From 557f3d9e2c3074649ac7a26a56a283b87cc88f2c Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 23 Nov 2022 14:32:32 +0100
Subject: [PATCH 001/700] Initial commit

---
 lib/SimpleNonlinearSolve/README.md | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 lib/SimpleNonlinearSolve/README.md

diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
new file mode 100644
index 000000000..ef116ffa8
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -0,0 +1 @@
+# SimpleNonlinearSolve

From 046c7173d5f766812719a38245fda8081f1fd2e3 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 23 Nov 2022 14:33:12 +0100
Subject: [PATCH 002/700] really start repo

---
 lib/SimpleNonlinearSolve/.JuliaFormatter.toml |   1 +
 lib/SimpleNonlinearSolve/LICENSE              |  21 +++
 lib/SimpleNonlinearSolve/Project.toml         |  38 +++++
 lib/SimpleNonlinearSolve/README.md            |  39 ++++-
 .../src/SimpleNonlinearSolve.jl               |  29 ++++
 lib/SimpleNonlinearSolve/src/ad.jl            |  63 ++++++++
 lib/SimpleNonlinearSolve/src/bisection.jl     |  65 ++++++++
 lib/SimpleNonlinearSolve/src/falsi.jl         |  68 ++++++++
 lib/SimpleNonlinearSolve/src/raphson.jl       |  51 ++++++
 lib/SimpleNonlinearSolve/src/utils.jl         |  35 ++++
 lib/SimpleNonlinearSolve/test/basictests.jl   | 152 ++++++++++++++++++
 lib/SimpleNonlinearSolve/test/runtests.jl     |  12 ++
 lib/SimpleNonlinearSolve/workflows/CI.yml     |  42 +++++
 .../workflows/CompatHelper.yml                |  26 +++
 .../workflows/Documentation.yml               |  29 ++++
 .../workflows/Downstream.yml                  |  53 ++++++
 .../workflows/FormatCheck.yml                 |  42 +++++
 .../workflows/Invalidations.yml               |  40 +++++
 lib/SimpleNonlinearSolve/workflows/TagBot.yml |  15 ++
 19 files changed, 820 insertions(+), 1 deletion(-)
 create mode 100644 lib/SimpleNonlinearSolve/.JuliaFormatter.toml
 create mode 100644 lib/SimpleNonlinearSolve/LICENSE
 create mode 100644 lib/SimpleNonlinearSolve/Project.toml
 create mode 100644 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/ad.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/bisection.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/falsi.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/raphson.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/utils.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/basictests.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/runtests.jl
 create mode 100644 lib/SimpleNonlinearSolve/workflows/CI.yml
 create mode 100644 lib/SimpleNonlinearSolve/workflows/CompatHelper.yml
 create mode 100644 lib/SimpleNonlinearSolve/workflows/Documentation.yml
 create mode 100644 lib/SimpleNonlinearSolve/workflows/Downstream.yml
 create mode 100644 lib/SimpleNonlinearSolve/workflows/FormatCheck.yml
 create mode 100644 lib/SimpleNonlinearSolve/workflows/Invalidations.yml
 create mode 100644 lib/SimpleNonlinearSolve/workflows/TagBot.yml

diff --git a/lib/SimpleNonlinearSolve/.JuliaFormatter.toml b/lib/SimpleNonlinearSolve/.JuliaFormatter.toml
new file mode 100644
index 000000000..453925c3f
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/.JuliaFormatter.toml
@@ -0,0 +1 @@
+style = "sciml"
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/LICENSE b/lib/SimpleNonlinearSolve/LICENSE
new file mode 100644
index 000000000..4d2bf6e69
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2020 Julia Computing, Inc.
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
new file mode 100644
index 000000000..0e3a98cd2
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -0,0 +1,38 @@
+name = "SimpleNonlinearSolve"
+uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
+authors = ["Kanav Gupta <kanav0610@gmail.com>"]
+version = "0.1.0"
+
+[deps]
+ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"
+FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
+Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
+
+[compat]
+ArrayInterfaceCore = "0.1.1"
+FiniteDiff = "2"
+ForwardDiff = "0.10.3"
+RecursiveArrayTools = "2"
+Reexport = "0.2, 1"
+SciMLBase = "1.32"
+Setfield = "0.7, 0.8, 1"
+StaticArrays = "0.12,1.0"
+UnPack = "1.0"
+julia = "1.6"
+
+[extras]
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[targets]
+test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "ForwardDiff"]
diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
index ef116ffa8..ef305c0c8 100644
--- a/lib/SimpleNonlinearSolve/README.md
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -1 +1,38 @@
-# SimpleNonlinearSolve
+# NonlinearSolve.jl
+
+[![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
+[![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/NonlinearSolve/stable/)
+
+[![codecov](https://codecov.io/gh/SciML/NonlinearSolve.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/SciML/NonlinearSolve.jl)
+[![Build Status](https://github.com/SciML/NonlinearSolve.jl/workflows/CI/badge.svg)](https://github.com/SciML/NonlinearSolve.jl/actions?query=workflow%3ACI)
+
+[![ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://img.shields.io/badge/ColPrac-Contributor's%20Guide-blueviolet)](https://github.com/SciML/ColPrac)
+[![SciML Code Style](https://img.shields.io/static/v1?label=code%20style&message=SciML&color=9558b2&labelColor=389826)](https://github.com/SciML/SciMLStyle)
+
+
+
+
+Fast implementations of root finding algorithms in Julia that satisfy the SciML common interface.
+
+For information on using the package,
+[see the stable documentation](https://docs.sciml.ai/NonlinearSolve/stable/). Use the
+[in-development documentation](https://docs.sciml.ai/NonlinearSolve/dev/) for the version of
+the documentation which contains the unreleased features.
+
+## High Level Examples
+
+```julia
+using NonlinearSolve, StaticArrays
+
+f(u,p) = u .* u .- 2
+u0 = @SVector[1.0, 1.0]
+probN = NonlinearProblem{false}(f, u0)
+solver = solve(probN, NewtonRaphson(), tol = 1e-9)
+
+## Bracketing Methods
+
+f(u, p) = u .* u .- 2.0
+u0 = (1.0, 2.0) # brackets
+probB = NonlinearProblem(f, u0)
+sol = solve(probB, Falsi())
+```
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
new file mode 100644
index 000000000..191bb8731
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -0,0 +1,29 @@
+module SimpleNonlinearSolve
+
+using Reexport
+using UnPack: @unpack
+using FiniteDiff, ForwardDiff
+using ForwardDiff: Dual
+using Setfield
+using StaticArrays
+using RecursiveArrayTools
+using LinearAlgebra
+import ArrayInterfaceCore
+
+@reexport using SciMLBase
+
+abstract type AbstractSimpleNonlinearSolveAlgorithm <: SciMLBase.AbstractNonlinearAlgorithm end
+abstract type AbstractBracketingAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
+abstract type AbstractNewtonAlgorithm{CS, AD, FDT} <: AbstractSimpleNonlinearSolveAlgorithm end
+abstract type AbstractImmutableNonlinearSolver <: AbstractSimpleNonlinearSolveAlgorithm end
+
+include("utils.jl")
+include("bisection.jl")
+include("falsi.jl")
+include("raphson.jl")
+include("ad.jl")
+
+# DiffEq styled algorithms
+export Bisection, Falsi, SimpleNewtonRaphson
+
+end # module
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
new file mode 100644
index 000000000..07a0620d0
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -0,0 +1,63 @@
+function scalar_nlsolve_ad(prob, alg, args...; kwargs...)
+    f = prob.f
+    p = value(prob.p)
+    u0 = value(prob.u0)
+
+    newprob = NonlinearProblem(f, u0, p; prob.kwargs...)
+    sol = solve(newprob, alg, args...; kwargs...)
+
+    uu = sol.u
+    if p isa Number
+        f_p = ForwardDiff.derivative(Base.Fix1(f, uu), p)
+    else
+        f_p = ForwardDiff.gradient(Base.Fix1(f, uu), p)
+    end
+
+    f_x = ForwardDiff.derivative(Base.Fix2(f, p), uu)
+    pp = prob.p
+    sumfun = let f_x′ = -f_x
+        ((fp, p),) -> (fp / f_x′) * ForwardDiff.partials(p)
+    end
+    partials = sum(sumfun, zip(f_p, pp))
+    return sol, partials
+end
+
+function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, SVector}, iip,
+                                                <:Dual{T, V, P}}, alg::SimpleNewtonRaphson,
+                         args...; kwargs...) where {iip, T, V, P}
+    sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
+    return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
+                                    retcode = sol.retcode)
+end
+function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, SVector}, iip,
+                                                <:AbstractArray{<:Dual{T, V, P}}},
+                         alg::SimpleNewtonRaphson, args...; kwargs...) where {iip, T, V, P}
+    sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
+    return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
+                                    retcode = sol.retcode)
+end
+
+# avoid ambiguities
+for Alg in [Bisection]
+    @eval function SciMLBase.solve(prob::NonlinearProblem{uType, iip, <:Dual{T, V, P}},
+                                   alg::$Alg, args...;
+                                   kwargs...) where {uType, iip, T, V, P}
+        sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
+        return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials),
+                                        sol.resid; retcode = sol.retcode,
+                                        left = Dual{T, V, P}(sol.left, partials),
+                                        right = Dual{T, V, P}(sol.right, partials))
+        #return BracketingSolution(Dual{T,V,P}(sol.left, partials), Dual{T,V,P}(sol.right, partials), sol.retcode, sol.resid)
+    end
+    @eval function SciMLBase.solve(prob::NonlinearProblem{uType, iip,
+                                                          <:AbstractArray{<:Dual{T, V, P}}},
+                                   alg::$Alg, args...;
+                                   kwargs...) where {uType, iip, T, V, P}
+        sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
+        return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials),
+                                        sol.resid; retcode = sol.retcode,
+                                        left = Dual{T, V, P}(sol.left, partials),
+                                        right = Dual{T, V, P}(sol.right, partials))
+        #return BracketingSolution(Dual{T,V,P}(sol.left, partials), Dual{T,V,P}(sol.right, partials), sol.retcode, sol.resid)
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
new file mode 100644
index 000000000..6e00afba7
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -0,0 +1,65 @@
+struct Bisection <: AbstractBracketingAlgorithm
+    exact_left::Bool
+    exact_right::Bool
+end
+
+function Bisection(; exact_left = false, exact_right = false)
+    Bisection(exact_left, exact_right)
+end
+
+function SciMLBase.solve(prob::NonlinearProblem, alg::Bisection, args...; maxiters = 1000,
+                         kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    left, right = prob.u0
+    fl, fr = f(left), f(right)
+
+    if iszero(fl)
+        return SciMLBase.build_solution(prob, alg, left, fl;
+                                        retcode = ReturnCode.ExactSolutionLeft, left = left,
+                                        right = right)
+    end
+
+    i = 1
+    if !iszero(fr)
+        while i < maxiters
+            mid = (left + right) / 2
+            (mid == left || mid == right) &&
+                return SciMLBase.build_solution(prob, alg, left, fl;
+                                                retcode = ReturnCode.FloatingPointLimit,
+                                                left = left, right = right)
+            fm = f(mid)
+            if iszero(fm)
+                right = mid
+                break
+            end
+            if sign(fl) == sign(fm)
+                fl = fm
+                left = mid
+            else
+                fr = fm
+                right = mid
+            end
+            i += 1
+        end
+    end
+
+    while i < maxiters
+        mid = (left + right) / 2
+        (mid == left || mid == right) &&
+            return SciMLBase.build_solution(prob, alg, left, fl;
+                                            retcode = ReturnCode.FloatingPointLimit,
+                                            left = left, right = right)
+        fm = f(mid)
+        if iszero(fm)
+            right = mid
+            fr = fm
+        else
+            left = mid
+            fl = fm
+        end
+        i += 1
+    end
+
+    return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
+                                    left = left, right = right)
+end
diff --git a/lib/SimpleNonlinearSolve/src/falsi.jl b/lib/SimpleNonlinearSolve/src/falsi.jl
new file mode 100644
index 000000000..0536ece19
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/falsi.jl
@@ -0,0 +1,68 @@
+struct Falsi <: AbstractBracketingAlgorithm end
+
+function SciMLBase.solve(prob::NonlinearProblem, alg::Falsi, args...; maxiters = 1000,
+                         kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    left, right = prob.u0
+    fl, fr = f(left), f(right)
+
+    if iszero(fl)
+        return SciMLBase.build_solution(prob, alg, left, fl;
+                                        retcode = ReturnCode.ExactSolutionLeft, left = left,
+                                        right = right)
+    end
+
+    i = 1
+    if !iszero(fr)
+        while i < maxiters
+            if nextfloat_tdir(left, prob.u0...) == right
+                return SciMLBase.build_solution(prob, alg, left, fl;
+                                                retcode = ReturnCode.FloatingPointLimit,
+                                                left = left, right = right)
+            end
+            mid = (fr * left - fl * right) / (fr - fl)
+            for i in 1:10
+                mid = max_tdir(left, prevfloat_tdir(mid, prob.u0...), prob.u0...)
+            end
+            if mid == right || mid == left
+                break
+            end
+            fm = f(mid)
+            if iszero(fm)
+                right = mid
+                break
+            end
+            if sign(fl) == sign(fm)
+                fl = fm
+                left = mid
+            else
+                fr = fm
+                right = mid
+            end
+            i += 1
+        end
+    end
+
+    while i < maxiters
+        mid = (left + right) / 2
+        (mid == left || mid == right) &&
+            return SciMLBase.build_solution(prob, alg, left, fl;
+                                            retcode = ReturnCode.FloatingPointLimit,
+                                            left = left, right = right)
+        fm = f(mid)
+        if iszero(fm)
+            right = mid
+            fr = fm
+        elseif sign(fm) == sign(fl)
+            left = mid
+            fl = fm
+        else
+            right = mid
+            fr = fm
+        end
+        i += 1
+    end
+
+    return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
+                                    left = left, right = right)
+end
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
new file mode 100644
index 000000000..8ed325a86
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -0,0 +1,51 @@
+struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
+    function SimpleNewtonRaphson(; chunk_size = Val{0}(), autodiff = Val{true}(),
+                                   diff_type = Val{:forward})
+        new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
+        SciMLBase._unwrap_val(diff_type)}()
+    end
+end
+
+function SciMLBase.solve(prob::NonlinearProblem,
+                         alg::SimpleNewtonRaphson, args...; xatol = nothing, xrtol = nothing,
+                         maxiters = 1000, kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    x = float(prob.u0)
+    fx = float(prob.u0)
+    T = typeof(x)
+
+    if SciMLBase.isinplace(prob)
+        error("SimpleNewtonRaphson currently only supports out-of-place nonlinear problems")
+    end
+
+    atol = xatol !== nothing ? xatol : oneunit(eltype(T)) * (eps(one(eltype(T))))^(4 // 5)
+    rtol = xrtol !== nothing ? xrtol : eps(one(eltype(T)))^(4 // 5)
+
+    if typeof(x) <: Number
+        xo = oftype(one(eltype(x)), Inf)
+    else
+        xo = map(x -> oftype(one(eltype(x)), Inf), x)
+    end
+
+    for i in 1:maxiters
+        if alg_autodiff(alg)
+            fx, dfx = value_derivative(f, x)
+        elseif x isa AbstractArray
+            fx = f(x)
+            dfx = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x), fx)
+        else
+            fx = f(x)
+            dfx = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x),
+                                                          fx)
+        end
+        iszero(fx) &&
+            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Default)
+        Δx = dfx \ fx
+        x -= Δx
+        if isapprox(x, xo, atol = atol, rtol = rtol)
+            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Default)
+        end
+        xo = x
+    end
+    return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
new file mode 100644
index 000000000..25f6ba358
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -0,0 +1,35 @@
+"""
+  prevfloat_tdir(x, x0, x1)
+
+Move `x` one floating point towards x0.
+"""
+function prevfloat_tdir(x, x0, x1)
+    x1 > x0 ? prevfloat(x) : nextfloat(x)
+end
+
+function nextfloat_tdir(x, x0, x1)
+    x1 > x0 ? nextfloat(x) : prevfloat(x)
+end
+
+function max_tdir(a, b, x0, x1)
+    x1 > x0 ? max(a, b) : min(a, b)
+end
+
+alg_autodiff(alg::AbstractNewtonAlgorithm{CS, AD, FDT}) where {CS, AD, FDT} = AD
+diff_type(alg::AbstractNewtonAlgorithm{CS, AD, FDT}) where {CS, AD, FDT} = FDT
+
+"""
+  value_derivative(f, x)
+
+Compute `f(x), d/dx f(x)` in the most efficient way.
+"""
+function value_derivative(f::F, x::R) where {F, R}
+    T = typeof(ForwardDiff.Tag(f, R))
+    out = f(ForwardDiff.Dual{T}(x, one(x)))
+    ForwardDiff.value(out), ForwardDiff.extract_derivative(T, out)
+end
+value_derivative(f::F, x::AbstractArray) where {F} = f(x), ForwardDiff.jacobian(f, x)
+
+value(x) = x
+value(x::Dual) = ForwardDiff.value(x)
+value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
new file mode 100644
index 000000000..47143dbce
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -0,0 +1,152 @@
+using SimpleNonlinearSolve
+using StaticArrays
+using BenchmarkTools
+using Test
+
+function benchmark_scalar(f, u0)
+    probN = NonlinearProblem{false}(f, u0)
+    sol = (solve(probN, SimpleNewtonRaphson()))
+end
+
+function ff(u, p)
+    u .* u .- 2
+end
+const cu0 = @SVector[1.0, 1.0]
+function sf(u, p)
+    u * u - 2
+end
+const csu0 = 1.0
+
+sol = benchmark_scalar(sf, csu0)
+@test sol.retcode === ReturnCode.Default
+@test sol.u * sol.u - 2 < 1e-9
+
+@test (@ballocated benchmark_scalar(sf, csu0)) == 0
+
+# AD Tests
+using ForwardDiff
+
+# Immutable
+f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
+
+g = function (p)
+    probN = NonlinearProblem{false}(f, csu0, p)
+    sol = solve(probN, SimpleNewtonRaphson(), tol = 1e-9)
+    return sol.u[end]
+end
+
+for p in 1.0:0.1:100.0
+    @test g(p) ≈ sqrt(p)
+    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+end
+
+# Scalar
+f, u0 = (u, p) -> u * u - p, 1.0
+
+# SimpleNewtonRaphson
+g = function (p)
+    probN = NonlinearProblem{false}(f, oftype(p, u0), p)
+    sol = solve(probN, SimpleNewtonRaphson())
+    return sol.u
+end
+
+@test ForwardDiff.derivative(g, 1.0) ≈ 0.5
+
+for p in 1.1:0.1:100.0
+    @test g(p) ≈ sqrt(p)
+    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+end
+
+u0 = (1.0, 20.0)
+# Falsi
+g = function (p)
+    probN = NonlinearProblem{false}(f, typeof(p).(u0), p)
+    sol = solve(probN, Falsi())
+    return sol.left
+end
+
+for p in 1.1:0.1:100.0
+    @test g(p) ≈ sqrt(p)
+    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+end
+
+f, u0 = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
+t = (p) -> [sqrt(p[2] / p[1])]
+p = [0.9, 50.0]
+for alg in [Bisection(), Falsi()]
+    global g, p
+    g = function (p)
+        probN = NonlinearProblem{false}(f, u0, p)
+        sol = solve(probN, Bisection())
+        return [sol.left]
+    end
+
+    @test g(p) ≈ [sqrt(p[2] / p[1])]
+    @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
+end
+
+gnewton = function (p)
+    probN = NonlinearProblem{false}(f, 0.5, p)
+    sol = solve(probN, SimpleNewtonRaphson())
+    return [sol.u]
+end
+@test gnewton(p) ≈ [sqrt(p[2] / p[1])]
+@test ForwardDiff.jacobian(gnewton, p) ≈ ForwardDiff.jacobian(t, p)
+
+# Error Checks
+
+f, u0 = (u, p) -> u .* u .- 2.0, @SVector[1.0, 1.0]
+probN = NonlinearProblem(f, u0)
+
+@test solve(probN, SimpleNewtonRaphson()).u[end] ≈ sqrt(2.0)
+@test solve(probN, SimpleNewtonRaphson(); immutable = false).u[end] ≈ sqrt(2.0)
+@test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
+@test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
+
+for u0 in [1.0, [1, 1.0]]
+    local f, probN, sol
+    f = (u, p) -> u .* u .- 2.0
+    probN = NonlinearProblem(f, u0)
+    sol = sqrt(2) * u0
+
+    @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
+    @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
+    @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u ≈ sol
+end
+
+# Bisection Tests
+f, u0 = (u, p) -> u .* u .- 2.0, (1.0, 2.0)
+probB = NonlinearProblem(f, u0)
+
+# Falsi
+sol = solve(probB, Falsi())
+@test sol.left ≈ sqrt(2.0)
+
+sol = solve(probB, Bisection())
+@test sol.left ≈ sqrt(2.0)
+
+# Garuntee Tests for Bisection
+f = function (u, p)
+    if u < 2.0
+        return u - 2.0
+    elseif u > 3.0
+        return u - 3.0
+    else
+        return 0.0
+    end
+end
+probB = NonlinearProblem(f, (0.0, 4.0))
+
+sol = solve(probB, Bisection(; exact_left = true))
+@test f(sol.left, nothing) < 0.0
+@test f(nextfloat(sol.left), nothing) >= 0.0
+
+sol = solve(probB, Bisection(; exact_right = true))
+@test f(sol.right, nothing) >= 0.0
+@test f(prevfloat(sol.right), nothing) <= 0.0
+
+sol = solve(probB, Bisection(; exact_left = true, exact_right = true); immutable = false)
+@test f(sol.left, nothing) < 0.0
+@test f(nextfloat(sol.left), nothing) >= 0.0
+@test f(sol.right, nothing) >= 0.0
+@test f(prevfloat(sol.right), nothing) <= 0.0
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
new file mode 100644
index 000000000..7269ed6bf
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -0,0 +1,12 @@
+using Pkg
+using SafeTestsets
+const LONGER_TESTS = false
+
+const GROUP = get(ENV, "GROUP", "All")
+const is_APPVEYOR = Sys.iswindows() && haskey(ENV, "APPVEYOR")
+
+@time begin
+
+if GROUP == "All" || GROUP == "Core"
+    @time @safetestset "Basic Tests + Some AD" begin include("basictests.jl") end
+end end
diff --git a/lib/SimpleNonlinearSolve/workflows/CI.yml b/lib/SimpleNonlinearSolve/workflows/CI.yml
new file mode 100644
index 000000000..c8d041ecf
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/workflows/CI.yml
@@ -0,0 +1,42 @@
+name: CI
+on:
+  pull_request:
+    branches:
+      - master
+  push:
+    branches:
+      - master
+jobs:
+  test:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        group:
+          - Core
+        version:
+          - '1'
+          - '1.6'
+    steps:
+      - uses: actions/checkout@v2
+      - uses: julia-actions/setup-julia@v1
+        with:
+          version: ${{ matrix.version }}
+      - uses: actions/cache@v1
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - uses: julia-actions/julia-buildpkg@v1
+      - uses: julia-actions/julia-runtest@v1
+        env:
+          GROUP: ${{ matrix.group }}
+          JULIA_NUM_THREADS: 11
+      - uses: julia-actions/julia-processcoverage@v1
+      - uses: codecov/codecov-action@v1
+        with:
+          file: lcov.info
diff --git a/lib/SimpleNonlinearSolve/workflows/CompatHelper.yml b/lib/SimpleNonlinearSolve/workflows/CompatHelper.yml
new file mode 100644
index 000000000..73494545f
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/workflows/CompatHelper.yml
@@ -0,0 +1,26 @@
+name: CompatHelper
+
+on:
+  schedule:
+    - cron: '00 * * * *'
+  issues:
+    types: [opened, reopened]
+
+jobs:
+  build:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      matrix:
+        julia-version: [1]
+        julia-arch: [x86]
+        os: [ubuntu-latest]
+    steps:
+      - uses: julia-actions/setup-julia@latest
+        with:
+          version: ${{ matrix.julia-version }}
+      - name: Pkg.add("CompatHelper")
+        run: julia -e 'using Pkg; Pkg.add("CompatHelper")'
+      - name: CompatHelper.main()
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+        run: julia -e 'using CompatHelper; CompatHelper.main(;subdirs=["", "docs"])'
diff --git a/lib/SimpleNonlinearSolve/workflows/Documentation.yml b/lib/SimpleNonlinearSolve/workflows/Documentation.yml
new file mode 100644
index 000000000..f64a315b6
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/workflows/Documentation.yml
@@ -0,0 +1,29 @@
+name: Documentation
+
+on:
+  push:
+    branches:
+      - master
+      - 'release-'
+    tags: '*'
+  pull_request:
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v2
+      - uses: julia-actions/setup-julia@latest
+        with:
+          version: '1'
+      - name: Install dependencies
+        run: julia --project=docs/ -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'
+      - name: Build and deploy
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} # For authentication with GitHub Actions token
+          DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }} # For authentication with SSH deploy key
+        run: julia --project=docs/ --code-coverage=user docs/make.jl
+      - uses: julia-actions/julia-processcoverage@v1
+      - uses: codecov/codecov-action@v1
+        with:
+          file: lcov.info
diff --git a/lib/SimpleNonlinearSolve/workflows/Downstream.yml b/lib/SimpleNonlinearSolve/workflows/Downstream.yml
new file mode 100644
index 000000000..916a33b4b
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/workflows/Downstream.yml
@@ -0,0 +1,53 @@
+name: IntegrationTest
+on:
+  push:
+    branches: [master]
+    tags: [v*]
+  pull_request:
+
+jobs:
+  test:
+    name: ${{ matrix.package.repo }}/${{ matrix.package.group }}/${{ matrix.julia-version }}
+    runs-on: ${{ matrix.os }}
+    env:
+      GROUP: ${{ matrix.package.group }}
+    strategy:
+      fail-fast: false
+      matrix:
+        julia-version: [1,1.6]
+        os: [ubuntu-latest]
+        package:
+          - {user: SciML, repo: ModelingToolkit.jl, group: All}
+    steps:
+      - uses: actions/checkout@v2
+      - uses: julia-actions/setup-julia@v1
+        with:
+          version: ${{ matrix.julia-version }}
+          arch: x64
+      - uses: julia-actions/julia-buildpkg@latest
+      - name: Clone Downstream
+        uses: actions/checkout@v2
+        with:
+          repository: ${{ matrix.package.user }}/${{ matrix.package.repo }}
+          path: downstream
+      - name: Load this and run the downstream tests
+        shell: julia --color=yes --project=downstream {0}
+        run: |
+          using Pkg
+          try
+            # force it to use this PR's version of the package
+            Pkg.develop(PackageSpec(path="."))  # resolver may fail with main deps
+            Pkg.update()
+            Pkg.test(coverage=true)  # resolver may fail with test time deps
+          catch err
+            err isa Pkg.Resolve.ResolverError || rethrow()
+            # If we can't resolve that means this is incompatible by SemVer and this is fine
+            # It means we marked this as a breaking change, so we don't need to worry about
+            # Mistakenly introducing a breaking change, as we have intentionally made one
+            @info "Not compatible with this release. No problem." exception=err
+            exit(0)  # Exit immediately, as a success
+          end
+      - uses: julia-actions/julia-processcoverage@v1
+      - uses: codecov/codecov-action@v1
+        with:
+          file: lcov.info
diff --git a/lib/SimpleNonlinearSolve/workflows/FormatCheck.yml b/lib/SimpleNonlinearSolve/workflows/FormatCheck.yml
new file mode 100644
index 000000000..2a3517a0f
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/workflows/FormatCheck.yml
@@ -0,0 +1,42 @@
+name: format-check
+
+on:
+  push:
+    branches:
+      - 'master'
+      - 'release-'
+    tags: '*'
+  pull_request:
+
+jobs:
+  build:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      matrix:
+        julia-version: [1]
+        julia-arch: [x86]
+        os: [ubuntu-latest]
+    steps:
+      - uses: julia-actions/setup-julia@latest
+        with:
+          version: ${{ matrix.julia-version }}
+
+      - uses: actions/checkout@v1
+      - name: Install JuliaFormatter and format
+        # This will use the latest version by default but you can set the version like so:
+        #
+        # julia  -e 'using Pkg; Pkg.add(PackageSpec(name="JuliaFormatter", version="0.13.0"))'
+        run: |
+          julia  -e 'using Pkg; Pkg.add(PackageSpec(name="JuliaFormatter"))'
+          julia  -e 'using JuliaFormatter; format(".", verbose=true)'
+      - name: Format check
+        run: |
+          julia -e '
+          out = Cmd(`git diff --name-only`) |> read |> String
+          if out == ""
+              exit(0)
+          else
+              @error "Some files have not been formatted !!!"
+              write(stdout, out)
+              exit(1)
+          end'
diff --git a/lib/SimpleNonlinearSolve/workflows/Invalidations.yml b/lib/SimpleNonlinearSolve/workflows/Invalidations.yml
new file mode 100644
index 000000000..4d0004e83
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/workflows/Invalidations.yml
@@ -0,0 +1,40 @@
+name: Invalidations
+
+on:
+  pull_request:
+
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: always.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  evaluate:
+    # Only run on PRs to the default branch.
+    # In the PR trigger above branches can be specified only explicitly whereas this check should work for master, main, or any other default branch
+    if: github.base_ref == github.event.repository.default_branch
+    runs-on: ubuntu-latest
+    steps:
+    - uses: julia-actions/setup-julia@v1
+      with:
+        version: '1'
+    - uses: actions/checkout@v3
+    - uses: julia-actions/julia-buildpkg@v1
+    - uses: julia-actions/julia-invalidations@v1
+      id: invs_pr
+
+    - uses: actions/checkout@v3
+      with:
+        ref: ${{ github.event.repository.default_branch }}
+    - uses: julia-actions/julia-buildpkg@v1
+    - uses: julia-actions/julia-invalidations@v1
+      id: invs_default
+    
+    - name: Report invalidation counts
+      run: |
+        echo "Invalidations on default branch: ${{ steps.invs_default.outputs.total }} (${{ steps.invs_default.outputs.deps }} via deps)" >> $GITHUB_STEP_SUMMARY
+        echo "This branch: ${{ steps.invs_pr.outputs.total }} (${{ steps.invs_pr.outputs.deps }} via deps)" >> $GITHUB_STEP_SUMMARY
+    - name: Check if the PR does increase number of invalidations
+      if: steps.invs_pr.outputs.total > steps.invs_default.outputs.total
+      run: exit 1
diff --git a/lib/SimpleNonlinearSolve/workflows/TagBot.yml b/lib/SimpleNonlinearSolve/workflows/TagBot.yml
new file mode 100644
index 000000000..f49313b66
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/workflows/TagBot.yml
@@ -0,0 +1,15 @@
+name: TagBot
+on:
+  issue_comment:
+    types:
+      - created
+  workflow_dispatch:
+jobs:
+  TagBot:
+    if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot'
+    runs-on: ubuntu-latest
+    steps:
+      - uses: JuliaRegistries/TagBot@v1
+        with:
+          token: ${{ secrets.GITHUB_TOKEN }}
+          ssh: ${{ secrets.DOCUMENTER_KEY }}

From 78996f8c4e5320d393466a8c30d890ac645d265b Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 23 Nov 2022 19:17:40 +0100
Subject: [PATCH 003/700] setup with IntervalNonlinearProblem

---
 lib/SimpleNonlinearSolve/Project.toml       |  4 ++--
 lib/SimpleNonlinearSolve/src/ad.jl          | 21 ++++++++++++++++-----
 lib/SimpleNonlinearSolve/src/bisection.jl   |  5 +++--
 lib/SimpleNonlinearSolve/src/falsi.jl       |  9 +++++----
 lib/SimpleNonlinearSolve/src/raphson.jl     |  7 ++++---
 lib/SimpleNonlinearSolve/test/basictests.jl | 14 +++++++-------
 6 files changed, 37 insertions(+), 23 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 0e3a98cd2..ca2fe2c05 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,6 +1,6 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
-authors = ["Kanav Gupta <kanav0610@gmail.com>"]
+authors = ["SciML"]
 version = "0.1.0"
 
 [deps]
@@ -21,7 +21,7 @@ FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 RecursiveArrayTools = "2"
 Reexport = "0.2, 1"
-SciMLBase = "1.32"
+SciMLBase = "1.73"
 Setfield = "0.7, 0.8, 1"
 StaticArrays = "0.12,1.0"
 UnPack = "1.0"
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index 07a0620d0..501324299 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -1,9 +1,15 @@
 function scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     f = prob.f
     p = value(prob.p)
-    u0 = value(prob.u0)
 
-    newprob = NonlinearProblem(f, u0, p; prob.kwargs...)
+    if prob isa IntervalNonlinearProblem
+        tspan = value(prob.tspan)
+        newprob = IntervalNonlinearProblem(f, tspan, p; prob.kwargs...)
+    else
+        u0 = value(prob.u0)
+        newprob = NonlinearProblem(f, u0, p; prob.kwargs...)
+    end
+
     sol = solve(newprob, alg, args...; kwargs...)
 
     uu = sol.u
@@ -39,7 +45,8 @@ end
 
 # avoid ambiguities
 for Alg in [Bisection]
-    @eval function SciMLBase.solve(prob::NonlinearProblem{uType, iip, <:Dual{T, V, P}},
+    @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
+                                                                  <:Dual{T, V, P}},
                                    alg::$Alg, args...;
                                    kwargs...) where {uType, iip, T, V, P}
         sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
@@ -49,8 +56,12 @@ for Alg in [Bisection]
                                         right = Dual{T, V, P}(sol.right, partials))
         #return BracketingSolution(Dual{T,V,P}(sol.left, partials), Dual{T,V,P}(sol.right, partials), sol.retcode, sol.resid)
     end
-    @eval function SciMLBase.solve(prob::NonlinearProblem{uType, iip,
-                                                          <:AbstractArray{<:Dual{T, V, P}}},
+    @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
+                                                                  <:AbstractArray{
+                                                                                  <:Dual{T,
+                                                                                         V,
+                                                                                         P}
+                                                                                  }},
                                    alg::$Alg, args...;
                                    kwargs...) where {uType, iip, T, V, P}
         sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index 6e00afba7..2440ea3c0 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -7,10 +7,11 @@ function Bisection(; exact_left = false, exact_right = false)
     Bisection(exact_left, exact_right)
 end
 
-function SciMLBase.solve(prob::NonlinearProblem, alg::Bisection, args...; maxiters = 1000,
+function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...;
+                         maxiters = 1000,
                          kwargs...)
     f = Base.Fix2(prob.f, prob.p)
-    left, right = prob.u0
+    left, right = prob.tspan
     fl, fr = f(left), f(right)
 
     if iszero(fl)
diff --git a/lib/SimpleNonlinearSolve/src/falsi.jl b/lib/SimpleNonlinearSolve/src/falsi.jl
index 0536ece19..d431a9251 100644
--- a/lib/SimpleNonlinearSolve/src/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/falsi.jl
@@ -1,9 +1,10 @@
 struct Falsi <: AbstractBracketingAlgorithm end
 
-function SciMLBase.solve(prob::NonlinearProblem, alg::Falsi, args...; maxiters = 1000,
+function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
+                         maxiters = 1000,
                          kwargs...)
     f = Base.Fix2(prob.f, prob.p)
-    left, right = prob.u0
+    left, right = prob.tspan
     fl, fr = f(left), f(right)
 
     if iszero(fl)
@@ -15,14 +16,14 @@ function SciMLBase.solve(prob::NonlinearProblem, alg::Falsi, args...; maxiters =
     i = 1
     if !iszero(fr)
         while i < maxiters
-            if nextfloat_tdir(left, prob.u0...) == right
+            if nextfloat_tdir(left, prob.tspan...) == right
                 return SciMLBase.build_solution(prob, alg, left, fl;
                                                 retcode = ReturnCode.FloatingPointLimit,
                                                 left = left, right = right)
             end
             mid = (fr * left - fl * right) / (fr - fl)
             for i in 1:10
-                mid = max_tdir(left, prevfloat_tdir(mid, prob.u0...), prob.u0...)
+                mid = max_tdir(left, prevfloat_tdir(mid, prob.tspan...), prob.tspan...)
             end
             if mid == right || mid == left
                 break
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 8ed325a86..6a5d235e0 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -1,13 +1,14 @@
 struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     function SimpleNewtonRaphson(; chunk_size = Val{0}(), autodiff = Val{true}(),
-                                   diff_type = Val{:forward})
+                                 diff_type = Val{:forward})
         new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
-        SciMLBase._unwrap_val(diff_type)}()
+            SciMLBase._unwrap_val(diff_type)}()
     end
 end
 
 function SciMLBase.solve(prob::NonlinearProblem,
-                         alg::SimpleNewtonRaphson, args...; xatol = nothing, xrtol = nothing,
+                         alg::SimpleNewtonRaphson, args...; xatol = nothing,
+                         xrtol = nothing,
                          maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 47143dbce..0a0716173 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -57,10 +57,10 @@ for p in 1.1:0.1:100.0
     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
 end
 
-u0 = (1.0, 20.0)
+tspan = (1.0, 20.0)
 # Falsi
 g = function (p)
-    probN = NonlinearProblem{false}(f, typeof(p).(u0), p)
+    probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
     sol = solve(probN, Falsi())
     return sol.left
 end
@@ -70,13 +70,13 @@ for p in 1.1:0.1:100.0
     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
 end
 
-f, u0 = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
+f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
 t = (p) -> [sqrt(p[2] / p[1])]
 p = [0.9, 50.0]
 for alg in [Bisection(), Falsi()]
     global g, p
     g = function (p)
-        probN = NonlinearProblem{false}(f, u0, p)
+        probN = IntervalNonlinearProblem{false}(f, tspan, p)
         sol = solve(probN, Bisection())
         return [sol.left]
     end
@@ -115,8 +115,8 @@ for u0 in [1.0, [1, 1.0]]
 end
 
 # Bisection Tests
-f, u0 = (u, p) -> u .* u .- 2.0, (1.0, 2.0)
-probB = NonlinearProblem(f, u0)
+f, tspan = (u, p) -> u .* u .- 2.0, (1.0, 2.0)
+probB = IntervalNonlinearProblem(f, tspan)
 
 # Falsi
 sol = solve(probB, Falsi())
@@ -135,7 +135,7 @@ f = function (u, p)
         return 0.0
     end
 end
-probB = NonlinearProblem(f, (0.0, 4.0))
+probB = IntervalNonlinearProblem(f, (0.0, 4.0))
 
 sol = solve(probB, Bisection(; exact_left = true))
 @test f(sol.left, nothing) < 0.0

From 7c6e65419c621940b67cf913277c80c202f8cb88 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 23 Nov 2022 19:19:04 +0100
Subject: [PATCH 004/700] fix workflow location

---
 lib/SimpleNonlinearSolve/{ => .github}/workflows/CI.yml           | 0
 lib/SimpleNonlinearSolve/{ => .github}/workflows/CompatHelper.yml | 0
 .../{ => .github}/workflows/Documentation.yml                     | 0
 lib/SimpleNonlinearSolve/{ => .github}/workflows/Downstream.yml   | 0
 lib/SimpleNonlinearSolve/{ => .github}/workflows/FormatCheck.yml  | 0
 .../{ => .github}/workflows/Invalidations.yml                     | 0
 lib/SimpleNonlinearSolve/{ => .github}/workflows/TagBot.yml       | 0
 7 files changed, 0 insertions(+), 0 deletions(-)
 rename lib/SimpleNonlinearSolve/{ => .github}/workflows/CI.yml (100%)
 rename lib/SimpleNonlinearSolve/{ => .github}/workflows/CompatHelper.yml (100%)
 rename lib/SimpleNonlinearSolve/{ => .github}/workflows/Documentation.yml (100%)
 rename lib/SimpleNonlinearSolve/{ => .github}/workflows/Downstream.yml (100%)
 rename lib/SimpleNonlinearSolve/{ => .github}/workflows/FormatCheck.yml (100%)
 rename lib/SimpleNonlinearSolve/{ => .github}/workflows/Invalidations.yml (100%)
 rename lib/SimpleNonlinearSolve/{ => .github}/workflows/TagBot.yml (100%)

diff --git a/lib/SimpleNonlinearSolve/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
similarity index 100%
rename from lib/SimpleNonlinearSolve/workflows/CI.yml
rename to lib/SimpleNonlinearSolve/.github/workflows/CI.yml
diff --git a/lib/SimpleNonlinearSolve/workflows/CompatHelper.yml b/lib/SimpleNonlinearSolve/.github/workflows/CompatHelper.yml
similarity index 100%
rename from lib/SimpleNonlinearSolve/workflows/CompatHelper.yml
rename to lib/SimpleNonlinearSolve/.github/workflows/CompatHelper.yml
diff --git a/lib/SimpleNonlinearSolve/workflows/Documentation.yml b/lib/SimpleNonlinearSolve/.github/workflows/Documentation.yml
similarity index 100%
rename from lib/SimpleNonlinearSolve/workflows/Documentation.yml
rename to lib/SimpleNonlinearSolve/.github/workflows/Documentation.yml
diff --git a/lib/SimpleNonlinearSolve/workflows/Downstream.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
similarity index 100%
rename from lib/SimpleNonlinearSolve/workflows/Downstream.yml
rename to lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
diff --git a/lib/SimpleNonlinearSolve/workflows/FormatCheck.yml b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
similarity index 100%
rename from lib/SimpleNonlinearSolve/workflows/FormatCheck.yml
rename to lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
diff --git a/lib/SimpleNonlinearSolve/workflows/Invalidations.yml b/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml
similarity index 100%
rename from lib/SimpleNonlinearSolve/workflows/Invalidations.yml
rename to lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml
diff --git a/lib/SimpleNonlinearSolve/workflows/TagBot.yml b/lib/SimpleNonlinearSolve/.github/workflows/TagBot.yml
similarity index 100%
rename from lib/SimpleNonlinearSolve/workflows/TagBot.yml
rename to lib/SimpleNonlinearSolve/.github/workflows/TagBot.yml

From 8a56da945e0ab04cd02610af3c6d2be1406e73dd Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 23 Nov 2022 19:39:15 +0100
Subject: [PATCH 005/700] fix tolerances

---
 lib/SimpleNonlinearSolve/src/raphson.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 6a5d235e0..1f23debd7 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -7,8 +7,8 @@ struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
 end
 
 function SciMLBase.solve(prob::NonlinearProblem,
-                         alg::SimpleNewtonRaphson, args...; xatol = nothing,
-                         xrtol = nothing,
+                         alg::SimpleNewtonRaphson, args...; abstol = nothing,
+                         reltol = nothing,
                          maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
@@ -19,8 +19,8 @@ function SciMLBase.solve(prob::NonlinearProblem,
         error("SimpleNewtonRaphson currently only supports out-of-place nonlinear problems")
     end
 
-    atol = xatol !== nothing ? xatol : oneunit(eltype(T)) * (eps(one(eltype(T))))^(4 // 5)
-    rtol = xrtol !== nothing ? xrtol : eps(one(eltype(T)))^(4 // 5)
+    atol = abstol !== nothing ? abstol : oneunit(eltype(T)) * (eps(one(eltype(T))))^(4 // 5)
+    rtol = reltol !== nothing ? reltol : eps(one(eltype(T)))^(4 // 5)
 
     if typeof(x) <: Number
         xo = oftype(one(eltype(x)), Inf)

From b7b67719f1794120b144dd0e87e5fc276e5887f8 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 23 Nov 2022 19:45:54 +0100
Subject: [PATCH 006/700] master -> main

---
 .../.github/workflows/CI.yml                  |  4 +--
 .../.github/workflows/Documentation.yml       | 29 -------------------
 .../.github/workflows/Downstream.yml          |  2 +-
 .../.github/workflows/FormatCheck.yml         |  2 +-
 4 files changed, 4 insertions(+), 33 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/.github/workflows/Documentation.yml

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
index c8d041ecf..80a2aea7b 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
@@ -2,10 +2,10 @@ name: CI
 on:
   pull_request:
     branches:
-      - master
+      - main
   push:
     branches:
-      - master
+      - main
 jobs:
   test:
     runs-on: ubuntu-latest
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Documentation.yml b/lib/SimpleNonlinearSolve/.github/workflows/Documentation.yml
deleted file mode 100644
index f64a315b6..000000000
--- a/lib/SimpleNonlinearSolve/.github/workflows/Documentation.yml
+++ /dev/null
@@ -1,29 +0,0 @@
-name: Documentation
-
-on:
-  push:
-    branches:
-      - master
-      - 'release-'
-    tags: '*'
-  pull_request:
-
-jobs:
-  build:
-    runs-on: ubuntu-latest
-    steps:
-      - uses: actions/checkout@v2
-      - uses: julia-actions/setup-julia@latest
-        with:
-          version: '1'
-      - name: Install dependencies
-        run: julia --project=docs/ -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'
-      - name: Build and deploy
-        env:
-          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} # For authentication with GitHub Actions token
-          DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }} # For authentication with SSH deploy key
-        run: julia --project=docs/ --code-coverage=user docs/make.jl
-      - uses: julia-actions/julia-processcoverage@v1
-      - uses: codecov/codecov-action@v1
-        with:
-          file: lcov.info
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
index 916a33b4b..122cccf4d 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
@@ -1,7 +1,7 @@
 name: IntegrationTest
 on:
   push:
-    branches: [master]
+    branches: [main]
     tags: [v*]
   pull_request:
 
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
index 2a3517a0f..e4e3512e2 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
@@ -3,7 +3,7 @@ name: format-check
 on:
   push:
     branches:
-      - 'master'
+      - 'main'
       - 'release-'
     tags: '*'
   pull_request:

From 4dcd7a76853dc8ac94e73374c3caa284a548dce0 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 23 Nov 2022 22:37:17 +0100
Subject: [PATCH 007/700] better readme

---
 lib/SimpleNonlinearSolve/README.md | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
index ef305c0c8..a7febbeb4 100644
--- a/lib/SimpleNonlinearSolve/README.md
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -9,10 +9,10 @@
 [![ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://img.shields.io/badge/ColPrac-Contributor's%20Guide-blueviolet)](https://github.com/SciML/ColPrac)
 [![SciML Code Style](https://img.shields.io/static/v1?label=code%20style&message=SciML&color=9558b2&labelColor=389826)](https://github.com/SciML/SciMLStyle)
 
-
-
-
 Fast implementations of root finding algorithms in Julia that satisfy the SciML common interface.
+SimpleNonlinearSolve.jl focuses on low-dependency implementations of very fast methods for
+very small and simple problems. For the full set of solvers, see NonlinearSolve.jl, of which
+SimpleNonlinearSolve.jl is just one solver set.
 
 For information on using the package,
 [see the stable documentation](https://docs.sciml.ai/NonlinearSolve/stable/). Use the
@@ -22,17 +22,17 @@ the documentation which contains the unreleased features.
 ## High Level Examples
 
 ```julia
-using NonlinearSolve, StaticArrays
+using SimpleNonlinearSolve, StaticArrays
 
 f(u,p) = u .* u .- 2
 u0 = @SVector[1.0, 1.0]
 probN = NonlinearProblem{false}(f, u0)
-solver = solve(probN, NewtonRaphson(), tol = 1e-9)
+solver = solve(probN, SimpleNewtonRaphson(), tol = 1e-9)
 
 ## Bracketing Methods
 
 f(u, p) = u .* u .- 2.0
 u0 = (1.0, 2.0) # brackets
-probB = NonlinearProblem(f, u0)
+probB = IntervalNonlinearProblem(f, u0)
 sol = solve(probB, Falsi())
 ```

From 26cee49125e1ac6cabce0962bfebd02255184bda Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 24 Nov 2022 10:14:37 +0100
Subject: [PATCH 008/700] Dramatically reduce dependencies

---
 lib/SimpleNonlinearSolve/Project.toml           | 17 +++++------------
 .../src/SimpleNonlinearSolve.jl                 |  6 +-----
 lib/SimpleNonlinearSolve/src/ad.jl              |  6 ++++--
 3 files changed, 10 insertions(+), 19 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index ca2fe2c05..0c9ebc040 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,38 +1,31 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.0"
+version = "0.1.1"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
-LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
-Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
-StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
-UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
+StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [compat]
 ArrayInterfaceCore = "0.1.1"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
-RecursiveArrayTools = "2"
 Reexport = "0.2, 1"
 SciMLBase = "1.73"
-Setfield = "0.7, 0.8, 1"
-StaticArrays = "0.12,1.0"
-UnPack = "1.0"
+StaticArraysCore = "1.4"
 julia = "1.6"
 
 [extras]
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
-ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "ForwardDiff"]
+test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays"]
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 191bb8731..164f99cf8 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -1,13 +1,9 @@
 module SimpleNonlinearSolve
 
 using Reexport
-using UnPack: @unpack
 using FiniteDiff, ForwardDiff
 using ForwardDiff: Dual
-using Setfield
-using StaticArrays
-using RecursiveArrayTools
-using LinearAlgebra
+using StaticArraysCore
 import ArrayInterfaceCore
 
 @reexport using SciMLBase
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index 501324299..3b8d3fee0 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -28,14 +28,16 @@ function scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return sol, partials
 end
 
-function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, SVector}, iip,
+function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
+                                                iip,
                                                 <:Dual{T, V, P}}, alg::SimpleNewtonRaphson,
                          args...; kwargs...) where {iip, T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
                                     retcode = sol.retcode)
 end
-function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, SVector}, iip,
+function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
+                                                iip,
                                                 <:AbstractArray{<:Dual{T, V, P}}},
                          alg::SimpleNewtonRaphson, args...; kwargs...) where {iip, T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)

From 41a1d01ce3ede0d1b0fe13a8e6f0b69b4a2bc855 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 24 Nov 2022 10:37:29 +0100
Subject: [PATCH 009/700] snoopprecompile

---
 lib/SimpleNonlinearSolve/Project.toml         |  2 ++
 .../src/SimpleNonlinearSolve.jl               | 24 +++++++++++++++++++
 2 files changed, 26 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 0c9ebc040..71f516462 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -9,6 +9,7 @@ FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+SnoopPrecompile = "66db9d55-30c0-4569-8b51-7e840670fc0c"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [compat]
@@ -17,6 +18,7 @@ FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 Reexport = "0.2, 1"
 SciMLBase = "1.73"
+SnoopPrecompile = "1"
 StaticArraysCore = "1.4"
 julia = "1.6"
 
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 164f99cf8..bd4788193 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -19,6 +19,30 @@ include("falsi.jl")
 include("raphson.jl")
 include("ad.jl")
 
+import SnoopPrecompile
+
+SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
+    prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
+    for alg in (SimpleNewtonRaphson,)
+        solve(prob_no_brack, alg(), tol = T(1e-2))
+    end
+
+    #=
+    for alg in (SimpleNewtonRaphson,)
+        for u0 in ([1., 1.], StaticArraysCore.SA[1.0, 1.0])
+            u0 = T.(.1)
+            probN = NonlinearProblem{false}((u,p) -> u .* u .- p, u0, T(2))
+            solve(probN, alg(), tol = T(1e-2))
+        end
+    end
+    =#
+
+    prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p, T.((0.0, 2.0)), T(2))
+    for alg in (Bisection, Falsi)
+        solve(prob_brack, alg(), tol = T(1e-2))
+    end
+end end
+
 # DiffEq styled algorithms
 export Bisection, Falsi, SimpleNewtonRaphson
 

From 9667029500fff3a92b97767ba9f6ecdb35dc7e7c Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 24 Nov 2022 10:55:52 +0100
Subject: [PATCH 010/700] Fix return codes

---
 lib/SimpleNonlinearSolve/Project.toml       | 2 +-
 lib/SimpleNonlinearSolve/src/raphson.jl     | 4 ++--
 lib/SimpleNonlinearSolve/test/basictests.jl | 2 +-
 3 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 71f516462..8b87181da 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.1"
+version = "0.1.2"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 1f23debd7..3db5b62bc 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -40,11 +40,11 @@ function SciMLBase.solve(prob::NonlinearProblem,
                                                           fx)
         end
         iszero(fx) &&
-            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Default)
+            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
         Δx = dfx \ fx
         x -= Δx
         if isapprox(x, xo, atol = atol, rtol = rtol)
-            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Default)
+            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
         end
         xo = x
     end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 0a0716173..0c4194675 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -18,7 +18,7 @@ end
 const csu0 = 1.0
 
 sol = benchmark_scalar(sf, csu0)
-@test sol.retcode === ReturnCode.Default
+@test sol.retcode === ReturnCode.Success
 @test sol.u * sol.u - 2 < 1e-9
 
 @test (@ballocated benchmark_scalar(sf, csu0)) == 0

From 70edef753fdf52eda16db1bd1b0d98e71f718460 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 24 Nov 2022 11:07:36 +0100
Subject: [PATCH 011/700] Update Downstream.yml

---
 lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
index 122cccf4d..6abfcfddc 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
@@ -18,6 +18,12 @@ jobs:
         os: [ubuntu-latest]
         package:
           - {user: SciML, repo: ModelingToolkit.jl, group: All}
+          - {user: SciML, repo: DiffEqBase.jl, group: Core}
+          - {user: SciML, repo: OrdinaryDiffEq.jl, group: InterfaceI}
+          - {user: SciML, repo: OrdinaryDiffEq.jl, group: InterfaceII}
+          - {user: SciML, repo: OrdinaryDiffEq.jl, group: InterfaceIII}
+          - {user: SciML, repo: OrdinaryDiffEq.jl, group: InterfaceIV}
+          - {user: SciML, repo: OrdinaryDiffEq.jl, group: InterfaceV}
     steps:
       - uses: actions/checkout@v2
       - uses: julia-actions/setup-julia@v1

From 5134d41672be3a274712bb8d51787311c7a3ce64 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 24 Nov 2022 15:31:27 +0100
Subject: [PATCH 012/700] Update README.md

---
 lib/SimpleNonlinearSolve/README.md | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
index a7febbeb4..818872c0b 100644
--- a/lib/SimpleNonlinearSolve/README.md
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -1,4 +1,4 @@
-# NonlinearSolve.jl
+# SimpleNonlinearSolve.jl
 
 [![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
 [![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/NonlinearSolve/stable/)
@@ -11,7 +11,8 @@
 
 Fast implementations of root finding algorithms in Julia that satisfy the SciML common interface.
 SimpleNonlinearSolve.jl focuses on low-dependency implementations of very fast methods for
-very small and simple problems. For the full set of solvers, see NonlinearSolve.jl, of which
+very small and simple problems. For the full set of solvers, see 
+[NonlinearSolve.jl](https://github.com/SciML/NonlinearSolve.jl), of which
 SimpleNonlinearSolve.jl is just one solver set.
 
 For information on using the package,

From 0bd99235ed3655dde1cc52eabcd89cff721e73cf Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 24 Nov 2022 21:04:13 +0100
Subject: [PATCH 013/700] Update CompatHelper.yml

---
 lib/SimpleNonlinearSolve/.github/workflows/CompatHelper.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CompatHelper.yml b/lib/SimpleNonlinearSolve/.github/workflows/CompatHelper.yml
index 73494545f..0fe6c3748 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CompatHelper.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CompatHelper.yml
@@ -23,4 +23,4 @@ jobs:
       - name: CompatHelper.main()
         env:
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
-        run: julia -e 'using CompatHelper; CompatHelper.main(;subdirs=["", "docs"])'
+        run: julia -e 'using CompatHelper; CompatHelper.main()'

From 92732e73d7c28c6bd41bd11da00e1bd540728cf1 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Sun, 4 Dec 2022 13:46:21 +0100
Subject: [PATCH 014/700] improve docstrings

---
 lib/SimpleNonlinearSolve/Project.toml     |  2 +-
 lib/SimpleNonlinearSolve/src/bisection.jl | 12 +++++++++
 lib/SimpleNonlinearSolve/src/falsi.jl     |  3 +++
 lib/SimpleNonlinearSolve/src/raphson.jl   | 30 +++++++++++++++++++++++
 4 files changed, 46 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 8b87181da..f04d3a6c3 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.2"
+version = "0.1.3"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"
diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index 2440ea3c0..e90f28f9e 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -1,3 +1,15 @@
+"""
+`Bisection(; exact_left = false, exact_right = false)`
+
+A common bisection method.
+
+### Keyword Arguments
+
+- `exact_left`: whether to enforce whether the left side of the interval must be exactly
+  zero for the returned result. Defualts to false.
+- `exact_right`: whether to enforce whether the right side of the interval must be exactly
+  zero for the returned result. Defualts to false.
+"""
 struct Bisection <: AbstractBracketingAlgorithm
     exact_left::Bool
     exact_right::Bool
diff --git a/lib/SimpleNonlinearSolve/src/falsi.jl b/lib/SimpleNonlinearSolve/src/falsi.jl
index d431a9251..81ce68ffa 100644
--- a/lib/SimpleNonlinearSolve/src/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/falsi.jl
@@ -1,3 +1,6 @@
+"""
+`Falsi`: A non-allocating regula falsi method
+"""
 struct Falsi <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 3db5b62bc..ed00fad30 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -1,3 +1,33 @@
+"""
+```julia
+SimpleNewtonRaphson(; chunk_size = Val{0}(), autodiff = Val{true}(),
+                                 diff_type = Val{:forward})
+```
+
+A low-overhead implementation of Newton-Raphson. This method is non-allocating on scalar
+and static array problems.
+
+!!! note
+
+    As part of the decreased overhead, this method omits some of the higher level error
+    catching of the other methods. Thus to see better error messages, use one of the other
+    methods like `NewtonRaphson`
+
+### Keyword Arguments
+
+- `chunk_size`: the chunk size used by the internal ForwardDiff.jl automatic differentiation
+  system. This allows for multiple derivative columns to be computed simultaniously,
+  improving performance. Defaults to `0`, which is equivalent to using ForwardDiff.jl's
+  default chunk size mechanism. For more details, see the documentation for
+  [ForwardDiff.jl](https://juliadiff.org/ForwardDiff.jl/stable/).
+- `autodiff`: whether to use forward-mode automatic differentiation for the Jacobian.
+  Note that this argument is ignored if an analytical Jacobian is passed as that will be
+  used instead. Defaults to `Val{true}`, which means ForwardDiff.jl is used by default.
+  If `Val{false}`, then FiniteDiff.jl is used for finite differencing.
+- `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
+  `Val{:forward}` for forward finite differences. For more details on the choices, see the
+  [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
+"""
 struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     function SimpleNewtonRaphson(; chunk_size = Val{0}(), autodiff = Val{true}(),
                                  diff_type = Val{:forward})

From db4cf617354e5f825db181ce3cf39f9f83cd357f Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 24 Dec 2022 10:24:57 -0500
Subject: [PATCH 015/700] Support complex in newton

---
 lib/SimpleNonlinearSolve/Project.toml   | 2 +-
 lib/SimpleNonlinearSolve/src/raphson.jl | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index f04d3a6c3..fa4f7f015 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.3"
+version = "0.1.4"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index ed00fad30..2848d6d1a 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -49,8 +49,8 @@ function SciMLBase.solve(prob::NonlinearProblem,
         error("SimpleNewtonRaphson currently only supports out-of-place nonlinear problems")
     end
 
-    atol = abstol !== nothing ? abstol : oneunit(eltype(T)) * (eps(one(eltype(T))))^(4 // 5)
-    rtol = reltol !== nothing ? reltol : eps(one(eltype(T)))^(4 // 5)
+    atol = abstol !== nothing ? abstol : real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
+    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
 
     if typeof(x) <: Number
         xo = oftype(one(eltype(x)), Inf)

From 28ac6845c3cac8c246dc47c7df0982e200c3a5e9 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 24 Dec 2022 10:42:51 -0500
Subject: [PATCH 016/700] format

---
 lib/SimpleNonlinearSolve/src/raphson.jl | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 2848d6d1a..47ae6eaf8 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -49,7 +49,8 @@ function SciMLBase.solve(prob::NonlinearProblem,
         error("SimpleNewtonRaphson currently only supports out-of-place nonlinear problems")
     end
 
-    atol = abstol !== nothing ? abstol : real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
+    atol = abstol !== nothing ? abstol :
+           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
     rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
 
     if typeof(x) <: Number
@@ -78,5 +79,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
         end
         xo = x
     end
+
+    @show x, fx
     return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
 end

From 15c2593e652e03a1821730b078a1ac2df78326cd Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Sat, 31 Dec 2022 06:24:29 +0100
Subject: [PATCH 017/700] inital commit, started to implement Broyden

---
 .../src/SimpleNonlinearSolve.jl               |  6 ++-
 lib/SimpleNonlinearSolve/src/broyden.jl       | 43 +++++++++++++++++++
 lib/SimpleNonlinearSolve/test/basictests.jl   |  4 +-
 3 files changed, 50 insertions(+), 3 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/broyden.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index bd4788193..213ba2317 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -4,6 +4,7 @@ using Reexport
 using FiniteDiff, ForwardDiff
 using ForwardDiff: Dual
 using StaticArraysCore
+using LinearAlgebra # TODO check if it is ok to add this
 import ArrayInterfaceCore
 
 @reexport using SciMLBase
@@ -18,12 +19,13 @@ include("bisection.jl")
 include("falsi.jl")
 include("raphson.jl")
 include("ad.jl")
+include("broyden.jl")
 
 import SnoopPrecompile
 
 SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
     prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-    for alg in (SimpleNewtonRaphson,)
+    for alg in (SimpleNewtonRaphson, Broyden)
         solve(prob_no_brack, alg(), tol = T(1e-2))
     end
 
@@ -44,6 +46,6 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
 end end
 
 # DiffEq styled algorithms
-export Bisection, Falsi, SimpleNewtonRaphson
+export Bisection, Broyden, Falsi, SimpleNewtonRaphson
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
new file mode 100644
index 000000000..9f9388bad
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -0,0 +1,43 @@
+# TODO add docstrings
+
+# TODO check what the supertype should be
+# TODO check if this should be defined as in raphson.jl
+struct Broyden <: AbstractSimpleNonlinearSolveAlgorithm end
+
+function SciMLBase.solve(prob::NonlinearProblem,
+                         alg::Broyden, args...; abstol = nothing,
+                         reltol = nothing,
+                         maxiters = 1000, kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    xₙ = float(prob.u0)
+    T = typeof(xₙ)
+    J⁻¹ = Matrix{T}(I, length(xₙ), length(xₙ))
+
+    if SciMLBase.isinplace(prob)
+        error("Broyden currently only supports out-of-place nonlinear problems")
+    end
+
+    atol = abstol !== nothing ? abstol :
+           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
+    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
+
+    for _ in 1:maxiters
+        # TODO check if nameing with heavy use of subscrips is ok
+        fₙ = f(xₙ)
+        xₙ₊₁ = xₙ + J⁻¹ * fₙ
+        Δxₙ = xₙ₊₁ - xₙ
+        Δfₙ = f(xₙ₊₁) - fₙ
+        J⁻¹ .+= ((Δxₙ .- J⁻¹ * Δfₙ) ./ (Δxₙ' * J⁻¹ * Δfₙ)) * (Δxₙ' * J⁻¹)
+
+        iszero(fₙ) &&
+            return SciMLBase.build_solution(prob, alg, xₙ₊₁, fₙ; retcode = ReturnCode.Success)
+
+        if isapprox(xₙ₊₁, xₙ, atol = atol, rtol = rtol)
+            return SciMLBase.build_solution(prob, alg, xₙ₊₁, fₙ; retcode = ReturnCode.Success)
+        end
+        xₙ = xₙ₊₁
+    end
+
+    @show xₙ, fₙ
+    return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
+end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 0c4194675..bc5a3902a 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -77,7 +77,7 @@ for alg in [Bisection(), Falsi()]
     global g, p
     g = function (p)
         probN = IntervalNonlinearProblem{false}(f, tspan, p)
-        sol = solve(probN, Bisection())
+        sol = solve(probN, Bisection())  # TODO check if "alg" should replace "Bisection()"
         return [sol.left]
     end
 
@@ -102,6 +102,7 @@ probN = NonlinearProblem(f, u0)
 @test solve(probN, SimpleNewtonRaphson(); immutable = false).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
+# TODO check why the 2 lines above are identical
 
 for u0 in [1.0, [1, 1.0]]
     local f, probN, sol
@@ -109,6 +110,7 @@ for u0 in [1.0, [1, 1.0]]
     probN = NonlinearProblem(f, u0)
     sol = sqrt(2) * u0
 
+    # TODO check why the two lines below are identical
     @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
     @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
     @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u ≈ sol

From 2d0c7d55a428019d78f259a3a890d2bb8ea67d83 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Mon, 2 Jan 2023 20:20:26 +0100
Subject: [PATCH 018/700] Implemented Broyden and tests

---
 lib/SimpleNonlinearSolve/Project.toml       |  1 +
 lib/SimpleNonlinearSolve/src/broyden.jl     | 45 ++++++++-----
 lib/SimpleNonlinearSolve/test/basictests.jl | 73 +++++++++++++--------
 3 files changed, 77 insertions(+), 42 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index fa4f7f015..3f4c0d749 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -7,6 +7,7 @@ version = "0.1.4"
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SnoopPrecompile = "66db9d55-30c0-4569-8b51-7e840670fc0c"
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 9f9388bad..7664cf6c8 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -5,13 +5,19 @@
 struct Broyden <: AbstractSimpleNonlinearSolveAlgorithm end
 
 function SciMLBase.solve(prob::NonlinearProblem,
-                         alg::Broyden, args...; abstol = nothing,
-                         reltol = nothing,
-                         maxiters = 1000, kwargs...)
+    alg::Broyden, args...; abstol = nothing,
+    reltol = nothing,
+    maxiters = 1000, kwargs...)
+
     f = Base.Fix2(prob.f, prob.p)
-    xₙ = float(prob.u0)
-    T = typeof(xₙ)
-    J⁻¹ = Matrix{T}(I, length(xₙ), length(xₙ))
+    x = float(prob.u0)
+    fₙ = f(x)
+    T = eltype(x)
+    if length(x) > 1
+        J⁻¹ = Matrix{T}(I, length(x), length(x))
+    else
+        J⁻¹ = 1
+    end
 
     if SciMLBase.isinplace(prob)
         error("Broyden currently only supports out-of-place nonlinear problems")
@@ -21,23 +27,30 @@ function SciMLBase.solve(prob::NonlinearProblem,
            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
     rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
 
-    for _ in 1:maxiters
-        # TODO check if nameing with heavy use of subscrips is ok
+    xₙ = x
+    xₙ₋₁ = x
+    fₙ₋₁ = fₙ
+    for n in 1:maxiters
+
+        xₙ = xₙ₋₁ - J⁻¹ * fₙ₋₁
         fₙ = f(xₙ)
-        xₙ₊₁ = xₙ + J⁻¹ * fₙ
-        Δxₙ = xₙ₊₁ - xₙ
-        Δfₙ = f(xₙ₊₁) - fₙ
-        J⁻¹ .+= ((Δxₙ .- J⁻¹ * Δfₙ) ./ (Δxₙ' * J⁻¹ * Δfₙ)) * (Δxₙ' * J⁻¹)
+        Δxₙ = xₙ - xₙ₋₁
+        Δfₙ = fₙ - fₙ₋₁
+        J⁻¹ += ((Δxₙ - J⁻¹ * Δfₙ) ./ (Δxₙ' * J⁻¹ * Δfₙ)) * (Δxₙ' * J⁻¹)
 
         iszero(fₙ) &&
-            return SciMLBase.build_solution(prob, alg, xₙ₊₁, fₙ; retcode = ReturnCode.Success)
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
+                                            retcode = ReturnCode.Success)
 
-        if isapprox(xₙ₊₁, xₙ, atol = atol, rtol = rtol)
-            return SciMLBase.build_solution(prob, alg, xₙ₊₁, fₙ; retcode = ReturnCode.Success)
+        if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
+                                            retcode = ReturnCode.Success)
         end
-        xₙ = xₙ₊₁
+        xₙ₋₁ = xₙ
+        fₙ₋₁ = fₙ
     end
 
     @show xₙ, fₙ
+
     return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index bc5a3902a..5518fb47c 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -3,6 +3,7 @@ using StaticArrays
 using BenchmarkTools
 using Test
 
+# SimpleNewtonRaphson
 function benchmark_scalar(f, u0)
     probN = NonlinearProblem{false}(f, u0)
     sol = (solve(probN, SimpleNewtonRaphson()))
@@ -23,38 +24,53 @@ sol = benchmark_scalar(sf, csu0)
 
 @test (@ballocated benchmark_scalar(sf, csu0)) == 0
 
+# Broyden
+function benchmark_scalar(f, u0)
+    probN = NonlinearProblem{false}(f, u0)
+    sol = (solve(probN, Broyden()))
+end
+
+sol = benchmark_scalar(sf, csu0)
+@test sol.retcode === ReturnCode.Success
+@test sol.u * sol.u - 2 < 1e-9
+@test (@ballocated benchmark_scalar(sf, csu0)) == 0
+
 # AD Tests
 using ForwardDiff
 
 # Immutable
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
-g = function (p)
-    probN = NonlinearProblem{false}(f, csu0, p)
-    sol = solve(probN, SimpleNewtonRaphson(), tol = 1e-9)
-    return sol.u[end]
-end
+for alg in [SimpleNewtonRaphson(), Broyden()]
+    g = function (p)
+        probN = NonlinearProblem{false}(f, csu0, p)
+        sol = solve(probN, alg, tol = 1e-9)
+        return sol.u[end]
+    end
 
-for p in 1.0:0.1:100.0
-    @test g(p) ≈ sqrt(p)
-    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+    for p in 1.1:0.1:100.0
+        @test g(p) ≈ sqrt(p)
+        @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+    end
 end
 
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
+for alg in [SimpleNewtonRaphson(), Broyden()]
 
-# SimpleNewtonRaphson
-g = function (p)
-    probN = NonlinearProblem{false}(f, oftype(p, u0), p)
-    sol = solve(probN, SimpleNewtonRaphson())
-    return sol.u
-end
-
-@test ForwardDiff.derivative(g, 1.0) ≈ 0.5
+    g = function (p)
+        probN = NonlinearProblem{false}(f, oftype(p, u0), p)
+        sol = solve(probN, alg)
+        return sol.u
+    end
 
-for p in 1.1:0.1:100.0
-    @test g(p) ≈ sqrt(p)
+    p = 1.1
     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+
+    for p in 1.1:0.1:100.0
+        @test g(p) ≈ sqrt(p)
+        @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+    end
 end
 
 tspan = (1.0, 20.0)
@@ -77,7 +93,7 @@ for alg in [Bisection(), Falsi()]
     global g, p
     g = function (p)
         probN = IntervalNonlinearProblem{false}(f, tspan, p)
-        sol = solve(probN, Bisection())  # TODO check if "alg" should replace "Bisection()"
+        sol = solve(probN, alg)
         return [sol.left]
     end
 
@@ -85,16 +101,18 @@ for alg in [Bisection(), Falsi()]
     @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
 end
 
-gnewton = function (p)
-    probN = NonlinearProblem{false}(f, 0.5, p)
-    sol = solve(probN, SimpleNewtonRaphson())
-    return [sol.u]
+for alg in [SimpleNewtonRaphson(), Broyden()]
+    global g, p
+    g = function (p)
+        probN = NonlinearProblem{false}(f, 0.5, p)
+        sol = solve(probN, alg)
+        return [sol.u]
+    end
+    @test g(p) ≈ [sqrt(p[2] / p[1])]
+    @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
 end
-@test gnewton(p) ≈ [sqrt(p[2] / p[1])]
-@test ForwardDiff.jacobian(gnewton, p) ≈ ForwardDiff.jacobian(t, p)
 
 # Error Checks
-
 f, u0 = (u, p) -> u .* u .- 2.0, @SVector[1.0, 1.0]
 probN = NonlinearProblem(f, u0)
 
@@ -103,6 +121,8 @@ probN = NonlinearProblem(f, u0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
 # TODO check why the 2 lines above are identical
+@test solve(probN, Broyden()).u[end] ≈ sqrt(2.0)
+@test solve(probN, Broyden(); immutable = false).u[end] ≈ sqrt(2.0)
 
 for u0 in [1.0, [1, 1.0]]
     local f, probN, sol
@@ -114,6 +134,7 @@ for u0 in [1.0, [1, 1.0]]
     @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
     @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
     @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u ≈ sol
+    @test solve(probN, Broyden()).u ≈ sol
 end
 
 # Bisection Tests

From 37522c934da12068ac02d5b401cc0f18449ba043 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Mon, 2 Jan 2023 22:24:29 +0100
Subject: [PATCH 019/700] Cleanup

---
 .../src/SimpleNonlinearSolve.jl               |  2 +-
 lib/SimpleNonlinearSolve/src/broyden.jl       | 21 +++++++++++--------
 lib/SimpleNonlinearSolve/test/basictests.jl   |  8 ++-----
 3 files changed, 15 insertions(+), 16 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 213ba2317..0b2fd0b48 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -4,7 +4,7 @@ using Reexport
 using FiniteDiff, ForwardDiff
 using ForwardDiff: Dual
 using StaticArraysCore
-using LinearAlgebra # TODO check if it is ok to add this
+using LinearAlgebra
 import ArrayInterfaceCore
 
 @reexport using SciMLBase
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 7664cf6c8..35d4adbbc 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -1,14 +1,18 @@
-# TODO add docstrings
+"""
+```julia
+Broyden()
+```
+
+A low-overhead implementation of Broyden. This method is non-allocating on scalar
+and static array problems.
+"""
 
-# TODO check what the supertype should be
-# TODO check if this should be defined as in raphson.jl
 struct Broyden <: AbstractSimpleNonlinearSolveAlgorithm end
 
 function SciMLBase.solve(prob::NonlinearProblem,
-    alg::Broyden, args...; abstol = nothing,
-    reltol = nothing,
-    maxiters = 1000, kwargs...)
-
+                         alg::Broyden, args...; abstol = nothing,
+                         reltol = nothing,
+                         maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     fₙ = f(x)
@@ -30,8 +34,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
     xₙ = x
     xₙ₋₁ = x
     fₙ₋₁ = fₙ
-    for n in 1:maxiters
-
+    for _ in 1:maxiters
         xₙ = xₙ₋₁ - J⁻¹ * fₙ₋₁
         fₙ = f(xₙ)
         Δxₙ = xₙ - xₙ₋₁
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 5518fb47c..6a5f69b3f 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -57,16 +57,12 @@ end
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
 for alg in [SimpleNewtonRaphson(), Broyden()]
-
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
         return sol.u
     end
 
-    p = 1.1
-    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
-
     for p in 1.1:0.1:100.0
         @test g(p) ≈ sqrt(p)
         @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
@@ -120,7 +116,7 @@ probN = NonlinearProblem(f, u0)
 @test solve(probN, SimpleNewtonRaphson(); immutable = false).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
-# TODO check why the 2 lines above are identical
+
 @test solve(probN, Broyden()).u[end] ≈ sqrt(2.0)
 @test solve(probN, Broyden(); immutable = false).u[end] ≈ sqrt(2.0)
 
@@ -130,10 +126,10 @@ for u0 in [1.0, [1, 1.0]]
     probN = NonlinearProblem(f, u0)
     sol = sqrt(2) * u0
 
-    # TODO check why the two lines below are identical
     @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
     @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
     @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u ≈ sol
+
     @test solve(probN, Broyden()).u ≈ sol
 end
 

From 93750f5c78e6dc26f013363e9a13779ef4c03650 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 2 Jan 2023 17:28:03 -0500
Subject: [PATCH 020/700] Update src/broyden.jl

---
 lib/SimpleNonlinearSolve/src/broyden.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 35d4adbbc..242ec674e 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -6,7 +6,6 @@ Broyden()
 A low-overhead implementation of Broyden. This method is non-allocating on scalar
 and static array problems.
 """
-
 struct Broyden <: AbstractSimpleNonlinearSolveAlgorithm end
 
 function SciMLBase.solve(prob::NonlinearProblem,

From 6c673bf4a0b3eabcee1583f9b644ce941a739a35 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 2 Jan 2023 17:34:06 -0500
Subject: [PATCH 021/700] Update src/broyden.jl

---
 lib/SimpleNonlinearSolve/src/broyden.jl | 2 --
 1 file changed, 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 242ec674e..ddeba8d1d 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -52,7 +52,5 @@ function SciMLBase.solve(prob::NonlinearProblem,
         fₙ₋₁ = fₙ
     end
 
-    @show xₙ, fₙ
-
     return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
 end

From f0d69b08abd916ae6e15db76e32699298614bdce Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 2 Jan 2023 17:43:43 -0500
Subject: [PATCH 022/700] Update src/broyden.jl

---
 lib/SimpleNonlinearSolve/src/broyden.jl | 6 +-----
 1 file changed, 1 insertion(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index ddeba8d1d..ab4d313b9 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -16,11 +16,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
     x = float(prob.u0)
     fₙ = f(x)
     T = eltype(x)
-    if length(x) > 1
-        J⁻¹ = Matrix{T}(I, length(x), length(x))
-    else
-        J⁻¹ = 1
-    end
+    J⁻¹ = ArrayInterfaceCore.zeromatrix(x)
 
     if SciMLBase.isinplace(prob)
         error("Broyden currently only supports out-of-place nonlinear problems")

From ae9d41774c4cdedd88a78d4be121d7170e087948 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 2 Jan 2023 17:44:26 -0500
Subject: [PATCH 023/700] Update src/broyden.jl

---
 lib/SimpleNonlinearSolve/src/broyden.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index ab4d313b9..49f53950a 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -16,7 +16,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
     x = float(prob.u0)
     fₙ = f(x)
     T = eltype(x)
-    J⁻¹ = ArrayInterfaceCore.zeromatrix(x)
+    J⁻¹ = ArrayInterfaceCore.zeromatrix(x) + I
 
     if SciMLBase.isinplace(prob)
         error("Broyden currently only supports out-of-place nonlinear problems")

From 8aa03478958812b50065c36b8ae564e0d03b339c Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Tue, 3 Jan 2023 17:33:45 +0100
Subject: [PATCH 024/700] Implemented and tested the Klement solver

---
 .../src/SimpleNonlinearSolve.jl               |  3 +-
 lib/SimpleNonlinearSolve/src/klement.jl       | 65 +++++++++++++++++++
 lib/SimpleNonlinearSolve/test/basictests.jl   | 22 ++++++-
 3 files changed, 86 insertions(+), 4 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/klement.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 0b2fd0b48..04309465b 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -20,6 +20,7 @@ include("falsi.jl")
 include("raphson.jl")
 include("ad.jl")
 include("broyden.jl")
+include("klement.jl")
 
 import SnoopPrecompile
 
@@ -46,6 +47,6 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
 end end
 
 # DiffEq styled algorithms
-export Bisection, Broyden, Falsi, SimpleNewtonRaphson
+export Bisection, Broyden, Falsi, Klement, SimpleNewtonRaphson
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
new file mode 100644
index 000000000..86ecd7ef8
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -0,0 +1,65 @@
+"""
+```julia
+Klement()
+```
+
+A low-overhead implementation of [Klement](https://jatm.com.br/jatm/article/view/373).
+This method is non-allocating on scalar and static array problems.
+
+
+"""
+struct Klement <: AbstractSimpleNonlinearSolveAlgorithm end
+
+function SciMLBase.solve(prob::NonlinearProblem,
+                         alg::Klement, args...; abstol = nothing,
+                         reltol = nothing,
+                         maxiters = 1000, kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    x = float(prob.u0)
+    fₙ = f(x)
+    T = eltype(x)
+    J = ArrayInterfaceCore.zeromatrix(x) + I
+
+    if SciMLBase.isinplace(prob)
+        error("Klement currently only supports out-of-place nonlinear problems")
+    end
+
+    atol = abstol !== nothing ? abstol :
+           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
+    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
+
+    xₙ = x
+    xₙ₋₁ = x
+    fₙ₋₁ = fₙ
+    for _ in 1:maxiters
+
+        xₙ = xₙ₋₁ - inv(J) * fₙ₋₁
+        fₙ = f(xₙ)
+        Δxₙ = xₙ - xₙ₋₁
+        Δfₙ = fₙ - fₙ₋₁
+
+        # Prevent division by 0
+        denominator = max.(J' .^ 2 * Δxₙ .^ 2, 1e-9)
+
+        k = (Δfₙ - J * Δxₙ) ./ denominator
+        J += (k * Δxₙ' .* J) * J
+
+        # Prevent inverting singular matrix
+        if det(J) ≈ 0
+            J = ArrayInterfaceCore.zeromatrix(x) + I
+        end
+
+        iszero(fₙ) &&
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
+                                            retcode = ReturnCode.Success)
+
+        if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
+                                            retcode = ReturnCode.Success)
+        end
+        xₙ₋₁ = xₙ
+        fₙ₋₁ = fₙ
+    end
+
+    return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
+end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 6a5f69b3f..648c16fb4 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -35,13 +35,24 @@ sol = benchmark_scalar(sf, csu0)
 @test sol.u * sol.u - 2 < 1e-9
 @test (@ballocated benchmark_scalar(sf, csu0)) == 0
 
+# Klement
+function benchmark_scalar(f, u0)
+    probN = NonlinearProblem{false}(f, u0)
+    sol = (solve(probN, Klement()))
+end
+
+sol = benchmark_scalar(sf, csu0)
+@test sol.retcode === ReturnCode.Success
+@test sol.u * sol.u - 2 < 1e-9
+@test (@ballocated benchmark_scalar(sf, csu0)) == 0
+
 # AD Tests
 using ForwardDiff
 
 # Immutable
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
-for alg in [SimpleNewtonRaphson(), Broyden()]
+for alg in [SimpleNewtonRaphson(), Broyden(), Klement()]
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
         sol = solve(probN, alg, tol = 1e-9)
@@ -56,7 +67,7 @@ end
 
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
-for alg in [SimpleNewtonRaphson(), Broyden()]
+for alg in [SimpleNewtonRaphson(), Broyden(), Klement()]
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
@@ -97,7 +108,7 @@ for alg in [Bisection(), Falsi()]
     @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
 end
 
-for alg in [SimpleNewtonRaphson(), Broyden()]
+for alg in [SimpleNewtonRaphson(), Broyden(), Klement()]
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -120,6 +131,9 @@ probN = NonlinearProblem(f, u0)
 @test solve(probN, Broyden()).u[end] ≈ sqrt(2.0)
 @test solve(probN, Broyden(); immutable = false).u[end] ≈ sqrt(2.0)
 
+@test solve(probN, Klement()).u[end] ≈ sqrt(2.0)
+@test solve(probN, Klement(); immutable = false).u[end] ≈ sqrt(2.0)
+
 for u0 in [1.0, [1, 1.0]]
     local f, probN, sol
     f = (u, p) -> u .* u .- 2.0
@@ -131,6 +145,8 @@ for u0 in [1.0, [1, 1.0]]
     @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u ≈ sol
 
     @test solve(probN, Broyden()).u ≈ sol
+
+    @test solve(probN, Klement()).u ≈ sol
 end
 
 # Bisection Tests

From ac619dc25f8599d39240c84f9a00c98da50747a8 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Tue, 3 Jan 2023 17:36:18 +0100
Subject: [PATCH 025/700] format fix

---
 lib/SimpleNonlinearSolve/src/klement.jl | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 86ecd7ef8..603516751 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -5,8 +5,6 @@ Klement()
 
 A low-overhead implementation of [Klement](https://jatm.com.br/jatm/article/view/373).
 This method is non-allocating on scalar and static array problems.
-
-
 """
 struct Klement <: AbstractSimpleNonlinearSolveAlgorithm end
 
@@ -32,7 +30,6 @@ function SciMLBase.solve(prob::NonlinearProblem,
     xₙ₋₁ = x
     fₙ₋₁ = fₙ
     for _ in 1:maxiters
-
         xₙ = xₙ₋₁ - inv(J) * fₙ₋₁
         fₙ = f(xₙ)
         Δxₙ = xₙ - xₙ₋₁

From 433e7c7bc712422c0f2423a5c277e1687081ce20 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Wed, 4 Jan 2023 12:15:57 +0100
Subject: [PATCH 026/700] change singularity handeling, and init of J

---
 lib/SimpleNonlinearSolve/src/klement.jl | 29 ++++++++++++++-----------
 lib/SimpleNonlinearSolve/src/utils.jl   | 10 +++++++++
 2 files changed, 26 insertions(+), 13 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 603516751..77e0fa14f 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -16,7 +16,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
     x = float(prob.u0)
     fₙ = f(x)
     T = eltype(x)
-    J = ArrayInterfaceCore.zeromatrix(x) + I
+    J = init_J(x)
 
     if SciMLBase.isinplace(prob)
         error("Klement currently only supports out-of-place nonlinear problems")
@@ -30,8 +30,19 @@ function SciMLBase.solve(prob::NonlinearProblem,
     xₙ₋₁ = x
     fₙ₋₁ = fₙ
     for _ in 1:maxiters
-        xₙ = xₙ₋₁ - inv(J) * fₙ₋₁
+        tmp = J \ fₙ₋₁
+        xₙ = xₙ₋₁ - tmp
         fₙ = f(xₙ)
+
+        iszero(fₙ) &&
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
+                                            retcode = ReturnCode.Success)
+
+        if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
+                                            retcode = ReturnCode.Success)
+        end
+
         Δxₙ = xₙ - xₙ₋₁
         Δfₙ = fₙ - fₙ₋₁
 
@@ -41,19 +52,11 @@ function SciMLBase.solve(prob::NonlinearProblem,
         k = (Δfₙ - J * Δxₙ) ./ denominator
         J += (k * Δxₙ' .* J) * J
 
-        # Prevent inverting singular matrix
-        if det(J) ≈ 0
-            J = ArrayInterfaceCore.zeromatrix(x) + I
+        # Singularity test
+        if cond(J) > 1e9
+            J = init_J(xₙ)
         end
 
-        iszero(fₙ) &&
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                                            retcode = ReturnCode.Success)
-
-        if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                                            retcode = ReturnCode.Success)
-        end
         xₙ₋₁ = xₙ
         fₙ₋₁ = fₙ
     end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 25f6ba358..a4d86e2f8 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -33,3 +33,13 @@ value_derivative(f::F, x::AbstractArray) where {F} = f(x), ForwardDiff.jacobian(
 value(x) = x
 value(x::Dual) = ForwardDiff.value(x)
 value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
+
+function init_J(x)
+    J = ArrayInterfaceCore.zeromatrix(x)
+    if ismutable(x)
+        J[diagind(J)] .= one(eltype(x))
+    else
+        J += I
+    end
+    return J
+end

From 27f5502d02313835dedd42ec74f81c43ca0a67b0 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Wed, 4 Jan 2023 18:57:58 +0100
Subject: [PATCH 027/700] using lu-factorization

---
 lib/SimpleNonlinearSolve/src/broyden.jl |  2 +-
 lib/SimpleNonlinearSolve/src/klement.jl | 94 ++++++++++++++++++-------
 2 files changed, 69 insertions(+), 27 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 49f53950a..06f923de2 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -16,7 +16,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
     x = float(prob.u0)
     fₙ = f(x)
     T = eltype(x)
-    J⁻¹ = ArrayInterfaceCore.zeromatrix(x) + I
+    J⁻¹ = init_J(x)
 
     if SciMLBase.isinplace(prob)
         error("Broyden currently only supports out-of-place nonlinear problems")
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 77e0fa14f..1209e9590 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -4,7 +4,7 @@ Klement()
 ```
 
 A low-overhead implementation of [Klement](https://jatm.com.br/jatm/article/view/373).
-This method is non-allocating on scalar and static array problems.
+This method is non-allocating on scalar problems.
 """
 struct Klement <: AbstractSimpleNonlinearSolveAlgorithm end
 
@@ -16,7 +16,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
     x = float(prob.u0)
     fₙ = f(x)
     T = eltype(x)
-    J = init_J(x)
+    singular_tol = 1e-9
 
     if SciMLBase.isinplace(prob)
         error("Klement currently only supports out-of-place nonlinear problems")
@@ -29,36 +29,78 @@ function SciMLBase.solve(prob::NonlinearProblem,
     xₙ = x
     xₙ₋₁ = x
     fₙ₋₁ = fₙ
-    for _ in 1:maxiters
-        tmp = J \ fₙ₋₁
-        xₙ = xₙ₋₁ - tmp
-        fₙ = f(xₙ)
-
-        iszero(fₙ) &&
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                                            retcode = ReturnCode.Success)
-
-        if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                                            retcode = ReturnCode.Success)
-        end
 
-        Δxₙ = xₙ - xₙ₋₁
-        Δfₙ = fₙ - fₙ₋₁
+    # x is scalar
+    if isa(x, Number)
+        J = 1.0
+        for _ in 1:maxiters
+
+            xₙ = xₙ₋₁ - fₙ₋₁/J
+            fₙ = f(xₙ)
+
+            iszero(fₙ) &&
+                return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
+                                                retcode = ReturnCode.Success)
+
+            if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
+                return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
+                                                retcode = ReturnCode.Success)
+            end
 
-        # Prevent division by 0
-        denominator = max.(J' .^ 2 * Δxₙ .^ 2, 1e-9)
+            Δxₙ = xₙ - xₙ₋₁
+            Δfₙ = fₙ - fₙ₋₁
 
-        k = (Δfₙ - J * Δxₙ) ./ denominator
-        J += (k * Δxₙ' .* J) * J
+            # Prevent division by 0
+            denominator = max(J ^ 2 * Δxₙ ^ 2, 1e-9)
 
-        # Singularity test
-        if cond(J) > 1e9
-            J = init_J(xₙ)
+            k = (Δfₙ - J * Δxₙ) / denominator
+            J += (k * Δxₙ * J) * J
+
+            # Singularity test
+            if J < singular_tol
+                J = 1.0
+            end
+
+            xₙ₋₁ = xₙ
+            fₙ₋₁ = fₙ
         end
+    # x is a vector
+    else
+        J = init_J(x)
+        F = lu(J, check = false)
+        for _ in 1:maxiters
+            tmp = F \ fₙ₋₁
+            xₙ = xₙ₋₁ - tmp
+            fₙ = f(xₙ)
+
+            iszero(fₙ) &&
+                return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
+                                                retcode = ReturnCode.Success)
 
-        xₙ₋₁ = xₙ
-        fₙ₋₁ = fₙ
+            if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
+                return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
+                                                retcode = ReturnCode.Success)
+            end
+
+            Δxₙ = xₙ - xₙ₋₁
+            Δfₙ = fₙ - fₙ₋₁
+
+            # Prevent division by 0
+            denominator = max.(J' .^ 2 * Δxₙ .^ 2, 1e-9)
+
+            k = (Δfₙ - J * Δxₙ) ./ denominator
+            J += (k * Δxₙ' .* J) * J
+            F = lu(J, check = false)
+
+            # Singularity test
+            if any(abs.(F.U[diagind(F.U)]) .< singular_tol)
+                J = init_J(xₙ)
+                F = lu(J, check = false)
+            end
+
+            xₙ₋₁ = xₙ
+            fₙ₋₁ = fₙ
+        end
     end
 
     return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)

From 17bb068288b5fd47fed2ff12493451e471e8c701 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Wed, 4 Jan 2023 19:41:03 +0100
Subject: [PATCH 028/700] formating

---
 lib/SimpleNonlinearSolve/src/klement.jl | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 1209e9590..4804e0922 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -34,8 +34,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
     if isa(x, Number)
         J = 1.0
         for _ in 1:maxiters
-
-            xₙ = xₙ₋₁ - fₙ₋₁/J
+            xₙ = xₙ₋₁ - fₙ₋₁ / J
             fₙ = f(xₙ)
 
             iszero(fₙ) &&
@@ -51,7 +50,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
             Δfₙ = fₙ - fₙ₋₁
 
             # Prevent division by 0
-            denominator = max(J ^ 2 * Δxₙ ^ 2, 1e-9)
+            denominator = max(J^2 * Δxₙ^2, 1e-9)
 
             k = (Δfₙ - J * Δxₙ) / denominator
             J += (k * Δxₙ * J) * J
@@ -64,7 +63,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
             xₙ₋₁ = xₙ
             fₙ₋₁ = fₙ
         end
-    # x is a vector
+        # x is a vector
     else
         J = init_J(x)
         F = lu(J, check = false)

From d71882cf01b419d61fc5849103b5b74a27f5d5d6 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 4 Jan 2023 15:25:04 -0500
Subject: [PATCH 029/700] Update src/klement.jl

---
 lib/SimpleNonlinearSolve/src/klement.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 4804e0922..04b5787b8 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -31,7 +31,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
     fₙ₋₁ = fₙ
 
     # x is scalar
-    if isa(x, Number)
+    if x isa Number
         J = 1.0
         for _ in 1:maxiters
             xₙ = xₙ₋₁ - fₙ₋₁ / J

From 0cb28987e7671c10427e5e7eb888605c8e2400cf Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Wed, 4 Jan 2023 22:05:44 +0100
Subject: [PATCH 030/700] moving the rows around => 1 less lu-factorization

---
 lib/SimpleNonlinearSolve/src/klement.jl | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 4804e0922..1d8b8afc7 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -66,8 +66,15 @@ function SciMLBase.solve(prob::NonlinearProblem,
         # x is a vector
     else
         J = init_J(x)
-        F = lu(J, check = false)
         for _ in 1:maxiters
+            F = lu(J, check = false)
+
+            # Singularity test
+            if any(abs.(F.U[diagind(F.U)]) .< singular_tol)
+                J = init_J(xₙ)
+                F = lu(J, check = false)
+            end
+
             tmp = F \ fₙ₋₁
             xₙ = xₙ₋₁ - tmp
             fₙ = f(xₙ)
@@ -89,13 +96,6 @@ function SciMLBase.solve(prob::NonlinearProblem,
 
             k = (Δfₙ - J * Δxₙ) ./ denominator
             J += (k * Δxₙ' .* J) * J
-            F = lu(J, check = false)
-
-            # Singularity test
-            if any(abs.(F.U[diagind(F.U)]) .< singular_tol)
-                J = init_J(xₙ)
-                F = lu(J, check = false)
-            end
 
             xₙ₋₁ = xₙ
             fₙ₋₁ = fₙ

From 1595d0ee77bd4e0f43eda0fac8d281b1a64514bb Mon Sep 17 00:00:00 2001
From: Arno Strouwen <arno.strouwen@telenet.be>
Date: Wed, 4 Jan 2023 23:10:54 +0100
Subject: [PATCH 031/700] [skip ci] spelling

---
 lib/SimpleNonlinearSolve/src/bisection.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index e90f28f9e..4e2b232e6 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -6,9 +6,9 @@ A common bisection method.
 ### Keyword Arguments
 
 - `exact_left`: whether to enforce whether the left side of the interval must be exactly
-  zero for the returned result. Defualts to false.
+  zero for the returned result. Defaults to false.
 - `exact_right`: whether to enforce whether the right side of the interval must be exactly
-  zero for the returned result. Defualts to false.
+  zero for the returned result. Defaults to false.
 """
 struct Bisection <: AbstractBracketingAlgorithm
     exact_left::Bool

From f419c140cbbb6f9d9d49db9a8e68e6aff685fabe Mon Sep 17 00:00:00 2001
From: Arno Strouwen <arno.strouwen@telenet.be>
Date: Wed, 4 Jan 2023 23:12:52 +0100
Subject: [PATCH 032/700] [skip ci] spelling

---
 lib/SimpleNonlinearSolve/src/raphson.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 47ae6eaf8..711f7766e 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -10,18 +10,18 @@ and static array problems.
 !!! note
 
     As part of the decreased overhead, this method omits some of the higher level error
-    catching of the other methods. Thus to see better error messages, use one of the other
+    catching of the other methods. Thus, to see better error messages, use one of the other
     methods like `NewtonRaphson`
 
 ### Keyword Arguments
 
 - `chunk_size`: the chunk size used by the internal ForwardDiff.jl automatic differentiation
-  system. This allows for multiple derivative columns to be computed simultaniously,
+  system. This allows for multiple derivative columns to be computed simultaneously,
   improving performance. Defaults to `0`, which is equivalent to using ForwardDiff.jl's
   default chunk size mechanism. For more details, see the documentation for
   [ForwardDiff.jl](https://juliadiff.org/ForwardDiff.jl/stable/).
 - `autodiff`: whether to use forward-mode automatic differentiation for the Jacobian.
-  Note that this argument is ignored if an analytical Jacobian is passed as that will be
+  Note that this argument is ignored if an analytical Jacobian is passed; as that will be
   used instead. Defaults to `Val{true}`, which means ForwardDiff.jl is used by default.
   If `Val{false}`, then FiniteDiff.jl is used for finite differencing.
 - `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to

From 2a8b42cf8a385d5ed3bb80e418138c6c7bfc8ef7 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Thu, 5 Jan 2023 14:06:16 +0100
Subject: [PATCH 033/700] Missed to precompile Klement

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 04309465b..a91b05719 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -26,7 +26,7 @@ import SnoopPrecompile
 
 SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
     prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-    for alg in (SimpleNewtonRaphson, Broyden)
+    for alg in (SimpleNewtonRaphson, Broyden, Klement)
         solve(prob_no_brack, alg(), tol = T(1e-2))
     end
 

From 175d656f5133d02a1e4fc43ce65d5363e80023a8 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Tue, 10 Jan 2023 20:33:50 +0100
Subject: [PATCH 034/700] Implementation of a trust-region solver

---
 .../src/SimpleNonlinearSolve.jl               |   8 +-
 lib/SimpleNonlinearSolve/src/trustRegion.jl   | 125 ++++++++++++++++++
 lib/SimpleNonlinearSolve/src/utils.jl         |  25 ++++
 lib/SimpleNonlinearSolve/test/basictests.jl   |  28 +++-
 4 files changed, 182 insertions(+), 4 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/trustRegion.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index a91b05719..4937ae119 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -21,6 +21,7 @@ include("raphson.jl")
 include("ad.jl")
 include("broyden.jl")
 include("klement.jl")
+include("trustRegion.jl")
 
 import SnoopPrecompile
 
@@ -30,6 +31,10 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
         solve(prob_no_brack, alg(), tol = T(1e-2))
     end
 
+    for alg in (TrustRegion(1.0),)
+        solve(prob_no_brack, alg, tol = T(1e-2))
+    end
+
     #=
     for alg in (SimpleNewtonRaphson,)
         for u0 in ([1., 1.], StaticArraysCore.SA[1.0, 1.0])
@@ -47,6 +52,7 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
 end end
 
 # DiffEq styled algorithms
-export Bisection, Broyden, Falsi, Klement, SimpleNewtonRaphson
+export Bisection, Broyden, Falsi, Klement, SimpleNewtonRaphson,
+       TrustRegion
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
new file mode 100644
index 000000000..1d017a80d
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -0,0 +1,125 @@
+"""
+```julia
+TrustRegion(max_trust_radius::Number; chunk_size = Val{0}(),
+                               autodiff = Val{true}(), diff_type = Val{:forward})
+```
+
+A low-overhead implementation of a
+[trust-region](https://optimization.mccormick.northwestern.edu/index.php/Trust-region_methods)
+solver
+
+
+### Keyword Arguments
+- `max_trust_radius`: the maximum radius of the trust region. The step size in the algorithm
+  will change dynamically. However, it will never be greater than the `max_trust_radius`.
+
+### Keyword Arguments
+
+- `chunk_size`: the chunk size used by the internal ForwardDiff.jl automatic differentiation
+  system. This allows for multiple derivative columns to be computed simultaneously,
+  improving performance. Defaults to `0`, which is equivalent to using ForwardDiff.jl's
+  default chunk size mechanism. For more details, see the documentation for
+  [ForwardDiff.jl](https://juliadiff.org/ForwardDiff.jl/stable/).
+- `autodiff`: whether to use forward-mode automatic differentiation for the Jacobian.
+  Note that this argument is ignored if an analytical Jacobian is passed; as that will be
+  used instead. Defaults to `Val{true}`, which means ForwardDiff.jl is used by default.
+  If `Val{false}`, then FiniteDiff.jl is used for finite differencing.
+- `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
+  `Val{:forward}` for forward finite differences. For more details on the choices, see the
+  [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
+"""
+struct TrustRegion{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
+    max_trust_radius::Number
+    function TrustRegion(max_turst_radius::Number; chunk_size = Val{0}(),
+                                            autodiff = Val{true}(),
+                                            diff_type = Val{:forward})
+        new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
+            SciMLBase._unwrap_val(diff_type)}(max_trust_radius)
+    end
+end
+
+function SciMLBase.solve(prob::NonlinearProblem,
+                         alg::TrustRegion, args...; abstol = nothing,
+                         reltol = nothing,
+                         maxiters = 1000, kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    x = float(prob.u0)
+    T = typeof(x)
+    Δₘₐₓ = float(alg.max_trust_radius)  # The maximum trust region radius.
+    Δ = Δₘₐₓ / 5  # Initial trust region radius.
+    η₁ = 0.1   # Threshold for taking a step.
+    η₂ = 0.25  # Threshold for shrinking the trust region.
+    η₃ = 0.75  # Threshold for expanding the trust region.
+    t₁ = 0.25  # Factor to shrink the trust region with.
+    t₂ = 2.0   # Factor to expand the trust region with.
+
+    if SciMLBase.isinplace(prob)
+        error("TrustRegion currently only supports out-of-place nonlinear problems")
+    end
+
+    atol = abstol !== nothing ? abstol :
+           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
+    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
+
+    if alg_autodiff(alg)
+        F, ∇f = value_derivative(f, x)
+    elseif x isa AbstractArray
+        F = f(x)
+        ∇f = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x), F)
+    else
+        F = f(x)
+        ∇f = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x), F)
+    end
+
+    fₖ = 0.5 * norm(F)^2
+    H = ∇f * ∇f
+    g = ∇f * F
+
+    for k in 1:maxiters
+        # Solve the trust region subproblem.
+        δ = dogleg_method(H, g, Δ)
+        xₖ₊₁ = x + δ
+        Fₖ₊₁ = f(xₖ₊₁)
+        fₖ₊₁ = 0.5 * norm(Fₖ₊₁)^2
+
+        # Compute the ratio of the actual to predicted reduction.
+        model = -(δ' * g + 0.5 * δ' * H * δ)
+        r = (fₖ - fₖ₊₁) / model
+
+        # Update the trust region radius.
+        if r < η₂
+            Δ *= t₁
+        if r > η₁
+            if isapprox(x̂, x, atol = atol, rtol = rtol)
+                return SciMLBase.build_solution(prob, alg, x, F;
+                                                retcode = ReturnCode.Success)
+            end
+
+            x = xₖ₊₁
+            F = Fₖ₊₁
+            if alg_autodiff(alg)
+                F, ∇f = value_derivative(f, x)
+            elseif x isa AbstractArray
+                ∇f = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x),
+                                                            F)
+            else
+                ∇f = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg),
+                                                              eltype(x),
+                                                              F)
+            end
+
+            iszero(F) &&
+                return SciMLBase.build_solution(prob, alg, x, F;
+                                                retcode = ReturnCode.Success)
+            # Update the trust region radius.
+            if r > η₃ && norm(δ) ≈ Δ
+                Δ = min(t₂ * Δ, Δₘₐₓ)
+            end
+            fₖ = f̂
+            H = ∇f * ∇f
+            g = ∇f * F
+        end
+    end
+
+    return SciMLBase.build_solution(prob, alg, x, F; retcode = ReturnCode.MaxIters)
+end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index a4d86e2f8..f3b7de9f6 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -43,3 +43,28 @@ function init_J(x)
     end
     return J
 end
+
+function dogleg_method(H, g, Δ)
+    # Compute the Newton step.
+    δN = -H \ g
+    # Test if the full step is within the trust region.
+    if norm(δN) ≤ Δ
+        return δN
+    end
+
+    # Calcualte Cauchy point, optimum along the steepest descent direction.
+    δsd = -g
+    norm_δsd = norm(δsd)
+    if norm_δsd ≥ Δ
+        return δsd .* Δ / norm_δsd
+    end
+
+    # Find the intersection point on the boundary.
+    δN_δsd = δN - δsd
+    dot_δN_δsd = dot(δN_δsd, δN_δsd)
+    dot_δsd_δN_δsd = dot(δsd, δN_δsd)
+    dot_δsd = dot(δsd, δsd)
+    fact = dot_δsd_δN_δsd^2 - dot_δN_δsd * (dot_δsd - Δ^2)
+    tau = (-dot_δsd_δN_δsd + sqrt(fact)) / dot_δN_δsd
+    return δsd + tau * δN_δsd
+end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 648c16fb4..9122519f8 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -46,13 +46,24 @@ sol = benchmark_scalar(sf, csu0)
 @test sol.u * sol.u - 2 < 1e-9
 @test (@ballocated benchmark_scalar(sf, csu0)) == 0
 
+# SimpleNewtonRaphsonTrustRegion
+function benchmark_scalar(f, u0)
+    probN = NonlinearProblem{false}(f, u0)
+    sol = (solve(probN, SimpleNewtonRaphsonTrustRegion(1.0)))
+end
+
+sol = benchmark_scalar(sf, csu0)
+@test sol.retcode === ReturnCode.Success
+@test sol.u * sol.u - 2 < 1e-9
+
 # AD Tests
 using ForwardDiff
 
 # Immutable
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
-for alg in [SimpleNewtonRaphson(), Broyden(), Klement()]
+for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
+            SimpleNewtonRaphsonTrustRegion(10.0)]
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
         sol = solve(probN, alg, tol = 1e-9)
@@ -67,7 +78,8 @@ end
 
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
-for alg in [SimpleNewtonRaphson(), Broyden(), Klement()]
+for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
+            SimpleNewtonRaphsonTrustRegion(10.0)]
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
@@ -108,7 +120,8 @@ for alg in [Bisection(), Falsi()]
     @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
 end
 
-for alg in [SimpleNewtonRaphson(), Broyden(), Klement()]
+for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
+            SimpleNewtonRaphsonTrustRegion(1.0)]
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -128,6 +141,11 @@ probN = NonlinearProblem(f, u0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
 
+@test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0)).u[end] ≈ sqrt(2.0)
+@test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0); immutable = false).u[end] ≈ sqrt(2.0)
+@test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0; autodiff = false)).u[end] ≈ sqrt(2.0)
+@test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0; autodiff = false)).u[end] ≈ sqrt(2.0)
+
 @test solve(probN, Broyden()).u[end] ≈ sqrt(2.0)
 @test solve(probN, Broyden(); immutable = false).u[end] ≈ sqrt(2.0)
 
@@ -144,6 +162,10 @@ for u0 in [1.0, [1, 1.0]]
     @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
     @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u ≈ sol
 
+    @test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0)).u ≈ sol
+    @test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0)).u ≈ sol
+    @test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0; autodiff = false)).u ≈ sol
+
     @test solve(probN, Broyden()).u ≈ sol
 
     @test solve(probN, Klement()).u ≈ sol

From bc4ab2d33200eb0c192502ed83aacee088c611d5 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Tue, 10 Jan 2023 21:46:51 +0100
Subject: [PATCH 035/700] bug fix

---
 .../src/SimpleNonlinearSolve.jl               |  2 +-
 lib/SimpleNonlinearSolve/src/trustRegion.jl   | 34 +++++++++++--------
 lib/SimpleNonlinearSolve/test/basictests.jl   | 24 ++++++-------
 3 files changed, 33 insertions(+), 27 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 4937ae119..b4c094493 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -31,7 +31,7 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
         solve(prob_no_brack, alg(), tol = T(1e-2))
     end
 
-    for alg in (TrustRegion(1.0),)
+    for alg in (TrustRegion(10.0),)
         solve(prob_no_brack, alg, tol = T(1e-2))
     end
 
diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 1d017a80d..cfdf9887d 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -30,9 +30,9 @@ solver
 """
 struct TrustRegion{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     max_trust_radius::Number
-    function TrustRegion(max_turst_radius::Number; chunk_size = Val{0}(),
-                                            autodiff = Val{true}(),
-                                            diff_type = Val{:forward})
+    function TrustRegion(max_trust_radius::Number; chunk_size = Val{0}(),
+                         autodiff = Val{true}(),
+                         diff_type = Val{:forward})
         new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
             SciMLBase._unwrap_val(diff_type)}(max_trust_radius)
     end
@@ -46,8 +46,8 @@ function SciMLBase.solve(prob::NonlinearProblem,
     x = float(prob.u0)
     T = typeof(x)
     Δₘₐₓ = float(alg.max_trust_radius)  # The maximum trust region radius.
-    Δ = Δₘₐₓ / 5  # Initial trust region radius.
-    η₁ = 0.1   # Threshold for taking a step.
+    Δ = Δₘₐₓ / 11  # Initial trust region radius.
+    η₁ = 0.0   # Threshold for taking a step.
     η₂ = 0.25  # Threshold for shrinking the trust region.
     η₃ = 0.75  # Threshold for expanding the trust region.
     t₁ = 0.25  # Factor to shrink the trust region with.
@@ -88,38 +88,44 @@ function SciMLBase.solve(prob::NonlinearProblem,
 
         # Update the trust region radius.
         if r < η₂
-            Δ *= t₁
-        if r > η₁
-            if isapprox(x̂, x, atol = atol, rtol = rtol)
+            Δ = t₁ * Δ
+
+            if Δ < 1e-10
                 return SciMLBase.build_solution(prob, alg, x, F;
                                                 retcode = ReturnCode.Success)
             end
-
+        end
+        if r > η₁
+            if isapprox(xₖ₊₁, x, atol = atol, rtol = rtol)
+                return SciMLBase.build_solution(prob, alg, xₖ₊₁, Fₖ₊₁;
+                                                retcode = ReturnCode.Success)
+            end
+            # Take the step.
             x = xₖ₊₁
             F = Fₖ₊₁
             if alg_autodiff(alg)
                 F, ∇f = value_derivative(f, x)
             elseif x isa AbstractArray
                 ∇f = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x),
-                                                            F)
+                                                           F)
             else
                 ∇f = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg),
-                                                              eltype(x),
-                                                              F)
+                                                             eltype(x),
+                                                             F)
             end
 
             iszero(F) &&
                 return SciMLBase.build_solution(prob, alg, x, F;
                                                 retcode = ReturnCode.Success)
+
             # Update the trust region radius.
             if r > η₃ && norm(δ) ≈ Δ
                 Δ = min(t₂ * Δ, Δₘₐₓ)
             end
-            fₖ = f̂
+            fₖ = fₖ₊₁
             H = ∇f * ∇f
             g = ∇f * F
         end
     end
-
     return SciMLBase.build_solution(prob, alg, x, F; retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 9122519f8..f30586c22 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -46,10 +46,10 @@ sol = benchmark_scalar(sf, csu0)
 @test sol.u * sol.u - 2 < 1e-9
 @test (@ballocated benchmark_scalar(sf, csu0)) == 0
 
-# SimpleNewtonRaphsonTrustRegion
+# TrustRegion
 function benchmark_scalar(f, u0)
     probN = NonlinearProblem{false}(f, u0)
-    sol = (solve(probN, SimpleNewtonRaphsonTrustRegion(1.0)))
+    sol = (solve(probN, TrustRegion(10.0)))
 end
 
 sol = benchmark_scalar(sf, csu0)
@@ -63,7 +63,7 @@ using ForwardDiff
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
 for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
-            SimpleNewtonRaphsonTrustRegion(10.0)]
+            TrustRegion(10.0)]
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
         sol = solve(probN, alg, tol = 1e-9)
@@ -79,7 +79,7 @@ end
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
 for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
-            SimpleNewtonRaphsonTrustRegion(10.0)]
+            TrustRegion(10.0)]
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
@@ -121,7 +121,7 @@ for alg in [Bisection(), Falsi()]
 end
 
 for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
-            SimpleNewtonRaphsonTrustRegion(1.0)]
+            TrustRegion(10.0)]
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -141,10 +141,10 @@ probN = NonlinearProblem(f, u0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
 
-@test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0)).u[end] ≈ sqrt(2.0)
-@test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0); immutable = false).u[end] ≈ sqrt(2.0)
-@test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0; autodiff = false)).u[end] ≈ sqrt(2.0)
-@test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0; autodiff = false)).u[end] ≈ sqrt(2.0)
+@test solve(probN, TrustRegion(10.0)).u[end] ≈ sqrt(2.0)
+@test solve(probN, TrustRegion(10.0); immutable = false).u[end] ≈ sqrt(2.0)
+@test solve(probN, TrustRegion(10.0; autodiff = false)).u[end] ≈ sqrt(2.0)
+@test solve(probN, TrustRegion(10.0; autodiff = false)).u[end] ≈ sqrt(2.0)
 
 @test solve(probN, Broyden()).u[end] ≈ sqrt(2.0)
 @test solve(probN, Broyden(); immutable = false).u[end] ≈ sqrt(2.0)
@@ -162,9 +162,9 @@ for u0 in [1.0, [1, 1.0]]
     @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
     @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u ≈ sol
 
-    @test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0)).u ≈ sol
-    @test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0)).u ≈ sol
-    @test solve(probN, SimpleNewtonRaphsonTrustRegion(1.0; autodiff = false)).u ≈ sol
+    @test solve(probN, TrustRegion(10.0)).u ≈ sol
+    @test solve(probN, TrustRegion(10.0)).u ≈ sol
+    @test solve(probN, TrustRegion(10.0; autodiff = false)).u ≈ sol
 
     @test solve(probN, Broyden()).u ≈ sol
 

From 28aebe68542271d374db284cf7ac8f2ef64facff Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Tue, 10 Jan 2023 21:49:09 +0100
Subject: [PATCH 036/700] update of parameter

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index cfdf9887d..781085cc1 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -47,7 +47,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
     T = typeof(x)
     Δₘₐₓ = float(alg.max_trust_radius)  # The maximum trust region radius.
     Δ = Δₘₐₓ / 11  # Initial trust region radius.
-    η₁ = 0.0   # Threshold for taking a step.
+    η₁ = 0.1   # Threshold for taking a step.
     η₂ = 0.25  # Threshold for shrinking the trust region.
     η₃ = 0.75  # Threshold for expanding the trust region.
     t₁ = 0.25  # Factor to shrink the trust region with.

From 883aeacd3ff5276c4b662b315180f8cbea8a6f48 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Tue, 10 Jan 2023 21:51:08 +0100
Subject: [PATCH 037/700] format

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index b4c094493..5f269fe12 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -52,7 +52,6 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
 end end
 
 # DiffEq styled algorithms
-export Bisection, Broyden, Falsi, Klement, SimpleNewtonRaphson,
-       TrustRegion
+export Bisection, Broyden, Falsi, Klement, SimpleNewtonRaphson, TrustRegion
 
 end # module

From c555f51833cde8c3d7113b88096068d9045118a9 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Tue, 10 Jan 2023 21:58:40 +0100
Subject: [PATCH 038/700] Implemented max allowed shrink of trust-region

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 781085cc1..dd91353e6 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -74,6 +74,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
     fₖ = 0.5 * norm(F)^2
     H = ∇f * ∇f
     g = ∇f * F
+    counter = 0
 
     for k in 1:maxiters
         # Solve the trust region subproblem.
@@ -89,11 +90,13 @@ function SciMLBase.solve(prob::NonlinearProblem,
         # Update the trust region radius.
         if r < η₂
             Δ = t₁ * Δ
-
-            if Δ < 1e-10
+            counter += 1
+            if counter > 32
                 return SciMLBase.build_solution(prob, alg, x, F;
                                                 retcode = ReturnCode.Success)
             end
+        else
+            counter = 0
         end
         if r > η₁
             if isapprox(xₖ₊₁, x, atol = atol, rtol = rtol)

From 36a3f3cc54819fab66975a23f6e33155337a8a9a Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Wed, 11 Jan 2023 09:11:38 +0100
Subject: [PATCH 039/700] Made kwargs of parameters

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 72 ++++++++++++++++-----
 lib/SimpleNonlinearSolve/test/basictests.jl | 57 +++++++++++++++-
 2 files changed, 110 insertions(+), 19 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index dd91353e6..efc30969f 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -8,8 +8,7 @@ A low-overhead implementation of a
 [trust-region](https://optimization.mccormick.northwestern.edu/index.php/Trust-region_methods)
 solver
 
-
-### Keyword Arguments
+### Arguments
 - `max_trust_radius`: the maximum radius of the trust region. The step size in the algorithm
   will change dynamically. However, it will never be greater than the `max_trust_radius`.
 
@@ -27,14 +26,54 @@ solver
 - `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
   `Val{:forward}` for forward finite differences. For more details on the choices, see the
   [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
+- `initial_trust_radius`: the initial trust region radius. Defaults to
+  `max_trust_radius / 11`.
+- `step_threshold`: the threshold for taking a step. In every iteration, the threshold is
+  compared with a value `r`, which is the actual reduction in the objective function divided
+  by the predicted reduction. If `step_threshold > r` the model is not a good approximation,
+  and the step is rejected. Defaults to `0.1`. For more details, see
+  [Trust-region methods](https://optimization.mccormick.northwestern.edu/index.php/Trust-region_methods)
+- `shrink_threshold`: the threshold for shrinking the trust region radius. In every
+  iteration, the threshold is compared with a value `r` which is the actual reduction in the
+  objective function divided by the predicted reduction. If `shrink_threshold > r` the trust
+  region radius is shrunk by `shrink_factor`. Defaults to `0.25`. For more details, see
+  [Trust-region methods](https://optimization.mccormick.northwestern.edu/index.php/Trust-region_methods)
+- `expand_threshold`: the threshold for expanding the trust region radius. If a step is
+  taken, i.e `step_threshold < r` (with `r` defined in `shrink_threshold`), a check is also
+  made to see if `expand_threshold < r`. If that is true, the trust region radius is
+  expanded by `expand_factor`. Defaults to `0.75`.
+- `shrink_factor`: the factor to shrink the trust region radius with if
+  `shrink_threshold > r` (with `r` defined in `shrink_threshold`). Defaults to `0.25`.
+- `expand_factor`: the factor to expand the trust region radius with if
+  `expand_threshold < r` (with `r` defined in `shrink_threshold`). Defaults to `2.0`.
+- `max_shrink_times`: the maximum number of times to shrink the trust region radius in a
+  row, `max_shrink_times` is exceeded, the algorithm returns. Defaults to `32`.
 """
 struct TrustRegion{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     max_trust_radius::Number
+    initial_trust_radius::Number
+    step_threshold::Number
+    shrink_threshold::Number
+    expand_threshold::Number
+    shrink_factor::Number
+    expand_factor::Number
+    max_shrink_times::Int
     function TrustRegion(max_trust_radius::Number; chunk_size = Val{0}(),
                          autodiff = Val{true}(),
-                         diff_type = Val{:forward})
+                         diff_type = Val{:forward},
+                         initial_trust_radius::Number = max_trust_radius / 11,
+                         step_threshold::Number = 0.1,
+                         shrink_threshold::Number = 0.25,
+                         expand_threshold::Number = 0.75,
+                         shrink_factor::Number = 0.25,
+                         expand_factor::Number = 2.0,
+                         max_shrink_times::Int = 32)
         new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
-            SciMLBase._unwrap_val(diff_type)}(max_trust_radius)
+            SciMLBase._unwrap_val(diff_type)}(max_trust_radius, initial_trust_radius,
+                                              step_threshold,
+                                              shrink_threshold, expand_threshold,
+                                              shrink_factor,
+                                              expand_factor, max_shrink_times)
     end
 end
 
@@ -45,13 +84,14 @@ function SciMLBase.solve(prob::NonlinearProblem,
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     T = typeof(x)
-    Δₘₐₓ = float(alg.max_trust_radius)  # The maximum trust region radius.
-    Δ = Δₘₐₓ / 11  # Initial trust region radius.
-    η₁ = 0.1   # Threshold for taking a step.
-    η₂ = 0.25  # Threshold for shrinking the trust region.
-    η₃ = 0.75  # Threshold for expanding the trust region.
-    t₁ = 0.25  # Factor to shrink the trust region with.
-    t₂ = 2.0   # Factor to expand the trust region with.
+    Δₘₐₓ = float(alg.max_trust_radius)
+    Δ = float(alg.initial_trust_radius)
+    η₁ = float(alg.step_threshold)
+    η₂ = float(alg.shrink_threshold)
+    η₃ = float(alg.expand_threshold)
+    t₁ = float(alg.shrink_factor)
+    t₂ = float(alg.expand_factor)
+    max_shrink_times = alg.max_shrink_times
 
     if SciMLBase.isinplace(prob)
         error("TrustRegion currently only supports out-of-place nonlinear problems")
@@ -74,7 +114,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
     fₖ = 0.5 * norm(F)^2
     H = ∇f * ∇f
     g = ∇f * F
-    counter = 0
+    shrink_counter = 0
 
     for k in 1:maxiters
         # Solve the trust region subproblem.
@@ -85,18 +125,18 @@ function SciMLBase.solve(prob::NonlinearProblem,
 
         # Compute the ratio of the actual to predicted reduction.
         model = -(δ' * g + 0.5 * δ' * H * δ)
-        r = (fₖ - fₖ₊₁) / model
+        r = model \ (fₖ - fₖ₊₁)
 
         # Update the trust region radius.
         if r < η₂
             Δ = t₁ * Δ
-            counter += 1
-            if counter > 32
+            shrink_counter += 1
+            if shrink_counter > max_shrink_times
                 return SciMLBase.build_solution(prob, alg, x, F;
                                                 retcode = ReturnCode.Success)
             end
         else
-            counter = 0
+            shrink_counter = 0
         end
         if r > η₁
             if isapprox(xₖ₊₁, x, atol = atol, rtol = rtol)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index f30586c22..d2a030253 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -63,7 +63,7 @@ using ForwardDiff
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
 for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
-            TrustRegion(10.0)]
+    TrustRegion(10.0)]
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
         sol = solve(probN, alg, tol = 1e-9)
@@ -79,7 +79,7 @@ end
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
 for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
-            TrustRegion(10.0)]
+    TrustRegion(10.0)]
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
@@ -121,7 +121,7 @@ for alg in [Bisection(), Falsi()]
 end
 
 for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
-            TrustRegion(10.0)]
+    TrustRegion(10.0)]
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -207,3 +207,54 @@ sol = solve(probB, Bisection(; exact_left = true, exact_right = true); immutable
 @test f(nextfloat(sol.left), nothing) >= 0.0
 @test f(sol.right, nothing) >= 0.0
 @test f(prevfloat(sol.right), nothing) <= 0.0
+
+# Test that `TrustRegion` passes a test that `SimpleNewtonRaphson` fails on.
+u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
+global g, f
+f = (u, p) -> 0.010000000000000002 .+
+              10.000000000000002 ./ (1 .+
+               (0.21640425613334457 .+
+                216.40425613334457 ./ (1 .+
+                 (0.21640425613334457 .+
+                  216.40425613334457 ./
+                  (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^ 2.0) .-
+              0.0011552453009332421u
+.-p
+g = function (p)
+    probN = NonlinearProblem{false}(f, u0, p)
+    sol = solve(probN, TrustRegion(100.0))
+    return sol.u
+end
+p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+u = g(p)
+f(u, p)
+@test all(f(u, p) .< 1e-10)
+
+# Test kwars in `TrustRegion`
+max_trust_radius = [10.0, 100.0, 1000.0]
+initial_trust_radius = [10.0, 1.0, 0.1]
+step_threshold = [0.0, 0.01, 0.25]
+shrink_threshold = [0.25, 0.3, 0.5]
+expand_threshold = [0.5, 0.8, 0.9]
+shrink_factor = [0.1, 0.3, 0.5]
+expand_factor = [1.5, 2.0, 3.0]
+max_shrink_times = [10, 20, 30]
+
+list_of_options = zip(max_trust_radius, initial_trust_radius, step_threshold,
+                      shrink_threshold, expand_threshold, shrink_factor,
+                      expand_factor, max_shrink_times)
+for options in list_of_options
+    local probN, sol, alg
+    alg = TrustRegion(options[1];
+                      initial_trust_radius = options[2],
+                      step_threshold = options[3],
+                      shrink_threshold = options[4],
+                      expand_threshold = options[5],
+                      shrink_factor = options[6],
+                      expand_factor = options[7],
+                      max_shrink_times = options[8])
+
+    probN = NonlinearProblem(f, u0, p)
+    sol = solve(probN, alg)
+    @test all(f(u, p) .< 1e-10)
+end

From d163535fa32ccc9e816fd509dcc8c2c7ed221b1a Mon Sep 17 00:00:00 2001
From: Wonseok Shin <wsshin97@gmail.com>
Date: Sat, 14 Jan 2023 15:14:25 -0500
Subject: [PATCH 040/700] Remove unnecessary @show

---
 lib/SimpleNonlinearSolve/src/raphson.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 711f7766e..52888de99 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -80,6 +80,5 @@ function SciMLBase.solve(prob::NonlinearProblem,
         xo = x
     end
 
-    @show x, fx
     return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
 end

From 85bc0d7c5d4432ad8e01856a195926e94c907ec2 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 14 Jan 2023 15:23:00 -0500
Subject: [PATCH 041/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 3f4c0d749..4dcd425ba 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.4"
+version = "0.1.5"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"

From b47d1d8c4029b35dc3694349a2d1196733af90ee Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 16 Jan 2023 19:35:03 -0500
Subject: [PATCH 042/700] Use DiffEqBase high level handling

---
 lib/SimpleNonlinearSolve/Project.toml                | 2 ++
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 7 ++++---
 lib/SimpleNonlinearSolve/src/broyden.jl              | 2 +-
 lib/SimpleNonlinearSolve/src/klement.jl              | 2 +-
 lib/SimpleNonlinearSolve/src/raphson.jl              | 2 +-
 lib/SimpleNonlinearSolve/src/trustRegion.jl          | 2 +-
 6 files changed, 10 insertions(+), 7 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 4dcd425ba..1afc7746f 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -5,6 +5,7 @@ version = "0.1.5"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"
+DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -15,6 +16,7 @@ StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [compat]
 ArrayInterfaceCore = "0.1.1"
+DiffEqBase = "6.115"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 Reexport = "0.2, 1"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 5f269fe12..dbe856365 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -6,6 +6,7 @@ using ForwardDiff: Dual
 using StaticArraysCore
 using LinearAlgebra
 import ArrayInterfaceCore
+using DiffEqBase
 
 @reexport using SciMLBase
 
@@ -28,11 +29,11 @@ import SnoopPrecompile
 SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
     prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
     for alg in (SimpleNewtonRaphson, Broyden, Klement)
-        solve(prob_no_brack, alg(), tol = T(1e-2))
+        solve(prob_no_brack, alg(), abstol = T(1e-2))
     end
 
     for alg in (TrustRegion(10.0),)
-        solve(prob_no_brack, alg, tol = T(1e-2))
+        solve(prob_no_brack, alg, abstol = T(1e-2))
     end
 
     #=
@@ -47,7 +48,7 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
 
     prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p, T.((0.0, 2.0)), T(2))
     for alg in (Bisection, Falsi)
-        solve(prob_brack, alg(), tol = T(1e-2))
+        solve(prob_brack, alg(), abstol = T(1e-2))
     end
 end end
 
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 06f923de2..c51e5d1db 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -8,7 +8,7 @@ and static array problems.
 """
 struct Broyden <: AbstractSimpleNonlinearSolveAlgorithm end
 
-function SciMLBase.solve(prob::NonlinearProblem,
+function SciMLBase.__solve(prob::NonlinearProblem,
                          alg::Broyden, args...; abstol = nothing,
                          reltol = nothing,
                          maxiters = 1000, kwargs...)
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 9e2821dcb..bc07d664b 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -8,7 +8,7 @@ This method is non-allocating on scalar problems.
 """
 struct Klement <: AbstractSimpleNonlinearSolveAlgorithm end
 
-function SciMLBase.solve(prob::NonlinearProblem,
+function SciMLBase.__solve(prob::NonlinearProblem,
                          alg::Klement, args...; abstol = nothing,
                          reltol = nothing,
                          maxiters = 1000, kwargs...)
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 52888de99..4ccc4fbbd 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -36,7 +36,7 @@ struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     end
 end
 
-function SciMLBase.solve(prob::NonlinearProblem,
+function SciMLBase.__solve(prob::NonlinearProblem,
                          alg::SimpleNewtonRaphson, args...; abstol = nothing,
                          reltol = nothing,
                          maxiters = 1000, kwargs...)
diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index efc30969f..7db6f460f 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -77,7 +77,7 @@ struct TrustRegion{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     end
 end
 
-function SciMLBase.solve(prob::NonlinearProblem,
+function SciMLBase.__solve(prob::NonlinearProblem,
                          alg::TrustRegion, args...; abstol = nothing,
                          reltol = nothing,
                          maxiters = 1000, kwargs...)

From 6fbef92b8afd445885f5c132f069364648f850a3 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 16 Jan 2023 20:14:11 -0500
Subject: [PATCH 043/700] fix bound

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 1afc7746f..3095dabff 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -16,7 +16,7 @@ StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [compat]
 ArrayInterfaceCore = "0.1.1"
-DiffEqBase = "6.115"
+DiffEqBase = "6.114"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 Reexport = "0.2, 1"

From 96b2e2e57eaab88f0aaf6b4f4ba8f18bfe40f54a Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 16 Jan 2023 20:16:10 -0500
Subject: [PATCH 044/700] format

---
 lib/SimpleNonlinearSolve/src/broyden.jl     | 6 +++---
 lib/SimpleNonlinearSolve/src/klement.jl     | 6 +++---
 lib/SimpleNonlinearSolve/src/raphson.jl     | 6 +++---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 6 +++---
 4 files changed, 12 insertions(+), 12 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index c51e5d1db..a05caa00a 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -9,9 +9,9 @@ and static array problems.
 struct Broyden <: AbstractSimpleNonlinearSolveAlgorithm end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-                         alg::Broyden, args...; abstol = nothing,
-                         reltol = nothing,
-                         maxiters = 1000, kwargs...)
+                           alg::Broyden, args...; abstol = nothing,
+                           reltol = nothing,
+                           maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     fₙ = f(x)
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index bc07d664b..4d59377df 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -9,9 +9,9 @@ This method is non-allocating on scalar problems.
 struct Klement <: AbstractSimpleNonlinearSolveAlgorithm end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-                         alg::Klement, args...; abstol = nothing,
-                         reltol = nothing,
-                         maxiters = 1000, kwargs...)
+                           alg::Klement, args...; abstol = nothing,
+                           reltol = nothing,
+                           maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     fₙ = f(x)
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 4ccc4fbbd..57d66b005 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -37,9 +37,9 @@ struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-                         alg::SimpleNewtonRaphson, args...; abstol = nothing,
-                         reltol = nothing,
-                         maxiters = 1000, kwargs...)
+                           alg::SimpleNewtonRaphson, args...; abstol = nothing,
+                           reltol = nothing,
+                           maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     fx = float(prob.u0)
diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 7db6f460f..289987b31 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -78,9 +78,9 @@ struct TrustRegion{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-                         alg::TrustRegion, args...; abstol = nothing,
-                         reltol = nothing,
-                         maxiters = 1000, kwargs...)
+                           alg::TrustRegion, args...; abstol = nothing,
+                           reltol = nothing,
+                           maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     T = typeof(x)

From fd87a491162b69231909e9e1248d69b975aa2885 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 16 Jan 2023 20:54:57 -0500
Subject: [PATCH 045/700] fix tests

---
 lib/SimpleNonlinearSolve/test/basictests.jl | 11 +----------
 1 file changed, 1 insertion(+), 10 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index d2a030253..5b0c2f396 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -66,7 +66,7 @@ for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
     TrustRegion(10.0)]
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
-        sol = solve(probN, alg, tol = 1e-9)
+        sol = solve(probN, alg, abstol = 1e-9)
         return sol.u[end]
     end
 
@@ -137,20 +137,11 @@ f, u0 = (u, p) -> u .* u .- 2.0, @SVector[1.0, 1.0]
 probN = NonlinearProblem(f, u0)
 
 @test solve(probN, SimpleNewtonRaphson()).u[end] ≈ sqrt(2.0)
-@test solve(probN, SimpleNewtonRaphson(); immutable = false).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
-@test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
-
 @test solve(probN, TrustRegion(10.0)).u[end] ≈ sqrt(2.0)
-@test solve(probN, TrustRegion(10.0); immutable = false).u[end] ≈ sqrt(2.0)
-@test solve(probN, TrustRegion(10.0; autodiff = false)).u[end] ≈ sqrt(2.0)
 @test solve(probN, TrustRegion(10.0; autodiff = false)).u[end] ≈ sqrt(2.0)
-
 @test solve(probN, Broyden()).u[end] ≈ sqrt(2.0)
-@test solve(probN, Broyden(); immutable = false).u[end] ≈ sqrt(2.0)
-
 @test solve(probN, Klement()).u[end] ≈ sqrt(2.0)
-@test solve(probN, Klement(); immutable = false).u[end] ≈ sqrt(2.0)
 
 for u0 in [1.0, [1, 1.0]]
     local f, probN, sol

From 604b5b71ec8dbd14f401646c709212ddfbc39848 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 16 Jan 2023 21:21:40 -0500
Subject: [PATCH 046/700] non-allocating on v1.7+

ugh v1.6 is now getting old lol
---
 lib/SimpleNonlinearSolve/test/basictests.jl | 12 +++++++++---
 1 file changed, 9 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 5b0c2f396..cd960b664 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -22,7 +22,9 @@ sol = benchmark_scalar(sf, csu0)
 @test sol.retcode === ReturnCode.Success
 @test sol.u * sol.u - 2 < 1e-9
 
-@test (@ballocated benchmark_scalar(sf, csu0)) == 0
+if VERSION >= v"1.7"
+    @test (@ballocated benchmark_scalar(sf, csu0)) == 0
+end
 
 # Broyden
 function benchmark_scalar(f, u0)
@@ -33,7 +35,9 @@ end
 sol = benchmark_scalar(sf, csu0)
 @test sol.retcode === ReturnCode.Success
 @test sol.u * sol.u - 2 < 1e-9
-@test (@ballocated benchmark_scalar(sf, csu0)) == 0
+if VERSION >= v"1.7"
+    @test (@ballocated benchmark_scalar(sf, csu0)) == 0
+end
 
 # Klement
 function benchmark_scalar(f, u0)
@@ -44,7 +48,9 @@ end
 sol = benchmark_scalar(sf, csu0)
 @test sol.retcode === ReturnCode.Success
 @test sol.u * sol.u - 2 < 1e-9
-@test (@ballocated benchmark_scalar(sf, csu0)) == 0
+if VERSION >= v"1.7"
+    @test (@ballocated benchmark_scalar(sf, csu0)) == 0
+end
 
 # TrustRegion
 function benchmark_scalar(f, u0)

From ab567dd5ca1899edfde1bb66c57142cf77b9d104 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 16 Jan 2023 22:10:22 -0500
Subject: [PATCH 047/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 3095dabff..6444085b3 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.5"
+version = "0.1.6"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"

From c8daa1fc30f2ab77e3d60ea8d633455a2b48d09d Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 17 Jan 2023 08:31:50 -0500
Subject: [PATCH 048/700] TrustRegion -> SimpleTrustRegion and specialize the
 number types

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 27 +++++++++++----------
 1 file changed, 14 insertions(+), 13 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 289987b31..2bfb633f1 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -1,6 +1,6 @@
 """
 ```julia
-TrustRegion(max_trust_radius::Number; chunk_size = Val{0}(),
+SimpleTrustRegion(max_trust_radius::Number; chunk_size = Val{0}(),
                                autodiff = Val{true}(), diff_type = Val{:forward})
 ```
 
@@ -49,16 +49,16 @@ solver
 - `max_shrink_times`: the maximum number of times to shrink the trust region radius in a
   row, `max_shrink_times` is exceeded, the algorithm returns. Defaults to `32`.
 """
-struct TrustRegion{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
-    max_trust_radius::Number
-    initial_trust_radius::Number
-    step_threshold::Number
-    shrink_threshold::Number
-    expand_threshold::Number
-    shrink_factor::Number
-    expand_factor::Number
+struct SimpleTrustRegion{T, CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
+    max_trust_radius::T
+    initial_trust_radius::T
+    step_threshold::T
+    shrink_threshold::T
+    expand_threshold::T
+    shrink_factor::T
+    expand_factor::T
     max_shrink_times::Int
-    function TrustRegion(max_trust_radius::Number; chunk_size = Val{0}(),
+    function SimpleTrustRegion(max_trust_radius::Number; chunk_size = Val{0}(),
                          autodiff = Val{true}(),
                          diff_type = Val{:forward},
                          initial_trust_radius::Number = max_trust_radius / 11,
@@ -68,8 +68,9 @@ struct TrustRegion{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
                          shrink_factor::Number = 0.25,
                          expand_factor::Number = 2.0,
                          max_shrink_times::Int = 32)
-        new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
-            SciMLBase._unwrap_val(diff_type)}(max_trust_radius, initial_trust_radius,
+        new{typeof(initial_trust_radius), SciMLBase._unwrap_val(chunk_size), 
+            SciMLBase._unwrap_val(autodiff), SciMLBase._unwrap_val(diff_type)}(
+                                              max_trust_radius, initial_trust_radius,
                                               step_threshold,
                                               shrink_threshold, expand_threshold,
                                               shrink_factor,
@@ -78,7 +79,7 @@ struct TrustRegion{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-                           alg::TrustRegion, args...; abstol = nothing,
+                           alg::SimpleTrustRegion, args...; abstol = nothing,
                            reltol = nothing,
                            maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)

From b313722e4671363430ec5a39cbabd9b8476fcdd1 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 17 Jan 2023 08:37:50 -0500
Subject: [PATCH 049/700] Complete the name change

---
 lib/SimpleNonlinearSolve/test/basictests.jl | 28 ++++++++++-----------
 1 file changed, 14 insertions(+), 14 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index cd960b664..bbee5ff09 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -52,10 +52,10 @@ if VERSION >= v"1.7"
     @test (@ballocated benchmark_scalar(sf, csu0)) == 0
 end
 
-# TrustRegion
+# SimpleTrustRegion
 function benchmark_scalar(f, u0)
     probN = NonlinearProblem{false}(f, u0)
-    sol = (solve(probN, TrustRegion(10.0)))
+    sol = (solve(probN, SimpleTrustRegion(10.0)))
 end
 
 sol = benchmark_scalar(sf, csu0)
@@ -69,7 +69,7 @@ using ForwardDiff
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
 for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
-    TrustRegion(10.0)]
+    SimpleTrustRegion(10.0)]
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
         sol = solve(probN, alg, abstol = 1e-9)
@@ -85,7 +85,7 @@ end
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
 for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
-    TrustRegion(10.0)]
+    SimpleTrustRegion(10.0)]
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
@@ -127,7 +127,7 @@ for alg in [Bisection(), Falsi()]
 end
 
 for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
-    TrustRegion(10.0)]
+    SimpleTrustRegion(10.0)]
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -144,8 +144,8 @@ probN = NonlinearProblem(f, u0)
 
 @test solve(probN, SimpleNewtonRaphson()).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
-@test solve(probN, TrustRegion(10.0)).u[end] ≈ sqrt(2.0)
-@test solve(probN, TrustRegion(10.0; autodiff = false)).u[end] ≈ sqrt(2.0)
+@test solve(probN, SimpleTrustRegion(10.0)).u[end] ≈ sqrt(2.0)
+@test solve(probN, SimpleTrustRegion(10.0; autodiff = false)).u[end] ≈ sqrt(2.0)
 @test solve(probN, Broyden()).u[end] ≈ sqrt(2.0)
 @test solve(probN, Klement()).u[end] ≈ sqrt(2.0)
 
@@ -159,9 +159,9 @@ for u0 in [1.0, [1, 1.0]]
     @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
     @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u ≈ sol
 
-    @test solve(probN, TrustRegion(10.0)).u ≈ sol
-    @test solve(probN, TrustRegion(10.0)).u ≈ sol
-    @test solve(probN, TrustRegion(10.0; autodiff = false)).u ≈ sol
+    @test solve(probN, SimpleTrustRegion(10.0)).u ≈ sol
+    @test solve(probN, SimpleTrustRegion(10.0)).u ≈ sol
+    @test solve(probN, SimpleTrustRegion(10.0; autodiff = false)).u ≈ sol
 
     @test solve(probN, Broyden()).u ≈ sol
 
@@ -205,7 +205,7 @@ sol = solve(probB, Bisection(; exact_left = true, exact_right = true); immutable
 @test f(sol.right, nothing) >= 0.0
 @test f(prevfloat(sol.right), nothing) <= 0.0
 
-# Test that `TrustRegion` passes a test that `SimpleNewtonRaphson` fails on.
+# Test that `SimpleTrustRegion` passes a test that `SimpleNewtonRaphson` fails on.
 u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
 global g, f
 f = (u, p) -> 0.010000000000000002 .+
@@ -219,7 +219,7 @@ f = (u, p) -> 0.010000000000000002 .+
 .-p
 g = function (p)
     probN = NonlinearProblem{false}(f, u0, p)
-    sol = solve(probN, TrustRegion(100.0))
+    sol = solve(probN, SimpleTrustRegion(100.0))
     return sol.u
 end
 p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
@@ -227,7 +227,7 @@ u = g(p)
 f(u, p)
 @test all(f(u, p) .< 1e-10)
 
-# Test kwars in `TrustRegion`
+# Test kwars in `SimpleTrustRegion`
 max_trust_radius = [10.0, 100.0, 1000.0]
 initial_trust_radius = [10.0, 1.0, 0.1]
 step_threshold = [0.0, 0.01, 0.25]
@@ -242,7 +242,7 @@ list_of_options = zip(max_trust_radius, initial_trust_radius, step_threshold,
                       expand_factor, max_shrink_times)
 for options in list_of_options
     local probN, sol, alg
-    alg = TrustRegion(options[1];
+    alg = SimpleTrustRegion(options[1];
                       initial_trust_radius = options[2],
                       step_threshold = options[3],
                       shrink_threshold = options[4],

From c251bfdafeba7f09d395938e19da93ced94800b6 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 17 Jan 2023 08:40:36 -0500
Subject: [PATCH 050/700] format

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 34 +++++++++++----------
 lib/SimpleNonlinearSolve/test/basictests.jl | 14 ++++-----
 2 files changed, 25 insertions(+), 23 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 2bfb633f1..4d0fcc09e 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -59,22 +59,24 @@ struct SimpleTrustRegion{T, CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     expand_factor::T
     max_shrink_times::Int
     function SimpleTrustRegion(max_trust_radius::Number; chunk_size = Val{0}(),
-                         autodiff = Val{true}(),
-                         diff_type = Val{:forward},
-                         initial_trust_radius::Number = max_trust_radius / 11,
-                         step_threshold::Number = 0.1,
-                         shrink_threshold::Number = 0.25,
-                         expand_threshold::Number = 0.75,
-                         shrink_factor::Number = 0.25,
-                         expand_factor::Number = 2.0,
-                         max_shrink_times::Int = 32)
-        new{typeof(initial_trust_radius), SciMLBase._unwrap_val(chunk_size), 
-            SciMLBase._unwrap_val(autodiff), SciMLBase._unwrap_val(diff_type)}(
-                                              max_trust_radius, initial_trust_radius,
-                                              step_threshold,
-                                              shrink_threshold, expand_threshold,
-                                              shrink_factor,
-                                              expand_factor, max_shrink_times)
+                               autodiff = Val{true}(),
+                               diff_type = Val{:forward},
+                               initial_trust_radius::Number = max_trust_radius / 11,
+                               step_threshold::Number = 0.1,
+                               shrink_threshold::Number = 0.25,
+                               expand_threshold::Number = 0.75,
+                               shrink_factor::Number = 0.25,
+                               expand_factor::Number = 2.0,
+                               max_shrink_times::Int = 32)
+        new{typeof(initial_trust_radius), SciMLBase._unwrap_val(chunk_size),
+            SciMLBase._unwrap_val(autodiff), SciMLBase._unwrap_val(diff_type)}(max_trust_radius,
+                                                                               initial_trust_radius,
+                                                                               step_threshold,
+                                                                               shrink_threshold,
+                                                                               expand_threshold,
+                                                                               shrink_factor,
+                                                                               expand_factor,
+                                                                               max_shrink_times)
     end
 end
 
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index bbee5ff09..39a4f3888 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -243,13 +243,13 @@ list_of_options = zip(max_trust_radius, initial_trust_radius, step_threshold,
 for options in list_of_options
     local probN, sol, alg
     alg = SimpleTrustRegion(options[1];
-                      initial_trust_radius = options[2],
-                      step_threshold = options[3],
-                      shrink_threshold = options[4],
-                      expand_threshold = options[5],
-                      shrink_factor = options[6],
-                      expand_factor = options[7],
-                      max_shrink_times = options[8])
+                            initial_trust_radius = options[2],
+                            step_threshold = options[3],
+                            shrink_threshold = options[4],
+                            expand_threshold = options[5],
+                            shrink_factor = options[6],
+                            expand_factor = options[7],
+                            max_shrink_times = options[8])
 
     probN = NonlinearProblem(f, u0, p)
     sol = solve(probN, alg)

From 52fd1e8d1daf2ca65d267692b5d7d3393cbec382 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 17 Jan 2023 09:02:16 -0500
Subject: [PATCH 051/700] last few TrustRegions

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 4 ++--
 lib/SimpleNonlinearSolve/src/trustRegion.jl          | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index dbe856365..c077d833d 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -32,7 +32,7 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
         solve(prob_no_brack, alg(), abstol = T(1e-2))
     end
 
-    for alg in (TrustRegion(10.0),)
+    for alg in (SimpleTrustRegion(10.0),)
         solve(prob_no_brack, alg, abstol = T(1e-2))
     end
 
@@ -53,6 +53,6 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
 end end
 
 # DiffEq styled algorithms
-export Bisection, Broyden, Falsi, Klement, SimpleNewtonRaphson, TrustRegion
+export Bisection, Broyden, Falsi, Klement, SimpleNewtonRaphson, SimpleTrustRegion
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 4d0fcc09e..08d5d5129 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -97,7 +97,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
     max_shrink_times = alg.max_shrink_times
 
     if SciMLBase.isinplace(prob)
-        error("TrustRegion currently only supports out-of-place nonlinear problems")
+        error("SimpleTrustRegion currently only supports out-of-place nonlinear problems")
     end
 
     atol = abstol !== nothing ? abstol :

From c9205260c4806bc3e9455c02edb86711462fc2e7 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 17 Jan 2023 09:54:36 -0500
Subject: [PATCH 052/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 6444085b3..696240832 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.6"
+version = "0.1.7"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"

From 4809a8c0e467865a7476074bb0c9bf241287be61 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Wed, 18 Jan 2023 20:57:20 +0100
Subject: [PATCH 053/700] Automatic choice for maximum trust region radius

---
 .../src/SimpleNonlinearSolve.jl               |  8 +--
 lib/SimpleNonlinearSolve/src/ad.jl            |  6 +-
 lib/SimpleNonlinearSolve/src/trustRegion.jl   | 62 ++++++++++++-------
 lib/SimpleNonlinearSolve/test/basictests.jl   | 32 +++++-----
 4 files changed, 60 insertions(+), 48 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index c077d833d..622595e1e 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -19,23 +19,19 @@ include("utils.jl")
 include("bisection.jl")
 include("falsi.jl")
 include("raphson.jl")
-include("ad.jl")
 include("broyden.jl")
 include("klement.jl")
 include("trustRegion.jl")
+include("ad.jl")
 
 import SnoopPrecompile
 
 SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
     prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-    for alg in (SimpleNewtonRaphson, Broyden, Klement)
+    for alg in (SimpleNewtonRaphson, Broyden, Klement, SimpleTrustRegion)
         solve(prob_no_brack, alg(), abstol = T(1e-2))
     end
 
-    for alg in (SimpleTrustRegion(10.0),)
-        solve(prob_no_brack, alg, abstol = T(1e-2))
-    end
-
     #=
     for alg in (SimpleNewtonRaphson,)
         for u0 in ([1., 1.], StaticArraysCore.SA[1.0, 1.0])
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index 3b8d3fee0..58a6181ea 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -30,7 +30,8 @@ end
 
 function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
                                                 iip,
-                                                <:Dual{T, V, P}}, alg::SimpleNewtonRaphson,
+                                                <:Dual{T, V, P}},
+                         alg::Union{SimpleNewtonRaphson, SimpleTrustRegion},
                          args...; kwargs...) where {iip, T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
@@ -39,7 +40,8 @@ end
 function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
                                                 iip,
                                                 <:AbstractArray{<:Dual{T, V, P}}},
-                         alg::SimpleNewtonRaphson, args...; kwargs...) where {iip, T, V, P}
+                         alg::Union{SimpleNewtonRaphson, SimpleTrustRegion}, args...;
+                         kwargs...) where {iip, T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
                                     retcode = sol.retcode)
diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 08d5d5129..329eb8808 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -1,17 +1,22 @@
 """
 ```julia
-SimpleTrustRegion(max_trust_radius::Number; chunk_size = Val{0}(),
-                               autodiff = Val{true}(), diff_type = Val{:forward})
+SimpleTrustRegion(; chunk_size = Val{0}(),
+                    autodiff = Val{true}(),
+                    diff_type = Val{:forward},
+                    max_trust_radius::Real = 0.0,
+                    initial_trust_radius::Real = 0.0,
+                    step_threshold::Real = 0.1,
+                    shrink_threshold::Real = 0.25,
+                    expand_threshold::Real = 0.75,
+                    shrink_factor::Real = 0.25,
+                    expand_factor::Real = 2.0,
+                    max_shrink_times::Int = 32
 ```
 
 A low-overhead implementation of a
 [trust-region](https://optimization.mccormick.northwestern.edu/index.php/Trust-region_methods)
 solver
 
-### Arguments
-- `max_trust_radius`: the maximum radius of the trust region. The step size in the algorithm
-  will change dynamically. However, it will never be greater than the `max_trust_radius`.
-
 ### Keyword Arguments
 
 - `chunk_size`: the chunk size used by the internal ForwardDiff.jl automatic differentiation
@@ -26,6 +31,8 @@ solver
 - `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
   `Val{:forward}` for forward finite differences. For more details on the choices, see the
   [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
+- `max_trust_radius`: the maximum radius of the trust region. Defaults to
+  `max(norm(f(u0)), maximum(u0) - minimum(u0))`.
 - `initial_trust_radius`: the initial trust region radius. Defaults to
   `max_trust_radius / 11`.
 - `step_threshold`: the threshold for taking a step. In every iteration, the threshold is
@@ -58,25 +65,28 @@ struct SimpleTrustRegion{T, CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     shrink_factor::T
     expand_factor::T
     max_shrink_times::Int
-    function SimpleTrustRegion(max_trust_radius::Number; chunk_size = Val{0}(),
+    function SimpleTrustRegion(; chunk_size = Val{0}(),
                                autodiff = Val{true}(),
                                diff_type = Val{:forward},
-                               initial_trust_radius::Number = max_trust_radius / 11,
-                               step_threshold::Number = 0.1,
-                               shrink_threshold::Number = 0.25,
-                               expand_threshold::Number = 0.75,
-                               shrink_factor::Number = 0.25,
-                               expand_factor::Number = 2.0,
+                               max_trust_radius::Real = 0.0,
+                               initial_trust_radius::Real = 0.0,
+                               step_threshold::Real = 0.1,
+                               shrink_threshold::Real = 0.25,
+                               expand_threshold::Real = 0.75,
+                               shrink_factor::Real = 0.25,
+                               expand_factor::Real = 2.0,
                                max_shrink_times::Int = 32)
-        new{typeof(initial_trust_radius), SciMLBase._unwrap_val(chunk_size),
-            SciMLBase._unwrap_val(autodiff), SciMLBase._unwrap_val(diff_type)}(max_trust_radius,
-                                                                               initial_trust_radius,
-                                                                               step_threshold,
-                                                                               shrink_threshold,
-                                                                               expand_threshold,
-                                                                               shrink_factor,
-                                                                               expand_factor,
-                                                                               max_shrink_times)
+        new{typeof(initial_trust_radius),
+            SciMLBase._unwrap_val(chunk_size),
+            SciMLBase._unwrap_val(autodiff),
+            SciMLBase._unwrap_val(diff_type)}(max_trust_radius,
+                                              initial_trust_radius,
+                                              step_threshold,
+                                              shrink_threshold,
+                                              expand_threshold,
+                                              shrink_factor,
+                                              expand_factor,
+                                              max_shrink_times)
     end
 end
 
@@ -114,6 +124,14 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         ∇f = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x), F)
     end
 
+    # Set default trust region radius if not specified by user.
+    if Δₘₐₓ == 0.0
+        Δₘₐₓ = max(norm(F), maximum(x) - minimum(x))
+    end
+    if Δ == 0.0
+        Δ = Δₘₐₓ / 11
+    end
+
     fₖ = 0.5 * norm(F)^2
     H = ∇f * ∇f
     g = ∇f * F
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 39a4f3888..98687bc07 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -55,7 +55,7 @@ end
 # SimpleTrustRegion
 function benchmark_scalar(f, u0)
     probN = NonlinearProblem{false}(f, u0)
-    sol = (solve(probN, SimpleTrustRegion(10.0)))
+    sol = (solve(probN, SimpleTrustRegion()))
 end
 
 sol = benchmark_scalar(sf, csu0)
@@ -68,8 +68,7 @@ using ForwardDiff
 # Immutable
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
-for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
-    SimpleTrustRegion(10.0)]
+for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion())
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
         sol = solve(probN, alg, abstol = 1e-9)
@@ -84,8 +83,7 @@ end
 
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
-for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
-    SimpleTrustRegion(10.0)]
+for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion())
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
@@ -126,8 +124,7 @@ for alg in [Bisection(), Falsi()]
     @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
 end
 
-for alg in [SimpleNewtonRaphson(), Broyden(), Klement(),
-    SimpleTrustRegion(10.0)]
+for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion())
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -144,8 +141,8 @@ probN = NonlinearProblem(f, u0)
 
 @test solve(probN, SimpleNewtonRaphson()).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
-@test solve(probN, SimpleTrustRegion(10.0)).u[end] ≈ sqrt(2.0)
-@test solve(probN, SimpleTrustRegion(10.0; autodiff = false)).u[end] ≈ sqrt(2.0)
+@test solve(probN, SimpleTrustRegion()).u[end] ≈ sqrt(2.0)
+@test solve(probN, SimpleTrustRegion(; autodiff = false)).u[end] ≈ sqrt(2.0)
 @test solve(probN, Broyden()).u[end] ≈ sqrt(2.0)
 @test solve(probN, Klement()).u[end] ≈ sqrt(2.0)
 
@@ -159,9 +156,9 @@ for u0 in [1.0, [1, 1.0]]
     @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
     @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u ≈ sol
 
-    @test solve(probN, SimpleTrustRegion(10.0)).u ≈ sol
-    @test solve(probN, SimpleTrustRegion(10.0)).u ≈ sol
-    @test solve(probN, SimpleTrustRegion(10.0; autodiff = false)).u ≈ sol
+    @test solve(probN, SimpleTrustRegion()).u ≈ sol
+    @test solve(probN, SimpleTrustRegion()).u ≈ sol
+    @test solve(probN, SimpleTrustRegion(; autodiff = false)).u ≈ sol
 
     @test solve(probN, Broyden()).u ≈ sol
 
@@ -215,17 +212,16 @@ f = (u, p) -> 0.010000000000000002 .+
                  (0.21640425613334457 .+
                   216.40425613334457 ./
                   (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^ 2.0) .-
-              0.0011552453009332421u
-.-p
+              0.0011552453009332421u .- p
 g = function (p)
     probN = NonlinearProblem{false}(f, u0, p)
-    sol = solve(probN, SimpleTrustRegion(100.0))
+    sol = solve(probN, SimpleTrustRegion())
     return sol.u
 end
 p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 u = g(p)
 f(u, p)
-@test all(f(u, p) .< 1e-10)
+@test all(abs.(f(u, p)) .< 1e-10)
 
 # Test kwars in `SimpleTrustRegion`
 max_trust_radius = [10.0, 100.0, 1000.0]
@@ -242,7 +238,7 @@ list_of_options = zip(max_trust_radius, initial_trust_radius, step_threshold,
                       expand_factor, max_shrink_times)
 for options in list_of_options
     local probN, sol, alg
-    alg = SimpleTrustRegion(options[1];
+    alg = SimpleTrustRegion(max_trust_radius = options[1],
                             initial_trust_radius = options[2],
                             step_threshold = options[3],
                             shrink_threshold = options[4],
@@ -253,5 +249,5 @@ for options in list_of_options
 
     probN = NonlinearProblem(f, u0, p)
     sol = solve(probN, alg)
-    @test all(f(u, p) .< 1e-10)
+    @test all(abs.(f(u, p)) .< 1e-10)
 end

From 84e2dd1cf58dfd7b2331b72434b3072059a83862 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 18 Jan 2023 15:19:19 -0500
Subject: [PATCH 054/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 696240832..a12faeac9 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.7"
+version = "0.1.8"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"

From ea3a2bfc91a50730b652541c5b3d5ee83e10a458 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Sun, 29 Jan 2023 15:40:32 +0100
Subject: [PATCH 055/700] Implementation of Ridder

---
 .../src/SimpleNonlinearSolve.jl               |  5 +-
 lib/SimpleNonlinearSolve/src/ridder.jl        | 84 +++++++++++++++++++
 lib/SimpleNonlinearSolve/test/basictests.jl   | 18 +++-
 3 files changed, 104 insertions(+), 3 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/ridder.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 622595e1e..c29fe63d6 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -22,6 +22,7 @@ include("raphson.jl")
 include("broyden.jl")
 include("klement.jl")
 include("trustRegion.jl")
+include("ridder.jl")
 include("ad.jl")
 
 import SnoopPrecompile
@@ -43,12 +44,12 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
     =#
 
     prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p, T.((0.0, 2.0)), T(2))
-    for alg in (Bisection, Falsi)
+    for alg in (Bisection, Falsi, Ridder)
         solve(prob_brack, alg(), abstol = T(1e-2))
     end
 end end
 
 # DiffEq styled algorithms
-export Bisection, Broyden, Falsi, Klement, SimpleNewtonRaphson, SimpleTrustRegion
+export Bisection, Broyden, Falsi, Klement, Ridder, SimpleNewtonRaphson, SimpleTrustRegion
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/ridder.jl b/lib/SimpleNonlinearSolve/src/ridder.jl
new file mode 100644
index 000000000..bb5c8d4db
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/ridder.jl
@@ -0,0 +1,84 @@
+"""
+`Ridder()`
+
+A non-allocating ridder method
+
+"""
+struct Ridder <: AbstractBracketingAlgorithm end
+
+function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
+                         maxiters = 1000,
+                         kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    left, right = prob.tspan
+    fl, fr = f(left), f(right)
+
+    if iszero(fl)
+        return SciMLBase.build_solution(prob, alg, left, fl;
+                                        retcode = ReturnCode.ExactSolutionLeft, left = left,
+                                        right = right)
+    end
+
+    xo = oftype(left, Inf)
+    i = 1
+    if !iszero(fr)
+        while i < maxiters
+            mid = (left + right) / 2
+            (mid == left || mid == right) &&
+                return SciMLBase.build_solution(prob, alg, left, fl;
+                                                retcode = ReturnCode.FloatingPointLimit,
+                                                left = left, right = right)
+            fm = f(mid)
+            s = sqrt(fm^2 - fl * fr)
+            iszero(s) &&
+                return SciMLBase.build_solution(prob, alg, left, fl;
+                                                retcode = ReturnCode.Failure,
+                                                left = left, right = right)
+            x = mid + (mid - left) * sign(fl - fr) * fm / s
+            fx = f(x)
+            xo = x
+            if iszero(fx)
+                right = x
+                fr = fx
+                break
+            end
+            if sign(fx) != sign(fm)
+                left = mid
+                fl = fm
+                right = x
+                fr = fx
+            elseif sign(fx) != sign(fl)
+                right = x
+                fr = fx
+            else
+                @assert sign(fx) != sign(fr)
+                left = x
+                fl = fx
+            end
+            i += 1
+        end
+    end
+
+    while i < maxiters
+        mid = (left + right) / 2
+        (mid == left || mid == right) &&
+            return SciMLBase.build_solution(prob, alg, left, fl;
+                                            retcode = ReturnCode.FloatingPointLimit,
+                                            left = left, right = right)
+        fm = f(mid)
+        if iszero(fm)
+            right = mid
+            fr = fm
+        elseif sign(fm) == sign(fl)
+            left = mid
+            fl = fm
+        else
+            right = mid
+            fr = fm
+        end
+        i += 1
+    end
+
+    return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
+                                    left = left, right = right)
+end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 98687bc07..d68b3f42c 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -109,10 +109,22 @@ for p in 1.1:0.1:100.0
     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
 end
 
+# Ridder
+g = function (p)
+    probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
+    sol = solve(probN, Ridder())
+    return sol.left
+end
+
+for p in 1.1:0.1:100.0
+    @test g(p) ≈ sqrt(p)
+    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+end
+
 f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
 t = (p) -> [sqrt(p[2] / p[1])]
 p = [0.9, 50.0]
-for alg in [Bisection(), Falsi()]
+for alg in [Bisection(), Falsi(), Ridder()]
     global g, p
     g = function (p)
         probN = IntervalNonlinearProblem{false}(f, tspan, p)
@@ -173,6 +185,10 @@ probB = IntervalNonlinearProblem(f, tspan)
 sol = solve(probB, Falsi())
 @test sol.left ≈ sqrt(2.0)
 
+# Ridder
+sol = solve(probB, Ridder())
+@test sol.left ≈ sqrt(2.0)
+
 sol = solve(probB, Bisection())
 @test sol.left ≈ sqrt(2.0)
 

From e84be4680dadadc1fcca5bf4bd37b6742934f348 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Sun, 29 Jan 2023 15:57:54 +0100
Subject: [PATCH 056/700] Small change to Ridder

---
 lib/SimpleNonlinearSolve/src/ridder.jl | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/ridder.jl b/lib/SimpleNonlinearSolve/src/ridder.jl
index bb5c8d4db..9fe7bccfe 100644
--- a/lib/SimpleNonlinearSolve/src/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/ridder.jl
@@ -69,12 +69,9 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
         if iszero(fm)
             right = mid
             fr = fm
-        elseif sign(fm) == sign(fl)
+        else
             left = mid
             fl = fm
-        else
-            right = mid
-            fr = fm
         end
         i += 1
     end

From fdfb03b7ccab66b2bf683997df97b8f20a9480a7 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Sun, 29 Jan 2023 17:19:35 +0100
Subject: [PATCH 057/700] Added more tests

---
 lib/SimpleNonlinearSolve/test/basictests.jl | 13 +++++++++++--
 1 file changed, 11 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index d68b3f42c..4ee2c3ab7 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -185,12 +185,21 @@ probB = IntervalNonlinearProblem(f, tspan)
 sol = solve(probB, Falsi())
 @test sol.left ≈ sqrt(2.0)
 
+sol = solve(probB, Bisection())
+@test sol.left ≈ sqrt(2.0)
+
 # Ridder
 sol = solve(probB, Ridder())
 @test sol.left ≈ sqrt(2.0)
-
-sol = solve(probB, Bisection())
+tspan = (sqrt(2.0), 10.0)
+probB = IntervalNonlinearProblem(f, tspan)
+sol = solve(probB, Ridder())
 @test sol.left ≈ sqrt(2.0)
+tspan = (0.0, sqrt(2.0))
+probB = IntervalNonlinearProblem(f, tspan)
+sol = solve(probB, Ridder())
+@test sol.left ≈ sqrt(2.0)
+probB = IntervalNonlinearProblem(f, tspan)
 
 # Garuntee Tests for Bisection
 f = function (u, p)

From 2959eda04792582ef18379016af3a2703ae94415 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Sun, 29 Jan 2023 17:21:33 +0100
Subject: [PATCH 058/700] Small fix in the tests

---
 lib/SimpleNonlinearSolve/test/basictests.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 4ee2c3ab7..017569227 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -199,7 +199,6 @@ tspan = (0.0, sqrt(2.0))
 probB = IntervalNonlinearProblem(f, tspan)
 sol = solve(probB, Ridder())
 @test sol.left ≈ sqrt(2.0)
-probB = IntervalNonlinearProblem(f, tspan)
 
 # Garuntee Tests for Bisection
 f = function (u, p)

From 8e57137551ad9b7360d9294fcfc84a287d80f042 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Mon, 30 Jan 2023 13:02:03 +0100
Subject: [PATCH 059/700] Adding a Brent method

---
 .../src/SimpleNonlinearSolve.jl               |   6 +-
 lib/SimpleNonlinearSolve/src/brent.jl         | 109 ++++++++++++++++++
 lib/SimpleNonlinearSolve/test/basictests.jl   |  26 ++++-
 3 files changed, 138 insertions(+), 3 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/brent.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index c29fe63d6..33f5895d7 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -23,6 +23,7 @@ include("broyden.jl")
 include("klement.jl")
 include("trustRegion.jl")
 include("ridder.jl")
+include("brent.jl")
 include("ad.jl")
 
 import SnoopPrecompile
@@ -44,12 +45,13 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
     =#
 
     prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p, T.((0.0, 2.0)), T(2))
-    for alg in (Bisection, Falsi, Ridder)
+    for alg in (Bisection, Falsi, Ridder, Brent)
         solve(prob_brack, alg(), abstol = T(1e-2))
     end
 end end
 
 # DiffEq styled algorithms
-export Bisection, Broyden, Falsi, Klement, Ridder, SimpleNewtonRaphson, SimpleTrustRegion
+export Bisection, Brent, Broyden, Falsi, Klement, Ridder, SimpleNewtonRaphson,
+       SimpleTrustRegion
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/brent.jl
new file mode 100644
index 000000000..9a60abfee
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/brent.jl
@@ -0,0 +1,109 @@
+"""
+`Brent()`
+
+A non-allocating Brent method
+
+"""
+struct Brent <: AbstractBracketingAlgorithm end
+
+function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
+                         maxiters = 1000,
+                         kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    a, b = prob.tspan
+    fa, fb = f(a), f(b)
+
+    if iszero(fa)
+        return SciMLBase.build_solution(prob, alg, a, fa;
+                                        retcode = ReturnCode.ExactSolutionLeft, left = a,
+                                        right = b)
+    end
+    if abs(fa) < abs(fb)
+        c = b
+        b = a
+        a = c
+        tmp = fa
+        fa = fb
+        fb = tmp
+    end
+
+    c = a
+    d = c
+    i = 1
+    cond = true
+    if !iszero(fb)
+        while i < maxiters
+            fc = f(c)
+            if fa != fc && fb != fc
+                # Inverse quadratic interpolation
+                s = a * fb * fc / ((fa - fb) * (fa - fc)) +
+                    b * fa * fc / ((fb - fa) * (fb - fc)) +
+                    c * fa * fb / ((fc - fa) * (fc - fb))
+            else
+                # Secant method
+                s = b - fb * (b - a) / (fb - fa)
+            end
+            if (s < min((3 * a + b) / 4, b) || s > max((3 * a + b) / 4, b)) ||
+               (cond && abs(s - b) ≥ abs(b - c) / 2) ||
+               (!cond && abs(s - b) ≥ abs(c - d) / 2) ||
+               (cond && abs(b - c) ≤ eps(a)) ||
+               (!cond && abs(c - d) ≤ eps(a))
+                # Bisection method
+                s = (a + b) / 2
+                (s == a || s == b) &&
+                    return SciMLBase.build_solution(prob, alg, a, fa;
+                                                    retcode = ReturnCode.FloatingPointLimit,
+                                                    left = a, right = b)
+                cond = true
+            else
+                cond = false
+            end
+            fs = f(s)
+            if iszero(fs)
+                a = b
+                b = s
+                break
+            end
+            if fa * fs < 0
+                d = c
+                c = b
+                b = s
+                fb = fs
+            else
+                a = s
+                fa = fs
+            end
+            if abs(fa) < abs(fb)
+                d = c
+                c = b
+                b = a
+                a = c
+                fc = fb
+                fb = fa
+                fa = fc
+            end
+            i += 1
+        end
+    end
+
+    while i < maxiters
+        c = (a + b) / 2
+        if (c == a || c == b)
+            return SciMLBase.build_solution(prob, alg, a, fa;
+                                            retcode = ReturnCode.FloatingPointLimit,
+                                            left = a, right = b)
+        end
+        fc = f(c)
+        if iszero(fc)
+            b = c
+            fb = fc
+        else
+            a = c
+            fa = fc
+        end
+        i += 1
+    end
+    
+    return SciMLBase.build_solution(prob, alg, a, fa; retcode = ReturnCode.MaxIters,
+                                    left = a, right = b)
+end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 017569227..fa15e798e 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -121,10 +121,22 @@ for p in 1.1:0.1:100.0
     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
 end
 
+# Brent
+g = function (p)
+    probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
+    sol = solve(probN, Brent())
+    return sol.left
+end
+
+for p in 1.1:0.1:100.0
+    @test g(p) ≈ sqrt(p)
+    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+end
+
 f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
 t = (p) -> [sqrt(p[2] / p[1])]
 p = [0.9, 50.0]
-for alg in [Bisection(), Falsi(), Ridder()]
+for alg in [Bisection(), Falsi(), Ridder(), Brent()]
     global g, p
     g = function (p)
         probN = IntervalNonlinearProblem{false}(f, tspan, p)
@@ -200,6 +212,18 @@ probB = IntervalNonlinearProblem(f, tspan)
 sol = solve(probB, Ridder())
 @test sol.left ≈ sqrt(2.0)
 
+# Brent
+sol = solve(probB, Brent())
+@test sol.left ≈ sqrt(2.0)
+tspan = (sqrt(2.0), 10.0)
+probB = IntervalNonlinearProblem(f, tspan)
+sol = solve(probB, Brent())
+@test sol.left ≈ sqrt(2.0)
+tspan = (0.0, sqrt(2.0))
+probB = IntervalNonlinearProblem(f, tspan)
+sol = solve(probB, Brent())
+@test sol.left ≈ sqrt(2.0)
+
 # Garuntee Tests for Bisection
 f = function (u, p)
     if u < 2.0

From c9ae3799c6134b5ec2dff75f2459f75b2a67f87a Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Mon, 30 Jan 2023 16:21:00 +0100
Subject: [PATCH 060/700] Updating Brent

---
 lib/SimpleNonlinearSolve/src/brent.jl | 13 +++++++++----
 1 file changed, 9 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/brent.jl
index 9a60abfee..99f645f6a 100644
--- a/lib/SimpleNonlinearSolve/src/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/brent.jl
@@ -12,6 +12,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
     f = Base.Fix2(prob.f, prob.p)
     a, b = prob.tspan
     fa, fb = f(a), f(b)
+    ϵ = eps(convert(typeof(fa), 1.0))
 
     if iszero(fa)
         return SciMLBase.build_solution(prob, alg, a, fa;
@@ -46,8 +47,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
             if (s < min((3 * a + b) / 4, b) || s > max((3 * a + b) / 4, b)) ||
                (cond && abs(s - b) ≥ abs(b - c) / 2) ||
                (!cond && abs(s - b) ≥ abs(c - d) / 2) ||
-               (cond && abs(b - c) ≤ eps(a)) ||
-               (!cond && abs(c - d) ≤ eps(a))
+               (cond && abs(b - c) ≤ ϵ) ||
+               (!cond && abs(c - d) ≤ ϵ)
                 # Bisection method
                 s = (a + b) / 2
                 (s == a || s == b) &&
@@ -60,8 +61,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
             end
             fs = f(s)
             if iszero(fs)
-                a = b
+                if b < a
+                    a = b
+                    fa = fb
+                end
                 b = s
+                fb = fs
                 break
             end
             if fa * fs < 0
@@ -103,7 +108,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
         end
         i += 1
     end
-    
+
     return SciMLBase.build_solution(prob, alg, a, fa; retcode = ReturnCode.MaxIters,
                                     left = a, right = b)
 end

From b7eb5620f4074f277fd9ac25cf61aac3b6f2fcb0 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 31 Jan 2023 06:03:21 -0500
Subject: [PATCH 061/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index a12faeac9..3b8b5d859 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.8"
+version = "0.1.9"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"

From 2f6e0838c80b6d433e982803dc9623a7283cd494 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Mon, 6 Feb 2023 13:03:47 +0100
Subject: [PATCH 062/700] Started to implement DFSane

---
 .../src/SimpleNonlinearSolve.jl               |   5 +-
 lib/SimpleNonlinearSolve/src/ad.jl            |   6 +-
 lib/SimpleNonlinearSolve/src/dfsane.jl        | 135 ++++++++++++++++++
 lib/SimpleNonlinearSolve/test/basictests.jl   |  72 ++++++++--
 4 files changed, 205 insertions(+), 13 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/dfsane.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 33f5895d7..940db0835 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -24,13 +24,14 @@ include("klement.jl")
 include("trustRegion.jl")
 include("ridder.jl")
 include("brent.jl")
+include("dfsane.jl")
 include("ad.jl")
 
 import SnoopPrecompile
 
 SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
     prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-    for alg in (SimpleNewtonRaphson, Broyden, Klement, SimpleTrustRegion)
+    for alg in (SimpleNewtonRaphson, Broyden, Klement, SimpleTrustRegion, SimpleDFSane)
         solve(prob_no_brack, alg(), abstol = T(1e-2))
     end
 
@@ -51,7 +52,7 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
 end end
 
 # DiffEq styled algorithms
-export Bisection, Brent, Broyden, Falsi, Klement, Ridder, SimpleNewtonRaphson,
+export Bisection, Brent, Broyden, SimpleDFSane, Falsi, Klement, Ridder, SimpleNewtonRaphson,
        SimpleTrustRegion
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index 58a6181ea..47713439c 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -31,16 +31,16 @@ end
 function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
                                                 iip,
                                                 <:Dual{T, V, P}},
-                         alg::Union{SimpleNewtonRaphson, SimpleTrustRegion},
+                         alg::Union{SimpleNewtonRaphson, SimpleTrustRegion, SimpleDFSane}, # TODO make this to one variable
                          args...; kwargs...) where {iip, T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
                                     retcode = sol.retcode)
 end
-function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
+function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector}, # TODO make this to one variable
                                                 iip,
                                                 <:AbstractArray{<:Dual{T, V, P}}},
-                         alg::Union{SimpleNewtonRaphson, SimpleTrustRegion}, args...;
+                         alg::Union{SimpleNewtonRaphson, SimpleTrustRegion, SimpleDFSane}, args...;
                          kwargs...) where {iip, T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
new file mode 100644
index 000000000..a66703dab
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -0,0 +1,135 @@
+"""
+```julia
+SimpleDFSane(; σ_min::Real = 1e-10, σ_0::Real = 1.0, M::Int = 10,
+            γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
+            nexp::Int = 2)
+```
+
+A low-overhead implementation of the df-sane method. For more information, see [1].
+References:
+    W LaCruz, JM Martinez, and M Raydan (2006), Spectral residual mathod without gradient information for solving large-scale nonlinear systems of equations, Mathematics of Computation, 75, 1429-1448.
+### Keyword Arguments
+
+
+- `σ_min`: the minimum value of `σ_k`. Defaults to `1e-10`. # TODO write about this...
+- `σ_0`: the initial value of `σ_k`. Defaults to `1.0`. # TODO write about this...
+- `M`: the value of `M` in the paper. Defaults to `10`. # TODO write about this...
+- `γ`: the value of `γ` in the paper. Defaults to `1e-4`. # TODO write about this...
+- `τ_min`: the minimum value of `τ_k`. Defaults to `0.1`. # TODO write about this...
+- `τ_max`: the maximum value of `τ_k`. Defaults to `0.5`. # TODO write about this...
+- `nexp`: the value of `nexp` in the paper. Defaults to `2`. # TODO write about this...
+
+"""
+struct SimpleDFSane{T} <: AbstractSimpleNonlinearSolveAlgorithm
+    σ_min::T
+    σ_0::T
+    M::Int
+    γ::T
+    τ_min::T
+    τ_max::T
+    nexp::Int
+
+    function SimpleDFSane(; σ_min::Real = 1e-10, σ_0::Real = 1.0, M::Int = 10,
+                          γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
+                          nexp::Int = 2)
+        new{typeof(σ_min)}(σ_min, σ_0, M, γ, τ_min, τ_max, nexp)
+    end
+end
+
+function SciMLBase.__solve(prob::NonlinearProblem,
+                           alg::SimpleDFSane, args...; abstol = nothing,
+                           reltol = nothing,
+                           maxiters = 1000, kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    x = float(prob.u0)
+    T = eltype(x)
+    σ_min = float(alg.σ_min)
+    σ_k = float(alg.σ_0)
+    M = alg.M
+    γ = float(alg.γ)
+    τ_min = float(alg.τ_min)
+    τ_max = float(alg.τ_max)
+    nexp = alg.nexp
+
+    if SciMLBase.isinplace(prob)
+        error("SimpleDFSane currently only supports out-of-place nonlinear problems")
+    end
+
+    atol = abstol !== nothing ? abstol :
+           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
+    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
+
+    function ff(x)
+        F = f(x)
+        f_k = norm(F)^nexp
+        return f_k, F
+    end
+
+    f_k, F_k = ff(x)
+    α_0 = convert(T, 1.0)
+    f_0 = f_k
+    prev_fs = fill(f_k, M)
+
+    for k in 1:maxiters
+        iszero(F_k) &&
+            return SciMLBase.build_solution(prob, alg, x, F_k;
+                                            retcode = ReturnCode.Success)
+
+        # Control spectral parameter
+        if abs(σ_k) > 1 / σ_min
+            σ_k = 1 / σ_min * sign(σ_k)
+        elseif abs(σ_k) < σ_min
+            σ_k = σ_min
+        end
+
+        # Line search direction
+        d = -σ_k * F_k
+
+        # Nonmonotone line search
+        η = f_0 / k^2
+
+        f_bar = maximum(prev_fs)
+        α_p = α_0
+        α_m = α_0
+        xp = x + α_p * d
+        fp, Fp = ff(xp)
+        while true
+            if fp ≤ f_bar + η - γ * α_p^2 * f_k
+                break
+            end
+
+            α_tp = α_p^2 * f_k / (fp + (2 * α_p - 1) * f_k)
+            xp = x - α_m * d
+            fp, Fp = ff(xp)
+
+            if fp ≤ f_bar + η - γ * α_m^2 * f_k
+                break
+            end
+
+            α_tm = α_m^2 * f_k / (fp + (2 * α_m - 1) * f_k)
+            α_p = min(τ_max * α_p, max(α_tp, τ_min * α_p))
+            α_m = min(τ_max * α_m, max(α_tm, τ_min * α_m))
+            xp = x + α_p * d
+            fp, Fp = ff(xp)
+        end
+
+        if isapprox(xp, x, atol = atol, rtol = rtol)
+            return SciMLBase.build_solution(prob, alg, xp, Fp;
+                                            retcode = ReturnCode.Success)
+        end
+        # Update spectral parameter
+        s_k = xp - x
+        y_k = Fp - F_k
+        σ_k = dot(s_k, s_k) / dot(s_k, y_k)
+
+        # Take step
+        x = xp
+        F_k = Fp
+        f_k = fp
+
+        # Store function value
+        idx_to_replace = k % M + 1
+        prev_fs[idx_to_replace] = fp
+    end
+    return SciMLBase.build_solution(prob, alg, x, F_k; retcode = ReturnCode.MaxIters)
+end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index fa15e798e..782c26625 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -62,13 +62,24 @@ sol = benchmark_scalar(sf, csu0)
 @test sol.retcode === ReturnCode.Success
 @test sol.u * sol.u - 2 < 1e-9
 
+# SimpleDFSane
+function benchmark_scalar(f, u0)
+    probN = NonlinearProblem{false}(f, u0)
+    sol = (solve(probN, SimpleDFSane()))
+end
+
+sol = benchmark_scalar(sf, csu0)
+@test sol.retcode === ReturnCode.Success
+@test sol.u * sol.u - 2 < 1e-9
+
 # AD Tests
 using ForwardDiff
 
 # Immutable
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
-for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion())
+for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion(),
+            SimpleDFSane())
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
         sol = solve(probN, alg, abstol = 1e-9)
@@ -76,14 +87,15 @@ for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion())
     end
 
     for p in 1.1:0.1:100.0
-        @test g(p) ≈ sqrt(p)
-        @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+        @test abs.(g(p)) ≈ sqrt(p)
+        @test abs.(ForwardDiff.derivative(g, p)) ≈ 1 / (2 * sqrt(p))
     end
 end
 
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
-for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion())
+for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion(),
+            SimpleDFSane())
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
@@ -91,8 +103,8 @@ for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion())
     end
 
     for p in 1.1:0.1:100.0
-        @test g(p) ≈ sqrt(p)
-        @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+        @test abs(g(p)) ≈ sqrt(p)
+        @test abs(ForwardDiff.derivative(g, p)) ≈ 1 / (2 * sqrt(p))
     end
 end
 
@@ -148,7 +160,7 @@ for alg in [Bisection(), Falsi(), Ridder(), Brent()]
     @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
 end
 
-for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion())
+for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion(), SimpleDFSane())
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -169,6 +181,7 @@ probN = NonlinearProblem(f, u0)
 @test solve(probN, SimpleTrustRegion(; autodiff = false)).u[end] ≈ sqrt(2.0)
 @test solve(probN, Broyden()).u[end] ≈ sqrt(2.0)
 @test solve(probN, Klement()).u[end] ≈ sqrt(2.0)
+@test solve(probN, SimpleDFSane()).u[end] ≈ sqrt(2.0)
 
 for u0 in [1.0, [1, 1.0]]
     local f, probN, sol
@@ -185,8 +198,8 @@ for u0 in [1.0, [1, 1.0]]
     @test solve(probN, SimpleTrustRegion(; autodiff = false)).u ≈ sol
 
     @test solve(probN, Broyden()).u ≈ sol
-
     @test solve(probN, Klement()).u ≈ sol
+    @test solve(probN, SimpleDFSane()).u ≈ sol
 end
 
 # Bisection Tests
@@ -299,3 +312,46 @@ for options in list_of_options
     sol = solve(probN, alg)
     @test all(abs.(f(u, p)) .< 1e-10)
 end
+
+# # Test that `SimpleDFSane` passes a test that `SimpleNewtonRaphson` fails on.
+# u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
+# global g, f
+# f = (u, p) -> 0.010000000000000002 .+
+#               10.000000000000002 ./ (1 .+
+#                (0.21640425613334457 .+
+#                 216.40425613334457 ./ (1 .+
+#                  (0.21640425613334457 .+
+#                   216.40425613334457 ./
+#                   (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^ 2.0) .-
+#               0.0011552453009332421u .- p
+# g = function (p)
+#     probN = NonlinearProblem{false}(f, u0, p)
+#     sol = solve(probN, SimpleDFSane())
+#     return sol.u
+# end
+# p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+# u = g(p)
+# f(u, p)
+# @test all(abs.(f(u, p)) .< 1e-10)
+
+# # Test kwars in `SimpleDFSane`
+
+
+# list_of_options = zip(max_trust_radius, initial_trust_radius, step_threshold,
+#                       shrink_threshold, expand_threshold, shrink_factor,
+#                       expand_factor, max_shrink_times)
+# for options in list_of_options
+#     local probN, sol, alg
+#     alg = SimpleDFSane(max_trust_radius = options[1],
+#                             initial_trust_radius = options[2],
+#                             step_threshold = options[3],
+#                             shrink_threshold = options[4],
+#                             expand_threshold = options[5],
+#                             shrink_factor = options[6],
+#                             expand_factor = options[7],
+#                             max_shrink_times = options[8])
+
+#     probN = NonlinearProblem(f, u0, p)
+#     sol = solve(probN, alg)
+#     @test all(abs.(f(u, p)) .< 1e-10)
+# end

From f816305756032dc14aa4ed6992c95ba6e96cbf2d Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Mon, 6 Feb 2023 19:51:25 +0100
Subject: [PATCH 063/700] DFSane implementation

---
 lib/SimpleNonlinearSolve/src/ad.jl          |   6 +-
 lib/SimpleNonlinearSolve/src/dfsane.jl      | 136 +++++++++++---------
 lib/SimpleNonlinearSolve/test/basictests.jl |  99 +++++++-------
 3 files changed, 137 insertions(+), 104 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index 47713439c..dbd90243a 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -31,16 +31,16 @@ end
 function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
                                                 iip,
                                                 <:Dual{T, V, P}},
-                         alg::Union{SimpleNewtonRaphson, SimpleTrustRegion, SimpleDFSane}, # TODO make this to one variable
+                         alg::AbstractSimpleNonlinearSolveAlgorithm,
                          args...; kwargs...) where {iip, T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
                                     retcode = sol.retcode)
 end
-function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector}, # TODO make this to one variable
+function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
                                                 iip,
                                                 <:AbstractArray{<:Dual{T, V, P}}},
-                         alg::Union{SimpleNewtonRaphson, SimpleTrustRegion, SimpleDFSane}, args...;
+                         alg::AbstractSimpleNonlinearSolveAlgorithm, args...;
                          kwargs...) where {iip, T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index a66703dab..3d2e9c8aa 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -1,55 +1,78 @@
 """
 ```julia
-SimpleDFSane(; σ_min::Real = 1e-10, σ_0::Real = 1.0, M::Int = 10,
-            γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
-            nexp::Int = 2)
+SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
+             M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
+             nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 / k^2)
 ```
 
-A low-overhead implementation of the df-sane method. For more information, see [1].
-References:
-    W LaCruz, JM Martinez, and M Raydan (2006), Spectral residual mathod without gradient information for solving large-scale nonlinear systems of equations, Mathematics of Computation, 75, 1429-1448.
-### Keyword Arguments
-
+A low-overhead implementation of the df-sane method for solving large-scale nonlinear
+systems of equations. For in depth information about all the parameters and the algorithm,
+see the paper: [W LaCruz, JM Martinez, and M Raydan (2006), Spectral residual mathod without
+gradient information for solving large-scale nonlinear systems of equations, Mathematics of
+Computation, 75, 1429-1448.](https://www.researchgate.net/publication/220576479_Spectral_Residual_Method_without_Gradient_Information_for_Solving_Large-Scale_Nonlinear_Systems_of_Equations)
 
-- `σ_min`: the minimum value of `σ_k`. Defaults to `1e-10`. # TODO write about this...
-- `σ_0`: the initial value of `σ_k`. Defaults to `1.0`. # TODO write about this...
-- `M`: the value of `M` in the paper. Defaults to `10`. # TODO write about this...
-- `γ`: the value of `γ` in the paper. Defaults to `1e-4`. # TODO write about this...
-- `τ_min`: the minimum value of `τ_k`. Defaults to `0.1`. # TODO write about this...
-- `τ_max`: the maximum value of `τ_k`. Defaults to `0.5`. # TODO write about this...
-- `nexp`: the value of `nexp` in the paper. Defaults to `2`. # TODO write about this...
+### Keyword Arguments
 
+- `σ_min`: the minimum value of the spectral coefficient `σ_k` which is related to the step
+  size in the algorithm. Defaults to `1e-10`.
+- `σ_max`: the maximum value of the spectral coefficient `σ_k` which is related to the step
+  size in the algorithm. Defaults to `1e10`.
+- `σ_1`: the initial value of the spectral coefficient `σ_k` which is related to the step
+  size in the algorithm.. Defaults to `1.0`.
+- `M`: The monotonicity of the algorithm is determined by a this positive integer.
+  A value of 1 for `M` would result in strict monotonicity in the decrease of the L2-norm
+  of the function `f`. However, higher values allow for more flexibility in this reduction.
+  Despite this, the algorithm still ensures global convergence through the use of a
+  non-monotone line-search algorithm that adheres to the Grippo-Lampariello-Lucidi
+  condition. Values in the range of 5 to 20 are usually sufficient, but some cases may call
+  for a higher value of `M`. The default setting is 10.
+- `γ`: a parameter that influences if a proposed step will be accepted. Higher value of `γ`
+  will make the algorithm more restrictive in accepting steps. Defaults to `1e-4`.
+- `τ_min`: if a step is rejected the new step size will get multiplied by factor, and this
+  parameter is the minimum value of that factor. Defaults to `0.1`.
+- `τ_max`: if a step is rejected the new step size will get multiplied by factor, and this
+  parameter is the maximum value of that factor. Defaults to `0.5`.
+- `nexp`: the exponent of the loss, i.e. ``f_k=||F(x_k)||^{nexp}``. The paper uses
+  `nexp ∈ {1,2}`. Defaults to `2`.
+- `η_strategy`:  function to determine the parameter `η_k`, which enables growth
+  of ``||F||^2``. Called as ``η_k = η_strategy(f_1, k, x, F)`` with `f_1` initialized as
+  ``f_1=||F(x_1)||^{nexp}``, `k` is the iteration number, `x` is the current `x`-value and
+  `F` the current residual. Should satisfy ``η_k > 0`` and ``∑ₖ ηₖ < ∞``. Defaults to
+  ``||F||^2 / k^2``.
 """
 struct SimpleDFSane{T} <: AbstractSimpleNonlinearSolveAlgorithm
     σ_min::T
-    σ_0::T
+    σ_max::T
+    σ_1::T
     M::Int
     γ::T
     τ_min::T
     τ_max::T
     nexp::Int
+    η_strategy::Function
 
-    function SimpleDFSane(; σ_min::Real = 1e-10, σ_0::Real = 1.0, M::Int = 10,
-                          γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
-                          nexp::Int = 2)
-        new{typeof(σ_min)}(σ_min, σ_0, M, γ, τ_min, τ_max, nexp)
+    function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
+                          M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
+                          nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 / k^2)
+        new{typeof(σ_min)}(σ_min, σ_max, σ_1, M, γ, τ_min, τ_max, nexp, η_strategy)
     end
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem,
-                           alg::SimpleDFSane, args...; abstol = nothing,
-                           reltol = nothing,
-                           maxiters = 1000, kwargs...)
+function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane,
+                           args...; abstol = nothing, reltol = nothing, maxiters = 1000,
+                           kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     T = eltype(x)
     σ_min = float(alg.σ_min)
-    σ_k = float(alg.σ_0)
+    σ_max = float(alg.σ_max)
+    σ_k = float(alg.σ_1)
     M = alg.M
     γ = float(alg.γ)
     τ_min = float(alg.τ_min)
     τ_max = float(alg.τ_max)
     nexp = alg.nexp
+    η_strategy = alg.η_strategy
 
     if SciMLBase.isinplace(prob)
         error("SimpleDFSane currently only supports out-of-place nonlinear problems")
@@ -66,70 +89,67 @@ function SciMLBase.__solve(prob::NonlinearProblem,
     end
 
     f_k, F_k = ff(x)
-    α_0 = convert(T, 1.0)
-    f_0 = f_k
-    prev_fs = fill(f_k, M)
+    α_1 = convert(T, 1.0)
+    f_1 = f_k
+    history_f_k = fill(f_k, M)
 
     for k in 1:maxiters
         iszero(F_k) &&
             return SciMLBase.build_solution(prob, alg, x, F_k;
                                             retcode = ReturnCode.Success)
 
-        # Control spectral parameter
-        if abs(σ_k) > 1 / σ_min
-            σ_k = 1 / σ_min * sign(σ_k)
+        # Spectral parameter range check
+        if abs(σ_k) > σ_max
+            σ_k = sign(σ_k) * σ_max
         elseif abs(σ_k) < σ_min
-            σ_k = σ_min
+            σ_k = sign(σ_k) * σ_min
         end
 
         # Line search direction
         d = -σ_k * F_k
 
-        # Nonmonotone line search
-        η = f_0 / k^2
-
-        f_bar = maximum(prev_fs)
-        α_p = α_0
-        α_m = α_0
-        xp = x + α_p * d
-        fp, Fp = ff(xp)
+        η = η_strategy(f_1, k, x, F_k)
+        f̄ = maximum(history_f_k)
+        α_p = α_1
+        α_m = α_1
+        x_new = x + α_p * d
+        f_new, F_new = ff(x_new)
         while true
-            if fp ≤ f_bar + η - γ * α_p^2 * f_k
+            if f_new ≤ f̄ + η - γ * α_p^2 * f_k
                 break
             end
 
-            α_tp = α_p^2 * f_k / (fp + (2 * α_p - 1) * f_k)
-            xp = x - α_m * d
-            fp, Fp = ff(xp)
+            α_tp = α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
+            x_new = x - α_m * d
+            f_new, F_new = ff(x_new)
 
-            if fp ≤ f_bar + η - γ * α_m^2 * f_k
+            if f_new ≤ f̄ + η - γ * α_m^2 * f_k
                 break
             end
 
-            α_tm = α_m^2 * f_k / (fp + (2 * α_m - 1) * f_k)
+            α_tm = α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
             α_p = min(τ_max * α_p, max(α_tp, τ_min * α_p))
             α_m = min(τ_max * α_m, max(α_tm, τ_min * α_m))
-            xp = x + α_p * d
-            fp, Fp = ff(xp)
+            x_new = x + α_p * d
+            f_new, F_new = ff(x_new)
         end
 
-        if isapprox(xp, x, atol = atol, rtol = rtol)
-            return SciMLBase.build_solution(prob, alg, xp, Fp;
+        if isapprox(x_new, x, atol = atol, rtol = rtol)
+            return SciMLBase.build_solution(prob, alg, x_new, F_new;
                                             retcode = ReturnCode.Success)
         end
         # Update spectral parameter
-        s_k = xp - x
-        y_k = Fp - F_k
-        σ_k = dot(s_k, s_k) / dot(s_k, y_k)
+        s_k = x_new - x
+        y_k = F_new - F_k
+        σ_k = (s_k' * s_k) / (s_k' * y_k)
 
         # Take step
-        x = xp
-        F_k = Fp
-        f_k = fp
+        x = x_new
+        F_k = F_new
+        f_k = f_new
 
         # Store function value
-        idx_to_replace = k % M + 1
-        prev_fs[idx_to_replace] = fp
+        history_f_k[k % M + 1] = f_new
     end
     return SciMLBase.build_solution(prob, alg, x, F_k; retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 782c26625..d8fb583f4 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -160,7 +160,8 @@ for alg in [Bisection(), Falsi(), Ridder(), Brent()]
     @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
 end
 
-for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion(), SimpleDFSane())
+for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion(),
+            SimpleDFSane())
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -313,45 +314,57 @@ for options in list_of_options
     @test all(abs.(f(u, p)) .< 1e-10)
 end
 
-# # Test that `SimpleDFSane` passes a test that `SimpleNewtonRaphson` fails on.
-# u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
-# global g, f
-# f = (u, p) -> 0.010000000000000002 .+
-#               10.000000000000002 ./ (1 .+
-#                (0.21640425613334457 .+
-#                 216.40425613334457 ./ (1 .+
-#                  (0.21640425613334457 .+
-#                   216.40425613334457 ./
-#                   (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^ 2.0) .-
-#               0.0011552453009332421u .- p
-# g = function (p)
-#     probN = NonlinearProblem{false}(f, u0, p)
-#     sol = solve(probN, SimpleDFSane())
-#     return sol.u
-# end
-# p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
-# u = g(p)
-# f(u, p)
-# @test all(abs.(f(u, p)) .< 1e-10)
-
-# # Test kwars in `SimpleDFSane`
-
-
-# list_of_options = zip(max_trust_radius, initial_trust_radius, step_threshold,
-#                       shrink_threshold, expand_threshold, shrink_factor,
-#                       expand_factor, max_shrink_times)
-# for options in list_of_options
-#     local probN, sol, alg
-#     alg = SimpleDFSane(max_trust_radius = options[1],
-#                             initial_trust_radius = options[2],
-#                             step_threshold = options[3],
-#                             shrink_threshold = options[4],
-#                             expand_threshold = options[5],
-#                             shrink_factor = options[6],
-#                             expand_factor = options[7],
-#                             max_shrink_times = options[8])
-
-#     probN = NonlinearProblem(f, u0, p)
-#     sol = solve(probN, alg)
-#     @test all(abs.(f(u, p)) .< 1e-10)
-# end
+# Test that `SimpleDFSane` passes a test that `SimpleNewtonRaphson` fails on.
+u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
+global g, f
+f = (u, p) -> 0.010000000000000002 .+
+              10.000000000000002 ./ (1 .+
+               (0.21640425613334457 .+
+                216.40425613334457 ./ (1 .+
+                 (0.21640425613334457 .+
+                  216.40425613334457 ./
+                  (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^ 2.0) .-
+              0.0011552453009332421u .- p
+g = function (p)
+    probN = NonlinearProblem{false}(f, u0, p)
+    sol = solve(probN, SimpleDFSane())
+    return sol.u
+end
+p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+u = g(p)
+f(u, p)
+@test all(abs.(f(u, p)) .< 1e-10)
+
+# Test kwars in `SimpleDFSane`
+σ_min = [1e-10, 1e-5, 1e-4]
+σ_max = [1e10, 1e5, 1e4]
+σ_1 = [1.0, 0.5, 2.0]
+M = [10, 1, 100]
+γ = [1e-4, 1e-3, 1e-5]
+τ_min = [0.1, 0.2, 0.3]
+τ_max = [0.5, 0.8, 0.9]
+nexp = [2, 1, 2]
+η_strategy = [
+    (f_1, k, x, F) -> f_1 / k^2,
+    (f_1, k, x, F) -> f_1 / k^3,
+    (f_1, k, x, F) -> f_1 / k^4,
+]
+
+list_of_options = zip(σ_min, σ_max, σ_1, M, γ, τ_min, τ_max, nexp,
+                      η_strategy)
+for options in list_of_options
+    local probN, sol, alg
+    alg = SimpleDFSane(σ_min = options[1],
+                       σ_max = options[2],
+                       σ_1 = options[3],
+                       M = options[4],
+                       γ = options[5],
+                       τ_min = options[6],
+                       τ_max = options[7],
+                       nexp = options[8],
+                       η_strategy = options[9])
+
+    probN = NonlinearProblem(f, u0, p)
+    sol = solve(probN, alg)
+    @test all(abs.(f(u, p)) .< 1e-10)
+end

From d8c13cfa26771e468220871f2f506220bf0952a2 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 6 Feb 2023 16:32:37 -0500
Subject: [PATCH 064/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 3b8b5d859..2a953148a 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.9"
+version = "0.1.10"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"

From 4199b52bb66f81e8680500663a9ffa7bbfbe7134 Mon Sep 17 00:00:00 2001
From: Simon Carlson <ccsimon123@gmail.com>
Date: Tue, 7 Feb 2023 13:01:28 +0100
Subject: [PATCH 065/700] Dead links in Trust Region fix

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 329eb8808..edd143215 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -13,9 +13,7 @@ SimpleTrustRegion(; chunk_size = Val{0}(),
                     max_shrink_times::Int = 32
 ```
 
-A low-overhead implementation of a
-[trust-region](https://optimization.mccormick.northwestern.edu/index.php/Trust-region_methods)
-solver
+A low-overhead implementation of a trust-region solver.
 
 ### Keyword Arguments
 
@@ -39,12 +37,12 @@ solver
   compared with a value `r`, which is the actual reduction in the objective function divided
   by the predicted reduction. If `step_threshold > r` the model is not a good approximation,
   and the step is rejected. Defaults to `0.1`. For more details, see
-  [Trust-region methods](https://optimization.mccormick.northwestern.edu/index.php/Trust-region_methods)
+  [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
 - `shrink_threshold`: the threshold for shrinking the trust region radius. In every
   iteration, the threshold is compared with a value `r` which is the actual reduction in the
   objective function divided by the predicted reduction. If `shrink_threshold > r` the trust
   region radius is shrunk by `shrink_factor`. Defaults to `0.25`. For more details, see
-  [Trust-region methods](https://optimization.mccormick.northwestern.edu/index.php/Trust-region_methods)
+  [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
 - `expand_threshold`: the threshold for expanding the trust region radius. If a step is
   taken, i.e `step_threshold < r` (with `r` defined in `shrink_threshold`), a check is also
   made to see if `expand_threshold < r`. If that is true, the trust region radius is

From 50d348f89b5e851b6b7db3055b9dc91852a270da Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 10 Feb 2023 16:32:42 -0500
Subject: [PATCH 066/700] Add limited memory broyden implementation

---
 .../src/SimpleNonlinearSolve.jl               |  5 +-
 lib/SimpleNonlinearSolve/src/lbroyden.jl      | 83 +++++++++++++++++++
 2 files changed, 86 insertions(+), 2 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/lbroyden.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 940db0835..5b170ce6c 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -20,6 +20,7 @@ include("bisection.jl")
 include("falsi.jl")
 include("raphson.jl")
 include("broyden.jl")
+include("lbroyden.jl")
 include("klement.jl")
 include("trustRegion.jl")
 include("ridder.jl")
@@ -52,7 +53,7 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
 end end
 
 # DiffEq styled algorithms
-export Bisection, Brent, Broyden, SimpleDFSane, Falsi, Klement, Ridder, SimpleNewtonRaphson,
-       SimpleTrustRegion
+export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, Klement,
+       Ridder, SimpleNewtonRaphson, SimpleTrustRegion
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
new file mode 100644
index 000000000..61423d8ce
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -0,0 +1,83 @@
+Base.@kwdef struct LBroyden <: AbstractSimpleNonlinearSolveAlgorithm
+    threshold::Int = 27
+end
+
+@views function SciMLBase.__solve(prob::NonlinearProblem,
+                                  alg::LBroyden, args...; abstol = nothing,
+                                  reltol = nothing,
+                                  maxiters = 1000, kwargs...)
+    threshold = min(maxiters, alg.threshold)
+    x = float(prob.u0)
+
+    if x isa Number
+        restore_scalar = true
+        x = [x]
+        f = u -> prob.f(u[], prob.p)
+    else
+        f = Base.Fix2(prob.f, prob.p)
+        restore_scalar = false
+    end
+
+    fₙ = f(x)
+    T = eltype(x)
+
+    if SciMLBase.isinplace(prob)
+        error("LBroyden currently only supports out-of-place nonlinear problems")
+    end
+
+    U = fill!(similar(x, (threshold, length(x))), zero(T))
+    Vᵀ = fill!(similar(x, (length(x), threshold)), zero(T))
+
+    atol = abstol !== nothing ? abstol :
+           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
+    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
+
+    xₙ = x
+    xₙ₋₁ = x
+    fₙ₋₁ = fₙ
+    update = fₙ
+    for i in 1:maxiters
+        xₙ = xₙ₋₁ .+ update
+        fₙ = f(xₙ)
+        Δxₙ = xₙ .- xₙ₋₁
+        Δfₙ = fₙ .- fₙ₋₁
+
+        if iszero(fₙ)
+            xₙ = restore_scalar ? xₙ[] : xₙ
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
+        end
+
+        if isapprox(xₙ, xₙ₋₁; atol, rtol)
+            xₙ = restore_scalar ? xₙ[] : xₙ
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
+        end
+
+        _U = U[1:min(threshold, i), :]
+        _Vᵀ = Vᵀ[:, 1:min(threshold, i)]
+
+        vᵀ = _rmatvec(_U, _Vᵀ, Δxₙ)
+        mvec = _matvec(_U, _Vᵀ, Δfₙ)
+        Δxₙ = (Δxₙ .- mvec) ./ (sum(vᵀ .* Δfₙ) .+ eps(T))
+
+        Vᵀ[:, mod1(i, threshold)] .= vᵀ
+        U[mod1(i, threshold), :] .= Δxₙ
+
+        update = -_matvec(U[1:min(threshold, i + 1), :], Vᵀ[:, 1:min(threshold, i + 1)], fₙ)
+
+        xₙ₋₁ = xₙ
+        fₙ₋₁ = fₙ
+    end
+
+    xₙ = restore_scalar ? xₙ[] : xₙ
+    return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
+end
+
+function _rmatvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
+                  x::Union{<:AbstractVector, <:Number})
+    return -x .+ dropdims(sum(U .* sum(Vᵀ .* x; dims = 1)'; dims = 1); dims = 1)
+end
+
+function _matvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
+                 x::Union{<:AbstractVector, <:Number})
+    return -x .+ dropdims(sum(sum(x .* U'; dims = 1) .* Vᵀ; dims = 2); dims = 2)
+end

From 87ea1bcec19460971ce8b74047d5d4e2e1d1a3f8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 10 Feb 2023 16:58:47 -0500
Subject: [PATCH 067/700] Add some tests

---
 lib/SimpleNonlinearSolve/Project.toml       | 2 +-
 lib/SimpleNonlinearSolve/src/lbroyden.jl    | 8 +++++++-
 lib/SimpleNonlinearSolve/test/basictests.jl | 8 +++++---
 3 files changed, 13 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 2a953148a..6288c3ecc 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.10"
+version = "0.1.11"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index 61423d8ce..f983bbd66 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -1,3 +1,9 @@
+"""
+    LBroyden(threshold::Int = 27)
+
+A limited memory implementation of Broyden. This method applies the L-BFGS scheme to
+Broyden's method.
+"""
 Base.@kwdef struct LBroyden <: AbstractSimpleNonlinearSolveAlgorithm
     threshold::Int = 27
 end
@@ -57,7 +63,7 @@ end
 
         vᵀ = _rmatvec(_U, _Vᵀ, Δxₙ)
         mvec = _matvec(_U, _Vᵀ, Δfₙ)
-        Δxₙ = (Δxₙ .- mvec) ./ (sum(vᵀ .* Δfₙ) .+ eps(T))
+        Δxₙ = (Δxₙ .- mvec) ./ (sum(vᵀ .* Δfₙ) .+ convert(T, 1e-5))
 
         Vᵀ[:, mod1(i, threshold)] .= vᵀ
         U[mod1(i, threshold), :] .= Δxₙ
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index d8fb583f4..ad83fd224 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -78,7 +78,7 @@ using ForwardDiff
 # Immutable
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
-for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion(),
+for alg in (SimpleNewtonRaphson(), Broyden(), LBroyden(), Klement(), SimpleTrustRegion(),
             SimpleDFSane())
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
@@ -94,7 +94,7 @@ end
 
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
-for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion(),
+for alg in (SimpleNewtonRaphson(), Broyden(), LBroyden(), Klement(), SimpleTrustRegion(),
             SimpleDFSane())
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
@@ -160,7 +160,7 @@ for alg in [Bisection(), Falsi(), Ridder(), Brent()]
     @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
 end
 
-for alg in (SimpleNewtonRaphson(), Broyden(), Klement(), SimpleTrustRegion(),
+for alg in (SimpleNewtonRaphson(), Broyden(), LBroyden(), Klement(), SimpleTrustRegion(),
             SimpleDFSane())
     global g, p
     g = function (p)
@@ -181,6 +181,7 @@ probN = NonlinearProblem(f, u0)
 @test solve(probN, SimpleTrustRegion()).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleTrustRegion(; autodiff = false)).u[end] ≈ sqrt(2.0)
 @test solve(probN, Broyden()).u[end] ≈ sqrt(2.0)
+@test solve(probN, LBroyden()).u[end] ≈ sqrt(2.0)
 @test solve(probN, Klement()).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleDFSane()).u[end] ≈ sqrt(2.0)
 
@@ -199,6 +200,7 @@ for u0 in [1.0, [1, 1.0]]
     @test solve(probN, SimpleTrustRegion(; autodiff = false)).u ≈ sol
 
     @test solve(probN, Broyden()).u ≈ sol
+    @test solve(probN, LBroyden()).u ≈ sol
     @test solve(probN, Klement()).u ≈ sol
     @test solve(probN, SimpleDFSane()).u ≈ sol
 end

From 775005604e2bd31c7215c3b0217b524903a7be08 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 11 Feb 2023 08:56:52 -0500
Subject: [PATCH 068/700] Update basictests.jl

---
 lib/SimpleNonlinearSolve/test/basictests.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index ad83fd224..3f386d276 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -166,7 +166,7 @@ for alg in (SimpleNewtonRaphson(), Broyden(), LBroyden(), Klement(), SimpleTrust
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
         sol = solve(probN, alg)
-        return [sol.u]
+        return [abs(sol.u)]
     end
     @test g(p) ≈ [sqrt(p[2] / p[1])]
     @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)

From 245a6d7be9332fc1ef195889b0f9dfc78a9ab045 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 12 Feb 2023 13:02:27 -0500
Subject: [PATCH 069/700] Make broyden batched

---
 lib/SimpleNonlinearSolve/Project.toml         |  4 ++-
 .../src/SimpleNonlinearSolve.jl               |  1 +
 lib/SimpleNonlinearSolve/src/broyden.jl       | 29 +++++++++++++------
 lib/SimpleNonlinearSolve/src/lbroyden.jl      |  7 ++---
 lib/SimpleNonlinearSolve/src/utils.jl         | 28 ++++++++++++++----
 5 files changed, 50 insertions(+), 19 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 6288c3ecc..351bb62a4 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.11"
+version = "0.1.12"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"
@@ -9,6 +9,7 @@ DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SnoopPrecompile = "66db9d55-30c0-4569-8b51-7e840670fc0c"
@@ -19,6 +20,7 @@ ArrayInterfaceCore = "0.1.1"
 DiffEqBase = "6.114"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
+NNlib = "0.8"
 Reexport = "0.2, 1"
 SciMLBase = "1.73"
 SnoopPrecompile = "1"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 5b170ce6c..b48e33ed2 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -7,6 +7,7 @@ using StaticArraysCore
 using LinearAlgebra
 import ArrayInterfaceCore
 using DiffEqBase
+using NNlib  # Batched Matrix Multiplication
 
 @reexport using SciMLBase
 
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index a05caa00a..7539a2bfe 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -8,15 +8,18 @@ and static array problems.
 """
 struct Broyden <: AbstractSimpleNonlinearSolveAlgorithm end
 
-function SciMLBase.__solve(prob::NonlinearProblem,
-                           alg::Broyden, args...; abstol = nothing,
-                           reltol = nothing,
-                           maxiters = 1000, kwargs...)
+function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...; abstol = nothing,
+                           reltol = nothing, maxiters = 1000, batch = false, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
+
+    if batch && ndims(x) != 2
+        error("`batch` mode works only if `ndims(prob.u0) == 2`")
+    end
+
     fₙ = f(x)
     T = eltype(x)
-    J⁻¹ = init_J(x)
+    J⁻¹ = init_J(x; batch)
 
     if SciMLBase.isinplace(prob)
         error("Broyden currently only supports out-of-place nonlinear problems")
@@ -30,11 +33,14 @@ function SciMLBase.__solve(prob::NonlinearProblem,
     xₙ₋₁ = x
     fₙ₋₁ = fₙ
     for _ in 1:maxiters
-        xₙ = xₙ₋₁ - J⁻¹ * fₙ₋₁
+        xₙ = xₙ₋₁ .- _batched_mul(J⁻¹, fₙ₋₁, batch)
         fₙ = f(xₙ)
-        Δxₙ = xₙ - xₙ₋₁
-        Δfₙ = fₙ - fₙ₋₁
-        J⁻¹ += ((Δxₙ - J⁻¹ * Δfₙ) ./ (Δxₙ' * J⁻¹ * Δfₙ)) * (Δxₙ' * J⁻¹)
+        Δxₙ = xₙ .- xₙ₋₁
+        Δfₙ = fₙ .- fₙ₋₁
+        J⁻¹Δfₙ = _batched_mul(J⁻¹, Δfₙ, batch)
+        J⁻¹ += _batched_mul(((Δxₙ .- J⁻¹Δfₙ, batch) ./
+                             (_batched_mul(_batch_transpose(Δxₙ, batch), J⁻¹Δfₙ, batch))),
+                            _batched_mul(_batch_transpose(Δxₙ, batch), J⁻¹, batch), batch)
 
         iszero(fₙ) &&
             return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
@@ -50,3 +56,8 @@ function SciMLBase.__solve(prob::NonlinearProblem,
 
     return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
 end
+
+function _batch_transpose(x, batch)
+    !batch && return x'
+    return reshape(x, 1, size(x)...)
+end
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index f983bbd66..f8ed9f5d3 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -8,10 +8,9 @@ Base.@kwdef struct LBroyden <: AbstractSimpleNonlinearSolveAlgorithm
     threshold::Int = 27
 end
 
-@views function SciMLBase.__solve(prob::NonlinearProblem,
-                                  alg::LBroyden, args...; abstol = nothing,
-                                  reltol = nothing,
-                                  maxiters = 1000, kwargs...)
+@views function SciMLBase.__solve(prob::NonlinearProblem, alg::LBroyden, args...;
+                                  abstol = nothing, reltol = nothing, maxiters = 1000,
+                                  batch = false, kwargs...)
     threshold = min(maxiters, alg.threshold)
     x = float(prob.u0)
 
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index f3b7de9f6..6f12b829f 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -34,14 +34,17 @@ value(x) = x
 value(x::Dual) = ForwardDiff.value(x)
 value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
 
-function init_J(x)
-    J = ArrayInterfaceCore.zeromatrix(x)
-    if ismutable(x)
-        J[diagind(J)] .= one(eltype(x))
+function init_J(x; batch = false)
+    x_ = batch ? x[:, 1] : x
+
+    J = ArrayInterfaceCore.zeromatrix(x_)
+    if ismutable(x_)
+        J[diagind(J)] .= one(eltype(x_))
     else
         J += I
     end
-    return J
+
+    return batch ? repeat(J, 1, 1, size(x, 2)) : J
 end
 
 function dogleg_method(H, g, Δ)
@@ -68,3 +71,18 @@ function dogleg_method(H, g, Δ)
     tau = (-dot_δsd_δN_δsd + sqrt(fact)) / dot_δN_δsd
     return δsd + tau * δN_δsd
 end
+
+_batched_mul(x, y, batch) = x * y
+function _batched_mul(x::AbstractArray{T, 3}, y::AbstractMatrix, batch) where {T}
+    !batch && return x * y
+    return dropdims(batched_mul(x, reshape(y, size(y, 1), 1, size(y, 2))); dims = 2)
+end
+function _batched_mul(x::AbstractMatrix, y::AbstractArray{T, 3}, batch) where {T}
+    !batch && return x * y
+    return batched_mul(reshape(x, size(x, 1), 1, size(x, 2)), y)
+end
+function _batched_mul(x::AbstractArray{T1, 3}, y::AbstractArray{T2, 3},
+                      batch) where {T1, T2}
+    !batch && return x * y
+    return batched_mul(x, y)
+end
\ No newline at end of file

From 3bd1c85c9ad148a7b86d32b9d15f55951e0233c8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 13 Feb 2023 11:07:39 -0500
Subject: [PATCH 070/700] Make it an extension

---
 lib/SimpleNonlinearSolve/Project.toml         |  7 ++-
 .../SimpleBatchedNonlinearSolveExt.jl         |  9 ++++
 .../SimpleBatchedNonlinearSolveExt/broyden.jl | 48 +++++++++++++++++++
 .../lbroyden.jl                               |  0
 .../SimpleBatchedNonlinearSolveExt/utils.jl   | 25 ++++++++++
 .../src/SimpleNonlinearSolve.jl               |  1 -
 lib/SimpleNonlinearSolve/src/broyden.jl       | 38 +++++++--------
 lib/SimpleNonlinearSolve/src/utils.jl         | 28 ++---------
 8 files changed, 109 insertions(+), 47 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/SimpleBatchedNonlinearSolveExt.jl
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/broyden.jl
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/lbroyden.jl
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/utils.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 351bb62a4..4852c1f78 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -9,12 +9,17 @@ DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SnoopPrecompile = "66db9d55-30c0-4569-8b51-7e840670fc0c"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
+[weakdeps]
+NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
+
+[extensions]
+SimpleBatchedNonlinearSolveExt = "NNlib"
+
 [compat]
 ArrayInterfaceCore = "0.1.1"
 DiffEqBase = "6.114"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/SimpleBatchedNonlinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/SimpleBatchedNonlinearSolveExt.jl
new file mode 100644
index 000000000..5a7483e3f
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/SimpleBatchedNonlinearSolveExt.jl
@@ -0,0 +1,9 @@
+module SimpleBatchedNonlinearSolveExt
+
+using SimpleNonlinearSolve, SciMLBase, NNlib
+
+include("utils.jl")
+include("broyden.jl")
+include("lbroyden.jl")
+
+end
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/broyden.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/broyden.jl
new file mode 100644
index 000000000..2476e9570
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/broyden.jl
@@ -0,0 +1,48 @@
+function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{true}, args...;
+                           abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    x = float(prob.u0)
+
+    if ndims(x) != 2
+        error("`batch` mode works only if `ndims(prob.u0) == 2`")
+    end
+
+    fₙ = f(x)
+    T = eltype(x)
+    J⁻¹ = _init_J_batched(x)
+
+    if SciMLBase.isinplace(prob)
+        error("Broyden currently only supports out-of-place nonlinear problems")
+    end
+
+    atol = abstol !== nothing ? abstol :
+           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
+    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
+
+    xₙ = x
+    xₙ₋₁ = x
+    fₙ₋₁ = fₙ
+    for _ in 1:maxiters
+        xₙ = xₙ₋₁ .- _batched_mul(J⁻¹, fₙ₋₁, batch)
+        fₙ = f(xₙ)
+        Δxₙ = xₙ .- xₙ₋₁
+        Δfₙ = fₙ .- fₙ₋₁
+        J⁻¹Δfₙ = _batched_mul(J⁻¹, Δfₙ, batch)
+        J⁻¹ += _batched_mul(((Δxₙ .- J⁻¹Δfₙ, batch) ./
+                             (_batched_mul(_batch_transpose(Δxₙ, batch), J⁻¹Δfₙ, batch))),
+                            _batched_mul(_batch_transpose(Δxₙ, batch), J⁻¹, batch), batch)
+
+        iszero(fₙ) &&
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
+                                            retcode = ReturnCode.Success)
+
+        if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
+                                            retcode = ReturnCode.Success)
+        end
+        xₙ₋₁ = xₙ
+        fₙ₋₁ = fₙ
+    end
+
+    return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
+end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/lbroyden.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/lbroyden.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/utils.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/utils.jl
new file mode 100644
index 000000000..4dfd4f34e
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/utils.jl
@@ -0,0 +1,25 @@
+_batch_transpose(x) = reshape(x, 1, size(x)...)
+
+_batched_mul(x, y) = x * y
+
+function _batched_mul(x::AbstractArray{T, 3}, y::AbstractMatrix) where {T}
+    return dropdims(batched_mul(x, reshape(y, size(y, 1), 1, size(y, 2))); dims = 2)
+end
+
+function _batched_mul(x::AbstractMatrix, y::AbstractArray{T, 3}) where {T}
+    return batched_mul(reshape(x, size(x, 1), 1, size(x, 2)), y)
+end
+
+function _batched_mul(x::AbstractArray{T1, 3}, y::AbstractArray{T2, 3}) where {T1, T2}
+    return batched_mul(x, y)
+end
+
+function _init_J_batched(x::AbstractMatrix{T}) where {T}
+    J = ArrayInterfaceCore.zeromatrix(x[:, 1])
+    if ismutable(x)
+        J[diagind(J)] .= one(eltype(x))
+    else
+        J += I
+    end
+    return repeat(J, 1, 1, size(x, 2))
+end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index b48e33ed2..5b170ce6c 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -7,7 +7,6 @@ using StaticArraysCore
 using LinearAlgebra
 import ArrayInterfaceCore
 using DiffEqBase
-using NNlib  # Batched Matrix Multiplication
 
 @reexport using SciMLBase
 
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 7539a2bfe..7820be8e9 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -1,25 +1,26 @@
 """
-```julia
-Broyden()
-```
+    Broyden()
 
 A low-overhead implementation of Broyden. This method is non-allocating on scalar
 and static array problems.
 """
-struct Broyden <: AbstractSimpleNonlinearSolveAlgorithm end
+struct Broyden{batched} <: AbstractSimpleNonlinearSolveAlgorithm
+    Broyden(batched = false) = new{batched}()
+end
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...; abstol = nothing,
-                           reltol = nothing, maxiters = 1000, batch = false, kwargs...)
+function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{false}, args...;
+                           abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
 
-    if batch && ndims(x) != 2
-        error("`batch` mode works only if `ndims(prob.u0) == 2`")
-    end
+    # if batch && ndims(x) != 2
+    #     error("`batch` mode works only if `ndims(prob.u0) == 2`")
+    # end
 
     fₙ = f(x)
     T = eltype(x)
-    J⁻¹ = init_J(x; batch)
+    # J⁻¹ = init_J(x; batch)
+    J⁻¹ = init_J(x)
 
     if SciMLBase.isinplace(prob)
         error("Broyden currently only supports out-of-place nonlinear problems")
@@ -33,14 +34,12 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...; abstol
     xₙ₋₁ = x
     fₙ₋₁ = fₙ
     for _ in 1:maxiters
-        xₙ = xₙ₋₁ .- _batched_mul(J⁻¹, fₙ₋₁, batch)
+        xₙ = xₙ₋₁ - J⁻¹ * fₙ₋₁
         fₙ = f(xₙ)
-        Δxₙ = xₙ .- xₙ₋₁
-        Δfₙ = fₙ .- fₙ₋₁
-        J⁻¹Δfₙ = _batched_mul(J⁻¹, Δfₙ, batch)
-        J⁻¹ += _batched_mul(((Δxₙ .- J⁻¹Δfₙ, batch) ./
-                             (_batched_mul(_batch_transpose(Δxₙ, batch), J⁻¹Δfₙ, batch))),
-                            _batched_mul(_batch_transpose(Δxₙ, batch), J⁻¹, batch), batch)
+        Δxₙ = xₙ - xₙ₋₁
+        Δfₙ = fₙ - fₙ₋₁
+        J⁻¹Δfₙ = J⁻¹ * Δfₙ
+        J⁻¹ += ((Δxₙ .- J⁻¹Δfₙ) ./ (Δxₙ' * J⁻¹Δfₙ)) * (Δxₙ' * J⁻¹)
 
         iszero(fₙ) &&
             return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
@@ -56,8 +55,3 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...; abstol
 
     return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
 end
-
-function _batch_transpose(x, batch)
-    !batch && return x'
-    return reshape(x, 1, size(x)...)
-end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 6f12b829f..f3b7de9f6 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -34,17 +34,14 @@ value(x) = x
 value(x::Dual) = ForwardDiff.value(x)
 value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
 
-function init_J(x; batch = false)
-    x_ = batch ? x[:, 1] : x
-
-    J = ArrayInterfaceCore.zeromatrix(x_)
-    if ismutable(x_)
-        J[diagind(J)] .= one(eltype(x_))
+function init_J(x)
+    J = ArrayInterfaceCore.zeromatrix(x)
+    if ismutable(x)
+        J[diagind(J)] .= one(eltype(x))
     else
         J += I
     end
-
-    return batch ? repeat(J, 1, 1, size(x, 2)) : J
+    return J
 end
 
 function dogleg_method(H, g, Δ)
@@ -71,18 +68,3 @@ function dogleg_method(H, g, Δ)
     tau = (-dot_δsd_δN_δsd + sqrt(fact)) / dot_δN_δsd
     return δsd + tau * δN_δsd
 end
-
-_batched_mul(x, y, batch) = x * y
-function _batched_mul(x::AbstractArray{T, 3}, y::AbstractMatrix, batch) where {T}
-    !batch && return x * y
-    return dropdims(batched_mul(x, reshape(y, size(y, 1), 1, size(y, 2))); dims = 2)
-end
-function _batched_mul(x::AbstractMatrix, y::AbstractArray{T, 3}, batch) where {T}
-    !batch && return x * y
-    return batched_mul(reshape(x, size(x, 1), 1, size(x, 2)), y)
-end
-function _batched_mul(x::AbstractArray{T1, 3}, y::AbstractArray{T2, 3},
-                      batch) where {T1, T2}
-    !batch && return x * y
-    return batched_mul(x, y)
-end
\ No newline at end of file

From 33cf8b36ac746c877e492cd67bd0cc3f28cc9ced Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 15 Feb 2023 11:28:44 -0500
Subject: [PATCH 071/700] Add requires for backward compat

---
 lib/SimpleNonlinearSolve/Project.toml         |  4 ++-
 ...n.jl => SimpleBatchedNonlinearSolveExt.jl} | 34 +++++++++++++++++++
 .../SimpleBatchedNonlinearSolveExt.jl         |  9 -----
 .../lbroyden.jl                               |  0
 .../SimpleBatchedNonlinearSolveExt/utils.jl   | 25 --------------
 .../src/SimpleNonlinearSolve.jl               | 12 +++++++
 lib/SimpleNonlinearSolve/src/broyden.jl       |  9 ++---
 7 files changed, 51 insertions(+), 42 deletions(-)
 rename lib/SimpleNonlinearSolve/ext/{SimpleBatchedNonlinearSolveExt/broyden.jl => SimpleBatchedNonlinearSolveExt.jl} (66%)
 delete mode 100644 lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/SimpleBatchedNonlinearSolveExt.jl
 delete mode 100644 lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/lbroyden.jl
 delete mode 100644 lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/utils.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 4852c1f78..28e3410a9 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -10,6 +10,7 @@ FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+Requires = "ae029012-a4dd-5104-9daa-d747884805df"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SnoopPrecompile = "66db9d55-30c0-4569-8b51-7e840670fc0c"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
@@ -34,10 +35,11 @@ julia = "1.6"
 
 [extras]
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays"]
+test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays", "NNlib"]
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/broyden.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
similarity index 66%
rename from lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/broyden.jl
rename to lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
index 2476e9570..88de48871 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/broyden.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
@@ -1,3 +1,34 @@
+module SimpleBatchedNonlinearSolveExt
+
+using SimpleNonlinearSolve, SciMLBase
+isdefined(Base, :get_extension) ? (using NNlib) : (using ..NNlib)
+
+_batch_transpose(x) = reshape(x, 1, size(x)...)
+
+_batched_mul(x, y) = x * y
+
+function _batched_mul(x::AbstractArray{T, 3}, y::AbstractMatrix) where {T}
+    return dropdims(batched_mul(x, reshape(y, size(y, 1), 1, size(y, 2))); dims = 2)
+end
+
+function _batched_mul(x::AbstractMatrix, y::AbstractArray{T, 3}) where {T}
+    return batched_mul(reshape(x, size(x, 1), 1, size(x, 2)), y)
+end
+
+function _batched_mul(x::AbstractArray{T1, 3}, y::AbstractArray{T2, 3}) where {T1, T2}
+    return batched_mul(x, y)
+end
+
+function _init_J_batched(x::AbstractMatrix{T}) where {T}
+    J = ArrayInterfaceCore.zeromatrix(x[:, 1])
+    if ismutable(x)
+        J[diagind(J)] .= one(eltype(x))
+    else
+        J += I
+    end
+    return repeat(J, 1, 1, size(x, 2))
+end
+
 function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{true}, args...;
                            abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
@@ -46,3 +77,6 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{true}, args...;
 
     return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
 end
+
+
+end
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/SimpleBatchedNonlinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/SimpleBatchedNonlinearSolveExt.jl
deleted file mode 100644
index 5a7483e3f..000000000
--- a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/SimpleBatchedNonlinearSolveExt.jl
+++ /dev/null
@@ -1,9 +0,0 @@
-module SimpleBatchedNonlinearSolveExt
-
-using SimpleNonlinearSolve, SciMLBase, NNlib
-
-include("utils.jl")
-include("broyden.jl")
-include("lbroyden.jl")
-
-end
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/lbroyden.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/lbroyden.jl
deleted file mode 100644
index e69de29bb..000000000
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/utils.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/utils.jl
deleted file mode 100644
index 4dfd4f34e..000000000
--- a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt/utils.jl
+++ /dev/null
@@ -1,25 +0,0 @@
-_batch_transpose(x) = reshape(x, 1, size(x)...)
-
-_batched_mul(x, y) = x * y
-
-function _batched_mul(x::AbstractArray{T, 3}, y::AbstractMatrix) where {T}
-    return dropdims(batched_mul(x, reshape(y, size(y, 1), 1, size(y, 2))); dims = 2)
-end
-
-function _batched_mul(x::AbstractMatrix, y::AbstractArray{T, 3}) where {T}
-    return batched_mul(reshape(x, size(x, 1), 1, size(x, 2)), y)
-end
-
-function _batched_mul(x::AbstractArray{T1, 3}, y::AbstractArray{T2, 3}) where {T1, T2}
-    return batched_mul(x, y)
-end
-
-function _init_J_batched(x::AbstractMatrix{T}) where {T}
-    J = ArrayInterfaceCore.zeromatrix(x[:, 1])
-    if ismutable(x)
-        J[diagind(J)] .= one(eltype(x))
-    else
-        J += I
-    end
-    return repeat(J, 1, 1, size(x, 2))
-end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 5b170ce6c..51785e323 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -10,6 +10,18 @@ using DiffEqBase
 
 @reexport using SciMLBase
 
+if !isdefined(Base, :get_extension)
+    using Requires
+end
+
+function __init__()
+    @static if !isdefined(Base, :get_extension)
+        @require NNlib="872c559c-99b0-510c-b3b7-b6c96a88d5cd" begin
+            include("../ext/SimpleBatchedNonlinearSolveExt.jl")
+        end
+    end
+end
+
 abstract type AbstractSimpleNonlinearSolveAlgorithm <: SciMLBase.AbstractNonlinearAlgorithm end
 abstract type AbstractBracketingAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 abstract type AbstractNewtonAlgorithm{CS, AD, FDT} <: AbstractSimpleNonlinearSolveAlgorithm end
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 7820be8e9..15da8a77e 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -1,11 +1,11 @@
 """
-    Broyden()
+    Broyden(; batched = false)
 
 A low-overhead implementation of Broyden. This method is non-allocating on scalar
 and static array problems.
 """
 struct Broyden{batched} <: AbstractSimpleNonlinearSolveAlgorithm
-    Broyden(batched = false) = new{batched}()
+    Broyden(; batched = false) = new{batched}()
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{false}, args...;
@@ -13,13 +13,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{false}, args...;
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
 
-    # if batch && ndims(x) != 2
-    #     error("`batch` mode works only if `ndims(prob.u0) == 2`")
-    # end
-
     fₙ = f(x)
     T = eltype(x)
-    # J⁻¹ = init_J(x; batch)
     J⁻¹ = init_J(x)
 
     if SciMLBase.isinplace(prob)

From e88d64dd60c95b5cba5c29786363db08aa0a6ccd Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 16 Feb 2023 14:51:45 -0500
Subject: [PATCH 072/700] Add tests for batched broyden

---
 lib/SimpleNonlinearSolve/.gitignore             |  3 +++
 .../ext/SimpleBatchedNonlinearSolveExt.jl       | 17 ++++++++---------
 .../src/SimpleNonlinearSolve.jl                 |  4 +---
 lib/SimpleNonlinearSolve/src/broyden.jl         |  5 +++++
 lib/SimpleNonlinearSolve/test/basictests.jl     | 12 ++++++++++++
 5 files changed, 29 insertions(+), 12 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/.gitignore

diff --git a/lib/SimpleNonlinearSolve/.gitignore b/lib/SimpleNonlinearSolve/.gitignore
new file mode 100644
index 000000000..e4cfbfe81
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/.gitignore
@@ -0,0 +1,3 @@
+Manifest.toml
+
+wip
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
index 88de48871..d59970471 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
@@ -1,6 +1,6 @@
 module SimpleBatchedNonlinearSolveExt
 
-using SimpleNonlinearSolve, SciMLBase
+using ArrayInterfaceCore, LinearAlgebra, SimpleNonlinearSolve, SciMLBase
 isdefined(Base, :get_extension) ? (using NNlib) : (using ..NNlib)
 
 _batch_transpose(x) = reshape(x, 1, size(x)...)
@@ -53,15 +53,15 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{true}, args...;
     xₙ = x
     xₙ₋₁ = x
     fₙ₋₁ = fₙ
-    for _ in 1:maxiters
-        xₙ = xₙ₋₁ .- _batched_mul(J⁻¹, fₙ₋₁, batch)
+    for i in 1:maxiters
+        xₙ = xₙ₋₁ .- _batched_mul(J⁻¹, fₙ₋₁)
         fₙ = f(xₙ)
         Δxₙ = xₙ .- xₙ₋₁
         Δfₙ = fₙ .- fₙ₋₁
-        J⁻¹Δfₙ = _batched_mul(J⁻¹, Δfₙ, batch)
-        J⁻¹ += _batched_mul(((Δxₙ .- J⁻¹Δfₙ, batch) ./
-                             (_batched_mul(_batch_transpose(Δxₙ, batch), J⁻¹Δfₙ, batch))),
-                            _batched_mul(_batch_transpose(Δxₙ, batch), J⁻¹, batch), batch)
+        J⁻¹Δfₙ = _batched_mul(J⁻¹, Δfₙ)
+        J⁻¹ += _batched_mul(((Δxₙ .- J⁻¹Δfₙ) ./
+                             (_batched_mul(_batch_transpose(Δxₙ), J⁻¹Δfₙ) .+ T(1e-5))),
+                            _batched_mul(_batch_transpose(Δxₙ), J⁻¹))
 
         iszero(fₙ) &&
             return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
@@ -78,5 +78,4 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{true}, args...;
     return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
 end
 
-
-end
\ No newline at end of file
+end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 51785e323..b82a7d0c6 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -16,9 +16,7 @@ end
 
 function __init__()
     @static if !isdefined(Base, :get_extension)
-        @require NNlib="872c559c-99b0-510c-b3b7-b6c96a88d5cd" begin
-            include("../ext/SimpleBatchedNonlinearSolveExt.jl")
-        end
+        @require NNlib="872c559c-99b0-510c-b3b7-b6c96a88d5cd" begin include("../ext/SimpleBatchedNonlinearSolveExt.jl") end
     end
 end
 
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 15da8a77e..d0ae233b3 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -3,6 +3,11 @@
 
 A low-overhead implementation of Broyden. This method is non-allocating on scalar
 and static array problems.
+
+!!! note
+
+    To use the `batched` version, remember to load `NNlib`, i.e., `using NNlib` or
+    `import NNlib` must be present in your code.
 """
 struct Broyden{batched} <: AbstractSimpleNonlinearSolveAlgorithm
     Broyden(; batched = false) = new{batched}()
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 3f386d276..12525d814 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -370,3 +370,15 @@ for options in list_of_options
     sol = solve(probN, alg)
     @test all(abs.(f(u, p)) .< 1e-10)
 end
+
+# Batched Broyden
+using NNlib
+
+f, u0 = (u, p) -> u .* u .- p, randn(1, 3)
+
+p = [2.0 1.0 5.0];
+probN = NonlinearProblem{false}(f, u0, p);
+
+sol = solve(probN, Broyden(batched = true))
+
+@test abs.(sol.u) ≈ sqrt.(p)

From 940fef52dc8618ee56cb0d229f22de9c3ad44d3e Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 16 Feb 2023 17:25:51 -0500
Subject: [PATCH 073/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 28e3410a9..2d99b8849 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.12"
+version = "0.1.13"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"

From 918f72e311e78bebaebc9a48cd8195df896cd9b8 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 16 Feb 2023 17:26:40 -0500
Subject: [PATCH 074/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 2d99b8849..0e05f54ba 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.13"
+version = "0.1.11"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"

From 9c7f959366f5b2f48dd39a23d6b950cd95d3e874 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 16 Feb 2023 17:37:09 -0500
Subject: [PATCH 075/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 0e05f54ba..aac1c5413 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -28,6 +28,7 @@ FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 NNlib = "0.8"
 Reexport = "0.2, 1"
+Requires = "1"
 SciMLBase = "1.73"
 SnoopPrecompile = "1"
 StaticArraysCore = "1.4"

From cf4449795dd7b11c09a1de686a51a6dede708edb Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 17 Feb 2023 17:45:59 -0500
Subject: [PATCH 076/700] Add Termination Conditions to Broyden

---
 lib/SimpleNonlinearSolve/Project.toml         |  6 +-
 .../ext/SimpleBatchedNonlinearSolveExt.jl     | 27 +++---
 lib/SimpleNonlinearSolve/src/broyden.jl       | 41 ++++++---
 lib/SimpleNonlinearSolve/test/basictests.jl   | 90 ++++++++++++-------
 4 files changed, 107 insertions(+), 57 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index aac1c5413..0368644a4 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.11"
+version = "0.1.12"
 
 [deps]
 ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"
@@ -23,7 +23,7 @@ SimpleBatchedNonlinearSolveExt = "NNlib"
 
 [compat]
 ArrayInterfaceCore = "0.1.1"
-DiffEqBase = "6.114"
+DiffEqBase = "6.118.1"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 NNlib = "0.8"
@@ -43,4 +43,4 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays", "NNlib"]
+test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays", "NNlib", "DiffEqBase"]
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
index d59970471..76c81efc4 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
@@ -1,6 +1,6 @@
 module SimpleBatchedNonlinearSolveExt
 
-using ArrayInterfaceCore, LinearAlgebra, SimpleNonlinearSolve, SciMLBase
+using ArrayInterfaceCore, DiffEqBase, LinearAlgebra, SimpleNonlinearSolve, SciMLBase
 isdefined(Base, :get_extension) ? (using NNlib) : (using ..NNlib)
 
 _batch_transpose(x) = reshape(x, 1, size(x)...)
@@ -31,6 +31,8 @@ end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{true}, args...;
                            abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
+    tc = alg.termination_condition
+    mode = DiffEqBase.get_termination_mode(tc)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
 
@@ -47,8 +49,17 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{true}, args...;
     end
 
     atol = abstol !== nothing ? abstol :
-           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
-    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
+           (tc.abstol !== nothing ? tc.abstol :
+            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5))
+    rtol = reltol !== nothing ? reltol :
+           (tc.reltol !== nothing ? tc.reltol : eps(real(one(eltype(T))))^(4 // 5))
+
+    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
+        error("Broyden currently doesn't support SAFE_BEST termination modes")
+    end
+
+    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? Dict() : nothing
+    termination_condition = tc(storage)
 
     xₙ = x
     xₙ₋₁ = x
@@ -63,14 +74,10 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{true}, args...;
                              (_batched_mul(_batch_transpose(Δxₙ), J⁻¹Δfₙ) .+ T(1e-5))),
                             _batched_mul(_batch_transpose(Δxₙ), J⁻¹))
 
-        iszero(fₙ) &&
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                                            retcode = ReturnCode.Success)
-
-        if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                                            retcode = ReturnCode.Success)
+        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
         end
+
         xₙ₋₁ = xₙ
         fₙ₋₁ = fₙ
     end
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index d0ae233b3..e8d339c4c 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -1,5 +1,7 @@
 """
-    Broyden(; batched = false)
+    Broyden(; batched = false,
+            termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+                                                                abstol = nothing, reltol = nothing))
 
 A low-overhead implementation of Broyden. This method is non-allocating on scalar
 and static array problems.
@@ -9,12 +11,22 @@ and static array problems.
     To use the `batched` version, remember to load `NNlib`, i.e., `using NNlib` or
     `import NNlib` must be present in your code.
 """
-struct Broyden{batched} <: AbstractSimpleNonlinearSolveAlgorithm
-    Broyden(; batched = false) = new{batched}()
+struct Broyden{batched, TC <: NLSolveTerminationCondition} <:
+       AbstractSimpleNonlinearSolveAlgorithm
+    termination_condition::TC
+
+    function Broyden(; batched = false,
+                     termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+                                                                         abstol = nothing,
+                                                                         reltol = nothing))
+        return new{batched, typeof(termination_condition)}(termination_condition)
+    end
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{false}, args...;
                            abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
+    tc = alg.termination_condition
+    mode = DiffEqBase.get_termination_mode(tc)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
 
@@ -27,8 +39,17 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{false}, args...;
     end
 
     atol = abstol !== nothing ? abstol :
-           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
-    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
+           (tc.abstol !== nothing ? tc.abstol :
+            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5))
+    rtol = reltol !== nothing ? reltol :
+           (tc.reltol !== nothing ? tc.reltol : eps(real(one(eltype(T))))^(4 // 5))
+
+    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
+        error("Broyden currently doesn't support SAFE_BEST termination modes")
+    end
+
+    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? Dict() : nothing
+    termination_condition = tc(storage)
 
     xₙ = x
     xₙ₋₁ = x
@@ -41,14 +62,10 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{false}, args...;
         J⁻¹Δfₙ = J⁻¹ * Δfₙ
         J⁻¹ += ((Δxₙ .- J⁻¹Δfₙ) ./ (Δxₙ' * J⁻¹Δfₙ)) * (Δxₙ' * J⁻¹)
 
-        iszero(fₙ) &&
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                                            retcode = ReturnCode.Success)
-
-        if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                                            retcode = ReturnCode.Success)
+        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
         end
+
         xₙ₋₁ = xₙ
         fₙ₋₁ = fₙ
     end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 12525d814..819621202 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -1,8 +1,25 @@
 using SimpleNonlinearSolve
 using StaticArrays
 using BenchmarkTools
+using DiffEqBase
 using Test
 
+const BATCHED_BROYDEN_SOLVERS = Broyden[]
+const BROYDEN_SOLVERS = Broyden[]
+
+for mode in instances(NLSolveTerminationMode.T)
+    if mode ∈
+       (NLSolveTerminationMode.SteadyStateDefault, NLSolveTerminationMode.RelSafeBest,
+        NLSolveTerminationMode.AbsSafeBest)
+        continue
+    end
+
+    termination_condition = NLSolveTerminationCondition(mode; abstol = nothing,
+                                                        reltol = nothing)
+    push!(BROYDEN_SOLVERS, Broyden(; batched = false, termination_condition))
+    push!(BATCHED_BROYDEN_SOLVERS, Broyden(; batched = true, termination_condition))
+end
+
 # SimpleNewtonRaphson
 function benchmark_scalar(f, u0)
     probN = NonlinearProblem{false}(f, u0)
@@ -27,16 +44,19 @@ if VERSION >= v"1.7"
 end
 
 # Broyden
-function benchmark_scalar(f, u0)
+function benchmark_scalar(f, u0, alg)
     probN = NonlinearProblem{false}(f, u0)
-    sol = (solve(probN, Broyden()))
+    sol = (solve(probN, alg))
 end
 
-sol = benchmark_scalar(sf, csu0)
-@test sol.retcode === ReturnCode.Success
-@test sol.u * sol.u - 2 < 1e-9
-if VERSION >= v"1.7"
-    @test (@ballocated benchmark_scalar(sf, csu0)) == 0
+for alg in BROYDEN_SOLVERS
+    sol = benchmark_scalar(sf, csu0, alg)
+    @test sol.retcode === ReturnCode.Success
+    @test sol.u * sol.u - 2 < 1e-9
+    # FIXME: Termination Condition Implementation is allocating. Not sure how to fix it.
+    # if VERSION >= v"1.7"
+    #     @test (@ballocated benchmark_scalar($sf, $csu0, $termination_condition)) == 0
+    # end
 end
 
 # Klement
@@ -78,8 +98,8 @@ using ForwardDiff
 # Immutable
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
-for alg in (SimpleNewtonRaphson(), Broyden(), LBroyden(), Klement(), SimpleTrustRegion(),
-            SimpleDFSane())
+for alg in (SimpleNewtonRaphson(), LBroyden(), Klement(), SimpleTrustRegion(),
+            SimpleDFSane(), BROYDEN_SOLVERS...)
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
         sol = solve(probN, alg, abstol = 1e-9)
@@ -94,8 +114,8 @@ end
 
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
-for alg in (SimpleNewtonRaphson(), Broyden(), LBroyden(), Klement(), SimpleTrustRegion(),
-            SimpleDFSane())
+for alg in (SimpleNewtonRaphson(), LBroyden(), Klement(), SimpleTrustRegion(),
+            SimpleDFSane(), BROYDEN_SOLVERS...)
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
@@ -160,8 +180,8 @@ for alg in [Bisection(), Falsi(), Ridder(), Brent()]
     @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
 end
 
-for alg in (SimpleNewtonRaphson(), Broyden(), LBroyden(), Klement(), SimpleTrustRegion(),
-            SimpleDFSane())
+for alg in (SimpleNewtonRaphson(), LBroyden(), Klement(), SimpleTrustRegion(),
+            SimpleDFSane(), BROYDEN_SOLVERS...)
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -176,14 +196,15 @@ end
 f, u0 = (u, p) -> u .* u .- 2.0, @SVector[1.0, 1.0]
 probN = NonlinearProblem(f, u0)
 
-@test solve(probN, SimpleNewtonRaphson()).u[end] ≈ sqrt(2.0)
-@test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u[end] ≈ sqrt(2.0)
-@test solve(probN, SimpleTrustRegion()).u[end] ≈ sqrt(2.0)
-@test solve(probN, SimpleTrustRegion(; autodiff = false)).u[end] ≈ sqrt(2.0)
-@test solve(probN, Broyden()).u[end] ≈ sqrt(2.0)
-@test solve(probN, LBroyden()).u[end] ≈ sqrt(2.0)
-@test solve(probN, Klement()).u[end] ≈ sqrt(2.0)
-@test solve(probN, SimpleDFSane()).u[end] ≈ sqrt(2.0)
+for alg in (SimpleNewtonRaphson(), SimpleNewtonRaphson(; autodiff = false),
+            SimpleTrustRegion(),
+            SimpleTrustRegion(; autodiff = false), LBroyden(), Klement(), SimpleDFSane(),
+            BROYDEN_SOLVERS...)
+    sol = solve(probN, alg)
+
+    @test sol.retcode == ReturnCode.Success
+    @test sol.u[end] ≈ sqrt(2.0)
+end
 
 for u0 in [1.0, [1, 1.0]]
     local f, probN, sol
@@ -191,18 +212,16 @@ for u0 in [1.0, [1, 1.0]]
     probN = NonlinearProblem(f, u0)
     sol = sqrt(2) * u0
 
-    @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
-    @test solve(probN, SimpleNewtonRaphson()).u ≈ sol
-    @test solve(probN, SimpleNewtonRaphson(; autodiff = false)).u ≈ sol
-
-    @test solve(probN, SimpleTrustRegion()).u ≈ sol
-    @test solve(probN, SimpleTrustRegion()).u ≈ sol
-    @test solve(probN, SimpleTrustRegion(; autodiff = false)).u ≈ sol
+    for alg in (SimpleNewtonRaphson(), SimpleNewtonRaphson(; autodiff = false),
+                SimpleTrustRegion(),
+                SimpleTrustRegion(; autodiff = false), LBroyden(), Klement(),
+                SimpleDFSane(),
+                BROYDEN_SOLVERS...)
+        sol2 = solve(probN, alg)
 
-    @test solve(probN, Broyden()).u ≈ sol
-    @test solve(probN, LBroyden()).u ≈ sol
-    @test solve(probN, Klement()).u ≈ sol
-    @test solve(probN, SimpleDFSane()).u ≈ sol
+        @test sol2.retcode == ReturnCode.Success
+        @test sol2.u ≈ sol
+    end
 end
 
 # Bisection Tests
@@ -382,3 +401,10 @@ probN = NonlinearProblem{false}(f, u0, p);
 sol = solve(probN, Broyden(batched = true))
 
 @test abs.(sol.u) ≈ sqrt.(p)
+
+for alg in BATCHED_BROYDEN_SOLVERS
+    sol = solve(probN, alg)
+
+    @test sol.retcode == ReturnCode.Success
+    @test abs.(sol.u) ≈ sqrt.(p)
+end

From 94eaa39e62d6481895b1ba8cded4226be12a6d7a Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 18 Feb 2023 09:21:18 -0500
Subject: [PATCH 077/700] update to ArrayInterface v7

---
 lib/SimpleNonlinearSolve/Project.toml                         | 4 ++--
 .../ext/SimpleBatchedNonlinearSolveExt.jl                     | 4 ++--
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl          | 2 +-
 lib/SimpleNonlinearSolve/src/utils.jl                         | 2 +-
 4 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index aac1c5413..87936fe44 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -4,7 +4,7 @@ authors = ["SciML"]
 version = "0.1.11"
 
 [deps]
-ArrayInterfaceCore = "30b0a656-2188-435a-8636-2ec0e6a096e2"
+ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -22,7 +22,7 @@ NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 SimpleBatchedNonlinearSolveExt = "NNlib"
 
 [compat]
-ArrayInterfaceCore = "0.1.1"
+ArrayInterface = "7"
 DiffEqBase = "6.114"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
index d59970471..4d5b45551 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
@@ -1,6 +1,6 @@
 module SimpleBatchedNonlinearSolveExt
 
-using ArrayInterfaceCore, LinearAlgebra, SimpleNonlinearSolve, SciMLBase
+using ArrayInterface, LinearAlgebra, SimpleNonlinearSolve, SciMLBase
 isdefined(Base, :get_extension) ? (using NNlib) : (using ..NNlib)
 
 _batch_transpose(x) = reshape(x, 1, size(x)...)
@@ -20,7 +20,7 @@ function _batched_mul(x::AbstractArray{T1, 3}, y::AbstractArray{T2, 3}) where {T
 end
 
 function _init_J_batched(x::AbstractMatrix{T}) where {T}
-    J = ArrayInterfaceCore.zeromatrix(x[:, 1])
+    J = ArrayInterface.zeromatrix(x[:, 1])
     if ismutable(x)
         J[diagind(J)] .= one(eltype(x))
     else
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index b82a7d0c6..7e6ef3441 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -5,7 +5,7 @@ using FiniteDiff, ForwardDiff
 using ForwardDiff: Dual
 using StaticArraysCore
 using LinearAlgebra
-import ArrayInterfaceCore
+import ArrayInterface
 using DiffEqBase
 
 @reexport using SciMLBase
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index f3b7de9f6..890aa2415 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -35,7 +35,7 @@ value(x::Dual) = ForwardDiff.value(x)
 value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
 
 function init_J(x)
-    J = ArrayInterfaceCore.zeromatrix(x)
+    J = ArrayInterface.zeromatrix(x)
     if ismutable(x)
         J[diagind(J)] .= one(eltype(x))
     else

From 6b9a5b2f6fb9d21a60532eacfbc718894579915a Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 18 Feb 2023 09:47:28 -0500
Subject: [PATCH 078/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 87936fe44..be3a13cba 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.11"
+version = "0.1.12"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"

From 4724ed3eb4262c0f8436809e5f1425bcc9c44160 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 18 Feb 2023 23:13:09 -0500
Subject: [PATCH 079/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index be3a13cba..4d78f7d62 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -22,7 +22,7 @@ NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 SimpleBatchedNonlinearSolveExt = "NNlib"
 
 [compat]
-ArrayInterface = "7"
+ArrayInterface = "6, 7"
 DiffEqBase = "6.114"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"

From 6ff49047886de4d2c1de6fa33351bec5d086ad9f Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Sun, 19 Feb 2023 00:29:16 +0100
Subject: [PATCH 080/700] Added halley's method

---
 lib/SimpleNonlinearSolve/src/halley.jl | 90 ++++++++++++++++++++++++++
 1 file changed, 90 insertions(+)
 create mode 100644 lib/SimpleNonlinearSolve/src/halley.jl

diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
new file mode 100644
index 000000000..f428db336
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -0,0 +1,90 @@
+"""
+```julia
+Halley(; chunk_size = Val{0}(), autodiff = Val{true}(),
+                                 diff_type = Val{:forward})
+```
+
+A low-overhead implementation of Halley's Method. This method is non-allocating on scalar
+and static array problems.
+
+!!! note
+
+    As part of the decreased overhead, this method omits some of the higher level error
+    catching of the other methods. Thus, to see better error messages, use one of the other
+    methods like `NewtonRaphson`
+
+### Keyword Arguments
+
+- `chunk_size`: the chunk size used by the internal ForwardDiff.jl automatic differentiation
+  system. This allows for multiple derivative columns to be computed simultaneously,
+  improving performance. Defaults to `0`, which is equivalent to using ForwardDiff.jl's
+  default chunk size mechanism. For more details, see the documentation for
+  [ForwardDiff.jl](https://juliadiff.org/ForwardDiff.jl/stable/).
+- `autodiff`: whether to use forward-mode automatic differentiation for the Jacobian.
+  Note that this argument is ignored if an analytical Jacobian is passed; as that will be
+  used instead. Defaults to `Val{true}`, which means ForwardDiff.jl is used by default.
+  If `Val{false}`, then FiniteDiff.jl is used for finite differencing.
+- `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
+  `Val{:forward}` for forward finite differences. For more details on the choices, see the
+  [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
+"""
+struct Halley{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
+    function Halley(; chunk_size = Val{0}(), autodiff = Val{true}(),
+                                 diff_type = Val{:forward})
+        new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
+            SciMLBase._unwrap_val(diff_type)}()
+    end
+end
+
+function SciMLBase.__solve(prob::NonlinearProblem,
+                           alg::Halley, args...; abstol = nothing,
+                           reltol = nothing,
+                           maxiters = 1000, kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    x = float(prob.u0)
+    fx = f(x)
+    # fx = float(prob.u0)
+    if !isa(fx, Number) || !isa(x, Number)
+        error("Halley currently only supports scalar-valued single-variable functions")
+    end
+    T = typeof(x)
+
+    if SciMLBase.isinplace(prob)
+        error("Halley currently only supports out-of-place nonlinear problems")
+    end
+
+    atol = abstol !== nothing ? abstol :
+           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
+    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
+
+    if typeof(x) <: Number
+        xo = oftype(one(eltype(x)), Inf)
+    else
+        xo = map(x -> oftype(one(eltype(x)), Inf), x)
+    end
+
+    for i in 1:maxiters
+        if alg_autodiff(alg)
+            fx = f(x)
+            dfdx(x) = ForwardDiff.derivative(f, x)
+            dfx = dfdx(x)
+            d2fx = ForwardDiff.derivative(dfdx, x)
+        else
+            fx = f(x)
+            dfx = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x),
+                                                          fx)
+            d2fx = FiniteDiff.finite_difference_derivative(x -> FiniteDiff.finite_difference_derivative(f, x),
+                                                           x, diff_type(alg), eltype(x), fx)
+        end
+        iszero(fx) &&
+            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
+        Δx = (2*dfx^2 - fx*d2fx) \ 2fx*dfx
+        x -= Δx
+        if isapprox(x, xo, atol = atol, rtol = rtol)
+            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
+        end
+        xo = x
+    end
+
+    return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+end

From becd1e6660cc3bde0c6197aeb70062ce4caf51b2 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Sun, 19 Feb 2023 00:34:00 +0100
Subject: [PATCH 081/700] added some tests for halley

---
 .../src/SimpleNonlinearSolve.jl               |  7 ++--
 lib/SimpleNonlinearSolve/test/basictests.jl   | 34 +++++++++++++++++--
 2 files changed, 36 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 7e6ef3441..dfc825c52 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -5,7 +5,7 @@ using FiniteDiff, ForwardDiff
 using ForwardDiff: Dual
 using StaticArraysCore
 using LinearAlgebra
-import ArrayInterface
+import ArrayInterfaceCore
 using DiffEqBase
 
 @reexport using SciMLBase
@@ -37,12 +37,13 @@ include("ridder.jl")
 include("brent.jl")
 include("dfsane.jl")
 include("ad.jl")
+include("halley.jl")
 
 import SnoopPrecompile
 
 SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
     prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-    for alg in (SimpleNewtonRaphson, Broyden, Klement, SimpleTrustRegion, SimpleDFSane)
+    for alg in (SimpleNewtonRaphson, Halley, Broyden, Klement, SimpleTrustRegion, SimpleDFSane)
         solve(prob_no_brack, alg(), abstol = T(1e-2))
     end
 
@@ -63,7 +64,7 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
 end end
 
 # DiffEq styled algorithms
-export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, Klement,
+export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, Halley, Klement,
        Ridder, SimpleNewtonRaphson, SimpleTrustRegion
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 12525d814..199e55579 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -26,6 +26,29 @@ if VERSION >= v"1.7"
     @test (@ballocated benchmark_scalar(sf, csu0)) == 0
 end
 
+# Halley
+function benchmark_scalar(f, u0)
+    probN = NonlinearProblem{false}(f, u0)
+    sol = (solve(probN, Halley()))
+end
+
+# function ff(u, p)
+#     u .* u .- 2
+# end
+# const cu0 = @SVector[1.0, 1.0]
+function sf(u, p)
+    u * u - 2
+end
+const csu0 = 1.0
+
+sol = benchmark_scalar(sf, csu0)
+@test sol.retcode === ReturnCode.Success
+@test sol.u * sol.u - 2 < 1e-9
+
+if VERSION >= v"1.7"
+    @test (@ballocated benchmark_scalar(sf, csu0)) == 0
+end
+
 # Broyden
 function benchmark_scalar(f, u0)
     probN = NonlinearProblem{false}(f, u0)
@@ -95,7 +118,7 @@ end
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
 for alg in (SimpleNewtonRaphson(), Broyden(), LBroyden(), Klement(), SimpleTrustRegion(),
-            SimpleDFSane())
+            SimpleDFSane(), Halley())
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
@@ -161,7 +184,7 @@ for alg in [Bisection(), Falsi(), Ridder(), Brent()]
 end
 
 for alg in (SimpleNewtonRaphson(), Broyden(), LBroyden(), Klement(), SimpleTrustRegion(),
-            SimpleDFSane())
+            SimpleDFSane(), Halley())
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -185,6 +208,13 @@ probN = NonlinearProblem(f, u0)
 @test solve(probN, Klement()).u[end] ≈ sqrt(2.0)
 @test solve(probN, SimpleDFSane()).u[end] ≈ sqrt(2.0)
 
+# Separate Error check for Halley; will be included in above error checks for the improved Halley
+f, u0 = (u, p) -> u * u - 2.0, 1.0
+probN = NonlinearProblem(f, u0)
+
+@test solve(probN, Halley()).u ≈ sqrt(2.0)
+
+
 for u0 in [1.0, [1, 1.0]]
     local f, probN, sol
     f = (u, p) -> u .* u .- 2.0

From b1c5f63e0fed3241ade13862c3a2a7728e9abfb2 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Sun, 19 Feb 2023 00:52:32 +0100
Subject: [PATCH 082/700] added tests

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index dfc825c52..e80c7cff2 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -5,7 +5,7 @@ using FiniteDiff, ForwardDiff
 using ForwardDiff: Dual
 using StaticArraysCore
 using LinearAlgebra
-import ArrayInterfaceCore
+import ArrayInterface
 using DiffEqBase
 
 @reexport using SciMLBase

From b07f0d7bc3709fca5203764569cdd77e187a8403 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 18 Feb 2023 23:10:37 -0500
Subject: [PATCH 083/700] Update src/halley.jl

---
 lib/SimpleNonlinearSolve/src/halley.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index f428db336..5c85afe20 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -78,7 +78,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         end
         iszero(fx) &&
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
-        Δx = (2*dfx^2 - fx*d2fx) \ 2fx*dfx
+        Δx = (2*dfx^2 - fx*d2fx) \ (2fx*dfx)
         x -= Δx
         if isapprox(x, xo, atol = atol, rtol = rtol)
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)

From 6cdd257d63335e6162f999cd489317aaa853f24e Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Sun, 19 Feb 2023 07:59:38 -0500
Subject: [PATCH 084/700] format

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 3 ++-
 lib/SimpleNonlinearSolve/src/halley.jl               | 7 ++++---
 lib/SimpleNonlinearSolve/test/basictests.jl          | 1 -
 3 files changed, 6 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index e80c7cff2..4c90b094f 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -43,7 +43,8 @@ import SnoopPrecompile
 
 SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
     prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-    for alg in (SimpleNewtonRaphson, Halley, Broyden, Klement, SimpleTrustRegion, SimpleDFSane)
+    for alg in (SimpleNewtonRaphson, Halley, Broyden, Klement, SimpleTrustRegion,
+                SimpleDFSane)
         solve(prob_no_brack, alg(), abstol = T(1e-2))
     end
 
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 5c85afe20..77ea3a4a1 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -30,7 +30,7 @@ and static array problems.
 """
 struct Halley{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     function Halley(; chunk_size = Val{0}(), autodiff = Val{true}(),
-                                 diff_type = Val{:forward})
+                    diff_type = Val{:forward})
         new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
             SciMLBase._unwrap_val(diff_type)}()
     end
@@ -73,12 +73,13 @@ function SciMLBase.__solve(prob::NonlinearProblem,
             fx = f(x)
             dfx = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x),
                                                           fx)
-            d2fx = FiniteDiff.finite_difference_derivative(x -> FiniteDiff.finite_difference_derivative(f, x),
+            d2fx = FiniteDiff.finite_difference_derivative(x -> FiniteDiff.finite_difference_derivative(f,
+                                                                                                        x),
                                                            x, diff_type(alg), eltype(x), fx)
         end
         iszero(fx) &&
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
-        Δx = (2*dfx^2 - fx*d2fx) \ (2fx*dfx)
+        Δx = (2 * dfx^2 - fx * d2fx) \ (2fx * dfx)
         x -= Δx
         if isapprox(x, xo, atol = atol, rtol = rtol)
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 199e55579..5f8f17a89 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -214,7 +214,6 @@ probN = NonlinearProblem(f, u0)
 
 @test solve(probN, Halley()).u ≈ sqrt(2.0)
 
-
 for u0 in [1.0, [1, 1.0]]
     local f, probN, sol
     f = (u, p) -> u .* u .- 2.0

From 427fae30024c9fbe62228edeea3caebe3cc561ee Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sun, 19 Feb 2023 10:01:24 -0500
Subject: [PATCH 085/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 1 -
 1 file changed, 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 9ad93b17c..796e5416b 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -23,7 +23,6 @@ SimpleBatchedNonlinearSolveExt = "NNlib"
 
 [compat]
 ArrayInterface = "6, 7"
-ArrayInterfaceCore = "0.1.1"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 NNlib = "0.8"

From e0ff9fc09d3a61d60d0de56ee8ec0adf35555092 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sun, 19 Feb 2023 10:10:37 -0500
Subject: [PATCH 086/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 796e5416b..78f3fcc88 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -42,4 +42,4 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays", "NNlib", "DiffEqBase"]
+test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays", "NNlib"]

From 2a3c9e1f7c4e81d1d6d9baa77bc4e044d60d2c7a Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sun, 19 Feb 2023 10:33:18 -0500
Subject: [PATCH 087/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 78f3fcc88..8f52dbdc6 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.12"
+version = "0.1.13"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"

From 9b04692b2e84006cfef1cafe9ad5c8e319d83f4a Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sun, 19 Feb 2023 12:06:11 -0500
Subject: [PATCH 088/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 8f52dbdc6..92e852cb9 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -23,6 +23,7 @@ SimpleBatchedNonlinearSolveExt = "NNlib"
 
 [compat]
 ArrayInterface = "6, 7"
+DiffEqBase = "6.119"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 NNlib = "0.8"

From 3ec0acc1e2c3d68248727b9097e11c85d56599b8 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Mon, 20 Feb 2023 23:47:57 +0100
Subject: [PATCH 089/700] multivariate halley and some tests

---
 lib/SimpleNonlinearSolve/src/halley.jl      | 77 ++++++++++++++++-----
 lib/SimpleNonlinearSolve/test/basictests.jl | 21 +++---
 2 files changed, 71 insertions(+), 27 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 77ea3a4a1..557f43473 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -42,10 +42,28 @@ function SciMLBase.__solve(prob::NonlinearProblem,
                            maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
-    fx = f(x)
-    # fx = float(prob.u0)
-    if !isa(fx, Number) || !isa(x, Number)
-        error("Halley currently only supports scalar-valued single-variable functions")
+    # Defining all derivative expressions in one place before the iterations
+    if isa(x, AbstractArray)
+        if alg_autodiff(alg)
+            n = length(x)
+            a_dfdx(x) = ForwardDiff.jacobian(f, x)
+            a_d2fdx(x) = ForwardDiff.jacobian(a_dfdx, x)
+            A = Array{Union{Nothing, Number}}(nothing, n, n)
+            #fx = f(x)
+        else
+            n = length(x)
+            f_dfdx(x) = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x))
+            f_d2fdx(x) = FiniteDiff.finite_difference_jacobian(f_dfdx, x, diff_type(alg), eltype(x))
+            A = Array{Union{Nothing, Number}}(nothing, n, n)
+        end
+    elseif isa(x, Number)
+        if alg_autodiff(alg)
+            sa_dfdx(x) = ForwardDiff.derivative(f, x)
+            sa_d2fdx(x) = ForwardDiff.derivative(sa_dfdx, x)
+        else
+            sf_dfdx(x) = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x))
+            sf_d2fdx(x) = FiniteDiff.finite_difference_derivative(sf_dfdx, x, diff_type(alg), eltype(x))
+        end
     end
     T = typeof(x)
 
@@ -65,22 +83,49 @@ function SciMLBase.__solve(prob::NonlinearProblem,
 
     for i in 1:maxiters
         if alg_autodiff(alg)
-            fx = f(x)
-            dfdx(x) = ForwardDiff.derivative(f, x)
-            dfx = dfdx(x)
-            d2fx = ForwardDiff.derivative(dfdx, x)
+            if isa(x, Number)
+                fx = f(x)
+                dfx = sa_dfdx(x)
+                d2fx = sa_d2fdx(x)
+            else
+                fx = f(x)
+                dfx = a_dfdx(x)
+                d2fx = reshape(a_d2fdx(x), (n,n,n)) # A 3-dim Hessian Tensor
+                ai = -(dfx \ fx)
+                for j in 1:n
+                    tmp = transpose(d2fx[:, :, j] * ai)
+                    A[j, :] = tmp
+                end
+                bi = (dfx) \ (A * ai)
+                ci = (ai .* ai) ./ (ai .+ (0.5 .* bi))
+            end
         else
-            fx = f(x)
-            dfx = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x),
-                                                          fx)
-            d2fx = FiniteDiff.finite_difference_derivative(x -> FiniteDiff.finite_difference_derivative(f,
-                                                                                                        x),
-                                                           x, diff_type(alg), eltype(x), fx)
+            if isa(x, Number)
+                fx = f(x)
+                dfx = sf_dfdx(x)
+                d2fx = sf_d2fdx(x)
+            else
+                fx = f(x)
+                dfx = f_dfdx(x)
+                d2fx = reshape(f_d2fdx(x), (n,n,n)) # A 3-dim Hessian Tensor
+                ai = -(dfx \ fx)
+                for j in 1:n
+                    tmp = transpose(d2fx[:, :, j] * ai)
+                    A[j, :] = tmp
+                end
+                bi = (dfx) \ (A * ai)
+                ci = (ai .* ai) ./ (ai .+ (0.5 .* bi))
+            end
         end
         iszero(fx) &&
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
-        Δx = (2 * dfx^2 - fx * d2fx) \ (2fx * dfx)
-        x -= Δx
+        if isa(x, Number)
+            Δx = (2 * dfx^2 - fx * d2fx) \ (2fx * dfx)
+            x -= Δx
+        else
+            Δx = ci
+            x += Δx
+        end
         if isapprox(x, xo, atol = atol, rtol = rtol)
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
         end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 26e92dfe8..8fbdfffaf 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -49,10 +49,10 @@ function benchmark_scalar(f, u0)
     sol = (solve(probN, Halley()))
 end
 
-# function ff(u, p)
-#     u .* u .- 2
-# end
-# const cu0 = @SVector[1.0, 1.0]
+function ff(u, p)
+    u .* u .- 2
+end
+const cu0 = @SVector[1.0, 1.0]
 function sf(u, p)
     u * u - 2
 end
@@ -62,6 +62,10 @@ sol = benchmark_scalar(sf, csu0)
 @test sol.retcode === ReturnCode.Success
 @test sol.u * sol.u - 2 < 1e-9
 
+sol = benchmark_scalar(ff, cu0)
+@test sol.retcode === ReturnCode.Success
+@test sol.u .* sol.u .- 2 < [1e-9, 1e-9]
+
 if VERSION >= v"1.7"
     @test (@ballocated benchmark_scalar(sf, csu0)) == 0
 end
@@ -122,7 +126,7 @@ using ForwardDiff
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
 for alg in (SimpleNewtonRaphson(), LBroyden(), Klement(), SimpleTrustRegion(),
-            SimpleDFSane(), BROYDEN_SOLVERS...)
+            SimpleDFSane(), Halley(), BROYDEN_SOLVERS...)
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
         sol = solve(probN, alg, abstol = 1e-9)
@@ -221,7 +225,7 @@ probN = NonlinearProblem(f, u0)
 
 for alg in (SimpleNewtonRaphson(), SimpleNewtonRaphson(; autodiff = false),
             SimpleTrustRegion(),
-            SimpleTrustRegion(; autodiff = false), LBroyden(), Klement(), SimpleDFSane(),
+            SimpleTrustRegion(; autodiff = false), Halley(), Halley(; autodiff = false), LBroyden(), Klement(), SimpleDFSane(),
             BROYDEN_SOLVERS...)
     sol = solve(probN, alg)
 
@@ -229,11 +233,6 @@ for alg in (SimpleNewtonRaphson(), SimpleNewtonRaphson(; autodiff = false),
     @test sol.u[end] ≈ sqrt(2.0)
 end
 
-# Separate Error check for Halley; will be included in above error checks for the improved Halley
-f, u0 = (u, p) -> u * u - 2.0, 1.0
-probN = NonlinearProblem(f, u0)
-
-@test solve(probN, Halley()).u ≈ sqrt(2.0)
 
 for u0 in [1.0, [1, 1.0]]
     local f, probN, sol

From 5f531f7f1e923dd68dbd009142d89116f0c7bb67 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Tue, 21 Feb 2023 22:42:23 +0100
Subject: [PATCH 090/700] modified allocations

---
 lib/SimpleNonlinearSolve/src/halley.jl | 50 +++++++-------------------
 1 file changed, 13 insertions(+), 37 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 557f43473..70b8a7f8c 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -42,28 +42,8 @@ function SciMLBase.__solve(prob::NonlinearProblem,
                            maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
-    # Defining all derivative expressions in one place before the iterations
     if isa(x, AbstractArray)
-        if alg_autodiff(alg)
-            n = length(x)
-            a_dfdx(x) = ForwardDiff.jacobian(f, x)
-            a_d2fdx(x) = ForwardDiff.jacobian(a_dfdx, x)
-            A = Array{Union{Nothing, Number}}(nothing, n, n)
-            #fx = f(x)
-        else
-            n = length(x)
-            f_dfdx(x) = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x))
-            f_d2fdx(x) = FiniteDiff.finite_difference_jacobian(f_dfdx, x, diff_type(alg), eltype(x))
-            A = Array{Union{Nothing, Number}}(nothing, n, n)
-        end
-    elseif isa(x, Number)
-        if alg_autodiff(alg)
-            sa_dfdx(x) = ForwardDiff.derivative(f, x)
-            sa_d2fdx(x) = ForwardDiff.derivative(sa_dfdx, x)
-        else
-            sf_dfdx(x) = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x))
-            sf_d2fdx(x) = FiniteDiff.finite_difference_derivative(sf_dfdx, x, diff_type(alg), eltype(x))
-        end
+        n = length(x)
     end
     T = typeof(x)
 
@@ -85,34 +65,30 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         if alg_autodiff(alg)
             if isa(x, Number)
                 fx = f(x)
-                dfx = sa_dfdx(x)
-                d2fx = sa_d2fdx(x)
+                dfx = ForwardDiff.derivative(f, x)
+                d2fx = ForwardDiff.derivative(x -> ForwardDiff.derivative(f, x), x)
             else
                 fx = f(x)
-                dfx = a_dfdx(x)
-                d2fx = reshape(a_d2fdx(x), (n,n,n)) # A 3-dim Hessian Tensor
+                dfx = ForwardDiff.jacobian(f, x)
+                d2fx = ForwardDiff.jacobian(x -> ForwardDiff.jacobian(f, x), x) #  n^2 by n matrix
                 ai = -(dfx \ fx)
-                for j in 1:n
-                    tmp = transpose(d2fx[:, :, j] * ai)
-                    A[j, :] = tmp
-                end
+                A = reshape(d2fx * ai, (n, n))
                 bi = (dfx) \ (A * ai)
                 ci = (ai .* ai) ./ (ai .+ (0.5 .* bi))
             end
         else
             if isa(x, Number)
                 fx = f(x)
-                dfx = sf_dfdx(x)
-                d2fx = sf_d2fdx(x)
+                dfx = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x))
+                d2fx = FiniteDiff.finite_difference_derivative(x -> FiniteDiff.finite_difference_derivative(f, x), x,
+                                                                                            diff_type(alg), eltype(x))
             else
                 fx = f(x)
-                dfx = f_dfdx(x)
-                d2fx = reshape(f_d2fdx(x), (n,n,n)) # A 3-dim Hessian Tensor
+                dfx = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x))
+                d2fx = FiniteDiff.finite_difference_jacobian(x -> FiniteDiff.finite_difference_jacobian(f, x), x, 
+                                                                        diff_type(alg), eltype(x))
                 ai = -(dfx \ fx)
-                for j in 1:n
-                    tmp = transpose(d2fx[:, :, j] * ai)
-                    A[j, :] = tmp
-                end
+                A = reshape(d2fx * ai, (n, n))
                 bi = (dfx) \ (A * ai)
                 ci = (ai .* ai) ./ (ai .+ (0.5 .* bi))
             end

From 7f542660bbeeb2db088f70db93a90c6f970d8a64 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Thu, 23 Feb 2023 01:29:26 +0100
Subject: [PATCH 091/700] fixed allocations and tests pass

---
 lib/SimpleNonlinearSolve/src/halley.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 70b8a7f8c..0e5417642 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -42,6 +42,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
                            maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
+    fx = f(x)
     if isa(x, AbstractArray)
         n = length(x)
     end
@@ -70,7 +71,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
             else
                 fx = f(x)
                 dfx = ForwardDiff.jacobian(f, x)
-                d2fx = ForwardDiff.jacobian(x -> ForwardDiff.jacobian(f, x), x) #  n^2 by n matrix
+                d2fx = ForwardDiff.jacobian(x -> ForwardDiff.jacobian(f, x), x)
                 ai = -(dfx \ fx)
                 A = reshape(d2fx * ai, (n, n))
                 bi = (dfx) \ (A * ai)

From 0882d7629ef0e32ec0bd7a34f1015159272192ca Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 8 Mar 2023 12:39:57 -0500
Subject: [PATCH 092/700] Add batched lbroyden

---
 lib/SimpleNonlinearSolve/Project.toml       |   2 +-
 lib/SimpleNonlinearSolve/src/halley.jl      |  15 ++-
 lib/SimpleNonlinearSolve/src/lbroyden.jl    | 101 +++++++++++++++-----
 lib/SimpleNonlinearSolve/test/basictests.jl |  48 ++++++----
 4 files changed, 121 insertions(+), 45 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 92e852cb9..55ccee5c4 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.13"
+version = "0.1.14"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 0e5417642..cdda7beda 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -80,14 +80,19 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         else
             if isa(x, Number)
                 fx = f(x)
-                dfx = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x))
-                d2fx = FiniteDiff.finite_difference_derivative(x -> FiniteDiff.finite_difference_derivative(f, x), x,
-                                                                                            diff_type(alg), eltype(x))
+                dfx = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg),
+                                                              eltype(x))
+                d2fx = FiniteDiff.finite_difference_derivative(x -> FiniteDiff.finite_difference_derivative(f,
+                                                                                                            x),
+                                                               x,
+                                                               diff_type(alg), eltype(x))
             else
                 fx = f(x)
                 dfx = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x))
-                d2fx = FiniteDiff.finite_difference_jacobian(x -> FiniteDiff.finite_difference_jacobian(f, x), x, 
-                                                                        diff_type(alg), eltype(x))
+                d2fx = FiniteDiff.finite_difference_jacobian(x -> FiniteDiff.finite_difference_jacobian(f,
+                                                                                                        x),
+                                                             x,
+                                                             diff_type(alg), eltype(x))
                 ai = -(dfx \ fx)
                 A = reshape(d2fx * ai, (n, n))
                 bi = (dfx) \ (A * ai)
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index f8ed9f5d3..6a3fc0947 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -1,19 +1,40 @@
 """
-    LBroyden(threshold::Int = 27)
+    LBroyden(; batched = false,
+              termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+                                                                  abstol = nothing, reltol = nothing),
+              threshold::Int = 27)
 
 A limited memory implementation of Broyden. This method applies the L-BFGS scheme to
 Broyden's method.
+
+!!! warn
+
+    This method is not very stable and can diverge even for very simple problems. This has mostly been
+    tested for neural networks in DeepEquilibriumNetworks.jl.
 """
-Base.@kwdef struct LBroyden <: AbstractSimpleNonlinearSolveAlgorithm
-    threshold::Int = 27
+struct LBroyden{batched, TC <: NLSolveTerminationCondition} <:
+       AbstractSimpleNonlinearSolveAlgorithm
+    termination_condition::TC
+    threshold::Int
+
+    function LBroyden(; batched = false, threshold::Int = 27,
+                      termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+                                                                          abstol = nothing,
+                                                                          reltol = nothing))
+        return new{batched, typeof(termination_condition)}(termination_condition, threshold)
+    end
 end
 
-@views function SciMLBase.__solve(prob::NonlinearProblem, alg::LBroyden, args...;
+@views function SciMLBase.__solve(prob::NonlinearProblem, alg::LBroyden{batched}, args...;
                                   abstol = nothing, reltol = nothing, maxiters = 1000,
-                                  batch = false, kwargs...)
+                                  kwargs...) where {batched}
+    tc = alg.termination_condition
+    mode = DiffEqBase.get_termination_mode(tc)
     threshold = min(maxiters, alg.threshold)
     x = float(prob.u0)
 
+    batched && @assert ndims(x)==2 "Batched LBroyden only supports 2D arrays"
+
     if x isa Number
         restore_scalar = true
         x = [x]
@@ -30,12 +51,20 @@ end
         error("LBroyden currently only supports out-of-place nonlinear problems")
     end
 
-    U = fill!(similar(x, (threshold, length(x))), zero(T))
-    Vᵀ = fill!(similar(x, (length(x), threshold)), zero(T))
+    U, Vᵀ = _init_lbroyden_state(batched, x, threshold)
 
     atol = abstol !== nothing ? abstol :
-           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
-    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
+           (tc.abstol !== nothing ? tc.abstol :
+            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5))
+    rtol = reltol !== nothing ? reltol :
+           (tc.reltol !== nothing ? tc.reltol : eps(real(one(eltype(T))))^(4 // 5))
+
+    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
+        error("LBroyden currently doesn't support SAFE_BEST termination modes")
+    end
+
+    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? Dict() : nothing
+    termination_condition = tc(storage)
 
     xₙ = x
     xₙ₋₁ = x
@@ -47,27 +76,23 @@ end
         Δxₙ = xₙ .- xₙ₋₁
         Δfₙ = fₙ .- fₙ₋₁
 
-        if iszero(fₙ)
-            xₙ = restore_scalar ? xₙ[] : xₙ
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
-        end
-
-        if isapprox(xₙ, xₙ₋₁; atol, rtol)
+        if termination_condition(restore_scalar ? [fₙ] : fₙ, xₙ, xₙ₋₁, atol, rtol)
             xₙ = restore_scalar ? xₙ[] : xₙ
             return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
         end
 
-        _U = U[1:min(threshold, i), :]
-        _Vᵀ = Vᵀ[:, 1:min(threshold, i)]
+        _U = selectdim(U, 1, 1:min(threshold, i))
+        _Vᵀ = selectdim(Vᵀ, 2, 1:min(threshold, i))
 
         vᵀ = _rmatvec(_U, _Vᵀ, Δxₙ)
         mvec = _matvec(_U, _Vᵀ, Δfₙ)
-        Δxₙ = (Δxₙ .- mvec) ./ (sum(vᵀ .* Δfₙ) .+ convert(T, 1e-5))
+        u = (Δxₙ .- mvec) ./ (sum(vᵀ .* Δfₙ) .+ convert(T, 1e-5))
 
-        Vᵀ[:, mod1(i, threshold)] .= vᵀ
-        U[mod1(i, threshold), :] .= Δxₙ
+        selectdim(Vᵀ, 2, mod1(i, threshold)) .= vᵀ
+        selectdim(U, 1, mod1(i, threshold)) .= u
 
-        update = -_matvec(U[1:min(threshold, i + 1), :], Vᵀ[:, 1:min(threshold, i + 1)], fₙ)
+        update = -_matvec(selectdim(U, 1, 1:min(threshold, i + 1)),
+                          selectdim(Vᵀ, 2, 1:min(threshold, i + 1)), fₙ)
 
         xₙ₋₁ = xₙ
         fₙ₋₁ = fₙ
@@ -77,12 +102,42 @@ end
     return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
 end
 
+function _init_lbroyden_state(batched::Bool, x, threshold)
+    T = eltype(x)
+    if batched
+        U = fill!(similar(x, (threshold, size(x, 1), size(x, 2))), zero(T))
+        Vᵀ = fill!(similar(x, (size(x, 1), threshold, size(x, 2))), zero(T))
+    else
+        U = fill!(similar(x, (threshold, length(x))), zero(T))
+        Vᵀ = fill!(similar(x, (length(x), threshold)), zero(T))
+    end
+    return U, Vᵀ
+end
+
 function _rmatvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
                   x::Union{<:AbstractVector, <:Number})
-    return -x .+ dropdims(sum(U .* sum(Vᵀ .* x; dims = 1)'; dims = 1); dims = 1)
+    length(U) == 0 && return x
+    return -x .+ vec((x' * Vᵀ) * U)
+end
+
+function _rmatvec(U::AbstractArray{T1, 3}, Vᵀ::AbstractArray{T2, 3},
+                  x::AbstractMatrix) where {T1, T2}
+    length(U) == 0 && return x
+    Vᵀx = sum(Vᵀ .* reshape(x, size(x, 1), 1, size(x, 2)); dims = 1)
+    return -x .+ _drdims_sum(U .* permutedims(Vᵀx, (2, 1, 3)); dims = 1)
 end
 
 function _matvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
                  x::Union{<:AbstractVector, <:Number})
-    return -x .+ dropdims(sum(sum(x .* U'; dims = 1) .* Vᵀ; dims = 2); dims = 2)
+    length(U) == 0 && return x
+    return -x .+ vec(Vᵀ * (U * x))
 end
+
+function _matvec(U::AbstractArray{T1, 3}, Vᵀ::AbstractArray{T2, 3},
+                 x::AbstractMatrix) where {T1, T2}
+    length(U) == 0 && return x
+    xUᵀ = sum(reshape(x, size(x, 1), 1, size(x, 2)) .* permutedims(U, (2, 1, 3)); dims = 1)
+    return -x .+ _drdims_sum(xUᵀ .* Vᵀ; dims = 2)
+end
+
+_drdims_sum(args...; dims = :) = dropdims(sum(args...; dims); dims)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 8fbdfffaf..6906b6f2d 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -6,6 +6,8 @@ using Test
 
 const BATCHED_BROYDEN_SOLVERS = Broyden[]
 const BROYDEN_SOLVERS = Broyden[]
+const BATCHED_LBROYDEN_SOLVERS = LBroyden[]
+const LBROYDEN_SOLVERS = LBroyden[]
 
 for mode in instances(NLSolveTerminationMode.T)
     if mode ∈
@@ -18,6 +20,8 @@ for mode in instances(NLSolveTerminationMode.T)
                                                         reltol = nothing)
     push!(BROYDEN_SOLVERS, Broyden(; batched = false, termination_condition))
     push!(BATCHED_BROYDEN_SOLVERS, Broyden(; batched = true, termination_condition))
+    push!(LBROYDEN_SOLVERS, LBroyden(; batched = false, termination_condition))
+    push!(BATCHED_LBROYDEN_SOLVERS, LBroyden(; batched = true, termination_condition))
 end
 
 # SimpleNewtonRaphson
@@ -134,15 +138,22 @@ for alg in (SimpleNewtonRaphson(), LBroyden(), Klement(), SimpleTrustRegion(),
     end
 
     for p in 1.1:0.1:100.0
-        @test abs.(g(p)) ≈ sqrt(p)
-        @test abs.(ForwardDiff.derivative(g, p)) ≈ 1 / (2 * sqrt(p))
+        res = abs.(g(p))
+        # Not surprising if LBrouden fails to converge
+        if any(x -> isnan(x) || x <= 1e-5 || x >= 1e5, res) && alg isa LBroyden
+            @test_broken res ≈ sqrt(p)
+            @test_broken abs.(ForwardDiff.derivative(g, p)) ≈ 1 / (2 * sqrt(p))
+        else
+            @test res ≈ sqrt(p)
+            @test abs.(ForwardDiff.derivative(g, p)) ≈ 1 / (2 * sqrt(p))
+        end
     end
 end
 
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
-for alg in (SimpleNewtonRaphson(), LBroyden(), Klement(), SimpleTrustRegion(),
-            SimpleDFSane(), Halley(), BROYDEN_SOLVERS...)
+for alg in (SimpleNewtonRaphson(), Klement(), SimpleTrustRegion(),
+            SimpleDFSane(), Halley(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
@@ -150,8 +161,15 @@ for alg in (SimpleNewtonRaphson(), LBroyden(), Klement(), SimpleTrustRegion(),
     end
 
     for p in 1.1:0.1:100.0
-        @test abs(g(p)) ≈ sqrt(p)
-        @test abs(ForwardDiff.derivative(g, p)) ≈ 1 / (2 * sqrt(p))
+        res = abs.(g(p))
+        # Not surprising if LBrouden fails to converge
+        if any(x -> isnan(x) || x <= 1e-5 || x >= 1e5, res) && alg isa LBroyden
+            @test_broken res ≈ sqrt(p)
+            @test_broken abs.(ForwardDiff.derivative(g, p)) ≈ 1 / (2 * sqrt(p))
+        else
+            @test res ≈ sqrt(p)
+            @test abs.(ForwardDiff.derivative(g, p)) ≈ 1 / (2 * sqrt(p))
+        end
     end
 end
 
@@ -207,8 +225,8 @@ for alg in [Bisection(), Falsi(), Ridder(), Brent()]
     @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
 end
 
-for alg in (SimpleNewtonRaphson(), LBroyden(), Klement(), SimpleTrustRegion(),
-            SimpleDFSane(), Halley(), BROYDEN_SOLVERS...)
+for alg in (SimpleNewtonRaphson(), Klement(), SimpleTrustRegion(),
+            SimpleDFSane(), Halley(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -225,15 +243,15 @@ probN = NonlinearProblem(f, u0)
 
 for alg in (SimpleNewtonRaphson(), SimpleNewtonRaphson(; autodiff = false),
             SimpleTrustRegion(),
-            SimpleTrustRegion(; autodiff = false), Halley(), Halley(; autodiff = false), LBroyden(), Klement(), SimpleDFSane(),
-            BROYDEN_SOLVERS...)
+            SimpleTrustRegion(; autodiff = false), Halley(), Halley(; autodiff = false),
+            Klement(), SimpleDFSane(),
+            BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
     sol = solve(probN, alg)
 
     @test sol.retcode == ReturnCode.Success
     @test sol.u[end] ≈ sqrt(2.0)
 end
 
-
 for u0 in [1.0, [1, 1.0]]
     local f, probN, sol
     f = (u, p) -> u .* u .- 2.0
@@ -241,10 +259,8 @@ for u0 in [1.0, [1, 1.0]]
     sol = sqrt(2) * u0
 
     for alg in (SimpleNewtonRaphson(), SimpleNewtonRaphson(; autodiff = false),
-                SimpleTrustRegion(),
-                SimpleTrustRegion(; autodiff = false), LBroyden(), Klement(),
-                SimpleDFSane(),
-                BROYDEN_SOLVERS...)
+                SimpleTrustRegion(), SimpleTrustRegion(; autodiff = false), Klement(),
+                SimpleDFSane(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
         sol2 = solve(probN, alg)
 
         @test sol2.retcode == ReturnCode.Success
@@ -430,7 +446,7 @@ sol = solve(probN, Broyden(batched = true))
 
 @test abs.(sol.u) ≈ sqrt.(p)
 
-for alg in BATCHED_BROYDEN_SOLVERS
+for alg in (BATCHED_BROYDEN_SOLVERS..., BATCHED_LBROYDEN_SOLVERS...)
     sol = solve(probN, alg)
 
     @test sol.retcode == ReturnCode.Success

From 810634d6f1067b213e1fc464efaaa5fea71986b8 Mon Sep 17 00:00:00 2001
From: Hendrik Ranocha <mail@ranocha.de>
Date: Mon, 13 Mar 2023 13:43:27 +0100
Subject: [PATCH 093/700] enable dependabot for GitHub actions

---
 lib/SimpleNonlinearSolve/.github/dependabot.yml | 7 +++++++
 1 file changed, 7 insertions(+)
 create mode 100644 lib/SimpleNonlinearSolve/.github/dependabot.yml

diff --git a/lib/SimpleNonlinearSolve/.github/dependabot.yml b/lib/SimpleNonlinearSolve/.github/dependabot.yml
new file mode 100644
index 000000000..700707ced
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/.github/dependabot.yml
@@ -0,0 +1,7 @@
+# https://docs.github.com/github/administering-a-repository/configuration-options-for-dependency-updates
+version: 2
+updates:
+  - package-ecosystem: "github-actions"
+    directory: "/" # Location of package manifests
+    schedule:
+      interval: "weekly"

From 03fb55dcf78274c8cd1cb7c8dfd1ae08da14d4d8 Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Mon, 13 Mar 2023 13:03:07 +0000
Subject: [PATCH 094/700] Bump actions/checkout from 1 to 3

Bumps [actions/checkout](https://github.com/actions/checkout) from 1 to 3.
- [Release notes](https://github.com/actions/checkout/releases)
- [Changelog](https://github.com/actions/checkout/blob/main/CHANGELOG.md)
- [Commits](https://github.com/actions/checkout/compare/v1...v3)

---
updated-dependencies:
- dependency-name: actions/checkout
  dependency-type: direct:production
  update-type: version-update:semver-major
...

Signed-off-by: dependabot[bot] <support@github.com>
---
 lib/SimpleNonlinearSolve/.github/workflows/CI.yml          | 2 +-
 lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml  | 4 ++--
 lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml | 2 +-
 3 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
index 80a2aea7b..9888c0d5a 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
@@ -17,7 +17,7 @@ jobs:
           - '1'
           - '1.6'
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v3
       - uses: julia-actions/setup-julia@v1
         with:
           version: ${{ matrix.version }}
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
index 6abfcfddc..34f258354 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
@@ -25,14 +25,14 @@ jobs:
           - {user: SciML, repo: OrdinaryDiffEq.jl, group: InterfaceIV}
           - {user: SciML, repo: OrdinaryDiffEq.jl, group: InterfaceV}
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v3
       - uses: julia-actions/setup-julia@v1
         with:
           version: ${{ matrix.julia-version }}
           arch: x64
       - uses: julia-actions/julia-buildpkg@latest
       - name: Clone Downstream
-        uses: actions/checkout@v2
+        uses: actions/checkout@v3
         with:
           repository: ${{ matrix.package.user }}/${{ matrix.package.repo }}
           path: downstream
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
index e4e3512e2..521b8c2b2 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
@@ -21,7 +21,7 @@ jobs:
         with:
           version: ${{ matrix.julia-version }}
 
-      - uses: actions/checkout@v1
+      - uses: actions/checkout@v3
       - name: Install JuliaFormatter and format
         # This will use the latest version by default but you can set the version like so:
         #

From 442b3055a4f397e18e9ac80b1ad6f8822f307cab Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Mon, 13 Mar 2023 13:03:13 +0000
Subject: [PATCH 095/700] Bump actions/cache from 1 to 3

Bumps [actions/cache](https://github.com/actions/cache) from 1 to 3.
- [Release notes](https://github.com/actions/cache/releases)
- [Changelog](https://github.com/actions/cache/blob/main/RELEASES.md)
- [Commits](https://github.com/actions/cache/compare/v1...v3)

---
updated-dependencies:
- dependency-name: actions/cache
  dependency-type: direct:production
  update-type: version-update:semver-major
...

Signed-off-by: dependabot[bot] <support@github.com>
---
 lib/SimpleNonlinearSolve/.github/workflows/CI.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
index 80a2aea7b..5eca1216b 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
@@ -21,7 +21,7 @@ jobs:
       - uses: julia-actions/setup-julia@v1
         with:
           version: ${{ matrix.version }}
-      - uses: actions/cache@v1
+      - uses: actions/cache@v3
         env:
           cache-name: cache-artifacts
         with:

From da193e5a148dd4ab3db99559db3d8414a45f837f Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Mon, 13 Mar 2023 13:03:17 +0000
Subject: [PATCH 096/700] Bump codecov/codecov-action from 1 to 3

Bumps [codecov/codecov-action](https://github.com/codecov/codecov-action) from 1 to 3.
- [Release notes](https://github.com/codecov/codecov-action/releases)
- [Changelog](https://github.com/codecov/codecov-action/blob/main/CHANGELOG.md)
- [Commits](https://github.com/codecov/codecov-action/compare/v1...v3)

---
updated-dependencies:
- dependency-name: codecov/codecov-action
  dependency-type: direct:production
  update-type: version-update:semver-major
...

Signed-off-by: dependabot[bot] <support@github.com>
---
 lib/SimpleNonlinearSolve/.github/workflows/CI.yml         | 2 +-
 lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
index 80a2aea7b..6d7dedf46 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
@@ -37,6 +37,6 @@ jobs:
           GROUP: ${{ matrix.group }}
           JULIA_NUM_THREADS: 11
       - uses: julia-actions/julia-processcoverage@v1
-      - uses: codecov/codecov-action@v1
+      - uses: codecov/codecov-action@v3
         with:
           file: lcov.info
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
index 6abfcfddc..8215d41a5 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
@@ -54,6 +54,6 @@ jobs:
             exit(0)  # Exit immediately, as a success
           end
       - uses: julia-actions/julia-processcoverage@v1
-      - uses: codecov/codecov-action@v1
+      - uses: codecov/codecov-action@v3
         with:
           file: lcov.info

From 81cfc3771cfb36ba9db3c0909347d42bcf206462 Mon Sep 17 00:00:00 2001
From: Huiyu Xie <huiyuxie@Huiyus-MacBook-Pro.local>
Date: Fri, 24 Mar 2023 16:55:26 -0700
Subject: [PATCH 097/700] bracket

---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 29 +++++++++++++++++++++++++
 1 file changed, 29 insertions(+)
 create mode 100644 lib/SimpleNonlinearSolve/src/alefeld.jl

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
new file mode 100644
index 000000000..020b17f8a
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -0,0 +1,29 @@
+#struct Alefeld <: AbstractSimpleNonlinearSolveAlgorithm end
+
+# Define subrotine function bracket, check d to see whether the zero is found when using.
+function _bracket(f::Function, a, b, c)
+    fc = f(c)
+    if fc == 0
+        ā, b̄, d = a, b, c
+    else
+        fa, fb = f(a), f(b)
+        if fa * fc < 0 
+            ā, b̄, d = a, c, b
+        elseif fb * fc < 0
+            ā, b̄, d = c, b, a
+        end
+    end
+    return ā, b̄, d 
+end
+
+# Define subrotine function 
+#function _newton_quadratic()
+
+
+
+# test 
+function fk(x)
+    return 2 * x
+end
+
+_bracket(fk, -2, 2, 0)
\ No newline at end of file

From f2191d60247bd4c6aede40e5a8e8d7c10dbab63c Mon Sep 17 00:00:00 2001
From: Huiyu Xie <huiyuxie@Huiyus-MacBook-Pro.local>
Date: Fri, 24 Mar 2023 18:20:23 -0700
Subject: [PATCH 098/700] newton

---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 35 +++++++++++++++++--------
 1 file changed, 24 insertions(+), 11 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 020b17f8a..9f5e2670d 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -1,29 +1,42 @@
 #struct Alefeld <: AbstractSimpleNonlinearSolveAlgorithm end
 
-# Define subrotine function bracket, check d to see whether the zero is found when using.
+# Define subrotine function bracket, check d to see whether the zero is found.
 function _bracket(f::Function, a, b, c)
-    fc = f(c)
-    if fc == 0
+    if f(c) == 0
         ā, b̄, d = a, b, c
     else
-        fa, fb = f(a), f(b)
-        if fa * fc < 0 
+        if f(a) * f(c) < 0 
             ā, b̄, d = a, c, b
-        elseif fb * fc < 0
+        elseif f(b) * f(c) < 0
             ā, b̄, d = c, b, a
         end
     end
     return ā, b̄, d 
 end
 
-# Define subrotine function 
-#function _newton_quadratic()
-
+# Define subrotine function newton quadratic, return the approximation of unique zero.
+function _newton_quadratic(f::Function, a, b, d, k)
+    A = ((f(b) - f(d)) / (b - d) - (f(a) - f(b)) / (a - b)) / (d - a) 
+    B = (f(b) - f(a)) / (b - a)
+    if A == 0
+        return a - (1 / B) * f(a)
+    elseif A * f(a) > 0
+        rᵢ₋₁ = a 
+    else 
+        rᵢ₋₁ = b
+    end 
+    for i in 1:k
+        rᵢ = rᵢ₋₁ - B * rᵢ₋₁ / (B + A * (2 * rᵢ₋₁ - a - b))
+        rᵢ₋₁ = rᵢ
+    end
+    return rᵢ₋₁
+end
 
 
 # test 
 function fk(x)
-    return 2 * x
+    return x^3
 end
 
-_bracket(fk, -2, 2, 0)
\ No newline at end of file
+_newton_quadratic(fk, -2, 4, 100, 2)
+

From 9fad692d07d92ba10d4d35585da1bec12747c6b1 Mon Sep 17 00:00:00 2001
From: Huiyu Xie <huiyuxie@Huiyus-MacBook-Pro.local>
Date: Fri, 24 Mar 2023 20:34:47 -0700
Subject: [PATCH 099/700] ipzero

---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 20 +++++++++++++++++++-
 1 file changed, 19 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 9f5e2670d..5e39281c5 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -11,13 +11,15 @@ function _bracket(f::Function, a, b, c)
             ā, b̄, d = c, b, a
         end
     end
+
     return ā, b̄, d 
 end
 
-# Define subrotine function newton quadratic, return the approximation of unique zero.
+# Define subrotine function newton quadratic, return the approximation of zero.
 function _newton_quadratic(f::Function, a, b, d, k)
     A = ((f(b) - f(d)) / (b - d) - (f(a) - f(b)) / (a - b)) / (d - a) 
     B = (f(b) - f(a)) / (b - a)
+
     if A == 0
         return a - (1 / B) * f(a)
     elseif A * f(a) > 0
@@ -25,13 +27,29 @@ function _newton_quadratic(f::Function, a, b, d, k)
     else 
         rᵢ₋₁ = b
     end 
+
     for i in 1:k
         rᵢ = rᵢ₋₁ - B * rᵢ₋₁ / (B + A * (2 * rᵢ₋₁ - a - b))
         rᵢ₋₁ = rᵢ
     end
+
     return rᵢ₋₁
 end
 
+# Define subrotine function ipzero, also return the approximation of zero.
+function _ipzero(f::Function, a, b, c, d)
+    Q₁₁ = (c - d) * f(c) / (f(d) - f(c))
+    Q₂₁ = (b - c) * f(b) / (f(c) - f(b))
+    Q₃₁ = (a - b) * f(a) / (f(b) - f(a))
+    D₂₁ = (b - c) * f(c) / (f(c) - f(b))
+    D₃₁ = (a - b) * f(b) / (f(b) - f(a))
+    Q₂₂ = (D₂₁ - Q₁₁) * f(b) / (f(d) - f(b))
+    Q₃₂ = (D₃₁ - Q₂₁) * f(a) / (f(c) - f(a))
+    D₃₂ = (D₃₁ - Q₂₁) * f(c) / (f(c) - f(a))
+    Q₃₃ = (D₃₂ - Q₂₂) * f(a) / (f(d) - f(a))
+
+    return a + Q₃₁ + Q₃₂ + Q₃₃
+end
 
 # test 
 function fk(x)

From d2c82b214de0230225b26e125efd66d02a53527d Mon Sep 17 00:00:00 2001
From: Huiyu Xie <huiyuxie@Huiyus-MacBook-Pro.local>
Date: Sat, 25 Mar 2023 23:55:18 -0700
Subject: [PATCH 100/700] add solve

---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 125 +++++++++++++++++++++---
 1 file changed, 110 insertions(+), 15 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 5e39281c5..ce726ea15 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -1,8 +1,111 @@
-#struct Alefeld <: AbstractSimpleNonlinearSolveAlgorithm end
+struct Alefeld <: AbstractBracketingAlgorithm end
 
-# Define subrotine function bracket, check d to see whether the zero is found.
+function SciMLBase.__solve(prob::NonlinearProblem,
+                            alg::Alefeld, args...; abstol = nothing,
+                            reltol = nothing,
+                            maxiters = 1000, kwargs...)
+                            
+    f = Base.Fix2(prob.f, prob.p)
+    a, b = prob.tspan
+    c = a - (b - a) / (f(b) - f(a)) * f(a)
+    
+    fc = f(c)
+    if iszero(fc)
+        return SciMLBase.build_solution(prob, alg, c, fc;
+                                        retcode = ReturnCode.Success, 
+                                        left = a,
+                                        right = b)
+    end
+    a, b, d = _bracket(f, a, b, c)
+    e = 0   # Set e as 0 before interation to avoid a non-value f(e)
+
+    for i in 2:maxiters
+        # The first bracketing block
+        f₁, f₂, f₃, f₄ = f(a), f(b), f(d), f(e)
+        if i == 2 || (f₁ == f₂ || f₁ == f₃ || f₁ == f₄ || f₂ == f₃ || f₂ == f₄ || f₃ == f₄)
+            c = _newton_quadratic(f, a, b, d, 2)
+        else 
+            c = _ipzero(f, a, b, d, e)
+            if (c - a) * (c - b) ≥ 0
+                c = _newton_quadratic(f, a, b, d, 2)
+            end
+        end 
+        ē, fc = d, f(c)   
+        iszero(fc) &&
+            return SciMLBase.build_solution(prob, alg, c, fc;
+                                        retcode = ReturnCode.Success, 
+                                        left = a,
+                                        right = b)
+        ā, b̄, d̄ = _bracket(f, a, b, c) 
+
+        # The second bracketing block
+        f₁, f₂, f₃, f₄ = f(ā), f(b̄), f(d̄), f(ē)
+        if f₁ == f₂ || f₁ == f₃ || f₁ == f₄ || f₂ == f₃ || f₂ == f₄ || f₃ == f₄
+            c = _newton_quadratic(f, ā, b̄, d̄, 3)
+        else 
+            c = _ipzero(f, ā, b̄, d̄, ē)
+            if (c - ā) * (c - b̄) ≥ 0
+                c = _newton_quadratic(f, ā, b̄, d̄, 3)
+            end
+        end
+        fc = f(c)
+        iszero(fc) &&
+            return SciMLBase.build_solution(prob, alg, c, fc;
+                                        retcode = ReturnCode.Success, 
+                                        left = a,
+                                        right = b)
+        ā, b̄, d̄ = _bracket(f, ā, b̄, c) 
+
+        # The third bracketing block
+        if abs(f(ā)) < abs(f(b̄))
+            u = ā
+        else
+            u = b̄
+        end
+        c = u - 2 * (b̄ - ā) / (f(b̄) - f(ā)) * f(u)
+        if (abs(c - u)) > 0.5 * (b̄ - ā)
+            c = 0.5 * (ā + b̄)
+        end
+        fc = f(c)
+        iszero(fc) &&
+            return SciMLBase.build_solution(prob, alg, c, fc;
+                                        retcode = ReturnCode.Success, 
+                                        left = a,
+                                        right = b)
+        ā, b̄, d = _bracket(f, ā, b̄, c) 
+
+        # The last bracketing block
+        if b̄ - ā < 0.5 * (b - a)
+            a, b, e = ā, b̄, d̄
+        else
+            e = d
+            c = 0.5 * (ā + b̄)
+            fc = f(c)
+            iszero(fc) &&
+            return SciMLBase.build_solution(prob, alg, c, fc;
+                                        retcode = ReturnCode.Success, 
+                                        left = a,
+                                        right = b)
+            a, b, d = _bracket(f, ā, b̄, c)
+        end
+    end
+
+    # Reassign the value a, b, and c
+    if b == c
+        b = d
+    elseif a == c
+        a = d
+    end
+    fc = f(c)
+
+    # Reuturn solution when run out of max interation
+    return SciMLBase.build_solution(prob, alg, c, fc; retcode = ReturnCode.MaxIters,
+                                    left = a, right = b)
+end
+
+# Define subrotine function bracket, check fc before bracket to return solution
 function _bracket(f::Function, a, b, c)
-    if f(c) == 0
+    if iszero(f(c))
         ā, b̄, d = a, b, c
     else
         if f(a) * f(c) < 0 
@@ -15,12 +118,12 @@ function _bracket(f::Function, a, b, c)
     return ā, b̄, d 
 end
 
-# Define subrotine function newton quadratic, return the approximation of zero.
+# Define subrotine function newton quadratic, return the approximation of zero
 function _newton_quadratic(f::Function, a, b, d, k)
     A = ((f(b) - f(d)) / (b - d) - (f(a) - f(b)) / (a - b)) / (d - a) 
     B = (f(b) - f(a)) / (b - a)
 
-    if A == 0
+    if iszero(A)
         return a - (1 / B) * f(a)
     elseif A * f(a) > 0
         rᵢ₋₁ = a 
@@ -36,7 +139,7 @@ function _newton_quadratic(f::Function, a, b, d, k)
     return rᵢ₋₁
 end
 
-# Define subrotine function ipzero, also return the approximation of zero.
+# Define subrotine function ipzero, also return the approximation of zero
 function _ipzero(f::Function, a, b, c, d)
     Q₁₁ = (c - d) * f(c) / (f(d) - f(c))
     Q₂₁ = (b - c) * f(b) / (f(c) - f(b))
@@ -49,12 +152,4 @@ function _ipzero(f::Function, a, b, c, d)
     Q₃₃ = (D₃₂ - Q₂₂) * f(a) / (f(d) - f(a))
 
     return a + Q₃₁ + Q₃₂ + Q₃₃
-end
-
-# test 
-function fk(x)
-    return x^3
-end
-
-_newton_quadratic(fk, -2, 4, 100, 2)
-
+end
\ No newline at end of file

From 918dd1dd345a5546ee94e317a275d8644c6b5e59 Mon Sep 17 00:00:00 2001
From: Huiyu <xhy19127@gmail.com>
Date: Sun, 26 Mar 2023 00:00:04 -0700
Subject: [PATCH 101/700] solve

---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index ce726ea15..1d9b9bfef 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -17,8 +17,9 @@ function SciMLBase.__solve(prob::NonlinearProblem,
                                         right = b)
     end
     a, b, d = _bracket(f, a, b, c)
-    e = 0   # Set e as 0 before interation to avoid a non-value f(e)
+    e = 0   # Set e as 0 before iteration to avoid a non-value f(e)
 
+    # Begin algorithm iteration
     for i in 2:maxiters
         # The first bracketing block
         f₁, f₂, f₃, f₄ = f(a), f(b), f(d), f(e)

From 43b0902ba41dbba6799a7ea282598e264adaf10d Mon Sep 17 00:00:00 2001
From: Huiyu <huiyuxie.sde@gmail.com>
Date: Sun, 26 Mar 2023 00:07:10 -0700
Subject: [PATCH 102/700] comment

---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 1d9b9bfef..e58005b4a 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -1,3 +1,7 @@
+'''
+# add annotation here
+'''
+
 struct Alefeld <: AbstractBracketingAlgorithm end
 
 function SciMLBase.__solve(prob::NonlinearProblem,

From b1195953732557f546b6e3004456bc1c4db49aa1 Mon Sep 17 00:00:00 2001
From: Huiyu <huiyuxie.sde@gmail.com>
Date: Sun, 26 Mar 2023 21:16:44 -0700
Subject: [PATCH 103/700] add alefeld

---
 lib/SimpleNonlinearSolve/Project.toml            | 16 ++++++++++------
 .../src/SimpleNonlinearSolve.jl                  |  5 +++--
 lib/SimpleNonlinearSolve/src/alefeld.jl          | 15 ++++++++++-----
 lib/SimpleNonlinearSolve/test/basictests.jl      | 12 ++++++++++++
 4 files changed, 35 insertions(+), 13 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 55ccee5c4..b34c4387c 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -5,22 +5,20 @@ version = "0.1.14"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
+SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SnoopPrecompile = "66db9d55-30c0-4569-8b51-7e840670fc0c"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
-[weakdeps]
-NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
-
-[extensions]
-SimpleBatchedNonlinearSolveExt = "NNlib"
-
 [compat]
 ArrayInterface = "6, 7"
 DiffEqBase = "6.119"
@@ -34,6 +32,9 @@ SnoopPrecompile = "1"
 StaticArraysCore = "1.4"
 julia = "1.6"
 
+[extensions]
+SimpleBatchedNonlinearSolveExt = "NNlib"
+
 [extras]
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
@@ -44,3 +45,6 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
 test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays", "NNlib"]
+
+[weakdeps]
+NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 4c90b094f..a33dd9297 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -38,6 +38,7 @@ include("brent.jl")
 include("dfsane.jl")
 include("ad.jl")
 include("halley.jl")
+include("alefeld.jl")
 
 import SnoopPrecompile
 
@@ -59,13 +60,13 @@ SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
     =#
 
     prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p, T.((0.0, 2.0)), T(2))
-    for alg in (Bisection, Falsi, Ridder, Brent)
+    for alg in (Bisection, Falsi, Ridder, Brent, Alefeld)
         solve(prob_brack, alg(), abstol = T(1e-2))
     end
 end end
 
 # DiffEq styled algorithms
 export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, Halley, Klement,
-       Ridder, SimpleNewtonRaphson, SimpleTrustRegion
+       Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index e58005b4a..1164875e7 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -1,10 +1,15 @@
-'''
-# add annotation here
-'''
+"""
+`Alefeld()` 
+
+An implementation of algorithm 4.2 from [Alefeld](https://dl.acm.org/doi/10.1145/210089.210111).
+
+The paper brought up two new algorithms. Here choose to implement algorithm 4.2 rather than 
+algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal procedure.
+"""
 
 struct Alefeld <: AbstractBracketingAlgorithm end
 
-function SciMLBase.__solve(prob::NonlinearProblem,
+function SciMLBase.solve(prob::NonlinearProblem,
                             alg::Alefeld, args...; abstol = nothing,
                             reltol = nothing,
                             maxiters = 1000, kwargs...)
@@ -23,7 +28,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
     a, b, d = _bracket(f, a, b, c)
     e = 0   # Set e as 0 before iteration to avoid a non-value f(e)
 
-    # Begin algorithm iteration
+    # Begin of algorithm iteration
     for i in 2:maxiters
         # The first bracketing block
         f₁, f₂, f₃, f₄ = f(a), f(b), f(d), f(e)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 6906b6f2d..5b76ce15f 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -210,6 +210,18 @@ for p in 1.1:0.1:100.0
     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
 end
 
+# Alefeld
+g = function (p)
+    probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
+    sol = solve(probN, Alefeld())
+    return sol.u
+end
+
+for p in 1.1:0.1:100.0
+    @test g(p) ≈ sqrt(p)
+    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+end
+
 f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
 t = (p) -> [sqrt(p[2] / p[1])]
 p = [0.9, 50.0]

From a81aa30389d6235a4ed6b3bb2c0a6fe40883dc7b Mon Sep 17 00:00:00 2001
From: Huiyu Xie <huiyuxie.sde@gmail.com>
Date: Wed, 29 Mar 2023 09:14:51 -0700
Subject: [PATCH 104/700] Update src/alefeld.jl

Co-authored-by: Christopher Rackauckas <accounts@chrisrackauckas.com>
---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 1164875e7..93d72d514 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -150,7 +150,7 @@ function _newton_quadratic(f::Function, a, b, d, k)
 end
 
 # Define subrotine function ipzero, also return the approximation of zero
-function _ipzero(f::Function, a, b, c, d)
+function _ipzero(f::F, a, b, c, d) where F
     Q₁₁ = (c - d) * f(c) / (f(d) - f(c))
     Q₂₁ = (b - c) * f(b) / (f(c) - f(b))
     Q₃₁ = (a - b) * f(a) / (f(b) - f(a))

From f618dfccb81811f25f9e8b3ab8b552ee97789b62 Mon Sep 17 00:00:00 2001
From: Huiyu Xie <huiyuxie.sde@gmail.com>
Date: Wed, 29 Mar 2023 09:20:32 -0700
Subject: [PATCH 105/700] Update src/alefeld.jl

Co-authored-by: Christopher Rackauckas <accounts@chrisrackauckas.com>
---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 93d72d514..1f53df0c9 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -114,7 +114,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
 end
 
 # Define subrotine function bracket, check fc before bracket to return solution
-function _bracket(f::Function, a, b, c)
+function _bracket(f::F, a, b, c) where F
     if iszero(f(c))
         ā, b̄, d = a, b, c
     else
@@ -129,7 +129,7 @@ function _bracket(f::Function, a, b, c)
 end
 
 # Define subrotine function newton quadratic, return the approximation of zero
-function _newton_quadratic(f::Function, a, b, d, k)
+function _newton_quadratic(f::F, a, b, d, k) where F
     A = ((f(b) - f(d)) / (b - d) - (f(a) - f(b)) / (a - b)) / (d - a) 
     B = (f(b) - f(a)) / (b - a)
 

From 0bb2ee41586dd35bf48f642511ff6b1bd334befa Mon Sep 17 00:00:00 2001
From: Huiyu Xie <huiyuxie.sde@gmail.com>
Date: Wed, 29 Mar 2023 09:21:22 -0700
Subject: [PATCH 106/700] Update src/alefeld.jl

Co-authored-by: Christopher Rackauckas <accounts@chrisrackauckas.com>
---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 1f53df0c9..bcc78f50d 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -6,7 +6,6 @@ An implementation of algorithm 4.2 from [Alefeld](https://dl.acm.org/doi/10.1145
 The paper brought up two new algorithms. Here choose to implement algorithm 4.2 rather than 
 algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal procedure.
 """
-
 struct Alefeld <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::NonlinearProblem,

From 4cdcb84052c0b95cc8294021ae8328aa649d3668 Mon Sep 17 00:00:00 2001
From: huiyuxie <huiyuxie.sde@gmail.com>
Date: Wed, 29 Mar 2023 12:34:56 -0400
Subject: [PATCH 107/700] resolve

---
 lib/SimpleNonlinearSolve/Project.toml   | 18 +++++++-----------
 lib/SimpleNonlinearSolve/src/alefeld.jl |  7 +++----
 2 files changed, 10 insertions(+), 15 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index b34c4387c..0be404135 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -5,20 +5,22 @@ version = "0.1.14"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
-BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
-SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SnoopPrecompile = "66db9d55-30c0-4569-8b51-7e840670fc0c"
-StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
+[weakdeps]
+NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
+
+[extensions]
+SimpleBatchedNonlinearSolveExt = "NNlib"
+
 [compat]
 ArrayInterface = "6, 7"
 DiffEqBase = "6.119"
@@ -32,9 +34,6 @@ SnoopPrecompile = "1"
 StaticArraysCore = "1.4"
 julia = "1.6"
 
-[extensions]
-SimpleBatchedNonlinearSolveExt = "NNlib"
-
 [extras]
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
@@ -44,7 +43,4 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays", "NNlib"]
-
-[weakdeps]
-NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
+test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays", "NNlib"]
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 1164875e7..bcc78f50d 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -6,7 +6,6 @@ An implementation of algorithm 4.2 from [Alefeld](https://dl.acm.org/doi/10.1145
 The paper brought up two new algorithms. Here choose to implement algorithm 4.2 rather than 
 algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal procedure.
 """
-
 struct Alefeld <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::NonlinearProblem,
@@ -114,7 +113,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
 end
 
 # Define subrotine function bracket, check fc before bracket to return solution
-function _bracket(f::Function, a, b, c)
+function _bracket(f::F, a, b, c) where F
     if iszero(f(c))
         ā, b̄, d = a, b, c
     else
@@ -129,7 +128,7 @@ function _bracket(f::Function, a, b, c)
 end
 
 # Define subrotine function newton quadratic, return the approximation of zero
-function _newton_quadratic(f::Function, a, b, d, k)
+function _newton_quadratic(f::F, a, b, d, k) where F
     A = ((f(b) - f(d)) / (b - d) - (f(a) - f(b)) / (a - b)) / (d - a) 
     B = (f(b) - f(a)) / (b - a)
 
@@ -150,7 +149,7 @@ function _newton_quadratic(f::Function, a, b, d, k)
 end
 
 # Define subrotine function ipzero, also return the approximation of zero
-function _ipzero(f::Function, a, b, c, d)
+function _ipzero(f::F, a, b, c, d) where F
     Q₁₁ = (c - d) * f(c) / (f(d) - f(c))
     Q₂₁ = (b - c) * f(b) / (f(c) - f(b))
     Q₃₁ = (a - b) * f(a) / (f(b) - f(a))

From 093e901d06ece01db3d1cf21e0b8f5aa2a11fb88 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 29 Mar 2023 16:12:42 -0400
Subject: [PATCH 108/700] Update src/alefeld.jl

---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index bcc78f50d..9bad1eadc 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -8,7 +8,7 @@ algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal
 """
 struct Alefeld <: AbstractBracketingAlgorithm end
 
-function SciMLBase.solve(prob::NonlinearProblem,
+function SciMLBase.solve(prob::IntervalNonlinearProblem,
                             alg::Alefeld, args...; abstol = nothing,
                             reltol = nothing,
                             maxiters = 1000, kwargs...)

From 76d04fc63ad5278cc4161f963b21efe5f1796710 Mon Sep 17 00:00:00 2001
From: huiyuxie <huiyuxie.sde@gmail.com>
Date: Wed, 29 Mar 2023 17:11:31 -0400
Subject: [PATCH 109/700] fix

---
 lib/SimpleNonlinearSolve/src/alefeld.jl |   5 +-
 lib/SimpleNonlinearSolve/src/test.jl    | 168 ++++++++++++++++++++++++
 2 files changed, 171 insertions(+), 2 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/test.jl

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index bcc78f50d..2c11a2749 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -8,7 +8,7 @@ algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal
 """
 struct Alefeld <: AbstractBracketingAlgorithm end
 
-function SciMLBase.solve(prob::NonlinearProblem,
+function SciMLBase.solve(prob::IntervalNonlinearProblem,
                             alg::Alefeld, args...; abstol = nothing,
                             reltol = nothing,
                             maxiters = 1000, kwargs...)
@@ -16,6 +16,7 @@ function SciMLBase.solve(prob::NonlinearProblem,
     f = Base.Fix2(prob.f, prob.p)
     a, b = prob.tspan
     c = a - (b - a) / (f(b) - f(a)) * f(a)
+    @show c
     
     fc = f(c)
     if iszero(fc)
@@ -129,7 +130,7 @@ end
 
 # Define subrotine function newton quadratic, return the approximation of zero
 function _newton_quadratic(f::F, a, b, d, k) where F
-    A = ((f(b) - f(d)) / (b - d) - (f(a) - f(b)) / (a - b)) / (d - a) 
+    A = ((f(d) - f(b)) / (d - b) - (f(b) - f(a)) / (b - a)) / (d - a) 
     B = (f(b) - f(a)) / (b - a)
 
     if iszero(A)
diff --git a/lib/SimpleNonlinearSolve/src/test.jl b/lib/SimpleNonlinearSolve/src/test.jl
new file mode 100644
index 000000000..ce543dede
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/test.jl
@@ -0,0 +1,168 @@
+using SimpleNonlinearSolve
+using StaticArrays
+using BenchmarkTools
+using DiffEqBase
+using Test
+
+function test(f::Function, a, b) 
+    c = a - (b - a) / (f(b) - f(a)) * f(a)
+    println("0  ", c)
+    
+    fc = f(c)
+    if iszero(fc)
+        return c
+    end
+    a, b, d = _bracket(f, a, b, c)
+    println("a   ", a, "b   ", b, "d   ", d)
+    e = 0   # Set e as 0 before iteration to avoid a non-value f(e)
+
+    # Begin of algorithm iteration
+    for i in 2:1000
+        # The first bracketing block
+        f₁, f₂, f₃, f₄ = f(a), f(b), f(d), f(e)
+        if i == 2 || (f₁ == f₂ || f₁ == f₃ || f₁ == f₄ || f₂ == f₃ || f₂ == f₄ || f₃ == f₄)
+            c = _newton_quadratic(f, a, b, d, 2)
+            println("1 ", "a   ", a, "b   ", b, "c   ", c)
+        else 
+            c = _ipzero(f, a, b, d, e)
+            if (c - a) * (c - b) ≥ 0
+                c = _newton_quadratic(f, a, b, d, 2)
+            end
+        end 
+        ē, fc = d, f(c)   
+        iszero(fc) &&
+            return c
+        ā, b̄, d̄ = _bracket(f, a, b, c) 
+
+        # The second bracketing block
+        f₁, f₂, f₃, f₄ = f(ā), f(b̄), f(d̄), f(ē)
+        if f₁ == f₂ || f₁ == f₃ || f₁ == f₄ || f₂ == f₃ || f₂ == f₄ || f₃ == f₄
+            c = _newton_quadratic(f, ā, b̄, d̄, 3)
+        else 
+            c = _ipzero(f, ā, b̄, d̄, ē)
+            if (c - ā) * (c - b̄) ≥ 0
+                c = _newton_quadratic(f, ā, b̄, d̄, 3)
+            end
+        end
+        fc = f(c)
+        iszero(fc) &&
+            return c
+        ā, b̄, d̄ = _bracket(f, ā, b̄, c) 
+
+        # The third bracketing block
+        if abs(f(ā)) < abs(f(b̄))
+            u = ā
+        else
+            u = b̄
+        end
+        c = u - 2 * (b̄ - ā) / (f(b̄) - f(ā)) * f(u)
+        if (abs(c - u)) > 0.5 * (b̄ - ā)
+            c = 0.5 * (ā + b̄)
+        end
+        fc = f(c)
+        iszero(fc) &&
+            return c
+        ā, b̄, d = _bracket(f, ā, b̄, c) 
+
+        # The last bracketing block
+        if b̄ - ā < 0.5 * (b - a)
+            a, b, e = ā, b̄, d̄
+        else
+            e = d
+            c = 0.5 * (ā + b̄)
+            fc = f(c)
+            iszero(fc) &&
+            return c
+            a, b, d = _bracket(f, ā, b̄, c)
+        end
+        println("i   ", i)
+    end
+
+    # Reassign the value a, b, and c
+    if b == c
+        b = d
+    elseif a == c
+        a = d
+    end
+    fc = f(c)
+
+    # Reuturn solution when run out of max interation
+    return c
+end
+
+# Define subrotine function bracket, check fc before bracket to return solution
+function _bracket(f::F, a, b, c) where F
+    if iszero(f(c))
+        ā, b̄, d = a, b, c
+    else
+        if f(a) * f(c) < 0 
+            ā, b̄, d = a, c, b
+        elseif f(b) * f(c) < 0
+            ā, b̄, d = c, b, a
+        end
+    end
+
+    return ā, b̄, d 
+end
+
+# Define subrotine function newton quadratic, return the approximation of zero
+function _newton_quadratic(f::F, a, b, d, k) where F
+    A = ((f(d) - f(b)) / (d - b) - (f(b) - f(a)) / (b - a)) / (d - a) 
+    B = (f(b) - f(a)) / (b - a)
+    println("A   ", A)
+    println("B   ", B)
+
+
+    if iszero(A)
+        return a - (1 / B) * f(a)
+    elseif A * f(a) > 0
+        rᵢ₋₁ = a 
+    else 
+        rᵢ₋₁ = b    
+    end 
+
+    for i in 1:k
+        rᵢ = rᵢ₋₁ - B * rᵢ₋₁ / (B + A * (2 * rᵢ₋₁ - a - b))
+        rᵢ₋₁ = rᵢ
+    end
+
+    return rᵢ₋₁
+end
+
+# Define subrotine function ipzero, also return the approximation of zero
+function _ipzero(f::F, a, b, c, d) where F
+    Q₁₁ = (c - d) * f(c) / (f(d) - f(c))
+    Q₂₁ = (b - c) * f(b) / (f(c) - f(b))
+    Q₃₁ = (a - b) * f(a) / (f(b) - f(a))
+    D₂₁ = (b - c) * f(c) / (f(c) - f(b))
+    D₃₁ = (a - b) * f(b) / (f(b) - f(a))
+    Q₂₂ = (D₂₁ - Q₁₁) * f(b) / (f(d) - f(b))
+    Q₃₂ = (D₃₁ - Q₂₁) * f(a) / (f(c) - f(a))
+    D₃₂ = (D₃₁ - Q₂₁) * f(c) / (f(c) - f(a))
+    Q₃₃ = (D₃₂ - Q₂₂) * f(a) / (f(d) - f(a))
+
+    return a + Q₃₁ + Q₃₂ + Q₃₃
+end
+
+
+
+
+
+
+function f0(x)
+    return x^2 - 1.1
+end
+
+a = 1.0
+b = 20.0
+
+#= global i = 0
+for p in 1:100
+    println(i)
+    test(f0, a, b)
+    #@test g(p) ≈ sqrt(p)
+    #@test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+    global i += 1
+end =#
+
+test(f0, a, b)
\ No newline at end of file

From 76d3904cabf122beb07a254baff753ba8f721e9e Mon Sep 17 00:00:00 2001
From: huiyuxie <huiyuxie.sde@gmail.com>
Date: Wed, 29 Mar 2023 21:30:21 -0400
Subject: [PATCH 110/700] clean test

---
 lib/SimpleNonlinearSolve/src/test.jl | 168 ---------------------------
 1 file changed, 168 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/src/test.jl

diff --git a/lib/SimpleNonlinearSolve/src/test.jl b/lib/SimpleNonlinearSolve/src/test.jl
deleted file mode 100644
index ce543dede..000000000
--- a/lib/SimpleNonlinearSolve/src/test.jl
+++ /dev/null
@@ -1,168 +0,0 @@
-using SimpleNonlinearSolve
-using StaticArrays
-using BenchmarkTools
-using DiffEqBase
-using Test
-
-function test(f::Function, a, b) 
-    c = a - (b - a) / (f(b) - f(a)) * f(a)
-    println("0  ", c)
-    
-    fc = f(c)
-    if iszero(fc)
-        return c
-    end
-    a, b, d = _bracket(f, a, b, c)
-    println("a   ", a, "b   ", b, "d   ", d)
-    e = 0   # Set e as 0 before iteration to avoid a non-value f(e)
-
-    # Begin of algorithm iteration
-    for i in 2:1000
-        # The first bracketing block
-        f₁, f₂, f₃, f₄ = f(a), f(b), f(d), f(e)
-        if i == 2 || (f₁ == f₂ || f₁ == f₃ || f₁ == f₄ || f₂ == f₃ || f₂ == f₄ || f₃ == f₄)
-            c = _newton_quadratic(f, a, b, d, 2)
-            println("1 ", "a   ", a, "b   ", b, "c   ", c)
-        else 
-            c = _ipzero(f, a, b, d, e)
-            if (c - a) * (c - b) ≥ 0
-                c = _newton_quadratic(f, a, b, d, 2)
-            end
-        end 
-        ē, fc = d, f(c)   
-        iszero(fc) &&
-            return c
-        ā, b̄, d̄ = _bracket(f, a, b, c) 
-
-        # The second bracketing block
-        f₁, f₂, f₃, f₄ = f(ā), f(b̄), f(d̄), f(ē)
-        if f₁ == f₂ || f₁ == f₃ || f₁ == f₄ || f₂ == f₃ || f₂ == f₄ || f₃ == f₄
-            c = _newton_quadratic(f, ā, b̄, d̄, 3)
-        else 
-            c = _ipzero(f, ā, b̄, d̄, ē)
-            if (c - ā) * (c - b̄) ≥ 0
-                c = _newton_quadratic(f, ā, b̄, d̄, 3)
-            end
-        end
-        fc = f(c)
-        iszero(fc) &&
-            return c
-        ā, b̄, d̄ = _bracket(f, ā, b̄, c) 
-
-        # The third bracketing block
-        if abs(f(ā)) < abs(f(b̄))
-            u = ā
-        else
-            u = b̄
-        end
-        c = u - 2 * (b̄ - ā) / (f(b̄) - f(ā)) * f(u)
-        if (abs(c - u)) > 0.5 * (b̄ - ā)
-            c = 0.5 * (ā + b̄)
-        end
-        fc = f(c)
-        iszero(fc) &&
-            return c
-        ā, b̄, d = _bracket(f, ā, b̄, c) 
-
-        # The last bracketing block
-        if b̄ - ā < 0.5 * (b - a)
-            a, b, e = ā, b̄, d̄
-        else
-            e = d
-            c = 0.5 * (ā + b̄)
-            fc = f(c)
-            iszero(fc) &&
-            return c
-            a, b, d = _bracket(f, ā, b̄, c)
-        end
-        println("i   ", i)
-    end
-
-    # Reassign the value a, b, and c
-    if b == c
-        b = d
-    elseif a == c
-        a = d
-    end
-    fc = f(c)
-
-    # Reuturn solution when run out of max interation
-    return c
-end
-
-# Define subrotine function bracket, check fc before bracket to return solution
-function _bracket(f::F, a, b, c) where F
-    if iszero(f(c))
-        ā, b̄, d = a, b, c
-    else
-        if f(a) * f(c) < 0 
-            ā, b̄, d = a, c, b
-        elseif f(b) * f(c) < 0
-            ā, b̄, d = c, b, a
-        end
-    end
-
-    return ā, b̄, d 
-end
-
-# Define subrotine function newton quadratic, return the approximation of zero
-function _newton_quadratic(f::F, a, b, d, k) where F
-    A = ((f(d) - f(b)) / (d - b) - (f(b) - f(a)) / (b - a)) / (d - a) 
-    B = (f(b) - f(a)) / (b - a)
-    println("A   ", A)
-    println("B   ", B)
-
-
-    if iszero(A)
-        return a - (1 / B) * f(a)
-    elseif A * f(a) > 0
-        rᵢ₋₁ = a 
-    else 
-        rᵢ₋₁ = b    
-    end 
-
-    for i in 1:k
-        rᵢ = rᵢ₋₁ - B * rᵢ₋₁ / (B + A * (2 * rᵢ₋₁ - a - b))
-        rᵢ₋₁ = rᵢ
-    end
-
-    return rᵢ₋₁
-end
-
-# Define subrotine function ipzero, also return the approximation of zero
-function _ipzero(f::F, a, b, c, d) where F
-    Q₁₁ = (c - d) * f(c) / (f(d) - f(c))
-    Q₂₁ = (b - c) * f(b) / (f(c) - f(b))
-    Q₃₁ = (a - b) * f(a) / (f(b) - f(a))
-    D₂₁ = (b - c) * f(c) / (f(c) - f(b))
-    D₃₁ = (a - b) * f(b) / (f(b) - f(a))
-    Q₂₂ = (D₂₁ - Q₁₁) * f(b) / (f(d) - f(b))
-    Q₃₂ = (D₃₁ - Q₂₁) * f(a) / (f(c) - f(a))
-    D₃₂ = (D₃₁ - Q₂₁) * f(c) / (f(c) - f(a))
-    Q₃₃ = (D₃₂ - Q₂₂) * f(a) / (f(d) - f(a))
-
-    return a + Q₃₁ + Q₃₂ + Q₃₃
-end
-
-
-
-
-
-
-function f0(x)
-    return x^2 - 1.1
-end
-
-a = 1.0
-b = 20.0
-
-#= global i = 0
-for p in 1:100
-    println(i)
-    test(f0, a, b)
-    #@test g(p) ≈ sqrt(p)
-    #@test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
-    global i += 1
-end =#
-
-test(f0, a, b)
\ No newline at end of file

From 4d332029757c814a1cbfec26db610e7dc59eedac Mon Sep 17 00:00:00 2001
From: Huiyu Xie <huiyuxie.sde@gmail.com>
Date: Thu, 30 Mar 2023 09:00:45 -0700
Subject: [PATCH 111/700] Update src/alefeld.jl

Co-authored-by: Christopher Rackauckas <accounts@chrisrackauckas.com>
---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 2c11a2749..77fa30921 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -26,7 +26,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
                                         right = b)
     end
     a, b, d = _bracket(f, a, b, c)
-    e = 0   # Set e as 0 before iteration to avoid a non-value f(e)
+    e = zero(a)   # Set e as 0 before iteration to avoid a non-value f(e)
 
     # Begin of algorithm iteration
     for i in 2:maxiters

From 15b6c13745d70624076f35083c08595e216bab52 Mon Sep 17 00:00:00 2001
From: huiyuxie <huiyuxie.sde@gmail.com>
Date: Thu, 30 Mar 2023 13:47:56 -0400
Subject: [PATCH 112/700] fix bugs

---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 43 ++++++++++++++++++-------
 1 file changed, 31 insertions(+), 12 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 2c11a2749..542bff8b6 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -16,7 +16,6 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
     f = Base.Fix2(prob.f, prob.p)
     a, b = prob.tspan
     c = a - (b - a) / (f(b) - f(a)) * f(a)
-    @show c
     
     fc = f(c)
     if iszero(fc)
@@ -26,7 +25,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
                                         right = b)
     end
     a, b, d = _bracket(f, a, b, c)
-    e = 0   # Set e as 0 before iteration to avoid a non-value f(e)
+    e = zero(a)    # Set e as 0 before iteration to avoid a non-value f(e)
 
     # Begin of algorithm iteration
     for i in 2:maxiters
@@ -40,7 +39,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
                 c = _newton_quadratic(f, a, b, d, 2)
             end
         end 
-        ē, fc = d, f(c)   
+        ē, fc = d, f(c)
+        (a == c || b == c) && 
+            return SciMLBase.build_solution(prob, alg, c, fc;
+                                            retcode = ReturnCode.FloatingPointLimit,
+                                            left = a, 
+                                            right = b)   
         iszero(fc) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
                                         retcode = ReturnCode.Success, 
@@ -59,11 +63,16 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
             end
         end
         fc = f(c)
+        (ā == c || b̄ == c) && 
+            return SciMLBase.build_solution(prob, alg, c, fc;
+                                            retcode = ReturnCode.FloatingPointLimit,
+                                            left = ā, 
+                                            right = b̄)
         iszero(fc) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
                                         retcode = ReturnCode.Success, 
-                                        left = a,
-                                        right = b)
+                                        left = ā,
+                                        right = b̄)
         ā, b̄, d̄ = _bracket(f, ā, b̄, c) 
 
         # The third bracketing block
@@ -77,11 +86,16 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
             c = 0.5 * (ā + b̄)
         end
         fc = f(c)
+        (ā == c || b̄ == c) && 
+            return SciMLBase.build_solution(prob, alg, c, fc;
+                                            retcode = ReturnCode.FloatingPointLimit,
+                                            left = ā, 
+                                            right = b̄)
         iszero(fc) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
                                         retcode = ReturnCode.Success, 
-                                        left = a,
-                                        right = b)
+                                        left = ā, 
+                                        right = b̄)
         ā, b̄, d = _bracket(f, ā, b̄, c) 
 
         # The last bracketing block
@@ -91,11 +105,16 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
             e = d
             c = 0.5 * (ā + b̄)
             fc = f(c)
+            (ā == c || b̄ == c) && 
+                return SciMLBase.build_solution(prob, alg, c, fc;
+                                                retcode = ReturnCode.FloatingPointLimit,
+                                                left = ā, 
+                                                right = b̄)
             iszero(fc) &&
-            return SciMLBase.build_solution(prob, alg, c, fc;
-                                        retcode = ReturnCode.Success, 
-                                        left = a,
-                                        right = b)
+                return SciMLBase.build_solution(prob, alg, c, fc;
+                                                retcode = ReturnCode.Success, 
+                                                left = ā,
+                                                right = b̄)
             a, b, d = _bracket(f, ā, b̄, c)
         end
     end
@@ -142,7 +161,7 @@ function _newton_quadratic(f::F, a, b, d, k) where F
     end 
 
     for i in 1:k
-        rᵢ = rᵢ₋₁ - B * rᵢ₋₁ / (B + A * (2 * rᵢ₋₁ - a - b))
+        rᵢ = rᵢ₋₁ - (f(a) + B * (rᵢ₋₁ - a) + A * (rᵢ₋₁ - a) * (rᵢ₋₁ - b)) / (B + A * (2 * rᵢ₋₁ - a - b))
         rᵢ₋₁ = rᵢ
     end
 

From 755fec85bc0c5401884352359ad36c65c6146db1 Mon Sep 17 00:00:00 2001
From: huiyuxie <huiyuxie.sde@gmail.com>
Date: Thu, 30 Mar 2023 17:12:18 -0400
Subject: [PATCH 113/700] more tests

---
 lib/SimpleNonlinearSolve/src/alefeld.jl     |  8 +++++--
 lib/SimpleNonlinearSolve/test/basictests.jl | 25 +++++++++++++++++++++
 2 files changed, 31 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 47b01d9ce..f468add9f 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -18,12 +18,16 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
     c = a - (b - a) / (f(b) - f(a)) * f(a)
     
     fc = f(c)
-    if iszero(fc)
+    (a == c || b == c) && 
+        return SciMLBase.build_solution(prob, alg, c, fc;
+                                        retcode = ReturnCode.FloatingPointLimit,
+                                        left = a, 
+                                        right = b)
+    iszero(fc) &&
         return SciMLBase.build_solution(prob, alg, c, fc;
                                         retcode = ReturnCode.Success, 
                                         left = a,
                                         right = b)
-    end
     a, b, d = _bracket(f, a, b, c)
     e = zero(a)   # Set e as 0 before iteration to avoid a non-value f(e)
 
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 5b76ce15f..310ca0638 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -222,6 +222,18 @@ for p in 1.1:0.1:100.0
     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
 end
 
+f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
+t = (p) -> [sqrt(p[2] / p[1])]
+p = [0.9, 50.0]
+g = function (p)
+    probN = IntervalNonlinearProblem{false}(f, tspan, p)
+    sol = solve(probN, Alefeld())
+    return [sol.u]
+end
+
+@test g(p) ≈ [sqrt(p[2] / p[1])]
+@test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
+
 f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
 t = (p) -> [sqrt(p[2] / p[1])]
 p = [0.9, 50.0]
@@ -288,6 +300,7 @@ probB = IntervalNonlinearProblem(f, tspan)
 sol = solve(probB, Falsi())
 @test sol.left ≈ sqrt(2.0)
 
+# Bisection
 sol = solve(probB, Bisection())
 @test sol.left ≈ sqrt(2.0)
 
@@ -315,6 +328,18 @@ probB = IntervalNonlinearProblem(f, tspan)
 sol = solve(probB, Brent())
 @test sol.left ≈ sqrt(2.0)
 
+# Alefeld
+sol = solve(probB, Alefeld())
+@test sol.u ≈ sqrt(2.0)
+tspan = (sqrt(2.0), 10.0)
+probB = IntervalNonlinearProblem(f, tspan)
+sol = solve(probB, Alefeld())
+@test sol.u ≈ sqrt(2.0)
+tspan = (0.0, sqrt(2.0))
+probB = IntervalNonlinearProblem(f, tspan)
+sol = solve(probB, Alefeld())
+@test sol.u ≈ sqrt(2.0)
+
 # Garuntee Tests for Bisection
 f = function (u, p)
     if u < 2.0

From 9cca5371c4df904eb64c1558e00148bbfa969ee3 Mon Sep 17 00:00:00 2001
From: Hendrik Ranocha <mail@ranocha.de>
Date: Fri, 31 Mar 2023 10:43:55 +0200
Subject: [PATCH 114/700] format

---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 85 +++++++++++++------------
 1 file changed, 43 insertions(+), 42 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 47b01d9ce..e573c59d1 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -9,18 +9,17 @@ algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal
 struct Alefeld <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem,
-                            alg::Alefeld, args...; abstol = nothing,
-                            reltol = nothing,
-                            maxiters = 1000, kwargs...)
-                            
+                         alg::Alefeld, args...; abstol = nothing,
+                         reltol = nothing,
+                         maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     a, b = prob.tspan
     c = a - (b - a) / (f(b) - f(a)) * f(a)
-    
+
     fc = f(c)
     if iszero(fc)
         return SciMLBase.build_solution(prob, alg, c, fc;
-                                        retcode = ReturnCode.Success, 
+                                        retcode = ReturnCode.Success,
                                         left = a,
                                         right = b)
     end
@@ -33,47 +32,47 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
         f₁, f₂, f₃, f₄ = f(a), f(b), f(d), f(e)
         if i == 2 || (f₁ == f₂ || f₁ == f₃ || f₁ == f₄ || f₂ == f₃ || f₂ == f₄ || f₃ == f₄)
             c = _newton_quadratic(f, a, b, d, 2)
-        else 
+        else
             c = _ipzero(f, a, b, d, e)
             if (c - a) * (c - b) ≥ 0
                 c = _newton_quadratic(f, a, b, d, 2)
             end
-        end 
+        end
         ē, fc = d, f(c)
-        (a == c || b == c) && 
+        (a == c || b == c) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
                                             retcode = ReturnCode.FloatingPointLimit,
-                                            left = a, 
-                                            right = b)   
+                                            left = a,
+                                            right = b)
         iszero(fc) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
-                                        retcode = ReturnCode.Success, 
-                                        left = a,
-                                        right = b)
-        ā, b̄, d̄ = _bracket(f, a, b, c) 
+                                            retcode = ReturnCode.Success,
+                                            left = a,
+                                            right = b)
+        ā, b̄, d̄ = _bracket(f, a, b, c)
 
         # The second bracketing block
         f₁, f₂, f₃, f₄ = f(ā), f(b̄), f(d̄), f(ē)
         if f₁ == f₂ || f₁ == f₃ || f₁ == f₄ || f₂ == f₃ || f₂ == f₄ || f₃ == f₄
             c = _newton_quadratic(f, ā, b̄, d̄, 3)
-        else 
+        else
             c = _ipzero(f, ā, b̄, d̄, ē)
             if (c - ā) * (c - b̄) ≥ 0
                 c = _newton_quadratic(f, ā, b̄, d̄, 3)
             end
         end
         fc = f(c)
-        (ā == c || b̄ == c) && 
+        (ā == c || b̄ == c) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
                                             retcode = ReturnCode.FloatingPointLimit,
-                                            left = ā, 
+                                            left = ā,
                                             right = b̄)
         iszero(fc) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
-                                        retcode = ReturnCode.Success, 
-                                        left = ā,
-                                        right = b̄)
-        ā, b̄, d̄ = _bracket(f, ā, b̄, c) 
+                                            retcode = ReturnCode.Success,
+                                            left = ā,
+                                            right = b̄)
+        ā, b̄, d̄ = _bracket(f, ā, b̄, c)
 
         # The third bracketing block
         if abs(f(ā)) < abs(f(b̄))
@@ -86,17 +85,17 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
             c = 0.5 * (ā + b̄)
         end
         fc = f(c)
-        (ā == c || b̄ == c) && 
+        (ā == c || b̄ == c) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
                                             retcode = ReturnCode.FloatingPointLimit,
-                                            left = ā, 
+                                            left = ā,
                                             right = b̄)
         iszero(fc) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
-                                        retcode = ReturnCode.Success, 
-                                        left = ā, 
-                                        right = b̄)
-        ā, b̄, d = _bracket(f, ā, b̄, c) 
+                                            retcode = ReturnCode.Success,
+                                            left = ā,
+                                            right = b̄)
+        ā, b̄, d = _bracket(f, ā, b̄, c)
 
         # The last bracketing block
         if b̄ - ā < 0.5 * (b - a)
@@ -105,14 +104,14 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
             e = d
             c = 0.5 * (ā + b̄)
             fc = f(c)
-            (ā == c || b̄ == c) && 
+            (ā == c || b̄ == c) &&
                 return SciMLBase.build_solution(prob, alg, c, fc;
                                                 retcode = ReturnCode.FloatingPointLimit,
-                                                left = ā, 
+                                                left = ā,
                                                 right = b̄)
             iszero(fc) &&
                 return SciMLBase.build_solution(prob, alg, c, fc;
-                                                retcode = ReturnCode.Success, 
+                                                retcode = ReturnCode.Success,
                                                 left = ā,
                                                 right = b̄)
             a, b, d = _bracket(f, ā, b̄, c)
@@ -133,35 +132,37 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
 end
 
 # Define subrotine function bracket, check fc before bracket to return solution
-function _bracket(f::F, a, b, c) where F
+function _bracket(f::F, a, b, c) where {F}
     if iszero(f(c))
         ā, b̄, d = a, b, c
     else
-        if f(a) * f(c) < 0 
+        if f(a) * f(c) < 0
             ā, b̄, d = a, c, b
         elseif f(b) * f(c) < 0
             ā, b̄, d = c, b, a
         end
     end
 
-    return ā, b̄, d 
+    return ā, b̄, d
 end
 
 # Define subrotine function newton quadratic, return the approximation of zero
-function _newton_quadratic(f::F, a, b, d, k) where F
-    A = ((f(d) - f(b)) / (d - b) - (f(b) - f(a)) / (b - a)) / (d - a) 
+function _newton_quadratic(f::F, a, b, d, k) where {F}
+    A = ((f(d) - f(b)) / (d - b) - (f(b) - f(a)) / (b - a)) / (d - a)
     B = (f(b) - f(a)) / (b - a)
 
     if iszero(A)
         return a - (1 / B) * f(a)
     elseif A * f(a) > 0
-        rᵢ₋₁ = a 
-    else 
+        rᵢ₋₁ = a
+    else
         rᵢ₋₁ = b
-    end 
+    end
 
     for i in 1:k
-        rᵢ = rᵢ₋₁ - (f(a) + B * (rᵢ₋₁ - a) + A * (rᵢ₋₁ - a) * (rᵢ₋₁ - b)) / (B + A * (2 * rᵢ₋₁ - a - b))
+        rᵢ = rᵢ₋₁ -
+             (f(a) + B * (rᵢ₋₁ - a) + A * (rᵢ₋₁ - a) * (rᵢ₋₁ - b)) /
+             (B + A * (2 * rᵢ₋₁ - a - b))
         rᵢ₋₁ = rᵢ
     end
 
@@ -169,7 +170,7 @@ function _newton_quadratic(f::F, a, b, d, k) where F
 end
 
 # Define subrotine function ipzero, also return the approximation of zero
-function _ipzero(f::F, a, b, c, d) where F
+function _ipzero(f::F, a, b, c, d) where {F}
     Q₁₁ = (c - d) * f(c) / (f(d) - f(c))
     Q₂₁ = (b - c) * f(b) / (f(c) - f(b))
     Q₃₁ = (a - b) * f(a) / (f(b) - f(a))
@@ -181,4 +182,4 @@ function _ipzero(f::F, a, b, c, d) where F
     Q₃₃ = (D₃₂ - Q₂₂) * f(a) / (f(d) - f(a))
 
     return a + Q₃₁ + Q₃₂ + Q₃₃
-end
\ No newline at end of file
+end

From 56c21013462f167c876ae645c6008e9be82e12cf Mon Sep 17 00:00:00 2001
From: Hendrik Ranocha <mail@ranocha.de>
Date: Fri, 31 Mar 2023 11:35:31 +0200
Subject: [PATCH 115/700] format

---
 lib/SimpleNonlinearSolve/src/alefeld.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index ad2604058..61861a4a7 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -17,10 +17,10 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
     c = a - (b - a) / (f(b) - f(a)) * f(a)
 
     fc = f(c)
-    (a == c || b == c) && 
+    (a == c || b == c) &&
         return SciMLBase.build_solution(prob, alg, c, fc;
                                         retcode = ReturnCode.FloatingPointLimit,
-                                        left = a, 
+                                        left = a,
                                         right = b)
     iszero(fc) &&
         return SciMLBase.build_solution(prob, alg, c, fc;

From 6c4cf4d69ffb2e5915a169b2dc74f97db0fb79cb Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 6 Apr 2023 11:32:47 -0400
Subject: [PATCH 116/700] Use a mutable struct instead of Dict for Safe
 termination

---
 lib/SimpleNonlinearSolve/.gitignore                            | 2 +-
 lib/SimpleNonlinearSolve/Project.toml                          | 2 +-
 lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl | 3 ++-
 lib/SimpleNonlinearSolve/src/broyden.jl                        | 3 ++-
 lib/SimpleNonlinearSolve/src/lbroyden.jl                       | 3 ++-
 5 files changed, 8 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.gitignore b/lib/SimpleNonlinearSolve/.gitignore
index e4cfbfe81..42affce03 100644
--- a/lib/SimpleNonlinearSolve/.gitignore
+++ b/lib/SimpleNonlinearSolve/.gitignore
@@ -1,3 +1,3 @@
 Manifest.toml
-
+.vscode
 wip
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 0be404135..a0becaaca 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -23,7 +23,7 @@ SimpleBatchedNonlinearSolveExt = "NNlib"
 
 [compat]
 ArrayInterface = "6, 7"
-DiffEqBase = "6.119"
+DiffEqBase = "6.123.0"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 NNlib = "0.8"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
index 07c117f4f..e3f394c3b 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
@@ -59,7 +59,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{true}, args...;
         error("Broyden currently doesn't support SAFE_BEST termination modes")
     end
 
-    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? Dict() : nothing
+    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? NLSolveSafeTerminationResult() :
+              nothing
     termination_condition = tc(storage)
 
     xₙ = x
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index e8d339c4c..e46469619 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -48,7 +48,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{false}, args...;
         error("Broyden currently doesn't support SAFE_BEST termination modes")
     end
 
-    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? Dict() : nothing
+    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? NLSolveSafeTerminationResult() :
+              nothing
     termination_condition = tc(storage)
 
     xₙ = x
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index 6a3fc0947..6cca7c11e 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -63,7 +63,8 @@ end
         error("LBroyden currently doesn't support SAFE_BEST termination modes")
     end
 
-    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? Dict() : nothing
+    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? NLSolveSafeTerminationResult() :
+              nothing
     termination_condition = tc(storage)
 
     xₙ = x

From 0ba9b91f91bea5dd67e2b641532a8050cbe1e049 Mon Sep 17 00:00:00 2001
From: Tim Holy <tim.holy@gmail.com>
Date: Mon, 24 Apr 2023 16:38:40 -0500
Subject: [PATCH 117/700] Migrate from SnoopPrecompile to PrecompileTools

---
 lib/SimpleNonlinearSolve/Project.toml                | 4 ++--
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index a0becaaca..aeb58ac43 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -12,7 +12,7 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
-SnoopPrecompile = "66db9d55-30c0-4569-8b51-7e840670fc0c"
+PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [weakdeps]
@@ -30,7 +30,7 @@ NNlib = "0.8"
 Reexport = "0.2, 1"
 Requires = "1"
 SciMLBase = "1.73"
-SnoopPrecompile = "1"
+PrecompileTools = "1"
 StaticArraysCore = "1.4"
 julia = "1.6"
 
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index a33dd9297..46f1ab3c4 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -40,9 +40,9 @@ include("ad.jl")
 include("halley.jl")
 include("alefeld.jl")
 
-import SnoopPrecompile
+import PrecompileTools
 
-SnoopPrecompile.@precompile_all_calls begin for T in (Float32, Float64)
+PrecompileTools.@compile_workload begin for T in (Float32, Float64)
     prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
     for alg in (SimpleNewtonRaphson, Halley, Broyden, Klement, SimpleTrustRegion,
                 SimpleDFSane)

From 0659f6a5eb9b352c24be53fbd7af98c20f2344ec Mon Sep 17 00:00:00 2001
From: Utkarsh <rajpututkarsh530@gmail.com>
Date: Fri, 19 May 2023 19:28:53 -0400
Subject: [PATCH 118/700] Add support for f.jac in SimpleNewtonRaphson

---
 lib/SimpleNonlinearSolve/src/raphson.jl     |  5 ++++-
 lib/SimpleNonlinearSolve/test/basictests.jl | 15 +++++++++++++++
 2 files changed, 19 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 57d66b005..8d2d9796c 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -60,7 +60,10 @@ function SciMLBase.__solve(prob::NonlinearProblem,
     end
 
     for i in 1:maxiters
-        if alg_autodiff(alg)
+        if DiffEqBase.has_jac(prob.f)
+            dfx = prob.f.jac(x, prob.p)
+            fx = f(x)
+        elseif alg_autodiff(alg)
             fx, dfx = value_derivative(f, x)
         elseif x isa AbstractArray
             fx = f(x)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 310ca0638..81a047e0a 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -2,6 +2,7 @@ using SimpleNonlinearSolve
 using StaticArrays
 using BenchmarkTools
 using DiffEqBase
+using LinearAlgebra
 using Test
 
 const BATCHED_BROYDEN_SOLVERS = Broyden[]
@@ -489,3 +490,17 @@ for alg in (BATCHED_BROYDEN_SOLVERS..., BATCHED_LBROYDEN_SOLVERS...)
     @test sol.retcode == ReturnCode.Success
     @test abs.(sol.u) ≈ sqrt.(p)
 end
+
+## Specified Jacobian
+
+f, u0 = (u, p) -> u .* u .- p, randn(3)
+
+f_jac(u, p) = begin diagm(2 * u) end
+
+p = [2.0, 1.0, 5.0];
+
+probN = NonlinearProblem(NonlinearFunction(f, jac = f_jac), u0, p)
+
+sol = solve(probN, SimpleNewtonRaphson())
+
+@test abs.(sol.u) ≈ sqrt.(p)

From 4411caef1c0740f8d7effdff1a9940233069e887 Mon Sep 17 00:00:00 2001
From: Utkarsh <rajpututkarsh530@gmail.com>
Date: Wed, 24 May 2023 15:54:24 -0400
Subject: [PATCH 119/700] Add custom jac in SimpleTrustRegion

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 6 +++++-
 lib/SimpleNonlinearSolve/test/basictests.jl | 9 +++++----
 2 files changed, 10 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index edd143215..aa893ffc1 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -112,7 +112,11 @@ function SciMLBase.__solve(prob::NonlinearProblem,
            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
     rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
 
-    if alg_autodiff(alg)
+
+    if DiffEqBase.has_jac(prob.f)
+        ∇f = prob.f.jac(x, prob.p)
+        F = f(x)
+    elseif alg_autodiff(alg)
         F, ∇f = value_derivative(f, x)
     elseif x isa AbstractArray
         F = f(x)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 81a047e0a..1a0249b65 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -491,7 +491,7 @@ for alg in (BATCHED_BROYDEN_SOLVERS..., BATCHED_LBROYDEN_SOLVERS...)
     @test abs.(sol.u) ≈ sqrt.(p)
 end
 
-## Specified Jacobian
+## User specified Jacobian
 
 f, u0 = (u, p) -> u .* u .- p, randn(3)
 
@@ -501,6 +501,7 @@ p = [2.0, 1.0, 5.0];
 
 probN = NonlinearProblem(NonlinearFunction(f, jac = f_jac), u0, p)
 
-sol = solve(probN, SimpleNewtonRaphson())
-
-@test abs.(sol.u) ≈ sqrt.(p)
+for alg in (SimpleNewtonRaphson(), SimpleTrustRegion())
+    sol = solve(probN, alg)
+    @test abs.(sol.u) ≈ sqrt.(p)
+end

From b1d8bea57a35c4e7a035ea68508563d3334b43c3 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Fri, 26 May 2023 14:32:16 -0700
Subject: [PATCH 120/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index aeb58ac43..c1f21c72e 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.14"
+version = "0.1.15"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
@@ -43,4 +43,4 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays", "NNlib"]
\ No newline at end of file
+test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays", "NNlib"]

From 0ca6ab0b9efb4b71ae1719451a9858cc0b6ce83e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 8 Jun 2023 15:08:39 -0400
Subject: [PATCH 121/700] Format and add a format CI

---
 .../.github/workflows/FormatPR.yml            | 29 ++++++++
 .../ext/SimpleBatchedNonlinearSolveExt.jl     |  4 +-
 .../src/SimpleNonlinearSolve.jl               | 46 +++++++------
 lib/SimpleNonlinearSolve/src/ad.jl            | 52 +++++++-------
 lib/SimpleNonlinearSolve/src/alefeld.jl       | 68 +++++++++----------
 lib/SimpleNonlinearSolve/src/bisection.jl     | 18 ++---
 lib/SimpleNonlinearSolve/src/brent.jl         | 18 ++---
 lib/SimpleNonlinearSolve/src/broyden.jl       |  8 +--
 lib/SimpleNonlinearSolve/src/dfsane.jl        | 12 ++--
 lib/SimpleNonlinearSolve/src/falsi.jl         | 18 ++---
 lib/SimpleNonlinearSolve/src/halley.jl        | 22 +++---
 lib/SimpleNonlinearSolve/src/klement.jl       | 14 ++--
 lib/SimpleNonlinearSolve/src/lbroyden.jl      | 20 +++---
 lib/SimpleNonlinearSolve/src/raphson.jl       | 10 +--
 lib/SimpleNonlinearSolve/src/ridder.jl        | 22 +++---
 lib/SimpleNonlinearSolve/src/trustRegion.jl   | 53 +++++++--------
 lib/SimpleNonlinearSolve/test/basictests.jl   | 60 ++++++++--------
 lib/SimpleNonlinearSolve/test/runtests.jl     | 10 +--
 18 files changed, 261 insertions(+), 223 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml b/lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml
new file mode 100644
index 000000000..b0cb28af5
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml
@@ -0,0 +1,29 @@
+name: format-pr
+on:
+  schedule:
+    - cron: '0 0 * * *'
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v3
+      - name: Install JuliaFormatter and format
+        run: |
+          julia  -e 'using Pkg; Pkg.add(PackageSpec(name="JuliaFormatter"))'
+          julia  -e 'using JuliaFormatter; format(".")'
+      # https://github.com/marketplace/actions/create-pull-request
+      # https://github.com/peter-evans/create-pull-request#reference-example
+      - name: Create Pull Request
+        id: cpr
+        uses: peter-evans/create-pull-request@v5
+        with:
+          token: ${{ secrets.GITHUB_TOKEN }}
+          commit-message: Format .jl files
+          title: 'Automatic JuliaFormatter.jl run'
+          branch: auto-juliaformatter-pr
+          delete-branch: true
+          labels: formatting, automated pr, no changelog
+      - name: Check outputs
+        run: |
+          echo "Pull Request Number - ${{ steps.cpr.outputs.pull-request-number }}"
+          echo "Pull Request URL - ${{ steps.cpr.outputs.pull-request-url }}"
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
index e3f394c3b..dd7628888 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
@@ -31,7 +31,7 @@ function _init_J_batched(x::AbstractMatrix{T}) where {T}
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{true}, args...;
-                           abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
+    abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
     f = Base.Fix2(prob.f, prob.p)
@@ -74,7 +74,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{true}, args...;
         J⁻¹Δfₙ = _batched_mul(J⁻¹, Δfₙ)
         J⁻¹ += _batched_mul(((Δxₙ .- J⁻¹Δfₙ) ./
                              (_batched_mul(_batch_transpose(Δxₙ), J⁻¹Δfₙ) .+ T(1e-5))),
-                            _batched_mul(_batch_transpose(Δxₙ), J⁻¹))
+            _batched_mul(_batch_transpose(Δxₙ), J⁻¹))
 
         if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
             return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 46f1ab3c4..8749aa72b 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -16,7 +16,9 @@ end
 
 function __init__()
     @static if !isdefined(Base, :get_extension)
-        @require NNlib="872c559c-99b0-510c-b3b7-b6c96a88d5cd" begin include("../ext/SimpleBatchedNonlinearSolveExt.jl") end
+        @require NNlib="872c559c-99b0-510c-b3b7-b6c96a88d5cd" begin
+            include("../ext/SimpleBatchedNonlinearSolveExt.jl")
+        end
     end
 end
 
@@ -42,31 +44,35 @@ include("alefeld.jl")
 
 import PrecompileTools
 
-PrecompileTools.@compile_workload begin for T in (Float32, Float64)
-    prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-    for alg in (SimpleNewtonRaphson, Halley, Broyden, Klement, SimpleTrustRegion,
-                SimpleDFSane)
-        solve(prob_no_brack, alg(), abstol = T(1e-2))
-    end
+PrecompileTools.@compile_workload begin
+    for T in (Float32, Float64)
+        prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
+        for alg in (SimpleNewtonRaphson, Halley, Broyden, Klement, SimpleTrustRegion,
+            SimpleDFSane)
+            solve(prob_no_brack, alg(), abstol = T(1e-2))
+        end
 
-    #=
-    for alg in (SimpleNewtonRaphson,)
-        for u0 in ([1., 1.], StaticArraysCore.SA[1.0, 1.0])
-            u0 = T.(.1)
-            probN = NonlinearProblem{false}((u,p) -> u .* u .- p, u0, T(2))
-            solve(probN, alg(), tol = T(1e-2))
+        #=
+        for alg in (SimpleNewtonRaphson,)
+            for u0 in ([1., 1.], StaticArraysCore.SA[1.0, 1.0])
+                u0 = T.(.1)
+                probN = NonlinearProblem{false}((u,p) -> u .* u .- p, u0, T(2))
+                solve(probN, alg(), tol = T(1e-2))
+            end
         end
-    end
-    =#
+        =#
 
-    prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p, T.((0.0, 2.0)), T(2))
-    for alg in (Bisection, Falsi, Ridder, Brent, Alefeld)
-        solve(prob_brack, alg(), abstol = T(1e-2))
+        prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p,
+            T.((0.0, 2.0)),
+            T(2))
+        for alg in (Bisection, Falsi, Ridder, Brent, Alefeld)
+            solve(prob_brack, alg(), abstol = T(1e-2))
+        end
     end
-end end
+end
 
 # DiffEq styled algorithms
 export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, Halley, Klement,
-       Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld
+    Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index dbd90243a..009cd227b 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -29,50 +29,50 @@ function scalar_nlsolve_ad(prob, alg, args...; kwargs...)
 end
 
 function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
-                                                iip,
-                                                <:Dual{T, V, P}},
-                         alg::AbstractSimpleNonlinearSolveAlgorithm,
-                         args...; kwargs...) where {iip, T, V, P}
+        iip,
+        <:Dual{T, V, P}},
+    alg::AbstractSimpleNonlinearSolveAlgorithm,
+    args...; kwargs...) where {iip, T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
-                                    retcode = sol.retcode)
+        retcode = sol.retcode)
 end
 function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
-                                                iip,
-                                                <:AbstractArray{<:Dual{T, V, P}}},
-                         alg::AbstractSimpleNonlinearSolveAlgorithm, args...;
-                         kwargs...) where {iip, T, V, P}
+        iip,
+        <:AbstractArray{<:Dual{T, V, P}}},
+    alg::AbstractSimpleNonlinearSolveAlgorithm, args...;
+    kwargs...) where {iip, T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
-                                    retcode = sol.retcode)
+        retcode = sol.retcode)
 end
 
 # avoid ambiguities
 for Alg in [Bisection]
     @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
-                                                                  <:Dual{T, V, P}},
-                                   alg::$Alg, args...;
-                                   kwargs...) where {uType, iip, T, V, P}
+            <:Dual{T, V, P}},
+        alg::$Alg, args...;
+        kwargs...) where {uType, iip, T, V, P}
         sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
         return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials),
-                                        sol.resid; retcode = sol.retcode,
-                                        left = Dual{T, V, P}(sol.left, partials),
-                                        right = Dual{T, V, P}(sol.right, partials))
+            sol.resid; retcode = sol.retcode,
+            left = Dual{T, V, P}(sol.left, partials),
+            right = Dual{T, V, P}(sol.right, partials))
         #return BracketingSolution(Dual{T,V,P}(sol.left, partials), Dual{T,V,P}(sol.right, partials), sol.retcode, sol.resid)
     end
     @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
-                                                                  <:AbstractArray{
-                                                                                  <:Dual{T,
-                                                                                         V,
-                                                                                         P}
-                                                                                  }},
-                                   alg::$Alg, args...;
-                                   kwargs...) where {uType, iip, T, V, P}
+            <:AbstractArray{
+                <:Dual{T,
+                    V,
+                    P},
+            }},
+        alg::$Alg, args...;
+        kwargs...) where {uType, iip, T, V, P}
         sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
         return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials),
-                                        sol.resid; retcode = sol.retcode,
-                                        left = Dual{T, V, P}(sol.left, partials),
-                                        right = Dual{T, V, P}(sol.right, partials))
+            sol.resid; retcode = sol.retcode,
+            left = Dual{T, V, P}(sol.left, partials),
+            right = Dual{T, V, P}(sol.right, partials))
         #return BracketingSolution(Dual{T,V,P}(sol.left, partials), Dual{T,V,P}(sol.right, partials), sol.retcode, sol.resid)
     end
 end
diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 61861a4a7..a2669ca96 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -9,9 +9,9 @@ algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal
 struct Alefeld <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem,
-                         alg::Alefeld, args...; abstol = nothing,
-                         reltol = nothing,
-                         maxiters = 1000, kwargs...)
+    alg::Alefeld, args...; abstol = nothing,
+    reltol = nothing,
+    maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     a, b = prob.tspan
     c = a - (b - a) / (f(b) - f(a)) * f(a)
@@ -19,14 +19,14 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
     fc = f(c)
     (a == c || b == c) &&
         return SciMLBase.build_solution(prob, alg, c, fc;
-                                        retcode = ReturnCode.FloatingPointLimit,
-                                        left = a,
-                                        right = b)
+            retcode = ReturnCode.FloatingPointLimit,
+            left = a,
+            right = b)
     iszero(fc) &&
         return SciMLBase.build_solution(prob, alg, c, fc;
-                                        retcode = ReturnCode.Success,
-                                        left = a,
-                                        right = b)
+            retcode = ReturnCode.Success,
+            left = a,
+            right = b)
     a, b, d = _bracket(f, a, b, c)
     e = zero(a)   # Set e as 0 before iteration to avoid a non-value f(e)
 
@@ -45,14 +45,14 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
         ē, fc = d, f(c)
         (a == c || b == c) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
-                                            retcode = ReturnCode.FloatingPointLimit,
-                                            left = a,
-                                            right = b)
+                retcode = ReturnCode.FloatingPointLimit,
+                left = a,
+                right = b)
         iszero(fc) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
-                                            retcode = ReturnCode.Success,
-                                            left = a,
-                                            right = b)
+                retcode = ReturnCode.Success,
+                left = a,
+                right = b)
         ā, b̄, d̄ = _bracket(f, a, b, c)
 
         # The second bracketing block
@@ -68,14 +68,14 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
         fc = f(c)
         (ā == c || b̄ == c) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
-                                            retcode = ReturnCode.FloatingPointLimit,
-                                            left = ā,
-                                            right = b̄)
+                retcode = ReturnCode.FloatingPointLimit,
+                left = ā,
+                right = b̄)
         iszero(fc) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
-                                            retcode = ReturnCode.Success,
-                                            left = ā,
-                                            right = b̄)
+                retcode = ReturnCode.Success,
+                left = ā,
+                right = b̄)
         ā, b̄, d̄ = _bracket(f, ā, b̄, c)
 
         # The third bracketing block
@@ -91,14 +91,14 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
         fc = f(c)
         (ā == c || b̄ == c) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
-                                            retcode = ReturnCode.FloatingPointLimit,
-                                            left = ā,
-                                            right = b̄)
+                retcode = ReturnCode.FloatingPointLimit,
+                left = ā,
+                right = b̄)
         iszero(fc) &&
             return SciMLBase.build_solution(prob, alg, c, fc;
-                                            retcode = ReturnCode.Success,
-                                            left = ā,
-                                            right = b̄)
+                retcode = ReturnCode.Success,
+                left = ā,
+                right = b̄)
         ā, b̄, d = _bracket(f, ā, b̄, c)
 
         # The last bracketing block
@@ -110,14 +110,14 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
             fc = f(c)
             (ā == c || b̄ == c) &&
                 return SciMLBase.build_solution(prob, alg, c, fc;
-                                                retcode = ReturnCode.FloatingPointLimit,
-                                                left = ā,
-                                                right = b̄)
+                    retcode = ReturnCode.FloatingPointLimit,
+                    left = ā,
+                    right = b̄)
             iszero(fc) &&
                 return SciMLBase.build_solution(prob, alg, c, fc;
-                                                retcode = ReturnCode.Success,
-                                                left = ā,
-                                                right = b̄)
+                    retcode = ReturnCode.Success,
+                    left = ā,
+                    right = b̄)
             a, b, d = _bracket(f, ā, b̄, c)
         end
     end
@@ -132,7 +132,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
 
     # Reuturn solution when run out of max interation
     return SciMLBase.build_solution(prob, alg, c, fc; retcode = ReturnCode.MaxIters,
-                                    left = a, right = b)
+        left = a, right = b)
 end
 
 # Define subrotine function bracket, check fc before bracket to return solution
diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index 4e2b232e6..673f77067 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -20,16 +20,16 @@ function Bisection(; exact_left = false, exact_right = false)
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...;
-                         maxiters = 1000,
-                         kwargs...)
+    maxiters = 1000,
+    kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
-                                        retcode = ReturnCode.ExactSolutionLeft, left = left,
-                                        right = right)
+            retcode = ReturnCode.ExactSolutionLeft, left = left,
+            right = right)
     end
 
     i = 1
@@ -38,8 +38,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
             mid = (left + right) / 2
             (mid == left || mid == right) &&
                 return SciMLBase.build_solution(prob, alg, left, fl;
-                                                retcode = ReturnCode.FloatingPointLimit,
-                                                left = left, right = right)
+                    retcode = ReturnCode.FloatingPointLimit,
+                    left = left, right = right)
             fm = f(mid)
             if iszero(fm)
                 right = mid
@@ -60,8 +60,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
         mid = (left + right) / 2
         (mid == left || mid == right) &&
             return SciMLBase.build_solution(prob, alg, left, fl;
-                                            retcode = ReturnCode.FloatingPointLimit,
-                                            left = left, right = right)
+                retcode = ReturnCode.FloatingPointLimit,
+                left = left, right = right)
         fm = f(mid)
         if iszero(fm)
             right = mid
@@ -74,5 +74,5 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
     end
 
     return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
-                                    left = left, right = right)
+        left = left, right = right)
 end
diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/brent.jl
index 99f645f6a..1cedad134 100644
--- a/lib/SimpleNonlinearSolve/src/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/brent.jl
@@ -7,8 +7,8 @@ A non-allocating Brent method
 struct Brent <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
-                         maxiters = 1000,
-                         kwargs...)
+    maxiters = 1000,
+    kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     a, b = prob.tspan
     fa, fb = f(a), f(b)
@@ -16,8 +16,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
 
     if iszero(fa)
         return SciMLBase.build_solution(prob, alg, a, fa;
-                                        retcode = ReturnCode.ExactSolutionLeft, left = a,
-                                        right = b)
+            retcode = ReturnCode.ExactSolutionLeft, left = a,
+            right = b)
     end
     if abs(fa) < abs(fb)
         c = b
@@ -53,8 +53,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
                 s = (a + b) / 2
                 (s == a || s == b) &&
                     return SciMLBase.build_solution(prob, alg, a, fa;
-                                                    retcode = ReturnCode.FloatingPointLimit,
-                                                    left = a, right = b)
+                        retcode = ReturnCode.FloatingPointLimit,
+                        left = a, right = b)
                 cond = true
             else
                 cond = false
@@ -95,8 +95,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
         c = (a + b) / 2
         if (c == a || c == b)
             return SciMLBase.build_solution(prob, alg, a, fa;
-                                            retcode = ReturnCode.FloatingPointLimit,
-                                            left = a, right = b)
+                retcode = ReturnCode.FloatingPointLimit,
+                left = a, right = b)
         end
         fc = f(c)
         if iszero(fc)
@@ -110,5 +110,5 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
     end
 
     return SciMLBase.build_solution(prob, alg, a, fa; retcode = ReturnCode.MaxIters,
-                                    left = a, right = b)
+        left = a, right = b)
 end
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index e46469619..8ce0d66b5 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -16,15 +16,15 @@ struct Broyden{batched, TC <: NLSolveTerminationCondition} <:
     termination_condition::TC
 
     function Broyden(; batched = false,
-                     termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-                                                                         abstol = nothing,
-                                                                         reltol = nothing))
+        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+            abstol = nothing,
+            reltol = nothing))
         return new{batched, typeof(termination_condition)}(termination_condition)
     end
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{false}, args...;
-                           abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
+    abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
     f = Base.Fix2(prob.f, prob.p)
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index 3d2e9c8aa..e898f060b 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -52,15 +52,15 @@ struct SimpleDFSane{T} <: AbstractSimpleNonlinearSolveAlgorithm
     η_strategy::Function
 
     function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
-                          M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
-                          nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 / k^2)
+        M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
+        nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 / k^2)
         new{typeof(σ_min)}(σ_min, σ_max, σ_1, M, γ, τ_min, τ_max, nexp, η_strategy)
     end
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane,
-                           args...; abstol = nothing, reltol = nothing, maxiters = 1000,
-                           kwargs...)
+    args...; abstol = nothing, reltol = nothing, maxiters = 1000,
+    kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     T = eltype(x)
@@ -96,7 +96,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane,
     for k in 1:maxiters
         iszero(F_k) &&
             return SciMLBase.build_solution(prob, alg, x, F_k;
-                                            retcode = ReturnCode.Success)
+                retcode = ReturnCode.Success)
 
         # Spectral parameter range check
         if abs(σ_k) > σ_max
@@ -136,7 +136,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane,
 
         if isapprox(x_new, x, atol = atol, rtol = rtol)
             return SciMLBase.build_solution(prob, alg, x_new, F_new;
-                                            retcode = ReturnCode.Success)
+                retcode = ReturnCode.Success)
         end
         # Update spectral parameter
         s_k = x_new - x
diff --git a/lib/SimpleNonlinearSolve/src/falsi.jl b/lib/SimpleNonlinearSolve/src/falsi.jl
index 81ce68ffa..cce11a811 100644
--- a/lib/SimpleNonlinearSolve/src/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/falsi.jl
@@ -4,16 +4,16 @@
 struct Falsi <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
-                         maxiters = 1000,
-                         kwargs...)
+    maxiters = 1000,
+    kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
-                                        retcode = ReturnCode.ExactSolutionLeft, left = left,
-                                        right = right)
+            retcode = ReturnCode.ExactSolutionLeft, left = left,
+            right = right)
     end
 
     i = 1
@@ -21,8 +21,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
         while i < maxiters
             if nextfloat_tdir(left, prob.tspan...) == right
                 return SciMLBase.build_solution(prob, alg, left, fl;
-                                                retcode = ReturnCode.FloatingPointLimit,
-                                                left = left, right = right)
+                    retcode = ReturnCode.FloatingPointLimit,
+                    left = left, right = right)
             end
             mid = (fr * left - fl * right) / (fr - fl)
             for i in 1:10
@@ -51,8 +51,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
         mid = (left + right) / 2
         (mid == left || mid == right) &&
             return SciMLBase.build_solution(prob, alg, left, fl;
-                                            retcode = ReturnCode.FloatingPointLimit,
-                                            left = left, right = right)
+                retcode = ReturnCode.FloatingPointLimit,
+                left = left, right = right)
         fm = f(mid)
         if iszero(fm)
             right = mid
@@ -68,5 +68,5 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
     end
 
     return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
-                                    left = left, right = right)
+        left = left, right = right)
 end
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index cdda7beda..9e97a57cd 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -30,16 +30,16 @@ and static array problems.
 """
 struct Halley{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     function Halley(; chunk_size = Val{0}(), autodiff = Val{true}(),
-                    diff_type = Val{:forward})
+        diff_type = Val{:forward})
         new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
             SciMLBase._unwrap_val(diff_type)}()
     end
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-                           alg::Halley, args...; abstol = nothing,
-                           reltol = nothing,
-                           maxiters = 1000, kwargs...)
+    alg::Halley, args...; abstol = nothing,
+    reltol = nothing,
+    maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     fx = f(x)
@@ -81,18 +81,18 @@ function SciMLBase.__solve(prob::NonlinearProblem,
             if isa(x, Number)
                 fx = f(x)
                 dfx = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg),
-                                                              eltype(x))
+                    eltype(x))
                 d2fx = FiniteDiff.finite_difference_derivative(x -> FiniteDiff.finite_difference_derivative(f,
-                                                                                                            x),
-                                                               x,
-                                                               diff_type(alg), eltype(x))
+                        x),
+                    x,
+                    diff_type(alg), eltype(x))
             else
                 fx = f(x)
                 dfx = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x))
                 d2fx = FiniteDiff.finite_difference_jacobian(x -> FiniteDiff.finite_difference_jacobian(f,
-                                                                                                        x),
-                                                             x,
-                                                             diff_type(alg), eltype(x))
+                        x),
+                    x,
+                    diff_type(alg), eltype(x))
                 ai = -(dfx \ fx)
                 A = reshape(d2fx * ai, (n, n))
                 bi = (dfx) \ (A * ai)
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 4d59377df..00264d32f 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -9,9 +9,9 @@ This method is non-allocating on scalar problems.
 struct Klement <: AbstractSimpleNonlinearSolveAlgorithm end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-                           alg::Klement, args...; abstol = nothing,
-                           reltol = nothing,
-                           maxiters = 1000, kwargs...)
+    alg::Klement, args...; abstol = nothing,
+    reltol = nothing,
+    maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     fₙ = f(x)
@@ -39,11 +39,11 @@ function SciMLBase.__solve(prob::NonlinearProblem,
 
             iszero(fₙ) &&
                 return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                                                retcode = ReturnCode.Success)
+                    retcode = ReturnCode.Success)
 
             if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
                 return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                                                retcode = ReturnCode.Success)
+                    retcode = ReturnCode.Success)
             end
 
             Δxₙ = xₙ - xₙ₋₁
@@ -81,11 +81,11 @@ function SciMLBase.__solve(prob::NonlinearProblem,
 
             iszero(fₙ) &&
                 return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                                                retcode = ReturnCode.Success)
+                    retcode = ReturnCode.Success)
 
             if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
                 return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                                                retcode = ReturnCode.Success)
+                    retcode = ReturnCode.Success)
             end
 
             Δxₙ = xₙ - xₙ₋₁
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index 6cca7c11e..fc2b51a88 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -18,16 +18,16 @@ struct LBroyden{batched, TC <: NLSolveTerminationCondition} <:
     threshold::Int
 
     function LBroyden(; batched = false, threshold::Int = 27,
-                      termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-                                                                          abstol = nothing,
-                                                                          reltol = nothing))
+        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+            abstol = nothing,
+            reltol = nothing))
         return new{batched, typeof(termination_condition)}(termination_condition, threshold)
     end
 end
 
 @views function SciMLBase.__solve(prob::NonlinearProblem, alg::LBroyden{batched}, args...;
-                                  abstol = nothing, reltol = nothing, maxiters = 1000,
-                                  kwargs...) where {batched}
+    abstol = nothing, reltol = nothing, maxiters = 1000,
+    kwargs...) where {batched}
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
     threshold = min(maxiters, alg.threshold)
@@ -93,7 +93,7 @@ end
         selectdim(U, 1, mod1(i, threshold)) .= u
 
         update = -_matvec(selectdim(U, 1, 1:min(threshold, i + 1)),
-                          selectdim(Vᵀ, 2, 1:min(threshold, i + 1)), fₙ)
+            selectdim(Vᵀ, 2, 1:min(threshold, i + 1)), fₙ)
 
         xₙ₋₁ = xₙ
         fₙ₋₁ = fₙ
@@ -116,26 +116,26 @@ function _init_lbroyden_state(batched::Bool, x, threshold)
 end
 
 function _rmatvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
-                  x::Union{<:AbstractVector, <:Number})
+    x::Union{<:AbstractVector, <:Number})
     length(U) == 0 && return x
     return -x .+ vec((x' * Vᵀ) * U)
 end
 
 function _rmatvec(U::AbstractArray{T1, 3}, Vᵀ::AbstractArray{T2, 3},
-                  x::AbstractMatrix) where {T1, T2}
+    x::AbstractMatrix) where {T1, T2}
     length(U) == 0 && return x
     Vᵀx = sum(Vᵀ .* reshape(x, size(x, 1), 1, size(x, 2)); dims = 1)
     return -x .+ _drdims_sum(U .* permutedims(Vᵀx, (2, 1, 3)); dims = 1)
 end
 
 function _matvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
-                 x::Union{<:AbstractVector, <:Number})
+    x::Union{<:AbstractVector, <:Number})
     length(U) == 0 && return x
     return -x .+ vec(Vᵀ * (U * x))
 end
 
 function _matvec(U::AbstractArray{T1, 3}, Vᵀ::AbstractArray{T2, 3},
-                 x::AbstractMatrix) where {T1, T2}
+    x::AbstractMatrix) where {T1, T2}
     length(U) == 0 && return x
     xUᵀ = sum(reshape(x, size(x, 1), 1, size(x, 2)) .* permutedims(U, (2, 1, 3)); dims = 1)
     return -x .+ _drdims_sum(xUᵀ .* Vᵀ; dims = 2)
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 8d2d9796c..386c35053 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -30,16 +30,16 @@ and static array problems.
 """
 struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     function SimpleNewtonRaphson(; chunk_size = Val{0}(), autodiff = Val{true}(),
-                                 diff_type = Val{:forward})
+        diff_type = Val{:forward})
         new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
             SciMLBase._unwrap_val(diff_type)}()
     end
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-                           alg::SimpleNewtonRaphson, args...; abstol = nothing,
-                           reltol = nothing,
-                           maxiters = 1000, kwargs...)
+    alg::SimpleNewtonRaphson, args...; abstol = nothing,
+    reltol = nothing,
+    maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     fx = float(prob.u0)
@@ -71,7 +71,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         else
             fx = f(x)
             dfx = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x),
-                                                          fx)
+                fx)
         end
         iszero(fx) &&
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
diff --git a/lib/SimpleNonlinearSolve/src/ridder.jl b/lib/SimpleNonlinearSolve/src/ridder.jl
index 9fe7bccfe..62b5a931a 100644
--- a/lib/SimpleNonlinearSolve/src/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/ridder.jl
@@ -7,16 +7,16 @@ A non-allocating ridder method
 struct Ridder <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
-                         maxiters = 1000,
-                         kwargs...)
+    maxiters = 1000,
+    kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
-                                        retcode = ReturnCode.ExactSolutionLeft, left = left,
-                                        right = right)
+            retcode = ReturnCode.ExactSolutionLeft, left = left,
+            right = right)
     end
 
     xo = oftype(left, Inf)
@@ -26,14 +26,14 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
             mid = (left + right) / 2
             (mid == left || mid == right) &&
                 return SciMLBase.build_solution(prob, alg, left, fl;
-                                                retcode = ReturnCode.FloatingPointLimit,
-                                                left = left, right = right)
+                    retcode = ReturnCode.FloatingPointLimit,
+                    left = left, right = right)
             fm = f(mid)
             s = sqrt(fm^2 - fl * fr)
             iszero(s) &&
                 return SciMLBase.build_solution(prob, alg, left, fl;
-                                                retcode = ReturnCode.Failure,
-                                                left = left, right = right)
+                    retcode = ReturnCode.Failure,
+                    left = left, right = right)
             x = mid + (mid - left) * sign(fl - fr) * fm / s
             fx = f(x)
             xo = x
@@ -63,8 +63,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
         mid = (left + right) / 2
         (mid == left || mid == right) &&
             return SciMLBase.build_solution(prob, alg, left, fl;
-                                            retcode = ReturnCode.FloatingPointLimit,
-                                            left = left, right = right)
+                retcode = ReturnCode.FloatingPointLimit,
+                left = left, right = right)
         fm = f(mid)
         if iszero(fm)
             right = mid
@@ -77,5 +77,5 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
     end
 
     return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
-                                    left = left, right = right)
+        left = left, right = right)
 end
diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index aa893ffc1..1423d59b8 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -64,34 +64,34 @@ struct SimpleTrustRegion{T, CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     expand_factor::T
     max_shrink_times::Int
     function SimpleTrustRegion(; chunk_size = Val{0}(),
-                               autodiff = Val{true}(),
-                               diff_type = Val{:forward},
-                               max_trust_radius::Real = 0.0,
-                               initial_trust_radius::Real = 0.0,
-                               step_threshold::Real = 0.1,
-                               shrink_threshold::Real = 0.25,
-                               expand_threshold::Real = 0.75,
-                               shrink_factor::Real = 0.25,
-                               expand_factor::Real = 2.0,
-                               max_shrink_times::Int = 32)
+        autodiff = Val{true}(),
+        diff_type = Val{:forward},
+        max_trust_radius::Real = 0.0,
+        initial_trust_radius::Real = 0.0,
+        step_threshold::Real = 0.1,
+        shrink_threshold::Real = 0.25,
+        expand_threshold::Real = 0.75,
+        shrink_factor::Real = 0.25,
+        expand_factor::Real = 2.0,
+        max_shrink_times::Int = 32)
         new{typeof(initial_trust_radius),
             SciMLBase._unwrap_val(chunk_size),
             SciMLBase._unwrap_val(autodiff),
             SciMLBase._unwrap_val(diff_type)}(max_trust_radius,
-                                              initial_trust_radius,
-                                              step_threshold,
-                                              shrink_threshold,
-                                              expand_threshold,
-                                              shrink_factor,
-                                              expand_factor,
-                                              max_shrink_times)
+            initial_trust_radius,
+            step_threshold,
+            shrink_threshold,
+            expand_threshold,
+            shrink_factor,
+            expand_factor,
+            max_shrink_times)
     end
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-                           alg::SimpleTrustRegion, args...; abstol = nothing,
-                           reltol = nothing,
-                           maxiters = 1000, kwargs...)
+    alg::SimpleTrustRegion, args...; abstol = nothing,
+    reltol = nothing,
+    maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     T = typeof(x)
@@ -112,7 +112,6 @@ function SciMLBase.__solve(prob::NonlinearProblem,
            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
     rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
 
-
     if DiffEqBase.has_jac(prob.f)
         ∇f = prob.f.jac(x, prob.p)
         F = f(x)
@@ -156,7 +155,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
             shrink_counter += 1
             if shrink_counter > max_shrink_times
                 return SciMLBase.build_solution(prob, alg, x, F;
-                                                retcode = ReturnCode.Success)
+                    retcode = ReturnCode.Success)
             end
         else
             shrink_counter = 0
@@ -164,7 +163,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         if r > η₁
             if isapprox(xₖ₊₁, x, atol = atol, rtol = rtol)
                 return SciMLBase.build_solution(prob, alg, xₖ₊₁, Fₖ₊₁;
-                                                retcode = ReturnCode.Success)
+                    retcode = ReturnCode.Success)
             end
             # Take the step.
             x = xₖ₊₁
@@ -173,16 +172,16 @@ function SciMLBase.__solve(prob::NonlinearProblem,
                 F, ∇f = value_derivative(f, x)
             elseif x isa AbstractArray
                 ∇f = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x),
-                                                           F)
+                    F)
             else
                 ∇f = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg),
-                                                             eltype(x),
-                                                             F)
+                    eltype(x),
+                    F)
             end
 
             iszero(F) &&
                 return SciMLBase.build_solution(prob, alg, x, F;
-                                                retcode = ReturnCode.Success)
+                    retcode = ReturnCode.Success)
 
             # Update the trust region radius.
             if r > η₃ && norm(δ) ≈ Δ
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 1a0249b65..e1d6f9bf8 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -18,7 +18,7 @@ for mode in instances(NLSolveTerminationMode.T)
     end
 
     termination_condition = NLSolveTerminationCondition(mode; abstol = nothing,
-                                                        reltol = nothing)
+        reltol = nothing)
     push!(BROYDEN_SOLVERS, Broyden(; batched = false, termination_condition))
     push!(BATCHED_BROYDEN_SOLVERS, Broyden(; batched = true, termination_condition))
     push!(LBROYDEN_SOLVERS, LBroyden(; batched = false, termination_condition))
@@ -131,7 +131,7 @@ using ForwardDiff
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
 for alg in (SimpleNewtonRaphson(), LBroyden(), Klement(), SimpleTrustRegion(),
-            SimpleDFSane(), Halley(), BROYDEN_SOLVERS...)
+    SimpleDFSane(), Halley(), BROYDEN_SOLVERS...)
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
         sol = solve(probN, alg, abstol = 1e-9)
@@ -154,7 +154,7 @@ end
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
 for alg in (SimpleNewtonRaphson(), Klement(), SimpleTrustRegion(),
-            SimpleDFSane(), Halley(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
+    SimpleDFSane(), Halley(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
@@ -251,7 +251,7 @@ for alg in [Bisection(), Falsi(), Ridder(), Brent()]
 end
 
 for alg in (SimpleNewtonRaphson(), Klement(), SimpleTrustRegion(),
-            SimpleDFSane(), Halley(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
+    SimpleDFSane(), Halley(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -267,10 +267,10 @@ f, u0 = (u, p) -> u .* u .- 2.0, @SVector[1.0, 1.0]
 probN = NonlinearProblem(f, u0)
 
 for alg in (SimpleNewtonRaphson(), SimpleNewtonRaphson(; autodiff = false),
-            SimpleTrustRegion(),
-            SimpleTrustRegion(; autodiff = false), Halley(), Halley(; autodiff = false),
-            Klement(), SimpleDFSane(),
-            BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
+    SimpleTrustRegion(),
+    SimpleTrustRegion(; autodiff = false), Halley(), Halley(; autodiff = false),
+    Klement(), SimpleDFSane(),
+    BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
     sol = solve(probN, alg)
 
     @test sol.retcode == ReturnCode.Success
@@ -284,8 +284,8 @@ for u0 in [1.0, [1, 1.0]]
     sol = sqrt(2) * u0
 
     for alg in (SimpleNewtonRaphson(), SimpleNewtonRaphson(; autodiff = false),
-                SimpleTrustRegion(), SimpleTrustRegion(; autodiff = false), Klement(),
-                SimpleDFSane(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
+        SimpleTrustRegion(), SimpleTrustRegion(; autodiff = false), Klement(),
+        SimpleDFSane(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
         sol2 = solve(probN, alg)
 
         @test sol2.retcode == ReturnCode.Success
@@ -399,18 +399,18 @@ expand_factor = [1.5, 2.0, 3.0]
 max_shrink_times = [10, 20, 30]
 
 list_of_options = zip(max_trust_radius, initial_trust_radius, step_threshold,
-                      shrink_threshold, expand_threshold, shrink_factor,
-                      expand_factor, max_shrink_times)
+    shrink_threshold, expand_threshold, shrink_factor,
+    expand_factor, max_shrink_times)
 for options in list_of_options
     local probN, sol, alg
     alg = SimpleTrustRegion(max_trust_radius = options[1],
-                            initial_trust_radius = options[2],
-                            step_threshold = options[3],
-                            shrink_threshold = options[4],
-                            expand_threshold = options[5],
-                            shrink_factor = options[6],
-                            expand_factor = options[7],
-                            max_shrink_times = options[8])
+        initial_trust_radius = options[2],
+        step_threshold = options[3],
+        shrink_threshold = options[4],
+        expand_threshold = options[5],
+        shrink_factor = options[6],
+        expand_factor = options[7],
+        max_shrink_times = options[8])
 
     probN = NonlinearProblem(f, u0, p)
     sol = solve(probN, alg)
@@ -454,18 +454,18 @@ nexp = [2, 1, 2]
 ]
 
 list_of_options = zip(σ_min, σ_max, σ_1, M, γ, τ_min, τ_max, nexp,
-                      η_strategy)
+    η_strategy)
 for options in list_of_options
     local probN, sol, alg
     alg = SimpleDFSane(σ_min = options[1],
-                       σ_max = options[2],
-                       σ_1 = options[3],
-                       M = options[4],
-                       γ = options[5],
-                       τ_min = options[6],
-                       τ_max = options[7],
-                       nexp = options[8],
-                       η_strategy = options[9])
+        σ_max = options[2],
+        σ_1 = options[3],
+        M = options[4],
+        γ = options[5],
+        τ_min = options[6],
+        τ_max = options[7],
+        nexp = options[8],
+        η_strategy = options[9])
 
     probN = NonlinearProblem(f, u0, p)
     sol = solve(probN, alg)
@@ -495,7 +495,9 @@ end
 
 f, u0 = (u, p) -> u .* u .- p, randn(3)
 
-f_jac(u, p) = begin diagm(2 * u) end
+f_jac(u, p) = begin
+    diagm(2 * u)
+end
 
 p = [2.0, 1.0, 5.0];
 
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 7269ed6bf..94a0086e4 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -6,7 +6,9 @@ const GROUP = get(ENV, "GROUP", "All")
 const is_APPVEYOR = Sys.iswindows() && haskey(ENV, "APPVEYOR")
 
 @time begin
-
-if GROUP == "All" || GROUP == "Core"
-    @time @safetestset "Basic Tests + Some AD" begin include("basictests.jl") end
-end end
+    if GROUP == "All" || GROUP == "Core"
+        @time @safetestset "Basic Tests + Some AD" begin
+            include("basictests.jl")
+        end
+    end
+end

From 31820602e7051f74232dbbe15120b858ba75419b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 8 Jun 2023 17:17:23 -0400
Subject: [PATCH 122/700] Batched DFSane

---
 lib/SimpleNonlinearSolve/Project.toml       |   2 +-
 lib/SimpleNonlinearSolve/src/dfsane.jl      | 174 +++++++++++++++-----
 lib/SimpleNonlinearSolve/test/basictests.jl |  12 +-
 3 files changed, 142 insertions(+), 46 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index c1f21c72e..cf5a675af 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.15"
+version = "0.1.16"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index e898f060b..388ebfe89 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -1,9 +1,12 @@
 """
-```julia
-SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
-             M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
-             nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 / k^2)
-```
+    SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
+        M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
+        nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2,
+        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+            abstol = nothing,
+            reltol = nothing),
+        batched::Bool = false,
+        max_inner_iterations::Int = 1000)
 
 A low-overhead implementation of the df-sane method for solving large-scale nonlinear
 systems of equations. For in depth information about all the parameters and the algorithm,
@@ -39,8 +42,16 @@ Computation, 75, 1429-1448.](https://www.researchgate.net/publication/220576479_
   ``f_1=||F(x_1)||^{nexp}``, `k` is the iteration number, `x` is the current `x`-value and
   `F` the current residual. Should satisfy ``η_k > 0`` and ``∑ₖ ηₖ < ∞``. Defaults to
   ``||F||^2 / k^2``.
+- `termination_condition`: a `NLSolveTerminationCondition` that determines when the solver
+  should terminate. Defaults to `NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+  abstol = nothing, reltol = nothing)`.
+- `batched`: if `true`, the algorithm will use a batched version of the algorithm that treats each
+  column of `x` as a separate problem. This can be useful nonlinear problems involing neural
+  networks. Defaults to `false`.
+- `max_inner_iterations`: the maximum number of iterations allowed for the inner loop of the
+  algorithm. Used exclusively in `batched` mode. Defaults to `1000`.
 """
-struct SimpleDFSane{T} <: AbstractSimpleNonlinearSolveAlgorithm
+struct SimpleDFSane{batched, T, TC} <: AbstractSimpleNonlinearSolveAlgorithm
     σ_min::T
     σ_max::T
     σ_1::T
@@ -50,23 +61,49 @@ struct SimpleDFSane{T} <: AbstractSimpleNonlinearSolveAlgorithm
     τ_max::T
     nexp::Int
     η_strategy::Function
+    termination_condition::TC
+    max_inner_iterations::Int
 
     function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
         M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
-        nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 / k^2)
-        new{typeof(σ_min)}(σ_min, σ_max, σ_1, M, γ, τ_min, τ_max, nexp, η_strategy)
+        nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2,
+        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+            abstol = nothing,
+            reltol = nothing),
+        batched::Bool = false,
+        max_inner_iterations = 1000)
+        return new{batched, typeof(σ_min), typeof(termination_condition)}(σ_min,
+            σ_max,
+            σ_1,
+            M,
+            γ,
+            τ_min,
+            τ_max,
+            nexp,
+            η_strategy,
+            termination_condition,
+            max_inner_iterations)
     end
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane,
+function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{batched},
     args...; abstol = nothing, reltol = nothing, maxiters = 1000,
-    kwargs...)
+    kwargs...) where {batched}
+    tc = alg.termination_condition
+    mode = DiffEqBase.get_termination_mode(tc)
+
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
+
+    if batched
+        batch_size = size(x, 2)
+    end
+
     T = eltype(x)
     σ_min = float(alg.σ_min)
     σ_max = float(alg.σ_max)
-    σ_k = float(alg.σ_1)
+    σ_k = batched ? fill(float(alg.σ_1), 1, batch_size) : float(alg.σ_1)
+
     M = alg.M
     γ = float(alg.γ)
     τ_min = float(alg.τ_min)
@@ -74,74 +111,123 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane,
     nexp = alg.nexp
     η_strategy = alg.η_strategy
 
+    batched && @assert ndims(x)==2 "Batched SimpleDFSane only supports 2D arrays"
+
     if SciMLBase.isinplace(prob)
         error("SimpleDFSane currently only supports out-of-place nonlinear problems")
     end
 
     atol = abstol !== nothing ? abstol :
-           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
-    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
+           (tc.abstol !== nothing ? tc.abstol :
+            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5))
+    rtol = reltol !== nothing ? reltol :
+           (tc.reltol !== nothing ? tc.reltol : eps(real(one(eltype(T))))^(4 // 5))
+
+    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
+        error("SimpleDFSane currently doesn't support SAFE_BEST termination modes")
+    end
+
+    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? NLSolveSafeTerminationResult() :
+              nothing
+    termination_condition = tc(storage)
 
     function ff(x)
         F = f(x)
-        f_k = norm(F)^nexp
+        f_k = if batched
+            sum(abs2, F; dims = 1) .^ (nexp / 2)
+        else
+            norm(F)^nexp
+        end
         return f_k, F
     end
 
+    function generate_history(f_k, M)
+        if batched
+            history = similar(f_k, (M, length(f_k)))
+            history .= reshape(f_k, 1, :)
+            return history
+        else
+            return fill(f_k, M)
+        end
+    end
+
     f_k, F_k = ff(x)
     α_1 = convert(T, 1.0)
     f_1 = f_k
-    history_f_k = fill(f_k, M)
+    history_f_k = generate_history(f_k, M)
 
     for k in 1:maxiters
-        iszero(F_k) &&
-            return SciMLBase.build_solution(prob, alg, x, F_k;
-                retcode = ReturnCode.Success)
-
         # Spectral parameter range check
-        if abs(σ_k) > σ_max
-            σ_k = sign(σ_k) * σ_max
-        elseif abs(σ_k) < σ_min
-            σ_k = sign(σ_k) * σ_min
+        if batched
+            @. σ_k = sign(σ_k) * clamp(abs(σ_k), σ_min, σ_max)
+        else
+            σ_k = sign(σ_k) * clamp(abs(σ_k), σ_min, σ_max)
         end
 
         # Line search direction
-        d = -σ_k * F_k
+        d = -σ_k .* F_k
 
         η = η_strategy(f_1, k, x, F_k)
-        f̄ = maximum(history_f_k)
+        f̄ = batched ? maximum(history_f_k; dims = 1) : maximum(history_f_k)
         α_p = α_1
         α_m = α_1
-        x_new = x + α_p * d
+        x_new = @. x + α_p * d
+
         f_new, F_new = ff(x_new)
+
+        inner_iterations = 0
         while true
-            if f_new ≤ f̄ + η - γ * α_p^2 * f_k
-                break
+            inner_iterations += 1
+
+            if batched
+                # NOTE: This is simply a heuristic, ideally we check using `all` but that is
+                #       typically very expensive for large problems
+                norm(f_new) ≤ norm(@. f̄ + η - γ * α_p^2 * f_k) && break
+            else
+                f_new ≤ f̄ + η - γ * α_p^2 * f_k && break
             end
 
-            α_tp = α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
-            x_new = x - α_m * d
+            α_tp = @. α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
+            x_new = @. x - α_m * d
             f_new, F_new = ff(x_new)
 
-            if f_new ≤ f̄ + η - γ * α_m^2 * f_k
-                break
+            if batched
+                # NOTE: This is simply a heuristic, ideally we check using `all` but that is
+                #       typically very expensive for large problems
+                norm(f_new) ≤ norm(@. f̄ + η - γ * α_p^2 * f_k) && break
+            else
+                f_new ≤ f̄ + η - γ * α_p^2 * f_k && break
             end
 
-            α_tm = α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
-            α_p = min(τ_max * α_p, max(α_tp, τ_min * α_p))
-            α_m = min(τ_max * α_m, max(α_tm, τ_min * α_m))
-            x_new = x + α_p * d
+            α_tm = @. α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
+            α_p = @. clamp(α_tp, τ_min * α_p, τ_max * α_p)
+            α_m = @. clamp(α_tm, τ_min * α_m, τ_max * α_m)
+            x_new = @. x + α_p * d
             f_new, F_new = ff(x_new)
+
+            # NOTE: The original algorithm runs till either condition is satisfied, however,
+            #       for most batched problems like neural networks we only care about
+            #       approximate convergence
+            batched && (inner_iterations ≥ alg.max_inner_iterations) && break
         end
 
-        if isapprox(x_new, x, atol = atol, rtol = rtol)
-            return SciMLBase.build_solution(prob, alg, x_new, F_new;
+        if termination_condition(F_new, x_new, x, atol, rtol)
+            return SciMLBase.build_solution(prob,
+                alg,
+                x_new,
+                F_new;
                 retcode = ReturnCode.Success)
         end
+
         # Update spectral parameter
-        s_k = x_new - x
-        y_k = F_new - F_k
-        σ_k = (s_k' * s_k) / (s_k' * y_k)
+        s_k = @. x_new - x
+        y_k = @. F_new - F_k
+
+        if batched
+            σ_k = sum(abs2, s_k; dims = 1) ./ (sum(s_k .* y_k; dims = 1) .+ T(1e-5))
+        else
+            σ_k = (s_k' * s_k) / (s_k' * y_k)
+        end
 
         # Take step
         x = x_new
@@ -149,7 +235,11 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane,
         f_k = f_new
 
         # Store function value
-        history_f_k[k % M + 1] = f_new
+        if batched
+            history_f_k[k % M + 1, :] .= vec(f_new)
+        else
+            history_f_k[k % M + 1] = f_new
+        end
     end
     return SciMLBase.build_solution(prob, alg, x, F_k; retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index e1d6f9bf8..aea173157 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -9,6 +9,8 @@ const BATCHED_BROYDEN_SOLVERS = Broyden[]
 const BROYDEN_SOLVERS = Broyden[]
 const BATCHED_LBROYDEN_SOLVERS = LBroyden[]
 const LBROYDEN_SOLVERS = LBroyden[]
+const BATCHED_DFSANE_SOLVERS = SimpleDFSane[]
+const DFSANE_SOLVERS = SimpleDFSane[]
 
 for mode in instances(NLSolveTerminationMode.T)
     if mode ∈
@@ -23,6 +25,8 @@ for mode in instances(NLSolveTerminationMode.T)
     push!(BATCHED_BROYDEN_SOLVERS, Broyden(; batched = true, termination_condition))
     push!(LBROYDEN_SOLVERS, LBroyden(; batched = false, termination_condition))
     push!(BATCHED_LBROYDEN_SOLVERS, LBroyden(; batched = true, termination_condition))
+    push!(DFSANE_SOLVERS, SimpleDFSane(; batched = false, termination_condition))
+    push!(BATCHED_DFSANE_SOLVERS, SimpleDFSane(; batched = true, termination_condition))
 end
 
 # SimpleNewtonRaphson
@@ -484,11 +488,13 @@ sol = solve(probN, Broyden(batched = true))
 
 @test abs.(sol.u) ≈ sqrt.(p)
 
-for alg in (BATCHED_BROYDEN_SOLVERS..., BATCHED_LBROYDEN_SOLVERS...)
-    sol = solve(probN, alg)
+for alg in (BATCHED_BROYDEN_SOLVERS...,
+    BATCHED_LBROYDEN_SOLVERS...,
+    BATCHED_DFSANE_SOLVERS...)
+    sol = solve(probN, alg; abstol = 1e-3, reltol = 1e-3)
 
     @test sol.retcode == ReturnCode.Success
-    @test abs.(sol.u) ≈ sqrt.(p)
+    @test abs.(sol.u)≈sqrt.(p) atol=1e-3 rtol=1e-3
 end
 
 ## User specified Jacobian

From 044b7431ea07b8beb79808e65eb455636593ef0b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 21 Jun 2023 12:40:57 -0400
Subject: [PATCH 123/700] Reuse criteria computation

---
 lib/SimpleNonlinearSolve/src/dfsane.jl | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index 388ebfe89..b5e2b8200 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -180,11 +180,13 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{batched},
             inner_iterations += 1
 
             if batched
+                criteria = @. f̄ + η - γ * α_p^2 * f_k
                 # NOTE: This is simply a heuristic, ideally we check using `all` but that is
                 #       typically very expensive for large problems
-                norm(f_new) ≤ norm(@. f̄ + η - γ * α_p^2 * f_k) && break
+                (sum(f_new .≤ criteria) ≥ batch_size ÷ 2) && break
             else
-                f_new ≤ f̄ + η - γ * α_p^2 * f_k && break
+                criteria = f̄ + η - γ * α_p^2 * f_k
+                f_new ≤ criteria && break
             end
 
             α_tp = @. α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
@@ -194,9 +196,9 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{batched},
             if batched
                 # NOTE: This is simply a heuristic, ideally we check using `all` but that is
                 #       typically very expensive for large problems
-                norm(f_new) ≤ norm(@. f̄ + η - γ * α_p^2 * f_k) && break
+                (sum(f_new .≤ criteria) ≥ batch_size ÷ 2) && break
             else
-                f_new ≤ f̄ + η - γ * α_p^2 * f_k && break
+                f_new ≤ criteria && break
             end
 
             α_tm = @. α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)

From feeb4386a1401178a0105ea762cae6e544d5f2c5 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Wed, 21 Jun 2023 23:49:30 +0200
Subject: [PATCH 124/700] itp method begin

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 1 +
 lib/SimpleNonlinearSolve/src/itp.jl                  | 0
 2 files changed, 1 insertion(+)
 create mode 100644 lib/SimpleNonlinearSolve/src/itp.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 8749aa72b..5074d449d 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -41,6 +41,7 @@ include("dfsane.jl")
 include("ad.jl")
 include("halley.jl")
 include("alefeld.jl")
+include("itp.jl")
 
 import PrecompileTools
 
diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
new file mode 100644
index 000000000..e69de29bb

From c3132f0d9a015d186049ab5d364730859c796a00 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Fri, 23 Jun 2023 02:10:44 +0200
Subject: [PATCH 125/700] ipt alg

---
 lib/SimpleNonlinearSolve/src/itp.jl | 31 +++++++++++++++++++++++++++++
 1 file changed, 31 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index e69de29bb..49a565628 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -0,0 +1,31 @@
+"""
+```julia
+Itp(; k1 = Val{1}(), k2 = Val{2}(), n0 = Val{1}())
+```
+ITP (Interpolate Truncate & Project)
+
+
+"""
+
+struct Itp <: AbstractBracketingAlgorithm
+    k1::Real
+    k2::Real
+    n0::Int
+end
+
+function Itp(k1::Real = Val{1}(), k2::Real = Val{2}(), n0::Int = Val{1}())
+    if k1 < 0
+        ArgumentError("Hyper-parameter κ₁ should not be negative")
+    end
+    if !isa(n0, Int)
+        ArgumentError("Hyper-parameter n₀ should be an Integer")
+    end
+    Itp(k1, k2, n0)
+end
+
+function SciMLBase.__solve(prob::NonlinearProblem, alg::Itp,
+                            args..., abstol = nothing, reltol = nothing, 
+                            maxiters = 1000, kwargs...)
+
+                               
+end
\ No newline at end of file

From ab87f17a789f179366a0f276c8c0bb1a209b7de7 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Tue, 27 Jun 2023 01:26:46 +0200
Subject: [PATCH 126/700] minor fix

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 5074d449d..8177dd2e6 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -74,6 +74,6 @@ end
 
 # DiffEq styled algorithms
 export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, Halley, Klement,
-    Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld
+    Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld, Itp
 
 end # module

From c3dab197778a1c5bf663475b123093fb5cec311c Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Tue, 27 Jun 2023 02:33:25 +0200
Subject: [PATCH 127/700] defined cache

---
 lib/SimpleNonlinearSolve/src/itp.jl | 31 ++++++++++++++++++++++++++++-
 1 file changed, 30 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 49a565628..ff848484d 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -23,9 +23,38 @@ function Itp(k1::Real = Val{1}(), k2::Real = Val{2}(), n0::Int = Val{1}())
     Itp(k1, k2, n0)
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::Itp,
+function SciMLBase.__solve(prob::IntervalNonlinearProblem, alg::Itp,
                             args..., abstol = nothing, reltol = nothing, 
                             maxiters = 1000, kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    left, right = prob.tspan # a and b
+    fl, fr = f(left), f(right)
+    ϵ = abstol
+    if iszero(fl)
+        return SciMLBase.build_solution(prob, alg, left, fl;
+            retcode = ReturnCode.ExactSolutionLeft, left = left,
+            right = right)
+    end
+
+    if iszero(fr)
 
+    end
+    #defining variables/cache
+    k1 = alg.k1
+    k2 = alg.k2
+    n0 = alg.k3
+    n_h = ceil(log2((right - left) / (2 * ϵ)))
+    n_max = n_h + n0
+    mid = (left + right) / 2
+    x_f = (fr * left - fl * right) / (fr - fl)
+    r = zero(left)
+    δ = zero(left)
+    σ = sign(mid - x_f)
+    i = 0 #iteration
+    while i <= maxiters
+        mid = (left + right) / 2
+        r = ϵ * 2 ^ (n_max - i) - ((right - left) / 2)
+        δ = k1 * (right - left) ^ k2
+    end
                                
 end
\ No newline at end of file

From c1da36d6fa0d3fab0e1a2cf57e1fa92364c08d9c Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Tue, 27 Jun 2023 03:01:21 +0200
Subject: [PATCH 128/700] complete alg

---
 lib/SimpleNonlinearSolve/src/itp.jl | 51 ++++++++++++++++++++++++++---
 1 file changed, 47 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index ff848484d..2df125a74 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -47,14 +47,57 @@ function SciMLBase.__solve(prob::IntervalNonlinearProblem, alg::Itp,
     n_max = n_h + n0
     mid = (left + right) / 2
     x_f = (fr * left - fl * right) / (fr - fl)
-    r = zero(left)
-    δ = zero(left)
-    σ = sign(mid - x_f)
+    xt = left
+    xp = left
+    r = zero(left) #minmax radius
+    δ = zero(left) # truncation error
+    σ = 1.0
     i = 0 #iteration
     while i <= maxiters
-        mid = (left + right) / 2
+        #mid = (left + right) / 2
         r = ϵ * 2 ^ (n_max - i) - ((right - left) / 2)
         δ = k1 * (right - left) ^ k2
+
+        ## Interpolation step ##
+        x_f =  (fr * left - fl * right) / (fr - fl)
+
+        ## Truncation step ##
+        σ = sign(mid - x_f)
+        if δ <= abs(mid - x_f)
+            xt = x_f + (σ * δ)
+        else
+            xt = mid
+        end
+
+        ## Projection step ##
+        if abs(xt - mid) <= r
+            xp = xt
+        else
+            xp = mid - (σ * r)
+        end
+
+        ## Update ##
+        yp = f(xp)
+        if yp > 0
+            right = xp
+            fr = yp
+        elseif yp < 0
+            left = xp
+            fl = yp
+        else
+            left = xp
+            right = xp
+        end
+        i += 1
+        mid = (left + right) / 2
+
+        if (right - left < 2 * ϵ)
+            return SciMLBase.build_solution(prob, alg, mid, fl;
+            retcode = ReturnCode.Success, left = left,
+            right = right)
+        end
     end
+    return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
+        left = left, right = right)
                                
 end
\ No newline at end of file

From 6b9dee4d1c0cb4d087f2b5b909ab4c731d275b88 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Tue, 27 Jun 2023 03:09:56 +0200
Subject: [PATCH 129/700] hyperparams checks

---
 lib/SimpleNonlinearSolve/src/itp.jl | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 2df125a74..853c3aa77 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -20,7 +20,13 @@ function Itp(k1::Real = Val{1}(), k2::Real = Val{2}(), n0::Int = Val{1}())
     if !isa(n0, Int)
         ArgumentError("Hyper-parameter n₀ should be an Integer")
     end
-    Itp(k1, k2, n0)
+    if n0 < 0
+        ArgumentError("Hyper-parameter n₀ should not be negative")
+    end
+    if k2 < 1 || k2 > (1.5 + sqrt(5) / 2)
+        ArgumentError("Hyper-parameter κ₂ should be between 1 and 1 + ϕ where ϕ ≈ 1.618... is the golden ratio")
+    end
+    return Itp(k1, k2, n0)
 end
 
 function SciMLBase.__solve(prob::IntervalNonlinearProblem, alg::Itp,

From f6702fcce1c95bd0c4219419b06fa0692018522f Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Tue, 27 Jun 2023 03:16:58 +0200
Subject: [PATCH 130/700] abstol fix

---
 lib/SimpleNonlinearSolve/src/itp.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 853c3aa77..8eed6d92c 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -30,7 +30,7 @@ function Itp(k1::Real = Val{1}(), k2::Real = Val{2}(), n0::Int = Val{1}())
 end
 
 function SciMLBase.__solve(prob::IntervalNonlinearProblem, alg::Itp,
-                            args..., abstol = nothing, reltol = nothing, 
+                            args..., abstol = 1e-8, reltol = nothing, 
                             maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan # a and b

From 483a6d7da6f8c21c499f92ccbc992c43d6656821 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Tue, 27 Jun 2023 03:24:00 +0200
Subject: [PATCH 131/700] right retcode

---
 lib/SimpleNonlinearSolve/src/itp.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 8eed6d92c..014e321ca 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -40,10 +40,10 @@ function SciMLBase.__solve(prob::IntervalNonlinearProblem, alg::Itp,
         return SciMLBase.build_solution(prob, alg, left, fl;
             retcode = ReturnCode.ExactSolutionLeft, left = left,
             right = right)
-    end
-
-    if iszero(fr)
-
+    elseif iszero(fr)
+        return SciMLBase.build_solution(prob, alg, right, fr;
+            retcode = ReturnCode.ExactSolutionRight, left = left,
+            right = right)
     end
     #defining variables/cache
     k1 = alg.k1

From 603106b7d70cfc9b1aa4855c4eb5305495505c4d Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Wed, 28 Jun 2023 03:25:27 +0200
Subject: [PATCH 132/700] update SimpleNonlinearSolve.jl

---
 .../src/SimpleNonlinearSolve.jl               |  2 +-
 lib/SimpleNonlinearSolve/src/itp.jl           | 31 +++++++++----------
 2 files changed, 16 insertions(+), 17 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 8177dd2e6..ca787c245 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -66,7 +66,7 @@ PrecompileTools.@compile_workload begin
         prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p,
             T.((0.0, 2.0)),
             T(2))
-        for alg in (Bisection, Falsi, Ridder, Brent, Alefeld)
+        for alg in (Bisection, Falsi, Ridder, Brent, Alefeld, Itp)
             solve(prob_brack, alg(), abstol = T(1e-2))
         end
     end
diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 014e321ca..085f80f53 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -11,26 +11,25 @@ struct Itp <: AbstractBracketingAlgorithm
     k1::Real
     k2::Real
     n0::Int
-end
-
-function Itp(k1::Real = Val{1}(), k2::Real = Val{2}(), n0::Int = Val{1}())
-    if k1 < 0
-        ArgumentError("Hyper-parameter κ₁ should not be negative")
-    end
-    if !isa(n0, Int)
-        ArgumentError("Hyper-parameter n₀ should be an Integer")
-    end
-    if n0 < 0
-        ArgumentError("Hyper-parameter n₀ should not be negative")
-    end
-    if k2 < 1 || k2 > (1.5 + sqrt(5) / 2)
-        ArgumentError("Hyper-parameter κ₂ should be between 1 and 1 + ϕ where ϕ ≈ 1.618... is the golden ratio")
+    function Itp(;k1::Real = 0.1, k2::Real = 2.0, n0::Int = 1)
+        if k1 < 0
+            ArgumentError("Hyper-parameter κ₁ should not be negative")
+        end
+        if !isa(n0, Int)
+            ArgumentError("Hyper-parameter n₀ should be an Integer")
+        end
+        if n0 < 0
+            ArgumentError("Hyper-parameter n₀ should not be negative")
+        end
+        if k2 < 1 || k2 > (1.5 + sqrt(5) / 2)
+            ArgumentError("Hyper-parameter κ₂ should be between 1 and 1 + ϕ where ϕ ≈ 1.618... is the golden ratio")
+        end
+        return new(k1, k2, n0)
     end
-    return Itp(k1, k2, n0)
 end
 
 function SciMLBase.__solve(prob::IntervalNonlinearProblem, alg::Itp,
-                            args..., abstol = 1e-8, reltol = nothing, 
+                            args...; abstol = nothing,
                             maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan # a and b

From 8882c457c4f66ad6cf8ddc69d3032cea1809a64a Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 28 Jun 2023 09:00:35 -0400
Subject: [PATCH 133/700] Update src/itp.jl

---
 lib/SimpleNonlinearSolve/src/itp.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 085f80f53..bd5f888dd 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -28,7 +28,7 @@ struct Itp <: AbstractBracketingAlgorithm
     end
 end
 
-function SciMLBase.__solve(prob::IntervalNonlinearProblem, alg::Itp,
+function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
                             args...; abstol = nothing,
                             maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)

From a4069d2e3180b773c205a3faaff624df4d4b15ef Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 27 Jun 2023 11:21:41 -0400
Subject: [PATCH 134/700] Use PackageExtensionCompat

---
 lib/SimpleNonlinearSolve/Project.toml                | 10 +++++-----
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 11 ++---------
 2 files changed, 7 insertions(+), 14 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index cf5a675af..d2551032d 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -9,10 +9,10 @@ DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+PackageExtensionCompat = "65ce6f38-6b18-4e1d-a461-8949797d7930"
+PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
-Requires = "ae029012-a4dd-5104-9daa-d747884805df"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
-PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [weakdeps]
@@ -23,14 +23,14 @@ SimpleBatchedNonlinearSolveExt = "NNlib"
 
 [compat]
 ArrayInterface = "6, 7"
-DiffEqBase = "6.123.0"
+DiffEqBase = "6.126"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 NNlib = "0.8"
+PackageExtensionCompat = "1"
+PrecompileTools = "1"
 Reexport = "0.2, 1"
-Requires = "1"
 SciMLBase = "1.73"
-PrecompileTools = "1"
 StaticArraysCore = "1.4"
 julia = "1.6"
 
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 8749aa72b..97ce20379 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -10,16 +10,9 @@ using DiffEqBase
 
 @reexport using SciMLBase
 
-if !isdefined(Base, :get_extension)
-    using Requires
-end
-
+using PackageExtensionCompat
 function __init__()
-    @static if !isdefined(Base, :get_extension)
-        @require NNlib="872c559c-99b0-510c-b3b7-b6c96a88d5cd" begin
-            include("../ext/SimpleBatchedNonlinearSolveExt.jl")
-        end
-    end
+    @require_extensions
 end
 
 abstract type AbstractSimpleNonlinearSolveAlgorithm <: SciMLBase.AbstractNonlinearAlgorithm end

From 4e2de7a1877b05dda15fa16b4d03681e79fb1c3e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 27 Jun 2023 11:51:36 -0400
Subject: [PATCH 135/700] Rework BatchedBroyden to be more efficient

---
 lib/SimpleNonlinearSolve/Project.toml         |   4 +-
 .../ext/SimpleBatchedNonlinearSolveExt.jl     | 120 ++++++++----------
 .../src/SimpleNonlinearSolve.jl               |   9 ++
 .../src/batched/broyden.jl                    |  20 +++
 .../src/batched/dfsane.jl                     |   0
 .../src/batched/lbroyden.jl                   |   0
 .../src/batched/raphson.jl                    |   0
 lib/SimpleNonlinearSolve/src/batched/utils.jl |  78 ++++++++++++
 lib/SimpleNonlinearSolve/src/broyden.jl       |  16 +--
 lib/SimpleNonlinearSolve/test/basictests.jl   |  12 +-
 10 files changed, 176 insertions(+), 83 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/batched/broyden.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/batched/dfsane.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/batched/raphson.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/batched/utils.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index d2551032d..b1b3a422c 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.16"
+version = "0.1.17"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
@@ -26,7 +26,7 @@ ArrayInterface = "6, 7"
 DiffEqBase = "6.126"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
-NNlib = "0.8"
+NNlib = "0.8, 0.9"
 PackageExtensionCompat = "1"
 PrecompileTools = "1"
 Reexport = "0.2, 1"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
index dd7628888..9e1ba59ad 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
@@ -1,90 +1,76 @@
 module SimpleBatchedNonlinearSolveExt
 
-using ArrayInterface, DiffEqBase, LinearAlgebra, SimpleNonlinearSolve, SciMLBase
+using ArrayInterface, DiffEqBase, LinearAlgebra, SimpleNonlinearSolve, SciMLBase, NNlib
+import SimpleNonlinearSolve: _construct_batched_problem_structure, _get_storage, _init_𝓙, _result_from_storage, _get_tolerance, @maybeinplace
 
-isdefined(Base, :get_extension) ? (using NNlib) : (using ..NNlib)
+@views function SciMLBase.__solve(prob::NonlinearProblem,
+    alg::BatchedBroyden;
+    abstol=nothing,
+    reltol=nothing,
+    maxiters=1000,
+    kwargs...)
+    iip = isinplace(prob)
+    u0 = prob.u0
 
-_batch_transpose(x) = reshape(x, 1, size(x)...)
+    u, f, reconstruct = _construct_batched_problem_structure(prob)
+    L, N = size(u)
 
-_batched_mul(x, y) = x * y
-
-function _batched_mul(x::AbstractArray{T, 3}, y::AbstractMatrix) where {T}
-    return dropdims(batched_mul(x, reshape(y, size(y, 1), 1, size(y, 2))); dims = 2)
-end
-
-function _batched_mul(x::AbstractMatrix, y::AbstractArray{T, 3}) where {T}
-    return batched_mul(reshape(x, size(x, 1), 1, size(x, 2)), y)
-end
-
-function _batched_mul(x::AbstractArray{T1, 3}, y::AbstractArray{T2, 3}) where {T1, T2}
-    return batched_mul(x, y)
-end
-
-function _init_J_batched(x::AbstractMatrix{T}) where {T}
-    J = ArrayInterface.zeromatrix(x[:, 1])
-    if ismutable(x)
-        J[diagind(J)] .= one(eltype(x))
-    else
-        J += I
-    end
-    return repeat(J, 1, 1, size(x, 2))
-end
-
-function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{true}, args...;
-    abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
-    f = Base.Fix2(prob.f, prob.p)
-    x = float(prob.u0)
 
-    if ndims(x) != 2
-        error("`batch` mode works only if `ndims(prob.u0) == 2`")
-    end
+    storage = _get_storage(mode, u)
 
-    fₙ = f(x)
-    T = eltype(x)
-    J⁻¹ = _init_J_batched(x)
+    xₙ, xₙ₋₁, δx, δf = ntuple(_ -> copy(u), 4)
+    T = eltype(u)
 
-    if SciMLBase.isinplace(prob)
-        error("Broyden currently only supports out-of-place nonlinear problems")
-    end
+    atol = _get_tolerance(abstol, tc.abstol, T)
+    rtol = _get_tolerance(reltol, tc.reltol, T)
+    termination_condition = tc(storage)
 
-    atol = abstol !== nothing ? abstol :
-           (tc.abstol !== nothing ? tc.abstol :
-            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5))
-    rtol = reltol !== nothing ? reltol :
-           (tc.reltol !== nothing ? tc.reltol : eps(real(one(eltype(T))))^(4 // 5))
+    𝓙⁻¹ = _init_𝓙(xₙ)  # L × L × N
+    𝓙⁻¹f, xᵀ𝓙⁻¹δf, xᵀ𝓙⁻¹ = similar(𝓙⁻¹, L, N), similar(𝓙⁻¹, 1, N), similar(𝓙⁻¹, 1, L, N)
 
-    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-        error("Broyden currently doesn't support SAFE_BEST termination modes")
-    end
+    @maybeinplace iip fₙ₋₁=f(xₙ) u
+    iip && (fₙ = copy(fₙ₋₁))
+    for n in 1:maxiters
+        batched_mul!(reshape(𝓙⁻¹f, L, 1, N), 𝓙⁻¹, reshape(fₙ₋₁, L, 1, N))
+        xₙ .= xₙ₋₁ .- 𝓙⁻¹f
 
-    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? NLSolveSafeTerminationResult() :
-              nothing
-    termination_condition = tc(storage)
+        @maybeinplace iip fₙ=f(xₙ)
+        δx .= xₙ .- xₙ₋₁
+        δf .= fₙ .- fₙ₋₁
+
+        batched_mul!(reshape(𝓙⁻¹f, L, 1, N), 𝓙⁻¹, reshape(δf, L, 1, N))
+        δxᵀ = reshape(δx, 1, L, N)
 
-    xₙ = x
-    xₙ₋₁ = x
-    fₙ₋₁ = fₙ
-    for i in 1:maxiters
-        xₙ = xₙ₋₁ .- _batched_mul(J⁻¹, fₙ₋₁)
-        fₙ = f(xₙ)
-        Δxₙ = xₙ .- xₙ₋₁
-        Δfₙ = fₙ .- fₙ₋₁
-        J⁻¹Δfₙ = _batched_mul(J⁻¹, Δfₙ)
-        J⁻¹ += _batched_mul(((Δxₙ .- J⁻¹Δfₙ) ./
-                             (_batched_mul(_batch_transpose(Δxₙ), J⁻¹Δfₙ) .+ T(1e-5))),
-            _batched_mul(_batch_transpose(Δxₙ), J⁻¹))
+        batched_mul!(reshape(xᵀ𝓙⁻¹δf, 1, 1, N), δxᵀ, reshape(𝓙⁻¹f, L, 1, N))
+        batched_mul!(xᵀ𝓙⁻¹, δxᵀ, 𝓙⁻¹)
+        δx .= (δx .- 𝓙⁻¹f) ./ (xᵀ𝓙⁻¹δf .+ T(1e-5))
+        batched_mul!(𝓙⁻¹, reshape(δx, L, 1, N), xᵀ𝓙⁻¹, one(T), one(T))
 
         if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
+            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode)
+            return DiffEqBase.build_solution(prob,
+                alg,
+                reconstruct(xₙ),
+                reconstruct(fₙ);
+                retcode)
         end
 
-        xₙ₋₁ = xₙ
-        fₙ₋₁ = fₙ
+        xₙ₋₁ .= xₙ
+        fₙ₋₁ .= fₙ
+    end
+
+    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
+        xₙ = storage.u
+        @maybeinplace iip fₙ=f(xₙ)
     end
 
-    return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
+    return DiffEqBase.build_solution(prob,
+        alg,
+        reconstruct(xₙ),
+        reconstruct(fₙ);
+        retcode=ReturnCode.MaxIters)
 end
 
 end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 97ce20379..ab2033622 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -19,6 +19,7 @@ abstract type AbstractSimpleNonlinearSolveAlgorithm <: SciMLBase.AbstractNonline
 abstract type AbstractBracketingAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 abstract type AbstractNewtonAlgorithm{CS, AD, FDT} <: AbstractSimpleNonlinearSolveAlgorithm end
 abstract type AbstractImmutableNonlinearSolver <: AbstractSimpleNonlinearSolveAlgorithm end
+abstract type AbstractBatchedNonlinearSolveAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 
 include("utils.jl")
 include("bisection.jl")
@@ -35,6 +36,13 @@ include("ad.jl")
 include("halley.jl")
 include("alefeld.jl")
 
+# Batched Solver Support
+include("batched/utils.jl")
+include("batched/raphson.jl")
+include("batched/dfsane.jl")
+include("batched/broyden.jl")
+include("batched/lbroyden.jl")
+
 import PrecompileTools
 
 PrecompileTools.@compile_workload begin
@@ -67,5 +75,6 @@ end
 # DiffEq styled algorithms
 export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, Halley, Klement,
     Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld
+export BatchedBroyden
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/batched/broyden.jl b/lib/SimpleNonlinearSolve/src/batched/broyden.jl
new file mode 100644
index 000000000..a301c4e14
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/batched/broyden.jl
@@ -0,0 +1,20 @@
+"""
+    BatchedBroyden(;
+        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+            abstol = nothing,
+            reltol = nothing))
+
+A low-overhead batched implementation of Broyden capable of solving multiple nonlinear
+problems simultaneously.
+
+!!! note
+
+    To use this version, remember to load `NNlib`, i.e., `using NNlib` or
+    `import NNlib` must be present in your code.
+"""
+struct BatchedBroyden{TC <: NLSolveTerminationCondition} <:
+    AbstractBatchedNonlinearSolveAlgorithm
+    termination_condition::TC
+end
+
+# Implementation of solve using Package Extensions
diff --git a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl b/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/SimpleNonlinearSolve/src/batched/raphson.jl b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/SimpleNonlinearSolve/src/batched/utils.jl b/lib/SimpleNonlinearSolve/src/batched/utils.jl
new file mode 100644
index 000000000..9ed91345f
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/batched/utils.jl
@@ -0,0 +1,78 @@
+function _get_tolerance(η, tc_η, ::Type{T}) where {T}
+    fallback_η = real(oneunit(T)) * (eps(real(one(T))))^(4 // 5)
+    return ifelse(η !== nothing, η, ifelse(tc_η !== nothing, tc_η, fallback_η))
+end
+
+function _construct_batched_problem_structure(prob)
+    return _construct_batched_problem_structure(prob.u0,
+        prob.f,
+        prob.p,
+        Val(SciMLBase.isinplace(prob)))
+end
+
+function _construct_batched_problem_structure(u0::AbstractArray{T, N},
+    f,
+    p,
+    ::Val{iip}) where {T, N, iip}
+    # Reconstruct `u`
+    reconstruct = N == 2 ? identity : Base.Fix2(reshape, size(u0))
+    # Standardize `u`
+    standardize = N == 2 ? identity :
+                  (N == 1 ? Base.Fix2(reshape, (:, 1)) :
+                   Base.Fix2(reshape, (:, size(u0, ndims(u0)))))
+    # Updated Function
+    f_modified = if iip
+        function f_modified_iip(du, u)
+            f(reconstruct(du), reconstruct(u), p)
+            return standardize(du)
+        end
+    else
+        f_modified_oop(u) = standardize(f(reconstruct(u), p))
+    end
+    return standardize(u0), f_modified, reconstruct
+end
+
+@views function _init_𝓙(x::AbstractMatrix)
+    𝓙 = ArrayInterface.zeromatrix(x[:, 1])
+    if ismutable(x)
+        𝓙[diagind(𝓙)] .= one(eltype(x))
+    else
+        𝓙 .+= I
+    end
+    return repeat(𝓙, 1, 1, size(x, 2))
+end
+
+_result_from_storage(::Nothing, xₙ, fₙ, f, mode) = ReturnCode.Success, xₙ, fₙ
+function _result_from_storage(storage::NLSolveSafeTerminationResult, xₙ, fₙ, f, mode)
+    if storage.return_code == DiffEqBase.NLSolveSafeTerminationReturnCode.Success
+        return ReturnCode.Success, xₙ, fₙ
+    else
+        if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
+            return ReturnCode.Terminated, storage.u, f(storage.u)
+        else
+            return ReturnCode.Terminated, xₙ, fₙ
+        end
+    end
+end
+
+function _get_storage(mode, u)
+    return mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ?
+           NLSolveSafeTerminationResult(mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES ? u :
+                                        nothing) : nothing
+end
+
+macro maybeinplace(iip::Symbol, expr::Expr, u0::Union{Symbol, Nothing}=nothing)
+    @assert expr.head == :(=)
+    x1, x2 = expr.args
+    @assert x2.head == :call
+    f, x = x2.args
+    define_expr = u0 === nothing ? :() : :($(x1) = similar($(u0)))
+    return quote
+        if $(esc(iip))
+            $(esc(define_expr))
+            $(esc(f))($(esc(x1)), $(esc(x)))
+        else
+            $(esc(expr))
+        end
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 8ce0d66b5..56fa2efea 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -11,19 +11,19 @@ and static array problems.
     To use the `batched` version, remember to load `NNlib`, i.e., `using NNlib` or
     `import NNlib` must be present in your code.
 """
-struct Broyden{batched, TC <: NLSolveTerminationCondition} <:
+struct Broyden{TC <: NLSolveTerminationCondition} <:
        AbstractSimpleNonlinearSolveAlgorithm
     termination_condition::TC
+end
 
-    function Broyden(; batched = false,
-        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-            abstol = nothing,
-            reltol = nothing))
-        return new{batched, typeof(termination_condition)}(termination_condition)
-    end
+function Broyden(; batched = false,
+    termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+        abstol = nothing,
+        reltol = nothing))
+    return (batched ? BatchedBroyden : Broyden)(termination_condition)
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden{false}, args...;
+function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
     abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index aea173157..dd54527a5 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -5,12 +5,12 @@ using DiffEqBase
 using LinearAlgebra
 using Test
 
-const BATCHED_BROYDEN_SOLVERS = Broyden[]
-const BROYDEN_SOLVERS = Broyden[]
-const BATCHED_LBROYDEN_SOLVERS = LBroyden[]
-const LBROYDEN_SOLVERS = LBroyden[]
-const BATCHED_DFSANE_SOLVERS = SimpleDFSane[]
-const DFSANE_SOLVERS = SimpleDFSane[]
+const BATCHED_BROYDEN_SOLVERS = []
+const BROYDEN_SOLVERS = []
+const BATCHED_LBROYDEN_SOLVERS = []
+const LBROYDEN_SOLVERS = []
+const BATCHED_DFSANE_SOLVERS = []
+const DFSANE_SOLVERS = []
 
 for mode in instances(NLSolveTerminationMode.T)
     if mode ∈

From dcd54a77cde48207983ced207954319febf9dbca Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 27 Jun 2023 15:29:45 -0400
Subject: [PATCH 136/700] Add Batching to Newton Raphson

---
 lib/SimpleNonlinearSolve/Project.toml         |  9 +-
 .../SimpleNonlinearSolveADLinearSolveExt.jl   | 89 +++++++++++++++++++
 ...Ext.jl => SimpleNonlinearSolveNNlibExt.jl} | 12 ++-
 .../src/SimpleNonlinearSolve.jl               |  6 +-
 .../src/batched/raphson.jl                    | 24 +++++
 lib/SimpleNonlinearSolve/src/batched/utils.jl | 39 ++++----
 lib/SimpleNonlinearSolve/src/broyden.jl       | 11 ++-
 lib/SimpleNonlinearSolve/src/raphson.jl       | 42 +++++++--
 8 files changed, 195 insertions(+), 37 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
 rename lib/SimpleNonlinearSolve/ext/{SimpleBatchedNonlinearSolveExt.jl => SimpleNonlinearSolveNNlibExt.jl} (90%)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index b1b3a422c..901708505 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -16,16 +16,21 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [weakdeps]
+AbstractDifferentiation = "c29ec348-61ec-40c8-8164-b8c60e9d9f3d"
+LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 
 [extensions]
-SimpleBatchedNonlinearSolveExt = "NNlib"
+SimpleNonlinearSolveNNlibExt = "NNlib"
+SimpleNonlinearSolveADLinearSolveExt = ["AbstractDifferentiation", "LinearSolve"]
 
 [compat]
+AbstractDifferentiation = "0.5"
 ArrayInterface = "6, 7"
 DiffEqBase = "6.126"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
+LinearSolve = "2"
 NNlib = "0.8, 0.9"
 PackageExtensionCompat = "1"
 PrecompileTools = "1"
@@ -35,7 +40,9 @@ StaticArraysCore = "1.4"
 julia = "1.6"
 
 [extras]
+AbstractDifferentiation = "c29ec348-61ec-40c8-8164-b8c60e9d9f3d"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
new file mode 100644
index 000000000..96ba9168a
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
@@ -0,0 +1,89 @@
+module SimpleNonlinearSolveADLinearSolveExt
+
+using AbstractDifferentiation, ArrayInterface, DiffEqBase, LinearAlgebra, LinearSolve,
+    SimpleNonlinearSolve, SciMLBase
+import SimpleNonlinearSolve: _construct_batched_problem_structure, _get_storage, _result_from_storage, _get_tolerance, @maybeinplace
+
+const AD = AbstractDifferentiation
+
+function __init__()
+    SimpleNonlinearSolve.ADLinearSolveExtLoaded[] = true
+    return
+end
+
+function SimpleNonlinearSolve.SimpleBatchedNewtonRaphson(; chunk_size = Val{0}(),
+    autodiff = Val{true}(),
+    diff_type = Val{:forward},
+    termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+        abstol = nothing,
+        reltol = nothing))
+    # TODO: Use `diff_type`. FiniteDiff.jl is currently not available in AD.jl
+    chunksize = SciMLBase._unwrap_val(chunk_size) == 0 ? nothing : chunk_size
+    ad = SciMLBase._unwrap_val(autodiff) ?
+        AD.ForwardDiffBackend(; chunksize) :
+        AD.FiniteDifferencesBackend()
+    return SimpleBatchedNewtonRaphson{typeof(ad), Nothing, typeof(termination_condition)}(
+        ad,
+        nothing,
+        termination_condition)
+end
+
+function SciMLBase.__solve(prob::NonlinearProblem,
+    alg::SimpleBatchedNewtonRaphson;
+    abstol=nothing,
+    reltol=nothing,
+    maxiters=1000,
+    kwargs...)
+    iip = isinplace(prob)
+    @assert !iip "SimpleBatchedNewtonRaphson currently only supports out-of-place nonlinear problems."
+    u, f, reconstruct = _construct_batched_problem_structure(prob)
+
+    tc = alg.termination_condition
+    mode = DiffEqBase.get_termination_mode(tc)
+
+    storage = _get_storage(mode, u)
+
+    xₙ, xₙ₋₁, δx = copy(u), copy(u), copy(u)
+    T = eltype(u)
+
+    atol = _get_tolerance(abstol, tc.abstol, T)
+    rtol = _get_tolerance(reltol, tc.reltol, T)
+    termination_condition = tc(storage)
+
+    for i in 1:maxiters
+        fₙ, (𝓙,) = AD.value_and_jacobian(alg.autodiff, f, xₙ)
+
+        iszero(fₙ) && return DiffEqBase.build_solution(prob,
+            alg,
+            reconstruct(xₙ),
+            reconstruct(fₙ);
+            retcode=ReturnCode.Success)
+
+        solve(LinearProblem(𝓙, vec(fₙ); u0=vec(δx)), alg.linsolve; kwargs...)
+        xₙ .-= δx
+
+        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
+            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, iip)
+            return DiffEqBase.build_solution(prob,
+                alg,
+                reconstruct(xₙ),
+                reconstruct(fₙ);
+                retcode)
+        end
+
+        xₙ₋₁ .= xₙ
+    end
+
+    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
+        xₙ = storage.u
+        fₙ = f(xₙ)
+    end
+
+    return DiffEqBase.build_solution(prob,
+        alg,
+        reconstruct(xₙ),
+        reconstruct(fₙ);
+        retcode=ReturnCode.MaxIters)
+end
+
+end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
similarity index 90%
rename from lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
rename to lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
index 9e1ba59ad..e62e2bda7 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleBatchedNonlinearSolveExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
@@ -1,8 +1,13 @@
-module SimpleBatchedNonlinearSolveExt
+module SimpleNonlinearSolveNNlibExt
 
-using ArrayInterface, DiffEqBase, LinearAlgebra, SimpleNonlinearSolve, SciMLBase, NNlib
+using ArrayInterface, DiffEqBase, LinearAlgebra, NNlib, SimpleNonlinearSolve, SciMLBase
 import SimpleNonlinearSolve: _construct_batched_problem_structure, _get_storage, _init_𝓙, _result_from_storage, _get_tolerance, @maybeinplace
 
+function __init__()
+    SimpleNonlinearSolve.NNlibExtLoaded[] = true
+    return
+end
+
 @views function SciMLBase.__solve(prob::NonlinearProblem,
     alg::BatchedBroyden;
     abstol=nothing,
@@ -10,7 +15,6 @@ import SimpleNonlinearSolve: _construct_batched_problem_structure, _get_storage,
     maxiters=1000,
     kwargs...)
     iip = isinplace(prob)
-    u0 = prob.u0
 
     u, f, reconstruct = _construct_batched_problem_structure(prob)
     L, N = size(u)
@@ -49,7 +53,7 @@ import SimpleNonlinearSolve: _construct_batched_problem_structure, _get_storage,
         batched_mul!(𝓙⁻¹, reshape(δx, L, 1, N), xᵀ𝓙⁻¹, one(T), one(T))
 
         if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
-            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode)
+            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, iip)
             return DiffEqBase.build_solution(prob,
                 alg,
                 reconstruct(xₙ),
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index ab2033622..49aef9fc8 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -15,6 +15,9 @@ function __init__()
     @require_extensions
 end
 
+const ADLinearSolveExtLoaded = Ref{Bool}(false)
+const NNlibExtLoaded = Ref{Bool}(false)
+
 abstract type AbstractSimpleNonlinearSolveAlgorithm <: SciMLBase.AbstractNonlinearAlgorithm end
 abstract type AbstractBracketingAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 abstract type AbstractNewtonAlgorithm{CS, AD, FDT} <: AbstractSimpleNonlinearSolveAlgorithm end
@@ -75,6 +78,7 @@ end
 # DiffEq styled algorithms
 export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, Halley, Klement,
     Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld
-export BatchedBroyden
+export BatchedBroyden, SimpleBatchedNewtonRaphson, SimpleBatchedDFSane,
+    BatchedLBroyden
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/batched/raphson.jl b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
index e69de29bb..0a28e338f 100644
--- a/lib/SimpleNonlinearSolve/src/batched/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
@@ -0,0 +1,24 @@
+"""
+    SimpleBatchedNewtonRaphson(; chunk_size = Val{0}(),
+        autodiff = Val{true}(),
+        diff_type = Val{:forward},
+        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+            abstol = nothing,
+            reltol = nothing))
+
+A low-overhead batched implementation of Newton-Raphson capable of solving multiple
+nonlinear problems simultaneously.
+
+!!! note
+
+    To use the `batched` version, remember to load `AbstractDifferentiation` and
+    `LinearSolve`.
+"""
+struct SimpleBatchedNewtonRaphson{AD, LS, TC <: NLSolveTerminationCondition} <:
+    AbstractBatchedNonlinearSolveAlgorithm
+    autodiff::AD
+    linsolve::LS
+    termination_condition::TC
+end
+
+# Implementation of solve using Package Extensions
diff --git a/lib/SimpleNonlinearSolve/src/batched/utils.jl b/lib/SimpleNonlinearSolve/src/batched/utils.jl
index 9ed91345f..33441e985 100644
--- a/lib/SimpleNonlinearSolve/src/batched/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/utils.jl
@@ -1,3 +1,19 @@
+macro maybeinplace(iip::Symbol, expr::Expr, u0::Union{Symbol, Nothing}=nothing)
+    @assert expr.head == :(=)
+    x1, x2 = expr.args
+    @assert x2.head == :call
+    f, x = x2.args
+    define_expr = u0 === nothing ? :() : :($(x1) = similar($(u0)))
+    return quote
+        if $(esc(iip))
+            $(esc(define_expr))
+            $(esc(f))($(esc(x1)), $(esc(x)))
+        else
+            $(esc(expr))
+        end
+    end
+end
+
 function _get_tolerance(η, tc_η, ::Type{T}) where {T}
     fallback_η = real(oneunit(T)) * (eps(real(one(T))))^(4 // 5)
     return ifelse(η !== nothing, η, ifelse(tc_η !== nothing, tc_η, fallback_η))
@@ -42,13 +58,14 @@ end
     return repeat(𝓙, 1, 1, size(x, 2))
 end
 
-_result_from_storage(::Nothing, xₙ, fₙ, f, mode) = ReturnCode.Success, xₙ, fₙ
-function _result_from_storage(storage::NLSolveSafeTerminationResult, xₙ, fₙ, f, mode)
+_result_from_storage(::Nothing, xₙ, fₙ, args...) = ReturnCode.Success, xₙ, fₙ
+function _result_from_storage(storage::NLSolveSafeTerminationResult, xₙ, fₙ, f, mode, iip)
     if storage.return_code == DiffEqBase.NLSolveSafeTerminationReturnCode.Success
         return ReturnCode.Success, xₙ, fₙ
     else
         if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-            return ReturnCode.Terminated, storage.u, f(storage.u)
+            @maybeinplace iip fₙ = f(xₙ)
+            return ReturnCode.Terminated, storage.u, fₙ
         else
             return ReturnCode.Terminated, xₙ, fₙ
         end
@@ -60,19 +77,3 @@ function _get_storage(mode, u)
            NLSolveSafeTerminationResult(mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES ? u :
                                         nothing) : nothing
 end
-
-macro maybeinplace(iip::Symbol, expr::Expr, u0::Union{Symbol, Nothing}=nothing)
-    @assert expr.head == :(=)
-    x1, x2 = expr.args
-    @assert x2.head == :call
-    f, x = x2.args
-    define_expr = u0 === nothing ? :() : :($(x1) = similar($(u0)))
-    return quote
-        if $(esc(iip))
-            $(esc(define_expr))
-            $(esc(f))($(esc(x1)), $(esc(x)))
-        else
-            $(esc(expr))
-        end
-    end
-end
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 56fa2efea..74566e8c3 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -1,7 +1,8 @@
 """
     Broyden(; batched = false,
-            termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-                                                                abstol = nothing, reltol = nothing))
+        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+            abstol = nothing,
+            reltol = nothing))
 
 A low-overhead implementation of Broyden. This method is non-allocating on scalar
 and static array problems.
@@ -20,7 +21,11 @@ function Broyden(; batched = false,
     termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
         abstol = nothing,
         reltol = nothing))
-    return (batched ? BatchedBroyden : Broyden)(termination_condition)
+    if batched
+        @assert NNlibExtLoaded[] "Please install and load `NNlib.jl` to use batched Broyden."
+        return BatchedBroyden(termination_condition)
+    end
+    return Broyden(termination_condition)
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 386c35053..59eb1ed6d 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -1,8 +1,8 @@
 """
-```julia
-SimpleNewtonRaphson(; chunk_size = Val{0}(), autodiff = Val{true}(),
-                                 diff_type = Val{:forward})
-```
+    SimpleNewtonRaphson(; batched = false,
+        chunk_size = Val{0}(),
+        autodiff = Val{true}(),
+        diff_type = Val{:forward})
 
 A low-overhead implementation of Newton-Raphson. This method is non-allocating on scalar
 and static array problems.
@@ -27,13 +27,37 @@ and static array problems.
 - `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
   `Val{:forward}` for forward finite differences. For more details on the choices, see the
   [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
+
+!!! note
+
+    To use the `batched` version, remember to load `AbstractDifferentiation` and
+    `LinearSolve`.
 """
-struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
-    function SimpleNewtonRaphson(; chunk_size = Val{0}(), autodiff = Val{true}(),
-        diff_type = Val{:forward})
-        new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
-            SciMLBase._unwrap_val(diff_type)}()
+struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT} end
+
+function SimpleNewtonRaphson(; batched=false,
+    chunk_size = Val{0}(),
+    autodiff = Val{true}(),
+    diff_type = Val{:forward},
+    termination_condition = missing)
+    if !ismissing(termination_condition) && !batched
+        throw(ArgumentError("`termination_condition` is currently only supported for batched problems"))
+    end
+    if batched
+        @assert ADLinearSolveExtLoaded[] "Please install and load `LinearSolve.jl` and `AbstractDifferentiation.jl` to use batched Newton-Raphson."
+        termination_condition = ismissing(termination_condition) ?
+            NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+                abstol = nothing,
+                reltol = nothing) :
+            termination_condition
+        return SimpleBatchedNewtonRaphson(; chunk_size,
+            autodiff,
+            diff_type,
+            termination_condition)
     end
+    return SimpleNewtonRaphson{SciMLBase._unwrap_val(chunk_size),
+        SciMLBase._unwrap_val(autodiff),
+        SciMLBase._unwrap_val(diff_type)}()
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,

From 51005e053741fa5c82601415ee70d6074aa3404c Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 27 Jun 2023 16:59:54 -0400
Subject: [PATCH 137/700] Update SimpleDFSane Batching

---
 lib/SimpleNonlinearSolve/Project.toml         |   8 -
 .../src/batched/dfsane.jl                     | 140 ++++++++++++++++++
 lib/SimpleNonlinearSolve/src/batched/utils.jl |   4 +-
 lib/SimpleNonlinearSolve/src/broyden.jl       |   7 +-
 lib/SimpleNonlinearSolve/src/dfsane.jl        | 122 ++++++---------
 lib/SimpleNonlinearSolve/test/Project.toml    |  12 ++
 lib/SimpleNonlinearSolve/test/basictests.jl   |  13 +-
 7 files changed, 201 insertions(+), 105 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/test/Project.toml

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 901708505..f1f472d08 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -41,13 +41,5 @@ julia = "1.6"
 
 [extras]
 AbstractDifferentiation = "c29ec348-61ec-40c8-8164-b8c60e9d9f3d"
-BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
-Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
-SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
-StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-
-[targets]
-test = ["BenchmarkTools", "SafeTestsets", "Pkg", "Test", "StaticArrays", "NNlib"]
diff --git a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
index e69de29bb..fe7cbcddf 100644
--- a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
@@ -0,0 +1,140 @@
+@kwdef struct SimpleBatchedDFSane{T, F, TC <: NLSolveTerminationCondition} <:
+              AbstractBatchedNonlinearSolveAlgorithm
+    σₘᵢₙ::T = 1.0f-10
+    σₘₐₓ::T = 1.0f+10
+    σ₁::T = 1.0f0
+    M::Int = 10
+    γ::T = 1.0f-4
+    τₘᵢₙ::T = 0.1f0
+    τₘₐₓ::T = 0.5f0
+    nₑₓₚ::Int = 2
+    ηₛ::F = (f₍ₙₒᵣₘ₎₁, n, xₙ, fₙ) -> f₍ₙₒᵣₘ₎₁ ./ n .^ 2
+    termination_condition::TC = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+        abstol=nothing,
+        reltol=nothing)
+    max_inner_iterations::Int = 1000
+end
+
+function SciMLBase.__solve(prob::NonlinearProblem,
+    alg::SimpleBatchedDFSane,
+    args...;
+    abstol=nothing,
+    reltol=nothing,
+    maxiters=100,
+    kwargs...)
+    iip = isinplace(prob)
+
+    u, f, reconstruct = _construct_batched_problem_structure(prob)
+    L, N = size(u)
+    T = eltype(u)
+
+    tc = alg.termination_condition
+    mode = DiffEqBase.get_termination_mode(tc)
+
+    storage = _get_storage(mode, u)
+
+    atol = _get_tolerance(abstol, tc.abstol, T)
+    rtol = _get_tolerance(reltol, tc.reltol, T)
+    termination_condition = tc(storage)
+
+    σₘᵢₙ, σₘₐₓ, γ, τₘᵢₙ, τₘₐₓ = T(alg.σₘᵢₙ), T(alg.σₘₐₓ), T(alg.γ), T(alg.τₘᵢₙ), T(alg.τₘₐₓ)
+    α₁ = one(T)
+    α₊, α₋ = similar(u, 1, N), similar(u, 1, N)
+    σₙ = fill(T(alg.σ₁), 1, N)
+    𝒹 = similar(σₙ, L, N)
+    (; M, nₑₓₚ) = alg
+
+    xₙ, xₙ₋₁, f₍ₙₒᵣₘ₎ₙ₋₁, f₍ₙₒᵣₘ₎ₙ = copy(u), copy(u), similar(u, 1, N), similar(u, 1, N)
+
+    function ff!(fₓ, fₙₒᵣₘ, x)
+        f(fₓ, x)
+        sum!(abs2, fₙₒᵣₘ, fₓ)
+        fₙₒᵣₘ .^= (nₑₓₚ / 2)
+        return fₓ
+    end
+
+    function ff!(fₙₒᵣₘ, x)
+        fₓ = f(x)
+        sum!(abs2, fₙₒᵣₘ, fₓ)
+        fₙₒᵣₘ .^= (nₑₓₚ / 2)
+        return fₓ
+    end
+
+    @maybeinplace iip fₙ₋₁ = ff!(f₍ₙₒᵣₘ₎ₙ₋₁, xₙ) xₙ
+    iip && (fₙ = similar(fₙ₋₁))
+    ℋ = repeat(f₍ₙₒᵣₘ₎ₙ₋₁, M, 1)
+    f̄ = similar(ℋ, 1, N)
+    ηₛ = (n, xₙ, fₙ) -> alg.ηₛ(f₍ₙₒᵣₘ₎ₙ₋₁, n, xₙ, fₙ)
+
+    for n in 1:maxiters
+        # Spectral parameter range check
+        @. σₙ = sign(σₙ) * clamp(abs(σₙ), σₘᵢₙ, σₘₐₓ)
+
+        # Line search direction
+        @. 𝒹 = -σₙ * fₙ₋₁
+
+        η = ηₛ(n, xₙ₋₁, fₙ₋₁)
+        maximum!(f̄, ℋ)
+        fill!(α₊, α₁)
+        fill!(α₋, α₁)
+        @. xₙ = xₙ₋₁ + α₊ * 𝒹
+
+        @maybeinplace iip fₙ = ff!(f₍ₙₒᵣₘ₎ₙ, xₙ)
+
+        for _ in 1:(alg.max_inner_iterations)
+            𝒸 = @. f̄ + η - γ * α₊^2 * f₍ₙₒᵣₘ₎ₙ₋₁
+
+            (sum(f₍ₙₒᵣₘ₎ₙ .≤ 𝒸) ≥ N ÷ 2) && break
+
+            @. α₊ = clamp(α₊^2 * f₍ₙₒᵣₘ₎ₙ₋₁ / (f₍ₙₒᵣₘ₎ₙ + (T(2) * α₊ - T(1)) * f₍ₙₒᵣₘ₎ₙ₋₁),
+                τₘᵢₙ * α₊,
+                τₘₐₓ * α₊)
+            @. xₙ = xₙ₋₁ - α₋ * 𝒹
+            @maybeinplace iip fₙ = ff!(f₍ₙₒᵣₘ₎ₙ, xₙ)
+
+            (sum(f₍ₙₒᵣₘ₎ₙ .≤ 𝒸) ≥ N ÷ 2) && break
+
+            @. α₋ = clamp(α₋^2 * f₍ₙₒᵣₘ₎ₙ₋₁ / (f₍ₙₒᵣₘ₎ₙ + (T(2) * α₋ - T(1)) * f₍ₙₒᵣₘ₎ₙ₋₁),
+                τₘᵢₙ * α₋,
+                τₘₐₓ * α₋)
+            @. xₙ = xₙ₋₁ + α₊ * 𝒹
+            @maybeinplace iip fₙ = ff!(f₍ₙₒᵣₘ₎ₙ, xₙ)
+        end
+
+        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
+            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, iip)
+            return DiffEqBase.build_solution(prob,
+                alg,
+                reconstruct(xₙ),
+                reconstruct(fₙ);
+                retcode)
+        end
+
+        # Update spectral parameter
+        @. xₙ₋₁ = xₙ - xₙ₋₁
+        @. fₙ₋₁ = fₙ - fₙ₋₁
+
+        sum!(abs2, α₊, xₙ₋₁)
+        sum!(α₋, xₙ₋₁ .* fₙ₋₁)
+        σₙ .= α₊ ./ (α₋ .+ T(1e-5))
+
+        # Take step
+        @. xₙ₋₁ = xₙ
+        @. fₙ₋₁ = fₙ
+        @. f₍ₙₒᵣₘ₎ₙ₋₁ = f₍ₙₒᵣₘ₎ₙ
+
+        # Update history
+        ℋ[n % M + 1, :] .= view(f₍ₙₒᵣₘ₎ₙ, 1, :)
+    end
+
+    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
+        xₙ = storage.u
+        @maybeinplace iip fₙ = f(xₙ)
+    end
+
+    return DiffEqBase.build_solution(prob,
+        alg,
+        reconstruct(xₙ),
+        reconstruct(fₙ);
+        retcode=ReturnCode.MaxIters)
+end
diff --git a/lib/SimpleNonlinearSolve/src/batched/utils.jl b/lib/SimpleNonlinearSolve/src/batched/utils.jl
index 33441e985..b5dbd597f 100644
--- a/lib/SimpleNonlinearSolve/src/batched/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/utils.jl
@@ -2,12 +2,12 @@ macro maybeinplace(iip::Symbol, expr::Expr, u0::Union{Symbol, Nothing}=nothing)
     @assert expr.head == :(=)
     x1, x2 = expr.args
     @assert x2.head == :call
-    f, x = x2.args
+    f, x... = x2.args
     define_expr = u0 === nothing ? :() : :($(x1) = similar($(u0)))
     return quote
         if $(esc(iip))
             $(esc(define_expr))
-            $(esc(f))($(esc(x1)), $(esc(x)))
+            $(esc(f))($(esc(x1)), $(esc.(x)...))
         else
             $(esc(expr))
         end
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 74566e8c3..6c5c3ce7f 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -43,11 +43,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
         error("Broyden currently only supports out-of-place nonlinear problems")
     end
 
-    atol = abstol !== nothing ? abstol :
-           (tc.abstol !== nothing ? tc.abstol :
-            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5))
-    rtol = reltol !== nothing ? reltol :
-           (tc.reltol !== nothing ? tc.reltol : eps(real(one(eltype(T))))^(4 // 5))
+    atol = _get_tolerance(abstol, tc.abstol, T)
+    rtol = _get_tolerance(reltol, tc.reltol, T)
 
     if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
         error("Broyden currently doesn't support SAFE_BEST termination modes")
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index b5e2b8200..d4bc77709 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -51,7 +51,7 @@ Computation, 75, 1429-1448.](https://www.researchgate.net/publication/220576479_
 - `max_inner_iterations`: the maximum number of iterations allowed for the inner loop of the
   algorithm. Used exclusively in `batched` mode. Defaults to `1000`.
 """
-struct SimpleDFSane{batched, T, TC} <: AbstractSimpleNonlinearSolveAlgorithm
+struct SimpleDFSane{T, TC} <: AbstractSimpleNonlinearSolveAlgorithm
     σ_min::T
     σ_max::T
     σ_1::T
@@ -62,47 +62,54 @@ struct SimpleDFSane{batched, T, TC} <: AbstractSimpleNonlinearSolveAlgorithm
     nexp::Int
     η_strategy::Function
     termination_condition::TC
-    max_inner_iterations::Int
+end
 
-    function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
-        M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
-        nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2,
-        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-            abstol = nothing,
-            reltol = nothing),
-        batched::Bool = false,
-        max_inner_iterations = 1000)
-        return new{batched, typeof(σ_min), typeof(termination_condition)}(σ_min,
-            σ_max,
-            σ_1,
+function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
+    M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
+    nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2,
+    termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+        abstol = nothing,
+        reltol = nothing),
+    batched::Bool = false,
+    max_inner_iterations = 1000)
+    if batched
+        return SimpleBatchedDFSane(; σₘᵢₙ = σ_min,
+            σₘₐₓ = σ_max,
+            σ₁ = σ_1,
             M,
             γ,
-            τ_min,
-            τ_max,
-            nexp,
-            η_strategy,
+            τₘᵢₙ = τ_min,
+            τₘₐₓ = τ_max,
+            nₑₓₚ = nexp,
+            ηₛ = η_strategy,
             termination_condition,
             max_inner_iterations)
     end
+    return SimpleDFSane{typeof(σ_min), typeof(termination_condition)}(σ_min,
+        σ_max,
+        σ_1,
+        M,
+        γ,
+        τ_min,
+        τ_max,
+        nexp,
+        η_strategy,
+        termination_condition)
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{batched},
+function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane,
     args...; abstol = nothing, reltol = nothing, maxiters = 1000,
-    kwargs...) where {batched}
+    kwargs...)
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
 
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
 
-    if batched
-        batch_size = size(x, 2)
-    end
-
     T = eltype(x)
     σ_min = float(alg.σ_min)
     σ_max = float(alg.σ_max)
-    σ_k = batched ? fill(float(alg.σ_1), 1, batch_size) : float(alg.σ_1)
+    σ_k = float(alg.σ_1)
 
     M = alg.M
     γ = float(alg.γ)
@@ -111,17 +118,12 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{batched},
     nexp = alg.nexp
     η_strategy = alg.η_strategy
 
-    batched && @assert ndims(x)==2 "Batched SimpleDFSane only supports 2D arrays"
-
     if SciMLBase.isinplace(prob)
         error("SimpleDFSane currently only supports out-of-place nonlinear problems")
     end
 
-    atol = abstol !== nothing ? abstol :
-           (tc.abstol !== nothing ? tc.abstol :
-            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5))
-    rtol = reltol !== nothing ? reltol :
-           (tc.reltol !== nothing ? tc.reltol : eps(real(one(eltype(T))))^(4 // 5))
+    atol = _get_tolerance(abstol, tc.abstol, T)
+    rtol = _get_tolerance(reltol, tc.reltol, T)
 
     if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
         error("SimpleDFSane currently doesn't support SAFE_BEST termination modes")
@@ -133,22 +135,12 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{batched},
 
     function ff(x)
         F = f(x)
-        f_k = if batched
-            sum(abs2, F; dims = 1) .^ (nexp / 2)
-        else
-            norm(F)^nexp
-        end
+        f_k = norm(F)^nexp
         return f_k, F
     end
 
     function generate_history(f_k, M)
-        if batched
-            history = similar(f_k, (M, length(f_k)))
-            history .= reshape(f_k, 1, :)
-            return history
-        else
-            return fill(f_k, M)
-        end
+        return fill(f_k, M)
     end
 
     f_k, F_k = ff(x)
@@ -158,17 +150,13 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{batched},
 
     for k in 1:maxiters
         # Spectral parameter range check
-        if batched
-            @. σ_k = sign(σ_k) * clamp(abs(σ_k), σ_min, σ_max)
-        else
-            σ_k = sign(σ_k) * clamp(abs(σ_k), σ_min, σ_max)
-        end
+        σ_k = sign(σ_k) * clamp(abs(σ_k), σ_min, σ_max)
 
         # Line search direction
         d = -σ_k .* F_k
 
         η = η_strategy(f_1, k, x, F_k)
-        f̄ = batched ? maximum(history_f_k; dims = 1) : maximum(history_f_k)
+        f̄ = maximum(history_f_k)
         α_p = α_1
         α_m = α_1
         x_new = @. x + α_p * d
@@ -179,38 +167,20 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{batched},
         while true
             inner_iterations += 1
 
-            if batched
-                criteria = @. f̄ + η - γ * α_p^2 * f_k
-                # NOTE: This is simply a heuristic, ideally we check using `all` but that is
-                #       typically very expensive for large problems
-                (sum(f_new .≤ criteria) ≥ batch_size ÷ 2) && break
-            else
-                criteria = f̄ + η - γ * α_p^2 * f_k
-                f_new ≤ criteria && break
-            end
+            criteria = f̄ + η - γ * α_p^2 * f_k
+            f_new ≤ criteria && break
 
             α_tp = @. α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
             x_new = @. x - α_m * d
             f_new, F_new = ff(x_new)
 
-            if batched
-                # NOTE: This is simply a heuristic, ideally we check using `all` but that is
-                #       typically very expensive for large problems
-                (sum(f_new .≤ criteria) ≥ batch_size ÷ 2) && break
-            else
-                f_new ≤ criteria && break
-            end
+            f_new ≤ criteria && break
 
             α_tm = @. α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
             α_p = @. clamp(α_tp, τ_min * α_p, τ_max * α_p)
             α_m = @. clamp(α_tm, τ_min * α_m, τ_max * α_m)
             x_new = @. x + α_p * d
             f_new, F_new = ff(x_new)
-
-            # NOTE: The original algorithm runs till either condition is satisfied, however,
-            #       for most batched problems like neural networks we only care about
-            #       approximate convergence
-            batched && (inner_iterations ≥ alg.max_inner_iterations) && break
         end
 
         if termination_condition(F_new, x_new, x, atol, rtol)
@@ -225,11 +195,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{batched},
         s_k = @. x_new - x
         y_k = @. F_new - F_k
 
-        if batched
-            σ_k = sum(abs2, s_k; dims = 1) ./ (sum(s_k .* y_k; dims = 1) .+ T(1e-5))
-        else
-            σ_k = (s_k' * s_k) / (s_k' * y_k)
-        end
+        σ_k = (s_k' * s_k) / (s_k' * y_k)
 
         # Take step
         x = x_new
@@ -237,11 +203,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{batched},
         f_k = f_new
 
         # Store function value
-        if batched
-            history_f_k[k % M + 1, :] .= vec(f_new)
-        else
-            history_f_k[k % M + 1] = f_new
-        end
+        history_f_k[k % M + 1] = f_new
     end
     return SciMLBase.build_solution(prob, alg, x, F_k; retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/test/Project.toml b/lib/SimpleNonlinearSolve/test/Project.toml
new file mode 100644
index 000000000..280bf2a39
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/Project.toml
@@ -0,0 +1,12 @@
+[deps]
+AbstractDifferentiation = "c29ec348-61ec-40c8-8164-b8c60e9d9f3d"
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
+NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
+Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index dd54527a5..4fe316b34 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -1,9 +1,5 @@
-using SimpleNonlinearSolve
-using StaticArrays
-using BenchmarkTools
-using DiffEqBase
-using LinearAlgebra
-using Test
+using SimpleNonlinearSolve, StaticArrays, BenchmarkTools, DiffEqBase, LinearAlgebra, Test,
+    NNlib, AbstractDifferentiation, LinearSolve
 
 const BATCHED_BROYDEN_SOLVERS = []
 const BROYDEN_SOLVERS = []
@@ -476,9 +472,6 @@ for options in list_of_options
     @test all(abs.(f(u, p)) .< 1e-10)
 end
 
-# Batched Broyden
-using NNlib
-
 f, u0 = (u, p) -> u .* u .- p, randn(1, 3)
 
 p = [2.0 1.0 5.0];
@@ -488,7 +481,7 @@ sol = solve(probN, Broyden(batched = true))
 
 @test abs.(sol.u) ≈ sqrt.(p)
 
-for alg in (BATCHED_BROYDEN_SOLVERS...,
+@testset "Batched Solver: $(nameof(typeof(alg)))" for alg in (BATCHED_BROYDEN_SOLVERS...,
     BATCHED_LBROYDEN_SOLVERS...,
     BATCHED_DFSANE_SOLVERS...)
     sol = solve(probN, alg; abstol = 1e-3, reltol = 1e-3)

From 52b5bacf974cd41ed37ef292ba7edd4431d65411 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 27 Jun 2023 17:01:35 -0400
Subject: [PATCH 138/700] Remove docstrings to ensure users don't directly
 construct the batched solvers

---
 lib/SimpleNonlinearSolve/src/batched/broyden.jl | 14 --------------
 lib/SimpleNonlinearSolve/src/batched/raphson.jl | 16 ----------------
 2 files changed, 30 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/batched/broyden.jl b/lib/SimpleNonlinearSolve/src/batched/broyden.jl
index a301c4e14..85754880f 100644
--- a/lib/SimpleNonlinearSolve/src/batched/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/broyden.jl
@@ -1,17 +1,3 @@
-"""
-    BatchedBroyden(;
-        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-            abstol = nothing,
-            reltol = nothing))
-
-A low-overhead batched implementation of Broyden capable of solving multiple nonlinear
-problems simultaneously.
-
-!!! note
-
-    To use this version, remember to load `NNlib`, i.e., `using NNlib` or
-    `import NNlib` must be present in your code.
-"""
 struct BatchedBroyden{TC <: NLSolveTerminationCondition} <:
     AbstractBatchedNonlinearSolveAlgorithm
     termination_condition::TC
diff --git a/lib/SimpleNonlinearSolve/src/batched/raphson.jl b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
index 0a28e338f..2be565fc5 100644
--- a/lib/SimpleNonlinearSolve/src/batched/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
@@ -1,19 +1,3 @@
-"""
-    SimpleBatchedNewtonRaphson(; chunk_size = Val{0}(),
-        autodiff = Val{true}(),
-        diff_type = Val{:forward},
-        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-            abstol = nothing,
-            reltol = nothing))
-
-A low-overhead batched implementation of Newton-Raphson capable of solving multiple
-nonlinear problems simultaneously.
-
-!!! note
-
-    To use the `batched` version, remember to load `AbstractDifferentiation` and
-    `LinearSolve`.
-"""
 struct SimpleBatchedNewtonRaphson{AD, LS, TC <: NLSolveTerminationCondition} <:
     AbstractBatchedNonlinearSolveAlgorithm
     autodiff::AD

From c98922be35229fb0e0835c9eecb3b948aaa60b54 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 27 Jun 2023 18:38:35 -0400
Subject: [PATCH 139/700] LBroyden

---
 .../SimpleNonlinearSolveADLinearSolveExt.jl   |  25 +--
 .../ext/SimpleNonlinearSolveNNlibExt.jl       | 122 +++++++++++--
 .../src/batched/dfsane.jl                     |   2 +-
 .../src/batched/lbroyden.jl                   |   7 +
 lib/SimpleNonlinearSolve/src/broyden.jl       |  10 +-
 lib/SimpleNonlinearSolve/src/lbroyden.jl      | 163 ++++++++----------
 6 files changed, 210 insertions(+), 119 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
index 96ba9168a..d0a97eb86 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
@@ -1,8 +1,10 @@
 module SimpleNonlinearSolveADLinearSolveExt
 
-using AbstractDifferentiation, ArrayInterface, DiffEqBase, LinearAlgebra, LinearSolve,
+using AbstractDifferentiation,
+    ArrayInterface, DiffEqBase, LinearAlgebra, LinearSolve,
     SimpleNonlinearSolve, SciMLBase
-import SimpleNonlinearSolve: _construct_batched_problem_structure, _get_storage, _result_from_storage, _get_tolerance, @maybeinplace
+import SimpleNonlinearSolve: _construct_batched_problem_structure,
+    _get_storage, _result_from_storage, _get_tolerance, @maybeinplace
 
 const AD = AbstractDifferentiation
 
@@ -20,19 +22,18 @@ function SimpleNonlinearSolve.SimpleBatchedNewtonRaphson(; chunk_size = Val{0}()
     # TODO: Use `diff_type`. FiniteDiff.jl is currently not available in AD.jl
     chunksize = SciMLBase._unwrap_val(chunk_size) == 0 ? nothing : chunk_size
     ad = SciMLBase._unwrap_val(autodiff) ?
-        AD.ForwardDiffBackend(; chunksize) :
-        AD.FiniteDifferencesBackend()
-    return SimpleBatchedNewtonRaphson{typeof(ad), Nothing, typeof(termination_condition)}(
-        ad,
+         AD.ForwardDiffBackend(; chunksize) :
+         AD.FiniteDifferencesBackend()
+    return SimpleBatchedNewtonRaphson{typeof(ad), Nothing, typeof(termination_condition)}(ad,
         nothing,
         termination_condition)
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
     alg::SimpleBatchedNewtonRaphson;
-    abstol=nothing,
-    reltol=nothing,
-    maxiters=1000,
+    abstol = nothing,
+    reltol = nothing,
+    maxiters = 1000,
     kwargs...)
     iip = isinplace(prob)
     @assert !iip "SimpleBatchedNewtonRaphson currently only supports out-of-place nonlinear problems."
@@ -57,9 +58,9 @@ function SciMLBase.__solve(prob::NonlinearProblem,
             alg,
             reconstruct(xₙ),
             reconstruct(fₙ);
-            retcode=ReturnCode.Success)
+            retcode = ReturnCode.Success)
 
-        solve(LinearProblem(𝓙, vec(fₙ); u0=vec(δx)), alg.linsolve; kwargs...)
+        solve(LinearProblem(𝓙, vec(fₙ); u0 = vec(δx)), alg.linsolve; kwargs...)
         xₙ .-= δx
 
         if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
@@ -83,7 +84,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         alg,
         reconstruct(xₙ),
         reconstruct(fₙ);
-        retcode=ReturnCode.MaxIters)
+        retcode = ReturnCode.MaxIters)
 end
 
 end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
index e62e2bda7..c0faefd9b 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
@@ -1,18 +1,20 @@
 module SimpleNonlinearSolveNNlibExt
 
 using ArrayInterface, DiffEqBase, LinearAlgebra, NNlib, SimpleNonlinearSolve, SciMLBase
-import SimpleNonlinearSolve: _construct_batched_problem_structure, _get_storage, _init_𝓙, _result_from_storage, _get_tolerance, @maybeinplace
+import SimpleNonlinearSolve: _construct_batched_problem_structure,
+    _get_storage, _init_𝓙, _result_from_storage, _get_tolerance, @maybeinplace
 
 function __init__()
     SimpleNonlinearSolve.NNlibExtLoaded[] = true
     return
 end
 
+# Broyden's method
 @views function SciMLBase.__solve(prob::NonlinearProblem,
     alg::BatchedBroyden;
-    abstol=nothing,
-    reltol=nothing,
-    maxiters=1000,
+    abstol = nothing,
+    reltol = nothing,
+    maxiters = 1000,
     kwargs...)
     iip = isinplace(prob)
 
@@ -24,7 +26,7 @@ end
 
     storage = _get_storage(mode, u)
 
-    xₙ, xₙ₋₁, δx, δf = ntuple(_ -> copy(u), 4)
+    xₙ, xₙ₋₁, δxₙ, δf = ntuple(_ -> copy(u), 4)
     T = eltype(u)
 
     atol = _get_tolerance(abstol, tc.abstol, T)
@@ -41,16 +43,16 @@ end
         xₙ .= xₙ₋₁ .- 𝓙⁻¹f
 
         @maybeinplace iip fₙ=f(xₙ)
-        δx .= xₙ .- xₙ₋₁
+        δxₙ .= xₙ .- xₙ₋₁
         δf .= fₙ .- fₙ₋₁
 
         batched_mul!(reshape(𝓙⁻¹f, L, 1, N), 𝓙⁻¹, reshape(δf, L, 1, N))
-        δxᵀ = reshape(δx, 1, L, N)
+        δxₙᵀ = reshape(δxₙ, 1, L, N)
 
-        batched_mul!(reshape(xᵀ𝓙⁻¹δf, 1, 1, N), δxᵀ, reshape(𝓙⁻¹f, L, 1, N))
-        batched_mul!(xᵀ𝓙⁻¹, δxᵀ, 𝓙⁻¹)
-        δx .= (δx .- 𝓙⁻¹f) ./ (xᵀ𝓙⁻¹δf .+ T(1e-5))
-        batched_mul!(𝓙⁻¹, reshape(δx, L, 1, N), xᵀ𝓙⁻¹, one(T), one(T))
+        batched_mul!(reshape(xᵀ𝓙⁻¹δf, 1, 1, N), δxₙᵀ, reshape(𝓙⁻¹f, L, 1, N))
+        batched_mul!(xᵀ𝓙⁻¹, δxₙᵀ, 𝓙⁻¹)
+        δxₙ .= (δxₙ .- 𝓙⁻¹f) ./ (xᵀ𝓙⁻¹δf .+ T(1e-5))
+        batched_mul!(𝓙⁻¹, reshape(δxₙ, L, 1, N), xᵀ𝓙⁻¹, one(T), one(T))
 
         if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
             retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, iip)
@@ -74,7 +76,103 @@ end
         alg,
         reconstruct(xₙ),
         reconstruct(fₙ);
-        retcode=ReturnCode.MaxIters)
+        retcode = ReturnCode.MaxIters)
+end
+
+# Limited Memory Broyden's method
+@views function SciMLBase.__solve(prob::NonlinearProblem,
+    alg::BatchedLBroyden;
+    abstol = nothing,
+    reltol = nothing,
+    maxiters = 1000,
+    kwargs...)
+    iip = isinplace(prob)
+
+    u, f, reconstruct = _construct_batched_problem_structure(prob)
+    L, N = size(u)
+    T = eltype(u)
+
+    tc = alg.termination_condition
+    mode = DiffEqBase.get_termination_mode(tc)
+
+    storage = _get_storage(mode, u)
+
+    η = min(maxiters, alg.threshold)
+    U = fill!(similar(u, (η, L, N)), zero(T))
+    Vᵀ = fill!(similar(u, (L, η, N)), zero(T))
+
+    xₙ, xₙ₋₁, δfₙ = ntuple(_ -> copy(u), 3)
+
+    atol = _get_tolerance(abstol, tc.abstol, T)
+    rtol = _get_tolerance(reltol, tc.reltol, T)
+    termination_condition = tc(storage)
+
+    @maybeinplace iip fₙ₋₁=f(xₙ) u
+    iip && (fₙ = copy(fₙ₋₁))
+    δxₙ = -copy(fₙ₋₁)
+    ηNx = similar(xₙ, η, N)
+
+    for i in 1:maxiters
+        @. xₙ = xₙ₋₁ - δxₙ
+        @maybeinplace iip fₙ=f(xₙ)
+        @. δxₙ = xₙ - xₙ₋₁
+        @. δfₙ = fₙ - fₙ₋₁
+
+        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
+            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, iip)
+            return DiffEqBase.build_solution(prob,
+                alg,
+                reconstruct(xₙ),
+                reconstruct(fₙ);
+                retcode)
+        end
+
+        _L = min(i, η)
+        _U = U[1:_L, :, :]
+        _Vᵀ = Vᵀ[:, 1:_L, :]
+
+        idx = mod1(i, η)
+
+        if i > 1
+            partial_ηNx = ηNx[1:_L, :]
+
+            _ηNx = reshape(partial_ηNx, 1, :, N)
+            batched_mul!(_ηNx, reshape(δxₙ, 1, L, N), _Vᵀ)
+            batched_mul!(Vᵀ[:, idx:idx, :], _ηNx, _U)
+            Vᵀ[:, idx, :] .-= δxₙ
+
+            _ηNx = reshape(partial_ηNx, :, 1, N)
+            batched_mul!(_ηNx, _U, reshape(δfₙ, L, 1, N))
+            batched_mul!(U[idx:idx, :, :], _Vᵀ, _ηNx)
+            U[idx, :, :] .-= δfₙ
+        else
+            Vᵀ[:, idx, :] .= -δxₙ
+            U[idx, :, :] .= -δfₙ
+        end
+
+        U[idx, :, :] .= (δxₙ .- U[idx, :, :]) ./
+                        (sum(Vᵀ[:, idx, :] .* δfₙ; dims = 1) .+
+                         convert(T, 1e-5))
+
+        _L = min(i + 1, η)
+        _ηNx = reshape(ηNx[1:_L, :], :, 1, N)
+        batched_mul!(_ηNx, U[1:_L, :, :], reshape(δfₙ, L, 1, N))
+        batched_mul!(reshape(δxₙ, L, 1, N), Vᵀ[:, 1:_L, :], _ηNx)
+
+        xₙ₋₁ .= xₙ
+        fₙ₋₁ .= fₙ
+    end
+
+    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
+        xₙ = storage.u
+        @maybeinplace iip fₙ=f(xₙ)
+    end
+
+    return DiffEqBase.build_solution(prob,
+        alg,
+        reconstruct(xₙ),
+        reconstruct(fₙ);
+        retcode = ReturnCode.MaxIters)
 end
 
 end
diff --git a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
index fe7cbcddf..88f02ebe7 100644
--- a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
@@ -1,4 +1,4 @@
-@kwdef struct SimpleBatchedDFSane{T, F, TC <: NLSolveTerminationCondition} <:
+Base.@kwdef struct SimpleBatchedDFSane{T, F, TC <: NLSolveTerminationCondition} <:
               AbstractBatchedNonlinearSolveAlgorithm
     σₘᵢₙ::T = 1.0f-10
     σₘₐₓ::T = 1.0f+10
diff --git a/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl b/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
index e69de29bb..5934c8fe0 100644
--- a/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
@@ -0,0 +1,7 @@
+struct BatchedLBroyden{TC <: NLSolveTerminationCondition} <:
+    AbstractBatchedNonlinearSolveAlgorithm
+    termination_condition::TC
+    threshold::Int
+end
+
+# Implementation of solve using Package Extensions
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 6c5c3ce7f..adf94b033 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -30,6 +30,9 @@ end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
     abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
+    if SciMLBase.isinplace(prob)
+        error("Broyden currently only supports out-of-place nonlinear problems")
+    end
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
     f = Base.Fix2(prob.f, prob.p)
@@ -39,10 +42,6 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
     T = eltype(x)
     J⁻¹ = init_J(x)
 
-    if SciMLBase.isinplace(prob)
-        error("Broyden currently only supports out-of-place nonlinear problems")
-    end
-
     atol = _get_tolerance(abstol, tc.abstol, T)
     rtol = _get_tolerance(reltol, tc.reltol, T)
 
@@ -50,8 +49,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
         error("Broyden currently doesn't support SAFE_BEST termination modes")
     end
 
-    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? NLSolveSafeTerminationResult() :
-              nothing
+    storage = _get_storage(mode, x)
     termination_condition = tc(storage)
 
     xₙ = x
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index fc2b51a88..95ec3895e 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -11,134 +11,121 @@ Broyden's method.
 
     This method is not very stable and can diverge even for very simple problems. This has mostly been
     tested for neural networks in DeepEquilibriumNetworks.jl.
+
+!!! note
+
+    To use the `batched` version, remember to load `NNlib`, i.e., `using NNlib` or
+    `import NNlib` must be present in your code.
 """
 struct LBroyden{batched, TC <: NLSolveTerminationCondition} <:
        AbstractSimpleNonlinearSolveAlgorithm
     termination_condition::TC
     threshold::Int
+end
 
-    function LBroyden(; batched = false, threshold::Int = 27,
-        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-            abstol = nothing,
-            reltol = nothing))
-        return new{batched, typeof(termination_condition)}(termination_condition, threshold)
+function LBroyden(; batched = false, threshold::Int = 27,
+    termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+        abstol = nothing,
+        reltol = nothing))
+    if batched
+        @assert NNlibExtLoaded[] "Please install and load `NNlib.jl` to use batched Broyden."
+        return BatchedLBroyden(termination_condition, threshold)
     end
+    return LBroyden{true, typeof(termination_condition)}(termination_condition, threshold)
 end
 
-@views function SciMLBase.__solve(prob::NonlinearProblem, alg::LBroyden{batched}, args...;
+@views function SciMLBase.__solve(prob::NonlinearProblem, alg::LBroyden, args...;
     abstol = nothing, reltol = nothing, maxiters = 1000,
-    kwargs...) where {batched}
+    kwargs...)
+    if SciMLBase.isinplace(prob)
+        error("LBroyden currently only supports out-of-place nonlinear problems")
+    end
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
-    threshold = min(maxiters, alg.threshold)
+    η = min(maxiters, alg.threshold)
     x = float(prob.u0)
 
-    batched && @assert ndims(x)==2 "Batched LBroyden only supports 2D arrays"
-
+    # FIXME: The scalar case currently is very inefficient
     if x isa Number
         restore_scalar = true
         x = [x]
-        f = u -> prob.f(u[], prob.p)
+        f = u -> [prob.f(u[], prob.p)]
     else
         f = Base.Fix2(prob.f, prob.p)
         restore_scalar = false
     end
 
-    fₙ = f(x)
+    L = length(x)
     T = eltype(x)
 
-    if SciMLBase.isinplace(prob)
-        error("LBroyden currently only supports out-of-place nonlinear problems")
-    end
-
-    U, Vᵀ = _init_lbroyden_state(batched, x, threshold)
+    U = fill!(similar(x, (η, L)), zero(T))
+    Vᵀ = fill!(similar(x, (L, η)), zero(T))
 
-    atol = abstol !== nothing ? abstol :
-           (tc.abstol !== nothing ? tc.abstol :
-            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5))
-    rtol = reltol !== nothing ? reltol :
-           (tc.reltol !== nothing ? tc.reltol : eps(real(one(eltype(T))))^(4 // 5))
-
-    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-        error("LBroyden currently doesn't support SAFE_BEST termination modes")
-    end
-
-    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? NLSolveSafeTerminationResult() :
-              nothing
+    atol = _get_tolerance(abstol, tc.abstol, T)
+    rtol = _get_tolerance(reltol, tc.reltol, T)
+    storage = _get_storage(mode, x)
     termination_condition = tc(storage)
 
-    xₙ = x
-    xₙ₋₁ = x
-    fₙ₋₁ = fₙ
-    update = fₙ
+    xₙ, xₙ₋₁, δfₙ = ntuple(_ -> copy(x), 3)
+    fₙ₋₁ = f(x)
+    δxₙ = -copy(fₙ₋₁)
+    ηNx = similar(xₙ, η)
+
     for i in 1:maxiters
-        xₙ = xₙ₋₁ .+ update
+        @. xₙ = xₙ₋₁ - δxₙ
         fₙ = f(xₙ)
-        Δxₙ = xₙ .- xₙ₋₁
-        Δfₙ = fₙ .- fₙ₋₁
+        @. δxₙ = xₙ - xₙ₋₁
+        @. δfₙ = fₙ - fₙ₋₁
 
-        if termination_condition(restore_scalar ? [fₙ] : fₙ, xₙ, xₙ₋₁, atol, rtol)
+        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
+            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, Val(false))
             xₙ = restore_scalar ? xₙ[] : xₙ
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
+            fₙ = restore_scalar ? fₙ[] : fₙ
+            return DiffEqBase.build_solution(prob, alg, xₙ, fₙ; retcode)
         end
 
-        _U = selectdim(U, 1, 1:min(threshold, i))
-        _Vᵀ = selectdim(Vᵀ, 2, 1:min(threshold, i))
-
-        vᵀ = _rmatvec(_U, _Vᵀ, Δxₙ)
-        mvec = _matvec(_U, _Vᵀ, Δfₙ)
-        u = (Δxₙ .- mvec) ./ (sum(vᵀ .* Δfₙ) .+ convert(T, 1e-5))
+        _L = min(i, η)
+        _U = U[1:_L, :]
+        _Vᵀ = Vᵀ[:, 1:_L]
 
-        selectdim(Vᵀ, 2, mod1(i, threshold)) .= vᵀ
-        selectdim(U, 1, mod1(i, threshold)) .= u
+        idx = mod1(i, η)
 
-        update = -_matvec(selectdim(U, 1, 1:min(threshold, i + 1)),
-            selectdim(Vᵀ, 2, 1:min(threshold, i + 1)), fₙ)
+        partial_ηNx = ηNx[1:_L]
 
-        xₙ₋₁ = xₙ
-        fₙ₋₁ = fₙ
-    end
+        if i > 1
+            _ηNx = reshape(partial_ηNx, 1, :)
+            mul!(_ηNx, reshape(δxₙ, 1, L), _Vᵀ)
+            mul!(Vᵀ[:, idx:idx], _ηNx, _U)
+            Vᵀ[:, idx] .-= δxₙ
 
-    xₙ = restore_scalar ? xₙ[] : xₙ
-    return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
-end
+            _ηNx = reshape(partial_ηNx, :, 1)
+            mul!(_ηNx, _U, reshape(δfₙ, L, 1))
+            mul!(U[idx:idx, :], _Vᵀ, _ηNx)
+            U[idx, :] .-= δfₙ
+        else
+            Vᵀ[:, idx] .= -δxₙ
+            U[idx, :] .= -δfₙ
+        end
 
-function _init_lbroyden_state(batched::Bool, x, threshold)
-    T = eltype(x)
-    if batched
-        U = fill!(similar(x, (threshold, size(x, 1), size(x, 2))), zero(T))
-        Vᵀ = fill!(similar(x, (size(x, 1), threshold, size(x, 2))), zero(T))
-    else
-        U = fill!(similar(x, (threshold, length(x))), zero(T))
-        Vᵀ = fill!(similar(x, (length(x), threshold)), zero(T))
-    end
-    return U, Vᵀ
-end
+        U[idx, :] .= (δxₙ .- U[idx, :]) ./
+                     (sum(Vᵀ[:, idx] .* δfₙ) .+
+                      convert(T, 1e-5))
 
-function _rmatvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
-    x::Union{<:AbstractVector, <:Number})
-    length(U) == 0 && return x
-    return -x .+ vec((x' * Vᵀ) * U)
-end
+        _L = min(i + 1, η)
+        _ηNx = reshape(ηNx[1:_L], :, 1)
+        mul!(_ηNx, U[1:_L, :], reshape(δfₙ, L, 1))
+        mul!(reshape(δxₙ, L, 1), Vᵀ[:, 1:_L], _ηNx)
 
-function _rmatvec(U::AbstractArray{T1, 3}, Vᵀ::AbstractArray{T2, 3},
-    x::AbstractMatrix) where {T1, T2}
-    length(U) == 0 && return x
-    Vᵀx = sum(Vᵀ .* reshape(x, size(x, 1), 1, size(x, 2)); dims = 1)
-    return -x .+ _drdims_sum(U .* permutedims(Vᵀx, (2, 1, 3)); dims = 1)
-end
+        xₙ₋₁ .= xₙ
+        fₙ₋₁ .= fₙ
+    end
 
-function _matvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
-    x::Union{<:AbstractVector, <:Number})
-    length(U) == 0 && return x
-    return -x .+ vec(Vᵀ * (U * x))
-end
+    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
+        xₙ = storage.u
+        fₙ = f(xₙ)
+    end
 
-function _matvec(U::AbstractArray{T1, 3}, Vᵀ::AbstractArray{T2, 3},
-    x::AbstractMatrix) where {T1, T2}
-    length(U) == 0 && return x
-    xUᵀ = sum(reshape(x, size(x, 1), 1, size(x, 2)) .* permutedims(U, (2, 1, 3)); dims = 1)
-    return -x .+ _drdims_sum(xUᵀ .* Vᵀ; dims = 2)
+    xₙ = restore_scalar ? xₙ[] : xₙ
+    fₙ = restore_scalar ? fₙ[] : fₙ
+    return DiffEqBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
 end
-
-_drdims_sum(args...; dims = :) = dropdims(sum(args...; dims); dims)

From 48b84df7c8ac470a691c63ecaa4f9ca2d5f0178f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 28 Jun 2023 11:31:09 -0400
Subject: [PATCH 140/700] Revert "LBroyden"

This reverts commit c98922be35229fb0e0835c9eecb3b948aaa60b54.
---
 .../SimpleNonlinearSolveADLinearSolveExt.jl   |  25 ++-
 .../ext/SimpleNonlinearSolveNNlibExt.jl       | 122 ++-----------
 .../src/batched/dfsane.jl                     |   2 +-
 .../src/batched/lbroyden.jl                   |   7 -
 lib/SimpleNonlinearSolve/src/broyden.jl       |  10 +-
 lib/SimpleNonlinearSolve/src/lbroyden.jl      | 163 ++++++++++--------
 6 files changed, 119 insertions(+), 210 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
index d0a97eb86..96ba9168a 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
@@ -1,10 +1,8 @@
 module SimpleNonlinearSolveADLinearSolveExt
 
-using AbstractDifferentiation,
-    ArrayInterface, DiffEqBase, LinearAlgebra, LinearSolve,
+using AbstractDifferentiation, ArrayInterface, DiffEqBase, LinearAlgebra, LinearSolve,
     SimpleNonlinearSolve, SciMLBase
-import SimpleNonlinearSolve: _construct_batched_problem_structure,
-    _get_storage, _result_from_storage, _get_tolerance, @maybeinplace
+import SimpleNonlinearSolve: _construct_batched_problem_structure, _get_storage, _result_from_storage, _get_tolerance, @maybeinplace
 
 const AD = AbstractDifferentiation
 
@@ -22,18 +20,19 @@ function SimpleNonlinearSolve.SimpleBatchedNewtonRaphson(; chunk_size = Val{0}()
     # TODO: Use `diff_type`. FiniteDiff.jl is currently not available in AD.jl
     chunksize = SciMLBase._unwrap_val(chunk_size) == 0 ? nothing : chunk_size
     ad = SciMLBase._unwrap_val(autodiff) ?
-         AD.ForwardDiffBackend(; chunksize) :
-         AD.FiniteDifferencesBackend()
-    return SimpleBatchedNewtonRaphson{typeof(ad), Nothing, typeof(termination_condition)}(ad,
+        AD.ForwardDiffBackend(; chunksize) :
+        AD.FiniteDifferencesBackend()
+    return SimpleBatchedNewtonRaphson{typeof(ad), Nothing, typeof(termination_condition)}(
+        ad,
         nothing,
         termination_condition)
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
     alg::SimpleBatchedNewtonRaphson;
-    abstol = nothing,
-    reltol = nothing,
-    maxiters = 1000,
+    abstol=nothing,
+    reltol=nothing,
+    maxiters=1000,
     kwargs...)
     iip = isinplace(prob)
     @assert !iip "SimpleBatchedNewtonRaphson currently only supports out-of-place nonlinear problems."
@@ -58,9 +57,9 @@ function SciMLBase.__solve(prob::NonlinearProblem,
             alg,
             reconstruct(xₙ),
             reconstruct(fₙ);
-            retcode = ReturnCode.Success)
+            retcode=ReturnCode.Success)
 
-        solve(LinearProblem(𝓙, vec(fₙ); u0 = vec(δx)), alg.linsolve; kwargs...)
+        solve(LinearProblem(𝓙, vec(fₙ); u0=vec(δx)), alg.linsolve; kwargs...)
         xₙ .-= δx
 
         if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
@@ -84,7 +83,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         alg,
         reconstruct(xₙ),
         reconstruct(fₙ);
-        retcode = ReturnCode.MaxIters)
+        retcode=ReturnCode.MaxIters)
 end
 
 end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
index c0faefd9b..e62e2bda7 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
@@ -1,20 +1,18 @@
 module SimpleNonlinearSolveNNlibExt
 
 using ArrayInterface, DiffEqBase, LinearAlgebra, NNlib, SimpleNonlinearSolve, SciMLBase
-import SimpleNonlinearSolve: _construct_batched_problem_structure,
-    _get_storage, _init_𝓙, _result_from_storage, _get_tolerance, @maybeinplace
+import SimpleNonlinearSolve: _construct_batched_problem_structure, _get_storage, _init_𝓙, _result_from_storage, _get_tolerance, @maybeinplace
 
 function __init__()
     SimpleNonlinearSolve.NNlibExtLoaded[] = true
     return
 end
 
-# Broyden's method
 @views function SciMLBase.__solve(prob::NonlinearProblem,
     alg::BatchedBroyden;
-    abstol = nothing,
-    reltol = nothing,
-    maxiters = 1000,
+    abstol=nothing,
+    reltol=nothing,
+    maxiters=1000,
     kwargs...)
     iip = isinplace(prob)
 
@@ -26,7 +24,7 @@ end
 
     storage = _get_storage(mode, u)
 
-    xₙ, xₙ₋₁, δxₙ, δf = ntuple(_ -> copy(u), 4)
+    xₙ, xₙ₋₁, δx, δf = ntuple(_ -> copy(u), 4)
     T = eltype(u)
 
     atol = _get_tolerance(abstol, tc.abstol, T)
@@ -43,16 +41,16 @@ end
         xₙ .= xₙ₋₁ .- 𝓙⁻¹f
 
         @maybeinplace iip fₙ=f(xₙ)
-        δxₙ .= xₙ .- xₙ₋₁
+        δx .= xₙ .- xₙ₋₁
         δf .= fₙ .- fₙ₋₁
 
         batched_mul!(reshape(𝓙⁻¹f, L, 1, N), 𝓙⁻¹, reshape(δf, L, 1, N))
-        δxₙᵀ = reshape(δxₙ, 1, L, N)
+        δxᵀ = reshape(δx, 1, L, N)
 
-        batched_mul!(reshape(xᵀ𝓙⁻¹δf, 1, 1, N), δxₙᵀ, reshape(𝓙⁻¹f, L, 1, N))
-        batched_mul!(xᵀ𝓙⁻¹, δxₙᵀ, 𝓙⁻¹)
-        δxₙ .= (δxₙ .- 𝓙⁻¹f) ./ (xᵀ𝓙⁻¹δf .+ T(1e-5))
-        batched_mul!(𝓙⁻¹, reshape(δxₙ, L, 1, N), xᵀ𝓙⁻¹, one(T), one(T))
+        batched_mul!(reshape(xᵀ𝓙⁻¹δf, 1, 1, N), δxᵀ, reshape(𝓙⁻¹f, L, 1, N))
+        batched_mul!(xᵀ𝓙⁻¹, δxᵀ, 𝓙⁻¹)
+        δx .= (δx .- 𝓙⁻¹f) ./ (xᵀ𝓙⁻¹δf .+ T(1e-5))
+        batched_mul!(𝓙⁻¹, reshape(δx, L, 1, N), xᵀ𝓙⁻¹, one(T), one(T))
 
         if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
             retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, iip)
@@ -76,103 +74,7 @@ end
         alg,
         reconstruct(xₙ),
         reconstruct(fₙ);
-        retcode = ReturnCode.MaxIters)
-end
-
-# Limited Memory Broyden's method
-@views function SciMLBase.__solve(prob::NonlinearProblem,
-    alg::BatchedLBroyden;
-    abstol = nothing,
-    reltol = nothing,
-    maxiters = 1000,
-    kwargs...)
-    iip = isinplace(prob)
-
-    u, f, reconstruct = _construct_batched_problem_structure(prob)
-    L, N = size(u)
-    T = eltype(u)
-
-    tc = alg.termination_condition
-    mode = DiffEqBase.get_termination_mode(tc)
-
-    storage = _get_storage(mode, u)
-
-    η = min(maxiters, alg.threshold)
-    U = fill!(similar(u, (η, L, N)), zero(T))
-    Vᵀ = fill!(similar(u, (L, η, N)), zero(T))
-
-    xₙ, xₙ₋₁, δfₙ = ntuple(_ -> copy(u), 3)
-
-    atol = _get_tolerance(abstol, tc.abstol, T)
-    rtol = _get_tolerance(reltol, tc.reltol, T)
-    termination_condition = tc(storage)
-
-    @maybeinplace iip fₙ₋₁=f(xₙ) u
-    iip && (fₙ = copy(fₙ₋₁))
-    δxₙ = -copy(fₙ₋₁)
-    ηNx = similar(xₙ, η, N)
-
-    for i in 1:maxiters
-        @. xₙ = xₙ₋₁ - δxₙ
-        @maybeinplace iip fₙ=f(xₙ)
-        @. δxₙ = xₙ - xₙ₋₁
-        @. δfₙ = fₙ - fₙ₋₁
-
-        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
-            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, iip)
-            return DiffEqBase.build_solution(prob,
-                alg,
-                reconstruct(xₙ),
-                reconstruct(fₙ);
-                retcode)
-        end
-
-        _L = min(i, η)
-        _U = U[1:_L, :, :]
-        _Vᵀ = Vᵀ[:, 1:_L, :]
-
-        idx = mod1(i, η)
-
-        if i > 1
-            partial_ηNx = ηNx[1:_L, :]
-
-            _ηNx = reshape(partial_ηNx, 1, :, N)
-            batched_mul!(_ηNx, reshape(δxₙ, 1, L, N), _Vᵀ)
-            batched_mul!(Vᵀ[:, idx:idx, :], _ηNx, _U)
-            Vᵀ[:, idx, :] .-= δxₙ
-
-            _ηNx = reshape(partial_ηNx, :, 1, N)
-            batched_mul!(_ηNx, _U, reshape(δfₙ, L, 1, N))
-            batched_mul!(U[idx:idx, :, :], _Vᵀ, _ηNx)
-            U[idx, :, :] .-= δfₙ
-        else
-            Vᵀ[:, idx, :] .= -δxₙ
-            U[idx, :, :] .= -δfₙ
-        end
-
-        U[idx, :, :] .= (δxₙ .- U[idx, :, :]) ./
-                        (sum(Vᵀ[:, idx, :] .* δfₙ; dims = 1) .+
-                         convert(T, 1e-5))
-
-        _L = min(i + 1, η)
-        _ηNx = reshape(ηNx[1:_L, :], :, 1, N)
-        batched_mul!(_ηNx, U[1:_L, :, :], reshape(δfₙ, L, 1, N))
-        batched_mul!(reshape(δxₙ, L, 1, N), Vᵀ[:, 1:_L, :], _ηNx)
-
-        xₙ₋₁ .= xₙ
-        fₙ₋₁ .= fₙ
-    end
-
-    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-        xₙ = storage.u
-        @maybeinplace iip fₙ=f(xₙ)
-    end
-
-    return DiffEqBase.build_solution(prob,
-        alg,
-        reconstruct(xₙ),
-        reconstruct(fₙ);
-        retcode = ReturnCode.MaxIters)
+        retcode=ReturnCode.MaxIters)
 end
 
 end
diff --git a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
index 88f02ebe7..fe7cbcddf 100644
--- a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
@@ -1,4 +1,4 @@
-Base.@kwdef struct SimpleBatchedDFSane{T, F, TC <: NLSolveTerminationCondition} <:
+@kwdef struct SimpleBatchedDFSane{T, F, TC <: NLSolveTerminationCondition} <:
               AbstractBatchedNonlinearSolveAlgorithm
     σₘᵢₙ::T = 1.0f-10
     σₘₐₓ::T = 1.0f+10
diff --git a/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl b/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
index 5934c8fe0..e69de29bb 100644
--- a/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
@@ -1,7 +0,0 @@
-struct BatchedLBroyden{TC <: NLSolveTerminationCondition} <:
-    AbstractBatchedNonlinearSolveAlgorithm
-    termination_condition::TC
-    threshold::Int
-end
-
-# Implementation of solve using Package Extensions
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index adf94b033..6c5c3ce7f 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -30,9 +30,6 @@ end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
     abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
-    if SciMLBase.isinplace(prob)
-        error("Broyden currently only supports out-of-place nonlinear problems")
-    end
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
     f = Base.Fix2(prob.f, prob.p)
@@ -42,6 +39,10 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
     T = eltype(x)
     J⁻¹ = init_J(x)
 
+    if SciMLBase.isinplace(prob)
+        error("Broyden currently only supports out-of-place nonlinear problems")
+    end
+
     atol = _get_tolerance(abstol, tc.abstol, T)
     rtol = _get_tolerance(reltol, tc.reltol, T)
 
@@ -49,7 +50,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
         error("Broyden currently doesn't support SAFE_BEST termination modes")
     end
 
-    storage = _get_storage(mode, x)
+    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? NLSolveSafeTerminationResult() :
+              nothing
     termination_condition = tc(storage)
 
     xₙ = x
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index 95ec3895e..fc2b51a88 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -11,121 +11,134 @@ Broyden's method.
 
     This method is not very stable and can diverge even for very simple problems. This has mostly been
     tested for neural networks in DeepEquilibriumNetworks.jl.
-
-!!! note
-
-    To use the `batched` version, remember to load `NNlib`, i.e., `using NNlib` or
-    `import NNlib` must be present in your code.
 """
 struct LBroyden{batched, TC <: NLSolveTerminationCondition} <:
        AbstractSimpleNonlinearSolveAlgorithm
     termination_condition::TC
     threshold::Int
-end
 
-function LBroyden(; batched = false, threshold::Int = 27,
-    termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-        abstol = nothing,
-        reltol = nothing))
-    if batched
-        @assert NNlibExtLoaded[] "Please install and load `NNlib.jl` to use batched Broyden."
-        return BatchedLBroyden(termination_condition, threshold)
+    function LBroyden(; batched = false, threshold::Int = 27,
+        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+            abstol = nothing,
+            reltol = nothing))
+        return new{batched, typeof(termination_condition)}(termination_condition, threshold)
     end
-    return LBroyden{true, typeof(termination_condition)}(termination_condition, threshold)
 end
 
-@views function SciMLBase.__solve(prob::NonlinearProblem, alg::LBroyden, args...;
+@views function SciMLBase.__solve(prob::NonlinearProblem, alg::LBroyden{batched}, args...;
     abstol = nothing, reltol = nothing, maxiters = 1000,
-    kwargs...)
-    if SciMLBase.isinplace(prob)
-        error("LBroyden currently only supports out-of-place nonlinear problems")
-    end
+    kwargs...) where {batched}
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
-    η = min(maxiters, alg.threshold)
+    threshold = min(maxiters, alg.threshold)
     x = float(prob.u0)
 
-    # FIXME: The scalar case currently is very inefficient
+    batched && @assert ndims(x)==2 "Batched LBroyden only supports 2D arrays"
+
     if x isa Number
         restore_scalar = true
         x = [x]
-        f = u -> [prob.f(u[], prob.p)]
+        f = u -> prob.f(u[], prob.p)
     else
         f = Base.Fix2(prob.f, prob.p)
         restore_scalar = false
     end
 
-    L = length(x)
+    fₙ = f(x)
     T = eltype(x)
 
-    U = fill!(similar(x, (η, L)), zero(T))
-    Vᵀ = fill!(similar(x, (L, η)), zero(T))
+    if SciMLBase.isinplace(prob)
+        error("LBroyden currently only supports out-of-place nonlinear problems")
+    end
+
+    U, Vᵀ = _init_lbroyden_state(batched, x, threshold)
 
-    atol = _get_tolerance(abstol, tc.abstol, T)
-    rtol = _get_tolerance(reltol, tc.reltol, T)
-    storage = _get_storage(mode, x)
-    termination_condition = tc(storage)
+    atol = abstol !== nothing ? abstol :
+           (tc.abstol !== nothing ? tc.abstol :
+            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5))
+    rtol = reltol !== nothing ? reltol :
+           (tc.reltol !== nothing ? tc.reltol : eps(real(one(eltype(T))))^(4 // 5))
 
-    xₙ, xₙ₋₁, δfₙ = ntuple(_ -> copy(x), 3)
-    fₙ₋₁ = f(x)
-    δxₙ = -copy(fₙ₋₁)
-    ηNx = similar(xₙ, η)
+    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
+        error("LBroyden currently doesn't support SAFE_BEST termination modes")
+    end
+
+    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? NLSolveSafeTerminationResult() :
+              nothing
+    termination_condition = tc(storage)
 
+    xₙ = x
+    xₙ₋₁ = x
+    fₙ₋₁ = fₙ
+    update = fₙ
     for i in 1:maxiters
-        @. xₙ = xₙ₋₁ - δxₙ
+        xₙ = xₙ₋₁ .+ update
         fₙ = f(xₙ)
-        @. δxₙ = xₙ - xₙ₋₁
-        @. δfₙ = fₙ - fₙ₋₁
+        Δxₙ = xₙ .- xₙ₋₁
+        Δfₙ = fₙ .- fₙ₋₁
 
-        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
-            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, Val(false))
+        if termination_condition(restore_scalar ? [fₙ] : fₙ, xₙ, xₙ₋₁, atol, rtol)
             xₙ = restore_scalar ? xₙ[] : xₙ
-            fₙ = restore_scalar ? fₙ[] : fₙ
-            return DiffEqBase.build_solution(prob, alg, xₙ, fₙ; retcode)
+            return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
         end
 
-        _L = min(i, η)
-        _U = U[1:_L, :]
-        _Vᵀ = Vᵀ[:, 1:_L]
-
-        idx = mod1(i, η)
+        _U = selectdim(U, 1, 1:min(threshold, i))
+        _Vᵀ = selectdim(Vᵀ, 2, 1:min(threshold, i))
 
-        partial_ηNx = ηNx[1:_L]
+        vᵀ = _rmatvec(_U, _Vᵀ, Δxₙ)
+        mvec = _matvec(_U, _Vᵀ, Δfₙ)
+        u = (Δxₙ .- mvec) ./ (sum(vᵀ .* Δfₙ) .+ convert(T, 1e-5))
 
-        if i > 1
-            _ηNx = reshape(partial_ηNx, 1, :)
-            mul!(_ηNx, reshape(δxₙ, 1, L), _Vᵀ)
-            mul!(Vᵀ[:, idx:idx], _ηNx, _U)
-            Vᵀ[:, idx] .-= δxₙ
+        selectdim(Vᵀ, 2, mod1(i, threshold)) .= vᵀ
+        selectdim(U, 1, mod1(i, threshold)) .= u
 
-            _ηNx = reshape(partial_ηNx, :, 1)
-            mul!(_ηNx, _U, reshape(δfₙ, L, 1))
-            mul!(U[idx:idx, :], _Vᵀ, _ηNx)
-            U[idx, :] .-= δfₙ
-        else
-            Vᵀ[:, idx] .= -δxₙ
-            U[idx, :] .= -δfₙ
-        end
+        update = -_matvec(selectdim(U, 1, 1:min(threshold, i + 1)),
+            selectdim(Vᵀ, 2, 1:min(threshold, i + 1)), fₙ)
 
-        U[idx, :] .= (δxₙ .- U[idx, :]) ./
-                     (sum(Vᵀ[:, idx] .* δfₙ) .+
-                      convert(T, 1e-5))
+        xₙ₋₁ = xₙ
+        fₙ₋₁ = fₙ
+    end
 
-        _L = min(i + 1, η)
-        _ηNx = reshape(ηNx[1:_L], :, 1)
-        mul!(_ηNx, U[1:_L, :], reshape(δfₙ, L, 1))
-        mul!(reshape(δxₙ, L, 1), Vᵀ[:, 1:_L], _ηNx)
+    xₙ = restore_scalar ? xₙ[] : xₙ
+    return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
+end
 
-        xₙ₋₁ .= xₙ
-        fₙ₋₁ .= fₙ
+function _init_lbroyden_state(batched::Bool, x, threshold)
+    T = eltype(x)
+    if batched
+        U = fill!(similar(x, (threshold, size(x, 1), size(x, 2))), zero(T))
+        Vᵀ = fill!(similar(x, (size(x, 1), threshold, size(x, 2))), zero(T))
+    else
+        U = fill!(similar(x, (threshold, length(x))), zero(T))
+        Vᵀ = fill!(similar(x, (length(x), threshold)), zero(T))
     end
+    return U, Vᵀ
+end
 
-    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-        xₙ = storage.u
-        fₙ = f(xₙ)
-    end
+function _rmatvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
+    x::Union{<:AbstractVector, <:Number})
+    length(U) == 0 && return x
+    return -x .+ vec((x' * Vᵀ) * U)
+end
 
-    xₙ = restore_scalar ? xₙ[] : xₙ
-    fₙ = restore_scalar ? fₙ[] : fₙ
-    return DiffEqBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
+function _rmatvec(U::AbstractArray{T1, 3}, Vᵀ::AbstractArray{T2, 3},
+    x::AbstractMatrix) where {T1, T2}
+    length(U) == 0 && return x
+    Vᵀx = sum(Vᵀ .* reshape(x, size(x, 1), 1, size(x, 2)); dims = 1)
+    return -x .+ _drdims_sum(U .* permutedims(Vᵀx, (2, 1, 3)); dims = 1)
 end
+
+function _matvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
+    x::Union{<:AbstractVector, <:Number})
+    length(U) == 0 && return x
+    return -x .+ vec(Vᵀ * (U * x))
+end
+
+function _matvec(U::AbstractArray{T1, 3}, Vᵀ::AbstractArray{T2, 3},
+    x::AbstractMatrix) where {T1, T2}
+    length(U) == 0 && return x
+    xUᵀ = sum(reshape(x, size(x, 1), 1, size(x, 2)) .* permutedims(U, (2, 1, 3)); dims = 1)
+    return -x .+ _drdims_sum(xUᵀ .* Vᵀ; dims = 2)
+end
+
+_drdims_sum(args...; dims = :) = dropdims(sum(args...; dims); dims)

From 4455c08bfdad3f8c5118bc8a9138b9e95bda3545 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 28 Jun 2023 11:31:24 -0400
Subject: [PATCH 141/700] Format

---
 .../SimpleNonlinearSolveADLinearSolveExt.jl   | 25 ++++++++++---------
 .../ext/SimpleNonlinearSolveNNlibExt.jl       | 11 ++++----
 .../src/SimpleNonlinearSolve.jl               |  3 ++-
 .../src/batched/broyden.jl                    |  2 +-
 .../src/batched/dfsane.jl                     | 24 +++++++++---------
 .../src/batched/lbroyden.jl                   |  1 +
 .../src/batched/raphson.jl                    |  2 +-
 lib/SimpleNonlinearSolve/src/batched/utils.jl |  4 +--
 lib/SimpleNonlinearSolve/src/raphson.jl       | 10 ++++----
 9 files changed, 43 insertions(+), 39 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
index 96ba9168a..d0a97eb86 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
@@ -1,8 +1,10 @@
 module SimpleNonlinearSolveADLinearSolveExt
 
-using AbstractDifferentiation, ArrayInterface, DiffEqBase, LinearAlgebra, LinearSolve,
+using AbstractDifferentiation,
+    ArrayInterface, DiffEqBase, LinearAlgebra, LinearSolve,
     SimpleNonlinearSolve, SciMLBase
-import SimpleNonlinearSolve: _construct_batched_problem_structure, _get_storage, _result_from_storage, _get_tolerance, @maybeinplace
+import SimpleNonlinearSolve: _construct_batched_problem_structure,
+    _get_storage, _result_from_storage, _get_tolerance, @maybeinplace
 
 const AD = AbstractDifferentiation
 
@@ -20,19 +22,18 @@ function SimpleNonlinearSolve.SimpleBatchedNewtonRaphson(; chunk_size = Val{0}()
     # TODO: Use `diff_type`. FiniteDiff.jl is currently not available in AD.jl
     chunksize = SciMLBase._unwrap_val(chunk_size) == 0 ? nothing : chunk_size
     ad = SciMLBase._unwrap_val(autodiff) ?
-        AD.ForwardDiffBackend(; chunksize) :
-        AD.FiniteDifferencesBackend()
-    return SimpleBatchedNewtonRaphson{typeof(ad), Nothing, typeof(termination_condition)}(
-        ad,
+         AD.ForwardDiffBackend(; chunksize) :
+         AD.FiniteDifferencesBackend()
+    return SimpleBatchedNewtonRaphson{typeof(ad), Nothing, typeof(termination_condition)}(ad,
         nothing,
         termination_condition)
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
     alg::SimpleBatchedNewtonRaphson;
-    abstol=nothing,
-    reltol=nothing,
-    maxiters=1000,
+    abstol = nothing,
+    reltol = nothing,
+    maxiters = 1000,
     kwargs...)
     iip = isinplace(prob)
     @assert !iip "SimpleBatchedNewtonRaphson currently only supports out-of-place nonlinear problems."
@@ -57,9 +58,9 @@ function SciMLBase.__solve(prob::NonlinearProblem,
             alg,
             reconstruct(xₙ),
             reconstruct(fₙ);
-            retcode=ReturnCode.Success)
+            retcode = ReturnCode.Success)
 
-        solve(LinearProblem(𝓙, vec(fₙ); u0=vec(δx)), alg.linsolve; kwargs...)
+        solve(LinearProblem(𝓙, vec(fₙ); u0 = vec(δx)), alg.linsolve; kwargs...)
         xₙ .-= δx
 
         if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
@@ -83,7 +84,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         alg,
         reconstruct(xₙ),
         reconstruct(fₙ);
-        retcode=ReturnCode.MaxIters)
+        retcode = ReturnCode.MaxIters)
 end
 
 end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
index e62e2bda7..5b06530a6 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
@@ -1,7 +1,8 @@
 module SimpleNonlinearSolveNNlibExt
 
 using ArrayInterface, DiffEqBase, LinearAlgebra, NNlib, SimpleNonlinearSolve, SciMLBase
-import SimpleNonlinearSolve: _construct_batched_problem_structure, _get_storage, _init_𝓙, _result_from_storage, _get_tolerance, @maybeinplace
+import SimpleNonlinearSolve: _construct_batched_problem_structure,
+    _get_storage, _init_𝓙, _result_from_storage, _get_tolerance, @maybeinplace
 
 function __init__()
     SimpleNonlinearSolve.NNlibExtLoaded[] = true
@@ -10,9 +11,9 @@ end
 
 @views function SciMLBase.__solve(prob::NonlinearProblem,
     alg::BatchedBroyden;
-    abstol=nothing,
-    reltol=nothing,
-    maxiters=1000,
+    abstol = nothing,
+    reltol = nothing,
+    maxiters = 1000,
     kwargs...)
     iip = isinplace(prob)
 
@@ -74,7 +75,7 @@ end
         alg,
         reconstruct(xₙ),
         reconstruct(fₙ);
-        retcode=ReturnCode.MaxIters)
+        retcode = ReturnCode.MaxIters)
 end
 
 end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 49aef9fc8..23b332fb3 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -22,7 +22,8 @@ abstract type AbstractSimpleNonlinearSolveAlgorithm <: SciMLBase.AbstractNonline
 abstract type AbstractBracketingAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 abstract type AbstractNewtonAlgorithm{CS, AD, FDT} <: AbstractSimpleNonlinearSolveAlgorithm end
 abstract type AbstractImmutableNonlinearSolver <: AbstractSimpleNonlinearSolveAlgorithm end
-abstract type AbstractBatchedNonlinearSolveAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
+abstract type AbstractBatchedNonlinearSolveAlgorithm <:
+              AbstractSimpleNonlinearSolveAlgorithm end
 
 include("utils.jl")
 include("bisection.jl")
diff --git a/lib/SimpleNonlinearSolve/src/batched/broyden.jl b/lib/SimpleNonlinearSolve/src/batched/broyden.jl
index 85754880f..ed3cd5dfc 100644
--- a/lib/SimpleNonlinearSolve/src/batched/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/broyden.jl
@@ -1,5 +1,5 @@
 struct BatchedBroyden{TC <: NLSolveTerminationCondition} <:
-    AbstractBatchedNonlinearSolveAlgorithm
+       AbstractBatchedNonlinearSolveAlgorithm
     termination_condition::TC
 end
 
diff --git a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
index fe7cbcddf..09fc37f8d 100644
--- a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
@@ -1,4 +1,4 @@
-@kwdef struct SimpleBatchedDFSane{T, F, TC <: NLSolveTerminationCondition} <:
+Base.@kwdef struct SimpleBatchedDFSane{T, F, TC <: NLSolveTerminationCondition} <:
               AbstractBatchedNonlinearSolveAlgorithm
     σₘᵢₙ::T = 1.0f-10
     σₘₐₓ::T = 1.0f+10
@@ -10,17 +10,17 @@
     nₑₓₚ::Int = 2
     ηₛ::F = (f₍ₙₒᵣₘ₎₁, n, xₙ, fₙ) -> f₍ₙₒᵣₘ₎₁ ./ n .^ 2
     termination_condition::TC = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-        abstol=nothing,
-        reltol=nothing)
+        abstol = nothing,
+        reltol = nothing)
     max_inner_iterations::Int = 1000
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
     alg::SimpleBatchedDFSane,
     args...;
-    abstol=nothing,
-    reltol=nothing,
-    maxiters=100,
+    abstol = nothing,
+    reltol = nothing,
+    maxiters = 100,
     kwargs...)
     iip = isinplace(prob)
 
@@ -60,7 +60,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         return fₓ
     end
 
-    @maybeinplace iip fₙ₋₁ = ff!(f₍ₙₒᵣₘ₎ₙ₋₁, xₙ) xₙ
+    @maybeinplace iip fₙ₋₁=ff!(f₍ₙₒᵣₘ₎ₙ₋₁, xₙ) xₙ
     iip && (fₙ = similar(fₙ₋₁))
     ℋ = repeat(f₍ₙₒᵣₘ₎ₙ₋₁, M, 1)
     f̄ = similar(ℋ, 1, N)
@@ -79,7 +79,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         fill!(α₋, α₁)
         @. xₙ = xₙ₋₁ + α₊ * 𝒹
 
-        @maybeinplace iip fₙ = ff!(f₍ₙₒᵣₘ₎ₙ, xₙ)
+        @maybeinplace iip fₙ=ff!(f₍ₙₒᵣₘ₎ₙ, xₙ)
 
         for _ in 1:(alg.max_inner_iterations)
             𝒸 = @. f̄ + η - γ * α₊^2 * f₍ₙₒᵣₘ₎ₙ₋₁
@@ -90,7 +90,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
                 τₘᵢₙ * α₊,
                 τₘₐₓ * α₊)
             @. xₙ = xₙ₋₁ - α₋ * 𝒹
-            @maybeinplace iip fₙ = ff!(f₍ₙₒᵣₘ₎ₙ, xₙ)
+            @maybeinplace iip fₙ=ff!(f₍ₙₒᵣₘ₎ₙ, xₙ)
 
             (sum(f₍ₙₒᵣₘ₎ₙ .≤ 𝒸) ≥ N ÷ 2) && break
 
@@ -98,7 +98,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
                 τₘᵢₙ * α₋,
                 τₘₐₓ * α₋)
             @. xₙ = xₙ₋₁ + α₊ * 𝒹
-            @maybeinplace iip fₙ = ff!(f₍ₙₒᵣₘ₎ₙ, xₙ)
+            @maybeinplace iip fₙ=ff!(f₍ₙₒᵣₘ₎ₙ, xₙ)
         end
 
         if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
@@ -129,12 +129,12 @@ function SciMLBase.__solve(prob::NonlinearProblem,
 
     if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
         xₙ = storage.u
-        @maybeinplace iip fₙ = f(xₙ)
+        @maybeinplace iip fₙ=f(xₙ)
     end
 
     return DiffEqBase.build_solution(prob,
         alg,
         reconstruct(xₙ),
         reconstruct(fₙ);
-        retcode=ReturnCode.MaxIters)
+        retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl b/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
index e69de29bb..8b1378917 100644
--- a/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
@@ -0,0 +1 @@
+
diff --git a/lib/SimpleNonlinearSolve/src/batched/raphson.jl b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
index 2be565fc5..63c03ec89 100644
--- a/lib/SimpleNonlinearSolve/src/batched/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
@@ -1,5 +1,5 @@
 struct SimpleBatchedNewtonRaphson{AD, LS, TC <: NLSolveTerminationCondition} <:
-    AbstractBatchedNonlinearSolveAlgorithm
+       AbstractBatchedNonlinearSolveAlgorithm
     autodiff::AD
     linsolve::LS
     termination_condition::TC
diff --git a/lib/SimpleNonlinearSolve/src/batched/utils.jl b/lib/SimpleNonlinearSolve/src/batched/utils.jl
index b5dbd597f..7b85011f1 100644
--- a/lib/SimpleNonlinearSolve/src/batched/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/utils.jl
@@ -1,4 +1,4 @@
-macro maybeinplace(iip::Symbol, expr::Expr, u0::Union{Symbol, Nothing}=nothing)
+macro maybeinplace(iip::Symbol, expr::Expr, u0::Union{Symbol, Nothing} = nothing)
     @assert expr.head == :(=)
     x1, x2 = expr.args
     @assert x2.head == :call
@@ -64,7 +64,7 @@ function _result_from_storage(storage::NLSolveSafeTerminationResult, xₙ, fₙ,
         return ReturnCode.Success, xₙ, fₙ
     else
         if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-            @maybeinplace iip fₙ = f(xₙ)
+            @maybeinplace iip fₙ=f(xₙ)
             return ReturnCode.Terminated, storage.u, fₙ
         else
             return ReturnCode.Terminated, xₙ, fₙ
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 59eb1ed6d..2621c587e 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -35,7 +35,7 @@ and static array problems.
 """
 struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT} end
 
-function SimpleNewtonRaphson(; batched=false,
+function SimpleNewtonRaphson(; batched = false,
     chunk_size = Val{0}(),
     autodiff = Val{true}(),
     diff_type = Val{:forward},
@@ -46,10 +46,10 @@ function SimpleNewtonRaphson(; batched=false,
     if batched
         @assert ADLinearSolveExtLoaded[] "Please install and load `LinearSolve.jl` and `AbstractDifferentiation.jl` to use batched Newton-Raphson."
         termination_condition = ismissing(termination_condition) ?
-            NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-                abstol = nothing,
-                reltol = nothing) :
-            termination_condition
+                                NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+            abstol = nothing,
+            reltol = nothing) :
+                                termination_condition
         return SimpleBatchedNewtonRaphson(; chunk_size,
             autodiff,
             diff_type,

From cf90edd9cabdce2c1c7908e78986816f53187794 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Wed, 28 Jun 2023 21:31:34 +0200
Subject: [PATCH 142/700] final fixes

---
 lib/SimpleNonlinearSolve/src/itp.jl | 11 ++++-------
 1 file changed, 4 insertions(+), 7 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index bd5f888dd..b233c4f6b 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -13,13 +13,10 @@ struct Itp <: AbstractBracketingAlgorithm
     n0::Int
     function Itp(;k1::Real = 0.1, k2::Real = 2.0, n0::Int = 1)
         if k1 < 0
-            ArgumentError("Hyper-parameter κ₁ should not be negative")
-        end
-        if !isa(n0, Int)
-            ArgumentError("Hyper-parameter n₀ should be an Integer")
+            error("Hyper-parameter κ₁ should not be negative")
         end
         if n0 < 0
-            ArgumentError("Hyper-parameter n₀ should not be negative")
+            error("Hyper-parameter n₀ should not be negative")
         end
         if k2 < 1 || k2 > (1.5 + sqrt(5) / 2)
             ArgumentError("Hyper-parameter κ₂ should be between 1 and 1 + ϕ where ϕ ≈ 1.618... is the golden ratio")
@@ -29,7 +26,7 @@ struct Itp <: AbstractBracketingAlgorithm
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
-                            args...; abstol = nothing,
+                            args...; abstol = 1.0e-8,
                             maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan # a and b
@@ -47,7 +44,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
     #defining variables/cache
     k1 = alg.k1
     k2 = alg.k2
-    n0 = alg.k3
+    n0 = alg.n0
     n_h = ceil(log2((right - left) / (2 * ϵ)))
     n_max = n_h + n0
     mid = (left + right) / 2

From b550942242cb0e9b39b31e92dc83de0c8a8296e6 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Thu, 29 Jun 2023 01:59:30 +0200
Subject: [PATCH 143/700] added itp tests

---
 lib/SimpleNonlinearSolve/src/itp.jl         |  4 ++--
 lib/SimpleNonlinearSolve/test/basictests.jl | 14 +++++++++++++-
 2 files changed, 15 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index b233c4f6b..c0d69f595 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -26,7 +26,7 @@ struct Itp <: AbstractBracketingAlgorithm
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
-                            args...; abstol = 1.0e-8,
+                            args...; abstol = 1.0e-10,
                             maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan # a and b
@@ -94,7 +94,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
         mid = (left + right) / 2
 
         if (right - left < 2 * ϵ)
-            return SciMLBase.build_solution(prob, alg, mid, fl;
+            return SciMLBase.build_solution(prob, alg, mid, f(mid);
             retcode = ReturnCode.Success, left = left,
             right = right)
         end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index aea173157..34ef7096f 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -215,6 +215,18 @@ for p in 1.1:0.1:100.0
     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
 end
 
+# ITP
+g = function (p)
+    probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
+    sol = solve(probN, Itp())
+    return sol.u
+end
+
+for p in 1.1:0.1:100.0
+    @test g(p) ≈ sqrt(p)
+    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+end
+
 # Alefeld
 g = function (p)
     probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
@@ -242,7 +254,7 @@ end
 f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
 t = (p) -> [sqrt(p[2] / p[1])]
 p = [0.9, 50.0]
-for alg in [Bisection(), Falsi(), Ridder(), Brent()]
+for alg in [Bisection(), Falsi(), Ridder(), Brent(), Itp()]
     global g, p
     g = function (p)
         probN = IntervalNonlinearProblem{false}(f, tspan, p)

From 0517f94f213c963fb5a4354e3a4e9a356f3cc547 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Fri, 30 Jun 2023 14:55:58 +0200
Subject: [PATCH 144/700] hyper param change

---
 lib/SimpleNonlinearSolve/src/itp.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index c0d69f595..568bb71b8 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -11,7 +11,7 @@ struct Itp <: AbstractBracketingAlgorithm
     k1::Real
     k2::Real
     n0::Int
-    function Itp(;k1::Real = 0.1, k2::Real = 2.0, n0::Int = 1)
+    function Itp(;k1::Real = 0.3, k2::Real = 2.0, n0::Int = 1)
         if k1 < 0
             error("Hyper-parameter κ₁ should not be negative")
         end
@@ -26,7 +26,7 @@ struct Itp <: AbstractBracketingAlgorithm
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
-                            args...; abstol = 1.0e-10,
+                            args...; abstol = 1.0e-8,
                             maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan # a and b

From 28aef82d10b7e4578b6b8ab9423fc1532090bd1a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 30 Jun 2023 15:15:54 -0400
Subject: [PATCH 145/700] Add Inplace tests

---
 lib/SimpleNonlinearSolve/Project.toml         |  2 +-
 .../src/SimpleNonlinearSolve.jl               |  4 +-
 .../src/batched/dfsane.jl                     |  2 +-
 .../src/batched/lbroyden.jl                   |  1 -
 lib/SimpleNonlinearSolve/test/inplace.jl      | 52 +++++++++++++++++++
 lib/SimpleNonlinearSolve/test/runtests.jl     |  7 +--
 6 files changed, 59 insertions(+), 9 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/inplace.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index f1f472d08..258f009d0 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -21,8 +21,8 @@ LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 
 [extensions]
-SimpleNonlinearSolveNNlibExt = "NNlib"
 SimpleNonlinearSolveADLinearSolveExt = ["AbstractDifferentiation", "LinearSolve"]
+SimpleNonlinearSolveNNlibExt = "NNlib"
 
 [compat]
 AbstractDifferentiation = "0.5"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 23b332fb3..cd4855612 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -45,7 +45,6 @@ include("batched/utils.jl")
 include("batched/raphson.jl")
 include("batched/dfsane.jl")
 include("batched/broyden.jl")
-include("batched/lbroyden.jl")
 
 import PrecompileTools
 
@@ -79,7 +78,6 @@ end
 # DiffEq styled algorithms
 export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, Halley, Klement,
     Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld
-export BatchedBroyden, SimpleBatchedNewtonRaphson, SimpleBatchedDFSane,
-    BatchedLBroyden
+export BatchedBroyden, SimpleBatchedNewtonRaphson, SimpleBatchedDFSane
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
index 09fc37f8d..a394517a0 100644
--- a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
@@ -1,5 +1,5 @@
 Base.@kwdef struct SimpleBatchedDFSane{T, F, TC <: NLSolveTerminationCondition} <:
-              AbstractBatchedNonlinearSolveAlgorithm
+                   AbstractBatchedNonlinearSolveAlgorithm
     σₘᵢₙ::T = 1.0f-10
     σₘₐₓ::T = 1.0f+10
     σ₁::T = 1.0f0
diff --git a/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl b/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
deleted file mode 100644
index 8b1378917..000000000
--- a/lib/SimpleNonlinearSolve/src/batched/lbroyden.jl
+++ /dev/null
@@ -1 +0,0 @@
-
diff --git a/lib/SimpleNonlinearSolve/test/inplace.jl b/lib/SimpleNonlinearSolve/test/inplace.jl
new file mode 100644
index 000000000..4c43a1da8
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/inplace.jl
@@ -0,0 +1,52 @@
+using SimpleNonlinearSolve, StaticArrays, BenchmarkTools, DiffEqBase, LinearAlgebra, Test,
+    NNlib, AbstractDifferentiation, LinearSolve
+
+# Supported Solvers: BatchedBroyden, SimpleBatchedDFSane
+function f!(du::AbstractArray{<:Number, N},
+    u::AbstractArray{<:Number, N},
+    p::AbstractVector) where {N}
+    u_ = reshape(u, :, size(u, N))
+    du .= reshape(sum(abs2, u_; dims = 1) .- reshape(p, 1, :),
+        ntuple(_ -> 1, N - 1)...,
+        size(u, N))
+    return du
+end
+
+function f!(du::AbstractMatrix, u::AbstractMatrix, p::AbstractVector)
+    du .= sum(abs2, u; dims = 1) .- reshape(p, 1, :)
+    return du
+end
+
+function f!(du::AbstractVector, u::AbstractVector, p::AbstractVector)
+    du .= sum(abs2, u) .- p
+    return du
+end
+
+@testset "Solver: $(nameof(typeof(solver)))" for solver in (Broyden(batched = true),
+    SimpleDFSane(batched = true))
+    @testset "T: $T" for T in (Float32, Float64)
+        p = rand(T, 5)
+        @testset "size(u0): $sz" for sz in ((2, 5), (1, 5), (2, 3, 5))
+            u0 = ones(T, sz)
+            prob = NonlinearProblem{true}(f!, u0, p)
+
+            sol = solve(prob, solver)
+
+            @test SciMLBase.successful_retcode(sol.retcode)
+
+            @test sol.resid≈zero(sol.resid) atol=5e-3
+        end
+
+        p = rand(T, 1)
+        @testset "size(u0): $sz" for sz in ((3,), (5,), (10,))
+            u0 = ones(T, sz)
+            prob = NonlinearProblem{true}(f!, u0, p)
+
+            sol = solve(prob, solver)
+
+            @test SciMLBase.successful_retcode(sol.retcode)
+
+            @test sol.resid≈zero(sol.resid) atol=5e-3
+        end
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 94a0086e4..bea57ea0a 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -1,14 +1,15 @@
-using Pkg
 using SafeTestsets
-const LONGER_TESTS = false
 
 const GROUP = get(ENV, "GROUP", "All")
-const is_APPVEYOR = Sys.iswindows() && haskey(ENV, "APPVEYOR")
 
 @time begin
     if GROUP == "All" || GROUP == "Core"
         @time @safetestset "Basic Tests + Some AD" begin
             include("basictests.jl")
         end
+
+        @time @safetestset "Inplace Tests" begin
+            include("inplace.jl")
+        end
     end
 end

From 6c3223915e6a8c0551aea0ebc3667c6c4813fb89 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 30 Jun 2023 15:29:46 -0400
Subject: [PATCH 146/700] Allow v1.6 to work

---
 lib/SimpleNonlinearSolve/src/batched/dfsane.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
index a394517a0..a76c768c2 100644
--- a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
@@ -42,7 +42,8 @@ function SciMLBase.__solve(prob::NonlinearProblem,
     α₊, α₋ = similar(u, 1, N), similar(u, 1, N)
     σₙ = fill(T(alg.σ₁), 1, N)
     𝒹 = similar(σₙ, L, N)
-    (; M, nₑₓₚ) = alg
+    M = alg.M
+    nₑₓₚ = alg.nₑₓₚ
 
     xₙ, xₙ₋₁, f₍ₙₒᵣₘ₎ₙ₋₁, f₍ₙₒᵣₘ₎ₙ = copy(u), copy(u), similar(u, 1, N), similar(u, 1, N)
 

From 504ab19c750efa76093d3ef00a41d843777667a7 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Fri, 7 Jul 2023 02:26:37 +0200
Subject: [PATCH 147/700] final hyper params, tol and some modifications

---
 lib/SimpleNonlinearSolve/src/itp.jl | 11 ++++++-----
 1 file changed, 6 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 568bb71b8..5a91df004 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -11,7 +11,7 @@ struct Itp <: AbstractBracketingAlgorithm
     k1::Real
     k2::Real
     n0::Int
-    function Itp(;k1::Real = 0.3, k2::Real = 2.0, n0::Int = 1)
+    function Itp(;k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
         if k1 < 0
             error("Hyper-parameter κ₁ should not be negative")
         end
@@ -26,7 +26,7 @@ struct Itp <: AbstractBracketingAlgorithm
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
-                            args...; abstol = 1.0e-8,
+                            args...; abstol = 1.0e-15,
                             maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan # a and b
@@ -46,7 +46,6 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
     k2 = alg.k2
     n0 = alg.n0
     n_h = ceil(log2((right - left) / (2 * ϵ)))
-    n_max = n_h + n0
     mid = (left + right) / 2
     x_f = (fr * left - fl * right) / (fr - fl)
     xt = left
@@ -54,11 +53,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
     r = zero(left) #minmax radius
     δ = zero(left) # truncation error
     σ = 1.0
+    ϵ_s = ϵ * 2^(n_h + n0)
     i = 0 #iteration
     while i <= maxiters
         #mid = (left + right) / 2
-        r = ϵ * 2 ^ (n_max - i) - ((right - left) / 2)
-        δ = k1 * (right - left) ^ k2
+        r = ϵ_s - ((right - left) / 2)
+        δ = k1 * ((right - left) ^ k2)
 
         ## Interpolation step ##
         x_f =  (fr * left - fl * right) / (fr - fl)
@@ -92,6 +92,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
         end
         i += 1
         mid = (left + right) / 2
+        ϵ_s /= 2
 
         if (right - left < 2 * ϵ)
             return SciMLBase.build_solution(prob, alg, mid, f(mid);

From bd3d622f519c95266c026aebcd7d2e35e0e9ffa4 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Fri, 7 Jul 2023 02:26:51 +0200
Subject: [PATCH 148/700] error check tests

---
 lib/SimpleNonlinearSolve/test/basictests.jl | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 34ef7096f..151536005 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -357,6 +357,18 @@ probB = IntervalNonlinearProblem(f, tspan)
 sol = solve(probB, Alefeld())
 @test sol.u ≈ sqrt(2.0)
 
+# Itp
+sol = solve(probB, Itp())
+@test sol.u ≈ sqrt(2.0)
+tspan = (sqrt(2.0), 10.0)
+probB = IntervalNonlinearProblem(f, tspan)
+sol = solve(probB, Itp())
+@test sol.u ≈ sqrt(2.0)
+tspan = (0.0, sqrt(2.0))
+probB = IntervalNonlinearProblem(f, tspan)
+sol = solve(probB, Itp())
+@test sol.u ≈ sqrt(2.0)
+
 # Garuntee Tests for Bisection
 f = function (u, p)
     if u < 2.0

From 8356a887777ba0be091492d2b4d86fee08e8b309 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Fri, 7 Jul 2023 02:35:09 +0200
Subject: [PATCH 149/700] format

---
 lib/SimpleNonlinearSolve/src/itp.jl | 17 ++++++++---------
 1 file changed, 8 insertions(+), 9 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 5a91df004..9968cbab1 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -11,7 +11,7 @@ struct Itp <: AbstractBracketingAlgorithm
     k1::Real
     k2::Real
     n0::Int
-    function Itp(;k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
+    function Itp(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
         if k1 < 0
             error("Hyper-parameter κ₁ should not be negative")
         end
@@ -26,8 +26,8 @@ struct Itp <: AbstractBracketingAlgorithm
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
-                            args...; abstol = 1.0e-15,
-                            maxiters = 1000, kwargs...)
+    args...; abstol = 1.0e-15,
+    maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan # a and b
     fl, fr = f(left), f(right)
@@ -58,10 +58,10 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
     while i <= maxiters
         #mid = (left + right) / 2
         r = ϵ_s - ((right - left) / 2)
-        δ = k1 * ((right - left) ^ k2)
+        δ = k1 * ((right - left)^k2)
 
         ## Interpolation step ##
-        x_f =  (fr * left - fl * right) / (fr - fl)
+        x_f = (fr * left - fl * right) / (fr - fl)
 
         ## Truncation step ##
         σ = sign(mid - x_f)
@@ -96,11 +96,10 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
 
         if (right - left < 2 * ϵ)
             return SciMLBase.build_solution(prob, alg, mid, f(mid);
-            retcode = ReturnCode.Success, left = left,
-            right = right)
+                retcode = ReturnCode.Success, left = left,
+                right = right)
         end
     end
     return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
         left = left, right = right)
-                               
-end
\ No newline at end of file
+end

From 4140c20e2cc4872e0d41025279e9a7eb04145bb7 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 10 Jul 2023 12:47:02 -0400
Subject: [PATCH 150/700] Update batched Raphson to use same parameters as
 unbatched

---
 lib/SimpleNonlinearSolve/Project.toml         |  7 --
 .../SimpleNonlinearSolveADLinearSolveExt.jl   | 90 -------------------
 .../src/SimpleNonlinearSolve.jl               |  3 +-
 .../src/batched/dfsane.jl                     |  4 +-
 .../src/batched/raphson.jl                    | 77 +++++++++++++++-
 lib/SimpleNonlinearSolve/src/dfsane.jl        |  2 +-
 lib/SimpleNonlinearSolve/src/raphson.jl       | 17 ++--
 lib/SimpleNonlinearSolve/test/Project.toml    |  2 -
 lib/SimpleNonlinearSolve/test/basictests.jl   | 12 ++-
 lib/SimpleNonlinearSolve/test/inplace.jl      |  4 +-
 10 files changed, 98 insertions(+), 120 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 258f009d0..89848eb78 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -16,21 +16,16 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [weakdeps]
-AbstractDifferentiation = "c29ec348-61ec-40c8-8164-b8c60e9d9f3d"
-LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 
 [extensions]
-SimpleNonlinearSolveADLinearSolveExt = ["AbstractDifferentiation", "LinearSolve"]
 SimpleNonlinearSolveNNlibExt = "NNlib"
 
 [compat]
-AbstractDifferentiation = "0.5"
 ArrayInterface = "6, 7"
 DiffEqBase = "6.126"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
-LinearSolve = "2"
 NNlib = "0.8, 0.9"
 PackageExtensionCompat = "1"
 PrecompileTools = "1"
@@ -40,6 +35,4 @@ StaticArraysCore = "1.4"
 julia = "1.6"
 
 [extras]
-AbstractDifferentiation = "c29ec348-61ec-40c8-8164-b8c60e9d9f3d"
-LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
deleted file mode 100644
index d0a97eb86..000000000
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveADLinearSolveExt.jl
+++ /dev/null
@@ -1,90 +0,0 @@
-module SimpleNonlinearSolveADLinearSolveExt
-
-using AbstractDifferentiation,
-    ArrayInterface, DiffEqBase, LinearAlgebra, LinearSolve,
-    SimpleNonlinearSolve, SciMLBase
-import SimpleNonlinearSolve: _construct_batched_problem_structure,
-    _get_storage, _result_from_storage, _get_tolerance, @maybeinplace
-
-const AD = AbstractDifferentiation
-
-function __init__()
-    SimpleNonlinearSolve.ADLinearSolveExtLoaded[] = true
-    return
-end
-
-function SimpleNonlinearSolve.SimpleBatchedNewtonRaphson(; chunk_size = Val{0}(),
-    autodiff = Val{true}(),
-    diff_type = Val{:forward},
-    termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-        abstol = nothing,
-        reltol = nothing))
-    # TODO: Use `diff_type`. FiniteDiff.jl is currently not available in AD.jl
-    chunksize = SciMLBase._unwrap_val(chunk_size) == 0 ? nothing : chunk_size
-    ad = SciMLBase._unwrap_val(autodiff) ?
-         AD.ForwardDiffBackend(; chunksize) :
-         AD.FiniteDifferencesBackend()
-    return SimpleBatchedNewtonRaphson{typeof(ad), Nothing, typeof(termination_condition)}(ad,
-        nothing,
-        termination_condition)
-end
-
-function SciMLBase.__solve(prob::NonlinearProblem,
-    alg::SimpleBatchedNewtonRaphson;
-    abstol = nothing,
-    reltol = nothing,
-    maxiters = 1000,
-    kwargs...)
-    iip = isinplace(prob)
-    @assert !iip "SimpleBatchedNewtonRaphson currently only supports out-of-place nonlinear problems."
-    u, f, reconstruct = _construct_batched_problem_structure(prob)
-
-    tc = alg.termination_condition
-    mode = DiffEqBase.get_termination_mode(tc)
-
-    storage = _get_storage(mode, u)
-
-    xₙ, xₙ₋₁, δx = copy(u), copy(u), copy(u)
-    T = eltype(u)
-
-    atol = _get_tolerance(abstol, tc.abstol, T)
-    rtol = _get_tolerance(reltol, tc.reltol, T)
-    termination_condition = tc(storage)
-
-    for i in 1:maxiters
-        fₙ, (𝓙,) = AD.value_and_jacobian(alg.autodiff, f, xₙ)
-
-        iszero(fₙ) && return DiffEqBase.build_solution(prob,
-            alg,
-            reconstruct(xₙ),
-            reconstruct(fₙ);
-            retcode = ReturnCode.Success)
-
-        solve(LinearProblem(𝓙, vec(fₙ); u0 = vec(δx)), alg.linsolve; kwargs...)
-        xₙ .-= δx
-
-        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
-            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, iip)
-            return DiffEqBase.build_solution(prob,
-                alg,
-                reconstruct(xₙ),
-                reconstruct(fₙ);
-                retcode)
-        end
-
-        xₙ₋₁ .= xₙ
-    end
-
-    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-        xₙ = storage.u
-        fₙ = f(xₙ)
-    end
-
-    return DiffEqBase.build_solution(prob,
-        alg,
-        reconstruct(xₙ),
-        reconstruct(fₙ);
-        retcode = ReturnCode.MaxIters)
-end
-
-end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index cd4855612..bc57d12cb 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -15,7 +15,6 @@ function __init__()
     @require_extensions
 end
 
-const ADLinearSolveExtLoaded = Ref{Bool}(false)
 const NNlibExtLoaded = Ref{Bool}(false)
 
 abstract type AbstractSimpleNonlinearSolveAlgorithm <: SciMLBase.AbstractNonlinearAlgorithm end
@@ -78,6 +77,6 @@ end
 # DiffEq styled algorithms
 export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, Halley, Klement,
     Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld
-export BatchedBroyden, SimpleBatchedNewtonRaphson, SimpleBatchedDFSane
+export BatchedBroyden, BatchedSimpleNewtonRaphson, BatchedSimpleDFSane
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
index a76c768c2..60bb6ae12 100644
--- a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
@@ -1,4 +1,4 @@
-Base.@kwdef struct SimpleBatchedDFSane{T, F, TC <: NLSolveTerminationCondition} <:
+Base.@kwdef struct BatchedSimpleDFSane{T, F, TC <: NLSolveTerminationCondition} <:
                    AbstractBatchedNonlinearSolveAlgorithm
     σₘᵢₙ::T = 1.0f-10
     σₘₐₓ::T = 1.0f+10
@@ -16,7 +16,7 @@ Base.@kwdef struct SimpleBatchedDFSane{T, F, TC <: NLSolveTerminationCondition}
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-    alg::SimpleBatchedDFSane,
+    alg::BatchedSimpleDFSane,
     args...;
     abstol = nothing,
     reltol = nothing,
diff --git a/lib/SimpleNonlinearSolve/src/batched/raphson.jl b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
index 63c03ec89..323c07e73 100644
--- a/lib/SimpleNonlinearSolve/src/batched/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
@@ -1,8 +1,77 @@
-struct SimpleBatchedNewtonRaphson{AD, LS, TC <: NLSolveTerminationCondition} <:
+struct BatchedSimpleNewtonRaphson{CS, AD, FDT, TC <: NLSolveTerminationCondition} <:
        AbstractBatchedNonlinearSolveAlgorithm
-    autodiff::AD
-    linsolve::LS
     termination_condition::TC
 end
 
-# Implementation of solve using Package Extensions
+alg_autodiff(alg::BatchedSimpleNewtonRaphson{CS, AD, FDT}) where {CS, AD, FDT} = AD
+diff_type(alg::BatchedSimpleNewtonRaphson{CS, AD, FDT}) where {CS, AD, FDT} = FDT
+
+function BatchedSimpleNewtonRaphson(; chunk_size = Val{0}(),
+    autodiff = Val{true}(),
+    diff_type = Val{:forward},
+    termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+        abstol = nothing,
+        reltol = nothing))
+    return BatchedSimpleNewtonRaphson{SciMLBase._unwrap_val(chunk_size),
+        SciMLBase._unwrap_val(autodiff),
+        SciMLBase._unwrap_val(diff_type), typeof(termination_condition)}(termination_condition)
+end
+
+function SciMLBase.__solve(prob::NonlinearProblem, alg::BatchedSimpleNewtonRaphson;
+    abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
+    iip = SciMLBase.isinplace(prob)
+    @assert !iip "BatchedSimpleNewtonRaphson currently only supports out-of-place nonlinear problems."
+    u, f, reconstruct = _construct_batched_problem_structure(prob)
+
+    tc = alg.termination_condition
+    mode = DiffEqBase.get_termination_mode(tc)
+
+    storage = _get_storage(mode, u)
+
+    xₙ, xₙ₋₁ = copy(u), copy(u)
+    T = eltype(u)
+
+    atol = _get_tolerance(abstol, tc.abstol, T)
+    rtol = _get_tolerance(reltol, tc.reltol, T)
+    termination_condition = tc(storage)
+
+    for i in 1:maxiters
+        if alg_autodiff(alg)
+            fₙ, 𝓙 = value_derivative(f, xₙ)
+        else
+            fₙ = f(xₙ)
+            𝓙 = FiniteDiff.finite_difference_jacobian(f, xₙ, diff_type(alg), eltype(xₙ), fₙ)
+        end
+
+        iszero(fₙ) && return DiffEqBase.build_solution(prob,
+            alg,
+            reconstruct(xₙ),
+            reconstruct(fₙ);
+            retcode = ReturnCode.Success)
+
+        δx = reshape(𝓙 \ vec(fₙ), size(xₙ))
+        xₙ .-= δx
+
+        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
+            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, iip)
+            return DiffEqBase.build_solution(prob,
+                alg,
+                reconstruct(xₙ),
+                reconstruct(fₙ);
+                retcode)
+        end
+
+        xₙ₋₁ .= xₙ
+    end
+
+    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
+        xₙ = storage.u
+        fₙ = f(xₙ)
+    end
+
+    return DiffEqBase.build_solution(prob,
+        alg,
+        reconstruct(xₙ),
+        reconstruct(fₙ);
+        retcode = ReturnCode.MaxIters)
+end
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index d4bc77709..2e52cde4f 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -73,7 +73,7 @@ function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real =
     batched::Bool = false,
     max_inner_iterations = 1000)
     if batched
-        return SimpleBatchedDFSane(; σₘᵢₙ = σ_min,
+        return BatchedSimpleDFSane(; σₘᵢₙ = σ_min,
             σₘₐₓ = σ_max,
             σ₁ = σ_1,
             M,
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 2621c587e..48b8f7591 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -2,7 +2,8 @@
     SimpleNewtonRaphson(; batched = false,
         chunk_size = Val{0}(),
         autodiff = Val{true}(),
-        diff_type = Val{:forward})
+        diff_type = Val{:forward},
+        termination_condition = missing)
 
 A low-overhead implementation of Newton-Raphson. This method is non-allocating on scalar
 and static array problems.
@@ -27,11 +28,8 @@ and static array problems.
 - `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
   `Val{:forward}` for forward finite differences. For more details on the choices, see the
   [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
-
-!!! note
-
-    To use the `batched` version, remember to load `AbstractDifferentiation` and
-    `LinearSolve`.
+- `termination_condition`: control the termination of the algorithm. (Only works for batched
+  problems)
 """
 struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT} end
 
@@ -44,16 +42,19 @@ function SimpleNewtonRaphson(; batched = false,
         throw(ArgumentError("`termination_condition` is currently only supported for batched problems"))
     end
     if batched
-        @assert ADLinearSolveExtLoaded[] "Please install and load `LinearSolve.jl` and `AbstractDifferentiation.jl` to use batched Newton-Raphson."
+        # @assert ADLinearSolveFDExtLoaded[] "Please install and load `LinearSolve.jl`, `FiniteDifferences.jl` and `AbstractDifferentiation.jl` to use batched Newton-Raphson."
         termination_condition = ismissing(termination_condition) ?
                                 NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
             abstol = nothing,
             reltol = nothing) :
                                 termination_condition
-        return SimpleBatchedNewtonRaphson(; chunk_size,
+        return BatchedSimpleNewtonRaphson(; chunk_size,
             autodiff,
             diff_type,
             termination_condition)
+        return SimpleNewtonRaphson{SciMLBase._unwrap_val(chunk_size),
+            SciMLBase._unwrap_val(autodiff),
+            SciMLBase._unwrap_val(diff_type)}()
     end
     return SimpleNewtonRaphson{SciMLBase._unwrap_val(chunk_size),
         SciMLBase._unwrap_val(autodiff),
diff --git a/lib/SimpleNonlinearSolve/test/Project.toml b/lib/SimpleNonlinearSolve/test/Project.toml
index 280bf2a39..469f302ee 100644
--- a/lib/SimpleNonlinearSolve/test/Project.toml
+++ b/lib/SimpleNonlinearSolve/test/Project.toml
@@ -1,10 +1,8 @@
 [deps]
-AbstractDifferentiation = "c29ec348-61ec-40c8-8164-b8c60e9d9f3d"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 4fe316b34..4b47c6aaa 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -1,5 +1,5 @@
 using SimpleNonlinearSolve, StaticArrays, BenchmarkTools, DiffEqBase, LinearAlgebra, Test,
-    NNlib, AbstractDifferentiation, LinearSolve
+    NNlib
 
 const BATCHED_BROYDEN_SOLVERS = []
 const BROYDEN_SOLVERS = []
@@ -7,6 +7,7 @@ const BATCHED_LBROYDEN_SOLVERS = []
 const LBROYDEN_SOLVERS = []
 const BATCHED_DFSANE_SOLVERS = []
 const DFSANE_SOLVERS = []
+const BATCHED_RAPHSON_SOLVERS = []
 
 for mode in instances(NLSolveTerminationMode.T)
     if mode ∈
@@ -23,6 +24,12 @@ for mode in instances(NLSolveTerminationMode.T)
     push!(BATCHED_LBROYDEN_SOLVERS, LBroyden(; batched = true, termination_condition))
     push!(DFSANE_SOLVERS, SimpleDFSane(; batched = false, termination_condition))
     push!(BATCHED_DFSANE_SOLVERS, SimpleDFSane(; batched = true, termination_condition))
+    push!(BATCHED_RAPHSON_SOLVERS,
+        SimpleNewtonRaphson(; batched = true,
+            termination_condition))
+    push!(BATCHED_RAPHSON_SOLVERS,
+        SimpleNewtonRaphson(; batched = true, autodiff = false,
+            termination_condition))
 end
 
 # SimpleNewtonRaphson
@@ -483,7 +490,8 @@ sol = solve(probN, Broyden(batched = true))
 
 @testset "Batched Solver: $(nameof(typeof(alg)))" for alg in (BATCHED_BROYDEN_SOLVERS...,
     BATCHED_LBROYDEN_SOLVERS...,
-    BATCHED_DFSANE_SOLVERS...)
+    BATCHED_DFSANE_SOLVERS...,
+    BATCHED_RAPHSON_SOLVERS...)
     sol = solve(probN, alg; abstol = 1e-3, reltol = 1e-3)
 
     @test sol.retcode == ReturnCode.Success
diff --git a/lib/SimpleNonlinearSolve/test/inplace.jl b/lib/SimpleNonlinearSolve/test/inplace.jl
index 4c43a1da8..0f2d74719 100644
--- a/lib/SimpleNonlinearSolve/test/inplace.jl
+++ b/lib/SimpleNonlinearSolve/test/inplace.jl
@@ -1,7 +1,7 @@
 using SimpleNonlinearSolve, StaticArrays, BenchmarkTools, DiffEqBase, LinearAlgebra, Test,
-    NNlib, AbstractDifferentiation, LinearSolve
+    NNlib
 
-# Supported Solvers: BatchedBroyden, SimpleBatchedDFSane
+# Supported Solvers: BatchedBroyden, BatchedSimpleDFSane
 function f!(du::AbstractArray{<:Number, N},
     u::AbstractArray{<:Number, N},
     p::AbstractVector) where {N}

From 43a87a722da006250f2edcc0136b8f134fda9991 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 10 Jul 2023 12:49:53 -0400
Subject: [PATCH 151/700] formatting

---
 lib/SimpleNonlinearSolve/test/basictests.jl | 3 ++-
 lib/SimpleNonlinearSolve/test/inplace.jl    | 3 ++-
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 4b47c6aaa..d5f85cdae 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -1,4 +1,5 @@
-using SimpleNonlinearSolve, StaticArrays, BenchmarkTools, DiffEqBase, LinearAlgebra, Test,
+using SimpleNonlinearSolve,
+    StaticArrays, BenchmarkTools, DiffEqBase, LinearAlgebra, Test,
     NNlib
 
 const BATCHED_BROYDEN_SOLVERS = []
diff --git a/lib/SimpleNonlinearSolve/test/inplace.jl b/lib/SimpleNonlinearSolve/test/inplace.jl
index 0f2d74719..886e8206a 100644
--- a/lib/SimpleNonlinearSolve/test/inplace.jl
+++ b/lib/SimpleNonlinearSolve/test/inplace.jl
@@ -1,4 +1,5 @@
-using SimpleNonlinearSolve, StaticArrays, BenchmarkTools, DiffEqBase, LinearAlgebra, Test,
+using SimpleNonlinearSolve,
+    StaticArrays, BenchmarkTools, DiffEqBase, LinearAlgebra, Test,
     NNlib
 
 # Supported Solvers: BatchedBroyden, BatchedSimpleDFSane

From f4431a1cf63e0aa3f6c8acc3e3905026c855df36 Mon Sep 17 00:00:00 2001
From: Hossein Pourbozorg <prbzrg@gmail.com>
Date: Mon, 17 Jul 2023 10:58:59 +0330
Subject: [PATCH 152/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index cf5a675af..28d6e7537 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -26,7 +26,7 @@ ArrayInterface = "6, 7"
 DiffEqBase = "6.123.0"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
-NNlib = "0.8"
+NNlib = "0.8, 0.9"
 Reexport = "0.2, 1"
 Requires = "1"
 SciMLBase = "1.73"

From 5cc8b123889524c90da2066ea6203638a442ee2f Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 18 Jul 2023 11:33:30 -0400
Subject: [PATCH 153/700] Update itp.jl

---
 lib/SimpleNonlinearSolve/src/itp.jl | 42 +++++++++++++++++++++++++----
 1 file changed, 37 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 9968cbab1..0a38f312d 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -1,15 +1,47 @@
 """
 ```julia
-Itp(; k1 = Val{1}(), k2 = Val{2}(), n0 = Val{1}())
+Itp(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
 ```
+
 ITP (Interpolate Truncate & Project)
 
+Use the [ITP method](https://en.wikipedia.org/wiki/ITP_method) to find
+a root of a bracketed function, with a convergence rate between 1 and 1.62.
 
-"""
+This method was introduced in the paper "An Enhancement of the Bisection Method
+Average Performance Preserving Minmax Optimality"
+(https://doi.org/10.1145/3423597) by I. F. D. Oliveira and R. H. C. Takahashi.
+
+# Tuning Parameters
+
+The following keyword parameters are accepted.
+
+- `n₀::Int = 1`, the 'slack'. Must not be negative.\n
+  When n₀ = 0 the worst-case is identical to that of bisection,
+  but increacing n₀ provides greater oppotunity for superlinearity.
+- `κ₁::Float64 = 0.1`. Must not be negative.\n
+  The recomended value is `0.2/(x₂ - x₁)`.
+  Lower values produce tighter asymptotic behaviour, while higher values
+  improve the steady-state behaviour when truncation is not helpful.
+- `κ₂::Real = 2`. Must lie in [1, 1+ϕ ≈ 2.62).\n
+  Higher values allow for a greater convergence rate,
+  but also make the method more succeptable to worst-case performance.
+  In practice, κ=1,2 seems to work well due to the computational simplicity,
+  as κ₂ is used as an exponent in the method.
 
-struct Itp <: AbstractBracketingAlgorithm
-    k1::Real
-    k2::Real
+### Worst Case Performance
+
+n½ + `n₀` iterations, where n½ is the number of iterations using bisection
+(n½ = ⌈log2(Δx)/2`tol`⌉).
+
+### Asymptotic Performance
+
+If `f` is twice differentiable and the root is simple,
+then with `n₀` > 0 the convergence rate is √`κ₂`.
+"""
+struct Itp <: AbstractBracketingAlgorithm{T}
+    k1::T
+    k2::T
     n0::Int
     function Itp(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
         if k1 < 0

From 3d52cd68699876c1328e194b1aa5c964ea943a6f Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 18 Jul 2023 12:10:10 -0400
Subject: [PATCH 154/700] Update src/itp.jl

---
 lib/SimpleNonlinearSolve/src/itp.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 0a38f312d..b9cc28cda 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -39,7 +39,7 @@ n½ + `n₀` iterations, where n½ is the number of iterations using bisection
 If `f` is twice differentiable and the root is simple,
 then with `n₀` > 0 the convergence rate is √`κ₂`.
 """
-struct Itp <: AbstractBracketingAlgorithm{T}
+struct Itp{T} <: AbstractBracketingAlgorithm
     k1::T
     k2::T
     n0::Int

From c01cf7b6d802fea7d6444c0d3d55c940ef28975c Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 18 Jul 2023 12:22:21 -0400
Subject: [PATCH 155/700] Update src/itp.jl

---
 lib/SimpleNonlinearSolve/src/itp.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index b9cc28cda..8e60ff1ad 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -53,7 +53,8 @@ struct Itp{T} <: AbstractBracketingAlgorithm
         if k2 < 1 || k2 > (1.5 + sqrt(5) / 2)
             ArgumentError("Hyper-parameter κ₂ should be between 1 and 1 + ϕ where ϕ ≈ 1.618... is the golden ratio")
         end
-        return new(k1, k2, n0)
+        T = promote_type(eltype(k1), eltype(k2))
+        return new{T}(k1, k2, n0)
     end
 end
 

From 091a9239cda887750ac1d8e6ce3070a17f7a8b49 Mon Sep 17 00:00:00 2001
From: oscarddssmith <oscar.smith@juliacomputing.com>
Date: Tue, 18 Jul 2023 13:50:48 -0400
Subject: [PATCH 156/700] capitalize ITP

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl |  4 ++--
 lib/SimpleNonlinearSolve/src/itp.jl                  |  8 ++++----
 lib/SimpleNonlinearSolve/test/basictests.jl          | 12 ++++++------
 3 files changed, 12 insertions(+), 12 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index bebbc6143..5c500d500 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -69,7 +69,7 @@ PrecompileTools.@compile_workload begin
         prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p,
             T.((0.0, 2.0)),
             T(2))
-        for alg in (Bisection, Falsi, Ridder, Brent, Alefeld, Itp)
+        for alg in (Bisection, Falsi, Ridder, Brent, Alefeld, ITP)
             solve(prob_brack, alg(), abstol = T(1e-2))
         end
     end
@@ -77,7 +77,7 @@ end
 
 # DiffEq styled algorithms
 export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, Halley, Klement,
-    Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld, Itp
+    Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld, ITP
 export BatchedBroyden, BatchedSimpleNewtonRaphson, BatchedSimpleDFSane
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 8e60ff1ad..4483fc0ab 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -1,6 +1,6 @@
 """
 ```julia
-Itp(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
+ITP(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
 ```
 
 ITP (Interpolate Truncate & Project)
@@ -39,11 +39,11 @@ n½ + `n₀` iterations, where n½ is the number of iterations using bisection
 If `f` is twice differentiable and the root is simple,
 then with `n₀` > 0 the convergence rate is √`κ₂`.
 """
-struct Itp{T} <: AbstractBracketingAlgorithm
+struct ITP{T} <: AbstractBracketingAlgorithm
     k1::T
     k2::T
     n0::Int
-    function Itp(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
+    function ITP(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
         if k1 < 0
             error("Hyper-parameter κ₁ should not be negative")
         end
@@ -58,7 +58,7 @@ struct Itp{T} <: AbstractBracketingAlgorithm
     end
 end
 
-function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Itp,
+function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
     args...; abstol = 1.0e-15,
     maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 72545af06..38dce60da 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -222,7 +222,7 @@ end
 # ITP
 g = function (p)
     probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
-    sol = solve(probN, Itp())
+    sol = solve(probN, ITP())
     return sol.u
 end
 
@@ -258,7 +258,7 @@ end
 f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
 t = (p) -> [sqrt(p[2] / p[1])]
 p = [0.9, 50.0]
-for alg in [Bisection(), Falsi(), Ridder(), Brent(), Itp()]
+for alg in [Bisection(), Falsi(), Ridder(), Brent(), ITP()]
     global g, p
     g = function (p)
         probN = IntervalNonlinearProblem{false}(f, tspan, p)
@@ -361,16 +361,16 @@ probB = IntervalNonlinearProblem(f, tspan)
 sol = solve(probB, Alefeld())
 @test sol.u ≈ sqrt(2.0)
 
-# Itp
-sol = solve(probB, Itp())
+# ITP
+sol = solve(probB, ITP())
 @test sol.u ≈ sqrt(2.0)
 tspan = (sqrt(2.0), 10.0)
 probB = IntervalNonlinearProblem(f, tspan)
-sol = solve(probB, Itp())
+sol = solve(probB, ITP())
 @test sol.u ≈ sqrt(2.0)
 tspan = (0.0, sqrt(2.0))
 probB = IntervalNonlinearProblem(f, tspan)
-sol = solve(probB, Itp())
+sol = solve(probB, ITP())
 @test sol.u ≈ sqrt(2.0)
 
 # Garuntee Tests for Bisection

From feb39a24d050f28df0fb87d86453d46ab4fd719c Mon Sep 17 00:00:00 2001
From: oscarddssmith <oscar.smith@juliacomputing.com>
Date: Tue, 18 Jul 2023 13:51:49 -0400
Subject: [PATCH 157/700] bump version

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 89848eb78..e4c556f47 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.17"
+version = "0.1.18"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"

From a6757d6444548f535014c95f391bfb64bc6b3f6b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Daniel=20Gonz=C3=A1lez?= <daniel.glez.arribas@gmail.com>
Date: Fri, 21 Jul 2023 14:22:03 +0200
Subject: [PATCH 158/700] Fix ITP for problems with flipped sign

---
 lib/SimpleNonlinearSolve/src/itp.jl         |  5 +++--
 lib/SimpleNonlinearSolve/test/basictests.jl | 16 ++++++++++++++++
 2 files changed, 19 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 4483fc0ab..648208b80 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -113,10 +113,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
 
         ## Update ##
         yp = f(xp)
-        if yp > 0
+        yps = yp * sign(fr)
+        if yps > 0
             right = xp
             fr = yp
-        elseif yp < 0
+        elseif yps < 0
             left = xp
             fl = yp
         else
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 38dce60da..ee3170ffb 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -539,3 +539,19 @@ for alg in (SimpleNewtonRaphson(), SimpleTrustRegion())
     sol = solve(probN, alg)
     @test abs.(sol.u) ≈ sqrt.(p)
 end
+
+# Flipped signs test
+f1(u, p) = u * u - p 
+f2(u, p) = p - u * u
+
+for Alg in (Alefeld, Bisection, Falsi, Brent, ITP, Ridder)
+    alg = Alg()
+    for p ∈ 1:4
+        inp1 = IntervalNonlinearProblem(f1, (1.0, 2.0), p)
+        inp2 = IntervalNonlinearProblem(f2, (1.0, 2.0), p)
+        sol = solve(inp1, alg)
+        @test abs.(sol.u) ≈ sqrt.(p)
+        sol = solve(inp2, alg)
+        @test abs.(sol.u) ≈ sqrt.(p)
+    end
+end
\ No newline at end of file

From 245483e4104840f66273bf20255b3e1b09ecffb6 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Fri, 21 Jul 2023 09:03:11 -0400
Subject: [PATCH 159/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index e4c556f47..ce68fc7b5 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.18"
+version = "0.1.19"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"

From 56c8669745b188e768986bc874de0fd3dbb78731 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Fri, 21 Jul 2023 09:03:57 -0400
Subject: [PATCH 160/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index ce68fc7b5..e4c556f47 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.19"
+version = "0.1.18"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"

From 15f05934655ef03ad02895d54bcc563d99704f63 Mon Sep 17 00:00:00 2001
From: ChrisRackauckas <ChrisRackauckas@users.noreply.github.com>
Date: Sat, 22 Jul 2023 00:20:08 +0000
Subject: [PATCH 161/700] Format .jl files

---
 lib/SimpleNonlinearSolve/test/basictests.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index ee3170ffb..9dc681f3a 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -541,12 +541,12 @@ for alg in (SimpleNewtonRaphson(), SimpleTrustRegion())
 end
 
 # Flipped signs test
-f1(u, p) = u * u - p 
+f1(u, p) = u * u - p
 f2(u, p) = p - u * u
 
 for Alg in (Alefeld, Bisection, Falsi, Brent, ITP, Ridder)
     alg = Alg()
-    for p ∈ 1:4
+    for p in 1:4
         inp1 = IntervalNonlinearProblem(f1, (1.0, 2.0), p)
         inp2 = IntervalNonlinearProblem(f2, (1.0, 2.0), p)
         sol = solve(inp1, alg)
@@ -554,4 +554,4 @@ for Alg in (Alefeld, Bisection, Falsi, Brent, ITP, Ridder)
         sol = solve(inp2, alg)
         @test abs.(sol.u) ≈ sqrt.(p)
     end
-end
\ No newline at end of file
+end

From 319e95b6ec8313554f51433fe5163da03f3292bf Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Daniel=20Gonz=C3=A1lez?= <daniel.glez.arribas@gmail.com>
Date: Sun, 23 Jul 2023 14:32:29 +0200
Subject: [PATCH 162/700] ITP improvements

---
 lib/SimpleNonlinearSolve/src/itp.jl         | 22 ++++++++++++---------
 lib/SimpleNonlinearSolve/test/basictests.jl | 15 +++++++-------
 2 files changed, 21 insertions(+), 16 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 648208b80..b762eaea9 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -78,7 +78,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
     k1 = alg.k1
     k2 = alg.k2
     n0 = alg.n0
-    n_h = ceil(log2((right - left) / (2 * ϵ)))
+    n_h = ceil(log2(abs(right - left) / (2 * ϵ)))
     mid = (left + right) / 2
     x_f = (fr * left - fl * right) / (fr - fl)
     xt = left
@@ -89,9 +89,9 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
     ϵ_s = ϵ * 2^(n_h + n0)
     i = 0 #iteration
     while i <= maxiters
-        #mid = (left + right) / 2
-        r = ϵ_s - ((right - left) / 2)
-        δ = k1 * ((right - left)^k2)
+        span = abs(right - left)
+        r = ϵ_s - (span / 2)
+        δ = k1 * (span^k2)
 
         ## Interpolation step ##
         x_f = (fr * left - fl * right) / (fr - fl)
@@ -112,6 +112,9 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
         end
 
         ## Update ##
+        tmin, tmax = minmax(left, right)
+        xp >= tmax && (xp = prevfloat(tmax))
+        xp <= tmin && (xp = nextfloat(tmin))
         yp = f(xp)
         yps = yp * sign(fr)
         if yps > 0
@@ -121,16 +124,17 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
             left = xp
             fl = yp
         else
-            left = xp
-            right = xp
+            return SciMLBase.build_solution(prob, alg, xp, yps;
+                                            retcode = ReturnCode.Success, left = left,
+                                            right = right)
         end
         i += 1
         mid = (left + right) / 2
         ϵ_s /= 2
 
-        if (right - left < 2 * ϵ)
-            return SciMLBase.build_solution(prob, alg, mid, f(mid);
-                retcode = ReturnCode.Success, left = left,
+        if nextfloat_tdir(left, prob.tspan...) == right
+            return SciMLBase.build_solution(prob, alg, left, fl;
+                retcode = ReturnCode.FloatingPointLimit, left = left,
                 right = right)
         end
     end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index ee3170ffb..678cf3a6a 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -540,18 +540,19 @@ for alg in (SimpleNewtonRaphson(), SimpleTrustRegion())
     @test abs.(sol.u) ≈ sqrt.(p)
 end
 
-# Flipped signs test
+# Flipped signs & reversed tsoan test for bracketing algorithms
 f1(u, p) = u * u - p 
 f2(u, p) = p - u * u
 
-for Alg in (Alefeld, Bisection, Falsi, Brent, ITP, Ridder)
-    alg = Alg()
+for alg in (Alefeld(), Bisection(), Falsi(), Brent(), ITP(), Ridder())
     for p ∈ 1:4
         inp1 = IntervalNonlinearProblem(f1, (1.0, 2.0), p)
         inp2 = IntervalNonlinearProblem(f2, (1.0, 2.0), p)
-        sol = solve(inp1, alg)
-        @test abs.(sol.u) ≈ sqrt.(p)
-        sol = solve(inp2, alg)
-        @test abs.(sol.u) ≈ sqrt.(p)
+        inp3 = IntervalNonlinearProblem(f1, (2.0, 1.0), p)
+        inp4 = IntervalNonlinearProblem(f2, (2.0, 1.0), p)
+        @test abs.(solve(inp1, alg).u) ≈ sqrt.(p)
+        @test abs.(solve(inp2, alg).u) ≈ sqrt.(p)
+        @test abs.(solve(inp3, alg).u) ≈ sqrt.(p)
+        @test abs.(solve(inp4, alg).u) ≈ sqrt.(p)
     end
 end
\ No newline at end of file

From 8e8ef86e67b9f0ce264fdfe5389cc407970834f6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Daniel=20Gonz=C3=A1lez?= <daniel.glez.arribas@gmail.com>
Date: Sun, 23 Jul 2023 14:39:15 +0200
Subject: [PATCH 163/700] Use safer formula for falsi point in ITP

---
 lib/SimpleNonlinearSolve/src/itp.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index b762eaea9..2d8c0a69f 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -80,7 +80,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
     n0 = alg.n0
     n_h = ceil(log2(abs(right - left) / (2 * ϵ)))
     mid = (left + right) / 2
-    x_f = (fr * left - fl * right) / (fr - fl)
+    x_f = left + (right - left) * (fl/(fl - fr))
     xt = left
     xp = left
     r = zero(left) #minmax radius
@@ -94,7 +94,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
         δ = k1 * (span^k2)
 
         ## Interpolation step ##
-        x_f = (fr * left - fl * right) / (fr - fl)
+        x_f = left + (right - left) * (fl/(fl - fr))
 
         ## Truncation step ##
         σ = sign(mid - x_f)

From 65f24fe17c1e3bb8106fb06c6c6bc5935165c71e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Daniel=20Gonz=C3=A1lez?= <daniel.glez.arribas@gmail.com>
Date: Sun, 23 Jul 2023 14:45:08 +0200
Subject: [PATCH 164/700] =?UTF-8?q?Refine=20ITP=20return=20solution=20on?=
 =?UTF-8?q?=20hitting=20f(=C2=B7)=20zero?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 lib/SimpleNonlinearSolve/src/itp.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 2d8c0a69f..1f1efbafe 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -125,8 +125,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
             fl = yp
         else
             return SciMLBase.build_solution(prob, alg, xp, yps;
-                                            retcode = ReturnCode.Success, left = left,
-                                            right = right)
+                                            retcode = ReturnCode.Success, left = xp,
+                                            right = xp)
         end
         i += 1
         mid = (left + right) / 2

From fbd4f68614d02689c080a2af173ed863da660a87 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Daniel=20Gonz=C3=A1lez?= <daniel.glez.arribas@gmail.com>
Date: Sun, 23 Jul 2023 14:45:45 +0200
Subject: [PATCH 165/700] typo

---
 lib/SimpleNonlinearSolve/test/basictests.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 95f8d58e2..6ab9e56d8 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -540,7 +540,7 @@ for alg in (SimpleNewtonRaphson(), SimpleTrustRegion())
     @test abs.(sol.u) ≈ sqrt.(p)
 end
 
-# Flipped signs & reversed tsoan test for bracketing algorithms
+# Flipped signs & reversed tspan test for bracketing algorithms
 f1(u, p) = u * u - p
 f2(u, p) = p - u * u
 

From 1fdd283990f06aacf31480397013bd70d1664526 Mon Sep 17 00:00:00 2001
From: ChrisRackauckas <ChrisRackauckas@users.noreply.github.com>
Date: Tue, 25 Jul 2023 00:20:59 +0000
Subject: [PATCH 166/700] Format .jl files

---
 lib/SimpleNonlinearSolve/src/itp.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 1f1efbafe..fa390aa45 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -80,7 +80,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
     n0 = alg.n0
     n_h = ceil(log2(abs(right - left) / (2 * ϵ)))
     mid = (left + right) / 2
-    x_f = left + (right - left) * (fl/(fl - fr))
+    x_f = left + (right - left) * (fl / (fl - fr))
     xt = left
     xp = left
     r = zero(left) #minmax radius
@@ -94,7 +94,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
         δ = k1 * (span^k2)
 
         ## Interpolation step ##
-        x_f = left + (right - left) * (fl/(fl - fr))
+        x_f = left + (right - left) * (fl / (fl - fr))
 
         ## Truncation step ##
         σ = sign(mid - x_f)
@@ -125,8 +125,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
             fl = yp
         else
             return SciMLBase.build_solution(prob, alg, xp, yps;
-                                            retcode = ReturnCode.Success, left = xp,
-                                            right = xp)
+                retcode = ReturnCode.Success, left = xp,
+                right = xp)
         end
         i += 1
         mid = (left + right) / 2

From dfb620f74b8d97f992d0077f9c0378e135e22799 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 1 Aug 2023 11:43:55 -0400
Subject: [PATCH 167/700] Add support for inplace BatchedSimpleNewtonRaphson

---
 lib/SimpleNonlinearSolve/Project.toml         |  2 +-
 .../src/batched/raphson.jl                    | 27 ++++++++++++++-----
 lib/SimpleNonlinearSolve/src/utils.jl         | 14 ++++++++++
 lib/SimpleNonlinearSolve/test/inplace.jl      | 15 +++++------
 4 files changed, 43 insertions(+), 15 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index e4c556f47..ce68fc7b5 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.18"
+version = "0.1.19"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
diff --git a/lib/SimpleNonlinearSolve/src/batched/raphson.jl b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
index 323c07e73..a141819bc 100644
--- a/lib/SimpleNonlinearSolve/src/batched/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
@@ -20,7 +20,8 @@ end
 function SciMLBase.__solve(prob::NonlinearProblem, alg::BatchedSimpleNewtonRaphson;
     abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
     iip = SciMLBase.isinplace(prob)
-    @assert !iip "BatchedSimpleNewtonRaphson currently only supports out-of-place nonlinear problems."
+    iip &&
+        @assert alg_autodiff(alg) "Inplace BatchedSimpleNewtonRaphson currently only supports autodiff."
     u, f, reconstruct = _construct_batched_problem_structure(prob)
 
     tc = alg.termination_condition
@@ -35,12 +36,26 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::BatchedSimpleNewtonRaphs
     rtol = _get_tolerance(reltol, tc.reltol, T)
     termination_condition = tc(storage)
 
+    if iip
+        𝓙 = similar(xₙ, length(xₙ), length(xₙ))
+        fₙ = similar(xₙ)
+        jac_cfg = ForwardDiff.JacobianConfig(f, fₙ, xₙ)
+    end
+
     for i in 1:maxiters
-        if alg_autodiff(alg)
-            fₙ, 𝓙 = value_derivative(f, xₙ)
+        if iip
+            value_derivative!(𝓙, fₙ, f, xₙ, jac_cfg)
         else
-            fₙ = f(xₙ)
-            𝓙 = FiniteDiff.finite_difference_jacobian(f, xₙ, diff_type(alg), eltype(xₙ), fₙ)
+            if alg_autodiff(alg)
+                fₙ, 𝓙 = value_derivative(f, xₙ)
+            else
+                fₙ = f(xₙ)
+                𝓙 = FiniteDiff.finite_difference_jacobian(f,
+                    xₙ,
+                    diff_type(alg),
+                    eltype(xₙ),
+                    fₙ)
+            end
         end
 
         iszero(fₙ) && return DiffEqBase.build_solution(prob,
@@ -66,7 +81,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::BatchedSimpleNewtonRaphs
 
     if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
         xₙ = storage.u
-        fₙ = f(xₙ)
+        @maybeinplace iip fₙ=f(xₙ)
     end
 
     return DiffEqBase.build_solution(prob,
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 890aa2415..12462a05c 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -30,6 +30,20 @@ function value_derivative(f::F, x::R) where {F, R}
 end
 value_derivative(f::F, x::AbstractArray) where {F} = f(x), ForwardDiff.jacobian(f, x)
 
+"""
+    value_derivative!(J, y, f!, x, cfg = JacobianConfig(f!, y, x))
+
+Inplace version of [`SimpleNonlinearSolve.value_derivative`](@ref).
+"""
+function value_derivative!(J::AbstractMatrix,
+    y::AbstractArray,
+    f!::F,
+    x::AbstractArray,
+    cfg::ForwardDiff.JacobianConfig = ForwardDiff.JacobianConfig(f!, y, x)) where {F}
+    ForwardDiff.jacobian!(J, f!, y, x, cfg)
+    return y, J
+end
+
 value(x) = x
 value(x::Dual) = ForwardDiff.value(x)
 value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
diff --git a/lib/SimpleNonlinearSolve/test/inplace.jl b/lib/SimpleNonlinearSolve/test/inplace.jl
index 886e8206a..d4882105b 100644
--- a/lib/SimpleNonlinearSolve/test/inplace.jl
+++ b/lib/SimpleNonlinearSolve/test/inplace.jl
@@ -2,29 +2,28 @@ using SimpleNonlinearSolve,
     StaticArrays, BenchmarkTools, DiffEqBase, LinearAlgebra, Test,
     NNlib
 
-# Supported Solvers: BatchedBroyden, BatchedSimpleDFSane
+# Supported Solvers: BatchedBroyden, BatchedSimpleDFSane, BatchedSimpleNewtonRaphson
 function f!(du::AbstractArray{<:Number, N},
     u::AbstractArray{<:Number, N},
     p::AbstractVector) where {N}
     u_ = reshape(u, :, size(u, N))
-    du .= reshape(sum(abs2, u_; dims = 1) .- reshape(p, 1, :),
-        ntuple(_ -> 1, N - 1)...,
-        size(u, N))
+    du .= reshape(sum(abs2, u_; dims = 1) .- u_ .- reshape(p, 1, :), size(u))
     return du
 end
 
 function f!(du::AbstractMatrix, u::AbstractMatrix, p::AbstractVector)
-    du .= sum(abs2, u; dims = 1) .- reshape(p, 1, :)
+    du .= sum(abs2, u; dims = 1) .- u .- reshape(p, 1, :)
     return du
 end
 
 function f!(du::AbstractVector, u::AbstractVector, p::AbstractVector)
-    du .= sum(abs2, u) .- p
+    du .= sum(abs2, u) .- u .- p
     return du
 end
 
-@testset "Solver: $(nameof(typeof(solver)))" for solver in (Broyden(batched = true),
-    SimpleDFSane(batched = true))
+@testset "Solver: $(nameof(typeof(solver)))" for solver in (Broyden(; batched = true),
+    SimpleDFSane(; batched = true),
+    SimpleNewtonRaphson(; batched = true))
     @testset "T: $T" for T in (Float32, Float64)
         p = rand(T, 5)
         @testset "size(u0): $sz" for sz in ((2, 5), (1, 5), (2, 3, 5))

From 5b0ec527e2c74dd778ba31924556a4905fb18780 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Fri, 1 Sep 2023 02:03:41 +0200
Subject: [PATCH 168/700] tolerance fix bisection

---
 lib/SimpleNonlinearSolve/src/bisection.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index 673f77067..6e39afda9 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -20,12 +20,12 @@ function Bisection(; exact_left = false, exact_right = false)
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...;
-    maxiters = 1000,
+    maxiters = 1000, abstol = nothing,
     kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
-
+    atol = abstol !== nothing ? abstol : eps(1.0)^(3 // 5)
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
             retcode = ReturnCode.ExactSolutionLeft, left = left,

From 12267cd4cb751ac612abe0e1e7c3a19f1fb16865 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Fri, 1 Sep 2023 02:28:42 +0200
Subject: [PATCH 169/700] right exact solution

---
 lib/SimpleNonlinearSolve/src/bisection.jl | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index 6e39afda9..58f31f184 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -31,6 +31,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
             retcode = ReturnCode.ExactSolutionLeft, left = left,
             right = right)
     end
+    if iszero(fr)
+        return SciMLBase.build_solution(prob, alg, right, fr;
+            retcode = ReturnCode.ExactSolutionRight, left = left,
+            right = right)
+    end
 
     i = 1
     if !iszero(fr)

From b44c6438b0494da485e4997af3955e83f8ea388f Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Mon, 4 Sep 2023 21:25:34 +0000
Subject: [PATCH 170/700] Bump actions/checkout from 3 to 4

Bumps [actions/checkout](https://github.com/actions/checkout) from 3 to 4.
- [Release notes](https://github.com/actions/checkout/releases)
- [Changelog](https://github.com/actions/checkout/blob/main/CHANGELOG.md)
- [Commits](https://github.com/actions/checkout/compare/v3...v4)

---
updated-dependencies:
- dependency-name: actions/checkout
  dependency-type: direct:production
  update-type: version-update:semver-major
...

Signed-off-by: dependabot[bot] <support@github.com>
---
 lib/SimpleNonlinearSolve/.github/workflows/CI.yml            | 2 +-
 lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml    | 4 ++--
 lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml   | 2 +-
 lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml      | 2 +-
 lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml | 4 ++--
 5 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
index fc96a93a4..1a6859e3a 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
@@ -17,7 +17,7 @@ jobs:
           - '1'
           - '1.6'
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v1
         with:
           version: ${{ matrix.version }}
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
index c6648dfb4..4b1032411 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
@@ -25,14 +25,14 @@ jobs:
           - {user: SciML, repo: OrdinaryDiffEq.jl, group: InterfaceIV}
           - {user: SciML, repo: OrdinaryDiffEq.jl, group: InterfaceV}
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v1
         with:
           version: ${{ matrix.julia-version }}
           arch: x64
       - uses: julia-actions/julia-buildpkg@latest
       - name: Clone Downstream
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
         with:
           repository: ${{ matrix.package.user }}/${{ matrix.package.repo }}
           path: downstream
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
index 521b8c2b2..45bd09c47 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
@@ -21,7 +21,7 @@ jobs:
         with:
           version: ${{ matrix.julia-version }}
 
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
       - name: Install JuliaFormatter and format
         # This will use the latest version by default but you can set the version like so:
         #
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml b/lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml
index b0cb28af5..eea22ebce 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml
@@ -6,7 +6,7 @@ jobs:
   build:
     runs-on: ubuntu-latest
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
       - name: Install JuliaFormatter and format
         run: |
           julia  -e 'using Pkg; Pkg.add(PackageSpec(name="JuliaFormatter"))'
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml b/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml
index 4d0004e83..28b9ce2fa 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml
@@ -19,12 +19,12 @@ jobs:
     - uses: julia-actions/setup-julia@v1
       with:
         version: '1'
-    - uses: actions/checkout@v3
+    - uses: actions/checkout@v4
     - uses: julia-actions/julia-buildpkg@v1
     - uses: julia-actions/julia-invalidations@v1
       id: invs_pr
 
-    - uses: actions/checkout@v3
+    - uses: actions/checkout@v4
       with:
         ref: ${{ github.event.repository.default_branch }}
     - uses: julia-actions/julia-buildpkg@v1

From 0d54cc553a886ff12b6ff61e150fad995feda58f Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Tue, 5 Sep 2023 00:37:54 +0200
Subject: [PATCH 171/700] tol for Bisection()

---
 lib/SimpleNonlinearSolve/src/bisection.jl | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index 58f31f184..1cb0e5d54 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -46,6 +46,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
                     retcode = ReturnCode.FloatingPointLimit,
                     left = left, right = right)
             fm = f(mid)
+            if abs((right - left) / 2) < atol
+                return SciMLBase.build_solution(prob, alg, mid, fm;
+                    retcode = ReturnCode.Success,
+                    left = left, right = right)
+            end
             if iszero(fm)
                 right = mid
                 break
@@ -68,6 +73,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
                 retcode = ReturnCode.FloatingPointLimit,
                 left = left, right = right)
         fm = f(mid)
+        if abs((right - left) / 2) < atol
+            return SciMLBase.build_solution(prob, alg, mid, fm;
+                retcode = ReturnCode.Success,
+                left = left, right = right)
+        end
         if iszero(fm)
             right = mid
             fr = fm

From a76441b54c2f302eaa2ec319c7981b2a61f6e57b Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Wed, 6 Sep 2023 00:09:42 +0200
Subject: [PATCH 172/700] tests for tol

changed default tol to machine epsilon
---
 lib/SimpleNonlinearSolve/src/bisection.jl   | 2 +-
 lib/SimpleNonlinearSolve/test/basictests.jl | 9 +++++++++
 2 files changed, 10 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index 1cb0e5d54..17836caf4 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -25,7 +25,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
-    atol = abstol !== nothing ? abstol : eps(1.0)^(3 // 5)
+    atol = abstol !== nothing ? abstol : eps(1.0)
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
             retcode = ReturnCode.ExactSolutionLeft, left = left,
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 6ab9e56d8..a1e2c5669 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -373,6 +373,15 @@ probB = IntervalNonlinearProblem(f, tspan)
 sol = solve(probB, ITP())
 @test sol.u ≈ sqrt(2.0)
 
+# Tolerance tests for Interval methods
+
+tols = [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6, 1e-7]
+
+for abstol in tols
+    sol = solve(probB, Bisection())
+    @test abs(sol.u - sqrt(2)) < abstol
+end
+
 # Garuntee Tests for Bisection
 f = function (u, p)
     if u < 2.0

From 1dfb5dc0edf8467601668fa8996fef1e7cd79717 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Thu, 7 Sep 2023 21:01:04 +0200
Subject: [PATCH 173/700] tol fix for brent, ridder and falsi

---
 lib/SimpleNonlinearSolve/src/brent.jl  | 13 ++++++++++++-
 lib/SimpleNonlinearSolve/src/falsi.jl  | 17 ++++++++++++++++-
 lib/SimpleNonlinearSolve/src/ridder.jl | 17 ++++++++++++++++-
 3 files changed, 44 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/brent.jl
index 1cedad134..2618211bd 100644
--- a/lib/SimpleNonlinearSolve/src/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/brent.jl
@@ -7,12 +7,13 @@ A non-allocating Brent method
 struct Brent <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
-    maxiters = 1000,
+    maxiters = 1000, abstol = nothing,
     kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     a, b = prob.tspan
     fa, fb = f(a), f(b)
     ϵ = eps(convert(typeof(fa), 1.0))
+    atol = abstol !== nothing ? abstol : eps(1.0)
 
     if iszero(fa)
         return SciMLBase.build_solution(prob, alg, a, fa;
@@ -60,6 +61,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
                 cond = false
             end
             fs = f(s)
+            if abs((b - a) / 2) < atol
+                return SciMLBase.build_solution(prob, alg, s, fs;
+                    retcode = ReturnCode.Success,
+                    left = a, right = b)
+            end
             if iszero(fs)
                 if b < a
                     a = b
@@ -99,6 +105,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
                 left = a, right = b)
         end
         fc = f(c)
+        if abs((b - a) / 2) < atol
+            return SciMLBase.build_solution(prob, alg, c, fc;
+                retcode = ReturnCode.Success,
+                left = a, right = b)
+        end
         if iszero(fc)
             b = c
             fb = fc
diff --git a/lib/SimpleNonlinearSolve/src/falsi.jl b/lib/SimpleNonlinearSolve/src/falsi.jl
index cce11a811..b08a2a1d1 100644
--- a/lib/SimpleNonlinearSolve/src/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/falsi.jl
@@ -4,16 +4,21 @@
 struct Falsi <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
-    maxiters = 1000,
+    maxiters = 1000, abstol = nothing,
     kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
+    atol = abstol !== nothing ? abstol : eps(1.0)
 
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
             retcode = ReturnCode.ExactSolutionLeft, left = left,
             right = right)
+    elseif iszero(fr)
+        return SciMLBase.build_solution(prob, alg, right, fr;
+            retcode = ReturnCode.ExactSolutionRight, left = left,
+            right = right)
     end
 
     i = 1
@@ -32,6 +37,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
                 break
             end
             fm = f(mid)
+            if abs((right - left) / 2) < atol
+                return SciMLBase.build_solution(prob, alg, mid, fm;
+                    retcode = ReturnCode.Success,
+                    left = left, right = right)
+            end
             if iszero(fm)
                 right = mid
                 break
@@ -54,6 +64,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
                 retcode = ReturnCode.FloatingPointLimit,
                 left = left, right = right)
         fm = f(mid)
+        if abs((right - left) / 2) < atol
+            return SciMLBase.build_solution(prob, alg, mid, fm;
+                retcode = ReturnCode.Success,
+                left = left, right = right)
+        end
         if iszero(fm)
             right = mid
             fr = fm
diff --git a/lib/SimpleNonlinearSolve/src/ridder.jl b/lib/SimpleNonlinearSolve/src/ridder.jl
index 62b5a931a..099891ddd 100644
--- a/lib/SimpleNonlinearSolve/src/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/ridder.jl
@@ -7,16 +7,21 @@ A non-allocating ridder method
 struct Ridder <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
-    maxiters = 1000,
+    maxiters = 1000, abstol = nothing,
     kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
+    atol = abstol !== nothing ? abstol : eps(1.0)
 
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
             retcode = ReturnCode.ExactSolutionLeft, left = left,
             right = right)
+    elseif iszero(fr)
+        return SciMLBase.build_solution(prob, alg, right, fr;
+            retcode = ReturnCode.ExactSolutionRight, left = left,
+            right = right)
     end
 
     xo = oftype(left, Inf)
@@ -37,6 +42,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
             x = mid + (mid - left) * sign(fl - fr) * fm / s
             fx = f(x)
             xo = x
+            if abs((right - left) / 2) < atol
+                return SciMLBase.build_solution(prob, alg, mid, fm;
+                    retcode = ReturnCode.Success,
+                    left = left, right = right)
+            end
             if iszero(fx)
                 right = x
                 fr = fx
@@ -66,6 +76,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
                 retcode = ReturnCode.FloatingPointLimit,
                 left = left, right = right)
         fm = f(mid)
+        if abs((right - left) / 2) < atol
+            return SciMLBase.build_solution(prob, alg, mid, fm;
+                retcode = ReturnCode.Success,
+                left = left, right = right)
+        end
         if iszero(fm)
             right = mid
             fr = fm

From c0d76ac6296046490993e03f933aabd9e4738af4 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Thu, 7 Sep 2023 21:01:31 +0200
Subject: [PATCH 174/700] tol tests - both upper and lower bounds

---
 lib/SimpleNonlinearSolve/test/basictests.jl | 26 +++++++++++++++++----
 1 file changed, 21 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index a1e2c5669..23253240a 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -374,12 +374,28 @@ sol = solve(probB, ITP())
 @test sol.u ≈ sqrt(2.0)
 
 # Tolerance tests for Interval methods
-
+f, tspan = (u, p) -> u .* u .- 2.0, (1.0, 10.0)
+probB = IntervalNonlinearProblem(f, tspan)
 tols = [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6, 1e-7]
-
-for abstol in tols
-    sol = solve(probB, Bisection())
-    @test abs(sol.u - sqrt(2)) < abstol
+ϵ = eps(1.0) #least possible tol for all methods
+
+for atol in tols
+    sol = solve(probB, Bisection(), abstol = atol)
+    @test abs(sol.u - sqrt(2)) < atol
+    @test abs(sol.u - sqrt(2)) > ϵ #test that the solution is not calculated upto max precision
+    sol = solve(probB, Falsi(), abstol = atol)
+    @test abs(sol.u - sqrt(2)) < atol
+    @test abs(sol.u - sqrt(2)) > ϵ
+end
+
+tols = [0.1] # Ridder and Brent converge rapidly so as we lower tolerance below 0.01, it converges with max precision to the solution
+for atol in tols
+    sol = solve(probB, Ridder(), abstol = atol)
+    @test abs(sol.u - sqrt(2)) < atol
+    @test abs(sol.u - sqrt(2)) > ϵ
+    sol = solve(probB, Brent(), abstol = atol)
+    @test abs(sol.u - sqrt(2)) < atol
+    @test abs(sol.u - sqrt(2)) > ϵ
 end
 
 # Garuntee Tests for Bisection

From 10bb570b40a631e9e038b40a621f1165b2915fd7 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Thu, 7 Sep 2023 21:03:36 +0200
Subject: [PATCH 175/700] right check for brent

---
 lib/SimpleNonlinearSolve/src/brent.jl | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/brent.jl
index 2618211bd..a6706248a 100644
--- a/lib/SimpleNonlinearSolve/src/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/brent.jl
@@ -19,6 +19,10 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
         return SciMLBase.build_solution(prob, alg, a, fa;
             retcode = ReturnCode.ExactSolutionLeft, left = a,
             right = b)
+    elseif iszero(fb)
+        return SciMLBase.build_solution(prob, alg, b, fb;
+            retcode = ReturnCode.ExactSolutionRight, left = a,
+            right = b)
     end
     if abs(fa) < abs(fb)
         c = b

From 62e0845bbe44b8a2c11215157cd7e65d7da8ce58 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 9 Sep 2023 05:09:32 -0400
Subject: [PATCH 176/700] Update src/ridder.jl

---
 lib/SimpleNonlinearSolve/src/ridder.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/ridder.jl b/lib/SimpleNonlinearSolve/src/ridder.jl
index 099891ddd..190a37153 100644
--- a/lib/SimpleNonlinearSolve/src/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/ridder.jl
@@ -12,7 +12,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
-    atol = abstol !== nothing ? abstol : eps(1.0)
+    atol = abstol !== nothing ? abstol : minimum(eps(left), eps(right))
 
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;

From 703d984c6de1b4830e697e0f9d223252d117e18f Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 9 Sep 2023 05:09:38 -0400
Subject: [PATCH 177/700] Update src/falsi.jl

---
 lib/SimpleNonlinearSolve/src/falsi.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/falsi.jl b/lib/SimpleNonlinearSolve/src/falsi.jl
index b08a2a1d1..549a52c13 100644
--- a/lib/SimpleNonlinearSolve/src/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/falsi.jl
@@ -9,7 +9,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
-    atol = abstol !== nothing ? abstol : eps(1.0)
+    atol = abstol !== nothing ? abstol : minimum(eps(left), eps(right))
 
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;

From c378fad4c50d686951c45712af7c6a18a7cc7681 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 9 Sep 2023 05:09:47 -0400
Subject: [PATCH 178/700] Update src/brent.jl

---
 lib/SimpleNonlinearSolve/src/brent.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/brent.jl
index a6706248a..1ddc0f348 100644
--- a/lib/SimpleNonlinearSolve/src/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/brent.jl
@@ -13,7 +13,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
     a, b = prob.tspan
     fa, fb = f(a), f(b)
     ϵ = eps(convert(typeof(fa), 1.0))
-    atol = abstol !== nothing ? abstol : eps(1.0)
+    atol = abstol !== nothing ? abstol : minimum(eps(left), eps(right))
 
     if iszero(fa)
         return SciMLBase.build_solution(prob, alg, a, fa;

From 11b7d02b0c9d4f890cce360c8dff542817536040 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 9 Sep 2023 05:09:50 -0400
Subject: [PATCH 179/700] Update src/bisection.jl

---
 lib/SimpleNonlinearSolve/src/bisection.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index 17836caf4..d0c134c04 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -25,7 +25,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
-    atol = abstol !== nothing ? abstol : eps(1.0)
+    atol = abstol !== nothing ? abstol : minimum(eps(left), eps(right))
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
             retcode = ReturnCode.ExactSolutionLeft, left = left,

From f5f61047cbb8cbc5e16562971d03d1c7ccdf585a Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 9 Sep 2023 05:10:34 -0400
Subject: [PATCH 180/700] Update src/bisection.jl

---
 lib/SimpleNonlinearSolve/src/bisection.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index d0c134c04..f1b69bd7b 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -25,7 +25,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
-    atol = abstol !== nothing ? abstol : minimum(eps(left), eps(right))
+    atol = abstol !== nothing ? abstol : min(eps(left), eps(right))
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
             retcode = ReturnCode.ExactSolutionLeft, left = left,

From 0a94645e7670ac580b9a6c70a62b801e21e4472c Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 9 Sep 2023 05:11:07 -0400
Subject: [PATCH 181/700] Update src/ridder.jl

---
 lib/SimpleNonlinearSolve/src/ridder.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/ridder.jl b/lib/SimpleNonlinearSolve/src/ridder.jl
index 190a37153..6e6e9464e 100644
--- a/lib/SimpleNonlinearSolve/src/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/ridder.jl
@@ -12,7 +12,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
-    atol = abstol !== nothing ? abstol : minimum(eps(left), eps(right))
+    atol = abstol !== nothing ? abstol : min(eps(left), eps(right))
 
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;

From f1564c92973d1449a72d9db26ded8c99a9706f3a Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 9 Sep 2023 05:11:10 -0400
Subject: [PATCH 182/700] Update src/falsi.jl

---
 lib/SimpleNonlinearSolve/src/falsi.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/falsi.jl b/lib/SimpleNonlinearSolve/src/falsi.jl
index 549a52c13..52506f871 100644
--- a/lib/SimpleNonlinearSolve/src/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/falsi.jl
@@ -9,7 +9,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
-    atol = abstol !== nothing ? abstol : minimum(eps(left), eps(right))
+    atol = abstol !== nothing ? abstol : min(eps(left), eps(right))
 
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;

From 4f89b5060f02ca61c55f57c9613c3c3c1decbeb5 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 9 Sep 2023 05:11:19 -0400
Subject: [PATCH 183/700] Update src/brent.jl

---
 lib/SimpleNonlinearSolve/src/brent.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/brent.jl
index 1ddc0f348..11fcd5f34 100644
--- a/lib/SimpleNonlinearSolve/src/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/brent.jl
@@ -13,7 +13,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
     a, b = prob.tspan
     fa, fb = f(a), f(b)
     ϵ = eps(convert(typeof(fa), 1.0))
-    atol = abstol !== nothing ? abstol : minimum(eps(left), eps(right))
+    atol = abstol !== nothing ? abstol : min(eps(left), eps(right))
 
     if iszero(fa)
         return SciMLBase.build_solution(prob, alg, a, fa;

From de98fe98a1dd57512d6748957d7d9001f9e4a7f7 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Mon, 11 Sep 2023 01:10:58 +0200
Subject: [PATCH 184/700] tol fix for itp

---
 lib/SimpleNonlinearSolve/src/brent.jl |  2 +-
 lib/SimpleNonlinearSolve/src/itp.jl   | 10 ++++++++--
 2 files changed, 9 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/brent.jl
index 11fcd5f34..df2cd1d7d 100644
--- a/lib/SimpleNonlinearSolve/src/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/brent.jl
@@ -13,7 +13,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
     a, b = prob.tspan
     fa, fb = f(a), f(b)
     ϵ = eps(convert(typeof(fa), 1.0))
-    atol = abstol !== nothing ? abstol : min(eps(left), eps(right))
+    atol = abstol !== nothing ? abstol : min(eps(a), eps(b))
 
     if iszero(fa)
         return SciMLBase.build_solution(prob, alg, a, fa;
diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index fa390aa45..fa3bebe26 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -59,12 +59,12 @@ struct ITP{T} <: AbstractBracketingAlgorithm
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
-    args...; abstol = 1.0e-15,
+    args...; abstol = nothing,
     maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan # a and b
     fl, fr = f(left), f(right)
-    ϵ = abstol
+    ϵ = abstol !== nothing ? abstol : min(eps(left), eps(right))
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
             retcode = ReturnCode.ExactSolutionLeft, left = left,
@@ -111,6 +111,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
             xp = mid - (σ * r)
         end
 
+        if abs((left - right) / 2) < ϵ
+            return SciMLBase.build_solution(prob, alg, mid, f(mid);
+            retcode = ReturnCode.Success,
+            left = left, right = right)
+        end
+    
         ## Update ##
         tmin, tmax = minmax(left, right)
         xp >= tmax && (xp = prevfloat(tmax))

From 8a32ee67c571029ba6eeb6c106ce7c78d3e8663c Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Mon, 11 Sep 2023 01:11:07 +0200
Subject: [PATCH 185/700] test for itp

---
 lib/SimpleNonlinearSolve/test/basictests.jl | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 23253240a..34468be58 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -386,6 +386,9 @@ for atol in tols
     sol = solve(probB, Falsi(), abstol = atol)
     @test abs(sol.u - sqrt(2)) < atol
     @test abs(sol.u - sqrt(2)) > ϵ
+    sol = solve(probB, ITP(), abstol = atol)
+    @test abs(sol.u - sqrt(2)) < atol
+    @test abs(sol.u - sqrt(2)) > ϵ
 end
 
 tols = [0.1] # Ridder and Brent converge rapidly so as we lower tolerance below 0.01, it converges with max precision to the solution

From 4402777519f9c1dd6469a09d8d923493a6824efd Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Tue, 12 Sep 2023 00:06:25 +0200
Subject: [PATCH 186/700] minor arg fix

---
 lib/SimpleNonlinearSolve/src/bisection.jl | 8 ++++----
 lib/SimpleNonlinearSolve/src/brent.jl     | 7 +++----
 lib/SimpleNonlinearSolve/src/falsi.jl     | 7 +++----
 lib/SimpleNonlinearSolve/src/itp.jl       | 4 ++--
 lib/SimpleNonlinearSolve/src/ridder.jl    | 7 +++----
 5 files changed, 15 insertions(+), 18 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index f1b69bd7b..d583bd35d 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -20,12 +20,12 @@ function Bisection(; exact_left = false, exact_right = false)
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...;
-    maxiters = 1000, abstol = nothing,
+    maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
     kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
-    atol = abstol !== nothing ? abstol : min(eps(left), eps(right))
+    #atol = abstol
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
             retcode = ReturnCode.ExactSolutionLeft, left = left,
@@ -46,7 +46,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
                     retcode = ReturnCode.FloatingPointLimit,
                     left = left, right = right)
             fm = f(mid)
-            if abs((right - left) / 2) < atol
+            if abs((right - left) / 2) < abstol
                 return SciMLBase.build_solution(prob, alg, mid, fm;
                     retcode = ReturnCode.Success,
                     left = left, right = right)
@@ -73,7 +73,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
                 retcode = ReturnCode.FloatingPointLimit,
                 left = left, right = right)
         fm = f(mid)
-        if abs((right - left) / 2) < atol
+        if abs((right - left) / 2) < abstol
             return SciMLBase.build_solution(prob, alg, mid, fm;
                 retcode = ReturnCode.Success,
                 left = left, right = right)
diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/brent.jl
index df2cd1d7d..47e5495f0 100644
--- a/lib/SimpleNonlinearSolve/src/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/brent.jl
@@ -7,13 +7,12 @@ A non-allocating Brent method
 struct Brent <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
-    maxiters = 1000, abstol = nothing,
+    maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
     kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     a, b = prob.tspan
     fa, fb = f(a), f(b)
     ϵ = eps(convert(typeof(fa), 1.0))
-    atol = abstol !== nothing ? abstol : min(eps(a), eps(b))
 
     if iszero(fa)
         return SciMLBase.build_solution(prob, alg, a, fa;
@@ -65,7 +64,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
                 cond = false
             end
             fs = f(s)
-            if abs((b - a) / 2) < atol
+            if abs((b - a) / 2) < abstol
                 return SciMLBase.build_solution(prob, alg, s, fs;
                     retcode = ReturnCode.Success,
                     left = a, right = b)
@@ -109,7 +108,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
                 left = a, right = b)
         end
         fc = f(c)
-        if abs((b - a) / 2) < atol
+        if abs((b - a) / 2) < abstol
             return SciMLBase.build_solution(prob, alg, c, fc;
                 retcode = ReturnCode.Success,
                 left = a, right = b)
diff --git a/lib/SimpleNonlinearSolve/src/falsi.jl b/lib/SimpleNonlinearSolve/src/falsi.jl
index 52506f871..de1079beb 100644
--- a/lib/SimpleNonlinearSolve/src/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/falsi.jl
@@ -4,12 +4,11 @@
 struct Falsi <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
-    maxiters = 1000, abstol = nothing,
+    maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
     kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
-    atol = abstol !== nothing ? abstol : min(eps(left), eps(right))
 
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
@@ -37,7 +36,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
                 break
             end
             fm = f(mid)
-            if abs((right - left) / 2) < atol
+            if abs((right - left) / 2) < abstol
                 return SciMLBase.build_solution(prob, alg, mid, fm;
                     retcode = ReturnCode.Success,
                     left = left, right = right)
@@ -64,7 +63,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
                 retcode = ReturnCode.FloatingPointLimit,
                 left = left, right = right)
         fm = f(mid)
-        if abs((right - left) / 2) < atol
+        if abs((right - left) / 2) < abstol
             return SciMLBase.build_solution(prob, alg, mid, fm;
                 retcode = ReturnCode.Success,
                 left = left, right = right)
diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index fa3bebe26..c5d87bbbe 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -59,12 +59,12 @@ struct ITP{T} <: AbstractBracketingAlgorithm
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
-    args...; abstol = nothing,
+    args...; abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
     maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan # a and b
     fl, fr = f(left), f(right)
-    ϵ = abstol !== nothing ? abstol : min(eps(left), eps(right))
+    ϵ = abstol
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
             retcode = ReturnCode.ExactSolutionLeft, left = left,
diff --git a/lib/SimpleNonlinearSolve/src/ridder.jl b/lib/SimpleNonlinearSolve/src/ridder.jl
index 6e6e9464e..ce95a178a 100644
--- a/lib/SimpleNonlinearSolve/src/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/ridder.jl
@@ -7,12 +7,11 @@ A non-allocating ridder method
 struct Ridder <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
-    maxiters = 1000, abstol = nothing,
+    maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
     kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
-    atol = abstol !== nothing ? abstol : min(eps(left), eps(right))
 
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
@@ -42,7 +41,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
             x = mid + (mid - left) * sign(fl - fr) * fm / s
             fx = f(x)
             xo = x
-            if abs((right - left) / 2) < atol
+            if abs((right - left) / 2) < abstol
                 return SciMLBase.build_solution(prob, alg, mid, fm;
                     retcode = ReturnCode.Success,
                     left = left, right = right)
@@ -76,7 +75,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
                 retcode = ReturnCode.FloatingPointLimit,
                 left = left, right = right)
         fm = f(mid)
-        if abs((right - left) / 2) < atol
+        if abs((right - left) / 2) < abstol
             return SciMLBase.build_solution(prob, alg, mid, fm;
                 retcode = ReturnCode.Success,
                 left = left, right = right)

From 35247e6daa819071fbd884cc96fa8e9e9b67e38e Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Tue, 12 Sep 2023 00:10:45 +0200
Subject: [PATCH 187/700] format

---
 lib/SimpleNonlinearSolve/src/bisection.jl | 1 -
 lib/SimpleNonlinearSolve/src/itp.jl       | 6 +++---
 2 files changed, 3 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index d583bd35d..24db4adcc 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -25,7 +25,6 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
-    #atol = abstol
     if iszero(fl)
         return SciMLBase.build_solution(prob, alg, left, fl;
             retcode = ReturnCode.ExactSolutionLeft, left = left,
diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index c5d87bbbe..f6688381c 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -113,10 +113,10 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
 
         if abs((left - right) / 2) < ϵ
             return SciMLBase.build_solution(prob, alg, mid, f(mid);
-            retcode = ReturnCode.Success,
-            left = left, right = right)
+                retcode = ReturnCode.Success,
+                left = left, right = right)
         end
-    
+
         ## Update ##
         tmin, tmax = minmax(left, right)
         xp >= tmax && (xp = prevfloat(tmax))

From 09180cec58cacc2cd35ab9b1518ce20e94f21608 Mon Sep 17 00:00:00 2001
From: Yash Raj Singh <yash.raj270998@gmail.com>
Date: Fri, 15 Sep 2023 02:14:07 +0200
Subject: [PATCH 188/700] readme fix

---
 lib/SimpleNonlinearSolve/README.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
index 818872c0b..f6715e696 100644
--- a/lib/SimpleNonlinearSolve/README.md
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -35,5 +35,7 @@ solver = solve(probN, SimpleNewtonRaphson(), tol = 1e-9)
 f(u, p) = u .* u .- 2.0
 u0 = (1.0, 2.0) # brackets
 probB = IntervalNonlinearProblem(f, u0)
-sol = solve(probB, Falsi())
+sol = solve(probB, ITP())
 ```
+
+For more details on the bracketing methods, refer to the [Tutorials](https://docs.sciml.ai/NonlinearSolve/stable/tutorials/nonlinear/#Using-Bracketing-Methods) and detailed [APIs](https://docs.sciml.ai/NonlinearSolve/stable/api/simplenonlinearsolve/#Solver-API)

From 8ea0f0efa7e43e54b93ecc2abbdfb3cd396c0138 Mon Sep 17 00:00:00 2001
From: CompatHelper Julia <compathelper_noreply@julialang.org>
Date: Fri, 22 Sep 2023 02:47:49 +0000
Subject: [PATCH 189/700] CompatHelper: bump compat for SciMLBase to 2, (keep
 existing compat)

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index ce68fc7b5..69e35abef 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -30,7 +30,7 @@ NNlib = "0.8, 0.9"
 PackageExtensionCompat = "1"
 PrecompileTools = "1"
 Reexport = "0.2, 1"
-SciMLBase = "1.73"
+SciMLBase = "1.73, 2"
 StaticArraysCore = "1.4"
 julia = "1.6"
 

From a6e6c0d9e1b2ba49a7727d806f77aac5c8fc11b2 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Fri, 22 Sep 2023 00:30:23 -0400
Subject: [PATCH 190/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 69e35abef..d72f9d000 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.19"
+version = "0.1.20"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"

From c6a641376b40b00c97173b6039e24583ed44810e Mon Sep 17 00:00:00 2001
From: Tom Rottier <39778698+TomRottier@users.noreply.github.com>
Date: Mon, 16 Oct 2023 15:42:08 -0400
Subject: [PATCH 191/700] Fix error in README example

Used keyword tol
---
 lib/SimpleNonlinearSolve/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
index f6715e696..c75b8ed62 100644
--- a/lib/SimpleNonlinearSolve/README.md
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -28,7 +28,7 @@ using SimpleNonlinearSolve, StaticArrays
 f(u,p) = u .* u .- 2
 u0 = @SVector[1.0, 1.0]
 probN = NonlinearProblem{false}(f, u0)
-solver = solve(probN, SimpleNewtonRaphson(), tol = 1e-9)
+solver = solve(probN, SimpleNewtonRaphson(), abstol = 1e-9)
 
 ## Bracketing Methods
 

From 65bcea052a9fd20633fdbed6c1c43cb910fa8b4b Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 17 Oct 2023 04:12:33 -0400
Subject: [PATCH 192/700] Set ITP as the default method for interval problems

---
 .../src/SimpleNonlinearSolve.jl                     | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 5c500d500..85052e5ff 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -46,6 +46,19 @@ include("batched/raphson.jl")
 include("batched/dfsane.jl")
 include("batched/broyden.jl")
 
+## Default algorithm
+
+# Set the default bracketing method to ITP
+
+function SciMLBase.solve(prob::IntervalNonlinearProblem; kwargs...)
+    SciMLBase.solve(prob, ITP(); kwargs...)
+end
+
+function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing,
+    args...; kwargs...)
+    SciMLBase.solve(prob, ITP(), args...; kwargs...)
+end
+
 import PrecompileTools
 
 PrecompileTools.@compile_workload begin

From e2f84c68dd0a8fddb3e744398cf28f9b8ee2a9dc Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 17 Oct 2023 04:28:20 -0400
Subject: [PATCH 193/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index d72f9d000..11285a623 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.20"
+version = "0.1.21"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"

From 1db1c982d612300fb471d62b1a9233337b50be85 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 17 Oct 2023 06:11:55 -0400
Subject: [PATCH 194/700] Halley -> SimpleHalley

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 3 +--
 lib/SimpleNonlinearSolve/src/halley.jl               | 8 ++++----
 2 files changed, 5 insertions(+), 6 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 85052e5ff..9c9c70fc6 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -88,8 +88,7 @@ PrecompileTools.@compile_workload begin
     end
 end
 
-# DiffEq styled algorithms
-export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, Halley, Klement,
+export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, SimpleHalley, Klement,
     Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld, ITP
 export BatchedBroyden, BatchedSimpleNewtonRaphson, BatchedSimpleDFSane
 
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 9e97a57cd..d307f99e9 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -1,6 +1,6 @@
 """
 ```julia
-Halley(; chunk_size = Val{0}(), autodiff = Val{true}(),
+SimpleHalley(; chunk_size = Val{0}(), autodiff = Val{true}(),
                                  diff_type = Val{:forward})
 ```
 
@@ -28,8 +28,8 @@ and static array problems.
   `Val{:forward}` for forward finite differences. For more details on the choices, see the
   [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
 """
-struct Halley{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
-    function Halley(; chunk_size = Val{0}(), autodiff = Val{true}(),
+struct SimpleHalley{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
+    function SimpleHalley(; chunk_size = Val{0}(), autodiff = Val{true}(),
         diff_type = Val{:forward})
         new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
             SciMLBase._unwrap_val(diff_type)}()
@@ -37,7 +37,7 @@ struct Halley{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-    alg::Halley, args...; abstol = nothing,
+    alg::SimpleHalley, args...; abstol = nothing,
     reltol = nothing,
     maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)

From 6d975f4391fb95a7a5a8c88763aafaf10bd73636 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 17 Oct 2023 06:16:53 -0400
Subject: [PATCH 195/700] fix naming

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl |  4 ++--
 lib/SimpleNonlinearSolve/src/halley.jl               |  4 ++--
 lib/SimpleNonlinearSolve/test/basictests.jl          | 12 ++++++------
 3 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 9c9c70fc6..c5632d7b8 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -36,7 +36,7 @@ include("ridder.jl")
 include("brent.jl")
 include("dfsane.jl")
 include("ad.jl")
-include("halley.jl")
+include("SimpleHalley.jl")
 include("alefeld.jl")
 include("itp.jl")
 
@@ -64,7 +64,7 @@ import PrecompileTools
 PrecompileTools.@compile_workload begin
     for T in (Float32, Float64)
         prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-        for alg in (SimpleNewtonRaphson, Halley, Broyden, Klement, SimpleTrustRegion,
+        for alg in (SimpleNewtonRaphson, SimpleHalley, Broyden, Klement, SimpleTrustRegion,
             SimpleDFSane)
             solve(prob_no_brack, alg(), abstol = T(1e-2))
         end
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index d307f99e9..29cc1e54f 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -4,7 +4,7 @@ SimpleHalley(; chunk_size = Val{0}(), autodiff = Val{true}(),
                                  diff_type = Val{:forward})
 ```
 
-A low-overhead implementation of Halley's Method. This method is non-allocating on scalar
+A low-overhead implementation of SimpleHalley's Method. This method is non-allocating on scalar
 and static array problems.
 
 !!! note
@@ -49,7 +49,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
     T = typeof(x)
 
     if SciMLBase.isinplace(prob)
-        error("Halley currently only supports out-of-place nonlinear problems")
+        error("SimpleHalley currently only supports out-of-place nonlinear problems")
     end
 
     atol = abstol !== nothing ? abstol :
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 34468be58..027f766ed 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -56,10 +56,10 @@ if VERSION >= v"1.7"
     @test (@ballocated benchmark_scalar(sf, csu0)) == 0
 end
 
-# Halley
+# SimpleHalley
 function benchmark_scalar(f, u0)
     probN = NonlinearProblem{false}(f, u0)
-    sol = (solve(probN, Halley()))
+    sol = (solve(probN, SimpleHalley()))
 end
 
 function ff(u, p)
@@ -139,7 +139,7 @@ using ForwardDiff
 f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
 
 for alg in (SimpleNewtonRaphson(), LBroyden(), Klement(), SimpleTrustRegion(),
-    SimpleDFSane(), Halley(), BROYDEN_SOLVERS...)
+    SimpleDFSane(), SimpleHalley(), BROYDEN_SOLVERS...)
     g = function (p)
         probN = NonlinearProblem{false}(f, csu0, p)
         sol = solve(probN, alg, abstol = 1e-9)
@@ -162,7 +162,7 @@ end
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
 for alg in (SimpleNewtonRaphson(), Klement(), SimpleTrustRegion(),
-    SimpleDFSane(), Halley(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
+    SimpleDFSane(), SimpleHalley(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
     g = function (p)
         probN = NonlinearProblem{false}(f, oftype(p, u0), p)
         sol = solve(probN, alg)
@@ -271,7 +271,7 @@ for alg in [Bisection(), Falsi(), Ridder(), Brent(), ITP()]
 end
 
 for alg in (SimpleNewtonRaphson(), Klement(), SimpleTrustRegion(),
-    SimpleDFSane(), Halley(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
+    SimpleDFSane(), SimpleHalley(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
     global g, p
     g = function (p)
         probN = NonlinearProblem{false}(f, 0.5, p)
@@ -288,7 +288,7 @@ probN = NonlinearProblem(f, u0)
 
 for alg in (SimpleNewtonRaphson(), SimpleNewtonRaphson(; autodiff = false),
     SimpleTrustRegion(),
-    SimpleTrustRegion(; autodiff = false), Halley(), Halley(; autodiff = false),
+    SimpleTrustRegion(; autodiff = false), SimpleHalley(), SimpleHalley(; autodiff = false),
     Klement(), SimpleDFSane(),
     BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
     sol = solve(probN, alg)

From ebb501f929c665aa9ff175ae521dcaacf8532fd3 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 17 Oct 2023 06:19:41 -0400
Subject: [PATCH 196/700] fix page name

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index c5632d7b8..96d76d92e 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -36,7 +36,7 @@ include("ridder.jl")
 include("brent.jl")
 include("dfsane.jl")
 include("ad.jl")
-include("SimpleHalley.jl")
+include("halley.jl")
 include("alefeld.jl")
 include("itp.jl")
 

From d7d9c458dbc3ab8d645a199149e07442c7e93c49 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 17 Oct 2023 06:29:34 -0400
Subject: [PATCH 197/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 11285a623..61fe5f16a 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.21"
+version = "0.1.22"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"

From 0f94ddadcb18be8c572cb29d7e2b1ba287b7a908 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Fri, 20 Oct 2023 08:08:08 -0400
Subject: [PATCH 198/700] Add matrix resizing and fix cases with u0 as a matrix

---
 lib/SimpleNonlinearSolve/Project.toml                 |  2 +-
 lib/SimpleNonlinearSolve/src/broyden.jl               |  6 +++---
 lib/SimpleNonlinearSolve/src/klement.jl               |  8 ++++----
 lib/SimpleNonlinearSolve/src/raphson.jl               |  2 +-
 lib/SimpleNonlinearSolve/src/utils.jl                 |  4 ++++
 .../test/matrix_resizing_tests.jl                     | 11 +++++++++++
 lib/SimpleNonlinearSolve/test/runtests.jl             | 10 +++-------
 7 files changed, 27 insertions(+), 16 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 61fe5f16a..28a6b0ed7 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.22"
+version = "0.1.23"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 6c5c3ce7f..2f518df83 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -58,12 +58,12 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
     xₙ₋₁ = x
     fₙ₋₁ = fₙ
     for _ in 1:maxiters
-        xₙ = xₙ₋₁ - J⁻¹ * fₙ₋₁
+        xₙ = xₙ₋₁ - ArrayInterface.restructure(xₙ₋₁, J⁻¹ * _vec(fₙ₋₁))
         fₙ = f(xₙ)
         Δxₙ = xₙ - xₙ₋₁
         Δfₙ = fₙ - fₙ₋₁
-        J⁻¹Δfₙ = J⁻¹ * Δfₙ
-        J⁻¹ += ((Δxₙ .- J⁻¹Δfₙ) ./ (Δxₙ' * J⁻¹Δfₙ)) * (Δxₙ' * J⁻¹)
+        J⁻¹Δfₙ = ArrayInterface.restructure(Δfₙ, J⁻¹ * _vec(Δfₙ))
+        J⁻¹ += ArrayInterface.restructure(J⁻¹, ((_vec(Δxₙ) .- _vec(J⁻¹Δfₙ)) ./ (_vec(Δxₙ)' * _vec(J⁻¹Δfₙ))) * (_vec(Δxₙ)' * J⁻¹))
 
         if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
             return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 00264d32f..7235487c5 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -75,7 +75,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
                 F = lu(J, check = false)
             end
 
-            tmp = F \ fₙ₋₁
+            tmp = ArrayInterface.restructure(fₙ₋₁, F \ _vec(fₙ₋₁))
             xₙ = xₙ₋₁ - tmp
             fₙ = f(xₙ)
 
@@ -92,10 +92,10 @@ function SciMLBase.__solve(prob::NonlinearProblem,
             Δfₙ = fₙ - fₙ₋₁
 
             # Prevent division by 0
-            denominator = max.(J' .^ 2 * Δxₙ .^ 2, 1e-9)
+            denominator = ArrayInterface.restructure(Δxₙ, max.(J' .^ 2 * _vec(Δxₙ) .^ 2, 1e-9))
 
-            k = (Δfₙ - J * Δxₙ) ./ denominator
-            J += (k * Δxₙ' .* J) * J
+            k = (Δfₙ - ArrayInterface.restructure(Δxₙ, J * _vec(Δxₙ))) ./ denominator
+            J += (_vec(k) * _vec(Δxₙ)' .* J) * J
 
             xₙ₋₁ = xₙ
             fₙ₋₁ = fₙ
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 48b8f7591..a7d9858bb 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -100,7 +100,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         end
         iszero(fx) &&
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
-        Δx = dfx \ fx
+        Δx = ArrayInterface.restructure(fx, dfx \ _vec(fx))
         x -= Δx
         if isapprox(x, xo, atol = atol, rtol = rtol)
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 12462a05c..4f5617786 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -82,3 +82,7 @@ function dogleg_method(H, g, Δ)
     tau = (-dot_δsd_δN_δsd + sqrt(fact)) / dot_δN_δsd
     return δsd + tau * δN_δsd
 end
+
+@inline _vec(v) = vec(v)
+@inline _vec(v::Number) = v
+@inline _vec(v::AbstractVector) = v
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
new file mode 100644
index 000000000..9612cbb68
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
@@ -0,0 +1,11 @@
+using SimpleNonlinearSolve
+
+ff(u, p) = u .* u .- p
+u0 = rand(2,2)
+p = 2.0
+vecprob = NonlinearProblem(ff, vec(u0), p)
+prob = NonlinearProblem(ff, u0, p)
+
+for alg in (Klement(), Broyden(), SimpleNewtonRaphson())
+    @test vec(solve(prob, alg).u) == solve(vecprob, alg).u
+end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index bea57ea0a..98a01bdba 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -4,12 +4,8 @@ const GROUP = get(ENV, "GROUP", "All")
 
 @time begin
     if GROUP == "All" || GROUP == "Core"
-        @time @safetestset "Basic Tests + Some AD" begin
-            include("basictests.jl")
-        end
-
-        @time @safetestset "Inplace Tests" begin
-            include("inplace.jl")
-        end
+        @time @safetestset "Basic Tests + Some AD" include("basictests.jl")
+        @time @safetestset "Inplace Tests" include("inplace.jl")
+        @time @safetestset "Matrix Resizing Tests" include("matrix_resizing_tests.jl")
     end
 end

From 580c439b58999e6552a25e1236836e539eccf986 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Fri, 20 Oct 2023 08:57:38 -0400
Subject: [PATCH 199/700] don't restructure on number

---
 lib/SimpleNonlinearSolve/src/broyden.jl | 6 +++---
 lib/SimpleNonlinearSolve/src/klement.jl | 6 +++---
 lib/SimpleNonlinearSolve/src/raphson.jl | 2 +-
 lib/SimpleNonlinearSolve/src/utils.jl   | 5 ++++-
 4 files changed, 11 insertions(+), 8 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 2f518df83..9f3c22505 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -58,12 +58,12 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
     xₙ₋₁ = x
     fₙ₋₁ = fₙ
     for _ in 1:maxiters
-        xₙ = xₙ₋₁ - ArrayInterface.restructure(xₙ₋₁, J⁻¹ * _vec(fₙ₋₁))
+        xₙ = xₙ₋₁ - _restructure(xₙ₋₁, J⁻¹ * _vec(fₙ₋₁))
         fₙ = f(xₙ)
         Δxₙ = xₙ - xₙ₋₁
         Δfₙ = fₙ - fₙ₋₁
-        J⁻¹Δfₙ = ArrayInterface.restructure(Δfₙ, J⁻¹ * _vec(Δfₙ))
-        J⁻¹ += ArrayInterface.restructure(J⁻¹, ((_vec(Δxₙ) .- _vec(J⁻¹Δfₙ)) ./ (_vec(Δxₙ)' * _vec(J⁻¹Δfₙ))) * (_vec(Δxₙ)' * J⁻¹))
+        J⁻¹Δfₙ = _restructure(Δfₙ, J⁻¹ * _vec(Δfₙ))
+        J⁻¹ += _restructure(J⁻¹, ((_vec(Δxₙ) .- _vec(J⁻¹Δfₙ)) ./ (_vec(Δxₙ)' * _vec(J⁻¹Δfₙ))) * (_vec(Δxₙ)' * J⁻¹))
 
         if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
             return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 7235487c5..799ba5987 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -75,7 +75,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
                 F = lu(J, check = false)
             end
 
-            tmp = ArrayInterface.restructure(fₙ₋₁, F \ _vec(fₙ₋₁))
+            tmp = _restructure(fₙ₋₁, F \ _vec(fₙ₋₁))
             xₙ = xₙ₋₁ - tmp
             fₙ = f(xₙ)
 
@@ -92,9 +92,9 @@ function SciMLBase.__solve(prob::NonlinearProblem,
             Δfₙ = fₙ - fₙ₋₁
 
             # Prevent division by 0
-            denominator = ArrayInterface.restructure(Δxₙ, max.(J' .^ 2 * _vec(Δxₙ) .^ 2, 1e-9))
+            denominator = _restructure(Δxₙ, max.(J' .^ 2 * _vec(Δxₙ) .^ 2, 1e-9))
 
-            k = (Δfₙ - ArrayInterface.restructure(Δxₙ, J * _vec(Δxₙ))) ./ denominator
+            k = (Δfₙ - _restructure(Δxₙ, J * _vec(Δxₙ))) ./ denominator
             J += (_vec(k) * _vec(Δxₙ)' .* J) * J
 
             xₙ₋₁ = xₙ
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index a7d9858bb..c36dc3504 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -100,7 +100,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         end
         iszero(fx) &&
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
-        Δx = ArrayInterface.restructure(fx, dfx \ _vec(fx))
+        Δx = _restructure(fx, dfx \ _vec(fx))
         x -= Δx
         if isapprox(x, xo, atol = atol, rtol = rtol)
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 4f5617786..c0245ece0 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -85,4 +85,7 @@ end
 
 @inline _vec(v) = vec(v)
 @inline _vec(v::Number) = v
-@inline _vec(v::AbstractVector) = v
\ No newline at end of file
+@inline _vec(v::AbstractVector) = v
+
+@inline _restructure(y::Number, x::Number) = x
+@inline _restructure(y, x) = ArrayInterface.restructure(y,x)
\ No newline at end of file

From 0e6aba39e0b82b2a1cedd42f8ae315236b3837ad Mon Sep 17 00:00:00 2001
From: ChrisRackauckas <ChrisRackauckas@users.noreply.github.com>
Date: Sat, 21 Oct 2023 00:18:21 +0000
Subject: [PATCH 200/700] Format .jl files

---
 lib/SimpleNonlinearSolve/src/broyden.jl                | 4 +++-
 lib/SimpleNonlinearSolve/src/utils.jl                  | 2 +-
 lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl | 2 +-
 3 files changed, 5 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 9f3c22505..045345f29 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -63,7 +63,9 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
         Δxₙ = xₙ - xₙ₋₁
         Δfₙ = fₙ - fₙ₋₁
         J⁻¹Δfₙ = _restructure(Δfₙ, J⁻¹ * _vec(Δfₙ))
-        J⁻¹ += _restructure(J⁻¹, ((_vec(Δxₙ) .- _vec(J⁻¹Δfₙ)) ./ (_vec(Δxₙ)' * _vec(J⁻¹Δfₙ))) * (_vec(Δxₙ)' * J⁻¹))
+        J⁻¹ += _restructure(J⁻¹,
+            ((_vec(Δxₙ) .- _vec(J⁻¹Δfₙ)) ./ (_vec(Δxₙ)' * _vec(J⁻¹Δfₙ))) *
+            (_vec(Δxₙ)' * J⁻¹))
 
         if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
             return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index c0245ece0..1c4400026 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -88,4 +88,4 @@ end
 @inline _vec(v::AbstractVector) = v
 
 @inline _restructure(y::Number, x::Number) = x
-@inline _restructure(y, x) = ArrayInterface.restructure(y,x)
\ No newline at end of file
+@inline _restructure(y, x) = ArrayInterface.restructure(y, x)
diff --git a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
index 9612cbb68..9a1989b71 100644
--- a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
@@ -1,7 +1,7 @@
 using SimpleNonlinearSolve
 
 ff(u, p) = u .* u .- p
-u0 = rand(2,2)
+u0 = rand(2, 2)
 p = 2.0
 vecprob = NonlinearProblem(ff, vec(u0), p)
 prob = NonlinearProblem(ff, u0, p)

From cca90d051fa0dff9a57825cb0fe1b74a68c2a00e Mon Sep 17 00:00:00 2001
From: Pepijn de Vos <pepijn.devos@juliacomputing.com>
Date: Thu, 2 Nov 2023 18:21:32 +0100
Subject: [PATCH 201/700] Change typeof(x) <: y to x isa y

---
 lib/SimpleNonlinearSolve/src/halley.jl  | 2 +-
 lib/SimpleNonlinearSolve/src/raphson.jl | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 29cc1e54f..2c0496cfe 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -56,7 +56,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
     rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
 
-    if typeof(x) <: Number
+    if x isa Number
         xo = oftype(one(eltype(x)), Inf)
     else
         xo = map(x -> oftype(one(eltype(x)), Inf), x)
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index c36dc3504..6af24b733 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -78,7 +78,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
     rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
 
-    if typeof(x) <: Number
+    if x isa Number
         xo = oftype(one(eltype(x)), Inf)
     else
         xo = map(x -> oftype(one(eltype(x)), Inf), x)

From ad12493fdb3ca8ee7dbfed3ac8588ca41b4d1433 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 30 Oct 2023 04:29:54 -0400
Subject: [PATCH 202/700] Add a dispatch to SimpleNewtonRaphson for NNLS and
 SimpleGaussNewton

Fixes https://github.com/SciML/SimpleNonlinearSolve.jl/issues/82
---
 .../src/SimpleNonlinearSolve.jl               |  2 +-
 lib/SimpleNonlinearSolve/src/raphson.jl       | 16 ++++++++++++++--
 .../test/least_squares.jl                     | 19 +++++++++++++++++++
 lib/SimpleNonlinearSolve/test/runtests.jl     |  1 +
 4 files changed, 35 insertions(+), 3 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/test/least_squares.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 96d76d92e..0713ea2c6 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -89,7 +89,7 @@ PrecompileTools.@compile_workload begin
 end
 
 export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, SimpleHalley, Klement,
-    Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld, ITP
+    Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld, ITP, SimpleGaussNewton
 export BatchedBroyden, BatchedSimpleNewtonRaphson, BatchedSimpleDFSane
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 6af24b733..d5bad8d13 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -61,7 +61,9 @@ function SimpleNewtonRaphson(; batched = false,
         SciMLBase._unwrap_val(diff_type)}()
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem,
+const SimpleGaussNewton = SimpleNewtonRaphson
+
+function SciMLBase.__solve(prob::Union{NonlinearProblem,NonlinearLeastSquaresProblem},
     alg::SimpleNewtonRaphson, args...; abstol = nothing,
     reltol = nothing,
     maxiters = 1000, kwargs...)
@@ -74,6 +76,10 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         error("SimpleNewtonRaphson currently only supports out-of-place nonlinear problems")
     end
 
+    if prob isa NonlinearLeastSquaresProblem && !(typeof(prob.u0) <: Union{Number, AbstractVector})
+        error("SimpleGaussNewton only supports Number and AbstactVector types. Please convert any problem of AbstractArray into one with u0 as AbstractVector")
+    end
+
     atol = abstol !== nothing ? abstol :
            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
     rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
@@ -100,7 +106,13 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         end
         iszero(fx) &&
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
-        Δx = _restructure(fx, dfx \ _vec(fx))
+
+        if prob isa NonlinearProblem
+            Δx = _restructure(fx, dfx \ _vec(fx))
+        else
+            Δx = dfx \ fx
+        end
+
         x -= Δx
         if isapprox(x, xo, atol = atol, rtol = rtol)
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
diff --git a/lib/SimpleNonlinearSolve/test/least_squares.jl b/lib/SimpleNonlinearSolve/test/least_squares.jl
new file mode 100644
index 000000000..64b656e8c
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/least_squares.jl
@@ -0,0 +1,19 @@
+using SimpleNonlinearSolve, Random, LinearAlgebra, Test
+
+true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
+
+θ_true = [1.0, 0.1, 2.0, 0.5]
+x = [-1.0, -0.5, 0.0, 0.5, 1.0]
+y_target = true_function(x, θ_true)
+
+function loss_function(θ, p)
+    ŷ = true_function(p, θ)
+    return abs2.(ŷ .- y_target)
+end
+
+θ_init = θ_true .+ randn!(similar(θ_true)) * 0.1
+prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
+sol = solve(prob_oop, SimpleNewtonRaphson())
+sol = solve(prob_oop, SimpleGaussNewton())
+
+@test norm(sol.resid) < 1e-12
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 98a01bdba..0c2a3dfde 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -7,5 +7,6 @@ const GROUP = get(ENV, "GROUP", "All")
         @time @safetestset "Basic Tests + Some AD" include("basictests.jl")
         @time @safetestset "Inplace Tests" include("inplace.jl")
         @time @safetestset "Matrix Resizing Tests" include("matrix_resizing_tests.jl")
+        @time @safetestset "Least Squares Tests" include("least_sqaures.jl")
     end
 end

From 754b15e1ad37885e3c06a7fb2f85a55d8ad5d66e Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Fri, 3 Nov 2023 10:05:30 -0400
Subject: [PATCH 203/700] Update runtests.jl

---
 lib/SimpleNonlinearSolve/test/runtests.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 0c2a3dfde..d0fd1ff9b 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -7,6 +7,6 @@ const GROUP = get(ENV, "GROUP", "All")
         @time @safetestset "Basic Tests + Some AD" include("basictests.jl")
         @time @safetestset "Inplace Tests" include("inplace.jl")
         @time @safetestset "Matrix Resizing Tests" include("matrix_resizing_tests.jl")
-        @time @safetestset "Least Squares Tests" include("least_sqaures.jl")
+        @time @safetestset "Least Squares Tests" include("least_squares.jl")
     end
 end

From f40bc46ebd31a71ba0e727b1bdd8c5808a342045 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Fri, 3 Nov 2023 10:16:49 -0400
Subject: [PATCH 204/700] Update test/least_squares.jl

---
 lib/SimpleNonlinearSolve/test/least_squares.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/least_squares.jl b/lib/SimpleNonlinearSolve/test/least_squares.jl
index 64b656e8c..1e0f135ef 100644
--- a/lib/SimpleNonlinearSolve/test/least_squares.jl
+++ b/lib/SimpleNonlinearSolve/test/least_squares.jl
@@ -11,7 +11,7 @@ function loss_function(θ, p)
     return abs2.(ŷ .- y_target)
 end
 
-θ_init = θ_true .+ randn!(similar(θ_true)) * 0.1
+θ_init = θ_true .+ 0.1
 prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
 sol = solve(prob_oop, SimpleNewtonRaphson())
 sol = solve(prob_oop, SimpleGaussNewton())

From 27af8bdd317c00680427d24e9883892247fae96e Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Fri, 3 Nov 2023 10:44:46 -0400
Subject: [PATCH 205/700] Update least_squares.jl

---
 lib/SimpleNonlinearSolve/test/least_squares.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/least_squares.jl b/lib/SimpleNonlinearSolve/test/least_squares.jl
index 1e0f135ef..0b6647372 100644
--- a/lib/SimpleNonlinearSolve/test/least_squares.jl
+++ b/lib/SimpleNonlinearSolve/test/least_squares.jl
@@ -1,4 +1,4 @@
-using SimpleNonlinearSolve, Random, LinearAlgebra, Test
+using SimpleNonlinearSolve, LinearAlgebra, Test
 
 true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
 
@@ -16,4 +16,4 @@ prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
 sol = solve(prob_oop, SimpleNewtonRaphson())
 sol = solve(prob_oop, SimpleGaussNewton())
 
-@test norm(sol.resid) < 1e-12
\ No newline at end of file
+@test norm(sol.resid) < 1e-12

From cdbc5674bb388ba5e41177117d4730009a97b0d1 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Fri, 3 Nov 2023 11:06:24 -0400
Subject: [PATCH 206/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 28a6b0ed7..baf991736 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.23"
+version = "0.1.24"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"

From 2292fbe7a072547b6f89ea6498f399f9b5ac2c92 Mon Sep 17 00:00:00 2001
From: Hendrik Ranocha <ranocha@users.noreply.github.com>
Date: Fri, 3 Nov 2023 16:44:50 +0100
Subject: [PATCH 207/700] fix badges in README.md

---
 lib/SimpleNonlinearSolve/README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
index c75b8ed62..53b32e311 100644
--- a/lib/SimpleNonlinearSolve/README.md
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -3,8 +3,8 @@
 [![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
 [![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/NonlinearSolve/stable/)
 
-[![codecov](https://codecov.io/gh/SciML/NonlinearSolve.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/SciML/NonlinearSolve.jl)
-[![Build Status](https://github.com/SciML/NonlinearSolve.jl/workflows/CI/badge.svg)](https://github.com/SciML/NonlinearSolve.jl/actions?query=workflow%3ACI)
+[![codecov](https://codecov.io/gh/SciML/SimpleNonlinearSolve.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/SciML/SimpleNonlinearSolve.jl)
+[![Build Status](https://github.com/SciML/SimpleNonlinearSolve.jl/workflows/CI/badge.svg)](https://github.com/SciML/SimpleNonlinearSolve.jl/actions?query=workflow%3ACI)
 
 [![ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://img.shields.io/badge/ColPrac-Contributor's%20Guide-blueviolet)](https://github.com/SciML/ColPrac)
 [![SciML Code Style](https://img.shields.io/static/v1?label=code%20style&message=SciML&color=9558b2&labelColor=389826)](https://github.com/SciML/SciMLStyle)

From c6ee5418d111b227d76bbf7261879803f29a1840 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sun, 5 Nov 2023 18:43:11 -0500
Subject: [PATCH 208/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index baf991736..acad73005 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -26,6 +26,7 @@ ArrayInterface = "6, 7"
 DiffEqBase = "6.126"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
+LinearAlgebra = "1.6"
 NNlib = "0.8, 0.9"
 PackageExtensionCompat = "1"
 PrecompileTools = "1"

From 77c359fd37ce6f999d85a3dab966ab669408ee19 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 7 Nov 2023 11:15:24 +0100
Subject: [PATCH 209/700] Require v1.9 and drop backwards compat

---
 lib/SimpleNonlinearSolve/.github/workflows/CI.yml  |  1 -
 .../.github/workflows/Downstream.yml               |  2 +-
 lib/SimpleNonlinearSolve/Project.toml              | 14 ++++++--------
 .../src/SimpleNonlinearSolve.jl                    |  5 -----
 4 files changed, 7 insertions(+), 15 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
index 1a6859e3a..ba2974f47 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
@@ -15,7 +15,6 @@ jobs:
           - Core
         version:
           - '1'
-          - '1.6'
     steps:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v1
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
index 4b1032411..affe2fd97 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
@@ -14,7 +14,7 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        julia-version: [1,1.6]
+        julia-version: [1]
         os: [ubuntu-latest]
         package:
           - {user: SciML, repo: ModelingToolkit.jl, group: All}
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index acad73005..86ae7359e 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.24"
+version = "0.1.25"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
@@ -9,7 +9,6 @@ DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-PackageExtensionCompat = "65ce6f38-6b18-4e1d-a461-8949797d7930"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
@@ -22,18 +21,17 @@ NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 SimpleNonlinearSolveNNlibExt = "NNlib"
 
 [compat]
-ArrayInterface = "6, 7"
+ArrayInterface = "7"
 DiffEqBase = "6.126"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
-LinearAlgebra = "1.6"
+LinearAlgebra = "1.9"
 NNlib = "0.8, 0.9"
-PackageExtensionCompat = "1"
 PrecompileTools = "1"
-Reexport = "0.2, 1"
-SciMLBase = "1.73, 2"
+Reexport = "1"
+SciMLBase = "2"
 StaticArraysCore = "1.4"
-julia = "1.6"
+julia = "1.9"
 
 [extras]
 NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 0713ea2c6..cfd73e3b1 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -10,11 +10,6 @@ using DiffEqBase
 
 @reexport using SciMLBase
 
-using PackageExtensionCompat
-function __init__()
-    @require_extensions
-end
-
 const NNlibExtLoaded = Ref{Bool}(false)
 
 abstract type AbstractSimpleNonlinearSolveAlgorithm <: SciMLBase.AbstractNonlinearAlgorithm end

From 960ed93d4606bd391bfcddbde2c953c2abf8d853 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 7 Nov 2023 14:02:43 +0100
Subject: [PATCH 210/700] Require SciMLBase with v2.7 for NonlinearLeastSquares

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 86ae7359e..aa45b60af 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -29,7 +29,7 @@ LinearAlgebra = "1.9"
 NNlib = "0.8, 0.9"
 PrecompileTools = "1"
 Reexport = "1"
-SciMLBase = "2"
+SciMLBase = "2.7"
 StaticArraysCore = "1.4"
 julia = "1.9"
 

From 7f16738609088005891f5dd05f7bd56939e5266c Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 7 Nov 2023 14:25:32 +0100
Subject: [PATCH 211/700] Update least_squares.jl

Fix residual definition in test
---
 lib/SimpleNonlinearSolve/test/least_squares.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/least_squares.jl b/lib/SimpleNonlinearSolve/test/least_squares.jl
index 0b6647372..a7003f697 100644
--- a/lib/SimpleNonlinearSolve/test/least_squares.jl
+++ b/lib/SimpleNonlinearSolve/test/least_squares.jl
@@ -8,7 +8,7 @@ y_target = true_function(x, θ_true)
 
 function loss_function(θ, p)
     ŷ = true_function(p, θ)
-    return abs2.(ŷ .- y_target)
+    return ŷ .- y_target
 end
 
 θ_init = θ_true .+ 0.1

From 9387e5f09d8df8d676a685561010de23d9d587f4 Mon Sep 17 00:00:00 2001
From: FHoltorf <holtorf93@gmail.com>
Date: Sat, 18 Nov 2023 11:32:54 -0500
Subject: [PATCH 212/700] fixed gradient and GN Hessian approximation

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 1423d59b8..0a97e7d92 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -134,8 +134,8 @@ function SciMLBase.__solve(prob::NonlinearProblem,
     end
 
     fₖ = 0.5 * norm(F)^2
-    H = ∇f * ∇f
-    g = ∇f * F
+    H = ∇f' * ∇f
+    g = ∇f' * F
     shrink_counter = 0
 
     for k in 1:maxiters
@@ -188,8 +188,8 @@ function SciMLBase.__solve(prob::NonlinearProblem,
                 Δ = min(t₂ * Δ, Δₘₐₓ)
             end
             fₖ = fₖ₊₁
-            H = ∇f * ∇f
-            g = ∇f * F
+            H = ∇f' * ∇f
+            g = ∇f' * F
         end
     end
     return SciMLBase.build_solution(prob, alg, x, F; retcode = ReturnCode.MaxIters)

From 5b9100a8358efcf48eadcc0fe3e660e9861b9dd0 Mon Sep 17 00:00:00 2001
From: FHoltorf <holtorf93@gmail.com>
Date: Sat, 18 Nov 2023 11:33:55 -0500
Subject: [PATCH 213/700] make step accepteance less consersative for better
 performance

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 0a97e7d92..f1e992572 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -68,7 +68,7 @@ struct SimpleTrustRegion{T, CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
         diff_type = Val{:forward},
         max_trust_radius::Real = 0.0,
         initial_trust_radius::Real = 0.0,
-        step_threshold::Real = 0.1,
+        step_threshold::Real = 0.0001,
         shrink_threshold::Real = 0.25,
         expand_threshold::Real = 0.75,
         shrink_factor::Real = 0.25,

From 7c6b5724b6c9c68629d718bfc72c1a7b4a9c471f Mon Sep 17 00:00:00 2001
From: FHoltorf <holtorf93@gmail.com>
Date: Tue, 21 Nov 2023 22:19:30 -0500
Subject: [PATCH 214/700] simple fraction with forward slash instead of
 backslash (for otherwise rather subtle)

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index f1e992572..ab28e1ce3 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -147,7 +147,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
 
         # Compute the ratio of the actual to predicted reduction.
         model = -(δ' * g + 0.5 * δ' * H * δ)
-        r = model \ (fₖ - fₖ₊₁)
+        r = (fₖ - fₖ₊₁) / model 
 
         # Update the trust region radius.
         if r < η₂

From 66a073214d2fa4b3786f3310536ce92b2fc7a277 Mon Sep 17 00:00:00 2001
From: FHoltorf <holtorf93@gmail.com>
Date: Tue, 21 Nov 2023 22:20:46 -0500
Subject: [PATCH 215/700] run formatter

---
 .../ext/SimpleNonlinearSolveNNlibExt.jl       | 10 +++---
 .../src/SimpleNonlinearSolve.jl               |  2 +-
 lib/SimpleNonlinearSolve/src/ad.jl            | 36 +++++++++----------
 lib/SimpleNonlinearSolve/src/alefeld.jl       |  6 ++--
 .../src/batched/dfsane.jl                     | 12 +++----
 .../src/batched/raphson.jl                    | 12 +++----
 lib/SimpleNonlinearSolve/src/batched/utils.jl |  6 ++--
 lib/SimpleNonlinearSolve/src/bisection.jl     |  4 +--
 lib/SimpleNonlinearSolve/src/brent.jl         |  4 +--
 lib/SimpleNonlinearSolve/src/broyden.jl       |  8 ++---
 lib/SimpleNonlinearSolve/src/dfsane.jl        | 18 +++++-----
 lib/SimpleNonlinearSolve/src/falsi.jl         |  4 +--
 lib/SimpleNonlinearSolve/src/halley.jl        |  8 ++---
 lib/SimpleNonlinearSolve/src/itp.jl           |  4 +--
 lib/SimpleNonlinearSolve/src/klement.jl       |  6 ++--
 lib/SimpleNonlinearSolve/src/lbroyden.jl      | 18 +++++-----
 lib/SimpleNonlinearSolve/src/raphson.jl       | 19 +++++-----
 lib/SimpleNonlinearSolve/src/ridder.jl        |  4 +--
 lib/SimpleNonlinearSolve/src/trustRegion.jl   | 28 +++++++--------
 lib/SimpleNonlinearSolve/src/utils.jl         |  8 ++---
 lib/SimpleNonlinearSolve/test/inplace.jl      |  4 +--
 21 files changed, 111 insertions(+), 110 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
index 5b06530a6..1132b64b7 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
@@ -10,11 +10,11 @@ function __init__()
 end
 
 @views function SciMLBase.__solve(prob::NonlinearProblem,
-    alg::BatchedBroyden;
-    abstol = nothing,
-    reltol = nothing,
-    maxiters = 1000,
-    kwargs...)
+        alg::BatchedBroyden;
+        abstol = nothing,
+        reltol = nothing,
+        maxiters = 1000,
+        kwargs...)
     iip = isinplace(prob)
 
     u, f, reconstruct = _construct_batched_problem_structure(prob)
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index cfd73e3b1..8c84c4377 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -50,7 +50,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem; kwargs...)
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing,
-    args...; kwargs...)
+        args...; kwargs...)
     SciMLBase.solve(prob, ITP(), args...; kwargs...)
 end
 
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index 009cd227b..b0fd9f11c 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -29,19 +29,19 @@ function scalar_nlsolve_ad(prob, alg, args...; kwargs...)
 end
 
 function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
-        iip,
-        <:Dual{T, V, P}},
-    alg::AbstractSimpleNonlinearSolveAlgorithm,
-    args...; kwargs...) where {iip, T, V, P}
+            iip,
+            <:Dual{T, V, P}},
+        alg::AbstractSimpleNonlinearSolveAlgorithm,
+        args...; kwargs...) where {iip, T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
         retcode = sol.retcode)
 end
 function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
-        iip,
-        <:AbstractArray{<:Dual{T, V, P}}},
-    alg::AbstractSimpleNonlinearSolveAlgorithm, args...;
-    kwargs...) where {iip, T, V, P}
+            iip,
+            <:AbstractArray{<:Dual{T, V, P}}},
+        alg::AbstractSimpleNonlinearSolveAlgorithm, args...;
+        kwargs...) where {iip, T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
         retcode = sol.retcode)
@@ -50,9 +50,9 @@ end
 # avoid ambiguities
 for Alg in [Bisection]
     @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
-            <:Dual{T, V, P}},
-        alg::$Alg, args...;
-        kwargs...) where {uType, iip, T, V, P}
+                <:Dual{T, V, P}},
+            alg::$Alg, args...;
+            kwargs...) where {uType, iip, T, V, P}
         sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
         return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials),
             sol.resid; retcode = sol.retcode,
@@ -61,13 +61,13 @@ for Alg in [Bisection]
         #return BracketingSolution(Dual{T,V,P}(sol.left, partials), Dual{T,V,P}(sol.right, partials), sol.retcode, sol.resid)
     end
     @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
-            <:AbstractArray{
-                <:Dual{T,
-                    V,
-                    P},
-            }},
-        alg::$Alg, args...;
-        kwargs...) where {uType, iip, T, V, P}
+                <:AbstractArray{
+                    <:Dual{T,
+                        V,
+                        P},
+                }},
+            alg::$Alg, args...;
+            kwargs...) where {uType, iip, T, V, P}
         sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
         return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials),
             sol.resid; retcode = sol.retcode,
diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index a2669ca96..0d4f56116 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -9,9 +9,9 @@ algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal
 struct Alefeld <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem,
-    alg::Alefeld, args...; abstol = nothing,
-    reltol = nothing,
-    maxiters = 1000, kwargs...)
+        alg::Alefeld, args...; abstol = nothing,
+        reltol = nothing,
+        maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     a, b = prob.tspan
     c = a - (b - a) / (f(b) - f(a)) * f(a)
diff --git a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
index 60bb6ae12..01b3b1996 100644
--- a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
@@ -16,12 +16,12 @@ Base.@kwdef struct BatchedSimpleDFSane{T, F, TC <: NLSolveTerminationCondition}
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-    alg::BatchedSimpleDFSane,
-    args...;
-    abstol = nothing,
-    reltol = nothing,
-    maxiters = 100,
-    kwargs...)
+        alg::BatchedSimpleDFSane,
+        args...;
+        abstol = nothing,
+        reltol = nothing,
+        maxiters = 100,
+        kwargs...)
     iip = isinplace(prob)
 
     u, f, reconstruct = _construct_batched_problem_structure(prob)
diff --git a/lib/SimpleNonlinearSolve/src/batched/raphson.jl b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
index a141819bc..7bc7b8c4a 100644
--- a/lib/SimpleNonlinearSolve/src/batched/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
@@ -7,18 +7,18 @@ alg_autodiff(alg::BatchedSimpleNewtonRaphson{CS, AD, FDT}) where {CS, AD, FDT} =
 diff_type(alg::BatchedSimpleNewtonRaphson{CS, AD, FDT}) where {CS, AD, FDT} = FDT
 
 function BatchedSimpleNewtonRaphson(; chunk_size = Val{0}(),
-    autodiff = Val{true}(),
-    diff_type = Val{:forward},
-    termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-        abstol = nothing,
-        reltol = nothing))
+        autodiff = Val{true}(),
+        diff_type = Val{:forward},
+        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+            abstol = nothing,
+            reltol = nothing))
     return BatchedSimpleNewtonRaphson{SciMLBase._unwrap_val(chunk_size),
         SciMLBase._unwrap_val(autodiff),
         SciMLBase._unwrap_val(diff_type), typeof(termination_condition)}(termination_condition)
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::BatchedSimpleNewtonRaphson;
-    abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
+        abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
     iip = SciMLBase.isinplace(prob)
     iip &&
         @assert alg_autodiff(alg) "Inplace BatchedSimpleNewtonRaphson currently only supports autodiff."
diff --git a/lib/SimpleNonlinearSolve/src/batched/utils.jl b/lib/SimpleNonlinearSolve/src/batched/utils.jl
index 7b85011f1..b8e66fe80 100644
--- a/lib/SimpleNonlinearSolve/src/batched/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/batched/utils.jl
@@ -27,9 +27,9 @@ function _construct_batched_problem_structure(prob)
 end
 
 function _construct_batched_problem_structure(u0::AbstractArray{T, N},
-    f,
-    p,
-    ::Val{iip}) where {T, N, iip}
+        f,
+        p,
+        ::Val{iip}) where {T, N, iip}
     # Reconstruct `u`
     reconstruct = N == 2 ? identity : Base.Fix2(reshape, size(u0))
     # Standardize `u`
diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index 24db4adcc..f7c98aa65 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -20,8 +20,8 @@ function Bisection(; exact_left = false, exact_right = false)
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...;
-    maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
-    kwargs...)
+        maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
+        kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/brent.jl
index 47e5495f0..7d7a6bcf9 100644
--- a/lib/SimpleNonlinearSolve/src/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/brent.jl
@@ -7,8 +7,8 @@ A non-allocating Brent method
 struct Brent <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
-    maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
-    kwargs...)
+        maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
+        kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     a, b = prob.tspan
     fa, fb = f(a), f(b)
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 045345f29..07b2609f9 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -18,9 +18,9 @@ struct Broyden{TC <: NLSolveTerminationCondition} <:
 end
 
 function Broyden(; batched = false,
-    termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-        abstol = nothing,
-        reltol = nothing))
+        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+            abstol = nothing,
+            reltol = nothing))
     if batched
         @assert NNlibExtLoaded[] "Please install and load `NNlib.jl` to use batched Broyden."
         return BatchedBroyden(termination_condition)
@@ -29,7 +29,7 @@ function Broyden(; batched = false,
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
-    abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
+        abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
     f = Base.Fix2(prob.f, prob.p)
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index 2e52cde4f..49c50bca3 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -65,13 +65,13 @@ struct SimpleDFSane{T, TC} <: AbstractSimpleNonlinearSolveAlgorithm
 end
 
 function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
-    M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
-    nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2,
-    termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-        abstol = nothing,
-        reltol = nothing),
-    batched::Bool = false,
-    max_inner_iterations = 1000)
+        M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
+        nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2,
+        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+            abstol = nothing,
+            reltol = nothing),
+        batched::Bool = false,
+        max_inner_iterations = 1000)
     if batched
         return BatchedSimpleDFSane(; σₘᵢₙ = σ_min,
             σₘₐₓ = σ_max,
@@ -98,8 +98,8 @@ function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real =
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane,
-    args...; abstol = nothing, reltol = nothing, maxiters = 1000,
-    kwargs...)
+        args...; abstol = nothing, reltol = nothing, maxiters = 1000,
+        kwargs...)
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
 
diff --git a/lib/SimpleNonlinearSolve/src/falsi.jl b/lib/SimpleNonlinearSolve/src/falsi.jl
index de1079beb..eb2ea1f5f 100644
--- a/lib/SimpleNonlinearSolve/src/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/falsi.jl
@@ -4,8 +4,8 @@
 struct Falsi <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
-    maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
-    kwargs...)
+        maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
+        kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 2c0496cfe..8107dde31 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -30,16 +30,16 @@ and static array problems.
 """
 struct SimpleHalley{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     function SimpleHalley(; chunk_size = Val{0}(), autodiff = Val{true}(),
-        diff_type = Val{:forward})
+            diff_type = Val{:forward})
         new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
             SciMLBase._unwrap_val(diff_type)}()
     end
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-    alg::SimpleHalley, args...; abstol = nothing,
-    reltol = nothing,
-    maxiters = 1000, kwargs...)
+        alg::SimpleHalley, args...; abstol = nothing,
+        reltol = nothing,
+        maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     fx = f(x)
diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index f6688381c..3147c526e 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -59,8 +59,8 @@ struct ITP{T} <: AbstractBracketingAlgorithm
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
-    args...; abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
-    maxiters = 1000, kwargs...)
+        args...; abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
+        maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan # a and b
     fl, fr = f(left), f(right)
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 799ba5987..e6a38ecc2 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -9,9 +9,9 @@ This method is non-allocating on scalar problems.
 struct Klement <: AbstractSimpleNonlinearSolveAlgorithm end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-    alg::Klement, args...; abstol = nothing,
-    reltol = nothing,
-    maxiters = 1000, kwargs...)
+        alg::Klement, args...; abstol = nothing,
+        reltol = nothing,
+        maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     fₙ = f(x)
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index fc2b51a88..482092151 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -18,16 +18,16 @@ struct LBroyden{batched, TC <: NLSolveTerminationCondition} <:
     threshold::Int
 
     function LBroyden(; batched = false, threshold::Int = 27,
-        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-            abstol = nothing,
-            reltol = nothing))
+            termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
+                abstol = nothing,
+                reltol = nothing))
         return new{batched, typeof(termination_condition)}(termination_condition, threshold)
     end
 end
 
 @views function SciMLBase.__solve(prob::NonlinearProblem, alg::LBroyden{batched}, args...;
-    abstol = nothing, reltol = nothing, maxiters = 1000,
-    kwargs...) where {batched}
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        kwargs...) where {batched}
     tc = alg.termination_condition
     mode = DiffEqBase.get_termination_mode(tc)
     threshold = min(maxiters, alg.threshold)
@@ -116,26 +116,26 @@ function _init_lbroyden_state(batched::Bool, x, threshold)
 end
 
 function _rmatvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
-    x::Union{<:AbstractVector, <:Number})
+        x::Union{<:AbstractVector, <:Number})
     length(U) == 0 && return x
     return -x .+ vec((x' * Vᵀ) * U)
 end
 
 function _rmatvec(U::AbstractArray{T1, 3}, Vᵀ::AbstractArray{T2, 3},
-    x::AbstractMatrix) where {T1, T2}
+        x::AbstractMatrix) where {T1, T2}
     length(U) == 0 && return x
     Vᵀx = sum(Vᵀ .* reshape(x, size(x, 1), 1, size(x, 2)); dims = 1)
     return -x .+ _drdims_sum(U .* permutedims(Vᵀx, (2, 1, 3)); dims = 1)
 end
 
 function _matvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
-    x::Union{<:AbstractVector, <:Number})
+        x::Union{<:AbstractVector, <:Number})
     length(U) == 0 && return x
     return -x .+ vec(Vᵀ * (U * x))
 end
 
 function _matvec(U::AbstractArray{T1, 3}, Vᵀ::AbstractArray{T2, 3},
-    x::AbstractMatrix) where {T1, T2}
+        x::AbstractMatrix) where {T1, T2}
     length(U) == 0 && return x
     xUᵀ = sum(reshape(x, size(x, 1), 1, size(x, 2)) .* permutedims(U, (2, 1, 3)); dims = 1)
     return -x .+ _drdims_sum(xUᵀ .* Vᵀ; dims = 2)
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index d5bad8d13..138e6724d 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -34,10 +34,10 @@ and static array problems.
 struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT} end
 
 function SimpleNewtonRaphson(; batched = false,
-    chunk_size = Val{0}(),
-    autodiff = Val{true}(),
-    diff_type = Val{:forward},
-    termination_condition = missing)
+        chunk_size = Val{0}(),
+        autodiff = Val{true}(),
+        diff_type = Val{:forward},
+        termination_condition = missing)
     if !ismissing(termination_condition) && !batched
         throw(ArgumentError("`termination_condition` is currently only supported for batched problems"))
     end
@@ -63,10 +63,10 @@ end
 
 const SimpleGaussNewton = SimpleNewtonRaphson
 
-function SciMLBase.__solve(prob::Union{NonlinearProblem,NonlinearLeastSquaresProblem},
-    alg::SimpleNewtonRaphson, args...; abstol = nothing,
-    reltol = nothing,
-    maxiters = 1000, kwargs...)
+function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+        alg::SimpleNewtonRaphson, args...; abstol = nothing,
+        reltol = nothing,
+        maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     fx = float(prob.u0)
@@ -76,7 +76,8 @@ function SciMLBase.__solve(prob::Union{NonlinearProblem,NonlinearLeastSquaresPro
         error("SimpleNewtonRaphson currently only supports out-of-place nonlinear problems")
     end
 
-    if prob isa NonlinearLeastSquaresProblem && !(typeof(prob.u0) <: Union{Number, AbstractVector})
+    if prob isa NonlinearLeastSquaresProblem &&
+       !(typeof(prob.u0) <: Union{Number, AbstractVector})
         error("SimpleGaussNewton only supports Number and AbstactVector types. Please convert any problem of AbstractArray into one with u0 as AbstractVector")
     end
 
diff --git a/lib/SimpleNonlinearSolve/src/ridder.jl b/lib/SimpleNonlinearSolve/src/ridder.jl
index ce95a178a..eabd7b2ac 100644
--- a/lib/SimpleNonlinearSolve/src/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/ridder.jl
@@ -7,8 +7,8 @@ A non-allocating ridder method
 struct Ridder <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
-    maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
-    kwargs...)
+        maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
+        kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index ab28e1ce3..98a36d063 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -64,16 +64,16 @@ struct SimpleTrustRegion{T, CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     expand_factor::T
     max_shrink_times::Int
     function SimpleTrustRegion(; chunk_size = Val{0}(),
-        autodiff = Val{true}(),
-        diff_type = Val{:forward},
-        max_trust_radius::Real = 0.0,
-        initial_trust_radius::Real = 0.0,
-        step_threshold::Real = 0.0001,
-        shrink_threshold::Real = 0.25,
-        expand_threshold::Real = 0.75,
-        shrink_factor::Real = 0.25,
-        expand_factor::Real = 2.0,
-        max_shrink_times::Int = 32)
+            autodiff = Val{true}(),
+            diff_type = Val{:forward},
+            max_trust_radius::Real = 0.0,
+            initial_trust_radius::Real = 0.0,
+            step_threshold::Real = 0.0001,
+            shrink_threshold::Real = 0.25,
+            expand_threshold::Real = 0.75,
+            shrink_factor::Real = 0.25,
+            expand_factor::Real = 2.0,
+            max_shrink_times::Int = 32)
         new{typeof(initial_trust_radius),
             SciMLBase._unwrap_val(chunk_size),
             SciMLBase._unwrap_val(autodiff),
@@ -89,9 +89,9 @@ struct SimpleTrustRegion{T, CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem,
-    alg::SimpleTrustRegion, args...; abstol = nothing,
-    reltol = nothing,
-    maxiters = 1000, kwargs...)
+        alg::SimpleTrustRegion, args...; abstol = nothing,
+        reltol = nothing,
+        maxiters = 1000, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
     T = typeof(x)
@@ -147,7 +147,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
 
         # Compute the ratio of the actual to predicted reduction.
         model = -(δ' * g + 0.5 * δ' * H * δ)
-        r = (fₖ - fₖ₊₁) / model 
+        r = (fₖ - fₖ₊₁) / model
 
         # Update the trust region radius.
         if r < η₂
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 1c4400026..45df96410 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -36,10 +36,10 @@ value_derivative(f::F, x::AbstractArray) where {F} = f(x), ForwardDiff.jacobian(
 Inplace version of [`SimpleNonlinearSolve.value_derivative`](@ref).
 """
 function value_derivative!(J::AbstractMatrix,
-    y::AbstractArray,
-    f!::F,
-    x::AbstractArray,
-    cfg::ForwardDiff.JacobianConfig = ForwardDiff.JacobianConfig(f!, y, x)) where {F}
+        y::AbstractArray,
+        f!::F,
+        x::AbstractArray,
+        cfg::ForwardDiff.JacobianConfig = ForwardDiff.JacobianConfig(f!, y, x)) where {F}
     ForwardDiff.jacobian!(J, f!, y, x, cfg)
     return y, J
 end
diff --git a/lib/SimpleNonlinearSolve/test/inplace.jl b/lib/SimpleNonlinearSolve/test/inplace.jl
index d4882105b..2e9d033a8 100644
--- a/lib/SimpleNonlinearSolve/test/inplace.jl
+++ b/lib/SimpleNonlinearSolve/test/inplace.jl
@@ -4,8 +4,8 @@ using SimpleNonlinearSolve,
 
 # Supported Solvers: BatchedBroyden, BatchedSimpleDFSane, BatchedSimpleNewtonRaphson
 function f!(du::AbstractArray{<:Number, N},
-    u::AbstractArray{<:Number, N},
-    p::AbstractVector) where {N}
+        u::AbstractArray{<:Number, N},
+        p::AbstractVector) where {N}
     u_ = reshape(u, :, size(u, N))
     du .= reshape(sum(abs2, u_; dims = 1) .- u_ .- reshape(p, 1, :), size(u))
     return du

From 000f4db4c8214115bff743a3045cf7a93edfb39a Mon Sep 17 00:00:00 2001
From: FHoltorf <holtorf93@gmail.com>
Date: Tue, 21 Nov 2023 22:44:59 -0500
Subject: [PATCH 216/700] Incorrect RetCode upon termination due to stalling of
 iterates or repeated shrinking of TR

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 98a36d063..72d8efa88 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -155,7 +155,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
             shrink_counter += 1
             if shrink_counter > max_shrink_times
                 return SciMLBase.build_solution(prob, alg, x, F;
-                    retcode = ReturnCode.Success)
+                    retcode = ReturnCode.ConvergenceFailure)
             end
         else
             shrink_counter = 0
@@ -163,7 +163,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         if r > η₁
             if isapprox(xₖ₊₁, x, atol = atol, rtol = rtol)
                 return SciMLBase.build_solution(prob, alg, xₖ₊₁, Fₖ₊₁;
-                    retcode = ReturnCode.Success)
+                    retcode = ReturnCode.ConvergenceFailure)
             end
             # Take the step.
             x = xₖ₊₁

From 0cc84ab6f167f967808ec76f67c9c149ead2186c Mon Sep 17 00:00:00 2001
From: FHoltorf <holtorf93@gmail.com>
Date: Wed, 22 Nov 2023 11:51:38 -0500
Subject: [PATCH 217/700] compute Newton step as opposed to Gauss-Newton step
 when J is square and full rank

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 2 +-
 lib/SimpleNonlinearSolve/src/utils.jl       | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 72d8efa88..011ececd8 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -140,7 +140,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
 
     for k in 1:maxiters
         # Solve the trust region subproblem.
-        δ = dogleg_method(H, g, Δ)
+        δ = dogleg_method(∇f, F, g, Δ)
         xₖ₊₁ = x + δ
         Fₖ₊₁ = f(xₖ₊₁)
         fₖ₊₁ = 0.5 * norm(Fₖ₊₁)^2
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 45df96410..af66f63f8 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -58,9 +58,9 @@ function init_J(x)
     return J
 end
 
-function dogleg_method(H, g, Δ)
+function dogleg_method(J, f, g, Δ)
     # Compute the Newton step.
-    δN = -H \ g
+    δN = J \ (-f)
     # Test if the full step is within the trust region.
     if norm(δN) ≤ Δ
         return δN

From 8fba768946b1fdf1bae918f9808f131ea1b4ec91 Mon Sep 17 00:00:00 2001
From: FHoltorf <holtorf93@gmail.com>
Date: Wed, 22 Nov 2023 11:54:23 -0500
Subject: [PATCH 218/700] undo ReturnCode changes => treat in another issue

---
 lib/SimpleNonlinearSolve/src/trustRegion.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 011ececd8..0fba7b12f 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -155,7 +155,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
             shrink_counter += 1
             if shrink_counter > max_shrink_times
                 return SciMLBase.build_solution(prob, alg, x, F;
-                    retcode = ReturnCode.ConvergenceFailure)
+                    retcode = ReturnCode.Success)
             end
         else
             shrink_counter = 0
@@ -163,7 +163,7 @@ function SciMLBase.__solve(prob::NonlinearProblem,
         if r > η₁
             if isapprox(xₖ₊₁, x, atol = atol, rtol = rtol)
                 return SciMLBase.build_solution(prob, alg, xₖ₊₁, Fₖ₊₁;
-                    retcode = ReturnCode.ConvergenceFailure)
+                    retcode = ReturnCode.Success)
             end
             # Take the step.
             x = xₖ₊₁

From 19436d1842233a527cc6186ded6530fd22e9c701 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 21 Nov 2023 18:54:23 -0500
Subject: [PATCH 219/700] Start cleaning up simplenonlinearsolve

---
 lib/SimpleNonlinearSolve/.JuliaFormatter.toml |   5 +-
 lib/SimpleNonlinearSolve/Project.toml         |   4 +-
 lib/SimpleNonlinearSolve/README.md            |  17 +-
 .../src/SimpleNonlinearSolve.jl               | 162 ++++----
 lib/SimpleNonlinearSolve/src/alefeld.jl       |   4 +-
 lib/SimpleNonlinearSolve/src/bisection.jl     |   8 +-
 lib/SimpleNonlinearSolve/src/brent.jl         |   1 -
 lib/SimpleNonlinearSolve/src/broyden.jl       |  99 ++---
 lib/SimpleNonlinearSolve/src/dfsane.jl        |  67 ++--
 lib/SimpleNonlinearSolve/src/halley.jl        |  26 +-
 lib/SimpleNonlinearSolve/src/itp.jl           |  24 +-
 lib/SimpleNonlinearSolve/src/raphson.jl       | 122 ++----
 lib/SimpleNonlinearSolve/src/ridder.jl        |   1 -
 lib/SimpleNonlinearSolve/src/utils.jl         | 360 ++++++++++++++----
 14 files changed, 528 insertions(+), 372 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.JuliaFormatter.toml b/lib/SimpleNonlinearSolve/.JuliaFormatter.toml
index 453925c3f..4d06911d7 100644
--- a/lib/SimpleNonlinearSolve/.JuliaFormatter.toml
+++ b/lib/SimpleNonlinearSolve/.JuliaFormatter.toml
@@ -1 +1,4 @@
-style = "sciml"
\ No newline at end of file
+style = "sciml"
+format_markdown = true
+annotate_untyped_fields_with_any = false
+format_docstrings = true
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index aa45b60af..f9242c69f 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,10 +1,12 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.25"
+version = "0.1.26"
 
 [deps]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
index 53b32e311..efa1fdd63 100644
--- a/lib/SimpleNonlinearSolve/README.md
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -6,12 +6,12 @@
 [![codecov](https://codecov.io/gh/SciML/SimpleNonlinearSolve.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/SciML/SimpleNonlinearSolve.jl)
 [![Build Status](https://github.com/SciML/SimpleNonlinearSolve.jl/workflows/CI/badge.svg)](https://github.com/SciML/SimpleNonlinearSolve.jl/actions?query=workflow%3ACI)
 
-[![ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://img.shields.io/badge/ColPrac-Contributor's%20Guide-blueviolet)](https://github.com/SciML/ColPrac)
+[![ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://img.shields.io/badge/ColPrac-Contributor%27s%20Guide-blueviolet)](https://github.com/SciML/ColPrac)
 [![SciML Code Style](https://img.shields.io/static/v1?label=code%20style&message=SciML&color=9558b2&labelColor=389826)](https://github.com/SciML/SciMLStyle)
 
 Fast implementations of root finding algorithms in Julia that satisfy the SciML common interface.
 SimpleNonlinearSolve.jl focuses on low-dependency implementations of very fast methods for
-very small and simple problems. For the full set of solvers, see 
+very small and simple problems. For the full set of solvers, see
 [NonlinearSolve.jl](https://github.com/SciML/NonlinearSolve.jl), of which
 SimpleNonlinearSolve.jl is just one solver set.
 
@@ -25,7 +25,7 @@ the documentation which contains the unreleased features.
 ```julia
 using SimpleNonlinearSolve, StaticArrays
 
-f(u,p) = u .* u .- 2
+f(u, p) = u .* u .- 2
 u0 = @SVector[1.0, 1.0]
 probN = NonlinearProblem{false}(f, u0)
 solver = solve(probN, SimpleNewtonRaphson(), abstol = 1e-9)
@@ -39,3 +39,14 @@ sol = solve(probB, ITP())
 ```
 
 For more details on the bracketing methods, refer to the [Tutorials](https://docs.sciml.ai/NonlinearSolve/stable/tutorials/nonlinear/#Using-Bracketing-Methods) and detailed [APIs](https://docs.sciml.ai/NonlinearSolve/stable/api/simplenonlinearsolve/#Solver-API)
+
+## Breaking Changes in v2
+
+* Batched solvers have been removed in favor of `BatchedArrays.jl`. Stay tuned for detailed
+  tutorials on how to use `BatchedArrays.jl` with `NonlinearSolve` & `SimpleNonlinearSolve`
+  solvers.
+* The old style of specifying autodiff with `chunksize`, `standardtag`, etc. has been
+  deprecated in favor of directly specifying the autodiff type, like `AutoForwardDiff`.
+* `Broyden` and `Klement` have been renamed to `SimpleBroyden` and `SimpleKlement` to
+  avoid conflicts with `NonlinearSolve.jl`'s `GeneralBroyden` and `GeneralKlement`, which
+  will be renamed to `Broyden` and `Klement` in the future.
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 8c84c4377..7d04c1037 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -1,90 +1,96 @@
 module SimpleNonlinearSolve
 
-using Reexport
-using FiniteDiff, ForwardDiff
-using ForwardDiff: Dual
-using StaticArraysCore
-using LinearAlgebra
-import ArrayInterface
-using DiffEqBase
+import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidations
+
+@recompile_invalidations begin
+    using ADTypes,
+        ArrayInterface, ConcreteStructs, DiffEqBase, Reexport, LinearAlgebra,
+        SciMLBase
+
+    import DiffEqBase: AbstractNonlinearTerminationMode,
+        AbstractSafeNonlinearTerminationMode, AbstractSafeBestNonlinearTerminationMode,
+        NonlinearSafeTerminationReturnCode, get_termination_mode
+    using FiniteDiff, ForwardDiff
+    import ForwardDiff: Dual
+    import SciMLBase: AbstractNonlinearAlgorithm, build_solution, isinplace
+    import StaticArraysCore: StaticArray, SVector, SArray, MArray
+end
 
-@reexport using SciMLBase
+@reexport using ADTypes, SciMLBase
 
-const NNlibExtLoaded = Ref{Bool}(false)
+# const NNlibExtLoaded = Ref{Bool}(false)
 
-abstract type AbstractSimpleNonlinearSolveAlgorithm <: SciMLBase.AbstractNonlinearAlgorithm end
+abstract type AbstractSimpleNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm end
 abstract type AbstractBracketingAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
-abstract type AbstractNewtonAlgorithm{CS, AD, FDT} <: AbstractSimpleNonlinearSolveAlgorithm end
-abstract type AbstractImmutableNonlinearSolver <: AbstractSimpleNonlinearSolveAlgorithm end
-abstract type AbstractBatchedNonlinearSolveAlgorithm <:
-              AbstractSimpleNonlinearSolveAlgorithm end
+abstract type AbstractNewtonAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 
 include("utils.jl")
-include("bisection.jl")
-include("falsi.jl")
+# include("bisection.jl")
+# include("falsi.jl")
 include("raphson.jl")
 include("broyden.jl")
-include("lbroyden.jl")
-include("klement.jl")
-include("trustRegion.jl")
-include("ridder.jl")
-include("brent.jl")
-include("dfsane.jl")
-include("ad.jl")
-include("halley.jl")
-include("alefeld.jl")
-include("itp.jl")
-
-# Batched Solver Support
-include("batched/utils.jl")
-include("batched/raphson.jl")
-include("batched/dfsane.jl")
-include("batched/broyden.jl")
-
-## Default algorithm
-
-# Set the default bracketing method to ITP
-
-function SciMLBase.solve(prob::IntervalNonlinearProblem; kwargs...)
-    SciMLBase.solve(prob, ITP(); kwargs...)
-end
-
-function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing,
-        args...; kwargs...)
-    SciMLBase.solve(prob, ITP(), args...; kwargs...)
-end
-
-import PrecompileTools
-
-PrecompileTools.@compile_workload begin
-    for T in (Float32, Float64)
-        prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-        for alg in (SimpleNewtonRaphson, SimpleHalley, Broyden, Klement, SimpleTrustRegion,
-            SimpleDFSane)
-            solve(prob_no_brack, alg(), abstol = T(1e-2))
-        end
-
-        #=
-        for alg in (SimpleNewtonRaphson,)
-            for u0 in ([1., 1.], StaticArraysCore.SA[1.0, 1.0])
-                u0 = T.(.1)
-                probN = NonlinearProblem{false}((u,p) -> u .* u .- p, u0, T(2))
-                solve(probN, alg(), tol = T(1e-2))
-            end
-        end
-        =#
-
-        prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p,
-            T.((0.0, 2.0)),
-            T(2))
-        for alg in (Bisection, Falsi, Ridder, Brent, Alefeld, ITP)
-            solve(prob_brack, alg(), abstol = T(1e-2))
-        end
-    end
-end
-
-export Bisection, Brent, Broyden, LBroyden, SimpleDFSane, Falsi, SimpleHalley, Klement,
-    Ridder, SimpleNewtonRaphson, SimpleTrustRegion, Alefeld, ITP, SimpleGaussNewton
-export BatchedBroyden, BatchedSimpleNewtonRaphson, BatchedSimpleDFSane
+# include("lbroyden.jl")
+# include("klement.jl")
+# include("trustRegion.jl")
+# include("ridder.jl")
+# include("brent.jl")
+# include("dfsane.jl")
+# include("ad.jl")
+# include("halley.jl")
+# include("alefeld.jl")
+# include("itp.jl")
+
+# # Batched Solver Support
+# include("batched/utils.jl")
+# include("batched/raphson.jl")
+# include("batched/dfsane.jl")
+# include("batched/broyden.jl")
+
+# ## Default algorithm
+
+# # Set the default bracketing method to ITP
+
+# function SciMLBase.solve(prob::IntervalNonlinearProblem; kwargs...)
+#     SciMLBase.solve(prob, ITP(); kwargs...)
+# end
+
+# function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing,
+#     args...; kwargs...)
+#     SciMLBase.solve(prob, ITP(), args...; kwargs...)
+# end
+
+# import PrecompileTools
+
+# PrecompileTools.@compile_workload begin
+#     for T in (Float32, Float64)
+#         prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
+#         for alg in (SimpleNewtonRaphson, SimpleHalley, Broyden, Klement, SimpleTrustRegion,
+#             SimpleDFSane)
+#             solve(prob_no_brack, alg(), abstol = T(1e-2))
+#         end
+
+#         #=
+#         for alg in (SimpleNewtonRaphson,)
+#             for u0 in ([1., 1.], StaticArraysCore.SA[1.0, 1.0])
+#                 u0 = T.(.1)
+#                 probN = NonlinearProblem{false}((u,p) -> u .* u .- p, u0, T(2))
+#                 solve(probN, alg(), tol = T(1e-2))
+#             end
+#         end
+#         =#
+
+#         prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p,
+#             T.((0.0, 2.0)),
+#             T(2))
+#         for alg in (Bisection, Falsi, Ridder, Brent, Alefeld, ITP)
+#             solve(prob_brack, alg(), abstol = T(1e-2))
+#         end
+#     end
+# end
+
+export SimpleBroyden, SimpleGaussNewton, SimpleNewtonRaphson
+# export Bisection, Brent, LBroyden, SimpleDFSane, Falsi, SimpleHalley, Klement,
+#     Ridder, SimpleTrustRegion, Alefeld, ITP
+# export BatchedBroyden, BatchedSimpleDFSane
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 0d4f56116..3d3b2ada8 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -1,9 +1,9 @@
 """
-`Alefeld()` 
+`Alefeld()`
 
 An implementation of algorithm 4.2 from [Alefeld](https://dl.acm.org/doi/10.1145/210089.210111).
 
-The paper brought up two new algorithms. Here choose to implement algorithm 4.2 rather than 
+The paper brought up two new algorithms. Here choose to implement algorithm 4.2 rather than
 algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal procedure.
 """
 struct Alefeld <: AbstractBracketingAlgorithm end
diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index f7c98aa65..93b1cbeb0 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -5,10 +5,10 @@ A common bisection method.
 
 ### Keyword Arguments
 
-- `exact_left`: whether to enforce whether the left side of the interval must be exactly
-  zero for the returned result. Defaults to false.
-- `exact_right`: whether to enforce whether the right side of the interval must be exactly
-  zero for the returned result. Defaults to false.
+  - `exact_left`: whether to enforce whether the left side of the interval must be exactly
+    zero for the returned result. Defaults to false.
+  - `exact_right`: whether to enforce whether the right side of the interval must be exactly
+    zero for the returned result. Defaults to false.
 """
 struct Bisection <: AbstractBracketingAlgorithm
     exact_left::Bool
diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/brent.jl
index 7d7a6bcf9..1319ed979 100644
--- a/lib/SimpleNonlinearSolve/src/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/brent.jl
@@ -2,7 +2,6 @@
 `Brent()`
 
 A non-allocating Brent method
-
 """
 struct Brent <: AbstractBracketingAlgorithm end
 
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 07b2609f9..4b7d5d902 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -1,79 +1,52 @@
 """
-    Broyden(; batched = false,
-        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-            abstol = nothing,
-            reltol = nothing))
+    SimpleBroyden()
 
 A low-overhead implementation of Broyden. This method is non-allocating on scalar
 and static array problems.
-
-!!! note
-
-    To use the `batched` version, remember to load `NNlib`, i.e., `using NNlib` or
-    `import NNlib` must be present in your code.
 """
-struct Broyden{TC <: NLSolveTerminationCondition} <:
-       AbstractSimpleNonlinearSolveAlgorithm
-    termination_condition::TC
-end
+struct SimpleBroyden <: AbstractSimpleNonlinearSolveAlgorithm end
 
-function Broyden(; batched = false,
-        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-            abstol = nothing,
-            reltol = nothing))
-    if batched
-        @assert NNlibExtLoaded[] "Please install and load `NNlib.jl` to use batched Broyden."
-        return BatchedBroyden(termination_condition)
-    end
-    return Broyden(termination_condition)
-end
-
-function SciMLBase.__solve(prob::NonlinearProblem, alg::Broyden, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
-    tc = alg.termination_condition
-    mode = DiffEqBase.get_termination_mode(tc)
-    f = Base.Fix2(prob.f, prob.p)
+function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        termination_condition = nothing, kwargs...)
+    f = isinplace(prob) ? (du, u) -> prob.f(du, u, prob.p) : u -> prob.f(u, prob.p)
     x = float(prob.u0)
+    fx = _get_fx(prob, x)
+    xo, δx, fprev, δf = __copy(x), __copy(x), __copy(fx), __copy(fx)
 
-    fₙ = f(x)
-    T = eltype(x)
-    J⁻¹ = init_J(x)
+    J⁻¹ = __init_identity_jacobian(fx, x)
+    J⁻¹δf, xᵀJ⁻¹ = __copy(x), __copy(x)
+    δJ⁻¹, δJ⁻¹n = __copy(x, J⁻¹), __copy(x)
 
-    if SciMLBase.isinplace(prob)
-        error("Broyden currently only supports out-of-place nonlinear problems")
-    end
+    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+        termination_condition)
 
-    atol = _get_tolerance(abstol, tc.abstol, T)
-    rtol = _get_tolerance(reltol, tc.reltol, T)
-
-    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-        error("Broyden currently doesn't support SAFE_BEST termination modes")
-    end
-
-    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? NLSolveSafeTerminationResult() :
-              nothing
-    termination_condition = tc(storage)
-
-    xₙ = x
-    xₙ₋₁ = x
-    fₙ₋₁ = fₙ
     for _ in 1:maxiters
-        xₙ = xₙ₋₁ - _restructure(xₙ₋₁, J⁻¹ * _vec(fₙ₋₁))
-        fₙ = f(xₙ)
-        Δxₙ = xₙ - xₙ₋₁
-        Δfₙ = fₙ - fₙ₋₁
-        J⁻¹Δfₙ = _restructure(Δfₙ, J⁻¹ * _vec(Δfₙ))
-        J⁻¹ += _restructure(J⁻¹,
-            ((_vec(Δxₙ) .- _vec(J⁻¹Δfₙ)) ./ (_vec(Δxₙ)' * _vec(J⁻¹Δfₙ))) *
-            (_vec(Δxₙ)' * J⁻¹))
-
-        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
+        δx = _restructure(δx, __mul!!(_vec(δx), J⁻¹, _vec(fprev)))
+        x = __sub!!(x, xo, δx)
+        fx = __eval_f(prob, f, fx, x)
+        δf = __sub!!(δf, fx, fprev)
+
+        # Termination Checks
+        tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
+        tc_sol !== nothing && return tc_sol
+
+        J⁻¹δf = _restructure(J⁻¹δf, __mul!!(_vec(J⁻¹δf), J⁻¹, _vec(δf)))
+        d = dot(δx, J⁻¹δf)
+        xᵀJ⁻¹ = _restructure(xᵀJ⁻¹, __mul!!(_vec(xᵀJ⁻¹), _vec(δx)', J⁻¹))
+
+        if ArrayInterface.can_setindex(δJ⁻¹n)
+            @. δJ⁻¹n = (δx - J⁻¹δf) / d
+        else
+            δJ⁻¹n = @. (δx - J⁻¹δf) / d
         end
 
-        xₙ₋₁ = xₙ
-        fₙ₋₁ = fₙ
+        δJ⁻¹ = __mul!!(δJ⁻¹, δJ⁻¹n, xᵀJ⁻¹')
+        J⁻¹ = __add!!(J⁻¹, δJ⁻¹)
+
+        xo = __copyto!!(xo, x)
+        fprev = __copyto!!(fprev, fx)
     end
 
-    return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
+    return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index 49c50bca3..e7fda8629 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -16,40 +16,39 @@ Computation, 75, 1429-1448.](https://www.researchgate.net/publication/220576479_
 
 ### Keyword Arguments
 
-- `σ_min`: the minimum value of the spectral coefficient `σ_k` which is related to the step
-  size in the algorithm. Defaults to `1e-10`.
-- `σ_max`: the maximum value of the spectral coefficient `σ_k` which is related to the step
-  size in the algorithm. Defaults to `1e10`.
-- `σ_1`: the initial value of the spectral coefficient `σ_k` which is related to the step
-  size in the algorithm.. Defaults to `1.0`.
-- `M`: The monotonicity of the algorithm is determined by a this positive integer.
-  A value of 1 for `M` would result in strict monotonicity in the decrease of the L2-norm
-  of the function `f`. However, higher values allow for more flexibility in this reduction.
-  Despite this, the algorithm still ensures global convergence through the use of a
-  non-monotone line-search algorithm that adheres to the Grippo-Lampariello-Lucidi
-  condition. Values in the range of 5 to 20 are usually sufficient, but some cases may call
-  for a higher value of `M`. The default setting is 10.
-- `γ`: a parameter that influences if a proposed step will be accepted. Higher value of `γ`
-  will make the algorithm more restrictive in accepting steps. Defaults to `1e-4`.
-- `τ_min`: if a step is rejected the new step size will get multiplied by factor, and this
-  parameter is the minimum value of that factor. Defaults to `0.1`.
-- `τ_max`: if a step is rejected the new step size will get multiplied by factor, and this
-  parameter is the maximum value of that factor. Defaults to `0.5`.
-- `nexp`: the exponent of the loss, i.e. ``f_k=||F(x_k)||^{nexp}``. The paper uses
-  `nexp ∈ {1,2}`. Defaults to `2`.
-- `η_strategy`:  function to determine the parameter `η_k`, which enables growth
-  of ``||F||^2``. Called as ``η_k = η_strategy(f_1, k, x, F)`` with `f_1` initialized as
-  ``f_1=||F(x_1)||^{nexp}``, `k` is the iteration number, `x` is the current `x`-value and
-  `F` the current residual. Should satisfy ``η_k > 0`` and ``∑ₖ ηₖ < ∞``. Defaults to
-  ``||F||^2 / k^2``.
-- `termination_condition`: a `NLSolveTerminationCondition` that determines when the solver
-  should terminate. Defaults to `NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-  abstol = nothing, reltol = nothing)`.
-- `batched`: if `true`, the algorithm will use a batched version of the algorithm that treats each
-  column of `x` as a separate problem. This can be useful nonlinear problems involing neural
-  networks. Defaults to `false`.
-- `max_inner_iterations`: the maximum number of iterations allowed for the inner loop of the
-  algorithm. Used exclusively in `batched` mode. Defaults to `1000`.
+  - `σ_min`: the minimum value of the spectral coefficient `σ_k` which is related to the step
+    size in the algorithm. Defaults to `1e-10`.
+  - `σ_max`: the maximum value of the spectral coefficient `σ_k` which is related to the step
+    size in the algorithm. Defaults to `1e10`.
+  - `σ_1`: the initial value of the spectral coefficient `σ_k` which is related to the step
+    size in the algorithm.. Defaults to `1.0`.
+  - `M`: The monotonicity of the algorithm is determined by a this positive integer.
+    A value of 1 for `M` would result in strict monotonicity in the decrease of the L2-norm
+    of the function `f`. However, higher values allow for more flexibility in this reduction.
+    Despite this, the algorithm still ensures global convergence through the use of a
+    non-monotone line-search algorithm that adheres to the Grippo-Lampariello-Lucidi
+    condition. Values in the range of 5 to 20 are usually sufficient, but some cases may call
+    for a higher value of `M`. The default setting is 10.
+  - `γ`: a parameter that influences if a proposed step will be accepted. Higher value of `γ`
+    will make the algorithm more restrictive in accepting steps. Defaults to `1e-4`.
+  - `τ_min`: if a step is rejected the new step size will get multiplied by factor, and this
+    parameter is the minimum value of that factor. Defaults to `0.1`.
+  - `τ_max`: if a step is rejected the new step size will get multiplied by factor, and this
+    parameter is the maximum value of that factor. Defaults to `0.5`.
+  - `nexp`: the exponent of the loss, i.e. ``f_k=||F(x_k)||^{nexp}``. The paper uses
+    `nexp ∈ {1,2}`. Defaults to `2`.
+  - `η_strategy`:  function to determine the parameter `η_k`, which enables growth
+    of ``||F||^2``. Called as ``η_k = η_strategy(f_1, k, x, F)`` with `f_1` initialized as
+    ``f_1=||F(x_1)||^{nexp}``, `k` is the iteration number, `x` is the current `x`-value and
+    `F` the current residual. Should satisfy ``η_k > 0`` and ``∑ₖ ηₖ < ∞``. Defaults to
+    ``||F||^2 / k^2``.
+  - `termination_condition`: a `NLSolveTerminationCondition` that determines when the solver
+    should terminate. Defaults to `NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault; abstol = nothing, reltol = nothing)`.
+  - `batched`: if `true`, the algorithm will use a batched version of the algorithm that treats each
+    column of `x` as a separate problem. This can be useful nonlinear problems involing neural
+    networks. Defaults to `false`.
+  - `max_inner_iterations`: the maximum number of iterations allowed for the inner loop of the
+    algorithm. Used exclusively in `batched` mode. Defaults to `1000`.
 """
 struct SimpleDFSane{T, TC} <: AbstractSimpleNonlinearSolveAlgorithm
     σ_min::T
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 8107dde31..8131acada 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -1,7 +1,7 @@
 """
 ```julia
 SimpleHalley(; chunk_size = Val{0}(), autodiff = Val{true}(),
-                                 diff_type = Val{:forward})
+    diff_type = Val{:forward})
 ```
 
 A low-overhead implementation of SimpleHalley's Method. This method is non-allocating on scalar
@@ -15,18 +15,18 @@ and static array problems.
 
 ### Keyword Arguments
 
-- `chunk_size`: the chunk size used by the internal ForwardDiff.jl automatic differentiation
-  system. This allows for multiple derivative columns to be computed simultaneously,
-  improving performance. Defaults to `0`, which is equivalent to using ForwardDiff.jl's
-  default chunk size mechanism. For more details, see the documentation for
-  [ForwardDiff.jl](https://juliadiff.org/ForwardDiff.jl/stable/).
-- `autodiff`: whether to use forward-mode automatic differentiation for the Jacobian.
-  Note that this argument is ignored if an analytical Jacobian is passed; as that will be
-  used instead. Defaults to `Val{true}`, which means ForwardDiff.jl is used by default.
-  If `Val{false}`, then FiniteDiff.jl is used for finite differencing.
-- `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
-  `Val{:forward}` for forward finite differences. For more details on the choices, see the
-  [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
+  - `chunk_size`: the chunk size used by the internal ForwardDiff.jl automatic differentiation
+    system. This allows for multiple derivative columns to be computed simultaneously,
+    improving performance. Defaults to `0`, which is equivalent to using ForwardDiff.jl's
+    default chunk size mechanism. For more details, see the documentation for
+    [ForwardDiff.jl](https://juliadiff.org/ForwardDiff.jl/stable/).
+  - `autodiff`: whether to use forward-mode automatic differentiation for the Jacobian.
+    Note that this argument is ignored if an analytical Jacobian is passed; as that will be
+    used instead. Defaults to `Val{true}`, which means ForwardDiff.jl is used by default.
+    If `Val{false}`, then FiniteDiff.jl is used for finite differencing.
+  - `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
+    `Val{:forward}` for forward finite differences. For more details on the choices, see the
+    [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
 """
 struct SimpleHalley{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     function SimpleHalley(; chunk_size = Val{0}(), autodiff = Val{true}(),
diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 3147c526e..933995cec 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -16,18 +16,18 @@ Average Performance Preserving Minmax Optimality"
 
 The following keyword parameters are accepted.
 
-- `n₀::Int = 1`, the 'slack'. Must not be negative.\n
-  When n₀ = 0 the worst-case is identical to that of bisection,
-  but increacing n₀ provides greater oppotunity for superlinearity.
-- `κ₁::Float64 = 0.1`. Must not be negative.\n
-  The recomended value is `0.2/(x₂ - x₁)`.
-  Lower values produce tighter asymptotic behaviour, while higher values
-  improve the steady-state behaviour when truncation is not helpful.
-- `κ₂::Real = 2`. Must lie in [1, 1+ϕ ≈ 2.62).\n
-  Higher values allow for a greater convergence rate,
-  but also make the method more succeptable to worst-case performance.
-  In practice, κ=1,2 seems to work well due to the computational simplicity,
-  as κ₂ is used as an exponent in the method.
+  - `n₀::Int = 1`, the 'slack'. Must not be negative.\n
+    When n₀ = 0 the worst-case is identical to that of bisection,
+    but increacing n₀ provides greater oppotunity for superlinearity.
+  - `κ₁::Float64 = 0.1`. Must not be negative.\n
+    The recomended value is `0.2/(x₂ - x₁)`.
+    Lower values produce tighter asymptotic behaviour, while higher values
+    improve the steady-state behaviour when truncation is not helpful.
+  - `κ₂::Real = 2`. Must lie in [1, 1+ϕ ≈ 2.62).\n
+    Higher values allow for a greater convergence rate,
+    but also make the method more succeptable to worst-case performance.
+    In practice, κ=1,2 seems to work well due to the computational simplicity,
+    as κ₂ is used as an exponent in the method.
 
 ### Worst Case Performance
 
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 138e6724d..a1974ba88 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -1,9 +1,6 @@
 """
-    SimpleNewtonRaphson(; batched = false,
-        chunk_size = Val{0}(),
-        autodiff = Val{true}(),
-        diff_type = Val{:forward},
-        termination_condition = missing)
+    SimpleNewtonRaphson(autodiff)
+    SimpleNewtonRaphson(; autodiff = AutoForwardDiff())
 
 A low-overhead implementation of Newton-Raphson. This method is non-allocating on scalar
 and static array problems.
@@ -16,110 +13,45 @@ and static array problems.
 
 ### Keyword Arguments
 
-- `chunk_size`: the chunk size used by the internal ForwardDiff.jl automatic differentiation
-  system. This allows for multiple derivative columns to be computed simultaneously,
-  improving performance. Defaults to `0`, which is equivalent to using ForwardDiff.jl's
-  default chunk size mechanism. For more details, see the documentation for
-  [ForwardDiff.jl](https://juliadiff.org/ForwardDiff.jl/stable/).
-- `autodiff`: whether to use forward-mode automatic differentiation for the Jacobian.
-  Note that this argument is ignored if an analytical Jacobian is passed; as that will be
-  used instead. Defaults to `Val{true}`, which means ForwardDiff.jl is used by default.
-  If `Val{false}`, then FiniteDiff.jl is used for finite differencing.
-- `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
-  `Val{:forward}` for forward finite differences. For more details on the choices, see the
-  [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
-- `termination_condition`: control the termination of the algorithm. (Only works for batched
-  problems)
+  - `autodiff`: determines the backend used for the Jacobian. Defaults to
+    `AutoForwardDiff()`. Valid choices are `AutoForwardDiff()` or `AutoFiniteDiff()`.
 """
-struct SimpleNewtonRaphson{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT} end
-
-function SimpleNewtonRaphson(; batched = false,
-        chunk_size = Val{0}(),
-        autodiff = Val{true}(),
-        diff_type = Val{:forward},
-        termination_condition = missing)
-    if !ismissing(termination_condition) && !batched
-        throw(ArgumentError("`termination_condition` is currently only supported for batched problems"))
-    end
-    if batched
-        # @assert ADLinearSolveFDExtLoaded[] "Please install and load `LinearSolve.jl`, `FiniteDifferences.jl` and `AbstractDifferentiation.jl` to use batched Newton-Raphson."
-        termination_condition = ismissing(termination_condition) ?
-                                NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-            abstol = nothing,
-            reltol = nothing) :
-                                termination_condition
-        return BatchedSimpleNewtonRaphson(; chunk_size,
-            autodiff,
-            diff_type,
-            termination_condition)
-        return SimpleNewtonRaphson{SciMLBase._unwrap_val(chunk_size),
-            SciMLBase._unwrap_val(autodiff),
-            SciMLBase._unwrap_val(diff_type)}()
-    end
-    return SimpleNewtonRaphson{SciMLBase._unwrap_val(chunk_size),
-        SciMLBase._unwrap_val(autodiff),
-        SciMLBase._unwrap_val(diff_type)}()
+@concrete struct SimpleNewtonRaphson <: AbstractNewtonAlgorithm
+    ad
 end
 
+SimpleNewtonRaphson(; autodiff = AutoForwardDiff()) = SimpleNewtonRaphson(autodiff)
+
 const SimpleGaussNewton = SimpleNewtonRaphson
 
 function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
-        alg::SimpleNewtonRaphson, args...; abstol = nothing,
-        reltol = nothing,
-        maxiters = 1000, kwargs...)
-    f = Base.Fix2(prob.f, prob.p)
+        alg::SimpleNewtonRaphson, args...; abstol = nothing, reltol = nothing,
+        maxiters = 1000, termination_condition = nothing, kwargs...)
     x = float(prob.u0)
-    fx = float(prob.u0)
-    T = typeof(x)
+    fx = _get_fx(prob, x)
+    xo = __copy(x)
+    J, jac_cache = jacobian_cache(alg.ad, prob.f, fx, x, prob.p)
 
-    if SciMLBase.isinplace(prob)
-        error("SimpleNewtonRaphson currently only supports out-of-place nonlinear problems")
-    end
-
-    if prob isa NonlinearLeastSquaresProblem &&
-       !(typeof(prob.u0) <: Union{Number, AbstractVector})
-        error("SimpleGaussNewton only supports Number and AbstactVector types. Please convert any problem of AbstractArray into one with u0 as AbstractVector")
-    end
-
-    atol = abstol !== nothing ? abstol :
-           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
-    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
-
-    if x isa Number
-        xo = oftype(one(eltype(x)), Inf)
-    else
-        xo = map(x -> oftype(one(eltype(x)), Inf), x)
-    end
+    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+        termination_condition)
 
     for i in 1:maxiters
-        if DiffEqBase.has_jac(prob.f)
-            dfx = prob.f.jac(x, prob.p)
-            fx = f(x)
-        elseif alg_autodiff(alg)
-            fx, dfx = value_derivative(f, x)
-        elseif x isa AbstractArray
-            fx = f(x)
-            dfx = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x), fx)
-        else
-            fx = f(x)
-            dfx = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x),
-                fx)
-        end
-        iszero(fx) &&
-            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
+        fx, dfx = value_and_jacobian(alg.ad, prob.f, fx, x, prob.p, jac_cache; J)
 
-        if prob isa NonlinearProblem
-            Δx = _restructure(fx, dfx \ _vec(fx))
+        if i == 1
+            if iszero(fx)
+                return build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
+            end
         else
-            Δx = dfx \ fx
+            # Termination Checks
+            tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
+            tc_sol !== nothing && return tc_sol
         end
 
-        x -= Δx
-        if isapprox(x, xo, atol = atol, rtol = rtol)
-            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
-        end
-        xo = x
+        xo = __copyto!!(xo, x)
+        Δx = _restructure(x, dfx \ _vec(fx))
+        x = __sub!!(x, Δx)
     end
 
-    return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+    return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/src/ridder.jl b/lib/SimpleNonlinearSolve/src/ridder.jl
index eabd7b2ac..41b43200e 100644
--- a/lib/SimpleNonlinearSolve/src/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/ridder.jl
@@ -2,7 +2,6 @@
 `Ridder()`
 
 A non-allocating ridder method
-
 """
 struct Ridder <: AbstractBracketingAlgorithm end
 
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index af66f63f8..6a35aae25 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -1,91 +1,323 @@
-"""
-  prevfloat_tdir(x, x0, x1)
+struct SimpleNonlinearSolveTag end
 
-Move `x` one floating point towards x0.
-"""
-function prevfloat_tdir(x, x0, x1)
-    x1 > x0 ? prevfloat(x) : nextfloat(x)
+function ForwardDiff.checktag(::Type{<:ForwardDiff.Tag{<:SimpleNonlinearSolveTag, <:T}},
+        f::F, x::AbstractArray{T}) where {T, F}
+    return true
 end
 
-function nextfloat_tdir(x, x0, x1)
-    x1 > x0 ? nextfloat(x) : prevfloat(x)
-end
+# """
+#   prevfloat_tdir(x, x0, x1)
 
-function max_tdir(a, b, x0, x1)
-    x1 > x0 ? max(a, b) : min(a, b)
-end
+# Move `x` one floating point towards x0.
+# """
+# function prevfloat_tdir(x, x0, x1)
+#     x1 > x0 ? prevfloat(x) : nextfloat(x)
+# end
 
-alg_autodiff(alg::AbstractNewtonAlgorithm{CS, AD, FDT}) where {CS, AD, FDT} = AD
-diff_type(alg::AbstractNewtonAlgorithm{CS, AD, FDT}) where {CS, AD, FDT} = FDT
+# function nextfloat_tdir(x, x0, x1)
+#     x1 > x0 ? nextfloat(x) : prevfloat(x)
+# end
 
-"""
-  value_derivative(f, x)
+# function max_tdir(a, b, x0, x1)
+#     x1 > x0 ? max(a, b) : min(a, b)
+# end
 
-Compute `f(x), d/dx f(x)` in the most efficient way.
-"""
-function value_derivative(f::F, x::R) where {F, R}
-    T = typeof(ForwardDiff.Tag(f, R))
-    out = f(ForwardDiff.Dual{T}(x, one(x)))
-    ForwardDiff.value(out), ForwardDiff.extract_derivative(T, out)
+# alg_autodiff(alg::AbstractNewtonAlgorithm{CS, AD, FDT}) where {CS, AD, FDT} = AD
+# diff_type(alg::AbstractNewtonAlgorithm{CS, AD, FDT}) where {CS, AD, FDT} = FDT
+
+__standard_tag(::Nothing, x) = ForwardDiff.Tag(SimpleNonlinearSolveTag(), eltype(x))
+__standard_tag(tag::ForwardDiff.Tag, _) = tag
+__standard_tag(tag, x) = ForwardDiff.Tag(tag, eltype(x))
+
+function __get_jacobian_config(ad::AutoForwardDiff{CS}, f, x) where {CS}
+    ck = (CS === nothing || CS ≤ 0) ? ForwardDiff.Chunk(length(x)) : ForwardDiff.Chunk{CS}()
+    tag = __standard_tag(ad.tag, x)
+    return ForwardDiff.JacobianConfig(f, x, ck, tag)
+end
+function __get_jacobian_config(ad::AutoForwardDiff{CS}, f!, y, x) where {CS}
+    ck = (CS === nothing || CS ≤ 0) ? ForwardDiff.Chunk(length(x)) : ForwardDiff.Chunk{CS}()
+    tag = __standard_tag(ad.tag, x)
+    return ForwardDiff.JacobianConfig(f!, y, x, ck, tag)
 end
-value_derivative(f::F, x::AbstractArray) where {F} = f(x), ForwardDiff.jacobian(f, x)
 
 """
-    value_derivative!(J, y, f!, x, cfg = JacobianConfig(f!, y, x))
+    value_and_jacobian(ad, f, y, x, p, cache; J = nothing)
 
-Inplace version of [`SimpleNonlinearSolve.value_derivative`](@ref).
+Compute `f(x), d/dx f(x)` in the most efficient way based on `ad`. None of the arguments
+except `cache` (& `J` if not nothing) are mutated.
 """
-function value_derivative!(J::AbstractMatrix,
-        y::AbstractArray,
-        f!::F,
-        x::AbstractArray,
-        cfg::ForwardDiff.JacobianConfig = ForwardDiff.JacobianConfig(f!, y, x)) where {F}
-    ForwardDiff.jacobian!(J, f!, y, x, cfg)
-    return y, J
-end
-
-value(x) = x
-value(x::Dual) = ForwardDiff.value(x)
-value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
-
-function init_J(x)
-    J = ArrayInterface.zeromatrix(x)
-    if ismutable(x)
-        J[diagind(J)] .= one(eltype(x))
+function value_and_jacobian(ad, f::F, y, x::X, p, cache; J = nothing) where {F, X}
+    if isinplace(f)
+        _f = (du, u) -> f(du, u, p)
+        if DiffEqBase.has_jac(f)
+            f.jac(J, x, p)
+            _f(y, x)
+            return y, J
+        elseif ad isa AutoForwardDiff
+            res = DiffResults.DiffResult(y, J)
+            ForwardDiff.jacobian!(res, _f, y, x, cache)
+            return DiffResults.value(res), DiffResults.jacobian(res)
+        elseif ad isa AutoFiniteDiff
+            FiniteDiff.finite_difference_jacobian!(J, _f, x, cache)
+            _f(y, x)
+            return y, J
+        else
+            throw(ArgumentError("Unsupported AD method: $(ad)"))
+        end
     else
-        J += I
+        _f = Base.Fix2(f, p)
+        if DiffEqBase.has_jac(f)
+            return _f(x), f.jac(x, p)
+        elseif ad isa AutoForwardDiff
+            if ArrayInterface.can_setindex(x)
+                res = DiffResults.DiffResult(y, J)
+                ForwardDiff.jacobian!(res, _f, x, cache)
+                return DiffResults.value(res), DiffResults.jacobian(res)
+            else
+                J_fd = ForwardDiff.jacobian(_f, x, cache)
+                return _f(x), J_fd
+            end
+        elseif ad isa AutoFiniteDiff
+            J_fd = FiniteDiff.finite_difference_jacobian(_f, x, cache)
+            return _f(x), J_fd
+        else
+            throw(ArgumentError("Unsupported AD method: $(ad)"))
+        end
     end
-    return J
 end
 
-function dogleg_method(J, f, g, Δ)
-    # Compute the Newton step.
-    δN = J \ (-f)
-    # Test if the full step is within the trust region.
-    if norm(δN) ≤ Δ
-        return δN
+function jacobian_cache(ad, f::F, y, x::X, p) where {F, X <: AbstractArray}
+    if isinplace(f)
+        _f = (du, u) -> f(du, u, p)
+        J = similar(y, length(y), length(x))
+        if DiffEqBase.has_jac(f)
+            return J, nothing
+        elseif ad isa AutoForwardDiff
+            return J, __get_jacobian_config(ad, _f, y, x)
+        elseif ad isa AutoFiniteDiff
+            return J, FiniteDiff.JacobianCache(copy(x), copy(y), copy(y), ad.fdtype)
+        else
+            throw(ArgumentError("Unsupported AD method: $(ad)"))
+        end
+    else
+        _f = Base.Fix2(f, p)
+        if DiffEqBase.has_jac(f)
+            return nothing, nothing
+        elseif ad isa AutoForwardDiff
+            J = ArrayInterface.can_setindex(x) ? similar(y, length(fx), length(x)) : nothing
+            return J, __get_jacobian_config(ad, _f, x)
+        elseif ad isa AutoFiniteDiff
+            return nothing, FiniteDiff.JacobianCache(copy(x), copy(y), copy(y), ad.fdtype)
+        else
+            throw(ArgumentError("Unsupported AD method: $(ad)"))
+        end
     end
+end
 
-    # Calcualte Cauchy point, optimum along the steepest descent direction.
-    δsd = -g
-    norm_δsd = norm(δsd)
-    if norm_δsd ≥ Δ
-        return δsd .* Δ / norm_δsd
-    end
+# """
+#   value_derivative(f, x)
 
-    # Find the intersection point on the boundary.
-    δN_δsd = δN - δsd
-    dot_δN_δsd = dot(δN_δsd, δN_δsd)
-    dot_δsd_δN_δsd = dot(δsd, δN_δsd)
-    dot_δsd = dot(δsd, δsd)
-    fact = dot_δsd_δN_δsd^2 - dot_δN_δsd * (dot_δsd - Δ^2)
-    tau = (-dot_δsd_δN_δsd + sqrt(fact)) / dot_δN_δsd
-    return δsd + tau * δN_δsd
+# Compute `f(x), d/dx f(x)` in the most efficient way.
+# """
+# function value_derivative(f::F, x::R) where {F, R}
+#     T = typeof(ForwardDiff.Tag(f, R))
+#     out = f(ForwardDiff.Dual{T}(x, one(x)))
+#     ForwardDiff.value(out), ForwardDiff.extract_derivative(T, out)
+# end
+# value_derivative(f::F, x::AbstractArray) where {F} = f(x), ForwardDiff.jacobian(f, x)
+
+# """
+#     value_derivative!(J, y, f!, x, cfg = JacobianConfig(f!, y, x))
+
+# Inplace version of [`SimpleNonlinearSolve.value_derivative`](@ref).
+# """
+# function value_derivative!(J::AbstractMatrix,
+#     y::AbstractArray,
+#     f!::F,
+#     x::AbstractArray,
+#     cfg::ForwardDiff.JacobianConfig = ForwardDiff.JacobianConfig(f!, y, x)) where {F}
+#     ForwardDiff.jacobian!(J, f!, y, x, cfg)
+#     return y, J
+# end
+
+# value(x) = x
+# value(x::Dual) = ForwardDiff.value(x)
+# value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
+
+__init_identity_jacobian(u::Number, _) = u
+function __init_identity_jacobian(u, fu)
+    J = similar(u, promote_type(eltype(u), eltype(fu)), length(fu), length(u))
+    J[diagind(J)] .= one(eltype(J))
+    return J
+end
+function __init_identity_jacobian(u::StaticArray, fu)
+    return convert(MArray{Tuple{length(fu), length(u)}},
+        Matrix{eltype(u)}(I, length(fu), length(u)))
 end
 
+# function dogleg_method(J, f, g, Δ)
+#     # Compute the Newton step.
+#     δN = J \ (-f)
+#     # Test if the full step is within the trust region.
+#     if norm(δN) ≤ Δ
+#         return δN
+#     end
+
+#     # Calcualte Cauchy point, optimum along the steepest descent direction.
+#     δsd = -g
+#     norm_δsd = norm(δsd)
+#     if norm_δsd ≥ Δ
+#         return δsd .* Δ / norm_δsd
+#     end
+
+#     # Find the intersection point on the boundary.
+#     δN_δsd = δN - δsd
+#     dot_δN_δsd = dot(δN_δsd, δN_δsd)
+#     dot_δsd_δN_δsd = dot(δsd, δN_δsd)
+#     dot_δsd = dot(δsd, δsd)
+#     fact = dot_δsd_δN_δsd^2 - dot_δN_δsd * (dot_δsd - Δ^2)
+#     tau = (-dot_δsd_δN_δsd + sqrt(fact)) / dot_δN_δsd
+#     return δsd + tau * δN_δsd
+# end
+
 @inline _vec(v) = vec(v)
 @inline _vec(v::Number) = v
 @inline _vec(v::AbstractVector) = v
 
 @inline _restructure(y::Number, x::Number) = x
 @inline _restructure(y, x) = ArrayInterface.restructure(y, x)
+
+@inline function _get_fx(prob::NonlinearLeastSquaresProblem, x)
+    isinplace(prob) && prob.f.resid_prototype === nothing &&
+        error("Inplace NonlinearLeastSquaresProblem requires a `resid_prototype`")
+    return _get_fx(prob.f, x, prob.p)
+end
+@inline _get_fx(prob::NonlinearProblem, x) = _get_fx(prob.f, x, prob.p)
+@inline function _get_fx(f::NonlinearFunction, x, p)
+    if isinplace(f)
+        if f.resid_prototype !== nothing
+            T = eltype(x)
+            return T.(f.resid_prototype)
+        else
+            fx = similar(x)
+            f(fx, x, p)
+            return fx
+        end
+    else
+        return f(x, p)
+    end
+end
+
+# Termination Conditions Support
+# Taken directly from NonlinearSolve.jl
+function init_termination_cache(abstol, reltol, du, u, ::Nothing)
+    return init_termination_cache(abstol, reltol, du, u, AbsSafeBestTerminationMode())
+end
+function init_termination_cache(abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
+    tc_cache = init(du, u, tc; abstol, reltol)
+    return DiffEqBase.get_abstol(tc_cache), DiffEqBase.get_reltol(tc_cache), tc_cache
+end
+
+function check_termination(tc_cache, fx, x, xo, prob, alg)
+    return check_termination(tc_cache, fx, x, xo, prob, alg,
+        DiffEqBase.get_termination_mode(tc_cache))
+end
+function check_termination(tc_cache, fx, x, xo, prob, alg,
+        ::AbstractNonlinearTerminationMode)
+    if tc_cache(fx, x, xo)
+        return build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
+    end
+    return nothing
+end
+function check_termination(tc_cache, fx, x, xo, prob, alg,
+        ::AbstractSafeNonlinearTerminationMode)
+    if tc_cache(fx, x, xo)
+        if tc_cache.retcode == NonlinearSafeTerminationReturnCode.Success
+            retcode = ReturnCode.Success
+        elseif tc_cache.retcode == NonlinearSafeTerminationReturnCode.PatienceTermination
+            retcode = ReturnCode.ConvergenceFailure
+        elseif tc_cache.retcode == NonlinearSafeTerminationReturnCode.ProtectiveTermination
+            retcode = ReturnCode.Unstable
+        else
+            error("Unknown termination code: $(tc_cache.retcode)")
+        end
+        return build_solution(prob, alg, x, fx; retcode)
+    end
+    return nothing
+end
+function check_termination(tc_cache, fx, x, xo, prob, alg,
+        ::AbstractSafeBestNonlinearTerminationMode)
+    if tc_cache(fx, x, xo)
+        if tc_cache.retcode == NonlinearSafeTerminationReturnCode.Success
+            retcode = ReturnCode.Success
+        elseif tc_cache.retcode == NonlinearSafeTerminationReturnCode.PatienceTermination
+            retcode = ReturnCode.ConvergenceFailure
+        elseif tc_cache.retcode == NonlinearSafeTerminationReturnCode.ProtectiveTermination
+            retcode = ReturnCode.Unstable
+        else
+            error("Unknown termination code: $(tc_cache.retcode)")
+        end
+        if isinplace(prob)
+            prob.f(fx, x, prob.p)
+        else
+            fx = prob.f(x, prob.p)
+        end
+        return build_solution(prob, alg, tc_cache.u, fx; retcode)
+    end
+    return nothing
+end
+
+# MaybeInplace
+@inline __copyto!!(::Number, x) = x
+@inline __copyto!!(::SArray, x) = x
+@inline __copyto!!(y::Union{MArray, Array}, x) = copyto!(y, x)
+@inline function __copyto!!(y::AbstractArray, x)
+    ArrayInterface.can_setindex(y) && return copyto!(y, x)
+    return x
+end
+
+@inline __sub!!(x::Number, Δx) = x - Δx
+@inline __sub!!(x::SArray, Δx) = x .- Δx
+@inline __sub!!(x::Union{MArray, Array}, Δx) = (x .-= Δx)
+@inline function __sub!!(x::AbstractArray, Δx)
+    ArrayInterface.can_setindex(x) && return (x .-= Δx)
+    return x .- Δx
+end
+
+@inline __sub!!(::Number, x, Δx) = x - Δx
+@inline __sub!!(::SArray, x, Δx) = x .- Δx
+@inline __sub!!(y::Union{MArray, Array}, x, Δx) = (@. y = x - Δx)
+@inline function __sub!!(y::AbstractArray, x, Δx)
+    ArrayInterface.can_setindex(y) && return (@. y = x - Δx)
+    return x .- Δx
+end
+
+@inline __add!!(x::Number, Δx) = x + Δx
+@inline __add!!(x::SArray, Δx) = x .+ Δx
+@inline __add!!(x::Union{MArray, Array}, Δx) = (x .+= Δx)
+@inline function __add!!(x::AbstractArray, Δx)
+    ArrayInterface.can_setindex(x) && return (x .+= Δx)
+    return x .+ Δx
+end
+
+@inline __copy(x::Union{Number, SArray}) = x
+@inline __copy(x::Union{Number, SArray}, _) = x
+@inline __copy(x::Union{MArray, Array}) = copy(x)
+@inline __copy(::Union{MArray, Array}, y) = copy(y)
+@inline function __copy(x::AbstractArray)
+    ArrayInterface.can_setindex(x) && return copy(x)
+    return x
+end
+@inline function __copy(x::AbstractArray, y)
+    ArrayInterface.can_setindex(x) && return copy(y)
+    return x
+end
+
+@inline __mul!!(::Union{Number, SArray}, A, b) = A * b
+@inline __mul!!(y::Union{MArray, Array}, A, b) = (mul!(y, A, b); y)
+@inline function __mul!!(y::AbstractArray, A, b)
+    ArrayInterface.can_setindex(y) && return (mul!(y, A, b); y)
+    return A * b
+end
+
+@inline __eval_f(prob, f, fx, x) = isinplace(prob) ? (f(fx, x); fx) : f(x)

From 0915379559c50a3a695ed45e51f891f959320446 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 21 Nov 2023 22:15:53 -0500
Subject: [PATCH 220/700] Update Klement

---
 lib/SimpleNonlinearSolve/Project.toml         |  10 --
 lib/SimpleNonlinearSolve/README.md            |  16 +--
 .../ext/SimpleNonlinearSolveNNlibExt.jl       |  81 ------------
 .../src/SimpleNonlinearSolve.jl               |  13 +-
 .../src/batched/broyden.jl                    |   6 -
 lib/SimpleNonlinearSolve/src/batched/utils.jl |  79 -----------
 lib/SimpleNonlinearSolve/src/broyden.jl       |   1 +
 lib/SimpleNonlinearSolve/src/klement.jl       | 125 ++++++------------
 lib/SimpleNonlinearSolve/src/utils.jl         | 103 ++++++++++-----
 9 files changed, 126 insertions(+), 308 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
 delete mode 100644 lib/SimpleNonlinearSolve/src/batched/broyden.jl
 delete mode 100644 lib/SimpleNonlinearSolve/src/batched/utils.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index f9242c69f..75af93414 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -16,24 +16,14 @@ Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
-[weakdeps]
-NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
-
-[extensions]
-SimpleNonlinearSolveNNlibExt = "NNlib"
-
 [compat]
 ArrayInterface = "7"
 DiffEqBase = "6.126"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 LinearAlgebra = "1.9"
-NNlib = "0.8, 0.9"
 PrecompileTools = "1"
 Reexport = "1"
 SciMLBase = "2.7"
 StaticArraysCore = "1.4"
 julia = "1.9"
-
-[extras]
-NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
index efa1fdd63..0f52b1065 100644
--- a/lib/SimpleNonlinearSolve/README.md
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -42,11 +42,11 @@ For more details on the bracketing methods, refer to the [Tutorials](https://doc
 
 ## Breaking Changes in v2
 
-* Batched solvers have been removed in favor of `BatchedArrays.jl`. Stay tuned for detailed
-  tutorials on how to use `BatchedArrays.jl` with `NonlinearSolve` & `SimpleNonlinearSolve`
-  solvers.
-* The old style of specifying autodiff with `chunksize`, `standardtag`, etc. has been
-  deprecated in favor of directly specifying the autodiff type, like `AutoForwardDiff`.
-* `Broyden` and `Klement` have been renamed to `SimpleBroyden` and `SimpleKlement` to
-  avoid conflicts with `NonlinearSolve.jl`'s `GeneralBroyden` and `GeneralKlement`, which
-  will be renamed to `Broyden` and `Klement` in the future.
+  - Batched solvers have been removed in favor of `BatchedArrays.jl`. Stay tuned for detailed
+    tutorials on how to use `BatchedArrays.jl` with `NonlinearSolve` & `SimpleNonlinearSolve`
+    solvers.
+  - The old style of specifying autodiff with `chunksize`, `standardtag`, etc. has been
+    deprecated in favor of directly specifying the autodiff type, like `AutoForwardDiff`.
+  - `Broyden` and `Klement` have been renamed to `SimpleBroyden` and `SimpleKlement` to
+    avoid conflicts with `NonlinearSolve.jl`'s `GeneralBroyden` and `GeneralKlement`, which
+    will be renamed to `Broyden` and `Klement` in the future.
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
deleted file mode 100644
index 1132b64b7..000000000
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveNNlibExt.jl
+++ /dev/null
@@ -1,81 +0,0 @@
-module SimpleNonlinearSolveNNlibExt
-
-using ArrayInterface, DiffEqBase, LinearAlgebra, NNlib, SimpleNonlinearSolve, SciMLBase
-import SimpleNonlinearSolve: _construct_batched_problem_structure,
-    _get_storage, _init_𝓙, _result_from_storage, _get_tolerance, @maybeinplace
-
-function __init__()
-    SimpleNonlinearSolve.NNlibExtLoaded[] = true
-    return
-end
-
-@views function SciMLBase.__solve(prob::NonlinearProblem,
-        alg::BatchedBroyden;
-        abstol = nothing,
-        reltol = nothing,
-        maxiters = 1000,
-        kwargs...)
-    iip = isinplace(prob)
-
-    u, f, reconstruct = _construct_batched_problem_structure(prob)
-    L, N = size(u)
-
-    tc = alg.termination_condition
-    mode = DiffEqBase.get_termination_mode(tc)
-
-    storage = _get_storage(mode, u)
-
-    xₙ, xₙ₋₁, δx, δf = ntuple(_ -> copy(u), 4)
-    T = eltype(u)
-
-    atol = _get_tolerance(abstol, tc.abstol, T)
-    rtol = _get_tolerance(reltol, tc.reltol, T)
-    termination_condition = tc(storage)
-
-    𝓙⁻¹ = _init_𝓙(xₙ)  # L × L × N
-    𝓙⁻¹f, xᵀ𝓙⁻¹δf, xᵀ𝓙⁻¹ = similar(𝓙⁻¹, L, N), similar(𝓙⁻¹, 1, N), similar(𝓙⁻¹, 1, L, N)
-
-    @maybeinplace iip fₙ₋₁=f(xₙ) u
-    iip && (fₙ = copy(fₙ₋₁))
-    for n in 1:maxiters
-        batched_mul!(reshape(𝓙⁻¹f, L, 1, N), 𝓙⁻¹, reshape(fₙ₋₁, L, 1, N))
-        xₙ .= xₙ₋₁ .- 𝓙⁻¹f
-
-        @maybeinplace iip fₙ=f(xₙ)
-        δx .= xₙ .- xₙ₋₁
-        δf .= fₙ .- fₙ₋₁
-
-        batched_mul!(reshape(𝓙⁻¹f, L, 1, N), 𝓙⁻¹, reshape(δf, L, 1, N))
-        δxᵀ = reshape(δx, 1, L, N)
-
-        batched_mul!(reshape(xᵀ𝓙⁻¹δf, 1, 1, N), δxᵀ, reshape(𝓙⁻¹f, L, 1, N))
-        batched_mul!(xᵀ𝓙⁻¹, δxᵀ, 𝓙⁻¹)
-        δx .= (δx .- 𝓙⁻¹f) ./ (xᵀ𝓙⁻¹δf .+ T(1e-5))
-        batched_mul!(𝓙⁻¹, reshape(δx, L, 1, N), xᵀ𝓙⁻¹, one(T), one(T))
-
-        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
-            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, iip)
-            return DiffEqBase.build_solution(prob,
-                alg,
-                reconstruct(xₙ),
-                reconstruct(fₙ);
-                retcode)
-        end
-
-        xₙ₋₁ .= xₙ
-        fₙ₋₁ .= fₙ
-    end
-
-    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-        xₙ = storage.u
-        @maybeinplace iip fₙ=f(xₙ)
-    end
-
-    return DiffEqBase.build_solution(prob,
-        alg,
-        reconstruct(xₙ),
-        reconstruct(fₙ);
-        retcode = ReturnCode.MaxIters)
-end
-
-end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 7d04c1037..5ba71e994 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -13,7 +13,7 @@ import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidat
     using FiniteDiff, ForwardDiff
     import ForwardDiff: Dual
     import SciMLBase: AbstractNonlinearAlgorithm, build_solution, isinplace
-    import StaticArraysCore: StaticArray, SVector, SArray, MArray
+    import StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray
 end
 
 @reexport using ADTypes, SciMLBase
@@ -30,7 +30,7 @@ include("utils.jl")
 include("raphson.jl")
 include("broyden.jl")
 # include("lbroyden.jl")
-# include("klement.jl")
+include("klement.jl")
 # include("trustRegion.jl")
 # include("ridder.jl")
 # include("brent.jl")
@@ -41,10 +41,7 @@ include("broyden.jl")
 # include("itp.jl")
 
 # # Batched Solver Support
-# include("batched/utils.jl")
-# include("batched/raphson.jl")
 # include("batched/dfsane.jl")
-# include("batched/broyden.jl")
 
 # ## Default algorithm
 
@@ -88,9 +85,9 @@ include("broyden.jl")
 #     end
 # end
 
-export SimpleBroyden, SimpleGaussNewton, SimpleNewtonRaphson
-# export Bisection, Brent, LBroyden, SimpleDFSane, Falsi, SimpleHalley, Klement,
+export SimpleBroyden, SimpleGaussNewton, SimpleKlement, SimpleNewtonRaphson
+# export Bisection, Brent, LBroyden, SimpleDFSane, Falsi, SimpleHalley,
 #     Ridder, SimpleTrustRegion, Alefeld, ITP
-# export BatchedBroyden, BatchedSimpleDFSane
+# export BatchedSimpleDFSane
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/batched/broyden.jl b/lib/SimpleNonlinearSolve/src/batched/broyden.jl
deleted file mode 100644
index ed3cd5dfc..000000000
--- a/lib/SimpleNonlinearSolve/src/batched/broyden.jl
+++ /dev/null
@@ -1,6 +0,0 @@
-struct BatchedBroyden{TC <: NLSolveTerminationCondition} <:
-       AbstractBatchedNonlinearSolveAlgorithm
-    termination_condition::TC
-end
-
-# Implementation of solve using Package Extensions
diff --git a/lib/SimpleNonlinearSolve/src/batched/utils.jl b/lib/SimpleNonlinearSolve/src/batched/utils.jl
deleted file mode 100644
index b8e66fe80..000000000
--- a/lib/SimpleNonlinearSolve/src/batched/utils.jl
+++ /dev/null
@@ -1,79 +0,0 @@
-macro maybeinplace(iip::Symbol, expr::Expr, u0::Union{Symbol, Nothing} = nothing)
-    @assert expr.head == :(=)
-    x1, x2 = expr.args
-    @assert x2.head == :call
-    f, x... = x2.args
-    define_expr = u0 === nothing ? :() : :($(x1) = similar($(u0)))
-    return quote
-        if $(esc(iip))
-            $(esc(define_expr))
-            $(esc(f))($(esc(x1)), $(esc.(x)...))
-        else
-            $(esc(expr))
-        end
-    end
-end
-
-function _get_tolerance(η, tc_η, ::Type{T}) where {T}
-    fallback_η = real(oneunit(T)) * (eps(real(one(T))))^(4 // 5)
-    return ifelse(η !== nothing, η, ifelse(tc_η !== nothing, tc_η, fallback_η))
-end
-
-function _construct_batched_problem_structure(prob)
-    return _construct_batched_problem_structure(prob.u0,
-        prob.f,
-        prob.p,
-        Val(SciMLBase.isinplace(prob)))
-end
-
-function _construct_batched_problem_structure(u0::AbstractArray{T, N},
-        f,
-        p,
-        ::Val{iip}) where {T, N, iip}
-    # Reconstruct `u`
-    reconstruct = N == 2 ? identity : Base.Fix2(reshape, size(u0))
-    # Standardize `u`
-    standardize = N == 2 ? identity :
-                  (N == 1 ? Base.Fix2(reshape, (:, 1)) :
-                   Base.Fix2(reshape, (:, size(u0, ndims(u0)))))
-    # Updated Function
-    f_modified = if iip
-        function f_modified_iip(du, u)
-            f(reconstruct(du), reconstruct(u), p)
-            return standardize(du)
-        end
-    else
-        f_modified_oop(u) = standardize(f(reconstruct(u), p))
-    end
-    return standardize(u0), f_modified, reconstruct
-end
-
-@views function _init_𝓙(x::AbstractMatrix)
-    𝓙 = ArrayInterface.zeromatrix(x[:, 1])
-    if ismutable(x)
-        𝓙[diagind(𝓙)] .= one(eltype(x))
-    else
-        𝓙 .+= I
-    end
-    return repeat(𝓙, 1, 1, size(x, 2))
-end
-
-_result_from_storage(::Nothing, xₙ, fₙ, args...) = ReturnCode.Success, xₙ, fₙ
-function _result_from_storage(storage::NLSolveSafeTerminationResult, xₙ, fₙ, f, mode, iip)
-    if storage.return_code == DiffEqBase.NLSolveSafeTerminationReturnCode.Success
-        return ReturnCode.Success, xₙ, fₙ
-    else
-        if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-            @maybeinplace iip fₙ=f(xₙ)
-            return ReturnCode.Terminated, storage.u, fₙ
-        else
-            return ReturnCode.Terminated, xₙ, fₙ
-        end
-    end
-end
-
-function _get_storage(mode, u)
-    return mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ?
-           NLSolveSafeTerminationResult(mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES ? u :
-                                        nothing) : nothing
-end
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 4b7d5d902..7587168a4 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -32,6 +32,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
         tc_sol !== nothing && return tc_sol
 
         J⁻¹δf = _restructure(J⁻¹δf, __mul!!(_vec(J⁻¹δf), J⁻¹, _vec(δf)))
+        δx = __neg!!(δx)
         d = dot(δx, J⁻¹δf)
         xᵀJ⁻¹ = _restructure(xᵀJ⁻¹, __mul!!(_vec(xᵀJ⁻¹), _vec(δx)', J⁻¹))
 
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index e6a38ecc2..3d22d1c07 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -1,106 +1,69 @@
 """
-```julia
-Klement()
-```
+    SimpleKlement()
 
 A low-overhead implementation of [Klement](https://jatm.com.br/jatm/article/view/373).
-This method is non-allocating on scalar problems.
 """
-struct Klement <: AbstractSimpleNonlinearSolveAlgorithm end
+struct SimpleKlement <: AbstractSimpleNonlinearSolveAlgorithm end
 
-function SciMLBase.__solve(prob::NonlinearProblem,
-        alg::Klement, args...; abstol = nothing,
-        reltol = nothing,
-        maxiters = 1000, kwargs...)
-    f = Base.Fix2(prob.f, prob.p)
+function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        termination_condition = nothing, kwargs...)
+    f = isinplace(prob) ? (du, u) -> prob.f(du, u, prob.p) : u -> prob.f(u, prob.p)
     x = float(prob.u0)
-    fₙ = f(x)
     T = eltype(x)
-    singular_tol = 1e-9
+    fx = _get_fx(prob, x)
 
-    if SciMLBase.isinplace(prob)
-        error("Klement currently only supports out-of-place nonlinear problems")
-    end
-
-    atol = abstol !== nothing ? abstol :
-           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
-    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
-
-    xₙ = x
-    xₙ₋₁ = x
-    fₙ₋₁ = fₙ
-
-    # x is scalar
-    if x isa Number
-        J = 1.0
-        for _ in 1:maxiters
-            xₙ = xₙ₋₁ - fₙ₋₁ / J
-            fₙ = f(xₙ)
-
-            iszero(fₙ) &&
-                return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                    retcode = ReturnCode.Success)
-
-            if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
-                return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                    retcode = ReturnCode.Success)
-            end
+    singular_tol = eps(T)^(2 // 3)
 
-            Δxₙ = xₙ - xₙ₋₁
-            Δfₙ = fₙ - fₙ₋₁
+    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+        termination_condition)
 
-            # Prevent division by 0
-            denominator = max(J^2 * Δxₙ^2, 1e-9)
+    δx, fprev, xo, δf, d = __copy(fx), __copy(fx), __copy(x), __copy(fx), __copy(x)
+    J = __init_identity_jacobian(fx, x)
+    J_cache, δx² = __copy(J), __copy(x)
 
-            k = (Δfₙ - J * Δxₙ) / denominator
-            J += (k * Δxₙ * J) * J
+    for _ in 1:maxiters
+        if x isa Number
+            J < singular_tol && (J = __init_identity_jacobian!!(J))
+            F = J
+        else
+            F = lu(J; check = false)
 
             # Singularity test
-            if J < singular_tol
-                J = 1.0
+            if any(x -> abs(x) < singular_tol, @view(F.U[diagind(F.U)]))
+                J = __init_identity_jacobian!!(J)
+                F = lu(J; check = false)
             end
-
-            xₙ₋₁ = xₙ
-            fₙ₋₁ = fₙ
         end
-        # x is a vector
-    else
-        J = init_J(x)
-        for _ in 1:maxiters
-            F = lu(J, check = false)
-
-            # Singularity test
-            if any(abs.(F.U[diagind(F.U)]) .< singular_tol)
-                J = init_J(xₙ)
-                F = lu(J, check = false)
-            end
 
-            tmp = _restructure(fₙ₋₁, F \ _vec(fₙ₋₁))
-            xₙ = xₙ₋₁ - tmp
-            fₙ = f(xₙ)
+        δx = __copyto!!(δx, fprev)
+        δx = __ldiv!!(F, δx)
+        x = __sub!!(x, xo, δx)
+        fx = __eval_f(prob, f, fx, x)
 
-            iszero(fₙ) &&
-                return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                    retcode = ReturnCode.Success)
+        # Termination Checks
+        tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
+        tc_sol !== nothing && return tc_sol
 
-            if isapprox(xₙ, xₙ₋₁, atol = atol, rtol = rtol)
-                return SciMLBase.build_solution(prob, alg, xₙ, fₙ;
-                    retcode = ReturnCode.Success)
-            end
+        δx = __neg!!(δx)
+        δf = __sub!!(δf, fx, fprev)
 
-            Δxₙ = xₙ - xₙ₋₁
-            Δfₙ = fₙ - fₙ₋₁
+        # Prevent division by 0
+        δx² = __broadcast!!(δx², abs2, δx)
+        J_cache = __broadcast!!(J_cache, abs2, J)
+        d = _restructure(d, __mul!!(_vec(d), J_cache', _vec(δx²)))
+        d = __broadcast!!(d, Base.Fix2(max, singular_tol), d)
 
-            # Prevent division by 0
-            denominator = _restructure(Δxₙ, max.(J' .^ 2 * _vec(Δxₙ) .^ 2, 1e-9))
+        δx² = _restructure(δx², __mul!!(_vec(δx²), J, _vec(δx)))
+        δf = __sub!!(δf, δx²)
+        δf = __broadcast!!(δf, /, δf, d)
 
-            k = (Δfₙ - _restructure(Δxₙ, J * _vec(Δxₙ))) ./ denominator
-            J += (_vec(k) * _vec(Δxₙ)' .* J) * J
+        J_cache = __mul!!(J_cache, _vec(δf), _vec(δx)')
+        J_cache = __broadcast!!(J_cache, *, J_cache, J)
+        J_cache = __mul!!(J_cache, J_cache, J)
 
-            xₙ₋₁ = xₙ
-            fₙ₋₁ = fₙ
-        end
+        J = __add!!(J, J_cache)
     end
 
-    return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
+    return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 6a35aae25..228006409 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -22,9 +22,6 @@ end
 #     x1 > x0 ? max(a, b) : min(a, b)
 # end
 
-# alg_autodiff(alg::AbstractNewtonAlgorithm{CS, AD, FDT}) where {CS, AD, FDT} = AD
-# diff_type(alg::AbstractNewtonAlgorithm{CS, AD, FDT}) where {CS, AD, FDT} = FDT
-
 __standard_tag(::Nothing, x) = ForwardDiff.Tag(SimpleNonlinearSolveTag(), eltype(x))
 __standard_tag(tag::ForwardDiff.Tag, _) = tag
 __standard_tag(tag, x) = ForwardDiff.Tag(tag, eltype(x))
@@ -86,6 +83,26 @@ function value_and_jacobian(ad, f::F, y, x::X, p, cache; J = nothing) where {F,
     end
 end
 
+function value_and_jacobian(ad, f::F, y, x::Number, p, cache; J = nothing) where {F}
+    if DiffEqBase.has_jac(f)
+        return f(x, p), f.jac(x, p)
+    elseif ad isa AutoForwardDiff
+        T = typeof(__standard_tag(ad.tag, x))
+        out = f(ForwardDiff.Dual{T}(x, one(x)), p)
+        return ForwardDiff.value(out), ForwardDiff.extract_derivative(T, out)
+    elseif ad isa AutoFiniteDiff
+        _f = Base.Fix2(f, p)
+        return _f(x), FiniteDiff.finite_difference_derivative(_f, x, ad.fdtype)
+    else
+        throw(ArgumentError("Unsupported AD method: $(ad)"))
+    end
+end
+
+"""
+    jacobian_cache(ad, f, y, x, p) --> J, cache
+
+Returns a Jacobian Matrix and a cache for the Jacobian computation.
+"""
 function jacobian_cache(ad, f::F, y, x::X, p) where {F, X <: AbstractArray}
     if isinplace(f)
         _f = (du, u) -> f(du, u, p)
@@ -114,45 +131,29 @@ function jacobian_cache(ad, f::F, y, x::X, p) where {F, X <: AbstractArray}
     end
 end
 
-# """
-#   value_derivative(f, x)
-
-# Compute `f(x), d/dx f(x)` in the most efficient way.
-# """
-# function value_derivative(f::F, x::R) where {F, R}
-#     T = typeof(ForwardDiff.Tag(f, R))
-#     out = f(ForwardDiff.Dual{T}(x, one(x)))
-#     ForwardDiff.value(out), ForwardDiff.extract_derivative(T, out)
-# end
-# value_derivative(f::F, x::AbstractArray) where {F} = f(x), ForwardDiff.jacobian(f, x)
-
-# """
-#     value_derivative!(J, y, f!, x, cfg = JacobianConfig(f!, y, x))
-
-# Inplace version of [`SimpleNonlinearSolve.value_derivative`](@ref).
-# """
-# function value_derivative!(J::AbstractMatrix,
-#     y::AbstractArray,
-#     f!::F,
-#     x::AbstractArray,
-#     cfg::ForwardDiff.JacobianConfig = ForwardDiff.JacobianConfig(f!, y, x)) where {F}
-#     ForwardDiff.jacobian!(J, f!, y, x, cfg)
-#     return y, J
-# end
-
-# value(x) = x
-# value(x::Dual) = ForwardDiff.value(x)
-# value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
+jacobian_cache(ad, f::F, y, x::Number, p) where {F} = nothing, nothing
 
-__init_identity_jacobian(u::Number, _) = u
+__init_identity_jacobian(u::Number, _) = one(u)
+__init_identity_jacobian!!(J::Number) = one(J)
 function __init_identity_jacobian(u, fu)
     J = similar(u, promote_type(eltype(u), eltype(fu)), length(fu), length(u))
     J[diagind(J)] .= one(eltype(J))
     return J
 end
+function __init_identity_jacobian!!(J)
+    fill!(J, zero(eltype(J)))
+    J[diagind(J)] .= one(eltype(J))
+    return J
+end
 function __init_identity_jacobian(u::StaticArray, fu)
-    return convert(MArray{Tuple{length(fu), length(u)}},
-        Matrix{eltype(u)}(I, length(fu), length(u)))
+    S1, S2 = length(fu), length(u)
+    J = SMatrix{S1, S2, eltype(u)}(ntuple(i -> ifelse(i ∈ 1:(S1 + 1):(S1 * S2), 1, 0),
+        S1 * S2))
+    return J
+end
+function __init_identity_jacobian!!(J::StaticArray{S1, S2}) where {S1, S2}
+    return SMMatrix{S1, S2, eltype(J)}(ntuple(i -> ifelse(i ∈ 1:(S1 + 1):(S1 * S2), 1, 0),
+        S1 * S2))
 end
 
 # function dogleg_method(J, f, g, Δ)
@@ -300,6 +301,14 @@ end
     return x .+ Δx
 end
 
+@inline __add!!(::Number, x, Δx) = x + Δx
+@inline __add!!(::SArray, x, Δx) = x .+ Δx
+@inline __add!!(y::Union{MArray, Array}, x, Δx) = (@. y = x + Δx)
+@inline function __add!!(y::AbstractArray, x, Δx)
+    ArrayInterface.can_setindex(y) && return (@. y = x + Δx)
+    return x .+ Δx
+end
+
 @inline __copy(x::Union{Number, SArray}) = x
 @inline __copy(x::Union{Number, SArray}, _) = x
 @inline __copy(x::Union{MArray, Array}) = copy(x)
@@ -320,4 +329,28 @@ end
     return A * b
 end
 
+@inline __neg!!(x::Union{Number, SArray}) = -x
+@inline __neg!!(x::Union{MArray, Array}) = (@. x .*= -one(eltype(x)))
+@inline function __neg!!(x::AbstractArray)
+    ArrayInterface.can_setindex(x) && return (@. x .*= -one(eltype(x)))
+    return -x
+end
+
+@inline __ldiv!!(A, b::Union{Number, SArray}) = A \ b
+@inline __ldiv!!(A, b::Union{MArray, Array}) = (ldiv!(A, b); b)
+@inline function __ldiv!!(A, b::AbstractArray)
+    ArrayInterface.can_setindex(b) && return (ldiv!(A, b); b)
+    return A \ b
+end
+
+@inline __broadcast!!(y::Union{Number, SArray}, f::F, x, args...) where {F} = f.(x, args...)
+@inline function __broadcast!!(y::Union{MArray, Array}, f::F, x, args...) where {F}
+    @. y = f(x, args...)
+    return y
+end
+@inline function __broadcast!!(y::AbstractArray, f::F, x, args...) where {F}
+    ArrayInterface.can_setindex(y) && return (@. y = f(x, args...))
+    return f.(x, args...)
+end
+
 @inline __eval_f(prob, f, fx, x) = isinplace(prob) ? (f(fx, x); fx) : f(x)

From d3af9e1eb533c0b237883e284129a639238fb558 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 21 Nov 2023 22:41:08 -0500
Subject: [PATCH 221/700] CLeanup bisection

---
 .../src/SimpleNonlinearSolve.jl               |  19 ++-
 .../src/batched/dfsane.jl                     | 141 ------------------
 lib/SimpleNonlinearSolve/src/bisection.jl     |  83 +++--------
 3 files changed, 35 insertions(+), 208 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/src/batched/dfsane.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 5ba71e994..8564a2805 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -25,23 +25,26 @@ abstract type AbstractBracketingAlgorithm <: AbstractSimpleNonlinearSolveAlgorit
 abstract type AbstractNewtonAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 
 include("utils.jl")
-# include("bisection.jl")
-# include("falsi.jl")
+
+# Nonlinear Solvera
 include("raphson.jl")
 include("broyden.jl")
 # include("lbroyden.jl")
 include("klement.jl")
 # include("trustRegion.jl")
+# include("halley.jl")
+# include("dfsane.jl")
+
+# Interval Nonlinear Solvers
+include("bisection.jl")
+# include("falsi.jl")
 # include("ridder.jl")
 # include("brent.jl")
-# include("dfsane.jl")
-# include("ad.jl")
-# include("halley.jl")
 # include("alefeld.jl")
 # include("itp.jl")
 
-# # Batched Solver Support
-# include("batched/dfsane.jl")
+# AD
+# include("ad.jl")
 
 # ## Default algorithm
 
@@ -86,8 +89,8 @@ include("klement.jl")
 # end
 
 export SimpleBroyden, SimpleGaussNewton, SimpleKlement, SimpleNewtonRaphson
+export Bisection
 # export Bisection, Brent, LBroyden, SimpleDFSane, Falsi, SimpleHalley,
 #     Ridder, SimpleTrustRegion, Alefeld, ITP
-# export BatchedSimpleDFSane
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl b/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
deleted file mode 100644
index 01b3b1996..000000000
--- a/lib/SimpleNonlinearSolve/src/batched/dfsane.jl
+++ /dev/null
@@ -1,141 +0,0 @@
-Base.@kwdef struct BatchedSimpleDFSane{T, F, TC <: NLSolveTerminationCondition} <:
-                   AbstractBatchedNonlinearSolveAlgorithm
-    σₘᵢₙ::T = 1.0f-10
-    σₘₐₓ::T = 1.0f+10
-    σ₁::T = 1.0f0
-    M::Int = 10
-    γ::T = 1.0f-4
-    τₘᵢₙ::T = 0.1f0
-    τₘₐₓ::T = 0.5f0
-    nₑₓₚ::Int = 2
-    ηₛ::F = (f₍ₙₒᵣₘ₎₁, n, xₙ, fₙ) -> f₍ₙₒᵣₘ₎₁ ./ n .^ 2
-    termination_condition::TC = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-        abstol = nothing,
-        reltol = nothing)
-    max_inner_iterations::Int = 1000
-end
-
-function SciMLBase.__solve(prob::NonlinearProblem,
-        alg::BatchedSimpleDFSane,
-        args...;
-        abstol = nothing,
-        reltol = nothing,
-        maxiters = 100,
-        kwargs...)
-    iip = isinplace(prob)
-
-    u, f, reconstruct = _construct_batched_problem_structure(prob)
-    L, N = size(u)
-    T = eltype(u)
-
-    tc = alg.termination_condition
-    mode = DiffEqBase.get_termination_mode(tc)
-
-    storage = _get_storage(mode, u)
-
-    atol = _get_tolerance(abstol, tc.abstol, T)
-    rtol = _get_tolerance(reltol, tc.reltol, T)
-    termination_condition = tc(storage)
-
-    σₘᵢₙ, σₘₐₓ, γ, τₘᵢₙ, τₘₐₓ = T(alg.σₘᵢₙ), T(alg.σₘₐₓ), T(alg.γ), T(alg.τₘᵢₙ), T(alg.τₘₐₓ)
-    α₁ = one(T)
-    α₊, α₋ = similar(u, 1, N), similar(u, 1, N)
-    σₙ = fill(T(alg.σ₁), 1, N)
-    𝒹 = similar(σₙ, L, N)
-    M = alg.M
-    nₑₓₚ = alg.nₑₓₚ
-
-    xₙ, xₙ₋₁, f₍ₙₒᵣₘ₎ₙ₋₁, f₍ₙₒᵣₘ₎ₙ = copy(u), copy(u), similar(u, 1, N), similar(u, 1, N)
-
-    function ff!(fₓ, fₙₒᵣₘ, x)
-        f(fₓ, x)
-        sum!(abs2, fₙₒᵣₘ, fₓ)
-        fₙₒᵣₘ .^= (nₑₓₚ / 2)
-        return fₓ
-    end
-
-    function ff!(fₙₒᵣₘ, x)
-        fₓ = f(x)
-        sum!(abs2, fₙₒᵣₘ, fₓ)
-        fₙₒᵣₘ .^= (nₑₓₚ / 2)
-        return fₓ
-    end
-
-    @maybeinplace iip fₙ₋₁=ff!(f₍ₙₒᵣₘ₎ₙ₋₁, xₙ) xₙ
-    iip && (fₙ = similar(fₙ₋₁))
-    ℋ = repeat(f₍ₙₒᵣₘ₎ₙ₋₁, M, 1)
-    f̄ = similar(ℋ, 1, N)
-    ηₛ = (n, xₙ, fₙ) -> alg.ηₛ(f₍ₙₒᵣₘ₎ₙ₋₁, n, xₙ, fₙ)
-
-    for n in 1:maxiters
-        # Spectral parameter range check
-        @. σₙ = sign(σₙ) * clamp(abs(σₙ), σₘᵢₙ, σₘₐₓ)
-
-        # Line search direction
-        @. 𝒹 = -σₙ * fₙ₋₁
-
-        η = ηₛ(n, xₙ₋₁, fₙ₋₁)
-        maximum!(f̄, ℋ)
-        fill!(α₊, α₁)
-        fill!(α₋, α₁)
-        @. xₙ = xₙ₋₁ + α₊ * 𝒹
-
-        @maybeinplace iip fₙ=ff!(f₍ₙₒᵣₘ₎ₙ, xₙ)
-
-        for _ in 1:(alg.max_inner_iterations)
-            𝒸 = @. f̄ + η - γ * α₊^2 * f₍ₙₒᵣₘ₎ₙ₋₁
-
-            (sum(f₍ₙₒᵣₘ₎ₙ .≤ 𝒸) ≥ N ÷ 2) && break
-
-            @. α₊ = clamp(α₊^2 * f₍ₙₒᵣₘ₎ₙ₋₁ / (f₍ₙₒᵣₘ₎ₙ + (T(2) * α₊ - T(1)) * f₍ₙₒᵣₘ₎ₙ₋₁),
-                τₘᵢₙ * α₊,
-                τₘₐₓ * α₊)
-            @. xₙ = xₙ₋₁ - α₋ * 𝒹
-            @maybeinplace iip fₙ=ff!(f₍ₙₒᵣₘ₎ₙ, xₙ)
-
-            (sum(f₍ₙₒᵣₘ₎ₙ .≤ 𝒸) ≥ N ÷ 2) && break
-
-            @. α₋ = clamp(α₋^2 * f₍ₙₒᵣₘ₎ₙ₋₁ / (f₍ₙₒᵣₘ₎ₙ + (T(2) * α₋ - T(1)) * f₍ₙₒᵣₘ₎ₙ₋₁),
-                τₘᵢₙ * α₋,
-                τₘₐₓ * α₋)
-            @. xₙ = xₙ₋₁ + α₊ * 𝒹
-            @maybeinplace iip fₙ=ff!(f₍ₙₒᵣₘ₎ₙ, xₙ)
-        end
-
-        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
-            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, iip)
-            return DiffEqBase.build_solution(prob,
-                alg,
-                reconstruct(xₙ),
-                reconstruct(fₙ);
-                retcode)
-        end
-
-        # Update spectral parameter
-        @. xₙ₋₁ = xₙ - xₙ₋₁
-        @. fₙ₋₁ = fₙ - fₙ₋₁
-
-        sum!(abs2, α₊, xₙ₋₁)
-        sum!(α₋, xₙ₋₁ .* fₙ₋₁)
-        σₙ .= α₊ ./ (α₋ .+ T(1e-5))
-
-        # Take step
-        @. xₙ₋₁ = xₙ
-        @. fₙ₋₁ = fₙ
-        @. f₍ₙₒᵣₘ₎ₙ₋₁ = f₍ₙₒᵣₘ₎ₙ
-
-        # Update history
-        ℋ[n % M + 1, :] .= view(f₍ₙₒᵣₘ₎ₙ, 1, :)
-    end
-
-    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-        xₙ = storage.u
-        @maybeinplace iip fₙ=f(xₙ)
-    end
-
-    return DiffEqBase.build_solution(prob,
-        alg,
-        reconstruct(xₙ),
-        reconstruct(fₙ);
-        retcode = ReturnCode.MaxIters)
-end
diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index 93b1cbeb0..7e8404451 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -1,5 +1,5 @@
 """
-`Bisection(; exact_left = false, exact_right = false)`
+    Bisection(; exact_left = false, exact_right = false)
 
 A common bisection method.
 
@@ -10,83 +10,48 @@ A common bisection method.
   - `exact_right`: whether to enforce whether the right side of the interval must be exactly
     zero for the returned result. Defaults to false.
 """
-struct Bisection <: AbstractBracketingAlgorithm
-    exact_left::Bool
-    exact_right::Bool
-end
-
-function Bisection(; exact_left = false, exact_right = false)
-    Bisection(exact_left, exact_right)
+@kwdef struct Bisection <: AbstractBracketingAlgorithm
+    exact_left::Bool = false
+    exact_right::Bool = false
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...;
         maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
         kwargs...)
+    @assert !isinplace(prob) "Bisection only supports OOP problems."
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
+
     if iszero(fl)
-        return SciMLBase.build_solution(prob, alg, left, fl;
-            retcode = ReturnCode.ExactSolutionLeft, left = left,
-            right = right)
+        return build_solution(prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft,
+            left, right)
     end
+
     if iszero(fr)
-        return SciMLBase.build_solution(prob, alg, right, fr;
-            retcode = ReturnCode.ExactSolutionRight, left = left,
-            right = right)
+        return build_solution(prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
+            left, right)
     end
 
-    i = 1
-    if !iszero(fr)
-        while i < maxiters
-            mid = (left + right) / 2
-            (mid == left || mid == right) &&
-                return SciMLBase.build_solution(prob, alg, left, fl;
-                    retcode = ReturnCode.FloatingPointLimit,
-                    left = left, right = right)
-            fm = f(mid)
-            if abs((right - left) / 2) < abstol
-                return SciMLBase.build_solution(prob, alg, mid, fm;
-                    retcode = ReturnCode.Success,
-                    left = left, right = right)
-            end
-            if iszero(fm)
-                right = mid
-                break
-            end
-            if sign(fl) == sign(fm)
-                fl = fm
-                left = mid
-            else
-                fr = fm
-                right = mid
-            end
-            i += 1
+    for _ in 1:maxiters
+        mid = (left + right) / 2
+        if (mid == left || mid == right)
+            return build_solution(prob, alg, left, fl; left, right,
+                retcode = ReturnCode.FloatingPointLimit)
         end
-    end
 
-    while i < maxiters
-        mid = (left + right) / 2
-        (mid == left || mid == right) &&
-            return SciMLBase.build_solution(prob, alg, left, fl;
-                retcode = ReturnCode.FloatingPointLimit,
-                left = left, right = right)
         fm = f(mid)
-        if abs((right - left) / 2) < abstol
-            return SciMLBase.build_solution(prob, alg, mid, fm;
-                retcode = ReturnCode.Success,
-                left = left, right = right)
+        if abs((right - left) / 2) < abstol || iszero(fm)
+            return build_solution(prob, alg, mid, fm; left, right,
+                retcode = ReturnCode.Success)
         end
-        if iszero(fm)
-            right = mid
-            fr = fm
+
+        if sign(fl * fm) < 0
+            right, fr = mid, fm
         else
-            left = mid
-            fl = fm
+            left, fl = mid, fm
         end
-        i += 1
     end
 
-    return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
-        left = left, right = right)
+    return build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
 end

From 71ed2fe54951aaf7fc008292150d08543136a7be Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 22 Nov 2023 02:44:43 -0500
Subject: [PATCH 222/700] Make some progress on Falsi and SimpleDFSane

---
 .../src/SimpleNonlinearSolve.jl               |  10 +-
 lib/SimpleNonlinearSolve/src/bisection.jl     |  14 +-
 lib/SimpleNonlinearSolve/src/dfsane.jl        | 199 +++++++-----------
 lib/SimpleNonlinearSolve/src/falsi.jl         | 117 +++++-----
 lib/SimpleNonlinearSolve/src/trustRegion.jl   |  91 ++++----
 lib/SimpleNonlinearSolve/src/utils.jl         |  39 ++--
 6 files changed, 221 insertions(+), 249 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 8564a2805..e0293ee6c 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -33,11 +33,11 @@ include("broyden.jl")
 include("klement.jl")
 # include("trustRegion.jl")
 # include("halley.jl")
-# include("dfsane.jl")
+include("dfsane.jl")
 
 # Interval Nonlinear Solvers
 include("bisection.jl")
-# include("falsi.jl")
+include("falsi.jl")
 # include("ridder.jl")
 # include("brent.jl")
 # include("alefeld.jl")
@@ -88,9 +88,9 @@ include("bisection.jl")
 #     end
 # end
 
-export SimpleBroyden, SimpleGaussNewton, SimpleKlement, SimpleNewtonRaphson
-export Bisection
-# export Bisection, Brent, LBroyden, SimpleDFSane, Falsi, SimpleHalley,
+export SimpleBroyden, SimpleDFSane, SimpleGaussNewton, SimpleKlement, SimpleNewtonRaphson
+export Bisection, Falsi
+# export Bisection, Brent, LBroyden, SimpleHalley,
 #     Ridder, SimpleTrustRegion, Alefeld, ITP
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index 7e8404451..9b1394bc6 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -9,6 +9,10 @@ A common bisection method.
     zero for the returned result. Defaults to false.
   - `exact_right`: whether to enforce whether the right side of the interval must be exactly
     zero for the returned result. Defaults to false.
+
+!!! warning
+
+    Currently, the keyword arguments are not implemented.
 """
 @kwdef struct Bisection <: AbstractBracketingAlgorithm
     exact_left::Bool = false
@@ -16,13 +20,15 @@ A common bisection method.
 end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...;
-        maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
-        kwargs...)
-    @assert !isinplace(prob) "Bisection only supports OOP problems."
+        maxiters = 1000, abstol = nothing, kwargs...)
+    @assert !isinplace(prob) "`Bisection` only supports OOP problems."
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
+    abstol = _get_tolerance(abstol,
+        promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
+
     if iszero(fl)
         return build_solution(prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft,
             left, right)
@@ -41,7 +47,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
         end
 
         fm = f(mid)
-        if abs((right - left) / 2) < abstol || iszero(fm)
+        if abs((right - left) / 2) < abstol || abs(fm) < abstol
             return build_solution(prob, alg, mid, fm; left, right,
                 retcode = ReturnCode.Success)
         end
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index e7fda8629..d646171d5 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -1,12 +1,7 @@
 """
     SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
         M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
-        nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2,
-        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-            abstol = nothing,
-            reltol = nothing),
-        batched::Bool = false,
-        max_inner_iterations::Int = 1000)
+        nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2)
 
 A low-overhead implementation of the df-sane method for solving large-scale nonlinear
 systems of equations. For in depth information about all the parameters and the algorithm,
@@ -42,167 +37,133 @@ Computation, 75, 1429-1448.](https://www.researchgate.net/publication/220576479_
     ``f_1=||F(x_1)||^{nexp}``, `k` is the iteration number, `x` is the current `x`-value and
     `F` the current residual. Should satisfy ``η_k > 0`` and ``∑ₖ ηₖ < ∞``. Defaults to
     ``||F||^2 / k^2``.
-  - `termination_condition`: a `NLSolveTerminationCondition` that determines when the solver
-    should terminate. Defaults to `NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault; abstol = nothing, reltol = nothing)`.
-  - `batched`: if `true`, the algorithm will use a batched version of the algorithm that treats each
-    column of `x` as a separate problem. This can be useful nonlinear problems involing neural
-    networks. Defaults to `false`.
-  - `max_inner_iterations`: the maximum number of iterations allowed for the inner loop of the
-    algorithm. Used exclusively in `batched` mode. Defaults to `1000`.
 """
-struct SimpleDFSane{T, TC} <: AbstractSimpleNonlinearSolveAlgorithm
-    σ_min::T
-    σ_max::T
-    σ_1::T
-    M::Int
-    γ::T
-    τ_min::T
-    τ_max::T
-    nexp::Int
-    η_strategy::Function
-    termination_condition::TC
+@kwdef @concrete struct SimpleDFSane <: AbstractSimpleNonlinearSolveAlgorithm
+    σ_min = 1e-10
+    σ_max = 1e10
+    σ_1 = 1.0
+    M::Int = 10
+    γ = 1e-4
+    τ_min = 0.1
+    τ_max = 0.5
+    nexp::Int = 2
+    η_strategy = (f_1, k, x, F) -> f_1 ./ k^2
 end
 
-function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
-        M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
-        nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2,
-        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-            abstol = nothing,
-            reltol = nothing),
-        batched::Bool = false,
-        max_inner_iterations = 1000)
-    if batched
-        return BatchedSimpleDFSane(; σₘᵢₙ = σ_min,
-            σₘₐₓ = σ_max,
-            σ₁ = σ_1,
-            M,
-            γ,
-            τₘᵢₙ = τ_min,
-            τₘₐₓ = τ_max,
-            nₑₓₚ = nexp,
-            ηₛ = η_strategy,
-            termination_condition,
-            max_inner_iterations)
-    end
-    return SimpleDFSane{typeof(σ_min), typeof(termination_condition)}(σ_min,
-        σ_max,
-        σ_1,
-        M,
-        γ,
-        τ_min,
-        τ_max,
-        nexp,
-        η_strategy,
-        termination_condition)
-end
+function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        termination_condition = nothing, kwargs...)
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane,
-        args...; abstol = nothing, reltol = nothing, maxiters = 1000,
-        kwargs...)
-    tc = alg.termination_condition
-    mode = DiffEqBase.get_termination_mode(tc)
+    f = isinplace(prob) ? (du, u) -> prob.f(du, u, prob.p) : u -> prob.f(u, prob.p)
 
-    f = Base.Fix2(prob.f, prob.p)
     x = float(prob.u0)
-
+    fx = _get_fx(prob, x)
     T = eltype(x)
-    σ_min = float(alg.σ_min)
-    σ_max = float(alg.σ_max)
-    σ_k = float(alg.σ_1)
+
+    σ_min = T(alg.σ_min)
+    σ_max = T(alg.σ_max)
+    σ_k = T(alg.σ_1)
 
     M = alg.M
-    γ = float(alg.γ)
-    τ_min = float(alg.τ_min)
-    τ_max = float(alg.τ_max)
+    γ = T(alg.γ)
+    τ_min = T(alg.τ_min)
+    τ_max = T(alg.τ_max)
     nexp = alg.nexp
     η_strategy = alg.η_strategy
 
-    if SciMLBase.isinplace(prob)
-        error("SimpleDFSane currently only supports out-of-place nonlinear problems")
-    end
-
-    atol = _get_tolerance(abstol, tc.abstol, T)
-    rtol = _get_tolerance(reltol, tc.reltol, T)
-
-    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-        error("SimpleDFSane currently doesn't support SAFE_BEST termination modes")
-    end
-
-    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? NLSolveSafeTerminationResult() :
-              nothing
-    termination_condition = tc(storage)
+    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+        termination_condition)
 
-    function ff(x)
-        F = f(x)
-        f_k = norm(F)^nexp
-        return f_k, F
+    ff = if isinplace(prob)
+        function (_fx, x)
+            f(_fx, x)
+            f_k = norm(_fx)^nexp
+            return f_k, _fx
+        end
+    else
+        function (x)
+            _fx = f(x)
+            f_k = norm(_fx)^nexp
+            return f_k, _fx
+        end
     end
 
-    function generate_history(f_k, M)
-        return fill(f_k, M)
-    end
+    generate_history(f_k, M) = fill(f_k, M)
 
-    f_k, F_k = ff(x)
-    α_1 = convert(T, 1.0)
+    f_k, F_k = isinplace(prob) ? ff(fx, x) : ff(x)
+    F_k = __copy(F_k)
+    α_1 = one(T)
     f_1 = f_k
     history_f_k = generate_history(f_k, M)
 
+    # Generate the cache
+    d, xo, x_cache, δx, δf = __copy(x), __copy(x), __copy(x), __copy(x), __copy(x)
+    α_tp, α_tm = __copy(x), __copy(x)
+
     for k in 1:maxiters
         # Spectral parameter range check
         σ_k = sign(σ_k) * clamp(abs(σ_k), σ_min, σ_max)
 
         # Line search direction
-        d = -σ_k .* F_k
+        d = __broadcast!!(d, *, -σ_k, F_k)
 
         η = η_strategy(f_1, k, x, F_k)
         f̄ = maximum(history_f_k)
         α_p = α_1
         α_m = α_1
-        x_new = @. x + α_p * d
 
-        f_new, F_new = ff(x_new)
+        x_cache = __broadcast!!(x_cache, *, α_p, d)
+        x = __broadcast!!(x, +, x_cache)
 
-        inner_iterations = 0
-        while true
-            inner_iterations += 1
+        f_new, F_new = isinplace(prob) ? ff(fx, x) : ff(x)
 
+        # FIXME: This part is not correctly implemented
+        while true
             criteria = f̄ + η - γ * α_p^2 * f_k
             f_new ≤ criteria && break
 
-            α_tp = @. α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
-            x_new = @. x - α_m * d
-            f_new, F_new = ff(x_new)
+            if ArrayInterface.can_setindex(α_tp) && !(x isa Number)
+                @. α_tp = α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
+            else
+                α_tp = @. α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
+            end
+            x_cache = __broadcast!!(x_cache, *, α_m, d)
+            x = __broadcast!!(x, -, x_cache)
+            f_new, F_new = isinplace(prob) ? ff(fx, x) : ff(x)
 
             f_new ≤ criteria && break
 
-            α_tm = @. α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
-            α_p = @. clamp(α_tp, τ_min * α_p, τ_max * α_p)
-            α_m = @. clamp(α_tm, τ_min * α_m, τ_max * α_m)
-            x_new = @. x + α_p * d
-            f_new, F_new = ff(x_new)
+            if ArrayInterface.can_setindex(α_tm) && !(x isa Number)
+                @. α_tm = α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
+                @. α_p = clamp(α_tp, τ_min * α_p, τ_max * α_p)
+                @. α_m = clamp(α_tm, τ_min * α_m, τ_max * α_m)
+            else
+                α_tm = @. α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
+                α_p = @. clamp(α_tp, τ_min * α_p, τ_max * α_p)
+                α_m = @. clamp(α_tm, τ_min * α_m, τ_max * α_m)
+            end
+            x_cache = __broadcast!!(x_cache, *, α_p, d)
+            x = __broadcast!!(x, +, x_cache)
+            f_new, F_new = isinplace(prob) ? ff(fx, x) : ff(x)
         end
 
-        if termination_condition(F_new, x_new, x, atol, rtol)
-            return SciMLBase.build_solution(prob,
-                alg,
-                x_new,
-                F_new;
-                retcode = ReturnCode.Success)
-        end
+        tc_sol = check_termination(tc_cache, f_new, x, xo, prob, alg)
+        tc_sol !== nothing && return tc_sol
 
         # Update spectral parameter
-        s_k = @. x_new - x
-        y_k = @. F_new - F_k
+        δx = __broadcast!!(δx, -, x, xo)
+        δf = __broadcast!!(δf, -, F_new, F_k)
 
-        σ_k = (s_k' * s_k) / (s_k' * y_k)
+        σ_k = dot(δx, δx) / dot(δx, δf)
 
         # Take step
-        x = x_new
-        F_k = F_new
+        xo = __copyto!!(xo, x)
+        F_k = __copyto!!(F_k, F_new)
         f_k = f_new
 
         # Store function value
         history_f_k[k % M + 1] = f_new
     end
-    return SciMLBase.build_solution(prob, alg, x, F_k; retcode = ReturnCode.MaxIters)
+
+    return build_solution(prob, alg, x, F_k; retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/src/falsi.jl b/lib/SimpleNonlinearSolve/src/falsi.jl
index eb2ea1f5f..5cc7cdbbb 100644
--- a/lib/SimpleNonlinearSolve/src/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/falsi.jl
@@ -1,86 +1,85 @@
 """
-`Falsi`: A non-allocating regula falsi method
+    Falsi()
+
+A non-allocating regula falsi method
 """
 struct Falsi <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
-        maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
-        kwargs...)
+        maxiters = 1000, abstol = nothing, kwargs...)
+    @assert !isinplace(prob) "`Falsi` only supports OOP problems."
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
+    abstol = _get_tolerance(abstol,
+        promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
+
     if iszero(fl)
-        return SciMLBase.build_solution(prob, alg, left, fl;
-            retcode = ReturnCode.ExactSolutionLeft, left = left,
-            right = right)
-    elseif iszero(fr)
-        return SciMLBase.build_solution(prob, alg, right, fr;
-            retcode = ReturnCode.ExactSolutionRight, left = left,
-            right = right)
+        return build_solution(prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft,
+            left, right)
+    end
+
+    if iszero(fr)
+        return build_solution(prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
+            left, right)
     end
 
+    # Regula Falsi Steps
     i = 1
-    if !iszero(fr)
-        while i < maxiters
-            if nextfloat_tdir(left, prob.tspan...) == right
-                return SciMLBase.build_solution(prob, alg, left, fl;
-                    retcode = ReturnCode.FloatingPointLimit,
-                    left = left, right = right)
-            end
-            mid = (fr * left - fl * right) / (fr - fl)
-            for i in 1:10
-                mid = max_tdir(left, prevfloat_tdir(mid, prob.tspan...), prob.tspan...)
-            end
-            if mid == right || mid == left
-                break
-            end
-            fm = f(mid)
-            if abs((right - left) / 2) < abstol
-                return SciMLBase.build_solution(prob, alg, mid, fm;
-                    retcode = ReturnCode.Success,
-                    left = left, right = right)
-            end
-            if iszero(fm)
-                right = mid
-                break
-            end
-            if sign(fl) == sign(fm)
-                fl = fm
-                left = mid
-            else
-                fr = fm
-                right = mid
-            end
-            i += 1
+    while i < maxiters
+        if __nextfloat_tdir(left, prob.tspan...) == right
+            return build_solution(prob, alg, left, fl; left, right,
+                retcode = ReturnCode.FloatingPointLimit)
+        end
+
+        mid = (fr * left - fl * right) / (fr - fl)
+        for _ in 1:10
+            mid = __max_tdir(left, __prevfloat_tdir(mid, prob.tspan...), prob.tspan...)
         end
+
+        (mid == left || mid == right) && break
+
+        fm = f(mid)
+        if abs((right - left) / 2) < abstol
+            return build_solution(prob, alg, mid, fm; left, right,
+                retcode = ReturnCode.Success)
+        end
+
+        if abs(fm) < abstol
+            right = mid
+            break
+        end
+
+        if sign(fl) == sign(fm)
+            fl, left = fm, mid
+        else
+            fr, right = fm, mid
+        end
+        i += 1
     end
 
     while i < maxiters
         mid = (left + right) / 2
-        (mid == left || mid == right) &&
-            return SciMLBase.build_solution(prob, alg, left, fl;
-                retcode = ReturnCode.FloatingPointLimit,
-                left = left, right = right)
+        if (mid == left || mid == right)
+            return build_solution(prob, alg, left, fl; left, right,
+                retcode = ReturnCode.FloatingPointLimit)
+        end
+
         fm = f(mid)
-        if abs((right - left) / 2) < abstol
-            return SciMLBase.build_solution(prob, alg, mid, fm;
-                retcode = ReturnCode.Success,
-                left = left, right = right)
+        if abs((right - left) / 2) < abstol || abs(fm) < abstol
+            return build_solution(prob, alg, mid, fm; left, right,
+                retcode = ReturnCode.Success)
         end
-        if iszero(fm)
-            right = mid
-            fr = fm
-        elseif sign(fm) == sign(fl)
-            left = mid
-            fl = fm
+
+        if sign(fl * fm) < 0
+            right, fr = mid, fm
         else
-            right = mid
-            fr = fm
+            left, fl = mid, fm
         end
         i += 1
     end
 
     return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
-        left = left, right = right)
+        left, right)
 end
diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/trustRegion.jl
index 0fba7b12f..d644f5fb7 100644
--- a/lib/SimpleNonlinearSolve/src/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/trustRegion.jl
@@ -1,58 +1,51 @@
 """
-```julia
-SimpleTrustRegion(; chunk_size = Val{0}(),
-                    autodiff = Val{true}(),
-                    diff_type = Val{:forward},
-                    max_trust_radius::Real = 0.0,
-                    initial_trust_radius::Real = 0.0,
-                    step_threshold::Real = 0.1,
-                    shrink_threshold::Real = 0.25,
-                    expand_threshold::Real = 0.75,
-                    shrink_factor::Real = 0.25,
-                    expand_factor::Real = 2.0,
-                    max_shrink_times::Int = 32
-```
+    SimpleTrustRegion(; chunk_size = Val{0}(), autodiff = Val{true}(),
+                        diff_type = Val{:forward}, max_trust_radius::Real = 0.0,
+                        initial_trust_radius::Real = 0.0, step_threshold::Real = 0.1,
+                        shrink_threshold::Real = 0.25, expand_threshold::Real = 0.75,
+                        shrink_factor::Real = 0.25, expand_factor::Real = 2.0,
+                        max_shrink_times::Int = 32)
 
 A low-overhead implementation of a trust-region solver.
 
 ### Keyword Arguments
 
-- `chunk_size`: the chunk size used by the internal ForwardDiff.jl automatic differentiation
-  system. This allows for multiple derivative columns to be computed simultaneously,
-  improving performance. Defaults to `0`, which is equivalent to using ForwardDiff.jl's
-  default chunk size mechanism. For more details, see the documentation for
-  [ForwardDiff.jl](https://juliadiff.org/ForwardDiff.jl/stable/).
-- `autodiff`: whether to use forward-mode automatic differentiation for the Jacobian.
-  Note that this argument is ignored if an analytical Jacobian is passed; as that will be
-  used instead. Defaults to `Val{true}`, which means ForwardDiff.jl is used by default.
-  If `Val{false}`, then FiniteDiff.jl is used for finite differencing.
-- `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
-  `Val{:forward}` for forward finite differences. For more details on the choices, see the
-  [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
-- `max_trust_radius`: the maximum radius of the trust region. Defaults to
-  `max(norm(f(u0)), maximum(u0) - minimum(u0))`.
-- `initial_trust_radius`: the initial trust region radius. Defaults to
-  `max_trust_radius / 11`.
-- `step_threshold`: the threshold for taking a step. In every iteration, the threshold is
-  compared with a value `r`, which is the actual reduction in the objective function divided
-  by the predicted reduction. If `step_threshold > r` the model is not a good approximation,
-  and the step is rejected. Defaults to `0.1`. For more details, see
-  [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
-- `shrink_threshold`: the threshold for shrinking the trust region radius. In every
-  iteration, the threshold is compared with a value `r` which is the actual reduction in the
-  objective function divided by the predicted reduction. If `shrink_threshold > r` the trust
-  region radius is shrunk by `shrink_factor`. Defaults to `0.25`. For more details, see
-  [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
-- `expand_threshold`: the threshold for expanding the trust region radius. If a step is
-  taken, i.e `step_threshold < r` (with `r` defined in `shrink_threshold`), a check is also
-  made to see if `expand_threshold < r`. If that is true, the trust region radius is
-  expanded by `expand_factor`. Defaults to `0.75`.
-- `shrink_factor`: the factor to shrink the trust region radius with if
-  `shrink_threshold > r` (with `r` defined in `shrink_threshold`). Defaults to `0.25`.
-- `expand_factor`: the factor to expand the trust region radius with if
-  `expand_threshold < r` (with `r` defined in `shrink_threshold`). Defaults to `2.0`.
-- `max_shrink_times`: the maximum number of times to shrink the trust region radius in a
-  row, `max_shrink_times` is exceeded, the algorithm returns. Defaults to `32`.
+  - `chunk_size`: the chunk size used by the internal ForwardDiff.jl automatic differentiation
+    system. This allows for multiple derivative columns to be computed simultaneously,
+    improving performance. Defaults to `0`, which is equivalent to using ForwardDiff.jl's
+    default chunk size mechanism. For more details, see the documentation for
+    [ForwardDiff.jl](https://juliadiff.org/ForwardDiff.jl/stable/).
+  - `autodiff`: whether to use forward-mode automatic differentiation for the Jacobian.
+    Note that this argument is ignored if an analytical Jacobian is passed; as that will be
+    used instead. Defaults to `Val{true}`, which means ForwardDiff.jl is used by default.
+    If `Val{false}`, then FiniteDiff.jl is used for finite differencing.
+  - `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
+    `Val{:forward}` for forward finite differences. For more details on the choices, see the
+    [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
+  - `max_trust_radius`: the maximum radius of the trust region. Defaults to
+    `max(norm(f(u0)), maximum(u0) - minimum(u0))`.
+  - `initial_trust_radius`: the initial trust region radius. Defaults to
+    `max_trust_radius / 11`.
+  - `step_threshold`: the threshold for taking a step. In every iteration, the threshold is
+    compared with a value `r`, which is the actual reduction in the objective function divided
+    by the predicted reduction. If `step_threshold > r` the model is not a good approximation,
+    and the step is rejected. Defaults to `0.1`. For more details, see
+    [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
+  - `shrink_threshold`: the threshold for shrinking the trust region radius. In every
+    iteration, the threshold is compared with a value `r` which is the actual reduction in the
+    objective function divided by the predicted reduction. If `shrink_threshold > r` the trust
+    region radius is shrunk by `shrink_factor`. Defaults to `0.25`. For more details, see
+    [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
+  - `expand_threshold`: the threshold for expanding the trust region radius. If a step is
+    taken, i.e `step_threshold < r` (with `r` defined in `shrink_threshold`), a check is also
+    made to see if `expand_threshold < r`. If that is true, the trust region radius is
+    expanded by `expand_factor`. Defaults to `0.75`.
+  - `shrink_factor`: the factor to shrink the trust region radius with if
+    `shrink_threshold > r` (with `r` defined in `shrink_threshold`). Defaults to `0.25`.
+  - `expand_factor`: the factor to expand the trust region radius with if
+    `expand_threshold < r` (with `r` defined in `shrink_threshold`). Defaults to `2.0`.
+  - `max_shrink_times`: the maximum number of times to shrink the trust region radius in a
+    row, `max_shrink_times` is exceeded, the algorithm returns. Defaults to `32`.
 """
 struct SimpleTrustRegion{T, CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
     max_trust_radius::T
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 228006409..df3374d86 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -5,22 +5,35 @@ function ForwardDiff.checktag(::Type{<:ForwardDiff.Tag{<:SimpleNonlinearSolveTag
     return true
 end
 
-# """
-#   prevfloat_tdir(x, x0, x1)
+"""
+    __prevfloat_tdir(x, x0, x1)
 
-# Move `x` one floating point towards x0.
-# """
-# function prevfloat_tdir(x, x0, x1)
-#     x1 > x0 ? prevfloat(x) : nextfloat(x)
-# end
+Move `x` one floating point towards x0.
+"""
+__prevfloat_tdir(x, x0, x1) = ifelse(x1 > x0, prevfloat(x), nextfloat(x))
 
-# function nextfloat_tdir(x, x0, x1)
-#     x1 > x0 ? nextfloat(x) : prevfloat(x)
-# end
+"""
+    __nextfloat_tdir(x, x0, x1)
 
-# function max_tdir(a, b, x0, x1)
-#     x1 > x0 ? max(a, b) : min(a, b)
-# end
+Move `x` one floating point towards x1.
+"""
+__nextfloat_tdir(x, x0, x1) = ifelse(x1 > x0, nextfloat(x), prevfloat(x))
+
+"""
+    __max_tdir(a, b, x0, x1)
+
+Return the maximum of `a` and `b` if `x1 > x0`, otherwise return the minimum.
+"""
+__max_tdir(a, b, x0, x1) = ifelse(x1 > x0, max(a, b), min(a, b))
+
+__cvt_real(::Type{T}, ::Nothing) where {T} = nothing
+__cvt_real(::Type{T}, x) where {T} = real(T(x))
+
+_get_tolerance(η, ::Type{T}) where {T} = __cvt_real(T, η)
+function _get_tolerance(::Nothing, ::Type{T}) where {T}
+    η = real(oneunit(T)) * (eps(real(one(T))))^(4 // 5)
+    return _get_tolerance(η, T)
+end
 
 __standard_tag(::Nothing, x) = ForwardDiff.Tag(SimpleNonlinearSolveTag(), eltype(x))
 __standard_tag(tag::ForwardDiff.Tag, _) = tag

From 408243e1456b0e95bbb92cfd3dbf09bb57121743 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 23 Nov 2023 02:43:44 -0500
Subject: [PATCH 223/700] Use a macro for compile time compatibility between
 inplace and oop versions

---
 .../src/SimpleNonlinearSolve.jl               |  13 +-
 lib/SimpleNonlinearSolve/src/bisection.jl     |  50 +++-
 lib/SimpleNonlinearSolve/src/broyden.jl       |  43 ++--
 lib/SimpleNonlinearSolve/src/dfsane.jl        | 224 +++++++++---------
 lib/SimpleNonlinearSolve/src/falsi.jl         |  77 +++---
 lib/SimpleNonlinearSolve/src/klement.jl       |  67 ++++--
 lib/SimpleNonlinearSolve/src/raphson.jl       |  10 +-
 .../src/rewrite_inplace.jl                    | 161 +++++++++++++
 lib/SimpleNonlinearSolve/src/ridder.jl        |  71 +++---
 lib/SimpleNonlinearSolve/src/utils.jl         |  91 +------
 10 files changed, 457 insertions(+), 350 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/rewrite_inplace.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index e0293ee6c..208e0e15f 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -25,6 +25,7 @@ abstract type AbstractBracketingAlgorithm <: AbstractSimpleNonlinearSolveAlgorit
 abstract type AbstractNewtonAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 
 include("utils.jl")
+include("rewrite_inplace.jl")
 
 # Nonlinear Solvera
 include("raphson.jl")
@@ -33,12 +34,12 @@ include("broyden.jl")
 include("klement.jl")
 # include("trustRegion.jl")
 # include("halley.jl")
-include("dfsane.jl")
+# include("dfsane.jl")
 
 # Interval Nonlinear Solvers
 include("bisection.jl")
 include("falsi.jl")
-# include("ridder.jl")
+include("ridder.jl")
 # include("brent.jl")
 # include("alefeld.jl")
 # include("itp.jl")
@@ -88,9 +89,9 @@ include("falsi.jl")
 #     end
 # end
 
-export SimpleBroyden, SimpleDFSane, SimpleGaussNewton, SimpleKlement, SimpleNewtonRaphson
-export Bisection, Falsi
-# export Bisection, Brent, LBroyden, SimpleHalley,
-#     Ridder, SimpleTrustRegion, Alefeld, ITP
+export SimpleBroyden, SimpleGaussNewton, SimpleKlement, SimpleNewtonRaphson
+# SimpleDFSane, SimpleTrustRegion, SimpleHalley
+export Bisection, Falsi, Ridder
+# export , Brent, LBroyden, Alefeld, ITP
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bisection.jl
index 9b1394bc6..42bb2cad0 100644
--- a/lib/SimpleNonlinearSolve/src/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bisection.jl
@@ -39,17 +39,57 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
             left, right)
     end
 
-    for _ in 1:maxiters
+    i = 1
+    if !iszero(fr)
+        while i < maxiters
+            mid = (left + right) / 2
+            (mid == left || mid == right) &&
+                return build_solution(prob, alg, left, fl; left, right,
+                    retcode = ReturnCode.FloatingPointLimit)
+            fm = f(mid)
+            if abs((right - left) / 2) < abstol
+                return build_solution(prob, alg, mid, fm; retcode = ReturnCode.Success,
+                    left, right)
+            end
+            if iszero(fm)
+                right = mid
+                break
+            end
+            if sign(fl) == sign(fm)
+                fl = fm
+                left = mid
+            else
+                fr = fm
+                right = mid
+            end
+            i += 1
+        end
+    end
+
+    sol, i, left, right, fl, fr = __bisection(left, right, fl, fr, f; abstol,
+        maxiters = maxiters - i, prob, alg)
+
+    sol !== nothing && return sol
+
+    return build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
+end
+
+function __bisection(left, right, fl, fr, f::F; abstol, maxiters, prob, alg) where {F}
+    i = 1
+    sol = nothing
+    while i < maxiters
         mid = (left + right) / 2
         if (mid == left || mid == right)
-            return build_solution(prob, alg, left, fl; left, right,
+            sol = build_solution(prob, alg, left, fl; left, right,
                 retcode = ReturnCode.FloatingPointLimit)
+            break
         end
 
         fm = f(mid)
         if abs((right - left) / 2) < abstol || abs(fm) < abstol
-            return build_solution(prob, alg, mid, fm; left, right,
+            sol = build_solution(prob, alg, mid, fm; left, right,
                 retcode = ReturnCode.Success)
+            break
         end
 
         if sign(fl * fm) < 0
@@ -57,7 +97,9 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
         else
             left, fl = mid, fm
         end
+
+        i += 1
     end
 
-    return build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
+    return sol, i, left, right, fl, fr
 end
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 7587168a4..aaf959cb5 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -9,44 +9,45 @@ struct SimpleBroyden <: AbstractSimpleNonlinearSolveAlgorithm end
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
         termination_condition = nothing, kwargs...)
-    f = isinplace(prob) ? (du, u) -> prob.f(du, u, prob.p) : u -> prob.f(u, prob.p)
-    x = float(prob.u0)
+    @bb x = copy(float(prob.u0))
     fx = _get_fx(prob, x)
-    xo, δx, fprev, δf = __copy(x), __copy(x), __copy(fx), __copy(fx)
+
+    @bb xo = copy(x)
+    @bb δx = copy(x)
+    @bb δf = copy(fx)
+    @bb fprev = copy(fx)
 
     J⁻¹ = __init_identity_jacobian(fx, x)
-    J⁻¹δf, xᵀJ⁻¹ = __copy(x), __copy(x)
-    δJ⁻¹, δJ⁻¹n = __copy(x, J⁻¹), __copy(x)
+    @bb J⁻¹δf = copy(x)
+    @bb xᵀJ⁻¹ = copy(x)
+    @bb δJ⁻¹n = copy(x)
+    @bb δJ⁻¹ = copy(J⁻¹)
 
     abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
         termination_condition)
 
     for _ in 1:maxiters
-        δx = _restructure(δx, __mul!!(_vec(δx), J⁻¹, _vec(fprev)))
-        x = __sub!!(x, xo, δx)
-        fx = __eval_f(prob, f, fx, x)
-        δf = __sub!!(δf, fx, fprev)
+        @bb δx = J⁻¹ × vec(fprev)
+        @bb @. x = xo - δx
+        fx = __eval_f(prob, fx, x)
+        @bb @. δf = fx - fprev
 
         # Termination Checks
         tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
         tc_sol !== nothing && return tc_sol
 
-        J⁻¹δf = _restructure(J⁻¹δf, __mul!!(_vec(J⁻¹δf), J⁻¹, _vec(δf)))
-        δx = __neg!!(δx)
+        @bb J⁻¹δf = J⁻¹ × vec(δf)
+        @bb δx .*= -1
         d = dot(δx, J⁻¹δf)
-        xᵀJ⁻¹ = _restructure(xᵀJ⁻¹, __mul!!(_vec(xᵀJ⁻¹), _vec(δx)', J⁻¹))
+        @bb xᵀJ⁻¹ = transpose(J⁻¹) × vec(δx)
 
-        if ArrayInterface.can_setindex(δJ⁻¹n)
-            @. δJ⁻¹n = (δx - J⁻¹δf) / d
-        else
-            δJ⁻¹n = @. (δx - J⁻¹δf) / d
-        end
+        @bb @. δJ⁻¹n = (δx - J⁻¹δf) / d
 
-        δJ⁻¹ = __mul!!(δJ⁻¹, δJ⁻¹n, xᵀJ⁻¹')
-        J⁻¹ = __add!!(J⁻¹, δJ⁻¹)
+        @bb δJ⁻¹ = δJ⁻¹n × transpose(xᵀJ⁻¹)
+        @bb J⁻¹ .+= δJ⁻¹
 
-        xo = __copyto!!(xo, x)
-        fprev = __copyto!!(fprev, fx)
+        @bb copyto!(xo, x)
+        @bb copyto!(fprev, fx)
     end
 
     return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index d646171d5..0ecc545f6 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -54,116 +54,116 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
         termination_condition = nothing, kwargs...)
 
-    f = isinplace(prob) ? (du, u) -> prob.f(du, u, prob.p) : u -> prob.f(u, prob.p)
-
-    x = float(prob.u0)
-    fx = _get_fx(prob, x)
-    T = eltype(x)
-
-    σ_min = T(alg.σ_min)
-    σ_max = T(alg.σ_max)
-    σ_k = T(alg.σ_1)
-
-    M = alg.M
-    γ = T(alg.γ)
-    τ_min = T(alg.τ_min)
-    τ_max = T(alg.τ_max)
-    nexp = alg.nexp
-    η_strategy = alg.η_strategy
-
-    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
-        termination_condition)
-
-    ff = if isinplace(prob)
-        function (_fx, x)
-            f(_fx, x)
-            f_k = norm(_fx)^nexp
-            return f_k, _fx
-        end
-    else
-        function (x)
-            _fx = f(x)
-            f_k = norm(_fx)^nexp
-            return f_k, _fx
-        end
-    end
-
-    generate_history(f_k, M) = fill(f_k, M)
-
-    f_k, F_k = isinplace(prob) ? ff(fx, x) : ff(x)
-    F_k = __copy(F_k)
-    α_1 = one(T)
-    f_1 = f_k
-    history_f_k = generate_history(f_k, M)
-
-    # Generate the cache
-    d, xo, x_cache, δx, δf = __copy(x), __copy(x), __copy(x), __copy(x), __copy(x)
-    α_tp, α_tm = __copy(x), __copy(x)
-
-    for k in 1:maxiters
-        # Spectral parameter range check
-        σ_k = sign(σ_k) * clamp(abs(σ_k), σ_min, σ_max)
-
-        # Line search direction
-        d = __broadcast!!(d, *, -σ_k, F_k)
-
-        η = η_strategy(f_1, k, x, F_k)
-        f̄ = maximum(history_f_k)
-        α_p = α_1
-        α_m = α_1
-
-        x_cache = __broadcast!!(x_cache, *, α_p, d)
-        x = __broadcast!!(x, +, x_cache)
-
-        f_new, F_new = isinplace(prob) ? ff(fx, x) : ff(x)
-
-        # FIXME: This part is not correctly implemented
-        while true
-            criteria = f̄ + η - γ * α_p^2 * f_k
-            f_new ≤ criteria && break
-
-            if ArrayInterface.can_setindex(α_tp) && !(x isa Number)
-                @. α_tp = α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
-            else
-                α_tp = @. α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
-            end
-            x_cache = __broadcast!!(x_cache, *, α_m, d)
-            x = __broadcast!!(x, -, x_cache)
-            f_new, F_new = isinplace(prob) ? ff(fx, x) : ff(x)
-
-            f_new ≤ criteria && break
-
-            if ArrayInterface.can_setindex(α_tm) && !(x isa Number)
-                @. α_tm = α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
-                @. α_p = clamp(α_tp, τ_min * α_p, τ_max * α_p)
-                @. α_m = clamp(α_tm, τ_min * α_m, τ_max * α_m)
-            else
-                α_tm = @. α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
-                α_p = @. clamp(α_tp, τ_min * α_p, τ_max * α_p)
-                α_m = @. clamp(α_tm, τ_min * α_m, τ_max * α_m)
-            end
-            x_cache = __broadcast!!(x_cache, *, α_p, d)
-            x = __broadcast!!(x, +, x_cache)
-            f_new, F_new = isinplace(prob) ? ff(fx, x) : ff(x)
-        end
-
-        tc_sol = check_termination(tc_cache, f_new, x, xo, prob, alg)
-        tc_sol !== nothing && return tc_sol
-
-        # Update spectral parameter
-        δx = __broadcast!!(δx, -, x, xo)
-        δf = __broadcast!!(δf, -, F_new, F_k)
-
-        σ_k = dot(δx, δx) / dot(δx, δf)
-
-        # Take step
-        xo = __copyto!!(xo, x)
-        F_k = __copyto!!(F_k, F_new)
-        f_k = f_new
-
-        # Store function value
-        history_f_k[k % M + 1] = f_new
-    end
-
-    return build_solution(prob, alg, x, F_k; retcode = ReturnCode.MaxIters)
+    # f = isinplace(prob) ? (du, u) -> prob.f(du, u, prob.p) : u -> prob.f(u, prob.p)
+
+    # x = float(prob.u0)
+    # fx = _get_fx(prob, x)
+    # T = eltype(x)
+
+    # σ_min = T(alg.σ_min)
+    # σ_max = T(alg.σ_max)
+    # σ_k = T(alg.σ_1)
+
+    # M = alg.M
+    # γ = T(alg.γ)
+    # τ_min = T(alg.τ_min)
+    # τ_max = T(alg.τ_max)
+    # nexp = alg.nexp
+    # η_strategy = alg.η_strategy
+
+    # abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+    #     termination_condition)
+
+    # ff = if isinplace(prob)
+    #     function (_fx, x)
+    #         f(_fx, x)
+    #         f_k = norm(_fx)^nexp
+    #         return f_k, _fx
+    #     end
+    # else
+    #     function (x)
+    #         _fx = f(x)
+    #         f_k = norm(_fx)^nexp
+    #         return f_k, _fx
+    #     end
+    # end
+
+    # generate_history(f_k, M) = fill(f_k, M)
+
+    # f_k, F_k = isinplace(prob) ? ff(fx, x) : ff(x)
+    # F_k = __copy(F_k)
+    # α_1 = one(T)
+    # f_1 = f_k
+    # history_f_k = generate_history(f_k, M)
+
+    # # Generate the cache
+    # d, xo, x_cache, δx, δf = __copy(x), __copy(x), __copy(x), __copy(x), __copy(x)
+    # α_tp, α_tm = __copy(x), __copy(x)
+
+    # for k in 1:maxiters
+    #     # Spectral parameter range check
+    #     σ_k = sign(σ_k) * clamp(abs(σ_k), σ_min, σ_max)
+
+    #     # Line search direction
+    #     d = __broadcast!!(d, *, -σ_k, F_k)
+
+    #     η = η_strategy(f_1, k, x, F_k)
+    #     f̄ = maximum(history_f_k)
+    #     α_p = α_1
+    #     α_m = α_1
+
+    #     x_cache = __broadcast!!(x_cache, *, α_p, d)
+    #     x = __broadcast!!(x, +, x_cache)
+
+    #     f_new, F_new = isinplace(prob) ? ff(fx, x) : ff(x)
+
+    #     # FIXME: This part is not correctly implemented
+    #     while true
+    #         criteria = f̄ + η - γ * α_p^2 * f_k
+    #         f_new ≤ criteria && break
+
+    #         if ArrayInterface.can_setindex(α_tp) && !(x isa Number)
+    #             @. α_tp = α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
+    #         else
+    #             α_tp = @. α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
+    #         end
+    #         x_cache = __broadcast!!(x_cache, *, α_m, d)
+    #         x = __broadcast!!(x, -, x_cache)
+    #         f_new, F_new = isinplace(prob) ? ff(fx, x) : ff(x)
+
+    #         f_new ≤ criteria && break
+
+    #         if ArrayInterface.can_setindex(α_tm) && !(x isa Number)
+    #             @. α_tm = α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
+    #             @. α_p = clamp(α_tp, τ_min * α_p, τ_max * α_p)
+    #             @. α_m = clamp(α_tm, τ_min * α_m, τ_max * α_m)
+    #         else
+    #             α_tm = @. α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
+    #             α_p = @. clamp(α_tp, τ_min * α_p, τ_max * α_p)
+    #             α_m = @. clamp(α_tm, τ_min * α_m, τ_max * α_m)
+    #         end
+    #         x_cache = __broadcast!!(x_cache, *, α_p, d)
+    #         x = __broadcast!!(x, +, x_cache)
+    #         f_new, F_new = isinplace(prob) ? ff(fx, x) : ff(x)
+    #     end
+
+    #     tc_sol = check_termination(tc_cache, f_new, x, xo, prob, alg)
+    #     tc_sol !== nothing && return tc_sol
+
+    #     # Update spectral parameter
+    #     δx = __broadcast!!(δx, -, x, xo)
+    #     δf = __broadcast!!(δf, -, F_new, F_k)
+
+    #     σ_k = dot(δx, δx) / dot(δx, δf)
+
+    #     # Take step
+    #     xo = __copyto!!(xo, x)
+    #     F_k = __copyto!!(F_k, F_new)
+    #     f_k = f_new
+
+    #     # Store function value
+    #     history_f_k[k % M + 1] = f_new
+    # end
+
+    # return build_solution(prob, alg, x, F_k; retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/src/falsi.jl b/lib/SimpleNonlinearSolve/src/falsi.jl
index 5cc7cdbbb..9db7d6cf1 100644
--- a/lib/SimpleNonlinearSolve/src/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/falsi.jl
@@ -1,7 +1,7 @@
 """
     Falsi()
 
-A non-allocating regula falsi method
+A non-allocating regula falsi method.
 """
 struct Falsi <: AbstractBracketingAlgorithm end
 
@@ -26,59 +26,44 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
     end
 
     # Regula Falsi Steps
-    i = 1
-    while i < maxiters
-        if __nextfloat_tdir(left, prob.tspan...) == right
-            return build_solution(prob, alg, left, fl; left, right,
-                retcode = ReturnCode.FloatingPointLimit)
-        end
+    i = 0
+    if !iszero(fr)
+        while i < maxiters
+            if __nextfloat_tdir(left, prob.tspan...) == right
+                return build_solution(prob, alg, left, fl; left, right,
+                    retcode = ReturnCode.FloatingPointLimit)
+            end
 
-        mid = (fr * left - fl * right) / (fr - fl)
-        for _ in 1:10
-            mid = __max_tdir(left, __prevfloat_tdir(mid, prob.tspan...), prob.tspan...)
-        end
+            mid = (fr * left - fl * right) / (fr - fl)
+            for _ in 1:10
+                mid = __max_tdir(left, __prevfloat_tdir(mid, prob.tspan...), prob.tspan...)
+            end
 
-        (mid == left || mid == right) && break
+            (mid == left || mid == right) && break
 
-        fm = f(mid)
-        if abs((right - left) / 2) < abstol
-            return build_solution(prob, alg, mid, fm; left, right,
-                retcode = ReturnCode.Success)
-        end
+            fm = f(mid)
+            if abs((right - left) / 2) < abstol
+                return build_solution(prob, alg, mid, fm; left, right,
+                    retcode = ReturnCode.Success)
+            end
 
-        if abs(fm) < abstol
-            right = mid
-            break
-        end
+            if abs(fm) < abstol
+                right = mid
+                break
+            end
 
-        if sign(fl) == sign(fm)
-            fl, left = fm, mid
-        else
-            fr, right = fm, mid
+            if sign(fl) == sign(fm)
+                fl, left = fm, mid
+            else
+                fr, right = fm, mid
+            end
+            i += 1
         end
-        i += 1
     end
 
-    while i < maxiters
-        mid = (left + right) / 2
-        if (mid == left || mid == right)
-            return build_solution(prob, alg, left, fl; left, right,
-                retcode = ReturnCode.FloatingPointLimit)
-        end
-
-        fm = f(mid)
-        if abs((right - left) / 2) < abstol || abs(fm) < abstol
-            return build_solution(prob, alg, mid, fm; left, right,
-                retcode = ReturnCode.Success)
-        end
-
-        if sign(fl * fm) < 0
-            right, fr = mid, fm
-        else
-            left, fl = mid, fm
-        end
-        i += 1
-    end
+    sol, i, left, right, fl, fr = __bisection(left, right, fl, fr, f; abstol,
+        maxiters = maxiters - i, prob, alg)
+    sol !== nothing && return sol
 
     return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
         left, right)
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 3d22d1c07..7b9a878ad 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -1,14 +1,14 @@
 """
     SimpleKlement()
 
-A low-overhead implementation of [Klement](https://jatm.com.br/jatm/article/view/373).
+A low-overhead implementation of [Klement](https://jatm.com.br/jatm/article/view/373). This
+method is non-allocating on scalar and static array problems.
 """
 struct SimpleKlement <: AbstractSimpleNonlinearSolveAlgorithm end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
         termination_condition = nothing, kwargs...)
-    f = isinplace(prob) ? (du, u) -> prob.f(du, u, prob.p) : u -> prob.f(u, prob.p)
     x = float(prob.u0)
     T = eltype(x)
     fx = _get_fx(prob, x)
@@ -18,51 +18,68 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
     abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
         termination_condition)
 
-    δx, fprev, xo, δf, d = __copy(fx), __copy(fx), __copy(x), __copy(fx), __copy(x)
+    @bb δx = copy(x)
+    @bb fprev = copy(fx)
+    @bb xo = copy(x)
+    @bb δf = copy(fx)
+    @bb d = copy(x)
+
     J = __init_identity_jacobian(fx, x)
-    J_cache, δx² = __copy(J), __copy(x)
+    @bb J_cache = copy(J)
+    @bb δx² = copy(x)
+    @bb J_cache2 = copy(J)
+    @bb F = copy(J)
 
     for _ in 1:maxiters
         if x isa Number
             J < singular_tol && (J = __init_identity_jacobian!!(J))
-            F = J
+            F_ = J
         else
-            F = lu(J; check = false)
+            @bb copyto!(F, J)
+            if setindex_trait(F) === CanSetindex()
+                F_ = lu!(F; check = false)
+            else
+                F_ = lu(F; check = false)
+            end
 
             # Singularity test
-            if any(x -> abs(x) < singular_tol, @view(F.U[diagind(F.U)]))
+            if !issuccess(F_)
                 J = __init_identity_jacobian!!(J)
-                F = lu(J; check = false)
+                if setindex_trait(J) === CanSetindex()
+                    lu!(J; check = false)
+                else
+                    J = lu(J; check = false)
+                end
             end
         end
 
-        δx = __copyto!!(δx, fprev)
-        δx = __ldiv!!(F, δx)
-        x = __sub!!(x, xo, δx)
-        fx = __eval_f(prob, f, fx, x)
+        @bb copyto!(δx, fprev)
+        δx = __ldiv!!(F_, δx)
+        @bb @. x = xo - δx
+        fx = __eval_f(prob, fx, x)
 
         # Termination Checks
         tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
         tc_sol !== nothing && return tc_sol
 
-        δx = __neg!!(δx)
-        δf = __sub!!(δf, fx, fprev)
+        @bb δx .*= -1
+        @bb @. δf = fx - fprev
 
         # Prevent division by 0
-        δx² = __broadcast!!(δx², abs2, δx)
-        J_cache = __broadcast!!(J_cache, abs2, J)
-        d = _restructure(d, __mul!!(_vec(d), J_cache', _vec(δx²)))
-        d = __broadcast!!(d, Base.Fix2(max, singular_tol), d)
+        @bb @. δx² = δx^2
+        @bb @. J_cache = J^2
+        @bb d = transpose(J_cache) × vec(δx²)
+        @bb @. d = max(d, singular_tol)
 
-        δx² = _restructure(δx², __mul!!(_vec(δx²), J, _vec(δx)))
-        δf = __sub!!(δf, δx²)
-        δf = __broadcast!!(δf, /, δf, d)
+        @bb δx² = J × vec(δx)
+        @bb @. δf = (δf - δx²) / d
 
-        J_cache = __mul!!(J_cache, _vec(δf), _vec(δx)')
-        J_cache = __broadcast!!(J_cache, *, J_cache, J)
-        J_cache = __mul!!(J_cache, J_cache, J)
+        _vδf, _vδx = vec(δf), vec(δx)
+        @bb J_cache = _vδf × transpose(_vδx)
+        @bb @. J_cache *= J
+        @bb J_cache2 = J_cache × J
 
-        J = __add!!(J, J_cache)
+        @bb @. J += J_cache2
     end
 
     return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index a1974ba88..1b63656de 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -9,7 +9,7 @@ and static array problems.
 
     As part of the decreased overhead, this method omits some of the higher level error
     catching of the other methods. Thus, to see better error messages, use one of the other
-    methods like `NewtonRaphson`
+    methods like `NewtonRaphson`.
 
 ### Keyword Arguments
 
@@ -27,9 +27,9 @@ const SimpleGaussNewton = SimpleNewtonRaphson
 function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
         alg::SimpleNewtonRaphson, args...; abstol = nothing, reltol = nothing,
         maxiters = 1000, termination_condition = nothing, kwargs...)
-    x = float(prob.u0)
+    @bb x = copy(float(prob.u0))
     fx = _get_fx(prob, x)
-    xo = __copy(x)
+    @bb xo = copy(x)
     J, jac_cache = jacobian_cache(alg.ad, prob.f, fx, x, prob.p)
 
     abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
@@ -48,9 +48,9 @@ function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresPr
             tc_sol !== nothing && return tc_sol
         end
 
-        xo = __copyto!!(xo, x)
+        @bb copyto!(xo, x)
         Δx = _restructure(x, dfx \ _vec(fx))
-        x = __sub!!(x, Δx)
+        @bb x .-= Δx
     end
 
     return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
diff --git a/lib/SimpleNonlinearSolve/src/rewrite_inplace.jl b/lib/SimpleNonlinearSolve/src/rewrite_inplace.jl
new file mode 100644
index 000000000..f0d80af23
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/rewrite_inplace.jl
@@ -0,0 +1,161 @@
+# Take a inplace code and rewrite it to be maybe-inplace
+# I will take this code out into a separate package because this is useful even in
+# NonlinearSolve.jl
+function __bangbang(M, expr; depth = 1)
+    new_expr = nothing
+    if expr.head == :call
+        @assert length(expr.args)≥2 "Expected a function call with atleast 1 argument. \
+                                     Got `$(expr)`."
+        f, a, args... = expr.args
+        g = get(OP_MAPPING, f, nothing)
+        if f == :copy && length(args) == 0
+            # Special case for copy with single argument
+            new_expr = :($(g)($(setindex_trait)($(a)), $(a)))
+        elseif g !== nothing
+            new_expr = :($(a) = $(g)($(setindex_trait)($(a)), $(a), $(args...)))
+        end
+    elseif expr.head == :(=)
+        a, rhs_expr = expr.args
+        if rhs_expr.head == :call
+            f, b, args... = rhs_expr.args
+            g = get(OP_MAPPING, f, nothing)
+            if g !== nothing
+                new_expr = :($(a) = $(g)($(setindex_trait)($(b)), $(b), $(args...)))
+            elseif f == :×
+                @debug "Custom operator `×` detected in `$(expr)`."
+                c, args... = args
+                @assert length(args)==0 "Expected `×` to have only 2 arguments. \
+                                        Got `$(expr)`."
+                is_b_vec = b isa Expr && b.head == :call && b.args[1] == :vec
+                is_c_vec = c isa Expr && c.head == :call && c.args[1] == :vec
+                a_sym = gensym("a")
+                if is_b_vec
+                    if is_c_vec
+                        error("2 `vec`s detected with `×` in `$(expr)`. Use `dot` instead.")
+                    else
+                        new_expr = quote
+                            if $(setindex_trait)($(a)) === CanSetindex()
+                                $(a_sym) = $(_vec)($a)
+                                mul!($(a_sym), $(_vec)($(b.args[2])), $(c))
+                                $(a) = $(_restructure)($a, $(a_sym))
+                            else
+                                $(a) = $(_restructure)($a, $(_vec)($(b.args[2])) * $(c))
+                            end
+                        end
+                    end
+                else
+                    if is_c_vec
+                        new_expr = quote
+                            if $(setindex_trait)($(a)) === CanSetindex()
+                                $(a_sym) = $(_vec)($a)
+                                mul!($(a), $(b), $(_vec)($(c.args[2])))
+                                $(a) = $(_restructure)($a, $(a_sym))
+                            else
+                                $(a) = $(_restructure)($a, $(b) * $(_vec)($(c.args[2])))
+                            end
+                        end
+                    else
+                        new_expr = quote
+                            if $(setindex_trait)($(a)) === CanSetindex()
+                                mul!($(a), $(b), $(c))
+                            else
+                                $(a) = $(b) * $(c)
+                            end
+                        end
+                    end
+                end
+            end
+        end
+    elseif expr.head == :(.=)
+        a, rhs_expr = expr.args
+        if rhs_expr isa Expr && rhs_expr.head == :(.)
+            f, arg_expr = rhs_expr.args
+            # f_broadcast = :(Base.Broadcast.BroadcastFunction($(f)))
+            new_expr = quote
+                if $(setindex_trait)($(a)) === CanSetindex()
+                    broadcast!($(f), $(a), $(arg_expr)...)
+                else
+                    $(a) = broadcast($(f), $(arg_expr)...)
+                end
+            end
+        end
+    elseif expr.head == :macrocall
+        # For @__dot__ there is a easier alternative
+        if expr.args[1] == Symbol("@__dot__")
+            main_expr = last(expr.args)
+            if main_expr isa Expr && main_expr.head == :(=)
+                a, rhs_expr = main_expr.args
+                new_expr = quote
+                    if $(setindex_trait)($(a)) === CanSetindex()
+                        @. $(main_expr)
+                    else
+                        $(a) = @. $(rhs_expr)
+                    end
+                end
+            end
+        end
+        if new_expr === nothing
+            new_expr = __bangbang(M, Base.macroexpand(M, expr; recursive = true);
+                depth = depth + 1)
+        end
+    else
+        f = expr.head # Things like :.-=, etc.
+        a, args... = expr.args
+        g = get(OP_MAPPING, f, nothing)
+        if g !== nothing
+            new_expr = :($(a) = $(g)($(setindex_trait)($(a)), $(a), $(args...)))
+        end
+    end
+    if new_expr !== nothing
+        if depth == 1
+            @debug "Replacing `$(expr)` with `$(new_expr)`"
+            return esc(new_expr)
+        else
+            return new_expr
+        end
+    end
+    error("`$(expr)` cannot be handled. Check the documentation for allowed expressions.")
+end
+
+macro bangbang(expr)
+    return __bangbang(__module__, expr)
+end
+
+# `bb` is the short form of bang-bang
+macro bb(expr)
+    return __bangbang(__module__, expr)
+end
+
+# Is Mutable or Not?
+abstract type AbstractMaybeSetindex end
+struct CannotSetindex <: AbstractMaybeSetindex end
+struct CanSetindex <: AbstractMaybeSetindex end
+
+# Common types should overload this via extensions, else it butchers type-inference
+setindex_trait(::Union{Number, SArray}) = CannotSetindex()
+setindex_trait(::Union{MArray, Array}) = CanSetindex()
+setindex_trait(A) = ifelse(ArrayInterface.can_setindex(A), CanSetindex(), CannotSetindex())
+
+# Operations
+const OP_MAPPING = Dict{Symbol, Symbol}(:copyto! => :__copyto!!,
+    :.-= => :__sub!!,
+    :.+= => :__add!!,
+    :.*= => :__mul!!,
+    :./= => :__div!!,
+    :copy => :__copy)
+
+@inline __copyto!!(::CannotSetindex, x, y) = y
+@inline __copyto!!(::CanSetindex, x, y) = (copyto!(x, y); x)
+
+@inline __broadcast!!(::CannotSetindex, op, x, args...) = broadcast(op, args...)
+@inline __broadcast!!(::CanSetindex, op, x, args...) = (broadcast!(op, x, args...); x)
+
+@inline __sub!!(S, x, args...) = __broadcast!!(S, -, x, x, args...)
+@inline __add!!(S, x, args...) = __broadcast!!(S, +, x, x, args...)
+@inline __mul!!(S, x, args...) = __broadcast!!(S, *, x, x, args...)
+@inline __div!!(S, x, args...) = __broadcast!!(S, /, x, x, args...)
+
+@inline __copy(::CannotSetindex, x) = x
+@inline __copy(::CanSetindex, x) = copy(x)
+@inline __copy(::CannotSetindex, x, y) = y
+@inline __copy(::CanSetindex, x, y) = copy(y)
diff --git a/lib/SimpleNonlinearSolve/src/ridder.jl b/lib/SimpleNonlinearSolve/src/ridder.jl
index 41b43200e..0bed8ee75 100644
--- a/lib/SimpleNonlinearSolve/src/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/ridder.jl
@@ -1,25 +1,28 @@
 """
-`Ridder()`
+    Ridder()
 
-A non-allocating ridder method
+A non-allocating ridder method.
 """
 struct Ridder <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
-        maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
-        kwargs...)
+        maxiters = 1000, abstol = nothing, kwargs...)
+    @assert !isinplace(prob) "`Ridder` only supports OOP problems."
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
+    abstol = _get_tolerance(abstol,
+        promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
+
     if iszero(fl)
-        return SciMLBase.build_solution(prob, alg, left, fl;
-            retcode = ReturnCode.ExactSolutionLeft, left = left,
-            right = right)
-    elseif iszero(fr)
-        return SciMLBase.build_solution(prob, alg, right, fr;
-            retcode = ReturnCode.ExactSolutionRight, left = left,
-            right = right)
+        return build_solution(prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft,
+            left, right)
+    end
+
+    if iszero(fr)
+        return build_solution(prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
+            left, right)
     end
 
     xo = oftype(left, Inf)
@@ -27,23 +30,21 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
     if !iszero(fr)
         while i < maxiters
             mid = (left + right) / 2
-            (mid == left || mid == right) &&
-                return SciMLBase.build_solution(prob, alg, left, fl;
-                    retcode = ReturnCode.FloatingPointLimit,
-                    left = left, right = right)
+            if (mid == left || mid == right)
+                return build_solution(prob, alg, left, fl; left, right,
+                    retcode = ReturnCode.FloatingPointLimit)
             fm = f(mid)
             s = sqrt(fm^2 - fl * fr)
-            iszero(s) &&
-                return SciMLBase.build_solution(prob, alg, left, fl;
-                    retcode = ReturnCode.Failure,
-                    left = left, right = right)
+            if iszero(s)
+                return build_solution(prob, alg, left, fl; left, right,
+                    retcode = ReturnCode.Failure)
+            end
             x = mid + (mid - left) * sign(fl - fr) * fm / s
             fx = f(x)
             xo = x
             if abs((right - left) / 2) < abstol
-                return SciMLBase.build_solution(prob, alg, mid, fm;
-                    retcode = ReturnCode.Success,
-                    left = left, right = right)
+                return build_solution(prob, alg, mid, fm; retcode = ReturnCode.Success,
+                    left, right)
             end
             if iszero(fx)
                 right = x
@@ -67,28 +68,10 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
         end
     end
 
-    while i < maxiters
-        mid = (left + right) / 2
-        (mid == left || mid == right) &&
-            return SciMLBase.build_solution(prob, alg, left, fl;
-                retcode = ReturnCode.FloatingPointLimit,
-                left = left, right = right)
-        fm = f(mid)
-        if abs((right - left) / 2) < abstol
-            return SciMLBase.build_solution(prob, alg, mid, fm;
-                retcode = ReturnCode.Success,
-                left = left, right = right)
-        end
-        if iszero(fm)
-            right = mid
-            fr = fm
-        else
-            left = mid
-            fl = fm
-        end
-        i += 1
-    end
+    sol, i, left, right, fl, fr = __bisection(left, right, fl, fr, f; abstol,
+        maxiters = maxiters - i, prob, alg)
+    sol !== nothing && return sol
 
     return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
-        left = left, right = right)
+        left, right)
 end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index df3374d86..11caa7073 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -134,7 +134,7 @@ function jacobian_cache(ad, f::F, y, x::X, p) where {F, X <: AbstractArray}
         if DiffEqBase.has_jac(f)
             return nothing, nothing
         elseif ad isa AutoForwardDiff
-            J = ArrayInterface.can_setindex(x) ? similar(y, length(fx), length(x)) : nothing
+            J = ArrayInterface.can_setindex(x) ? similar(y, length(y), length(x)) : nothing
             return J, __get_jacobian_config(ad, _f, x)
         elseif ad isa AutoFiniteDiff
             return nothing, FiniteDiff.JacobianCache(copy(x), copy(y), copy(y), ad.fdtype)
@@ -150,6 +150,7 @@ __init_identity_jacobian(u::Number, _) = one(u)
 __init_identity_jacobian!!(J::Number) = one(J)
 function __init_identity_jacobian(u, fu)
     J = similar(u, promote_type(eltype(u), eltype(fu)), length(fu), length(u))
+    fill!(J, zero(eltype(J)))
     J[diagind(J)] .= one(eltype(J))
     return J
 end
@@ -281,89 +282,5 @@ function check_termination(tc_cache, fx, x, xo, prob, alg,
     return nothing
 end
 
-# MaybeInplace
-@inline __copyto!!(::Number, x) = x
-@inline __copyto!!(::SArray, x) = x
-@inline __copyto!!(y::Union{MArray, Array}, x) = copyto!(y, x)
-@inline function __copyto!!(y::AbstractArray, x)
-    ArrayInterface.can_setindex(y) && return copyto!(y, x)
-    return x
-end
-
-@inline __sub!!(x::Number, Δx) = x - Δx
-@inline __sub!!(x::SArray, Δx) = x .- Δx
-@inline __sub!!(x::Union{MArray, Array}, Δx) = (x .-= Δx)
-@inline function __sub!!(x::AbstractArray, Δx)
-    ArrayInterface.can_setindex(x) && return (x .-= Δx)
-    return x .- Δx
-end
-
-@inline __sub!!(::Number, x, Δx) = x - Δx
-@inline __sub!!(::SArray, x, Δx) = x .- Δx
-@inline __sub!!(y::Union{MArray, Array}, x, Δx) = (@. y = x - Δx)
-@inline function __sub!!(y::AbstractArray, x, Δx)
-    ArrayInterface.can_setindex(y) && return (@. y = x - Δx)
-    return x .- Δx
-end
-
-@inline __add!!(x::Number, Δx) = x + Δx
-@inline __add!!(x::SArray, Δx) = x .+ Δx
-@inline __add!!(x::Union{MArray, Array}, Δx) = (x .+= Δx)
-@inline function __add!!(x::AbstractArray, Δx)
-    ArrayInterface.can_setindex(x) && return (x .+= Δx)
-    return x .+ Δx
-end
-
-@inline __add!!(::Number, x, Δx) = x + Δx
-@inline __add!!(::SArray, x, Δx) = x .+ Δx
-@inline __add!!(y::Union{MArray, Array}, x, Δx) = (@. y = x + Δx)
-@inline function __add!!(y::AbstractArray, x, Δx)
-    ArrayInterface.can_setindex(y) && return (@. y = x + Δx)
-    return x .+ Δx
-end
-
-@inline __copy(x::Union{Number, SArray}) = x
-@inline __copy(x::Union{Number, SArray}, _) = x
-@inline __copy(x::Union{MArray, Array}) = copy(x)
-@inline __copy(::Union{MArray, Array}, y) = copy(y)
-@inline function __copy(x::AbstractArray)
-    ArrayInterface.can_setindex(x) && return copy(x)
-    return x
-end
-@inline function __copy(x::AbstractArray, y)
-    ArrayInterface.can_setindex(x) && return copy(y)
-    return x
-end
-
-@inline __mul!!(::Union{Number, SArray}, A, b) = A * b
-@inline __mul!!(y::Union{MArray, Array}, A, b) = (mul!(y, A, b); y)
-@inline function __mul!!(y::AbstractArray, A, b)
-    ArrayInterface.can_setindex(y) && return (mul!(y, A, b); y)
-    return A * b
-end
-
-@inline __neg!!(x::Union{Number, SArray}) = -x
-@inline __neg!!(x::Union{MArray, Array}) = (@. x .*= -one(eltype(x)))
-@inline function __neg!!(x::AbstractArray)
-    ArrayInterface.can_setindex(x) && return (@. x .*= -one(eltype(x)))
-    return -x
-end
-
-@inline __ldiv!!(A, b::Union{Number, SArray}) = A \ b
-@inline __ldiv!!(A, b::Union{MArray, Array}) = (ldiv!(A, b); b)
-@inline function __ldiv!!(A, b::AbstractArray)
-    ArrayInterface.can_setindex(b) && return (ldiv!(A, b); b)
-    return A \ b
-end
-
-@inline __broadcast!!(y::Union{Number, SArray}, f::F, x, args...) where {F} = f.(x, args...)
-@inline function __broadcast!!(y::Union{MArray, Array}, f::F, x, args...) where {F}
-    @. y = f(x, args...)
-    return y
-end
-@inline function __broadcast!!(y::AbstractArray, f::F, x, args...) where {F}
-    ArrayInterface.can_setindex(y) && return (@. y = f(x, args...))
-    return f.(x, args...)
-end
-
-@inline __eval_f(prob, f, fx, x) = isinplace(prob) ? (f(fx, x); fx) : f(x)
+@inline __eval_f(prob, fx, x) = isinplace(prob) ? (prob.f(fx, x, prob.p); fx) :
+                                prob.f(x, prob.p)

From f22923177f95af945cc9a2f9a8ca6855d242d90f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 23 Nov 2023 02:50:28 -0500
Subject: [PATCH 224/700] Fix brent

---
 .../src/SimpleNonlinearSolve.jl               |   8 +-
 lib/SimpleNonlinearSolve/src/brent.jl         | 148 ++++++++----------
 2 files changed, 71 insertions(+), 85 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 208e0e15f..34d2b0728 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -40,7 +40,7 @@ include("klement.jl")
 include("bisection.jl")
 include("falsi.jl")
 include("ridder.jl")
-# include("brent.jl")
+include("brent.jl")
 # include("alefeld.jl")
 # include("itp.jl")
 
@@ -90,8 +90,8 @@ include("ridder.jl")
 # end
 
 export SimpleBroyden, SimpleGaussNewton, SimpleKlement, SimpleNewtonRaphson
-# SimpleDFSane, SimpleTrustRegion, SimpleHalley
-export Bisection, Falsi, Ridder
-# export , Brent, LBroyden, Alefeld, ITP
+# SimpleDFSane, SimpleTrustRegion, SimpleHalley, LBroyden
+export Bisection, Brent, Falsi, Ridder
+# export  Alefeld, ITP
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/brent.jl
index 1319ed979..75497f379 100644
--- a/lib/SimpleNonlinearSolve/src/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/brent.jl
@@ -1,127 +1,113 @@
 """
-`Brent()`
+    Brent()
 
-A non-allocating Brent method
+left non-allocating Brent method.
 """
 struct Brent <: AbstractBracketingAlgorithm end
 
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
-        maxiters = 1000, abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
-        kwargs...)
+        maxiters = 1000, abstol = nothing, kwargs...)
+    @assert !isinplace(prob) "`Brent` only supports OOP problems."
     f = Base.Fix2(prob.f, prob.p)
-    a, b = prob.tspan
-    fa, fb = f(a), f(b)
-    ϵ = eps(convert(typeof(fa), 1.0))
+    left, right = prob.tspan
+    fl, fr = f(left), f(right)
+    ϵ = eps(convert(typeof(fl), 1))
 
-    if iszero(fa)
-        return SciMLBase.build_solution(prob, alg, a, fa;
-            retcode = ReturnCode.ExactSolutionLeft, left = a,
-            right = b)
-    elseif iszero(fb)
-        return SciMLBase.build_solution(prob, alg, b, fb;
-            retcode = ReturnCode.ExactSolutionRight, left = a,
-            right = b)
+    abstol = _get_tolerance(abstol,
+        promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
+
+    if iszero(fl)
+        return build_solution(prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft,
+            left, right)
     end
-    if abs(fa) < abs(fb)
-        c = b
-        b = a
-        a = c
-        tmp = fa
-        fa = fb
-        fb = tmp
+
+    if iszero(fr)
+        return build_solution(prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
+            left, right)
     end
 
-    c = a
+    if abs(fl) < abs(fr)
+        c = right
+        right = left
+        left = c
+        tmp = fl
+        fl = fr
+        fr = tmp
+    end
+
+    c = left
     d = c
     i = 1
     cond = true
-    if !iszero(fb)
+    if !iszero(fr)
         while i < maxiters
             fc = f(c)
-            if fa != fc && fb != fc
+            if fl != fc && fr != fc
                 # Inverse quadratic interpolation
-                s = a * fb * fc / ((fa - fb) * (fa - fc)) +
-                    b * fa * fc / ((fb - fa) * (fb - fc)) +
-                    c * fa * fb / ((fc - fa) * (fc - fb))
+                s = left * fr * fc / ((fl - fr) * (fl - fc)) +
+                    right * fl * fc / ((fr - fl) * (fr - fc)) +
+                    c * fl * fr / ((fc - fl) * (fc - fr))
             else
                 # Secant method
-                s = b - fb * (b - a) / (fb - fa)
+                s = right - fr * (right - left) / (fr - fl)
             end
-            if (s < min((3 * a + b) / 4, b) || s > max((3 * a + b) / 4, b)) ||
-               (cond && abs(s - b) ≥ abs(b - c) / 2) ||
-               (!cond && abs(s - b) ≥ abs(c - d) / 2) ||
-               (cond && abs(b - c) ≤ ϵ) ||
+            if (s < min((3 * left + right) / 4, right) ||
+                s > max((3 * left + right) / 4, right)) ||
+               (cond && abs(s - right) ≥ abs(right - c) / 2) ||
+               (!cond && abs(s - right) ≥ abs(c - d) / 2) ||
+               (cond && abs(right - c) ≤ ϵ) ||
                (!cond && abs(c - d) ≤ ϵ)
                 # Bisection method
-                s = (a + b) / 2
-                (s == a || s == b) &&
-                    return SciMLBase.build_solution(prob, alg, a, fa;
+                s = (left + right) / 2
+                (s == left || s == right) &&
+                    return SciMLBase.build_solution(prob, alg, left, fl;
                         retcode = ReturnCode.FloatingPointLimit,
-                        left = a, right = b)
+                        left = left, right = right)
                 cond = true
             else
                 cond = false
             end
             fs = f(s)
-            if abs((b - a) / 2) < abstol
+            if abs((right - left) / 2) < abstol
                 return SciMLBase.build_solution(prob, alg, s, fs;
                     retcode = ReturnCode.Success,
-                    left = a, right = b)
+                    left = left, right = right)
             end
             if iszero(fs)
-                if b < a
-                    a = b
-                    fa = fb
+                if right < left
+                    left = right
+                    fl = fr
                 end
-                b = s
-                fb = fs
+                right = s
+                fr = fs
                 break
             end
-            if fa * fs < 0
+            if fl * fs < 0
                 d = c
-                c = b
-                b = s
-                fb = fs
+                c = right
+                right = s
+                fr = fs
             else
-                a = s
-                fa = fs
+                left = s
+                fl = fs
             end
-            if abs(fa) < abs(fb)
+            if abs(fl) < abs(fr)
                 d = c
-                c = b
-                b = a
-                a = c
-                fc = fb
-                fb = fa
-                fa = fc
+                c = right
+                right = left
+                left = c
+                fc = fr
+                fr = fl
+                fl = fc
             end
             i += 1
         end
     end
 
-    while i < maxiters
-        c = (a + b) / 2
-        if (c == a || c == b)
-            return SciMLBase.build_solution(prob, alg, a, fa;
-                retcode = ReturnCode.FloatingPointLimit,
-                left = a, right = b)
-        end
-        fc = f(c)
-        if abs((b - a) / 2) < abstol
-            return SciMLBase.build_solution(prob, alg, c, fc;
-                retcode = ReturnCode.Success,
-                left = a, right = b)
-        end
-        if iszero(fc)
-            b = c
-            fb = fc
-        else
-            a = c
-            fa = fc
-        end
-        i += 1
-    end
+    sol, i, left, right, fl, fr = __bisection(left, right, fl, fr, f; abstol,
+        maxiters = maxiters - i, prob, alg)
+
+    sol !== nothing && return sol
 
-    return SciMLBase.build_solution(prob, alg, a, fa; retcode = ReturnCode.MaxIters,
-        left = a, right = b)
+    return build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
 end

From 190ca22c9592793feff2d15639965bc353a15f17 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 23 Nov 2023 03:10:29 -0500
Subject: [PATCH 225/700] Fix the interval methods

---
 .../src/SimpleNonlinearSolve.jl               |  31 +++---
 lib/SimpleNonlinearSolve/src/alefeld.jl       |  68 ++++--------
 lib/SimpleNonlinearSolve/src/itp.jl           | 100 ++++++++----------
 lib/SimpleNonlinearSolve/src/ridder.jl        |   4 +-
 4 files changed, 88 insertions(+), 115 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 34d2b0728..695094805 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -41,8 +41,8 @@ include("bisection.jl")
 include("falsi.jl")
 include("ridder.jl")
 include("brent.jl")
-# include("alefeld.jl")
-# include("itp.jl")
+include("alefeld.jl")
+include("itp.jl")
 
 # AD
 # include("ad.jl")
@@ -62,9 +62,9 @@ include("brent.jl")
 
 # import PrecompileTools
 
-# PrecompileTools.@compile_workload begin
-#     for T in (Float32, Float64)
-#         prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
+@setup_workload begin
+    for T in (Float32, Float64)
+        # prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
 #         for alg in (SimpleNewtonRaphson, SimpleHalley, Broyden, Klement, SimpleTrustRegion,
 #             SimpleDFSane)
 #             solve(prob_no_brack, alg(), abstol = T(1e-2))
@@ -80,18 +80,19 @@ include("brent.jl")
 #         end
 #         =#
 
-#         prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p,
-#             T.((0.0, 2.0)),
-#             T(2))
-#         for alg in (Bisection, Falsi, Ridder, Brent, Alefeld, ITP)
-#             solve(prob_brack, alg(), abstol = T(1e-2))
-#         end
-#     end
-# end
+        prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p,
+            T.((0.0, 2.0)), T(2))
+        algs = [Bisection(), Falsi(), Ridder(), Brent(), Alefeld(), ITP()]
+        @compile_workload begin
+            for alg in algs
+                solve(prob_brack, alg, abstol = T(1e-2))
+            end
+        end
+    end
+end
 
 export SimpleBroyden, SimpleGaussNewton, SimpleKlement, SimpleNewtonRaphson
 # SimpleDFSane, SimpleTrustRegion, SimpleHalley, LBroyden
-export Bisection, Brent, Falsi, Ridder
-# export  Alefeld, ITP
+export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/alefeld.jl
index 3d3b2ada8..39c984fd5 100644
--- a/lib/SimpleNonlinearSolve/src/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/alefeld.jl
@@ -1,5 +1,5 @@
 """
-`Alefeld()`
+    Alefeld()
 
 An implementation of algorithm 4.2 from [Alefeld](https://dl.acm.org/doi/10.1145/210089.210111).
 
@@ -8,24 +8,18 @@ algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal
 """
 struct Alefeld <: AbstractBracketingAlgorithm end
 
-function SciMLBase.solve(prob::IntervalNonlinearProblem,
-        alg::Alefeld, args...; abstol = nothing,
-        reltol = nothing,
-        maxiters = 1000, kwargs...)
+function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...;
+        maxiters = 1000, abstol = nothing, kwargs...)
     f = Base.Fix2(prob.f, prob.p)
     a, b = prob.tspan
     c = a - (b - a) / (f(b) - f(a)) * f(a)
 
     fc = f(c)
     (a == c || b == c) &&
-        return SciMLBase.build_solution(prob, alg, c, fc;
-            retcode = ReturnCode.FloatingPointLimit,
-            left = a,
-            right = b)
+        return build_solution(prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
+            left = a, right = b)
     iszero(fc) &&
-        return SciMLBase.build_solution(prob, alg, c, fc;
-            retcode = ReturnCode.Success,
-            left = a,
+        return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success, left = a,
             right = b)
     a, b, d = _bracket(f, a, b, c)
     e = zero(a)   # Set e as 0 before iteration to avoid a non-value f(e)
@@ -44,15 +38,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
         end
         ē, fc = d, f(c)
         (a == c || b == c) &&
-            return SciMLBase.build_solution(prob, alg, c, fc;
-                retcode = ReturnCode.FloatingPointLimit,
-                left = a,
-                right = b)
+            return build_solution(prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
+                left = a, right = b)
         iszero(fc) &&
-            return SciMLBase.build_solution(prob, alg, c, fc;
-                retcode = ReturnCode.Success,
-                left = a,
-                right = b)
+            return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success,
+                left = a, right = b)
         ā, b̄, d̄ = _bracket(f, a, b, c)
 
         # The second bracketing block
@@ -67,15 +57,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
         end
         fc = f(c)
         (ā == c || b̄ == c) &&
-            return SciMLBase.build_solution(prob, alg, c, fc;
-                retcode = ReturnCode.FloatingPointLimit,
-                left = ā,
-                right = b̄)
+            return build_solution(prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
+                left = ā, right = b̄)
         iszero(fc) &&
-            return SciMLBase.build_solution(prob, alg, c, fc;
-                retcode = ReturnCode.Success,
-                left = ā,
-                right = b̄)
+            return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success,
+                left = ā, right = b̄)
         ā, b̄, d̄ = _bracket(f, ā, b̄, c)
 
         # The third bracketing block
@@ -90,15 +76,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
         end
         fc = f(c)
         (ā == c || b̄ == c) &&
-            return SciMLBase.build_solution(prob, alg, c, fc;
-                retcode = ReturnCode.FloatingPointLimit,
-                left = ā,
-                right = b̄)
+            return build_solution(prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
+                left = ā, right = b̄)
         iszero(fc) &&
-            return SciMLBase.build_solution(prob, alg, c, fc;
-                retcode = ReturnCode.Success,
-                left = ā,
-                right = b̄)
+            return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success,
+                left = ā, right = b̄)
         ā, b̄, d = _bracket(f, ā, b̄, c)
 
         # The last bracketing block
@@ -109,15 +91,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
             c = 0.5 * (ā + b̄)
             fc = f(c)
             (ā == c || b̄ == c) &&
-                return SciMLBase.build_solution(prob, alg, c, fc;
-                    retcode = ReturnCode.FloatingPointLimit,
-                    left = ā,
-                    right = b̄)
+                return build_solution(prob, alg, c, fc;
+                    retcode = ReturnCode.FloatingPointLimit, left = ā, right = b̄)
             iszero(fc) &&
-                return SciMLBase.build_solution(prob, alg, c, fc;
-                    retcode = ReturnCode.Success,
-                    left = ā,
-                    right = b̄)
+                return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success,
+                    left = ā, right = b̄)
             a, b, d = _bracket(f, ā, b̄, c)
         end
     end
@@ -131,7 +109,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem,
     fc = f(c)
 
     # Reuturn solution when run out of max interation
-    return SciMLBase.build_solution(prob, alg, c, fc; retcode = ReturnCode.MaxIters,
+    return build_solution(prob, alg, c, fc; retcode = ReturnCode.MaxIters,
         left = a, right = b)
 end
 
diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/itp.jl
index 933995cec..fd46de6c3 100644
--- a/lib/SimpleNonlinearSolve/src/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/itp.jl
@@ -1,33 +1,29 @@
 """
-```julia
-ITP(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
-```
+    ITP(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
 
 ITP (Interpolate Truncate & Project)
 
-Use the [ITP method](https://en.wikipedia.org/wiki/ITP_method) to find
-a root of a bracketed function, with a convergence rate between 1 and 1.62.
+Use the [ITP method](https://en.wikipedia.org/wiki/ITP_method) to find a root of a bracketed
+function, with a convergence rate between 1 and 1.62.
 
-This method was introduced in the paper "An Enhancement of the Bisection Method
-Average Performance Preserving Minmax Optimality"
-(https://doi.org/10.1145/3423597) by I. F. D. Oliveira and R. H. C. Takahashi.
+This method was introduced in the paper "An Enhancement of the Bisection Method Average
+Performance Preserving Minmax Optimality" (https://doi.org/10.1145/3423597) by
+I. F. D. Oliveira and R. H. C. Takahashi.
 
 # Tuning Parameters
 
 The following keyword parameters are accepted.
 
-  - `n₀::Int = 1`, the 'slack'. Must not be negative.\n
-    When n₀ = 0 the worst-case is identical to that of bisection,
-    but increacing n₀ provides greater oppotunity for superlinearity.
-  - `κ₁::Float64 = 0.1`. Must not be negative.\n
-    The recomended value is `0.2/(x₂ - x₁)`.
-    Lower values produce tighter asymptotic behaviour, while higher values
-    improve the steady-state behaviour when truncation is not helpful.
-  - `κ₂::Real = 2`. Must lie in [1, 1+ϕ ≈ 2.62).\n
-    Higher values allow for a greater convergence rate,
-    but also make the method more succeptable to worst-case performance.
-    In practice, κ=1,2 seems to work well due to the computational simplicity,
-    as κ₂ is used as an exponent in the method.
+  - `n₀::Int = 1`, the 'slack'. Must not be negative. When n₀ = 0 the worst-case is
+    identical to that of bisection, but increacing n₀ provides greater oppotunity for
+    superlinearity.
+  - `κ₁::Float64 = 0.1`. Must not be negative. The recomended value is `0.2/(x₂ - x₁)`.
+    Lower values produce tighter asymptotic behaviour, while higher values improve the
+    steady-state behaviour when truncation is not helpful.
+  - `κ₂::Real = 2`. Must lie in [1, 1+ϕ ≈ 2.62). Higher values allow for a greater
+    convergence rate, but also make the method more succeptable to worst-case performance.
+    In practice, κ=1,2 seems to work well due to the computational simplicity, as κ₂ is used
+    as an exponent in the method.
 
 ### Worst Case Performance
 
@@ -36,44 +32,45 @@ n½ + `n₀` iterations, where n½ is the number of iterations using bisection
 
 ### Asymptotic Performance
 
-If `f` is twice differentiable and the root is simple,
-then with `n₀` > 0 the convergence rate is √`κ₂`.
+If `f` is twice differentiable and the root is simple, then with `n₀` > 0 the convergence
+rate is √`κ₂`.
 """
 struct ITP{T} <: AbstractBracketingAlgorithm
     k1::T
     k2::T
     n0::Int
     function ITP(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
-        if k1 < 0
-            error("Hyper-parameter κ₁ should not be negative")
-        end
-        if n0 < 0
-            error("Hyper-parameter n₀ should not be negative")
-        end
+        k1 < 0 && error("Hyper-parameter κ₁ should not be negative")
+        n0 < 0 && error("Hyper-parameter n₀ should not be negative")
         if k2 < 1 || k2 > (1.5 + sqrt(5) / 2)
-            ArgumentError("Hyper-parameter κ₂ should be between 1 and 1 + ϕ where ϕ ≈ 1.618... is the golden ratio")
+            throw(ArgumentError("Hyper-parameter κ₂ should be between 1 and 1 + ϕ where \
+                                 ϕ ≈ 1.618... is the golden ratio"))
         end
         T = promote_type(eltype(k1), eltype(k2))
         return new{T}(k1, k2, n0)
     end
 end
 
-function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
-        args...; abstol = min(eps(prob.tspan[1]), eps(prob.tspan[2])),
-        maxiters = 1000, kwargs...)
+function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
+        maxiters = 1000, abstol = nothing, kwargs...)
+    @assert !isinplace(prob) "`Bisection` only supports OOP problems."
     f = Base.Fix2(prob.f, prob.p)
-    left, right = prob.tspan # a and b
+    left, right = prob.tspan
     fl, fr = f(left), f(right)
-    ϵ = abstol
+
+    abstol = _get_tolerance(abstol,
+        promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
+
     if iszero(fl)
-        return SciMLBase.build_solution(prob, alg, left, fl;
-            retcode = ReturnCode.ExactSolutionLeft, left = left,
-            right = right)
-    elseif iszero(fr)
-        return SciMLBase.build_solution(prob, alg, right, fr;
-            retcode = ReturnCode.ExactSolutionRight, left = left,
-            right = right)
+        return build_solution(prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft,
+            left, right)
     end
+
+    if iszero(fr)
+        return build_solution(prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
+            left, right)
+    end
+    ϵ = abstol
     #defining variables/cache
     k1 = alg.k1
     k2 = alg.k2
@@ -112,9 +109,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
         end
 
         if abs((left - right) / 2) < ϵ
-            return SciMLBase.build_solution(prob, alg, mid, f(mid);
-                retcode = ReturnCode.Success,
-                left = left, right = right)
+            return build_solution(prob, alg, mid, f(mid); retcode = ReturnCode.Success,
+                left, right)
         end
 
         ## Update ##
@@ -130,20 +126,18 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP,
             left = xp
             fl = yp
         else
-            return SciMLBase.build_solution(prob, alg, xp, yps;
-                retcode = ReturnCode.Success, left = xp,
-                right = xp)
+            return build_solution(prob, alg, xp, yps; retcode = ReturnCode.Success,
+                left = xp, right = xp)
         end
         i += 1
         mid = (left + right) / 2
         ϵ_s /= 2
 
-        if nextfloat_tdir(left, prob.tspan...) == right
-            return SciMLBase.build_solution(prob, alg, left, fl;
-                retcode = ReturnCode.FloatingPointLimit, left = left,
-                right = right)
+        if __nextfloat_tdir(left, prob.tspan...) == right
+            return build_solution(prob, alg, left, fl; left, right,
+                retcode = ReturnCode.FloatingPointLimit)
         end
     end
-    return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
-        left = left, right = right)
+
+    return build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
 end
diff --git a/lib/SimpleNonlinearSolve/src/ridder.jl b/lib/SimpleNonlinearSolve/src/ridder.jl
index 0bed8ee75..11b7604e1 100644
--- a/lib/SimpleNonlinearSolve/src/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/ridder.jl
@@ -30,7 +30,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
     if !iszero(fr)
         while i < maxiters
             mid = (left + right) / 2
-            if (mid == left || mid == right)
+            (mid == left || mid == right) &&
                 return build_solution(prob, alg, left, fl; left, right,
                     retcode = ReturnCode.FloatingPointLimit)
             fm = f(mid)
@@ -70,7 +70,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
 
     sol, i, left, right, fl, fr = __bisection(left, right, fl, fr, f; abstol,
         maxiters = maxiters - i, prob, alg)
-    sol !== nothing && return sol
+        sol !== nothing && return sol
 
     return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
         left, right)

From b50ece4301342fe9145301d00974d299f38cdc9d Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 23 Nov 2023 19:18:29 -0500
Subject: [PATCH 226/700] Move things around a bit

---
 .../src/SimpleNonlinearSolve.jl               | 72 +++++++++----------
 .../src/{ => bracketing}/alefeld.jl           |  0
 .../src/{ => bracketing}/bisection.jl         |  0
 .../src/{ => bracketing}/brent.jl             |  0
 .../src/{ => bracketing}/falsi.jl             |  0
 .../src/{ => bracketing}/itp.jl               |  0
 .../src/{ => bracketing}/ridder.jl            |  0
 .../src/{ => nlsolve}/broyden.jl              |  0
 .../src/{ => nlsolve}/dfsane.jl               |  0
 .../src/{ => nlsolve}/halley.jl               |  0
 .../src/{ => nlsolve}/klement.jl              |  0
 .../src/{ => nlsolve}/lbroyden.jl             |  0
 .../src/{ => nlsolve}/raphson.jl              |  0
 .../src/{ => nlsolve}/trustRegion.jl          |  0
 14 files changed, 36 insertions(+), 36 deletions(-)
 rename lib/SimpleNonlinearSolve/src/{ => bracketing}/alefeld.jl (100%)
 rename lib/SimpleNonlinearSolve/src/{ => bracketing}/bisection.jl (100%)
 rename lib/SimpleNonlinearSolve/src/{ => bracketing}/brent.jl (100%)
 rename lib/SimpleNonlinearSolve/src/{ => bracketing}/falsi.jl (100%)
 rename lib/SimpleNonlinearSolve/src/{ => bracketing}/itp.jl (100%)
 rename lib/SimpleNonlinearSolve/src/{ => bracketing}/ridder.jl (100%)
 rename lib/SimpleNonlinearSolve/src/{ => nlsolve}/broyden.jl (100%)
 rename lib/SimpleNonlinearSolve/src/{ => nlsolve}/dfsane.jl (100%)
 rename lib/SimpleNonlinearSolve/src/{ => nlsolve}/halley.jl (100%)
 rename lib/SimpleNonlinearSolve/src/{ => nlsolve}/klement.jl (100%)
 rename lib/SimpleNonlinearSolve/src/{ => nlsolve}/lbroyden.jl (100%)
 rename lib/SimpleNonlinearSolve/src/{ => nlsolve}/raphson.jl (100%)
 rename lib/SimpleNonlinearSolve/src/{ => nlsolve}/trustRegion.jl (100%)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 695094805..ab7026bf8 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -28,57 +28,57 @@ include("utils.jl")
 include("rewrite_inplace.jl")
 
 # Nonlinear Solvera
-include("raphson.jl")
-include("broyden.jl")
-# include("lbroyden.jl")
-include("klement.jl")
-# include("trustRegion.jl")
-# include("halley.jl")
-# include("dfsane.jl")
+include("nlsolve/raphson.jl")
+include("nlsolve/broyden.jl")
+# include("nlsolve/lbroyden.jl")
+include("nlsolve/klement.jl")
+# include("nlsolve/trustRegion.jl")
+# include("nlsolve/halley.jl")
+# include("nlsolve/dfsane.jl")
 
 # Interval Nonlinear Solvers
-include("bisection.jl")
-include("falsi.jl")
-include("ridder.jl")
-include("brent.jl")
-include("alefeld.jl")
-include("itp.jl")
+include("bracketing/bisection.jl")
+include("bracketing/falsi.jl")
+include("bracketing/ridder.jl")
+include("bracketing/brent.jl")
+include("bracketing/alefeld.jl")
+include("bracketing/itp.jl")
 
 # AD
 # include("ad.jl")
 
-# ## Default algorithm
+## Default algorithm
 
-# # Set the default bracketing method to ITP
+# Set the default bracketing method to ITP
 
-# function SciMLBase.solve(prob::IntervalNonlinearProblem; kwargs...)
-#     SciMLBase.solve(prob, ITP(); kwargs...)
-# end
+function SciMLBase.solve(prob::IntervalNonlinearProblem; kwargs...)
+    return solve(prob, ITP(); kwargs...)
+end
 
-# function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing,
-#     args...; kwargs...)
-#     SciMLBase.solve(prob, ITP(), args...; kwargs...)
-# end
+function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing,
+        args...; kwargs...)
+    return solve(prob, ITP(), args...; kwargs...)
+end
 
 # import PrecompileTools
 
 @setup_workload begin
     for T in (Float32, Float64)
         # prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-#         for alg in (SimpleNewtonRaphson, SimpleHalley, Broyden, Klement, SimpleTrustRegion,
-#             SimpleDFSane)
-#             solve(prob_no_brack, alg(), abstol = T(1e-2))
-#         end
-
-#         #=
-#         for alg in (SimpleNewtonRaphson,)
-#             for u0 in ([1., 1.], StaticArraysCore.SA[1.0, 1.0])
-#                 u0 = T.(.1)
-#                 probN = NonlinearProblem{false}((u,p) -> u .* u .- p, u0, T(2))
-#                 solve(probN, alg(), tol = T(1e-2))
-#             end
-#         end
-#         =#
+        #         for alg in (SimpleNewtonRaphson, SimpleHalley, Broyden, Klement, SimpleTrustRegion,
+        #             SimpleDFSane)
+        #             solve(prob_no_brack, alg(), abstol = T(1e-2))
+        #         end
+
+        #         #=
+        #         for alg in (SimpleNewtonRaphson,)
+        #             for u0 in ([1., 1.], StaticArraysCore.SA[1.0, 1.0])
+        #                 u0 = T.(.1)
+        #                 probN = NonlinearProblem{false}((u,p) -> u .* u .- p, u0, T(2))
+        #                 solve(probN, alg(), tol = T(1e-2))
+        #             end
+        #         end
+        #         =#
 
         prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p,
             T.((0.0, 2.0)), T(2))
diff --git a/lib/SimpleNonlinearSolve/src/alefeld.jl b/lib/SimpleNonlinearSolve/src/bracketing/alefeld.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/alefeld.jl
rename to lib/SimpleNonlinearSolve/src/bracketing/alefeld.jl
diff --git a/lib/SimpleNonlinearSolve/src/bisection.jl b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/bisection.jl
rename to lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
diff --git a/lib/SimpleNonlinearSolve/src/brent.jl b/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/brent.jl
rename to lib/SimpleNonlinearSolve/src/bracketing/brent.jl
diff --git a/lib/SimpleNonlinearSolve/src/falsi.jl b/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/falsi.jl
rename to lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
diff --git a/lib/SimpleNonlinearSolve/src/itp.jl b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/itp.jl
rename to lib/SimpleNonlinearSolve/src/bracketing/itp.jl
diff --git a/lib/SimpleNonlinearSolve/src/ridder.jl b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/ridder.jl
rename to lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/broyden.jl
rename to lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/dfsane.jl
rename to lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/halley.jl
rename to lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/klement.jl
rename to lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/lbroyden.jl
rename to lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/raphson.jl
rename to lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
diff --git a/lib/SimpleNonlinearSolve/src/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
similarity index 100%
rename from lib/SimpleNonlinearSolve/src/trustRegion.jl
rename to lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl

From 62d99e03a597ae2cac822337b829ab172b43a8f1 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 23 Nov 2023 22:51:03 -0500
Subject: [PATCH 227/700] Move out the @bb macro into a separate package

---
 lib/SimpleNonlinearSolve/Project.toml         |   1 +
 .../src/SimpleNonlinearSolve.jl               |  10 +-
 .../src/bracketing/ridder.jl                  |   2 +-
 .../src/nlsolve/klement.jl                    |   8 +-
 .../src/rewrite_inplace.jl                    | 161 ------------------
 5 files changed, 10 insertions(+), 172 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/src/rewrite_inplace.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 75af93414..8e6b0f510 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -11,6 +11,7 @@ DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index ab7026bf8..cdfc95b5c 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -4,28 +4,25 @@ import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidat
 
 @recompile_invalidations begin
     using ADTypes,
-        ArrayInterface, ConcreteStructs, DiffEqBase, Reexport, LinearAlgebra,
-        SciMLBase
+        ArrayInterface, ConcreteStructs, DiffEqBase, Reexport, LinearAlgebra, SciMLBase
 
     import DiffEqBase: AbstractNonlinearTerminationMode,
         AbstractSafeNonlinearTerminationMode, AbstractSafeBestNonlinearTerminationMode,
         NonlinearSafeTerminationReturnCode, get_termination_mode
     using FiniteDiff, ForwardDiff
     import ForwardDiff: Dual
+    import MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
     import SciMLBase: AbstractNonlinearAlgorithm, build_solution, isinplace
     import StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray
 end
 
 @reexport using ADTypes, SciMLBase
 
-# const NNlibExtLoaded = Ref{Bool}(false)
-
 abstract type AbstractSimpleNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm end
 abstract type AbstractBracketingAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 abstract type AbstractNewtonAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 
 include("utils.jl")
-include("rewrite_inplace.jl")
 
 # Nonlinear Solvera
 include("nlsolve/raphson.jl")
@@ -50,7 +47,6 @@ include("bracketing/itp.jl")
 ## Default algorithm
 
 # Set the default bracketing method to ITP
-
 function SciMLBase.solve(prob::IntervalNonlinearProblem; kwargs...)
     return solve(prob, ITP(); kwargs...)
 end
@@ -60,8 +56,6 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing,
     return solve(prob, ITP(), args...; kwargs...)
 end
 
-# import PrecompileTools
-
 @setup_workload begin
     for T in (Float32, Float64)
         # prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
index 11b7604e1..20e0db489 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
@@ -70,7 +70,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
 
     sol, i, left, right, fl, fr = __bisection(left, right, fl, fr, f; abstol,
         maxiters = maxiters - i, prob, alg)
-        sol !== nothing && return sol
+    sol !== nothing && return sol
 
     return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
         left, right)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
index 7b9a878ad..56d6ccd55 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
@@ -54,7 +54,11 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
         end
 
         @bb copyto!(δx, fprev)
-        δx = __ldiv!!(F_, δx)
+        if setindex_trait(δx) === CanSetindex()
+            ldiv!(F_, δx)
+        else
+            δx = F_ \ δx
+        end
         @bb @. x = xo - δx
         fx = __eval_f(prob, fx, x)
 
@@ -74,7 +78,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
         @bb δx² = J × vec(δx)
         @bb @. δf = (δf - δx²) / d
 
-        _vδf, _vδx = vec(δf), vec(δx)
+        _vδf, _vδx = _vec(δf), _vec(δx)
         @bb J_cache = _vδf × transpose(_vδx)
         @bb @. J_cache *= J
         @bb J_cache2 = J_cache × J
diff --git a/lib/SimpleNonlinearSolve/src/rewrite_inplace.jl b/lib/SimpleNonlinearSolve/src/rewrite_inplace.jl
deleted file mode 100644
index f0d80af23..000000000
--- a/lib/SimpleNonlinearSolve/src/rewrite_inplace.jl
+++ /dev/null
@@ -1,161 +0,0 @@
-# Take a inplace code and rewrite it to be maybe-inplace
-# I will take this code out into a separate package because this is useful even in
-# NonlinearSolve.jl
-function __bangbang(M, expr; depth = 1)
-    new_expr = nothing
-    if expr.head == :call
-        @assert length(expr.args)≥2 "Expected a function call with atleast 1 argument. \
-                                     Got `$(expr)`."
-        f, a, args... = expr.args
-        g = get(OP_MAPPING, f, nothing)
-        if f == :copy && length(args) == 0
-            # Special case for copy with single argument
-            new_expr = :($(g)($(setindex_trait)($(a)), $(a)))
-        elseif g !== nothing
-            new_expr = :($(a) = $(g)($(setindex_trait)($(a)), $(a), $(args...)))
-        end
-    elseif expr.head == :(=)
-        a, rhs_expr = expr.args
-        if rhs_expr.head == :call
-            f, b, args... = rhs_expr.args
-            g = get(OP_MAPPING, f, nothing)
-            if g !== nothing
-                new_expr = :($(a) = $(g)($(setindex_trait)($(b)), $(b), $(args...)))
-            elseif f == :×
-                @debug "Custom operator `×` detected in `$(expr)`."
-                c, args... = args
-                @assert length(args)==0 "Expected `×` to have only 2 arguments. \
-                                        Got `$(expr)`."
-                is_b_vec = b isa Expr && b.head == :call && b.args[1] == :vec
-                is_c_vec = c isa Expr && c.head == :call && c.args[1] == :vec
-                a_sym = gensym("a")
-                if is_b_vec
-                    if is_c_vec
-                        error("2 `vec`s detected with `×` in `$(expr)`. Use `dot` instead.")
-                    else
-                        new_expr = quote
-                            if $(setindex_trait)($(a)) === CanSetindex()
-                                $(a_sym) = $(_vec)($a)
-                                mul!($(a_sym), $(_vec)($(b.args[2])), $(c))
-                                $(a) = $(_restructure)($a, $(a_sym))
-                            else
-                                $(a) = $(_restructure)($a, $(_vec)($(b.args[2])) * $(c))
-                            end
-                        end
-                    end
-                else
-                    if is_c_vec
-                        new_expr = quote
-                            if $(setindex_trait)($(a)) === CanSetindex()
-                                $(a_sym) = $(_vec)($a)
-                                mul!($(a), $(b), $(_vec)($(c.args[2])))
-                                $(a) = $(_restructure)($a, $(a_sym))
-                            else
-                                $(a) = $(_restructure)($a, $(b) * $(_vec)($(c.args[2])))
-                            end
-                        end
-                    else
-                        new_expr = quote
-                            if $(setindex_trait)($(a)) === CanSetindex()
-                                mul!($(a), $(b), $(c))
-                            else
-                                $(a) = $(b) * $(c)
-                            end
-                        end
-                    end
-                end
-            end
-        end
-    elseif expr.head == :(.=)
-        a, rhs_expr = expr.args
-        if rhs_expr isa Expr && rhs_expr.head == :(.)
-            f, arg_expr = rhs_expr.args
-            # f_broadcast = :(Base.Broadcast.BroadcastFunction($(f)))
-            new_expr = quote
-                if $(setindex_trait)($(a)) === CanSetindex()
-                    broadcast!($(f), $(a), $(arg_expr)...)
-                else
-                    $(a) = broadcast($(f), $(arg_expr)...)
-                end
-            end
-        end
-    elseif expr.head == :macrocall
-        # For @__dot__ there is a easier alternative
-        if expr.args[1] == Symbol("@__dot__")
-            main_expr = last(expr.args)
-            if main_expr isa Expr && main_expr.head == :(=)
-                a, rhs_expr = main_expr.args
-                new_expr = quote
-                    if $(setindex_trait)($(a)) === CanSetindex()
-                        @. $(main_expr)
-                    else
-                        $(a) = @. $(rhs_expr)
-                    end
-                end
-            end
-        end
-        if new_expr === nothing
-            new_expr = __bangbang(M, Base.macroexpand(M, expr; recursive = true);
-                depth = depth + 1)
-        end
-    else
-        f = expr.head # Things like :.-=, etc.
-        a, args... = expr.args
-        g = get(OP_MAPPING, f, nothing)
-        if g !== nothing
-            new_expr = :($(a) = $(g)($(setindex_trait)($(a)), $(a), $(args...)))
-        end
-    end
-    if new_expr !== nothing
-        if depth == 1
-            @debug "Replacing `$(expr)` with `$(new_expr)`"
-            return esc(new_expr)
-        else
-            return new_expr
-        end
-    end
-    error("`$(expr)` cannot be handled. Check the documentation for allowed expressions.")
-end
-
-macro bangbang(expr)
-    return __bangbang(__module__, expr)
-end
-
-# `bb` is the short form of bang-bang
-macro bb(expr)
-    return __bangbang(__module__, expr)
-end
-
-# Is Mutable or Not?
-abstract type AbstractMaybeSetindex end
-struct CannotSetindex <: AbstractMaybeSetindex end
-struct CanSetindex <: AbstractMaybeSetindex end
-
-# Common types should overload this via extensions, else it butchers type-inference
-setindex_trait(::Union{Number, SArray}) = CannotSetindex()
-setindex_trait(::Union{MArray, Array}) = CanSetindex()
-setindex_trait(A) = ifelse(ArrayInterface.can_setindex(A), CanSetindex(), CannotSetindex())
-
-# Operations
-const OP_MAPPING = Dict{Symbol, Symbol}(:copyto! => :__copyto!!,
-    :.-= => :__sub!!,
-    :.+= => :__add!!,
-    :.*= => :__mul!!,
-    :./= => :__div!!,
-    :copy => :__copy)
-
-@inline __copyto!!(::CannotSetindex, x, y) = y
-@inline __copyto!!(::CanSetindex, x, y) = (copyto!(x, y); x)
-
-@inline __broadcast!!(::CannotSetindex, op, x, args...) = broadcast(op, args...)
-@inline __broadcast!!(::CanSetindex, op, x, args...) = (broadcast!(op, x, args...); x)
-
-@inline __sub!!(S, x, args...) = __broadcast!!(S, -, x, x, args...)
-@inline __add!!(S, x, args...) = __broadcast!!(S, +, x, x, args...)
-@inline __mul!!(S, x, args...) = __broadcast!!(S, *, x, x, args...)
-@inline __div!!(S, x, args...) = __broadcast!!(S, /, x, x, args...)
-
-@inline __copy(::CannotSetindex, x) = x
-@inline __copy(::CanSetindex, x) = copy(x)
-@inline __copy(::CannotSetindex, x, y) = y
-@inline __copy(::CanSetindex, x, y) = copy(y)

From 12006d11aab4c0369a1dd0c8ef331a553e732932 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 23 Nov 2023 23:07:45 -0500
Subject: [PATCH 228/700] Reenable some more compilation

---
 .../src/SimpleNonlinearSolve.jl               | 42 ++++++++++++-------
 1 file changed, 27 insertions(+), 15 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index cdfc95b5c..b74090a9f 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -58,21 +58,33 @@ end
 
 @setup_workload begin
     for T in (Float32, Float64)
-        # prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-        #         for alg in (SimpleNewtonRaphson, SimpleHalley, Broyden, Klement, SimpleTrustRegion,
-        #             SimpleDFSane)
-        #             solve(prob_no_brack, alg(), abstol = T(1e-2))
-        #         end
-
-        #         #=
-        #         for alg in (SimpleNewtonRaphson,)
-        #             for u0 in ([1., 1.], StaticArraysCore.SA[1.0, 1.0])
-        #                 u0 = T.(.1)
-        #                 probN = NonlinearProblem{false}((u,p) -> u .* u .- p, u0, T(2))
-        #                 solve(probN, alg(), tol = T(1e-2))
-        #             end
-        #         end
-        #         =#
+        prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
+        algs = [SimpleNewtonRaphson(), SimpleBroyden(), SimpleKlement()]
+
+        @compile_workload begin
+            for alg in algs
+                solve(prob_no_brack, alg, abstol = T(1e-2))
+            end
+        end
+
+        prob_no_brack = NonlinearProblem{true}((du, u, p) -> du .= u .* u .- p,
+            T.([1.0, 1.0]), T(2))
+
+        @compile_workload begin
+            for alg in algs
+                solve(prob_no_brack, alg, abstol = T(1e-2))
+            end
+        end
+
+        #=
+        for alg in (SimpleNewtonRaphson,)
+            for u0 in ([1., 1.], StaticArraysCore.SA[1.0, 1.0])
+                u0 = T.(.1)
+                probN = NonlinearProblem{false}((u,p) -> u .* u .- p, u0, T(2))
+                solve(probN, alg(), tol = T(1e-2))
+            end
+        end
+        =#
 
         prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p,
             T.((0.0, 2.0)), T(2))

From 1b1029e84c096c4aefbcd0620281173a0e705a8d Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 23 Nov 2023 23:10:26 -0500
Subject: [PATCH 229/700] bad rebase

---
 .../src/batched/raphson.jl                    | 92 -------------------
 1 file changed, 92 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/src/batched/raphson.jl

diff --git a/lib/SimpleNonlinearSolve/src/batched/raphson.jl b/lib/SimpleNonlinearSolve/src/batched/raphson.jl
deleted file mode 100644
index 7bc7b8c4a..000000000
--- a/lib/SimpleNonlinearSolve/src/batched/raphson.jl
+++ /dev/null
@@ -1,92 +0,0 @@
-struct BatchedSimpleNewtonRaphson{CS, AD, FDT, TC <: NLSolveTerminationCondition} <:
-       AbstractBatchedNonlinearSolveAlgorithm
-    termination_condition::TC
-end
-
-alg_autodiff(alg::BatchedSimpleNewtonRaphson{CS, AD, FDT}) where {CS, AD, FDT} = AD
-diff_type(alg::BatchedSimpleNewtonRaphson{CS, AD, FDT}) where {CS, AD, FDT} = FDT
-
-function BatchedSimpleNewtonRaphson(; chunk_size = Val{0}(),
-        autodiff = Val{true}(),
-        diff_type = Val{:forward},
-        termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-            abstol = nothing,
-            reltol = nothing))
-    return BatchedSimpleNewtonRaphson{SciMLBase._unwrap_val(chunk_size),
-        SciMLBase._unwrap_val(autodiff),
-        SciMLBase._unwrap_val(diff_type), typeof(termination_condition)}(termination_condition)
-end
-
-function SciMLBase.__solve(prob::NonlinearProblem, alg::BatchedSimpleNewtonRaphson;
-        abstol = nothing, reltol = nothing, maxiters = 1000, kwargs...)
-    iip = SciMLBase.isinplace(prob)
-    iip &&
-        @assert alg_autodiff(alg) "Inplace BatchedSimpleNewtonRaphson currently only supports autodiff."
-    u, f, reconstruct = _construct_batched_problem_structure(prob)
-
-    tc = alg.termination_condition
-    mode = DiffEqBase.get_termination_mode(tc)
-
-    storage = _get_storage(mode, u)
-
-    xₙ, xₙ₋₁ = copy(u), copy(u)
-    T = eltype(u)
-
-    atol = _get_tolerance(abstol, tc.abstol, T)
-    rtol = _get_tolerance(reltol, tc.reltol, T)
-    termination_condition = tc(storage)
-
-    if iip
-        𝓙 = similar(xₙ, length(xₙ), length(xₙ))
-        fₙ = similar(xₙ)
-        jac_cfg = ForwardDiff.JacobianConfig(f, fₙ, xₙ)
-    end
-
-    for i in 1:maxiters
-        if iip
-            value_derivative!(𝓙, fₙ, f, xₙ, jac_cfg)
-        else
-            if alg_autodiff(alg)
-                fₙ, 𝓙 = value_derivative(f, xₙ)
-            else
-                fₙ = f(xₙ)
-                𝓙 = FiniteDiff.finite_difference_jacobian(f,
-                    xₙ,
-                    diff_type(alg),
-                    eltype(xₙ),
-                    fₙ)
-            end
-        end
-
-        iszero(fₙ) && return DiffEqBase.build_solution(prob,
-            alg,
-            reconstruct(xₙ),
-            reconstruct(fₙ);
-            retcode = ReturnCode.Success)
-
-        δx = reshape(𝓙 \ vec(fₙ), size(xₙ))
-        xₙ .-= δx
-
-        if termination_condition(fₙ, xₙ, xₙ₋₁, atol, rtol)
-            retcode, xₙ, fₙ = _result_from_storage(storage, xₙ, fₙ, f, mode, iip)
-            return DiffEqBase.build_solution(prob,
-                alg,
-                reconstruct(xₙ),
-                reconstruct(fₙ);
-                retcode)
-        end
-
-        xₙ₋₁ .= xₙ
-    end
-
-    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-        xₙ = storage.u
-        @maybeinplace iip fₙ=f(xₙ)
-    end
-
-    return DiffEqBase.build_solution(prob,
-        alg,
-        reconstruct(xₙ),
-        reconstruct(fₙ);
-        retcode = ReturnCode.MaxIters)
-end

From 3c3e401eb8587e578674e19a5b3ccc04c9804aac Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 24 Nov 2023 01:25:56 -0500
Subject: [PATCH 230/700] More robust and allocated version of TrustRegion

---
 .../src/SimpleNonlinearSolve.jl               |  10 +-
 .../src/nlsolve/raphson.jl                    |  10 +-
 .../src/nlsolve/trustRegion.jl                | 221 ++++++++----------
 lib/SimpleNonlinearSolve/src/utils.jl         |  25 --
 4 files changed, 107 insertions(+), 159 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index b74090a9f..79a4d3f53 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -29,7 +29,7 @@ include("nlsolve/raphson.jl")
 include("nlsolve/broyden.jl")
 # include("nlsolve/lbroyden.jl")
 include("nlsolve/klement.jl")
-# include("nlsolve/trustRegion.jl")
+include("nlsolve/trustRegion.jl")
 # include("nlsolve/halley.jl")
 # include("nlsolve/dfsane.jl")
 
@@ -59,7 +59,8 @@ end
 @setup_workload begin
     for T in (Float32, Float64)
         prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-        algs = [SimpleNewtonRaphson(), SimpleBroyden(), SimpleKlement()]
+        algs = [SimpleNewtonRaphson(), SimpleBroyden(), SimpleKlement(),
+            SimpleTrustRegion()]
 
         @compile_workload begin
             for alg in algs
@@ -97,8 +98,9 @@ end
     end
 end
 
-export SimpleBroyden, SimpleGaussNewton, SimpleKlement, SimpleNewtonRaphson
-# SimpleDFSane, SimpleTrustRegion, SimpleHalley, LBroyden
+export SimpleBroyden,
+    SimpleGaussNewton, SimpleKlement, SimpleNewtonRaphson, SimpleTrustRegion
+# SimpleDFSane, SimpleHalley, LBroyden
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
index 1b63656de..3d8debfe4 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
@@ -16,12 +16,10 @@ and static array problems.
   - `autodiff`: determines the backend used for the Jacobian. Defaults to
     `AutoForwardDiff()`. Valid choices are `AutoForwardDiff()` or `AutoFiniteDiff()`.
 """
-@concrete struct SimpleNewtonRaphson <: AbstractNewtonAlgorithm
-    ad
+@kwdef @concrete struct SimpleNewtonRaphson <: AbstractNewtonAlgorithm
+    autodiff = AutoForwardDiff()
 end
 
-SimpleNewtonRaphson(; autodiff = AutoForwardDiff()) = SimpleNewtonRaphson(autodiff)
-
 const SimpleGaussNewton = SimpleNewtonRaphson
 
 function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
@@ -30,13 +28,13 @@ function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresPr
     @bb x = copy(float(prob.u0))
     fx = _get_fx(prob, x)
     @bb xo = copy(x)
-    J, jac_cache = jacobian_cache(alg.ad, prob.f, fx, x, prob.p)
+    J, jac_cache = jacobian_cache(alg.autodiff, prob.f, fx, x, prob.p)
 
     abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
         termination_condition)
 
     for i in 1:maxiters
-        fx, dfx = value_and_jacobian(alg.ad, prob.f, fx, x, prob.p, jac_cache; J)
+        fx, dfx = value_and_jacobian(alg.autodiff, prob.f, fx, x, prob.p, jac_cache; J)
 
         if i == 1
             if iszero(fx)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index d644f5fb7..2420b7226 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -1,27 +1,17 @@
 """
-    SimpleTrustRegion(; chunk_size = Val{0}(), autodiff = Val{true}(),
-                        diff_type = Val{:forward}, max_trust_radius::Real = 0.0,
+    SimpleTrustRegion(; autodiff = AutoForwardDiff(), max_trust_radius::Real = 0.0,
                         initial_trust_radius::Real = 0.0, step_threshold::Real = 0.1,
                         shrink_threshold::Real = 0.25, expand_threshold::Real = 0.75,
                         shrink_factor::Real = 0.25, expand_factor::Real = 2.0,
                         max_shrink_times::Int = 32)
 
-A low-overhead implementation of a trust-region solver.
+A low-overhead implementation of a trust-region solver. This method is non-allocating on
+scalar and static array problems.
 
 ### Keyword Arguments
 
-  - `chunk_size`: the chunk size used by the internal ForwardDiff.jl automatic differentiation
-    system. This allows for multiple derivative columns to be computed simultaneously,
-    improving performance. Defaults to `0`, which is equivalent to using ForwardDiff.jl's
-    default chunk size mechanism. For more details, see the documentation for
-    [ForwardDiff.jl](https://juliadiff.org/ForwardDiff.jl/stable/).
-  - `autodiff`: whether to use forward-mode automatic differentiation for the Jacobian.
-    Note that this argument is ignored if an analytical Jacobian is passed; as that will be
-    used instead. Defaults to `Val{true}`, which means ForwardDiff.jl is used by default.
-    If `Val{false}`, then FiniteDiff.jl is used for finite differencing.
-  - `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
-    `Val{:forward}` for forward finite differences. For more details on the choices, see the
-    [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
+  - `autodiff`: determines the backend used for the Jacobian. Defaults to
+    `AutoForwardDiff()`. Valid choices are `AutoForwardDiff()` or `AutoFiniteDiff()`.
   - `max_trust_radius`: the maximum radius of the trust region. Defaults to
     `max(norm(f(u0)), maximum(u0) - minimum(u0))`.
   - `initial_trust_radius`: the initial trust region radius. Defaults to
@@ -47,143 +37,126 @@ A low-overhead implementation of a trust-region solver.
   - `max_shrink_times`: the maximum number of times to shrink the trust region radius in a
     row, `max_shrink_times` is exceeded, the algorithm returns. Defaults to `32`.
 """
-struct SimpleTrustRegion{T, CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
-    max_trust_radius::T
-    initial_trust_radius::T
-    step_threshold::T
-    shrink_threshold::T
-    expand_threshold::T
-    shrink_factor::T
-    expand_factor::T
-    max_shrink_times::Int
-    function SimpleTrustRegion(; chunk_size = Val{0}(),
-            autodiff = Val{true}(),
-            diff_type = Val{:forward},
-            max_trust_radius::Real = 0.0,
-            initial_trust_radius::Real = 0.0,
-            step_threshold::Real = 0.0001,
-            shrink_threshold::Real = 0.25,
-            expand_threshold::Real = 0.75,
-            shrink_factor::Real = 0.25,
-            expand_factor::Real = 2.0,
-            max_shrink_times::Int = 32)
-        new{typeof(initial_trust_radius),
-            SciMLBase._unwrap_val(chunk_size),
-            SciMLBase._unwrap_val(autodiff),
-            SciMLBase._unwrap_val(diff_type)}(max_trust_radius,
-            initial_trust_radius,
-            step_threshold,
-            shrink_threshold,
-            expand_threshold,
-            shrink_factor,
-            expand_factor,
-            max_shrink_times)
-    end
+@kwdef @concrete struct SimpleTrustRegion <: AbstractNewtonAlgorithm
+    autodiff = AutoForwardDiff()
+    max_trust_radius = 0.0
+    initial_trust_radius = 0.0
+    step_threshold = 0.0001
+    shrink_threshold = 0.25
+    expand_threshold = 0.75
+    shrink_factor = 0.25
+    expand_factor = 2.0
+    max_shrink_times::Int = 32
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem,
-        alg::SimpleTrustRegion, args...; abstol = nothing,
-        reltol = nothing,
-        maxiters = 1000, kwargs...)
-    f = Base.Fix2(prob.f, prob.p)
-    x = float(prob.u0)
-    T = typeof(x)
-    Δₘₐₓ = float(alg.max_trust_radius)
-    Δ = float(alg.initial_trust_radius)
-    η₁ = float(alg.step_threshold)
-    η₂ = float(alg.shrink_threshold)
-    η₃ = float(alg.expand_threshold)
-    t₁ = float(alg.shrink_factor)
-    t₂ = float(alg.expand_factor)
+function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        termination_condition = nothing, kwargs...)
+    @bb x = copy(float(prob.u0))
+    T = eltype(real(x))
+    Δₘₐₓ = T(alg.max_trust_radius)
+    Δ = T(alg.initial_trust_radius)
+    η₁ = T(alg.step_threshold)
+    η₂ = T(alg.shrink_threshold)
+    η₃ = T(alg.expand_threshold)
+    t₁ = T(alg.shrink_factor)
+    t₂ = T(alg.expand_factor)
     max_shrink_times = alg.max_shrink_times
 
-    if SciMLBase.isinplace(prob)
-        error("SimpleTrustRegion currently only supports out-of-place nonlinear problems")
-    end
+    fx = _get_fx(prob, x)
+    @bb xo = copy(x)
+    J, jac_cache = jacobian_cache(alg.autodiff, prob.f, fx, x, prob.p)
+    fx, ∇f = value_and_jacobian(alg.autodiff, prob.f, fx, x, prob.p, jac_cache; J)
 
-    atol = abstol !== nothing ? abstol :
-           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
-    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
-
-    if DiffEqBase.has_jac(prob.f)
-        ∇f = prob.f.jac(x, prob.p)
-        F = f(x)
-    elseif alg_autodiff(alg)
-        F, ∇f = value_derivative(f, x)
-    elseif x isa AbstractArray
-        F = f(x)
-        ∇f = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x), F)
-    else
-        F = f(x)
-        ∇f = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg), eltype(x), F)
-    end
+    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+        termination_condition)
 
     # Set default trust region radius if not specified by user.
-    if Δₘₐₓ == 0.0
-        Δₘₐₓ = max(norm(F), maximum(x) - minimum(x))
-    end
-    if Δ == 0.0
-        Δ = Δₘₐₓ / 11
-    end
+    Δₘₐₓ == 0 && (Δₘₐₓ = max(norm(fx), maximum(x) - minimum(x)))
+    Δ == 0 && (Δ = Δₘₐₓ / 11)
 
-    fₖ = 0.5 * norm(F)^2
+    fₖ = 0.5 * norm(fx)^2
     H = ∇f' * ∇f
-    g = ∇f' * F
+    g = ∇f' * fx
     shrink_counter = 0
 
+    @bb δsd = copy(x)
+    @bb δN_δsd = copy(x)
+    @bb δN = copy(x)
+    @bb Hδ = copy(x)
+    dogleg_cache = (; δsd, δN_δsd, δN)
+
+    F = fx
     for k in 1:maxiters
         # Solve the trust region subproblem.
-        δ = dogleg_method(∇f, F, g, Δ)
-        xₖ₊₁ = x + δ
-        Fₖ₊₁ = f(xₖ₊₁)
-        fₖ₊₁ = 0.5 * norm(Fₖ₊₁)^2
+        δ = dogleg_method!!(dogleg_cache, ∇f, fx, g, Δ)
+        @bb @. x = xo + δ
+
+        fx = __eval_f(prob, fx, x)
+
+        fₖ₊₁ = norm(fx)^2 / T(2)
 
         # Compute the ratio of the actual to predicted reduction.
-        model = -(δ' * g + 0.5 * δ' * H * δ)
-        r = (fₖ - fₖ₊₁) / model
+        @bb Hδ = H × δ
+        r = (fₖ₊₁ - fₖ) / (dot(δ', g) + dot(δ', Hδ) / T(2))
 
         # Update the trust region radius.
         if r < η₂
             Δ = t₁ * Δ
             shrink_counter += 1
-            if shrink_counter > max_shrink_times
-                return SciMLBase.build_solution(prob, alg, x, F;
-                    retcode = ReturnCode.Success)
-            end
+            shrink_counter > max_shrink_times && return build_solution(prob, alg, x, fx;
+                    retcode = ReturnCode.ConvergenceFailure)
         else
             shrink_counter = 0
         end
+
         if r > η₁
-            if isapprox(xₖ₊₁, x, atol = atol, rtol = rtol)
-                return SciMLBase.build_solution(prob, alg, xₖ₊₁, Fₖ₊₁;
-                    retcode = ReturnCode.Success)
-            end
+            # Termination Checks
+            tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
+            tc_sol !== nothing && return tc_sol
+
             # Take the step.
-            x = xₖ₊₁
-            F = Fₖ₊₁
-            if alg_autodiff(alg)
-                F, ∇f = value_derivative(f, x)
-            elseif x isa AbstractArray
-                ∇f = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x),
-                    F)
-            else
-                ∇f = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg),
-                    eltype(x),
-                    F)
-            end
-
-            iszero(F) &&
-                return SciMLBase.build_solution(prob, alg, x, F;
-                    retcode = ReturnCode.Success)
+            @bb @. xo = x
+
+            fx, ∇f = value_and_jacobian(alg.autodiff, prob.f, fx, x, prob.p, jac_cache; J)
 
             # Update the trust region radius.
-            if r > η₃ && norm(δ) ≈ Δ
-                Δ = min(t₂ * Δ, Δₘₐₓ)
-            end
+            (r > η₃) && (norm(δ) ≈ Δ) && (Δ = min(t₂ * Δ, Δₘₐₓ))
             fₖ = fₖ₊₁
-            H = ∇f' * ∇f
-            g = ∇f' * F
+
+            @bb H = transpose(∇f) × ∇f
+            @bb g = transpose(∇f) × fx
         end
     end
-    return SciMLBase.build_solution(prob, alg, x, F; retcode = ReturnCode.MaxIters)
+
+    return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+end
+
+function dogleg_method!!(cache, J, f, g, Δ)
+    (; δsd, δN_δsd, δN) = cache
+
+    # Compute the Newton step.
+    @bb δN .= J \ f
+    @bb δN .*= -1
+    # Test if the full step is within the trust region.
+    (norm(δN) ≤ Δ) && return δN
+
+    # Calcualte Cauchy point, optimum along the steepest descent direction.
+    @bb δsd .= g
+    @bb @. δsd *= -1
+    norm_δsd = norm(δsd)
+    if (norm_δsd ≥ Δ)
+        @bb @. δsd *= Δ / norm_δsd
+        return δsd
+    end
+
+    # Find the intersection point on the boundary.
+    @bb @. δN_δsd = δN - δsd
+    dot_δN_δsd = dot(δN_δsd, δN_δsd)
+    dot_δsd_δN_δsd = dot(δsd, δN_δsd)
+    dot_δsd = dot(δsd, δsd)
+    fact = dot_δsd_δN_δsd^2 - dot_δN_δsd * (dot_δsd - Δ^2)
+    tau = (-dot_δsd_δN_δsd + sqrt(fact)) / dot_δN_δsd
+    @bb @. δsd += tau * δN_δsd
+    return δsd
 end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 11caa7073..7b39fd6c7 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -170,31 +170,6 @@ function __init_identity_jacobian!!(J::StaticArray{S1, S2}) where {S1, S2}
         S1 * S2))
 end
 
-# function dogleg_method(J, f, g, Δ)
-#     # Compute the Newton step.
-#     δN = J \ (-f)
-#     # Test if the full step is within the trust region.
-#     if norm(δN) ≤ Δ
-#         return δN
-#     end
-
-#     # Calcualte Cauchy point, optimum along the steepest descent direction.
-#     δsd = -g
-#     norm_δsd = norm(δsd)
-#     if norm_δsd ≥ Δ
-#         return δsd .* Δ / norm_δsd
-#     end
-
-#     # Find the intersection point on the boundary.
-#     δN_δsd = δN - δsd
-#     dot_δN_δsd = dot(δN_δsd, δN_δsd)
-#     dot_δsd_δN_δsd = dot(δsd, δN_δsd)
-#     dot_δsd = dot(δsd, δsd)
-#     fact = dot_δsd_δN_δsd^2 - dot_δN_δsd * (dot_δsd - Δ^2)
-#     tau = (-dot_δsd_δN_δsd + sqrt(fact)) / dot_δN_δsd
-#     return δsd + tau * δN_δsd
-# end
-
 @inline _vec(v) = vec(v)
 @inline _vec(v::Number) = v
 @inline _vec(v::AbstractVector) = v

From 82342fd64be1f18818a6c48043f68e7db89fca92 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 24 Nov 2023 14:58:00 -0500
Subject: [PATCH 231/700] Fix Limited Memory Broyden

---
 lib/SimpleNonlinearSolve/README.md            |   2 +
 .../src/SimpleNonlinearSolve.jl               |  48 ++---
 lib/SimpleNonlinearSolve/src/ad.jl            |  69 +++---
 .../src/nlsolve/lbroyden.jl                   | 199 ++++++++----------
 .../src/nlsolve/trustRegion.jl                |   9 +-
 lib/SimpleNonlinearSolve/src/utils.jl         |  27 ++-
 6 files changed, 167 insertions(+), 187 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
index 0f52b1065..6bba38ff1 100644
--- a/lib/SimpleNonlinearSolve/README.md
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -50,3 +50,5 @@ For more details on the bracketing methods, refer to the [Tutorials](https://doc
   - `Broyden` and `Klement` have been renamed to `SimpleBroyden` and `SimpleKlement` to
     avoid conflicts with `NonlinearSolve.jl`'s `GeneralBroyden` and `GeneralKlement`, which
     will be renamed to `Broyden` and `Klement` in the future.
+  - `LBroyden` has been renamed to `SimpleLimitedMemoryBroyden` to make it consistent with
+    `NonlinearSolve.jl`'s `LimitedMemoryBroyden`.
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 79a4d3f53..707f543a4 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -13,7 +13,7 @@ import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidat
     import ForwardDiff: Dual
     import MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
     import SciMLBase: AbstractNonlinearAlgorithm, build_solution, isinplace
-    import StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray
+    import StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, MMatrix, Size
 end
 
 @reexport using ADTypes, SciMLBase
@@ -24,16 +24,16 @@ abstract type AbstractNewtonAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm e
 
 include("utils.jl")
 
-# Nonlinear Solvera
+## Nonlinear Solvers
 include("nlsolve/raphson.jl")
 include("nlsolve/broyden.jl")
-# include("nlsolve/lbroyden.jl")
+include("nlsolve/lbroyden.jl")
 include("nlsolve/klement.jl")
 include("nlsolve/trustRegion.jl")
 # include("nlsolve/halley.jl")
 # include("nlsolve/dfsane.jl")
 
-# Interval Nonlinear Solvers
+## Interval Nonlinear Solvers
 include("bracketing/bisection.jl")
 include("bracketing/falsi.jl")
 include("bracketing/ridder.jl")
@@ -42,7 +42,7 @@ include("bracketing/alefeld.jl")
 include("bracketing/itp.jl")
 
 # AD
-# include("ad.jl")
+include("ad.jl")
 
 ## Default algorithm
 
@@ -58,34 +58,22 @@ end
 
 @setup_workload begin
     for T in (Float32, Float64)
-        prob_no_brack = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-        algs = [SimpleNewtonRaphson(), SimpleBroyden(), SimpleKlement(),
-            SimpleTrustRegion()]
-
-        @compile_workload begin
-            for alg in algs
-                solve(prob_no_brack, alg, abstol = T(1e-2))
-            end
-        end
+        prob_no_brack_scalar = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
+        prob_no_brack_iip = NonlinearProblem{true}((du, u, p) -> du .= u .* u .- p,
+            T.([1.0, 1.0, 1.0]), T(2))
+        prob_no_brack_oop = NonlinearProblem{false}((u, p) -> u .* u .- p,
+            T.([1.0, 1.0, 1.0]), T(2))
 
-        prob_no_brack = NonlinearProblem{true}((du, u, p) -> du .= u .* u .- p,
-            T.([1.0, 1.0]), T(2))
+        algs = [SimpleNewtonRaphson(), SimpleBroyden(), SimpleKlement(),
+            SimpleTrustRegion(), SimpleLimitedMemoryBroyden(; threshold = 2)]
 
         @compile_workload begin
             for alg in algs
-                solve(prob_no_brack, alg, abstol = T(1e-2))
-            end
-        end
-
-        #=
-        for alg in (SimpleNewtonRaphson,)
-            for u0 in ([1., 1.], StaticArraysCore.SA[1.0, 1.0])
-                u0 = T.(.1)
-                probN = NonlinearProblem{false}((u,p) -> u .* u .- p, u0, T(2))
-                solve(probN, alg(), tol = T(1e-2))
+                solve(prob_no_brack_scalar, alg, abstol = T(1e-2))
+                solve(prob_no_brack_iip, alg, abstol = T(1e-2))
+                solve(prob_no_brack_oop, alg, abstol = T(1e-2))
             end
         end
-        =#
 
         prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p,
             T.((0.0, 2.0)), T(2))
@@ -98,9 +86,9 @@ end
     end
 end
 
-export SimpleBroyden,
-    SimpleGaussNewton, SimpleKlement, SimpleNewtonRaphson, SimpleTrustRegion
-# SimpleDFSane, SimpleHalley, LBroyden
+export SimpleBroyden, SimpleGaussNewton, SimpleKlement, SimpleLimitedMemoryBroyden,
+    SimpleNewtonRaphson, SimpleTrustRegion
+# SimpleDFSane, SimpleHalley
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index b0fd9f11c..a13ae0e6f 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -1,7 +1,7 @@
 function scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     f = prob.f
     p = value(prob.p)
-
+    u0 = value(prob.u0)
     if prob isa IntervalNonlinearProblem
         tspan = value(prob.tspan)
         newprob = IntervalNonlinearProblem(f, tspan, p; prob.kwargs...)
@@ -13,66 +13,57 @@ function scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     sol = solve(newprob, alg, args...; kwargs...)
 
     uu = sol.u
-    if p isa Number
-        f_p = ForwardDiff.derivative(Base.Fix1(f, uu), p)
-    else
-        f_p = ForwardDiff.gradient(Base.Fix1(f, uu), p)
-    end
+    f_p = scalar_nlsolve_∂f_∂p(f, uu, p)
+    f_x = scalar_nlsolve_∂f_∂u(f, uu, p)
+
+    z_arr = -inv(f_x) * f_p
 
-    f_x = ForwardDiff.derivative(Base.Fix2(f, p), uu)
     pp = prob.p
-    sumfun = let f_x′ = -f_x
-        ((fp, p),) -> (fp / f_x′) * ForwardDiff.partials(p)
+    sumfun = ((z, p),) -> map(zᵢ -> zᵢ * ForwardDiff.partials(p), z)
+    if uu isa Number
+        partials = sum(sumfun, zip(z_arr, pp))
+    elseif p isa Number
+        partials = sumfun((z_arr, pp))
+    else
+        partials = sum(sumfun, zip(eachcol(z_arr), pp))
     end
-    partials = sum(sumfun, zip(f_p, pp))
+
     return sol, partials
 end
 
-function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
-            iip,
-            <:Dual{T, V, P}},
-        alg::AbstractSimpleNonlinearSolveAlgorithm,
-        args...; kwargs...) where {iip, T, V, P}
+function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, SVector, <:AbstractArray},
+            false, <:Dual{T, V, P}}, alg::AbstractSimpleNonlinearSolveAlgorithm, args...;
+        kwargs...) where {T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
-    return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
-        retcode = sol.retcode)
+    dual_soln = scalar_nlsolve_dual_soln(sol.u, partials, prob.p)
+    return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode)
 end
-function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, StaticArraysCore.SVector},
-            iip,
-            <:AbstractArray{<:Dual{T, V, P}}},
-        alg::AbstractSimpleNonlinearSolveAlgorithm, args...;
-        kwargs...) where {iip, T, V, P}
+
+function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, SVector, <:AbstractArray},
+            false, <:AbstractArray{<:Dual{T, V, P}}},
+        alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...) where {T, V, P}
     sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
-    return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials), sol.resid;
-        retcode = sol.retcode)
+    dual_soln = scalar_nlsolve_dual_soln(sol.u, partials, prob.p)
+    return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode)
 end
 
 # avoid ambiguities
 for Alg in [Bisection]
     @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
-                <:Dual{T, V, P}},
-            alg::$Alg, args...;
-            kwargs...) where {uType, iip, T, V, P}
+                <:Dual{T, V, P}}, alg::$Alg, args...; kwargs...) where {uType, iip, T, V, P}
         sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
-        return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials),
-            sol.resid; retcode = sol.retcode,
+        dual_soln = scalar_nlsolve_dual_soln(sol.u, partials, prob.p)
+        return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode,
             left = Dual{T, V, P}(sol.left, partials),
             right = Dual{T, V, P}(sol.right, partials))
-        #return BracketingSolution(Dual{T,V,P}(sol.left, partials), Dual{T,V,P}(sol.right, partials), sol.retcode, sol.resid)
     end
     @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
-                <:AbstractArray{
-                    <:Dual{T,
-                        V,
-                        P},
-                }},
-            alg::$Alg, args...;
+                <:AbstractArray{<:Dual{T, V, P}}}, alg::$Alg, args...;
             kwargs...) where {uType, iip, T, V, P}
         sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
-        return SciMLBase.build_solution(prob, alg, Dual{T, V, P}(sol.u, partials),
-            sol.resid; retcode = sol.retcode,
+        dual_soln = scalar_nlsolve_dual_soln(sol.u, partials, prob.p)
+        return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode,
             left = Dual{T, V, P}(sol.left, partials),
             right = Dual{T, V, P}(sol.right, partials))
-        #return BracketingSolution(Dual{T,V,P}(sol.left, partials), Dual{T,V,P}(sol.right, partials), sol.retcode, sol.resid)
     end
 end
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index 482092151..4cc8ee025 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -1,144 +1,119 @@
 """
-    LBroyden(; batched = false,
-              termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-                                                                  abstol = nothing, reltol = nothing),
-              threshold::Int = 27)
+    SimpleLimitedMemoryBroyden(; threshold::Int = 27)
+    SimpleLimitedMemoryBroyden(; threshold::Val = Val(27))
 
 A limited memory implementation of Broyden. This method applies the L-BFGS scheme to
-Broyden's method.
+Broyden's method. This Alogrithm unfortunately cannot non-allocating for StaticArrays
+without compromising on the "simple" aspect.
 
-!!! warn
+If the threshold is larger than the problem size, then this method will use `SimpleBroyden`.
 
-    This method is not very stable and can diverge even for very simple problems. This has mostly been
-    tested for neural networks in DeepEquilibriumNetworks.jl.
+!!! warning
+
+    This method is not very stable and can diverge even for very simple problems. This has
+    mostly been tested for neural networks in DeepEquilibriumNetworks.jl.
 """
-struct LBroyden{batched, TC <: NLSolveTerminationCondition} <:
-       AbstractSimpleNonlinearSolveAlgorithm
-    termination_condition::TC
-    threshold::Int
-
-    function LBroyden(; batched = false, threshold::Int = 27,
-            termination_condition = NLSolveTerminationCondition(NLSolveTerminationMode.NLSolveDefault;
-                abstol = nothing,
-                reltol = nothing))
-        return new{batched, typeof(termination_condition)}(termination_condition, threshold)
-    end
-end
+struct SimpleLimitedMemoryBroyden{threshold} <: AbstractSimpleNonlinearSolveAlgorithm end
 
-@views function SciMLBase.__solve(prob::NonlinearProblem, alg::LBroyden{batched}, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000,
-        kwargs...) where {batched}
-    tc = alg.termination_condition
-    mode = DiffEqBase.get_termination_mode(tc)
-    threshold = min(maxiters, alg.threshold)
-    x = float(prob.u0)
-
-    batched && @assert ndims(x)==2 "Batched LBroyden only supports 2D arrays"
-
-    if x isa Number
-        restore_scalar = true
-        x = [x]
-        f = u -> prob.f(u[], prob.p)
-    else
-        f = Base.Fix2(prob.f, prob.p)
-        restore_scalar = false
-    end
+__get_threshold(::SimpleLimitedMemoryBroyden{threshold}) where {threshold} = Val(threshold)
 
-    fₙ = f(x)
-    T = eltype(x)
+function SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27))
+    return SimpleLimitedMemoryBroyden{SciMLBase._unwrap_val(threshold)}()
+end
 
-    if SciMLBase.isinplace(prob)
-        error("LBroyden currently only supports out-of-place nonlinear problems")
+@views function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyden,
+        args...; abstol = nothing, reltol = nothing, maxiters = 1000,
+        termination_condition = nothing, kwargs...)
+    @bb x = copy(float(prob.u0))
+    threshold = __get_threshold(alg)
+    η = min(SciMLBase._unwrap_val(threshold), maxiters)
+
+    # For scalar problems / if the threshold is larger than problem size just use Broyden
+    if x isa Number || length(x) ≤ η
+        return SciMLBase.__solve(prob, SimpleBroyden(), args...;
+            abstol, reltol, maxiters, termination_condition, kwargs...)
     end
 
-    U, Vᵀ = _init_lbroyden_state(batched, x, threshold)
+    fx = _get_fx(prob, x)
 
-    atol = abstol !== nothing ? abstol :
-           (tc.abstol !== nothing ? tc.abstol :
-            real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5))
-    rtol = reltol !== nothing ? reltol :
-           (tc.reltol !== nothing ? tc.reltol : eps(real(one(eltype(T))))^(4 // 5))
+    U, Vᵀ = __init_low_rank_jacobian(x, fx, threshold)
 
-    if mode ∈ DiffEqBase.SAFE_BEST_TERMINATION_MODES
-        error("LBroyden currently doesn't support SAFE_BEST termination modes")
-    end
+    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+        termination_condition)
+
+    @bb xo = copy(x)
+    @bb δx = copy(fx)
+    @bb δx .*= -1
+    @bb fo = copy(fx)
+    @bb δf = copy(fx)
 
-    storage = mode ∈ DiffEqBase.SAFE_TERMINATION_MODES ? NLSolveSafeTerminationResult() :
-              nothing
-    termination_condition = tc(storage)
+    @bb vᵀ_cache = copy(x)
+    Tcache = __lbroyden_threshold_cache(x, threshold)
+    @bb mat_cache = copy(x)
 
-    xₙ = x
-    xₙ₋₁ = x
-    fₙ₋₁ = fₙ
-    update = fₙ
     for i in 1:maxiters
-        xₙ = xₙ₋₁ .+ update
-        fₙ = f(xₙ)
-        Δxₙ = xₙ .- xₙ₋₁
-        Δfₙ = fₙ .- fₙ₋₁
+        @bb @. x = xo + δx
+        fx = __eval_f(prob, fx, x)
+        @bb @. δf = fx - fo
 
-        if termination_condition(restore_scalar ? [fₙ] : fₙ, xₙ, xₙ₋₁, atol, rtol)
-            xₙ = restore_scalar ? xₙ[] : xₙ
-            return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.Success)
-        end
+        # Termination Checks
+        tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
+        tc_sol !== nothing && return tc_sol
 
-        _U = selectdim(U, 1, 1:min(threshold, i))
-        _Vᵀ = selectdim(Vᵀ, 2, 1:min(threshold, i))
+        _U = selectdim(U, 2, 1:min(η, i - 1))
+        _Vᵀ = selectdim(Vᵀ, 1, 1:min(η, i - 1))
 
-        vᵀ = _rmatvec(_U, _Vᵀ, Δxₙ)
-        mvec = _matvec(_U, _Vᵀ, Δfₙ)
-        u = (Δxₙ .- mvec) ./ (sum(vᵀ .* Δfₙ) .+ convert(T, 1e-5))
+        vᵀ = _rmatvec!!(vᵀ_cache, Tcache, _U, _Vᵀ, δx)
+        mvec = _matvec!!(mat_cache, Tcache, _U, _Vᵀ, δf)
+        d = dot(vᵀ, δf)
+        @bb @. δx = (δx - mvec) / d
 
-        selectdim(Vᵀ, 2, mod1(i, threshold)) .= vᵀ
-        selectdim(U, 1, mod1(i, threshold)) .= u
+        selectdim(U, 2, mod1(i, η)) .= δx
+        selectdim(Vᵀ, 1, mod1(i, η)) .= vᵀ
 
-        update = -_matvec(selectdim(U, 1, 1:min(threshold, i + 1)),
-            selectdim(Vᵀ, 2, 1:min(threshold, i + 1)), fₙ)
+        _U = selectdim(U, 2, 1:min(η, i))
+        _Vᵀ = selectdim(Vᵀ, 1, 1:min(η, i))
+        δx = _matvec!!(δx, Tcache, _U, _Vᵀ, fx)
+        @bb @. δx *= -1
 
-        xₙ₋₁ = xₙ
-        fₙ₋₁ = fₙ
+        @bb copyto!(xo, x)
+        @bb copyto!(fo, fx)
     end
 
-    xₙ = restore_scalar ? xₙ[] : xₙ
-    return SciMLBase.build_solution(prob, alg, xₙ, fₙ; retcode = ReturnCode.MaxIters)
+    return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
 end
 
-function _init_lbroyden_state(batched::Bool, x, threshold)
-    T = eltype(x)
-    if batched
-        U = fill!(similar(x, (threshold, size(x, 1), size(x, 2))), zero(T))
-        Vᵀ = fill!(similar(x, (size(x, 1), threshold, size(x, 2))), zero(T))
-    else
-        U = fill!(similar(x, (threshold, length(x))), zero(T))
-        Vᵀ = fill!(similar(x, (length(x), threshold)), zero(T))
+function _rmatvec!!(y, xᵀU, U, Vᵀ, x)
+    # xᵀ × (-I + UVᵀ)
+    η = size(U, 2)
+    if η == 0
+        @bb @. y = -x
+        return y
     end
-    return U, Vᵀ
+    x_ = vec(x)
+    xᵀU_ = view(xᵀU, 1:η)
+    @bb xᵀU_ = transpose(U) × x_
+    @bb y = transpose(Vᵀ) × xᵀU_
+    @bb @. y -= x
+    return y
 end
 
-function _rmatvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
-        x::Union{<:AbstractVector, <:Number})
-    length(U) == 0 && return x
-    return -x .+ vec((x' * Vᵀ) * U)
-end
-
-function _rmatvec(U::AbstractArray{T1, 3}, Vᵀ::AbstractArray{T2, 3},
-        x::AbstractMatrix) where {T1, T2}
-    length(U) == 0 && return x
-    Vᵀx = sum(Vᵀ .* reshape(x, size(x, 1), 1, size(x, 2)); dims = 1)
-    return -x .+ _drdims_sum(U .* permutedims(Vᵀx, (2, 1, 3)); dims = 1)
-end
-
-function _matvec(U::AbstractMatrix, Vᵀ::AbstractMatrix,
-        x::Union{<:AbstractVector, <:Number})
-    length(U) == 0 && return x
-    return -x .+ vec(Vᵀ * (U * x))
+function _matvec!!(y, Vᵀx, U, Vᵀ, x)
+    # (-I + UVᵀ) × x
+    η = size(U, 2)
+    if η == 0
+        @bb @. y = -x
+        return y
+    end
+    x_ = vec(x)
+    Vᵀx_ = view(Vᵀx, 1:η)
+    @bb Vᵀx_ = Vᵀ × x_
+    @bb y = U × Vᵀx_
+    @bb @. y -= x
+    return y
 end
 
-function _matvec(U::AbstractArray{T1, 3}, Vᵀ::AbstractArray{T2, 3},
-        x::AbstractMatrix) where {T1, T2}
-    length(U) == 0 && return x
-    xUᵀ = sum(reshape(x, size(x, 1), 1, size(x, 2)) .* permutedims(U, (2, 1, 3)); dims = 1)
-    return -x .+ _drdims_sum(xUᵀ .* Vᵀ; dims = 2)
+__lbroyden_threshold_cache(x, ::Val{threshold}) where {threshold} = similar(x, threshold)
+function __lbroyden_threshold_cache(x::SArray, ::Val{threshold}) where {threshold}
+    return SArray{Tuple{threshold}, eltype(x)}(ntuple(_ -> zero(eltype(x)), threshold))
 end
-
-_drdims_sum(args...; dims = :) = dropdims(sum(args...; dims); dims)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index 2420b7226..3c3ad60b4 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -1,9 +1,8 @@
 """
     SimpleTrustRegion(; autodiff = AutoForwardDiff(), max_trust_radius::Real = 0.0,
-                        initial_trust_radius::Real = 0.0, step_threshold::Real = 0.1,
-                        shrink_threshold::Real = 0.25, expand_threshold::Real = 0.75,
-                        shrink_factor::Real = 0.25, expand_factor::Real = 2.0,
-                        max_shrink_times::Int = 32)
+        initial_trust_radius::Real = 0.0, step_threshold::Real = 0.1,
+        shrink_threshold::Real = 0.25, expand_threshold::Real = 0.75,
+        shrink_factor::Real = 0.25, expand_factor::Real = 2.0, max_shrink_times::Int = 32)
 
 A low-overhead implementation of a trust-region solver. This method is non-allocating on
 scalar and static array problems.
@@ -105,7 +104,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
             Δ = t₁ * Δ
             shrink_counter += 1
             shrink_counter > max_shrink_times && return build_solution(prob, alg, x, fx;
-                    retcode = ReturnCode.ConvergenceFailure)
+                retcode = ReturnCode.ConvergenceFailure)
         else
             shrink_counter = 0
         end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 7b39fd6c7..396a134da 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -170,6 +170,20 @@ function __init_identity_jacobian!!(J::StaticArray{S1, S2}) where {S1, S2}
         S1 * S2))
 end
 
+function __init_low_rank_jacobian(u::StaticArray{S1, T1}, fu::StaticArray{S2, T2},
+        ::Val{threshold}) where {S1, S2, T1, T2, threshold}
+    T = promote_type(T1, T2)
+    fuSize, uSize = Size(fu), Size(u)
+    Vᵀ = MArray{Tuple{threshold, prod(uSize)}, T}(undef)
+    U = MArray{Tuple{prod(fuSize), threshold}, T}(undef)
+    return U, Vᵀ
+end
+function __init_low_rank_jacobian(u, fu, ::Val{threshold}) where {threshold}
+    Vᵀ = similar(u, threshold, length(u))
+    U = similar(u, length(fu), threshold)
+    return U, Vᵀ
+end
+
 @inline _vec(v) = vec(v)
 @inline _vec(v::Number) = v
 @inline _vec(v::AbstractVector) = v
@@ -200,10 +214,17 @@ end
 
 # Termination Conditions Support
 # Taken directly from NonlinearSolve.jl
+# The default here is different from NonlinearSolve since the userbases are assumed to be
+# different. NonlinearSolve is more for robust / cached solvers while SimpleNonlinearSolve
+# is meant for low overhead solvers, users can opt into the other termination modes but the
+# default is to use the least overhead version.
 function init_termination_cache(abstol, reltol, du, u, ::Nothing)
-    return init_termination_cache(abstol, reltol, du, u, AbsSafeBestTerminationMode())
+    return init_termination_cache(abstol, reltol, du, u, AbsNormTerminationMode())
 end
 function init_termination_cache(abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
+    T = promote_type(eltype(du), eltype(u))
+    abstol !== nothing && (abstol = T(abstol))
+    reltol !== nothing && (reltol = T(reltol))
     tc_cache = init(du, u, tc; abstol, reltol)
     return DiffEqBase.get_abstol(tc_cache), DiffEqBase.get_reltol(tc_cache), tc_cache
 end
@@ -257,5 +278,9 @@ function check_termination(tc_cache, fx, x, xo, prob, alg,
     return nothing
 end
 
+@inline value(x) = x
+@inline value(x::Dual) = ForwardDiff.value(x)
+@inline value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
+
 @inline __eval_f(prob, fx, x) = isinplace(prob) ? (prob.f(fx, x, prob.p); fx) :
                                 prob.f(x, prob.p)

From 0c2b3658e59c2a62218f4650d98346db50fd5be2 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 24 Nov 2023 15:50:33 -0500
Subject: [PATCH 232/700] Type stability fixes

---
 lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl | 4 ++--
 lib/SimpleNonlinearSolve/src/utils.jl           | 6 ++----
 2 files changed, 4 insertions(+), 6 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
index 3d8debfe4..22f7fba84 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
@@ -47,8 +47,8 @@ function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresPr
         end
 
         @bb copyto!(xo, x)
-        Δx = _restructure(x, dfx \ _vec(fx))
-        @bb x .-= Δx
+        δx = _restructure(x, dfx \ _vec(fx))
+        @bb x .-= δx
     end
 
     return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 396a134da..464495500 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -161,13 +161,11 @@ function __init_identity_jacobian!!(J)
 end
 function __init_identity_jacobian(u::StaticArray, fu)
     S1, S2 = length(fu), length(u)
-    J = SMatrix{S1, S2, eltype(u)}(ntuple(i -> ifelse(i ∈ 1:(S1 + 1):(S1 * S2), 1, 0),
-        S1 * S2))
+    J = SMatrix{S1, S2, eltype(u)}(I)
     return J
 end
 function __init_identity_jacobian!!(J::StaticArray{S1, S2}) where {S1, S2}
-    return SMMatrix{S1, S2, eltype(J)}(ntuple(i -> ifelse(i ∈ 1:(S1 + 1):(S1 * S2), 1, 0),
-        S1 * S2))
+    return SMMatrix{S1, S2, eltype(J)}(I)
 end
 
 function __init_low_rank_jacobian(u::StaticArray{S1, T1}, fu::StaticArray{S2, T2},

From 8f6d66db21219c233f1e0c1910275720c59b8335 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 24 Nov 2023 22:24:14 -0500
Subject: [PATCH 233/700] Fix Halley's method

---
 .../src/SimpleNonlinearSolve.jl               |  11 +-
 .../src/nlsolve/dfsane.jl                     | 198 ++++++++----------
 .../src/nlsolve/halley.jl                     | 143 +++++--------
 lib/SimpleNonlinearSolve/src/utils.jl         |  43 ++++
 4 files changed, 186 insertions(+), 209 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 707f543a4..a9e7d7b82 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -30,8 +30,8 @@ include("nlsolve/broyden.jl")
 include("nlsolve/lbroyden.jl")
 include("nlsolve/klement.jl")
 include("nlsolve/trustRegion.jl")
-# include("nlsolve/halley.jl")
-# include("nlsolve/dfsane.jl")
+include("nlsolve/halley.jl")
+include("nlsolve/dfsane.jl")
 
 ## Interval Nonlinear Solvers
 include("bracketing/bisection.jl")
@@ -64,7 +64,7 @@ end
         prob_no_brack_oop = NonlinearProblem{false}((u, p) -> u .* u .- p,
             T.([1.0, 1.0, 1.0]), T(2))
 
-        algs = [SimpleNewtonRaphson(), SimpleBroyden(), SimpleKlement(),
+        algs = [SimpleNewtonRaphson(), SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
             SimpleTrustRegion(), SimpleLimitedMemoryBroyden(; threshold = 2)]
 
         @compile_workload begin
@@ -86,9 +86,8 @@ end
     end
 end
 
-export SimpleBroyden, SimpleGaussNewton, SimpleKlement, SimpleLimitedMemoryBroyden,
-    SimpleNewtonRaphson, SimpleTrustRegion
-# SimpleDFSane, SimpleHalley
+export SimpleBroyden, SimpleDFSane, SimpleGaussNewton, SimpleHalley, SimpleKlement,
+    SimpleLimitedMemoryBroyden, SimpleNewtonRaphson, SimpleTrustRegion
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 0ecc545f6..657f760cb 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -53,117 +53,91 @@ end
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
         termination_condition = nothing, kwargs...)
+    x = float(copy(prob.u0))
+    fx = _get_fx(prob, x)
+    T = eltype(x)
 
-    # f = isinplace(prob) ? (du, u) -> prob.f(du, u, prob.p) : u -> prob.f(u, prob.p)
-
-    # x = float(prob.u0)
-    # fx = _get_fx(prob, x)
-    # T = eltype(x)
-
-    # σ_min = T(alg.σ_min)
-    # σ_max = T(alg.σ_max)
-    # σ_k = T(alg.σ_1)
-
-    # M = alg.M
-    # γ = T(alg.γ)
-    # τ_min = T(alg.τ_min)
-    # τ_max = T(alg.τ_max)
-    # nexp = alg.nexp
-    # η_strategy = alg.η_strategy
-
-    # abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
-    #     termination_condition)
-
-    # ff = if isinplace(prob)
-    #     function (_fx, x)
-    #         f(_fx, x)
-    #         f_k = norm(_fx)^nexp
-    #         return f_k, _fx
-    #     end
-    # else
-    #     function (x)
-    #         _fx = f(x)
-    #         f_k = norm(_fx)^nexp
-    #         return f_k, _fx
-    #     end
-    # end
-
-    # generate_history(f_k, M) = fill(f_k, M)
-
-    # f_k, F_k = isinplace(prob) ? ff(fx, x) : ff(x)
-    # F_k = __copy(F_k)
-    # α_1 = one(T)
-    # f_1 = f_k
-    # history_f_k = generate_history(f_k, M)
-
-    # # Generate the cache
-    # d, xo, x_cache, δx, δf = __copy(x), __copy(x), __copy(x), __copy(x), __copy(x)
-    # α_tp, α_tm = __copy(x), __copy(x)
-
-    # for k in 1:maxiters
-    #     # Spectral parameter range check
-    #     σ_k = sign(σ_k) * clamp(abs(σ_k), σ_min, σ_max)
-
-    #     # Line search direction
-    #     d = __broadcast!!(d, *, -σ_k, F_k)
-
-    #     η = η_strategy(f_1, k, x, F_k)
-    #     f̄ = maximum(history_f_k)
-    #     α_p = α_1
-    #     α_m = α_1
-
-    #     x_cache = __broadcast!!(x_cache, *, α_p, d)
-    #     x = __broadcast!!(x, +, x_cache)
-
-    #     f_new, F_new = isinplace(prob) ? ff(fx, x) : ff(x)
-
-    #     # FIXME: This part is not correctly implemented
-    #     while true
-    #         criteria = f̄ + η - γ * α_p^2 * f_k
-    #         f_new ≤ criteria && break
-
-    #         if ArrayInterface.can_setindex(α_tp) && !(x isa Number)
-    #             @. α_tp = α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
-    #         else
-    #             α_tp = @. α_p^2 * f_k / (f_new + (2 * α_p - 1) * f_k)
-    #         end
-    #         x_cache = __broadcast!!(x_cache, *, α_m, d)
-    #         x = __broadcast!!(x, -, x_cache)
-    #         f_new, F_new = isinplace(prob) ? ff(fx, x) : ff(x)
-
-    #         f_new ≤ criteria && break
-
-    #         if ArrayInterface.can_setindex(α_tm) && !(x isa Number)
-    #             @. α_tm = α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
-    #             @. α_p = clamp(α_tp, τ_min * α_p, τ_max * α_p)
-    #             @. α_m = clamp(α_tm, τ_min * α_m, τ_max * α_m)
-    #         else
-    #             α_tm = @. α_m^2 * f_k / (f_new + (2 * α_m - 1) * f_k)
-    #             α_p = @. clamp(α_tp, τ_min * α_p, τ_max * α_p)
-    #             α_m = @. clamp(α_tm, τ_min * α_m, τ_max * α_m)
-    #         end
-    #         x_cache = __broadcast!!(x_cache, *, α_p, d)
-    #         x = __broadcast!!(x, +, x_cache)
-    #         f_new, F_new = isinplace(prob) ? ff(fx, x) : ff(x)
-    #     end
-
-    #     tc_sol = check_termination(tc_cache, f_new, x, xo, prob, alg)
-    #     tc_sol !== nothing && return tc_sol
-
-    #     # Update spectral parameter
-    #     δx = __broadcast!!(δx, -, x, xo)
-    #     δf = __broadcast!!(δf, -, F_new, F_k)
-
-    #     σ_k = dot(δx, δx) / dot(δx, δf)
-
-    #     # Take step
-    #     xo = __copyto!!(xo, x)
-    #     F_k = __copyto!!(F_k, F_new)
-    #     f_k = f_new
-
-    #     # Store function value
-    #     history_f_k[k % M + 1] = f_new
-    # end
-
-    # return build_solution(prob, alg, x, F_k; retcode = ReturnCode.MaxIters)
+    σ_min = T(alg.σ_min)
+    σ_max = T(alg.σ_max)
+    σ_k = T(alg.σ_1)
+
+    (; M, nexp, η_strategy) = alg
+    γ = T(alg.γ)
+    τ_min = T(alg.τ_min)
+    τ_max = T(alg.τ_max)
+
+    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+        termination_condition)
+
+    fx_norm = norm(fx)^nexp
+    α_1 = one(T)
+    f_1 = fx_norm
+    history_f_k = fill(fx_norm, M)
+
+    # Generate the cache
+    @bb d = copy(x)
+    @bb xo = copy(x)
+    @bb x_cache = copy(x)
+    @bb δx = copy(x)
+    @bb fxo = copy(fx)
+    @bb δf = copy(fx)
+
+    k = 0
+    while k < maxiters
+        # Spectral parameter range check
+        σ_k = sign(σ_k) * clamp(abs(σ_k), σ_min, σ_max)
+
+        # Line search direction
+        @bb @. d = -σ_k * fx
+
+        η = η_strategy(f_1, k, x, fx)
+        f_bar = maximum(history_f_k)
+        α_p = α_1
+        α_m = α_1
+
+        @bb @. x += α_p * d
+
+        fx = __eval_f(prob, fx, x)
+        fx_norm_new = norm(fx)^nexp
+
+        while k < maxiters
+            fx_norm_new ≤ (f_bar + η - γ * α_p^2 * fx_norm) && break
+
+            α_p = α_p^2 * fx_norm / (fx_norm_new + (T(2) * α_p - T(1)) * fx_norm)
+            @bb @. x -= α_m * d
+
+            fx = __eval_f(prob, fx, x)
+            fx_norm_new = norm(fx)^nexp
+
+            fx_norm_new ≤ (f_bar + η - γ * α_m^2 * fx_norm) && break
+
+            α_tm = α_m^2 * fx_norm / (fx_norm_new + (T(2) * α_m - T(1)) * fx_norm)
+            α_p = clamp(α_p, τ_min * α_p, τ_max * α_p)
+            α_m = clamp(α_tm, τ_min * α_m, τ_max * α_m)
+            @bb @. x += α_p * d
+
+            fx = __eval_f(prob, fx, x)
+            fx_norm_new = norm(fx)^nexp
+        end
+
+        tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
+        tc_sol !== nothing && return tc_sol
+
+        # Update spectral parameter
+        @bb @. δx = x - xo
+        @bb @. δf = fx - fxo
+
+        σ_k = dot(δx, δx) / dot(δx, δf)
+
+        # Take step
+        @bb copyto!(xo, x)
+        @bb copyto!(fxo, fx)
+        fx_norm = fx_norm_new
+
+        # Store function value
+        history_f_k[mod1(k, M)] = fx_norm_new
+        k += 1
+    end
+
+    return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index 8131acada..3e6e4d55f 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -1,11 +1,8 @@
 """
-```julia
-SimpleHalley(; chunk_size = Val{0}(), autodiff = Val{true}(),
-    diff_type = Val{:forward})
-```
+    SimpleHalley(autodiff)
+    SimpleHalley(; autodiff = AutoForwardDiff())
 
-A low-overhead implementation of SimpleHalley's Method. This method is non-allocating on scalar
-and static array problems.
+A low-overhead implementation of Halley's Method.
 
 !!! note
 
@@ -15,104 +12,68 @@ and static array problems.
 
 ### Keyword Arguments
 
-  - `chunk_size`: the chunk size used by the internal ForwardDiff.jl automatic differentiation
-    system. This allows for multiple derivative columns to be computed simultaneously,
-    improving performance. Defaults to `0`, which is equivalent to using ForwardDiff.jl's
-    default chunk size mechanism. For more details, see the documentation for
-    [ForwardDiff.jl](https://juliadiff.org/ForwardDiff.jl/stable/).
-  - `autodiff`: whether to use forward-mode automatic differentiation for the Jacobian.
-    Note that this argument is ignored if an analytical Jacobian is passed; as that will be
-    used instead. Defaults to `Val{true}`, which means ForwardDiff.jl is used by default.
-    If `Val{false}`, then FiniteDiff.jl is used for finite differencing.
-  - `diff_type`: the type of finite differencing used if `autodiff = false`. Defaults to
-    `Val{:forward}` for forward finite differences. For more details on the choices, see the
-    [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) documentation.
+  - `autodiff`: determines the backend used for the Hessian. Defaults to
+    `AutoForwardDiff()`. Valid choices are `AutoForwardDiff()` or `AutoFiniteDiff()`.
 """
-struct SimpleHalley{CS, AD, FDT} <: AbstractNewtonAlgorithm{CS, AD, FDT}
-    function SimpleHalley(; chunk_size = Val{0}(), autodiff = Val{true}(),
-            diff_type = Val{:forward})
-        new{SciMLBase._unwrap_val(chunk_size), SciMLBase._unwrap_val(autodiff),
-            SciMLBase._unwrap_val(diff_type)}()
-    end
+@kwdef @concrete struct SimpleHalley <: AbstractNewtonAlgorithm
+    autodiff = AutoForwardDiff()
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem,
-        alg::SimpleHalley, args...; abstol = nothing,
-        reltol = nothing,
-        maxiters = 1000, kwargs...)
-    f = Base.Fix2(prob.f, prob.p)
-    x = float(prob.u0)
-    fx = f(x)
-    if isa(x, AbstractArray)
-        n = length(x)
-    end
-    T = typeof(x)
-
-    if SciMLBase.isinplace(prob)
+function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        termination_condition = nothing, kwargs...)
+    isinplace(prob) &&
         error("SimpleHalley currently only supports out-of-place nonlinear problems")
-    end
 
-    atol = abstol !== nothing ? abstol :
-           real(oneunit(eltype(T))) * (eps(real(one(eltype(T)))))^(4 // 5)
-    rtol = reltol !== nothing ? reltol : eps(real(one(eltype(T))))^(4 // 5)
+    x = copy(float(prob.u0))
+    fx = _get_fx(prob, x)
+    T = eltype(x)
 
-    if x isa Number
-        xo = oftype(one(eltype(x)), Inf)
+    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+        termination_condition)
+
+    @bb xo = copy(x)
+
+    if setindex_trait(x) === CanSetindex()
+        A = similar(x, length(x), length(x))
+        Aaᵢ = similar(x, length(x))
+        cᵢ = similar(x)
     else
-        xo = map(x -> oftype(one(eltype(x)), Inf), x)
+        A = x
+        Aaᵢ = x
+        cᵢ = x
     end
 
     for i in 1:maxiters
-        if alg_autodiff(alg)
-            if isa(x, Number)
-                fx = f(x)
-                dfx = ForwardDiff.derivative(f, x)
-                d2fx = ForwardDiff.derivative(x -> ForwardDiff.derivative(f, x), x)
-            else
-                fx = f(x)
-                dfx = ForwardDiff.jacobian(f, x)
-                d2fx = ForwardDiff.jacobian(x -> ForwardDiff.jacobian(f, x), x)
-                ai = -(dfx \ fx)
-                A = reshape(d2fx * ai, (n, n))
-                bi = (dfx) \ (A * ai)
-                ci = (ai .* ai) ./ (ai .+ (0.5 .* bi))
-            end
-        else
-            if isa(x, Number)
-                fx = f(x)
-                dfx = FiniteDiff.finite_difference_derivative(f, x, diff_type(alg),
-                    eltype(x))
-                d2fx = FiniteDiff.finite_difference_derivative(x -> FiniteDiff.finite_difference_derivative(f,
-                        x),
-                    x,
-                    diff_type(alg), eltype(x))
-            else
-                fx = f(x)
-                dfx = FiniteDiff.finite_difference_jacobian(f, x, diff_type(alg), eltype(x))
-                d2fx = FiniteDiff.finite_difference_jacobian(x -> FiniteDiff.finite_difference_jacobian(f,
-                        x),
-                    x,
-                    diff_type(alg), eltype(x))
-                ai = -(dfx \ fx)
-                A = reshape(d2fx * ai, (n, n))
-                bi = (dfx) \ (A * ai)
-                ci = (ai .* ai) ./ (ai .+ (0.5 .* bi))
+        # Hessian Computation is unfortunately type unstable
+        fx, dfx, d2fx = compute_jacobian_and_hessian(alg.autodiff, prob, fx, x)
+        setindex_trait(x) === CannotSetindex() && (A = dfx)
+
+        aᵢ = dfx \ _vec(fx)
+        A_ = _vec(A)
+        @bb A_ = d2fx × aᵢ
+        A = _restructure(A, A_)
+
+        @bb Aaᵢ = A × aᵢ
+        @bb A .*= -1
+        bᵢ = dfx \ Aaᵢ
+
+        @bb @. cᵢ = (aᵢ * aᵢ) / (-aᵢ + (T(0.5) * bᵢ))
+
+        if i == 1
+            if iszero(fx)
+                return build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
             end
-        end
-        iszero(fx) &&
-            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
-        if isa(x, Number)
-            Δx = (2 * dfx^2 - fx * d2fx) \ (2fx * dfx)
-            x -= Δx
         else
-            Δx = ci
-            x += Δx
-        end
-        if isapprox(x, xo, atol = atol, rtol = rtol)
-            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
+            # Termination Checks
+            tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
+            tc_sol !== nothing && return tc_sol
         end
-        xo = x
+
+        @bb @. x += cᵢ
+
+        @bb copyto!(xo, x)
     end
 
-    return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+    return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
 end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 464495500..7dbd8e422 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -146,6 +146,49 @@ end
 
 jacobian_cache(ad, f::F, y, x::Number, p) where {F} = nothing, nothing
 
+function compute_jacobian_and_hessian(ad::AutoForwardDiff, prob, _, x::Number)
+    fx = prob.f(x, prob.p)
+    J_fn = Base.Fix1(ForwardDiff.derivative, Base.Fix2(prob.f, prob.p))
+    dfx = J_fn(x)
+    d2fx = ForwardDiff.derivative(J_fn, x)
+    return fx, dfx, d2fx
+end
+
+function compute_jacobian_and_hessian(ad::AutoForwardDiff, prob, fx, x)
+    if isinplace(prob)
+        error("Inplace version for Nested ForwardDiff Not Implemented Yet!")
+    else
+        f = Base.Fix2(prob.f, prob.p)
+        fx = f(x)
+        J_fn = Base.Fix1(ForwardDiff.jacobian, f)
+        dfx = J_fn(x)
+        d2fx = ForwardDiff.jacobian(J_fn, x)
+        return fx, dfx, d2fx
+    end
+end
+
+function compute_jacobian_and_hessian(ad::AutoFiniteDiff, prob, _, x::Number)
+    fx = prob.f(x, prob.p)
+    J_fn = x -> FiniteDiff.finite_difference_derivative(Base.Fix2(prob.f, prob.p), x,
+        ad.fdtype)
+    dfx = J_fn(x)
+    d2fx = FiniteDiff.finite_difference_derivative(J_fn, x, ad.fdtype)
+    return fx, dfx, d2fx
+end
+
+function compute_jacobian_and_hessian(ad::AutoFiniteDiff, prob, fx, x)
+    if isinplace(prob)
+        error("Inplace version for Nested FiniteDiff Not Implemented Yet!")
+    else
+        f = Base.Fix2(prob.f, prob.p)
+        fx = f(x)
+        J_fn = x -> FiniteDiff.finite_difference_jacobian(f, x, ad.fdtype)
+        dfx = J_fn(x)
+        d2fx = FiniteDiff.finite_difference_jacobian(J_fn, x, ad.fdtype)
+        return fx, dfx, d2fx
+    end
+end
+
 __init_identity_jacobian(u::Number, _) = one(u)
 __init_identity_jacobian!!(J::Number) = one(J)
 function __init_identity_jacobian(u, fu)

From 83102b059b9a1778c3525a883e2738c89e273683 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 24 Nov 2023 23:32:50 -0500
Subject: [PATCH 234/700] Add tests for the nonlinear solvers

---
 .../src/SimpleNonlinearSolve.jl               |   7 +
 lib/SimpleNonlinearSolve/src/ad.jl            |  21 +
 lib/SimpleNonlinearSolve/src/utils.jl         |   4 +-
 lib/SimpleNonlinearSolve/test/Project.toml    |   3 +-
 lib/SimpleNonlinearSolve/test/basictests.jl   | 948 ++++++++----------
 lib/SimpleNonlinearSolve/test/inplace.jl      |  52 -
 .../test/least_squares.jl                     |   8 +-
 lib/SimpleNonlinearSolve/test/runtests.jl     |   1 -
 8 files changed, 445 insertions(+), 599 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/test/inplace.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index a9e7d7b82..66d7d4271 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -67,12 +67,19 @@ end
         algs = [SimpleNewtonRaphson(), SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
             SimpleTrustRegion(), SimpleLimitedMemoryBroyden(; threshold = 2)]
 
+        algs_no_iip = [SimpleHalley()]
+
         @compile_workload begin
             for alg in algs
                 solve(prob_no_brack_scalar, alg, abstol = T(1e-2))
                 solve(prob_no_brack_iip, alg, abstol = T(1e-2))
                 solve(prob_no_brack_oop, alg, abstol = T(1e-2))
             end
+
+            for alg in algs_no_iip
+                solve(prob_no_brack_scalar, alg, abstol = T(1e-2))
+                solve(prob_no_brack_oop, alg, abstol = T(1e-2))
+            end
         end
 
         prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p,
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index a13ae0e6f..8cbff710c 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -47,6 +47,27 @@ function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, SVector, <:Abstr
     return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode)
 end
 
+function scalar_nlsolve_∂f_∂p(f, u, p)
+    ff = p isa Number ? ForwardDiff.derivative :
+         (u isa Number ? ForwardDiff.gradient : ForwardDiff.jacobian)
+    return ff(Base.Fix1(f, u), p)
+end
+
+function scalar_nlsolve_∂f_∂u(f, u, p)
+    ff = u isa Number ? ForwardDiff.derivative : ForwardDiff.jacobian
+    return ff(Base.Fix2(f, p), u)
+end
+
+function scalar_nlsolve_dual_soln(u::Number, partials,
+        ::Union{<:AbstractArray{<:Dual{T, V, P}}, Dual{T, V, P}}) where {T, V, P}
+    return Dual{T, V, P}(u, partials)
+end
+
+function scalar_nlsolve_dual_soln(u::AbstractArray, partials,
+        ::Union{<:AbstractArray{<:Dual{T, V, P}}, Dual{T, V, P}}) where {T, V, P}
+    return map(((uᵢ, pᵢ),) -> Dual{T, V, P}(uᵢ, pᵢ), zip(u, partials))
+end
+
 # avoid ambiguities
 for Alg in [Bisection]
     @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 7dbd8e422..870b526f4 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -207,8 +207,8 @@ function __init_identity_jacobian(u::StaticArray, fu)
     J = SMatrix{S1, S2, eltype(u)}(I)
     return J
 end
-function __init_identity_jacobian!!(J::StaticArray{S1, S2}) where {S1, S2}
-    return SMMatrix{S1, S2, eltype(J)}(I)
+function __init_identity_jacobian!!(J::SMatrix{S1, S2}) where {S1, S2}
+    return SMatrix{S1, S2, eltype(J)}(I)
 end
 
 function __init_low_rank_jacobian(u::StaticArray{S1, T1}, fu::StaticArray{S2, T2},
diff --git a/lib/SimpleNonlinearSolve/test/Project.toml b/lib/SimpleNonlinearSolve/test/Project.toml
index 469f302ee..835a6aa43 100644
--- a/lib/SimpleNonlinearSolve/test/Project.toml
+++ b/lib/SimpleNonlinearSolve/test/Project.toml
@@ -3,8 +3,9 @@ BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
+LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 027f766ed..4963a52fe 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -1,586 +1,454 @@
-using SimpleNonlinearSolve,
-    StaticArrays, BenchmarkTools, DiffEqBase, LinearAlgebra, Test,
-    NNlib
-
-const BATCHED_BROYDEN_SOLVERS = []
-const BROYDEN_SOLVERS = []
-const BATCHED_LBROYDEN_SOLVERS = []
-const LBROYDEN_SOLVERS = []
-const BATCHED_DFSANE_SOLVERS = []
-const DFSANE_SOLVERS = []
-const BATCHED_RAPHSON_SOLVERS = []
-
-for mode in instances(NLSolveTerminationMode.T)
-    if mode ∈
-       (NLSolveTerminationMode.SteadyStateDefault, NLSolveTerminationMode.RelSafeBest,
-        NLSolveTerminationMode.AbsSafeBest)
-        continue
-    end
-
-    termination_condition = NLSolveTerminationCondition(mode; abstol = nothing,
-        reltol = nothing)
-    push!(BROYDEN_SOLVERS, Broyden(; batched = false, termination_condition))
-    push!(BATCHED_BROYDEN_SOLVERS, Broyden(; batched = true, termination_condition))
-    push!(LBROYDEN_SOLVERS, LBroyden(; batched = false, termination_condition))
-    push!(BATCHED_LBROYDEN_SOLVERS, LBroyden(; batched = true, termination_condition))
-    push!(DFSANE_SOLVERS, SimpleDFSane(; batched = false, termination_condition))
-    push!(BATCHED_DFSANE_SOLVERS, SimpleDFSane(; batched = true, termination_condition))
-    push!(BATCHED_RAPHSON_SOLVERS,
-        SimpleNewtonRaphson(; batched = true,
-            termination_condition))
-    push!(BATCHED_RAPHSON_SOLVERS,
-        SimpleNewtonRaphson(; batched = true, autodiff = false,
-            termination_condition))
-end
-
-# SimpleNewtonRaphson
-function benchmark_scalar(f, u0)
-    probN = NonlinearProblem{false}(f, u0)
-    sol = (solve(probN, SimpleNewtonRaphson()))
-end
-
-function ff(u, p)
-    u .* u .- 2
-end
-const cu0 = @SVector[1.0, 1.0]
-function sf(u, p)
-    u * u - 2
-end
-const csu0 = 1.0
-
-sol = benchmark_scalar(sf, csu0)
-@test sol.retcode === ReturnCode.Success
-@test sol.u * sol.u - 2 < 1e-9
-
-if VERSION >= v"1.7"
-    @test (@ballocated benchmark_scalar(sf, csu0)) == 0
-end
-
-# SimpleHalley
-function benchmark_scalar(f, u0)
-    probN = NonlinearProblem{false}(f, u0)
-    sol = (solve(probN, SimpleHalley()))
-end
+using BenchmarkTools, LinearSolve, NonlinearSolve, StaticArrays, Random, LinearAlgebra,
+    Test, ForwardDiff, DiffEqBase
+
+_nameof(x) = applicable(nameof, x) ? nameof(x) : _nameof(typeof(x))
+
+quadratic_f(u, p) = u .* u .- p
+quadratic_f!(du, u, p) = (du .= u .* u .- p)
+quadratic_f2(u, p) = @. p[1] * u * u - p[2]
+
+function newton_fails(u, p)
+    return 0.010000000000000002 .+
+           10.000000000000002 ./ (1 .+
+            (0.21640425613334457 .+
+             216.40425613334457 ./ (1 .+
+              (0.21640425613334457 .+
+               216.40425613334457 ./
+               (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^ 2.0) .-
+           0.0011552453009332421u .- p
+end
+
+const TERMINATION_CONDITIONS = [
+    NormTerminationMode(), RelTerminationMode(), RelNormTerminationMode(),
+    AbsTerminationMode(), AbsNormTerminationMode(), RelSafeTerminationMode(),
+    AbsSafeTerminationMode(), RelSafeBestTerminationMode(), AbsSafeBestTerminationMode(),
+]
 
-function ff(u, p)
-    u .* u .- 2
-end
-const cu0 = @SVector[1.0, 1.0]
-function sf(u, p)
-    u * u - 2
-end
-const csu0 = 1.0
+# --- SimpleNewtonRaphson tests ---
 
-sol = benchmark_scalar(sf, csu0)
-@test sol.retcode === ReturnCode.Success
-@test sol.u * sol.u - 2 < 1e-9
+@testset "$(alg)" for alg in (SimpleNewtonRaphson, SimpleTrustRegion)
+    # Eval else the alg is type unstable
+    @eval begin
+        function benchmark_nlsolve_oop(f, u0, p = 2.0; autodiff = AutoForwardDiff())
+            prob = NonlinearProblem{false}(f, u0, p)
+            return solve(prob, $(alg)(; autodiff), abstol = 1e-9)
+        end
 
-sol = benchmark_scalar(ff, cu0)
-@test sol.retcode === ReturnCode.Success
-@test sol.u .* sol.u .- 2 < [1e-9, 1e-9]
+        function benchmark_nlsolve_iip(f, u0, p = 2.0; autodiff = AutoForwardDiff())
+            prob = NonlinearProblem{true}(f, u0, p)
+            return solve(prob, $(alg)(; autodiff), abstol = 1e-9)
+        end
+    end
 
-if VERSION >= v"1.7"
-    @test (@ballocated benchmark_scalar(sf, csu0)) == 0
-end
+    @testset "AutoDiff: $(_nameof(autodiff))" for autodiff in (AutoFiniteDiff(),
+        AutoForwardDiff())
+        @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
+            sol = benchmark_nlsolve_oop(quadratic_f, u0; autodiff)
+            @test SciMLBase.successful_retcode(sol)
+            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+        end
 
-# Broyden
-function benchmark_scalar(f, u0, alg)
-    probN = NonlinearProblem{false}(f, u0)
-    sol = (solve(probN, alg))
-end
+        @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+            sol = benchmark_nlsolve_iip(quadratic_f!, u0; autodiff)
+            @test SciMLBase.successful_retcode(sol)
+            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+        end
+    end
 
-for alg in BROYDEN_SOLVERS
-    sol = benchmark_scalar(sf, csu0, alg)
-    @test sol.retcode === ReturnCode.Success
-    @test sol.u * sol.u - 2 < 1e-9
-    # FIXME: Termination Condition Implementation is allocating. Not sure how to fix it.
-    # if VERSION >= v"1.7"
-    #     @test (@ballocated benchmark_scalar($sf, $csu0, $termination_condition)) == 0
-    # end
-end
+    @testset "Allocations: Static Array and Scalars" begin
+        @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, $(@SVector[1.0, 1.0]),
+            2.0; autodiff = AutoForwardDiff())) < 200
+        @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, 1.0, 2.0;
+            autodiff = AutoForwardDiff())) == 0
+    end
 
-# Klement
-function benchmark_scalar(f, u0)
-    probN = NonlinearProblem{false}(f, u0)
-    sol = (solve(probN, Klement()))
-end
+    @testset "[OOP] Immutable AD" begin
+        for p in [1.0, 100.0]
+            @test begin
+                res = benchmark_nlsolve_oop(quadratic_f, @SVector[1.0, 1.0], p)
+                res_true = sqrt(p)
+                all(res.u .≈ res_true)
+            end
+            @test ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
+                @SVector[1.0, 1.0], p).u[end], p) ≈ 1 / (2 * sqrt(p))
+        end
+    end
 
-sol = benchmark_scalar(sf, csu0)
-@test sol.retcode === ReturnCode.Success
-@test sol.u * sol.u - 2 < 1e-9
-if VERSION >= v"1.7"
-    @test (@ballocated benchmark_scalar(sf, csu0)) == 0
-end
+    @testset "[OOP] Scalar AD" begin
+        for p in 1.0:0.1:100.0
+            @test begin
+                res = benchmark_nlsolve_oop(quadratic_f, 1.0, p)
+                res_true = sqrt(p)
+                res.u ≈ res_true
+            end
+            @test ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f, 1.0, p).u,
+                p) ≈ 1 / (2 * sqrt(p))
+        end
+    end
 
-# SimpleTrustRegion
-function benchmark_scalar(f, u0)
-    probN = NonlinearProblem{false}(f, u0)
-    sol = (solve(probN, SimpleTrustRegion()))
-end
+    t = (p) -> [sqrt(p[2] / p[1])]
+    p = [0.9, 50.0]
+    @test benchmark_nlsolve_oop(quadratic_f2, 0.5, p).u ≈ sqrt(p[2] / p[1])
+    @test ForwardDiff.jacobian(p -> [benchmark_nlsolve_oop(quadratic_f2, 0.5, p).u],
+        p) ≈ ForwardDiff.jacobian(t, p)
 
-sol = benchmark_scalar(sf, csu0)
-@test sol.retcode === ReturnCode.Success
-@test sol.u * sol.u - 2 < 1e-9
+    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
+        u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 
-# SimpleDFSane
-function benchmark_scalar(f, u0)
-    probN = NonlinearProblem{false}(f, u0)
-    sol = (solve(probN, SimpleDFSane()))
+        probN = NonlinearProblem(quadratic_f, u0, 2.0)
+        @test all(solve(probN, alg(); termination_condition).u .≈ sqrt(2.0))
+    end
 end
 
-sol = benchmark_scalar(sf, csu0)
-@test sol.retcode === ReturnCode.Success
-@test sol.u * sol.u - 2 < 1e-9
-
-# AD Tests
-using ForwardDiff
-
-# Immutable
-f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0]
+# --- SimpleHalley tests ---
 
-for alg in (SimpleNewtonRaphson(), LBroyden(), Klement(), SimpleTrustRegion(),
-    SimpleDFSane(), SimpleHalley(), BROYDEN_SOLVERS...)
-    g = function (p)
-        probN = NonlinearProblem{false}(f, csu0, p)
-        sol = solve(probN, alg, abstol = 1e-9)
-        return sol.u[end]
+@testset "SimpleHalley" begin
+    function benchmark_nlsolve_oop(f, u0, p = 2.0; autodiff = AutoForwardDiff())
+        prob = NonlinearProblem{false}(f, u0, p)
+        return solve(prob, SimpleHalley(; autodiff), abstol = 1e-9)
     end
 
-    for p in 1.1:0.1:100.0
-        res = abs.(g(p))
-        # Not surprising if LBrouden fails to converge
-        if any(x -> isnan(x) || x <= 1e-5 || x >= 1e5, res) && alg isa LBroyden
-            @test_broken res ≈ sqrt(p)
-            @test_broken abs.(ForwardDiff.derivative(g, p)) ≈ 1 / (2 * sqrt(p))
-        else
-            @test res ≈ sqrt(p)
-            @test abs.(ForwardDiff.derivative(g, p)) ≈ 1 / (2 * sqrt(p))
+    @testset "AutoDiff: $(_nameof(autodiff))" for autodiff in (AutoFiniteDiff(),
+        AutoForwardDiff())
+        @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
+            sol = benchmark_nlsolve_oop(quadratic_f, u0; autodiff)
+            @test SciMLBase.successful_retcode(sol)
+            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
         end
     end
-end
 
-# Scalar
-f, u0 = (u, p) -> u * u - p, 1.0
-for alg in (SimpleNewtonRaphson(), Klement(), SimpleTrustRegion(),
-    SimpleDFSane(), SimpleHalley(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
-    g = function (p)
-        probN = NonlinearProblem{false}(f, oftype(p, u0), p)
-        sol = solve(probN, alg)
-        return sol.u
+    @testset "Allocations: Static Array and Scalars" begin
+        @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, 1.0, 2.0;
+            autodiff = AutoForwardDiff())) == 0
     end
 
-    for p in 1.1:0.1:100.0
-        res = abs.(g(p))
-        # Not surprising if LBrouden fails to converge
-        if any(x -> isnan(x) || x <= 1e-5 || x >= 1e5, res) && alg isa LBroyden
-            @test_broken res ≈ sqrt(p)
-            @test_broken abs.(ForwardDiff.derivative(g, p)) ≈ 1 / (2 * sqrt(p))
-        else
-            @test res ≈ sqrt(p)
-            @test abs.(ForwardDiff.derivative(g, p)) ≈ 1 / (2 * sqrt(p))
+    @testset "[OOP] Immutable AD" begin
+        for p in [1.0, 100.0]
+            @test begin
+                res = benchmark_nlsolve_oop(quadratic_f, @SVector[1.0, 1.0], p)
+                res_true = sqrt(p)
+                all(res.u .≈ res_true)
+            end
+            @test ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
+                @SVector[1.0, 1.0], p).u[end], p) ≈ 1 / (2 * sqrt(p))
         end
     end
-end
-
-tspan = (1.0, 20.0)
-# Falsi
-g = function (p)
-    probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
-    sol = solve(probN, Falsi())
-    return sol.left
-end
-
-for p in 1.1:0.1:100.0
-    @test g(p) ≈ sqrt(p)
-    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
-end
-
-# Ridder
-g = function (p)
-    probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
-    sol = solve(probN, Ridder())
-    return sol.left
-end
-
-for p in 1.1:0.1:100.0
-    @test g(p) ≈ sqrt(p)
-    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
-end
-
-# Brent
-g = function (p)
-    probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
-    sol = solve(probN, Brent())
-    return sol.left
-end
-
-for p in 1.1:0.1:100.0
-    @test g(p) ≈ sqrt(p)
-    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
-end
 
-# ITP
-g = function (p)
-    probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
-    sol = solve(probN, ITP())
-    return sol.u
-end
+    @testset "[OOP] Scalar AD" begin
+        for p in 1.0:0.1:100.0
+            @test begin
+                res = benchmark_nlsolve_oop(quadratic_f, 1.0, p)
+                res_true = sqrt(p)
+                res.u ≈ res_true
+            end
+            @test ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f, 1.0, p).u,
+                p) ≈ 1 / (2 * sqrt(p))
+        end
+    end
 
-for p in 1.1:0.1:100.0
-    @test g(p) ≈ sqrt(p)
-    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
-end
+    t = (p) -> [sqrt(p[2] / p[1])]
+    p = [0.9, 50.0]
+    @test benchmark_nlsolve_oop(quadratic_f2, 0.5, p).u ≈ sqrt(p[2] / p[1])
+    @test ForwardDiff.jacobian(p -> [benchmark_nlsolve_oop(quadratic_f2, 0.5, p).u],
+        p) ≈ ForwardDiff.jacobian(t, p)
 
-# Alefeld
-g = function (p)
-    probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
-    sol = solve(probN, Alefeld())
-    return sol.u
-end
+    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
+        u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 
-for p in 1.1:0.1:100.0
-    @test g(p) ≈ sqrt(p)
-    @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+        probN = NonlinearProblem(quadratic_f, u0, 2.0)
+        @show solve(probN, SimpleHalley(); termination_condition).u
+        @test all(solve(probN, SimpleHalley(); termination_condition).u .≈ sqrt(2.0))
+    end
 end
 
-f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
-t = (p) -> [sqrt(p[2] / p[1])]
-p = [0.9, 50.0]
-g = function (p)
-    probN = IntervalNonlinearProblem{false}(f, tspan, p)
-    sol = solve(probN, Alefeld())
-    return [sol.u]
-end
+# --- SimpleBroyden / SimpleKlement / SimpleLimitedMemoryBroyden tests ---
 
-@test g(p) ≈ [sqrt(p[2] / p[1])]
-@test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
-
-f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
-t = (p) -> [sqrt(p[2] / p[1])]
-p = [0.9, 50.0]
-for alg in [Bisection(), Falsi(), Ridder(), Brent(), ITP()]
-    global g, p
-    g = function (p)
-        probN = IntervalNonlinearProblem{false}(f, tspan, p)
-        sol = solve(probN, alg)
-        return [sol.left]
+@testset "$(alg)" for alg in [SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
+        SimpleLimitedMemoryBroyden()]
+    function benchmark_nlsolve_oop(f, u0, p = 2.0)
+        prob = NonlinearProblem{false}(f, u0, p)
+        return solve(prob, alg, abstol = 1e-9)
     end
 
-    @test g(p) ≈ [sqrt(p[2] / p[1])]
-    @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
-end
-
-for alg in (SimpleNewtonRaphson(), Klement(), SimpleTrustRegion(),
-    SimpleDFSane(), SimpleHalley(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
-    global g, p
-    g = function (p)
-        probN = NonlinearProblem{false}(f, 0.5, p)
-        sol = solve(probN, alg)
-        return [abs(sol.u)]
+    function benchmark_nlsolve_iip(f, u0, p = 2.0)
+        prob = NonlinearProblem{true}(f, u0, p)
+        return solve(prob, alg, abstol = 1e-9)
     end
-    @test g(p) ≈ [sqrt(p[2] / p[1])]
-    @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
-end
-
-# Error Checks
-f, u0 = (u, p) -> u .* u .- 2.0, @SVector[1.0, 1.0]
-probN = NonlinearProblem(f, u0)
-
-for alg in (SimpleNewtonRaphson(), SimpleNewtonRaphson(; autodiff = false),
-    SimpleTrustRegion(),
-    SimpleTrustRegion(; autodiff = false), SimpleHalley(), SimpleHalley(; autodiff = false),
-    Klement(), SimpleDFSane(),
-    BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
-    sol = solve(probN, alg)
-
-    @test sol.retcode == ReturnCode.Success
-    @test sol.u[end] ≈ sqrt(2.0)
-end
-
-for u0 in [1.0, [1, 1.0]]
-    local f, probN, sol
-    f = (u, p) -> u .* u .- 2.0
-    probN = NonlinearProblem(f, u0)
-    sol = sqrt(2) * u0
 
-    for alg in (SimpleNewtonRaphson(), SimpleNewtonRaphson(; autodiff = false),
-        SimpleTrustRegion(), SimpleTrustRegion(; autodiff = false), Klement(),
-        SimpleDFSane(), BROYDEN_SOLVERS..., LBROYDEN_SOLVERS...)
-        sol2 = solve(probN, alg)
-
-        @test sol2.retcode == ReturnCode.Success
-        @test sol2.u ≈ sol
+    @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
+        sol = benchmark_nlsolve_oop(quadratic_f, u0)
+        @test SciMLBase.successful_retcode(sol)
+        @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
     end
-end
-
-# Bisection Tests
-f, tspan = (u, p) -> u .* u .- 2.0, (1.0, 2.0)
-probB = IntervalNonlinearProblem(f, tspan)
-
-# Falsi
-sol = solve(probB, Falsi())
-@test sol.left ≈ sqrt(2.0)
-
-# Bisection
-sol = solve(probB, Bisection())
-@test sol.left ≈ sqrt(2.0)
-
-# Ridder
-sol = solve(probB, Ridder())
-@test sol.left ≈ sqrt(2.0)
-tspan = (sqrt(2.0), 10.0)
-probB = IntervalNonlinearProblem(f, tspan)
-sol = solve(probB, Ridder())
-@test sol.left ≈ sqrt(2.0)
-tspan = (0.0, sqrt(2.0))
-probB = IntervalNonlinearProblem(f, tspan)
-sol = solve(probB, Ridder())
-@test sol.left ≈ sqrt(2.0)
-
-# Brent
-sol = solve(probB, Brent())
-@test sol.left ≈ sqrt(2.0)
-tspan = (sqrt(2.0), 10.0)
-probB = IntervalNonlinearProblem(f, tspan)
-sol = solve(probB, Brent())
-@test sol.left ≈ sqrt(2.0)
-tspan = (0.0, sqrt(2.0))
-probB = IntervalNonlinearProblem(f, tspan)
-sol = solve(probB, Brent())
-@test sol.left ≈ sqrt(2.0)
-
-# Alefeld
-sol = solve(probB, Alefeld())
-@test sol.u ≈ sqrt(2.0)
-tspan = (sqrt(2.0), 10.0)
-probB = IntervalNonlinearProblem(f, tspan)
-sol = solve(probB, Alefeld())
-@test sol.u ≈ sqrt(2.0)
-tspan = (0.0, sqrt(2.0))
-probB = IntervalNonlinearProblem(f, tspan)
-sol = solve(probB, Alefeld())
-@test sol.u ≈ sqrt(2.0)
-
-# ITP
-sol = solve(probB, ITP())
-@test sol.u ≈ sqrt(2.0)
-tspan = (sqrt(2.0), 10.0)
-probB = IntervalNonlinearProblem(f, tspan)
-sol = solve(probB, ITP())
-@test sol.u ≈ sqrt(2.0)
-tspan = (0.0, sqrt(2.0))
-probB = IntervalNonlinearProblem(f, tspan)
-sol = solve(probB, ITP())
-@test sol.u ≈ sqrt(2.0)
-
-# Tolerance tests for Interval methods
-f, tspan = (u, p) -> u .* u .- 2.0, (1.0, 10.0)
-probB = IntervalNonlinearProblem(f, tspan)
-tols = [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6, 1e-7]
-ϵ = eps(1.0) #least possible tol for all methods
-
-for atol in tols
-    sol = solve(probB, Bisection(), abstol = atol)
-    @test abs(sol.u - sqrt(2)) < atol
-    @test abs(sol.u - sqrt(2)) > ϵ #test that the solution is not calculated upto max precision
-    sol = solve(probB, Falsi(), abstol = atol)
-    @test abs(sol.u - sqrt(2)) < atol
-    @test abs(sol.u - sqrt(2)) > ϵ
-    sol = solve(probB, ITP(), abstol = atol)
-    @test abs(sol.u - sqrt(2)) < atol
-    @test abs(sol.u - sqrt(2)) > ϵ
-end
-
-tols = [0.1] # Ridder and Brent converge rapidly so as we lower tolerance below 0.01, it converges with max precision to the solution
-for atol in tols
-    sol = solve(probB, Ridder(), abstol = atol)
-    @test abs(sol.u - sqrt(2)) < atol
-    @test abs(sol.u - sqrt(2)) > ϵ
-    sol = solve(probB, Brent(), abstol = atol)
-    @test abs(sol.u - sqrt(2)) < atol
-    @test abs(sol.u - sqrt(2)) > ϵ
-end
 
-# Garuntee Tests for Bisection
-f = function (u, p)
-    if u < 2.0
-        return u - 2.0
-    elseif u > 3.0
-        return u - 3.0
-    else
-        return 0.0
+    @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+        sol = benchmark_nlsolve_iip(quadratic_f!, u0)
+        @test SciMLBase.successful_retcode(sol)
+        @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
     end
-end
-probB = IntervalNonlinearProblem(f, (0.0, 4.0))
-
-sol = solve(probB, Bisection(; exact_left = true))
-@test f(sol.left, nothing) < 0.0
-@test f(nextfloat(sol.left), nothing) >= 0.0
-
-sol = solve(probB, Bisection(; exact_right = true))
-@test f(sol.right, nothing) >= 0.0
-@test f(prevfloat(sol.right), nothing) <= 0.0
-
-sol = solve(probB, Bisection(; exact_left = true, exact_right = true); immutable = false)
-@test f(sol.left, nothing) < 0.0
-@test f(nextfloat(sol.left), nothing) >= 0.0
-@test f(sol.right, nothing) >= 0.0
-@test f(prevfloat(sol.right), nothing) <= 0.0
-
-# Test that `SimpleTrustRegion` passes a test that `SimpleNewtonRaphson` fails on.
-u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
-global g, f
-f = (u, p) -> 0.010000000000000002 .+
-              10.000000000000002 ./ (1 .+
-               (0.21640425613334457 .+
-                216.40425613334457 ./ (1 .+
-                 (0.21640425613334457 .+
-                  216.40425613334457 ./
-                  (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^ 2.0) .-
-              0.0011552453009332421u .- p
-g = function (p)
-    probN = NonlinearProblem{false}(f, u0, p)
-    sol = solve(probN, SimpleTrustRegion())
-    return sol.u
-end
-p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
-u = g(p)
-f(u, p)
-@test all(abs.(f(u, p)) .< 1e-10)
-
-# Test kwars in `SimpleTrustRegion`
-max_trust_radius = [10.0, 100.0, 1000.0]
-initial_trust_radius = [10.0, 1.0, 0.1]
-step_threshold = [0.0, 0.01, 0.25]
-shrink_threshold = [0.25, 0.3, 0.5]
-expand_threshold = [0.5, 0.8, 0.9]
-shrink_factor = [0.1, 0.3, 0.5]
-expand_factor = [1.5, 2.0, 3.0]
-max_shrink_times = [10, 20, 30]
-
-list_of_options = zip(max_trust_radius, initial_trust_radius, step_threshold,
-    shrink_threshold, expand_threshold, shrink_factor,
-    expand_factor, max_shrink_times)
-for options in list_of_options
-    local probN, sol, alg
-    alg = SimpleTrustRegion(max_trust_radius = options[1],
-        initial_trust_radius = options[2],
-        step_threshold = options[3],
-        shrink_threshold = options[4],
-        expand_threshold = options[5],
-        shrink_factor = options[6],
-        expand_factor = options[7],
-        max_shrink_times = options[8])
-
-    probN = NonlinearProblem(f, u0, p)
-    sol = solve(probN, alg)
-    @test all(abs.(f(u, p)) .< 1e-10)
-end
-
-# Test that `SimpleDFSane` passes a test that `SimpleNewtonRaphson` fails on.
-u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
-global g, f
-f = (u, p) -> 0.010000000000000002 .+
-              10.000000000000002 ./ (1 .+
-               (0.21640425613334457 .+
-                216.40425613334457 ./ (1 .+
-                 (0.21640425613334457 .+
-                  216.40425613334457 ./
-                  (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^ 2.0) .-
-              0.0011552453009332421u .- p
-g = function (p)
-    probN = NonlinearProblem{false}(f, u0, p)
-    sol = solve(probN, SimpleDFSane())
-    return sol.u
-end
-p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
-u = g(p)
-f(u, p)
-@test all(abs.(f(u, p)) .< 1e-10)
-
-# Test kwars in `SimpleDFSane`
-σ_min = [1e-10, 1e-5, 1e-4]
-σ_max = [1e10, 1e5, 1e4]
-σ_1 = [1.0, 0.5, 2.0]
-M = [10, 1, 100]
-γ = [1e-4, 1e-3, 1e-5]
-τ_min = [0.1, 0.2, 0.3]
-τ_max = [0.5, 0.8, 0.9]
-nexp = [2, 1, 2]
-η_strategy = [
-    (f_1, k, x, F) -> f_1 / k^2,
-    (f_1, k, x, F) -> f_1 / k^3,
-    (f_1, k, x, F) -> f_1 / k^4,
-]
 
-list_of_options = zip(σ_min, σ_max, σ_1, M, γ, τ_min, τ_max, nexp,
-    η_strategy)
-for options in list_of_options
-    local probN, sol, alg
-    alg = SimpleDFSane(σ_min = options[1],
-        σ_max = options[2],
-        σ_1 = options[3],
-        M = options[4],
-        γ = options[5],
-        τ_min = options[6],
-        τ_max = options[7],
-        nexp = options[8],
-        η_strategy = options[9])
-
-    probN = NonlinearProblem(f, u0, p)
-    sol = solve(probN, alg)
-    @test all(abs.(f(u, p)) .< 1e-10)
-end
-
-f, u0 = (u, p) -> u .* u .- p, randn(1, 3)
-
-p = [2.0 1.0 5.0];
-probN = NonlinearProblem{false}(f, u0, p);
-
-sol = solve(probN, Broyden(batched = true))
-
-@test abs.(sol.u) ≈ sqrt.(p)
+    @testset "Allocations: Static Array and Scalars" begin
+        @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, $(@SVector[1.0, 1.0]),
+            2.0)) < 200
+        @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, 1.0, 2.0)) == 0
+    end
 
-@testset "Batched Solver: $(nameof(typeof(alg)))" for alg in (BATCHED_BROYDEN_SOLVERS...,
-    BATCHED_LBROYDEN_SOLVERS...,
-    BATCHED_DFSANE_SOLVERS...,
-    BATCHED_RAPHSON_SOLVERS...)
-    sol = solve(probN, alg; abstol = 1e-3, reltol = 1e-3)
+    @testset "[OOP] Immutable AD" begin
+        for p in [1.0, 100.0]
+            @test begin
+                res = benchmark_nlsolve_oop(quadratic_f, @SVector[1.0, 1.0], p)
+                res_true = sqrt(p)
+                all(res.u .≈ res_true)
+            end
+            @test ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
+                @SVector[1.0, 1.0], p).u[end], p) ≈ 1 / (2 * sqrt(p))
+        end
+    end
 
-    @test sol.retcode == ReturnCode.Success
-    @test abs.(sol.u)≈sqrt.(p) atol=1e-3 rtol=1e-3
-end
+    @testset "[OOP] Scalar AD" begin
+        for p in 1.0:0.1:100.0
+            @test begin
+                res = benchmark_nlsolve_oop(quadratic_f, 1.0, p)
+                res_true = sqrt(p)
+                res.u ≈ res_true
+            end
+            @test ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f, 1.0, p).u,
+                p) ≈ 1 / (2 * sqrt(p))
+        end
+    end
 
-## User specified Jacobian
+    t = (p) -> [sqrt(p[2] / p[1])]
+    p = [0.9, 50.0]
+    @test benchmark_nlsolve_oop(quadratic_f2, 0.5, p).u ≈ sqrt(p[2] / p[1])
+    @test ForwardDiff.jacobian(p -> [benchmark_nlsolve_oop(quadratic_f2, 0.5, p).u],
+        p) ≈ ForwardDiff.jacobian(t, p)
 
-f, u0 = (u, p) -> u .* u .- p, randn(3)
+    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
+        u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 
-f_jac(u, p) = begin
-    diagm(2 * u)
+        probN = NonlinearProblem(quadratic_f, u0, 2.0)
+        @test all(solve(probN, alg; termination_condition).u .≈ sqrt(2.0))
+    end
 end
 
-p = [2.0, 1.0, 5.0];
 
-probN = NonlinearProblem(NonlinearFunction(f, jac = f_jac), u0, p)
-
-for alg in (SimpleNewtonRaphson(), SimpleTrustRegion())
-    sol = solve(probN, alg)
-    @test abs.(sol.u) ≈ sqrt.(p)
-end
-
-# Flipped signs & reversed tspan test for bracketing algorithms
-f1(u, p) = u * u - p
-f2(u, p) = p - u * u
-
-for alg in (Alefeld(), Bisection(), Falsi(), Brent(), ITP(), Ridder())
-    for p in 1:4
-        inp1 = IntervalNonlinearProblem(f1, (1.0, 2.0), p)
-        inp2 = IntervalNonlinearProblem(f2, (1.0, 2.0), p)
-        inp3 = IntervalNonlinearProblem(f1, (2.0, 1.0), p)
-        inp4 = IntervalNonlinearProblem(f2, (2.0, 1.0), p)
-        @test abs.(solve(inp1, alg).u) ≈ sqrt.(p)
-        @test abs.(solve(inp2, alg).u) ≈ sqrt.(p)
-        @test abs.(solve(inp3, alg).u) ≈ sqrt.(p)
-        @test abs.(solve(inp4, alg).u) ≈ sqrt.(p)
-    end
-end
+1 + 1 + 1
+
+# tspan = (1.0, 20.0)
+# # Falsi
+# g = function (p)
+#     probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
+#     sol = solve(probN, Falsi())
+#     return sol.left
+# end
+
+# for p in 1.1:0.1:100.0
+#     @test g(p) ≈ sqrt(p)
+#     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+# end
+
+# # Ridder
+# g = function (p)
+#     probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
+#     sol = solve(probN, Ridder())
+#     return sol.left
+# end
+
+# for p in 1.1:0.1:100.0
+#     @test g(p) ≈ sqrt(p)
+#     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+# end
+
+# # Brent
+# g = function (p)
+#     probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
+#     sol = solve(probN, Brent())
+#     return sol.left
+# end
+
+# for p in 1.1:0.1:100.0
+#     @test g(p) ≈ sqrt(p)
+#     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+# end
+
+# # ITP
+# g = function (p)
+#     probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
+#     sol = solve(probN, ITP())
+#     return sol.u
+# end
+
+# for p in 1.1:0.1:100.0
+#     @test g(p) ≈ sqrt(p)
+#     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+# end
+
+# # Alefeld
+# g = function (p)
+#     probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
+#     sol = solve(probN, Alefeld())
+#     return sol.u
+# end
+
+# for p in 1.1:0.1:100.0
+#     @test g(p) ≈ sqrt(p)
+#     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
+# end
+
+# f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
+# t = (p) -> [sqrt(p[2] / p[1])]
+# p = [0.9, 50.0]
+# g = function (p)
+#     probN = IntervalNonlinearProblem{false}(f, tspan, p)
+#     sol = solve(probN, Alefeld())
+#     return [sol.u]
+# end
+
+# @test g(p) ≈ [sqrt(p[2] / p[1])]
+# @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
+
+# f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
+# t = (p) -> [sqrt(p[2] / p[1])]
+# p = [0.9, 50.0]
+# for alg in [Bisection(), Falsi(), Ridder(), Brent(), ITP()]
+#     global g, p
+#     g = function (p)
+#         probN = IntervalNonlinearProblem{false}(f, tspan, p)
+#         sol = solve(probN, alg)
+#         return [sol.left]
+#     end
+
+#     @test g(p) ≈ [sqrt(p[2] / p[1])]
+#     @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
+# end
+
+# # Bisection Tests
+# f, tspan = (u, p) -> u .* u .- 2.0, (1.0, 2.0)
+# probB = IntervalNonlinearProblem(f, tspan)
+
+# # Falsi
+# sol = solve(probB, Falsi())
+# @test sol.left ≈ sqrt(2.0)
+
+# # Bisection
+# sol = solve(probB, Bisection())
+# @test sol.left ≈ sqrt(2.0)
+
+# # Ridder
+# sol = solve(probB, Ridder())
+# @test sol.left ≈ sqrt(2.0)
+# tspan = (sqrt(2.0), 10.0)
+# probB = IntervalNonlinearProblem(f, tspan)
+# sol = solve(probB, Ridder())
+# @test sol.left ≈ sqrt(2.0)
+# tspan = (0.0, sqrt(2.0))
+# probB = IntervalNonlinearProblem(f, tspan)
+# sol = solve(probB, Ridder())
+# @test sol.left ≈ sqrt(2.0)
+
+# # Brent
+# sol = solve(probB, Brent())
+# @test sol.left ≈ sqrt(2.0)
+# tspan = (sqrt(2.0), 10.0)
+# probB = IntervalNonlinearProblem(f, tspan)
+# sol = solve(probB, Brent())
+# @test sol.left ≈ sqrt(2.0)
+# tspan = (0.0, sqrt(2.0))
+# probB = IntervalNonlinearProblem(f, tspan)
+# sol = solve(probB, Brent())
+# @test sol.left ≈ sqrt(2.0)
+
+# # Alefeld
+# sol = solve(probB, Alefeld())
+# @test sol.u ≈ sqrt(2.0)
+# tspan = (sqrt(2.0), 10.0)
+# probB = IntervalNonlinearProblem(f, tspan)
+# sol = solve(probB, Alefeld())
+# @test sol.u ≈ sqrt(2.0)
+# tspan = (0.0, sqrt(2.0))
+# probB = IntervalNonlinearProblem(f, tspan)
+# sol = solve(probB, Alefeld())
+# @test sol.u ≈ sqrt(2.0)
+
+# # ITP
+# sol = solve(probB, ITP())
+# @test sol.u ≈ sqrt(2.0)
+# tspan = (sqrt(2.0), 10.0)
+# probB = IntervalNonlinearProblem(f, tspan)
+# sol = solve(probB, ITP())
+# @test sol.u ≈ sqrt(2.0)
+# tspan = (0.0, sqrt(2.0))
+# probB = IntervalNonlinearProblem(f, tspan)
+# sol = solve(probB, ITP())
+# @test sol.u ≈ sqrt(2.0)
+
+# # Tolerance tests for Interval methods
+# f, tspan = (u, p) -> u .* u .- 2.0, (1.0, 10.0)
+# probB = IntervalNonlinearProblem(f, tspan)
+# tols = [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6, 1e-7]
+# ϵ = eps(1.0) #least possible tol for all methods
+
+# for atol in tols
+#     sol = solve(probB, Bisection(), abstol = atol)
+#     @test abs(sol.u - sqrt(2)) < atol
+#     @test abs(sol.u - sqrt(2)) > ϵ #test that the solution is not calculated upto max precision
+#     sol = solve(probB, Falsi(), abstol = atol)
+#     @test abs(sol.u - sqrt(2)) < atol
+#     @test abs(sol.u - sqrt(2)) > ϵ
+#     sol = solve(probB, ITP(), abstol = atol)
+#     @test abs(sol.u - sqrt(2)) < atol
+#     @test abs(sol.u - sqrt(2)) > ϵ
+# end
+
+# tols = [0.1] # Ridder and Brent converge rapidly so as we lower tolerance below 0.01, it converges with max precision to the solution
+# for atol in tols
+#     sol = solve(probB, Ridder(), abstol = atol)
+#     @test abs(sol.u - sqrt(2)) < atol
+#     @test abs(sol.u - sqrt(2)) > ϵ
+#     sol = solve(probB, Brent(), abstol = atol)
+#     @test abs(sol.u - sqrt(2)) < atol
+#     @test abs(sol.u - sqrt(2)) > ϵ
+# end
+
+# # Garuntee Tests for Bisection
+# f = function (u, p)
+#     if u < 2.0
+#         return u - 2.0
+#     elseif u > 3.0
+#         return u - 3.0
+#     else
+#         return 0.0
+#     end
+# end
+# probB = IntervalNonlinearProblem(f, (0.0, 4.0))
+
+# sol = solve(probB, Bisection(; exact_left = true))
+# @test f(sol.left, nothing) < 0.0
+# @test f(nextfloat(sol.left), nothing) >= 0.0
+
+# sol = solve(probB, Bisection(; exact_right = true))
+# @test f(sol.right, nothing) >= 0.0
+# @test f(prevfloat(sol.right), nothing) <= 0.0
+
+# sol = solve(probB, Bisection(; exact_left = true, exact_right = true); immutable = false)
+# @test f(sol.left, nothing) < 0.0
+# @test f(nextfloat(sol.left), nothing) >= 0.0
+# @test f(sol.right, nothing) >= 0.0
+# @test f(prevfloat(sol.right), nothing) <= 0.0
+
+# # Flipped signs & reversed tspan test for bracketing algorithms
+# f1(u, p) = u * u - p
+# f2(u, p) = p - u * u
+
+# for alg in (Alefeld(), Bisection(), Falsi(), Brent(), ITP(), Ridder())
+#     for p in 1:4
+#         inp1 = IntervalNonlinearProblem(f1, (1.0, 2.0), p)
+#         inp2 = IntervalNonlinearProblem(f2, (1.0, 2.0), p)
+#         inp3 = IntervalNonlinearProblem(f1, (2.0, 1.0), p)
+#         inp4 = IntervalNonlinearProblem(f2, (2.0, 1.0), p)
+#         @test abs.(solve(inp1, alg).u) ≈ sqrt.(p)
+#         @test abs.(solve(inp2, alg).u) ≈ sqrt.(p)
+#         @test abs.(solve(inp3, alg).u) ≈ sqrt.(p)
+#         @test abs.(solve(inp4, alg).u) ≈ sqrt.(p)
+#     end
+# end
diff --git a/lib/SimpleNonlinearSolve/test/inplace.jl b/lib/SimpleNonlinearSolve/test/inplace.jl
deleted file mode 100644
index 2e9d033a8..000000000
--- a/lib/SimpleNonlinearSolve/test/inplace.jl
+++ /dev/null
@@ -1,52 +0,0 @@
-using SimpleNonlinearSolve,
-    StaticArrays, BenchmarkTools, DiffEqBase, LinearAlgebra, Test,
-    NNlib
-
-# Supported Solvers: BatchedBroyden, BatchedSimpleDFSane, BatchedSimpleNewtonRaphson
-function f!(du::AbstractArray{<:Number, N},
-        u::AbstractArray{<:Number, N},
-        p::AbstractVector) where {N}
-    u_ = reshape(u, :, size(u, N))
-    du .= reshape(sum(abs2, u_; dims = 1) .- u_ .- reshape(p, 1, :), size(u))
-    return du
-end
-
-function f!(du::AbstractMatrix, u::AbstractMatrix, p::AbstractVector)
-    du .= sum(abs2, u; dims = 1) .- u .- reshape(p, 1, :)
-    return du
-end
-
-function f!(du::AbstractVector, u::AbstractVector, p::AbstractVector)
-    du .= sum(abs2, u) .- u .- p
-    return du
-end
-
-@testset "Solver: $(nameof(typeof(solver)))" for solver in (Broyden(; batched = true),
-    SimpleDFSane(; batched = true),
-    SimpleNewtonRaphson(; batched = true))
-    @testset "T: $T" for T in (Float32, Float64)
-        p = rand(T, 5)
-        @testset "size(u0): $sz" for sz in ((2, 5), (1, 5), (2, 3, 5))
-            u0 = ones(T, sz)
-            prob = NonlinearProblem{true}(f!, u0, p)
-
-            sol = solve(prob, solver)
-
-            @test SciMLBase.successful_retcode(sol.retcode)
-
-            @test sol.resid≈zero(sol.resid) atol=5e-3
-        end
-
-        p = rand(T, 1)
-        @testset "size(u0): $sz" for sz in ((3,), (5,), (10,))
-            u0 = ones(T, sz)
-            prob = NonlinearProblem{true}(f!, u0, p)
-
-            sol = solve(prob, solver)
-
-            @test SciMLBase.successful_retcode(sol.retcode)
-
-            @test sol.resid≈zero(sol.resid) atol=5e-3
-        end
-    end
-end
diff --git a/lib/SimpleNonlinearSolve/test/least_squares.jl b/lib/SimpleNonlinearSolve/test/least_squares.jl
index a7003f697..e09ad92bc 100644
--- a/lib/SimpleNonlinearSolve/test/least_squares.jl
+++ b/lib/SimpleNonlinearSolve/test/least_squares.jl
@@ -13,7 +13,9 @@ end
 
 θ_init = θ_true .+ 0.1
 prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
-sol = solve(prob_oop, SimpleNewtonRaphson())
-sol = solve(prob_oop, SimpleGaussNewton())
 
-@test norm(sol.resid) < 1e-12
+for solver in [SimpleNewtonRaphson(AutoForwardDiff()), SimpleGaussNewton(AutoForwardDiff()),
+        SimpleNewtonRaphson(AutoFiniteDiff()), SimpleGaussNewton(AutoFiniteDiff())]
+    sol = solve(prob_oop, solver)
+    @test norm(sol.resid) < 1e-12
+end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index d0fd1ff9b..a38e954d8 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -5,7 +5,6 @@ const GROUP = get(ENV, "GROUP", "All")
 @time begin
     if GROUP == "All" || GROUP == "Core"
         @time @safetestset "Basic Tests + Some AD" include("basictests.jl")
-        @time @safetestset "Inplace Tests" include("inplace.jl")
         @time @safetestset "Matrix Resizing Tests" include("matrix_resizing_tests.jl")
         @time @safetestset "Least Squares Tests" include("least_squares.jl")
     end

From c1d3e8c14f2f5ae0def54d84499b8b6f4597046b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 Nov 2023 01:55:44 -0500
Subject: [PATCH 235/700] Fix the tests

---
 lib/SimpleNonlinearSolve/src/ad.jl            |   3 +-
 .../src/bracketing/bisection.jl               |  10 +-
 .../src/nlsolve/broyden.jl                    |   4 +-
 .../src/nlsolve/dfsane.jl                     |   3 +
 .../src/nlsolve/halley.jl                     |   4 +-
 .../src/nlsolve/klement.jl                    |   4 +-
 .../src/nlsolve/trustRegion.jl                |   9 +-
 .../test/23_test_problems.jl                  |  87 +++++
 lib/SimpleNonlinearSolve/test/Project.toml    |   1 +
 lib/SimpleNonlinearSolve/test/basictests.jl   | 308 +++++++-----------
 .../test/matrix_resizing_tests.jl             |   3 +-
 lib/SimpleNonlinearSolve/test/runtests.jl     |   5 +-
 12 files changed, 228 insertions(+), 213 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/test/23_test_problems.jl

diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index 8cbff710c..d4cbcf744 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -1,9 +1,8 @@
 function scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     f = prob.f
     p = value(prob.p)
-    u0 = value(prob.u0)
     if prob isa IntervalNonlinearProblem
-        tspan = value(prob.tspan)
+        tspan = value.(prob.tspan)
         newprob = IntervalNonlinearProblem(f, tspan, p; prob.kwargs...)
     else
         u0 = value(prob.u0)
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
index 42bb2cad0..66418b3e0 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
@@ -86,16 +86,18 @@ function __bisection(left, right, fl, fr, f::F; abstol, maxiters, prob, alg) whe
         end
 
         fm = f(mid)
-        if abs((right - left) / 2) < abstol || abs(fm) < abstol
+        if abs((right - left) / 2) < abstol
             sol = build_solution(prob, alg, mid, fm; left, right,
                 retcode = ReturnCode.Success)
             break
         end
 
-        if sign(fl * fm) < 0
-            right, fr = mid, fm
+        if iszero(fm)
+            right = mid
+            fr = fm
         else
-            left, fl = mid, fm
+            left = mid
+            fl = fm
         end
 
         i += 1
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index aaf959cb5..1e544a4d2 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -43,7 +43,9 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
 
         @bb @. δJ⁻¹n = (δx - J⁻¹δf) / d
 
-        @bb δJ⁻¹ = δJ⁻¹n × transpose(xᵀJ⁻¹)
+        δJ⁻¹n_ = _vec(δJ⁻¹n)
+        xᵀJ⁻¹_ = _vec(xᵀJ⁻¹)
+        @bb δJ⁻¹ = δJ⁻¹n_ × transpose(xᵀJ⁻¹_)
         @bb J⁻¹ .+= δJ⁻¹
 
         @bb copyto!(xo, x)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 657f760cb..77ee497a3 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -72,6 +72,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
     fx_norm = norm(fx)^nexp
     α_1 = one(T)
     f_1 = fx_norm
+
     history_f_k = fill(fx_norm, M)
 
     # Generate the cache
@@ -118,6 +119,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
 
             fx = __eval_f(prob, fx, x)
             fx_norm_new = norm(fx)^nexp
+
+            k += 1
         end
 
         tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index 3e6e4d55f..161abaed1 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -58,7 +58,9 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
         @bb A .*= -1
         bᵢ = dfx \ Aaᵢ
 
-        @bb @. cᵢ = (aᵢ * aᵢ) / (-aᵢ + (T(0.5) * bᵢ))
+        cᵢ_ = _vec(cᵢ)
+        @bb @. cᵢ_ = (aᵢ * aᵢ) / (-aᵢ + (T(0.5) * bᵢ))
+        cᵢ = _restructure(cᵢ, cᵢ_)
 
         if i == 1
             if iszero(fx)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
index 56d6ccd55..5041dc4df 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
@@ -55,9 +55,9 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
 
         @bb copyto!(δx, fprev)
         if setindex_trait(δx) === CanSetindex()
-            ldiv!(F_, δx)
+            ldiv!(F_, _vec(δx))
         else
-            δx = F_ \ δx
+            δx = _restructure(δx, F_ \ _vec(δx))
         end
         @bb @. x = xo - δx
         fx = __eval_f(prob, fx, x)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index 3c3ad60b4..bf85dcfe3 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -76,7 +76,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
 
     fₖ = 0.5 * norm(fx)^2
     H = ∇f' * ∇f
-    g = ∇f' * fx
+    g = _restructure(x, ∇f' * _vec(fx))
     shrink_counter = 0
 
     @bb δsd = copy(x)
@@ -96,7 +96,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
         fₖ₊₁ = norm(fx)^2 / T(2)
 
         # Compute the ratio of the actual to predicted reduction.
-        @bb Hδ = H × δ
+        # @show size(H), size(δ)
+        @bb Hδ = H × vec(δ)
         r = (fₖ₊₁ - fₖ) / (dot(δ', g) + dot(δ', Hδ) / T(2))
 
         # Update the trust region radius.
@@ -124,7 +125,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
             fₖ = fₖ₊₁
 
             @bb H = transpose(∇f) × ∇f
-            @bb g = transpose(∇f) × fx
+            @bb g = transpose(∇f) × vec(fx)
         end
     end
 
@@ -135,7 +136,7 @@ function dogleg_method!!(cache, J, f, g, Δ)
     (; δsd, δN_δsd, δN) = cache
 
     # Compute the Newton step.
-    @bb δN .= J \ f
+    @bb δN .= _restructure(δN, J \ _vec(f))
     @bb δN .*= -1
     # Test if the full step is within the trust region.
     (norm(δN) ≤ Δ) && return δN
diff --git a/lib/SimpleNonlinearSolve/test/23_test_problems.jl b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
new file mode 100644
index 000000000..5edd5710b
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
@@ -0,0 +1,87 @@
+using SimpleNonlinearSolve, LinearAlgebra, NonlinearProblemLibrary, Test
+
+problems = NonlinearProblemLibrary.problems
+dicts = NonlinearProblemLibrary.dicts
+
+function test_on_library(problems, dicts, alg_ops, broken_tests, ϵ = 1e-4;
+        skip_tests = nothing)
+    for (idx, (problem, dict)) in enumerate(zip(problems, dicts))
+        x = dict["start"]
+        res = similar(x)
+        nlprob = NonlinearProblem(problem, copy(x))
+        @testset "$idx: $(dict["title"])" begin
+            for alg in alg_ops
+                try
+                    sol = solve(nlprob, alg;
+                        termination_condition = AbsNormTerminationMode())
+                    problem(res, sol.u, nothing)
+
+                    skip = skip_tests !== nothing && idx in skip_tests[alg]
+                    if skip
+                        @test_skip norm(res) ≤ ϵ
+                        continue
+                    end
+                    broken = idx in broken_tests[alg] ? true : false
+                    @test norm(res)≤ϵ broken=broken
+                catch
+                    broken = idx in broken_tests[alg] ? true : false
+                    if broken
+                        @test false broken=true
+                    else
+                        @test 1 == 2
+                    end
+                end
+            end
+        end
+    end
+end
+
+@testset "SimpleNewtonRaphson 23 Test Problems" begin
+    alg_ops = (SimpleNewtonRaphson(),)
+
+    # dictionary with indices of test problems where method does not converge to small residual
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [6]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testset "SimpleTrustRegion 23 Test Problems" begin
+    alg_ops = (SimpleTrustRegion(),)
+
+    # dictionary with indices of test problems where method does not converge to small residual
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [3, 6, 15, 16, 21]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testset "SimpleDFSane 23 Test Problems" begin
+    alg_ops = (SimpleDFSane(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 15, 16, 17, 21, 22]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testset "SimpleBroyden 23 Test Problems" begin
+    alg_ops = (SimpleBroyden(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 6, 11, 12, 13, 14]
+
+    skip_tests = Dict(alg => Int[] for alg in alg_ops)
+    skip_tests[alg_ops[1]] = [22]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests; skip_tests)
+end
+
+@testset "SimpleKlement 23 Test Problems" begin
+    alg_ops = (SimpleKlement(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13, 19, 21, 22]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
diff --git a/lib/SimpleNonlinearSolve/test/Project.toml b/lib/SimpleNonlinearSolve/test/Project.toml
index 835a6aa43..b8072e68e 100644
--- a/lib/SimpleNonlinearSolve/test/Project.toml
+++ b/lib/SimpleNonlinearSolve/test/Project.toml
@@ -4,6 +4,7 @@ DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
+NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 4963a52fe..413a6a512 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -1,5 +1,5 @@
-using BenchmarkTools, LinearSolve, NonlinearSolve, StaticArrays, Random, LinearAlgebra,
-    Test, ForwardDiff, DiffEqBase
+using BenchmarkTools, LinearSolve, SimpleNonlinearSolve, StaticArrays, Random,
+    LinearAlgebra, Test, ForwardDiff, DiffEqBase
 
 _nameof(x) = applicable(nameof, x) ? nameof(x) : _nameof(typeof(x))
 
@@ -163,8 +163,8 @@ end
 
 # --- SimpleBroyden / SimpleKlement / SimpleLimitedMemoryBroyden tests ---
 
-@testset "$(alg)" for alg in [SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
-        SimpleLimitedMemoryBroyden()]
+@testset "$(_nameof(alg))" for alg in [SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
+    SimpleLimitedMemoryBroyden()]
     function benchmark_nlsolve_oop(f, u0, p = 2.0)
         prob = NonlinearProblem{false}(f, u0, p)
         return solve(prob, alg, abstol = 1e-9)
@@ -190,30 +190,39 @@ end
     @testset "Allocations: Static Array and Scalars" begin
         @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, $(@SVector[1.0, 1.0]),
             2.0)) < 200
-        @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, 1.0, 2.0)) == 0
+        allocs = alg isa SimpleDFSane ? 144 : 0
+        @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, 1.0, 2.0)) == allocs
     end
 
     @testset "[OOP] Immutable AD" begin
         for p in [1.0, 100.0]
-            @test begin
-                res = benchmark_nlsolve_oop(quadratic_f, @SVector[1.0, 1.0], p)
-                res_true = sqrt(p)
-                all(res.u .≈ res_true)
+            res = benchmark_nlsolve_oop(quadratic_f, @SVector[1.0, 1.0], p)
+
+            if any(x -> isnan(x) || x <= 1e-5 || x >= 1e5, res)
+                @test_broken all(res .≈ sqrt(p))
+                @test_broken abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
+                    @SVector[1.0, 1.0], p).u[end], p)) ≈ 1 / (2 * sqrt(p))
+            else
+                @test all(res .≈ sqrt(p))
+                @test isapprox(abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
+                        @SVector[1.0, 1.0], p).u[end], p)), 1 / (2 * sqrt(p)))
             end
-            @test ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
-                @SVector[1.0, 1.0], p).u[end], p) ≈ 1 / (2 * sqrt(p))
         end
     end
 
     @testset "[OOP] Scalar AD" begin
         for p in 1.0:0.1:100.0
-            @test begin
-                res = benchmark_nlsolve_oop(quadratic_f, 1.0, p)
-                res_true = sqrt(p)
-                res.u ≈ res_true
+            res = benchmark_nlsolve_oop(quadratic_f, 1.0, p)
+
+            if any(x -> isnan(x) || x <= 1e-5 || x >= 1e5, res)
+                @test_broken all(res .≈ sqrt(p))
+                @test_broken abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
+                        1.0, p).u, p)) ≈ 1 / (2 * sqrt(p))
+            else
+                @test all(res .≈ sqrt(p))
+                @test isapprox(abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
+                            1.0, p).u, p)), 1 / (2 * sqrt(p)))
             end
-            @test ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f, 1.0, p).u,
-                p) ≈ 1 / (2 * sqrt(p))
         end
     end
 
@@ -231,185 +240,109 @@ end
     end
 end
 
+@testset "Newton Fails" begin
+    function benchmark_nlsolve_oop(f, u0, p, alg)
+        prob = NonlinearProblem{false}(f, u0, p)
+        return solve(prob, alg; abstol = 1e-9)
+    end
 
-1 + 1 + 1
+    u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
+    p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 
-# tspan = (1.0, 20.0)
-# # Falsi
-# g = function (p)
-#     probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
-#     sol = solve(probN, Falsi())
-#     return sol.left
-# end
+    for alg in (SimpleDFSane(), SimpleTrustRegion(), SimpleHalley())
+        sol = benchmark_nlsolve_oop(newton_fails, u0, p, alg)
+        @test SciMLBase.successful_retcode(sol)
+        @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
+    end
+end
 
-# for p in 1.1:0.1:100.0
-#     @test g(p) ≈ sqrt(p)
-#     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
-# end
+# --- Interval Nonlinear Problems ---
 
-# # Ridder
-# g = function (p)
-#     probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
-#     sol = solve(probN, Ridder())
-#     return sol.left
-# end
+@testset "Interval Nonlinear Problem: $(alg)" for alg in (Bisection(), Falsi(), Ridder(),
+    Brent(), ITP(), Alefeld())
+    tspan = (1.0, 20.0)
 
-# for p in 1.1:0.1:100.0
-#     @test g(p) ≈ sqrt(p)
-#     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
-# end
+    function g(p)
+        probN = IntervalNonlinearProblem{false}(quadratic_f, typeof(p).(tspan), p)
+        sol = solve(probN, alg; abstol = 1e-9)
+        return sol.left
+    end
 
-# # Brent
-# g = function (p)
-#     probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
-#     sol = solve(probN, Brent())
-#     return sol.left
-# end
+    for p in 1.1:0.1:100.0
+        @test g(p)≈sqrt(p) atol=1e-3 rtol=1e-3
+        @test ForwardDiff.derivative(g, p)≈1 / (2 * sqrt(p)) atol=1e-3 rtol=1e-3
+    end
 
-# for p in 1.1:0.1:100.0
-#     @test g(p) ≈ sqrt(p)
-#     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
-# end
+    t = (p) -> [sqrt(p[2] / p[1])]
+    p = [0.9, 50.0]
 
-# # ITP
-# g = function (p)
-#     probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
-#     sol = solve(probN, ITP())
-#     return sol.u
-# end
+    function g2(p)
+        probN = IntervalNonlinearProblem{false}((u, p) -> p[1] * u * u - p[2], tspan, p)
+        sol = solve(probN, alg; abstol = 1e-9)
+        return [sol.u]
+    end
 
-# for p in 1.1:0.1:100.0
-#     @test g(p) ≈ sqrt(p)
-#     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
-# end
+    @test g2(p)≈[sqrt(p[2] / p[1])] atol=1e-3 rtol=1e-3
+    @test ForwardDiff.jacobian(g2, p)≈ForwardDiff.jacobian(t, p) atol=1e-3 rtol=1e-3
 
-# # Alefeld
-# g = function (p)
-#     probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
-#     sol = solve(probN, Alefeld())
-#     return sol.u
-# end
+    probB = IntervalNonlinearProblem{false}(quadratic_f, (1.0, 2.0), 2.0)
+    sol = solve(probB, alg; abstol = 1e-9)
+    @test sol.left≈sqrt(2.0) atol=1e-3 rtol=1e-3
 
-# for p in 1.1:0.1:100.0
-#     @test g(p) ≈ sqrt(p)
-#     @test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
-# end
+    if !(alg isa Bisection || alg isa Falsi)
+        probB = IntervalNonlinearProblem{false}(quadratic_f, (sqrt(2.0), 10.0), 2.0)
+        sol = solve(probB, alg; abstol = 1e-9)
+        @test sol.left≈sqrt(2.0) atol=1e-3 rtol=1e-3
 
-# f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
-# t = (p) -> [sqrt(p[2] / p[1])]
-# p = [0.9, 50.0]
-# g = function (p)
-#     probN = IntervalNonlinearProblem{false}(f, tspan, p)
-#     sol = solve(probN, Alefeld())
-#     return [sol.u]
-# end
+        probB = IntervalNonlinearProblem{false}(quadratic_f, (0.0, sqrt(2.0)), 2.0)
+        sol = solve(probB, alg; abstol = 1e-9)
+        @test sol.left≈sqrt(2.0) atol=1e-3 rtol=1e-3
+    end
+end
 
-# @test g(p) ≈ [sqrt(p[2] / p[1])]
-# @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
-
-# f, tspan = (u, p) -> p[1] * u * u - p[2], (1.0, 100.0)
-# t = (p) -> [sqrt(p[2] / p[1])]
-# p = [0.9, 50.0]
-# for alg in [Bisection(), Falsi(), Ridder(), Brent(), ITP()]
-#     global g, p
-#     g = function (p)
-#         probN = IntervalNonlinearProblem{false}(f, tspan, p)
-#         sol = solve(probN, alg)
-#         return [sol.left]
-#     end
+@testset "Tolerance Tests Interval Methods: $(alg)" for alg in (Bisection(), Falsi(), ITP())
+    probB = IntervalNonlinearProblem(quadratic_f, tspan, 2.0)
+    tols = [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6, 1e-7]
+    ϵ = eps(1.0) #least possible tol for all methods
 
-#     @test g(p) ≈ [sqrt(p[2] / p[1])]
-#     @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p)
-# end
+    for atol in tols
+        sol = solve(probB, alg; abstol = atol)
+        @test abs(sol.u - sqrt(2)) < atol
+        @test abs(sol.u - sqrt(2)) > ϵ #test that the solution is not calculated upto max precision
+    end
+end
 
-# # Bisection Tests
-# f, tspan = (u, p) -> u .* u .- 2.0, (1.0, 2.0)
-# probB = IntervalNonlinearProblem(f, tspan)
-
-# # Falsi
-# sol = solve(probB, Falsi())
-# @test sol.left ≈ sqrt(2.0)
-
-# # Bisection
-# sol = solve(probB, Bisection())
-# @test sol.left ≈ sqrt(2.0)
-
-# # Ridder
-# sol = solve(probB, Ridder())
-# @test sol.left ≈ sqrt(2.0)
-# tspan = (sqrt(2.0), 10.0)
-# probB = IntervalNonlinearProblem(f, tspan)
-# sol = solve(probB, Ridder())
-# @test sol.left ≈ sqrt(2.0)
-# tspan = (0.0, sqrt(2.0))
-# probB = IntervalNonlinearProblem(f, tspan)
-# sol = solve(probB, Ridder())
-# @test sol.left ≈ sqrt(2.0)
-
-# # Brent
-# sol = solve(probB, Brent())
-# @test sol.left ≈ sqrt(2.0)
-# tspan = (sqrt(2.0), 10.0)
-# probB = IntervalNonlinearProblem(f, tspan)
-# sol = solve(probB, Brent())
-# @test sol.left ≈ sqrt(2.0)
-# tspan = (0.0, sqrt(2.0))
-# probB = IntervalNonlinearProblem(f, tspan)
-# sol = solve(probB, Brent())
-# @test sol.left ≈ sqrt(2.0)
-
-# # Alefeld
-# sol = solve(probB, Alefeld())
-# @test sol.u ≈ sqrt(2.0)
-# tspan = (sqrt(2.0), 10.0)
-# probB = IntervalNonlinearProblem(f, tspan)
-# sol = solve(probB, Alefeld())
-# @test sol.u ≈ sqrt(2.0)
-# tspan = (0.0, sqrt(2.0))
-# probB = IntervalNonlinearProblem(f, tspan)
-# sol = solve(probB, Alefeld())
-# @test sol.u ≈ sqrt(2.0)
-
-# # ITP
-# sol = solve(probB, ITP())
-# @test sol.u ≈ sqrt(2.0)
-# tspan = (sqrt(2.0), 10.0)
-# probB = IntervalNonlinearProblem(f, tspan)
-# sol = solve(probB, ITP())
-# @test sol.u ≈ sqrt(2.0)
-# tspan = (0.0, sqrt(2.0))
-# probB = IntervalNonlinearProblem(f, tspan)
-# sol = solve(probB, ITP())
-# @test sol.u ≈ sqrt(2.0)
-
-# # Tolerance tests for Interval methods
-# f, tspan = (u, p) -> u .* u .- 2.0, (1.0, 10.0)
-# probB = IntervalNonlinearProblem(f, tspan)
-# tols = [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6, 1e-7]
-# ϵ = eps(1.0) #least possible tol for all methods
-
-# for atol in tols
-#     sol = solve(probB, Bisection(), abstol = atol)
-#     @test abs(sol.u - sqrt(2)) < atol
-#     @test abs(sol.u - sqrt(2)) > ϵ #test that the solution is not calculated upto max precision
-#     sol = solve(probB, Falsi(), abstol = atol)
-#     @test abs(sol.u - sqrt(2)) < atol
-#     @test abs(sol.u - sqrt(2)) > ϵ
-#     sol = solve(probB, ITP(), abstol = atol)
-#     @test abs(sol.u - sqrt(2)) < atol
-#     @test abs(sol.u - sqrt(2)) > ϵ
-# end
+@testset "Tolerance Tests Interval Methods: $(alg)" for alg in (Ridder(), Brent())
+    probB = IntervalNonlinearProblem(quadratic_f, tspan, 2.0)
+    tols = [0.1] # Ridder and Brent converge rapidly so as we lower tolerance below 0.01, it converges with max precision to the solution
+    ϵ = eps(1.0) #least possible tol for all methods
 
-# tols = [0.1] # Ridder and Brent converge rapidly so as we lower tolerance below 0.01, it converges with max precision to the solution
-# for atol in tols
-#     sol = solve(probB, Ridder(), abstol = atol)
-#     @test abs(sol.u - sqrt(2)) < atol
-#     @test abs(sol.u - sqrt(2)) > ϵ
-#     sol = solve(probB, Brent(), abstol = atol)
-#     @test abs(sol.u - sqrt(2)) < atol
-#     @test abs(sol.u - sqrt(2)) > ϵ
-# end
+    for atol in tols
+        sol = solve(probB, alg; abstol = atol)
+        @test abs(sol.u - sqrt(2)) < atol
+        @test abs(sol.u - sqrt(2)) > ϵ #test that the solution is not calculated upto max precision
+    end
+end
 
+@testset "Flipped Signs and Reversed Tspan: $(alg)" for alg in (Alefeld(), Bisection(),
+    Falsi(), Brent(), ITP(), Ridder())
+    f1(u, p) = u * u - p
+    f2(u, p) = p - u * u
+
+    for p in 1:4
+        inp1 = IntervalNonlinearProblem(f1, (1.0, 2.0), p)
+        inp2 = IntervalNonlinearProblem(f2, (1.0, 2.0), p)
+        inp3 = IntervalNonlinearProblem(f1, (2.0, 1.0), p)
+        inp4 = IntervalNonlinearProblem(f2, (2.0, 1.0), p)
+        @test abs.(solve(inp1, alg).u) ≈ sqrt.(p)
+        @test abs.(solve(inp2, alg).u) ≈ sqrt.(p)
+        @test abs.(solve(inp3, alg).u) ≈ sqrt.(p)
+        @test abs.(solve(inp4, alg).u) ≈ sqrt.(p)
+    end
+end
+
+# The following tests were included in the previos versions but these kwargs never did
+# anything!
 # # Garuntee Tests for Bisection
 # f = function (u, p)
 #     if u < 2.0
@@ -435,20 +368,3 @@ end
 # @test f(nextfloat(sol.left), nothing) >= 0.0
 # @test f(sol.right, nothing) >= 0.0
 # @test f(prevfloat(sol.right), nothing) <= 0.0
-
-# # Flipped signs & reversed tspan test for bracketing algorithms
-# f1(u, p) = u * u - p
-# f2(u, p) = p - u * u
-
-# for alg in (Alefeld(), Bisection(), Falsi(), Brent(), ITP(), Ridder())
-#     for p in 1:4
-#         inp1 = IntervalNonlinearProblem(f1, (1.0, 2.0), p)
-#         inp2 = IntervalNonlinearProblem(f2, (1.0, 2.0), p)
-#         inp3 = IntervalNonlinearProblem(f1, (2.0, 1.0), p)
-#         inp4 = IntervalNonlinearProblem(f2, (2.0, 1.0), p)
-#         @test abs.(solve(inp1, alg).u) ≈ sqrt.(p)
-#         @test abs.(solve(inp2, alg).u) ≈ sqrt.(p)
-#         @test abs.(solve(inp3, alg).u) ≈ sqrt.(p)
-#         @test abs.(solve(inp4, alg).u) ≈ sqrt.(p)
-#     end
-# end
diff --git a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
index 9a1989b71..9c81beb6b 100644
--- a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
@@ -6,6 +6,7 @@ p = 2.0
 vecprob = NonlinearProblem(ff, vec(u0), p)
 prob = NonlinearProblem(ff, u0, p)
 
-for alg in (Klement(), Broyden(), SimpleNewtonRaphson())
+@testset "$(alg)" for alg in (SimpleKlement(), SimpleBroyden(), SimpleNewtonRaphson(),
+    SimpleDFSane(), SimpleLimitedMemoryBroyden(), SimpleTrustRegion())
     @test vec(solve(prob, alg).u) == solve(vecprob, alg).u
 end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index a38e954d8..35a7d5c25 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -1,11 +1,12 @@
-using SafeTestsets
+using SafeTestsets, Test
 
 const GROUP = get(ENV, "GROUP", "All")
 
-@time begin
+@time @testset "SimpleNonlinearSolve.jl"
     if GROUP == "All" || GROUP == "Core"
         @time @safetestset "Basic Tests + Some AD" include("basictests.jl")
         @time @safetestset "Matrix Resizing Tests" include("matrix_resizing_tests.jl")
         @time @safetestset "Least Squares Tests" include("least_squares.jl")
+        @time @safetestset "23 Test Problems" include("23_test_problems.jl")
     end
 end

From 88e99f650f738cfee8134025bfb8f70290f44a05 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 Nov 2023 01:55:53 -0500
Subject: [PATCH 236/700] Bump version

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 8e6b0f510..3c6f51afa 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.1.26"
+version = "0.2.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 3111c2884ef870fefce814a6645691762e01a78f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 Nov 2023 02:00:40 -0500
Subject: [PATCH 237/700] Formatting fix

---
 lib/SimpleNonlinearSolve/test/least_squares.jl | 2 +-
 lib/SimpleNonlinearSolve/test/runtests.jl      | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/least_squares.jl b/lib/SimpleNonlinearSolve/test/least_squares.jl
index e09ad92bc..bc801421f 100644
--- a/lib/SimpleNonlinearSolve/test/least_squares.jl
+++ b/lib/SimpleNonlinearSolve/test/least_squares.jl
@@ -15,7 +15,7 @@ end
 prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
 
 for solver in [SimpleNewtonRaphson(AutoForwardDiff()), SimpleGaussNewton(AutoForwardDiff()),
-        SimpleNewtonRaphson(AutoFiniteDiff()), SimpleGaussNewton(AutoFiniteDiff())]
+    SimpleNewtonRaphson(AutoFiniteDiff()), SimpleGaussNewton(AutoFiniteDiff())]
     sol = solve(prob_oop, solver)
     @test norm(sol.resid) < 1e-12
 end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 35a7d5c25..cc4cd70b3 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -2,7 +2,7 @@ using SafeTestsets, Test
 
 const GROUP = get(ENV, "GROUP", "All")
 
-@time @testset "SimpleNonlinearSolve.jl"
+@time @testset "SimpleNonlinearSolve.jl" begin
     if GROUP == "All" || GROUP == "Core"
         @time @safetestset "Basic Tests + Some AD" include("basictests.jl")
         @time @safetestset "Matrix Resizing Tests" include("matrix_resizing_tests.jl")

From f6c952fbb683ca79509035ab91e1715e29bf9cb1 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 27 Nov 2023 09:03:46 -0500
Subject: [PATCH 238/700] Fix the tests

---
 lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl    | 1 -
 lib/SimpleNonlinearSolve/test/23_test_problems.jl      | 7 ++++---
 lib/SimpleNonlinearSolve/test/basictests.jl            | 3 ++-
 lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl | 2 +-
 4 files changed, 7 insertions(+), 6 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index bf85dcfe3..b4db39691 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -96,7 +96,6 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
         fₖ₊₁ = norm(fx)^2 / T(2)
 
         # Compute the ratio of the actual to predicted reduction.
-        # @show size(H), size(δ)
         @bb Hδ = H × vec(δ)
         r = (fₖ₊₁ - fₖ) / (dot(δ', g) + dot(δ', Hδ) / T(2))
 
diff --git a/lib/SimpleNonlinearSolve/test/23_test_problems.jl b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
index 5edd5710b..40b261c34 100644
--- a/lib/SimpleNonlinearSolve/test/23_test_problems.jl
+++ b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
@@ -1,4 +1,4 @@
-using SimpleNonlinearSolve, LinearAlgebra, NonlinearProblemLibrary, Test
+using SimpleNonlinearSolve, LinearAlgebra, NonlinearProblemLibrary, DiffEqBase, Test
 
 problems = NonlinearProblemLibrary.problems
 dicts = NonlinearProblemLibrary.dicts
@@ -23,7 +23,8 @@ function test_on_library(problems, dicts, alg_ops, broken_tests, ϵ = 1e-4;
                     end
                     broken = idx in broken_tests[alg] ? true : false
                     @test norm(res)≤ϵ broken=broken
-                catch
+                catch e
+                    @error e
                     broken = idx in broken_tests[alg] ? true : false
                     if broken
                         @test false broken=true
@@ -69,7 +70,7 @@ end
     alg_ops = (SimpleBroyden(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 6, 11, 12, 13, 14]
+    broken_tests[alg_ops[1]] = [1, 4, 5, 6, 11, 12, 13, 14]
 
     skip_tests = Dict(alg => Int[] for alg in alg_ops)
     skip_tests[alg_ops[1]] = [22]
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 413a6a512..e5f874569 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -156,7 +156,6 @@ end
         u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @show solve(probN, SimpleHalley(); termination_condition).u
         @test all(solve(probN, SimpleHalley(); termination_condition).u .≈ sqrt(2.0))
     end
 end
@@ -301,6 +300,7 @@ end
 end
 
 @testset "Tolerance Tests Interval Methods: $(alg)" for alg in (Bisection(), Falsi(), ITP())
+    tspan = (1.0, 20.0)
     probB = IntervalNonlinearProblem(quadratic_f, tspan, 2.0)
     tols = [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6, 1e-7]
     ϵ = eps(1.0) #least possible tol for all methods
@@ -313,6 +313,7 @@ end
 end
 
 @testset "Tolerance Tests Interval Methods: $(alg)" for alg in (Ridder(), Brent())
+    tspan = (1.0, 20.0)
     probB = IntervalNonlinearProblem(quadratic_f, tspan, 2.0)
     tols = [0.1] # Ridder and Brent converge rapidly so as we lower tolerance below 0.01, it converges with max precision to the solution
     ϵ = eps(1.0) #least possible tol for all methods
diff --git a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
index 9c81beb6b..66f6a3d0c 100644
--- a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
@@ -8,5 +8,5 @@ prob = NonlinearProblem(ff, u0, p)
 
 @testset "$(alg)" for alg in (SimpleKlement(), SimpleBroyden(), SimpleNewtonRaphson(),
     SimpleDFSane(), SimpleLimitedMemoryBroyden(), SimpleTrustRegion())
-    @test vec(solve(prob, alg).u) == solve(vecprob, alg).u
+    @test vec(solve(prob, alg).u) ≈ solve(vecprob, alg).u
 end

From ab95a667324e02645758200b5e9bb9f157e983fa Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 27 Nov 2023 10:05:32 -0500
Subject: [PATCH 239/700] Add AllocCheck.jl

---
 lib/SimpleNonlinearSolve/test/Project.toml  |  1 +
 lib/SimpleNonlinearSolve/test/basictests.jl | 35 ++++++++++++++++++++-
 2 files changed, 35 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/Project.toml b/lib/SimpleNonlinearSolve/test/Project.toml
index b8072e68e..230ab90ea 100644
--- a/lib/SimpleNonlinearSolve/test/Project.toml
+++ b/lib/SimpleNonlinearSolve/test/Project.toml
@@ -1,4 +1,5 @@
 [deps]
+AllocCheck = "9b6a8646-10ed-4001-bbdc-1d2f46dfbb1a"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index e5f874569..3643f5db3 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -1,4 +1,4 @@
-using BenchmarkTools, LinearSolve, SimpleNonlinearSolve, StaticArrays, Random,
+using AllocCheck, BenchmarkTools, LinearSolve, SimpleNonlinearSolve, StaticArrays, Random,
     LinearAlgebra, Test, ForwardDiff, DiffEqBase
 
 _nameof(x) = applicable(nameof, x) ? nameof(x) : _nameof(typeof(x))
@@ -255,6 +255,39 @@ end
     end
 end
 
+# --- Allocation Checks ---
+
+## SimpleDFSane needs to allocate a history vector
+@testset "Allocation Checks: $(_nameof(alg))" for alg in (
+        SimpleNewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 2)),
+        SimpleHalley(; autodiff = AutoForwardDiff(; chunksize = 2)),
+        SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
+        SimpleTrustRegion(; autodiff = AutoForwardDiff(; chunksize = 2)))
+    @check_allocs nlsolve(prob, alg) = DiffEqBase.__solve(prob, alg; abstol = 1e-9)
+
+    nlprob_scalar = NonlinearProblem{false}(quadratic_f, 1.0, 2.0)
+    nlprob_sa = NonlinearProblem{false}(quadratic_f, @SVector[1.0, 1.0], 2.0)
+
+    try
+        nlsolve(nlprob_scalar, alg)
+        @test true
+    catch e
+        @error e
+        @test false
+    end
+
+    # ForwardDiff allocates for hessian since we don't propagate the chunksize
+    # SimpleLimitedMemoryBroyden needs to do views on the low rank matrices so the sizes
+    # are dynamic. This can be fixed but no without maintaining the simplicity of the code
+    try
+        nlsolve(nlprob_sa, alg)
+        @test true
+    catch e
+        @error e
+        @test false broken=(alg isa SimpleHalley || alg isa SimpleLimitedMemoryBroyden)
+    end
+end
+
 # --- Interval Nonlinear Problems ---
 
 @testset "Interval Nonlinear Problem: $(alg)" for alg in (Bisection(), Falsi(), Ridder(),

From e908f1417982bbcbdc668e63ec7804e9ff7e2a1f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 27 Nov 2023 10:15:42 -0500
Subject: [PATCH 240/700] Fix chunk size picking for StaticArrays

---
 lib/SimpleNonlinearSolve/src/utils.jl       | 14 ++++++++++++--
 lib/SimpleNonlinearSolve/test/basictests.jl |  8 +++-----
 2 files changed, 15 insertions(+), 7 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 870b526f4..444128bf0 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -39,13 +39,23 @@ __standard_tag(::Nothing, x) = ForwardDiff.Tag(SimpleNonlinearSolveTag(), eltype
 __standard_tag(tag::ForwardDiff.Tag, _) = tag
 __standard_tag(tag, x) = ForwardDiff.Tag(tag, eltype(x))
 
+__pick_forwarddiff_chunk(x) = ForwardDiff.Chunk(length(x))
+function __pick_forwarddiff_chunk(x::StaticArray)
+    L = prod(Size(x))
+    if L ≤ ForwardDiff.DEFAULT_CHUNK_THRESHOLD
+        return ForwardDiff.Chunk{L}()
+    else
+        return ForwardDiff.Chunk{ForwardDiff.DEFAULT_CHUNK_THRESHOLD}()
+    end
+end
+
 function __get_jacobian_config(ad::AutoForwardDiff{CS}, f, x) where {CS}
-    ck = (CS === nothing || CS ≤ 0) ? ForwardDiff.Chunk(length(x)) : ForwardDiff.Chunk{CS}()
+    ck = (CS === nothing || CS ≤ 0) ? __pick_forwarddiff_chunk(x) : ForwardDiff.Chunk{CS}()
     tag = __standard_tag(ad.tag, x)
     return ForwardDiff.JacobianConfig(f, x, ck, tag)
 end
 function __get_jacobian_config(ad::AutoForwardDiff{CS}, f!, y, x) where {CS}
-    ck = (CS === nothing || CS ≤ 0) ? ForwardDiff.Chunk(length(x)) : ForwardDiff.Chunk{CS}()
+    ck = (CS === nothing || CS ≤ 0) ? __pick_forwarddiff_chunk(x) : ForwardDiff.Chunk{CS}()
     tag = __standard_tag(ad.tag, x)
     return ForwardDiff.JacobianConfig(f!, y, x, ck, tag)
 end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 3643f5db3..a9dc24c68 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -258,11 +258,9 @@ end
 # --- Allocation Checks ---
 
 ## SimpleDFSane needs to allocate a history vector
-@testset "Allocation Checks: $(_nameof(alg))" for alg in (
-        SimpleNewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 2)),
-        SimpleHalley(; autodiff = AutoForwardDiff(; chunksize = 2)),
-        SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
-        SimpleTrustRegion(; autodiff = AutoForwardDiff(; chunksize = 2)))
+@testset "Allocation Checks: $(_nameof(alg))" for alg in ( SimpleNewtonRaphson(),
+        SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
+        SimpleTrustRegion())
     @check_allocs nlsolve(prob, alg) = DiffEqBase.__solve(prob, alg; abstol = 1e-9)
 
     nlprob_scalar = NonlinearProblem{false}(quadratic_f, 1.0, 2.0)

From 23779dfa00e5c6f2f24ead25b5634665f3d0b348 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 27 Nov 2023 21:33:22 -0500
Subject: [PATCH 241/700] Skip 1 broyden test

---
 lib/SimpleNonlinearSolve/test/23_test_problems.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/23_test_problems.jl b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
index 40b261c34..a0d5bc68e 100644
--- a/lib/SimpleNonlinearSolve/test/23_test_problems.jl
+++ b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
@@ -73,7 +73,7 @@ end
     broken_tests[alg_ops[1]] = [1, 4, 5, 6, 11, 12, 13, 14]
 
     skip_tests = Dict(alg => Int[] for alg in alg_ops)
-    skip_tests[alg_ops[1]] = [22]
+    skip_tests[alg_ops[1]] = [2, 22]
 
     test_on_library(problems, dicts, alg_ops, broken_tests; skip_tests)
 end

From 32c20f1f7a85e843cae56c0813644870054a7a46 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 27 Nov 2023 21:56:22 -0500
Subject: [PATCH 242/700] Change the norm

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 3 ++-
 lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl       | 8 ++++----
 lib/SimpleNonlinearSolve/test/basictests.jl          | 6 +++---
 3 files changed, 9 insertions(+), 8 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 66d7d4271..a723b0a12 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -8,7 +8,8 @@ import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidat
 
     import DiffEqBase: AbstractNonlinearTerminationMode,
         AbstractSafeNonlinearTerminationMode, AbstractSafeBestNonlinearTerminationMode,
-        NonlinearSafeTerminationReturnCode, get_termination_mode
+        NonlinearSafeTerminationReturnCode, get_termination_mode,
+        NONLINEARSOLVE_DEFAULT_NORM
     using FiniteDiff, ForwardDiff
     import ForwardDiff: Dual
     import MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 77ee497a3..2cbbd163f 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -69,7 +69,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
     abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
         termination_condition)
 
-    fx_norm = norm(fx)^nexp
+    fx_norm = NONLINEARSOLVE_DEFAULT_NORM(fx)^nexp
     α_1 = one(T)
     f_1 = fx_norm
 
@@ -99,7 +99,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
         @bb @. x += α_p * d
 
         fx = __eval_f(prob, fx, x)
-        fx_norm_new = norm(fx)^nexp
+        fx_norm_new = NONLINEARSOLVE_DEFAULT_NORM(fx)^nexp
 
         while k < maxiters
             fx_norm_new ≤ (f_bar + η - γ * α_p^2 * fx_norm) && break
@@ -108,7 +108,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
             @bb @. x -= α_m * d
 
             fx = __eval_f(prob, fx, x)
-            fx_norm_new = norm(fx)^nexp
+            fx_norm_new = NONLINEARSOLVE_DEFAULT_NORM(fx)^nexp
 
             fx_norm_new ≤ (f_bar + η - γ * α_m^2 * fx_norm) && break
 
@@ -118,7 +118,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
             @bb @. x += α_p * d
 
             fx = __eval_f(prob, fx, x)
-            fx_norm_new = norm(fx)^nexp
+            fx_norm_new = NONLINEARSOLVE_DEFAULT_NORM(fx)^nexp
 
             k += 1
         end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index a9dc24c68..6b7040308 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -258,9 +258,9 @@ end
 # --- Allocation Checks ---
 
 ## SimpleDFSane needs to allocate a history vector
-@testset "Allocation Checks: $(_nameof(alg))" for alg in ( SimpleNewtonRaphson(),
-        SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
-        SimpleTrustRegion())
+@testset "Allocation Checks: $(_nameof(alg))" for alg in (SimpleNewtonRaphson(),
+    SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
+    SimpleTrustRegion())
     @check_allocs nlsolve(prob, alg) = DiffEqBase.__solve(prob, alg; abstol = 1e-9)
 
     nlprob_scalar = NonlinearProblem{false}(quadratic_f, 1.0, 2.0)

From cd2e8c990a36af2a4371c8b5952e2f987c3190f0 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 27 Nov 2023 22:38:35 -0500
Subject: [PATCH 243/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 3c6f51afa..b5838a949 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "0.2.0"
+version = "1.0.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 7f0cedd18a36a3b590c2988c3ddbe050b978f953 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 28 Nov 2023 11:23:49 -0500
Subject: [PATCH 244/700] Add compat entries and change default norm

---
 lib/SimpleNonlinearSolve/Project.toml               |  3 +++
 lib/SimpleNonlinearSolve/src/nlsolve/halley.jl      |  4 ++++
 lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl | 12 ++++++------
 3 files changed, 13 insertions(+), 6 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index b5838a949..7db247364 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -18,11 +18,14 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [compat]
+ADTypes = "0.2"
 ArrayInterface = "7"
+ConcreteStructs = "0.2"
 DiffEqBase = "6.126"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 LinearAlgebra = "1.9"
+MaybeInplace = "0.1"
 PrecompileTools = "1"
 Reexport = "1"
 SciMLBase = "2.7"
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index 161abaed1..37379764c 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -14,6 +14,10 @@ A low-overhead implementation of Halley's Method.
 
   - `autodiff`: determines the backend used for the Hessian. Defaults to
     `AutoForwardDiff()`. Valid choices are `AutoForwardDiff()` or `AutoFiniteDiff()`.
+
+!!! warning
+
+    Inplace Problems are currently not supported by this method.
 """
 @kwdef @concrete struct SimpleHalley <: AbstractNewtonAlgorithm
     autodiff = AutoForwardDiff()
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index b4db39691..35719ff21 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -71,10 +71,10 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
         termination_condition)
 
     # Set default trust region radius if not specified by user.
-    Δₘₐₓ == 0 && (Δₘₐₓ = max(norm(fx), maximum(x) - minimum(x)))
+    Δₘₐₓ == 0 && (Δₘₐₓ = max(NONLINEARSOLVE_DEFAULT_NORM(fx), maximum(x) - minimum(x)))
     Δ == 0 && (Δ = Δₘₐₓ / 11)
 
-    fₖ = 0.5 * norm(fx)^2
+    fₖ = 0.5 * NONLINEARSOLVE_DEFAULT_NORM(fx)^2
     H = ∇f' * ∇f
     g = _restructure(x, ∇f' * _vec(fx))
     shrink_counter = 0
@@ -93,7 +93,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
 
         fx = __eval_f(prob, fx, x)
 
-        fₖ₊₁ = norm(fx)^2 / T(2)
+        fₖ₊₁ = NONLINEARSOLVE_DEFAULT_NORM(fx)^2 / T(2)
 
         # Compute the ratio of the actual to predicted reduction.
         @bb Hδ = H × vec(δ)
@@ -120,7 +120,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
             fx, ∇f = value_and_jacobian(alg.autodiff, prob.f, fx, x, prob.p, jac_cache; J)
 
             # Update the trust region radius.
-            (r > η₃) && (norm(δ) ≈ Δ) && (Δ = min(t₂ * Δ, Δₘₐₓ))
+            (r > η₃) && (NONLINEARSOLVE_DEFAULT_NORM(δ) ≈ Δ) && (Δ = min(t₂ * Δ, Δₘₐₓ))
             fₖ = fₖ₊₁
 
             @bb H = transpose(∇f) × ∇f
@@ -138,12 +138,12 @@ function dogleg_method!!(cache, J, f, g, Δ)
     @bb δN .= _restructure(δN, J \ _vec(f))
     @bb δN .*= -1
     # Test if the full step is within the trust region.
-    (norm(δN) ≤ Δ) && return δN
+    (NONLINEARSOLVE_DEFAULT_NORM(δN) ≤ Δ) && return δN
 
     # Calcualte Cauchy point, optimum along the steepest descent direction.
     @bb δsd .= g
     @bb @. δsd *= -1
-    norm_δsd = norm(δsd)
+    norm_δsd = NONLINEARSOLVE_DEFAULT_NORM(δsd)
     if (norm_δsd ≥ Δ)
         @bb @. δsd *= Δ / norm_δsd
         return δsd

From f557f02ed49873dd85c2aad0655011f23aa734aa Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 28 Nov 2023 11:34:58 -0500
Subject: [PATCH 245/700] revert the norm change

---
 lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index 35719ff21..b4db39691 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -71,10 +71,10 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
         termination_condition)
 
     # Set default trust region radius if not specified by user.
-    Δₘₐₓ == 0 && (Δₘₐₓ = max(NONLINEARSOLVE_DEFAULT_NORM(fx), maximum(x) - minimum(x)))
+    Δₘₐₓ == 0 && (Δₘₐₓ = max(norm(fx), maximum(x) - minimum(x)))
     Δ == 0 && (Δ = Δₘₐₓ / 11)
 
-    fₖ = 0.5 * NONLINEARSOLVE_DEFAULT_NORM(fx)^2
+    fₖ = 0.5 * norm(fx)^2
     H = ∇f' * ∇f
     g = _restructure(x, ∇f' * _vec(fx))
     shrink_counter = 0
@@ -93,7 +93,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
 
         fx = __eval_f(prob, fx, x)
 
-        fₖ₊₁ = NONLINEARSOLVE_DEFAULT_NORM(fx)^2 / T(2)
+        fₖ₊₁ = norm(fx)^2 / T(2)
 
         # Compute the ratio of the actual to predicted reduction.
         @bb Hδ = H × vec(δ)
@@ -120,7 +120,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
             fx, ∇f = value_and_jacobian(alg.autodiff, prob.f, fx, x, prob.p, jac_cache; J)
 
             # Update the trust region radius.
-            (r > η₃) && (NONLINEARSOLVE_DEFAULT_NORM(δ) ≈ Δ) && (Δ = min(t₂ * Δ, Δₘₐₓ))
+            (r > η₃) && (norm(δ) ≈ Δ) && (Δ = min(t₂ * Δ, Δₘₐₓ))
             fₖ = fₖ₊₁
 
             @bb H = transpose(∇f) × ∇f
@@ -138,12 +138,12 @@ function dogleg_method!!(cache, J, f, g, Δ)
     @bb δN .= _restructure(δN, J \ _vec(f))
     @bb δN .*= -1
     # Test if the full step is within the trust region.
-    (NONLINEARSOLVE_DEFAULT_NORM(δN) ≤ Δ) && return δN
+    (norm(δN) ≤ Δ) && return δN
 
     # Calcualte Cauchy point, optimum along the steepest descent direction.
     @bb δsd .= g
     @bb @. δsd *= -1
-    norm_δsd = NONLINEARSOLVE_DEFAULT_NORM(δsd)
+    norm_δsd = norm(δsd)
     if (norm_δsd ≥ Δ)
         @bb @. δsd *= Δ / norm_δsd
         return δsd

From 6fe4ed6af8376381160e5d2a03a1d0f8e733e4fe Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 28 Nov 2023 12:42:10 -0500
Subject: [PATCH 246/700] No transpose

---
 lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index b4db39691..8cad64582 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -97,7 +97,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
 
         # Compute the ratio of the actual to predicted reduction.
         @bb Hδ = H × vec(δ)
-        r = (fₖ₊₁ - fₖ) / (dot(δ', g) + dot(δ', Hδ) / T(2))
+        r = (fₖ₊₁ - fₖ) / (dot(δ, g) + dot(δ, Hδ) / T(2))
 
         # Update the trust region radius.
         if r < η₂

From 338816074ffe8fe65a69f9556b202add5ccf86e6 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 28 Nov 2023 13:34:30 -0500
Subject: [PATCH 247/700] Disambiguate conditionals with `Bool`

---
 .../src/nlsolve/trustRegion.jl                     | 14 +++++++-------
 lib/SimpleNonlinearSolve/src/utils.jl              |  6 +++---
 2 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index 8cad64582..73f34357a 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -85,7 +85,6 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
     @bb Hδ = copy(x)
     dogleg_cache = (; δsd, δN_δsd, δN)
 
-    F = fx
     for k in 1:maxiters
         # Solve the trust region subproblem.
         δ = dogleg_method!!(dogleg_cache, ∇f, fx, g, Δ)
@@ -100,16 +99,16 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
         r = (fₖ₊₁ - fₖ) / (dot(δ, g) + dot(δ, Hδ) / T(2))
 
         # Update the trust region radius.
-        if r < η₂
+        if Bool(r ≥ η₂)
+            shrink_counter = 0
+        else
             Δ = t₁ * Δ
             shrink_counter += 1
             shrink_counter > max_shrink_times && return build_solution(prob, alg, x, fx;
                 retcode = ReturnCode.ConvergenceFailure)
-        else
-            shrink_counter = 0
         end
 
-        if r > η₁
+        if Bool(r ≥ η₁)
             # Termination Checks
             tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
             tc_sol !== nothing && return tc_sol
@@ -138,13 +137,14 @@ function dogleg_method!!(cache, J, f, g, Δ)
     @bb δN .= _restructure(δN, J \ _vec(f))
     @bb δN .*= -1
     # Test if the full step is within the trust region.
-    (norm(δN) ≤ Δ) && return δN
+    Bool(norm(δN) ≤ Δ) && return δN
 
     # Calcualte Cauchy point, optimum along the steepest descent direction.
     @bb δsd .= g
     @bb @. δsd *= -1
     norm_δsd = norm(δsd)
-    if (norm_δsd ≥ Δ)
+
+    if Bool(norm_δsd ≥ Δ)
         @bb @. δsd *= Δ / norm_δsd
         return δsd
     end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 444128bf0..b5381f33e 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -286,14 +286,14 @@ function check_termination(tc_cache, fx, x, xo, prob, alg)
 end
 function check_termination(tc_cache, fx, x, xo, prob, alg,
         ::AbstractNonlinearTerminationMode)
-    if tc_cache(fx, x, xo)
+    if Bool(tc_cache(fx, x, xo))
         return build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
     end
     return nothing
 end
 function check_termination(tc_cache, fx, x, xo, prob, alg,
         ::AbstractSafeNonlinearTerminationMode)
-    if tc_cache(fx, x, xo)
+    if Bool(tc_cache(fx, x, xo))
         if tc_cache.retcode == NonlinearSafeTerminationReturnCode.Success
             retcode = ReturnCode.Success
         elseif tc_cache.retcode == NonlinearSafeTerminationReturnCode.PatienceTermination
@@ -309,7 +309,7 @@ function check_termination(tc_cache, fx, x, xo, prob, alg,
 end
 function check_termination(tc_cache, fx, x, xo, prob, alg,
         ::AbstractSafeBestNonlinearTerminationMode)
-    if tc_cache(fx, x, xo)
+    if Bool(tc_cache(fx, x, xo))
         if tc_cache.retcode == NonlinearSafeTerminationReturnCode.Success
             retcode = ReturnCode.Success
         elseif tc_cache.retcode == NonlinearSafeTerminationReturnCode.PatienceTermination

From d64875d370fd1106bf3034cbec9c19f5faa97cb4 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 28 Nov 2023 14:47:44 -0500
Subject: [PATCH 248/700] Don't support Batched TR for correctness reasons

---
 lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl      | 4 ++--
 lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl | 8 ++++----
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 2cbbd163f..c3f00cd28 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -102,7 +102,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
         fx_norm_new = NONLINEARSOLVE_DEFAULT_NORM(fx)^nexp
 
         while k < maxiters
-            fx_norm_new ≤ (f_bar + η - γ * α_p^2 * fx_norm) && break
+            Bool(fx_norm_new ≤ (f_bar + η - γ * α_p^2 * fx_norm)) && break
 
             α_p = α_p^2 * fx_norm / (fx_norm_new + (T(2) * α_p - T(1)) * fx_norm)
             @bb @. x -= α_m * d
@@ -110,7 +110,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
             fx = __eval_f(prob, fx, x)
             fx_norm_new = NONLINEARSOLVE_DEFAULT_NORM(fx)^nexp
 
-            fx_norm_new ≤ (f_bar + η - γ * α_m^2 * fx_norm) && break
+            Bool(fx_norm_new ≤ (f_bar + η - γ * α_m^2 * fx_norm)) && break
 
             α_tm = α_m^2 * fx_norm / (fx_norm_new + (T(2) * α_m - T(1)) * fx_norm)
             α_p = clamp(α_p, τ_min * α_p, τ_max * α_p)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index 73f34357a..3976380b4 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -99,7 +99,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
         r = (fₖ₊₁ - fₖ) / (dot(δ, g) + dot(δ, Hδ) / T(2))
 
         # Update the trust region radius.
-        if Bool(r ≥ η₂)
+        if r ≥ η₂
             shrink_counter = 0
         else
             Δ = t₁ * Δ
@@ -108,7 +108,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
                 retcode = ReturnCode.ConvergenceFailure)
         end
 
-        if Bool(r ≥ η₁)
+        if r ≥ η₁
             # Termination Checks
             tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
             tc_sol !== nothing && return tc_sol
@@ -137,14 +137,14 @@ function dogleg_method!!(cache, J, f, g, Δ)
     @bb δN .= _restructure(δN, J \ _vec(f))
     @bb δN .*= -1
     # Test if the full step is within the trust region.
-    Bool(norm(δN) ≤ Δ) && return δN
+    (norm(δN) ≤ Δ) && return δN
 
     # Calcualte Cauchy point, optimum along the steepest descent direction.
     @bb δsd .= g
     @bb @. δsd *= -1
     norm_δsd = norm(δsd)
 
-    if Bool(norm_δsd ≥ Δ)
+    if (norm_δsd ≥ Δ)
         @bb @. δsd *= Δ / norm_δsd
         return δsd
     end

From 91304a756d2fdd5b4b5bb4d56ea8d4d95b7f0b20 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 30 Nov 2023 18:40:03 -0500
Subject: [PATCH 249/700] Needs a safety copy

---
 lib/SimpleNonlinearSolve/src/nlsolve/klement.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
index 5041dc4df..b4349425a 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
@@ -9,7 +9,7 @@ struct SimpleKlement <: AbstractSimpleNonlinearSolveAlgorithm end
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
         termination_condition = nothing, kwargs...)
-    x = float(prob.u0)
+    @bb x = copy(float(prob.u0))
     T = eltype(x)
     fx = _get_fx(prob, x)
 

From a7847537f9a4299baa6714b00a92d41104b1e1b3 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 30 Nov 2023 20:10:32 -0500
Subject: [PATCH 250/700] Extra cache in DFSane

---
 lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index c3f00cd28..f2cc13d6b 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -78,9 +78,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
     # Generate the cache
     @bb d = copy(x)
     @bb xo = copy(x)
-    @bb x_cache = copy(x)
     @bb δx = copy(x)
-    @bb fxo = copy(fx)
     @bb δf = copy(fx)
 
     k = 0
@@ -128,13 +126,13 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
 
         # Update spectral parameter
         @bb @. δx = x - xo
-        @bb @. δf = fx - fxo
+        @bb @. δf = fx - δf
 
         σ_k = dot(δx, δx) / dot(δx, δf)
 
         # Take step
         @bb copyto!(xo, x)
-        @bb copyto!(fxo, fx)
+        @bb copyto!(δf, fx)
         fx_norm = fx_norm_new
 
         # Store function value

From 6a7e3cee04a95dc001a9ce8a59f4fca62ee59225 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 4 Dec 2023 15:20:23 -0500
Subject: [PATCH 251/700] Bug fixes

---
 .../src/nlsolve/broyden.jl                    |  4 +--
 .../src/nlsolve/dfsane.jl                     | 25 +++++++++-------
 .../src/nlsolve/halley.jl                     |  4 +--
 .../src/nlsolve/klement.jl                    | 30 ++++++++-----------
 .../src/nlsolve/lbroyden.jl                   |  4 +--
 .../src/nlsolve/raphson.jl                    |  8 ++---
 .../src/nlsolve/trustRegion.jl                |  4 +--
 lib/SimpleNonlinearSolve/src/utils.jl         |  8 +++++
 .../test/23_test_problems.jl                  |  4 +--
 9 files changed, 47 insertions(+), 44 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index 1e544a4d2..5f2dccdc7 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -7,9 +7,9 @@ and static array problems.
 struct SimpleBroyden <: AbstractSimpleNonlinearSolveAlgorithm end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000,
+        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
         termination_condition = nothing, kwargs...)
-    @bb x = copy(float(prob.u0))
+    x = __maybe_unaliased(prob.u0, alias_u0)
     fx = _get_fx(prob, x)
 
     @bb xo = copy(x)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index f2cc13d6b..4f75cf9e6 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -51,9 +51,9 @@ Computation, 75, 1429-1448.](https://www.researchgate.net/publication/220576479_
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000,
+        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
         termination_condition = nothing, kwargs...)
-    x = float(copy(prob.u0))
+    x = __maybe_unaliased(prob.u0, alias_u0)
     fx = _get_fx(prob, x)
     T = eltype(x)
 
@@ -76,6 +76,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
     history_f_k = fill(fx_norm, M)
 
     # Generate the cache
+    @bb x_cache = similar(x)
     @bb d = copy(x)
     @bb xo = copy(x)
     @bb δx = copy(x)
@@ -89,38 +90,40 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
         # Line search direction
         @bb @. d = -σ_k * fx
 
-        η = η_strategy(f_1, k, x, fx)
+        η = η_strategy(f_1, k + 1, x, fx)
         f_bar = maximum(history_f_k)
         α_p = α_1
         α_m = α_1
 
-        @bb @. x += α_p * d
+        @bb @. x_cache = x + α_p * d
 
-        fx = __eval_f(prob, fx, x)
+        fx = __eval_f(prob, fx, x_cache)
         fx_norm_new = NONLINEARSOLVE_DEFAULT_NORM(fx)^nexp
 
         while k < maxiters
             Bool(fx_norm_new ≤ (f_bar + η - γ * α_p^2 * fx_norm)) && break
 
-            α_p = α_p^2 * fx_norm / (fx_norm_new + (T(2) * α_p - T(1)) * fx_norm)
-            @bb @. x -= α_m * d
+            α_tp = α_p^2 * fx_norm / (fx_norm_new + (T(2) * α_p - T(1)) * fx_norm)
+            @bb @. x_cache = x - α_m * d
 
-            fx = __eval_f(prob, fx, x)
+            fx = __eval_f(prob, fx, x_cache)
             fx_norm_new = NONLINEARSOLVE_DEFAULT_NORM(fx)^nexp
 
             Bool(fx_norm_new ≤ (f_bar + η - γ * α_m^2 * fx_norm)) && break
 
             α_tm = α_m^2 * fx_norm / (fx_norm_new + (T(2) * α_m - T(1)) * fx_norm)
-            α_p = clamp(α_p, τ_min * α_p, τ_max * α_p)
+            α_p = clamp(α_tp, τ_min * α_p, τ_max * α_p)
             α_m = clamp(α_tm, τ_min * α_m, τ_max * α_m)
-            @bb @. x += α_p * d
+            @bb @. x_cache = x + α_p * d
 
-            fx = __eval_f(prob, fx, x)
+            fx = __eval_f(prob, fx, x_cache)
             fx_norm_new = NONLINEARSOLVE_DEFAULT_NORM(fx)^nexp
 
             k += 1
         end
 
+        @bb copyto!(x, x_cache)
+
         tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
         tc_sol !== nothing && return tc_sol
 
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index 37379764c..88b30a032 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -24,12 +24,12 @@ A low-overhead implementation of Halley's Method.
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000,
+        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
         termination_condition = nothing, kwargs...)
     isinplace(prob) &&
         error("SimpleHalley currently only supports out-of-place nonlinear problems")
 
-    x = copy(float(prob.u0))
+    x = __maybe_unaliased(prob.u0, alias_u0)
     fx = _get_fx(prob, x)
     T = eltype(x)
 
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
index b4349425a..a4e6d917c 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
@@ -7,9 +7,9 @@ method is non-allocating on scalar and static array problems.
 struct SimpleKlement <: AbstractSimpleNonlinearSolveAlgorithm end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000,
+        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
         termination_condition = nothing, kwargs...)
-    @bb x = copy(float(prob.u0))
+    x = __maybe_unaliased(prob.u0, alias_u0)
     T = eltype(x)
     fx = _get_fx(prob, x)
 
@@ -21,13 +21,12 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
     @bb δx = copy(x)
     @bb fprev = copy(fx)
     @bb xo = copy(x)
-    @bb δf = copy(fx)
     @bb d = copy(x)
 
     J = __init_identity_jacobian(fx, x)
-    @bb J_cache = copy(J)
-    @bb δx² = copy(x)
-    @bb J_cache2 = copy(J)
+    @bb J_cache = similar(J)
+    @bb δx² = similar(x)
+    @bb J_cache2 = similar(J)
     @bb F = copy(J)
 
     for _ in 1:maxiters
@@ -67,23 +66,18 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
         tc_sol !== nothing && return tc_sol
 
         @bb δx .*= -1
-        @bb @. δf = fx - fprev
-
-        # Prevent division by 0
+        @bb J_cache .= J' .^ 2
         @bb @. δx² = δx^2
-        @bb @. J_cache = J^2
-        @bb d = transpose(J_cache) × vec(δx²)
-        @bb @. d = max(d, singular_tol)
-
+        @bb d = J_cache × vec(δx²)
         @bb δx² = J × vec(δx)
-        @bb @. δf = (δf - δx²) / d
-
-        _vδf, _vδx = _vec(δf), _vec(δx)
-        @bb J_cache = _vδf × transpose(_vδx)
+        @bb @. fprev = (fx - fprev - δx²) / ifelse(iszero(d), singular_tol, d)
+        @bb J_cache = vec(fprev) × transpose(_vec(δx))
         @bb @. J_cache *= J
         @bb J_cache2 = J_cache × J
-
         @bb @. J += J_cache2
+
+        @bb copyto!(fprev, fx)
+        @bb copyto!(xo, x)
     end
 
     return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index 4cc8ee025..6dcac6a37 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -22,9 +22,9 @@ function SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27))
 end
 
 @views function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyden,
-        args...; abstol = nothing, reltol = nothing, maxiters = 1000,
+        args...; abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
         termination_condition = nothing, kwargs...)
-    @bb x = copy(float(prob.u0))
+    x = __maybe_unaliased(prob.u0, alias_u0)
     threshold = __get_threshold(alg)
     η = min(SciMLBase._unwrap_val(threshold), maxiters)
 
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
index 22f7fba84..2ae14cddf 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
@@ -24,8 +24,8 @@ const SimpleGaussNewton = SimpleNewtonRaphson
 
 function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
         alg::SimpleNewtonRaphson, args...; abstol = nothing, reltol = nothing,
-        maxiters = 1000, termination_condition = nothing, kwargs...)
-    @bb x = copy(float(prob.u0))
+        maxiters = 1000, termination_condition = nothing, alias_u0 = false, kwargs...)
+    x = __maybe_unaliased(prob.u0, alias_u0)
     fx = _get_fx(prob, x)
     @bb xo = copy(x)
     J, jac_cache = jacobian_cache(alg.autodiff, prob.f, fx, x, prob.p)
@@ -37,9 +37,7 @@ function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresPr
         fx, dfx = value_and_jacobian(alg.autodiff, prob.f, fx, x, prob.p, jac_cache; J)
 
         if i == 1
-            if iszero(fx)
-                return build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
-            end
+            iszero(fx) && build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
         else
             # Termination Checks
             tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index 3976380b4..4f3baf37e 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -49,9 +49,9 @@ scalar and static array problems.
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000,
+        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
         termination_condition = nothing, kwargs...)
-    @bb x = copy(float(prob.u0))
+    x = __maybe_unaliased(prob.u0, alias_u0)
     T = eltype(real(x))
     Δₘₐₓ = T(alg.max_trust_radius)
     Δ = T(alg.initial_trust_radius)
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index b5381f33e..22b186255 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -335,3 +335,11 @@ end
 
 @inline __eval_f(prob, fx, x) = isinplace(prob) ? (prob.f(fx, x, prob.p); fx) :
                                 prob.f(x, prob.p)
+
+# Unalias
+@inline __maybe_unaliased(x::Union{Number, SArray}, ::Bool) = x
+@inline function __maybe_unaliased(x::AbstractArray, alias::Bool)
+    # Spend time coping iff we will mutate the array
+    (alias || !ArrayInterface.can_setindex(typeof(x))) && return x
+    return deepcopy(x)
+end
diff --git a/lib/SimpleNonlinearSolve/test/23_test_problems.jl b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
index a0d5bc68e..66b82fe9b 100644
--- a/lib/SimpleNonlinearSolve/test/23_test_problems.jl
+++ b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
@@ -61,7 +61,7 @@ end
     alg_ops = (SimpleDFSane(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 15, 16, 17, 21, 22]
+    broken_tests[alg_ops[1]] = [1, 2, 3, 4, 5, 6, 11, 21]
 
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
@@ -82,7 +82,7 @@ end
     alg_ops = (SimpleKlement(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13, 19, 21, 22]
+    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 6, 7, 11, 13, 22]
 
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end

From 54acf9fd94d6bff1845b3554b4ef66314e65a13b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 4 Dec 2023 16:17:47 -0500
Subject: [PATCH 252/700] Fix DFSane tests and Klement allocations

---
 lib/SimpleNonlinearSolve/src/nlsolve/klement.jl |  7 ++++---
 lib/SimpleNonlinearSolve/test/basictests.jl     | 10 +++++-----
 2 files changed, 9 insertions(+), 8 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
index a4e6d917c..262d3b4c3 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
@@ -44,10 +44,11 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
             # Singularity test
             if !issuccess(F_)
                 J = __init_identity_jacobian!!(J)
+                @bb copyto!(F, J)
                 if setindex_trait(J) === CanSetindex()
-                    lu!(J; check = false)
+                    F_ = lu!(F; check = false)
                 else
-                    J = lu(J; check = false)
+                    F_ = lu(F; check = false)
                 end
             end
         end
@@ -66,7 +67,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
         tc_sol !== nothing && return tc_sol
 
         @bb δx .*= -1
-        @bb J_cache .= J' .^ 2
+        @bb J_cache .= transpose(J) .^ 2
         @bb @. δx² = δx^2
         @bb d = J_cache × vec(δx²)
         @bb δx² = J × vec(δx)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 6b7040308..26038cd8c 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -198,11 +198,11 @@ end
             res = benchmark_nlsolve_oop(quadratic_f, @SVector[1.0, 1.0], p)
 
             if any(x -> isnan(x) || x <= 1e-5 || x >= 1e5, res)
-                @test_broken all(res .≈ sqrt(p))
+                @test_broken all(abs.(res) .≈ sqrt(p))
                 @test_broken abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
                     @SVector[1.0, 1.0], p).u[end], p)) ≈ 1 / (2 * sqrt(p))
             else
-                @test all(res .≈ sqrt(p))
+                @test all(abs.(res) .≈ sqrt(p))
                 @test isapprox(abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
                         @SVector[1.0, 1.0], p).u[end], p)), 1 / (2 * sqrt(p)))
             end
@@ -213,12 +213,12 @@ end
         for p in 1.0:0.1:100.0
             res = benchmark_nlsolve_oop(quadratic_f, 1.0, p)
 
-            if any(x -> isnan(x) || x <= 1e-5 || x >= 1e5, res)
-                @test_broken all(res .≈ sqrt(p))
+            if any(x -> isnan(x), res)
+                @test_broken abs(res.u) ≈ sqrt(p)
                 @test_broken abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
                         1.0, p).u, p)) ≈ 1 / (2 * sqrt(p))
             else
-                @test all(res .≈ sqrt(p))
+                @test abs(res.u) ≈ sqrt(p)
                 @test isapprox(abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
                             1.0, p).u, p)), 1 / (2 * sqrt(p)))
             end

From b8afd8d74eb637562e007938f15c822d3bbbe95f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 4 Dec 2023 16:26:37 -0500
Subject: [PATCH 253/700] Typo

---
 lib/SimpleNonlinearSolve/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
index 6bba38ff1..256a65ad4 100644
--- a/lib/SimpleNonlinearSolve/README.md
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -40,7 +40,7 @@ sol = solve(probB, ITP())
 
 For more details on the bracketing methods, refer to the [Tutorials](https://docs.sciml.ai/NonlinearSolve/stable/tutorials/nonlinear/#Using-Bracketing-Methods) and detailed [APIs](https://docs.sciml.ai/NonlinearSolve/stable/api/simplenonlinearsolve/#Solver-API)
 
-## Breaking Changes in v2
+## Breaking Changes in v1.0.0
 
   - Batched solvers have been removed in favor of `BatchedArrays.jl`. Stay tuned for detailed
     tutorials on how to use `BatchedArrays.jl` with `NonlinearSolve` & `SimpleNonlinearSolve`

From e196db7c0fad3c29b1de14bd18b607bc664c82e4 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 6 Dec 2023 14:48:20 -0500
Subject: [PATCH 254/700] Update Klement to exploit the diagonal structure

---
 lib/SimpleNonlinearSolve/Project.toml         |  2 +-
 .../src/nlsolve/klement.jl                    | 47 ++-----------------
 lib/SimpleNonlinearSolve/src/utils.jl         |  7 +++
 .../test/23_test_problems.jl                  |  2 +-
 4 files changed, 14 insertions(+), 44 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 7db247364..66caa1e17 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.0.0"
+version = "1.0.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
index 262d3b4c3..9351b45f1 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
@@ -13,8 +13,6 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
     T = eltype(x)
     fx = _get_fx(prob, x)
 
-    singular_tol = eps(T)^(2 // 3)
-
     abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
         termination_condition)
 
@@ -23,42 +21,14 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
     @bb xo = copy(x)
     @bb d = copy(x)
 
-    J = __init_identity_jacobian(fx, x)
-    @bb J_cache = similar(J)
+    J = one.(x)
     @bb δx² = similar(x)
-    @bb J_cache2 = similar(J)
-    @bb F = copy(J)
 
     for _ in 1:maxiters
-        if x isa Number
-            J < singular_tol && (J = __init_identity_jacobian!!(J))
-            F_ = J
-        else
-            @bb copyto!(F, J)
-            if setindex_trait(F) === CanSetindex()
-                F_ = lu!(F; check = false)
-            else
-                F_ = lu(F; check = false)
-            end
+        any(iszero, J) && (J = __init_identity_jacobian!!(J))
 
-            # Singularity test
-            if !issuccess(F_)
-                J = __init_identity_jacobian!!(J)
-                @bb copyto!(F, J)
-                if setindex_trait(J) === CanSetindex()
-                    F_ = lu!(F; check = false)
-                else
-                    F_ = lu(F; check = false)
-                end
-            end
-        end
+        @bb @. δx = fprev / J
 
-        @bb copyto!(δx, fprev)
-        if setindex_trait(δx) === CanSetindex()
-            ldiv!(F_, _vec(δx))
-        else
-            δx = _restructure(δx, F_ \ _vec(δx))
-        end
         @bb @. x = xo - δx
         fx = __eval_f(prob, fx, x)
 
@@ -67,15 +37,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
         tc_sol !== nothing && return tc_sol
 
         @bb δx .*= -1
-        @bb J_cache .= transpose(J) .^ 2
-        @bb @. δx² = δx^2
-        @bb d = J_cache × vec(δx²)
-        @bb δx² = J × vec(δx)
-        @bb @. fprev = (fx - fprev - δx²) / ifelse(iszero(d), singular_tol, d)
-        @bb J_cache = vec(fprev) × transpose(_vec(δx))
-        @bb @. J_cache *= J
-        @bb J_cache2 = J_cache × J
-        @bb @. J += J_cache2
+        @bb @. δx² = δx^2 * J^2
+        @bb @. J += (fx - fprev - J * δx) / ifelse(iszero(δx²), T(1e-5), δx²) * δx * (J^2)
 
         @bb copyto!(fprev, fx)
         @bb copyto!(xo, x)
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 22b186255..5ee5731f9 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -212,6 +212,10 @@ function __init_identity_jacobian!!(J)
     J[diagind(J)] .= one(eltype(J))
     return J
 end
+function __init_identity_jacobian!!(J::AbstractVector)
+    fill!(J, one(eltype(J)))
+    return J
+end
 function __init_identity_jacobian(u::StaticArray, fu)
     S1, S2 = length(fu), length(u)
     J = SMatrix{S1, S2, eltype(u)}(I)
@@ -220,6 +224,9 @@ end
 function __init_identity_jacobian!!(J::SMatrix{S1, S2}) where {S1, S2}
     return SMatrix{S1, S2, eltype(J)}(I)
 end
+function __init_identity_jacobian!!(J::SVector{S1}) where {S1}
+    return ones(SVector{S1, eltype(J)})
+end
 
 function __init_low_rank_jacobian(u::StaticArray{S1, T1}, fu::StaticArray{S2, T2},
         ::Val{threshold}) where {S1, S2, T1, T2, threshold}
diff --git a/lib/SimpleNonlinearSolve/test/23_test_problems.jl b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
index 66b82fe9b..bf85967d3 100644
--- a/lib/SimpleNonlinearSolve/test/23_test_problems.jl
+++ b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
@@ -82,7 +82,7 @@ end
     alg_ops = (SimpleKlement(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 6, 7, 11, 13, 22]
+    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 6, 11, 12, 22]
 
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end

From a86117d172e1284f467677ea10bcef6e1774a9cd Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 6 Dec 2023 21:07:18 -0500
Subject: [PATCH 255/700] Fix links

---
 lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl | 10 +++++++---
 1 file changed, 7 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 4f75cf9e6..11f3af1d5 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -5,9 +5,7 @@
 
 A low-overhead implementation of the df-sane method for solving large-scale nonlinear
 systems of equations. For in depth information about all the parameters and the algorithm,
-see the paper: [W LaCruz, JM Martinez, and M Raydan (2006), Spectral residual mathod without
-gradient information for solving large-scale nonlinear systems of equations, Mathematics of
-Computation, 75, 1429-1448.](https://www.researchgate.net/publication/220576479_Spectral_Residual_Method_without_Gradient_Information_for_Solving_Large-Scale_Nonlinear_Systems_of_Equations)
+see the paper [1].
 
 ### Keyword Arguments
 
@@ -37,6 +35,12 @@ Computation, 75, 1429-1448.](https://www.researchgate.net/publication/220576479_
     ``f_1=||F(x_1)||^{nexp}``, `k` is the iteration number, `x` is the current `x`-value and
     `F` the current residual. Should satisfy ``η_k > 0`` and ``∑ₖ ηₖ < ∞``. Defaults to
     ``||F||^2 / k^2``.
+
+### References
+
+[1] W LaCruz, JM Martinez, and M Raydan (2006), Spectral residual mathod without gradient
+information for solving large-scale nonlinear systems of equations, Mathematics of
+Computation, 75, 1429-1448.
 """
 @kwdef @concrete struct SimpleDFSane <: AbstractSimpleNonlinearSolveAlgorithm
     σ_min = 1e-10

From ca5d82f90ff85c7fb4d78e0acb377db0e045b542 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 6 Dec 2023 21:10:38 -0500
Subject: [PATCH 256/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 7db247364..66caa1e17 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.0.0"
+version = "1.0.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 171cf42016fa6de90a7b12eaceb41559c73f837f Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 7 Dec 2023 12:07:37 -0500
Subject: [PATCH 257/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 66caa1e17..f1608e1ce 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.0.1"
+version = "1.0.2"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From beabc41712c94a286ece4767b2023dd928fadfb4 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 17 Dec 2023 13:56:06 -0500
Subject: [PATCH 258/700] Fix non vec Limited Memory Broyden

---
 lib/SimpleNonlinearSolve/Project.toml                  | 2 +-
 lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl       | 8 ++++----
 lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl | 4 ++--
 3 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index f1608e1ce..53749a72f 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.0.2"
+version = "1.0.3"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index 6dcac6a37..a78611a0a 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -68,8 +68,8 @@ end
         d = dot(vᵀ, δf)
         @bb @. δx = (δx - mvec) / d
 
-        selectdim(U, 2, mod1(i, η)) .= δx
-        selectdim(Vᵀ, 1, mod1(i, η)) .= vᵀ
+        selectdim(U, 2, mod1(i, η)) .= _vec(δx)
+        selectdim(Vᵀ, 1, mod1(i, η)) .= _vec(vᵀ)
 
         _U = selectdim(U, 2, 1:min(η, i))
         _Vᵀ = selectdim(Vᵀ, 1, 1:min(η, i))
@@ -93,7 +93,7 @@ function _rmatvec!!(y, xᵀU, U, Vᵀ, x)
     x_ = vec(x)
     xᵀU_ = view(xᵀU, 1:η)
     @bb xᵀU_ = transpose(U) × x_
-    @bb y = transpose(Vᵀ) × xᵀU_
+    @bb y = transpose(Vᵀ) × vec(xᵀU_)
     @bb @. y -= x
     return y
 end
@@ -108,7 +108,7 @@ function _matvec!!(y, Vᵀx, U, Vᵀ, x)
     x_ = vec(x)
     Vᵀx_ = view(Vᵀx, 1:η)
     @bb Vᵀx_ = Vᵀ × x_
-    @bb y = U × Vᵀx_
+    @bb y = U × vec(Vᵀx_)
     @bb @. y -= x
     return y
 end
diff --git a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
index 66f6a3d0c..455aac91a 100644
--- a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
@@ -1,12 +1,12 @@
 using SimpleNonlinearSolve
 
 ff(u, p) = u .* u .- p
-u0 = rand(2, 2)
+u0 = ones(2, 3)
 p = 2.0
 vecprob = NonlinearProblem(ff, vec(u0), p)
 prob = NonlinearProblem(ff, u0, p)
 
 @testset "$(alg)" for alg in (SimpleKlement(), SimpleBroyden(), SimpleNewtonRaphson(),
-    SimpleDFSane(), SimpleLimitedMemoryBroyden(), SimpleTrustRegion())
+    SimpleDFSane(), SimpleLimitedMemoryBroyden(; threshold = Val(2)), SimpleTrustRegion())
     @test vec(solve(prob, alg).u) ≈ solve(vecprob, alg).u
 end

From d7deef5ab0b2e6c1b3857e4cb24344d2b8637788 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 25 Dec 2023 12:22:31 -0500
Subject: [PATCH 259/700] Fix the 23 test problems

---
 lib/SimpleNonlinearSolve/test/23_test_problems.jl | 4 ++--
 lib/SimpleNonlinearSolve/test/Project.toml        | 3 +++
 2 files changed, 5 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/23_test_problems.jl b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
index bf85967d3..bc82145a9 100644
--- a/lib/SimpleNonlinearSolve/test/23_test_problems.jl
+++ b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
@@ -42,7 +42,7 @@ end
 
     # dictionary with indices of test problems where method does not converge to small residual
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [6]
+    broken_tests[alg_ops[1]] = []
 
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
@@ -82,7 +82,7 @@ end
     alg_ops = (SimpleKlement(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 6, 11, 12, 22]
+    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 11, 12, 22]
 
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
diff --git a/lib/SimpleNonlinearSolve/test/Project.toml b/lib/SimpleNonlinearSolve/test/Project.toml
index 230ab90ea..993e98749 100644
--- a/lib/SimpleNonlinearSolve/test/Project.toml
+++ b/lib/SimpleNonlinearSolve/test/Project.toml
@@ -11,3 +11,6 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[compat]
+NonlinearProblemLibrary = "0.1.2"

From 703d6ca3ded3c313e61caa2abce0c054b8edec8b Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 25 Dec 2023 12:31:02 -0500
Subject: [PATCH 260/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 53749a72f..8cd72d57f 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.0.3"
+version = "1.0.4"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From ff3c7bebde65ab7bfd7850d744062829336c7fa5 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 25 Dec 2023 15:33:04 -0500
Subject: [PATCH 261/700] Add Polyester ForwardDiff support

---
 lib/SimpleNonlinearSolve/Project.toml         | 10 ++++-
 ...leNonlinearSolvePolyesterForwardDiffExt.jl | 13 ++++++
 .../src/SimpleNonlinearSolve.jl               |  4 +-
 .../src/nlsolve/halley.jl                     |  7 ++-
 .../src/nlsolve/raphson.jl                    | 12 ++---
 .../src/nlsolve/trustRegion.jl                | 12 ++---
 lib/SimpleNonlinearSolve/src/utils.jl         | 45 ++++++++++++++-----
 7 files changed, 78 insertions(+), 25 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 8cd72d57f..124e21010 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.0.4"
+version = "1.1.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -17,8 +17,14 @@ Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
+[extensions]
+SimpleNonlinearSolvePolyesterForwardDiffExt = "PolyesterForwardDiff"
+
+[weakdeps]
+PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
+
 [compat]
-ADTypes = "0.2"
+ADTypes = "0.2.6"
 ArrayInterface = "7"
 ConcreteStructs = "0.2"
 DiffEqBase = "6.126"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
new file mode 100644
index 000000000..c15738f11
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
@@ -0,0 +1,13 @@
+module SimpleNonlinearSolvePolyesterForwardDiffExt
+
+using SimpleNonlinearSolve, PolyesterForwardDiff
+
+@inline SimpleNonlinearSolve.__is_extension_loaded(::Val{:PolyesterForwardDiff}) = true
+
+@inline function SimpleNonlinearSolve.__polyester_forwarddiff_jacobian!(f!::F, y, J, x,
+        chunksize) where {F}
+    PolyesterForwardDiff.threaded_jacobian!(f!, y, J, x, chunksize)
+    return J
+end
+
+end
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index a723b0a12..6ffe25420 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -9,7 +9,7 @@ import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidat
     import DiffEqBase: AbstractNonlinearTerminationMode,
         AbstractSafeNonlinearTerminationMode, AbstractSafeBestNonlinearTerminationMode,
         NonlinearSafeTerminationReturnCode, get_termination_mode,
-        NONLINEARSOLVE_DEFAULT_NORM
+        NONLINEARSOLVE_DEFAULT_NORM, _get_tolerance
     using FiniteDiff, ForwardDiff
     import ForwardDiff: Dual
     import MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
@@ -23,6 +23,8 @@ abstract type AbstractSimpleNonlinearSolveAlgorithm <: AbstractNonlinearAlgorith
 abstract type AbstractBracketingAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 abstract type AbstractNewtonAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 
+@inline __is_extension_loaded(::Val) = false
+
 include("utils.jl")
 
 ## Nonlinear Solvers
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index 88b30a032..fe83c0cfa 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -53,14 +53,17 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
         fx, dfx, d2fx = compute_jacobian_and_hessian(alg.autodiff, prob, fx, x)
         setindex_trait(x) === CannotSetindex() && (A = dfx)
 
-        aᵢ = dfx \ _vec(fx)
+        # Factorize Once and Reuse
+        dfx_fact = factorize(dfx)
+
+        aᵢ = dfx_fact \ _vec(fx)
         A_ = _vec(A)
         @bb A_ = d2fx × aᵢ
         A = _restructure(A, A_)
 
         @bb Aaᵢ = A × aᵢ
         @bb A .*= -1
-        bᵢ = dfx \ Aaᵢ
+        bᵢ = dfx_fact \ Aaᵢ
 
         cᵢ_ = _vec(cᵢ)
         @bb @. cᵢ_ = (aᵢ * aᵢ) / (-aᵢ + (T(0.5) * bᵢ))
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
index 2ae14cddf..e84f59521 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
@@ -1,6 +1,6 @@
 """
     SimpleNewtonRaphson(autodiff)
-    SimpleNewtonRaphson(; autodiff = AutoForwardDiff())
+    SimpleNewtonRaphson(; autodiff = nothing)
 
 A low-overhead implementation of Newton-Raphson. This method is non-allocating on scalar
 and static array problems.
@@ -14,10 +14,11 @@ and static array problems.
 ### Keyword Arguments
 
   - `autodiff`: determines the backend used for the Jacobian. Defaults to
-    `AutoForwardDiff()`. Valid choices are `AutoForwardDiff()` or `AutoFiniteDiff()`.
+    `nothing`. Valid choices are `AutoPolyesterForwardDiff()`, `AutoForwardDiff()` or
+    `AutoFiniteDiff()`.
 """
 @kwdef @concrete struct SimpleNewtonRaphson <: AbstractNewtonAlgorithm
-    autodiff = AutoForwardDiff()
+    autodiff = nothing
 end
 
 const SimpleGaussNewton = SimpleNewtonRaphson
@@ -27,14 +28,15 @@ function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresPr
         maxiters = 1000, termination_condition = nothing, alias_u0 = false, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
     fx = _get_fx(prob, x)
+    autodiff = __get_concrete_autodiff(prob, alg.autodiff)
     @bb xo = copy(x)
-    J, jac_cache = jacobian_cache(alg.autodiff, prob.f, fx, x, prob.p)
+    J, jac_cache = jacobian_cache(autodiff, prob.f, fx, x, prob.p)
 
     abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
         termination_condition)
 
     for i in 1:maxiters
-        fx, dfx = value_and_jacobian(alg.autodiff, prob.f, fx, x, prob.p, jac_cache; J)
+        fx, dfx = value_and_jacobian(autodiff, prob.f, fx, x, prob.p, jac_cache; J)
 
         if i == 1
             iszero(fx) && build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index 4f3baf37e..e8a90cdbd 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -10,7 +10,8 @@ scalar and static array problems.
 ### Keyword Arguments
 
   - `autodiff`: determines the backend used for the Jacobian. Defaults to
-    `AutoForwardDiff()`. Valid choices are `AutoForwardDiff()` or `AutoFiniteDiff()`.
+    `nothing`. Valid choices are `AutoPolyesterForwardDiff()`, `AutoForwardDiff()` or
+    `AutoFiniteDiff()`.
   - `max_trust_radius`: the maximum radius of the trust region. Defaults to
     `max(norm(f(u0)), maximum(u0) - minimum(u0))`.
   - `initial_trust_radius`: the initial trust region radius. Defaults to
@@ -37,7 +38,7 @@ scalar and static array problems.
     row, `max_shrink_times` is exceeded, the algorithm returns. Defaults to `32`.
 """
 @kwdef @concrete struct SimpleTrustRegion <: AbstractNewtonAlgorithm
-    autodiff = AutoForwardDiff()
+    autodiff = nothing
     max_trust_radius = 0.0
     initial_trust_radius = 0.0
     step_threshold = 0.0001
@@ -61,11 +62,12 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
     t₁ = T(alg.shrink_factor)
     t₂ = T(alg.expand_factor)
     max_shrink_times = alg.max_shrink_times
+    autodiff = __get_concrete_autodiff(prob, alg.autodiff)
 
     fx = _get_fx(prob, x)
     @bb xo = copy(x)
-    J, jac_cache = jacobian_cache(alg.autodiff, prob.f, fx, x, prob.p)
-    fx, ∇f = value_and_jacobian(alg.autodiff, prob.f, fx, x, prob.p, jac_cache; J)
+    J, jac_cache = jacobian_cache(autodiff, prob.f, fx, x, prob.p)
+    fx, ∇f = value_and_jacobian(autodiff, prob.f, fx, x, prob.p, jac_cache; J)
 
     abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
         termination_condition)
@@ -116,7 +118,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
             # Take the step.
             @bb @. xo = x
 
-            fx, ∇f = value_and_jacobian(alg.autodiff, prob.f, fx, x, prob.p, jac_cache; J)
+            fx, ∇f = value_and_jacobian(autodiff, prob.f, fx, x, prob.p, jac_cache; J)
 
             # Update the trust region radius.
             (r > η₃) && (norm(δ) ≈ Δ) && (Δ = min(t₂ * Δ, Δₘₐₓ))
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 5ee5731f9..b4b21162e 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -26,15 +26,6 @@ Return the maximum of `a` and `b` if `x1 > x0`, otherwise return the minimum.
 """
 __max_tdir(a, b, x0, x1) = ifelse(x1 > x0, max(a, b), min(a, b))
 
-__cvt_real(::Type{T}, ::Nothing) where {T} = nothing
-__cvt_real(::Type{T}, x) where {T} = real(T(x))
-
-_get_tolerance(η, ::Type{T}) where {T} = __cvt_real(T, η)
-function _get_tolerance(::Nothing, ::Type{T}) where {T}
-    η = real(oneunit(T)) * (eps(real(one(T))))^(4 // 5)
-    return _get_tolerance(η, T)
-end
-
 __standard_tag(::Nothing, x) = ForwardDiff.Tag(SimpleNonlinearSolveTag(), eltype(x))
 __standard_tag(tag::ForwardDiff.Tag, _) = tag
 __standard_tag(tag, x) = ForwardDiff.Tag(tag, eltype(x))
@@ -60,6 +51,12 @@ function __get_jacobian_config(ad::AutoForwardDiff{CS}, f!, y, x) where {CS}
     return ForwardDiff.JacobianConfig(f!, y, x, ck, tag)
 end
 
+function __get_jacobian_config(ad::AutoPolyesterForwardDiff{CS}, args...) where {CS}
+    x = last(args)
+    return (CS === nothing || CS ≤ 0) ? __pick_forwarddiff_chunk(x) :
+           ForwardDiff.Chunk{CS}()
+end
+
 """
     value_and_jacobian(ad, f, y, x, p, cache; J = nothing)
 
@@ -81,6 +78,9 @@ function value_and_jacobian(ad, f::F, y, x::X, p, cache; J = nothing) where {F,
             FiniteDiff.finite_difference_jacobian!(J, _f, x, cache)
             _f(y, x)
             return y, J
+        elseif ad isa AutoPolyesterForwardDiff
+            __polyester_forwarddiff_jacobian!(_f, y, J, x, cache)
+            return y, J
         else
             throw(ArgumentError("Unsupported AD method: $(ad)"))
         end
@@ -100,12 +100,18 @@ function value_and_jacobian(ad, f::F, y, x::X, p, cache; J = nothing) where {F,
         elseif ad isa AutoFiniteDiff
             J_fd = FiniteDiff.finite_difference_jacobian(_f, x, cache)
             return _f(x), J_fd
+        elseif ad isa AutoPolyesterForwardDiff
+            __polyester_forwarddiff_jacobian!(_f, J, x, cache)
+            return _f(x), J
         else
             throw(ArgumentError("Unsupported AD method: $(ad)"))
         end
     end
 end
 
+# Declare functions
+function __polyester_forwarddiff_jacobian! end
+
 function value_and_jacobian(ad, f::F, y, x::Number, p, cache; J = nothing) where {F}
     if DiffEqBase.has_jac(f)
         return f(x, p), f.jac(x, p)
@@ -132,7 +138,7 @@ function jacobian_cache(ad, f::F, y, x::X, p) where {F, X <: AbstractArray}
         J = similar(y, length(y), length(x))
         if DiffEqBase.has_jac(f)
             return J, nothing
-        elseif ad isa AutoForwardDiff
+        elseif ad isa AutoForwardDiff || ad isa AutoPolyesterForwardDiff
             return J, __get_jacobian_config(ad, _f, y, x)
         elseif ad isa AutoFiniteDiff
             return J, FiniteDiff.JacobianCache(copy(x), copy(y), copy(y), ad.fdtype)
@@ -146,6 +152,10 @@ function jacobian_cache(ad, f::F, y, x::X, p) where {F, X <: AbstractArray}
         elseif ad isa AutoForwardDiff
             J = ArrayInterface.can_setindex(x) ? similar(y, length(y), length(x)) : nothing
             return J, __get_jacobian_config(ad, _f, x)
+        elseif ad isa AutoPolyesterForwardDiff
+            @assert ArrayInterface.can_setindex(x) "PolyesterForwardDiff requires mutable inputs."
+            J = similar(y, length(y), length(x))
+            return J, __get_jacobian_config(ad, _f, x)
         elseif ad isa AutoFiniteDiff
             return nothing, FiniteDiff.JacobianCache(copy(x), copy(y), copy(y), ad.fdtype)
         else
@@ -350,3 +360,18 @@ end
     (alias || !ArrayInterface.can_setindex(typeof(x))) && return x
     return deepcopy(x)
 end
+
+# Decide which AD backend to use
+@inline __get_concrete_autodiff(prob, ad::ADTypes.AbstractADType) = ad
+@inline function __get_concrete_autodiff(prob, ::Nothing)
+    if ForwardDiff.can_dual(eltype(prob.u0))
+        if __is_extension_loaded(Val(:PolyesterForwardDiff)) && !(prob.u0 isa Number) &&
+           ArrayInterface.can_setindex(prob.u0)
+            return AutoPolyesterForwardDiff()
+        else
+            return AutoForwardDiff()
+        end
+    else
+        return AutoFiniteDiff()
+    end
+end
\ No newline at end of file

From 31c596d7bd9a1c3c7699bf2f63ba8285d246c924 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 26 Dec 2023 14:40:55 -0500
Subject: [PATCH 262/700] Add tests

---
 ...pleNonlinearSolvePolyesterForwardDiffExt.jl |  8 +++++++-
 lib/SimpleNonlinearSolve/src/nlsolve/halley.jl |  9 +++++----
 lib/SimpleNonlinearSolve/src/utils.jl          | 18 ++++++++++++------
 lib/SimpleNonlinearSolve/test/Project.toml     |  1 +
 lib/SimpleNonlinearSolve/test/basictests.jl    | 10 ++++++----
 5 files changed, 31 insertions(+), 15 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
index c15738f11..81cee481d 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
@@ -10,4 +10,10 @@ using SimpleNonlinearSolve, PolyesterForwardDiff
     return J
 end
 
-end
\ No newline at end of file
+@inline function SimpleNonlinearSolve.__polyester_forwarddiff_jacobian!(f::F, J, x,
+        chunksize) where {F}
+    PolyesterForwardDiff.threaded_jacobian!(f, J, x, chunksize)
+    return J
+end
+
+end
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index fe83c0cfa..50f7d38d0 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -12,15 +12,15 @@ A low-overhead implementation of Halley's Method.
 
 ### Keyword Arguments
 
-  - `autodiff`: determines the backend used for the Hessian. Defaults to
-    `AutoForwardDiff()`. Valid choices are `AutoForwardDiff()` or `AutoFiniteDiff()`.
+  - `autodiff`: determines the backend used for the Hessian. Defaults to `nothing`. Valid
+    choices are `AutoForwardDiff()` or `AutoFiniteDiff()`.
 
 !!! warning
 
     Inplace Problems are currently not supported by this method.
 """
 @kwdef @concrete struct SimpleHalley <: AbstractNewtonAlgorithm
-    autodiff = AutoForwardDiff()
+    autodiff = nothing
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
@@ -33,6 +33,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
     fx = _get_fx(prob, x)
     T = eltype(x)
 
+    autodiff = __get_concrete_autodiff(prob, alg.autodiff; polyester = Val(false))
     abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
         termination_condition)
 
@@ -50,7 +51,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
 
     for i in 1:maxiters
         # Hessian Computation is unfortunately type unstable
-        fx, dfx, d2fx = compute_jacobian_and_hessian(alg.autodiff, prob, fx, x)
+        fx, dfx, d2fx = compute_jacobian_and_hessian(autodiff, prob, fx, x)
         setindex_trait(x) === CannotSetindex() && (A = dfx)
 
         # Factorize Once and Reuse
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index b4b21162e..4fb620a53 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -119,6 +119,11 @@ function value_and_jacobian(ad, f::F, y, x::Number, p, cache; J = nothing) where
         T = typeof(__standard_tag(ad.tag, x))
         out = f(ForwardDiff.Dual{T}(x, one(x)), p)
         return ForwardDiff.value(out), ForwardDiff.extract_derivative(T, out)
+    elseif ad isa AutoPolyesterForwardDiff
+        # Just use ForwardDiff
+        T = typeof(__standard_tag(nothing, x))
+        out = f(ForwardDiff.Dual{T}(x, one(x)), p)
+        return ForwardDiff.value(out), ForwardDiff.extract_derivative(T, out)
     elseif ad isa AutoFiniteDiff
         _f = Base.Fix2(f, p)
         return _f(x), FiniteDiff.finite_difference_derivative(_f, x, ad.fdtype)
@@ -153,7 +158,7 @@ function jacobian_cache(ad, f::F, y, x::X, p) where {F, X <: AbstractArray}
             J = ArrayInterface.can_setindex(x) ? similar(y, length(y), length(x)) : nothing
             return J, __get_jacobian_config(ad, _f, x)
         elseif ad isa AutoPolyesterForwardDiff
-            @assert ArrayInterface.can_setindex(x) "PolyesterForwardDiff requires mutable inputs."
+            @assert ArrayInterface.can_setindex(x) "PolyesterForwardDiff requires mutable inputs. Use AutoForwardDiff instead."
             J = similar(y, length(y), length(x))
             return J, __get_jacobian_config(ad, _f, x)
         elseif ad isa AutoFiniteDiff
@@ -362,11 +367,12 @@ end
 end
 
 # Decide which AD backend to use
-@inline __get_concrete_autodiff(prob, ad::ADTypes.AbstractADType) = ad
-@inline function __get_concrete_autodiff(prob, ::Nothing)
+@inline __get_concrete_autodiff(prob, ad::ADTypes.AbstractADType; kwargs...) = ad
+@inline function __get_concrete_autodiff(prob, ::Nothing; polyester::Val{P} = Val(true),
+        kwargs...) where {P}
     if ForwardDiff.can_dual(eltype(prob.u0))
-        if __is_extension_loaded(Val(:PolyesterForwardDiff)) && !(prob.u0 isa Number) &&
-           ArrayInterface.can_setindex(prob.u0)
+        if P && __is_extension_loaded(Val(:PolyesterForwardDiff)) &&
+           !(prob.u0 isa Number) && ArrayInterface.can_setindex(prob.u0)
             return AutoPolyesterForwardDiff()
         else
             return AutoForwardDiff()
@@ -374,4 +380,4 @@ end
     else
         return AutoFiniteDiff()
     end
-end
\ No newline at end of file
+end
diff --git a/lib/SimpleNonlinearSolve/test/Project.toml b/lib/SimpleNonlinearSolve/test/Project.toml
index 993e98749..4442a15a6 100644
--- a/lib/SimpleNonlinearSolve/test/Project.toml
+++ b/lib/SimpleNonlinearSolve/test/Project.toml
@@ -7,6 +7,7 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 26038cd8c..7b4e7bbc8 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -1,5 +1,6 @@
 using AllocCheck, BenchmarkTools, LinearSolve, SimpleNonlinearSolve, StaticArrays, Random,
     LinearAlgebra, Test, ForwardDiff, DiffEqBase
+import PolyesterForwardDiff
 
 _nameof(x) = applicable(nameof, x) ? nameof(x) : _nameof(typeof(x))
 
@@ -29,20 +30,21 @@ const TERMINATION_CONDITIONS = [
 @testset "$(alg)" for alg in (SimpleNewtonRaphson, SimpleTrustRegion)
     # Eval else the alg is type unstable
     @eval begin
-        function benchmark_nlsolve_oop(f, u0, p = 2.0; autodiff = AutoForwardDiff())
+        function benchmark_nlsolve_oop(f, u0, p = 2.0; autodiff = nothing)
             prob = NonlinearProblem{false}(f, u0, p)
             return solve(prob, $(alg)(; autodiff), abstol = 1e-9)
         end
 
-        function benchmark_nlsolve_iip(f, u0, p = 2.0; autodiff = AutoForwardDiff())
+        function benchmark_nlsolve_iip(f, u0, p = 2.0; autodiff = nothing)
             prob = NonlinearProblem{true}(f, u0, p)
             return solve(prob, $(alg)(; autodiff), abstol = 1e-9)
         end
     end
 
     @testset "AutoDiff: $(_nameof(autodiff))" for autodiff in (AutoFiniteDiff(),
-        AutoForwardDiff())
+        AutoForwardDiff(), AutoPolyesterForwardDiff())
         @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
+            u0 isa SVector && autodiff isa AutoPolyesterForwardDiff && continue
             sol = benchmark_nlsolve_oop(quadratic_f, u0; autodiff)
             @test SciMLBase.successful_retcode(sol)
             @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
@@ -103,7 +105,7 @@ end
 # --- SimpleHalley tests ---
 
 @testset "SimpleHalley" begin
-    function benchmark_nlsolve_oop(f, u0, p = 2.0; autodiff = AutoForwardDiff())
+    function benchmark_nlsolve_oop(f, u0, p = 2.0; autodiff = nothing)
         prob = NonlinearProblem{false}(f, u0, p)
         return solve(prob, SimpleHalley(; autodiff), abstol = 1e-9)
     end

From 0f8ce36158903aad36642ef8a842d7b29a23c520 Mon Sep 17 00:00:00 2001
From: ErikQQY <2283984853@qq.com>
Date: Mon, 25 Dec 2023 23:58:16 +0800
Subject: [PATCH 263/700] Add downgrade CI

Signed-off-by: ErikQQY <2283984853@qq.com>
---
 .../.github/workflows/Downgrade.yml           | 29 +++++++++++++++++++
 lib/SimpleNonlinearSolve/Project.toml         | 20 ++++++-------
 2 files changed, 39 insertions(+), 10 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml
new file mode 100644
index 000000000..01ff8cad5
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml
@@ -0,0 +1,29 @@
+name: Downgrade
+on:
+  pull_request:
+    branches:
+      - master
+    paths-ignore:
+      - 'docs/**'
+  push:
+    branches:
+      - master
+    paths-ignore:
+      - 'docs/**'
+jobs:
+  test:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        version: ['1']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v1
+        with:
+          version: ${{ matrix.version }}
+      - uses: cjdoris/julia-downgrade-compat-action@v1
+#        if: ${{ matrix.version == '1.6' }}
+        with:
+          skip: Pkg,TOML
+      - uses: julia-actions/julia-buildpkg@v1
+      - uses: julia-actions/julia-runtest@v1
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 124e21010..b28d90b98 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -25,15 +25,15 @@ PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
 
 [compat]
 ADTypes = "0.2.6"
-ArrayInterface = "7"
-ConcreteStructs = "0.2"
-DiffEqBase = "6.126"
-FiniteDiff = "2"
-ForwardDiff = "0.10.3"
+ArrayInterface = "7.7"
+ConcreteStructs = "0.2.2"
+DiffEqBase = "6.144"
+FiniteDiff = "2.21"
+ForwardDiff = "0.10.36"
 LinearAlgebra = "1.9"
-MaybeInplace = "0.1"
-PrecompileTools = "1"
-Reexport = "1"
-SciMLBase = "2.7"
-StaticArraysCore = "1.4"
+MaybeInplace = "0.1.1"
+PrecompileTools = "1.2"
+Reexport = "1.2"
+SciMLBase = "2.11"
+StaticArraysCore = "1.4.2"
 julia = "1.9"

From b35a140865f42c0a2ead9314b12bae911620f9d6 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 25 Dec 2023 11:47:12 -0500
Subject: [PATCH 264/700] Update .github/workflows/Downgrade.yml

---
 lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml
index 01ff8cad5..cbcc6ac06 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml
@@ -2,7 +2,7 @@ name: Downgrade
 on:
   pull_request:
     branches:
-      - master
+      - main
     paths-ignore:
       - 'docs/**'
   push:

From 77cade8edfba21ac69d81b108115703d7fb0748c Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 26 Dec 2023 18:07:56 -0500
Subject: [PATCH 265/700] Add ForwardDiff Inplace Overloads

---
 lib/SimpleNonlinearSolve/Project.toml         |  2 +-
 lib/SimpleNonlinearSolve/src/ad.jl            | 95 ++++++++++--------
 .../src/nlsolve/halley.jl                     |  9 +-
 lib/SimpleNonlinearSolve/src/utils.jl         |  3 +
 lib/SimpleNonlinearSolve/test/basictests.jl   | 98 -------------------
 lib/SimpleNonlinearSolve/test/forward_ad.jl   | 93 ++++++++++++++++++
 lib/SimpleNonlinearSolve/test/runtests.jl     |  3 +-
 7 files changed, 160 insertions(+), 143 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/test/forward_ad.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 124e21010..7a7ac60d2 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.1.0"
+version = "1.2.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index d4cbcf744..f6f5f5895 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -1,21 +1,24 @@
-function scalar_nlsolve_ad(prob, alg, args...; kwargs...)
-    f = prob.f
+function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, <:AbstractArray},
+            iip, <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
+        alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...) where {T, V, P, iip}
+    sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
+    dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
+    return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats,
+        sol.original)
+end
+
+function __nlsolve_ad(prob::NonlinearProblem{uType, iip}, alg, args...;
+        kwargs...) where {uType, iip}
     p = value(prob.p)
-    if prob isa IntervalNonlinearProblem
-        tspan = value.(prob.tspan)
-        newprob = IntervalNonlinearProblem(f, tspan, p; prob.kwargs...)
-    else
-        u0 = value(prob.u0)
-        newprob = NonlinearProblem(f, u0, p; prob.kwargs...)
-    end
+    newprob = NonlinearProblem(prob.f, value(prob.u0), p; prob.kwargs...)
 
     sol = solve(newprob, alg, args...; kwargs...)
 
     uu = sol.u
-    f_p = scalar_nlsolve_∂f_∂p(f, uu, p)
-    f_x = scalar_nlsolve_∂f_∂u(f, uu, p)
+    f_p = __nlsolve_∂f_∂p(prob, prob.f, uu, p)
+    f_x = __nlsolve_∂f_∂u(prob, prob.f, uu, p)
 
-    z_arr = -inv(f_x) * f_p
+    z_arr = -f_x \ f_p
 
     pp = prob.p
     sumfun = ((z, p),) -> map(zᵢ -> zᵢ * ForwardDiff.partials(p), z)
@@ -30,49 +33,57 @@ function scalar_nlsolve_ad(prob, alg, args...; kwargs...)
     return sol, partials
 end
 
-function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, SVector, <:AbstractArray},
-            false, <:Dual{T, V, P}}, alg::AbstractSimpleNonlinearSolveAlgorithm, args...;
-        kwargs...) where {T, V, P}
-    sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
-    dual_soln = scalar_nlsolve_dual_soln(sol.u, partials, prob.p)
-    return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode)
-end
-
-function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, SVector, <:AbstractArray},
-            false, <:AbstractArray{<:Dual{T, V, P}}},
-        alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...) where {T, V, P}
-    sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
-    dual_soln = scalar_nlsolve_dual_soln(sol.u, partials, prob.p)
-    return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode)
-end
-
-function scalar_nlsolve_∂f_∂p(f, u, p)
-    ff = p isa Number ? ForwardDiff.derivative :
-         (u isa Number ? ForwardDiff.gradient : ForwardDiff.jacobian)
-    return ff(Base.Fix1(f, u), p)
+@inline function __nlsolve_∂f_∂p(prob, f::F, u, p) where {F}
+    if isinplace(prob)
+        __f = p -> begin
+            du = similar(u, promote_type(eltype(u), eltype(p)))
+            f(du, u, p)
+            return du
+        end
+    else
+        __f = Base.Fix1(f, u)
+    end
+    if p isa Number
+        return __reshape(ForwardDiff.derivative(__f, p), :, 1)
+    elseif u isa Number
+        return __reshape(ForwardDiff.gradient(__f, p), 1, :)
+    else
+        return ForwardDiff.jacobian(__f, p)
+    end
 end
 
-function scalar_nlsolve_∂f_∂u(f, u, p)
-    ff = u isa Number ? ForwardDiff.derivative : ForwardDiff.jacobian
-    return ff(Base.Fix2(f, p), u)
+@inline function __nlsolve_∂f_∂u(prob, f::F, u, p) where {F}
+    if isinplace(prob)
+        du = similar(u)
+        __f = (du, u) -> f(du, u, p)
+        ForwardDiff.jacobian(__f, du, u)
+    else
+        __f = Base.Fix2(f, p)
+        if u isa Number
+            return ForwardDiff.derivative(__f, u)
+        else
+            return ForwardDiff.jacobian(__f, u)
+        end
+    end
 end
 
-function scalar_nlsolve_dual_soln(u::Number, partials,
+@inline function __nlsolve_dual_soln(u::Number, partials,
         ::Union{<:AbstractArray{<:Dual{T, V, P}}, Dual{T, V, P}}) where {T, V, P}
     return Dual{T, V, P}(u, partials)
 end
 
-function scalar_nlsolve_dual_soln(u::AbstractArray, partials,
+@inline function __nlsolve_dual_soln(u::AbstractArray, partials,
         ::Union{<:AbstractArray{<:Dual{T, V, P}}, Dual{T, V, P}}) where {T, V, P}
-    return map(((uᵢ, pᵢ),) -> Dual{T, V, P}(uᵢ, pᵢ), zip(u, partials))
+    _partials = _restructure(u, partials)
+    return map(((uᵢ, pᵢ),) -> Dual{T, V, P}(uᵢ, pᵢ), zip(u, _partials))
 end
 
 # avoid ambiguities
 for Alg in [Bisection]
     @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
                 <:Dual{T, V, P}}, alg::$Alg, args...; kwargs...) where {uType, iip, T, V, P}
-        sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
-        dual_soln = scalar_nlsolve_dual_soln(sol.u, partials, prob.p)
+        sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
+        dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
         return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode,
             left = Dual{T, V, P}(sol.left, partials),
             right = Dual{T, V, P}(sol.right, partials))
@@ -80,8 +91,8 @@ for Alg in [Bisection]
     @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
                 <:AbstractArray{<:Dual{T, V, P}}}, alg::$Alg, args...;
             kwargs...) where {uType, iip, T, V, P}
-        sol, partials = scalar_nlsolve_ad(prob, alg, args...; kwargs...)
-        dual_soln = scalar_nlsolve_dual_soln(sol.u, partials, prob.p)
+        sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
+        dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
         return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode,
             left = Dual{T, V, P}(sol.left, partials),
             right = Dual{T, V, P}(sol.right, partials))
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index 50f7d38d0..491a340e3 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -55,7 +55,14 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
         setindex_trait(x) === CannotSetindex() && (A = dfx)
 
         # Factorize Once and Reuse
-        dfx_fact = factorize(dfx)
+        dfx_fact = if dfx isa Number
+            dfx
+        else
+            fact = lu(dfx; check = false)
+            !issuccess(fact) && return build_solution(prob, alg, x, fx;
+                retcode = ReturnCode.Unstable)
+            fact
+        end
 
         aᵢ = dfx_fact \ _vec(fx)
         A_ = _vec(A)
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 4fb620a53..b3018f5ac 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -381,3 +381,6 @@ end
         return AutoFiniteDiff()
     end
 end
+
+@inline __reshape(x::Number, args...) = x
+@inline __reshape(x::AbstractArray, args...) = reshape(x, args...)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 7b4e7bbc8..e43a90761 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -64,36 +64,6 @@ const TERMINATION_CONDITIONS = [
             autodiff = AutoForwardDiff())) == 0
     end
 
-    @testset "[OOP] Immutable AD" begin
-        for p in [1.0, 100.0]
-            @test begin
-                res = benchmark_nlsolve_oop(quadratic_f, @SVector[1.0, 1.0], p)
-                res_true = sqrt(p)
-                all(res.u .≈ res_true)
-            end
-            @test ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
-                @SVector[1.0, 1.0], p).u[end], p) ≈ 1 / (2 * sqrt(p))
-        end
-    end
-
-    @testset "[OOP] Scalar AD" begin
-        for p in 1.0:0.1:100.0
-            @test begin
-                res = benchmark_nlsolve_oop(quadratic_f, 1.0, p)
-                res_true = sqrt(p)
-                res.u ≈ res_true
-            end
-            @test ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f, 1.0, p).u,
-                p) ≈ 1 / (2 * sqrt(p))
-        end
-    end
-
-    t = (p) -> [sqrt(p[2] / p[1])]
-    p = [0.9, 50.0]
-    @test benchmark_nlsolve_oop(quadratic_f2, 0.5, p).u ≈ sqrt(p[2] / p[1])
-    @test ForwardDiff.jacobian(p -> [benchmark_nlsolve_oop(quadratic_f2, 0.5, p).u],
-        p) ≈ ForwardDiff.jacobian(t, p)
-
     @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 
@@ -124,36 +94,6 @@ end
             autodiff = AutoForwardDiff())) == 0
     end
 
-    @testset "[OOP] Immutable AD" begin
-        for p in [1.0, 100.0]
-            @test begin
-                res = benchmark_nlsolve_oop(quadratic_f, @SVector[1.0, 1.0], p)
-                res_true = sqrt(p)
-                all(res.u .≈ res_true)
-            end
-            @test ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
-                @SVector[1.0, 1.0], p).u[end], p) ≈ 1 / (2 * sqrt(p))
-        end
-    end
-
-    @testset "[OOP] Scalar AD" begin
-        for p in 1.0:0.1:100.0
-            @test begin
-                res = benchmark_nlsolve_oop(quadratic_f, 1.0, p)
-                res_true = sqrt(p)
-                res.u ≈ res_true
-            end
-            @test ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f, 1.0, p).u,
-                p) ≈ 1 / (2 * sqrt(p))
-        end
-    end
-
-    t = (p) -> [sqrt(p[2] / p[1])]
-    p = [0.9, 50.0]
-    @test benchmark_nlsolve_oop(quadratic_f2, 0.5, p).u ≈ sqrt(p[2] / p[1])
-    @test ForwardDiff.jacobian(p -> [benchmark_nlsolve_oop(quadratic_f2, 0.5, p).u],
-        p) ≈ ForwardDiff.jacobian(t, p)
-
     @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 
@@ -195,44 +135,6 @@ end
         @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, 1.0, 2.0)) == allocs
     end
 
-    @testset "[OOP] Immutable AD" begin
-        for p in [1.0, 100.0]
-            res = benchmark_nlsolve_oop(quadratic_f, @SVector[1.0, 1.0], p)
-
-            if any(x -> isnan(x) || x <= 1e-5 || x >= 1e5, res)
-                @test_broken all(abs.(res) .≈ sqrt(p))
-                @test_broken abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
-                    @SVector[1.0, 1.0], p).u[end], p)) ≈ 1 / (2 * sqrt(p))
-            else
-                @test all(abs.(res) .≈ sqrt(p))
-                @test isapprox(abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
-                        @SVector[1.0, 1.0], p).u[end], p)), 1 / (2 * sqrt(p)))
-            end
-        end
-    end
-
-    @testset "[OOP] Scalar AD" begin
-        for p in 1.0:0.1:100.0
-            res = benchmark_nlsolve_oop(quadratic_f, 1.0, p)
-
-            if any(x -> isnan(x), res)
-                @test_broken abs(res.u) ≈ sqrt(p)
-                @test_broken abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
-                        1.0, p).u, p)) ≈ 1 / (2 * sqrt(p))
-            else
-                @test abs(res.u) ≈ sqrt(p)
-                @test isapprox(abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
-                            1.0, p).u, p)), 1 / (2 * sqrt(p)))
-            end
-        end
-    end
-
-    t = (p) -> [sqrt(p[2] / p[1])]
-    p = [0.9, 50.0]
-    @test benchmark_nlsolve_oop(quadratic_f2, 0.5, p).u ≈ sqrt(p[2] / p[1])
-    @test ForwardDiff.jacobian(p -> [benchmark_nlsolve_oop(quadratic_f2, 0.5, p).u],
-        p) ≈ ForwardDiff.jacobian(t, p)
-
     @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 
diff --git a/lib/SimpleNonlinearSolve/test/forward_ad.jl b/lib/SimpleNonlinearSolve/test/forward_ad.jl
new file mode 100644
index 000000000..717c222df
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/forward_ad.jl
@@ -0,0 +1,93 @@
+using ForwardDiff, SimpleNonlinearSolve, StaticArrays, Test, LinearAlgebra
+
+test_f!(du, u, p) = (@. du = u^2 - p)
+test_f(u, p) = (@. u^2 - p)
+
+jacobian_f(::Number, p) = 1 / (2 * √p)
+jacobian_f(::Number, p::Number) = 1 / (2 * √p)
+jacobian_f(u, p::Number) = one.(u) .* (1 / (2 * √p))
+jacobian_f(u, p::AbstractArray) = diagm(vec(@. 1 / (2 * √p)))
+
+function solve_with(::Val{mode}, u, alg) where {mode}
+    f = if mode === :iip
+        solve_iip(p) = solve(NonlinearProblem(test_f!, u, p), alg).u
+    elseif mode === :oop
+        solve_oop(p) = solve(NonlinearProblem(test_f, u, p), alg).u
+    end
+    return f
+end
+
+__compatible(::Any, ::Val{:oop}) = true
+__compatible(::Number, ::Val{:iip}) = false
+__compatible(::AbstractArray, ::Val{:iip}) = true
+__compatible(::StaticArray, ::Val{:iip}) = false
+
+__compatible(::Any, ::Number) = true
+__compatible(::Number, ::AbstractArray) = false
+__compatible(u::AbstractArray, p::AbstractArray) = size(u) == size(p)
+
+__compatible(u::Number, ::SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm) = true
+function __compatible(u::AbstractArray,
+        ::SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm)
+    true
+end
+function __compatible(u::StaticArray,
+        ::SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm)
+    true
+end
+
+function __compatible(::SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm,
+        ::Val{:iip})
+    true
+end
+function __compatible(::SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm,
+        ::Val{:oop})
+    true
+end
+__compatible(::SimpleHalley, ::Val{:iip}) = false
+
+@testset "ForwardDiff.jl Integration: $(alg)" for alg in (SimpleNewtonRaphson(),
+    SimpleTrustRegion(), SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleDFSane())
+    us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
+
+    @testset "Scalar AD" begin
+        for p in 1.0:0.1:100.0, u0 in us, mode in (:iip, :oop)
+            __compatible(u0, alg) || continue
+            __compatible(u0, Val(mode)) || continue
+            __compatible(alg, Val(mode)) || continue
+
+            sol = solve(NonlinearProblem(test_f, u0, p), alg)
+            if SciMLBase.successful_retcode(sol)
+                gs = abs.(ForwardDiff.derivative(solve_with(Val{mode}(), u0, alg), p))
+                gs_true = abs.(jacobian_f(u0, p))
+                if !(isapprox(gs, gs_true, atol = 1e-5))
+                    @show sol.retcode, sol.u
+                    @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_gradient=gs true_gradient=gs_true
+                else
+                    @test abs.(gs)≈abs.(gs_true) atol=1e-5
+                end
+            end
+        end
+    end
+
+    @testset "Jacobian" begin
+        for u0 in us, p in ([2.0, 1.0], [2.0 1.0; 3.0 4.0]), mode in (:iip, :oop)
+            __compatible(u0, p) || continue
+            __compatible(u0, alg) || continue
+            __compatible(u0, Val(mode)) || continue
+            __compatible(alg, Val(mode)) || continue
+
+            sol = solve(NonlinearProblem(test_f, u0, p), alg)
+            if SciMLBase.successful_retcode(sol)
+                gs = abs.(ForwardDiff.jacobian(solve_with(Val{mode}(), u0, alg), p))
+                gs_true = abs.(jacobian_f(u0, p))
+                if !(isapprox(gs, gs_true, atol = 1e-5))
+                    @show sol.retcode, sol.u
+                    @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_jacobian=gs true_jacobian=gs_true
+                else
+                    @test abs.(gs)≈abs.(gs_true) atol=1e-5
+                end
+            end
+        end
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index cc4cd70b3..6cb730bc7 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -4,7 +4,8 @@ const GROUP = get(ENV, "GROUP", "All")
 
 @time @testset "SimpleNonlinearSolve.jl" begin
     if GROUP == "All" || GROUP == "Core"
-        @time @safetestset "Basic Tests + Some AD" include("basictests.jl")
+        @time @safetestset "Basic Tests" include("basictests.jl")
+        @time @safetestset "Forward AD" include("forward_ad.jl")
         @time @safetestset "Matrix Resizing Tests" include("matrix_resizing_tests.jl")
         @time @safetestset "Least Squares Tests" include("least_squares.jl")
         @time @safetestset "23 Test Problems" include("23_test_problems.jl")

From f66e91385dd2b8008b2d493c47d01673fc7b61fa Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 26 Dec 2023 19:01:44 -0500
Subject: [PATCH 266/700] Fix tests

---
 lib/SimpleNonlinearSolve/src/ad.jl            | 47 +++++++++----------
 .../src/nlsolve/halley.jl                     |  2 +-
 lib/SimpleNonlinearSolve/test/forward_ad.jl   | 23 +++------
 3 files changed, 30 insertions(+), 42 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index f6f5f5895..574904bcc 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -7,10 +7,30 @@ function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, <:AbstractArray}
         sol.original)
 end
 
-function __nlsolve_ad(prob::NonlinearProblem{uType, iip}, alg, args...;
-        kwargs...) where {uType, iip}
+# Handle Ambiguities
+for algType in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
+    @eval begin
+        function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
+                    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
+                alg::$(algType), args...; kwargs...) where {uType, T, V, P, iip}
+            sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
+            dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
+            return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode,
+                sol.stats, sol.original, left = Dual{T, V, P}(sol.left, partials),
+                right = Dual{T, V, P}(sol.right, partials))
+        end
+    end
+end
+
+function __nlsolve_ad(prob, alg, args...; kwargs...)
     p = value(prob.p)
-    newprob = NonlinearProblem(prob.f, value(prob.u0), p; prob.kwargs...)
+    if prob isa IntervalNonlinearProblem
+        tspan = value.(prob.tspan)
+        newprob = IntervalNonlinearProblem(prob.f, tspan, p; prob.kwargs...)
+    else
+        u0 = value(prob.u0)
+        newprob = NonlinearProblem(prob.f, u0, p; prob.kwargs...)
+    end
 
     sol = solve(newprob, alg, args...; kwargs...)
 
@@ -77,24 +97,3 @@ end
     _partials = _restructure(u, partials)
     return map(((uᵢ, pᵢ),) -> Dual{T, V, P}(uᵢ, pᵢ), zip(u, _partials))
 end
-
-# avoid ambiguities
-for Alg in [Bisection]
-    @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
-                <:Dual{T, V, P}}, alg::$Alg, args...; kwargs...) where {uType, iip, T, V, P}
-        sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
-        dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
-        return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode,
-            left = Dual{T, V, P}(sol.left, partials),
-            right = Dual{T, V, P}(sol.right, partials))
-    end
-    @eval function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
-                <:AbstractArray{<:Dual{T, V, P}}}, alg::$Alg, args...;
-            kwargs...) where {uType, iip, T, V, P}
-        sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
-        dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
-        return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode,
-            left = Dual{T, V, P}(sol.left, partials),
-            right = Dual{T, V, P}(sol.right, partials))
-    end
-end
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index 491a340e3..44877e097 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -71,7 +71,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
 
         @bb Aaᵢ = A × aᵢ
         @bb A .*= -1
-        bᵢ = dfx_fact \ Aaᵢ
+        bᵢ = dfx_fact \ _vec(Aaᵢ)
 
         cᵢ_ = _vec(cᵢ)
         @bb @. cᵢ_ = (aᵢ * aᵢ) / (-aᵢ + (T(0.5) * bᵢ))
diff --git a/lib/SimpleNonlinearSolve/test/forward_ad.jl b/lib/SimpleNonlinearSolve/test/forward_ad.jl
index 717c222df..f545ccb0c 100644
--- a/lib/SimpleNonlinearSolve/test/forward_ad.jl
+++ b/lib/SimpleNonlinearSolve/test/forward_ad.jl
@@ -1,4 +1,5 @@
 using ForwardDiff, SimpleNonlinearSolve, StaticArrays, Test, LinearAlgebra
+import SimpleNonlinearSolve: AbstractSimpleNonlinearSolveAlgorithm
 
 test_f!(du, u, p) = (@. du = u^2 - p)
 test_f(u, p) = (@. u^2 - p)
@@ -26,24 +27,12 @@ __compatible(::Any, ::Number) = true
 __compatible(::Number, ::AbstractArray) = false
 __compatible(u::AbstractArray, p::AbstractArray) = size(u) == size(p)
 
-__compatible(u::Number, ::SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm) = true
-function __compatible(u::AbstractArray,
-        ::SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm)
-    true
-end
-function __compatible(u::StaticArray,
-        ::SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm)
-    true
-end
+__compatible(u::Number, ::AbstractSimpleNonlinearSolveAlgorithm) = true
+__compatible(u::AbstractArray, ::AbstractSimpleNonlinearSolveAlgorithm) = true
+__compatible(u::StaticArray, ::AbstractSimpleNonlinearSolveAlgorithm) = true
 
-function __compatible(::SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm,
-        ::Val{:iip})
-    true
-end
-function __compatible(::SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm,
-        ::Val{:oop})
-    true
-end
+__compatible(::AbstractSimpleNonlinearSolveAlgorithm, ::Val{:iip}) = true
+__compatible(::AbstractSimpleNonlinearSolveAlgorithm, ::Val{:oop}) = true
 __compatible(::SimpleHalley, ::Val{:iip}) = false
 
 @testset "ForwardDiff.jl Integration: $(alg)" for alg in (SimpleNewtonRaphson(),

From 5d4d76630de74109da4d7d4f2aa500219174da1b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 12 Jan 2024 21:48:06 -0500
Subject: [PATCH 267/700] Dispatch on solve directly and forward to __solve

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 6ffe25420..356c0b51e 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -59,6 +59,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing,
     return solve(prob, ITP(), args...; kwargs...)
 end
 
+# By Pass the highlevel checks for NonlinearProblem for Simple Algorithms
+function SciMLBase.solve(prob::NonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
+        args...; kwargs...)
+    return SciMLBase.__solve(prob, alg, args...; kwargs...)
+end
+
 @setup_workload begin
     for T in (Float32, Float64)
         prob_no_brack_scalar = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))

From ec1d5b30d29bcd7debec61317b1d47db4209a4fc Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 13 Jan 2024 01:12:47 -0500
Subject: [PATCH 268/700] Non allocating version of LBroyden for StaticArrays

---
 .../src/nlsolve/lbroyden.jl                   | 160 +++++++++++++++++-
 lib/SimpleNonlinearSolve/src/utils.jl         |  14 --
 2 files changed, 156 insertions(+), 18 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index a78611a0a..390db2437 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -36,7 +36,7 @@ end
 
     fx = _get_fx(prob, x)
 
-    U, Vᵀ = __init_low_rank_jacobian(x, fx, threshold)
+    U, Vᵀ = __init_low_rank_jacobian(x, fx, x isa StaticArray ? threshold : Val(η))
 
     abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
         termination_condition)
@@ -48,7 +48,7 @@ end
     @bb δf = copy(fx)
 
     @bb vᵀ_cache = copy(x)
-    Tcache = __lbroyden_threshold_cache(x, threshold)
+    Tcache = __lbroyden_threshold_cache(x, x isa StaticArray ? threshold : Val(η))
     @bb mat_cache = copy(x)
 
     for i in 1:maxiters
@@ -83,6 +83,105 @@ end
     return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
 end
 
+# Non-allocating StaticArrays version of SimpleLimitedMemoryBroyden is actually quite
+# finicky, so we'll implement it separately from the generic version
+# We make an exception here and don't support termination conditions
+@views function SciMLBase.__solve(prob::NonlinearProblem{<:SArray},
+        alg::SimpleLimitedMemoryBroyden, args...; abstol = nothing,
+        termination_condition = nothing,
+        maxiters = 1000, kwargs...)
+    if termination_condition !== nothing &&
+       !(termination_condition isa AbsNormTerminationMode)
+        error("SimpleLimitedMemoryBroyden with StaticArrays does not support termination \
+               conditions!")
+    end
+
+    x = prob.u0
+    fx = _get_fx(prob, x)
+    threshold = __get_threshold(alg)
+
+    U, Vᵀ = __init_low_rank_jacobian(x, fx, threshold)
+
+    abstol = DiffEqBase._get_tolerance(abstol, eltype(x))
+
+    xo, δx, fo, δf = x, -fx, fx, fx
+
+    converged, res = __unrolled_lbroyden_initial_iterations(prob, xo, fo, δx, abstol, U, Vᵀ,
+        threshold)
+
+    converged &&
+        return build_solution(prob, alg, res.x, res.fx; retcode = ReturnCode.Success)
+
+    xo, fo, δx = res.x, res.fx, res.δx
+
+    for i in 1:(maxiters - SciMLBase._unwrap_val(threshold))
+        x = xo .+ δx
+        fx = prob.f(x, prob.p)
+        δf = fx - fo
+
+        maximum(abs, fx) ≤ abstol &&
+            return build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
+
+        vᵀ = _restructure(x, _rmatvec!!(U, Vᵀ, vec(δx)))
+        mvec = _restructure(x, _matvec!!(U, Vᵀ, vec(δf)))
+
+        d = dot(vᵀ, δf)
+        δx = @. (δx - mvec) / d
+
+        U = Base.setindex(U, vec(δx), mod1(i, SciMLBase._unwrap_val(threshold)))
+        Vᵀ = Base.setindex(Vᵀ, vec(vᵀ), mod1(i, SciMLBase._unwrap_val(threshold)))
+
+        δx = -_restructure(fx, _matvec!!(U, Vᵀ, vec(fx)))
+
+        xo = x
+        fo = fx
+    end
+
+    return build_solution(prob, alg, xo, fo; retcode = ReturnCode.MaxIters)
+end
+
+@generated function __unrolled_lbroyden_initial_iterations(prob, xo, fo, δx, abstol, U,
+        Vᵀ, ::Val{threshold}) where {threshold}
+    calls = []
+    for i in 1:threshold
+        static_idx, static_idx_p1 = Val(i - 1), Val(i)
+        push!(calls,
+            quote
+                x = xo .+ δx
+                fx = prob.f(x, prob.p)
+                δf = fx - fo
+
+                maximum(abs, fx) ≤ abstol && return true, (; x, fx, δx)
+
+                _U = __first_n_getindex(U, $(static_idx))
+                _Vᵀ = __first_n_getindex(Vᵀ, $(static_idx))
+
+                vᵀ = _restructure(x, _rmatvec!!(_U, _Vᵀ, vec(δx)))
+                mvec = _restructure(x, _matvec!!(_U, _Vᵀ, vec(δf)))
+
+                d = dot(vᵀ, δf)
+                δx = @. (δx - mvec) / d
+
+                U = Base.setindex(U, vec(δx), $(i))
+                Vᵀ = Base.setindex(Vᵀ, vec(vᵀ), $(i))
+
+                _U = __first_n_getindex(U, $(static_idx_p1))
+                _Vᵀ = __first_n_getindex(Vᵀ, $(static_idx_p1))
+                δx = -_restructure(fx, _matvec!!(_U, _Vᵀ, vec(fx)))
+
+                xo = x
+                fo = fx
+            end)
+    end
+    push!(calls, quote
+        # Termination Check
+        maximum(abs, fx) ≤ abstol && return true, (; x, fx, δx)
+
+        return false, (; x, fx, δx)
+    end)
+    return Expr(:block, calls...)
+end
+
 function _rmatvec!!(y, xᵀU, U, Vᵀ, x)
     # xᵀ × (-I + UVᵀ)
     η = size(U, 2)
@@ -98,6 +197,9 @@ function _rmatvec!!(y, xᵀU, U, Vᵀ, x)
     return y
 end
 
+@inline _rmatvec!!(::Nothing, Vᵀ, x) = -x
+@inline _rmatvec!!(U, Vᵀ, x) = __mapTdot(__mapdot(x, U), Vᵀ) .- x
+
 function _matvec!!(y, Vᵀx, U, Vᵀ, x)
     # (-I + UVᵀ) × x
     η = size(U, 2)
@@ -113,7 +215,57 @@ function _matvec!!(y, Vᵀx, U, Vᵀ, x)
     return y
 end
 
+@inline _matvec!!(::Nothing, Vᵀ, x) = -x
+@inline _matvec!!(U, Vᵀ, x) = __mapTdot(__mapdot(x, Vᵀ), U) .- x
+
+function __mapdot(x::SVector{S1}, Y::SVector{S2, <:SVector{S1}}) where {S1, S2}
+    return map(Base.Fix1(dot, x), Y)
+end
+@generated function __mapTdot(x::SVector{S1}, Y::SVector{S1, <:SVector{S2}}) where {S1, S2}
+    calls = []
+    syms = [gensym("m$(i)") for i in 1:length(Y)]
+    for i in 1:length(Y)
+        push!(calls, :($(syms[i]) = x[$(i)] .* Y[$i]))
+    end
+    push!(calls, :(return .+($(syms...))))
+    return Expr(:block, calls...)
+end
+
+@generated function __first_n_getindex(x::SVector{L, T}, ::Val{N}) where {L, T, N}
+    @assert N ≤ L
+    getcalls = ntuple(i -> :(x[$i]), N)
+    N == 0 && return :(return nothing)
+    return :(return SVector{$N, $T}(($(getcalls...))))
+end
+
 __lbroyden_threshold_cache(x, ::Val{threshold}) where {threshold} = similar(x, threshold)
-function __lbroyden_threshold_cache(x::SArray, ::Val{threshold}) where {threshold}
-    return SArray{Tuple{threshold}, eltype(x)}(ntuple(_ -> zero(eltype(x)), threshold))
+function __lbroyden_threshold_cache(x::StaticArray, ::Val{threshold}) where {threshold}
+    return zeros(MArray{Tuple{threshold}, eltype(x)})
+end
+__lbroyden_threshold_cache(x::SArray, ::Val{threshold}) where {threshold} = nothing
+
+function __init_low_rank_jacobian(u::StaticArray{S1, T1}, fu::StaticArray{S2, T2},
+        ::Val{threshold}) where {S1, S2, T1, T2, threshold}
+    T = promote_type(T1, T2)
+    fuSize, uSize = Size(fu), Size(u)
+    Vᵀ = MArray{Tuple{threshold, prod(uSize)}, T}(undef)
+    U = MArray{Tuple{prod(fuSize), threshold}, T}(undef)
+    return U, Vᵀ
+end
+@generated function __init_low_rank_jacobian(u::SArray{S1, T1}, fu::SArray{S2, T2},
+        ::Val{threshold}) where {S1, S2, T1, T2, threshold}
+    T = promote_type(T1, T2)
+    Lfu, Lu = prod(Size(fu)), prod(Size(u))
+    inner_inits_Vᵀ = [zeros(SVector{Lu, T}) for i in 1:threshold]
+    inner_inits_U = [zeros(SVector{Lfu, T}) for i in 1:threshold]
+    return quote
+        Vᵀ = SVector($(inner_inits_Vᵀ...))
+        U = SVector($(inner_inits_U...))
+        return U, Vᵀ
+    end
+end
+function __init_low_rank_jacobian(u, fu, ::Val{threshold}) where {threshold}
+    Vᵀ = similar(u, threshold, length(u))
+    U = similar(u, length(fu), threshold)
+    return U, Vᵀ
 end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index b3018f5ac..c6b9f2004 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -243,20 +243,6 @@ function __init_identity_jacobian!!(J::SVector{S1}) where {S1}
     return ones(SVector{S1, eltype(J)})
 end
 
-function __init_low_rank_jacobian(u::StaticArray{S1, T1}, fu::StaticArray{S2, T2},
-        ::Val{threshold}) where {S1, S2, T1, T2, threshold}
-    T = promote_type(T1, T2)
-    fuSize, uSize = Size(fu), Size(u)
-    Vᵀ = MArray{Tuple{threshold, prod(uSize)}, T}(undef)
-    U = MArray{Tuple{prod(fuSize), threshold}, T}(undef)
-    return U, Vᵀ
-end
-function __init_low_rank_jacobian(u, fu, ::Val{threshold}) where {threshold}
-    Vᵀ = similar(u, threshold, length(u))
-    U = similar(u, length(fu), threshold)
-    return U, Vᵀ
-end
-
 @inline _vec(v) = vec(v)
 @inline _vec(v::Number) = v
 @inline _vec(v::AbstractVector) = v

From ebfcffd4548729c5ce1c79348a2f37a47687697c Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 13 Jan 2024 01:44:43 -0500
Subject: [PATCH 269/700] Allow allocations for the termination condition
 version

---
 .../.buildkite/pipeline.yml                   | 15 ++++++++
 .../src/nlsolve/lbroyden.jl                   | 31 +++++++++-------
 lib/SimpleNonlinearSolve/test/cuda.jl         | 35 +++++++++++++++++++
 .../test/cuda/Project.toml                    |  5 +++
 lib/SimpleNonlinearSolve/test/runtests.jl     | 11 ++++++
 5 files changed, 85 insertions(+), 12 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
 create mode 100644 lib/SimpleNonlinearSolve/test/cuda.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/cuda/Project.toml

diff --git a/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml b/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
new file mode 100644
index 000000000..5705ed5ab
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
@@ -0,0 +1,15 @@
+steps:
+  - label: "Julia 1"
+    plugins:
+      - JuliaCI/julia#v1:
+          version: "1"
+    agents:
+      queue: "juliagpu"
+      cuda: "*"
+    timeout_in_minutes: 30
+    # Don't run Buildkite if the commit message includes the text [skip tests]
+    if: build.message !~ /\[skip tests\]/
+
+env:
+  GROUP: CUDA
+  JULIA_PKG_SERVER: ""
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index 390db2437..fab444329 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -21,7 +21,22 @@ function SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27))
     return SimpleLimitedMemoryBroyden{SciMLBase._unwrap_val(threshold)}()
 end
 
-@views function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyden,
+function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyden,
+        args...; termination_condition = nothing, kwargs...)
+    if prob.u0 isa SArray
+        if termination_condition === nothing ||
+           termination_condition isa AbsNormTerminationMode
+            return __static_solve(prob, alg, args...; termination_condition, kwargs...)
+        end
+        @warn "Specifying `termination_condition = $(termination_condition)` for \
+               `SimpleLimitedMemoryBroyden` with `SArray` is not non-allocating. Use \
+               either `termination_condition = AbsNormTerminationMode()` or \
+               `termination_condition = nothing`." maxlog=1
+    end
+    return __generic_solve(prob, alg, args...; termination_condition, kwargs...)
+end
+
+@views function __generic_solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyden,
         args...; abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
         termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
@@ -85,17 +100,9 @@ end
 
 # Non-allocating StaticArrays version of SimpleLimitedMemoryBroyden is actually quite
 # finicky, so we'll implement it separately from the generic version
-# We make an exception here and don't support termination conditions
-@views function SciMLBase.__solve(prob::NonlinearProblem{<:SArray},
-        alg::SimpleLimitedMemoryBroyden, args...; abstol = nothing,
-        termination_condition = nothing,
-        maxiters = 1000, kwargs...)
-    if termination_condition !== nothing &&
-       !(termination_condition isa AbsNormTerminationMode)
-        error("SimpleLimitedMemoryBroyden with StaticArrays does not support termination \
-               conditions!")
-    end
-
+# Ignore termination_condition. Don't pass things into internal functions
+function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemoryBroyden,
+        args...; abstol = nothing, maxiters = 1000, kwargs...)
     x = prob.u0
     fx = _get_fx(prob, x)
     threshold = __get_threshold(alg)
diff --git a/lib/SimpleNonlinearSolve/test/cuda.jl b/lib/SimpleNonlinearSolve/test/cuda.jl
new file mode 100644
index 000000000..f34ec5914
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/cuda.jl
@@ -0,0 +1,35 @@
+using SimpleNonlinearSolve, StaticArrays, CUDA, Test
+
+CUDA.allowscalar(false)
+
+f(u, p) = u .* u .- 2
+f!(du, u, p) = du .= u .* u .- 2
+
+@testset "Solving on GPUs" begin
+    for alg in (SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(), SimpleBroyden(),
+        SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley())
+        @info "Testing $alg on CUDA"
+
+        # Static Arrays
+        u0 = @SVector[1.0f0, 1.0f0]
+        probN = NonlinearProblem{false}(f, u0)
+        sol = solve(probN, alg; abstol = 1.0f-6)
+        @test SciMLBase.successful_retcode(sol)
+        @test maximum(abs, sol.resid) ≤ 1.0f-6
+
+        # Regular Arrays
+        u0 = [1.0, 1.0]
+        probN = NonlinearProblem{false}(f, u0)
+        sol = solve(probN, alg; abstol = 1.0f-6)
+        @test SciMLBase.successful_retcode(sol)
+        @test maximum(abs, sol.resid) ≤ 1.0f-6
+
+        # Regular Arrays Inplace
+        alg isa SimpleHalley && continue
+        u0 = [1.0, 1.0]
+        probN = NonlinearProblem{true}(f!, u0)
+        sol = solve(probN, alg; abstol = 1.0f-6)
+        @test SciMLBase.successful_retcode(sol)
+        @test maximum(abs, sol.resid) ≤ 1.0f-6
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/test/cuda/Project.toml b/lib/SimpleNonlinearSolve/test/cuda/Project.toml
new file mode 100644
index 000000000..36c63059b
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/cuda/Project.toml
@@ -0,0 +1,5 @@
+[deps]
+CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 6cb730bc7..cfd91f8b6 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -2,6 +2,12 @@ using SafeTestsets, Test
 
 const GROUP = get(ENV, "GROUP", "All")
 
+function activate_env(env)
+    Pkg.activate(env)
+    Pkg.develop(PackageSpec(path = dirname(@__DIR__)))
+    Pkg.instantiate()
+end
+
 @time @testset "SimpleNonlinearSolve.jl" begin
     if GROUP == "All" || GROUP == "Core"
         @time @safetestset "Basic Tests" include("basictests.jl")
@@ -10,4 +16,9 @@ const GROUP = get(ENV, "GROUP", "All")
         @time @safetestset "Least Squares Tests" include("least_squares.jl")
         @time @safetestset "23 Test Problems" include("23_test_problems.jl")
     end
+
+    if GROUP == "CUDA"
+        activate_env("cuda")
+        @time @safetestset "CUDA Tests" include("cuda.jl")
+    end
 end

From 8ef96862d1ec067916f762dff390ec0f0048cb35 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 13 Jan 2024 01:51:41 -0500
Subject: [PATCH 270/700] AllocCheck for SimpleLimitedMemoryBroyden

---
 lib/SimpleNonlinearSolve/.buildkite/pipeline.yml | 1 +
 lib/SimpleNonlinearSolve/test/basictests.jl      | 6 ++----
 2 files changed, 3 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml b/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
index 5705ed5ab..e84559d00 100644
--- a/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
+++ b/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
@@ -3,6 +3,7 @@ steps:
     plugins:
       - JuliaCI/julia#v1:
           version: "1"
+      - JuliaCI/julia-test#v1:
     agents:
       queue: "juliagpu"
       cuda: "*"
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index e43a90761..99aa3df40 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -165,7 +165,7 @@ end
 @testset "Allocation Checks: $(_nameof(alg))" for alg in (SimpleNewtonRaphson(),
     SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
     SimpleTrustRegion())
-    @check_allocs nlsolve(prob, alg) = DiffEqBase.__solve(prob, alg; abstol = 1e-9)
+    @check_allocs nlsolve(prob, alg) = SciMLBase.solve(prob, alg; abstol = 1e-9)
 
     nlprob_scalar = NonlinearProblem{false}(quadratic_f, 1.0, 2.0)
     nlprob_sa = NonlinearProblem{false}(quadratic_f, @SVector[1.0, 1.0], 2.0)
@@ -179,14 +179,12 @@ end
     end
 
     # ForwardDiff allocates for hessian since we don't propagate the chunksize
-    # SimpleLimitedMemoryBroyden needs to do views on the low rank matrices so the sizes
-    # are dynamic. This can be fixed but no without maintaining the simplicity of the code
     try
         nlsolve(nlprob_sa, alg)
         @test true
     catch e
         @error e
-        @test false broken=(alg isa SimpleHalley || alg isa SimpleLimitedMemoryBroyden)
+        @test false broken=(alg isa SimpleHalley)
     end
 end
 

From 043336bf12ebc842a0c8f3f94cc353b76dcfd7d8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 13 Jan 2024 02:36:02 -0500
Subject: [PATCH 271/700] Make DFSane non-allocating as well

---
 .../src/nlsolve/dfsane.jl                     | 45 ++++++++++++-------
 .../src/nlsolve/lbroyden.jl                   | 19 ++++----
 lib/SimpleNonlinearSolve/test/basictests.jl   |  5 ++-
 3 files changed, 43 insertions(+), 26 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 11f3af1d5..46f2e86d1 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -1,6 +1,6 @@
 """
     SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
-        M::Int = 10, γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
+        M::Union{Int, Val} = Val(10), γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
         nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2)
 
 A low-overhead implementation of the df-sane method for solving large-scale nonlinear
@@ -42,21 +42,26 @@ see the paper [1].
 information for solving large-scale nonlinear systems of equations, Mathematics of
 Computation, 75, 1429-1448.
 """
-@kwdef @concrete struct SimpleDFSane <: AbstractSimpleNonlinearSolveAlgorithm
-    σ_min = 1e-10
-    σ_max = 1e10
-    σ_1 = 1.0
-    M::Int = 10
-    γ = 1e-4
-    τ_min = 0.1
-    τ_max = 0.5
-    nexp::Int = 2
-    η_strategy = (f_1, k, x, F) -> f_1 ./ k^2
+@concrete struct SimpleDFSane{M} <: AbstractSimpleNonlinearSolveAlgorithm
+    σ_min
+    σ_max
+    σ_1
+    γ
+    τ_min
+    τ_max
+    nexp::Int
+    η_strategy
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
+function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
+        M::Union{Int, Val} = Val(10), γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
+        nexp::Int = 2, η_strategy::F = (f_1, k, x, F) -> f_1 ./ k^2) where {F}
+    return SimpleDFSane{SciMLBase._unwrap_val(M)}(σ_min, σ_max, σ_1, γ, τ_min, τ_max, nexp, η_strategy)
+end
+
+function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{M}, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
-        termination_condition = nothing, kwargs...)
+        termination_condition = nothing, kwargs...) where {M}
     x = __maybe_unaliased(prob.u0, alias_u0)
     fx = _get_fx(prob, x)
     T = eltype(x)
@@ -65,7 +70,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
     σ_max = T(alg.σ_max)
     σ_k = T(alg.σ_1)
 
-    (; M, nexp, η_strategy) = alg
+    (; nexp, η_strategy) = alg
     γ = T(alg.γ)
     τ_min = T(alg.τ_min)
     τ_max = T(alg.τ_max)
@@ -77,7 +82,11 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
     α_1 = one(T)
     f_1 = fx_norm
 
-    history_f_k = fill(fx_norm, M)
+    history_f_k = if x isa SArray
+        ones(SVector{M, T}) * fx_norm
+    else
+        fill(fx_norm, M)
+    end
 
     # Generate the cache
     @bb x_cache = similar(x)
@@ -143,7 +152,11 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane, args...;
         fx_norm = fx_norm_new
 
         # Store function value
-        history_f_k[mod1(k, M)] = fx_norm_new
+        if history_f_k isa SVector
+            history_f_k = Base.setindex(history_f_k, fx_norm_new, mod1(k, M))
+        else
+            history_f_k[mod1(k, M)] = fx_norm_new
+        end
         k += 1
     end
 
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index fab444329..a919f5cab 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -107,7 +107,7 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
     fx = _get_fx(prob, x)
     threshold = __get_threshold(alg)
 
-    U, Vᵀ = __init_low_rank_jacobian(x, fx, threshold)
+    U, Vᵀ = __init_low_rank_jacobian(vec(x), vec(fx), threshold)
 
     abstol = DiffEqBase._get_tolerance(abstol, eltype(x))
 
@@ -230,8 +230,8 @@ function __mapdot(x::SVector{S1}, Y::SVector{S2, <:SVector{S1}}) where {S1, S2}
 end
 @generated function __mapTdot(x::SVector{S1}, Y::SVector{S1, <:SVector{S2}}) where {S1, S2}
     calls = []
-    syms = [gensym("m$(i)") for i in 1:length(Y)]
-    for i in 1:length(Y)
+    syms = [gensym("m$(i)") for i in 1:S1]
+    for i in 1:S1
         push!(calls, :($(syms[i]) = x[$(i)] .* Y[$i]))
     end
     push!(calls, :(return .+($(syms...))))
@@ -259,18 +259,21 @@ function __init_low_rank_jacobian(u::StaticArray{S1, T1}, fu::StaticArray{S2, T2
     U = MArray{Tuple{prod(fuSize), threshold}, T}(undef)
     return U, Vᵀ
 end
-@generated function __init_low_rank_jacobian(u::SArray{S1, T1}, fu::SArray{S2, T2},
-        ::Val{threshold}) where {S1, S2, T1, T2, threshold}
+
+@generated function __init_low_rank_jacobian(u::SVector{Lu, T1}, fu::SVector{Lfu, T2},
+        ::Val{threshold}) where {Lu, Lfu, T1, T2, threshold}
     T = promote_type(T1, T2)
-    Lfu, Lu = prod(Size(fu)), prod(Size(u))
-    inner_inits_Vᵀ = [zeros(SVector{Lu, T}) for i in 1:threshold]
-    inner_inits_U = [zeros(SVector{Lfu, T}) for i in 1:threshold]
+    # Lfu, Lu = __prod_size(S2), __prod_size(S1)
+    # Lfu, Lu = __prod(Size(fu)), __prod(Size(u))
+    inner_inits_Vᵀ = [:(zeros(SVector{$Lu, $T})) for i in 1:threshold]
+    inner_inits_U = [:(zeros(SVector{$Lfu, $T})) for i in 1:threshold]
     return quote
         Vᵀ = SVector($(inner_inits_Vᵀ...))
         U = SVector($(inner_inits_U...))
         return U, Vᵀ
     end
 end
+
 function __init_low_rank_jacobian(u, fu, ::Val{threshold}) where {threshold}
     Vᵀ = similar(u, threshold, length(u))
     U = similar(u, length(fu), threshold)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 99aa3df40..7da944e7b 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -164,7 +164,7 @@ end
 ## SimpleDFSane needs to allocate a history vector
 @testset "Allocation Checks: $(_nameof(alg))" for alg in (SimpleNewtonRaphson(),
     SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
-    SimpleTrustRegion())
+    SimpleTrustRegion(), SimpleDFSane())
     @check_allocs nlsolve(prob, alg) = SciMLBase.solve(prob, alg; abstol = 1e-9)
 
     nlprob_scalar = NonlinearProblem{false}(quadratic_f, 1.0, 2.0)
@@ -175,7 +175,8 @@ end
         @test true
     catch e
         @error e
-        @test false
+        # History Vector Allocates
+        @test false broken=(alg isa SimpleDFSane)
     end
 
     # ForwardDiff allocates for hessian since we don't propagate the chunksize

From 91a995d9ad7302572823f9a7caa5c8b9a335b41a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 13 Jan 2024 02:42:28 -0500
Subject: [PATCH 272/700] Add kernel launch tests

---
 lib/SimpleNonlinearSolve/Project.toml         |  2 +-
 lib/SimpleNonlinearSolve/README.md            |  1 +
 .../src/nlsolve/dfsane.jl                     |  3 ++-
 .../src/nlsolve/lbroyden.jl                   |  4 ----
 lib/SimpleNonlinearSolve/test/cuda.jl         | 23 +++++++++++++++++++
 lib/SimpleNonlinearSolve/test/runtests.jl     |  2 +-
 6 files changed, 28 insertions(+), 7 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 7a7ac60d2..d518e1686 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.2.0"
+version = "1.2.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
index 256a65ad4..3ef4868bb 100644
--- a/lib/SimpleNonlinearSolve/README.md
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -5,6 +5,7 @@
 
 [![codecov](https://codecov.io/gh/SciML/SimpleNonlinearSolve.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/SciML/SimpleNonlinearSolve.jl)
 [![Build Status](https://github.com/SciML/SimpleNonlinearSolve.jl/workflows/CI/badge.svg)](https://github.com/SciML/SimpleNonlinearSolve.jl/actions?query=workflow%3ACI)
+[![Build status](https://badge.buildkite.com/c5f7db4f1b5e8a592514378b6fc807d934546cc7d5aa79d645.svg?branch=main)](https://buildkite.com/julialang/simplenonlinearsolve-dot-jl)
 
 [![ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://img.shields.io/badge/ColPrac-Contributor%27s%20Guide-blueviolet)](https://github.com/SciML/ColPrac)
 [![SciML Code Style](https://img.shields.io/static/v1?label=code%20style&message=SciML&color=9558b2&labelColor=389826)](https://github.com/SciML/SciMLStyle)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 46f2e86d1..c6111b38c 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -56,7 +56,8 @@ end
 function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
         M::Union{Int, Val} = Val(10), γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
         nexp::Int = 2, η_strategy::F = (f_1, k, x, F) -> f_1 ./ k^2) where {F}
-    return SimpleDFSane{SciMLBase._unwrap_val(M)}(σ_min, σ_max, σ_1, γ, τ_min, τ_max, nexp, η_strategy)
+    return SimpleDFSane{SciMLBase._unwrap_val(M)}(σ_min, σ_max, σ_1, γ, τ_min, τ_max, nexp,
+        η_strategy)
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{M}, args...;
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index a919f5cab..3a0c11ded 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -259,12 +259,9 @@ function __init_low_rank_jacobian(u::StaticArray{S1, T1}, fu::StaticArray{S2, T2
     U = MArray{Tuple{prod(fuSize), threshold}, T}(undef)
     return U, Vᵀ
 end
-
 @generated function __init_low_rank_jacobian(u::SVector{Lu, T1}, fu::SVector{Lfu, T2},
         ::Val{threshold}) where {Lu, Lfu, T1, T2, threshold}
     T = promote_type(T1, T2)
-    # Lfu, Lu = __prod_size(S2), __prod_size(S1)
-    # Lfu, Lu = __prod(Size(fu)), __prod(Size(u))
     inner_inits_Vᵀ = [:(zeros(SVector{$Lu, $T})) for i in 1:threshold]
     inner_inits_U = [:(zeros(SVector{$Lfu, $T})) for i in 1:threshold]
     return quote
@@ -273,7 +270,6 @@ end
         return U, Vᵀ
     end
 end
-
 function __init_low_rank_jacobian(u, fu, ::Val{threshold}) where {threshold}
     Vᵀ = similar(u, threshold, length(u))
     U = similar(u, length(fu), threshold)
diff --git a/lib/SimpleNonlinearSolve/test/cuda.jl b/lib/SimpleNonlinearSolve/test/cuda.jl
index f34ec5914..9b984bc70 100644
--- a/lib/SimpleNonlinearSolve/test/cuda.jl
+++ b/lib/SimpleNonlinearSolve/test/cuda.jl
@@ -33,3 +33,26 @@ f!(du, u, p) = du .= u .* u .- 2
         @test maximum(abs, sol.resid) ≤ 1.0f-6
     end
 end
+
+function kernel_function(prob, alg)
+    solve(prob, alg; abstol = 1.0f-6, reltol = 1.0f-6)
+    return nothing
+end
+
+@testset "CUDA Kernel Launch Test" begin
+    prob = NonlinearProblem{false}(f, @SVector[1.0f0, 1.0f0])
+
+    for alg in (SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(), SimpleBroyden(),
+        SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley())
+        @test begin
+            try
+                @cuda kernel_function(prob, alg)
+                @info "Successfully launched kernel for $(alg)."
+                true
+            catch err
+                @error "Kernel Launch failed for $(alg)."
+                false
+            end
+        end broken=(alg isa SimpleHalley)
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index cfd91f8b6..4de514642 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -1,4 +1,4 @@
-using SafeTestsets, Test
+using Pkg, SafeTestsets, Test
 
 const GROUP = get(ENV, "GROUP", "All")
 

From 686c1cb372c71f12ef4edaba4c9a67d4f133ea67 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 10 Jan 2024 09:46:10 -0500
Subject: [PATCH 273/700] Add Line Search to Broyden

---
 lib/SimpleNonlinearSolve/Project.toml         | 10 ++-
 .../src/SimpleNonlinearSolve.jl               |  6 +-
 lib/SimpleNonlinearSolve/src/linesearch.jl    | 77 +++++++++++++++++++
 .../src/nlsolve/broyden.jl                    | 30 +++++++-
 .../src/nlsolve/lbroyden.jl                   | 29 ++++---
 5 files changed, 131 insertions(+), 21 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/linesearch.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index d518e1686..6373e9647 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,13 +1,14 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.2.1"
+version = "1.3.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -17,17 +18,18 @@ Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
-[extensions]
-SimpleNonlinearSolvePolyesterForwardDiffExt = "PolyesterForwardDiff"
-
 [weakdeps]
 PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
 
+[extensions]
+SimpleNonlinearSolvePolyesterForwardDiffExt = "PolyesterForwardDiff"
+
 [compat]
 ADTypes = "0.2.6"
 ArrayInterface = "7"
 ConcreteStructs = "0.2"
 DiffEqBase = "6.126"
+FastClosures = "0.3"
 FiniteDiff = "2"
 ForwardDiff = "0.10.3"
 LinearAlgebra = "1.9"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 356c0b51e..c8f515cc2 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -3,14 +3,13 @@ module SimpleNonlinearSolve
 import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidations
 
 @recompile_invalidations begin
-    using ADTypes,
-        ArrayInterface, ConcreteStructs, DiffEqBase, Reexport, LinearAlgebra, SciMLBase
+    using ADTypes, ArrayInterface, ConcreteStructs, DiffEqBase, FastClosures, FiniteDiff,
+        ForwardDiff, Reexport, LinearAlgebra, SciMLBase
 
     import DiffEqBase: AbstractNonlinearTerminationMode,
         AbstractSafeNonlinearTerminationMode, AbstractSafeBestNonlinearTerminationMode,
         NonlinearSafeTerminationReturnCode, get_termination_mode,
         NONLINEARSOLVE_DEFAULT_NORM, _get_tolerance
-    using FiniteDiff, ForwardDiff
     import ForwardDiff: Dual
     import MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
     import SciMLBase: AbstractNonlinearAlgorithm, build_solution, isinplace
@@ -26,6 +25,7 @@ abstract type AbstractNewtonAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm e
 @inline __is_extension_loaded(::Val) = false
 
 include("utils.jl")
+include("linesearch.jl")
 
 ## Nonlinear Solvers
 include("nlsolve/raphson.jl")
diff --git a/lib/SimpleNonlinearSolve/src/linesearch.jl b/lib/SimpleNonlinearSolve/src/linesearch.jl
new file mode 100644
index 000000000..fdab57bfd
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/linesearch.jl
@@ -0,0 +1,77 @@
+# This is a copy of the version in NonlinearSolve.jl. Temporarily kept here till we move
+# line searches into a dedicated package. Renamed to `__` to avoid conflicts.
+@kwdef @concrete struct __LiFukushimaLineSearch
+    lambda_0 = 1
+    beta = 1 // 2
+    sigma_1 = 1 // 1000
+    sigma_2 = 1 // 1000
+    eta = 1 // 10
+    rho = 9 // 10
+    nan_maxiters::Int = 5
+    maxiters::Int = 100
+end
+
+@concrete mutable struct __LiFukushimaLineSearchCache
+    ϕ
+    λ₀
+    β
+    σ₁
+    σ₂
+    η
+    ρ
+    α
+    nan_maxiters::Int
+    maxiters::Int
+end
+
+function (alg::__LiFukushimaLineSearch)(prob, fu, u)
+    @bb u_cache = similar(u)
+    @bb fu_cache = similar(fu)
+    T = promote_type(eltype(fu), eltype(u))
+
+    ϕ = @closure (u, δu, α) -> begin
+        @bb @. u_cache = u + α * δu
+        return norm(__eval_f(prob, fu_cache, u_cache), 2)
+    end
+
+    return __LiFukushimaLineSearchCache(ϕ, T(alg.lambda_0), T(alg.beta), T(alg.sigma_1),
+        T(alg.sigma_2), T(alg.eta), T(alg.rho), T(true), alg.nan_maxiters, alg.maxiters)
+end
+
+function (cache::__LiFukushimaLineSearchCache)(u, δu)
+    T = promote_type(eltype(u), eltype(δu))
+    ϕ = @closure α -> cache.ϕ(u, δu, α)
+
+    fx_norm = ϕ(T(0))
+
+    # Non-Blocking exit if the norm is NaN or Inf
+    !isfinite(fx_norm) && return cache.α
+
+    # Early Terminate based on Eq. 2.7
+    du_norm = norm(δu, 2)
+    fxλ_norm = ϕ(cache.α)
+    fxλ_norm ≤ cache.ρ * fx_norm - cache.σ₂ * du_norm^2 && return cache.α
+
+    λ₂, λ₁ = cache.λ₀, cache.λ₀
+    fxλp_norm = ϕ(λ₂)
+
+    if !isfinite(fxλp_norm)
+        nan_converged = false
+        for _ in 1:(cache.nan_maxiters)
+            λ₁, λ₂ = λ₂, cache.β * λ₂
+            fxλp_norm = ϕ(λ₂)
+            nan_converged = isfinite(fxλp_norm)
+            nan_converged && break
+        end
+        nan_converged || return cache.α
+    end
+
+    for i in 1:(cache.maxiters)
+        fxλp_norm = ϕ(λ₂)
+        converged = fxλp_norm ≤ (1 + cache.η) * fx_norm - cache.σ₁ * λ₂^2 * du_norm^2
+        converged && return λ₂
+        λ₁, λ₂ = λ₂, cache.β * λ₂
+    end
+
+    return cache.α
+end
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index 5f2dccdc7..82312a01d 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -1,10 +1,26 @@
 """
-    SimpleBroyden()
+    SimpleBroyden(; linesearch = Val(false))
 
 A low-overhead implementation of Broyden. This method is non-allocating on scalar
 and static array problems.
+
+If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch` [1] line search else
+no line search is used. For advanced customization of the line search, use the
+`Broyden` algorithm in `NonlinearSolve.jl`.
+
+### References
+
+[1] Li, Dong-Hui, and Masao Fukushima. "A derivative-free line search and global convergence
+of Broyden-like method for nonlinear equations." Optimization methods and software 13.3
+(2000): 181-201.
 """
-struct SimpleBroyden <: AbstractSimpleNonlinearSolveAlgorithm end
+struct SimpleBroyden{linesearch} <: AbstractSimpleNonlinearSolveAlgorithm end
+
+function SimpleBroyden(; linesearch = Val(false))
+    SimpleBroyden{SciMLBase._unwrap_val(linesearch)}()
+end
+
+__get_linesearch(::SimpleBroyden{LS}) where {LS} = Val(LS)
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
@@ -26,9 +42,16 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
     abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
         termination_condition)
 
+    ls_cache = __get_linesearch(alg) === Val(true) ?
+               __LiFukushimaLineSearch()(prob, fx, x) : nothing
+
     for _ in 1:maxiters
         @bb δx = J⁻¹ × vec(fprev)
-        @bb @. x = xo - δx
+        @bb δx .*= -1
+
+        α = ls_cache === nothing ? true : ls_cache(x, δx)
+
+        @bb @. x = xo + α * δx
         fx = __eval_f(prob, fx, x)
         @bb @. δf = fx - fprev
 
@@ -37,7 +60,6 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
         tc_sol !== nothing && return tc_sol
 
         @bb J⁻¹δf = J⁻¹ × vec(δf)
-        @bb δx .*= -1
         d = dot(δx, J⁻¹δf)
         @bb xᵀJ⁻¹ = transpose(J⁻¹) × vec(δx)
 
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index 3a0c11ded..d949fcc8b 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -1,6 +1,6 @@
 """
-    SimpleLimitedMemoryBroyden(; threshold::Int = 27)
-    SimpleLimitedMemoryBroyden(; threshold::Val = Val(27))
+    SimpleLimitedMemoryBroyden(; threshold::Int = 27, linesearch = Val(true))
+    SimpleLimitedMemoryBroyden(; threshold::Val = Val(27), linesearch = Val(true))
 
 A limited memory implementation of Broyden. This method applies the L-BFGS scheme to
 Broyden's method. This Alogrithm unfortunately cannot non-allocating for StaticArrays
@@ -8,17 +8,26 @@ without compromising on the "simple" aspect.
 
 If the threshold is larger than the problem size, then this method will use `SimpleBroyden`.
 
-!!! warning
+If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch` [1] line search else
+no line search is used. For advanced customization of the line search, use the
+`LimitedMemoryBroyden` algorithm in `NonlinearSolve.jl`.
 
-    This method is not very stable and can diverge even for very simple problems. This has
-    mostly been tested for neural networks in DeepEquilibriumNetworks.jl.
+### References
+
+[1] Li, Dong-Hui, and Masao Fukushima. "A derivative-free line search and global convergence
+of Broyden-like method for nonlinear equations." Optimization methods and software 13.3
+(2000): 181-201.
 """
-struct SimpleLimitedMemoryBroyden{threshold} <: AbstractSimpleNonlinearSolveAlgorithm end
+struct SimpleLimitedMemoryBroyden{threshold, linesearch} <:
+       AbstractSimpleNonlinearSolveAlgorithm end
 
 __get_threshold(::SimpleLimitedMemoryBroyden{threshold}) where {threshold} = Val(threshold)
+__use_linesearch(::SimpleLimitedMemoryBroyden{Th, LS}) where {Th, LS} = Val(LS)
 
-function SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27))
-    return SimpleLimitedMemoryBroyden{SciMLBase._unwrap_val(threshold)}()
+function SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27),
+        linesearch = Val(true))
+    return SimpleLimitedMemoryBroyden{SciMLBase._unwrap_val(threshold),
+        SciMLBase._unwrap_val(linesearch)}()
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyden,
@@ -45,8 +54,8 @@ end
 
     # For scalar problems / if the threshold is larger than problem size just use Broyden
     if x isa Number || length(x) ≤ η
-        return SciMLBase.__solve(prob, SimpleBroyden(), args...;
-            abstol, reltol, maxiters, termination_condition, kwargs...)
+        return SciMLBase.__solve(prob, SimpleBroyden(; linesearch = __use_linesearch(alg)),
+            args...; abstol, reltol, maxiters, termination_condition, kwargs...)
     end
 
     fx = _get_fx(prob, x)

From e822edd1287f89424bdd59a63741a3a38e5ba9d6 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 10 Jan 2024 10:24:01 -0500
Subject: [PATCH 274/700] Add Line Search to LBroyden

---
 lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl  | 1 -
 lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl | 6 +++++-
 2 files changed, 5 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index 82312a01d..cc505339f 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -50,7 +50,6 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
         @bb δx .*= -1
 
         α = ls_cache === nothing ? true : ls_cache(x, δx)
-
         @bb @. x = xo + α * δx
         fx = __eval_f(prob, fx, x)
         @bb @. δf = fx - fprev
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index d949fcc8b..ccd77d38e 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -75,8 +75,12 @@ end
     Tcache = __lbroyden_threshold_cache(x, x isa StaticArray ? threshold : Val(η))
     @bb mat_cache = copy(x)
 
+    ls_cache = __get_linesearch(alg) === Val(true) ?
+               __LiFukushimaLineSearch()(prob, fx, x) : nothing
+
     for i in 1:maxiters
-        @bb @. x = xo + δx
+        α = ls_cache === nothing ? true : ls_cache(x, δx)
+        @bb @. x = xo + α * δx
         fx = __eval_f(prob, fx, x)
         @bb @. δf = fx - fo
 

From ee1b66d9f7b45eda729f20e8d64005eaae5dd3ca Mon Sep 17 00:00:00 2001
From: Vaibhav Kumar Dixit <vaibhavyashdixit@gmail.com>
Date: Wed, 10 Jan 2024 14:28:32 -0500
Subject: [PATCH 275/700] Update src/nlsolve/lbroyden.jl

---
 lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index ccd77d38e..fa3b9d3cd 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -75,7 +75,7 @@ end
     Tcache = __lbroyden_threshold_cache(x, x isa StaticArray ? threshold : Val(η))
     @bb mat_cache = copy(x)
 
-    ls_cache = __get_linesearch(alg) === Val(true) ?
+    ls_cache = __use_linesearch(alg) === Val(true) ?
                __LiFukushimaLineSearch()(prob, fx, x) : nothing
 
     for i in 1:maxiters

From 7648d58cec5b39ffc9424b49098148135a4955c6 Mon Sep 17 00:00:00 2001
From: Vaibhav Dixit <vaibhavyashdixit@gmail.com>
Date: Fri, 12 Jan 2024 12:29:57 -0500
Subject: [PATCH 276/700] temp diable termination condition

---
 lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index cc505339f..fa0b17359 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -39,8 +39,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
     @bb δJ⁻¹n = copy(x)
     @bb δJ⁻¹ = copy(J⁻¹)
 
-    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
-        termination_condition)
+    # abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+    #     termination_condition)
 
     ls_cache = __get_linesearch(alg) === Val(true) ?
                __LiFukushimaLineSearch()(prob, fx, x) : nothing
@@ -55,8 +55,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
         @bb @. δf = fx - fprev
 
         # Termination Checks
-        tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
-        tc_sol !== nothing && return tc_sol
+        # tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
+        # tc_sol !== nothing && return tc_sol
 
         @bb J⁻¹δf = J⁻¹ × vec(δf)
         d = dot(δx, J⁻¹δf)

From 20296e803f8df726172c139f260b05ebc468189a Mon Sep 17 00:00:00 2001
From: Vaibhav Dixit <vaibhavyashdixit@gmail.com>
Date: Fri, 12 Jan 2024 13:48:05 -0500
Subject: [PATCH 277/700] isfinite not comiling

---
 lib/SimpleNonlinearSolve/src/linesearch.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/linesearch.jl b/lib/SimpleNonlinearSolve/src/linesearch.jl
index fdab57bfd..8a93410bd 100644
--- a/lib/SimpleNonlinearSolve/src/linesearch.jl
+++ b/lib/SimpleNonlinearSolve/src/linesearch.jl
@@ -45,7 +45,7 @@ function (cache::__LiFukushimaLineSearchCache)(u, δu)
     fx_norm = ϕ(T(0))
 
     # Non-Blocking exit if the norm is NaN or Inf
-    !isfinite(fx_norm) && return cache.α
+    (fx_norm == Inf || fx_norm == NaN) && return cache.α
 
     # Early Terminate based on Eq. 2.7
     du_norm = norm(δu, 2)

From c222e6412ff8a186f459d6695a64036a43887bc9 Mon Sep 17 00:00:00 2001
From: Vaibhav Dixit <vaibhavyashdixit@gmail.com>
Date: Fri, 12 Jan 2024 14:10:06 -0500
Subject: [PATCH 278/700] use DiffEqBase definitions of norm etc

---
 lib/SimpleNonlinearSolve/src/linesearch.jl | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/linesearch.jl b/lib/SimpleNonlinearSolve/src/linesearch.jl
index 8a93410bd..4d2ec4aa5 100644
--- a/lib/SimpleNonlinearSolve/src/linesearch.jl
+++ b/lib/SimpleNonlinearSolve/src/linesearch.jl
@@ -2,11 +2,11 @@
 # line searches into a dedicated package. Renamed to `__` to avoid conflicts.
 @kwdef @concrete struct __LiFukushimaLineSearch
     lambda_0 = 1
-    beta = 1 // 2
-    sigma_1 = 1 // 1000
-    sigma_2 = 1 // 1000
-    eta = 1 // 10
-    rho = 9 // 10
+    beta = 1.0 / 2.0
+    sigma_1 = 1.0 / 1000.0
+    sigma_2 = 1.0 / 1000.0
+    eta = 1.0 / 10.0
+    rho = 9.0 / 10.0
     nan_maxiters::Int = 5
     maxiters::Int = 100
 end
@@ -31,7 +31,7 @@ function (alg::__LiFukushimaLineSearch)(prob, fu, u)
 
     ϕ = @closure (u, δu, α) -> begin
         @bb @. u_cache = u + α * δu
-        return norm(__eval_f(prob, fu_cache, u_cache), 2)
+        return NONLINEARSOLVE_DEFAULT_NORM(__eval_f(prob, fu_cache, u_cache))
     end
 
     return __LiFukushimaLineSearchCache(ϕ, T(alg.lambda_0), T(alg.beta), T(alg.sigma_1),
@@ -42,25 +42,25 @@ function (cache::__LiFukushimaLineSearchCache)(u, δu)
     T = promote_type(eltype(u), eltype(δu))
     ϕ = @closure α -> cache.ϕ(u, δu, α)
 
-    fx_norm = ϕ(T(0))
+    fx_norm::T = ϕ(T(0))
 
     # Non-Blocking exit if the norm is NaN or Inf
-    (fx_norm == Inf || fx_norm == NaN) && return cache.α
+    DiffEqBase.NAN_CHECK(fx_norm) && return cache.α
 
     # Early Terminate based on Eq. 2.7
-    du_norm = norm(δu, 2)
+    du_norm = NONLINEARSOLVE_DEFAULT_NORM(δu)
     fxλ_norm = ϕ(cache.α)
     fxλ_norm ≤ cache.ρ * fx_norm - cache.σ₂ * du_norm^2 && return cache.α
 
     λ₂, λ₁ = cache.λ₀, cache.λ₀
     fxλp_norm = ϕ(λ₂)
 
-    if !isfinite(fxλp_norm)
+    if DiffEqBase.NAN_CHECK(fxλp_norm)
         nan_converged = false
         for _ in 1:(cache.nan_maxiters)
             λ₁, λ₂ = λ₂, cache.β * λ₂
             fxλp_norm = ϕ(λ₂)
-            nan_converged = isfinite(fxλp_norm)
+            nan_converged = DiffEqBase.NAN_CHECK(fxλp_norm)
             nan_converged && break
         end
         nan_converged || return cache.α

From 705ac0612dbc5da1982882900c22ee3a5914d0f0 Mon Sep 17 00:00:00 2001
From: Vaibhav Dixit <vaibhavyashdixit@gmail.com>
Date: Fri, 12 Jan 2024 15:24:05 -0500
Subject: [PATCH 279/700] T(phi)

---
 lib/SimpleNonlinearSolve/src/linesearch.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/linesearch.jl b/lib/SimpleNonlinearSolve/src/linesearch.jl
index 4d2ec4aa5..b93bd21de 100644
--- a/lib/SimpleNonlinearSolve/src/linesearch.jl
+++ b/lib/SimpleNonlinearSolve/src/linesearch.jl
@@ -42,7 +42,7 @@ function (cache::__LiFukushimaLineSearchCache)(u, δu)
     T = promote_type(eltype(u), eltype(δu))
     ϕ = @closure α -> cache.ϕ(u, δu, α)
 
-    fx_norm::T = ϕ(T(0))
+    fx_norm = ϕ(T(0))::T
 
     # Non-Blocking exit if the norm is NaN or Inf
     DiffEqBase.NAN_CHECK(fx_norm) && return cache.α

From 5a92d0f807c97c3734297cffe887830b42adf3d4 Mon Sep 17 00:00:00 2001
From: Vaibhav Dixit <vaibhavyashdixit@gmail.com>
Date: Fri, 12 Jan 2024 16:31:05 -0500
Subject: [PATCH 280/700] Typer assertions and simplify function eval all
 around

---
 lib/SimpleNonlinearSolve/src/linesearch.jl | 18 ++++++++----------
 1 file changed, 8 insertions(+), 10 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/linesearch.jl b/lib/SimpleNonlinearSolve/src/linesearch.jl
index b93bd21de..82ece8381 100644
--- a/lib/SimpleNonlinearSolve/src/linesearch.jl
+++ b/lib/SimpleNonlinearSolve/src/linesearch.jl
@@ -25,13 +25,11 @@ end
 end
 
 function (alg::__LiFukushimaLineSearch)(prob, fu, u)
-    @bb u_cache = similar(u)
-    @bb fu_cache = similar(fu)
     T = promote_type(eltype(fu), eltype(u))
 
     ϕ = @closure (u, δu, α) -> begin
-        @bb @. u_cache = u + α * δu
-        return NONLINEARSOLVE_DEFAULT_NORM(__eval_f(prob, fu_cache, u_cache))
+        u_cache = @. u + α * δu
+        return NONLINEARSOLVE_DEFAULT_NORM(prob.f(u_cache, prob.p))
     end
 
     return __LiFukushimaLineSearchCache(ϕ, T(alg.lambda_0), T(alg.beta), T(alg.sigma_1),
@@ -45,22 +43,22 @@ function (cache::__LiFukushimaLineSearchCache)(u, δu)
     fx_norm = ϕ(T(0))::T
 
     # Non-Blocking exit if the norm is NaN or Inf
-    DiffEqBase.NAN_CHECK(fx_norm) && return cache.α
+    DiffEqBase.NAN_CHECK(fx_norm)::Bool && return cache.α
 
     # Early Terminate based on Eq. 2.7
-    du_norm = NONLINEARSOLVE_DEFAULT_NORM(δu)
-    fxλ_norm = ϕ(cache.α)
+    du_norm = NONLINEARSOLVE_DEFAULT_NORM(δu)::T
+    fxλ_norm = ϕ(cache.α)::T
     fxλ_norm ≤ cache.ρ * fx_norm - cache.σ₂ * du_norm^2 && return cache.α
 
     λ₂, λ₁ = cache.λ₀, cache.λ₀
-    fxλp_norm = ϕ(λ₂)
+    fxλp_norm = ϕ(λ₂)::T
 
-    if DiffEqBase.NAN_CHECK(fxλp_norm)
+    if DiffEqBase.NAN_CHECK(fxλp_norm)::Bool
         nan_converged = false
         for _ in 1:(cache.nan_maxiters)
             λ₁, λ₂ = λ₂, cache.β * λ₂
             fxλp_norm = ϕ(λ₂)
-            nan_converged = DiffEqBase.NAN_CHECK(fxλp_norm)
+            nan_converged = DiffEqBase.NAN_CHECK(fxλp_norm)::Bool
             nan_converged && break
         end
         nan_converged || return cache.α

From f14726deb7624c1765425ef374b093b98ba134e0 Mon Sep 17 00:00:00 2001
From: Vaibhav Dixit <vaibhavyashdixit@gmail.com>
Date: Fri, 12 Jan 2024 16:53:29 -0500
Subject: [PATCH 281/700] Bring back bb

---
 lib/SimpleNonlinearSolve/src/linesearch.jl | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/linesearch.jl b/lib/SimpleNonlinearSolve/src/linesearch.jl
index 82ece8381..1b21974b9 100644
--- a/lib/SimpleNonlinearSolve/src/linesearch.jl
+++ b/lib/SimpleNonlinearSolve/src/linesearch.jl
@@ -25,11 +25,13 @@ end
 end
 
 function (alg::__LiFukushimaLineSearch)(prob, fu, u)
+    @bb u_cache = similar(u)
+    @bb fu_cache = similar(fu)
     T = promote_type(eltype(fu), eltype(u))
 
     ϕ = @closure (u, δu, α) -> begin
         u_cache = @. u + α * δu
-        return NONLINEARSOLVE_DEFAULT_NORM(prob.f(u_cache, prob.p))
+        return NONLINEARSOLVE_DEFAULT_NORM(__eval_f(prob, fu_cache, u_cache))
     end
 
     return __LiFukushimaLineSearchCache(ϕ, T(alg.lambda_0), T(alg.beta), T(alg.sigma_1),

From 8a5526a796622cb5526f361da6b135a8d70b005f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 14 Jan 2024 00:40:25 -0500
Subject: [PATCH 282/700] Broyden line search works inside kernels

---
 .../src/SimpleNonlinearSolve.jl               |   2 +-
 lib/SimpleNonlinearSolve/src/linesearch.jl    | 109 +++++++++++++-----
 .../src/nlsolve/broyden.jl                    |  14 +--
 .../src/nlsolve/dfsane.jl                     |   2 +-
 .../src/nlsolve/lbroyden.jl                   |  17 ++-
 5 files changed, 96 insertions(+), 48 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index c8f515cc2..c6dd6291f 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -12,7 +12,7 @@ import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidat
         NONLINEARSOLVE_DEFAULT_NORM, _get_tolerance
     import ForwardDiff: Dual
     import MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
-    import SciMLBase: AbstractNonlinearAlgorithm, build_solution, isinplace
+    import SciMLBase: AbstractNonlinearAlgorithm, build_solution, isinplace, _unwrap_val
     import StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, MMatrix, Size
 end
 
diff --git a/lib/SimpleNonlinearSolve/src/linesearch.jl b/lib/SimpleNonlinearSolve/src/linesearch.jl
index 1b21974b9..e5d2bb93c 100644
--- a/lib/SimpleNonlinearSolve/src/linesearch.jl
+++ b/lib/SimpleNonlinearSolve/src/linesearch.jl
@@ -1,17 +1,17 @@
 # This is a copy of the version in NonlinearSolve.jl. Temporarily kept here till we move
-# line searches into a dedicated package. Renamed to `__` to avoid conflicts.
-@kwdef @concrete struct __LiFukushimaLineSearch
+# line searches into a dedicated package.
+@kwdef @concrete struct LiFukushimaLineSearch
     lambda_0 = 1
-    beta = 1.0 / 2.0
-    sigma_1 = 1.0 / 1000.0
-    sigma_2 = 1.0 / 1000.0
-    eta = 1.0 / 10.0
-    rho = 9.0 / 10.0
-    nan_maxiters::Int = 5
+    beta = 0.5
+    sigma_1 = 0.001
+    sigma_2 = 0.001
+    eta = 0.1
+    rho = 0.1
+    nan_maxiters = missing
     maxiters::Int = 100
 end
 
-@concrete mutable struct __LiFukushimaLineSearchCache
+@concrete mutable struct LiFukushimaLineSearchCache{T <: Union{Nothing, Int}}
     ϕ
     λ₀
     β
@@ -20,11 +20,31 @@ end
     η
     ρ
     α
-    nan_maxiters::Int
+    nan_maxiters::T
     maxiters::Int
 end
 
-function (alg::__LiFukushimaLineSearch)(prob, fu, u)
+@concrete struct StaticLiFukushimaLineSearchCache
+    f
+    p
+    λ₀
+    β
+    σ₁
+    σ₂
+    η
+    ρ
+    maxiters::Int
+end
+
+(alg::LiFukushimaLineSearch)(prob, fu, u) = __generic_init(alg, prob, fu, u)
+function (alg::LiFukushimaLineSearch)(prob, fu::SArray, u::SArray)
+    (alg.nan_maxiters === missing || alg.nan_maxiters === nothing) &&
+        return __static_init(alg, prob, fu, u)
+    @warn "`LiFukushimaLineSearch` with NaN checking is not non-allocating" maxlog=1
+    return __generic_init(alg, prob, fu, u)
+end
+
+function __generic_init(alg::LiFukushimaLineSearch, prob, fu, u)
     @bb u_cache = similar(u)
     @bb fu_cache = similar(fu)
     T = promote_type(eltype(fu), eltype(u))
@@ -34,36 +54,45 @@ function (alg::__LiFukushimaLineSearch)(prob, fu, u)
         return NONLINEARSOLVE_DEFAULT_NORM(__eval_f(prob, fu_cache, u_cache))
     end
 
-    return __LiFukushimaLineSearchCache(ϕ, T(alg.lambda_0), T(alg.beta), T(alg.sigma_1),
-        T(alg.sigma_2), T(alg.eta), T(alg.rho), T(true), alg.nan_maxiters, alg.maxiters)
+    nan_maxiters = ifelse(alg.nan_maxiters === missing, 5, alg.nan_maxiters)
+
+    return LiFukushimaLineSearchCache(ϕ, T(alg.lambda_0), T(alg.beta), T(alg.sigma_1),
+        T(alg.sigma_2), T(alg.eta), T(alg.rho), T(true), nan_maxiters, alg.maxiters)
 end
 
-function (cache::__LiFukushimaLineSearchCache)(u, δu)
+function __static_init(alg::LiFukushimaLineSearch, prob, fu, u)
+    T = promote_type(eltype(fu), eltype(u))
+    return StaticLiFukushimaLineSearchCache(prob.f, prob.p, T(alg.lambda_0), T(alg.beta),
+        T(alg.sigma_1), T(alg.sigma_2), T(alg.eta), T(alg.rho), alg.maxiters)
+end
+
+function (cache::LiFukushimaLineSearchCache)(u, δu)
     T = promote_type(eltype(u), eltype(δu))
     ϕ = @closure α -> cache.ϕ(u, δu, α)
-
-    fx_norm = ϕ(T(0))::T
+    fx_norm = ϕ(T(0))
 
     # Non-Blocking exit if the norm is NaN or Inf
-    DiffEqBase.NAN_CHECK(fx_norm)::Bool && return cache.α
+    DiffEqBase.NAN_CHECK(fx_norm) && return cache.α
 
     # Early Terminate based on Eq. 2.7
-    du_norm = NONLINEARSOLVE_DEFAULT_NORM(δu)::T
-    fxλ_norm = ϕ(cache.α)::T
+    du_norm = NONLINEARSOLVE_DEFAULT_NORM(δu)
+    fxλ_norm = ϕ(cache.α)
     fxλ_norm ≤ cache.ρ * fx_norm - cache.σ₂ * du_norm^2 && return cache.α
 
     λ₂, λ₁ = cache.λ₀, cache.λ₀
-    fxλp_norm = ϕ(λ₂)::T
-
-    if DiffEqBase.NAN_CHECK(fxλp_norm)::Bool
-        nan_converged = false
-        for _ in 1:(cache.nan_maxiters)
-            λ₁, λ₂ = λ₂, cache.β * λ₂
-            fxλp_norm = ϕ(λ₂)
-            nan_converged = DiffEqBase.NAN_CHECK(fxλp_norm)::Bool
-            nan_converged && break
+    fxλp_norm = ϕ(λ₂)
+
+    if cache.nan_maxiters !== nothing
+        if DiffEqBase.NAN_CHECK(fxλp_norm)
+            nan_converged = false
+            for _ in 1:(cache.nan_maxiters)
+                λ₁, λ₂ = λ₂, cache.β * λ₂
+                fxλp_norm = ϕ(λ₂)
+                nan_converged = DiffEqBase.NAN_CHECK(fxλp_norm)::Bool
+                nan_converged && break
+            end
+            nan_converged || return cache.α
         end
-        nan_converged || return cache.α
     end
 
     for i in 1:(cache.maxiters)
@@ -75,3 +104,25 @@ function (cache::__LiFukushimaLineSearchCache)(u, δu)
 
     return cache.α
 end
+
+function (cache::StaticLiFukushimaLineSearchCache)(u, δu)
+    T = promote_type(eltype(u), eltype(δu))
+
+    # Early Terminate based on Eq. 2.7
+    fx_norm = NONLINEARSOLVE_DEFAULT_NORM(cache.f(u, cache.p))
+    du_norm = NONLINEARSOLVE_DEFAULT_NORM(δu)
+    fxλ_norm = NONLINEARSOLVE_DEFAULT_NORM(cache.f(u .+ cache.λ₀ .* δu, cache.p))
+    fxλ_norm ≤ cache.ρ * fx_norm - cache.σ₂ * du_norm^2 && return T(true)
+
+    λ₂, λ₁ = cache.λ₀, cache.λ₀
+    fxλp_norm = NONLINEARSOLVE_DEFAULT_NORM(cache.f(u .+ λ₂ .* δu, cache.p))
+
+    for i in 1:(cache.maxiters)
+        fxλp_norm = NONLINEARSOLVE_DEFAULT_NORM(cache.f(u .+ λ₂ .* δu, cache.p))
+        converged = fxλp_norm ≤ (1 + cache.η) * fx_norm - cache.σ₁ * λ₂^2 * du_norm^2
+        converged && return λ₂
+        λ₁, λ₂ = λ₂, cache.β * λ₂
+    end
+
+    return T(true)
+end
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index fa0b17359..8eebd9518 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -16,9 +16,7 @@ of Broyden-like method for nonlinear equations." Optimization methods and softwa
 """
 struct SimpleBroyden{linesearch} <: AbstractSimpleNonlinearSolveAlgorithm end
 
-function SimpleBroyden(; linesearch = Val(false))
-    SimpleBroyden{SciMLBase._unwrap_val(linesearch)}()
-end
+SimpleBroyden(; linesearch = Val(false)) = SimpleBroyden{_unwrap_val(linesearch)}()
 
 __get_linesearch(::SimpleBroyden{LS}) where {LS} = Val(LS)
 
@@ -39,11 +37,11 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
     @bb δJ⁻¹n = copy(x)
     @bb δJ⁻¹ = copy(J⁻¹)
 
-    # abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
-    #     termination_condition)
+    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+        termination_condition)
 
     ls_cache = __get_linesearch(alg) === Val(true) ?
-               __LiFukushimaLineSearch()(prob, fx, x) : nothing
+               LiFukushimaLineSearch()(prob, fx, x) : nothing
 
     for _ in 1:maxiters
         @bb δx = J⁻¹ × vec(fprev)
@@ -55,8 +53,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
         @bb @. δf = fx - fprev
 
         # Termination Checks
-        # tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
-        # tc_sol !== nothing && return tc_sol
+        tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
+        tc_sol !== nothing && return tc_sol
 
         @bb J⁻¹δf = J⁻¹ × vec(δf)
         d = dot(δx, J⁻¹δf)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index c6111b38c..9232c5445 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -56,7 +56,7 @@ end
 function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
         M::Union{Int, Val} = Val(10), γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
         nexp::Int = 2, η_strategy::F = (f_1, k, x, F) -> f_1 ./ k^2) where {F}
-    return SimpleDFSane{SciMLBase._unwrap_val(M)}(σ_min, σ_max, σ_1, γ, τ_min, τ_max, nexp,
+    return SimpleDFSane{_unwrap_val(M)}(σ_min, σ_max, σ_1, γ, τ_min, τ_max, nexp,
         η_strategy)
 end
 
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index fa3b9d3cd..5f144a3b6 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -1,6 +1,6 @@
 """
-    SimpleLimitedMemoryBroyden(; threshold::Int = 27, linesearch = Val(true))
-    SimpleLimitedMemoryBroyden(; threshold::Val = Val(27), linesearch = Val(true))
+    SimpleLimitedMemoryBroyden(; threshold::Int = 27, linesearch = Val(false))
+    SimpleLimitedMemoryBroyden(; threshold::Val = Val(27), linesearch = Val(false))
 
 A limited memory implementation of Broyden. This method applies the L-BFGS scheme to
 Broyden's method. This Alogrithm unfortunately cannot non-allocating for StaticArrays
@@ -25,9 +25,8 @@ __get_threshold(::SimpleLimitedMemoryBroyden{threshold}) where {threshold} = Val
 __use_linesearch(::SimpleLimitedMemoryBroyden{Th, LS}) where {Th, LS} = Val(LS)
 
 function SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27),
-        linesearch = Val(true))
-    return SimpleLimitedMemoryBroyden{SciMLBase._unwrap_val(threshold),
-        SciMLBase._unwrap_val(linesearch)}()
+        linesearch = Val(false))
+    return SimpleLimitedMemoryBroyden{_unwrap_val(threshold), _unwrap_val(linesearch)}()
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyden,
@@ -50,7 +49,7 @@ end
         termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
     threshold = __get_threshold(alg)
-    η = min(SciMLBase._unwrap_val(threshold), maxiters)
+    η = min(_unwrap_val(threshold), maxiters)
 
     # For scalar problems / if the threshold is larger than problem size just use Broyden
     if x isa Number || length(x) ≤ η
@@ -134,7 +133,7 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
 
     xo, fo, δx = res.x, res.fx, res.δx
 
-    for i in 1:(maxiters - SciMLBase._unwrap_val(threshold))
+    for i in 1:(maxiters - _unwrap_val(threshold))
         x = xo .+ δx
         fx = prob.f(x, prob.p)
         δf = fx - fo
@@ -148,8 +147,8 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
         d = dot(vᵀ, δf)
         δx = @. (δx - mvec) / d
 
-        U = Base.setindex(U, vec(δx), mod1(i, SciMLBase._unwrap_val(threshold)))
-        Vᵀ = Base.setindex(Vᵀ, vec(vᵀ), mod1(i, SciMLBase._unwrap_val(threshold)))
+        U = Base.setindex(U, vec(δx), mod1(i, _unwrap_val(threshold)))
+        Vᵀ = Base.setindex(Vᵀ, vec(vᵀ), mod1(i, _unwrap_val(threshold)))
 
         δx = -_restructure(fx, _matvec!!(U, Vᵀ, vec(fx)))
 

From cf2551b57d1f8d9b0c70ef60ea8b41a08a3ac4e4 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 14 Jan 2024 00:42:07 -0500
Subject: [PATCH 283/700] Add linesearch to the cuda tests

---
 lib/SimpleNonlinearSolve/test/basictests.jl | 4 ++--
 lib/SimpleNonlinearSolve/test/cuda.jl       | 6 ++++--
 2 files changed, 6 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 7da944e7b..b0b356daf 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -105,7 +105,7 @@ end
 # --- SimpleBroyden / SimpleKlement / SimpleLimitedMemoryBroyden tests ---
 
 @testset "$(_nameof(alg))" for alg in [SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
-    SimpleLimitedMemoryBroyden()]
+    SimpleLimitedMemoryBroyden(), SimpleBroyden(; linesearch = Val(true))]
     function benchmark_nlsolve_oop(f, u0, p = 2.0)
         prob = NonlinearProblem{false}(f, u0, p)
         return solve(prob, alg, abstol = 1e-9)
@@ -164,7 +164,7 @@ end
 ## SimpleDFSane needs to allocate a history vector
 @testset "Allocation Checks: $(_nameof(alg))" for alg in (SimpleNewtonRaphson(),
     SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
-    SimpleTrustRegion(), SimpleDFSane())
+    SimpleTrustRegion(), SimpleDFSane(), SimpleBroyden(; linesearch = Val(true)))
     @check_allocs nlsolve(prob, alg) = SciMLBase.solve(prob, alg; abstol = 1e-9)
 
     nlprob_scalar = NonlinearProblem{false}(quadratic_f, 1.0, 2.0)
diff --git a/lib/SimpleNonlinearSolve/test/cuda.jl b/lib/SimpleNonlinearSolve/test/cuda.jl
index 9b984bc70..19e67a081 100644
--- a/lib/SimpleNonlinearSolve/test/cuda.jl
+++ b/lib/SimpleNonlinearSolve/test/cuda.jl
@@ -7,7 +7,8 @@ f!(du, u, p) = du .= u .* u .- 2
 
 @testset "Solving on GPUs" begin
     for alg in (SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(), SimpleBroyden(),
-        SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley())
+        SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley(),
+        SimpleBroyden(; linesearch = Val(true)))
         @info "Testing $alg on CUDA"
 
         # Static Arrays
@@ -43,7 +44,8 @@ end
     prob = NonlinearProblem{false}(f, @SVector[1.0f0, 1.0f0])
 
     for alg in (SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(), SimpleBroyden(),
-        SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley())
+        SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley(),
+        SimpleBroyden(; linesearch = Val(true)))
         @test begin
             try
                 @cuda kernel_function(prob, alg)

From 1d5eeb817528ca103514a722fd7d26231ba2506f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 14 Jan 2024 00:55:36 -0500
Subject: [PATCH 284/700] Add linesearch to LBroyden

---
 .../src/nlsolve/broyden.jl                    |  2 +-
 .../src/nlsolve/lbroyden.jl                   | 20 +++++++++++--------
 lib/SimpleNonlinearSolve/test/basictests.jl   |  6 ++++--
 lib/SimpleNonlinearSolve/test/cuda.jl         |  6 ++++--
 4 files changed, 21 insertions(+), 13 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index 8eebd9518..327f2e2fb 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -6,7 +6,7 @@ and static array problems.
 
 If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch` [1] line search else
 no line search is used. For advanced customization of the line search, use the
-`Broyden` algorithm in `NonlinearSolve.jl`.
+[`Broyden`](@ref) algorithm in `NonlinearSolve.jl`.
 
 ### References
 
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index 5f144a3b6..5f5d481c2 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -3,14 +3,13 @@
     SimpleLimitedMemoryBroyden(; threshold::Val = Val(27), linesearch = Val(false))
 
 A limited memory implementation of Broyden. This method applies the L-BFGS scheme to
-Broyden's method. This Alogrithm unfortunately cannot non-allocating for StaticArrays
-without compromising on the "simple" aspect.
+Broyden's method.
 
 If the threshold is larger than the problem size, then this method will use `SimpleBroyden`.
 
 If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch` [1] line search else
 no line search is used. For advanced customization of the line search, use the
-`LimitedMemoryBroyden` algorithm in `NonlinearSolve.jl`.
+[`LimitedMemoryBroyden`](@ref) algorithm in `NonlinearSolve.jl`.
 
 ### References
 
@@ -75,7 +74,7 @@ end
     @bb mat_cache = copy(x)
 
     ls_cache = __use_linesearch(alg) === Val(true) ?
-               __LiFukushimaLineSearch()(prob, fx, x) : nothing
+               LiFukushimaLineSearch()(prob, fx, x) : nothing
 
     for i in 1:maxiters
         α = ls_cache === nothing ? true : ls_cache(x, δx)
@@ -125,8 +124,11 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
 
     xo, δx, fo, δf = x, -fx, fx, fx
 
+    ls_cache = __use_linesearch(alg) === Val(true) ?
+               LiFukushimaLineSearch()(prob, fx, x) : nothing
+
     converged, res = __unrolled_lbroyden_initial_iterations(prob, xo, fo, δx, abstol, U, Vᵀ,
-        threshold)
+        threshold, ls_cache)
 
     converged &&
         return build_solution(prob, alg, res.x, res.fx; retcode = ReturnCode.Success)
@@ -134,7 +136,8 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
     xo, fo, δx = res.x, res.fx, res.δx
 
     for i in 1:(maxiters - _unwrap_val(threshold))
-        x = xo .+ δx
+        α = ls_cache === nothing ? true : ls_cache(xo, δx)
+        x = xo .+ α .* δx
         fx = prob.f(x, prob.p)
         δf = fx - fo
 
@@ -160,13 +163,14 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
 end
 
 @generated function __unrolled_lbroyden_initial_iterations(prob, xo, fo, δx, abstol, U,
-        Vᵀ, ::Val{threshold}) where {threshold}
+        Vᵀ, ::Val{threshold}, ls_cache) where {threshold}
     calls = []
     for i in 1:threshold
         static_idx, static_idx_p1 = Val(i - 1), Val(i)
         push!(calls,
             quote
-                x = xo .+ δx
+                α = ls_cache === nothing ? true : ls_cache(xo, δx)
+                x = xo .+ α .* δx
                 fx = prob.f(x, prob.p)
                 δf = fx - fo
 
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index b0b356daf..2c4cd6be5 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -105,7 +105,8 @@ end
 # --- SimpleBroyden / SimpleKlement / SimpleLimitedMemoryBroyden tests ---
 
 @testset "$(_nameof(alg))" for alg in [SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
-    SimpleLimitedMemoryBroyden(), SimpleBroyden(; linesearch = Val(true))]
+    SimpleLimitedMemoryBroyden(), SimpleBroyden(; linesearch = Val(true)),
+    SimpleLimitedMemoryBroyden(; linesearch = Val(true))]
     function benchmark_nlsolve_oop(f, u0, p = 2.0)
         prob = NonlinearProblem{false}(f, u0, p)
         return solve(prob, alg, abstol = 1e-9)
@@ -164,7 +165,8 @@ end
 ## SimpleDFSane needs to allocate a history vector
 @testset "Allocation Checks: $(_nameof(alg))" for alg in (SimpleNewtonRaphson(),
     SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
-    SimpleTrustRegion(), SimpleDFSane(), SimpleBroyden(; linesearch = Val(true)))
+    SimpleTrustRegion(), SimpleDFSane(), SimpleBroyden(; linesearch = Val(true)),
+    SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
     @check_allocs nlsolve(prob, alg) = SciMLBase.solve(prob, alg; abstol = 1e-9)
 
     nlprob_scalar = NonlinearProblem{false}(quadratic_f, 1.0, 2.0)
diff --git a/lib/SimpleNonlinearSolve/test/cuda.jl b/lib/SimpleNonlinearSolve/test/cuda.jl
index 19e67a081..95ee60fb6 100644
--- a/lib/SimpleNonlinearSolve/test/cuda.jl
+++ b/lib/SimpleNonlinearSolve/test/cuda.jl
@@ -8,7 +8,8 @@ f!(du, u, p) = du .= u .* u .- 2
 @testset "Solving on GPUs" begin
     for alg in (SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(), SimpleBroyden(),
         SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley(),
-        SimpleBroyden(; linesearch = Val(true)))
+        SimpleBroyden(; linesearch = Val(true)),
+        SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
         @info "Testing $alg on CUDA"
 
         # Static Arrays
@@ -45,7 +46,8 @@ end
 
     for alg in (SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(), SimpleBroyden(),
         SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley(),
-        SimpleBroyden(; linesearch = Val(true)))
+        SimpleBroyden(; linesearch = Val(true)),
+        SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
         @test begin
             try
                 @cuda kernel_function(prob, alg)

From 223ca68a30f292910b27adde52a303c57aee73ae Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 14 Jan 2024 01:04:00 -0500
Subject: [PATCH 285/700] Remove the old flaky benchmarktools allocations tests

---
 lib/SimpleNonlinearSolve/test/Project.toml  |  1 -
 lib/SimpleNonlinearSolve/test/basictests.jl | 21 +--------------------
 2 files changed, 1 insertion(+), 21 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/Project.toml b/lib/SimpleNonlinearSolve/test/Project.toml
index 4442a15a6..cbf18f66c 100644
--- a/lib/SimpleNonlinearSolve/test/Project.toml
+++ b/lib/SimpleNonlinearSolve/test/Project.toml
@@ -1,6 +1,5 @@
 [deps]
 AllocCheck = "9b6a8646-10ed-4001-bbdc-1d2f46dfbb1a"
-BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 2c4cd6be5..726930072 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -1,4 +1,4 @@
-using AllocCheck, BenchmarkTools, LinearSolve, SimpleNonlinearSolve, StaticArrays, Random,
+using AllocCheck, LinearSolve, SimpleNonlinearSolve, StaticArrays, Random,
     LinearAlgebra, Test, ForwardDiff, DiffEqBase
 import PolyesterForwardDiff
 
@@ -57,13 +57,6 @@ const TERMINATION_CONDITIONS = [
         end
     end
 
-    @testset "Allocations: Static Array and Scalars" begin
-        @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, $(@SVector[1.0, 1.0]),
-            2.0; autodiff = AutoForwardDiff())) < 200
-        @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, 1.0, 2.0;
-            autodiff = AutoForwardDiff())) == 0
-    end
-
     @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 
@@ -89,11 +82,6 @@ end
         end
     end
 
-    @testset "Allocations: Static Array and Scalars" begin
-        @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, 1.0, 2.0;
-            autodiff = AutoForwardDiff())) == 0
-    end
-
     @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 
@@ -129,13 +117,6 @@ end
         @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
     end
 
-    @testset "Allocations: Static Array and Scalars" begin
-        @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, $(@SVector[1.0, 1.0]),
-            2.0)) < 200
-        allocs = alg isa SimpleDFSane ? 144 : 0
-        @test (@ballocated $(benchmark_nlsolve_oop)($quadratic_f, 1.0, 2.0)) == allocs
-    end
-
     @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 

From 545e3358f8967b4aeef3e38f24251129d5b9f77f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 14 Jan 2024 01:34:10 -0500
Subject: [PATCH 286/700] DFSane non-allocating for scalars now

---
 lib/SimpleNonlinearSolve/Project.toml         |  3 +++
 .../SimpleNonlinearSolveStaticArraysExt.jl    |  7 ++++++
 lib/SimpleNonlinearSolve/src/linesearch.jl    |  3 ++-
 .../src/nlsolve/dfsane.jl                     | 23 ++++++++++---------
 lib/SimpleNonlinearSolve/test/basictests.jl   |  3 +--
 5 files changed, 25 insertions(+), 14 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveStaticArraysExt.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 6373e9647..493766ead 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -20,9 +20,11 @@ StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [weakdeps]
 PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
 [extensions]
 SimpleNonlinearSolvePolyesterForwardDiffExt = "PolyesterForwardDiff"
+SimpleNonlinearSolveStaticArraysExt = "StaticArrays"
 
 [compat]
 ADTypes = "0.2.6"
@@ -38,4 +40,5 @@ PrecompileTools = "1"
 Reexport = "1"
 SciMLBase = "2.7"
 StaticArraysCore = "1.4"
+StaticArrays = "1"
 julia = "1.9"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveStaticArraysExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveStaticArraysExt.jl
new file mode 100644
index 000000000..90318a82a
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveStaticArraysExt.jl
@@ -0,0 +1,7 @@
+module SimpleNonlinearSolveStaticArraysExt
+
+using SimpleNonlinearSolve
+
+@inline SimpleNonlinearSolve.__is_extension_loaded(::Val{:StaticArrays}) = true
+
+end
diff --git a/lib/SimpleNonlinearSolve/src/linesearch.jl b/lib/SimpleNonlinearSolve/src/linesearch.jl
index e5d2bb93c..13f0c28af 100644
--- a/lib/SimpleNonlinearSolve/src/linesearch.jl
+++ b/lib/SimpleNonlinearSolve/src/linesearch.jl
@@ -37,7 +37,8 @@ end
 end
 
 (alg::LiFukushimaLineSearch)(prob, fu, u) = __generic_init(alg, prob, fu, u)
-function (alg::LiFukushimaLineSearch)(prob, fu::SArray, u::SArray)
+function (alg::LiFukushimaLineSearch)(prob, fu::Union{Number, SArray},
+        u::Union{Number, SArray})
     (alg.nan_maxiters === missing || alg.nan_maxiters === nothing) &&
         return __static_init(alg, prob, fu, u)
     @warn "`LiFukushimaLineSearch` with NaN checking is not non-allocating" maxlog=1
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 9232c5445..6931e6101 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -9,21 +9,21 @@ see the paper [1].
 
 ### Keyword Arguments
 
-  - `σ_min`: the minimum value of the spectral coefficient `σ_k` which is related to the step
-    size in the algorithm. Defaults to `1e-10`.
-  - `σ_max`: the maximum value of the spectral coefficient `σ_k` which is related to the step
-    size in the algorithm. Defaults to `1e10`.
+  - `σ_min`: the minimum value of the spectral coefficient `σ_k` which is related to the
+    step size in the algorithm. Defaults to `1e-10`.
+  - `σ_max`: the maximum value of the spectral coefficient `σ_k` which is related to the
+    step size in the algorithm. Defaults to `1e10`.
   - `σ_1`: the initial value of the spectral coefficient `σ_k` which is related to the step
     size in the algorithm.. Defaults to `1.0`.
   - `M`: The monotonicity of the algorithm is determined by a this positive integer.
     A value of 1 for `M` would result in strict monotonicity in the decrease of the L2-norm
-    of the function `f`. However, higher values allow for more flexibility in this reduction.
-    Despite this, the algorithm still ensures global convergence through the use of a
-    non-monotone line-search algorithm that adheres to the Grippo-Lampariello-Lucidi
+    of the function `f`. However, higher values allow for more flexibility in this
+    reduction. Despite this, the algorithm still ensures global convergence through the use
+    of a non-monotone line-search algorithm that adheres to the Grippo-Lampariello-Lucidi
     condition. Values in the range of 5 to 20 are usually sufficient, but some cases may call
     for a higher value of `M`. The default setting is 10.
-  - `γ`: a parameter that influences if a proposed step will be accepted. Higher value of `γ`
-    will make the algorithm more restrictive in accepting steps. Defaults to `1e-4`.
+  - `γ`: a parameter that influences if a proposed step will be accepted. Higher value of
+    `γ` will make the algorithm more restrictive in accepting steps. Defaults to `1e-4`.
   - `τ_min`: if a step is rejected the new step size will get multiplied by factor, and this
     parameter is the minimum value of that factor. Defaults to `0.1`.
   - `τ_max`: if a step is rejected the new step size will get multiplied by factor, and this
@@ -31,7 +31,7 @@ see the paper [1].
   - `nexp`: the exponent of the loss, i.e. ``f_k=||F(x_k)||^{nexp}``. The paper uses
     `nexp ∈ {1,2}`. Defaults to `2`.
   - `η_strategy`:  function to determine the parameter `η_k`, which enables growth
-    of ``||F||^2``. Called as ``η_k = η_strategy(f_1, k, x, F)`` with `f_1` initialized as
+    of ``||F||^2``. Called as `η_k = η_strategy(f_1, k, x, F)` with `f_1` initialized as
     ``f_1=||F(x_1)||^{nexp}``, `k` is the iteration number, `x` is the current `x`-value and
     `F` the current residual. Should satisfy ``η_k > 0`` and ``∑ₖ ηₖ < ∞``. Defaults to
     ``||F||^2 / k^2``.
@@ -83,7 +83,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{M}, args...
     α_1 = one(T)
     f_1 = fx_norm
 
-    history_f_k = if x isa SArray
+    history_f_k = if x isa SArray ||
+                     (x isa Number && __is_extension_loaded(Val(:StaticArrays)))
         ones(SVector{M, T}) * fx_norm
     else
         fill(fx_norm, M)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 726930072..5938197c7 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -158,8 +158,7 @@ end
         @test true
     catch e
         @error e
-        # History Vector Allocates
-        @test false broken=(alg isa SimpleDFSane)
+        @test false
     end
 
     # ForwardDiff allocates for hessian since we don't propagate the chunksize

From 2ff6536cbd928a0757348ccc8b427b256808ecdb Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 14 Jan 2024 02:53:14 -0500
Subject: [PATCH 287/700] Resolve tolerances differently for kernel launches

---
 .../src/SimpleNonlinearSolve.jl                    | 11 ++++++++++-
 lib/SimpleNonlinearSolve/src/ad.jl                 | 14 ++++++++++++++
 .../src/bracketing/bisection.jl                    |  2 +-
 lib/SimpleNonlinearSolve/src/bracketing/brent.jl   |  2 +-
 lib/SimpleNonlinearSolve/src/bracketing/falsi.jl   |  2 +-
 lib/SimpleNonlinearSolve/src/bracketing/itp.jl     |  2 +-
 lib/SimpleNonlinearSolve/src/bracketing/ridder.jl  |  2 +-
 lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl   |  8 +++++++-
 lib/SimpleNonlinearSolve/src/utils.jl              |  7 +++++++
 lib/SimpleNonlinearSolve/test/cuda.jl              |  2 +-
 10 files changed, 44 insertions(+), 8 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index c6dd6291f..8a4f2fe27 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -9,7 +9,7 @@ import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidat
     import DiffEqBase: AbstractNonlinearTerminationMode,
         AbstractSafeNonlinearTerminationMode, AbstractSafeBestNonlinearTerminationMode,
         NonlinearSafeTerminationReturnCode, get_termination_mode,
-        NONLINEARSOLVE_DEFAULT_NORM, _get_tolerance
+        NONLINEARSOLVE_DEFAULT_NORM
     import ForwardDiff: Dual
     import MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
     import SciMLBase: AbstractNonlinearAlgorithm, build_solution, isinplace, _unwrap_val
@@ -65,6 +65,15 @@ function SciMLBase.solve(prob::NonlinearProblem, alg::AbstractSimpleNonlinearSol
     return SciMLBase.__solve(prob, alg, args...; kwargs...)
 end
 
+function SciMLBase.solve(prob::NonlinearProblem{<:Union{<:Number, <:SArray}},
+        alg::AbstractSimpleNonlinearSolveAlgorithm, args...; abstol = nothing,
+        reltol = nothing, kwargs...)
+    _abstol = __get_tolerance(prob.u0, abstol, eltype(prob.u0))
+    _reltol = __get_tolerance(prob.u0, reltol, eltype(prob.u0))
+    return SciMLBase.__solve(prob, alg, args...; abstol = _abstol, reltol = _reltol,
+        kwargs...)
+end
+
 @setup_workload begin
     for T in (Float32, Float64)
         prob_no_brack_scalar = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index 574904bcc..11aa95476 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -8,6 +8,20 @@ function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, <:AbstractArray}
 end
 
 # Handle Ambiguities
+for algType in (SimpleNewtonRaphson, SimpleDFSane, SimpleTrustRegion, SimpleBroyden,
+    SimpleLimitedMemoryBroyden, SimpleKlement, SimpleHalley)
+    @eval begin
+        function SciMLBase.solve(prob::NonlinearProblem{uType, iip,
+                    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
+                alg::$(algType), args...; kwargs...) where {uType, T, V, P, iip}
+            sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
+            dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
+            return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode,
+                sol.stats, sol.original)
+        end
+    end
+end
+
 for algType in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
     @eval begin
         function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
index 66418b3e0..38f9cb9eb 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
@@ -26,7 +26,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
-    abstol = _get_tolerance(abstol,
+    abstol = __get_tolerance(nothing, abstol,
         promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
 
     if iszero(fl)
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/brent.jl b/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
index 75497f379..f37c45e4a 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
@@ -13,7 +13,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
     fl, fr = f(left), f(right)
     ϵ = eps(convert(typeof(fl), 1))
 
-    abstol = _get_tolerance(abstol,
+    abstol = __get_tolerance(nothing, abstol,
         promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
 
     if iszero(fl)
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl b/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
index 9db7d6cf1..86086f81a 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
@@ -12,7 +12,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
-    abstol = _get_tolerance(abstol,
+    abstol = __get_tolerance(nothing, abstol,
         promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
 
     if iszero(fl)
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
index fd46de6c3..cce5eafea 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
@@ -58,7 +58,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
-    abstol = _get_tolerance(abstol,
+    abstol = __get_tolerance(nothing, abstol,
         promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
 
     if iszero(fl)
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
index 20e0db489..cd18060d5 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
@@ -12,7 +12,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
-    abstol = _get_tolerance(abstol,
+    abstol = __get_tolerance(nothing, abstol,
         promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
 
     if iszero(fl)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index 5f5d481c2..c04fa20ee 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -28,6 +28,12 @@ function SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27),
     return SimpleLimitedMemoryBroyden{_unwrap_val(threshold), _unwrap_val(linesearch)}()
 end
 
+function SciMLBase.solve(prob::NonlinearProblem{<:Union{<:Number, <:SArray}},
+        alg::SimpleLimitedMemoryBroyden, args...; kwargs...)
+    # Don't resolve the `abstol` and `reltol` here
+    return SciMLBase.__solve(prob, alg, args...; kwargs...)
+end
+
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyden,
         args...; termination_condition = nothing, kwargs...)
     if prob.u0 isa SArray
@@ -120,7 +126,7 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
 
     U, Vᵀ = __init_low_rank_jacobian(vec(x), vec(fx), threshold)
 
-    abstol = DiffEqBase._get_tolerance(abstol, eltype(x))
+    abstol = __get_tolerance(x, abstol, eltype(x))
 
     xo, δx, fo, δf = x, -fx, fx, fx
 
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index c6b9f2004..de23e9c58 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -370,3 +370,10 @@ end
 
 @inline __reshape(x::Number, args...) = x
 @inline __reshape(x::AbstractArray, args...) = reshape(x, args...)
+
+# Override cases which might be used in a kernel launch
+__get_tolerance(x, η, ::Type{T}) where {T} = DiffEqBase._get_tolerance(η, T)
+function __get_tolerance(x::Union{SArray, Number}, ::Nothing, ::Type{T}) where {T}
+    η = real(oneunit(T)) * (eps(real(one(T))))^(real(T)(0.8))
+    return T(η)
+end
diff --git a/lib/SimpleNonlinearSolve/test/cuda.jl b/lib/SimpleNonlinearSolve/test/cuda.jl
index 95ee60fb6..fddf751de 100644
--- a/lib/SimpleNonlinearSolve/test/cuda.jl
+++ b/lib/SimpleNonlinearSolve/test/cuda.jl
@@ -37,7 +37,7 @@ f!(du, u, p) = du .= u .* u .- 2
 end
 
 function kernel_function(prob, alg)
-    solve(prob, alg; abstol = 1.0f-6, reltol = 1.0f-6)
+    solve(prob, alg)
     return nothing
 end
 

From a1ce1cfc6048c7c080de17345e6cc7b458c68dd8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 14 Jan 2024 04:55:41 -0500
Subject: [PATCH 288/700] Add alpha scaling

---
 lib/SimpleNonlinearSolve/src/linesearch.jl    |  3 +-
 .../src/nlsolve/broyden.jl                    | 33 +++++++---
 .../src/nlsolve/lbroyden.jl                   | 60 ++++++++++++-------
 lib/SimpleNonlinearSolve/src/utils.jl         | 10 ++--
 4 files changed, 69 insertions(+), 37 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/linesearch.jl b/lib/SimpleNonlinearSolve/src/linesearch.jl
index 13f0c28af..fadf69cdc 100644
--- a/lib/SimpleNonlinearSolve/src/linesearch.jl
+++ b/lib/SimpleNonlinearSolve/src/linesearch.jl
@@ -112,11 +112,10 @@ function (cache::StaticLiFukushimaLineSearchCache)(u, δu)
     # Early Terminate based on Eq. 2.7
     fx_norm = NONLINEARSOLVE_DEFAULT_NORM(cache.f(u, cache.p))
     du_norm = NONLINEARSOLVE_DEFAULT_NORM(δu)
-    fxλ_norm = NONLINEARSOLVE_DEFAULT_NORM(cache.f(u .+ cache.λ₀ .* δu, cache.p))
+    fxλ_norm = NONLINEARSOLVE_DEFAULT_NORM(cache.f(u .+ δu, cache.p))
     fxλ_norm ≤ cache.ρ * fx_norm - cache.σ₂ * du_norm^2 && return T(true)
 
     λ₂, λ₁ = cache.λ₀, cache.λ₀
-    fxλp_norm = NONLINEARSOLVE_DEFAULT_NORM(cache.f(u .+ λ₂ .* δu, cache.p))
 
     for i in 1:(cache.maxiters)
         fxλp_norm = NONLINEARSOLVE_DEFAULT_NORM(cache.f(u .+ λ₂ .* δu, cache.p))
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index 327f2e2fb..d670c0556 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -1,12 +1,16 @@
 """
-    SimpleBroyden(; linesearch = Val(false))
+    SimpleBroyden(; linesearch = Val(false), alpha = nothing)
 
 A low-overhead implementation of Broyden. This method is non-allocating on scalar
 and static array problems.
 
-If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch` [1] line search else
-no line search is used. For advanced customization of the line search, use the
-[`Broyden`](@ref) algorithm in `NonlinearSolve.jl`.
+### Keyword Arguments
+
+  * `linesearch`: If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch`
+    [1] line search else no line search is used. For advanced customization of the line
+    search, use the [`Broyden`](@ref) algorithm in `NonlinearSolve.jl`.
+  * `alpha`: Scale the initial jacobian initialization with `alpha`. If it is `nothing`, we
+    will compute the scaling using `2 * norm(fu) / max(norm(u), true)`.
 
 ### References
 
@@ -14,9 +18,13 @@ no line search is used. For advanced customization of the line search, use the
 of Broyden-like method for nonlinear equations." Optimization methods and software 13.3
 (2000): 181-201.
 """
-struct SimpleBroyden{linesearch} <: AbstractSimpleNonlinearSolveAlgorithm end
+@concrete struct SimpleBroyden{linesearch} <: AbstractSimpleNonlinearSolveAlgorithm
+    alpha
+end
 
-SimpleBroyden(; linesearch = Val(false)) = SimpleBroyden{_unwrap_val(linesearch)}()
+function SimpleBroyden(; linesearch = Val(false), alpha = nothing)
+    return SimpleBroyden{_unwrap_val(linesearch)}(alpha)
+end
 
 __get_linesearch(::SimpleBroyden{LS}) where {LS} = Val(LS)
 
@@ -25,13 +33,22 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
         termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
     fx = _get_fx(prob, x)
+    T = promote_type(eltype(x), eltype(fx))
 
     @bb xo = copy(x)
     @bb δx = copy(x)
     @bb δf = copy(fx)
     @bb fprev = copy(fx)
 
-    J⁻¹ = __init_identity_jacobian(fx, x)
+    if alg.alpha === nothing
+        fx_norm = NONLINEARSOLVE_DEFAULT_NORM(fx)
+        x_norm = NONLINEARSOLVE_DEFAULT_NORM(x)
+        init_α = ifelse(fx_norm ≥ 1e-5, max(x_norm, T(true)) / (2 * fx_norm), T(true))
+    else
+        init_α = inv(alg.alpha)
+    end
+
+    J⁻¹ = __init_identity_jacobian(fx, x, init_α)
     @bb J⁻¹δf = copy(x)
     @bb xᵀJ⁻¹ = copy(x)
     @bb δJ⁻¹n = copy(x)
@@ -47,7 +64,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
         @bb δx = J⁻¹ × vec(fprev)
         @bb δx .*= -1
 
-        α = ls_cache === nothing ? true : ls_cache(x, δx)
+        α = ls_cache === nothing ? true : ls_cache(xo, δx)
         @bb @. x = xo + α * δx
         fx = __eval_f(prob, fx, x)
         @bb @. δf = fx - fprev
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index c04fa20ee..c35dec388 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -1,15 +1,20 @@
 """
-    SimpleLimitedMemoryBroyden(; threshold::Int = 27, linesearch = Val(false))
-    SimpleLimitedMemoryBroyden(; threshold::Val = Val(27), linesearch = Val(false))
+    SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27),
+        linesearch = Val(false), alpha = nothing)
 
 A limited memory implementation of Broyden. This method applies the L-BFGS scheme to
 Broyden's method.
 
 If the threshold is larger than the problem size, then this method will use `SimpleBroyden`.
 
-If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch` [1] line search else
-no line search is used. For advanced customization of the line search, use the
-[`LimitedMemoryBroyden`](@ref) algorithm in `NonlinearSolve.jl`.
+### Keyword Arguments:
+
+  - `linesearch`: If `linesearch` is `Val(true)`, then we use the
+    `LiFukushimaLineSearch` [1] line search else no line search is used. For advanced
+    customization of the line search, use the [`LimitedMemoryBroyden`](@ref) algorithm in
+    `NonlinearSolve.jl`.
+  - `alpha`: Scale the initial jacobian initialization with `alpha`. If it is `nothing`, we
+    will compute the scaling using `2 * norm(fu) / max(norm(u), true)`.
 
 ### References
 
@@ -17,20 +22,22 @@ no line search is used. For advanced customization of the line search, use the
 of Broyden-like method for nonlinear equations." Optimization methods and software 13.3
 (2000): 181-201.
 """
-struct SimpleLimitedMemoryBroyden{threshold, linesearch} <:
-       AbstractSimpleNonlinearSolveAlgorithm end
+@concrete struct SimpleLimitedMemoryBroyden{threshold, linesearch} <:
+                 AbstractSimpleNonlinearSolveAlgorithm
+    alpha
+end
 
 __get_threshold(::SimpleLimitedMemoryBroyden{threshold}) where {threshold} = Val(threshold)
 __use_linesearch(::SimpleLimitedMemoryBroyden{Th, LS}) where {Th, LS} = Val(LS)
 
 function SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27),
-        linesearch = Val(false))
-    return SimpleLimitedMemoryBroyden{_unwrap_val(threshold), _unwrap_val(linesearch)}()
+        linesearch = Val(false), alpha = nothing)
+    return SimpleLimitedMemoryBroyden{_unwrap_val(threshold), _unwrap_val(linesearch)}(alpha)
 end
 
+# Don't resolve the `abstol` and `reltol` here
 function SciMLBase.solve(prob::NonlinearProblem{<:Union{<:Number, <:SArray}},
         alg::SimpleLimitedMemoryBroyden, args...; kwargs...)
-    # Don't resolve the `abstol` and `reltol` here
     return SciMLBase.__solve(prob, alg, args...; kwargs...)
 end
 
@@ -133,8 +140,17 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
     ls_cache = __use_linesearch(alg) === Val(true) ?
                LiFukushimaLineSearch()(prob, fx, x) : nothing
 
+    T = promote_type(eltype(x), eltype(fx))
+    if alg.alpha === nothing
+        fx_norm = NONLINEARSOLVE_DEFAULT_NORM(fx)
+        x_norm = NONLINEARSOLVE_DEFAULT_NORM(x)
+        init_α = ifelse(fx_norm ≥ 1e-5, max(x_norm, T(true)) / (2 * fx_norm), T(true))
+    else
+        init_α = inv(alg.alpha)
+    end
+
     converged, res = __unrolled_lbroyden_initial_iterations(prob, xo, fo, δx, abstol, U, Vᵀ,
-        threshold, ls_cache)
+        threshold, ls_cache, init_α)
 
     converged &&
         return build_solution(prob, alg, res.x, res.fx; retcode = ReturnCode.Success)
@@ -150,8 +166,8 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
         maximum(abs, fx) ≤ abstol &&
             return build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
 
-        vᵀ = _restructure(x, _rmatvec!!(U, Vᵀ, vec(δx)))
-        mvec = _restructure(x, _matvec!!(U, Vᵀ, vec(δf)))
+        vᵀ = _restructure(x, _rmatvec!!(U, Vᵀ, vec(δx), init_α))
+        mvec = _restructure(x, _matvec!!(U, Vᵀ, vec(δf), init_α))
 
         d = dot(vᵀ, δf)
         δx = @. (δx - mvec) / d
@@ -159,7 +175,7 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
         U = Base.setindex(U, vec(δx), mod1(i, _unwrap_val(threshold)))
         Vᵀ = Base.setindex(Vᵀ, vec(vᵀ), mod1(i, _unwrap_val(threshold)))
 
-        δx = -_restructure(fx, _matvec!!(U, Vᵀ, vec(fx)))
+        δx = -_restructure(fx, _matvec!!(U, Vᵀ, vec(fx), init_α))
 
         xo = x
         fo = fx
@@ -169,7 +185,7 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
 end
 
 @generated function __unrolled_lbroyden_initial_iterations(prob, xo, fo, δx, abstol, U,
-        Vᵀ, ::Val{threshold}, ls_cache) where {threshold}
+        Vᵀ, ::Val{threshold}, ls_cache, init_α) where {threshold}
     calls = []
     for i in 1:threshold
         static_idx, static_idx_p1 = Val(i - 1), Val(i)
@@ -185,8 +201,8 @@ end
                 _U = __first_n_getindex(U, $(static_idx))
                 _Vᵀ = __first_n_getindex(Vᵀ, $(static_idx))
 
-                vᵀ = _restructure(x, _rmatvec!!(_U, _Vᵀ, vec(δx)))
-                mvec = _restructure(x, _matvec!!(_U, _Vᵀ, vec(δf)))
+                vᵀ = _restructure(x, _rmatvec!!(_U, _Vᵀ, vec(δx), init_α))
+                mvec = _restructure(x, _matvec!!(_U, _Vᵀ, vec(δf), init_α))
 
                 d = dot(vᵀ, δf)
                 δx = @. (δx - mvec) / d
@@ -196,7 +212,7 @@ end
 
                 _U = __first_n_getindex(U, $(static_idx_p1))
                 _Vᵀ = __first_n_getindex(Vᵀ, $(static_idx_p1))
-                δx = -_restructure(fx, _matvec!!(_U, _Vᵀ, vec(fx)))
+                δx = -_restructure(fx, _matvec!!(_U, _Vᵀ, vec(fx), init_α))
 
                 xo = x
                 fo = fx
@@ -226,8 +242,8 @@ function _rmatvec!!(y, xᵀU, U, Vᵀ, x)
     return y
 end
 
-@inline _rmatvec!!(::Nothing, Vᵀ, x) = -x
-@inline _rmatvec!!(U, Vᵀ, x) = __mapTdot(__mapdot(x, U), Vᵀ) .- x
+@inline _rmatvec!!(::Nothing, Vᵀ, x, init_α) = -x .* init_α
+@inline _rmatvec!!(U, Vᵀ, x, init_α) = __mapTdot(__mapdot(x, U), Vᵀ) .- x .* init_α
 
 function _matvec!!(y, Vᵀx, U, Vᵀ, x)
     # (-I + UVᵀ) × x
@@ -244,8 +260,8 @@ function _matvec!!(y, Vᵀx, U, Vᵀ, x)
     return y
 end
 
-@inline _matvec!!(::Nothing, Vᵀ, x) = -x
-@inline _matvec!!(U, Vᵀ, x) = __mapTdot(__mapdot(x, Vᵀ), U) .- x
+@inline _matvec!!(::Nothing, Vᵀ, x, init_α) = -x .* init_α
+@inline _matvec!!(U, Vᵀ, x, init_α) = __mapTdot(__mapdot(x, Vᵀ), U) .- x .* init_α
 
 function __mapdot(x::SVector{S1}, Y::SVector{S2, <:SVector{S1}}) where {S1, S2}
     return map(Base.Fix1(dot, x), Y)
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index de23e9c58..c150522da 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -214,12 +214,12 @@ function compute_jacobian_and_hessian(ad::AutoFiniteDiff, prob, fx, x)
     end
 end
 
-__init_identity_jacobian(u::Number, _) = one(u)
+__init_identity_jacobian(u::Number, fu, α = true) = oftype(u, α)
 __init_identity_jacobian!!(J::Number) = one(J)
-function __init_identity_jacobian(u, fu)
+function __init_identity_jacobian(u, fu, α = true)
     J = similar(u, promote_type(eltype(u), eltype(fu)), length(fu), length(u))
     fill!(J, zero(eltype(J)))
-    J[diagind(J)] .= one(eltype(J))
+    J[diagind(J)] .= eltype(J)(α)
     return J
 end
 function __init_identity_jacobian!!(J)
@@ -231,9 +231,9 @@ function __init_identity_jacobian!!(J::AbstractVector)
     fill!(J, one(eltype(J)))
     return J
 end
-function __init_identity_jacobian(u::StaticArray, fu)
+function __init_identity_jacobian(u::StaticArray, fu, α = true)
     S1, S2 = length(fu), length(u)
-    J = SMatrix{S1, S2, eltype(u)}(I)
+    J = SMatrix{S1, S2, eltype(u)}(I * α)
     return J
 end
 function __init_identity_jacobian!!(J::SMatrix{S1, S2}) where {S1, S2}

From ba289bedc8bea004dcf785ffa1143965a58d707d Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 14 Jan 2024 05:50:30 -0500
Subject: [PATCH 289/700] Resolve ambiguities

---
 .../src/SimpleNonlinearSolve.jl                   |  9 ---------
 lib/SimpleNonlinearSolve/src/ad.jl                | 15 ---------------
 lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl   |  4 ++--
 lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl  |  6 ------
 lib/SimpleNonlinearSolve/src/utils.jl             |  4 ++--
 5 files changed, 4 insertions(+), 34 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 8a4f2fe27..73eda9977 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -65,15 +65,6 @@ function SciMLBase.solve(prob::NonlinearProblem, alg::AbstractSimpleNonlinearSol
     return SciMLBase.__solve(prob, alg, args...; kwargs...)
 end
 
-function SciMLBase.solve(prob::NonlinearProblem{<:Union{<:Number, <:SArray}},
-        alg::AbstractSimpleNonlinearSolveAlgorithm, args...; abstol = nothing,
-        reltol = nothing, kwargs...)
-    _abstol = __get_tolerance(prob.u0, abstol, eltype(prob.u0))
-    _reltol = __get_tolerance(prob.u0, reltol, eltype(prob.u0))
-    return SciMLBase.__solve(prob, alg, args...; abstol = _abstol, reltol = _reltol,
-        kwargs...)
-end
-
 @setup_workload begin
     for T in (Float32, Float64)
         prob_no_brack_scalar = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index 11aa95476..a4a777be6 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -7,21 +7,6 @@ function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, <:AbstractArray}
         sol.original)
 end
 
-# Handle Ambiguities
-for algType in (SimpleNewtonRaphson, SimpleDFSane, SimpleTrustRegion, SimpleBroyden,
-    SimpleLimitedMemoryBroyden, SimpleKlement, SimpleHalley)
-    @eval begin
-        function SciMLBase.solve(prob::NonlinearProblem{uType, iip,
-                    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
-                alg::$(algType), args...; kwargs...) where {uType, T, V, P, iip}
-            sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
-            dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
-            return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode,
-                sol.stats, sol.original)
-        end
-    end
-end
-
 for algType in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
     @eval begin
         function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index d670c0556..ad19d765b 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -6,10 +6,10 @@ and static array problems.
 
 ### Keyword Arguments
 
-  * `linesearch`: If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch`
+  - `linesearch`: If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch`
     [1] line search else no line search is used. For advanced customization of the line
     search, use the [`Broyden`](@ref) algorithm in `NonlinearSolve.jl`.
-  * `alpha`: Scale the initial jacobian initialization with `alpha`. If it is `nothing`, we
+  - `alpha`: Scale the initial jacobian initialization with `alpha`. If it is `nothing`, we
     will compute the scaling using `2 * norm(fu) / max(norm(u), true)`.
 
 ### References
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index c35dec388..eb7b1bbaf 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -35,12 +35,6 @@ function SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27),
     return SimpleLimitedMemoryBroyden{_unwrap_val(threshold), _unwrap_val(linesearch)}(alpha)
 end
 
-# Don't resolve the `abstol` and `reltol` here
-function SciMLBase.solve(prob::NonlinearProblem{<:Union{<:Number, <:SArray}},
-        alg::SimpleLimitedMemoryBroyden, args...; kwargs...)
-    return SciMLBase.__solve(prob, alg, args...; kwargs...)
-end
-
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyden,
         args...; termination_condition = nothing, kwargs...)
     if prob.u0 isa SArray
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index c150522da..7390f5e3c 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -282,8 +282,8 @@ function init_termination_cache(abstol, reltol, du, u, ::Nothing)
 end
 function init_termination_cache(abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
     T = promote_type(eltype(du), eltype(u))
-    abstol !== nothing && (abstol = T(abstol))
-    reltol !== nothing && (reltol = T(reltol))
+    abstol = __get_tolerance(u, abstol, T)
+    reltol = __get_tolerance(u, reltol, T)
     tc_cache = init(du, u, tc; abstol, reltol)
     return DiffEqBase.get_abstol(tc_cache), DiffEqBase.get_reltol(tc_cache), tc_cache
 end

From 4d35fc65b31b362a3114828ddc1bfaf5da0fb7cc Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 14 Jan 2024 06:04:49 -0500
Subject: [PATCH 290/700] More of the 23 tests are working

---
 lib/SimpleNonlinearSolve/test/23_test_problems.jl | 7 ++-----
 1 file changed, 2 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/23_test_problems.jl b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
index bc82145a9..18ac5e9bd 100644
--- a/lib/SimpleNonlinearSolve/test/23_test_problems.jl
+++ b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
@@ -70,12 +70,9 @@ end
     alg_ops = (SimpleBroyden(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 4, 5, 6, 11, 12, 13, 14]
+    broken_tests[alg_ops[1]] = [1, 5, 11]
 
-    skip_tests = Dict(alg => Int[] for alg in alg_ops)
-    skip_tests[alg_ops[1]] = [2, 22]
-
-    test_on_library(problems, dicts, alg_ops, broken_tests; skip_tests)
+    test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
 @testset "SimpleKlement 23 Test Problems" begin

From 7e2fc08021ccab73af2b716ddaecb68891f608dc Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 14 Jan 2024 09:26:45 -0500
Subject: [PATCH 291/700] Update src/linesearch.jl

Co-authored-by: Vaibhav Kumar Dixit <vaibhavyashdixit@gmail.com>
---
 lib/SimpleNonlinearSolve/src/linesearch.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/linesearch.jl b/lib/SimpleNonlinearSolve/src/linesearch.jl
index fadf69cdc..235ee0bba 100644
--- a/lib/SimpleNonlinearSolve/src/linesearch.jl
+++ b/lib/SimpleNonlinearSolve/src/linesearch.jl
@@ -51,7 +51,7 @@ function __generic_init(alg::LiFukushimaLineSearch, prob, fu, u)
     T = promote_type(eltype(fu), eltype(u))
 
     ϕ = @closure (u, δu, α) -> begin
-        u_cache = @. u + α * δu
+        @. u_cache = u + α * δu
         return NONLINEARSOLVE_DEFAULT_NORM(__eval_f(prob, fu_cache, u_cache))
     end
 

From 34289efb5e348c1e23f5d7933712a01ef10aee58 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 14 Jan 2024 09:27:34 -0500
Subject: [PATCH 292/700] Update src/linesearch.jl

---
 lib/SimpleNonlinearSolve/src/linesearch.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/linesearch.jl b/lib/SimpleNonlinearSolve/src/linesearch.jl
index 235ee0bba..c33253f63 100644
--- a/lib/SimpleNonlinearSolve/src/linesearch.jl
+++ b/lib/SimpleNonlinearSolve/src/linesearch.jl
@@ -51,7 +51,7 @@ function __generic_init(alg::LiFukushimaLineSearch, prob, fu, u)
     T = promote_type(eltype(fu), eltype(u))
 
     ϕ = @closure (u, δu, α) -> begin
-        @. u_cache = u + α * δu
+        @bb @. u_cache = u + α * δu
         return NONLINEARSOLVE_DEFAULT_NORM(__eval_f(prob, fu_cache, u_cache))
     end
 

From 36c2c838e329cf13d957778ac0797caab938d711 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 15 Jan 2024 02:58:55 -0500
Subject: [PATCH 293/700] Clean up some of the docs

---
 lib/SimpleNonlinearSolve/Project.toml            |  2 +-
 lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl  | 14 ++++----------
 lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl   |  8 +-------
 lib/SimpleNonlinearSolve/src/nlsolve/klement.jl  |  2 +-
 lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl | 12 +++---------
 5 files changed, 10 insertions(+), 28 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 493766ead..ca40b1ed6 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.3.0"
+version = "1.3.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index ad19d765b..15e544795 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -1,22 +1,16 @@
 """
     SimpleBroyden(; linesearch = Val(false), alpha = nothing)
 
-A low-overhead implementation of Broyden. This method is non-allocating on scalar
-and static array problems.
+A low-overhead implementation of Broyden. This method is non-allocating on scalar and static
+array problems.
 
 ### Keyword Arguments
 
   - `linesearch`: If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch`
-    [1] line search else no line search is used. For advanced customization of the line
-    search, use the [`Broyden`](@ref) algorithm in `NonlinearSolve.jl`.
+    [li2000derivative](@cite) line search else no line search is used. For advanced
+    customization of the line search, use `Broyden` from `NonlinearSolve.jl`.
   - `alpha`: Scale the initial jacobian initialization with `alpha`. If it is `nothing`, we
     will compute the scaling using `2 * norm(fu) / max(norm(u), true)`.
-
-### References
-
-[1] Li, Dong-Hui, and Masao Fukushima. "A derivative-free line search and global convergence
-of Broyden-like method for nonlinear equations." Optimization methods and software 13.3
-(2000): 181-201.
 """
 @concrete struct SimpleBroyden{linesearch} <: AbstractSimpleNonlinearSolveAlgorithm
     alpha
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 6931e6101..856e31fd4 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -5,7 +5,7 @@
 
 A low-overhead implementation of the df-sane method for solving large-scale nonlinear
 systems of equations. For in depth information about all the parameters and the algorithm,
-see the paper [1].
+see [la2006spectral](@citet).
 
 ### Keyword Arguments
 
@@ -35,12 +35,6 @@ see the paper [1].
     ``f_1=||F(x_1)||^{nexp}``, `k` is the iteration number, `x` is the current `x`-value and
     `F` the current residual. Should satisfy ``η_k > 0`` and ``∑ₖ ηₖ < ∞``. Defaults to
     ``||F||^2 / k^2``.
-
-### References
-
-[1] W LaCruz, JM Martinez, and M Raydan (2006), Spectral residual mathod without gradient
-information for solving large-scale nonlinear systems of equations, Mathematics of
-Computation, 75, 1429-1448.
 """
 @concrete struct SimpleDFSane{M} <: AbstractSimpleNonlinearSolveAlgorithm
     σ_min
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
index 9351b45f1..680b9cd7c 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
@@ -1,7 +1,7 @@
 """
     SimpleKlement()
 
-A low-overhead implementation of [Klement](https://jatm.com.br/jatm/article/view/373). This
+A low-overhead implementation of `Klement` [klement2014using](@citep). This
 method is non-allocating on scalar and static array problems.
 """
 struct SimpleKlement <: AbstractSimpleNonlinearSolveAlgorithm end
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index eb7b1bbaf..9f8896ed1 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -9,18 +9,12 @@ If the threshold is larger than the problem size, then this method will use `Sim
 
 ### Keyword Arguments:
 
-  - `linesearch`: If `linesearch` is `Val(true)`, then we use the
-    `LiFukushimaLineSearch` [1] line search else no line search is used. For advanced
-    customization of the line search, use the [`LimitedMemoryBroyden`](@ref) algorithm in
+  - `linesearch`: If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch`
+    [li2000derivative](@cite) line search else no line search is used. For advanced
+    customization of the line search, use the `LimitedMemoryBroyden` algorithm in
     `NonlinearSolve.jl`.
   - `alpha`: Scale the initial jacobian initialization with `alpha`. If it is `nothing`, we
     will compute the scaling using `2 * norm(fu) / max(norm(u), true)`.
-
-### References
-
-[1] Li, Dong-Hui, and Masao Fukushima. "A derivative-free line search and global convergence
-of Broyden-like method for nonlinear equations." Optimization methods and software 13.3
-(2000): 181-201.
 """
 @concrete struct SimpleLimitedMemoryBroyden{threshold, linesearch} <:
                  AbstractSimpleNonlinearSolveAlgorithm

From 6a022263490572abfe2deb412bbc4e5d770a98e1 Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Mon, 22 Jan 2024 21:22:00 +0000
Subject: [PATCH 294/700] Bump actions/cache from 3 to 4

Bumps [actions/cache](https://github.com/actions/cache) from 3 to 4.
- [Release notes](https://github.com/actions/cache/releases)
- [Changelog](https://github.com/actions/cache/blob/main/RELEASES.md)
- [Commits](https://github.com/actions/cache/compare/v3...v4)

---
updated-dependencies:
- dependency-name: actions/cache
  dependency-type: direct:production
  update-type: version-update:semver-major
...

Signed-off-by: dependabot[bot] <support@github.com>
---
 lib/SimpleNonlinearSolve/.github/workflows/CI.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
index ba2974f47..8855ab61a 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
@@ -20,7 +20,7 @@ jobs:
       - uses: julia-actions/setup-julia@v1
         with:
           version: ${{ matrix.version }}
-      - uses: actions/cache@v3
+      - uses: actions/cache@v4
         env:
           cache-name: cache-artifacts
         with:

From f86134d316a55095193623764788ffb27047a9c4 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 5 Feb 2024 18:35:51 -0500
Subject: [PATCH 295/700] Patch Adjoint Sensitivity for Simple Nonlinear Solve
 Algorithms

---
 lib/SimpleNonlinearSolve/Project.toml         |  7 ++++--
 .../SimpleNonlinearSolveChainRulesCoreExt.jl  | 21 ++++++++++++++++++
 .../src/SimpleNonlinearSolve.jl               | 22 +++++++++++++------
 lib/SimpleNonlinearSolve/test/Project.toml    |  2 ++
 lib/SimpleNonlinearSolve/test/adjoint.jl      | 14 ++++++++++++
 lib/SimpleNonlinearSolve/test/runtests.jl     |  1 +
 6 files changed, 58 insertions(+), 9 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/adjoint.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index ca40b1ed6..7390adc2c 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.3.1"
+version = "1.3.2"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -19,16 +19,19 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [weakdeps]
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
 [extensions]
+SimpleNonlinearSolveChainRulesCoreExt = "ChainRulesCore"
 SimpleNonlinearSolvePolyesterForwardDiffExt = "PolyesterForwardDiff"
 SimpleNonlinearSolveStaticArraysExt = "StaticArrays"
 
 [compat]
 ADTypes = "0.2.6"
 ArrayInterface = "7"
+ChainRulesCore = "1"
 ConcreteStructs = "0.2"
 DiffEqBase = "6.126"
 FastClosures = "0.3"
@@ -39,6 +42,6 @@ MaybeInplace = "0.1"
 PrecompileTools = "1"
 Reexport = "1"
 SciMLBase = "2.7"
-StaticArraysCore = "1.4"
 StaticArrays = "1"
+StaticArraysCore = "1.4"
 julia = "1.9"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
new file mode 100644
index 000000000..23cd25f33
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
@@ -0,0 +1,21 @@
+module SimpleNonlinearSolveChainRulesCoreExt
+
+using ChainRulesCore, DiffEqBase, SciMLBase, SimpleNonlinearSolve
+
+# The expectation here is that no-one is using this directly inside a GPU kernel. We can
+# eventually lift this requirement using a custom adjoint
+function ChainRulesCore.rrule(::typeof(SimpleNonlinearSolve.__internal_solve_up),
+        prob::NonlinearProblem,
+        sensealg::Union{Nothing, DiffEqBase.AbstractSensitivityAlgorithm}, u0, u0_changed,
+        p, p_changed, alg, args...; kwargs...)
+    out, ∇internal = DiffEqBase._solve_adjoint(prob, sensealg, u0, p,
+        SciMLBase.ChainRulesOriginator(), alg, args...; kwargs...)
+    function ∇__internal_solve_up(Δ)
+        ∂f, ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(Δ)
+        return (∂f, ∂prob, ∂sensealg, ∂u0, NoTangent(), ∂p, NoTangent(), ∂originator,
+            ∂args...)
+    end
+    return out, ∇__internal_solve_up
+end
+
+end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 73eda9977..3f12d8888 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -50,18 +50,26 @@ include("ad.jl")
 ## Default algorithm
 
 # Set the default bracketing method to ITP
-function SciMLBase.solve(prob::IntervalNonlinearProblem; kwargs...)
-    return solve(prob, ITP(); kwargs...)
-end
-
-function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing,
-        args...; kwargs...)
+SciMLBase.solve(prob::IntervalNonlinearProblem; kwargs...) = solve(prob, ITP(); kwargs...)
+function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing, args...; kwargs...)
     return solve(prob, ITP(), args...; kwargs...)
 end
 
 # By Pass the highlevel checks for NonlinearProblem for Simple Algorithms
 function SciMLBase.solve(prob::NonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
-        args...; kwargs...)
+        args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...)
+    if sensealg === nothing && haskey(prob.kwargs, :sensealg)
+        sensealg = prob.kwargs[:sensealg]
+    end
+    new_u0 = u0 !== nothing ? u0 : prob.u0
+    new_p = p !== nothing ? p : prob.p
+    return __internal_solve_up(prob, sensealg, new_u0, u0 === nothing, new_p, p === nothing,
+        alg, args...; kwargs...)
+end
+
+function __internal_solve_up(_prob::NonlinearProblem, sensealg, u0, u0_changed, p,
+        p_changed, alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...)
+    prob = u0_changed || p_changed ? remake(_prob; u0, p) : _prob
     return SciMLBase.__solve(prob, alg, args...; kwargs...)
 end
 
diff --git a/lib/SimpleNonlinearSolve/test/Project.toml b/lib/SimpleNonlinearSolve/test/Project.toml
index cbf18f66c..f690826d0 100644
--- a/lib/SimpleNonlinearSolve/test/Project.toml
+++ b/lib/SimpleNonlinearSolve/test/Project.toml
@@ -9,8 +9,10 @@ Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
+SciMLSensitivity = "1ed8b502-d754-442c-8d5d-10ac956f44a1"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [compat]
 NonlinearProblemLibrary = "0.1.2"
diff --git a/lib/SimpleNonlinearSolve/test/adjoint.jl b/lib/SimpleNonlinearSolve/test/adjoint.jl
new file mode 100644
index 000000000..27c746981
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/adjoint.jl
@@ -0,0 +1,14 @@
+using ForwardDiff, SciMLSensitivity, SimpleNonlinearSolve, Test, Zygote
+
+@testset "Simple Adjoint Test" begin
+    ff(u, p) = u .^ 2 .- p
+
+    function solve_nlprob(p)
+        prob = NonlinearProblem{false}(ff, [1.0, 2.0], p)
+        return sum(abs2, solve(prob, SimpleNewtonRaphson()).u)
+    end
+
+    p = [3.0, 2.0]
+
+    @test only(Zygote.gradient(solve_nlprob, p)) ≈ ForwardDiff.gradient(solve_nlprob, p)
+end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 4de514642..c9ff996dc 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -15,6 +15,7 @@ end
         @time @safetestset "Matrix Resizing Tests" include("matrix_resizing_tests.jl")
         @time @safetestset "Least Squares Tests" include("least_squares.jl")
         @time @safetestset "23 Test Problems" include("23_test_problems.jl")
+        @time @safetestset "Simple Adjoint Tests" include("adjoint.jl")
     end
 
     if GROUP == "CUDA"

From 9bdd4858e2a9299ce7a0d4cc7a3f0141c87e874b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 8 Feb 2024 10:49:08 -0500
Subject: [PATCH 296/700] Run tests in Parallel

---
 .../.github/workflows/CI.yml                  |  4 +-
 .../test/23_test_problems.jl                  | 66 ++++++++--------
 lib/SimpleNonlinearSolve/test/Project.toml    |  1 +
 lib/SimpleNonlinearSolve/test/adjoint.jl      |  4 +-
 lib/SimpleNonlinearSolve/test/basictests.jl   | 75 +++++++------------
 lib/SimpleNonlinearSolve/test/cuda.jl         | 26 +++----
 .../test/cuda/Project.toml                    |  1 +
 lib/SimpleNonlinearSolve/test/forward_ad.jl   |  4 +-
 .../test/least_squares.jl                     |  5 +-
 .../test/matrix_resizing_tests.jl             |  4 +-
 lib/SimpleNonlinearSolve/test/runtests.jl     | 18 ++---
 11 files changed, 96 insertions(+), 112 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
index 8855ab61a..3bc260f64 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
@@ -32,9 +32,11 @@ jobs:
             ${{ runner.os }}-
       - uses: julia-actions/julia-buildpkg@v1
       - uses: julia-actions/julia-runtest@v1
+        with:
+          annotate: true
         env:
           GROUP: ${{ matrix.group }}
-          JULIA_NUM_THREADS: 11
+          JULIA_NUM_THREADS: "auto"
       - uses: julia-actions/julia-processcoverage@v1
       - uses: codecov/codecov-action@v3
         with:
diff --git a/lib/SimpleNonlinearSolve/test/23_test_problems.jl b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
index 18ac5e9bd..73bb304ec 100644
--- a/lib/SimpleNonlinearSolve/test/23_test_problems.jl
+++ b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
@@ -1,4 +1,4 @@
-using SimpleNonlinearSolve, LinearAlgebra, NonlinearProblemLibrary, DiffEqBase, Test
+using SimpleNonlinearSolve, LinearAlgebra, NonlinearProblemLibrary, DiffEqBase, XUnit
 
 problems = NonlinearProblemLibrary.problems
 dicts = NonlinearProblemLibrary.dicts
@@ -37,49 +37,51 @@ function test_on_library(problems, dicts, alg_ops, broken_tests, ϵ = 1e-4;
     end
 end
 
-@testset "SimpleNewtonRaphson 23 Test Problems" begin
-    alg_ops = (SimpleNewtonRaphson(),)
+@testset "23 Test Problems" begin
+    @testcase "SimpleNewtonRaphson 23 Test Problems" begin
+        alg_ops = (SimpleNewtonRaphson(),)
 
-    # dictionary with indices of test problems where method does not converge to small residual
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = []
+        # dictionary with indices of test problems where method does not converge to small residual
+        broken_tests = Dict(alg => Int[] for alg in alg_ops)
+        broken_tests[alg_ops[1]] = []
 
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
+        test_on_library(problems, dicts, alg_ops, broken_tests)
+    end
 
-@testset "SimpleTrustRegion 23 Test Problems" begin
-    alg_ops = (SimpleTrustRegion(),)
+    @testcase "SimpleTrustRegion 23 Test Problems" begin
+        alg_ops = (SimpleTrustRegion(),)
 
-    # dictionary with indices of test problems where method does not converge to small residual
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [3, 6, 15, 16, 21]
+        # dictionary with indices of test problems where method does not converge to small residual
+        broken_tests = Dict(alg => Int[] for alg in alg_ops)
+        broken_tests[alg_ops[1]] = [3, 6, 15, 16, 21]
 
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
+        test_on_library(problems, dicts, alg_ops, broken_tests)
+    end
 
-@testset "SimpleDFSane 23 Test Problems" begin
-    alg_ops = (SimpleDFSane(),)
+    @testcase "SimpleDFSane 23 Test Problems" begin
+        alg_ops = (SimpleDFSane(),)
 
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 2, 3, 4, 5, 6, 11, 21]
+        broken_tests = Dict(alg => Int[] for alg in alg_ops)
+        broken_tests[alg_ops[1]] = [1, 2, 3, 4, 5, 6, 11, 21]
 
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
+        test_on_library(problems, dicts, alg_ops, broken_tests)
+    end
 
-@testset "SimpleBroyden 23 Test Problems" begin
-    alg_ops = (SimpleBroyden(),)
+    @testcase "SimpleBroyden 23 Test Problems" begin
+        alg_ops = (SimpleBroyden(),)
 
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 5, 11]
+        broken_tests = Dict(alg => Int[] for alg in alg_ops)
+        broken_tests[alg_ops[1]] = [1, 5, 11]
 
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
+        test_on_library(problems, dicts, alg_ops, broken_tests)
+    end
 
-@testset "SimpleKlement 23 Test Problems" begin
-    alg_ops = (SimpleKlement(),)
+    @testcase "SimpleKlement 23 Test Problems" begin
+        alg_ops = (SimpleKlement(),)
 
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 11, 12, 22]
+        broken_tests = Dict(alg => Int[] for alg in alg_ops)
+        broken_tests[alg_ops[1]] = [1, 2, 4, 5, 11, 12, 22]
 
-    test_on_library(problems, dicts, alg_ops, broken_tests)
+        test_on_library(problems, dicts, alg_ops, broken_tests)
+    end
 end
diff --git a/lib/SimpleNonlinearSolve/test/Project.toml b/lib/SimpleNonlinearSolve/test/Project.toml
index f690826d0..9077234a6 100644
--- a/lib/SimpleNonlinearSolve/test/Project.toml
+++ b/lib/SimpleNonlinearSolve/test/Project.toml
@@ -12,6 +12,7 @@ SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 SciMLSensitivity = "1ed8b502-d754-442c-8d5d-10ac956f44a1"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+XUnit = "3e3c03f2-1a94-11e9-2981-050a4ca824ab"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [compat]
diff --git a/lib/SimpleNonlinearSolve/test/adjoint.jl b/lib/SimpleNonlinearSolve/test/adjoint.jl
index 27c746981..cf2ef38d7 100644
--- a/lib/SimpleNonlinearSolve/test/adjoint.jl
+++ b/lib/SimpleNonlinearSolve/test/adjoint.jl
@@ -1,6 +1,6 @@
-using ForwardDiff, SciMLSensitivity, SimpleNonlinearSolve, Test, Zygote
+using ForwardDiff, SciMLSensitivity, SimpleNonlinearSolve, XUnit, Zygote
 
-@testset "Simple Adjoint Test" begin
+@testcase "Simple Adjoint Test" begin
     ff(u, p) = u .^ 2 .- p
 
     function solve_nlprob(p)
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index 5938197c7..c46230476 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -1,5 +1,5 @@
 using AllocCheck, LinearSolve, SimpleNonlinearSolve, StaticArrays, Random,
-    LinearAlgebra, Test, ForwardDiff, DiffEqBase
+    LinearAlgebra, XUnit, ForwardDiff, DiffEqBase
 import PolyesterForwardDiff
 
 _nameof(x) = applicable(nameof, x) ? nameof(x) : _nameof(typeof(x))
@@ -25,33 +25,29 @@ const TERMINATION_CONDITIONS = [
     AbsSafeTerminationMode(), RelSafeBestTerminationMode(), AbsSafeBestTerminationMode(),
 ]
 
-# --- SimpleNewtonRaphson tests ---
-
-@testset "$(alg)" for alg in (SimpleNewtonRaphson, SimpleTrustRegion)
-    # Eval else the alg is type unstable
-    @eval begin
-        function benchmark_nlsolve_oop(f, u0, p = 2.0; autodiff = nothing)
-            prob = NonlinearProblem{false}(f, u0, p)
-            return solve(prob, $(alg)(; autodiff), abstol = 1e-9)
-        end
+function benchmark_nlsolve_oop(f::F, u0, p = 2.0; solver) where {F}
+    prob = NonlinearProblem{false}(f, u0, p)
+    return solve(prob, solver; abstol = 1e-9)
+end
+function benchmark_nlsolve_iip(f!::F, u0, p = 2.0; solver) where {F}
+    prob = NonlinearProblem{true}(f!, u0, p)
+    return solve(prob, solver; abstol = 1e-9)
+end
 
-        function benchmark_nlsolve_iip(f, u0, p = 2.0; autodiff = nothing)
-            prob = NonlinearProblem{true}(f, u0, p)
-            return solve(prob, $(alg)(; autodiff), abstol = 1e-9)
-        end
-    end
+# --- SimpleNewtonRaphson tests ---
 
+@testcase "$(alg)" for alg in (SimpleNewtonRaphson, SimpleTrustRegion)
     @testset "AutoDiff: $(_nameof(autodiff))" for autodiff in (AutoFiniteDiff(),
         AutoForwardDiff(), AutoPolyesterForwardDiff())
         @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
             u0 isa SVector && autodiff isa AutoPolyesterForwardDiff && continue
-            sol = benchmark_nlsolve_oop(quadratic_f, u0; autodiff)
+            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = alg(; autodiff))
             @test SciMLBase.successful_retcode(sol)
             @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
         end
 
         @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
-            sol = benchmark_nlsolve_iip(quadratic_f!, u0; autodiff)
+            sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver = alg(; autodiff))
             @test SciMLBase.successful_retcode(sol)
             @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
         end
@@ -67,16 +63,11 @@ end
 
 # --- SimpleHalley tests ---
 
-@testset "SimpleHalley" begin
-    function benchmark_nlsolve_oop(f, u0, p = 2.0; autodiff = nothing)
-        prob = NonlinearProblem{false}(f, u0, p)
-        return solve(prob, SimpleHalley(; autodiff), abstol = 1e-9)
-    end
-
+@testcase "SimpleHalley" begin
     @testset "AutoDiff: $(_nameof(autodiff))" for autodiff in (AutoFiniteDiff(),
         AutoForwardDiff())
         @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-            sol = benchmark_nlsolve_oop(quadratic_f, u0; autodiff)
+            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = SimpleHalley(; autodiff))
             @test SciMLBase.successful_retcode(sol)
             @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
         end
@@ -92,27 +83,17 @@ end
 
 # --- SimpleBroyden / SimpleKlement / SimpleLimitedMemoryBroyden tests ---
 
-@testset "$(_nameof(alg))" for alg in [SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
+@testcase "$(_nameof(alg))" for alg in [SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
     SimpleLimitedMemoryBroyden(), SimpleBroyden(; linesearch = Val(true)),
     SimpleLimitedMemoryBroyden(; linesearch = Val(true))]
-    function benchmark_nlsolve_oop(f, u0, p = 2.0)
-        prob = NonlinearProblem{false}(f, u0, p)
-        return solve(prob, alg, abstol = 1e-9)
-    end
-
-    function benchmark_nlsolve_iip(f, u0, p = 2.0)
-        prob = NonlinearProblem{true}(f, u0, p)
-        return solve(prob, alg, abstol = 1e-9)
-    end
-
     @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-        sol = benchmark_nlsolve_oop(quadratic_f, u0)
+        sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = alg)
         @test SciMLBase.successful_retcode(sol)
         @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
     end
 
     @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
-        sol = benchmark_nlsolve_iip(quadratic_f!, u0)
+        sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver = alg)
         @test SciMLBase.successful_retcode(sol)
         @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
     end
@@ -126,16 +107,11 @@ end
 end
 
 @testset "Newton Fails" begin
-    function benchmark_nlsolve_oop(f, u0, p, alg)
-        prob = NonlinearProblem{false}(f, u0, p)
-        return solve(prob, alg; abstol = 1e-9)
-    end
-
     u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
     p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 
-    for alg in (SimpleDFSane(), SimpleTrustRegion(), SimpleHalley())
-        sol = benchmark_nlsolve_oop(newton_fails, u0, p, alg)
+    @testcase "$(alg)" for alg in (SimpleDFSane(), SimpleTrustRegion(), SimpleHalley())
+        sol = benchmark_nlsolve_oop(newton_fails, u0, p; solver = alg)
         @test SciMLBase.successful_retcode(sol)
         @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
     end
@@ -144,7 +120,7 @@ end
 # --- Allocation Checks ---
 
 ## SimpleDFSane needs to allocate a history vector
-@testset "Allocation Checks: $(_nameof(alg))" for alg in (SimpleNewtonRaphson(),
+@testcase "Allocation Checks: $(_nameof(alg))" for alg in (SimpleNewtonRaphson(),
     SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
     SimpleTrustRegion(), SimpleDFSane(), SimpleBroyden(; linesearch = Val(true)),
     SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
@@ -173,7 +149,7 @@ end
 
 # --- Interval Nonlinear Problems ---
 
-@testset "Interval Nonlinear Problem: $(alg)" for alg in (Bisection(), Falsi(), Ridder(),
+@testcase "Interval Nonlinear Problem: $(alg)" for alg in (Bisection(), Falsi(), Ridder(),
     Brent(), ITP(), Alefeld())
     tspan = (1.0, 20.0)
 
@@ -215,7 +191,8 @@ end
     end
 end
 
-@testset "Tolerance Tests Interval Methods: $(alg)" for alg in (Bisection(), Falsi(), ITP())
+@testcase "Tolerance Tests Interval Methods: $(alg)" for alg in (Bisection(), Falsi(),
+    ITP())
     tspan = (1.0, 20.0)
     probB = IntervalNonlinearProblem(quadratic_f, tspan, 2.0)
     tols = [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6, 1e-7]
@@ -228,7 +205,7 @@ end
     end
 end
 
-@testset "Tolerance Tests Interval Methods: $(alg)" for alg in (Ridder(), Brent())
+@testcase "Tolerance Tests Interval Methods: $(alg)" for alg in (Ridder(), Brent())
     tspan = (1.0, 20.0)
     probB = IntervalNonlinearProblem(quadratic_f, tspan, 2.0)
     tols = [0.1] # Ridder and Brent converge rapidly so as we lower tolerance below 0.01, it converges with max precision to the solution
@@ -241,7 +218,7 @@ end
     end
 end
 
-@testset "Flipped Signs and Reversed Tspan: $(alg)" for alg in (Alefeld(), Bisection(),
+@testcase "Flipped Signs and Reversed Tspan: $(alg)" for alg in (Alefeld(), Bisection(),
     Falsi(), Brent(), ITP(), Ridder())
     f1(u, p) = u * u - p
     f2(u, p) = p - u * u
diff --git a/lib/SimpleNonlinearSolve/test/cuda.jl b/lib/SimpleNonlinearSolve/test/cuda.jl
index fddf751de..7708ae5c4 100644
--- a/lib/SimpleNonlinearSolve/test/cuda.jl
+++ b/lib/SimpleNonlinearSolve/test/cuda.jl
@@ -1,4 +1,4 @@
-using SimpleNonlinearSolve, StaticArrays, CUDA, Test
+using SimpleNonlinearSolve, StaticArrays, CUDA, XUnit
 
 CUDA.allowscalar(false)
 
@@ -6,12 +6,10 @@ f(u, p) = u .* u .- 2
 f!(du, u, p) = du .= u .* u .- 2
 
 @testset "Solving on GPUs" begin
-    for alg in (SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(), SimpleBroyden(),
-        SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley(),
-        SimpleBroyden(; linesearch = Val(true)),
+    @testcase "$(alg)" for alg in (SimpleNewtonRaphson(), SimpleDFSane(),
+        SimpleTrustRegion(), SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(),
+        SimpleHalley(), SimpleBroyden(; linesearch = Val(true)),
         SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
-        @info "Testing $alg on CUDA"
-
         # Static Arrays
         u0 = @SVector[1.0f0, 1.0f0]
         probN = NonlinearProblem{false}(f, u0)
@@ -27,12 +25,13 @@ f!(du, u, p) = du .= u .* u .- 2
         @test maximum(abs, sol.resid) ≤ 1.0f-6
 
         # Regular Arrays Inplace
-        alg isa SimpleHalley && continue
-        u0 = [1.0, 1.0]
-        probN = NonlinearProblem{true}(f!, u0)
-        sol = solve(probN, alg; abstol = 1.0f-6)
-        @test SciMLBase.successful_retcode(sol)
-        @test maximum(abs, sol.resid) ≤ 1.0f-6
+        if !(alg isa SimpleHalley)
+            u0 = [1.0, 1.0]
+            probN = NonlinearProblem{true}(f!, u0)
+            sol = solve(probN, alg; abstol = 1.0f-6)
+            @test SciMLBase.successful_retcode(sol)
+            @test maximum(abs, sol.resid) ≤ 1.0f-6
+        end
     end
 end
 
@@ -44,7 +43,8 @@ end
 @testset "CUDA Kernel Launch Test" begin
     prob = NonlinearProblem{false}(f, @SVector[1.0f0, 1.0f0])
 
-    for alg in (SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(), SimpleBroyden(),
+    @testcase "$(alg)" for alg in (SimpleNewtonRaphson(), SimpleDFSane(),
+        SimpleTrustRegion(), SimpleBroyden(),
         SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley(),
         SimpleBroyden(; linesearch = Val(true)),
         SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
diff --git a/lib/SimpleNonlinearSolve/test/cuda/Project.toml b/lib/SimpleNonlinearSolve/test/cuda/Project.toml
index 36c63059b..4fdee40a7 100644
--- a/lib/SimpleNonlinearSolve/test/cuda/Project.toml
+++ b/lib/SimpleNonlinearSolve/test/cuda/Project.toml
@@ -3,3 +3,4 @@ CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+XUnit = "3e3c03f2-1a94-11e9-2981-050a4ca824ab"
diff --git a/lib/SimpleNonlinearSolve/test/forward_ad.jl b/lib/SimpleNonlinearSolve/test/forward_ad.jl
index f545ccb0c..78059c2f0 100644
--- a/lib/SimpleNonlinearSolve/test/forward_ad.jl
+++ b/lib/SimpleNonlinearSolve/test/forward_ad.jl
@@ -1,4 +1,4 @@
-using ForwardDiff, SimpleNonlinearSolve, StaticArrays, Test, LinearAlgebra
+using ForwardDiff, SimpleNonlinearSolve, StaticArrays, XUnit, LinearAlgebra
 import SimpleNonlinearSolve: AbstractSimpleNonlinearSolveAlgorithm
 
 test_f!(du, u, p) = (@. du = u^2 - p)
@@ -35,7 +35,7 @@ __compatible(::AbstractSimpleNonlinearSolveAlgorithm, ::Val{:iip}) = true
 __compatible(::AbstractSimpleNonlinearSolveAlgorithm, ::Val{:oop}) = true
 __compatible(::SimpleHalley, ::Val{:iip}) = false
 
-@testset "ForwardDiff.jl Integration: $(alg)" for alg in (SimpleNewtonRaphson(),
+@testcase "ForwardDiff.jl Integration: $(alg)" for alg in (SimpleNewtonRaphson(),
     SimpleTrustRegion(), SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleDFSane())
     us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
 
diff --git a/lib/SimpleNonlinearSolve/test/least_squares.jl b/lib/SimpleNonlinearSolve/test/least_squares.jl
index bc801421f..6c48a9807 100644
--- a/lib/SimpleNonlinearSolve/test/least_squares.jl
+++ b/lib/SimpleNonlinearSolve/test/least_squares.jl
@@ -1,4 +1,4 @@
-using SimpleNonlinearSolve, LinearAlgebra, Test
+using SimpleNonlinearSolve, LinearAlgebra, XUnit
 
 true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
 
@@ -14,7 +14,8 @@ end
 θ_init = θ_true .+ 0.1
 prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
 
-for solver in [SimpleNewtonRaphson(AutoForwardDiff()), SimpleGaussNewton(AutoForwardDiff()),
+@testcase "Solver: $(solver)" for solver in [SimpleNewtonRaphson(AutoForwardDiff()),
+    SimpleGaussNewton(AutoForwardDiff()),
     SimpleNewtonRaphson(AutoFiniteDiff()), SimpleGaussNewton(AutoFiniteDiff())]
     sol = solve(prob_oop, solver)
     @test norm(sol.resid) < 1e-12
diff --git a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
index 455aac91a..63a0a1735 100644
--- a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
@@ -1,4 +1,4 @@
-using SimpleNonlinearSolve
+using SimpleNonlinearSolve, XUnit
 
 ff(u, p) = u .* u .- p
 u0 = ones(2, 3)
@@ -6,7 +6,7 @@ p = 2.0
 vecprob = NonlinearProblem(ff, vec(u0), p)
 prob = NonlinearProblem(ff, u0, p)
 
-@testset "$(alg)" for alg in (SimpleKlement(), SimpleBroyden(), SimpleNewtonRaphson(),
+@testcase "$(alg)" for alg in (SimpleKlement(), SimpleBroyden(), SimpleNewtonRaphson(),
     SimpleDFSane(), SimpleLimitedMemoryBroyden(; threshold = Val(2)), SimpleTrustRegion())
     @test vec(solve(prob, alg).u) ≈ solve(vecprob, alg).u
 end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index c9ff996dc..5d9216ae3 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -1,4 +1,4 @@
-using Pkg, SafeTestsets, Test
+using Pkg, SafeTestsets, XUnit
 
 const GROUP = get(ENV, "GROUP", "All")
 
@@ -8,18 +8,18 @@ function activate_env(env)
     Pkg.instantiate()
 end
 
-@time @testset "SimpleNonlinearSolve.jl" begin
+@testset runner=ParallelTestRunner() "SimpleNonlinearSolve.jl" begin
     if GROUP == "All" || GROUP == "Core"
-        @time @safetestset "Basic Tests" include("basictests.jl")
-        @time @safetestset "Forward AD" include("forward_ad.jl")
-        @time @safetestset "Matrix Resizing Tests" include("matrix_resizing_tests.jl")
-        @time @safetestset "Least Squares Tests" include("least_squares.jl")
-        @time @safetestset "23 Test Problems" include("23_test_problems.jl")
-        @time @safetestset "Simple Adjoint Tests" include("adjoint.jl")
+        @safetestset "Basic Tests" include("basictests.jl")
+        @safetestset "Forward AD" include("forward_ad.jl")
+        @safetestset "Matrix Resizing Tests" include("matrix_resizing_tests.jl")
+        @safetestset "Least Squares Tests" include("least_squares.jl")
+        @safetestset "23 Test Problems" include("23_test_problems.jl")
+        @safetestset "Simple Adjoint Tests" include("adjoint.jl")
     end
 
     if GROUP == "CUDA"
         activate_env("cuda")
-        @time @safetestset "CUDA Tests" include("cuda.jl")
+        @safetestset "CUDA Tests" include("cuda.jl")
     end
 end

From 6ac95bda6a2838ad054531c548554df417243451 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 8 Feb 2024 13:43:29 -0500
Subject: [PATCH 297/700] Add NLsolve update rule to SimpleTrustRegion

---
 lib/SimpleNonlinearSolve/Project.toml         |  2 +-
 .../src/nlsolve/trustRegion.jl                | 68 ++++++++++++++-----
 .../test/23_test_problems.jl                  |  6 +-
 lib/SimpleNonlinearSolve/test/basictests.jl   | 10 ++-
 lib/SimpleNonlinearSolve/test/cuda.jl         |  7 +-
 lib/SimpleNonlinearSolve/test/forward_ad.jl   |  3 +-
 .../test/matrix_resizing_tests.jl             |  3 +-
 7 files changed, 72 insertions(+), 27 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 7390adc2c..b0cbd3739 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.3.2"
+version = "1.4.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index e8a90cdbd..03c4692e7 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -1,8 +1,9 @@
 """
-    SimpleTrustRegion(; autodiff = AutoForwardDiff(), max_trust_radius::Real = 0.0,
-        initial_trust_radius::Real = 0.0, step_threshold::Real = 0.1,
-        shrink_threshold::Real = 0.25, expand_threshold::Real = 0.75,
-        shrink_factor::Real = 0.25, expand_factor::Real = 2.0, max_shrink_times::Int = 32)
+    SimpleTrustRegion(; autodiff = AutoForwardDiff(), max_trust_radius = 0.0,
+        initial_trust_radius = 0.0, step_threshold = nothing,
+        shrink_threshold = nothing, expand_threshold = nothing,
+        shrink_factor = 0.25, expand_factor = 2.0, max_shrink_times::Int = 32,
+        nlsolve_update_rule = Val(false))
 
 A low-overhead implementation of a trust-region solver. This method is non-allocating on
 scalar and static array problems.
@@ -36,17 +37,22 @@ scalar and static array problems.
     `expand_threshold < r` (with `r` defined in `shrink_threshold`). Defaults to `2.0`.
   - `max_shrink_times`: the maximum number of times to shrink the trust region radius in a
     row, `max_shrink_times` is exceeded, the algorithm returns. Defaults to `32`.
+  - `nlsolve_update_rule`: If set to `Val(true)`, updates the trust region radius using the
+    update rule from NLSolve.jl. Defaults to `Val(false)`. If set to `Val(true)`, few of the
+    radius update parameters -- `step_threshold = 0.05`, `expand_threshold = 0.9`, and
+    `shrink_factor = 0.5` -- have different defaults.
 """
 @kwdef @concrete struct SimpleTrustRegion <: AbstractNewtonAlgorithm
     autodiff = nothing
     max_trust_radius = 0.0
     initial_trust_radius = 0.0
     step_threshold = 0.0001
-    shrink_threshold = 0.25
-    expand_threshold = 0.75
-    shrink_factor = 0.25
+    shrink_threshold = nothing
+    expand_threshold = nothing
+    shrink_factor = nothing
     expand_factor = 2.0
     max_shrink_times::Int = 32
+    nlsolve_update_rule = Val(false)
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args...;
@@ -57,14 +63,27 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
     Δₘₐₓ = T(alg.max_trust_radius)
     Δ = T(alg.initial_trust_radius)
     η₁ = T(alg.step_threshold)
-    η₂ = T(alg.shrink_threshold)
-    η₃ = T(alg.expand_threshold)
-    t₁ = T(alg.shrink_factor)
+    if alg.shrink_threshold === nothing
+        η₂ = _unwrap_val(alg.nlsolve_update_rule) ? T(0.05) : T(0.25)
+    else
+        η₂ = T(alg.shrink_threshold)
+    end
+    if alg.expand_threshold === nothing
+        η₃ = _unwrap_val(alg.nlsolve_update_rule) ? T(0.9) : T(0.75)
+    else
+        η₃ = T(alg.expand_threshold)
+    end
+    if alg.shrink_factor === nothing
+        t₁ = _unwrap_val(alg.nlsolve_update_rule) ? T(0.5) : T(0.25)
+    else
+        t₁ = T(alg.shrink_factor)
+    end
     t₂ = T(alg.expand_factor)
     max_shrink_times = alg.max_shrink_times
     autodiff = __get_concrete_autodiff(prob, alg.autodiff)
 
     fx = _get_fx(prob, x)
+    norm_fx = norm(fx)
     @bb xo = copy(x)
     J, jac_cache = jacobian_cache(autodiff, prob.f, fx, x, prob.p)
     fx, ∇f = value_and_jacobian(autodiff, prob.f, fx, x, prob.p, jac_cache; J)
@@ -73,10 +92,17 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
         termination_condition)
 
     # Set default trust region radius if not specified by user.
-    Δₘₐₓ == 0 && (Δₘₐₓ = max(norm(fx), maximum(x) - minimum(x)))
-    Δ == 0 && (Δ = Δₘₐₓ / 11)
+    Δₘₐₓ == 0 && (Δₘₐₓ = max(norm_fx, maximum(x) - minimum(x)))
+    if Δ == 0
+        if _unwrap_val(alg.nlsolve_update_rule)
+            norm_x = norm(x)
+            Δ = T(ifelse(norm_x > 0, norm_x, 1))
+        else
+            Δ = T(Δₘₐₓ / 11)
+        end
+    end
 
-    fₖ = 0.5 * norm(fx)^2
+    fₖ = 0.5 * norm_fx^2
     H = ∇f' * ∇f
     g = _restructure(x, ∇f' * _vec(fx))
     shrink_counter = 0
@@ -87,7 +113,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
     @bb Hδ = copy(x)
     dogleg_cache = (; δsd, δN_δsd, δN)
 
-    for k in 1:maxiters
+    for _ in 1:maxiters
         # Solve the trust region subproblem.
         δ = dogleg_method!!(dogleg_cache, ∇f, fx, g, Δ)
         @bb @. x = xo + δ
@@ -107,7 +133,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
             Δ = t₁ * Δ
             shrink_counter += 1
             shrink_counter > max_shrink_times && return build_solution(prob, alg, x, fx;
-                retcode = ReturnCode.ConvergenceFailure)
+                retcode = ReturnCode.ShrinkThresholdExceeded)
         end
 
         if r ≥ η₁
@@ -121,12 +147,22 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
             fx, ∇f = value_and_jacobian(autodiff, prob.f, fx, x, prob.p, jac_cache; J)
 
             # Update the trust region radius.
-            (r > η₃) && (norm(δ) ≈ Δ) && (Δ = min(t₂ * Δ, Δₘₐₓ))
+            if !_unwrap_val(alg.nlsolve_update_rule) && r > η₃
+                Δ = min(t₂ * Δ, Δₘₐₓ)
+            end
             fₖ = fₖ₊₁
 
             @bb H = transpose(∇f) × ∇f
             @bb g = transpose(∇f) × vec(fx)
         end
+
+        if _unwrap_val(alg.nlsolve_update_rule)
+            if r > η₃
+                Δ = t₂ * norm(δ)
+            elseif r > 0.5
+                Δ = max(Δ, t₂ * norm(δ))
+            end
+        end
     end
 
     return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
diff --git a/lib/SimpleNonlinearSolve/test/23_test_problems.jl b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
index 73bb304ec..c04998281 100644
--- a/lib/SimpleNonlinearSolve/test/23_test_problems.jl
+++ b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
@@ -49,11 +49,13 @@ end
     end
 
     @testcase "SimpleTrustRegion 23 Test Problems" begin
-        alg_ops = (SimpleTrustRegion(),)
+        alg_ops = (SimpleTrustRegion(),
+            SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
 
         # dictionary with indices of test problems where method does not converge to small residual
         broken_tests = Dict(alg => Int[] for alg in alg_ops)
-        broken_tests[alg_ops[1]] = [3, 6, 15, 16, 21]
+        broken_tests[alg_ops[1]] = [3, 15, 16, 21]
+        broken_tests[alg_ops[2]] = [15, 16]
 
         test_on_library(problems, dicts, alg_ops, broken_tests)
     end
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
index c46230476..3f59dfb45 100644
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ b/lib/SimpleNonlinearSolve/test/basictests.jl
@@ -36,7 +36,9 @@ end
 
 # --- SimpleNewtonRaphson tests ---
 
-@testcase "$(alg)" for alg in (SimpleNewtonRaphson, SimpleTrustRegion)
+@testcase "$(alg)" for alg in (SimpleNewtonRaphson, SimpleTrustRegion,
+    (args...; kwargs...) -> SimpleTrustRegion(args...; nlsolve_update_rule = Val(true),
+        kwargs...))
     @testset "AutoDiff: $(_nameof(autodiff))" for autodiff in (AutoFiniteDiff(),
         AutoForwardDiff(), AutoPolyesterForwardDiff())
         @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
@@ -110,7 +112,8 @@ end
     u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
     p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 
-    @testcase "$(alg)" for alg in (SimpleDFSane(), SimpleTrustRegion(), SimpleHalley())
+    @testcase "$(alg)" for alg in (SimpleDFSane(), SimpleTrustRegion(), SimpleHalley(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
         sol = benchmark_nlsolve_oop(newton_fails, u0, p; solver = alg)
         @test SciMLBase.successful_retcode(sol)
         @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
@@ -122,7 +125,8 @@ end
 ## SimpleDFSane needs to allocate a history vector
 @testcase "Allocation Checks: $(_nameof(alg))" for alg in (SimpleNewtonRaphson(),
     SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
-    SimpleTrustRegion(), SimpleDFSane(), SimpleBroyden(; linesearch = Val(true)),
+    SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+    SimpleDFSane(), SimpleBroyden(; linesearch = Val(true)),
     SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
     @check_allocs nlsolve(prob, alg) = SciMLBase.solve(prob, alg; abstol = 1e-9)
 
diff --git a/lib/SimpleNonlinearSolve/test/cuda.jl b/lib/SimpleNonlinearSolve/test/cuda.jl
index 7708ae5c4..f1f372f6a 100644
--- a/lib/SimpleNonlinearSolve/test/cuda.jl
+++ b/lib/SimpleNonlinearSolve/test/cuda.jl
@@ -7,7 +7,8 @@ f!(du, u, p) = du .= u .* u .- 2
 
 @testset "Solving on GPUs" begin
     @testcase "$(alg)" for alg in (SimpleNewtonRaphson(), SimpleDFSane(),
-        SimpleTrustRegion(), SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(),
+        SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+        SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(),
         SimpleHalley(), SimpleBroyden(; linesearch = Val(true)),
         SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
         # Static Arrays
@@ -44,8 +45,8 @@ end
     prob = NonlinearProblem{false}(f, @SVector[1.0f0, 1.0f0])
 
     @testcase "$(alg)" for alg in (SimpleNewtonRaphson(), SimpleDFSane(),
-        SimpleTrustRegion(), SimpleBroyden(),
-        SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley(),
+        SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+        SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley(),
         SimpleBroyden(; linesearch = Val(true)),
         SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
         @test begin
diff --git a/lib/SimpleNonlinearSolve/test/forward_ad.jl b/lib/SimpleNonlinearSolve/test/forward_ad.jl
index 78059c2f0..99b32c3cb 100644
--- a/lib/SimpleNonlinearSolve/test/forward_ad.jl
+++ b/lib/SimpleNonlinearSolve/test/forward_ad.jl
@@ -36,7 +36,8 @@ __compatible(::AbstractSimpleNonlinearSolveAlgorithm, ::Val{:oop}) = true
 __compatible(::SimpleHalley, ::Val{:iip}) = false
 
 @testcase "ForwardDiff.jl Integration: $(alg)" for alg in (SimpleNewtonRaphson(),
-    SimpleTrustRegion(), SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleDFSane())
+    SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+    SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleDFSane())
     us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
 
     @testset "Scalar AD" begin
diff --git a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
index 63a0a1735..778ec5185 100644
--- a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
@@ -7,6 +7,7 @@ vecprob = NonlinearProblem(ff, vec(u0), p)
 prob = NonlinearProblem(ff, u0, p)
 
 @testcase "$(alg)" for alg in (SimpleKlement(), SimpleBroyden(), SimpleNewtonRaphson(),
-    SimpleDFSane(), SimpleLimitedMemoryBroyden(; threshold = Val(2)), SimpleTrustRegion())
+    SimpleDFSane(), SimpleLimitedMemoryBroyden(; threshold = Val(2)), SimpleTrustRegion(),
+    SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
     @test vec(solve(prob, alg).u) ≈ solve(vecprob, alg).u
 end

From 1d8161837a6313067bf9e1baf79128f9a4b245a5 Mon Sep 17 00:00:00 2001
From: Avik Pal <avik.pal.2017@gmail.com>
Date: Thu, 8 Feb 2024 14:16:47 -0500
Subject: [PATCH 298/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 6dc0389c5..2d6167a0d 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -37,7 +37,7 @@ DiffEqBase = "6.144"
 FastClosures = "0.3"
 FiniteDiff = "2.21"
 ForwardDiff = "0.10.36"
-LinearAlgebra = "1.9"
+LinearAlgebra = "1.10"
 MaybeInplace = "0.1.1"
 PrecompileTools = "1.2"
 Reexport = "1.2"

From 03bab8ea1ef4e738fc379825ba8914fcde81868e Mon Sep 17 00:00:00 2001
From: Avik Pal <avik.pal.2017@gmail.com>
Date: Thu, 8 Feb 2024 14:19:02 -0500
Subject: [PATCH 299/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 2d6167a0d..f6d3ba7d5 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -42,6 +42,6 @@ MaybeInplace = "0.1.1"
 PrecompileTools = "1.2"
 Reexport = "1.2"
 SciMLBase = "2.23"
-StaticArrays = "1"
+StaticArrays = "1.8"
 StaticArraysCore = "1.4.2"
 julia = "1.10"

From 28a3c9b1d25187f66fb357019d8a87dbcaa7183d Mon Sep 17 00:00:00 2001
From: Avik Pal <avik.pal.2017@gmail.com>
Date: Thu, 8 Feb 2024 14:20:45 -0500
Subject: [PATCH 300/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index f6d3ba7d5..b2fb3baac 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -31,7 +31,7 @@ SimpleNonlinearSolveStaticArraysExt = "StaticArrays"
 [compat]
 ADTypes = "0.2.6"
 ArrayInterface = "7.7"
-ChainRulesCore = "1"
+ChainRulesCore = "1.18"
 ConcreteStructs = "0.2.2"
 DiffEqBase = "6.144"
 FastClosures = "0.3"

From fe60a39808615c41fad422398971eff88c9627d5 Mon Sep 17 00:00:00 2001
From: Avik Pal <avik.pal.2017@gmail.com>
Date: Thu, 8 Feb 2024 14:44:31 -0500
Subject: [PATCH 301/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index b2fb3baac..fc4f75e71 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -33,7 +33,7 @@ ADTypes = "0.2.6"
 ArrayInterface = "7.7"
 ChainRulesCore = "1.18"
 ConcreteStructs = "0.2.2"
-DiffEqBase = "6.144"
+DiffEqBase = "6.146"
 FastClosures = "0.3"
 FiniteDiff = "2.21"
 ForwardDiff = "0.10.36"

From cd4899dab84e736f3d5d92a763e4395cd524a2dd Mon Sep 17 00:00:00 2001
From: Avik Pal <avik.pal.2017@gmail.com>
Date: Thu, 8 Feb 2024 16:13:56 -0500
Subject: [PATCH 302/700] Apply suggestions from code review

---
 lib/SimpleNonlinearSolve/Project.toml | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index fc4f75e71..f5445b9d7 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -31,17 +31,17 @@ SimpleNonlinearSolveStaticArraysExt = "StaticArrays"
 [compat]
 ADTypes = "0.2.6"
 ArrayInterface = "7.7"
-ChainRulesCore = "1.18"
+ChainRulesCore = "1.21"
 ConcreteStructs = "0.2.2"
 DiffEqBase = "6.146"
 FastClosures = "0.3"
-FiniteDiff = "2.21"
+FiniteDiff = "2.22"
 ForwardDiff = "0.10.36"
 LinearAlgebra = "1.10"
 MaybeInplace = "0.1.1"
 PrecompileTools = "1.2"
 Reexport = "1.2"
 SciMLBase = "2.23"
-StaticArrays = "1.8"
+StaticArrays = "1.9"
 StaticArraysCore = "1.4.2"
 julia = "1.10"

From 07ec5739af11de447a5651c6636304986e12661d Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 9 Feb 2024 09:37:28 -0500
Subject: [PATCH 303/700] Use ReTestItems instead of XUnit

---
 .../.buildkite/pipeline.yml                   |  11 +-
 .../.github/workflows/CI.yml                  |   4 +-
 .../.github/workflows/Downstream.yml          |   4 +
 .../.github/workflows/FormatPR.yml            |   2 +-
 lib/SimpleNonlinearSolve/Project.toml         |  25 +-
 .../test/23_test_problems.jl                  |  89 ------
 lib/SimpleNonlinearSolve/test/Project.toml    |  19 --
 lib/SimpleNonlinearSolve/test/basictests.jl   | 268 -----------------
 .../test/core/23_test_problems_tests.jl       |  89 ++++++
 .../{adjoint.jl => core/adjoint_tests.jl}     |   4 +-
 .../test/core/forward_ad_tests.jl             |  90 ++++++
 .../test/core/least_squares_tests.jl          |  24 ++
 .../test/core/matrix_resizing_tests.jl        |  14 +
 .../test/core/rootfind_tests.jl               | 279 ++++++++++++++++++
 .../test/cuda/Project.toml                    |   6 -
 lib/SimpleNonlinearSolve/test/forward_ad.jl   |  83 ------
 .../test/{cuda.jl => gpu/cuda_tests.jl}       |  31 +-
 .../test/least_squares.jl                     |  22 --
 .../test/matrix_resizing_tests.jl             |  13 -
 lib/SimpleNonlinearSolve/test/runtests.jl     |  26 +-
 20 files changed, 564 insertions(+), 539 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/test/23_test_problems.jl
 delete mode 100644 lib/SimpleNonlinearSolve/test/Project.toml
 delete mode 100644 lib/SimpleNonlinearSolve/test/basictests.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
 rename lib/SimpleNonlinearSolve/test/{adjoint.jl => core/adjoint_tests.jl} (73%)
 create mode 100644 lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
 delete mode 100644 lib/SimpleNonlinearSolve/test/cuda/Project.toml
 delete mode 100644 lib/SimpleNonlinearSolve/test/forward_ad.jl
 rename lib/SimpleNonlinearSolve/test/{cuda.jl => gpu/cuda_tests.jl} (75%)
 delete mode 100644 lib/SimpleNonlinearSolve/test/least_squares.jl
 delete mode 100644 lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl

diff --git a/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml b/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
index e84559d00..ef04f99a6 100644
--- a/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
+++ b/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
@@ -4,6 +4,12 @@ steps:
       - JuliaCI/julia#v1:
           version: "1"
       - JuliaCI/julia-test#v1:
+          coverage: true
+      - JuliaCI/julia-coverage#v1:
+          codecov: true
+          dirs:
+            - src
+            - ext
     agents:
       queue: "juliagpu"
       cuda: "*"
@@ -13,4 +19,7 @@ steps:
 
 env:
   GROUP: CUDA
-  JULIA_PKG_SERVER: ""
\ No newline at end of file
+  JULIA_PKG_SERVER: ""
+  RETESTITEMS_NWORKERS: 4
+  RETESTITEMS_NWORKER_THREADS: 2
+  SECRET_CODECOV_TOKEN: "HsC3X/h3CrsRhMR199BUbw9xmASfTTEtdT2JMJlbkW6nsMtZXDIWxKzBNOpn0123zn3K+VE30i7+aLpcqZjlux0BQDMVLx5O5KudjrJmBE2G8KMMv1pra+UHEOFdFP3TzjHXGcHzpUrjpG8if8cHbsWdyQCV0Hdx2qAPnhX5haGPyMuIlRfoaWQfdxJPl5fDLXs1xe0LnMcYMx8uUsvvJZ/hhFtMYWJU0WFtqnAkCR8h/pQd6yZOaGP2SXJkOR8+1xbx+M8m6agH9idp2BjDPpXMOo27V3O2Gkoy3R4b5ouLdqOMaZSIOemoYCv6oh+EkbKaFvZydvm0xCW5YBFPPw==;U2FsdGVkX19FT0yFV6EMY/NVSQslXE6byckN0qa/HVU5dd3d4swmOCWBkBPtemRPGvCMP669iXSPfDTlw7ZSvw=="
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
index 3bc260f64..009bccfbf 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
@@ -36,7 +36,9 @@ jobs:
           annotate: true
         env:
           GROUP: ${{ matrix.group }}
-          JULIA_NUM_THREADS: "auto"
+          JULIA_NUM_THREADS: 11
+          RETESTITEMS_NWORKERS: 4
+          RETESTITEMS_NWORKER_THREADS: 2
       - uses: julia-actions/julia-processcoverage@v1
       - uses: codecov/codecov-action@v3
         with:
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
index affe2fd97..a3c5003c1 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
@@ -24,6 +24,7 @@ jobs:
           - {user: SciML, repo: OrdinaryDiffEq.jl, group: InterfaceIII}
           - {user: SciML, repo: OrdinaryDiffEq.jl, group: InterfaceIV}
           - {user: SciML, repo: OrdinaryDiffEq.jl, group: InterfaceV}
+          - {user: SciML, repo: NonlinearSolve.jl, group: All}
     steps:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v1
@@ -53,6 +54,9 @@ jobs:
             @info "Not compatible with this release. No problem." exception=err
             exit(0)  # Exit immediately, as a success
           end
+        env:
+          RETESTITEMS_NWORKERS: 4
+          RETESTITEMS_NWORKER_THREADS: 2
       - uses: julia-actions/julia-processcoverage@v1
       - uses: codecov/codecov-action@v3
         with:
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml b/lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml
index eea22ebce..05caa2ebc 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/FormatPR.yml
@@ -15,7 +15,7 @@ jobs:
       # https://github.com/peter-evans/create-pull-request#reference-example
       - name: Create Pull Request
         id: cpr
-        uses: peter-evans/create-pull-request@v5
+        uses: peter-evans/create-pull-request@v6
         with:
           token: ${{ secrets.GITHUB_TOKEN }}
           commit-message: Format .jl files
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index b0cbd3739..6d6d5a55f 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.4.0"
+version = "1.4.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -41,7 +41,28 @@ LinearAlgebra = "1.9"
 MaybeInplace = "0.1"
 PrecompileTools = "1"
 Reexport = "1"
-SciMLBase = "2.7"
+SciMLBase = "2.23"
 StaticArrays = "1"
 StaticArraysCore = "1.4"
 julia = "1.9"
+
+[extras]
+AllocCheck = "9b6a8646-10ed-4001-bbdc-1d2f46dfbb1a"
+CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
+NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
+Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
+Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+SciMLSensitivity = "1ed8b502-d754-442c-8d5d-10ac956f44a1"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+
+[targets]
+test = ["AllocCheck", "DiffEqBase", "ForwardDiff", "LinearAlgebra", "LinearSolve", "NonlinearProblemLibrary", "Pkg", "Random", "ReTestItems", "SciMLSensitivity", "StaticArrays", "Zygote", "CUDA", "PolyesterForwardDiff", "Reexport", "Test"]
diff --git a/lib/SimpleNonlinearSolve/test/23_test_problems.jl b/lib/SimpleNonlinearSolve/test/23_test_problems.jl
deleted file mode 100644
index c04998281..000000000
--- a/lib/SimpleNonlinearSolve/test/23_test_problems.jl
+++ /dev/null
@@ -1,89 +0,0 @@
-using SimpleNonlinearSolve, LinearAlgebra, NonlinearProblemLibrary, DiffEqBase, XUnit
-
-problems = NonlinearProblemLibrary.problems
-dicts = NonlinearProblemLibrary.dicts
-
-function test_on_library(problems, dicts, alg_ops, broken_tests, ϵ = 1e-4;
-        skip_tests = nothing)
-    for (idx, (problem, dict)) in enumerate(zip(problems, dicts))
-        x = dict["start"]
-        res = similar(x)
-        nlprob = NonlinearProblem(problem, copy(x))
-        @testset "$idx: $(dict["title"])" begin
-            for alg in alg_ops
-                try
-                    sol = solve(nlprob, alg;
-                        termination_condition = AbsNormTerminationMode())
-                    problem(res, sol.u, nothing)
-
-                    skip = skip_tests !== nothing && idx in skip_tests[alg]
-                    if skip
-                        @test_skip norm(res) ≤ ϵ
-                        continue
-                    end
-                    broken = idx in broken_tests[alg] ? true : false
-                    @test norm(res)≤ϵ broken=broken
-                catch e
-                    @error e
-                    broken = idx in broken_tests[alg] ? true : false
-                    if broken
-                        @test false broken=true
-                    else
-                        @test 1 == 2
-                    end
-                end
-            end
-        end
-    end
-end
-
-@testset "23 Test Problems" begin
-    @testcase "SimpleNewtonRaphson 23 Test Problems" begin
-        alg_ops = (SimpleNewtonRaphson(),)
-
-        # dictionary with indices of test problems where method does not converge to small residual
-        broken_tests = Dict(alg => Int[] for alg in alg_ops)
-        broken_tests[alg_ops[1]] = []
-
-        test_on_library(problems, dicts, alg_ops, broken_tests)
-    end
-
-    @testcase "SimpleTrustRegion 23 Test Problems" begin
-        alg_ops = (SimpleTrustRegion(),
-            SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
-
-        # dictionary with indices of test problems where method does not converge to small residual
-        broken_tests = Dict(alg => Int[] for alg in alg_ops)
-        broken_tests[alg_ops[1]] = [3, 15, 16, 21]
-        broken_tests[alg_ops[2]] = [15, 16]
-
-        test_on_library(problems, dicts, alg_ops, broken_tests)
-    end
-
-    @testcase "SimpleDFSane 23 Test Problems" begin
-        alg_ops = (SimpleDFSane(),)
-
-        broken_tests = Dict(alg => Int[] for alg in alg_ops)
-        broken_tests[alg_ops[1]] = [1, 2, 3, 4, 5, 6, 11, 21]
-
-        test_on_library(problems, dicts, alg_ops, broken_tests)
-    end
-
-    @testcase "SimpleBroyden 23 Test Problems" begin
-        alg_ops = (SimpleBroyden(),)
-
-        broken_tests = Dict(alg => Int[] for alg in alg_ops)
-        broken_tests[alg_ops[1]] = [1, 5, 11]
-
-        test_on_library(problems, dicts, alg_ops, broken_tests)
-    end
-
-    @testcase "SimpleKlement 23 Test Problems" begin
-        alg_ops = (SimpleKlement(),)
-
-        broken_tests = Dict(alg => Int[] for alg in alg_ops)
-        broken_tests[alg_ops[1]] = [1, 2, 4, 5, 11, 12, 22]
-
-        test_on_library(problems, dicts, alg_ops, broken_tests)
-    end
-end
diff --git a/lib/SimpleNonlinearSolve/test/Project.toml b/lib/SimpleNonlinearSolve/test/Project.toml
deleted file mode 100644
index 9077234a6..000000000
--- a/lib/SimpleNonlinearSolve/test/Project.toml
+++ /dev/null
@@ -1,19 +0,0 @@
-[deps]
-AllocCheck = "9b6a8646-10ed-4001-bbdc-1d2f46dfbb1a"
-DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
-ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
-LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
-NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
-Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
-PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
-Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
-SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
-SciMLSensitivity = "1ed8b502-d754-442c-8d5d-10ac956f44a1"
-StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-XUnit = "3e3c03f2-1a94-11e9-2981-050a4ca824ab"
-Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
-
-[compat]
-NonlinearProblemLibrary = "0.1.2"
diff --git a/lib/SimpleNonlinearSolve/test/basictests.jl b/lib/SimpleNonlinearSolve/test/basictests.jl
deleted file mode 100644
index 3f59dfb45..000000000
--- a/lib/SimpleNonlinearSolve/test/basictests.jl
+++ /dev/null
@@ -1,268 +0,0 @@
-using AllocCheck, LinearSolve, SimpleNonlinearSolve, StaticArrays, Random,
-    LinearAlgebra, XUnit, ForwardDiff, DiffEqBase
-import PolyesterForwardDiff
-
-_nameof(x) = applicable(nameof, x) ? nameof(x) : _nameof(typeof(x))
-
-quadratic_f(u, p) = u .* u .- p
-quadratic_f!(du, u, p) = (du .= u .* u .- p)
-quadratic_f2(u, p) = @. p[1] * u * u - p[2]
-
-function newton_fails(u, p)
-    return 0.010000000000000002 .+
-           10.000000000000002 ./ (1 .+
-            (0.21640425613334457 .+
-             216.40425613334457 ./ (1 .+
-              (0.21640425613334457 .+
-               216.40425613334457 ./
-               (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^ 2.0) .-
-           0.0011552453009332421u .- p
-end
-
-const TERMINATION_CONDITIONS = [
-    NormTerminationMode(), RelTerminationMode(), RelNormTerminationMode(),
-    AbsTerminationMode(), AbsNormTerminationMode(), RelSafeTerminationMode(),
-    AbsSafeTerminationMode(), RelSafeBestTerminationMode(), AbsSafeBestTerminationMode(),
-]
-
-function benchmark_nlsolve_oop(f::F, u0, p = 2.0; solver) where {F}
-    prob = NonlinearProblem{false}(f, u0, p)
-    return solve(prob, solver; abstol = 1e-9)
-end
-function benchmark_nlsolve_iip(f!::F, u0, p = 2.0; solver) where {F}
-    prob = NonlinearProblem{true}(f!, u0, p)
-    return solve(prob, solver; abstol = 1e-9)
-end
-
-# --- SimpleNewtonRaphson tests ---
-
-@testcase "$(alg)" for alg in (SimpleNewtonRaphson, SimpleTrustRegion,
-    (args...; kwargs...) -> SimpleTrustRegion(args...; nlsolve_update_rule = Val(true),
-        kwargs...))
-    @testset "AutoDiff: $(_nameof(autodiff))" for autodiff in (AutoFiniteDiff(),
-        AutoForwardDiff(), AutoPolyesterForwardDiff())
-        @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-            u0 isa SVector && autodiff isa AutoPolyesterForwardDiff && continue
-            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = alg(; autodiff))
-            @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-        end
-
-        @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
-            sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver = alg(; autodiff))
-            @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-        end
-    end
-
-    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
-        u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
-
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, alg(); termination_condition).u .≈ sqrt(2.0))
-    end
-end
-
-# --- SimpleHalley tests ---
-
-@testcase "SimpleHalley" begin
-    @testset "AutoDiff: $(_nameof(autodiff))" for autodiff in (AutoFiniteDiff(),
-        AutoForwardDiff())
-        @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = SimpleHalley(; autodiff))
-            @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-        end
-    end
-
-    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
-        u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
-
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, SimpleHalley(); termination_condition).u .≈ sqrt(2.0))
-    end
-end
-
-# --- SimpleBroyden / SimpleKlement / SimpleLimitedMemoryBroyden tests ---
-
-@testcase "$(_nameof(alg))" for alg in [SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
-    SimpleLimitedMemoryBroyden(), SimpleBroyden(; linesearch = Val(true)),
-    SimpleLimitedMemoryBroyden(; linesearch = Val(true))]
-    @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-        sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = alg)
-        @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-    end
-
-    @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
-        sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver = alg)
-        @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-    end
-
-    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
-        u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
-
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, alg; termination_condition).u .≈ sqrt(2.0))
-    end
-end
-
-@testset "Newton Fails" begin
-    u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
-    p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
-
-    @testcase "$(alg)" for alg in (SimpleDFSane(), SimpleTrustRegion(), SimpleHalley(),
-        SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
-        sol = benchmark_nlsolve_oop(newton_fails, u0, p; solver = alg)
-        @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
-    end
-end
-
-# --- Allocation Checks ---
-
-## SimpleDFSane needs to allocate a history vector
-@testcase "Allocation Checks: $(_nameof(alg))" for alg in (SimpleNewtonRaphson(),
-    SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
-    SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
-    SimpleDFSane(), SimpleBroyden(; linesearch = Val(true)),
-    SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
-    @check_allocs nlsolve(prob, alg) = SciMLBase.solve(prob, alg; abstol = 1e-9)
-
-    nlprob_scalar = NonlinearProblem{false}(quadratic_f, 1.0, 2.0)
-    nlprob_sa = NonlinearProblem{false}(quadratic_f, @SVector[1.0, 1.0], 2.0)
-
-    try
-        nlsolve(nlprob_scalar, alg)
-        @test true
-    catch e
-        @error e
-        @test false
-    end
-
-    # ForwardDiff allocates for hessian since we don't propagate the chunksize
-    try
-        nlsolve(nlprob_sa, alg)
-        @test true
-    catch e
-        @error e
-        @test false broken=(alg isa SimpleHalley)
-    end
-end
-
-# --- Interval Nonlinear Problems ---
-
-@testcase "Interval Nonlinear Problem: $(alg)" for alg in (Bisection(), Falsi(), Ridder(),
-    Brent(), ITP(), Alefeld())
-    tspan = (1.0, 20.0)
-
-    function g(p)
-        probN = IntervalNonlinearProblem{false}(quadratic_f, typeof(p).(tspan), p)
-        sol = solve(probN, alg; abstol = 1e-9)
-        return sol.left
-    end
-
-    for p in 1.1:0.1:100.0
-        @test g(p)≈sqrt(p) atol=1e-3 rtol=1e-3
-        @test ForwardDiff.derivative(g, p)≈1 / (2 * sqrt(p)) atol=1e-3 rtol=1e-3
-    end
-
-    t = (p) -> [sqrt(p[2] / p[1])]
-    p = [0.9, 50.0]
-
-    function g2(p)
-        probN = IntervalNonlinearProblem{false}((u, p) -> p[1] * u * u - p[2], tspan, p)
-        sol = solve(probN, alg; abstol = 1e-9)
-        return [sol.u]
-    end
-
-    @test g2(p)≈[sqrt(p[2] / p[1])] atol=1e-3 rtol=1e-3
-    @test ForwardDiff.jacobian(g2, p)≈ForwardDiff.jacobian(t, p) atol=1e-3 rtol=1e-3
-
-    probB = IntervalNonlinearProblem{false}(quadratic_f, (1.0, 2.0), 2.0)
-    sol = solve(probB, alg; abstol = 1e-9)
-    @test sol.left≈sqrt(2.0) atol=1e-3 rtol=1e-3
-
-    if !(alg isa Bisection || alg isa Falsi)
-        probB = IntervalNonlinearProblem{false}(quadratic_f, (sqrt(2.0), 10.0), 2.0)
-        sol = solve(probB, alg; abstol = 1e-9)
-        @test sol.left≈sqrt(2.0) atol=1e-3 rtol=1e-3
-
-        probB = IntervalNonlinearProblem{false}(quadratic_f, (0.0, sqrt(2.0)), 2.0)
-        sol = solve(probB, alg; abstol = 1e-9)
-        @test sol.left≈sqrt(2.0) atol=1e-3 rtol=1e-3
-    end
-end
-
-@testcase "Tolerance Tests Interval Methods: $(alg)" for alg in (Bisection(), Falsi(),
-    ITP())
-    tspan = (1.0, 20.0)
-    probB = IntervalNonlinearProblem(quadratic_f, tspan, 2.0)
-    tols = [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6, 1e-7]
-    ϵ = eps(1.0) #least possible tol for all methods
-
-    for atol in tols
-        sol = solve(probB, alg; abstol = atol)
-        @test abs(sol.u - sqrt(2)) < atol
-        @test abs(sol.u - sqrt(2)) > ϵ #test that the solution is not calculated upto max precision
-    end
-end
-
-@testcase "Tolerance Tests Interval Methods: $(alg)" for alg in (Ridder(), Brent())
-    tspan = (1.0, 20.0)
-    probB = IntervalNonlinearProblem(quadratic_f, tspan, 2.0)
-    tols = [0.1] # Ridder and Brent converge rapidly so as we lower tolerance below 0.01, it converges with max precision to the solution
-    ϵ = eps(1.0) #least possible tol for all methods
-
-    for atol in tols
-        sol = solve(probB, alg; abstol = atol)
-        @test abs(sol.u - sqrt(2)) < atol
-        @test abs(sol.u - sqrt(2)) > ϵ #test that the solution is not calculated upto max precision
-    end
-end
-
-@testcase "Flipped Signs and Reversed Tspan: $(alg)" for alg in (Alefeld(), Bisection(),
-    Falsi(), Brent(), ITP(), Ridder())
-    f1(u, p) = u * u - p
-    f2(u, p) = p - u * u
-
-    for p in 1:4
-        inp1 = IntervalNonlinearProblem(f1, (1.0, 2.0), p)
-        inp2 = IntervalNonlinearProblem(f2, (1.0, 2.0), p)
-        inp3 = IntervalNonlinearProblem(f1, (2.0, 1.0), p)
-        inp4 = IntervalNonlinearProblem(f2, (2.0, 1.0), p)
-        @test abs.(solve(inp1, alg).u) ≈ sqrt.(p)
-        @test abs.(solve(inp2, alg).u) ≈ sqrt.(p)
-        @test abs.(solve(inp3, alg).u) ≈ sqrt.(p)
-        @test abs.(solve(inp4, alg).u) ≈ sqrt.(p)
-    end
-end
-
-# The following tests were included in the previos versions but these kwargs never did
-# anything!
-# # Garuntee Tests for Bisection
-# f = function (u, p)
-#     if u < 2.0
-#         return u - 2.0
-#     elseif u > 3.0
-#         return u - 3.0
-#     else
-#         return 0.0
-#     end
-# end
-# probB = IntervalNonlinearProblem(f, (0.0, 4.0))
-
-# sol = solve(probB, Bisection(; exact_left = true))
-# @test f(sol.left, nothing) < 0.0
-# @test f(nextfloat(sol.left), nothing) >= 0.0
-
-# sol = solve(probB, Bisection(; exact_right = true))
-# @test f(sol.right, nothing) >= 0.0
-# @test f(prevfloat(sol.right), nothing) <= 0.0
-
-# sol = solve(probB, Bisection(; exact_left = true, exact_right = true); immutable = false)
-# @test f(sol.left, nothing) < 0.0
-# @test f(nextfloat(sol.left), nothing) >= 0.0
-# @test f(sol.right, nothing) >= 0.0
-# @test f(prevfloat(sol.right), nothing) <= 0.0
diff --git a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
new file mode 100644
index 000000000..4e5401a02
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
@@ -0,0 +1,89 @@
+@testsetup module RobustnessTesting
+using LinearAlgebra, NonlinearProblemLibrary, DiffEqBase, Test
+
+problems = NonlinearProblemLibrary.problems
+dicts = NonlinearProblemLibrary.dicts
+
+function test_on_library(problems, dicts, alg_ops, broken_tests, ϵ = 1e-4;
+        skip_tests = nothing)
+    for (idx, (problem, dict)) in enumerate(zip(problems, dicts))
+        x = dict["start"]
+        res = similar(x)
+        nlprob = NonlinearProblem(problem, copy(x))
+        @testset "$idx: $(dict["title"])" begin
+            for alg in alg_ops
+                try
+                    sol = solve(nlprob, alg;
+                        termination_condition = AbsNormTerminationMode())
+                    problem(res, sol.u, nothing)
+
+                    skip = skip_tests !== nothing && idx in skip_tests[alg]
+                    if skip
+                        @test_skip norm(res) ≤ ϵ
+                        continue
+                    end
+                    broken = idx in broken_tests[alg] ? true : false
+                    @test norm(res)≤ϵ broken=broken
+                catch e
+                    @error e
+                    broken = idx in broken_tests[alg] ? true : false
+                    if broken
+                        @test false broken=true
+                    else
+                        @test 1 == 2
+                    end
+                end
+            end
+        end
+    end
+end
+
+export problems, dicts, test_on_library
+end
+
+@testitem "SimpleNewtonRaphson" setup=[RobustnessTesting] begin
+    alg_ops = (SimpleNewtonRaphson(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = []
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "SimpleTrustRegion" setup=[RobustnessTesting] begin
+    alg_ops = (SimpleTrustRegion(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [3, 15, 16, 21]
+    broken_tests[alg_ops[2]] = [15, 16]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "SimpleDFSane" setup=[RobustnessTesting] begin
+    alg_ops = (SimpleDFSane(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [1, 2, 3, 4, 5, 6, 11, 21]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "SimpleBroyden" setup=[RobustnessTesting] begin
+    alg_ops = (SimpleBroyden(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [1, 5, 11]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "SimpleKlement" setup=[RobustnessTesting] begin
+    alg_ops = (SimpleKlement(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 11, 12, 22]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
diff --git a/lib/SimpleNonlinearSolve/test/adjoint.jl b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
similarity index 73%
rename from lib/SimpleNonlinearSolve/test/adjoint.jl
rename to lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
index cf2ef38d7..f96491449 100644
--- a/lib/SimpleNonlinearSolve/test/adjoint.jl
+++ b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
@@ -1,6 +1,6 @@
-using ForwardDiff, SciMLSensitivity, SimpleNonlinearSolve, XUnit, Zygote
+@testitem "Simple Adjoint Test" begin
+    using ForwardDiff, SciMLSensitivity, Zygote
 
-@testcase "Simple Adjoint Test" begin
     ff(u, p) = u .^ 2 .- p
 
     function solve_nlprob(p)
diff --git a/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl b/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
new file mode 100644
index 000000000..e7fc44f02
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
@@ -0,0 +1,90 @@
+@testsetup module ForwardADTesting
+using Reexport
+@reexport using ForwardDiff, SimpleNonlinearSolve, StaticArrays, LinearAlgebra
+import SimpleNonlinearSolve: AbstractSimpleNonlinearSolveAlgorithm
+
+test_f!(du, u, p) = (@. du = u^2 - p)
+test_f(u, p) = (@. u^2 - p)
+
+jacobian_f(::Number, p) = 1 / (2 * √p)
+jacobian_f(::Number, p::Number) = 1 / (2 * √p)
+jacobian_f(u, p::Number) = one.(u) .* (1 / (2 * √p))
+jacobian_f(u, p::AbstractArray) = diagm(vec(@. 1 / (2 * √p)))
+
+function solve_with(::Val{mode}, u, alg) where {mode}
+    f = if mode === :iip
+        solve_iip(p) = solve(NonlinearProblem(test_f!, u, p), alg).u
+    elseif mode === :oop
+        solve_oop(p) = solve(NonlinearProblem(test_f, u, p), alg).u
+    end
+    return f
+end
+
+__compatible(::Any, ::Val{:oop}) = true
+__compatible(::Number, ::Val{:iip}) = false
+__compatible(::AbstractArray, ::Val{:iip}) = true
+__compatible(::StaticArray, ::Val{:iip}) = false
+
+__compatible(::Any, ::Number) = true
+__compatible(::Number, ::AbstractArray) = false
+__compatible(u::AbstractArray, p::AbstractArray) = size(u) == size(p)
+
+__compatible(u::Number, ::AbstractSimpleNonlinearSolveAlgorithm) = true
+__compatible(u::AbstractArray, ::AbstractSimpleNonlinearSolveAlgorithm) = true
+__compatible(u::StaticArray, ::AbstractSimpleNonlinearSolveAlgorithm) = true
+
+__compatible(::AbstractSimpleNonlinearSolveAlgorithm, ::Val{:iip}) = true
+__compatible(::AbstractSimpleNonlinearSolveAlgorithm, ::Val{:oop}) = true
+__compatible(::SimpleHalley, ::Val{:iip}) = false
+
+export test_f, test_f!, jacobian_f, solve_with, __compatible
+end
+
+@testitem "ForwardDiff.jl Integration" setup=[ForwardADTesting] begin
+    @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(),
+        SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+        SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleDFSane())
+        us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
+
+        @testset "Scalar AD" begin
+            for p in 1.0:0.1:100.0, u0 in us, mode in (:iip, :oop)
+                __compatible(u0, alg) || continue
+                __compatible(u0, Val(mode)) || continue
+                __compatible(alg, Val(mode)) || continue
+
+                sol = solve(NonlinearProblem(test_f, u0, p), alg)
+                if SciMLBase.successful_retcode(sol)
+                    gs = abs.(ForwardDiff.derivative(solve_with(Val{mode}(), u0, alg), p))
+                    gs_true = abs.(jacobian_f(u0, p))
+                    if !(isapprox(gs, gs_true, atol = 1e-5))
+                        @show sol.retcode, sol.u
+                        @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_gradient=gs true_gradient=gs_true
+                    else
+                        @test abs.(gs)≈abs.(gs_true) atol=1e-5
+                    end
+                end
+            end
+        end
+
+        @testset "Jacobian" begin
+            for u0 in us, p in ([2.0, 1.0], [2.0 1.0; 3.0 4.0]), mode in (:iip, :oop)
+                __compatible(u0, p) || continue
+                __compatible(u0, alg) || continue
+                __compatible(u0, Val(mode)) || continue
+                __compatible(alg, Val(mode)) || continue
+
+                sol = solve(NonlinearProblem(test_f, u0, p), alg)
+                if SciMLBase.successful_retcode(sol)
+                    gs = abs.(ForwardDiff.jacobian(solve_with(Val{mode}(), u0, alg), p))
+                    gs_true = abs.(jacobian_f(u0, p))
+                    if !(isapprox(gs, gs_true, atol = 1e-5))
+                        @show sol.retcode, sol.u
+                        @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_jacobian=gs true_jacobian=gs_true
+                    else
+                        @test abs.(gs)≈abs.(gs_true) atol=1e-5
+                    end
+                end
+            end
+        end
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl b/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl
new file mode 100644
index 000000000..8d99d3544
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl
@@ -0,0 +1,24 @@
+@testitem "Nonlinear Least Squares" begin
+    using LinearAlgebra
+
+    true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
+
+    θ_true = [1.0, 0.1, 2.0, 0.5]
+    x = [-1.0, -0.5, 0.0, 0.5, 1.0]
+    y_target = true_function(x, θ_true)
+
+    function loss_function(θ, p)
+        ŷ = true_function(p, θ)
+        return ŷ .- y_target
+    end
+
+    θ_init = θ_true .+ 0.1
+    prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
+
+    @testset "Solver: $(nameof(typeof(solver)))" for solver in [
+        SimpleNewtonRaphson(AutoForwardDiff()), SimpleGaussNewton(AutoForwardDiff()),
+        SimpleNewtonRaphson(AutoFiniteDiff()), SimpleGaussNewton(AutoFiniteDiff())]
+        sol = solve(prob_oop, solver)
+        @test norm(sol.resid, Inf) < 1e-12
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl b/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl
new file mode 100644
index 000000000..54cf86b21
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl
@@ -0,0 +1,14 @@
+@testitem "Matrix Resizing" begin
+    ff(u, p) = u .* u .- p
+    u0 = ones(2, 3)
+    p = 2.0
+    vecprob = NonlinearProblem(ff, vec(u0), p)
+    prob = NonlinearProblem(ff, u0, p)
+
+    @testset "$(nameof(typeof(alg)))" for alg in (SimpleKlement(), SimpleBroyden(),
+        SimpleNewtonRaphson(), SimpleDFSane(),
+        SimpleLimitedMemoryBroyden(; threshold = Val(2)),
+        SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
+        @test vec(solve(prob, alg).u) ≈ solve(vecprob, alg).u
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
new file mode 100644
index 000000000..dc6054273
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -0,0 +1,279 @@
+@testsetup module RootfindingTesting
+using Reexport
+@reexport using AllocCheck,
+    LinearSolve, StaticArrays, Random, LinearAlgebra, ForwardDiff, DiffEqBase
+import PolyesterForwardDiff
+
+quadratic_f(u, p) = u .* u .- p
+quadratic_f!(du, u, p) = (du .= u .* u .- p)
+quadratic_f2(u, p) = @. p[1] * u * u - p[2]
+
+function newton_fails(u, p)
+    return 0.010000000000000002 .+
+           10.000000000000002 ./ (1 .+
+            (0.21640425613334457 .+
+             216.40425613334457 ./ (1 .+
+              (0.21640425613334457 .+
+               216.40425613334457 ./
+               (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^ 2.0) .-
+           0.0011552453009332421u .- p
+end
+
+const TERMINATION_CONDITIONS = [
+    NormTerminationMode(), RelTerminationMode(), RelNormTerminationMode(),
+    AbsTerminationMode(), AbsNormTerminationMode(), RelSafeTerminationMode(),
+    AbsSafeTerminationMode(), RelSafeBestTerminationMode(), AbsSafeBestTerminationMode(),
+]
+
+function benchmark_nlsolve_oop(f::F, u0, p = 2.0; solver) where {F}
+    prob = NonlinearProblem{false}(f, u0, p)
+    return solve(prob, solver; abstol = 1e-9)
+end
+function benchmark_nlsolve_iip(f!::F, u0, p = 2.0; solver) where {F}
+    prob = NonlinearProblem{true}(f!, u0, p)
+    return solve(prob, solver; abstol = 1e-9)
+end
+
+export quadratic_f, quadratic_f!, quadratic_f2, newton_fails, TERMINATION_CONDITIONS,
+    benchmark_nlsolve_oop, benchmark_nlsolve_iip
+
+end
+
+@testitem "First Order Methods" setup=[RootfindingTesting] begin
+    @testset "$(alg)" for alg in (SimpleNewtonRaphson, SimpleTrustRegion,
+        (args...; kwargs...) -> SimpleTrustRegion(args...; nlsolve_update_rule = Val(true),
+            kwargs...))
+        @testset "AutoDiff: $(nameof(typeof(autodiff))))" for autodiff in (AutoFiniteDiff(),
+            AutoForwardDiff(), AutoPolyesterForwardDiff())
+            @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],
+                @SVector[1.0, 1.0], 1.0)
+                u0 isa SVector && autodiff isa AutoPolyesterForwardDiff && continue
+                sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = alg(; autodiff))
+                @test SciMLBase.successful_retcode(sol)
+                @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+            end
+
+            @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+                sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver = alg(; autodiff))
+                @test SciMLBase.successful_retcode(sol)
+                @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+            end
+        end
+
+        @testset "Termination condition: $(termination_condition) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
+            u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
+
+            probN = NonlinearProblem(quadratic_f, u0, 2.0)
+            @test all(solve(probN, alg(); termination_condition).u .≈ sqrt(2.0))
+        end
+    end
+end
+
+@testitem "SimpleHalley" setup=[RootfindingTesting] begin
+    @testset "AutoDiff: $(nameof(typeof(autodiff)))" for autodiff in (AutoFiniteDiff(),
+        AutoForwardDiff())
+        @testset "[OOP] u0: $(nameof(typeof(u0)))" for u0 in ([1.0, 1.0],
+            @SVector[1.0, 1.0], 1.0)
+            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = SimpleHalley(; autodiff))
+            @test SciMLBase.successful_retcode(sol)
+            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+        end
+    end
+
+    @testset "Termination condition: $(termination_condition) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
+        u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
+
+        probN = NonlinearProblem(quadratic_f, u0, 2.0)
+        @test all(solve(probN, SimpleHalley(); termination_condition).u .≈ sqrt(2.0))
+    end
+end
+
+@testitem "Derivative Free Metods" setup=[RootfindingTesting] begin
+    @testset "$(nameof(typeof(alg)))" for alg in [SimpleBroyden(), SimpleKlement(),
+        SimpleDFSane(), SimpleLimitedMemoryBroyden(),
+        SimpleBroyden(; linesearch = Val(true)),
+        SimpleLimitedMemoryBroyden(; linesearch = Val(true))]
+        @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
+            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = alg)
+            @test SciMLBase.successful_retcode(sol)
+            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+        end
+
+        @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+            sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver = alg)
+            @test SciMLBase.successful_retcode(sol)
+            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+        end
+
+        @testset "Termination condition: $(termination_condition) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
+            u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
+
+            probN = NonlinearProblem(quadratic_f, u0, 2.0)
+            @test all(solve(probN, alg; termination_condition).u .≈ sqrt(2.0))
+        end
+    end
+end
+
+@testitem "Newton Fails" setup=[RootfindingTesting] begin
+    u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
+    p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+
+    @testset "$(nameof(typeof(alg)))" for alg in (SimpleDFSane(), SimpleTrustRegion(),
+        SimpleHalley(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
+        sol = benchmark_nlsolve_oop(newton_fails, u0, p; solver = alg)
+        @test SciMLBase.successful_retcode(sol)
+        @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
+    end
+end
+
+@testitem "Allocation Checks" setup=[RootfindingTesting] begin
+    @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(),
+        SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
+        SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+        SimpleDFSane(), SimpleBroyden(; linesearch = Val(true)),
+        SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
+        @check_allocs nlsolve(prob, alg) = SciMLBase.solve(prob, alg; abstol = 1e-9)
+
+        nlprob_scalar = NonlinearProblem{false}(quadratic_f, 1.0, 2.0)
+        nlprob_sa = NonlinearProblem{false}(quadratic_f, @SVector[1.0, 1.0], 2.0)
+
+        try
+            nlsolve(nlprob_scalar, alg)
+            @test true
+        catch e
+            @error e
+            @test false
+        end
+
+        # ForwardDiff allocates for hessian since we don't propagate the chunksize
+        try
+            nlsolve(nlprob_sa, alg)
+            @test true
+        catch e
+            @error e
+            @test false broken=(alg isa SimpleHalley)
+        end
+    end
+end
+
+@testitem "Interval Nonlinear Problems" setup=[RootfindingTesting] begin
+    @testset "$(nameof(typeof(alg)))" for alg in (Bisection(), Falsi(), Ridder(), Brent(),
+        ITP(), Alefeld())
+        tspan = (1.0, 20.0)
+
+        function g(p)
+            probN = IntervalNonlinearProblem{false}(quadratic_f, typeof(p).(tspan), p)
+            sol = solve(probN, alg; abstol = 1e-9)
+            return sol.left
+        end
+
+        for p in 1.1:0.1:100.0
+            @test g(p)≈sqrt(p) atol=1e-3 rtol=1e-3
+            @test ForwardDiff.derivative(g, p)≈1 / (2 * sqrt(p)) atol=1e-3 rtol=1e-3
+        end
+
+        t = (p) -> [sqrt(p[2] / p[1])]
+        p = [0.9, 50.0]
+
+        function g2(p)
+            probN = IntervalNonlinearProblem{false}((u, p) -> p[1] * u * u - p[2], tspan, p)
+            sol = solve(probN, alg; abstol = 1e-9)
+            return [sol.u]
+        end
+
+        @test g2(p)≈[sqrt(p[2] / p[1])] atol=1e-3 rtol=1e-3
+        @test ForwardDiff.jacobian(g2, p)≈ForwardDiff.jacobian(t, p) atol=1e-3 rtol=1e-3
+
+        probB = IntervalNonlinearProblem{false}(quadratic_f, (1.0, 2.0), 2.0)
+        sol = solve(probB, alg; abstol = 1e-9)
+        @test sol.left≈sqrt(2.0) atol=1e-3 rtol=1e-3
+
+        if !(alg isa Bisection || alg isa Falsi)
+            probB = IntervalNonlinearProblem{false}(quadratic_f, (sqrt(2.0), 10.0), 2.0)
+            sol = solve(probB, alg; abstol = 1e-9)
+            @test sol.left≈sqrt(2.0) atol=1e-3 rtol=1e-3
+
+            probB = IntervalNonlinearProblem{false}(quadratic_f, (0.0, sqrt(2.0)), 2.0)
+            sol = solve(probB, alg; abstol = 1e-9)
+            @test sol.left≈sqrt(2.0) atol=1e-3 rtol=1e-3
+        end
+    end
+end
+
+@testitem "Tolerance Tests Interval Methods" setup=[RootfindingTesting] begin
+    @testset "$(nameof(typeof(alg)))" for alg in (Bisection(), Falsi(), ITP())
+        tspan = (1.0, 20.0)
+        probB = IntervalNonlinearProblem(quadratic_f, tspan, 2.0)
+        tols = [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6, 1e-7]
+        ϵ = eps(1.0) #least possible tol for all methods
+
+        for atol in tols
+            sol = solve(probB, alg; abstol = atol)
+            @test abs(sol.u - sqrt(2)) < atol
+            @test abs(sol.u - sqrt(2)) > ϵ #test that the solution is not calculated upto max precision
+        end
+    end
+end
+
+@testitem "Tolerance Tests Interval Methods 2" setup=[RootfindingTesting] begin
+    @testset "$(nameof(typeof(alg)))" for alg in (Ridder(), Brent())
+        tspan = (1.0, 20.0)
+        probB = IntervalNonlinearProblem(quadratic_f, tspan, 2.0)
+        tols = [0.1] # Ridder and Brent converge rapidly so as we lower tolerance below 0.01, it converges with max precision to the solution
+        ϵ = eps(1.0) #least possible tol for all methods
+
+        for atol in tols
+            sol = solve(probB, alg; abstol = atol)
+            @test abs(sol.u - sqrt(2)) < atol
+            @test abs(sol.u - sqrt(2)) > ϵ #test that the solution is not calculated upto max precision
+        end
+    end
+end
+
+@testitem "Flipped Signs and Reversed Tspan" setup=[RootfindingTesting] begin
+    @testset "$(nameof(typeof(alg)))" for alg in (Alefeld(), Bisection(), Falsi(), Brent(),
+        ITP(), Ridder())
+        f1(u, p) = u * u - p
+        f2(u, p) = p - u * u
+
+        for p in 1:4
+            inp1 = IntervalNonlinearProblem(f1, (1.0, 2.0), p)
+            inp2 = IntervalNonlinearProblem(f2, (1.0, 2.0), p)
+            inp3 = IntervalNonlinearProblem(f1, (2.0, 1.0), p)
+            inp4 = IntervalNonlinearProblem(f2, (2.0, 1.0), p)
+            @test abs.(solve(inp1, alg).u) ≈ sqrt.(p)
+            @test abs.(solve(inp2, alg).u) ≈ sqrt.(p)
+            @test abs.(solve(inp3, alg).u) ≈ sqrt.(p)
+            @test abs.(solve(inp4, alg).u) ≈ sqrt.(p)
+        end
+    end
+end
+
+# The following tests were included in the previos versions but these kwargs never did
+# anything!
+# # Garuntee Tests for Bisection
+# f = function (u, p)
+#     if u < 2.0
+#         return u - 2.0
+#     elseif u > 3.0
+#         return u - 3.0
+#     else
+#         return 0.0
+#     end
+# end
+# probB = IntervalNonlinearProblem(f, (0.0, 4.0))
+
+# sol = solve(probB, Bisection(; exact_left = true))
+# @test f(sol.left, nothing) < 0.0
+# @test f(nextfloat(sol.left), nothing) >= 0.0
+
+# sol = solve(probB, Bisection(; exact_right = true))
+# @test f(sol.right, nothing) >= 0.0
+# @test f(prevfloat(sol.right), nothing) <= 0.0
+
+# sol = solve(probB, Bisection(; exact_left = true, exact_right = true); immutable = false)
+# @test f(sol.left, nothing) < 0.0
+# @test f(nextfloat(sol.left), nothing) >= 0.0
+# @test f(sol.right, nothing) >= 0.0
+# @test f(prevfloat(sol.right), nothing) <= 0.0
diff --git a/lib/SimpleNonlinearSolve/test/cuda/Project.toml b/lib/SimpleNonlinearSolve/test/cuda/Project.toml
deleted file mode 100644
index 4fdee40a7..000000000
--- a/lib/SimpleNonlinearSolve/test/cuda/Project.toml
+++ /dev/null
@@ -1,6 +0,0 @@
-[deps]
-CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
-SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
-StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-XUnit = "3e3c03f2-1a94-11e9-2981-050a4ca824ab"
diff --git a/lib/SimpleNonlinearSolve/test/forward_ad.jl b/lib/SimpleNonlinearSolve/test/forward_ad.jl
deleted file mode 100644
index 99b32c3cb..000000000
--- a/lib/SimpleNonlinearSolve/test/forward_ad.jl
+++ /dev/null
@@ -1,83 +0,0 @@
-using ForwardDiff, SimpleNonlinearSolve, StaticArrays, XUnit, LinearAlgebra
-import SimpleNonlinearSolve: AbstractSimpleNonlinearSolveAlgorithm
-
-test_f!(du, u, p) = (@. du = u^2 - p)
-test_f(u, p) = (@. u^2 - p)
-
-jacobian_f(::Number, p) = 1 / (2 * √p)
-jacobian_f(::Number, p::Number) = 1 / (2 * √p)
-jacobian_f(u, p::Number) = one.(u) .* (1 / (2 * √p))
-jacobian_f(u, p::AbstractArray) = diagm(vec(@. 1 / (2 * √p)))
-
-function solve_with(::Val{mode}, u, alg) where {mode}
-    f = if mode === :iip
-        solve_iip(p) = solve(NonlinearProblem(test_f!, u, p), alg).u
-    elseif mode === :oop
-        solve_oop(p) = solve(NonlinearProblem(test_f, u, p), alg).u
-    end
-    return f
-end
-
-__compatible(::Any, ::Val{:oop}) = true
-__compatible(::Number, ::Val{:iip}) = false
-__compatible(::AbstractArray, ::Val{:iip}) = true
-__compatible(::StaticArray, ::Val{:iip}) = false
-
-__compatible(::Any, ::Number) = true
-__compatible(::Number, ::AbstractArray) = false
-__compatible(u::AbstractArray, p::AbstractArray) = size(u) == size(p)
-
-__compatible(u::Number, ::AbstractSimpleNonlinearSolveAlgorithm) = true
-__compatible(u::AbstractArray, ::AbstractSimpleNonlinearSolveAlgorithm) = true
-__compatible(u::StaticArray, ::AbstractSimpleNonlinearSolveAlgorithm) = true
-
-__compatible(::AbstractSimpleNonlinearSolveAlgorithm, ::Val{:iip}) = true
-__compatible(::AbstractSimpleNonlinearSolveAlgorithm, ::Val{:oop}) = true
-__compatible(::SimpleHalley, ::Val{:iip}) = false
-
-@testcase "ForwardDiff.jl Integration: $(alg)" for alg in (SimpleNewtonRaphson(),
-    SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
-    SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleDFSane())
-    us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
-
-    @testset "Scalar AD" begin
-        for p in 1.0:0.1:100.0, u0 in us, mode in (:iip, :oop)
-            __compatible(u0, alg) || continue
-            __compatible(u0, Val(mode)) || continue
-            __compatible(alg, Val(mode)) || continue
-
-            sol = solve(NonlinearProblem(test_f, u0, p), alg)
-            if SciMLBase.successful_retcode(sol)
-                gs = abs.(ForwardDiff.derivative(solve_with(Val{mode}(), u0, alg), p))
-                gs_true = abs.(jacobian_f(u0, p))
-                if !(isapprox(gs, gs_true, atol = 1e-5))
-                    @show sol.retcode, sol.u
-                    @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_gradient=gs true_gradient=gs_true
-                else
-                    @test abs.(gs)≈abs.(gs_true) atol=1e-5
-                end
-            end
-        end
-    end
-
-    @testset "Jacobian" begin
-        for u0 in us, p in ([2.0, 1.0], [2.0 1.0; 3.0 4.0]), mode in (:iip, :oop)
-            __compatible(u0, p) || continue
-            __compatible(u0, alg) || continue
-            __compatible(u0, Val(mode)) || continue
-            __compatible(alg, Val(mode)) || continue
-
-            sol = solve(NonlinearProblem(test_f, u0, p), alg)
-            if SciMLBase.successful_retcode(sol)
-                gs = abs.(ForwardDiff.jacobian(solve_with(Val{mode}(), u0, alg), p))
-                gs_true = abs.(jacobian_f(u0, p))
-                if !(isapprox(gs, gs_true, atol = 1e-5))
-                    @show sol.retcode, sol.u
-                    @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_jacobian=gs true_jacobian=gs_true
-                else
-                    @test abs.(gs)≈abs.(gs_true) atol=1e-5
-                end
-            end
-        end
-    end
-end
diff --git a/lib/SimpleNonlinearSolve/test/cuda.jl b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
similarity index 75%
rename from lib/SimpleNonlinearSolve/test/cuda.jl
rename to lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
index f1f372f6a..37999dada 100644
--- a/lib/SimpleNonlinearSolve/test/cuda.jl
+++ b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
@@ -1,12 +1,12 @@
-using SimpleNonlinearSolve, StaticArrays, CUDA, XUnit
+@testitem "Solving on GPUs" begin
+    using StaticArrays, CUDA
 
-CUDA.allowscalar(false)
+    CUDA.allowscalar(false)
 
-f(u, p) = u .* u .- 2
-f!(du, u, p) = du .= u .* u .- 2
+    f(u, p) = u .* u .- 2
+    f!(du, u, p) = du .= u .* u .- 2
 
-@testset "Solving on GPUs" begin
-    @testcase "$(alg)" for alg in (SimpleNewtonRaphson(), SimpleDFSane(),
+    @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(), SimpleDFSane(),
         SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
         SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(),
         SimpleHalley(), SimpleBroyden(; linesearch = Val(true)),
@@ -36,15 +36,22 @@ f!(du, u, p) = du .= u .* u .- 2
     end
 end
 
-function kernel_function(prob, alg)
-    solve(prob, alg)
-    return nothing
-end
+@testitem "CUDA Kernel Launch Test" begin
+    using StaticArrays, CUDA
+
+    CUDA.allowscalar(false)
+
+    f(u, p) = u .* u .- 2
+    f!(du, u, p) = du .= u .* u .- 2
+
+    function kernel_function(prob, alg)
+        solve(prob, alg)
+        return nothing
+    end
 
-@testset "CUDA Kernel Launch Test" begin
     prob = NonlinearProblem{false}(f, @SVector[1.0f0, 1.0f0])
 
-    @testcase "$(alg)" for alg in (SimpleNewtonRaphson(), SimpleDFSane(),
+    @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(), SimpleDFSane(),
         SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
         SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley(),
         SimpleBroyden(; linesearch = Val(true)),
diff --git a/lib/SimpleNonlinearSolve/test/least_squares.jl b/lib/SimpleNonlinearSolve/test/least_squares.jl
deleted file mode 100644
index 6c48a9807..000000000
--- a/lib/SimpleNonlinearSolve/test/least_squares.jl
+++ /dev/null
@@ -1,22 +0,0 @@
-using SimpleNonlinearSolve, LinearAlgebra, XUnit
-
-true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
-
-θ_true = [1.0, 0.1, 2.0, 0.5]
-x = [-1.0, -0.5, 0.0, 0.5, 1.0]
-y_target = true_function(x, θ_true)
-
-function loss_function(θ, p)
-    ŷ = true_function(p, θ)
-    return ŷ .- y_target
-end
-
-θ_init = θ_true .+ 0.1
-prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
-
-@testcase "Solver: $(solver)" for solver in [SimpleNewtonRaphson(AutoForwardDiff()),
-    SimpleGaussNewton(AutoForwardDiff()),
-    SimpleNewtonRaphson(AutoFiniteDiff()), SimpleGaussNewton(AutoFiniteDiff())]
-    sol = solve(prob_oop, solver)
-    @test norm(sol.resid) < 1e-12
-end
diff --git a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl b/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
deleted file mode 100644
index 778ec5185..000000000
--- a/lib/SimpleNonlinearSolve/test/matrix_resizing_tests.jl
+++ /dev/null
@@ -1,13 +0,0 @@
-using SimpleNonlinearSolve, XUnit
-
-ff(u, p) = u .* u .- p
-u0 = ones(2, 3)
-p = 2.0
-vecprob = NonlinearProblem(ff, vec(u0), p)
-prob = NonlinearProblem(ff, u0, p)
-
-@testcase "$(alg)" for alg in (SimpleKlement(), SimpleBroyden(), SimpleNewtonRaphson(),
-    SimpleDFSane(), SimpleLimitedMemoryBroyden(; threshold = Val(2)), SimpleTrustRegion(),
-    SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
-    @test vec(solve(prob, alg).u) ≈ solve(vecprob, alg).u
-end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 5d9216ae3..56acdd0c5 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -1,25 +1,11 @@
-using Pkg, SafeTestsets, XUnit
+using ReTestItems
 
 const GROUP = get(ENV, "GROUP", "All")
 
-function activate_env(env)
-    Pkg.activate(env)
-    Pkg.develop(PackageSpec(path = dirname(@__DIR__)))
-    Pkg.instantiate()
+if GROUP == "All" || GROUP == "Core"
+    ReTestItems.runtests(joinpath(@__DIR__, "core/"))
 end
 
-@testset runner=ParallelTestRunner() "SimpleNonlinearSolve.jl" begin
-    if GROUP == "All" || GROUP == "Core"
-        @safetestset "Basic Tests" include("basictests.jl")
-        @safetestset "Forward AD" include("forward_ad.jl")
-        @safetestset "Matrix Resizing Tests" include("matrix_resizing_tests.jl")
-        @safetestset "Least Squares Tests" include("least_squares.jl")
-        @safetestset "23 Test Problems" include("23_test_problems.jl")
-        @safetestset "Simple Adjoint Tests" include("adjoint.jl")
-    end
-
-    if GROUP == "CUDA"
-        activate_env("cuda")
-        @safetestset "CUDA Tests" include("cuda.jl")
-    end
-end
+if GROUP == "GPU"
+    ReTestItems.runtests(joinpath(@__DIR__, "gpu/"))
+end
\ No newline at end of file

From 5fd1cd7bccbbcc720c83ad8cb748f43667c64011 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 9 Feb 2024 09:47:39 -0500
Subject: [PATCH 304/700] Test on multiple os

---
 lib/SimpleNonlinearSolve/.github/workflows/CI.yml | 13 +++++++++++--
 lib/SimpleNonlinearSolve/test/runtests.jl         |  2 +-
 2 files changed, 12 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
index 009bccfbf..8e0ab3bff 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
@@ -8,13 +8,17 @@ on:
       - main
 jobs:
   test:
-    runs-on: ubuntu-latest
+    runs-on: ${{ matrix.os }}
     strategy:
       matrix:
         group:
           - Core
         version:
           - '1'
+        os:
+          - ubuntu-latest
+          - macos-latest
+          - windows-latest
     steps:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v1
@@ -40,6 +44,11 @@ jobs:
           RETESTITEMS_NWORKERS: 4
           RETESTITEMS_NWORKER_THREADS: 2
       - uses: julia-actions/julia-processcoverage@v1
-      - uses: codecov/codecov-action@v3
+        with:
+          directories: src,ext
+      - uses: codecov/codecov-action@v4
         with:
           file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 56acdd0c5..1a2e93bb1 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -8,4 +8,4 @@ end
 
 if GROUP == "GPU"
     ReTestItems.runtests(joinpath(@__DIR__, "gpu/"))
-end
\ No newline at end of file
+end

From 75911566db61ee80a8dc39938b3000a654bb0e03 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 9 Feb 2024 10:13:46 -0500
Subject: [PATCH 305/700] Retry for Broyden

---
 lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
index 4e5401a02..8b8f2395d 100644
--- a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
@@ -70,7 +70,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "SimpleBroyden" setup=[RobustnessTesting] begin
+@testitem "SimpleBroyden" retries=5 setup=[RobustnessTesting] begin
     alg_ops = (SimpleBroyden(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)

From 2d216726aa1a0201ad3a4986676f22f9c44bbd2c Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 10 Feb 2024 12:02:07 -0500
Subject: [PATCH 306/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index b04fc411c..ca54b2515 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -32,7 +32,7 @@ SimpleNonlinearSolveStaticArraysExt = "StaticArrays"
 ADTypes = "0.2.6"
 ArrayInterface = "7.7"
 ChainRulesCore = "1.21"
-ConcreteStructs = "0.2.2"
+ConcreteStructs = "0.2.4"
 DiffEqBase = "6.146"
 FastClosures = "0.3"
 FiniteDiff = "2.22"

From ef11257832fb05d529c58065296450ab24779c13 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 10 Feb 2024 12:30:33 -0500
Subject: [PATCH 307/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index ca54b2515..bf943823d 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -32,7 +32,7 @@ SimpleNonlinearSolveStaticArraysExt = "StaticArrays"
 ADTypes = "0.2.6"
 ArrayInterface = "7.7"
 ChainRulesCore = "1.21"
-ConcreteStructs = "0.2.4"
+ConcreteStructs = "0.2.3"
 DiffEqBase = "6.146"
 FastClosures = "0.3"
 FiniteDiff = "2.22"

From 4d1c76191b7c5e58b17be42cefe5bbb0a1f5a929 Mon Sep 17 00:00:00 2001
From: ChrisRackauckas <1814174+ChrisRackauckas@users.noreply.github.com>
Date: Sun, 11 Feb 2024 00:19:29 +0000
Subject: [PATCH 308/700] Format .jl files

---
 .../src/SimpleNonlinearSolve.jl                 | 17 ++++++++++-------
 lib/SimpleNonlinearSolve/src/ad.jl              |  9 ++++++---
 .../src/bracketing/alefeld.jl                   |  9 ++++++---
 .../src/bracketing/bisection.jl                 |  3 ++-
 .../src/bracketing/brent.jl                     |  3 ++-
 .../src/bracketing/falsi.jl                     |  3 ++-
 lib/SimpleNonlinearSolve/src/bracketing/itp.jl  |  3 ++-
 .../src/bracketing/ridder.jl                    |  3 ++-
 .../src/nlsolve/lbroyden.jl                     |  3 ++-
 .../test/core/rootfind_tests.jl                 |  9 +++++----
 10 files changed, 39 insertions(+), 23 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 3f12d8888..894195106 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -4,12 +4,13 @@ import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidat
 
 @recompile_invalidations begin
     using ADTypes, ArrayInterface, ConcreteStructs, DiffEqBase, FastClosures, FiniteDiff,
-        ForwardDiff, Reexport, LinearAlgebra, SciMLBase
+          ForwardDiff, Reexport, LinearAlgebra, SciMLBase
 
     import DiffEqBase: AbstractNonlinearTerminationMode,
-        AbstractSafeNonlinearTerminationMode, AbstractSafeBestNonlinearTerminationMode,
-        NonlinearSafeTerminationReturnCode, get_termination_mode,
-        NONLINEARSOLVE_DEFAULT_NORM
+                       AbstractSafeNonlinearTerminationMode,
+                       AbstractSafeBestNonlinearTerminationMode,
+                       NonlinearSafeTerminationReturnCode, get_termination_mode,
+                       NONLINEARSOLVE_DEFAULT_NORM
     import ForwardDiff: Dual
     import MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
     import SciMLBase: AbstractNonlinearAlgorithm, build_solution, isinplace, _unwrap_val
@@ -56,14 +57,16 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing, args...;
 end
 
 # By Pass the highlevel checks for NonlinearProblem for Simple Algorithms
-function SciMLBase.solve(prob::NonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
+function SciMLBase.solve(
+        prob::NonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
         args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...)
     if sensealg === nothing && haskey(prob.kwargs, :sensealg)
         sensealg = prob.kwargs[:sensealg]
     end
     new_u0 = u0 !== nothing ? u0 : prob.u0
     new_p = p !== nothing ? p : prob.p
-    return __internal_solve_up(prob, sensealg, new_u0, u0 === nothing, new_p, p === nothing,
+    return __internal_solve_up(
+        prob, sensealg, new_u0, u0 === nothing, new_p, p === nothing,
         alg, args...; kwargs...)
 end
 
@@ -111,7 +114,7 @@ end
 end
 
 export SimpleBroyden, SimpleDFSane, SimpleGaussNewton, SimpleHalley, SimpleKlement,
-    SimpleLimitedMemoryBroyden, SimpleNewtonRaphson, SimpleTrustRegion
+       SimpleLimitedMemoryBroyden, SimpleNewtonRaphson, SimpleTrustRegion
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index a4a777be6..b4f7f41b9 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -1,15 +1,18 @@
-function SciMLBase.solve(prob::NonlinearProblem{<:Union{Number, <:AbstractArray},
+function SciMLBase.solve(
+        prob::NonlinearProblem{<:Union{Number, <:AbstractArray},
             iip, <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
         alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...) where {T, V, P, iip}
     sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
     dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
-    return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats,
+    return SciMLBase.build_solution(
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats,
         sol.original)
 end
 
 for algType in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
     @eval begin
-        function SciMLBase.solve(prob::IntervalNonlinearProblem{uType, iip,
+        function SciMLBase.solve(
+                prob::IntervalNonlinearProblem{uType, iip,
                     <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
                 alg::$(algType), args...; kwargs...) where {uType, T, V, P, iip}
             sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/alefeld.jl b/lib/SimpleNonlinearSolve/src/bracketing/alefeld.jl
index 39c984fd5..3b89751a7 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/alefeld.jl
@@ -38,7 +38,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...;
         end
         ē, fc = d, f(c)
         (a == c || b == c) &&
-            return build_solution(prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
+            return build_solution(
+                prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
                 left = a, right = b)
         iszero(fc) &&
             return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success,
@@ -57,7 +58,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...;
         end
         fc = f(c)
         (ā == c || b̄ == c) &&
-            return build_solution(prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
+            return build_solution(
+                prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
                 left = ā, right = b̄)
         iszero(fc) &&
             return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success,
@@ -76,7 +78,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...;
         end
         fc = f(c)
         (ā == c || b̄ == c) &&
-            return build_solution(prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
+            return build_solution(
+                prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
                 left = ā, right = b̄)
         iszero(fc) &&
             return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success,
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
index 38f9cb9eb..acadf6aa1 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
@@ -35,7 +35,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
     end
 
     if iszero(fr)
-        return build_solution(prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
+        return build_solution(
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
             left, right)
     end
 
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/brent.jl b/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
index f37c45e4a..89b2e60be 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
@@ -22,7 +22,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
     end
 
     if iszero(fr)
-        return build_solution(prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
+        return build_solution(
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
             left, right)
     end
 
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl b/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
index 86086f81a..896e07329 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
@@ -21,7 +21,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
     end
 
     if iszero(fr)
-        return build_solution(prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
+        return build_solution(
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
             left, right)
     end
 
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
index cce5eafea..3f2069b72 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
@@ -67,7 +67,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
     end
 
     if iszero(fr)
-        return build_solution(prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
+        return build_solution(
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
             left, right)
     end
     ϵ = abstol
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
index cd18060d5..3b23f4287 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
@@ -21,7 +21,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
     end
 
     if iszero(fr)
-        return build_solution(prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
+        return build_solution(
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
             left, right)
     end
 
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index 9f8896ed1..145a5467d 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -137,7 +137,8 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
         init_α = inv(alg.alpha)
     end
 
-    converged, res = __unrolled_lbroyden_initial_iterations(prob, xo, fo, δx, abstol, U, Vᵀ,
+    converged, res = __unrolled_lbroyden_initial_iterations(
+        prob, xo, fo, δx, abstol, U, Vᵀ,
         threshold, ls_cache, init_α)
 
     converged &&
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index dc6054273..005651568 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -1,7 +1,7 @@
 @testsetup module RootfindingTesting
 using Reexport
 @reexport using AllocCheck,
-    LinearSolve, StaticArrays, Random, LinearAlgebra, ForwardDiff, DiffEqBase
+                LinearSolve, StaticArrays, Random, LinearAlgebra, ForwardDiff, DiffEqBase
 import PolyesterForwardDiff
 
 quadratic_f(u, p) = u .* u .- p
@@ -22,7 +22,7 @@ end
 const TERMINATION_CONDITIONS = [
     NormTerminationMode(), RelTerminationMode(), RelNormTerminationMode(),
     AbsTerminationMode(), AbsNormTerminationMode(), RelSafeTerminationMode(),
-    AbsSafeTerminationMode(), RelSafeBestTerminationMode(), AbsSafeBestTerminationMode(),
+    AbsSafeTerminationMode(), RelSafeBestTerminationMode(), AbsSafeBestTerminationMode()
 ]
 
 function benchmark_nlsolve_oop(f::F, u0, p = 2.0; solver) where {F}
@@ -35,7 +35,7 @@ function benchmark_nlsolve_iip(f!::F, u0, p = 2.0; solver) where {F}
 end
 
 export quadratic_f, quadratic_f!, quadratic_f2, newton_fails, TERMINATION_CONDITIONS,
-    benchmark_nlsolve_oop, benchmark_nlsolve_iip
+       benchmark_nlsolve_oop, benchmark_nlsolve_iip
 
 end
 
@@ -43,7 +43,8 @@ end
     @testset "$(alg)" for alg in (SimpleNewtonRaphson, SimpleTrustRegion,
         (args...; kwargs...) -> SimpleTrustRegion(args...; nlsolve_update_rule = Val(true),
             kwargs...))
-        @testset "AutoDiff: $(nameof(typeof(autodiff))))" for autodiff in (AutoFiniteDiff(),
+        @testset "AutoDiff: $(nameof(typeof(autodiff))))" for autodiff in (
+            AutoFiniteDiff(),
             AutoForwardDiff(), AutoPolyesterForwardDiff())
             @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],
                 @SVector[1.0, 1.0], 1.0)

From 214fb0fd8e33963dbbd1940919fbdd9aa732b25c Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 9 Feb 2024 14:58:18 -0500
Subject: [PATCH 309/700] Dispatch didnot propagate problem kwargs

---
 lib/SimpleNonlinearSolve/Project.toml                | 2 +-
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index bf943823d..fdef9b8ee 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.4.1"
+version = "1.4.2"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 894195106..55b579e95 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -53,7 +53,7 @@ include("ad.jl")
 # Set the default bracketing method to ITP
 SciMLBase.solve(prob::IntervalNonlinearProblem; kwargs...) = solve(prob, ITP(); kwargs...)
 function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing, args...; kwargs...)
-    return solve(prob, ITP(), args...; kwargs...)
+    return solve(prob, ITP(), args...; prob.kwargs..., kwargs...)
 end
 
 # By Pass the highlevel checks for NonlinearProblem for Simple Algorithms
@@ -67,7 +67,7 @@ function SciMLBase.solve(
     new_p = p !== nothing ? p : prob.p
     return __internal_solve_up(
         prob, sensealg, new_u0, u0 === nothing, new_p, p === nothing,
-        alg, args...; kwargs...)
+        alg, args...; prob.kwargs..., kwargs...)
 end
 
 function __internal_solve_up(_prob::NonlinearProblem, sensealg, u0, u0_changed, p,

From 3e8ffd0309a2af7030b117a99927ab91d7f3a00a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 15 Feb 2024 11:06:29 -0500
Subject: [PATCH 310/700] Add a test for kwarg propagation

---
 lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl | 9 +++++++--
 1 file changed, 7 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index 005651568..f3ac188a9 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -120,14 +120,19 @@ end
     p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 
     @testset "$(nameof(typeof(alg)))" for alg in (SimpleDFSane(), SimpleTrustRegion(),
-        SimpleHalley(),
-        SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
+        SimpleHalley(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
         sol = benchmark_nlsolve_oop(newton_fails, u0, p; solver = alg)
         @test SciMLBase.successful_retcode(sol)
         @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
     end
 end
 
+@testitem "Kwargs Propagation" setup=[RootfindingTesting] begin
+    prob = NonlinearProblem(quadratic_f, ones(4), 2.0; maxiters = 2)
+    sol = solve(prob, SimpleNewtonRaphson())
+    @test sol.retcode === ReturnCode.MaxIters
+end
+
 @testitem "Allocation Checks" setup=[RootfindingTesting] begin
     @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(),
         SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),

From 05c80bb151a6714abdbd6de991c3ef8af4da6a10 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 15 Feb 2024 11:40:00 -0500
Subject: [PATCH 311/700] Dont fail fast

---
 lib/SimpleNonlinearSolve/.github/workflows/CI.yml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
index 8e0ab3bff..16ec1087c 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
@@ -10,6 +10,7 @@ jobs:
   test:
     runs-on: ${{ matrix.os }}
     strategy:
+      fail-fast: false
       matrix:
         group:
           - Core

From 05c6206a9f447f977eab033511ecf12d185db58c Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 14 Feb 2024 22:59:34 -0500
Subject: [PATCH 312/700] Static GPU compilation of Jacobian

---
 .../.buildkite/pipeline.yml                     |  2 +-
 lib/SimpleNonlinearSolve/Project.toml           |  2 +-
 lib/SimpleNonlinearSolve/src/utils.jl           | 17 ++++++++++++++---
 3 files changed, 16 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml b/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
index ef04f99a6..f95a8351f 100644
--- a/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
+++ b/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
@@ -13,7 +13,7 @@ steps:
     agents:
       queue: "juliagpu"
       cuda: "*"
-    timeout_in_minutes: 30
+    timeout_in_minutes: 120
     # Don't run Buildkite if the commit message includes the text [skip tests]
     if: build.message !~ /\[skip tests\]/
 
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index fdef9b8ee..4065b1fcf 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.4.2"
+version = "1.4.3"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 7390f5e3c..e89794b4c 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -40,17 +40,28 @@ function __pick_forwarddiff_chunk(x::StaticArray)
     end
 end
 
-function __get_jacobian_config(ad::AutoForwardDiff{CS}, f, x) where {CS}
+function __get_jacobian_config(ad::AutoForwardDiff{CS}, f::F, x) where {F, CS}
     ck = (CS === nothing || CS ≤ 0) ? __pick_forwarddiff_chunk(x) : ForwardDiff.Chunk{CS}()
     tag = __standard_tag(ad.tag, x)
-    return ForwardDiff.JacobianConfig(f, x, ck, tag)
+    return __forwarddiff_jacobian_config(f, x, ck, tag)
 end
-function __get_jacobian_config(ad::AutoForwardDiff{CS}, f!, y, x) where {CS}
+function __get_jacobian_config(ad::AutoForwardDiff{CS}, f!::F, y, x) where {F, CS}
     ck = (CS === nothing || CS ≤ 0) ? __pick_forwarddiff_chunk(x) : ForwardDiff.Chunk{CS}()
     tag = __standard_tag(ad.tag, x)
     return ForwardDiff.JacobianConfig(f!, y, x, ck, tag)
 end
 
+function __forwarddiff_jacobian_config(f::F, x, ck::ForwardDiff.Chunk, tag) where {F}
+    return ForwardDiff.JacobianConfig(f, x, ck, tag)
+end
+function __forwarddiff_jacobian_config(
+        f::F, x::SArray, ck::ForwardDiff.Chunk{N}, tag) where {F, N}
+    seeds = ForwardDiff.construct_seeds(ForwardDiff.Partials{N, eltype(x)})
+    duals = ForwardDiff.Dual{typeof(tag), eltype(x), N}.(x)
+    return ForwardDiff.JacobianConfig{typeof(tag), eltype(x), N, typeof(duals)}(seeds,
+        duals)
+end
+
 function __get_jacobian_config(ad::AutoPolyesterForwardDiff{CS}, args...) where {CS}
     x = last(args)
     return (CS === nothing || CS ≤ 0) ? __pick_forwarddiff_chunk(x) :

From 9203bc3216dd5866a93de10cd57916066071b1f9 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 16 Feb 2024 10:50:33 -0500
Subject: [PATCH 313/700] Julia version not allowed to be changed in patch
 release

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 4065b1fcf..58adfd46a 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.4.3"
+version = "1.5.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 36d4bb6b3da17424f7806c9ff49224e0c60c098b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 17 Feb 2024 10:21:55 -0500
Subject: [PATCH 314/700] Start wrapping NLSolvers

---
 Project.toml                      |  8 +++--
 ext/NonlinearSolveNLsolversExt.jl | 50 +++++++++++++++++++++++++++++++
 src/NonlinearSolve.jl             |  2 +-
 src/algorithms/extension_algs.jl  | 16 ++++++++++
 4 files changed, 73 insertions(+), 3 deletions(-)
 create mode 100644 ext/NonlinearSolveNLsolversExt.jl

diff --git a/Project.toml b/Project.toml
index 59b33a84d..e5afe2c2e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.5.6"
+version = "3.6.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -36,6 +36,7 @@ FixedPointAcceleration = "817d07cb-a79a-5c30-9a31-890123675176"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
 MINPACK = "4854310b-de5a-5eb6-a2a5-c1dee2bd17f9"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
+NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
 SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
 Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
@@ -48,6 +49,7 @@ NonlinearSolveFixedPointAccelerationExt = "FixedPointAcceleration"
 NonlinearSolveLeastSquaresOptimExt = "LeastSquaresOptim"
 NonlinearSolveMINPACKExt = "MINPACK"
 NonlinearSolveNLsolveExt = "NLsolve"
+NonlinearSolveNLSolversExt = "NLSolvers"
 NonlinearSolveSIAMFANLEquationsExt = "SIAMFANLEquations"
 NonlinearSolveSpeedMappingExt = "SpeedMapping"
 NonlinearSolveSymbolicsExt = "Symbolics"
@@ -77,6 +79,7 @@ LinearSolve = "2.21"
 MINPACK = "1.2"
 MaybeInplace = "0.1.1"
 NLsolve = "4.5"
+NLSolvers = "0.5"
 NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
 OrdinaryDiffEq = "6.63"
@@ -120,6 +123,7 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 MINPACK = "4854310b-de5a-5eb6-a2a5-c1dee2bd17f9"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
+NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
 NaNMath = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
 NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
@@ -139,4 +143,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "Enzyme", "BenchmarkTools", "SafeTestsets", "Pkg", "Test", "ForwardDiff", "StaticArrays", "Symbolics", "LinearSolve", "Random", "LinearAlgebra", "Zygote", "SparseDiffTools", "NonlinearProblemLibrary", "LeastSquaresOptim", "FastLevenbergMarquardt", "NaNMath", "BandedMatrices", "DiffEqBase", "StableRNGs", "MINPACK", "NLsolve", "OrdinaryDiffEq", "SpeedMapping", "FixedPointAcceleration", "SIAMFANLEquations", "Sundials", "ReTestItems", "Reexport", "CUDA"]
+test = ["Aqua", "Enzyme", "BenchmarkTools", "SafeTestsets", "Pkg", "Test", "ForwardDiff", "StaticArrays", "Symbolics", "LinearSolve", "Random", "LinearAlgebra", "Zygote", "SparseDiffTools", "NonlinearProblemLibrary", "LeastSquaresOptim", "FastLevenbergMarquardt", "NaNMath", "BandedMatrices", "DiffEqBase", "StableRNGs", "MINPACK", "NLsolve", "OrdinaryDiffEq", "SpeedMapping", "FixedPointAcceleration", "SIAMFANLEquations", "Sundials", "ReTestItems", "Reexport", "CUDA", "NLSolvers"]
diff --git a/ext/NonlinearSolveNLsolversExt.jl b/ext/NonlinearSolveNLsolversExt.jl
new file mode 100644
index 000000000..e8a1f849f
--- /dev/null
+++ b/ext/NonlinearSolveNLsolversExt.jl
@@ -0,0 +1,50 @@
+module NonlinearSolveNLSolversExt
+
+using NonlinearSolve, NLSolversJL, SciMLBase
+
+function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0::Bool = false,
+        termination_condition = nothing, kwargs...) where {StT, ShT}
+    NonlinearSolve.__test_termination_condition(termination_condition, :NLSolversJL)
+
+    if prob.u0 isa Number
+        error("Scalar Inputs for NLsolversJL is not yet handled.")
+    end
+
+    f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
+
+#     if prob.f.jac === nothing && alg.autodiff isa Symbol
+#         df = OnceDifferentiable(f!, u0, resid; alg.autodiff)
+#     else
+#         jac! = NonlinearSolve.__construct_extension_jac(prob, alg, u0, resid; alg.autodiff)
+#         if prob.f.jac_prototype === nothing
+#             J = similar(u0, promote_type(eltype(u0), eltype(resid)), length(u0),
+#                 length(resid))
+#         else
+#             J = zero(prob.f.jac_prototype)
+#         end
+#         df = OnceDifferentiable(f!, jac!, vec(u0), vec(resid), J)
+#     end
+
+#     abstol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u0))
+#     show_trace = ShT || alg.show_trace
+#     store_trace = StT || alg.store_trace
+#     extended_trace = !(trace_level isa TraceMinimal) || alg.extended_trace
+
+#     original = nlsolve(df, vec(u0); ftol = abstol, iterations = maxiters, alg.method,
+#         store_trace, extended_trace, alg.linesearch, alg.linsolve, alg.factor,
+#         alg.autoscale, alg.m, alg.beta, show_trace)
+
+#     f!(vec(resid), original.zero)
+#     u = prob.u0 isa Number ? original.zero[1] : reshape(original.zero, size(prob.u0))
+#     resid = prob.u0 isa Number ? resid[1] : resid
+
+#     retcode = original.x_converged || original.f_converged ? ReturnCode.Success :
+#               ReturnCode.Failure
+#     stats = SciMLBase.NLStats(original.f_calls, original.g_calls, original.g_calls,
+#         original.g_calls, original.iterations)
+
+#     return SciMLBase.build_solution(prob, alg, u, resid; retcode, original, stats)
+end
+
+end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index de46fe153..a84c9f4d6 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -144,7 +144,7 @@ export NonlinearSolvePolyAlgorithm,
        RobustMultiNewton, FastShortcutNonlinearPolyalg, FastShortcutNLLSPolyalg
 
 # Extension Algorithms
-export LeastSquaresOptimJL, FastLevenbergMarquardtJL, CMINPACK, NLsolveJL,
+export LeastSquaresOptimJL, FastLevenbergMarquardtJL, CMINPACK, NLsolveJL, NLSolversJL,
        FixedPointAccelerationJL, SpeedMappingJL, SIAMFANLEquationsJL
 
 # Advanced Algorithms -- Without Bells and Whistles
diff --git a/src/algorithms/extension_algs.jl b/src/algorithms/extension_algs.jl
index eeed0ea5b..a166b8987 100644
--- a/src/algorithms/extension_algs.jl
+++ b/src/algorithms/extension_algs.jl
@@ -281,6 +281,22 @@ function NLsolveJL(; method = :trust_region, autodiff = :central, store_trace =
         factor, autoscale, m, beta, show_trace)
 end
 
+@concrete struct NLSolversJL <: AbstractNonlinearSolveExtensionAlgorithm
+    method
+    autodiff
+
+    function NLSolversJL(method, autodiff)
+        if Base.get_extension(@__MODULE__, :NonlinearSolveNLsolversExt) === nothing
+            error("NLSolversJL requires NLSolvers.jl to be loaded")
+        end
+
+        return new{typeof(method), typeof(autodiff)}(method, autodiff)
+    end
+end
+
+NLSolversJL(method; autodiff = nothing) = NLSolversJL(method, autodiff)
+NLSolversJL(; method, autodiff = nothing) = NLSolversJL(method, autodiff)
+
 """
     SpeedMappingJL(; σ_min = 0.0, stabilize::Bool = false, check_obj::Bool = false,
         orders::Vector{Int} = [3, 3, 2], time_limit::Real = 1000)

From 9a6bdfb423a8b0311f7585091667edb37c36ea62 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 17 Feb 2024 15:56:44 -0500
Subject: [PATCH 315/700] Finish wrapping NLSolvers.jl

---
 docs/src/api/nlsolve.md                      |  2 +-
 docs/src/api/nlsolvers.md                    | 17 ++++
 docs/src/solvers/nonlinear_system_solvers.md |  9 +++
 ext/NonlinearSolveNLSolversExt.jl            | 84 ++++++++++++++++++++
 ext/NonlinearSolveNLsolversExt.jl            | 50 ------------
 src/algorithms/extension_algs.jl             | 24 +++++-
 test/wrappers/rootfind_tests.jl              | 26 ++++--
 7 files changed, 151 insertions(+), 61 deletions(-)
 create mode 100644 docs/src/api/nlsolvers.md
 create mode 100644 ext/NonlinearSolveNLSolversExt.jl
 delete mode 100644 ext/NonlinearSolveNLsolversExt.jl

diff --git a/docs/src/api/nlsolve.md b/docs/src/api/nlsolve.md
index 05db0937f..bea379953 100644
--- a/docs/src/api/nlsolve.md
+++ b/docs/src/api/nlsolve.md
@@ -7,7 +7,7 @@ using these solvers:
 ```julia
 using Pkg
 Pkg.add("NLsolve")
-using NLSolve, NonlinearSolve
+using NLsolve, NonlinearSolve
 ```
 
 ## Solver API
diff --git a/docs/src/api/nlsolvers.md b/docs/src/api/nlsolvers.md
new file mode 100644
index 000000000..a1cc72656
--- /dev/null
+++ b/docs/src/api/nlsolvers.md
@@ -0,0 +1,17 @@
+# NLSolvers.jl
+
+This is a extension for importing solvers from NLSolvers.jl into the SciML interface. Note
+that these solvers do not come by default, and thus one needs to install the package before
+using these solvers:
+
+```julia
+using Pkg
+Pkg.add("NLSolvers")
+using NLSolvers, NonlinearSolve
+```
+
+## Solver API
+
+```@docs
+NLSolversJL
+```
diff --git a/docs/src/solvers/nonlinear_system_solvers.md b/docs/src/solvers/nonlinear_system_solvers.md
index c0f4164c9..5b9e88e34 100644
--- a/docs/src/solvers/nonlinear_system_solvers.md
+++ b/docs/src/solvers/nonlinear_system_solvers.md
@@ -168,3 +168,12 @@ SIAMFANLEquations.jl is a wrapper for the methods in the SIAMFANLEquations.jl li
 Other solvers listed in [Fixed Point Solvers](@ref fixed_point_methods_full_list),
 [FastLevenbergMarquardt.jl](@ref fastlm_wrapper_summary) and
 [LeastSquaresOptim.jl](@ref lso_wrapper_summary) can also solve nonlinear systems.
+
+### NLSolvers.jl
+
+This is a wrapper package for importing solvers from NLSolvers.jl into the SciML interface.
+
+  - [`NLSolversJL()`](@ref): A wrapper for
+    [NLSolvers.jl](https://github.com/JuliaNLSolvers/NLSolvers.jl)
+
+For a list of possible solvers see the [NLSolvers.jl documentation](https://julianlsolvers.github.io/NLSolvers.jl/)
diff --git a/ext/NonlinearSolveNLSolversExt.jl b/ext/NonlinearSolveNLSolversExt.jl
new file mode 100644
index 000000000..fd75095c0
--- /dev/null
+++ b/ext/NonlinearSolveNLSolversExt.jl
@@ -0,0 +1,84 @@
+module NonlinearSolveNLSolversExt
+
+using ADTypes, FastClosures, NonlinearSolve, NLSolvers, SciMLBase, LinearAlgebra
+using FiniteDiff, ForwardDiff
+
+function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0::Bool = false,
+        termination_condition = nothing, kwargs...)
+    NonlinearSolve.__test_termination_condition(termination_condition, :NLSolversJL)
+
+    abstol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(prob.u0))
+    reltol = NonlinearSolve.DEFAULT_TOLERANCE(reltol, eltype(prob.u0))
+
+    options = NEqOptions(; maxiter = maxiters, f_abstol = abstol, f_reltol = reltol)
+
+    if prob.u0 isa Number
+        f_scalar = @closure x -> prob.f(x, prob.p)
+
+        if alg.autodiff === nothing
+            if ForwardDiff.can_dual(typeof(prob.u0))
+                autodiff_concrete = :forwarddiff
+            else
+                autodiff_concrete = :finitediff
+            end
+        else
+            if alg.autodiff isa AutoForwardDiff || alg.autodiff isa AutoPolyesterForwardDiff
+                autodiff_concrete = :forwarddiff
+            elseif alg.autodiff isa AutoFiniteDiff
+                autodiff_concrete = :finitediff
+            else
+                error("Only ForwardDiff or FiniteDiff autodiff is supported.")
+            end
+        end
+
+        if autodiff_concrete === :forwarddiff
+            fj_scalar = @closure (Jx, x) -> begin
+                T = typeof(NonlinearSolve.NonlinearSolveTag())
+                x_dual = ForwardDiff.Dual{T}(x, one(x))
+                y = prob.f(x_dual, prob.p)
+                return ForwardDiff.value(y), ForwardDiff.extract_derivative(T, y)
+            end
+        else
+            fj_scalar = @closure (Jx, x) -> begin
+                _f = Base.Fix2(prob.f, prob.p)
+                return _f(x), FiniteDiff.finite_difference_derivative(_f, x)
+            end
+        end
+
+        prob_obj = NLSolvers.ScalarObjective(; f = f_scalar, fg = fj_scalar)
+        prob_nlsolver = NEqProblem(prob_obj; inplace = false)
+        res = NLSolvers.solve(prob_nlsolver, prob.u0, alg.method, options)
+
+        retcode = ifelse(norm(res.info.best_residual, Inf) ≤ abstol, ReturnCode.Success,
+            ReturnCode.MaxIters)
+        stats = SciMLBase.NLStats(-1, -1, -1, -1, res.info.iter)
+
+        return SciMLBase.build_solution(prob, alg, res.info.solution,
+            res.info.best_residual; retcode, original = res, stats)
+    end
+
+    f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
+
+    jac! = NonlinearSolve.__construct_extension_jac(prob, alg, u0, resid; alg.autodiff)
+
+    FJ_vector! = @closure (Fx, Jx, x) -> begin
+        f!(Fx, x)
+        jac!(Jx, x)
+        return Fx, Jx
+    end
+
+    prob_obj = NLSolvers.VectorObjective(; F = f!, FJ = FJ_vector!)
+    prob_nlsolver = NEqProblem(prob_obj)
+
+    res = NLSolvers.solve(prob_nlsolver, u0, alg.method, options)
+
+    retcode = ifelse(norm(res.info.best_residual, Inf) ≤ abstol, ReturnCode.Success,
+        ReturnCode.MaxIters)
+    stats = SciMLBase.NLStats(-1, -1, -1, -1, res.info.iter)
+
+    return SciMLBase.build_solution(prob, alg, res.info.solution,
+        res.info.best_residual; retcode, original = res, stats)
+end
+
+end
diff --git a/ext/NonlinearSolveNLsolversExt.jl b/ext/NonlinearSolveNLsolversExt.jl
deleted file mode 100644
index e8a1f849f..000000000
--- a/ext/NonlinearSolveNLsolversExt.jl
+++ /dev/null
@@ -1,50 +0,0 @@
-module NonlinearSolveNLSolversExt
-
-using NonlinearSolve, NLSolversJL, SciMLBase
-
-function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0::Bool = false,
-        termination_condition = nothing, kwargs...) where {StT, ShT}
-    NonlinearSolve.__test_termination_condition(termination_condition, :NLSolversJL)
-
-    if prob.u0 isa Number
-        error("Scalar Inputs for NLsolversJL is not yet handled.")
-    end
-
-    f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
-
-#     if prob.f.jac === nothing && alg.autodiff isa Symbol
-#         df = OnceDifferentiable(f!, u0, resid; alg.autodiff)
-#     else
-#         jac! = NonlinearSolve.__construct_extension_jac(prob, alg, u0, resid; alg.autodiff)
-#         if prob.f.jac_prototype === nothing
-#             J = similar(u0, promote_type(eltype(u0), eltype(resid)), length(u0),
-#                 length(resid))
-#         else
-#             J = zero(prob.f.jac_prototype)
-#         end
-#         df = OnceDifferentiable(f!, jac!, vec(u0), vec(resid), J)
-#     end
-
-#     abstol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u0))
-#     show_trace = ShT || alg.show_trace
-#     store_trace = StT || alg.store_trace
-#     extended_trace = !(trace_level isa TraceMinimal) || alg.extended_trace
-
-#     original = nlsolve(df, vec(u0); ftol = abstol, iterations = maxiters, alg.method,
-#         store_trace, extended_trace, alg.linesearch, alg.linsolve, alg.factor,
-#         alg.autoscale, alg.m, alg.beta, show_trace)
-
-#     f!(vec(resid), original.zero)
-#     u = prob.u0 isa Number ? original.zero[1] : reshape(original.zero, size(prob.u0))
-#     resid = prob.u0 isa Number ? resid[1] : resid
-
-#     retcode = original.x_converged || original.f_converged ? ReturnCode.Success :
-#               ReturnCode.Failure
-#     stats = SciMLBase.NLStats(original.f_calls, original.g_calls, original.g_calls,
-#         original.g_calls, original.iterations)
-
-#     return SciMLBase.build_solution(prob, alg, u, resid; retcode, original, stats)
-end
-
-end
diff --git a/src/algorithms/extension_algs.jl b/src/algorithms/extension_algs.jl
index a166b8987..1821a7ef7 100644
--- a/src/algorithms/extension_algs.jl
+++ b/src/algorithms/extension_algs.jl
@@ -281,12 +281,28 @@ function NLsolveJL(; method = :trust_region, autodiff = :central, store_trace =
         factor, autoscale, m, beta, show_trace)
 end
 
-@concrete struct NLSolversJL <: AbstractNonlinearSolveExtensionAlgorithm
-    method
-    autodiff
+"""
+    NLSolversJL(method; autodiff = nothing)
+    NLSolversJL(; method, autodiff = nothing)
+
+Wrapper over NLSolvers.jl Nonlinear Equation Solvers. We automatically construct the
+jacobian function and supply it to the solver.
+
+### Arguments
+
+  - `method`: the choice of method for solving the nonlinear system. See the documentation
+    for NLSolvers.jl for more information.
+  - `autodiff`: the choice of method for generating the Jacobian. Defaults to `nothing`
+    which means that a default is selected according to the problem specification. Can be
+    any valid ADTypes.jl autodiff type (conditional on that backend being supported in
+    NonlinearSolve.jl).
+"""
+struct NLSolversJL{M, AD} <: AbstractNonlinearSolveExtensionAlgorithm
+    method::M
+    autodiff::AD
 
     function NLSolversJL(method, autodiff)
-        if Base.get_extension(@__MODULE__, :NonlinearSolveNLsolversExt) === nothing
+        if Base.get_extension(@__MODULE__, :NonlinearSolveNLSolversExt) === nothing
             error("NLSolversJL requires NLSolvers.jl to be loaded")
         end
 
diff --git a/test/wrappers/rootfind_tests.jl b/test/wrappers/rootfind_tests.jl
index 889fa8b57..0fa56d690 100644
--- a/test/wrappers/rootfind_tests.jl
+++ b/test/wrappers/rootfind_tests.jl
@@ -1,6 +1,9 @@
 @testsetup module WrapperRootfindImports
 using Reexport
-@reexport using LinearAlgebra, NLsolve, SIAMFANLEquations, MINPACK
+@reexport using LinearAlgebra
+import NLSolvers, NLsolve, SIAMFANLEquations, MINPACK
+
+export NLSolvers
 end
 
 @testitem "Steady State Problems" setup=[WrapperRootfindImports] begin
@@ -12,7 +15,8 @@ end
     u0 = zeros(2)
     prob_iip = SteadyStateProblem(f_iip, u0)
 
-    for alg in [NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+    for alg in [
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())), NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
         sol = solve(prob_iip, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
         @test maximum(abs, sol.resid) < 1e-6
@@ -23,7 +27,8 @@ end
     u0 = zeros(2)
     prob_oop = SteadyStateProblem(f_oop, u0)
 
-    for alg in [NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+    for alg in [
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())), NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
         sol = solve(prob_oop, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
         @test maximum(abs, sol.resid) < 1e-6
@@ -39,7 +44,8 @@ end
     u0 = zeros(2)
     prob_iip = NonlinearProblem{true}(f_iip, u0)
 
-    for alg in [NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+    for alg in [
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())), NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
         local sol
         sol = solve(prob_iip, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
@@ -50,7 +56,8 @@ end
     f_oop(u, p) = [2 - 2u[1], u[1] - 4u[2]]
     u0 = zeros(2)
     prob_oop = NonlinearProblem{false}(f_oop, u0)
-    for alg in [NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+    for alg in [
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())), NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
         local sol
         sol = solve(prob_oop, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
@@ -61,7 +68,10 @@ end
     f_tol(u, p) = u^2 - 2
     prob_tol = NonlinearProblem(f_tol, 1.0)
     for tol in [1e-1, 1e-3, 1e-6, 1e-10, 1e-15],
-        alg in [NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL(; method = :newton),
+        alg in [
+            NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
+            NLsolveJL(),
+            CMINPACK(), SIAMFANLEquationsJL(; method = :newton),
             SIAMFANLEquationsJL(; method = :pseudotransient),
             SIAMFANLEquationsJL(; method = :secant)]
 
@@ -107,6 +117,10 @@ end
 
     sol = solve(ProbN, NLsolveJL(); abstol = 1e-8)
     @test maximum(abs, sol.resid) < 1e-6
+    sol = solve(ProbN,
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking()));
+        abstol = 1e-8)
+    @test maximum(abs, sol.resid) < 1e-6
     sol = solve(ProbN, SIAMFANLEquationsJL(; method = :newton); abstol = 1e-8)
     @test maximum(abs, sol.resid) < 1e-6
     sol = solve(ProbN, SIAMFANLEquationsJL(; method = :pseudotransient); abstol = 1e-8)

From c7e10db5a2ed73791f7bec697c0d584732a0eeac Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 17 Feb 2024 22:06:30 -0500
Subject: [PATCH 316/700] Enable formatting with
 join_lines_based_on_source=false

---
 .JuliaFormatter.toml                          |   1 +
 docs/make.jl                                  |  24 ++-
 docs/pages.jl                                 |  63 ++----
 docs/src/basics/diagnostics_api.md            |   4 +-
 docs/src/basics/faq.md                        |  11 +-
 docs/src/basics/sparsity_detection.md         |  13 +-
 docs/src/index.md                             |  10 +-
 docs/src/tutorials/getting_started.md         |   4 +-
 docs/src/tutorials/large_systems.md           |  41 ++--
 docs/src/tutorials/modelingtoolkit.md         |  17 +-
 ...NonlinearSolveFastLevenbergMarquardtExt.jl |  24 +--
 ...NonlinearSolveFixedPointAccelerationExt.jl |  12 +-
 ext/NonlinearSolveLeastSquaresOptimExt.jl     |  17 +-
 ext/NonlinearSolveMINPACKExt.jl               |  19 +-
 ext/NonlinearSolveNLsolveExt.jl               |  18 +-
 ext/NonlinearSolveSIAMFANLEquationsExt.jl     |  50 ++---
 ext/NonlinearSolveSpeedMappingExt.jl          |  10 +-
 src/NonlinearSolve.jl                         |  19 +-
 src/abstract_types.jl                         |  70 ++++---
 src/algorithms/broyden.jl                     |  25 ++-
 src/algorithms/dfsane.jl                      |   4 +-
 src/algorithms/extension_algs.jl              |  48 +++--
 src/algorithms/gauss_newton.jl                |   4 +-
 src/algorithms/klement.jl                     |  13 +-
 src/algorithms/lbroyden.jl                    |  39 ++--
 src/algorithms/levenberg_marquardt.jl         |  51 ++---
 src/algorithms/pseudo_transient.jl            |  26 +--
 src/algorithms/raphson.jl                     |   4 +-
 src/algorithms/trust_region.jl                |  12 +-
 src/core/approximate_jacobian.jl              |  95 +++++----
 src/core/generalized_first_order.jl           |  73 ++++---
 src/core/generic.jl                           |  19 +-
 src/core/spectral_methods.jl                  |  29 ++-
 src/default.jl                                |  80 ++++----
 src/descent/damped_newton.jl                  |  37 ++--
 src/descent/dogleg.jl                         |  17 +-
 src/descent/geodesic_acceleration.jl          |  27 ++-
 src/descent/newton.jl                         |  40 ++--
 src/descent/steepest.jl                       |  14 +-
 src/globalization/line_search.jl              |  46 +++--
 src/globalization/trust_region.jl             |  86 ++++-----
 src/internal/approximate_initialization.jl    |  50 ++---
 src/internal/forward_diff.jl                  |  36 ++--
 src/internal/helpers.jl                       |  51 +++--
 src/internal/jacobian.jl                      |  32 ++--
 src/internal/linear_solve.jl                  |  30 +--
 src/internal/operators.jl                     |  43 ++---
 src/internal/termination.jl                   |  20 +-
 src/internal/tracing.jl                       |  51 ++---
 test/core/23_test_problems_tests.jl           |  10 +-
 test/core/forward_ad_tests.jl                 |  10 +-
 test/core/nlls_tests.jl                       |  30 ++-
 test/core/rootfind_tests.jl                   | 181 +++++++++---------
 test/gpu/core_tests.jl                        |   7 +-
 test/misc/bruss_tests.jl                      |  22 +--
 test/misc/matrix_resizing_tests.jl            |  12 +-
 test/misc/polyalg_tests.jl                    |   4 +-
 test/misc/qa_tests.jl                         |   4 +-
 test/runtests.jl                              |   3 +-
 test/wrappers/nlls_tests.jl                   |  31 ++-
 60 files changed, 897 insertions(+), 946 deletions(-)

diff --git a/.JuliaFormatter.toml b/.JuliaFormatter.toml
index 1768a1a7f..66c13bae3 100644
--- a/.JuliaFormatter.toml
+++ b/.JuliaFormatter.toml
@@ -2,3 +2,4 @@ style = "sciml"
 format_markdown = true
 annotate_untyped_fields_with_any = false
 format_docstrings = true
+join_lines_based_on_source = false
diff --git a/docs/make.jl b/docs/make.jl
index c42e05004..01b53ce8d 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,11 +1,11 @@
 using Documenter, DocumenterCitations
-using NonlinearSolve,
-      SimpleNonlinearSolve, Sundials, SteadyStateDiffEq, SciMLBase, DiffEqBase
+using NonlinearSolve, SimpleNonlinearSolve, Sundials, SteadyStateDiffEq, SciMLBase,
+      DiffEqBase
 
-cp(joinpath(@__DIR__, "Manifest.toml"), joinpath(@__DIR__, "src/assets/Manifest.toml"),
-    force = true)
-cp(joinpath(@__DIR__, "Project.toml"), joinpath(@__DIR__, "src/assets/Project.toml"),
-    force = true)
+cp(joinpath(@__DIR__, "Manifest.toml"),
+    joinpath(@__DIR__, "src/assets/Manifest.toml"), force = true)
+cp(joinpath(@__DIR__, "Project.toml"),
+    joinpath(@__DIR__, "src/assets/Project.toml"), force = true)
 
 include("pages.jl")
 
@@ -13,11 +13,15 @@ bib = CitationBibliography(joinpath(@__DIR__, "src", "refs.bib"))
 
 makedocs(; sitename = "NonlinearSolve.jl",
     authors = "Chris Rackauckas",
-    modules = [NonlinearSolve, SimpleNonlinearSolve, SteadyStateDiffEq, Sundials,
-        DiffEqBase, SciMLBase],
-    clean = true, doctest = false, linkcheck = true,
+    modules = [NonlinearSolve, SimpleNonlinearSolve,
+        SteadyStateDiffEq, Sundials, DiffEqBase, SciMLBase],
+    clean = true,
+    doctest = false,
+    linkcheck = true,
     linkcheck_ignore = ["https://twitter.com/ChrisRackauckas/status/1544743542094020615"],
-    checkdocs = :exports, warnonly = [:missing_docs], plugins = [bib],
+    checkdocs = :exports,
+    warnonly = [:missing_docs],
+    plugins = [bib],
     format = Documenter.HTML(assets = ["assets/favicon.ico", "assets/citations.css"],
         canonical = "https://docs.sciml.ai/NonlinearSolve/stable/"),
     pages)
diff --git a/docs/pages.jl b/docs/pages.jl
index 52791bc45..0706115f7 100644
--- a/docs/pages.jl
+++ b/docs/pages.jl
@@ -1,47 +1,26 @@
 # Put in a separate page so it can be used by SciMLDocs.jl
 
-pages = [
-    "index.md",
+pages = ["index.md",
     "Getting Started with Nonlinear Rootfinding in Julia" => "tutorials/getting_started.md",
-    "Tutorials" => Any["tutorials/code_optimization.md",
-        "tutorials/large_systems.md",
-        "tutorials/modelingtoolkit.md",
-        "tutorials/small_compile.md",
-        "tutorials/iterator_interface.md",
-        "tutorials/optimizing_parameterized_ode.md"],
-    "Basics" => Any["basics/nonlinear_problem.md",
-        "basics/nonlinear_functions.md",
-        "basics/solve.md",
-        "basics/nonlinear_solution.md",
-        "basics/autodiff.md",
-        "basics/termination_condition.md",
-        "basics/diagnostics_api.md",
-        "basics/sparsity_detection.md",
-        "basics/faq.md"],
+    "Tutorials" => Any["tutorials/code_optimization.md", "tutorials/large_systems.md",
+        "tutorials/modelingtoolkit.md", "tutorials/small_compile.md",
+        "tutorials/iterator_interface.md", "tutorials/optimizing_parameterized_ode.md"],
+    "Basics" => Any["basics/nonlinear_problem.md", "basics/nonlinear_functions.md",
+        "basics/solve.md", "basics/nonlinear_solution.md", "basics/autodiff.md",
+        "basics/termination_condition.md", "basics/diagnostics_api.md",
+        "basics/sparsity_detection.md", "basics/faq.md"],
     "Solver Summaries and Recommendations" => Any["solvers/nonlinear_system_solvers.md",
-        "solvers/bracketing_solvers.md",
-        "solvers/steady_state_solvers.md",
-        "solvers/nonlinear_least_squares_solvers.md",
-        "solvers/fixed_point_solvers.md"],
-    "Native Functionalities" => Any["native/solvers.md",
-        "native/simplenonlinearsolve.md",
-        "native/steadystatediffeq.md",
-        "native/descent.md",
-        "native/globalization.md",
-        "native/diagnostics.md"],
-    "Wrapped Solver APIs" => Any["api/fastlevenbergmarquardt.md",
-        "api/fixedpointacceleration.md",
-        "api/leastsquaresoptim.md",
-        "api/minpack.md",
-        "api/nlsolve.md",
-        "api/siamfanlequations.md",
-        "api/speedmapping.md",
-        "api/sundials.md"],
-    "Development Documentation" => ["devdocs/internal_interfaces.md",
-        "devdocs/linear_solve.md",
-        "devdocs/jacobian.md",
-        "devdocs/operators.md",
-        "devdocs/algorithm_helpers.md"],
+        "solvers/bracketing_solvers.md", "solvers/steady_state_solvers.md",
+        "solvers/nonlinear_least_squares_solvers.md", "solvers/fixed_point_solvers.md"],
+    "Native Functionalities" => Any["native/solvers.md", "native/simplenonlinearsolve.md",
+        "native/steadystatediffeq.md", "native/descent.md",
+        "native/globalization.md", "native/diagnostics.md"],
+    "Wrapped Solver APIs" => Any[
+        "api/fastlevenbergmarquardt.md", "api/fixedpointacceleration.md",
+        "api/leastsquaresoptim.md", "api/minpack.md", "api/nlsolve.md",
+        "api/siamfanlequations.md", "api/speedmapping.md", "api/sundials.md"],
+    "Development Documentation" => [
+        "devdocs/internal_interfaces.md", "devdocs/linear_solve.md",
+        "devdocs/jacobian.md", "devdocs/operators.md", "devdocs/algorithm_helpers.md"],
     "Release Notes" => "release_notes.md",
-    "References" => "references.md"
-]
+    "References" => "references.md"]
diff --git a/docs/src/basics/diagnostics_api.md b/docs/src/basics/diagnostics_api.md
index 993432a00..7da29c1f7 100644
--- a/docs/src/basics/diagnostics_api.md
+++ b/docs/src/basics/diagnostics_api.md
@@ -33,9 +33,7 @@ using ModelingToolkit, NonlinearSolve
 @parameters σ ρ β
 
 # Define a nonlinear system
-eqs = [0 ~ σ * (y - x),
-    0 ~ x * (ρ - z) - y,
-    0 ~ x * y - β * z]
+eqs = [0 ~ σ * (y - x), 0 ~ x * (ρ - z) - y, 0 ~ x * y - β * z]
 @named ns = NonlinearSystem(eqs, [x, y, z], [σ, ρ, β])
 
 u0 = [x => 1.0, y => 0.0, z => 0.0]
diff --git a/docs/src/basics/faq.md b/docs/src/basics/faq.md
index e40b57b33..265cee264 100644
--- a/docs/src/basics/faq.md
+++ b/docs/src/basics/faq.md
@@ -16,8 +16,8 @@ myfun(x, lv) = x * sin(x) - lv
 function f(out, levels, u0)
     for i in 1:N
         out[i] = solve(
-            IntervalNonlinearProblem{false}(IntervalNonlinearFunction{false}(myfun),
-                u0, levels[i]),
+            IntervalNonlinearProblem{false}(
+                IntervalNonlinearFunction{false}(myfun), u0, levels[i]),
             Falsi()).u
     end
 end
@@ -25,8 +25,7 @@ end
 function f2(out, levels, u0)
     for i in 1:N
         out[i] = solve(
-            NonlinearProblem{false}(NonlinearFunction{false}(myfun),
-                u0, levels[i]),
+            NonlinearProblem{false}(NonlinearFunction{false}(myfun), u0, levels[i]),
             SimpleNewtonRaphson()).u
     end
 end
@@ -75,8 +74,8 @@ be a Dual number. This causes the error. To fix it:
  1. Specify the `autodiff` to be `AutoFiniteDiff`
 
 ```@example dual_error_faq
-sol = solve(prob_oop, LevenbergMarquardt(; autodiff = AutoFiniteDiff()); maxiters = 10000,
-    abstol = 1e-8)
+sol = solve(prob_oop, LevenbergMarquardt(; autodiff = AutoFiniteDiff());
+    maxiters = 10000, abstol = 1e-8)
 ```
 
 This worked but, Finite Differencing is not the recommended approach in any scenario.
diff --git a/docs/src/basics/sparsity_detection.md b/docs/src/basics/sparsity_detection.md
index 222aebe19..208fc306e 100644
--- a/docs/src/basics/sparsity_detection.md
+++ b/docs/src/basics/sparsity_detection.md
@@ -23,12 +23,10 @@ Now you can help the solver further by providing the color vector. This can be d
 
 ```julia
 prob = NonlinearProblem(
-    NonlinearFunction(nlfunc; sparsity = jac_prototype,
-        colorvec = colorvec), x0)
+    NonlinearFunction(nlfunc; sparsity = jac_prototype, colorvec = colorvec), x0)
 # OR
 prob = NonlinearProblem(
-    NonlinearFunction(nlfunc; jac_prototype = jac_prototype,
-        colorvec = colorvec), x0)
+    NonlinearFunction(nlfunc; jac_prototype = jac_prototype, colorvec = colorvec), x0)
 ```
 
 If the `colorvec` is not provided, then it is computed on demand.
@@ -46,12 +44,11 @@ If you don't have a Sparse Jacobian Prototype, but you know the which sparsity d
 algorithm you want to use, then you can create your problem as follows:
 
 ```julia
-prob = NonlinearProblem(NonlinearFunction(nlfunc; sparsity = SymbolicsSparsityDetection()),
-    x0)  # Remember to have Symbolics.jl loaded
+prob = NonlinearProblem(
+    NonlinearFunction(nlfunc; sparsity = SymbolicsSparsityDetection()), x0)  # Remember to have Symbolics.jl loaded
 # OR
 prob = NonlinearProblem(
-    NonlinearFunction(nlfunc; sparsity = ApproximateJacobianSparsity()),
-    x0)
+    NonlinearFunction(nlfunc; sparsity = ApproximateJacobianSparsity()), x0)
 ```
 
 These Detection Algorithms are from [SparseDiffTools.jl](https://github.com/JuliaDiff/SparseDiffTools.jl),
diff --git a/docs/src/index.md b/docs/src/index.md
index b35f09f3a..bf1f52a43 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -84,9 +84,15 @@ using TOML
 using Markdown
 version = TOML.parse(read("../../Project.toml", String))["version"]
 name = TOML.parse(read("../../Project.toml", String))["name"]
-link_manifest = "https://github.com/SciML/" * name * ".jl/tree/gh-pages/v" * version *
+link_manifest = "https://github.com/SciML/" *
+                name *
+                ".jl/tree/gh-pages/v" *
+                version *
                 "/assets/Manifest.toml"
-link_project = "https://github.com/SciML/" * name * ".jl/tree/gh-pages/v" * version *
+link_project = "https://github.com/SciML/" *
+               name *
+               ".jl/tree/gh-pages/v" *
+               version *
                "/assets/Project.toml"
 Markdown.parse("""You can also download the
 [manifest]($link_manifest)
diff --git a/docs/src/tutorials/getting_started.md b/docs/src/tutorials/getting_started.md
index 26bf9faa9..d0729eeaf 100644
--- a/docs/src/tutorials/getting_started.md
+++ b/docs/src/tutorials/getting_started.md
@@ -180,8 +180,8 @@ be skipped for out of place problems):
 
 ```@example 1
 u0 = [0.0, 0.0]
-prob = NonlinearLeastSquaresProblem(NonlinearFunction(nlls!, resid_prototype = zeros(3)),
-    u0)
+prob = NonlinearLeastSquaresProblem(
+    NonlinearFunction(nlls!, resid_prototype = zeros(3)), u0)
 
 solve(prob)
 ```
diff --git a/docs/src/tutorials/large_systems.md b/docs/src/tutorials/large_systems.md
index aedd58445..19e7493d5 100644
--- a/docs/src/tutorials/large_systems.md
+++ b/docs/src/tutorials/large_systems.md
@@ -78,11 +78,10 @@ function brusselator_2d_loop(du, u, p)
         limit(j - 1, N)
         du[i, j, 1] = alpha * (u[im1, j, 1] + u[ip1, j, 1] + u[i, jp1, 1] + u[i, jm1, 1] -
                        4u[i, j, 1]) +
-                      B + u[i, j, 1]^2 * u[i, j, 2] - (A + 1) * u[i, j, 1] +
-                      brusselator_f(x, y)
+                      B +
+                      u[i, j, 1]^2 * u[i, j, 2] - (A + 1) * u[i, j, 1] + brusselator_f(x, y)
         du[i, j, 2] = alpha * (u[im1, j, 2] + u[ip1, j, 2] + u[i, jp1, 2] + u[i, jm1, 2] -
-                       4u[i, j, 2]) +
-                      A * u[i, j, 1] - u[i, j, 1]^2 * u[i, j, 2]
+                       4u[i, j, 2]) + A * u[i, j, 1] - u[i, j, 1]^2 * u[i, j, 2]
     end
 end
 p = (3.4, 1.0, 10.0, step(xyd_brusselator))
@@ -100,8 +99,8 @@ function init_brusselator_2d(xyd)
 end
 
 u0 = init_brusselator_2d(xyd_brusselator)
-prob_brusselator_2d = NonlinearProblem(brusselator_2d_loop, u0, p; abstol = 1e-10,
-    reltol = 1e-10)
+prob_brusselator_2d = NonlinearProblem(
+    brusselator_2d_loop, u0, p; abstol = 1e-10, reltol = 1e-10)
 ```
 
 ## Choosing Jacobian Types
@@ -140,11 +139,11 @@ using BenchmarkTools # for @btime
 @btime solve(prob_brusselator_2d,
     NewtonRaphson(; autodiff = AutoSparseForwardDiff(; chunksize = 32)));
 @btime solve(prob_brusselator_2d,
-    NewtonRaphson(; autodiff = AutoSparseForwardDiff(; chunksize = 32),
-        linsolve = KLUFactorization()));
+    NewtonRaphson(;
+        autodiff = AutoSparseForwardDiff(; chunksize = 32), linsolve = KLUFactorization()));
 @btime solve(prob_brusselator_2d,
-    NewtonRaphson(; autodiff = AutoSparseForwardDiff(; chunksize = 32),
-        linsolve = KrylovJL_GMRES()));
+    NewtonRaphson(;
+        autodiff = AutoSparseForwardDiff(; chunksize = 32), linsolve = KrylovJL_GMRES()));
 nothing # hide
 ```
 
@@ -164,8 +163,8 @@ kick out a sparse matrix with our pattern, that we can turn into our `jac_protot
 ```@example ill_conditioned_nlprob
 using Symbolics
 du0 = copy(u0)
-jac_sparsity = Symbolics.jacobian_sparsity((du, u) -> brusselator_2d_loop(du, u, p),
-    du0, u0)
+jac_sparsity = Symbolics.jacobian_sparsity(
+    (du, u) -> brusselator_2d_loop(du, u, p), du0, u0)
 ```
 
 Notice that Julia gives a nice print out of the sparsity pattern. That's neat, and would be
@@ -275,8 +274,8 @@ function algebraicmultigrid(W, du, u, p, t, newW, Plprev, Prprev, solverdata)
 end
 
 @btime solve(prob_brusselator_2d_sparse,
-    NewtonRaphson(linsolve = KrylovJL_GMRES(), precs = algebraicmultigrid,
-        concrete_jac = true));
+    NewtonRaphson(
+        linsolve = KrylovJL_GMRES(), precs = algebraicmultigrid, concrete_jac = true));
 nothing # hide
 ```
 
@@ -286,8 +285,8 @@ or with a Jacobi smoother:
 function algebraicmultigrid2(W, du, u, p, t, newW, Plprev, Prprev, solverdata)
     if newW === nothing || newW
         A = convert(AbstractMatrix, W)
-        Pl = AlgebraicMultigrid.aspreconditioner(AlgebraicMultigrid.ruge_stuben(A,
-            presmoother = AlgebraicMultigrid.Jacobi(rand(size(A, 1))),
+        Pl = AlgebraicMultigrid.aspreconditioner(AlgebraicMultigrid.ruge_stuben(
+            A, presmoother = AlgebraicMultigrid.Jacobi(rand(size(A, 1))),
             postsmoother = AlgebraicMultigrid.Jacobi(rand(size(A, 1)))))
     else
         Pl = Plprev
@@ -296,8 +295,8 @@ function algebraicmultigrid2(W, du, u, p, t, newW, Plprev, Prprev, solverdata)
 end
 
 @btime solve(prob_brusselator_2d_sparse,
-    NewtonRaphson(linsolve = KrylovJL_GMRES(), precs = algebraicmultigrid2,
-        concrete_jac = true));
+    NewtonRaphson(
+        linsolve = KrylovJL_GMRES(), precs = algebraicmultigrid2, concrete_jac = true));
 nothing # hide
 ```
 
@@ -309,12 +308,10 @@ sparsity detection. Let's compare the two by setting the sparsity detection algo
 
 ```@example ill_conditioned_nlprob
 prob_brusselator_2d_exact = NonlinearProblem(
-    NonlinearFunction(brusselator_2d_loop;
-        sparsity = SymbolicsSparsityDetection()),
+    NonlinearFunction(brusselator_2d_loop; sparsity = SymbolicsSparsityDetection()),
     u0, p; abstol = 1e-10, reltol = 1e-10)
 prob_brusselator_2d_approx = NonlinearProblem(
-    NonlinearFunction(brusselator_2d_loop;
-        sparsity = ApproximateJacobianSparsity()),
+    NonlinearFunction(brusselator_2d_loop; sparsity = ApproximateJacobianSparsity()),
     u0, p; abstol = 1e-10, reltol = 1e-10)
 
 @btime solve(prob_brusselator_2d_exact, NewtonRaphson());
diff --git a/docs/src/tutorials/modelingtoolkit.md b/docs/src/tutorials/modelingtoolkit.md
index 17dbc985e..845b727b7 100644
--- a/docs/src/tutorials/modelingtoolkit.md
+++ b/docs/src/tutorials/modelingtoolkit.md
@@ -12,14 +12,10 @@ using ModelingToolkit, NonlinearSolve
 @parameters σ ρ β
 
 # Define a nonlinear system
-eqs = [0 ~ σ * (y - x),
-    0 ~ x * (ρ - z) - y,
-    0 ~ x * y - β * z]
+eqs = [0 ~ σ * (y - x), 0 ~ x * (ρ - z) - y, 0 ~ x * y - β * z]
 @named ns = NonlinearSystem(eqs, [x, y, z], [σ, ρ, β])
 
-u0 = [x => 1.0,
-    y => 0.0,
-    z => 0.0]
+u0 = [x => 1.0, y => 0.0, z => 0.0]
 
 ps = [σ => 10.0
       ρ => 26.0
@@ -60,13 +56,8 @@ solved more simply. Let's take a look at a quick system:
 
 ```@example mtk
 @variables u1 u2 u3 u4 u5
-eqs = [
-    0 ~ u1 - sin(u5),
-    0 ~ u2 - cos(u1),
-    0 ~ u3 - hypot(u1, u2),
-    0 ~ u4 - hypot(u2, u3),
-    0 ~ u5 - hypot(u4, u1)
-]
+eqs = [0 ~ u1 - sin(u5), 0 ~ u2 - cos(u1), 0 ~ u3 - hypot(u1, u2),
+    0 ~ u4 - hypot(u2, u3), 0 ~ u5 - hypot(u4, u1)]
 @named sys = NonlinearSystem(eqs, [u1, u2, u3, u4, u5], [])
 ```
 
diff --git a/ext/NonlinearSolveFastLevenbergMarquardtExt.jl b/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
index 2cfb98020..6221883a7 100644
--- a/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
+++ b/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
@@ -20,11 +20,11 @@ end
 function SciMLBase.__solve(prob::Union{NonlinearLeastSquaresProblem, NonlinearProblem},
         alg::FastLevenbergMarquardtJL, args...; alias_u0 = false, abstol = nothing,
         reltol = nothing, maxiters = 1000, termination_condition = nothing, kwargs...)
-    NonlinearSolve.__test_termination_condition(termination_condition,
-        :FastLevenbergMarquardt)
+    NonlinearSolve.__test_termination_condition(
+        termination_condition, :FastLevenbergMarquardt)
 
-    fn, u, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0,
-        can_handle_oop = Val(prob.u0 isa SArray))
+    fn, u, resid = NonlinearSolve.__construct_extension_f(
+        prob; alias_u0, can_handle_oop = Val(prob.u0 isa SArray))
     f = if prob.u0 isa SArray
         @closure (u, p) -> fn(u)
     else
@@ -33,8 +33,8 @@ function SciMLBase.__solve(prob::Union{NonlinearLeastSquaresProblem, NonlinearPr
     abstol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u))
     reltol = NonlinearSolve.DEFAULT_TOLERANCE(reltol, eltype(u))
 
-    _jac_fn = NonlinearSolve.__construct_extension_jac(prob, alg, u, resid; alg.autodiff,
-        can_handle_oop = Val(prob.u0 isa SArray))
+    _jac_fn = NonlinearSolve.__construct_extension_jac(
+        prob, alg, u, resid; alg.autodiff, can_handle_oop = Val(prob.u0 isa SArray))
     jac_fn = if prob.u0 isa SArray
         @closure (u, p) -> _jac_fn(u)
     else
@@ -42,12 +42,12 @@ function SciMLBase.__solve(prob::Union{NonlinearLeastSquaresProblem, NonlinearPr
     end
 
     solver_kwargs = (; xtol = reltol, ftol = reltol, gtol = abstol, maxit = maxiters,
-        alg.factor, alg.factoraccept, alg.factorreject, alg.minscale, alg.maxscale,
-        alg.factorupdate, alg.minfactor, alg.maxfactor)
+        alg.factor, alg.factoraccept, alg.factorreject, alg.minscale,
+        alg.maxscale, alg.factorupdate, alg.minfactor, alg.maxfactor)
 
     if prob.u0 isa SArray
-        res, fx, info, iter, nfev, njev = FastLM.lmsolve(f, jac_fn, prob.u0;
-            solver_kwargs...)
+        res, fx, info, iter, nfev, njev = FastLM.lmsolve(
+            f, jac_fn, prob.u0; solver_kwargs...)
         LM, solver = nothing, nothing
     else
         J = prob.f.jac_prototype === nothing ? similar(u, length(resid), length(u)) :
@@ -55,8 +55,8 @@ function SciMLBase.__solve(prob::Union{NonlinearLeastSquaresProblem, NonlinearPr
         solver = _fast_lm_solver(alg, u)
         LM = FastLM.LMWorkspace(u, resid, J)
 
-        res, fx, info, iter, nfev, njev, LM, solver = FastLM.lmsolve!(f, jac_fn, LM;
-            solver, solver_kwargs...)
+        res, fx, info, iter, nfev, njev, LM, solver = FastLM.lmsolve!(
+            f, jac_fn, LM; solver, solver_kwargs...)
     end
 
     stats = SciMLBase.NLStats(nfev, njev, -1, -1, iter)
diff --git a/ext/NonlinearSolveFixedPointAccelerationExt.jl b/ext/NonlinearSolveFixedPointAccelerationExt.jl
index 0c8ff8371..9e7254886 100644
--- a/ext/NonlinearSolveFixedPointAccelerationExt.jl
+++ b/ext/NonlinearSolveFixedPointAccelerationExt.jl
@@ -4,13 +4,13 @@ using NonlinearSolve, FixedPointAcceleration, SciMLBase
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::FixedPointAccelerationJL, args...;
         abstol = nothing, maxiters = 1000, alias_u0::Bool = false,
-        show_trace::Val{PrintReports} = Val(false), termination_condition = nothing,
-        kwargs...) where {PrintReports}
-    NonlinearSolve.__test_termination_condition(termination_condition,
-        :FixedPointAccelerationJL)
+        show_trace::Val{PrintReports} = Val(false),
+        termination_condition = nothing, kwargs...) where {PrintReports}
+    NonlinearSolve.__test_termination_condition(
+        termination_condition, :FixedPointAccelerationJL)
 
-    f, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0,
-        make_fixed_point = Val(true), force_oop = Val(true))
+    f, u0, resid = NonlinearSolve.__construct_extension_f(
+        prob; alias_u0, make_fixed_point = Val(true), force_oop = Val(true))
     tol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u0))
 
     sol = fixed_point(f, u0; Algorithm = alg.algorithm, MaxIter = maxiters, MaxM = alg.m,
diff --git a/ext/NonlinearSolveLeastSquaresOptimExt.jl b/ext/NonlinearSolveLeastSquaresOptimExt.jl
index 6ce6eabd4..42ff7c9d3 100644
--- a/ext/NonlinearSolveLeastSquaresOptimExt.jl
+++ b/ext/NonlinearSolveLeastSquaresOptimExt.jl
@@ -29,8 +29,8 @@ end
 
 function SciMLBase.__init(prob::Union{NonlinearLeastSquaresProblem, NonlinearProblem},
         alg::LeastSquaresOptimJL, args...; alias_u0 = false, abstol = nothing,
-        show_trace::Val{ShT} = Val(false), trace_level = TraceMinimal(), reltol = nothing,
-        store_trace::Val{StT} = Val(false), maxiters = 1000,
+        show_trace::Val{ShT} = Val(false), trace_level = TraceMinimal(),
+        reltol = nothing, store_trace::Val{StT} = Val(false), maxiters = 1000,
         termination_condition = nothing, kwargs...) where {ShT, StT}
     NonlinearSolve.__test_termination_condition(termination_condition, :LeastSquaresOptim)
 
@@ -43,13 +43,16 @@ function SciMLBase.__init(prob::Union{NonlinearLeastSquaresProblem, NonlinearPro
             J = prob.f.jac_prototype, output_length = length(resid))
     else
         g! = NonlinearSolve.__construct_extension_jac(prob, alg, u, resid; alg.autodiff)
-        lsoprob = LSO.LeastSquaresProblem(; x = u, f!, y = resid, g!,
-            J = prob.f.jac_prototype, output_length = length(resid))
+        lsoprob = LSO.LeastSquaresProblem(;
+            x = u, f!, y = resid, g!, J = prob.f.jac_prototype,
+            output_length = length(resid))
     end
 
     allocated_prob = LSO.LeastSquaresProblemAllocated(lsoprob, _lso_solver(alg))
 
-    return LeastSquaresOptimJLCache(prob, alg, allocated_prob,
+    return LeastSquaresOptimJLCache(prob,
+        alg,
+        allocated_prob,
         (; x_tol = reltol, f_tol = abstol, g_tol = abstol, iterations = maxiters,
             show_trace = ShT, store_trace = StT, show_every = trace_level.print_frequency))
 end
@@ -61,8 +64,8 @@ function SciMLBase.solve!(cache::LeastSquaresOptimJLCache)
               (res.iterations ≥ maxiters ? ReturnCode.MaxIters :
                ReturnCode.ConvergenceFailure)
     stats = SciMLBase.NLStats(res.f_calls, res.g_calls, -1, -1, res.iterations)
-    return SciMLBase.build_solution(cache.prob, cache.alg, res.minimizer, res.ssr / 2;
-        retcode, original = res, stats)
+    return SciMLBase.build_solution(
+        cache.prob, cache.alg, res.minimizer, res.ssr / 2; retcode, original = res, stats)
 end
 
 end
diff --git a/ext/NonlinearSolveMINPACKExt.jl b/ext/NonlinearSolveMINPACKExt.jl
index 4465051ea..8be121c13 100644
--- a/ext/NonlinearSolveMINPACKExt.jl
+++ b/ext/NonlinearSolveMINPACKExt.jl
@@ -3,12 +3,11 @@ module NonlinearSolveMINPACKExt
 using MINPACK, NonlinearSolve, SciMLBase
 import FastClosures: @closure
 
-function SciMLBase.__solve(prob::Union{NonlinearLeastSquaresProblem,
-            NonlinearProblem},
-        alg::CMINPACK, args...; abstol = nothing, maxiters = 1000,
-        alias_u0::Bool = false, show_trace::Val{ShT} = Val(false),
-        store_trace::Val{StT} = Val(false), termination_condition = nothing,
-        kwargs...) where {ShT, StT}
+function SciMLBase.__solve(
+        prob::Union{NonlinearLeastSquaresProblem, NonlinearProblem}, alg::CMINPACK,
+        args...; abstol = nothing, maxiters = 1000, alias_u0::Bool = false,
+        show_trace::Val{ShT} = Val(false), store_trace::Val{StT} = Val(false),
+        termination_condition = nothing, kwargs...) where {ShT, StT}
     NonlinearSolve.__test_termination_condition(termination_condition, :CMINPACK)
 
     _f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
@@ -23,13 +22,13 @@ function SciMLBase.__solve(prob::Union{NonlinearLeastSquaresProblem,
     tol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u0))
 
     if alg.autodiff === missing && prob.f.jac === nothing
-        original = MINPACK.fsolve(f!, u0, m; tol, show_trace, tracing, method,
-            iterations = maxiters)
+        original = MINPACK.fsolve(
+            f!, u0, m; tol, show_trace, tracing, method, iterations = maxiters)
     else
         _jac! = NonlinearSolve.__construct_extension_jac(prob, alg, u0, resid; alg.autodiff)
         jac! = @closure (J, u) -> (_jac!(J, u); Cint(0))
-        original = MINPACK.fsolve(f!, jac!, u0, m; tol, show_trace, tracing, method,
-            iterations = maxiters)
+        original = MINPACK.fsolve(
+            f!, jac!, u0, m; tol, show_trace, tracing, method, iterations = maxiters)
     end
 
     u = original.x
diff --git a/ext/NonlinearSolveNLsolveExt.jl b/ext/NonlinearSolveNLsolveExt.jl
index 64886c021..2af1ab5a3 100644
--- a/ext/NonlinearSolveNLsolveExt.jl
+++ b/ext/NonlinearSolveNLsolveExt.jl
@@ -2,11 +2,11 @@ module NonlinearSolveNLsolveExt
 
 using NonlinearSolve, NLsolve, SciMLBase
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::NLsolveJL, args...;
-        abstol = nothing, maxiters = 1000, alias_u0::Bool = false,
-        termination_condition = nothing, store_trace::Val{StT} = Val(false),
-        show_trace::Val{ShT} = Val(false), trace_level = TraceMinimal(),
-        kwargs...) where {StT, ShT}
+function SciMLBase.__solve(
+        prob::NonlinearProblem, alg::NLsolveJL, args...; abstol = nothing,
+        maxiters = 1000, alias_u0::Bool = false, termination_condition = nothing,
+        store_trace::Val{StT} = Val(false), show_trace::Val{ShT} = Val(false),
+        trace_level = TraceMinimal(), kwargs...) where {StT, ShT}
     NonlinearSolve.__test_termination_condition(termination_condition, :NLsolveJL)
 
     f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
@@ -16,8 +16,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::NLsolveJL, args...;
     else
         jac! = NonlinearSolve.__construct_extension_jac(prob, alg, u0, resid; alg.autodiff)
         if prob.f.jac_prototype === nothing
-            J = similar(u0, promote_type(eltype(u0), eltype(resid)), length(u0),
-                length(resid))
+            J = similar(
+                u0, promote_type(eltype(u0), eltype(resid)), length(u0), length(resid))
         else
             J = zero(prob.f.jac_prototype)
         end
@@ -30,8 +30,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::NLsolveJL, args...;
     extended_trace = !(trace_level isa TraceMinimal) || alg.extended_trace
 
     original = nlsolve(df, vec(u0); ftol = abstol, iterations = maxiters, alg.method,
-        store_trace, extended_trace, alg.linesearch, alg.linsolve, alg.factor,
-        alg.autoscale, alg.m, alg.beta, show_trace)
+        store_trace, extended_trace, alg.linesearch, alg.linsolve,
+        alg.factor, alg.autoscale, alg.m, alg.beta, show_trace)
 
     f!(vec(resid), original.zero)
     u = prob.u0 isa Number ? original.zero[1] : reshape(original.zero, size(prob.u0))
diff --git a/ext/NonlinearSolveSIAMFANLEquationsExt.jl b/ext/NonlinearSolveSIAMFANLEquationsExt.jl
index c313477df..17fef4922 100644
--- a/ext/NonlinearSolveSIAMFANLEquationsExt.jl
+++ b/ext/NonlinearSolveSIAMFANLEquationsExt.jl
@@ -25,14 +25,14 @@ end
 # not interesting here.
 @inline function __siam_fanl_equations_stats_mapping(method, sol)
     ((method === :pseudotransient) || (method === :anderson)) && return nothing
-    return SciMLBase.NLStats(sum(sol.stats.ifun), sum(sol.stats.ijac), 0, 0,
-        sum(sol.stats.iarm))
+    return SciMLBase.NLStats(
+        sum(sol.stats.ifun), sum(sol.stats.ijac), 0, 0, sum(sol.stats.iarm))
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SIAMFANLEquationsJL, args...;
-        abstol = nothing, reltol = nothing, alias_u0::Bool = false, maxiters = 1000,
-        termination_condition = nothing, show_trace::Val{ShT} = Val(false),
-        kwargs...) where {ShT}
+        abstol = nothing, reltol = nothing, alias_u0::Bool = false,
+        maxiters = 1000, termination_condition = nothing,
+        show_trace::Val{ShT} = Val(false), kwargs...) where {ShT}
     NonlinearSolve.__test_termination_condition(termination_condition, :SIAMFANLEquationsJL)
 
     (; method, delta, linsolve, m, beta) = alg
@@ -45,19 +45,19 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SIAMFANLEquationsJL, arg
         if method == :newton
             sol = nsolsc(f, prob.u0; maxit = maxiters, atol, rtol, printerr = ShT)
         elseif method == :pseudotransient
-            sol = ptcsolsc(f, prob.u0; delta0 = delta, maxit = maxiters, atol, rtol,
-                printerr = ShT)
+            sol = ptcsolsc(
+                f, prob.u0; delta0 = delta, maxit = maxiters, atol, rtol, printerr = ShT)
         elseif method == :secant
             sol = secant(f, prob.u0; maxit = maxiters, atol, rtol, printerr = ShT)
         elseif method == :anderson
-            f_aa, u, _ = NonlinearSolve.__construct_extension_f(prob; alias_u0,
-                make_fixed_point = Val(true))
-            sol = aasol(f_aa, u, m, __zeros_like(u, 1, 2 * m + 4); maxit = maxiters,
-                atol, rtol, beta)
+            f_aa, u, _ = NonlinearSolve.__construct_extension_f(
+                prob; alias_u0, make_fixed_point = Val(true))
+            sol = aasol(f_aa, u, m, __zeros_like(u, 1, 2 * m + 4);
+                maxit = maxiters, atol, rtol, beta)
         end
     else
-        f, u, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0,
-            make_fixed_point = Val(method == :anderson))
+        f, u, resid = NonlinearSolve.__construct_extension_f(
+            prob; alias_u0, make_fixed_point = Val(method == :anderson))
         N = length(u)
         FS = __zeros_like(u, N)
 
@@ -67,34 +67,34 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SIAMFANLEquationsJL, arg
             JVS = linsolve == :gmres ? __zeros_like(u, N, 3) : __zeros_like(u, N)
             linsolve_alg = String(linsolve)
             if method == :newton
-                sol = nsoli(f, u, FS, JVS; lsolver = linsolve_alg, maxit = maxiters, atol,
-                    rtol, printerr = ShT)
+                sol = nsoli(f, u, FS, JVS; lsolver = linsolve_alg,
+                    maxit = maxiters, atol, rtol, printerr = ShT)
             elseif method == :pseudotransient
-                sol = ptcsoli(f, u, FS, JVS; lsolver = linsolve_alg, maxit = maxiters,
-                    atol, rtol, printerr = ShT)
+                sol = ptcsoli(f, u, FS, JVS; lsolver = linsolve_alg,
+                    maxit = maxiters, atol, rtol, printerr = ShT)
             end
         else
             if prob.f.jac === nothing && alg.autodiff === missing
                 FPS = __zeros_like(u, N, N)
                 if method == :newton
-                    sol = nsol(f, u, FS, FPS; sham = 1, atol, rtol, maxit = maxiters,
-                        printerr = ShT)
+                    sol = nsol(f, u, FS, FPS; sham = 1, atol, rtol,
+                        maxit = maxiters, printerr = ShT)
                 elseif method == :pseudotransient
                     sol = ptcsol(f, u, FS, FPS; atol, rtol, maxit = maxiters,
                         delta0 = delta, printerr = ShT)
                 elseif method == :anderson
-                    sol = aasol(f, u, m, zeros(T, N, 2 * m + 4); atol, rtol,
-                        maxit = maxiters, beta)
+                    sol = aasol(
+                        f, u, m, zeros(T, N, 2 * m + 4); atol, rtol, maxit = maxiters, beta)
                 end
             else
                 FPS = prob.f.jac_prototype !== nothing ? zero(prob.f.jac_prototype) :
                       __zeros_like(u, N, N)
-                jac = NonlinearSolve.__construct_extension_jac(prob, alg, u, resid;
-                    alg.autodiff)
+                jac = NonlinearSolve.__construct_extension_jac(
+                    prob, alg, u, resid; alg.autodiff)
                 AJ! = @closure (J, u, x) -> jac(J, x)
                 if method == :newton
-                    sol = nsol(f, u, FS, FPS, AJ!; sham = 1, atol, rtol, maxit = maxiters,
-                        printerr = ShT)
+                    sol = nsol(f, u, FS, FPS, AJ!; sham = 1, atol,
+                        rtol, maxit = maxiters, printerr = ShT)
                 elseif method == :pseudotransient
                     sol = ptcsol(f, u, FS, FPS, AJ!; atol, rtol, maxit = maxiters,
                         delta0 = delta, printerr = ShT)
diff --git a/ext/NonlinearSolveSpeedMappingExt.jl b/ext/NonlinearSolveSpeedMappingExt.jl
index 23f1cba98..286b2577c 100644
--- a/ext/NonlinearSolveSpeedMappingExt.jl
+++ b/ext/NonlinearSolveSpeedMappingExt.jl
@@ -3,13 +3,13 @@ module NonlinearSolveSpeedMappingExt
 using NonlinearSolve, SciMLBase, SpeedMapping
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SpeedMappingJL, args...;
-        abstol = nothing, maxiters = 1000, alias_u0::Bool = false, maxtime = nothing,
-        store_trace::Val{store_info} = Val(false), termination_condition = nothing,
-        kwargs...) where {store_info}
+        abstol = nothing, maxiters = 1000, alias_u0::Bool = false,
+        maxtime = nothing, store_trace::Val{store_info} = Val(false),
+        termination_condition = nothing, kwargs...) where {store_info}
     NonlinearSolve.__test_termination_condition(termination_condition, :SpeedMappingJL)
 
-    m!, u, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0,
-        make_fixed_point = Val(true))
+    m!, u, resid = NonlinearSolve.__construct_extension_f(
+        prob; alias_u0, make_fixed_point = Val(true))
     tol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u))
 
     time_limit = ifelse(maxtime === nothing, alg.time_limit, maxtime)
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index de46fe153..e30ce530c 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -90,15 +90,15 @@ include("default.jl")
         push!(probs_nls, NonlinearProblem(fn, T.(u0), T(2)))
     end
 
-    nls_algs = (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(), PseudoTransient(),
-        Broyden(), Klement(), DFSane(), nothing)
+    nls_algs = (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
+        PseudoTransient(), Broyden(), Klement(), DFSane(), nothing)
 
     probs_nlls = NonlinearLeastSquaresProblem[]
     nlfuncs = ((NonlinearFunction{false}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
         (NonlinearFunction{false}((u, p) -> vcat(u .* u .- p, u .* u .- p)), [0.1, 0.1]),
         (
-            NonlinearFunction{true}((du, u, p) -> du[1] = u[1] * u[1] - p,
-                resid_prototype = zeros(1)),
+            NonlinearFunction{true}(
+                (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(1)),
             [0.1, 0.0]),
         (
             NonlinearFunction{true}((du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p),
@@ -111,8 +111,8 @@ include("default.jl")
         (NonlinearFunction{false}((u, p) -> vcat(u .* u .- p, u .* u .- p)),
             Float32[0.1, 0.1]),
         (
-            NonlinearFunction{true}((du, u, p) -> du[1] = u[1] * u[1] - p,
-                resid_prototype = zeros(Float32, 1)),
+            NonlinearFunction{true}(
+                (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(Float32, 1)),
             Float32[0.1, 0.0]),
         (
             NonlinearFunction{true}((du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p),
@@ -140,8 +140,8 @@ end
 # Core Algorithms
 export NewtonRaphson, PseudoTransient, Klement, Broyden, LimitedMemoryBroyden, DFSane
 export GaussNewton, LevenbergMarquardt, TrustRegion
-export NonlinearSolvePolyAlgorithm,
-       RobustMultiNewton, FastShortcutNonlinearPolyalg, FastShortcutNLLSPolyalg
+export NonlinearSolvePolyAlgorithm, RobustMultiNewton, FastShortcutNonlinearPolyalg,
+       FastShortcutNLLSPolyalg
 
 # Extension Algorithms
 export LeastSquaresOptimJL, FastLevenbergMarquardtJL, CMINPACK, NLsolveJL,
@@ -151,8 +151,7 @@ export LeastSquaresOptimJL, FastLevenbergMarquardtJL, CMINPACK, NLsolveJL,
 export GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm, GeneralizedDFSane
 
 # Descent Algorithms
-export NewtonDescent, SteepestDescent, Dogleg, DampedNewtonDescent,
-       GeodesicAcceleration
+export NewtonDescent, SteepestDescent, Dogleg, DampedNewtonDescent, GeodesicAcceleration
 
 # Globalization
 ## Line Search Algorithms
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 1b30f2b9f..b7127cb2c 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -16,15 +16,15 @@ squares solver.
 ### `__internal_init` specification
 
 ```julia
+__internal_init(prob::NonlinearProblem{uType, iip}, alg::AbstractDescentAlgorithm, J,
+    fu, u; pre_inverted::Val{INV} = Val(false), linsolve_kwargs = (;),
+    abstol = nothing, reltol = nothing, alias_J::Bool = true,
+    shared::Val{N} = Val(1), kwargs...) where {INV, N, uType, iip} --> AbstractDescentCache
+
 __internal_init(
-    prob::NonlinearProblem{uType, iip}, alg::AbstractDescentAlgorithm, J, fu, u;
-    pre_inverted::Val{INV} = Val(false), linsolve_kwargs = (;), abstol = nothing,
-    reltol = nothing, alias_J::Bool = true, shared::Val{N} = Val(1),
-    kwargs...) where {INV, N, uType, iip} --> AbstractDescentCache
-
-__internal_init(prob::NonlinearLeastSquaresProblem{uType, iip},
-    alg::AbstractDescentAlgorithm, J, fu, u; pre_inverted::Val{INV} = Val(false),
-    linsolve_kwargs = (;), abstol = nothing, reltol = nothing, alias_J::Bool = true,
+    prob::NonlinearLeastSquaresProblem{uType, iip}, alg::AbstractDescentAlgorithm,
+    J, fu, u; pre_inverted::Val{INV} = Val(false), linsolve_kwargs = (;),
+    abstol = nothing, reltol = nothing, alias_J::Bool = true,
     shared::Val{N} = Val(1), kwargs...) where {INV, N, uType, iip} --> AbstractDescentCache
 ```
 
@@ -66,8 +66,8 @@ Abstract Type for all Descent Caches.
 ### `__internal_solve!` specification
 
 ```julia
-δu, success, intermediates = __internal_solve!(cache::AbstractDescentCache, J, fu, u,
-    idx::Val; skip_solve::Bool = false, kwargs...)
+δu, success, intermediates = __internal_solve!(
+    cache::AbstractDescentCache, J, fu, u, idx::Val; skip_solve::Bool = false, kwargs...)
 ```
 
   - `J`: Jacobian or Inverse Jacobian (if `pre_inverted = Val(true)`).
@@ -119,10 +119,10 @@ Abstract Type for all Line Search Algorithms used in NonlinearSolve.jl.
 ### `__internal_init` specification
 
 ```julia
-__internal_init(prob::AbstractNonlinearProblem,
-    alg::AbstractNonlinearSolveLineSearchAlgorithm, f::F, fu, u, p, args...;
-    internalnorm::IN = DEFAULT_NORM,
-    kwargs...) where {F, IN} --> AbstractNonlinearSolveLineSearchCache
+__internal_init(
+    prob::AbstractNonlinearProblem, alg::AbstractNonlinearSolveLineSearchAlgorithm, f::F,
+    fu, u, p, args...; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN} -->
+AbstractNonlinearSolveLineSearchCache
 ```
 """
 abstract type AbstractNonlinearSolveLineSearchAlgorithm end
@@ -145,8 +145,8 @@ Returns 2 values:
 """
 abstract type AbstractNonlinearSolveLineSearchCache end
 
-function reinit_cache!(cache::AbstractNonlinearSolveLineSearchCache, args...; p = cache.p,
-        kwargs...)
+function reinit_cache!(
+        cache::AbstractNonlinearSolveLineSearchCache, args...; p = cache.p, kwargs...)
     cache.nf[] = 0
     cache.p = p
 end
@@ -233,10 +233,9 @@ Abstract Type for Damping Functions in DampedNewton.
 ### `__internal_init` specification
 
 ```julia
-__internal_init(
-    prob::AbstractNonlinearProblem, f::AbstractDampingFunction, initial_damping,
-    J, fu, u, args...; internal_norm = DEFAULT_NORM,
-    kwargs...) --> AbstractDampingFunctionCache
+__internal_init(prob::AbstractNonlinearProblem, f::AbstractDampingFunction, initial_damping,
+    J, fu, u, args...; internal_norm = DEFAULT_NORM, kwargs...) -->
+AbstractDampingFunctionCache
 ```
 
 Returns a [`AbstractDampingFunctionCache`](@ref).
@@ -318,9 +317,8 @@ Abstract Type for all Jacobian Initialization Algorithms used in NonlinearSolve.
 ### `__internal_init` specification
 
 ```julia
-__internal_init(prob::AbstractNonlinearProblem, alg::AbstractJacobianInitialization,
-    solver, f::F, fu, u, p; linsolve = missing, internalnorm::IN = DEFAULT_NORM,
-    kwargs...)
+__internal_init(prob::AbstractNonlinearProblem, alg::AbstractJacobianInitialization, solver,
+    f::F, fu, u, p; linsolve = missing, internalnorm::IN = DEFAULT_NORM, kwargs...)
 ```
 
 Returns a [`NonlinearSolve.InitializedApproximateJacobianCache`](@ref).
@@ -353,10 +351,10 @@ Abstract Type for all Approximate Jacobian Update Rules used in NonlinearSolve.j
 ### `__internal_init` specification
 
 ```julia
-__internal_init(prob::AbstractNonlinearProblem,
-    alg::AbstractApproximateJacobianUpdateRule, J, fu, u, du, args...;
-    internalnorm::F = DEFAULT_NORM,
-    kwargs...) where {F} --> AbstractApproximateJacobianUpdateRuleCache{INV}
+__internal_init(
+    prob::AbstractNonlinearProblem, alg::AbstractApproximateJacobianUpdateRule, J,
+    fu, u, du, args...; internalnorm::F = DEFAULT_NORM, kwargs...) where {F} -->
+AbstractApproximateJacobianUpdateRuleCache{INV}
 ```
 """
 abstract type AbstractApproximateJacobianUpdateRule{INV} end
@@ -375,8 +373,8 @@ Abstract Type for all Approximate Jacobian Update Rule Caches used in NonlinearS
 ### `__internal_solve!` specification
 
 ```julia
-__internal_solve!(cache::AbstractApproximateJacobianUpdateRuleCache, J, fu, u, du;
-    kwargs...) --> J / J⁻¹
+__internal_solve!(
+    cache::AbstractApproximateJacobianUpdateRuleCache, J, fu, u, du; kwargs...) --> J / J⁻¹
 ```
 """
 abstract type AbstractApproximateJacobianUpdateRuleCache{INV} end
@@ -391,8 +389,8 @@ Condition for resetting the Jacobian in Quasi-Newton's methods.
 ### `__internal_init` specification
 
 ```julia
-__internal_init(alg::AbstractResetCondition, J, fu, u, du, args...;
-    kwargs...) --> ResetCache
+__internal_init(alg::AbstractResetCondition, J, fu, u, du, args...; kwargs...) -->
+ResetCache
 ```
 
 ### `__internal_solve!` specification
@@ -411,9 +409,9 @@ Abstract Type for all Trust Region Methods used in NonlinearSolve.jl.
 ### `__internal_init` specification
 
 ```julia
-__internal_init(prob::AbstractNonlinearProblem, alg::AbstractTrustRegionMethod,
-    f::F, fu, u, p, args...; internalnorm::IF = DEFAULT_NORM,
-    kwargs...) where {F, IF} --> AbstractTrustRegionMethodCache
+__internal_init(prob::AbstractNonlinearProblem, alg::AbstractTrustRegionMethod, f::F, fu, u,
+    p, args...; internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF} -->
+AbstractTrustRegionMethodCache
 ```
 """
 abstract type AbstractTrustRegionMethod end
@@ -468,8 +466,8 @@ abstract type AbstractNonlinearSolveTraceLevel end
 
 # Default Printing
 for aType in (AbstractTrustRegionMethod, AbstractNonlinearSolveLineSearchAlgorithm,
-    AbstractResetCondition, AbstractApproximateJacobianUpdateRule, AbstractDampingFunction,
-    AbstractNonlinearSolveExtensionAlgorithm)
+    AbstractResetCondition, AbstractApproximateJacobianUpdateRule,
+    AbstractDampingFunction, AbstractNonlinearSolveExtensionAlgorithm)
     @eval function Base.show(io::IO, alg::$(aType))
         print(io, "$(nameof(typeof(alg)))()")
     end
diff --git a/src/algorithms/broyden.jl b/src/algorithms/broyden.jl
index bd3b490e4..679897efa 100644
--- a/src/algorithms/broyden.jl
+++ b/src/algorithms/broyden.jl
@@ -28,10 +28,9 @@ search.
         useful for specific problems, but whether it will work may depend strongly on the
         problem
 """
-function Broyden(;
-        max_resets = 100, linesearch = NoLineSearch(), reset_tolerance = nothing,
-        init_jacobian::Val{IJ} = Val(:identity), autodiff = nothing, alpha = nothing,
-        update_rule::Val{UR} = Val(:good_broyden)) where {IJ, UR}
+function Broyden(; max_resets = 100, linesearch = NoLineSearch(), reset_tolerance = nothing,
+        init_jacobian::Val{IJ} = Val(:identity), autodiff = nothing,
+        alpha = nothing, update_rule::Val{UR} = Val(:good_broyden)) where {IJ, UR}
     if IJ === :identity
         if UR === :diagonal
             initialization = IdentityInitialization(alpha, DiagonalStructure())
@@ -56,9 +55,9 @@ function Broyden(;
                              or `:diagonal`"))
     end
 
-    return ApproximateJacobianSolveAlgorithm{IJ === :true_jacobian, :Broyden}(; linesearch,
-        descent = NewtonDescent(), update_rule, max_resets, initialization,
-        reinit_rule = NoChangeInStateReset(; reset_tolerance))
+    return ApproximateJacobianSolveAlgorithm{IJ === :true_jacobian, :Broyden}(;
+        linesearch, descent = NewtonDescent(), update_rule, max_resets,
+        initialization, reinit_rule = NoChangeInStateReset(; reset_tolerance))
 end
 
 # Checks for no significant change for `nsteps`
@@ -107,8 +106,8 @@ function __internal_init(alg::NoChangeInStateReset, J, fu, u, du, args...; kwarg
     end
     T = real(eltype(u))
     tol = alg.reset_tolerance === nothing ? eps(T)^(3 // 4) : T(alg.reset_tolerance)
-    return NoChangeInStateResetCache(dfu, tol, alg.check_du, alg.check_dfu, alg.nsteps, 0,
-        0)
+    return NoChangeInStateResetCache(
+        dfu, tol, alg.check_du, alg.check_dfu, alg.nsteps, 0, 0)
 end
 
 function __internal_solve!(cache::NoChangeInStateResetCache, J, fu, u, du)
@@ -170,8 +169,8 @@ Broyden Update Rule corresponding to "good broyden's method" [broyden1965class](
 end
 
 function __internal_init(prob::AbstractNonlinearProblem,
-        alg::Union{GoodBroydenUpdateRule, BadBroydenUpdateRule}, J, fu, u, du, args...;
-        internalnorm::F = DEFAULT_NORM, kwargs...) where {F}
+        alg::Union{GoodBroydenUpdateRule, BadBroydenUpdateRule}, J, fu, u,
+        du, args...; internalnorm::F = DEFAULT_NORM, kwargs...) where {F}
     @bb J⁻¹dfu = similar(u)
     @bb dfu = copy(fu)
     if alg isa GoodBroydenUpdateRule || J isa Diagonal
@@ -206,8 +205,8 @@ function __internal_solve!(cache::BroydenUpdateRuleCache{mode}, J⁻¹, fu, u, d
     return J⁻¹
 end
 
-function __internal_solve!(cache::BroydenUpdateRuleCache{mode}, J⁻¹::Diagonal, fu, u,
-        du) where {mode}
+function __internal_solve!(
+        cache::BroydenUpdateRuleCache{mode}, J⁻¹::Diagonal, fu, u, du) where {mode}
     T = eltype(u)
     @bb @. cache.dfu = fu - cache.dfu
     J⁻¹_diag = _restructure(cache.dfu, diag(J⁻¹))
diff --git a/src/algorithms/dfsane.jl b/src/algorithms/dfsane.jl
index 9122fb6a1..b42544055 100644
--- a/src/algorithms/dfsane.jl
+++ b/src/algorithms/dfsane.jl
@@ -20,7 +20,7 @@ function DFSane(; σ_min = 1 // 10^10, σ_max = 1e10, σ_1 = 1, M::Int = 10, γ
         τ_min = 1 // 10, τ_max = 1 // 2, n_exp::Int = 2, max_inner_iterations::Int = 100,
         η_strategy::ETA = (fn_1, n, x_n, f_n) -> fn_1 / n^2) where {ETA}
     linesearch = RobustNonMonotoneLineSearch(;
-        gamma = γ, sigma_1 = σ_1, M, tau_min = τ_min,
-        tau_max = τ_max, n_exp, η_strategy, maxiters = max_inner_iterations)
+        gamma = γ, sigma_1 = σ_1, M, tau_min = τ_min, tau_max = τ_max,
+        n_exp, η_strategy, maxiters = max_inner_iterations)
     return GeneralizedDFSane{:DFSane}(linesearch, σ_min, σ_max, nothing)
 end
diff --git a/src/algorithms/extension_algs.jl b/src/algorithms/extension_algs.jl
index eeed0ea5b..673af5314 100644
--- a/src/algorithms/extension_algs.jl
+++ b/src/algorithms/extension_algs.jl
@@ -80,10 +80,10 @@ see the documentation for `FastLevenbergMarquardt.jl`.
     maxfactor
 end
 
-function FastLevenbergMarquardtJL(linsolve::Symbol = :cholesky; factor = 1e-6,
-        factoraccept = 13.0, factorreject = 3.0, factorupdate = :marquardt,
-        minscale = 1e-12, maxscale = 1e16, minfactor = 1e-28, maxfactor = 1e32,
-        autodiff = nothing)
+function FastLevenbergMarquardtJL(
+        linsolve::Symbol = :cholesky; factor = 1e-6, factoraccept = 13.0,
+        factorreject = 3.0, factorupdate = :marquardt, minscale = 1e-12,
+        maxscale = 1e16, minfactor = 1e-28, maxfactor = 1e32, autodiff = nothing)
     @assert linsolve in (:qr, :cholesky)
     @assert factorupdate in (:marquardt, :nielson)
 
@@ -148,8 +148,8 @@ NonlinearLeastSquaresProblem.
     autodiff
 end
 
-function CMINPACK(; show_trace = missing, tracing = missing, method::Symbol = :auto,
-        autodiff = missing)
+function CMINPACK(; show_trace = missing, tracing = missing,
+        method::Symbol = :auto, autodiff = missing)
     if Base.get_extension(@__MODULE__, :NonlinearSolveMINPACKExt) === nothing
         error("CMINPACK requires MINPACK.jl to be loaded")
     end
@@ -235,8 +235,8 @@ end
 
 function NLsolveJL(; method = :trust_region, autodiff = :central, store_trace = missing,
         extended_trace = missing, linesearch = LineSearches.Static(),
-        linsolve = (x, A, b) -> copyto!(x, A \ b), factor = 1.0, autoscale = true, m = 10,
-        beta = one(Float64), show_trace = missing)
+        linsolve = (x, A, b) -> copyto!(x, A \ b), factor = 1.0,
+        autoscale = true, m = 10, beta = one(Float64), show_trace = missing)
     if Base.get_extension(@__MODULE__, :NonlinearSolveNLsolveExt) === nothing
         error("NLsolveJL requires NLsolve.jl to be loaded")
     end
@@ -252,22 +252,20 @@ function NLsolveJL(; method = :trust_region, autodiff = :central, store_trace =
     end
 
     if store_trace !== missing
-        Base.depwarn(
-            "`store_trace` for NLsolveJL has been deprecated and will be removed \
-             in v4. Use the `store_trace` keyword argument via the logging API \
-             https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ \
-             instead.",
+        Base.depwarn("`store_trace` for NLsolveJL has been deprecated and will be removed \
+                      in v4. Use the `store_trace` keyword argument via the logging API \
+                      https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ \
+                      instead.",
             :NLsolveJL)
     else
         store_trace = false
     end
 
     if extended_trace !== missing
-        Base.depwarn(
-            "`extended_trace` for NLsolveJL has been deprecated and will be \
-             removed in v4. Use the `trace_level = TraceAll()` keyword argument \
-             via the logging API \
-             https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ instead.",
+        Base.depwarn("`extended_trace` for NLsolveJL has been deprecated and will be \
+                      removed in v4. Use the `trace_level = TraceAll()` keyword argument \
+                      via the logging API \
+                      https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ instead.",
             :NLsolveJL)
     else
         extended_trace = false
@@ -277,8 +275,8 @@ function NLsolveJL(; method = :trust_region, autodiff = :central, store_trace =
         error("`autodiff` must be `:central` or `:forward`.")
     end
 
-    return NLsolveJL(method, autodiff, store_trace, extended_trace, linesearch, linsolve,
-        factor, autoscale, m, beta, show_trace)
+    return NLsolveJL(method, autodiff, store_trace, extended_trace, linesearch,
+        linsolve, factor, autoscale, m, beta, show_trace)
 end
 
 """
@@ -368,9 +366,9 @@ problems as well.
     condition_number_threshold
 end
 
-function FixedPointAccelerationJL(; algorithm = :Anderson, m = missing,
-        condition_number_threshold = missing, extrapolation_period = missing,
-        replace_invalids = :NoAction, dampening = 1.0)
+function FixedPointAccelerationJL(;
+        algorithm = :Anderson, m = missing, condition_number_threshold = missing,
+        extrapolation_period = missing, replace_invalids = :NoAction, dampening = 1.0)
     if Base.get_extension(@__MODULE__, :NonlinearSolveFixedPointAccelerationExt) === nothing
         error("FixedPointAccelerationJL requires FixedPointAcceleration.jl to be loaded")
     end
@@ -447,8 +445,8 @@ end
     autodiff
 end
 
-function SIAMFANLEquationsJL(; method = :newton, delta = 1e-3, linsolve = nothing, m = 0,
-        beta = 1.0, autodiff = missing)
+function SIAMFANLEquationsJL(; method = :newton, delta = 1e-3, linsolve = nothing,
+        m = 0, beta = 1.0, autodiff = missing)
     if Base.get_extension(@__MODULE__, :NonlinearSolveSIAMFANLEquationsExt) === nothing
         error("SIAMFANLEquationsJL requires SIAMFANLEquations.jl to be loaded")
     end
diff --git a/src/algorithms/gauss_newton.jl b/src/algorithms/gauss_newton.jl
index 1e6384788..4e826c130 100644
--- a/src/algorithms/gauss_newton.jl
+++ b/src/algorithms/gauss_newton.jl
@@ -9,6 +9,6 @@ for large-scale and numerically-difficult nonlinear least squares problems.
 function GaussNewton(; concrete_jac = nothing, linsolve = nothing, precs = DEFAULT_PRECS,
         linesearch = NoLineSearch(), vjp_autodiff = nothing, autodiff = nothing)
     descent = NewtonDescent(; linsolve, precs)
-    return GeneralizedFirstOrderAlgorithm(; concrete_jac, name = :GaussNewton,
-        descent, jacobian_ad = autodiff, reverse_ad = vjp_autodiff)
+    return GeneralizedFirstOrderAlgorithm(; concrete_jac, name = :GaussNewton, descent,
+        jacobian_ad = autodiff, reverse_ad = vjp_autodiff)
 end
diff --git a/src/algorithms/klement.jl b/src/algorithms/klement.jl
index 8aa94fbd1..428dc382c 100644
--- a/src/algorithms/klement.jl
+++ b/src/algorithms/klement.jl
@@ -47,8 +47,9 @@ function Klement(; max_resets::Int = 100, linsolve = nothing, alpha = nothing,
 
     CJ = IJ === :true_jacobian || IJ === :true_jacobian_diagonal
 
-    return ApproximateJacobianSolveAlgorithm{CJ, :Klement}(; linesearch,
-        descent = NewtonDescent(; linsolve, precs), update_rule = KlementUpdateRule(),
+    return ApproximateJacobianSolveAlgorithm{CJ, :Klement}(;
+        linesearch, descent = NewtonDescent(; linsolve, precs),
+        update_rule = KlementUpdateRule(),
         reinit_rule = IllConditionedJacobianReset(), max_resets, initialization)
 end
 
@@ -99,8 +100,8 @@ Update rule for [`Klement`](@ref).
     fu_cache
 end
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::KlementUpdateRule, J, fu, u,
-        du, args...; kwargs...)
+function __internal_init(prob::AbstractNonlinearProblem, alg::KlementUpdateRule,
+        J, fu, u, du, args...; kwargs...)
     @bb Jdu = similar(fu)
     if J isa Diagonal || J isa Number
         J_cache, J_cache_2, Jdu_cache = nothing, nothing, nothing
@@ -125,7 +126,9 @@ function __internal_solve!(cache::KlementUpdateRuleCache, J_::Diagonal, fu, u, d
     J = _restructure(u, diag(J_))
     @bb @. cache.Jdu = (J^2) * (du^2)
     @bb @. J += ((fu - cache.fu_cache - J * du) /
-                 ifelse(iszero(cache.Jdu), T(1e-5), cache.Jdu)) * du * (J^2)
+                 ifelse(iszero(cache.Jdu), T(1e-5), cache.Jdu)) *
+                du *
+                (J^2)
     @bb copyto!(cache.fu_cache, fu)
     return Diagonal(vec(J))
 end
diff --git a/src/algorithms/lbroyden.jl b/src/algorithms/lbroyden.jl
index 43b362819..499cc7c34 100644
--- a/src/algorithms/lbroyden.jl
+++ b/src/algorithms/lbroyden.jl
@@ -19,9 +19,12 @@ function LimitedMemoryBroyden(; max_resets::Int = 3, linesearch = NoLineSearch()
         threshold::Union{Val, Int} = Val(10), reset_tolerance = nothing, alpha = nothing)
     threshold isa Int && (threshold = Val(threshold))
     return ApproximateJacobianSolveAlgorithm{false, :LimitedMemoryBroyden}(; linesearch,
-        descent = NewtonDescent(), update_rule = GoodBroydenUpdateRule(), max_resets,
-        initialization = BroydenLowRankInitialization{_unwrap_val(threshold)}(alpha,
-            threshold), reinit_rule = NoChangeInStateReset(; reset_tolerance))
+        descent = NewtonDescent(),
+        update_rule = GoodBroydenUpdateRule(),
+        max_resets,
+        initialization = BroydenLowRankInitialization{_unwrap_val(threshold)}(
+            alpha, threshold),
+        reinit_rule = NoChangeInStateReset(; reset_tolerance))
 end
 
 """
@@ -38,13 +41,13 @@ end
 
 jacobian_initialized_preinverted(::BroydenLowRankInitialization) = true
 
-function __internal_init(prob::AbstractNonlinearProblem,
-        alg::BroydenLowRankInitialization{T}, solver, f::F, fu, u, p; maxiters = 1000,
+function __internal_init(
+        prob::AbstractNonlinearProblem, alg::BroydenLowRankInitialization{T},
+        solver, f::F, fu, u, p; maxiters = 1000,
         internalnorm::IN = DEFAULT_NORM, kwargs...) where {T, F, IN}
     if u isa Number # Use the standard broyden
-        return __internal_init(prob, IdentityInitialization(true, FullStructure()), solver,
-            f, fu, u,
-            p; maxiters, kwargs...)
+        return __internal_init(prob, IdentityInitialization(true, FullStructure()),
+            solver, f, fu, u, p; maxiters, kwargs...)
     end
     # Pay to cost of slightly more allocations to prevent type-instability for StaticArrays
     α = inv(__initial_alpha(alg.alpha, u, fu, internalnorm))
@@ -54,13 +57,12 @@ function __internal_init(prob::AbstractNonlinearProblem,
         threshold = min(_unwrap_val(alg.threshold), maxiters)
         J = BroydenLowRankJacobian(fu, u; threshold, alpha = α)
     end
-    return InitializedApproximateJacobianCache(J, FullStructure(), alg, nothing, true,
-        internalnorm)
+    return InitializedApproximateJacobianCache(
+        J, FullStructure(), alg, nothing, true, internalnorm)
 end
 
 function (cache::InitializedApproximateJacobianCache)(
-        alg::BroydenLowRankInitialization, fu,
-        u)
+        alg::BroydenLowRankInitialization, fu, u)
     α = __initial_alpha(alg.alpha, u, fu, cache.internalnorm)
     cache.J.idx = 0
     cache.J.alpha = inv(α)
@@ -97,14 +99,15 @@ end
 for op in (:adjoint, :transpose)
     # FIXME: adjoint might be a problem here. Fix if a complex number issue shows up
     @eval function Base.$(op)(operator::BroydenLowRankJacobian{T}) where {T}
-        return BroydenLowRankJacobian{T}(operator.Vᵀ, operator.U,
-            operator.idx, operator.cache, operator.alpha)
+        return BroydenLowRankJacobian{T}(
+            operator.Vᵀ, operator.U, operator.idx, operator.cache, operator.alpha)
     end
 end
 
 # Storing the transpose to ensure contiguous memory on splicing
-function BroydenLowRankJacobian(fu::StaticArray{S2, T2}, u::StaticArray{S1, T1};
-        alpha = true, threshold::Val{Th} = Val(10)) where {S1, S2, T1, T2, Th}
+function BroydenLowRankJacobian(
+        fu::StaticArray{S2, T2}, u::StaticArray{S1, T1}; alpha = true,
+        threshold::Val{Th} = Val(10)) where {S1, S2, T1, T2, Th}
     T = promote_type(T1, T2)
     fuSize, uSize = Size(fu), Size(u)
     U = MArray{Tuple{prod(fuSize), Th}, T}(undef)
@@ -156,8 +159,8 @@ function LinearAlgebra.mul!(y::AbstractVector, x::AbstractVector, J::BroydenLowR
     return y
 end
 
-function LinearAlgebra.mul!(J::BroydenLowRankJacobian, u,
-        vᵀ::LinearAlgebra.AdjOrTransAbsVec, α::Bool, β::Bool)
+function LinearAlgebra.mul!(
+        J::BroydenLowRankJacobian, u, vᵀ::LinearAlgebra.AdjOrTransAbsVec, α::Bool, β::Bool)
     @assert α & β
     idx_update = mod1(J.idx + 1, size(J.U, 2))
     copyto!(@view(J.U[:, idx_update]), _vec(u))
diff --git a/src/algorithms/levenberg_marquardt.jl b/src/algorithms/levenberg_marquardt.jl
index adb7ee9a4..510226d7d 100644
--- a/src/algorithms/levenberg_marquardt.jl
+++ b/src/algorithms/levenberg_marquardt.jl
@@ -30,11 +30,12 @@ nonlinear systems.
 For the remaining arguments, see [`GeodesicAcceleration`](@ref) and
 [`NonlinearSolve.LevenbergMarquardtTrustRegion`](@ref) documentations.
 """
-function LevenbergMarquardt(; concrete_jac = missing, linsolve = nothing,
-        precs = DEFAULT_PRECS, damping_initial::Real = 1.0, α_geodesic::Real = 0.75,
+function LevenbergMarquardt(;
+        concrete_jac = missing, linsolve = nothing, precs = DEFAULT_PRECS,
+        damping_initial::Real = 1.0, α_geodesic::Real = 0.75,
         damping_increase_factor::Real = 2.0, damping_decrease_factor::Real = 3.0,
-        finite_diff_step_geodesic = 0.1, b_uphill::Real = 1.0, autodiff = nothing,
-        min_damping_D::Real = 1e-8, disable_geodesic = False)
+        finite_diff_step_geodesic = 0.1, b_uphill::Real = 1.0,
+        autodiff = nothing, min_damping_D::Real = 1e-8, disable_geodesic = False)
     if concrete_jac !== missing
         Base.depwarn("The `concrete_jac` keyword argument is deprecated and will be \
                       removed in v0.4. This kwarg doesn't make sense (and is currently \
@@ -43,15 +44,16 @@ function LevenbergMarquardt(; concrete_jac = missing, linsolve = nothing,
             :LevenbergMarquardt)
     end
 
-    descent = DampedNewtonDescent(; linsolve, precs, initial_damping = damping_initial,
-        damping_fn = LevenbergMarquardtDampingFunction(damping_increase_factor,
-            damping_decrease_factor, min_damping_D))
+    descent = DampedNewtonDescent(; linsolve,
+        precs,
+        initial_damping = damping_initial,
+        damping_fn = LevenbergMarquardtDampingFunction(
+            damping_increase_factor, damping_decrease_factor, min_damping_D))
     if disable_geodesic === False
         descent = GeodesicAcceleration(descent, finite_diff_step_geodesic, α_geodesic)
     end
     trustregion = LevenbergMarquardtTrustRegion(b_uphill)
-    return GeneralizedFirstOrderAlgorithm(;
-        concrete_jac = true, name = :LevenbergMarquardt,
+    return GeneralizedFirstOrderAlgorithm(; concrete_jac = true, name = :LevenbergMarquardt,
         trustregion, descent, jacobian_ad = autodiff)
 end
 
@@ -87,21 +89,22 @@ function reinit_cache!(cache::LevenbergMarquardtDampingCache, args...; kwargs...
     cache.J_damped = cache.λ .* cache.DᵀD
 end
 
-function requires_normal_form_jacobian(::Union{LevenbergMarquardtDampingFunction,
-        LevenbergMarquardtDampingCache})
+function requires_normal_form_jacobian(::Union{
+        LevenbergMarquardtDampingFunction, LevenbergMarquardtDampingCache})
     return false
 end
-function requires_normal_form_rhs(::Union{LevenbergMarquardtDampingFunction,
-        LevenbergMarquardtDampingCache})
+function requires_normal_form_rhs(::Union{
+        LevenbergMarquardtDampingFunction, LevenbergMarquardtDampingCache})
     return false
 end
-function returns_norm_form_damping(::Union{LevenbergMarquardtDampingFunction,
-        LevenbergMarquardtDampingCache})
+function returns_norm_form_damping(::Union{
+        LevenbergMarquardtDampingFunction, LevenbergMarquardtDampingCache})
     return true
 end
 
-function __internal_init(prob::AbstractNonlinearProblem,
-        f::LevenbergMarquardtDampingFunction, initial_damping, J, fu, u, ::Val{NF};
+function __internal_init(
+        prob::AbstractNonlinearProblem, f::LevenbergMarquardtDampingFunction,
+        initial_damping, J, fu, u, ::Val{NF};
         internalnorm::F = DEFAULT_NORM, kwargs...) where {F, NF}
     T = promote_type(eltype(u), eltype(fu))
     DᵀD = __init_diagonal(u, T(f.min_damping))
@@ -111,15 +114,15 @@ function __internal_init(prob::AbstractNonlinearProblem,
         @bb J_diag_cache = similar(u)
     end
     J_damped = T(initial_damping) .* DᵀD
-    return LevenbergMarquardtDampingCache(T(f.increase_factor), T(f.decrease_factor),
-        T(f.min_damping), T(f.increase_factor), T(initial_damping), DᵀD, J_diag_cache,
-        J_damped, f, T(initial_damping))
+    return LevenbergMarquardtDampingCache(
+        T(f.increase_factor), T(f.decrease_factor), T(f.min_damping), T(f.increase_factor),
+        T(initial_damping), DᵀD, J_diag_cache, J_damped, f, T(initial_damping))
 end
 
 (damping::LevenbergMarquardtDampingCache)(::Nothing) = damping.J_damped
 
-function __internal_solve!(damping::LevenbergMarquardtDampingCache, J, fu, ::Val{false};
-        kwargs...)
+function __internal_solve!(
+        damping::LevenbergMarquardtDampingCache, J, fu, ::Val{false}; kwargs...)
     if __can_setindex(damping.J_diag_cache)
         sum!(abs2, _vec(damping.J_diag_cache), J')
     elseif damping.J_diag_cache isa Number
@@ -132,8 +135,8 @@ function __internal_solve!(damping::LevenbergMarquardtDampingCache, J, fu, ::Val
     return damping.J_damped
 end
 
-function __internal_solve!(damping::LevenbergMarquardtDampingCache, JᵀJ, fu, ::Val{true};
-        kwargs...)
+function __internal_solve!(
+        damping::LevenbergMarquardtDampingCache, JᵀJ, fu, ::Val{true}; kwargs...)
     damping.DᵀD = __update_LM_diagonal!!(damping.DᵀD, JᵀJ)
     @bb @. damping.J_damped = damping.λ * damping.DᵀD
     return damping.J_damped
diff --git a/src/algorithms/pseudo_transient.jl b/src/algorithms/pseudo_transient.jl
index 957cfc904..fda39a3b9 100644
--- a/src/algorithms/pseudo_transient.jl
+++ b/src/algorithms/pseudo_transient.jl
@@ -20,8 +20,8 @@ function PseudoTransient(; concrete_jac = nothing, linsolve = nothing,
         precs = DEFAULT_PRECS, autodiff = nothing, alpha_initial = 1e-3)
     descent = DampedNewtonDescent(; linsolve, precs, initial_damping = alpha_initial,
         damping_fn = SwitchedEvolutionRelaxation())
-    return GeneralizedFirstOrderAlgorithm(; concrete_jac,
-        name = :PseudoTransient, linesearch, descent, jacobian_ad = autodiff)
+    return GeneralizedFirstOrderAlgorithm(;
+        concrete_jac, name = :PseudoTransient, linesearch, descent, jacobian_ad = autodiff)
 end
 
 """
@@ -43,27 +43,27 @@ Cache for the [`SwitchedEvolutionRelaxation`](@ref) method.
     internalnorm
 end
 
-function requires_normal_form_jacobian(cache::Union{SwitchedEvolutionRelaxation,
-        SwitchedEvolutionRelaxationCache})
+function requires_normal_form_jacobian(cache::Union{
+        SwitchedEvolutionRelaxation, SwitchedEvolutionRelaxationCache})
     return false
 end
-function requires_normal_form_rhs(cache::Union{SwitchedEvolutionRelaxation,
-        SwitchedEvolutionRelaxationCache})
+function requires_normal_form_rhs(cache::Union{
+        SwitchedEvolutionRelaxation, SwitchedEvolutionRelaxationCache})
     return false
 end
 
-function __internal_init(prob::AbstractNonlinearProblem, f::SwitchedEvolutionRelaxation,
-        initial_damping, J, fu, u, args...; internalnorm::F = DEFAULT_NORM,
-        kwargs...) where {F}
+function __internal_init(
+        prob::AbstractNonlinearProblem, f::SwitchedEvolutionRelaxation, initial_damping,
+        J, fu, u, args...; internalnorm::F = DEFAULT_NORM, kwargs...) where {F}
     T = promote_type(eltype(u), eltype(fu))
-    return SwitchedEvolutionRelaxationCache(internalnorm(fu), T(1 / initial_damping),
-        internalnorm)
+    return SwitchedEvolutionRelaxationCache(
+        internalnorm(fu), T(1 / initial_damping), internalnorm)
 end
 
 (damping::SwitchedEvolutionRelaxationCache)(::Nothing) = damping.α⁻¹
 
-function __internal_solve!(damping::SwitchedEvolutionRelaxationCache, J, fu, args...;
-        kwargs...)
+function __internal_solve!(
+        damping::SwitchedEvolutionRelaxationCache, J, fu, args...; kwargs...)
     res_norm = damping.internalnorm(fu)
     damping.α⁻¹ *= res_norm / damping.res_norm
     damping.res_norm = res_norm
diff --git a/src/algorithms/raphson.jl b/src/algorithms/raphson.jl
index bc005f2b6..c6847f54c 100644
--- a/src/algorithms/raphson.jl
+++ b/src/algorithms/raphson.jl
@@ -9,6 +9,6 @@ for large-scale and numerically-difficult nonlinear systems.
 function NewtonRaphson(; concrete_jac = nothing, linsolve = nothing,
         linesearch = NoLineSearch(), precs = DEFAULT_PRECS, autodiff = nothing)
     descent = NewtonDescent(; linsolve, precs)
-    return GeneralizedFirstOrderAlgorithm(; concrete_jac, name = :NewtonRaphson,
-        linesearch, descent, jacobian_ad = autodiff)
+    return GeneralizedFirstOrderAlgorithm(;
+        concrete_jac, name = :NewtonRaphson, linesearch, descent, jacobian_ad = autodiff)
 end
diff --git a/src/algorithms/trust_region.jl b/src/algorithms/trust_region.jl
index 7f550a65c..ac8f42d35 100644
--- a/src/algorithms/trust_region.jl
+++ b/src/algorithms/trust_region.jl
@@ -35,10 +35,10 @@ function TrustRegion(; concrete_jac = nothing, linsolve = nothing, precs = DEFAU
     if isnothing(vjp_autodiff) && autodiff isa ADTypes.AbstractFiniteDifferencesMode
         vjp_autodiff = autodiff
     end
-    trustregion = GenericTrustRegionScheme(; method = radius_update_scheme, step_threshold,
-        shrink_threshold, expand_threshold, shrink_factor, expand_factor,
-        reverse_ad = vjp_autodiff, forward_ad)
-    return GeneralizedFirstOrderAlgorithm(; concrete_jac, name = :TrustRegion,
-        trustregion, descent, jacobian_ad = autodiff, reverse_ad = vjp_autodiff,
-        max_shrink_times)
+    trustregion = GenericTrustRegionScheme(;
+        method = radius_update_scheme, step_threshold, shrink_threshold, expand_threshold,
+        shrink_factor, expand_factor, reverse_ad = vjp_autodiff, forward_ad)
+    return GeneralizedFirstOrderAlgorithm(;
+        concrete_jac, name = :TrustRegion, trustregion, descent,
+        jacobian_ad = autodiff, reverse_ad = vjp_autodiff, max_shrink_times)
 end
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index ffc77cea8..d0471e99b 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -50,14 +50,14 @@ function __show_algorithm(io::IO, alg::ApproximateJacobianSolveAlgorithm, name,
     print(io, "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))")
 end
 
-function ApproximateJacobianSolveAlgorithm(; concrete_jac = nothing,
-        name::Symbol = :unknown, kwargs...)
+function ApproximateJacobianSolveAlgorithm(;
+        concrete_jac = nothing, name::Symbol = :unknown, kwargs...)
     return ApproximateJacobianSolveAlgorithm{concrete_jac, name}(; kwargs...)
 end
 
-function ApproximateJacobianSolveAlgorithm{concrete_jac, name}(; linesearch = missing,
-        trustregion = missing, descent, update_rule, reinit_rule, initialization,
-        max_resets::Int = typemax(Int),
+function ApproximateJacobianSolveAlgorithm{concrete_jac, name}(;
+        linesearch = missing, trustregion = missing, descent, update_rule,
+        reinit_rule, initialization, max_resets::Int = typemax(Int),
         max_shrink_times::Int = typemax(Int)) where {concrete_jac, name}
     if linesearch !== missing && !(linesearch isa AbstractNonlinearSolveLineSearchAlgorithm)
         Base.depwarn("Passing in a `LineSearches.jl` algorithm directly is deprecated. \
@@ -65,8 +65,9 @@ function ApproximateJacobianSolveAlgorithm{concrete_jac, name}(; linesearch = mi
             :GeneralizedFirstOrderAlgorithm)
         linesearch = LineSearchesJL(; method = linesearch)
     end
-    return ApproximateJacobianSolveAlgorithm{concrete_jac, name}(linesearch, trustregion,
-        descent, update_rule, reinit_rule, max_resets, max_shrink_times, initialization)
+    return ApproximateJacobianSolveAlgorithm{concrete_jac, name}(
+        linesearch, trustregion, descent, update_rule, reinit_rule,
+        max_resets, max_shrink_times, initialization)
 end
 
 @inline concrete_jac(::ApproximateJacobianSolveAlgorithm{CJ}) where {CJ} = CJ
@@ -117,9 +118,9 @@ end
 
 store_inverse_jacobian(::ApproximateJacobianSolveCache{INV}) where {INV} = INV
 
-function __reinit_internal!(cache::ApproximateJacobianSolveCache{INV, GB, iip}, args...;
-        p = cache.p, u0 = cache.u, alias_u0::Bool = false, maxiters = 1000,
-        maxtime = nothing, kwargs...) where {INV, GB, iip}
+function __reinit_internal!(cache::ApproximateJacobianSolveCache{INV, GB, iip},
+        args...; p = cache.p, u0 = cache.u, alias_u0::Bool = false,
+        maxiters = 1000, maxtime = nothing, kwargs...) where {INV, GB, iip}
     if iip
         recursivecopy!(cache.u, u0)
         cache.prob.f(cache.fu, cache.u, p)
@@ -147,10 +148,10 @@ end
 
 @internal_caches ApproximateJacobianSolveCache :initialization_cache :descent_cache :linesearch_cache :trustregion_cache :update_rule_cache :reinit_rule_cache
 
-function SciMLBase.__init(prob::AbstractNonlinearProblem{uType, iip},
-        alg::ApproximateJacobianSolveAlgorithm, args...; alias_u0 = false,
-        maxtime = nothing, maxiters = 1000, abstol = nothing, reltol = nothing,
-        linsolve_kwargs = (;), termination_condition = nothing,
+function SciMLBase.__init(
+        prob::AbstractNonlinearProblem{uType, iip}, alg::ApproximateJacobianSolveAlgorithm,
+        args...; alias_u0 = false, maxtime = nothing, maxiters = 1000, abstol = nothing,
+        reltol = nothing, linsolve_kwargs = (;), termination_condition = nothing,
         internalnorm::F = DEFAULT_NORM, kwargs...) where {uType, iip, F}
     timer = get_timer_output()
     @static_timeit timer "cache construction" begin
@@ -162,18 +163,18 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem{uType, iip},
         INV = store_inverse_jacobian(alg.update_rule)
 
         linsolve = get_linear_solver(alg.descent)
-        initialization_cache = __internal_init(prob, alg.initialization, alg, f, fu, u, p;
-            linsolve,
-            maxiters, internalnorm)
+        initialization_cache = __internal_init(
+            prob, alg.initialization, alg, f, fu, u, p; linsolve, maxiters, internalnorm)
 
-        abstol, reltol, termination_cache = init_termination_cache(abstol, reltol, fu, u,
-            termination_condition)
+        abstol, reltol, termination_cache = init_termination_cache(
+            abstol, reltol, fu, u, termination_condition)
         linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
 
         J = initialization_cache(nothing)
         inv_workspace, J = INV ? __safe_inv_workspace(J) : (nothing, J)
-        descent_cache = __internal_init(prob, alg.descent, J, fu, u; abstol, reltol,
-            internalnorm, linsolve_kwargs, pre_inverted = Val(INV), timer)
+        descent_cache = __internal_init(
+            prob, alg.descent, J, fu, u; abstol, reltol, internalnorm,
+            linsolve_kwargs, pre_inverted = Val(INV), timer)
         du = get_du(descent_cache)
 
         reinit_rule_cache = __internal_init(alg.reinit_rule, J, fu, u, du)
@@ -189,31 +190,31 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem{uType, iip},
         if alg.trustregion !== missing
             supports_trust_region(alg.descent) || error("Trust Region not supported by \
                                                         $(alg.descent).")
-            trustregion_cache = __internal_init(prob, alg.trustregion, f, fu, u, p;
-                internalnorm, kwargs...)
+            trustregion_cache = __internal_init(
+                prob, alg.trustregion, f, fu, u, p; internalnorm, kwargs...)
             GB = :TrustRegion
         end
 
         if alg.linesearch !== missing
             supports_line_search(alg.descent) || error("Line Search not supported by \
                                                         $(alg.descent).")
-            linesearch_cache = __internal_init(prob, alg.linesearch, f, fu, u, p;
-                internalnorm,
-                kwargs...)
+            linesearch_cache = __internal_init(
+                prob, alg.linesearch, f, fu, u, p; internalnorm, kwargs...)
             GB = :LineSearch
         end
 
-        update_rule_cache = __internal_init(prob, alg.update_rule, J, fu, u, du;
-            internalnorm)
+        update_rule_cache = __internal_init(
+            prob, alg.update_rule, J, fu, u, du; internalnorm)
 
         trace = init_nonlinearsolve_trace(alg, u, fu, ApplyArray(__zero, J), du;
             uses_jacobian_inverse = Val(INV), kwargs...)
 
-        return ApproximateJacobianSolveCache{INV, GB, iip, maxtime !== nothing}(fu, u,
-            u_cache, p, du, J, alg, prob, initialization_cache, descent_cache,
-            linesearch_cache, trustregion_cache, update_rule_cache, reinit_rule_cache,
-            inv_workspace, 0, 0, 0, alg.max_resets, maxiters, maxtime, alg.max_shrink_times,
-            0, timer, 0.0, termination_cache, trace, ReturnCode.Default, false, false)
+        return ApproximateJacobianSolveCache{INV, GB, iip, maxtime !== nothing}(
+            fu, u, u_cache, p, du, J, alg, prob, initialization_cache,
+            descent_cache, linesearch_cache, trustregion_cache,
+            update_rule_cache, reinit_rule_cache, inv_workspace, 0, 0, 0,
+            alg.max_resets, maxiters, maxtime, alg.max_shrink_times, 0, timer,
+            0.0, termination_cache, trace, ReturnCode.Default, false, false)
     end
 end
 
@@ -222,10 +223,8 @@ function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
     new_jacobian = true
     @static_timeit cache.timer "jacobian init/reinit" begin
         if get_nsteps(cache) == 0  # First Step is special ignore kwargs
-            J_init = __internal_solve!(cache.initialization_cache,
-                cache.fu,
-                cache.u,
-                Val(false))
+            J_init = __internal_solve!(
+                cache.initialization_cache, cache.fu, cache.u, Val(false))
             if INV
                 if jacobian_initialized_preinverted(cache.initialization_cache.alg)
                     cache.J = J_init
@@ -248,8 +247,8 @@ function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
                 cache.force_reinit = false
             elseif recompute_jacobian === nothing
                 # Standard Step
-                reinit = __internal_solve!(cache.reinit_rule_cache, cache.J, cache.fu,
-                    cache.u, cache.du)
+                reinit = __internal_solve!(
+                    cache.reinit_rule_cache, cache.J, cache.fu, cache.u, cache.du)
                 reinit && (countable_reinit = true)
             elseif recompute_jacobian
                 reinit = true  # Force ReInitialization: Don't count towards resetting
@@ -268,8 +267,8 @@ function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
             end
 
             if reinit
-                J_init = __internal_solve!(cache.initialization_cache, cache.fu, cache.u,
-                    Val(true))
+                J_init = __internal_solve!(
+                    cache.initialization_cache, cache.fu, cache.u, Val(true))
                 cache.J = INV ? __safe_inv!!(cache.inv_workspace, J_init) : J_init
                 J = cache.J
                 cache.steps_since_last_reset = 0
@@ -284,13 +283,11 @@ function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
         if cache.trustregion_cache !== nothing &&
            hasfield(typeof(cache.trustregion_cache), :trust_region)
             δu, descent_success, descent_intermediates = __internal_solve!(
-                cache.descent_cache,
-                J, cache.fu, cache.u; new_jacobian,
+                cache.descent_cache, J, cache.fu, cache.u; new_jacobian,
                 trust_region = cache.trustregion_cache.trust_region)
         else
             δu, descent_success, descent_intermediates = __internal_solve!(
-                cache.descent_cache,
-                J, cache.fu, cache.u; new_jacobian)
+                cache.descent_cache, J, cache.fu, cache.u; new_jacobian)
         end
     end
 
@@ -309,8 +306,9 @@ function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
             end
         elseif GB === :TrustRegion
             @static_timeit cache.timer "trustregion" begin
-                tr_accepted, u_new, fu_new = __internal_solve!(cache.trustregion_cache, J,
-                    cache.fu, cache.u, δu, descent_intermediates)
+                tr_accepted, u_new, fu_new = __internal_solve!(
+                    cache.trustregion_cache, J, cache.fu,
+                    cache.u, δu, descent_intermediates)
                 if tr_accepted
                     @bb copyto!(cache.u, u_new)
                     @bb copyto!(cache.fu, fu_new)
@@ -341,7 +339,8 @@ function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
     update_trace!(cache, α)
     @bb copyto!(cache.u_cache, cache.u)
 
-    if (cache.force_stop || cache.force_reinit ||
+    if (cache.force_stop ||
+        cache.force_reinit ||
         (recompute_jacobian !== nothing && !recompute_jacobian))
         callback_into_cache!(cache)
         return nothing
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 0812e7f05..753b7682f 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -46,14 +46,14 @@ function __show_algorithm(io::IO, alg::GeneralizedFirstOrderAlgorithm, name, ind
     print(io, "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))")
 end
 
-function GeneralizedFirstOrderAlgorithm(; concrete_jac = nothing,
-        name::Symbol = :unknown, kwargs...)
+function GeneralizedFirstOrderAlgorithm(;
+        concrete_jac = nothing, name::Symbol = :unknown, kwargs...)
     return GeneralizedFirstOrderAlgorithm{concrete_jac, name}(; kwargs...)
 end
 
-function GeneralizedFirstOrderAlgorithm{concrete_jac, name}(; descent,
-        linesearch = missing, trustregion = missing, jacobian_ad = nothing,
-        forward_ad = nothing, reverse_ad = nothing,
+function GeneralizedFirstOrderAlgorithm{concrete_jac, name}(;
+        descent, linesearch = missing, trustregion = missing,
+        jacobian_ad = nothing, forward_ad = nothing, reverse_ad = nothing,
         max_shrink_times::Int = typemax(Int)) where {concrete_jac, name}
     forward_ad = ifelse(forward_ad !== nothing, forward_ad,
         ifelse(jacobian_ad isa ADTypes.AbstractForwardMode, jacobian_ad, nothing))
@@ -67,8 +67,9 @@ function GeneralizedFirstOrderAlgorithm{concrete_jac, name}(; descent,
         linesearch = LineSearchesJL(; method = linesearch)
     end
 
-    return GeneralizedFirstOrderAlgorithm{concrete_jac, name}(linesearch,
-        trustregion, descent, max_shrink_times, jacobian_ad, forward_ad, reverse_ad)
+    return GeneralizedFirstOrderAlgorithm{concrete_jac, name}(
+        linesearch, trustregion, descent, max_shrink_times,
+        jacobian_ad, forward_ad, reverse_ad)
 end
 
 concrete_jac(::GeneralizedFirstOrderAlgorithm{CJ}) where {CJ} = CJ
@@ -112,9 +113,9 @@ concrete_jac(::GeneralizedFirstOrderAlgorithm{CJ}) where {CJ} = CJ
     force_stop::Bool
 end
 
-function __reinit_internal!(cache::GeneralizedFirstOrderAlgorithmCache{iip}, args...;
-        p = cache.p, u0 = cache.u, alias_u0::Bool = false, maxiters = 1000,
-        maxtime = nothing, kwargs...) where {iip}
+function __reinit_internal!(
+        cache::GeneralizedFirstOrderAlgorithmCache{iip}, args...; p = cache.p, u0 = cache.u,
+        alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...) where {iip}
     if iip
         recursivecopy!(cache.u, u0)
         cache.prob.f(cache.fu, cache.u, p)
@@ -140,11 +141,11 @@ end
 
 @internal_caches GeneralizedFirstOrderAlgorithmCache :jac_cache :descent_cache :linesearch_cache :trustregion_cache
 
-function SciMLBase.__init(prob::AbstractNonlinearProblem{uType, iip},
-        alg::GeneralizedFirstOrderAlgorithm, args...; alias_u0 = false, maxiters = 1000,
-        abstol = nothing, reltol = nothing, maxtime = nothing,
-        termination_condition = nothing, internalnorm = DEFAULT_NORM, linsolve_kwargs = (;),
-        kwargs...) where {uType, iip}
+function SciMLBase.__init(
+        prob::AbstractNonlinearProblem{uType, iip}, alg::GeneralizedFirstOrderAlgorithm,
+        args...; alias_u0 = false, maxiters = 1000, abstol = nothing,
+        reltol = nothing, maxtime = nothing, termination_condition = nothing,
+        internalnorm = DEFAULT_NORM, linsolve_kwargs = (;), kwargs...) where {uType, iip}
     timer = get_timer_output()
     @static_timeit timer "cache construction" begin
         (; f, u0, p) = prob
@@ -154,12 +155,13 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem{uType, iip},
 
         linsolve = get_linear_solver(alg.descent)
 
-        abstol, reltol, termination_cache = init_termination_cache(abstol, reltol, fu, u,
-            termination_condition)
+        abstol, reltol, termination_cache = init_termination_cache(
+            abstol, reltol, fu, u, termination_condition)
         linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
 
-        jac_cache = JacobianCache(prob, alg, f, fu, u, p; autodiff = alg.jacobian_ad,
-            linsolve, jvp_autodiff = alg.forward_ad, vjp_autodiff = alg.reverse_ad)
+        jac_cache = JacobianCache(
+            prob, alg, f, fu, u, p; autodiff = alg.jacobian_ad, linsolve,
+            jvp_autodiff = alg.forward_ad, vjp_autodiff = alg.reverse_ad)
         J = jac_cache(nothing)
         descent_cache = __internal_init(prob, alg.descent, J, fu, u; abstol, reltol,
             internalnorm, linsolve_kwargs, timer)
@@ -176,27 +178,25 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem{uType, iip},
         if alg.trustregion !== missing
             supports_trust_region(alg.descent) || error("Trust Region not supported by \
                                                         $(alg.descent).")
-            trustregion_cache = __internal_init(prob, alg.trustregion, f, fu, u, p;
-                internalnorm,
-                kwargs...)
+            trustregion_cache = __internal_init(
+                prob, alg.trustregion, f, fu, u, p; internalnorm, kwargs...)
             GB = :TrustRegion
         end
 
         if alg.linesearch !== missing
             supports_line_search(alg.descent) || error("Line Search not supported by \
                                                         $(alg.descent).")
-            linesearch_cache = __internal_init(prob, alg.linesearch, f, fu, u, p;
-                internalnorm,
-                kwargs...)
+            linesearch_cache = __internal_init(
+                prob, alg.linesearch, f, fu, u, p; internalnorm, kwargs...)
             GB = :LineSearch
         end
 
         trace = init_nonlinearsolve_trace(alg, u, fu, ApplyArray(__zero, J), du; kwargs...)
 
-        return GeneralizedFirstOrderAlgorithmCache{iip, GB, maxtime !== nothing}(fu, u,
-            u_cache, p, du, J, alg, prob, jac_cache, descent_cache, linesearch_cache,
-            trustregion_cache, 0, 0, maxiters, maxtime, alg.max_shrink_times, timer, 0.0,
-            true, termination_cache, trace, ReturnCode.Default, false)
+        return GeneralizedFirstOrderAlgorithmCache{iip, GB, maxtime !== nothing}(
+            fu, u, u_cache, p, du, J, alg, prob, jac_cache, descent_cache, linesearch_cache,
+            trustregion_cache, 0, 0, maxiters, maxtime, alg.max_shrink_times,
+            timer, 0.0, true, termination_cache, trace, ReturnCode.Default, false)
     end
 end
 
@@ -216,13 +216,11 @@ function __step!(cache::GeneralizedFirstOrderAlgorithmCache{iip, GB};
         if cache.trustregion_cache !== nothing &&
            hasfield(typeof(cache.trustregion_cache), :trust_region)
             δu, descent_success, descent_intermediates = __internal_solve!(
-                cache.descent_cache,
-                J, cache.fu, cache.u; new_jacobian,
+                cache.descent_cache, J, cache.fu, cache.u; new_jacobian,
                 trust_region = cache.trustregion_cache.trust_region)
         else
             δu, descent_success, descent_intermediates = __internal_solve!(
-                cache.descent_cache,
-                J, cache.fu, cache.u; new_jacobian)
+                cache.descent_cache, J, cache.fu, cache.u; new_jacobian)
         end
     end
 
@@ -230,8 +228,8 @@ function __step!(cache::GeneralizedFirstOrderAlgorithmCache{iip, GB};
         cache.make_new_jacobian = true
         if GB === :LineSearch
             @static_timeit cache.timer "linesearch" begin
-                linesearch_failed, α = __internal_solve!(cache.linesearch_cache,
-                    cache.u, δu)
+                linesearch_failed, α = __internal_solve!(
+                    cache.linesearch_cache, cache.u, δu)
             end
             if linesearch_failed
                 cache.retcode = ReturnCode.InternalLineSearchFailed
@@ -243,8 +241,9 @@ function __step!(cache::GeneralizedFirstOrderAlgorithmCache{iip, GB};
             end
         elseif GB === :TrustRegion
             @static_timeit cache.timer "trustregion" begin
-                tr_accepted, u_new, fu_new = __internal_solve!(cache.trustregion_cache, J,
-                    cache.fu, cache.u, δu, descent_intermediates)
+                tr_accepted, u_new, fu_new = __internal_solve!(
+                    cache.trustregion_cache, J, cache.fu,
+                    cache.u, δu, descent_intermediates)
                 if tr_accepted
                     @bb copyto!(cache.u, u_new)
                     @bb copyto!(cache.fu, fu_new)
diff --git a/src/core/generic.jl b/src/core/generic.jl
index 849a259f1..22fc3e9d0 100644
--- a/src/core/generic.jl
+++ b/src/core/generic.jl
@@ -15,20 +15,20 @@ function SciMLBase.solve!(cache::AbstractNonlinearSolveCache)
 
     # The solver might have set a different `retcode`
     if cache.retcode == ReturnCode.Default
-        cache.retcode = ifelse(get_nsteps(cache) ≥ cache.maxiters, ReturnCode.MaxIters,
-            ReturnCode.Success)
+        cache.retcode = ifelse(
+            get_nsteps(cache) ≥ cache.maxiters, ReturnCode.MaxIters, ReturnCode.Success)
     end
 
     update_from_termination_cache!(cache.termination_cache, cache)
 
-    update_trace!(cache.trace, get_nsteps(cache), get_u(cache), get_fu(cache), nothing,
-        nothing, nothing; last = True)
+    update_trace!(cache.trace, get_nsteps(cache), get_u(cache),
+        get_fu(cache), nothing, nothing, nothing; last = True)
 
     stats = ImmutableNLStats(get_nf(cache), get_njacs(cache), get_nfactors(cache),
         get_nsolve(cache), get_nsteps(cache))
 
-    return SciMLBase.build_solution(cache.prob, cache.alg, get_u(cache), get_fu(cache);
-        cache.retcode, stats, cache.trace)
+    return SciMLBase.build_solution(cache.prob, cache.alg, get_u(cache),
+        get_fu(cache); cache.retcode, stats, cache.trace)
 end
 
 """
@@ -45,8 +45,8 @@ Performs one step of the nonlinear solver.
     respectively. For algorithms that don't use jacobian information, this keyword is
     ignored with a one-time warning.
 """
-function SciMLBase.step!(cache::AbstractNonlinearSolveCache{iip, timeit}, args...;
-        kwargs...) where {iip, timeit}
+function SciMLBase.step!(cache::AbstractNonlinearSolveCache{iip, timeit},
+        args...; kwargs...) where {iip, timeit}
     timeit && (time_start = time())
     res = @static_timeit cache.timer "solve" begin
         __step!(cache, args...; kwargs...)
@@ -55,7 +55,8 @@ function SciMLBase.step!(cache::AbstractNonlinearSolveCache{iip, timeit}, args..
 
     if timeit
         cache.total_time += time() - time_start
-        if !cache.force_stop && cache.retcode == ReturnCode.Default &&
+        if !cache.force_stop &&
+           cache.retcode == ReturnCode.Default &&
            cache.total_time ≥ cache.maxtime
             cache.retcode = ReturnCode.MaxTime
             cache.force_stop = true
diff --git a/src/core/spectral_methods.jl b/src/core/spectral_methods.jl
index deab95b3f..a4e824744 100644
--- a/src/core/spectral_methods.jl
+++ b/src/core/spectral_methods.jl
@@ -76,9 +76,9 @@ concrete_jac(::GeneralizedDFSane) = nothing
     force_stop::Bool
 end
 
-function __reinit_internal!(cache::GeneralizedDFSaneCache{iip}, args...; p = cache.p,
-        u0 = cache.u, alias_u0::Bool = false, maxiters = 1000, maxtime = nothing,
-        kwargs...) where {iip}
+function __reinit_internal!(
+        cache::GeneralizedDFSaneCache{iip}, args...; p = cache.p, u0 = cache.u,
+        alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...) where {iip}
     if iip
         recursivecopy!(cache.u, u0)
         cache.prob.f(cache.fu, cache.u, p)
@@ -115,10 +115,10 @@ end
 
 @internal_caches GeneralizedDFSaneCache :linesearch_cache
 
-function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane, args...;
-        alias_u0 = false, maxiters = 1000, abstol = nothing, reltol = nothing,
-        termination_condition = nothing, internalnorm::F = DEFAULT_NORM, maxtime = nothing,
-        kwargs...) where {F}
+function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane,
+        args...; alias_u0 = false, maxiters = 1000, abstol = nothing,
+        reltol = nothing, termination_condition = nothing,
+        internalnorm::F = DEFAULT_NORM, maxtime = nothing, kwargs...) where {F}
     timer = get_timer_output()
     @static_timeit timer "cache construction" begin
         u = __maybe_unaliased(prob.u0, alias_u0)
@@ -129,11 +129,11 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane
         fu = evaluate_f(prob, u)
         @bb fu_cache = copy(fu)
 
-        linesearch_cache = __internal_init(prob, alg.linesearch, prob.f, fu, u, prob.p;
-            maxiters, internalnorm, kwargs...)
+        linesearch_cache = __internal_init(
+            prob, alg.linesearch, prob.f, fu, u, prob.p; maxiters, internalnorm, kwargs...)
 
-        abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fu, u_cache,
-            termination_condition)
+        abstol, reltol, tc_cache = init_termination_cache(
+            abstol, reltol, fu, u_cache, termination_condition)
         trace = init_nonlinearsolve_trace(alg, u, fu, nothing, du; kwargs...)
 
         if alg.σ_1 === nothing
@@ -148,10 +148,9 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane
         end
 
         return GeneralizedDFSaneCache{isinplace(prob), maxtime !== nothing}(
-            fu, fu_cache, u,
-            u_cache, prob.p, du, alg, prob, σ_n, T(alg.σ_min), T(alg.σ_max),
-            linesearch_cache, 0, 0, maxiters, maxtime, timer, 0.0, tc_cache, trace,
-            ReturnCode.Default, false)
+            fu, fu_cache, u, u_cache, prob.p, du, alg, prob, σ_n, T(alg.σ_min),
+            T(alg.σ_max), linesearch_cache, 0, 0, maxiters, maxtime,
+            timer, 0.0, tc_cache, trace, ReturnCode.Default, false)
     end
 end
 
diff --git a/src/default.jl b/src/default.jl
index dafdf7902..8b17a9393 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -59,24 +59,21 @@ end
 for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProblem, :NLLS))
     algType = NonlinearSolvePolyAlgorithm{pType}
     @eval begin
-        function SciMLBase.__init(prob::$probType, alg::$algType{N}, args...;
-                kwargs...) where {N}
+        function SciMLBase.__init(
+                prob::$probType, alg::$algType{N}, args...; kwargs...) where {N}
             return NonlinearSolvePolyAlgorithmCache{isinplace(prob), N}(
-                map(solver -> SciMLBase.__init(prob,
-                        solver, args...; kwargs...), alg.algs),
+                map(solver -> SciMLBase.__init(prob, solver, args...; kwargs...), alg.algs),
                 alg, 1)
         end
     end
 end
 
-@generated function SciMLBase.solve!(cache::NonlinearSolvePolyAlgorithmCache{iip,
-        N}) where {iip, N}
-    calls = [
-        quote
+@generated function SciMLBase.solve!(cache::NonlinearSolvePolyAlgorithmCache{
+        iip, N}) where {iip, N}
+    calls = [quote
         1 ≤ cache.current ≤ length(cache.caches) ||
             error("Current choices shouldn't get here!")
-    end
-    ]
+    end]
 
     cache_syms = [gensym("cache") for i in 1:N]
     sol_syms = [gensym("sol") for i in 1:N]
@@ -90,8 +87,9 @@ end
                         stats = $(sol_syms[i]).stats
                         u = $(sol_syms[i]).u
                         fu = get_fu($(cache_syms[i]))
-                        return SciMLBase.build_solution($(sol_syms[i]).prob, cache.alg, u,
-                            fu; retcode = ReturnCode.Success, stats,
+                        return SciMLBase.build_solution(
+                            $(sol_syms[i]).prob, cache.alg, u, fu;
+                            retcode = ReturnCode.Success, stats,
                             original = $(sol_syms[i]), trace = $(sol_syms[i]).trace)
                     end
                     cache.current = $(i + 1)
@@ -112,8 +110,8 @@ end
             stats = cache.caches[idx].stats
             u = cache.caches[idx].u
 
-            return SciMLBase.build_solution(cache.caches[idx].prob, cache.alg, u,
-                fus[idx]; retcode, stats, cache.caches[idx].trace)
+            return SciMLBase.build_solution(cache.caches[idx].prob, cache.alg, u, fus[idx];
+                retcode, stats, cache.caches[idx].trace)
         end)
 
     return Expr(:block, calls...)
@@ -122,19 +120,19 @@ end
 for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProblem, :NLLS))
     algType = NonlinearSolvePolyAlgorithm{pType}
     @eval begin
-        @generated function SciMLBase.__solve(prob::$probType, alg::$algType{N}, args...;
-                kwargs...) where {N}
+        @generated function SciMLBase.__solve(
+                prob::$probType, alg::$algType{N}, args...; kwargs...) where {N}
             calls = []
             sol_syms = [gensym("sol") for _ in 1:N]
             for i in 1:N
                 cur_sol = sol_syms[i]
                 push!(calls,
                     quote
-                        $(cur_sol) = SciMLBase.__solve(prob, alg.algs[$(i)], args...;
-                            kwargs...)
+                        $(cur_sol) = SciMLBase.__solve(prob, alg.algs[$(i)], args...; kwargs...)
                         if SciMLBase.successful_retcode($(cur_sol))
-                            return SciMLBase.build_solution(prob, alg, $(cur_sol).u,
-                                $(cur_sol).resid; $(cur_sol).retcode, $(cur_sol).stats,
+                            return SciMLBase.build_solution(
+                                prob, alg, $(cur_sol).u, $(cur_sol).resid;
+                                $(cur_sol).retcode, $(cur_sol).stats,
                                 original = $(cur_sol), trace = $(cur_sol).trace)
                         end
                     end)
@@ -145,11 +143,10 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
                 push!(calls, :($(resid) = $(sym).resid))
             end
 
-            push!(calls,
-                quote
-                    resids = tuple($(Tuple(resids)...))
-                    minfu, idx = __findmin(DEFAULT_NORM, resids)
-                end)
+            push!(calls, quote
+                resids = tuple($(Tuple(resids)...))
+                minfu, idx = __findmin(DEFAULT_NORM, resids)
+            end)
 
             for i in 1:N
                 push!(calls,
@@ -217,8 +214,9 @@ for more performance and then tries more robust techniques if the faster ones fa
   - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
     are compatible with the problem type. Defaults to `Float64`.
 """
-function FastShortcutNonlinearPolyalg(::Type{T} = Float64; concrete_jac = nothing,
-        linsolve = nothing, precs = DEFAULT_PRECS, must_use_jacobian::Val{JAC} = Val(false),
+function FastShortcutNonlinearPolyalg(
+        ::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
+        precs = DEFAULT_PRECS, must_use_jacobian::Val{JAC} = Val(false),
         prefer_simplenonlinearsolve::Val{SA} = Val(false),
         autodiff = nothing) where {T, JAC, SA}
     if JAC
@@ -237,8 +235,7 @@ function FastShortcutNonlinearPolyalg(::Type{T} = Float64; concrete_jac = nothin
         # and thus are not included in the polyalgorithm
         if SA
             if __is_complex(T)
-                algs = (SimpleBroyden(),
-                    Broyden(; init_jacobian = Val(:true_jacobian)),
+                algs = (SimpleBroyden(), Broyden(; init_jacobian = Val(:true_jacobian)),
                     SimpleKlement(),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff))
             else
@@ -253,8 +250,7 @@ function FastShortcutNonlinearPolyalg(::Type{T} = Float64; concrete_jac = nothin
             end
         else
             if __is_complex(T)
-                algs = (Broyden(),
-                    Broyden(; init_jacobian = Val(:true_jacobian)),
+                algs = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian)),
                     Klement(; linsolve, precs),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff))
             else
@@ -317,8 +313,8 @@ end
 ## can use that!
 function SciMLBase.__init(prob::NonlinearProblem, ::Nothing, args...; kwargs...)
     must_use_jacobian = Val(prob.f.jac !== nothing)
-    return SciMLBase.__init(prob,
-        FastShortcutNonlinearPolyalg(eltype(prob.u0); must_use_jacobian),
+    return SciMLBase.__init(
+        prob, FastShortcutNonlinearPolyalg(eltype(prob.u0); must_use_jacobian),
         args...; kwargs...)
 end
 
@@ -326,17 +322,19 @@ function SciMLBase.__solve(prob::NonlinearProblem, ::Nothing, args...; kwargs...
     must_use_jacobian = Val(prob.f.jac !== nothing)
     prefer_simplenonlinearsolve = Val(prob.u0 isa SArray)
     return SciMLBase.__solve(prob,
-        FastShortcutNonlinearPolyalg(eltype(prob.u0); must_use_jacobian,
-            prefer_simplenonlinearsolve), args...; kwargs...)
+        FastShortcutNonlinearPolyalg(
+            eltype(prob.u0); must_use_jacobian, prefer_simplenonlinearsolve),
+        args...;
+        kwargs...)
 end
 
 function SciMLBase.__init(prob::NonlinearLeastSquaresProblem, ::Nothing, args...; kwargs...)
-    return SciMLBase.__init(prob, FastShortcutNLLSPolyalg(eltype(prob.u0)), args...;
-        kwargs...)
+    return SciMLBase.__init(
+        prob, FastShortcutNLLSPolyalg(eltype(prob.u0)), args...; kwargs...)
 end
 
-function SciMLBase.__solve(prob::NonlinearLeastSquaresProblem, ::Nothing, args...;
-        kwargs...)
-    return SciMLBase.__solve(prob, FastShortcutNLLSPolyalg(eltype(prob.u0)), args...;
-        kwargs...)
+function SciMLBase.__solve(
+        prob::NonlinearLeastSquaresProblem, ::Nothing, args...; kwargs...)
+    return SciMLBase.__solve(
+        prob, FastShortcutNLLSPolyalg(eltype(prob.u0)), args...; kwargs...)
 end
diff --git a/src/descent/damped_newton.jl b/src/descent/damped_newton.jl
index 77ad95b54..3e21cc2d1 100644
--- a/src/descent/damped_newton.jl
+++ b/src/descent/damped_newton.jl
@@ -51,11 +51,10 @@ end
 
 @internal_caches DampedNewtonDescentCache :lincache :damping_fn_cache
 
-function __internal_init(
-        prob::AbstractNonlinearProblem, alg::DampedNewtonDescent, J, fu, u;
-        pre_inverted::Val{INV} = False, linsolve_kwargs = (;), abstol = nothing,
-        timer = get_timer_output(), reltol = nothing, alias_J = true,
-        shared::Val{N} = Val(1), kwargs...) where {INV, N}
+function __internal_init(prob::AbstractNonlinearProblem, alg::DampedNewtonDescent, J,
+        fu, u; pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
+        abstol = nothing, timer = get_timer_output(), reltol = nothing,
+        alias_J = true, shared::Val{N} = Val(1), kwargs...) where {INV, N}
     length(fu) != length(u) &&
         @assert !INV "Precomputed Inverse for Non-Square Jacobian doesn't make sense."
     @bb δu = similar(u)
@@ -103,8 +102,7 @@ function __internal_init(
         A, b = J_cache, rhs_cache
     elseif mode === :simple
         damping_fn_cache = __internal_init(
-            prob, alg.damping_fn, alg.initial_damping, J, fu,
-            u, False; kwargs...)
+            prob, alg.damping_fn, alg.initial_damping, J, fu, u, False; kwargs...)
         J_cache = __maybe_unaliased(J, alias_J)
         D = damping_fn_cache(nothing)
         J_damped = __dampen_jacobian!!(J_cache, J, D)
@@ -117,8 +115,7 @@ function __internal_init(
         jac_damp = requires_normal_form_jacobian(alg.damping_fn) ? JᵀJ : J
         rhs_damp = requires_normal_form_rhs(alg.damping_fn) ? Jᵀfu : fu
         damping_fn_cache = __internal_init(prob, alg.damping_fn, alg.initial_damping,
-            jac_damp,
-            rhs_damp, u, True; kwargs...)
+            jac_damp, rhs_damp, u, True; kwargs...)
         D = damping_fn_cache(nothing)
         @bb J_cache = similar(JᵀJ)
         @bb @. J_cache = 0
@@ -127,16 +124,16 @@ function __internal_init(
         rhs_cache = nothing
     end
 
-    lincache = LinearSolverCache(alg, alg.linsolve, A, b, _vec(u); abstol, reltol,
-        linsolve_kwargs...)
+    lincache = LinearSolverCache(
+        alg, alg.linsolve, A, b, _vec(u); abstol, reltol, linsolve_kwargs...)
 
-    return DampedNewtonDescentCache{INV, mode}(J_cache, δu, δus, lincache, JᵀJ, Jᵀfu,
-        rhs_cache, damping_fn_cache, timer)
+    return DampedNewtonDescentCache{INV, mode}(
+        J_cache, δu, δus, lincache, JᵀJ, Jᵀfu, rhs_cache, damping_fn_cache, timer)
 end
 
-function __internal_solve!(cache::DampedNewtonDescentCache{INV, mode}, J, fu, u,
-        idx::Val{N} = Val(1); skip_solve::Bool = false, new_jacobian::Bool = true,
-        kwargs...) where {INV, N, mode}
+function __internal_solve!(cache::DampedNewtonDescentCache{INV, mode}, J, fu,
+        u, idx::Val{N} = Val(1); skip_solve::Bool = false,
+        new_jacobian::Bool = true, kwargs...) where {INV, N, mode}
     δu = get_du(cache, idx)
     skip_solve && return δu, true, (;)
 
@@ -186,8 +183,8 @@ function __internal_solve!(cache::DampedNewtonDescentCache{INV, mode}, J, fu, u,
                 INV && (J = inv(J))
                 @bb cache.JᵀJ_cache = transpose(J) × J
                 @bb cache.Jᵀfu_cache = transpose(J) × vec(fu)
-                D = __internal_solve!(cache.damping_fn_cache, cache.JᵀJ_cache,
-                    cache.Jᵀfu_cache, True)
+                D = __internal_solve!(
+                    cache.damping_fn_cache, cache.JᵀJ_cache, cache.Jᵀfu_cache, True)
                 cache.J = __dampen_jacobian!!(cache.J, cache.JᵀJ_cache, D)
                 A = __maybe_symmetric(cache.J)
             elseif !recompute_A
@@ -203,8 +200,8 @@ function __internal_solve!(cache::DampedNewtonDescentCache{INV, mode}, J, fu, u,
     end
 
     @static_timeit cache.timer "linear solve" begin
-        δu = cache.lincache(; A, b,
-            reuse_A_if_factorization = !new_jacobian && !recompute_A,
+        δu = cache.lincache(;
+            A, b, reuse_A_if_factorization = !new_jacobian && !recompute_A,
             kwargs..., linu = _vec(δu))
         δu = _restructure(get_du(cache, idx), δu)
     end
diff --git a/src/descent/dogleg.jl b/src/descent/dogleg.jl
index e1a50832f..ee725988b 100644
--- a/src/descent/dogleg.jl
+++ b/src/descent/dogleg.jl
@@ -33,8 +33,7 @@ function Dogleg(; linsolve = nothing, precs = DEFAULT_PRECS, damping = False,
         SteepestDescent(; linsolve, precs))
 end
 
-@concrete mutable struct DoglegCache{pre_inverted, normalform} <:
-                         AbstractDescentCache
+@concrete mutable struct DoglegCache{pre_inverted, normalform} <: AbstractDescentCache
     δu
     δus
     newton_cache
@@ -49,9 +48,9 @@ end
 @internal_caches DoglegCache :newton_cache :cauchy_cache
 
 function __internal_init(prob::AbstractNonlinearProblem, alg::Dogleg, J, fu, u;
-        pre_inverted::Val{INV} = False, linsolve_kwargs = (;), abstol = nothing,
-        reltol = nothing, internalnorm::F = DEFAULT_NORM, shared::Val{N} = Val(1),
-        kwargs...) where {F, INV, N}
+        pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
+        abstol = nothing, reltol = nothing, internalnorm::F = DEFAULT_NORM,
+        shared::Val{N} = Val(1), kwargs...) where {F, INV, N}
     newton_cache = __internal_init(prob, alg.newton_descent, J, fu, u; pre_inverted,
         linsolve_kwargs, abstol, reltol, shared, kwargs...)
     cauchy_cache = __internal_init(prob, alg.steepest_descent, J, fu, u; pre_inverted,
@@ -82,8 +81,8 @@ function __internal_solve!(cache::DoglegCache{INV, NF}, J, fu, u, idx::Val{N} =
                                     want to use a Trust Region."
     δu = get_du(cache, idx)
     T = promote_type(eltype(u), eltype(fu))
-    δu_newton, _, _ = __internal_solve!(cache.newton_cache, J, fu, u, idx; skip_solve,
-        kwargs...)
+    δu_newton, _, _ = __internal_solve!(
+        cache.newton_cache, J, fu, u, idx; skip_solve, kwargs...)
 
     # Newton's Step within the trust region
     if cache.internalnorm(δu_newton) ≤ trust_region
@@ -103,8 +102,8 @@ function __internal_solve!(cache::DoglegCache{INV, NF}, J, fu, u, idx::Val{N} =
         @bb cache.δu_cache_mul = JᵀJ × vec(δu_cauchy)
         δuJᵀJδu = __dot(δu_cauchy, cache.δu_cache_mul)
     else
-        δu_cauchy, _, _ = __internal_solve!(cache.cauchy_cache, J, fu, u, idx; skip_solve,
-            kwargs...)
+        δu_cauchy, _, _ = __internal_solve!(
+            cache.cauchy_cache, J, fu, u, idx; skip_solve, kwargs...)
         J_ = INV ? inv(J) : J
         l_grad = cache.internalnorm(δu_cauchy)
         @bb cache.JᵀJ_cache = J × vec(δu_cauchy)  # TODO: Rename
diff --git a/src/descent/geodesic_acceleration.jl b/src/descent/geodesic_acceleration.jl
index 35764783c..6cba1202e 100644
--- a/src/descent/geodesic_acceleration.jl
+++ b/src/descent/geodesic_acceleration.jl
@@ -31,8 +31,7 @@ for other methods are not theorectically or experimentally verified.
 end
 
 function Base.show(io::IO, alg::GeodesicAcceleration)
-    print(
-        io, "GeodesicAcceleration(descent = $(alg.descent), finite_diff_step_geodesic = ",
+    print(io, "GeodesicAcceleration(descent = $(alg.descent), finite_diff_step_geodesic = ",
         "$(alg.finite_diff_step_geodesic), α = $(alg.α))")
 end
 
@@ -55,8 +54,8 @@ get_linear_solver(alg::GeodesicAcceleration) = get_linear_solver(alg.descent)
     last_step_accepted::Bool
 end
 
-function __reinit_internal!(cache::GeodesicAccelerationCache, args...; p = cache.p,
-        kwargs...)
+function __reinit_internal!(
+        cache::GeodesicAccelerationCache, args...; p = cache.p, kwargs...)
     cache.p = p
     cache.last_step_accepted = false
 end
@@ -84,10 +83,10 @@ function set_acceleration!(cache::GeodesicAccelerationCache, δa, ::Val{N}) wher
     set_du!(cache.descent_cache, δa, Val(2N))
 end
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::GeodesicAcceleration, J, fu,
-        u; shared::Val{N} = Val(1), pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
-        abstol = nothing, reltol = nothing, internalnorm::F = DEFAULT_NORM,
-        kwargs...) where {INV, N, F}
+function __internal_init(prob::AbstractNonlinearProblem, alg::GeodesicAcceleration, J,
+        fu, u; shared::Val{N} = Val(1), pre_inverted::Val{INV} = False,
+        linsolve_kwargs = (;), abstol = nothing, reltol = nothing,
+        internalnorm::F = DEFAULT_NORM, kwargs...) where {INV, N, F}
     T = promote_type(eltype(u), eltype(fu))
     @bb δu = similar(u)
     δus = N ≤ 1 ? nothing : map(2:N) do i
@@ -98,17 +97,17 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::GeodesicAccelerati
     @bb Jv = similar(fu)
     @bb fu_cache = copy(fu)
     @bb u_cache = similar(u)
-    return GeodesicAccelerationCache(δu, δus, descent_cache, prob.f, prob.p, T(alg.α),
-        internalnorm, T(alg.finite_diff_step_geodesic), Jv, fu_cache, u_cache, false)
+    return GeodesicAccelerationCache(
+        δu, δus, descent_cache, prob.f, prob.p, T(alg.α), internalnorm,
+        T(alg.finite_diff_step_geodesic), Jv, fu_cache, u_cache, false)
 end
 
-function __internal_solve!(
-        cache::GeodesicAccelerationCache, J, fu, u, idx::Val{N} = Val(1);
+function __internal_solve!(cache::GeodesicAccelerationCache, J, fu, u, idx::Val{N} = Val(1);
         skip_solve::Bool = false, kwargs...) where {N}
     a, v, δu = get_acceleration(cache, idx), get_velocity(cache, idx), get_du(cache, idx)
     skip_solve && return δu, true, (; a, v)
-    v, _, _ = __internal_solve!(cache.descent_cache, J, fu, u, Val(2N - 1); skip_solve,
-        kwargs...)
+    v, _, _ = __internal_solve!(
+        cache.descent_cache, J, fu, u, Val(2N - 1); skip_solve, kwargs...)
 
     @bb @. cache.u_cache = u + cache.h * v
     cache.fu_cache = evaluate_f!!(cache.f, cache.fu_cache, cache.u_cache, cache.p)
diff --git a/src/descent/newton.jl b/src/descent/newton.jl
index c8ba35ed9..cfbc1c239 100644
--- a/src/descent/newton.jl
+++ b/src/descent/newton.jl
@@ -32,24 +32,24 @@ end
 
 @internal_caches NewtonDescentCache :lincache
 
-function __internal_init(prob::NonlinearProblem, alg::NewtonDescent, J, fu, u;
-        shared::Val{N} = Val(1), pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
-        abstol = nothing, reltol = nothing, timer = get_timer_output(),
-        kwargs...) where {INV, N}
+function __internal_init(
+        prob::NonlinearProblem, alg::NewtonDescent, J, fu, u; shared::Val{N} = Val(1),
+        pre_inverted::Val{INV} = False, linsolve_kwargs = (;), abstol = nothing,
+        reltol = nothing, timer = get_timer_output(), kwargs...) where {INV, N}
     @bb δu = similar(u)
     δus = N ≤ 1 ? nothing : map(2:N) do i
         @bb δu_ = similar(u)
     end
     INV && return NewtonDescentCache{true, false}(δu, δus, nothing, nothing, nothing, timer)
-    lincache = LinearSolverCache(alg, alg.linsolve, J, _vec(fu), _vec(u); abstol, reltol,
-        linsolve_kwargs...)
+    lincache = LinearSolverCache(
+        alg, alg.linsolve, J, _vec(fu), _vec(u); abstol, reltol, linsolve_kwargs...)
     return NewtonDescentCache{false, false}(δu, δus, lincache, nothing, nothing, timer)
 end
 
-function __internal_init(prob::NonlinearLeastSquaresProblem, alg::NewtonDescent, J, fu, u;
-        pre_inverted::Val{INV} = False, linsolve_kwargs = (;), shared::Val{N} = Val(1),
-        abstol = nothing, reltol = nothing, timer = get_timer_output(),
-        kwargs...) where {INV, N}
+function __internal_init(prob::NonlinearLeastSquaresProblem, alg::NewtonDescent, J,
+        fu, u; pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
+        shared::Val{N} = Val(1), abstol = nothing, reltol = nothing,
+        timer = get_timer_output(), kwargs...) where {INV, N}
     length(fu) != length(u) &&
         @assert !INV "Precomputed Inverse for Non-Square Jacobian doesn't make sense."
 
@@ -62,8 +62,8 @@ function __internal_init(prob::NonlinearLeastSquaresProblem, alg::NewtonDescent,
         JᵀJ, Jᵀfu = nothing, nothing
         A, b = J, _vec(fu)
     end
-    lincache = LinearSolverCache(alg, alg.linsolve, A, b, _vec(u); abstol, reltol,
-        linsolve_kwargs...)
+    lincache = LinearSolverCache(
+        alg, alg.linsolve, A, b, _vec(u); abstol, reltol, linsolve_kwargs...)
     @bb δu = similar(u)
     δus = N ≤ 1 ? nothing : map(2:N) do i
         @bb δu_ = similar(u)
@@ -71,9 +71,9 @@ function __internal_init(prob::NonlinearLeastSquaresProblem, alg::NewtonDescent,
     return NewtonDescentCache{false, normal_form}(δu, δus, lincache, JᵀJ, Jᵀfu, timer)
 end
 
-function __internal_solve!(cache::NewtonDescentCache{INV, false}, J, fu, u,
-        idx::Val = Val(1); skip_solve::Bool = false, new_jacobian::Bool = true,
-        kwargs...) where {INV}
+function __internal_solve!(
+        cache::NewtonDescentCache{INV, false}, J, fu, u, idx::Val = Val(1);
+        skip_solve::Bool = false, new_jacobian::Bool = true, kwargs...) where {INV}
     δu = get_du(cache, idx)
     skip_solve && return δu, true, (;)
     if INV
@@ -81,8 +81,9 @@ function __internal_solve!(cache::NewtonDescentCache{INV, false}, J, fu, u,
         @bb δu = J × vec(fu)
     else
         @static_timeit cache.timer "linear solve" begin
-            δu = cache.lincache(; A = J, b = _vec(fu), kwargs..., linu = _vec(δu),
-                du = _vec(δu), reuse_A_if_factorization = !new_jacobian || (idx !== Val(1)))
+            δu = cache.lincache(;
+                A = J, b = _vec(fu), kwargs..., linu = _vec(δu), du = _vec(δu),
+                reuse_A_if_factorization = !new_jacobian || (idx !== Val(1)))
             δu = _restructure(get_du(cache, idx), δu)
         end
     end
@@ -91,8 +92,9 @@ function __internal_solve!(cache::NewtonDescentCache{INV, false}, J, fu, u,
     return δu, true, (;)
 end
 
-function __internal_solve!(cache::NewtonDescentCache{false, true}, J, fu, u,
-        idx::Val = Val(1); skip_solve::Bool = false, new_jacobian::Bool = true, kwargs...)
+function __internal_solve!(
+        cache::NewtonDescentCache{false, true}, J, fu, u, idx::Val = Val(1);
+        skip_solve::Bool = false, new_jacobian::Bool = true, kwargs...)
     δu = get_du(cache, idx)
     skip_solve && return δu, true, (;)
     if idx === Val(1)
diff --git a/src/descent/steepest.jl b/src/descent/steepest.jl
index d19505a86..40919cc6e 100644
--- a/src/descent/steepest.jl
+++ b/src/descent/steepest.jl
@@ -29,8 +29,9 @@ end
 
 @internal_caches SteepestDescentCache :lincache
 
-@inline function __internal_init(prob::AbstractNonlinearProblem, alg::SteepestDescent, J,
-        fu, u; shared::Val{N} = Val(1), pre_inverted::Val{INV} = False,
+@inline function __internal_init(
+        prob::AbstractNonlinearProblem, alg::SteepestDescent, J, fu,
+        u; shared::Val{N} = Val(1), pre_inverted::Val{INV} = False,
         linsolve_kwargs = (;), abstol = nothing, reltol = nothing,
         timer = get_timer_output(), kwargs...) where {INV, N}
     INV && @assert length(fu)==length(u) "Non-Square Jacobian Inverse doesn't make sense."
@@ -39,8 +40,8 @@ end
         @bb δu_ = similar(u)
     end
     if INV
-        lincache = LinearSolverCache(alg, alg.linsolve, transpose(J), _vec(fu), _vec(u);
-            abstol, reltol, linsolve_kwargs...)
+        lincache = LinearSolverCache(alg, alg.linsolve, transpose(J), _vec(fu),
+            _vec(u); abstol, reltol, linsolve_kwargs...)
     else
         lincache = nothing
     end
@@ -53,8 +54,9 @@ function __internal_solve!(cache::SteepestDescentCache{INV}, J, fu, u, idx::Val
     if INV
         A = J === nothing ? nothing : transpose(J)
         @static_timeit cache.timer "linear solve" begin
-            δu = cache.lincache(; A, b = _vec(fu), kwargs..., linu = _vec(δu),
-                du = _vec(δu), reuse_A_if_factorization = !new_jacobian || idx !== Val(1))
+            δu = cache.lincache(;
+                A, b = _vec(fu), kwargs..., linu = _vec(δu), du = _vec(δu),
+                reuse_A_if_factorization = !new_jacobian || idx !== Val(1))
             δu = _restructure(get_du(cache, idx), δu)
         end
     else
diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index 6e13043de..9d4f52e71 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -9,8 +9,8 @@ struct NoLineSearch <: AbstractNonlinearSolveLineSearchAlgorithm end
     α
 end
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::NoLineSearch, f::F, fu, u,
-        p, args...; kwargs...) where {F}
+function __internal_init(prob::AbstractNonlinearProblem, alg::NoLineSearch,
+        f::F, fu, u, p, args...; kwargs...) where {F}
     return NoLineSearchCache(promote_type(eltype(fu), eltype(u))(true))
 end
 
@@ -80,8 +80,9 @@ Base.@deprecate_binding LineSearch LineSearchesJL true
     nf::Base.RefValue{Int}
 end
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::LineSearchesJL, f::F, fu, u,
-        p, args...; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+function __internal_init(
+        prob::AbstractNonlinearProblem, alg::LineSearchesJL, f::F, fu, u, p,
+        args...; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     T = promote_type(eltype(fu), eltype(u))
     if u isa Number
         grad_op = @closure (u, fu, p) -> last(__value_derivative(Base.Fix2(f, p), u)) * fu
@@ -94,8 +95,8 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::LineSearchesJL, f:
                 grad_op = @closure (u, fu, p) -> f.vjp(fu, u, p)
             end
         else
-            autodiff = get_concrete_reverse_ad(alg.autodiff, prob;
-                check_forward_mode = true)
+            autodiff = get_concrete_reverse_ad(
+                alg.autodiff, prob; check_forward_mode = true)
             vjp_op = VecJacOperator(prob, fu, u; autodiff)
             if isinplace(prob)
                 g_cache = similar(u)
@@ -134,17 +135,16 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::LineSearchesJL, f:
         return obj, dot(g₀, du)
     end
 
-    return LineSearchesJLCache(f, p, ϕ, dϕ, ϕdϕ, alg.method, T(alg.initial_alpha), grad_op,
-        u_cache, fu_cache, nf)
+    return LineSearchesJLCache(
+        f, p, ϕ, dϕ, ϕdϕ, alg.method, T(alg.initial_alpha), grad_op, u_cache, fu_cache, nf)
 end
 
 function __internal_solve!(cache::LineSearchesJLCache, u, du; kwargs...)
     ϕ = @closure α -> cache.ϕ(cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache)
-    dϕ = @closure α -> cache.dϕ(cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache,
-        cache.grad_op)
+    dϕ = @closure α -> cache.dϕ(
+        cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache, cache.grad_op)
     ϕdϕ = @closure α -> cache.ϕdϕ(
-        cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache,
-        cache.grad_op)
+        cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache, cache.grad_op)
 
     ϕ₀, dϕ₀ = ϕdϕ(zero(eltype(u)))
 
@@ -225,8 +225,9 @@ end
     nf::Base.RefValue{Int}
 end
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::RobustNonMonotoneLineSearch,
-        f::F, fu, u, p, args...; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+function __internal_init(
+        prob::AbstractNonlinearProblem, alg::RobustNonMonotoneLineSearch, f::F, fu,
+        u, p, args...; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     @bb u_cache = similar(u)
     @bb fu_cache = similar(fu)
     T = promote_type(eltype(fu), eltype(u))
@@ -242,9 +243,10 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::RobustNonMonotoneL
     fn₁ = internalnorm(fu)^alg.n_exp
     η_strategy = @closure (n, xₙ, fₙ) -> alg.η_strategy(fn₁, n, xₙ, fₙ)
 
-    return RobustNonMonotoneLineSearchCache(f, p, ϕ, u_cache, fu_cache, internalnorm,
-        alg.maxiters, fill(fn₁, alg.M), T(alg.gamma), T(alg.sigma_1), alg.M, T(alg.tau_min),
-        T(alg.tau_max), 0, η_strategy, alg.n_exp, nf)
+    return RobustNonMonotoneLineSearchCache(
+        f, p, ϕ, u_cache, fu_cache, internalnorm, alg.maxiters,
+        fill(fn₁, alg.M), T(alg.gamma), T(alg.sigma_1), alg.M,
+        T(alg.tau_min), T(alg.tau_max), 0, η_strategy, alg.n_exp, nf)
 end
 
 function __internal_solve!(cache::RobustNonMonotoneLineSearchCache, u, du; kwargs...)
@@ -316,8 +318,9 @@ end
     nf::Base.RefValue{Int}
 end
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::LiFukushimaLineSearch,
-        f::F, fu, u, p, args...; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+function __internal_init(
+        prob::AbstractNonlinearProblem, alg::LiFukushimaLineSearch, f::F, fu, u,
+        p, args...; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     @bb u_cache = similar(u)
     @bb fu_cache = similar(fu)
     T = promote_type(eltype(fu), eltype(u))
@@ -330,8 +333,9 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::LiFukushimaLineSea
         return internalnorm(fu_cache)
     end
 
-    return LiFukushimaLineSearchCache(ϕ, f, p, internalnorm, u_cache, fu_cache,
-        T(alg.lambda_0), T(alg.beta), T(alg.sigma_1), T(alg.sigma_2), T(alg.eta),
+    return LiFukushimaLineSearchCache(
+        ϕ, f, p, internalnorm, u_cache, fu_cache, T(alg.lambda_0),
+        T(alg.beta), T(alg.sigma_1), T(alg.sigma_2), T(alg.eta),
         T(alg.rho), T(true), alg.nan_max_iter, alg.maxiters, nf)
 end
 
diff --git a/src/globalization/trust_region.jl b/src/globalization/trust_region.jl
index 891767a4a..6004695ec 100644
--- a/src/globalization/trust_region.jl
+++ b/src/globalization/trust_region.jl
@@ -46,8 +46,8 @@ end
     nf::Int
 end
 
-function reinit_cache!(cache::LevenbergMarquardtTrustRegionCache, args...; p = cache.p,
-        u0 = cache.v_cache, kwargs...)
+function reinit_cache!(cache::LevenbergMarquardtTrustRegionCache, args...;
+        p = cache.p, u0 = cache.v_cache, kwargs...)
     cache.p = p
     @bb copyto!(cache.v_cache, u0)
     cache.loss_old = oftype(cache.loss_old, Inf)
@@ -57,18 +57,18 @@ function reinit_cache!(cache::LevenbergMarquardtTrustRegionCache, args...; p = c
 end
 
 function __internal_init(
-        prob::AbstractNonlinearProblem, alg::LevenbergMarquardtTrustRegion,
-        f::F, fu, u, p, args...; internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF}
+        prob::AbstractNonlinearProblem, alg::LevenbergMarquardtTrustRegion, f::F,
+        fu, u, p, args...; internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF}
     T = promote_type(eltype(u), eltype(fu))
     @bb v = copy(u)
     @bb u_cache = similar(u)
     @bb fu_cache = similar(fu)
-    return LevenbergMarquardtTrustRegionCache(f, p, T(Inf), v, T(Inf), internalnorm,
-        alg.β_uphill, false, u_cache, fu_cache, 0)
+    return LevenbergMarquardtTrustRegionCache(
+        f, p, T(Inf), v, T(Inf), internalnorm, alg.β_uphill, false, u_cache, fu_cache, 0)
 end
 
-function __internal_solve!(cache::LevenbergMarquardtTrustRegionCache, J, fu, u, δu,
-        descent_stats)
+function __internal_solve!(
+        cache::LevenbergMarquardtTrustRegionCache, J, fu, u, δu, descent_stats)
     # This should be true if Geodesic Acceleration is being used
     v = hasfield(typeof(descent_stats), :v) ? descent_stats.v : δu
     norm_v = cache.internalnorm(v)
@@ -236,8 +236,8 @@ the value used in the respective paper.
   - `expand_factor`: the factor to expand the trust region radius with if
     `expand_threshold < r` (with `r` defined in `shrink_threshold`). Defaults to `2.0`.
 """
-@kwdef @concrete struct GenericTrustRegionScheme{
-    M <: RadiusUpdateSchemes.AbstractRadiusUpdateScheme}
+@kwdef @concrete struct GenericTrustRegionScheme{M <:
+                                                 RadiusUpdateSchemes.AbstractRadiusUpdateScheme}
     method::M = RadiusUpdateSchemes.Simple
     step_threshold = nothing
     shrink_threshold = nothing
@@ -286,14 +286,15 @@ end
     alg
 end
 
-function reinit_cache!(cache::GenericTrustRegionSchemeCache, args...; u0 = nothing,
-        p = cache.p, kwargs...)
+function reinit_cache!(
+        cache::GenericTrustRegionSchemeCache, args...; u0 = nothing, p = cache.p, kwargs...)
     T = eltype(cache.u_cache)
     cache.p = p
     if u0 !== nothing
         u0_norm = cache.internalnorm(u0)
-        cache.trust_region = __initial_trust_radius(cache.alg.initial_trust_radius, T,
-            cache.alg.method, cache.max_trust_radius, u0_norm, u0_norm)  # FIXME: scheme specific
+        cache.trust_region = __initial_trust_radius(
+            cache.alg.initial_trust_radius, T, cache.alg.method,
+            cache.max_trust_radius, u0_norm, u0_norm)  # FIXME: scheme specific
     end
     cache.last_step_accepted = false
     cache.shrink_counter = 0
@@ -313,14 +314,15 @@ for func in (:__max_trust_radius, :__initial_trust_radius, :__step_threshold,
 end
 
 @inline __max_trust_radius(::Nothing, ::Type{T}, method, u, fu_norm) where {T} = T(Inf)
-@inline function __max_trust_radius(::Nothing, ::Type{T},
-        ::Union{RUS.__Simple, RUS.__NocedalWright}, u, fu_norm) where {T}
+@inline function __max_trust_radius(
+        ::Nothing, ::Type{T}, ::Union{RUS.__Simple, RUS.__NocedalWright},
+        u, fu_norm) where {T}
     u_min, u_max = extrema(u)
     return max(T(fu_norm), u_max - u_min)
 end
 
-@inline function __initial_trust_radius(::Nothing, ::Type{T}, method, max_tr,
-        u0_norm, fu_norm) where {T}
+@inline function __initial_trust_radius(
+        ::Nothing, ::Type{T}, method, max_tr, u0_norm, fu_norm) where {T}
     method isa RUS.__NLsolve && return T(ifelse(u0_norm > 0, u0_norm, 1))
     (method isa RUS.__Hei || method isa RUS.__Bastin) && return T(1)
     method isa RUS.__Fan && return T((fu_norm^0.99) / 10)
@@ -365,16 +367,17 @@ end
 
 @inline __expand_factor(::Nothing, ::Type{T}, method) where {T} = T(2)
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::GenericTrustRegionScheme,
-        f::F, fu, u, p, args...; internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF}
+function __internal_init(
+        prob::AbstractNonlinearProblem, alg::GenericTrustRegionScheme, f::F, fu,
+        u, p, args...; internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF}
     T = promote_type(eltype(u), eltype(fu))
     u0_norm = internalnorm(u)
     fu_norm = internalnorm(fu)
 
     # Common Setup
     max_trust_radius = __max_trust_radius(alg.max_trust_radius, T, alg.method, u, fu_norm)
-    initial_trust_radius = __initial_trust_radius(alg.initial_trust_radius, T, alg.method,
-        max_trust_radius, u0_norm, fu_norm)
+    initial_trust_radius = __initial_trust_radius(
+        alg.initial_trust_radius, T, alg.method, max_trust_radius, u0_norm, fu_norm)
     step_threshold = __step_threshold(alg.step_threshold, T, alg.method)
     shrink_threshold = __shrink_threshold(alg.shrink_threshold, T, alg.method)
     expand_threshold = __expand_threshold(alg.expand_threshold, T, alg.method)
@@ -412,15 +415,15 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::GenericTrustRegion
     @bb fu_cache = similar(fu)
     @bb Jδu_cache = similar(fu)
 
-    return GenericTrustRegionSchemeCache(alg.method, f, p, max_trust_radius,
-        initial_trust_radius, initial_trust_radius, step_threshold, shrink_threshold,
-        expand_threshold, shrink_factor, expand_factor, p1, p2, p3, p4, ϵ, T(0),
-        vjp_operator, jvp_operator, Jᵀfu_cache, Jδu_cache, δu_cache, internalnorm,
-        u_cache, fu_cache, false, 0, 0, alg)
+    return GenericTrustRegionSchemeCache(
+        alg.method, f, p, max_trust_radius, initial_trust_radius, initial_trust_radius,
+        step_threshold, shrink_threshold, expand_threshold, shrink_factor,
+        expand_factor, p1, p2, p3, p4, ϵ, T(0), vjp_operator, jvp_operator, Jᵀfu_cache,
+        Jδu_cache, δu_cache, internalnorm, u_cache, fu_cache, false, 0, 0, alg)
 end
 
-function __internal_solve!(cache::GenericTrustRegionSchemeCache, J, fu, u, δu,
-        descent_stats)
+function __internal_solve!(
+        cache::GenericTrustRegionSchemeCache, J, fu, u, δu, descent_stats)
     T = promote_type(eltype(u), eltype(fu))
     @bb @. cache.u_cache = u + δu
     cache.fu_cache = evaluate_f!!(cache.f, cache.fu_cache, cache.u_cache, cache.p)
@@ -462,8 +465,8 @@ function __internal_solve!(cache::GenericTrustRegionSchemeCache, J, fu, u, δu,
             if cache.ρ ≥ cache.expand_threshold
                 cache.trust_region = cache.expand_factor * cache.internalnorm(δu)
             elseif cache.ρ ≥ cache.p1
-                cache.trust_region = max(cache.trust_region,
-                    cache.expand_factor * cache.internalnorm(δu))
+                cache.trust_region = max(
+                    cache.trust_region, cache.expand_factor * cache.internalnorm(δu))
             end
         end
     elseif cache.method isa RUS.__NocedalWright
@@ -473,14 +476,14 @@ function __internal_solve!(cache::GenericTrustRegionSchemeCache, J, fu, u, δu,
         else
             cache.shrink_counter = 0
             if cache.ρ > cache.expand_threshold &&
-               abs(cache.internalnorm(δu) - cache.trust_region) <
-               1e-6 * cache.trust_region
+               abs(cache.internalnorm(δu) - cache.trust_region) < 1e-6 * cache.trust_region
                 cache.trust_region = cache.expand_factor * cache.trust_region
             end
         end
     elseif cache.method isa RUS.__Hei
-        tr_new = __rfunc(cache.ρ, cache.shrink_threshold, cache.p1, cache.p3, cache.p4,
-            cache.p2) * cache.internalnorm(δu)
+        tr_new = __rfunc(
+            cache.ρ, cache.shrink_threshold, cache.p1, cache.p3, cache.p4, cache.p2) *
+                 cache.internalnorm(δu)
         if tr_new < cache.trust_region
             cache.shrink_counter += 1
         else
@@ -507,16 +510,14 @@ function __internal_solve!(cache::GenericTrustRegionSchemeCache, J, fu, u, δu,
             cache.shrink_counter += 1
         else
             cache.shrink_counter = 0
-            cache.ρ > cache.expand_threshold && (cache.p1 = min(cache.p1 * cache.p3,
-                cache.p4))
+            cache.ρ > cache.expand_threshold &&
+                (cache.p1 = min(cache.p1 * cache.p3, cache.p4))
         end
         cache.trust_region = cache.p1 * (cache.internalnorm(cache.fu_cache)^T(0.99))
     elseif cache.method isa RUS.__Bastin
         if cache.ρ > cache.step_threshold
-            jvp_op = StatefulJacobianOperator(cache.jvp_operator, cache.u_cache,
-                cache.p)
-            vjp_op = StatefulJacobianOperator(cache.vjp_operator, cache.u_cache,
-                cache.p)
+            jvp_op = StatefulJacobianOperator(cache.jvp_operator, cache.u_cache, cache.p)
+            vjp_op = StatefulJacobianOperator(cache.vjp_operator, cache.u_cache, cache.p)
             @bb cache.Jδu_cache = jvp_op × vec(δu)
             @bb cache.Jᵀfu_cache = vjp_op × vec(cache.fu_cache)
             denom_1 = dot(_vec(δu), cache.Jᵀfu_cache)
@@ -541,7 +542,6 @@ end
 
 # R-function for adaptive trust region method
 function __rfunc(r::R, c2::R, M::R, γ1::R, γ2::R, β::R) where {R <: Real}
-    return ifelse(r ≥ c2,
-        (2 * (M - 1 - γ2) * atan(r - c2) + (1 + γ2)) / R(π),
+    return ifelse(r ≥ c2, (2 * (M - 1 - γ2) * atan(r - c2) + (1 + γ2)) / R(π),
         (1 - γ1 - β) * (exp(r - c2) + β / (1 - γ1 - β)))
 end
diff --git a/src/internal/approximate_initialization.jl b/src/internal/approximate_initialization.jl
index bb9898009..60f4a7584 100644
--- a/src/internal/approximate_initialization.jl
+++ b/src/internal/approximate_initialization.jl
@@ -63,17 +63,16 @@ structure as specified by `structure`.
     structure
 end
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::IdentityInitialization,
-        solver,
-        f::F, fu, u::Number, p; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+function __internal_init(
+        prob::AbstractNonlinearProblem, alg::IdentityInitialization, solver, f::F,
+        fu, u::Number, p; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     α = __initial_alpha(alg.alpha, u, fu, internalnorm)
-    return InitializedApproximateJacobianCache(α, alg.structure, alg, nothing, true,
-        internalnorm)
+    return InitializedApproximateJacobianCache(
+        α, alg.structure, alg, nothing, true, internalnorm)
 end
 function __internal_init(prob::AbstractNonlinearProblem, alg::IdentityInitialization,
-        solver,
-        f::F, fu::StaticArray, u::StaticArray, p; internalnorm::IN = DEFAULT_NORM,
-        kwargs...) where {IN, F}
+        solver, f::F, fu::StaticArray, u::StaticArray, p;
+        internalnorm::IN = DEFAULT_NORM, kwargs...) where {IN, F}
     α = __initial_alpha(alg.alpha, u, fu, internalnorm)
     if alg.structure isa DiagonalStructure
         @assert length(u)==length(fu) "Diagonal Jacobian Structure must be square!"
@@ -87,11 +86,12 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::IdentityInitializa
         end
         J = alg.structure(J_; alias = true)
     end
-    return InitializedApproximateJacobianCache(J, alg.structure, alg, nothing, true,
-        internalnorm)
+    return InitializedApproximateJacobianCache(
+        J, alg.structure, alg, nothing, true, internalnorm)
 end
-function __internal_init(prob::AbstractNonlinearProblem, alg::IdentityInitialization,
-        solver, f::F, fu, u, p; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+function __internal_init(
+        prob::AbstractNonlinearProblem, alg::IdentityInitialization, solver,
+        f::F, fu, u, p; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     α = __initial_alpha(alg.alpha, u, fu, internalnorm)
     if alg.structure isa DiagonalStructure
         @assert length(u)==length(fu) "Diagonal Jacobian Structure must be square!"
@@ -100,8 +100,8 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::IdentityInitializa
         J_ = similar(fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u))
         J = alg.structure(__make_identity!!(J_, α); alias = true)
     end
-    return InitializedApproximateJacobianCache(J, alg.structure, alg, nothing, true,
-        internalnorm)
+    return InitializedApproximateJacobianCache(
+        J, alg.structure, alg, nothing, true, internalnorm)
 end
 
 @inline function __initial_alpha(α, u, fu, internalnorm::F) where {F}
@@ -145,15 +145,15 @@ make a selection automatically.
     autodiff
 end
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::TrueJacobianInitialization,
-        solver, f::F, fu, u, p; linsolve = missing, internalnorm::IN = DEFAULT_NORM,
-        kwargs...) where {F, IN}
-    autodiff = get_concrete_forward_ad(alg.autodiff, prob; check_reverse_mode = false,
-        kwargs...)
+function __internal_init(
+        prob::AbstractNonlinearProblem, alg::TrueJacobianInitialization, solver, f::F, fu,
+        u, p; linsolve = missing, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+    autodiff = get_concrete_forward_ad(
+        alg.autodiff, prob; check_reverse_mode = false, kwargs...)
     jac_cache = JacobianCache(prob, solver, prob.f, fu, u, p; autodiff, linsolve)
     J = alg.structure(jac_cache(nothing))
-    return InitializedApproximateJacobianCache(J, alg.structure, alg, jac_cache, false,
-        internalnorm)
+    return InitializedApproximateJacobianCache(
+        J, alg.structure, alg, jac_cache, false, internalnorm)
 end
 
 """
@@ -205,8 +205,8 @@ function (cache::InitializedApproximateJacobianCache)(::Nothing)
     return get_full_jacobian(cache, cache.structure, cache.J)
 end
 
-function __internal_solve!(cache::InitializedApproximateJacobianCache, fu, u,
-        ::Val{reinit}) where {reinit}
+function __internal_solve!(
+        cache::InitializedApproximateJacobianCache, fu, u, ::Val{reinit}) where {reinit}
     if reinit || !cache.initialized
         cache(cache.alg, fu, u)
         cache.initialized = true
@@ -225,8 +225,8 @@ function (cache::InitializedApproximateJacobianCache)(alg::IdentityInitializatio
     return
 end
 
-function (cache::InitializedApproximateJacobianCache)(alg::TrueJacobianInitialization, fu,
-        u)
+function (cache::InitializedApproximateJacobianCache)(
+        alg::TrueJacobianInitialization, fu, u)
     J_new = cache.cache(u)
     cache.J = cache.structure(cache.J, J_new)
     return
diff --git a/src/internal/forward_diff.jl b/src/internal/forward_diff.jl
index 4555c99a6..190c80645 100644
--- a/src/internal/forward_diff.jl
+++ b/src/internal/forward_diff.jl
@@ -1,17 +1,17 @@
 # Not part of public API but helps reduce code duplication
-import SimpleNonlinearSolve: __nlsolve_ad,
-                             __nlsolve_dual_soln, __nlsolve_∂f_∂p, __nlsolve_∂f_∂u
+import SimpleNonlinearSolve: __nlsolve_ad, __nlsolve_dual_soln, __nlsolve_∂f_∂p,
+                             __nlsolve_∂f_∂u
 
 function SciMLBase.solve(
-        prob::NonlinearProblem{<:Union{Number, <:AbstractArray},
-            iip, <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
-        alg::Union{Nothing, AbstractNonlinearAlgorithm}, args...;
+        prob::NonlinearProblem{<:Union{Number, <:AbstractArray}, iip,
+            <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
+        alg::Union{Nothing, AbstractNonlinearAlgorithm},
+        args...;
         kwargs...) where {T, V, P, iip}
     sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
     dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
     return SciMLBase.build_solution(
-        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats,
-        sol.original)
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
 end
 
 @concrete mutable struct NonlinearSolveForwardDiffCache
@@ -25,10 +25,9 @@ end
 
 @internal_caches NonlinearSolveForwardDiffCache :cache
 
-function reinit_cache!(cache::NonlinearSolveForwardDiffCache; p = cache.p,
-        u0 = get_u(cache.cache), kwargs...)
-    inner_cache = reinit_cache!(cache.cache; p = __value(p), u0 = __value(u0),
-        kwargs...)
+function reinit_cache!(cache::NonlinearSolveForwardDiffCache;
+        p = cache.p, u0 = get_u(cache.cache), kwargs...)
+    inner_cache = reinit_cache!(cache.cache; p = __value(p), u0 = __value(u0), kwargs...)
     cache.cache = inner_cache
     cache.p = p
     cache.values_p = __value(p)
@@ -37,15 +36,16 @@ function reinit_cache!(cache::NonlinearSolveForwardDiffCache; p = cache.p,
 end
 
 function SciMLBase.init(
-        prob::NonlinearProblem{<:Union{Number, <:AbstractArray},
-            iip, <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
-        alg::Union{Nothing, AbstractNonlinearAlgorithm}, args...;
+        prob::NonlinearProblem{<:Union{Number, <:AbstractArray}, iip,
+            <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
+        alg::Union{Nothing, AbstractNonlinearAlgorithm},
+        args...;
         kwargs...) where {T, V, P, iip}
     p = __value(prob.p)
     newprob = NonlinearProblem(prob.f, __value(prob.u0), p; prob.kwargs...)
     cache = init(newprob, alg, args...; kwargs...)
-    return NonlinearSolveForwardDiffCache(cache, newprob, alg, prob.p, p,
-        ForwardDiff.partials(prob.p))
+    return NonlinearSolveForwardDiffCache(
+        cache, newprob, alg, prob.p, p, ForwardDiff.partials(prob.p))
 end
 
 function SciMLBase.solve!(cache::NonlinearSolveForwardDiffCache)
@@ -66,8 +66,8 @@ function SciMLBase.solve!(cache::NonlinearSolveForwardDiffCache)
     end
 
     dual_soln = __nlsolve_dual_soln(sol.u, partials, cache.p)
-    return SciMLBase.build_solution(prob, cache.alg, dual_soln, sol.resid; sol.retcode,
-        sol.stats, sol.original)
+    return SciMLBase.build_solution(
+        prob, cache.alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
 end
 
 @inline __value(x) = x
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index 4f475214b..fc43543ec 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -32,29 +32,27 @@ end
 # AutoDiff Selection Functions
 struct NonlinearSolveTag end
 
-function ForwardDiff.checktag(::Type{<:ForwardDiff.Tag{<:NonlinearSolveTag, <:T}}, f::F,
-        x::AbstractArray{T}) where {T, F}
+function ForwardDiff.checktag(::Type{<:ForwardDiff.Tag{<:NonlinearSolveTag, <:T}},
+        f::F, x::AbstractArray{T}) where {T, F}
     return true
 end
 
 function get_concrete_forward_ad(
-        autodiff::Union{ADTypes.AbstractForwardMode,
-            ADTypes.AbstractFiniteDifferencesMode},
-        prob, sp::Val{test_sparse} = True,
-        args...; kwargs...) where {test_sparse}
+        autodiff::Union{ADTypes.AbstractForwardMode, ADTypes.AbstractFiniteDifferencesMode},
+        prob, sp::Val{test_sparse} = True, args...; kwargs...) where {test_sparse}
     return autodiff
 end
-function get_concrete_forward_ad(autodiff::ADTypes.AbstractADType, prob,
-        sp::Val{test_sparse} = True, args...;
-        check_reverse_mode = true, kwargs...) where {test_sparse}
+function get_concrete_forward_ad(
+        autodiff::ADTypes.AbstractADType, prob, sp::Val{test_sparse} = True,
+        args...; check_reverse_mode = true, kwargs...) where {test_sparse}
     if check_reverse_mode
         @warn "$(autodiff)::$(typeof(autodiff)) is not a \
                `Abstract(Forward/FiniteDifferences)Mode`. Use with caution." maxlog=1
     end
     return autodiff
 end
-function get_concrete_forward_ad(autodiff, prob, sp::Val{test_sparse} = True, args...;
-        kwargs...) where {test_sparse}
+function get_concrete_forward_ad(
+        autodiff, prob, sp::Val{test_sparse} = True, args...; kwargs...) where {test_sparse}
     if test_sparse
         (; sparsity, jac_prototype) = prob.f
         use_sparse_ad = sparsity !== nothing || jac_prototype !== nothing
@@ -71,10 +69,8 @@ function get_concrete_forward_ad(autodiff, prob, sp::Val{test_sparse} = True, ar
 end
 
 function get_concrete_reverse_ad(
-        autodiff::Union{ADTypes.AbstractReverseMode,
-            ADTypes.AbstractFiniteDifferencesMode},
-        prob, sp::Val{test_sparse} = True,
-        args...; kwargs...) where {test_sparse}
+        autodiff::Union{ADTypes.AbstractReverseMode, ADTypes.AbstractFiniteDifferencesMode},
+        prob, sp::Val{test_sparse} = True, args...; kwargs...) where {test_sparse}
     return autodiff
 end
 function get_concrete_reverse_ad(autodiff::Union{AutoZygote, AutoSparseZygote}, prob,
@@ -88,17 +84,17 @@ function get_concrete_reverse_ad(autodiff::Union{AutoZygote, AutoSparseZygote},
     end
     return autodiff
 end
-function get_concrete_reverse_ad(autodiff::ADTypes.AbstractADType, prob,
-        sp::Val{test_sparse} = True, args...; check_reverse_mode = true,
-        kwargs...) where {test_sparse}
+function get_concrete_reverse_ad(
+        autodiff::ADTypes.AbstractADType, prob, sp::Val{test_sparse} = True,
+        args...; check_reverse_mode = true, kwargs...) where {test_sparse}
     if check_reverse_mode
         @warn "$(autodiff)::$(typeof(autodiff)) is not a \
                `Abstract(Forward/FiniteDifferences)Mode`. Use with caution." maxlog=1
     end
     return autodiff
 end
-function get_concrete_reverse_ad(autodiff, prob, sp::Val{test_sparse} = True, args...;
-        kwargs...) where {test_sparse}
+function get_concrete_reverse_ad(
+        autodiff, prob, sp::Val{test_sparse} = True, args...; kwargs...) where {test_sparse}
     if test_sparse
         (; sparsity, jac_prototype) = prob.f
         use_sparse_ad = sparsity !== nothing || jac_prototype !== nothing
@@ -234,19 +230,18 @@ macro internal_caches(cType, internal_cache_names...)
 end
 
 function __internal_caches(__source__, __module__, cType, internal_cache_names::Tuple)
-    fields = map(name -> :($(__query_stat)(getproperty(cache, $(name)), ST)),
-        internal_cache_names)
+    fields = map(
+        name -> :($(__query_stat)(getproperty(cache, $(name)), ST)), internal_cache_names)
     callback_caches = map(
-        name -> :($(callback_into_cache!)(cache,
-            getproperty(internalcache, $(name)), internalcache, args...)),
+        name -> :($(callback_into_cache!)(
+            cache, getproperty(internalcache, $(name)), internalcache, args...)),
         internal_cache_names)
     callbacks_self = map(
-        name -> :($(callback_into_cache!)(internalcache,
-            getproperty(internalcache, $(name)))),
+        name -> :($(callback_into_cache!)(
+            internalcache, getproperty(internalcache, $(name)))),
         internal_cache_names)
     reinit_caches = map(
-        name -> :($(reinit_cache!)(getproperty(cache, $(name)),
-            args...; kwargs...)),
+        name -> :($(reinit_cache!)(getproperty(cache, $(name)), args...; kwargs...)),
         internal_cache_names)
     return esc(quote
         function __query_stat(cache::$(cType), ST::Val{stat}) where {stat}
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 6f28d5999..fc4f12f33 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -42,24 +42,25 @@ Construct a cache for the Jacobian of `f` w.r.t. `u`.
     jvp_autodiff
 end
 
-function reinit_cache!(cache::JacobianCache{iip}, args...; p = cache.p, u0 = cache.u,
-        kwargs...) where {iip}
+function reinit_cache!(cache::JacobianCache{iip}, args...; p = cache.p,
+        u0 = cache.u, kwargs...) where {iip}
     cache.njacs = 0
     cache.u = u0
     cache.p = p
     cache.uf = JacobianWrapper{iip}(cache.f, p)
 end
 
-function JacobianCache(prob, alg, f::F, fu_, u, p; autodiff = nothing,
-        vjp_autodiff = nothing, jvp_autodiff = nothing, linsolve = missing) where {F}
+function JacobianCache(
+        prob, alg, f::F, fu_, u, p; autodiff = nothing, vjp_autodiff = nothing,
+        jvp_autodiff = nothing, linsolve = missing) where {F}
     iip = isinplace(prob)
     uf = JacobianWrapper{iip}(f, p)
 
     autodiff = get_concrete_forward_ad(autodiff, prob; check_reverse_mode = false)
-    jvp_autodiff = get_concrete_forward_ad(jvp_autodiff, prob, Val(false);
-        check_reverse_mode = true)
-    vjp_autodiff = get_concrete_reverse_ad(vjp_autodiff, prob, Val(false);
-        check_forward_mode = false)
+    jvp_autodiff = get_concrete_forward_ad(
+        jvp_autodiff, prob, Val(false); check_reverse_mode = true)
+    vjp_autodiff = get_concrete_reverse_ad(
+        vjp_autodiff, prob, Val(false); check_forward_mode = false)
 
     has_analytic_jac = SciMLBase.has_jac(f)
     linsolve_needs_jac = concrete_jac(alg) === nothing && (linsolve === missing ||
@@ -72,8 +73,8 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; autodiff = nothing,
     if !has_analytic_jac && needs_jac
         sd = __sparsity_detection_alg(f, autodiff)
         jac_cache = iip ? sparse_jacobian_cache(autodiff, sd, uf, fu, u) :
-                    sparse_jacobian_cache(autodiff, sd, uf, __maybe_mutable(u, autodiff);
-            fx = fu)
+                    sparse_jacobian_cache(
+            autodiff, sd, uf, __maybe_mutable(u, autodiff); fx = fu)
     else
         jac_cache = nothing
     end
@@ -91,14 +92,13 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; autodiff = nothing,
     end
 
     return JacobianCache{iip}(
-        J, f, uf, fu, u, p, jac_cache, alg, 0, autodiff, vjp_autodiff,
-        jvp_autodiff)
+        J, f, uf, fu, u, p, jac_cache, alg, 0, autodiff, vjp_autodiff, jvp_autodiff)
 end
 
 function JacobianCache(prob, alg, f::F, ::Number, u::Number, p; kwargs...) where {F}
     uf = JacobianWrapper{false}(f, p)
-    return JacobianCache{false}(u, f, uf, u, u, p, nothing, alg, 0, nothing, nothing,
-        nothing)
+    return JacobianCache{false}(
+        u, f, uf, u, u, p, nothing, alg, 0, nothing, nothing, nothing)
 end
 
 @inline (cache::JacobianCache)(u = cache.u) = cache(cache.J, u, cache.p)
@@ -117,8 +117,8 @@ function (cache::JacobianCache)(::Number, u, p = cache.p) # Scalar
     return J
 end
 # Compute the Jacobian
-function (cache::JacobianCache{iip})(J::Union{AbstractMatrix, Nothing}, u,
-        p = cache.p) where {iip}
+function (cache::JacobianCache{iip})(
+        J::Union{AbstractMatrix, Nothing}, u, p = cache.p) where {iip}
     cache.njacs += 1
     if iip
         if has_jac(cache.f)
diff --git a/src/internal/linear_solve.jl b/src/internal/linear_solve.jl
index 319b80005..261d9e8dc 100644
--- a/src/internal/linear_solve.jl
+++ b/src/internal/linear_solve.jl
@@ -16,9 +16,9 @@ handled:
 ### Solving the System
 
 ```julia
-(cache::LinearSolverCache)(; A = nothing, b = nothing, linu = nothing,
-    du = nothing, p = nothing, weight = nothing, cachedata = nothing,
-    reuse_A_if_factorization = false, kwargs...)
+(cache::LinearSolverCache)(;
+    A = nothing, b = nothing, linu = nothing, du = nothing, p = nothing,
+    weight = nothing, cachedata = nothing, reuse_A_if_factorization = false, kwargs...)
 ```
 
 Returns the solution of the system `u` and stores the updated cache in `cache.lincache`.
@@ -67,8 +67,10 @@ end
 function LinearSolverCache(alg, linsolve, A, b, u; kwargs...)
     u_fixed = __fix_strange_type_combination(A, b, u)
 
-    if (A isa Number && b isa Number) || (linsolve === nothing && A isa SMatrix) ||
-       (A isa Diagonal) || (linsolve isa typeof(\))
+    if (A isa Number && b isa Number) ||
+       (linsolve === nothing && A isa SMatrix) ||
+       (A isa Diagonal) ||
+       (linsolve isa typeof(\))
         return LinearSolverCache(nothing, nothing, A, b, nothing, 0, 0)
     end
     @bb u_ = copy(u_fixed)
@@ -77,8 +79,8 @@ function LinearSolverCache(alg, linsolve, A, b, u; kwargs...)
     weight = __init_ones(u_fixed)
     if __hasfield(alg, Val(:precs))
         precs = alg.precs
-        Pl_, Pr_ = precs(A, nothing, u, nothing, nothing, nothing, nothing, nothing,
-            nothing)
+        Pl_, Pr_ = precs(
+            A, nothing, u, nothing, nothing, nothing, nothing, nothing, nothing)
     else
         precs, Pl_, Pr_ = nothing, nothing, nothing
     end
@@ -91,8 +93,8 @@ function LinearSolverCache(alg, linsolve, A, b, u; kwargs...)
 end
 
 # Direct Linear Solve Case without Caching
-function (cache::LinearSolverCache{Nothing})(; A = nothing, b = nothing, linu = nothing,
-        kwargs...)
+function (cache::LinearSolverCache{Nothing})(;
+        A = nothing, b = nothing, linu = nothing, kwargs...)
     cache.nsolve += 1
     cache.nfactors += 1
     A === nothing || (cache.A = A)
@@ -107,9 +109,9 @@ function (cache::LinearSolverCache{Nothing})(; A = nothing, b = nothing, linu =
     return res
 end
 # Use LinearSolve.jl
-function (cache::LinearSolverCache)(; A = nothing, b = nothing, linu = nothing,
-        du = nothing, p = nothing, weight = nothing, cachedata = nothing,
-        reuse_A_if_factorization = false, kwargs...)
+function (cache::LinearSolverCache)(;
+        A = nothing, b = nothing, linu = nothing, du = nothing, p = nothing,
+        weight = nothing, cachedata = nothing, reuse_A_if_factorization = false, kwargs...)
     cache.nsolve += 1
 
     __update_A!(cache, A, reuse_A_if_factorization)
@@ -124,8 +126,8 @@ function (cache::LinearSolverCache)(; A = nothing, b = nothing, linu = nothing,
     if cache.precs === nothing
         _Pl, _Pr = nothing, nothing
     else
-        _Pl, _Pr = cache.precs(cache.lincache.A, du, linu, p, nothing, A !== nothing,
-            Plprev, Prprev, cachedata)
+        _Pl, _Pr = cache.precs(cache.lincache.A, du, linu, p, nothing,
+            A !== nothing, Plprev, Prprev, cachedata)
     end
 
     if (_Pl !== nothing || _Pr !== nothing)
diff --git a/src/internal/operators.jl b/src/internal/operators.jl
index d5e6f4145..a34565a9d 100644
--- a/src/internal/operators.jl
+++ b/src/internal/operators.jl
@@ -16,9 +16,9 @@ transposed, and `T = false` means that the Jacobian is not transposed.
 ### Constructor
 
 ```julia
-JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff = nothing,
-    vjp_autodiff = nothing, skip_vjp::Val{NoVJP} = False,
-    skip_jvp::Val{NoJVP} = False) where {NoVJP, NoJVP}
+JacobianOperator(
+    prob::AbstractNonlinearProblem, fu, u; jvp_autodiff = nothing, vjp_autodiff = nothing,
+    skip_vjp::Val{NoVJP} = False, skip_jvp::Val{NoJVP} = False) where {NoVJP, NoJVP}
 ```
 
 See also [`NonlinearSolve.VecJacOperator`](@ref) and
@@ -45,8 +45,8 @@ end
 
 for op in (:adjoint, :transpose)
     @eval function Base.$(op)(operator::JacobianOperator{vjp, iip, T}) where {vjp, iip, T}
-        return JacobianOperator{!vjp, iip, T}(operator.jvp_op, operator.vjp_op,
-            operator.output_cache, operator.input_cache)
+        return JacobianOperator{!vjp, iip, T}(
+            operator.jvp_op, operator.vjp_op, operator.output_cache, operator.input_cache)
     end
 end
 
@@ -68,8 +68,8 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
             @closure (v, u, p) -> FiniteDiff.finite_difference_derivative(uf, u) * v
         end
     else
-        vjp_autodiff = __get_nonsparse_ad(get_concrete_reverse_ad(vjp_autodiff,
-            prob, False))
+        vjp_autodiff = __get_nonsparse_ad(get_concrete_reverse_ad(
+            vjp_autodiff, prob, False))
         if vjp_autodiff isa AutoZygote
             iip && error("`AutoZygote` cannot handle inplace problems.")
             @closure (v, u, p) -> auto_vecjac(uf, u, v)
@@ -98,17 +98,15 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
             @closure (v, u, p) -> FiniteDiff.finite_difference_derivative(uf, u) * v
         end
     else
-        jvp_autodiff = __get_nonsparse_ad(get_concrete_forward_ad(jvp_autodiff,
-            prob, False))
+        jvp_autodiff = __get_nonsparse_ad(get_concrete_forward_ad(
+            jvp_autodiff, prob, False))
         if jvp_autodiff isa AutoForwardDiff || jvp_autodiff isa AutoPolyesterForwardDiff
             if iip
                 # FIXME: Technically we should propagate the tag but ignoring that for now
-                cache1 = Dual{
-                    typeof(ForwardDiff.Tag(NonlinearSolveTag(), eltype(u))), eltype(u), 1
-                }.(similar(u), ForwardDiff.Partials.(tuple.(u)))
-                cache2 = Dual{
-                    typeof(ForwardDiff.Tag(NonlinearSolveTag(), eltype(fu))), eltype(fu), 1
-                }.(similar(fu), ForwardDiff.Partials.(tuple.(fu)))
+                cache1 = Dual{typeof(ForwardDiff.Tag(NonlinearSolveTag(), eltype(u))),
+                    eltype(u), 1}.(similar(u), ForwardDiff.Partials.(tuple.(u)))
+                cache2 = Dual{typeof(ForwardDiff.Tag(NonlinearSolveTag(), eltype(fu))),
+                    eltype(fu), 1}.(similar(fu), ForwardDiff.Partials.(tuple.(fu)))
                 @closure (Jv, v, u, p) -> auto_jacvec!(Jv, uf, u, v, cache1, cache2)
             else
                 @closure (v, u, p) -> auto_jacvec(uf, u, v)
@@ -128,8 +126,7 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
     end
 
     return JacobianOperator{false, iip, promote_type(eltype(fu), eltype(u))}(
-        jvp_op, vjp_op,
-        u, fu)
+        jvp_op, vjp_op, u, fu)
 end
 
 """
@@ -208,8 +205,8 @@ end
 Wrapper over a [`JacobianOperator`](@ref) which stores the input `u` and `p` and defines
 `mul!` and `*` for computing VJPs and JVPs.
 """
-@concrete struct StatefulJacobianOperator{vjp, iip, T,
-    J <: JacobianOperator{vjp, iip, T}} <: AbstractNonlinearSolveOperator{T}
+@concrete struct StatefulJacobianOperator{
+    vjp, iip, T, J <: JacobianOperator{vjp, iip, T}} <: AbstractNonlinearSolveOperator{T}
     jac_op::J
     u
     p
@@ -230,8 +227,8 @@ function Base.:*(J_op::StatefulJacobianOperator{vjp, iip, T, J, <:Number},
     return J_op.jac_op(v, J_op.u, J_op.p)
 end
 
-function LinearAlgebra.mul!(Jv::AbstractArray, J::StatefulJacobianOperator,
-        v::AbstractArray)
+function LinearAlgebra.mul!(
+        Jv::AbstractArray, J::StatefulJacobianOperator, v::AbstractArray)
     J.jac_op(Jv, v, J.u, J.p)
     return Jv
 end
@@ -271,8 +268,8 @@ function Base.:*(JᵀJ::StatefulJacobianNormalFormOperator, x::AbstractArray)
     return JᵀJ.vjp_operator * (JᵀJ.jvp_operator * x)
 end
 
-function LinearAlgebra.mul!(JᵀJx::AbstractArray, JᵀJ::StatefulJacobianNormalFormOperator,
-        x::AbstractArray)
+function LinearAlgebra.mul!(
+        JᵀJx::AbstractArray, JᵀJ::StatefulJacobianNormalFormOperator, x::AbstractArray)
     mul!(JᵀJ.cache, JᵀJ.jvp_operator, x)
     mul!(JᵀJx, JᵀJ.vjp_operator, JᵀJ.cache)
     return JᵀJx
diff --git a/src/internal/termination.jl b/src/internal/termination.jl
index 59d8905f5..e55e344f7 100644
--- a/src/internal/termination.jl
+++ b/src/internal/termination.jl
@@ -1,6 +1,6 @@
 function init_termination_cache(abstol, reltol, du, u, ::Nothing)
-    return init_termination_cache(abstol, reltol, du, u,
-        AbsSafeBestTerminationMode(; max_stalled_steps = 32))
+    return init_termination_cache(
+        abstol, reltol, du, u, AbsSafeBestTerminationMode(; max_stalled_steps = 32))
 end
 function init_termination_cache(abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
     tc_cache = init(du, u, tc; abstol, reltol, use_deprecated_retcodes = Val(false))
@@ -12,8 +12,8 @@ function check_and_update!(cache, fu, u, uprev)
 end
 
 function check_and_update!(tc_cache, cache, fu, u, uprev)
-    return check_and_update!(tc_cache, cache, fu, u, uprev,
-        DiffEqBase.get_termination_mode(tc_cache))
+    return check_and_update!(
+        tc_cache, cache, fu, u, uprev, DiffEqBase.get_termination_mode(tc_cache))
 end
 
 function check_and_update!(tc_cache, cache, fu, u, uprev, mode)
@@ -25,17 +25,17 @@ function check_and_update!(tc_cache, cache, fu, u, uprev, mode)
 end
 
 function update_from_termination_cache!(tc_cache, cache, u = get_u(cache))
-    return update_from_termination_cache!(tc_cache, cache,
-        DiffEqBase.get_termination_mode(tc_cache), u)
+    return update_from_termination_cache!(
+        tc_cache, cache, DiffEqBase.get_termination_mode(tc_cache), u)
 end
 
-function update_from_termination_cache!(tc_cache, cache,
-        mode::AbstractNonlinearTerminationMode, u = get_u(cache))
+function update_from_termination_cache!(
+        tc_cache, cache, mode::AbstractNonlinearTerminationMode, u = get_u(cache))
     evaluate_f!(cache, u, cache.p)
 end
 
-function update_from_termination_cache!(tc_cache, cache,
-        mode::AbstractSafeBestNonlinearTerminationMode, u = get_u(cache))
+function update_from_termination_cache!(
+        tc_cache, cache, mode::AbstractSafeBestNonlinearTerminationMode, u = get_u(cache))
     if isinplace(cache)
         copyto!(get_u(cache), tc_cache.u)
     else
diff --git a/src/internal/tracing.jl b/src/internal/tracing.jl
index 667c6ce07..8f0f10fb1 100644
--- a/src/internal/tracing.jl
+++ b/src/internal/tracing.jl
@@ -90,13 +90,13 @@ function Base.show(io::IO, entry::NonlinearSolveTraceEntry)
 end
 
 function NonlinearSolveTraceEntry(iteration, fu, δu)
-    return NonlinearSolveTraceEntry(iteration, norm(fu, Inf), norm(δu, 2), nothing,
-        nothing, nothing, nothing, nothing)
+    return NonlinearSolveTraceEntry(
+        iteration, norm(fu, Inf), norm(δu, 2), nothing, nothing, nothing, nothing, nothing)
 end
 
 function NonlinearSolveTraceEntry(iteration, fu, δu, J)
-    return NonlinearSolveTraceEntry(iteration, norm(fu, Inf), norm(δu, 2), __cond(J),
-        nothing, nothing, nothing, nothing)
+    return NonlinearSolveTraceEntry(iteration, norm(fu, Inf), norm(δu, 2),
+        __cond(J), nothing, nothing, nothing, nothing)
 end
 
 function NonlinearSolveTraceEntry(iteration, fu, δu, J, u)
@@ -104,8 +104,8 @@ function NonlinearSolveTraceEntry(iteration, fu, δu, J, u)
         __copy(J), __copy(u), __copy(fu), __copy(δu))
 end
 
-@concrete struct NonlinearSolveTrace{show_trace, store_trace,
-    Tr <: AbstractNonlinearSolveTraceLevel}
+@concrete struct NonlinearSolveTrace{
+    show_trace, store_trace, Tr <: AbstractNonlinearSolveTraceLevel}
     history
     trace_level::Tr
 end
@@ -126,25 +126,26 @@ end
 function init_nonlinearsolve_trace(alg, u, fu, J, δu; show_trace::Val = Val(false),
         trace_level::AbstractNonlinearSolveTraceLevel = TraceMinimal(),
         store_trace::Val = Val(false), uses_jac_inverse = Val(false), kwargs...)
-    return init_nonlinearsolve_trace(alg, show_trace, trace_level, store_trace, u, fu, J,
-        δu, uses_jac_inverse)
+    return init_nonlinearsolve_trace(
+        alg, show_trace, trace_level, store_trace, u, fu, J, δu, uses_jac_inverse)
 end
 
-function init_nonlinearsolve_trace(alg, ::Val{show_trace},
-        trace_level::AbstractNonlinearSolveTraceLevel, ::Val{store_trace}, u, fu, J,
-        δu, ::Val{uses_jac_inverse}) where {show_trace, store_trace, uses_jac_inverse}
+function init_nonlinearsolve_trace(
+        alg, ::Val{show_trace}, trace_level::AbstractNonlinearSolveTraceLevel,
+        ::Val{store_trace}, u, fu, J, δu,
+        ::Val{uses_jac_inverse}) where {show_trace, store_trace, uses_jac_inverse}
     if show_trace
         print("\nAlgorithm: ")
         Base.printstyled(alg, "\n\n"; color = :green, bold = true)
     end
     J_ = uses_jac_inverse ? (trace_level isa TraceMinimal ? J : __safe_inv(J)) : J
-    history = __init_trace_history(Val{show_trace}(), trace_level, Val{store_trace}(), u,
-        fu, J_, δu)
+    history = __init_trace_history(
+        Val{show_trace}(), trace_level, Val{store_trace}(), u, fu, J_, δu)
     return NonlinearSolveTrace{show_trace, store_trace}(history, trace_level)
 end
 
-function __init_trace_history(::Val{show_trace}, trace_level, ::Val{store_trace}, u, fu, J,
-        δu) where {show_trace, store_trace}
+function __init_trace_history(::Val{show_trace}, trace_level, ::Val{store_trace},
+        u, fu, J, δu) where {show_trace, store_trace}
     !store_trace && !show_trace && return nothing
     entry = __trace_entry(trace_level, 0, u, fu, J, δu)
     show_trace && show(entry)
@@ -167,16 +168,16 @@ function update_trace!(trace::NonlinearSolveTrace{ShT, StT}, iter, u, fu, J, δu
     !StT && !ShT && return nothing
 
     if L
-        entry = NonlinearSolveTraceEntry(-1, norm(fu, Inf), NaN32, nothing, nothing,
-            nothing, nothing, nothing)
+        entry = NonlinearSolveTraceEntry(
+            -1, norm(fu, Inf), NaN32, nothing, nothing, nothing, nothing, nothing)
         ShT && show(entry)
         return trace
     end
 
     show_now = ShT && (mod1(iter, trace.trace_level.print_frequency) == 1)
     store_now = StT && (mod1(iter, trace.trace_level.store_frequency) == 1)
-    (show_now || store_now) && (entry = __trace_entry(trace.trace_level, iter, u, fu, J,
-        δu, α))
+    (show_now || store_now) &&
+        (entry = __trace_entry(trace.trace_level, iter, u, fu, J, δu, α))
     store_now && push!(trace.history, entry)
     show_now && show(entry)
     return trace
@@ -188,13 +189,13 @@ function update_trace!(cache::AbstractNonlinearSolveCache, α = true)
 
     J = __getproperty(cache, Val(:J))
     if J === nothing
-        update_trace!(trace, get_nsteps(cache) + 1, get_u(cache), get_fu(cache),
-            nothing, cache.du, α)
+        update_trace!(
+            trace, get_nsteps(cache) + 1, get_u(cache), get_fu(cache), nothing, cache.du, α)
     elseif cache isa ApproximateJacobianSolveCache && store_inverse_jacobian(cache)
-        update_trace!(trace, get_nsteps(cache) + 1, get_u(cache), get_fu(cache),
-            ApplyArray(__safe_inv, J), cache.du, α)
+        update_trace!(trace, get_nsteps(cache) + 1, get_u(cache),
+            get_fu(cache), ApplyArray(__safe_inv, J), cache.du, α)
     else
-        update_trace!(trace, get_nsteps(cache) + 1, get_u(cache), get_fu(cache), J,
-            cache.du, α)
+        update_trace!(
+            trace, get_nsteps(cache) + 1, get_u(cache), get_fu(cache), J, cache.du, α)
     end
 end
diff --git a/test/core/23_test_problems_tests.jl b/test/core/23_test_problems_tests.jl
index 43a361958..7924e372d 100644
--- a/test/core/23_test_problems_tests.jl
+++ b/test/core/23_test_problems_tests.jl
@@ -4,8 +4,8 @@ using NonlinearSolve, LinearAlgebra, LinearSolve, NonlinearProblemLibrary, Test
 problems = NonlinearProblemLibrary.problems
 dicts = NonlinearProblemLibrary.dicts
 
-function test_on_library(problems, dicts, alg_ops, broken_tests, ϵ = 1e-4;
-        skip_tests = nothing)
+function test_on_library(
+        problems, dicts, alg_ops, broken_tests, ϵ = 1e-4; skip_tests = nothing)
     for (idx, (problem, dict)) in enumerate(zip(problems, dicts))
         x = dict["start"]
         res = similar(x)
@@ -71,8 +71,7 @@ end
 @testitem "LevenbergMarquardt" setup=[RobustnessTesting] begin
     using LinearSolve
 
-    alg_ops = (LevenbergMarquardt(),
-        LevenbergMarquardt(; α_geodesic = 0.1),
+    alg_ops = (LevenbergMarquardt(), LevenbergMarquardt(; α_geodesic = 0.1),
         LevenbergMarquardt(; linsolve = CholeskyFactorization()))
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -93,8 +92,7 @@ end
 end
 
 @testitem "Broyden" retries=5 setup=[RobustnessTesting] begin
-    alg_ops = (Broyden(),
-        Broyden(; init_jacobian = Val(:true_jacobian)),
+    alg_ops = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian)),
         Broyden(; update_rule = Val(:bad_broyden)),
         Broyden(; init_jacobian = Val(:true_jacobian), update_rule = Val(:bad_broyden)))
 
diff --git a/test/core/forward_ad_tests.jl b/test/core/forward_ad_tests.jl
index 22882cbec..a13259939 100644
--- a/test/core/forward_ad_tests.jl
+++ b/test/core/forward_ad_tests.jl
@@ -63,10 +63,9 @@ export test_f!, test_f, jacobian_f, solve_with, __compatible
 end
 
 @testitem "ForwardDiff.jl Integration" setup=[ForwardADTesting] begin
-    for alg in (NewtonRaphson(), TrustRegion(),
-        LevenbergMarquardt(), PseudoTransient(; alpha_initial = 10.0), Broyden(), Klement(),
-        DFSane(), nothing, NLsolveJL(), CMINPACK(),
-        KINSOL(; globalization_strategy = :LineSearch))
+    for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
+        PseudoTransient(; alpha_initial = 10.0), Broyden(), Klement(), DFSane(), nothing,
+        NLsolveJL(), CMINPACK(), KINSOL(; globalization_strategy = :LineSearch))
         us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
 
         @testset "Scalar AD" begin
@@ -90,7 +89,8 @@ end
         end
 
         @testset "Jacobian" begin
-            for u0 in us, p in ([2.0, 1.0], [2.0 1.0; 3.0 4.0]),
+            for u0 in us,
+                p in ([2.0, 1.0], [2.0 1.0; 3.0 4.0]),
                 mode in (:iip, :oop, :iip_cache, :oop_cache)
 
                 __compatible(u0, p) || continue
diff --git a/test/core/nlls_tests.jl b/test/core/nlls_tests.jl
index c95fd0de0..3722ca671 100644
--- a/test/core/nlls_tests.jl
+++ b/test/core/nlls_tests.jl
@@ -1,7 +1,7 @@
 @testsetup module CoreNLLSTesting
 using Reexport
-@reexport using NonlinearSolve,
-                LinearSolve, LinearAlgebra, StableRNGs, Random, ForwardDiff, Zygote
+@reexport using NonlinearSolve, LinearSolve, LinearAlgebra, StableRNGs, Random, ForwardDiff,
+                Zygote
 
 true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
 true_function(y, x, θ) = (@. y = θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4]))
@@ -36,16 +36,12 @@ for linsolve in [nothing, LUFactorization(), KrylovJL_GMRES(), KrylovJL_LSMR()]
     end
 end
 append!(solvers,
-    [
-        LevenbergMarquardt(),
-        LevenbergMarquardt(; linsolve = LUFactorization()),
+    [LevenbergMarquardt(), LevenbergMarquardt(; linsolve = LUFactorization()),
         LevenbergMarquardt(; linsolve = KrylovJL_GMRES()),
-        LevenbergMarquardt(; linsolve = KrylovJL_LSMR()),
-        nothing
-    ])
+        LevenbergMarquardt(; linsolve = KrylovJL_LSMR()), nothing])
 for radius_update_scheme in [RadiusUpdateSchemes.Simple, RadiusUpdateSchemes.NocedalWright,
-    RadiusUpdateSchemes.NLsolve, RadiusUpdateSchemes.Hei, RadiusUpdateSchemes.Yuan,
-    RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin]
+    RadiusUpdateSchemes.NLsolve, RadiusUpdateSchemes.Hei,
+    RadiusUpdateSchemes.Yuan, RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin]
     push!(solvers, TrustRegion(; radius_update_scheme))
 end
 
@@ -55,8 +51,7 @@ end
 @testitem "General NLLS Solvers" setup=[CoreNLLSTesting] begin
     prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
     prob_iip = NonlinearLeastSquaresProblem(
-        NonlinearFunction(loss_function;
-            resid_prototype = zero(y_target)), θ_init, x)
+        NonlinearFunction(loss_function; resid_prototype = zero(y_target)), θ_init, x)
 
     nlls_problems = [prob_oop, prob_iip]
 
@@ -84,16 +79,15 @@ end
 
     probs = [
         NonlinearLeastSquaresProblem(
-            NonlinearFunction{true}(loss_function;
-                resid_prototype = zero(y_target), vjp = vjp!),
+            NonlinearFunction{true}(
+                loss_function; resid_prototype = zero(y_target), vjp = vjp!),
             θ_init,
             x),
         NonlinearLeastSquaresProblem(
-            NonlinearFunction{false}(loss_function;
-                resid_prototype = zero(y_target), vjp = vjp),
+            NonlinearFunction{false}(
+                loss_function; resid_prototype = zero(y_target), vjp = vjp),
             θ_init,
-            x)
-    ]
+            x)]
 
     for prob in probs, solver in solvers
         sol = solve(prob, solver; maxiters = 10000, abstol = 1e-8)
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index 6a9402651..86dc5ff2c 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -25,17 +25,15 @@ function newton_fails(u, p)
             (0.21640425613334457 .+
              216.40425613334457 ./ (1 .+
               (0.21640425613334457 .+
-               216.40425613334457 ./
-               (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^ 2.0) .-
-           0.0011552453009332421u .- p
+               216.40425613334457 ./ (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^
+            2.0) .- 0.0011552453009332421u .- p
 end
 
 const TERMINATION_CONDITIONS = [
     SteadyStateDiffEqTerminationMode(), SimpleNonlinearSolveTerminationMode(),
     NormTerminationMode(), RelTerminationMode(), RelNormTerminationMode(),
     AbsTerminationMode(), AbsNormTerminationMode(), RelSafeTerminationMode(),
-    AbsSafeTerminationMode(), RelSafeBestTerminationMode(), AbsSafeBestTerminationMode()
-]
+    AbsSafeTerminationMode(), RelSafeBestTerminationMode(), AbsSafeBestTerminationMode()]
 
 function benchmark_nlsolve_oop(f, u0, p = 2.0; solver, kwargs...)
     prob = NonlinearProblem{false}(f, u0, p)
@@ -68,8 +66,7 @@ end
 
 @testitem "NewtonRaphson" setup=[CoreRootfindTesting] begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad))" for lsmethod in (
-            Static(),
-            StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
+            Static(), StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
         ad in (AutoFiniteDiff(), AutoZygote())
 
         linesearch = LineSearchesJL(; method = lsmethod, autodiff = ad)
@@ -81,18 +78,19 @@ end
             @test SciMLBase.successful_retcode(sol)
             @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
 
-            cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0), NewtonRaphson(),
-                abstol = 1e-9)
+            cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0),
+                NewtonRaphson(), abstol = 1e-9)
             @test (@ballocated solve!($cache)) < 200
         end
 
-        precs = [
-            (u0) -> NonlinearSolve.DEFAULT_PRECS,
-            u0 -> ((args...) -> (Diagonal(rand!(similar(u0))), nothing))
-        ]
+        precs = [(u0) -> NonlinearSolve.DEFAULT_PRECS,
+            u0 -> ((args...) -> (Diagonal(rand!(similar(u0))), nothing))]
 
         @testset "[IIP] u0: $(typeof(u0)) precs: $(_nameof(prec)) linsolve: $(_nameof(linsolve))" for u0 in ([
-                1.0, 1.0],), prec in precs, linsolve in (nothing, KrylovJL_GMRES(), \)
+                1.0, 1.0],),
+            prec in precs,
+            linsolve in (nothing, KrylovJL_GMRES(), \)
+
             ad isa AutoZygote && continue
             if prec === :Random
                 prec = (args...) -> (Diagonal(randn!(similar(u0))), nothing)
@@ -114,8 +112,8 @@ end
     @test nlprob_iterator_interface(quadratic_f!, p, Val(true), NewtonRaphson()) ≈ sqrt.(p)
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
-            AutoSparseForwardDiff(),
-            AutoSparseFiniteDiff(), AutoZygote(), AutoSparseZygote(), __autosparseenzyme()),
+            AutoSparseForwardDiff(), AutoSparseFiniteDiff(),
+            AutoZygote(), AutoSparseZygote(), __autosparseenzyme()),
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -134,13 +132,14 @@ end
 
 @testitem "TrustRegion" setup=[CoreRootfindTesting] begin
     radius_update_schemes = [RadiusUpdateSchemes.Simple, RadiusUpdateSchemes.NocedalWright,
-        RadiusUpdateSchemes.NLsolve, RadiusUpdateSchemes.Hei, RadiusUpdateSchemes.Yuan,
-        RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin]
+        RadiusUpdateSchemes.NLsolve, RadiusUpdateSchemes.Hei,
+        RadiusUpdateSchemes.Yuan, RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin]
     u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
     linear_solvers = [nothing, LUFactorization(), KrylovJL_GMRES(), \]
 
     @testset "[OOP] u0: $(typeof(u0)) radius_update_scheme: $(radius_update_scheme) linear_solver: $(linsolve)" for u0 in u0s,
-        radius_update_scheme in radius_update_schemes, linsolve in linear_solvers
+        radius_update_scheme in radius_update_schemes,
+        linsolve in linear_solvers
 
         abstol = ifelse(linsolve isa KrylovJL, 1e-6, 1e-9)
 
@@ -155,7 +154,8 @@ end
     end
 
     @testset "[IIP] u0: $(typeof(u0)) radius_update_scheme: $(radius_update_scheme) linear_solver: $(linsolve)" for u0 in ([
-            1.0, 1.0],), radius_update_scheme in radius_update_schemes,
+            1.0, 1.0],),
+        radius_update_scheme in radius_update_schemes,
         linsolve in linear_solvers
 
         abstol = ifelse(linsolve isa KrylovJL, 1e-6, 1e-9)
@@ -175,8 +175,8 @@ end
     @test nlprob_iterator_interface(quadratic_f!, p, Val(true), TrustRegion()) ≈ sqrt.(p)
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0)) radius_update_scheme: $(radius_update_scheme)" for autodiff in (
-            AutoSparseForwardDiff(),
-            AutoSparseFiniteDiff(), AutoZygote(), AutoSparseZygote(), __autosparseenzyme()),
+            AutoSparseForwardDiff(), AutoSparseFiniteDiff(),
+            AutoZygote(), AutoSparseZygote(), __autosparseenzyme()),
         u0 in (1.0, [1.0, 1.0]),
         radius_update_scheme in radius_update_schemes
 
@@ -207,16 +207,16 @@ end
         expand_factor = [1.5, 2.0, 3.0]
         max_shrink_times = [10, 20, 30]
 
-        list_of_options = zip(max_trust_radius, initial_trust_radius, step_threshold,
-            shrink_threshold, expand_threshold, shrink_factor,
-            expand_factor, max_shrink_times)
+        list_of_options = zip(
+            max_trust_radius, initial_trust_radius, step_threshold, shrink_threshold,
+            expand_threshold, shrink_factor, expand_factor, max_shrink_times)
         for options in list_of_options
             local probN, sol, alg
-            alg = TrustRegion(max_trust_radius = options[1],
-                initial_trust_radius = options[2], step_threshold = options[3],
-                shrink_threshold = options[4], expand_threshold = options[5],
-                shrink_factor = options[6], expand_factor = options[7],
-                max_shrink_times = options[8])
+            alg = TrustRegion(
+                max_trust_radius = options[1], initial_trust_radius = options[2],
+                step_threshold = options[3], shrink_threshold = options[4],
+                expand_threshold = options[5], shrink_factor = options[6],
+                expand_factor = options[7], max_shrink_times = options[8])
 
             probN = NonlinearProblem{false}(quadratic_f, [1.0, 1.0], 2.0)
             sol = solve(probN, alg, abstol = 1e-10)
@@ -255,8 +255,8 @@ end
         @test SciMLBase.successful_retcode(sol)
         @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
 
-        cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0), LevenbergMarquardt(),
-            abstol = 1e-9)
+        cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0),
+            LevenbergMarquardt(), abstol = 1e-9)
         @test (@ballocated solve!($cache)) < 200
     end
 
@@ -265,19 +265,20 @@ end
         @test SciMLBase.successful_retcode(sol)
         @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
 
-        cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0), LevenbergMarquardt(),
-            abstol = 1e-9)
+        cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0),
+            LevenbergMarquardt(), abstol = 1e-9)
         @test (@ballocated solve!($cache)) ≤ 64
     end
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
-            AutoSparseForwardDiff(),
-            AutoSparseFiniteDiff(), AutoZygote(), AutoSparseZygote(), __autosparseenzyme()),
+            AutoSparseForwardDiff(), AutoSparseFiniteDiff(),
+            AutoZygote(), AutoSparseZygote(), __autosparseenzyme()),
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, LevenbergMarquardt(; autodiff); abstol = 1e-9,
-            reltol = 1e-9).u .≈ sqrt(2.0))
+        @test all(solve(
+            probN, LevenbergMarquardt(; autodiff); abstol = 1e-9, reltol = 1e-9).u .≈
+                  sqrt(2.0))
     end
 
     # Test that `LevenbergMarquardt` passes a test that `NewtonRaphson` fails on.
@@ -291,10 +292,10 @@ end
 
     # Iterator interface
     p = range(0.01, 2, length = 200)
-    @test abs.(nlprob_iterator_interface(quadratic_f, p, Val(false),
-        LevenbergMarquardt())) ≈ sqrt.(p)
-    @test abs.(nlprob_iterator_interface(quadratic_f!, p, Val(true),
-        LevenbergMarquardt())) ≈ sqrt.(p)
+    @test abs.(nlprob_iterator_interface(
+        quadratic_f, p, Val(false), LevenbergMarquardt())) ≈ sqrt.(p)
+    @test abs.(nlprob_iterator_interface(
+        quadratic_f!, p, Val(true), LevenbergMarquardt())) ≈ sqrt.(p)
 
     # Test kwargs in `LevenbergMarquardt`
     @testset "Keyword Arguments" begin
@@ -306,13 +307,13 @@ end
         b_uphill = Float64[0, 1, 2]
         min_damping_D = [1e-12, 1e-9, 1e-4]
 
-        list_of_options = zip(damping_initial, damping_increase_factor,
-            damping_decrease_factor, finite_diff_step_geodesic, α_geodesic, b_uphill,
-            min_damping_D)
+        list_of_options = zip(
+            damping_initial, damping_increase_factor, damping_decrease_factor,
+            finite_diff_step_geodesic, α_geodesic, b_uphill, min_damping_D)
         for options in list_of_options
             local probN, sol, alg
-            alg = LevenbergMarquardt(; damping_initial = options[1],
-                damping_increase_factor = options[2],
+            alg = LevenbergMarquardt(;
+                damping_initial = options[1], damping_increase_factor = options[2],
                 damping_decrease_factor = options[3],
                 finite_diff_step_geodesic = options[4], α_geodesic = options[5],
                 b_uphill = options[6], min_damping_D = options[7])
@@ -341,8 +342,7 @@ end
         @test SciMLBase.successful_retcode(sol)
         @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
 
-        cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0), DFSane(),
-            abstol = 1e-9)
+        cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0), DFSane(), abstol = 1e-9)
         @test (@ballocated solve!($cache)) < 200
     end
 
@@ -379,19 +379,15 @@ end
         τ_min = [0.1, 0.2, 0.3]
         τ_max = [0.5, 0.8, 0.9]
         nexp = [2, 1, 2]
-        η_strategy = [
-            (f_1, k, x, F) -> f_1 / k^2,
-            (f_1, k, x, F) -> f_1 / k^3,
-            (f_1, k, x, F) -> f_1 / k^4
-        ]
-
-        list_of_options = zip(σ_min, σ_max, σ_1, M, γ, τ_min, τ_max, nexp,
-            η_strategy)
+        η_strategy = [(f_1, k, x, F) -> f_1 / k^2, (f_1, k, x, F) -> f_1 / k^3,
+            (f_1, k, x, F) -> f_1 / k^4]
+
+        list_of_options = zip(σ_min, σ_max, σ_1, M, γ, τ_min, τ_max, nexp, η_strategy)
         for options in list_of_options
             local probN, sol, alg
             alg = DFSane(σ_min = options[1], σ_max = options[2], σ_1 = options[3],
-                M = options[4], γ = options[5], τ_min = options[6], τ_max = options[7],
-                n_exp = options[8], η_strategy = options[9])
+                M = options[4], γ = options[5], τ_min = options[6],
+                τ_max = options[7], n_exp = options[8], η_strategy = options[9])
 
             probN = NonlinearProblem{false}(quadratic_f, [1.0, 1.0], 2.0)
             sol = solve(probN, alg, abstol = 1e-11)
@@ -412,8 +408,8 @@ end
 @testitem "PseudoTransient" setup=[CoreRootfindTesting] begin
     # These are tests for NewtonRaphson so we should set alpha_initial to be high so that we
     # converge quickly
-    @testset "PT: alpha_initial = 10.0 PT AD: $(ad)" for ad in (AutoFiniteDiff(),
-        AutoZygote())
+    @testset "PT: alpha_initial = 10.0 PT AD: $(ad)" for ad in (
+        AutoFiniteDiff(), AutoZygote())
         u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
 
         @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
@@ -431,7 +427,10 @@ end
         precs = [NonlinearSolve.DEFAULT_PRECS, :Random]
 
         @testset "[IIP] u0: $(typeof(u0)) precs: $(_nameof(prec)) linsolve: $(_nameof(linsolve))" for u0 in ([
-                1.0, 1.0],), prec in precs, linsolve in (nothing, KrylovJL_GMRES(), \)
+                1.0, 1.0],),
+            prec in precs,
+            linsolve in (nothing, KrylovJL_GMRES(), \)
+
             ad isa AutoZygote && continue
             if prec === :Random
                 prec = (args...) -> (Diagonal(randn!(similar(u0))), nothing)
@@ -441,21 +440,21 @@ end
             @test SciMLBase.successful_retcode(sol)
             @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
 
-            cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0), solver;
-                abstol = 1e-9)
+            cache = init(
+                NonlinearProblem{true}(quadratic_f!, u0, 2.0), solver; abstol = 1e-9)
             @test (@ballocated solve!($cache)) ≤ 64
         end
     end
 
     p = range(0.01, 2, length = 200)
-    @test nlprob_iterator_interface(quadratic_f, p, Val(false),
-        PseudoTransient(; alpha_initial = 10.0)) ≈ sqrt.(p)
-    @test nlprob_iterator_interface(quadratic_f!, p, Val(true),
-        PseudoTransient(; alpha_initial = 10.0)) ≈ sqrt.(p)
+    @test nlprob_iterator_interface(
+        quadratic_f, p, Val(false), PseudoTransient(; alpha_initial = 10.0)) ≈ sqrt.(p)
+    @test nlprob_iterator_interface(
+        quadratic_f!, p, Val(true), PseudoTransient(; alpha_initial = 10.0)) ≈ sqrt.(p)
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
-            AutoSparseForwardDiff(),
-            AutoSparseFiniteDiff(), AutoZygote(), AutoSparseZygote(), __autosparseenzyme()),
+            AutoSparseForwardDiff(), AutoSparseFiniteDiff(),
+            AutoZygote(), AutoSparseZygote(), __autosparseenzyme()),
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -467,8 +466,9 @@ end
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, PseudoTransient(; alpha_initial = 10.0);
-            termination_condition).u .≈ sqrt(2.0))
+        @test all(solve(
+            probN, PseudoTransient(; alpha_initial = 10.0); termination_condition).u .≈
+                  sqrt(2.0))
     end
 end
 
@@ -476,9 +476,8 @@ end
 
 @testitem "Broyden" setup=[CoreRootfindTesting] begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian) Update Rule: $(update_rule)" for lsmethod in (
-            Static(),
-            StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente(),
-            LiFukushimaLineSearch()),
+            Static(), StrongWolfe(), BackTracking(), HagerZhang(),
+            MoreThuente(), LiFukushimaLineSearch()),
         ad in (AutoFiniteDiff(), AutoZygote()),
         init_jacobian in (Val(:identity), Val(:true_jacobian)),
         update_rule in (Val(:good_broyden), Val(:bad_broyden), Val(:diagonal))
@@ -527,8 +526,7 @@ end
 
 @testitem "Klement" setup=[CoreRootfindTesting] begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian)" for lsmethod in (
-            Static(),
-            StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
+            Static(), StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
         ad in (AutoFiniteDiff(), AutoZygote()),
         init_jacobian in (Val(:identity), Val(:true_jacobian), Val(:true_jacobian_diagonal))
 
@@ -577,9 +575,8 @@ end
 
 @testitem "LimitedMemoryBroyden" setup=[CoreRootfindTesting] begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad))" for lsmethod in (
-            Static(),
-            StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente(),
-            LiFukushimaLineSearch()),
+            Static(), StrongWolfe(), BackTracking(), HagerZhang(),
+            MoreThuente(), LiFukushimaLineSearch()),
         ad in (AutoFiniteDiff(), AutoZygote())
 
         linesearch = LineSearchesJL(; method = lsmethod, autodiff = ad)
@@ -611,17 +608,17 @@ end
 
     # Iterator interface
     p = range(0.01, 2, length = 200)
-    @test nlprob_iterator_interface(quadratic_f, p, Val(false),
-        LimitedMemoryBroyden())≈sqrt.(p) atol=1e-2
-    @test nlprob_iterator_interface(quadratic_f!, p, Val(true),
-        LimitedMemoryBroyden())≈sqrt.(p) atol=1e-2
+    @test nlprob_iterator_interface(
+        quadratic_f, p, Val(false), LimitedMemoryBroyden())≈sqrt.(p) atol=1e-2
+    @test nlprob_iterator_interface(
+        quadratic_f!, p, Val(true), LimitedMemoryBroyden())≈sqrt.(p) atol=1e-2
 
     @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, LimitedMemoryBroyden();
-            termination_condition).u .≈ sqrt(2.0))
+        @test all(solve(probN, LimitedMemoryBroyden(); termination_condition).u .≈
+                  sqrt(2.0))
     end
 end
 
@@ -643,8 +640,8 @@ end
         return v + 0.1 * (u .* Δ * v + v .* Δ * u)
     end
 
-    function JVP!(du::Vector{Float64}, v::Vector{Float64}, u::Vector{Float64},
-            p::Vector{Float64})
+    function JVP!(
+            du::Vector{Float64}, v::Vector{Float64}, u::Vector{Float64}, p::Vector{Float64})
         Δ = Tridiagonal(-ones(99), 2 * ones(100), -ones(99))
         du .= v + 0.1 * (u .* Δ * v + v .* Δ * u)
         return nothing
@@ -655,16 +652,16 @@ end
     prob = NonlinearProblem(NonlinearFunction{false}(F; jvp = JVP), u0, u0)
     sol = solve(prob, NewtonRaphson(; linsolve = KrylovJL_GMRES()); abstol = 1e-13)
     @test norm(sol.resid, Inf) ≤ 1e-6
-    sol = solve(prob,
-        TrustRegion(; linsolve = KrylovJL_GMRES(), vjp_autodiff = AutoFiniteDiff());
+    sol = solve(
+        prob, TrustRegion(; linsolve = KrylovJL_GMRES(), vjp_autodiff = AutoFiniteDiff());
         abstol = 1e-13)
     @test norm(sol.resid, Inf) ≤ 1e-6
 
     prob = NonlinearProblem(NonlinearFunction{true}(F!; jvp = JVP!), u0, u0)
     sol = solve(prob, NewtonRaphson(; linsolve = KrylovJL_GMRES()); abstol = 1e-13)
     @test norm(sol.resid, Inf) ≤ 1e-6
-    sol = solve(prob,
-        TrustRegion(; linsolve = KrylovJL_GMRES(), vjp_autodiff = AutoFiniteDiff());
+    sol = solve(
+        prob, TrustRegion(; linsolve = KrylovJL_GMRES(), vjp_autodiff = AutoFiniteDiff());
         abstol = 1e-13)
     @test norm(sol.resid, Inf) ≤ 1e-6
 end
diff --git a/test/gpu/core_tests.jl b/test/gpu/core_tests.jl
index 074098072..6e9806498 100644
--- a/test/gpu/core_tests.jl
+++ b/test/gpu/core_tests.jl
@@ -12,12 +12,11 @@
     prob = NonlinearProblem(linear_f, u0)
 
     SOLVERS = (NewtonRaphson(), LevenbergMarquardt(; linsolve = QRFactorization()),
-        LevenbergMarquardt(; linsolve = KrylovJL_GMRES()), PseudoTransient(), Klement(),
-        Broyden(; linesearch = LiFukushimaLineSearch()),
+        LevenbergMarquardt(; linsolve = KrylovJL_GMRES()), PseudoTransient(),
+        Klement(), Broyden(; linesearch = LiFukushimaLineSearch()),
         LimitedMemoryBroyden(; threshold = 2, linesearch = LiFukushimaLineSearch()),
         DFSane(), TrustRegion(; linsolve = QRFactorization()),
-        TrustRegion(; linsolve = KrylovJL_GMRES(),
-            concrete_jac = true),  # Needed if Zygote not loaded
+        TrustRegion(; linsolve = KrylovJL_GMRES(), concrete_jac = true),  # Needed if Zygote not loaded
         nothing)
 
     @testset "[IIP] GPU Solvers" begin
diff --git a/test/misc/bruss_tests.jl b/test/misc/bruss_tests.jl
index a1fcd6761..08eae5436 100644
--- a/test/misc/bruss_tests.jl
+++ b/test/misc/bruss_tests.jl
@@ -18,12 +18,12 @@
             du[i, j, 1] = alpha *
                           (u[im1, j, 1] + u[ip1, j, 1] + u[i, jp1, 1] + u[i, jm1, 1] -
                            4u[i, j, 1]) +
-                          B + u[i, j, 1]^2 * u[i, j, 2] - (A + 1) * u[i, j, 1] +
+                          B +
+                          u[i, j, 1]^2 * u[i, j, 2] - (A + 1) * u[i, j, 1] +
                           brusselator_f(x, y)
             du[i, j, 2] = alpha *
                           (u[im1, j, 2] + u[ip1, j, 2] + u[i, jp1, 2] + u[i, jm1, 2] -
-                           4u[i, j, 2]) +
-                          A * u[i, j, 1] - u[i, j, 1]^2 * u[i, j, 2]
+                           4u[i, j, 2]) + A * u[i, j, 1] - u[i, j, 1]^2 * u[i, j, 2]
         end
     end
 
@@ -46,17 +46,17 @@
     sol = solve(prob_brusselator_2d, NewtonRaphson(); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
-    sol = solve(prob_brusselator_2d, NewtonRaphson(autodiff = AutoSparseForwardDiff());
-        abstol = 1e-8)
+    sol = solve(prob_brusselator_2d,
+        NewtonRaphson(autodiff = AutoSparseForwardDiff()); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
-    sol = solve(prob_brusselator_2d, NewtonRaphson(autodiff = AutoSparseFiniteDiff());
-        abstol = 1e-8)
+    sol = solve(prob_brusselator_2d,
+        NewtonRaphson(autodiff = AutoSparseFiniteDiff()); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
     du0 = copy(u0)
-    jac_sparsity = Symbolics.jacobian_sparsity((du, u) -> brusselator_2d_loop(du, u, p),
-        du0, u0)
+    jac_sparsity = Symbolics.jacobian_sparsity(
+        (du, u) -> brusselator_2d_loop(du, u, p), du0, u0)
     jac_prototype = float.(jac_sparsity)
     fill!(jac_prototype, 0)
     @test all(iszero, jac_prototype)
@@ -68,8 +68,8 @@
     @test norm(sol.resid, Inf) < 1e-8
     @test !all(iszero, jac_prototype)
 
-    sol = solve(prob_brusselator_2d, NewtonRaphson(autodiff = AutoSparseFiniteDiff());
-        abstol = 1e-8)
+    sol = solve(prob_brusselator_2d,
+        NewtonRaphson(autodiff = AutoSparseFiniteDiff()); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
     cache = init(prob_brusselator_2d, NewtonRaphson(; autodiff = AutoSparseForwardDiff()))
diff --git a/test/misc/matrix_resizing_tests.jl b/test/misc/matrix_resizing_tests.jl
index e13704c96..1d17a696a 100644
--- a/test/misc/matrix_resizing_tests.jl
+++ b/test/misc/matrix_resizing_tests.jl
@@ -7,9 +7,9 @@
     vecprob = NonlinearProblem(ff, vec(u0), p)
     prob = NonlinearProblem(ff, u0, p)
 
-    for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
-        PseudoTransient(), RobustMultiNewton(), FastShortcutNonlinearPolyalg(), Broyden(),
-        Klement(), LimitedMemoryBroyden(; threshold = 2))
+    for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(), PseudoTransient(),
+        RobustMultiNewton(), FastShortcutNonlinearPolyalg(),
+        Broyden(), Klement(), LimitedMemoryBroyden(; threshold = 2))
         @test vec(solve(prob, alg).u) == solve(vecprob, alg).u
     end
 end
@@ -23,9 +23,9 @@ end
     vecprob = NonlinearProblem(fiip, vec(u0), p)
     prob = NonlinearProblem(fiip, u0, p)
 
-    for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
-        PseudoTransient(), RobustMultiNewton(), FastShortcutNonlinearPolyalg(), Broyden(),
-        Klement(), LimitedMemoryBroyden(; threshold = 2))
+    for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(), PseudoTransient(),
+        RobustMultiNewton(), FastShortcutNonlinearPolyalg(),
+        Broyden(), Klement(), LimitedMemoryBroyden(; threshold = 2))
         @test vec(solve(prob, alg).u) == solve(vecprob, alg).u
     end
 end
diff --git a/test/misc/polyalg_tests.jl b/test/misc/polyalg_tests.jl
index 10df60429..d9433d494 100644
--- a/test/misc/polyalg_tests.jl
+++ b/test/misc/polyalg_tests.jl
@@ -91,8 +91,8 @@ end
     # This test is not meant to return success but test that all the default solvers can handle
     # complex valued problems
     @test_nowarn solve(prob; abstol = 1e-19, maxiters = 10)
-    @test_nowarn solve(prob, RobustMultiNewton(eltype(prob.u0)); abstol = 1e-19,
-        maxiters = 10)
+    @test_nowarn solve(
+        prob, RobustMultiNewton(eltype(prob.u0)); abstol = 1e-19, maxiters = 10)
 end
 
 @testitem "No AD" begin
diff --git a/test/misc/qa_tests.jl b/test/misc/qa_tests.jl
index e182ac22f..c43b9f027 100644
--- a/test/misc/qa_tests.jl
+++ b/test/misc/qa_tests.jl
@@ -4,8 +4,8 @@
     Aqua.find_persistent_tasks_deps(NonlinearSolve)
     Aqua.test_ambiguities(NonlinearSolve; recursive = false)
     Aqua.test_deps_compat(NonlinearSolve)
-    Aqua.test_piracies(NonlinearSolve,
-        treat_as_own = [NonlinearProblem, NonlinearLeastSquaresProblem])
+    Aqua.test_piracies(
+        NonlinearSolve, treat_as_own = [NonlinearProblem, NonlinearLeastSquaresProblem])
     Aqua.test_project_extras(NonlinearSolve)
     # Timer Outputs needs to be enabled via Preferences
     Aqua.test_stale_deps(NonlinearSolve; ignore = [:TimerOutputs])
diff --git a/test/runtests.jl b/test/runtests.jl
index 0c3f7d855..014e4cd0e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -3,8 +3,7 @@ using ReTestItems
 const GROUP = get(ENV, "GROUP", "All")
 
 if GROUP == "All" || GROUP == "Core"
-    ReTestItems.runtests(joinpath(@__DIR__, "core/"),
-        joinpath(@__DIR__, "misc/"),
+    ReTestItems.runtests(joinpath(@__DIR__, "core/"), joinpath(@__DIR__, "misc/"),
         joinpath(@__DIR__, "wrappers/"))
 end
 
diff --git a/test/wrappers/nlls_tests.jl b/test/wrappers/nlls_tests.jl
index f578b192c..a65ab5ec9 100644
--- a/test/wrappers/nlls_tests.jl
+++ b/test/wrappers/nlls_tests.jl
@@ -31,8 +31,7 @@ end
 @testitem "LeastSquaresOptim.jl" setup=[WrapperNLLSSetup] begin
     prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
     prob_iip = NonlinearLeastSquaresProblem(
-        NonlinearFunction(loss_function;
-            resid_prototype = zero(y_target)), θ_init, x)
+        NonlinearFunction(loss_function; resid_prototype = zero(y_target)), θ_init, x)
 
     nlls_problems = [prob_oop, prob_iip]
 
@@ -47,8 +46,7 @@ end
     end
 end
 
-@testitem "FastLevenbergMarquardt.jl + CMINPACK: Jacobian Provided" setup=[
-    WrapperNLLSSetup] begin
+@testitem "FastLevenbergMarquardt.jl + CMINPACK: Jacobian Provided" setup=[WrapperNLLSSetup] begin
     function jac!(J, θ, p)
         resid = zeros(length(p))
         ForwardDiff.jacobian!(J, (resid, θ) -> loss_function(resid, θ, p), resid, θ)
@@ -59,18 +57,17 @@ end
 
     probs = [
         NonlinearLeastSquaresProblem(
-            NonlinearFunction{true}(loss_function;
-                resid_prototype = zero(y_target), jac = jac!),
+            NonlinearFunction{true}(
+                loss_function; resid_prototype = zero(y_target), jac = jac!),
             θ_init,
             x),
         NonlinearLeastSquaresProblem(
-            NonlinearFunction{false}(loss_function;
-                resid_prototype = zero(y_target), jac = jac),
+            NonlinearFunction{false}(
+                loss_function; resid_prototype = zero(y_target), jac = jac),
             θ_init,
             x),
-        NonlinearLeastSquaresProblem(NonlinearFunction{false}(loss_function; jac),
-            θ_init, x)
-    ]
+        NonlinearLeastSquaresProblem(
+            NonlinearFunction{false}(loss_function; jac), θ_init, x)]
 
     solvers = Any[FastLevenbergMarquardtJL(linsolve) for linsolve in (:cholesky, :qr)]
     push!(solvers, CMINPACK())
@@ -80,19 +77,15 @@ end
     end
 end
 
-@testitem "FastLevenbergMarquardt.jl + CMINPACK: Jacobian Not Provided" setup=[
-    WrapperNLLSSetup] begin
+@testitem "FastLevenbergMarquardt.jl + CMINPACK: Jacobian Not Provided" setup=[WrapperNLLSSetup] begin
     probs = [
         NonlinearLeastSquaresProblem(
-            NonlinearFunction{true}(loss_function;
-                resid_prototype = zero(y_target)),
+            NonlinearFunction{true}(loss_function; resid_prototype = zero(y_target)),
             θ_init, x),
         NonlinearLeastSquaresProblem(
-            NonlinearFunction{false}(loss_function;
-                resid_prototype = zero(y_target)),
+            NonlinearFunction{false}(loss_function; resid_prototype = zero(y_target)),
             θ_init, x),
-        NonlinearLeastSquaresProblem(NonlinearFunction{false}(loss_function), θ_init, x)
-    ]
+        NonlinearLeastSquaresProblem(NonlinearFunction{false}(loss_function), θ_init, x)]
 
     solvers = vec(Any[FastLevenbergMarquardtJL(linsolve; autodiff)
                       for linsolve in (:cholesky, :qr),

From 97c232ba2f1f957fa49878ca2cf71a810945adc8 Mon Sep 17 00:00:00 2001
From: Arno Strouwen <arno.strouwen@telenet.be>
Date: Sun, 18 Feb 2024 13:26:44 +0100
Subject: [PATCH 317/700] [skip ci] update downgrade CI repo

---
 .github/workflows/Downgrade.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/workflows/Downgrade.yml b/.github/workflows/Downgrade.yml
index 8e5efd609..c1b0820f3 100644
--- a/.github/workflows/Downgrade.yml
+++ b/.github/workflows/Downgrade.yml
@@ -21,7 +21,7 @@ jobs:
       - uses: julia-actions/setup-julia@v1
         with:
           version: ${{ matrix.version }}
-      - uses: cjdoris/julia-downgrade-compat-action@v1
+      - uses: julia-actions/julia-downgrade-compat@v1
         with:
           skip: Pkg,TOML
       - uses: julia-actions/julia-buildpkg@v1

From 0166ee965368572b961b802a561258be8c03c84c Mon Sep 17 00:00:00 2001
From: Arno Strouwen <arno.strouwen@telenet.be>
Date: Sun, 18 Feb 2024 13:59:51 +0100
Subject: [PATCH 318/700] [skip ci] update downgrade CI repo

---
 lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml
index cbcc6ac06..0d225bb0b 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml
@@ -21,9 +21,9 @@ jobs:
       - uses: julia-actions/setup-julia@v1
         with:
           version: ${{ matrix.version }}
-      - uses: cjdoris/julia-downgrade-compat-action@v1
+      - uses: julia-actions/julia-downgrade-compat@v1
 #        if: ${{ matrix.version == '1.6' }}
         with:
           skip: Pkg,TOML
       - uses: julia-actions/julia-buildpkg@v1
-      - uses: julia-actions/julia-runtest@v1
\ No newline at end of file
+      - uses: julia-actions/julia-runtest@v1

From bf072d2b438c1c4ec25d987da608f395553d3a9b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 18 Feb 2024 09:16:36 -0500
Subject: [PATCH 319/700] Update pages.jl

---
 docs/pages.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/pages.jl b/docs/pages.jl
index 0706115f7..0d548cd60 100644
--- a/docs/pages.jl
+++ b/docs/pages.jl
@@ -17,7 +17,7 @@ pages = ["index.md",
         "native/globalization.md", "native/diagnostics.md"],
     "Wrapped Solver APIs" => Any[
         "api/fastlevenbergmarquardt.md", "api/fixedpointacceleration.md",
-        "api/leastsquaresoptim.md", "api/minpack.md", "api/nlsolve.md",
+        "api/leastsquaresoptim.md", "api/minpack.md", "api/nlsolve.md", "api/nlsolvers.md",
         "api/siamfanlequations.md", "api/speedmapping.md", "api/sundials.md"],
     "Development Documentation" => [
         "devdocs/internal_interfaces.md", "devdocs/linear_solve.md",

From 84a08dceb29b04fcc7e18d09f560d08aad17fbcc Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 16 Feb 2024 15:58:27 -0500
Subject: [PATCH 320/700] Add step! for polyalgorithms

---
 Project.toml               |  2 +-
 src/adtypes.jl             |  8 ++---
 src/core/generic.jl        |  3 +-
 src/default.jl             | 72 +++++++++++++++++++++++++++++++-------
 src/utils.jl               |  3 ++
 test/misc/polyalg_tests.jl | 25 +++++++++++++
 testing.jl                 | 14 ++++++++
 7 files changed, 108 insertions(+), 19 deletions(-)
 create mode 100644 testing.jl

diff --git a/Project.toml b/Project.toml
index e5afe2c2e..504eec23f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.6.0"
+version = "3.6.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/adtypes.jl b/src/adtypes.jl
index 45507ecdf..9ed3107c5 100644
--- a/src/adtypes.jl
+++ b/src/adtypes.jl
@@ -83,13 +83,13 @@ AutoSparseForwardDiff
 Uses [`PolyesterForwardDiff.jl`](https://github.com/JuliaDiff/PolyesterForwardDiff.jl)
 to compute the jacobian. This is essentially parallelized `ForwardDiff.jl`.
 
-    - Supports both inplace and out-of-place functions
+  - Supports both inplace and out-of-place functions
 
 ### Keyword Arguments
 
-    - `chunksize`: Count of dual numbers that can be propagated simultaneously. Setting
-      this number to a high value will lead to slowdowns. Use
-      [`NonlinearSolve.pickchunksize`](@ref) to get a proper value.
+  - `chunksize`: Count of dual numbers that can be propagated simultaneously. Setting
+    this number to a high value will lead to slowdowns. Use
+    [`NonlinearSolve.pickchunksize`](@ref) to get a proper value.
 """
 AutoPolyesterForwardDiff
 
diff --git a/src/core/generic.jl b/src/core/generic.jl
index 22fc3e9d0..972dc18a5 100644
--- a/src/core/generic.jl
+++ b/src/core/generic.jl
@@ -51,7 +51,8 @@ function SciMLBase.step!(cache::AbstractNonlinearSolveCache{iip, timeit},
     res = @static_timeit cache.timer "solve" begin
         __step!(cache, args...; kwargs...)
     end
-    cache.nsteps += 1
+
+    hasfield(typeof(cache), :nsteps) && (cache.nsteps += 1)
 
     if timeit
         cache.total_time += time() - time_start
diff --git a/src/default.jl b/src/default.jl
index 8b17a9393..46dcedeaa 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -44,26 +44,35 @@ function Base.show(io::IO, alg::NonlinearSolvePolyAlgorithm{pType, N}) where {pT
     end
 end
 
-@concrete mutable struct NonlinearSolvePolyAlgorithmCache{iip, N} <:
-                         AbstractNonlinearSolveCache{iip, false}
+@concrete mutable struct NonlinearSolvePolyAlgorithmCache{iip, N, timeit} <:
+                         AbstractNonlinearSolveCache{iip, timeit}
     caches
     alg
+    best::Int
     current::Int
+    nsteps::Int
+    total_time::Float64
+    maxtime
+    retcode::ReturnCode.T
+    force_stop::Bool
 end
 
 function reinit_cache!(cache::NonlinearSolvePolyAlgorithmCache, args...; kwargs...)
     foreach(c -> reinit_cache!(c, args...; kwargs...), cache.caches)
     cache.current = 1
+    cache.nsteps = 0
+    cache.total_time = 0.0
 end
 
 for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProblem, :NLLS))
     algType = NonlinearSolvePolyAlgorithm{pType}
     @eval begin
-        function SciMLBase.__init(
-                prob::$probType, alg::$algType{N}, args...; kwargs...) where {N}
-            return NonlinearSolvePolyAlgorithmCache{isinplace(prob), N}(
-                map(solver -> SciMLBase.__init(prob, solver, args...; kwargs...), alg.algs),
-                alg, 1)
+        function SciMLBase.__init(prob::$probType, alg::$algType{N}, args...;
+                maxtime = nothing, kwargs...) where {N}
+            return NonlinearSolvePolyAlgorithmCache{isinplace(prob), N, maxtime !== nothing}(
+                map(solver -> SciMLBase.__init(prob, solver, args...; maxtime, kwargs...),
+                    alg.algs), alg, -1, 1, 0, 0.0, maxtime,
+                ReturnCode.Default, false)
         end
     end
 end
@@ -87,9 +96,8 @@ end
                         stats = $(sol_syms[i]).stats
                         u = $(sol_syms[i]).u
                         fu = get_fu($(cache_syms[i]))
-                        return SciMLBase.build_solution(
-                            $(sol_syms[i]).prob, cache.alg, u, fu;
-                            retcode = ReturnCode.Success, stats,
+                        return SciMLBase.build_solution($(sol_syms[i]).prob, cache.alg, u,
+                            fu; retcode = $(sol_syms[i]).retcode, stats,
                             original = $(sol_syms[i]), trace = $(sol_syms[i]).trace)
                     end
                     cache.current = $(i + 1)
@@ -103,12 +111,11 @@ end
     end
     push!(calls,
         quote
-            retcode = ReturnCode.MaxIters
-
             fus = tuple($(Tuple(resids)...))
             minfu, idx = __findmin(cache.caches[1].internalnorm, fus)
             stats = cache.caches[idx].stats
-            u = cache.caches[idx].u
+            u = get_u(cache.caches[idx])
+            retcode = cache.caches[idx].retcode
 
             return SciMLBase.build_solution(cache.caches[idx].prob, cache.alg, u, fus[idx];
                 retcode, stats, cache.caches[idx].trace)
@@ -117,6 +124,45 @@ end
     return Expr(:block, calls...)
 end
 
+@generated function __step!(
+        cache::NonlinearSolvePolyAlgorithmCache{iip, N}, args...; kwargs...) where {iip, N}
+    calls = []
+    cache_syms = [gensym("cache") for i in 1:N]
+    for i in 1:N
+        push!(calls,
+            quote
+                $(cache_syms[i]) = cache.caches[$(i)]
+                if $(i) == cache.current
+                    __step!($(cache_syms[i]), args...; kwargs...)
+                    if !not_terminated($(cache_syms[i]))
+                        if SciMLBase.successful_retcode($(cache_syms[i]).retcode)
+                            cache.best = $(i)
+                            cache.force_stop = true
+                            cache.retcode = $(cache_syms[i]).retcode
+                        else
+                            cache.current = $(i + 1)
+                        end
+                    end
+                    return
+                end
+            end)
+    end
+
+    push!(calls,
+        quote
+            if !(1 ≤ cache.current ≤ length(cache.caches))
+                minfu, idx = __findmin(first(cache.caches).internalnorm, cache.caches)
+                cache.best = idx
+                cache.retcode = cache.caches[cache.best].retcode
+                cache.force_stop = true
+                return
+            end
+        end
+    )
+
+    return Expr(:block, calls...)
+end
+
 for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProblem, :NLLS))
     algType = NonlinearSolvePolyAlgorithm{pType}
     @eval begin
diff --git a/src/utils.jl b/src/utils.jl
index 7f4c2c439..aec66bdd4 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -94,6 +94,9 @@ LazyArrays.applied_axes(::typeof(__zero), x) = axes(x)
 @inline __is_complex(::Type{Complex}) = true
 @inline __is_complex(::Type{T}) where {T} = false
 
+function __findmin_caches(f, caches)
+    return __findmin(f ∘ get_fu, caches)
+end
 function __findmin(f, x)
     return findmin(x) do xᵢ
         fx = f(xᵢ)
diff --git a/test/misc/polyalg_tests.jl b/test/misc/polyalg_tests.jl
index d9433d494..6c1f17639 100644
--- a/test/misc/polyalg_tests.jl
+++ b/test/misc/polyalg_tests.jl
@@ -28,6 +28,31 @@
     cache = init(probN, custom_polyalg; abstol = 1e-9)
     solver = solve!(cache)
     @test SciMLBase.successful_retcode(solver)
+
+    # Test the step interface
+    cache = init(probN; abstol = 1e-9)
+    for i in 1:10000
+        step!(cache)
+        cache.force_stop && break
+    end
+    @test SciMLBase.successful_retcode(cache.retcode)
+    cache = init(probN, RobustMultiNewton(); abstol = 1e-9)
+    for i in 1:10000
+        step!(cache)
+        cache.force_stop && break
+    end
+    @test SciMLBase.successful_retcode(cache.retcode)
+    cache = init(probN, FastShortcutNonlinearPolyalg(); abstol = 1e-9)
+    for i in 1:10000
+        step!(cache)
+        cache.force_stop && break
+    end
+    @test SciMLBase.successful_retcode(cache.retcode)
+    cache = init(probN, custom_polyalg; abstol = 1e-9)
+    for i in 1:10000
+        step!(cache)
+        cache.force_stop && break
+    end
 end
 
 @testitem "Testing #153 Singular Exception" begin
diff --git a/testing.jl b/testing.jl
new file mode 100644
index 000000000..9a3110f40
--- /dev/null
+++ b/testing.jl
@@ -0,0 +1,14 @@
+using NonlinearSolve
+
+f(u, p) = u .* u .- 2
+
+u0 = [1.0, 1.0]
+
+prob = NonlinearProblem(f, u0)
+
+nlcache = init(prob);
+
+for i in 1:10
+    step!(nlcache)
+    @show nlcache.retcode
+end

From c7409c861ceda258d424848f1df0ff3d9f758001 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 16 Feb 2024 21:07:07 -0500
Subject: [PATCH 321/700] Add pretty printing for the cache

---
 src/abstract_types.jl | 22 ++++++++++++++++++++--
 src/core/generic.jl   |  5 +++--
 src/default.jl        | 25 +++++++++++++++++++------
 3 files changed, 42 insertions(+), 10 deletions(-)

diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index b7127cb2c..78063c19d 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -173,8 +173,8 @@ not applicable. Else a boolean value is returned.
 """
 concrete_jac(::AbstractNonlinearSolveAlgorithm) = nothing
 
-function Base.show(io::IO, alg::AbstractNonlinearSolveAlgorithm{name}) where {name}
-    __show_algorithm(io, alg, name, 0)
+function Base.show(io::IO, alg::AbstractNonlinearSolveAlgorithm)
+    __show_algorithm(io, alg, get_name(alg), 0)
 end
 
 get_name(::AbstractNonlinearSolveAlgorithm{name}) where {name} = name
@@ -207,6 +207,24 @@ Abstract Type for all NonlinearSolve.jl Caches.
 """
 abstract type AbstractNonlinearSolveCache{iip, timeit} end
 
+function Base.show(io::IO, cache::AbstractNonlinearSolveCache)
+    __show_cache(io, cache, 0)
+end
+
+function __show_cache(io::IO, cache::AbstractNonlinearSolveCache, indent = 0)
+    println(io, "$(nameof(typeof(cache)))(")
+    __show_algorithm(io, cache.alg,
+        (" "^(indent + 4)) * "alg = " * string(get_name(cache.alg)), indent +
+                                                                     4)
+    println(io, ",")
+    println(io, (" "^(indent + 4)) * "u = ", get_u(cache), ",")
+    println(io, (" "^(indent + 4)) * "residual = ", get_fu(cache), ",")
+    println(io, (" "^(indent + 4)) * "inf-norm(residual) = ", norm(get_fu(cache), Inf), ",")
+    println(io, " "^(indent + 4) * "nsteps = ", get_nsteps(cache), ",")
+    println(io, " "^(indent + 4) * "retcode = ", cache.retcode)
+    print(io, " "^(indent) * ")")
+end
+
 SciMLBase.isinplace(::AbstractNonlinearSolveCache{iip}) where {iip} = iip
 
 get_fu(cache::AbstractNonlinearSolveCache) = cache.fu
diff --git a/src/core/generic.jl b/src/core/generic.jl
index 972dc18a5..7f3dd3a8e 100644
--- a/src/core/generic.jl
+++ b/src/core/generic.jl
@@ -45,8 +45,9 @@ Performs one step of the nonlinear solver.
     respectively. For algorithms that don't use jacobian information, this keyword is
     ignored with a one-time warning.
 """
-function SciMLBase.step!(cache::AbstractNonlinearSolveCache{iip, timeit},
-        args...; kwargs...) where {iip, timeit}
+function SciMLBase.step!(cache::AbstractNonlinearSolveCache{iip, timeit}, args...;
+        kwargs...) where {iip, timeit}
+    not_terminated(cache) || return
     timeit && (time_start = time())
     res = @static_timeit cache.timer "solve" begin
         __step!(cache, args...; kwargs...)
diff --git a/src/default.jl b/src/default.jl
index 46dcedeaa..8544998f7 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -55,6 +55,19 @@ end
     maxtime
     retcode::ReturnCode.T
     force_stop::Bool
+    maxiters::Int
+end
+
+function Base.show(io::IO,
+        cache::NonlinearSolvePolyAlgorithmCache{pType, N}) where {pType, N}
+    problem_kind = ifelse(pType == :NLS, "NonlinearProblem", "NonlinearLeastSquaresProblem")
+    println(io, "NonlinearSolvePolyAlgorithmCache for $(problem_kind) with $(N) algorithms")
+    best_alg = ifelse(cache.best == -1, "nothing", cache.best)
+    println(io, "Best algorithm: $(best_alg)")
+    println(io, "Current algorithm: $(cache.current)")
+    println(io, "nsteps: $(cache.nsteps)")
+    println(io, "retcode: $(cache.retcode)")
+    __show_cache(io, cache.caches[cache.current], 0)
 end
 
 function reinit_cache!(cache::NonlinearSolvePolyAlgorithmCache, args...; kwargs...)
@@ -68,11 +81,11 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
     algType = NonlinearSolvePolyAlgorithm{pType}
     @eval begin
         function SciMLBase.__init(prob::$probType, alg::$algType{N}, args...;
-                maxtime = nothing, kwargs...) where {N}
+                maxtime = nothing, maxiters = 1000, kwargs...) where {N}
             return NonlinearSolvePolyAlgorithmCache{isinplace(prob), N, maxtime !== nothing}(
                 map(solver -> SciMLBase.__init(prob, solver, args...; maxtime, kwargs...),
                     alg.algs), alg, -1, 1, 0, 0.0, maxtime,
-                ReturnCode.Default, false)
+                ReturnCode.Default, false, maxiters)
         end
     end
 end
@@ -124,8 +137,8 @@ end
     return Expr(:block, calls...)
 end
 
-@generated function __step!(
-        cache::NonlinearSolvePolyAlgorithmCache{iip, N}, args...; kwargs...) where {iip, N}
+@generated function __step!(cache::NonlinearSolvePolyAlgorithmCache{iip, N}, args...;
+        kwargs...) where {iip, N}
     calls = []
     cache_syms = [gensym("cache") for i in 1:N]
     for i in 1:N
@@ -134,6 +147,7 @@ end
                 $(cache_syms[i]) = cache.caches[$(i)]
                 if $(i) == cache.current
                     __step!($(cache_syms[i]), args...; kwargs...)
+                    $(cache_syms[i]).nsteps += 1
                     if !not_terminated($(cache_syms[i]))
                         if SciMLBase.successful_retcode($(cache_syms[i]).retcode)
                             cache.best = $(i)
@@ -157,8 +171,7 @@ end
                 cache.force_stop = true
                 return
             end
-        end
-    )
+        end)
 
     return Expr(:block, calls...)
 end

From bd5d988f4825aa3c84b04710f1f3e7cec54f8b0f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 18 Feb 2024 11:59:00 -0500
Subject: [PATCH 322/700] Format

---
 ext/NonlinearSolveNLSolversExt.jl | 21 +++++++++++----------
 src/abstract_types.jl             |  3 +--
 src/core/generic.jl               |  4 ++--
 src/default.jl                    | 25 +++++++++++++++++--------
 test/wrappers/rootfind_tests.jl   | 15 +++++++++------
 5 files changed, 40 insertions(+), 28 deletions(-)

diff --git a/ext/NonlinearSolveNLSolversExt.jl b/ext/NonlinearSolveNLSolversExt.jl
index fd75095c0..b480578d0 100644
--- a/ext/NonlinearSolveNLSolversExt.jl
+++ b/ext/NonlinearSolveNLSolversExt.jl
@@ -4,8 +4,8 @@ using ADTypes, FastClosures, NonlinearSolve, NLSolvers, SciMLBase, LinearAlgebra
 using FiniteDiff, ForwardDiff
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0::Bool = false,
-        termination_condition = nothing, kwargs...)
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0::Bool = false, termination_condition = nothing, kwargs...)
     NonlinearSolve.__test_termination_condition(termination_condition, :NLSolversJL)
 
     abstol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(prob.u0))
@@ -50,12 +50,13 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
         prob_nlsolver = NEqProblem(prob_obj; inplace = false)
         res = NLSolvers.solve(prob_nlsolver, prob.u0, alg.method, options)
 
-        retcode = ifelse(norm(res.info.best_residual, Inf) ≤ abstol, ReturnCode.Success,
-            ReturnCode.MaxIters)
+        retcode = ifelse(norm(res.info.best_residual, Inf) ≤ abstol,
+            ReturnCode.Success, ReturnCode.MaxIters)
         stats = SciMLBase.NLStats(-1, -1, -1, -1, res.info.iter)
 
-        return SciMLBase.build_solution(prob, alg, res.info.solution,
-            res.info.best_residual; retcode, original = res, stats)
+        return SciMLBase.build_solution(
+            prob, alg, res.info.solution, res.info.best_residual;
+            retcode, original = res, stats)
     end
 
     f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
@@ -73,12 +74,12 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
 
     res = NLSolvers.solve(prob_nlsolver, u0, alg.method, options)
 
-    retcode = ifelse(norm(res.info.best_residual, Inf) ≤ abstol, ReturnCode.Success,
-        ReturnCode.MaxIters)
+    retcode = ifelse(
+        norm(res.info.best_residual, Inf) ≤ abstol, ReturnCode.Success, ReturnCode.MaxIters)
     stats = SciMLBase.NLStats(-1, -1, -1, -1, res.info.iter)
 
-    return SciMLBase.build_solution(prob, alg, res.info.solution,
-        res.info.best_residual; retcode, original = res, stats)
+    return SciMLBase.build_solution(prob, alg, res.info.solution, res.info.best_residual;
+        retcode, original = res, stats)
 end
 
 end
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 78063c19d..e9c2f4d7f 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -214,8 +214,7 @@ end
 function __show_cache(io::IO, cache::AbstractNonlinearSolveCache, indent = 0)
     println(io, "$(nameof(typeof(cache)))(")
     __show_algorithm(io, cache.alg,
-        (" "^(indent + 4)) * "alg = " * string(get_name(cache.alg)), indent +
-                                                                     4)
+        (" "^(indent + 4)) * "alg = " * string(get_name(cache.alg)), indent + 4)
     println(io, ",")
     println(io, (" "^(indent + 4)) * "u = ", get_u(cache), ",")
     println(io, (" "^(indent + 4)) * "residual = ", get_fu(cache), ",")
diff --git a/src/core/generic.jl b/src/core/generic.jl
index 7f3dd3a8e..9aafba49b 100644
--- a/src/core/generic.jl
+++ b/src/core/generic.jl
@@ -45,8 +45,8 @@ Performs one step of the nonlinear solver.
     respectively. For algorithms that don't use jacobian information, this keyword is
     ignored with a one-time warning.
 """
-function SciMLBase.step!(cache::AbstractNonlinearSolveCache{iip, timeit}, args...;
-        kwargs...) where {iip, timeit}
+function SciMLBase.step!(cache::AbstractNonlinearSolveCache{iip, timeit},
+        args...; kwargs...) where {iip, timeit}
     not_terminated(cache) || return
     timeit && (time_start = time())
     res = @static_timeit cache.timer "solve" begin
diff --git a/src/default.jl b/src/default.jl
index 8544998f7..da2420656 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -58,8 +58,8 @@ end
     maxiters::Int
 end
 
-function Base.show(io::IO,
-        cache::NonlinearSolvePolyAlgorithmCache{pType, N}) where {pType, N}
+function Base.show(
+        io::IO, cache::NonlinearSolvePolyAlgorithmCache{pType, N}) where {pType, N}
     problem_kind = ifelse(pType == :NLS, "NonlinearProblem", "NonlinearLeastSquaresProblem")
     println(io, "NonlinearSolvePolyAlgorithmCache for $(problem_kind) with $(N) algorithms")
     best_alg = ifelse(cache.best == -1, "nothing", cache.best)
@@ -84,8 +84,16 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
                 maxtime = nothing, maxiters = 1000, kwargs...) where {N}
             return NonlinearSolvePolyAlgorithmCache{isinplace(prob), N, maxtime !== nothing}(
                 map(solver -> SciMLBase.__init(prob, solver, args...; maxtime, kwargs...),
-                    alg.algs), alg, -1, 1, 0, 0.0, maxtime,
-                ReturnCode.Default, false, maxiters)
+                    alg.algs),
+                alg,
+                -1,
+                1,
+                0,
+                0.0,
+                maxtime,
+                ReturnCode.Default,
+                false,
+                maxiters)
         end
     end
 end
@@ -109,8 +117,9 @@ end
                         stats = $(sol_syms[i]).stats
                         u = $(sol_syms[i]).u
                         fu = get_fu($(cache_syms[i]))
-                        return SciMLBase.build_solution($(sol_syms[i]).prob, cache.alg, u,
-                            fu; retcode = $(sol_syms[i]).retcode, stats,
+                        return SciMLBase.build_solution(
+                            $(sol_syms[i]).prob, cache.alg, u, fu;
+                            retcode = $(sol_syms[i]).retcode, stats,
                             original = $(sol_syms[i]), trace = $(sol_syms[i]).trace)
                     end
                     cache.current = $(i + 1)
@@ -137,8 +146,8 @@ end
     return Expr(:block, calls...)
 end
 
-@generated function __step!(cache::NonlinearSolvePolyAlgorithmCache{iip, N}, args...;
-        kwargs...) where {iip, N}
+@generated function __step!(
+        cache::NonlinearSolvePolyAlgorithmCache{iip, N}, args...; kwargs...) where {iip, N}
     calls = []
     cache_syms = [gensym("cache") for i in 1:N]
     for i in 1:N
diff --git a/test/wrappers/rootfind_tests.jl b/test/wrappers/rootfind_tests.jl
index 0fa56d690..dcee9ceba 100644
--- a/test/wrappers/rootfind_tests.jl
+++ b/test/wrappers/rootfind_tests.jl
@@ -16,7 +16,8 @@ end
     prob_iip = SteadyStateProblem(f_iip, u0)
 
     for alg in [
-        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())), NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
+        NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
         sol = solve(prob_iip, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
         @test maximum(abs, sol.resid) < 1e-6
@@ -28,7 +29,8 @@ end
     prob_oop = SteadyStateProblem(f_oop, u0)
 
     for alg in [
-        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())), NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
+        NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
         sol = solve(prob_oop, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
         @test maximum(abs, sol.resid) < 1e-6
@@ -45,7 +47,8 @@ end
     prob_iip = NonlinearProblem{true}(f_iip, u0)
 
     for alg in [
-        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())), NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
+        NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
         local sol
         sol = solve(prob_iip, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
@@ -57,7 +60,8 @@ end
     u0 = zeros(2)
     prob_oop = NonlinearProblem{false}(f_oop, u0)
     for alg in [
-        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())), NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
+        NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
         local sol
         sol = solve(prob_oop, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
@@ -70,8 +74,7 @@ end
     for tol in [1e-1, 1e-3, 1e-6, 1e-10, 1e-15],
         alg in [
             NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
-            NLsolveJL(),
-            CMINPACK(), SIAMFANLEquationsJL(; method = :newton),
+            NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL(; method = :newton),
             SIAMFANLEquationsJL(; method = :pseudotransient),
             SIAMFANLEquationsJL(; method = :secant)]
 

From e37b70a2fba8717b41f6458584c9c194f073ebb7 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 20 Feb 2024 11:05:18 -0500
Subject: [PATCH 323/700] Add caching for solvers without init

---
 Project.toml                              |  2 +-
 ext/NonlinearSolveLeastSquaresOptimExt.jl |  4 +++
 ext/NonlinearSolveNLSolversExt.jl         | 21 +++++++------
 src/NonlinearSolve.jl                     |  1 +
 src/abstract_types.jl                     |  3 ++
 src/core/noinit.jl                        | 37 +++++++++++++++++++++++
 test/misc/noinit_caching_tests.jl         | 23 ++++++++++++++
 test/misc/qa_tests.jl                     |  7 +++--
 test/wrappers/rootfind_tests.jl           | 15 +++++----
 9 files changed, 93 insertions(+), 20 deletions(-)
 create mode 100644 src/core/noinit.jl
 create mode 100644 test/misc/noinit_caching_tests.jl

diff --git a/Project.toml b/Project.toml
index e5afe2c2e..20dd03f68 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.6.0"
+version = "3.7.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/ext/NonlinearSolveLeastSquaresOptimExt.jl b/ext/NonlinearSolveLeastSquaresOptimExt.jl
index 42ff7c9d3..b5c1a7426 100644
--- a/ext/NonlinearSolveLeastSquaresOptimExt.jl
+++ b/ext/NonlinearSolveLeastSquaresOptimExt.jl
@@ -23,6 +23,10 @@ end
     kwargs
 end
 
+function Base.show(io::IO, cache::LeastSquaresOptimJLCache)
+    print(io, "LeastSquaresOptimJLCache()")
+end
+
 function SciMLBase.reinit!(cache::LeastSquaresOptimJLCache, args...; kwargs...)
     error("Reinitialization not supported for LeastSquaresOptimJL.")
 end
diff --git a/ext/NonlinearSolveNLSolversExt.jl b/ext/NonlinearSolveNLSolversExt.jl
index fd75095c0..b480578d0 100644
--- a/ext/NonlinearSolveNLSolversExt.jl
+++ b/ext/NonlinearSolveNLSolversExt.jl
@@ -4,8 +4,8 @@ using ADTypes, FastClosures, NonlinearSolve, NLSolvers, SciMLBase, LinearAlgebra
 using FiniteDiff, ForwardDiff
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0::Bool = false,
-        termination_condition = nothing, kwargs...)
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0::Bool = false, termination_condition = nothing, kwargs...)
     NonlinearSolve.__test_termination_condition(termination_condition, :NLSolversJL)
 
     abstol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(prob.u0))
@@ -50,12 +50,13 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
         prob_nlsolver = NEqProblem(prob_obj; inplace = false)
         res = NLSolvers.solve(prob_nlsolver, prob.u0, alg.method, options)
 
-        retcode = ifelse(norm(res.info.best_residual, Inf) ≤ abstol, ReturnCode.Success,
-            ReturnCode.MaxIters)
+        retcode = ifelse(norm(res.info.best_residual, Inf) ≤ abstol,
+            ReturnCode.Success, ReturnCode.MaxIters)
         stats = SciMLBase.NLStats(-1, -1, -1, -1, res.info.iter)
 
-        return SciMLBase.build_solution(prob, alg, res.info.solution,
-            res.info.best_residual; retcode, original = res, stats)
+        return SciMLBase.build_solution(
+            prob, alg, res.info.solution, res.info.best_residual;
+            retcode, original = res, stats)
     end
 
     f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
@@ -73,12 +74,12 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
 
     res = NLSolvers.solve(prob_nlsolver, u0, alg.method, options)
 
-    retcode = ifelse(norm(res.info.best_residual, Inf) ≤ abstol, ReturnCode.Success,
-        ReturnCode.MaxIters)
+    retcode = ifelse(
+        norm(res.info.best_residual, Inf) ≤ abstol, ReturnCode.Success, ReturnCode.MaxIters)
     stats = SciMLBase.NLStats(-1, -1, -1, -1, res.info.iter)
 
-    return SciMLBase.build_solution(prob, alg, res.info.solution,
-        res.info.best_residual; retcode, original = res, stats)
+    return SciMLBase.build_solution(prob, alg, res.info.solution, res.info.best_residual;
+        retcode, original = res, stats)
 end
 
 end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 10645fad7..991783672 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -66,6 +66,7 @@ include("core/generic.jl")
 include("core/approximate_jacobian.jl")
 include("core/generalized_first_order.jl")
 include("core/spectral_methods.jl")
+include("core/noinit.jl")
 
 include("algorithms/raphson.jl")
 include("algorithms/pseudo_transient.jl")
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index b7127cb2c..a08f53317 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -214,6 +214,9 @@ get_u(cache::AbstractNonlinearSolveCache) = cache.u
 set_fu!(cache::AbstractNonlinearSolveCache, fu) = (cache.fu = fu)
 SciMLBase.set_u!(cache::AbstractNonlinearSolveCache, u) = (cache.u = u)
 
+function SciMLBase.reinit!(cache::AbstractNonlinearSolveCache; kwargs...)
+    return reinit_cache!(cache; kwargs...)
+end
 function SciMLBase.reinit!(cache::AbstractNonlinearSolveCache, u0; kwargs...)
     return reinit_cache!(cache; u0, kwargs...)
 end
diff --git a/src/core/noinit.jl b/src/core/noinit.jl
new file mode 100644
index 000000000..b51c09c23
--- /dev/null
+++ b/src/core/noinit.jl
@@ -0,0 +1,37 @@
+# Some algorithms don't support creating a cache and doing `solve!`, this unfortunately
+# makes it difficult to write generic code that supports caching. For the algorithms that
+# don't have a `__init` function defined, we create a "Fake Cache", which just calls
+# `__solve` from `solve!`
+@concrete mutable struct NonlinearSolveNoInitCache{iip, timeit} <:
+                         AbstractNonlinearSolveCache{iip, timeit}
+    prob
+    alg
+    args
+    kwargs::Any
+end
+
+function SciMLBase.reinit!(
+        cache::NonlinearSolveNoInitCache, u0 = cache.prob.u0; p = cache.prob.p, kwargs...)
+    prob = remake(cache.prob; u0, p)
+    cache.prob = prob
+    cache.kwargs = merge(cache.kwargs, kwargs)
+    return cache
+end
+
+function Base.show(io::IO, cache::NonlinearSolveNoInitCache)
+    print(io, "NonlinearSolveNoInitCache(alg = $(cache.alg))")
+end
+
+function SciMLBase.__init(prob::AbstractNonlinearProblem{uType, iip},
+        alg::Union{AbstractNonlinearSolveAlgorithm,
+            SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm},
+        args...;
+        maxtime = nothing,
+        kwargs...) where {uType, iip}
+    return NonlinearSolveNoInitCache{iip, maxtime !== nothing}(
+        prob, alg, args, merge((; maxtime), kwargs))
+end
+
+function SciMLBase.solve!(cache::NonlinearSolveNoInitCache)
+    return solve(cache.prob, cache.alg, cache.args...; cache.kwargs...)
+end
diff --git a/test/misc/noinit_caching_tests.jl b/test/misc/noinit_caching_tests.jl
new file mode 100644
index 000000000..f9207d82f
--- /dev/null
+++ b/test/misc/noinit_caching_tests.jl
@@ -0,0 +1,23 @@
+@testitem "NoInit Caching" begin
+    using LinearAlgebra
+    import NLsolve, NLSolvers
+
+    solvers = [SimpleNewtonRaphson(), SimpleTrustRegion(), SimpleDFSane(), NLsolveJL(),
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking()))]
+
+    prob = NonlinearProblem((u, p) -> u .^ 2 .- p, [0.1, 0.3], 2.0)
+
+    for alg in solvers
+        cache = init(prob, alg)
+        sol = solve!(cache)
+        @test SciMLBase.successful_retcode(sol)
+        @test norm(sol.resid, Inf) ≤ 1e-6
+
+        reinit!(cache; p = 5.0)
+        @test cache.prob.p == 5.0
+        sol = solve!(cache)
+        @test SciMLBase.successful_retcode(sol)
+        @test norm(sol.resid, Inf) ≤ 1e-6
+        @test norm(sol.u .^ 2 .- 5.0, Inf) ≤ 1e-6
+    end
+end
diff --git a/test/misc/qa_tests.jl b/test/misc/qa_tests.jl
index c43b9f027..28cf1dbf4 100644
--- a/test/misc/qa_tests.jl
+++ b/test/misc/qa_tests.jl
@@ -1,11 +1,12 @@
 @testitem "Aqua" begin
-    using NonlinearSolve, Aqua
+    using NonlinearSolve, SimpleNonlinearSolve, Aqua
 
     Aqua.find_persistent_tasks_deps(NonlinearSolve)
     Aqua.test_ambiguities(NonlinearSolve; recursive = false)
     Aqua.test_deps_compat(NonlinearSolve)
-    Aqua.test_piracies(
-        NonlinearSolve, treat_as_own = [NonlinearProblem, NonlinearLeastSquaresProblem])
+    Aqua.test_piracies(NonlinearSolve,
+        treat_as_own = [NonlinearProblem, NonlinearLeastSquaresProblem,
+            SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm])
     Aqua.test_project_extras(NonlinearSolve)
     # Timer Outputs needs to be enabled via Preferences
     Aqua.test_stale_deps(NonlinearSolve; ignore = [:TimerOutputs])
diff --git a/test/wrappers/rootfind_tests.jl b/test/wrappers/rootfind_tests.jl
index 0fa56d690..dcee9ceba 100644
--- a/test/wrappers/rootfind_tests.jl
+++ b/test/wrappers/rootfind_tests.jl
@@ -16,7 +16,8 @@ end
     prob_iip = SteadyStateProblem(f_iip, u0)
 
     for alg in [
-        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())), NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
+        NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
         sol = solve(prob_iip, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
         @test maximum(abs, sol.resid) < 1e-6
@@ -28,7 +29,8 @@ end
     prob_oop = SteadyStateProblem(f_oop, u0)
 
     for alg in [
-        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())), NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
+        NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
         sol = solve(prob_oop, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
         @test maximum(abs, sol.resid) < 1e-6
@@ -45,7 +47,8 @@ end
     prob_iip = NonlinearProblem{true}(f_iip, u0)
 
     for alg in [
-        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())), NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
+        NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
         local sol
         sol = solve(prob_iip, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
@@ -57,7 +60,8 @@ end
     u0 = zeros(2)
     prob_oop = NonlinearProblem{false}(f_oop, u0)
     for alg in [
-        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())), NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
+        NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
         local sol
         sol = solve(prob_oop, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
@@ -70,8 +74,7 @@ end
     for tol in [1e-1, 1e-3, 1e-6, 1e-10, 1e-15],
         alg in [
             NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
-            NLsolveJL(),
-            CMINPACK(), SIAMFANLEquationsJL(; method = :newton),
+            NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL(; method = :newton),
             SIAMFANLEquationsJL(; method = :pseudotransient),
             SIAMFANLEquationsJL(; method = :secant)]
 

From 156e65b76c495bc1c911f98d3a97680ff67f5406 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 21 Feb 2024 20:37:07 -0500
Subject: [PATCH 324/700] Delete testing.jl

---
 testing.jl | 14 --------------
 1 file changed, 14 deletions(-)
 delete mode 100644 testing.jl

diff --git a/testing.jl b/testing.jl
deleted file mode 100644
index 9a3110f40..000000000
--- a/testing.jl
+++ /dev/null
@@ -1,14 +0,0 @@
-using NonlinearSolve
-
-f(u, p) = u .* u .- 2
-
-u0 = [1.0, 1.0]
-
-prob = NonlinearProblem(f, u0)
-
-nlcache = init(prob);
-
-for i in 1:10
-    step!(nlcache)
-    @show nlcache.retcode
-end

From 50711d735abc3fdce78073ec638d189793e7fdbe Mon Sep 17 00:00:00 2001
From: CompatHelper Julia <compathelper_noreply@julialang.org>
Date: Thu, 22 Feb 2024 07:06:42 +0000
Subject: [PATCH 325/700] CompatHelper: bump compat for ModelingToolkit to 9
 for package docs, (keep existing compat)

---
 docs/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/Project.toml b/docs/Project.toml
index 1a82e485c..f62ef73aa 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -30,7 +30,7 @@ Documenter = "1"
 DocumenterCitations = "1"
 IncompleteLU = "0.2"
 LinearSolve = "2"
-ModelingToolkit = "8"
+ModelingToolkit = "8, 9"
 NonlinearSolve = "3"
 OrdinaryDiffEq = "6"
 Plots = "1"

From 8767492fecfec204bf4d017b5c2d10ce6b2d1a60 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 22 Feb 2024 15:45:27 -0500
Subject: [PATCH 326/700] Patches for DiffEqCallbacks

---
 .github/workflows/Downstream.yml |  1 +
 Project.toml                     |  2 +-
 src/core/generic.jl              | 10 +++++----
 src/default.jl                   | 38 ++++++++++++++++++--------------
 4 files changed, 30 insertions(+), 21 deletions(-)

diff --git a/.github/workflows/Downstream.yml b/.github/workflows/Downstream.yml
index e5b27bddf..b0c39af7a 100644
--- a/.github/workflows/Downstream.yml
+++ b/.github/workflows/Downstream.yml
@@ -25,6 +25,7 @@ jobs:
           - {user: SciML, repo: OrdinaryDiffEq.jl, group: Interface}
           - {user: SciML, repo: OrdinaryDiffEq.jl, group: Regression}
           - {user: SciML, repo: BoundaryValueDiffEq.jl, group: All}
+          - {user: SciML, repo: DiffEqCallbacks.jl, group: All}
     steps:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v1
diff --git a/Project.toml b/Project.toml
index 09059a431..a06689370 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.7.1"
+version = "3.7.2"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/core/generic.jl b/src/core/generic.jl
index 9aafba49b..75d494730 100644
--- a/src/core/generic.jl
+++ b/src/core/generic.jl
@@ -24,11 +24,13 @@ function SciMLBase.solve!(cache::AbstractNonlinearSolveCache)
     update_trace!(cache.trace, get_nsteps(cache), get_u(cache),
         get_fu(cache), nothing, nothing, nothing; last = True)
 
-    stats = ImmutableNLStats(get_nf(cache), get_njacs(cache), get_nfactors(cache),
-        get_nsolve(cache), get_nsteps(cache))
+    return SciMLBase.build_solution(cache.prob, cache.alg, get_u(cache), get_fu(cache);
+        cache.retcode, stats = __compile_stats(cache), cache.trace)
+end
 
-    return SciMLBase.build_solution(cache.prob, cache.alg, get_u(cache),
-        get_fu(cache); cache.retcode, stats, cache.trace)
+function __compile_stats(cache::AbstractNonlinearSolveCache)
+    return ImmutableNLStats(get_nf(cache), get_njacs(cache), get_nfactors(cache),
+        get_nsolve(cache), get_nsteps(cache))
 end
 
 """
diff --git a/src/default.jl b/src/default.jl
index da2420656..805001c0e 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -56,6 +56,7 @@ end
     retcode::ReturnCode.T
     force_stop::Bool
     maxiters::Int
+    internalnorm
 end
 
 function Base.show(
@@ -80,10 +81,13 @@ end
 for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProblem, :NLLS))
     algType = NonlinearSolvePolyAlgorithm{pType}
     @eval begin
-        function SciMLBase.__init(prob::$probType, alg::$algType{N}, args...;
-                maxtime = nothing, maxiters = 1000, kwargs...) where {N}
+        function SciMLBase.__init(
+                prob::$probType, alg::$algType{N}, args...; maxtime = nothing,
+                maxiters = 1000, internalnorm = DEFAULT_NORM, kwargs...) where {N}
             return NonlinearSolvePolyAlgorithmCache{isinplace(prob), N, maxtime !== nothing}(
-                map(solver -> SciMLBase.__init(prob, solver, args...; maxtime, kwargs...),
+                map(
+                    solver -> SciMLBase.__init(
+                        prob, solver, args...; maxtime, internalnorm, kwargs...),
                     alg.algs),
                 alg,
                 -1,
@@ -93,7 +97,8 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
                 maxtime,
                 ReturnCode.Default,
                 false,
-                maxiters)
+                maxiters,
+                internalnorm)
         end
     end
 end
@@ -134,8 +139,8 @@ end
     push!(calls,
         quote
             fus = tuple($(Tuple(resids)...))
-            minfu, idx = __findmin(cache.caches[1].internalnorm, fus)
-            stats = cache.caches[idx].stats
+            minfu, idx = __findmin(cache.internalnorm, fus)
+            stats = __compile_stats(cache.caches[idx])
             u = get_u(cache.caches[idx])
             retcode = cache.caches[idx].retcode
 
@@ -171,16 +176,15 @@ end
             end)
     end
 
-    push!(calls,
-        quote
-            if !(1 ≤ cache.current ≤ length(cache.caches))
-                minfu, idx = __findmin(first(cache.caches).internalnorm, cache.caches)
-                cache.best = idx
-                cache.retcode = cache.caches[cache.best].retcode
-                cache.force_stop = true
-                return
-            end
-        end)
+    push!(calls, quote
+        if !(1 ≤ cache.current ≤ length(cache.caches))
+            minfu, idx = __findmin(cache.internalnorm, cache.caches)
+            cache.best = idx
+            cache.retcode = cache.caches[cache.best].retcode
+            cache.force_stop = true
+            return
+        end
+    end)
 
     return Expr(:block, calls...)
 end
@@ -353,9 +357,11 @@ function FastShortcutNLLSPolyalg(::Type{T} = Float64; concrete_jac = nothing,
         linsolve = nothing, precs = DEFAULT_PRECS, kwargs...) where {T}
     if __is_complex(T)
         algs = (GaussNewton(; concrete_jac, linsolve, precs, kwargs...),
+            LevenbergMarquardt(; linsolve, precs, disable_geodesic = Val(true), kwargs...),
             LevenbergMarquardt(; linsolve, precs, kwargs...))
     else
         algs = (GaussNewton(; concrete_jac, linsolve, precs, kwargs...),
+            LevenbergMarquardt(; linsolve, precs, disable_geodesic = Val(true), kwargs...),
             TrustRegion(; concrete_jac, linsolve, precs, kwargs...),
             GaussNewton(; concrete_jac, linsolve, precs,
                 linesearch = LineSearchesJL(; method = BackTracking()), kwargs...),

From 9fad71e18795f034c792e19de2f57f60ca2f1874 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 24 Feb 2024 09:04:56 -0500
Subject: [PATCH 327/700] Update modelingtoolkit.md

---
 docs/src/tutorials/modelingtoolkit.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/src/tutorials/modelingtoolkit.md b/docs/src/tutorials/modelingtoolkit.md
index 845b727b7..87b0a4405 100644
--- a/docs/src/tutorials/modelingtoolkit.md
+++ b/docs/src/tutorials/modelingtoolkit.md
@@ -13,7 +13,7 @@ using ModelingToolkit, NonlinearSolve
 
 # Define a nonlinear system
 eqs = [0 ~ σ * (y - x), 0 ~ x * (ρ - z) - y, 0 ~ x * y - β * z]
-@named ns = NonlinearSystem(eqs, [x, y, z], [σ, ρ, β])
+@mtkbuild ns = NonlinearSystem(eqs, [x, y, z], [σ, ρ, β])
 
 u0 = [x => 1.0, y => 0.0, z => 0.0]
 

From fe891b625c75add19af17475eea007bc9dd8cde4 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 24 Feb 2024 09:34:09 -0500
Subject: [PATCH 328/700] Update diagnostics_api.md

---
 docs/src/basics/diagnostics_api.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/src/basics/diagnostics_api.md b/docs/src/basics/diagnostics_api.md
index 7da29c1f7..c8b207544 100644
--- a/docs/src/basics/diagnostics_api.md
+++ b/docs/src/basics/diagnostics_api.md
@@ -34,7 +34,7 @@ using ModelingToolkit, NonlinearSolve
 
 # Define a nonlinear system
 eqs = [0 ~ σ * (y - x), 0 ~ x * (ρ - z) - y, 0 ~ x * y - β * z]
-@named ns = NonlinearSystem(eqs, [x, y, z], [σ, ρ, β])
+@mtkbuild ns = NonlinearSystem(eqs, [x, y, z], [σ, ρ, β])
 
 u0 = [x => 1.0, y => 0.0, z => 0.0]
 

From 716209ff03a6de6d389b217a9215c58962b4d981 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 26 Feb 2024 04:53:22 -0600
Subject: [PATCH 329/700] Make default polyalgs respect autodiff

---
 Project.toml               |  2 +-
 src/default.jl             | 43 +++++++++++++++++++++-----------------
 test/misc/polyalg_tests.jl | 26 +++++++++++++++++++++++
 3 files changed, 51 insertions(+), 20 deletions(-)

diff --git a/Project.toml b/Project.toml
index a06689370..bc1919c29 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.7.2"
+version = "3.7.3"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/default.jl b/src/default.jl
index 805001c0e..bae3e2c57 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -307,12 +307,13 @@ function FastShortcutNonlinearPolyalg(
         # and thus are not included in the polyalgorithm
         if SA
             if __is_complex(T)
-                algs = (SimpleBroyden(), Broyden(; init_jacobian = Val(:true_jacobian)),
+                algs = (SimpleBroyden(),
+                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
                     SimpleKlement(),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff))
             else
                 algs = (SimpleBroyden(),
-                    Broyden(; init_jacobian = Val(:true_jacobian)),
+                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
                     SimpleKlement(),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs,
@@ -322,13 +323,13 @@ function FastShortcutNonlinearPolyalg(
             end
         else
             if __is_complex(T)
-                algs = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian)),
-                    Klement(; linsolve, precs),
+                algs = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
+                    Klement(; linsolve, prec, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff))
             else
-                algs = (Broyden(),
-                    Broyden(; init_jacobian = Val(:true_jacobian)),
-                    Klement(; linsolve, precs),
+                algs = (Broyden(; autodiff),
+                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
+                    Klement(; linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs,
                         linesearch = LineSearchesJL(; method = BackTracking()), autodiff),
@@ -343,7 +344,7 @@ end
 
 """
     FastShortcutNLLSPolyalg(::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
-        precs = DEFAULT_PRECS, kwargs...)
+        precs = DEFAULT_PRECS, autodiff = nothing, kwargs...)
 
 A polyalgorithm focused on balancing speed and robustness. It first tries less robust methods
 for more performance and then tries more robust techniques if the faster ones fail.
@@ -353,21 +354,25 @@ for more performance and then tries more robust techniques if the faster ones fa
   - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
     are compatible with the problem type. Defaults to `Float64`.
 """
-function FastShortcutNLLSPolyalg(::Type{T} = Float64; concrete_jac = nothing,
-        linsolve = nothing, precs = DEFAULT_PRECS, kwargs...) where {T}
+function FastShortcutNLLSPolyalg(
+        ::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
+        precs = DEFAULT_PRECS, autodiff = nothing, kwargs...) where {T}
     if __is_complex(T)
-        algs = (GaussNewton(; concrete_jac, linsolve, precs, kwargs...),
-            LevenbergMarquardt(; linsolve, precs, disable_geodesic = Val(true), kwargs...),
-            LevenbergMarquardt(; linsolve, precs, kwargs...))
+        algs = (GaussNewton(; concrete_jac, linsolve, precs, autodiff, kwargs...),
+            LevenbergMarquardt(;
+                linsolve, precs, autodiff, disable_geodesic = Val(true), kwargs...),
+            LevenbergMarquardt(; linsolve, precs, autodiff, kwargs...))
     else
-        algs = (GaussNewton(; concrete_jac, linsolve, precs, kwargs...),
-            LevenbergMarquardt(; linsolve, precs, disable_geodesic = Val(true), kwargs...),
-            TrustRegion(; concrete_jac, linsolve, precs, kwargs...),
+        algs = (GaussNewton(; concrete_jac, linsolve, precs, autodiff, kwargs...),
+            LevenbergMarquardt(;
+                linsolve, precs, disable_geodesic = Val(true), autodiff, kwargs...),
+            TrustRegion(; concrete_jac, linsolve, precs, autodiff, kwargs...),
             GaussNewton(; concrete_jac, linsolve, precs,
-                linesearch = LineSearchesJL(; method = BackTracking()), kwargs...),
+                linesearch = LineSearchesJL(; method = BackTracking()),
+                autodiff, kwargs...),
             TrustRegion(; concrete_jac, linsolve, precs,
-                radius_update_scheme = RadiusUpdateSchemes.Bastin, kwargs...),
-            LevenbergMarquardt(; linsolve, precs, kwargs...))
+                radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff, kwargs...),
+            LevenbergMarquardt(; linsolve, precs, autodiff, kwargs...))
     end
     return NonlinearSolvePolyAlgorithm(algs, Val(:NLLS))
 end
diff --git a/test/misc/polyalg_tests.jl b/test/misc/polyalg_tests.jl
index 6c1f17639..7b7fe6880 100644
--- a/test/misc/polyalg_tests.jl
+++ b/test/misc/polyalg_tests.jl
@@ -71,6 +71,32 @@ end
     @test SciMLBase.successful_retcode(sol)
 end
 
+@testitem "PolyAlgorithms Autodiff" begin
+    cache = zeros(2)
+    function f(du, u, p)
+        cache .= u .* u
+        du .= cache .- 2
+    end
+    u0 = [1.0, 1.0]
+    probN = NonlinearProblem{true}(f, u0)
+
+    custom_polyalg = NonlinearSolvePolyAlgorithm((
+        Broyden(; autodiff = AutoFiniteDiff()), LimitedMemoryBroyden()))
+
+    # Uses the `__solve` function
+    solver = solve(probN; abstol = 1e-9)
+    @test SciMLBase.successful_retcode(solver)
+    @test_throws MethodError solve(probN, RobustMultiNewton(); abstol = 1e-9)
+    @test SciMLBase.successful_retcode(solver)
+    solver = solve(probN, RobustMultiNewton(; autodiff = AutoFiniteDiff()); abstol = 1e-9)
+    @test SciMLBase.successful_retcode(solver)
+    solver = solve(
+        probN, FastShortcutNonlinearPolyalg(; autodiff = AutoFiniteDiff()); abstol = 1e-9)
+    @test SciMLBase.successful_retcode(solver)
+    solver = solve(probN, custom_polyalg; abstol = 1e-9)
+    @test SciMLBase.successful_retcode(solver)
+end
+
 @testitem "Simple Scalar Problem #187" begin
     using NaNMath
 

From 30697eede907444ca987f53543cf58053d1a9376 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 26 Feb 2024 05:17:58 -0600
Subject: [PATCH 330/700] fix typo

---
 src/default.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/default.jl b/src/default.jl
index bae3e2c57..4d40fb995 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -324,7 +324,7 @@ function FastShortcutNonlinearPolyalg(
         else
             if __is_complex(T)
                 algs = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
-                    Klement(; linsolve, prec, autodiff),
+                    Klement(; linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff))
             else
                 algs = (Broyden(; autodiff),

From e831d1ad65dbf81de23cb76031f9a3d167ba3528 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 26 Feb 2024 13:55:52 -0500
Subject: [PATCH 331/700] Forward Mode overloads for Least Squares Problem

---
 lib/SimpleNonlinearSolve/Project.toml            |  4 +++-
 .../ext/SimpleNonlinearSolveZygoteExt.jl         |  7 +++++++
 lib/SimpleNonlinearSolve/src/ad.jl               |  3 ++-
 .../test/core/least_squares_tests.jl             | 16 ++++++++++++++++
 4 files changed, 28 insertions(+), 2 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 4065b1fcf..390d37a23 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.4.3"
+version = "1.5.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -22,11 +22,13 @@ StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [extensions]
 SimpleNonlinearSolveChainRulesCoreExt = "ChainRulesCore"
 SimpleNonlinearSolvePolyesterForwardDiffExt = "PolyesterForwardDiff"
 SimpleNonlinearSolveStaticArraysExt = "StaticArrays"
+SimpleNonlinearSolveZygoteExt = "Zygote"
 
 [compat]
 ADTypes = "0.2.6"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl
new file mode 100644
index 000000000..ae3b61352
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl
@@ -0,0 +1,7 @@
+module SimpleNonlinearSolveZygoteExt
+
+import SimpleNonlinearSolve
+
+SimpleNonlinearSolve.__is_extension_loaded(::Val{:Zygote}) = true
+
+end
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index b4f7f41b9..579eef120 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -24,7 +24,8 @@ for algType in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
     end
 end
 
-function __nlsolve_ad(prob, alg, args...; kwargs...)
+function __nlsolve_ad(
+        prob::Union{IntervalNonlinearProblem, NonlinearProblem}, alg, args...; kwargs...)
     p = value(prob.p)
     if prob isa IntervalNonlinearProblem
         tspan = value.(prob.tspan)
diff --git a/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl b/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl
index 8d99d3544..840a4f277 100644
--- a/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl
@@ -12,6 +12,12 @@
         return ŷ .- y_target
     end
 
+    function loss_function!(resid, θ, p)
+        ŷ = true_function(p, θ)
+        @. resid = ŷ - y_target
+        return
+    end
+
     θ_init = θ_true .+ 0.1
     prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
 
@@ -21,4 +27,14 @@
         sol = solve(prob_oop, solver)
         @test norm(sol.resid, Inf) < 1e-12
     end
+
+    prob_iip = NonlinearLeastSquaresProblem(
+        NonlinearFunction{true}(loss_function!, resid_prototype = zeros(length(y_target))), θ_init, x)
+
+    @testset "Solver: $(nameof(typeof(solver)))" for solver in [
+        SimpleNewtonRaphson(AutoForwardDiff()), SimpleGaussNewton(AutoForwardDiff()),
+        SimpleNewtonRaphson(AutoFiniteDiff()), SimpleGaussNewton(AutoFiniteDiff())]
+        sol = solve(prob_iip, solver)
+        @test norm(sol.resid, Inf) < 1e-12
+    end
 end

From 9bf42c35b3ea9be9d6fc2db91a12f06d7ff8025f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 26 Feb 2024 15:20:51 -0500
Subject: [PATCH 332/700] Add implementation for NLLS Forward Mode

---
 lib/SimpleNonlinearSolve/Project.toml         | 18 +++-
 .../ext/SimpleNonlinearSolveZygoteExt.jl      |  7 +-
 .../src/SimpleNonlinearSolve.jl               |  1 +
 lib/SimpleNonlinearSolve/src/ad.jl            | 86 ++++++++++++++++++-
 lib/SimpleNonlinearSolve/src/utils.jl         |  3 +
 .../test/core/aqua_tests.jl                   |  9 ++
 .../test/core/forward_ad_tests.jl             |  4 +-
 .../test/core/rootfind_tests.jl               | 50 +++++------
 8 files changed, 148 insertions(+), 30 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/test/core/aqua_tests.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 390d37a23..a8b406cee 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -8,6 +8,7 @@ ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+DiffResults = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -32,26 +33,41 @@ SimpleNonlinearSolveZygoteExt = "Zygote"
 
 [compat]
 ADTypes = "0.2.6"
+AllocCheck = "0.1.1"
 ArrayInterface = "7.7"
+Aqua = "0.8"
+CUDA = "5.2"
 ChainRulesCore = "1.21"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.146"
+DiffResults = "1.1"
 FastClosures = "0.3"
 FiniteDiff = "2.22"
 ForwardDiff = "0.10.36"
 LinearAlgebra = "1.10"
+LinearSolve = "2.25"
 MaybeInplace = "0.1.1"
+NonlinearProblemLibrary = "0.1.2"
+Pkg = "1.10"
+PolyesterForwardDiff = "0.1.1"
 PrecompileTools = "1.2"
+Random = "1.10"
+ReTestItems = "1.23"
 Reexport = "1.2"
 SciMLBase = "2.23"
+SciMLSensitivity = "7.56"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4.2"
+Test = "1.10"
+Zygote = "0.6.69"
 julia = "1.10"
 
 [extras]
 AllocCheck = "9b6a8646-10ed-4001-bbdc-1d2f46dfbb1a"
+Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
@@ -67,4 +83,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["AllocCheck", "DiffEqBase", "ForwardDiff", "LinearAlgebra", "LinearSolve", "NonlinearProblemLibrary", "Pkg", "Random", "ReTestItems", "SciMLSensitivity", "StaticArrays", "Zygote", "CUDA", "PolyesterForwardDiff", "Reexport", "Test"]
+test = ["Aqua", "AllocCheck", "DiffEqBase", "ForwardDiff", "LinearAlgebra", "LinearSolve", "NonlinearProblemLibrary", "Pkg", "Random", "ReTestItems", "SciMLSensitivity", "StaticArrays", "Zygote", "CUDA", "PolyesterForwardDiff", "Reexport", "Test", "FiniteDiff"]
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl
index ae3b61352..d2caa8998 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl
@@ -1,7 +1,12 @@
 module SimpleNonlinearSolveZygoteExt
 
-import SimpleNonlinearSolve
+import SimpleNonlinearSolve, Zygote
 
 SimpleNonlinearSolve.__is_extension_loaded(::Val{:Zygote}) = true
 
+function SimpleNonlinearSolve.__zygote_compute_nlls_vjp(f::F, u, p) where {F}
+    y, pb = Zygote.pullback(Base.Fix2(f, p), u)
+    return 2 .* only(pb(y))
+end
+
 end
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 55b579e95..710f2d6c3 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -11,6 +11,7 @@ import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidat
                        AbstractSafeBestNonlinearTerminationMode,
                        NonlinearSafeTerminationReturnCode, get_termination_mode,
                        NONLINEARSOLVE_DEFAULT_NORM
+    import DiffResults
     import ForwardDiff: Dual
     import MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
     import SciMLBase: AbstractNonlinearAlgorithm, build_solution, isinplace, _unwrap_val
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index 579eef120..c8683ac71 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -5,8 +5,17 @@ function SciMLBase.solve(
     sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
     dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
     return SciMLBase.build_solution(
-        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats,
-        sol.original)
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+end
+
+function SciMLBase.solve(
+        prob::NonlinearLeastSquaresProblem{<:AbstractArray,
+            iip, <:Union{<:AbstractArray{<:Dual{T, V, P}}}},
+        alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...) where {T, V, P, iip}
+    sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
+    dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
+    return SciMLBase.build_solution(
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
 end
 
 for algType in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
@@ -56,6 +65,79 @@ function __nlsolve_ad(
     return sol, partials
 end
 
+function __nlsolve_ad(prob::NonlinearLeastSquaresProblem, alg, args...; kwargs...)
+    p = value(prob.p)
+    u0 = value(prob.u0)
+    newprob = NonlinearLeastSquaresProblem(prob.f, u0, p; prob.kwargs...)
+
+    sol = solve(newprob, alg, args...; kwargs...)
+
+    uu = sol.u
+
+    if !SciMLBase.has_jac(prob.f)
+        if isinplace(prob)
+            _F = @closure (du, u, p) -> begin
+                resid = similar(du, length(sol.resid))
+                res = DiffResults.DiffResult(
+                    resid, similar(du, length(sol.resid), length(u)))
+                _f = @closure (du, u) -> prob.f(du, u, p)
+                ForwardDiff.jacobian!(res, _f, resid, u)
+                mul!(reshape(du, 1, :), vec(DiffResults.value(res))',
+                    DiffResults.jacobian(res), 2, false)
+                return nothing
+            end
+        else
+            # For small problems, nesting ForwardDiff is actually quite fast
+            if __is_extension_loaded(Val(:Zygote)) && (length(uu) + length(sol.resid) ≥ 50)
+                _F = @closure (u, p) -> __zygote_compute_nlls_vjp(prob.f, u, p)
+            else
+                _F = @closure (u, p) -> begin
+                    T = promote_type(eltype(u), eltype(p))
+                    res = DiffResults.DiffResult(
+                        similar(u, T, size(sol.resid)), similar(
+                            u, T, length(sol.resid), length(u)))
+                    ForwardDiff.jacobian!(res, Base.Fix2(prob.f, p), u)
+                    return reshape(
+                        2 .* vec(DiffResults.value(res))' * DiffResults.jacobian(res),
+                        size(u))
+                end
+            end
+        end
+    else
+        if isinplace(prob)
+            _F = @closure (du, u, p) -> begin
+                J = similar(du, length(sol.resid), length(u))
+                prob.jac(J, u, p)
+                resid = similar(du, length(sol.resid))
+                prob.f(resid, u, p)
+                mul!(reshape(du, 1, :), vec(resid)', J, 2, false)
+                return nothing
+            end
+        else
+            _F = @closure (u, p) -> begin
+                return reshape(2 .* vec(prob.f(u, p))' * prob.jac(u, p), size(u))
+            end
+        end
+    end
+
+    f_p = __nlsolve_∂f_∂p(prob, _F, uu, p)
+    f_x = __nlsolve_∂f_∂u(prob, _F, uu, p)
+
+    z_arr = -f_x \ f_p
+
+    pp = prob.p
+    sumfun = ((z, p),) -> map(zᵢ -> zᵢ * ForwardDiff.partials(p), z)
+    if uu isa Number
+        partials = sum(sumfun, zip(z_arr, pp))
+    elseif p isa Number
+        partials = sumfun((z_arr, pp))
+    else
+        partials = sum(sumfun, zip(eachcol(z_arr), pp))
+    end
+
+    return sol, partials
+end
+
 @inline function __nlsolve_∂f_∂p(prob, f::F, u, p) where {F}
     if isinplace(prob)
         __f = p -> begin
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index e89794b4c..7a52fdedc 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -388,3 +388,6 @@ function __get_tolerance(x::Union{SArray, Number}, ::Nothing, ::Type{T}) where {
     η = real(oneunit(T)) * (eps(real(one(T))))^(real(T)(0.8))
     return T(η)
 end
+
+# Extension
+function __zygote_compute_nlls_vjp end
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/test/core/aqua_tests.jl b/lib/SimpleNonlinearSolve/test/core/aqua_tests.jl
new file mode 100644
index 000000000..72437ff37
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/aqua_tests.jl
@@ -0,0 +1,9 @@
+@testitem "Aqua" begin
+    using Aqua
+
+    Aqua.test_all(SimpleNonlinearSolve; piracies = false, ambiguities = false)
+    Aqua.test_piracies(SimpleNonlinearSolve;
+        treat_as_own = [
+            NonlinearProblem, NonlinearLeastSquaresProblem, IntervalNonlinearProblem])
+    Aqua.test_ambiguities(SimpleNonlinearSolve; recursive = false)
+end
diff --git a/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl b/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
index e7fc44f02..3d2c87da4 100644
--- a/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
@@ -1,4 +1,4 @@
-@testsetup module ForwardADTesting
+@testsetup module ForwardADRootfindingTesting
 using Reexport
 @reexport using ForwardDiff, SimpleNonlinearSolve, StaticArrays, LinearAlgebra
 import SimpleNonlinearSolve: AbstractSimpleNonlinearSolveAlgorithm
@@ -40,7 +40,7 @@ __compatible(::SimpleHalley, ::Val{:iip}) = false
 export test_f, test_f!, jacobian_f, solve_with, __compatible
 end
 
-@testitem "ForwardDiff.jl Integration" setup=[ForwardADTesting] begin
+@testitem "ForwardDiff.jl Integration: Rootfinding" setup=[ForwardADRootfindingTesting] begin
     @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(),
         SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
         SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleDFSane())
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index f3ac188a9..726a6dda7 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -134,31 +134,33 @@ end
 end
 
 @testitem "Allocation Checks" setup=[RootfindingTesting] begin
-    @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(),
-        SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
-        SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
-        SimpleDFSane(), SimpleBroyden(; linesearch = Val(true)),
-        SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
-        @check_allocs nlsolve(prob, alg) = SciMLBase.solve(prob, alg; abstol = 1e-9)
-
-        nlprob_scalar = NonlinearProblem{false}(quadratic_f, 1.0, 2.0)
-        nlprob_sa = NonlinearProblem{false}(quadratic_f, @SVector[1.0, 1.0], 2.0)
-
-        try
-            nlsolve(nlprob_scalar, alg)
-            @test true
-        catch e
-            @error e
-            @test false
-        end
+    if Sys.islinux()  # Very slow on other OS
+        @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(),
+            SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
+            SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+            SimpleDFSane(), SimpleBroyden(; linesearch = Val(true)),
+            SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
+            @check_allocs nlsolve(prob, alg) = SciMLBase.solve(prob, alg; abstol = 1e-9)
+
+            nlprob_scalar = NonlinearProblem{false}(quadratic_f, 1.0, 2.0)
+            nlprob_sa = NonlinearProblem{false}(quadratic_f, @SVector[1.0, 1.0], 2.0)
+
+            try
+                nlsolve(nlprob_scalar, alg)
+                @test true
+            catch e
+                @error e
+                @test false
+            end
 
-        # ForwardDiff allocates for hessian since we don't propagate the chunksize
-        try
-            nlsolve(nlprob_sa, alg)
-            @test true
-        catch e
-            @error e
-            @test false broken=(alg isa SimpleHalley)
+            # ForwardDiff allocates for hessian since we don't propagate the chunksize
+            try
+                nlsolve(nlprob_sa, alg)
+                @test true
+            catch e
+                @error e
+                @test false broken=(alg isa SimpleHalley)
+            end
         end
     end
 end

From c7930cc0c63d7d267d88f8bb00d273559874d58e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 26 Feb 2024 16:02:55 -0500
Subject: [PATCH 333/700] Use custom vjp

---
 lib/SimpleNonlinearSolve/src/ad.jl            |  49 +++++---
 .../test/core/forward_ad_tests.jl             | 118 ++++++++++++++++++
 2 files changed, 151 insertions(+), 16 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index c8683ac71..d4e091c43 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -74,7 +74,39 @@ function __nlsolve_ad(prob::NonlinearLeastSquaresProblem, alg, args...; kwargs..
 
     uu = sol.u
 
-    if !SciMLBase.has_jac(prob.f)
+    # First check for custom `vjp` then custom `Jacobian` and if nothing is provided use
+    # nested autodiff as the last resort
+    if SciMLBase.has_vjp(prob.f)
+        if isinplace(prob)
+            _F = @closure (du, u, p) -> begin
+                resid = similar(du, length(sol.resid))
+                prob.f(resid, u, p)
+                prob.f.vjp(du, resid, u, p)
+                du .*= 2
+                return nothing
+            end
+        else
+            _F = @closure (u, p) -> begin
+                resid = prob.f(u, p)
+                return reshape(2 .* prob.f.vjp(resid, u, p), size(u))
+            end
+        end
+    elseif SciMLBase.has_jac(prob.f)
+        if isinplace(prob)
+            _F = @closure (du, u, p) -> begin
+                J = similar(du, length(sol.resid), length(u))
+                prob.f.jac(J, u, p)
+                resid = similar(du, length(sol.resid))
+                prob.f(resid, u, p)
+                mul!(reshape(du, 1, :), vec(resid)', J, 2, false)
+                return nothing
+            end
+        else
+            _F = @closure (u, p) -> begin
+                return reshape(2 .* vec(prob.f(u, p))' * prob.f.jac(u, p), size(u))
+            end
+        end
+    else
         if isinplace(prob)
             _F = @closure (du, u, p) -> begin
                 resid = similar(du, length(sol.resid))
@@ -103,21 +135,6 @@ function __nlsolve_ad(prob::NonlinearLeastSquaresProblem, alg, args...; kwargs..
                 end
             end
         end
-    else
-        if isinplace(prob)
-            _F = @closure (du, u, p) -> begin
-                J = similar(du, length(sol.resid), length(u))
-                prob.jac(J, u, p)
-                resid = similar(du, length(sol.resid))
-                prob.f(resid, u, p)
-                mul!(reshape(du, 1, :), vec(resid)', J, 2, false)
-                return nothing
-            end
-        else
-            _F = @closure (u, p) -> begin
-                return reshape(2 .* vec(prob.f(u, p))' * prob.jac(u, p), size(u))
-            end
-        end
     end
 
     f_p = __nlsolve_∂f_∂p(prob, _F, uu, p)
diff --git a/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl b/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
index 3d2c87da4..e0852ba53 100644
--- a/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
@@ -88,3 +88,121 @@ end
         end
     end
 end
+
+@testsetup module ForwardADNLLSTesting
+using Reexport
+@reexport using ForwardDiff, FiniteDiff, SimpleNonlinearSolve, StaticArrays, LinearAlgebra,
+                Zygote
+
+true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
+
+const θ_true = [1.0, 0.1, 2.0, 0.5]
+const x = [-1.0, -0.5, 0.0, 0.5, 1.0]
+const y_target = true_function(x, θ_true)
+
+function loss_function(θ, p)
+    ŷ = true_function(p, θ)
+    return ŷ .- y_target
+end
+
+function loss_function_jac(θ, p)
+    return ForwardDiff.jacobian(θ -> loss_function(θ, p), θ)
+end
+
+loss_function_vjp(v, θ, p) = reshape(vec(v)' * loss_function_jac(θ, p), size(θ))
+
+function loss_function!(resid, θ, p)
+    ŷ = true_function(p, θ)
+    @. resid = ŷ - y_target
+    return
+end
+
+function loss_function_jac!(J, θ, p)
+    J .= ForwardDiff.jacobian(θ -> loss_function(θ, p), θ)
+    return
+end
+
+function loss_function_vjp!(vJ, v, θ, p)
+    vec(vJ) .= reshape(vec(v)' * loss_function_jac(θ, p), size(θ))
+    return
+end
+
+θ_init = θ_true .+ 0.1
+
+export loss_function, loss_function!, loss_function_jac, loss_function_vjp,
+       loss_function_jac!, loss_function_vjp!, θ_init, x, y_target
+end
+
+@testitem "ForwardDiff.jl Integration: NLLS" setup=[ForwardADNLLSTesting] begin
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        SimpleNewtonRaphson(), SimpleGaussNewton(),
+        SimpleNewtonRaphson(AutoFiniteDiff()), SimpleGaussNewton(AutoFiniteDiff()))
+        function obj_1(p)
+            prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, p)
+            sol = solve(prob_oop, alg)
+            return sum(abs2, sol.u)
+        end
+
+        function obj_2(p)
+            ff = NonlinearFunction{false}(loss_function; jac = loss_function_jac)
+            prob_oop = NonlinearLeastSquaresProblem{false}(ff, θ_init, p)
+            sol = solve(prob_oop, alg)
+            return sum(abs2, sol.u)
+        end
+
+        function obj_3(p)
+            ff = NonlinearFunction{false}(loss_function; vjp = loss_function_vjp)
+            prob_oop = NonlinearLeastSquaresProblem{false}(ff, θ_init, p)
+            sol = solve(prob_oop, alg)
+            return sum(abs2, sol.u)
+        end
+
+        finitediff = FiniteDiff.finite_difference_gradient(obj_1, x)
+
+        fdiff1 = ForwardDiff.gradient(obj_1, x)
+        fdiff2 = ForwardDiff.gradient(obj_2, x)
+        fdiff3 = ForwardDiff.gradient(obj_3, x)
+
+        @test finitediff≈fdiff1 atol=1e-5
+        @test finitediff≈fdiff2 atol=1e-5
+        @test finitediff≈fdiff3 atol=1e-5
+        @test fdiff1 ≈ fdiff2 ≈ fdiff3
+
+        function obj_4(p)
+            prob_iip = NonlinearLeastSquaresProblem(
+                NonlinearFunction{true}(
+                    loss_function!; resid_prototype = zeros(length(y_target))), θ_init, p)
+            sol = solve(prob_iip, alg)
+            return sum(abs2, sol.u)
+        end
+
+        function obj_5(p)
+            ff = NonlinearFunction{true}(
+                loss_function!; resid_prototype = zeros(length(y_target)), jac = loss_function_jac!)
+            prob_iip = NonlinearLeastSquaresProblem(
+                ff, θ_init, p)
+            sol = solve(prob_iip, alg)
+            return sum(abs2, sol.u)
+        end
+
+        function obj_6(p)
+            ff = NonlinearFunction{true}(
+                loss_function!; resid_prototype = zeros(length(y_target)), vjp = loss_function_vjp!)
+            prob_iip = NonlinearLeastSquaresProblem(
+                ff, θ_init, p)
+            sol = solve(prob_iip, alg)
+            return sum(abs2, sol.u)
+        end
+
+        finitediff = FiniteDiff.finite_difference_gradient(obj_4, x)
+
+        fdiff4 = ForwardDiff.gradient(obj_4, x)
+        fdiff5 = ForwardDiff.gradient(obj_5, x)
+        fdiff6 = ForwardDiff.gradient(obj_6, x)
+
+        @test finitediff≈fdiff4 atol=1e-5
+        @test finitediff≈fdiff5 atol=1e-5
+        @test finitediff≈fdiff6 atol=1e-5
+        @test fdiff4 ≈ fdiff5 ≈ fdiff6
+    end
+end

From 2b8b5e42d5281364fe04efd6552e3381160329a5 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 26 Feb 2024 16:06:57 -0500
Subject: [PATCH 334/700] Formatting and Downgrade

---
 lib/SimpleNonlinearSolve/Project.toml                         | 4 ++--
 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl | 2 +-
 lib/SimpleNonlinearSolve/src/utils.jl                         | 2 +-
 3 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index a8b406cee..a73771cce 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -37,7 +37,7 @@ AllocCheck = "0.1.1"
 ArrayInterface = "7.7"
 Aqua = "0.8"
 CUDA = "5.2"
-ChainRulesCore = "1.21"
+ChainRulesCore = "1.22"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.146"
 DiffResults = "1.1"
@@ -54,7 +54,7 @@ PrecompileTools = "1.2"
 Random = "1.10"
 ReTestItems = "1.23"
 Reexport = "1.2"
-SciMLBase = "2.23"
+SciMLBase = "2.26.3"
 SciMLSensitivity = "7.56"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4.2"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl
index d2caa8998..b29a1529a 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl
@@ -9,4 +9,4 @@ function SimpleNonlinearSolve.__zygote_compute_nlls_vjp(f::F, u, p) where {F}
     return 2 .* only(pb(y))
 end
 
-end
\ No newline at end of file
+end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 7a52fdedc..2876cedb2 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -390,4 +390,4 @@ function __get_tolerance(x::Union{SArray, Number}, ::Nothing, ::Type{T}) where {
 end
 
 # Extension
-function __zygote_compute_nlls_vjp end
\ No newline at end of file
+function __zygote_compute_nlls_vjp end

From 75c0fb610f9b93d2070290d3859e7d8a25843f6a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 5 Mar 2024 16:04:24 -0500
Subject: [PATCH 335/700] Export wrappers over LineSearches

---
 Project.toml                     |  2 +-
 src/NonlinearSolve.jl            |  8 +++++---
 src/globalization/line_search.jl | 16 ++++++++++++++++
 3 files changed, 22 insertions(+), 4 deletions(-)

diff --git a/Project.toml b/Project.toml
index bc1919c29..1294701b1 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.7.3"
+version = "3.8.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 991783672..e7fa9bd3e 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -9,8 +9,8 @@ import PrecompileTools: @recompile_invalidations, @compile_workload, @setup_work
 
 @recompile_invalidations begin
     using ADTypes, ConcreteStructs, DiffEqBase, FastBroadcast, FastClosures, LazyArrays,
-          LineSearches, LinearAlgebra, LinearSolve, MaybeInplace, Preferences, Printf,
-          SciMLBase, SimpleNonlinearSolve, SparseArrays, SparseDiffTools
+          LinearAlgebra, LinearSolve, MaybeInplace, Preferences, Printf, SciMLBase,
+          SimpleNonlinearSolve, SparseArrays, SparseDiffTools
 
     import ArrayInterface: undefmatrix, can_setindex, restructure, fast_scalar_indexing
     import DiffEqBase: AbstractNonlinearTerminationMode,
@@ -20,6 +20,7 @@ import PrecompileTools: @recompile_invalidations, @compile_workload, @setup_work
     import FiniteDiff
     import ForwardDiff
     import ForwardDiff: Dual
+    import LineSearches
     import LinearSolve: ComposePreconditioner, InvPreconditioner, needs_concrete_A
     import RecursiveArrayTools: recursivecopy!, recursivefill!
 
@@ -29,7 +30,7 @@ import PrecompileTools: @recompile_invalidations, @compile_workload, @setup_work
     import StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix, MMatrix
 end
 
-@reexport using ADTypes, LineSearches, SciMLBase, SimpleNonlinearSolve
+@reexport using ADTypes, SciMLBase, SimpleNonlinearSolve
 
 const AbstractSparseADType = Union{ADTypes.AbstractSparseFiniteDifferences,
     ADTypes.AbstractSparseForwardMode, ADTypes.AbstractSparseReverseMode}
@@ -157,6 +158,7 @@ export NewtonDescent, SteepestDescent, Dogleg, DampedNewtonDescent, GeodesicAcce
 # Globalization
 ## Line Search Algorithms
 export LineSearchesJL, NoLineSearch, RobustNonMonotoneLineSearch, LiFukushimaLineSearch
+export Static, HagerZhang, MoreThuente, StrongWolfe, BackTracking
 ## Trust Region Algorithms
 export RadiusUpdateSchemes
 
diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index 9d4f52e71..56bb98cf6 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -53,6 +53,10 @@ end
 
 LineSearchesJL(method; kwargs...) = LineSearchesJL(; method, kwargs...)
 function LineSearchesJL(; method = LineSearches.Static(), autodiff = nothing, α = true)
+    if method isa LineSearchesJL  # Prevent breaking old code
+        return LineSearchesJL(method.method, α, autodiff)
+    end
+
     if method isa AbstractNonlinearSolveLineSearchAlgorithm
         Base.depwarn("Passing a native NonlinearSolve line search algorithm to \
                       `LineSearchesJL` or `LineSearch` is deprecated. Pass the method \
@@ -65,6 +69,18 @@ end
 
 Base.@deprecate_binding LineSearch LineSearchesJL true
 
+Static(args...; kwargs...) = LineSearchesJL(LineSearches.Static(args...; kwargs...))
+HagerZhang(args...; kwargs...) = LineSearchesJL(LineSearches.HagerZhang(args...; kwargs...))
+function MoreThuente(args...; kwargs...)
+    return LineSearchesJL(LineSearches.MoreThuente(args...; kwargs...))
+end
+function BackTracking(args...; kwargs...)
+    return LineSearchesJL(LineSearches.BackTracking(args...; kwargs...))
+end
+function StrongWolfe(args...; kwargs...)
+    return LineSearchesJL(LineSearches.StrongWolfe(args...; kwargs...))
+end
+
 # Wrapper over LineSearches.jl algorithms
 @concrete mutable struct LineSearchesJLCache <: AbstractNonlinearSolveLineSearchCache
     f

From 59118352118cf08720533d534366293fc092dd08 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 5 Mar 2024 16:27:53 -0500
Subject: [PATCH 336/700] All polyalg in 23 test problems

---
 src/algorithms/lbroyden.jl          |  4 ++--
 test/core/23_test_problems_tests.jl | 12 +++++++++++-
 2 files changed, 13 insertions(+), 3 deletions(-)

diff --git a/src/algorithms/lbroyden.jl b/src/algorithms/lbroyden.jl
index 499cc7c34..f1959e7d0 100644
--- a/src/algorithms/lbroyden.jl
+++ b/src/algorithms/lbroyden.jl
@@ -159,8 +159,8 @@ function LinearAlgebra.mul!(y::AbstractVector, x::AbstractVector, J::BroydenLowR
     return y
 end
 
-function LinearAlgebra.mul!(
-        J::BroydenLowRankJacobian, u, vᵀ::LinearAlgebra.AdjOrTransAbsVec, α::Bool, β::Bool)
+function LinearAlgebra.mul!(J::BroydenLowRankJacobian, u::AbstractArray,
+        vᵀ::LinearAlgebra.AdjOrTransAbsVec, α::Bool, β::Bool)
     @assert α & β
     idx_update = mod1(J.idx + 1, size(J.U, 2))
     copyto!(@view(J.U[:, idx_update]), _vec(u))
diff --git a/test/core/23_test_problems_tests.jl b/test/core/23_test_problems_tests.jl
index 7924e372d..b0f17113a 100644
--- a/test/core/23_test_problems_tests.jl
+++ b/test/core/23_test_problems_tests.jl
@@ -40,6 +40,16 @@ end
 export test_on_library, problems, dicts
 end
 
+@testitem "PolyAlgorithms" setup=[RobustnessTesting] begin
+    alg_ops = (RobustMultiNewton(), FastShortcutNonlinearPolyalg())
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = []
+    broken_tests[alg_ops[2]] = []
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
 @testitem "NewtonRaphson" setup=[RobustnessTesting] begin
     alg_ops = (NewtonRaphson(),)
 
@@ -91,7 +101,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "Broyden" retries=5 setup=[RobustnessTesting] begin
+@testitem "Broyden" setup=[RobustnessTesting] begin
     alg_ops = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian)),
         Broyden(; update_rule = Val(:bad_broyden)),
         Broyden(; init_jacobian = Val(:true_jacobian), update_rule = Val(:bad_broyden)))

From 6f68b2aac3bbc00669c6c15fc9b9b2f08794ba5d Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 5 Mar 2024 17:32:11 -0500
Subject: [PATCH 337/700] Use start index

---
 src/algorithms/klement.jl          |  4 +-
 src/core/approximate_jacobian.jl   |  4 +-
 src/default.jl                     | 68 +++++++++++++++++++++---------
 test/core/forward_ad_tests.jl      |  4 +-
 test/core/rootfind_tests.jl        |  8 ++--
 test/misc/matrix_resizing_tests.jl |  8 ++--
 6 files changed, 62 insertions(+), 34 deletions(-)

diff --git a/src/algorithms/klement.jl b/src/algorithms/klement.jl
index 428dc382c..66daec1b7 100644
--- a/src/algorithms/klement.jl
+++ b/src/algorithms/klement.jl
@@ -25,8 +25,8 @@ over this.
         differentiable problems.
 """
 function Klement(; max_resets::Int = 100, linsolve = nothing, alpha = nothing,
-        linesearch = NoLineSearch(), precs = DEFAULT_PRECS, autodiff = nothing,
-        init_jacobian::Val{IJ} = Val(:identity)) where {IJ}
+        linesearch = NoLineSearch(), precs = DEFAULT_PRECS,
+        autodiff = nothing, init_jacobian::Val{IJ} = Val(:identity)) where {IJ}
     if !(linesearch isa AbstractNonlinearSolveLineSearchAlgorithm)
         Base.depwarn(
             "Passing in a `LineSearches.jl` algorithm directly is deprecated. \
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index d0471e99b..4204b2db7 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -66,8 +66,8 @@ function ApproximateJacobianSolveAlgorithm{concrete_jac, name}(;
         linesearch = LineSearchesJL(; method = linesearch)
     end
     return ApproximateJacobianSolveAlgorithm{concrete_jac, name}(
-        linesearch, trustregion, descent, update_rule, reinit_rule,
-        max_resets, max_shrink_times, initialization)
+        linesearch, trustregion, descent, update_rule,
+        reinit_rule, max_resets, max_shrink_times, initialization)
 end
 
 @inline concrete_jac(::ApproximateJacobianSolveAlgorithm{CJ}) where {CJ} = CJ
diff --git a/src/default.jl b/src/default.jl
index 4d40fb995..d7f00edb9 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -1,6 +1,7 @@
 # Poly Algorithms
 """
-    NonlinearSolvePolyAlgorithm(algs, ::Val{pType} = Val(:NLS)) where {pType}
+    NonlinearSolvePolyAlgorithm(algs, ::Val{pType} = Val(:NLS);
+        start_index = 1) where {pType}
 
 A general way to define PolyAlgorithms for `NonlinearProblem` and
 `NonlinearLeastSquaresProblem`. This is a container for a tuple of algorithms that will be
@@ -15,6 +16,10 @@ residual is returned.
     `NonlinearLeastSquaresProblem`. This is used to determine the correct problem type to
     dispatch on.
 
+### Keyword Arguments
+
+  - `start_index`: the index to start at. Defaults to `1`.
+
 ### Example
 
 ```julia
@@ -25,11 +30,14 @@ alg = NonlinearSolvePolyAlgorithm((NewtonRaphson(), Broyden()))
 """
 struct NonlinearSolvePolyAlgorithm{pType, N, A} <: AbstractNonlinearSolveAlgorithm{:PolyAlg}
     algs::A
+    start_index::Int
 
-    function NonlinearSolvePolyAlgorithm(algs, ::Val{pType} = Val(:NLS)) where {pType}
+    function NonlinearSolvePolyAlgorithm(
+            algs, ::Val{pType} = Val(:NLS); start_index::Int = 1) where {pType}
         @assert pType ∈ (:NLS, :NLLS)
+        @assert 0 < start_index ≤ length(algs)
         algs = Tuple(algs)
-        return new{pType, length(algs), typeof(algs)}(algs)
+        return new{pType, length(algs), typeof(algs)}(algs, start_index)
     end
 end
 
@@ -73,7 +81,7 @@ end
 
 function reinit_cache!(cache::NonlinearSolvePolyAlgorithmCache, args...; kwargs...)
     foreach(c -> reinit_cache!(c, args...; kwargs...), cache.caches)
-    cache.current = 1
+    cache.current = cache.alg.start_index
     cache.nsteps = 0
     cache.total_time = 0.0
 end
@@ -91,7 +99,7 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
                     alg.algs),
                 alg,
                 -1,
-                1,
+                alg.start_index,
                 0,
                 0.0,
                 maxtime,
@@ -140,6 +148,7 @@ end
         quote
             fus = tuple($(Tuple(resids)...))
             minfu, idx = __findmin(cache.internalnorm, fus)
+            idx += cache.alg.start_index - 1
             stats = __compile_stats(cache.caches[idx])
             u = get_u(cache.caches[idx])
             retcode = cache.caches[idx].retcode
@@ -194,18 +203,22 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
     @eval begin
         @generated function SciMLBase.__solve(
                 prob::$probType, alg::$algType{N}, args...; kwargs...) where {N}
-            calls = []
+            calls = [:(current = alg.start_index)]
             sol_syms = [gensym("sol") for _ in 1:N]
             for i in 1:N
                 cur_sol = sol_syms[i]
                 push!(calls,
                     quote
-                        $(cur_sol) = SciMLBase.__solve(prob, alg.algs[$(i)], args...; kwargs...)
-                        if SciMLBase.successful_retcode($(cur_sol))
-                            return SciMLBase.build_solution(
-                                prob, alg, $(cur_sol).u, $(cur_sol).resid;
-                                $(cur_sol).retcode, $(cur_sol).stats,
-                                original = $(cur_sol), trace = $(cur_sol).trace)
+                        if current == $i
+                            $(cur_sol) = SciMLBase.__solve(
+                                prob, alg.algs[$(i)], args...; kwargs...)
+                            if SciMLBase.successful_retcode($(cur_sol))
+                                return SciMLBase.build_solution(
+                                    prob, alg, $(cur_sol).u, $(cur_sol).resid;
+                                    $(cur_sol).retcode, $(cur_sol).stats,
+                                    original = $(cur_sol), trace = $(cur_sol).trace)
+                            end
+                            current = $(i + 1)
                         end
                     end)
             end
@@ -218,6 +231,7 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
             push!(calls, quote
                 resids = tuple($(Tuple(resids)...))
                 minfu, idx = __findmin(DEFAULT_NORM, resids)
+                idx += alg.start_index - 1
             end)
 
             for i in 1:N
@@ -263,6 +277,7 @@ function RobustMultiNewton(::Type{T} = Float64; concrete_jac = nothing, linsolve
         algs = (TrustRegion(; concrete_jac, linsolve, precs, autodiff),
             TrustRegion(; concrete_jac, linsolve, precs, autodiff,
                 radius_update_scheme = RadiusUpdateSchemes.Bastin),
+            NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
             NewtonRaphson(; concrete_jac, linsolve, precs,
                 linesearch = LineSearchesJL(; method = BackTracking()), autodiff),
             TrustRegion(; concrete_jac, linsolve, precs,
@@ -276,7 +291,8 @@ end
 """
     FastShortcutNonlinearPolyalg(::Type{T} = Float64; concrete_jac = nothing,
         linsolve = nothing, precs = DEFAULT_PRECS, must_use_jacobian::Val = Val(false),
-        prefer_simplenonlinearsolve::Val{SA} = Val(false), autodiff = nothing) where {T}
+        prefer_simplenonlinearsolve::Val{SA} = Val(false), autodiff = nothing,
+        u0_len::Union{Int, Nothing} = nothing) where {T}
 
 A polyalgorithm focused on balancing speed and robustness. It first tries less robust methods
 for more performance and then tries more robust techniques if the faster ones fail.
@@ -285,12 +301,19 @@ for more performance and then tries more robust techniques if the faster ones fa
 
   - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
     are compatible with the problem type. Defaults to `Float64`.
+
+### Keyword Arguments
+
+  - `u0_len`: The length of the initial guess. If this is `nothing`, then the length of the
+    initial guess is not checked. If this is an integer and it is less than `25`, we use
+    jacobian based methods.
 """
 function FastShortcutNonlinearPolyalg(
         ::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
         precs = DEFAULT_PRECS, must_use_jacobian::Val{JAC} = Val(false),
         prefer_simplenonlinearsolve::Val{SA} = Val(false),
-        autodiff = nothing) where {T, JAC, SA}
+        u0_len::Union{Int, Nothing} = nothing, autodiff = nothing) where {T, JAC, SA}
+    start_index = 1
     if JAC
         if __is_complex(T)
             algs = (NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),)
@@ -312,6 +335,7 @@ function FastShortcutNonlinearPolyalg(
                     SimpleKlement(),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff))
             else
+                start_index = u0_len !== nothing ? (u0_len ≤ 25 ? 4 : 1) : 1
                 algs = (SimpleBroyden(),
                     Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
                     SimpleKlement(),
@@ -327,6 +351,8 @@ function FastShortcutNonlinearPolyalg(
                     Klement(; linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff))
             else
+                # TODO: This number requires a bit rigorous testing
+                start_index = u0_len !== nothing ? (u0_len ≤ 25 ? 4 : 1) : 1
                 algs = (Broyden(; autodiff),
                     Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
                     Klement(; linsolve, precs, autodiff),
@@ -339,7 +365,7 @@ function FastShortcutNonlinearPolyalg(
             end
         end
     end
-    return NonlinearSolvePolyAlgorithm(algs, Val(:NLS))
+    return NonlinearSolvePolyAlgorithm(algs, Val(:NLS); start_index)
 end
 
 """
@@ -392,17 +418,19 @@ end
 ## can use that!
 function SciMLBase.__init(prob::NonlinearProblem, ::Nothing, args...; kwargs...)
     must_use_jacobian = Val(prob.f.jac !== nothing)
-    return SciMLBase.__init(
-        prob, FastShortcutNonlinearPolyalg(eltype(prob.u0); must_use_jacobian),
-        args...; kwargs...)
+    return SciMLBase.__init(prob,
+        FastShortcutNonlinearPolyalg(
+            eltype(prob.u0); must_use_jacobian, u0_len = length(prob.u0)),
+        args...;
+        kwargs...)
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, ::Nothing, args...; kwargs...)
     must_use_jacobian = Val(prob.f.jac !== nothing)
     prefer_simplenonlinearsolve = Val(prob.u0 isa SArray)
     return SciMLBase.__solve(prob,
-        FastShortcutNonlinearPolyalg(
-            eltype(prob.u0); must_use_jacobian, prefer_simplenonlinearsolve),
+        FastShortcutNonlinearPolyalg(eltype(prob.u0); must_use_jacobian,
+            prefer_simplenonlinearsolve, u0_len = length(prob.u0)),
         args...;
         kwargs...)
 end
diff --git a/test/core/forward_ad_tests.jl b/test/core/forward_ad_tests.jl
index a13259939..24258e157 100644
--- a/test/core/forward_ad_tests.jl
+++ b/test/core/forward_ad_tests.jl
@@ -64,8 +64,8 @@ end
 
 @testitem "ForwardDiff.jl Integration" setup=[ForwardADTesting] begin
     for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
-        PseudoTransient(; alpha_initial = 10.0), Broyden(), Klement(), DFSane(), nothing,
-        NLsolveJL(), CMINPACK(), KINSOL(; globalization_strategy = :LineSearch))
+        PseudoTransient(; alpha_initial = 10.0), Broyden(), Klement(), DFSane(),
+        nothing, NLsolveJL(), CMINPACK(), KINSOL(; globalization_strategy = :LineSearch))
         us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
 
         @testset "Scalar AD" begin
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index 86dc5ff2c..87ba7cd35 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -476,8 +476,8 @@ end
 
 @testitem "Broyden" setup=[CoreRootfindTesting] begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian) Update Rule: $(update_rule)" for lsmethod in (
-            Static(), StrongWolfe(), BackTracking(), HagerZhang(),
-            MoreThuente(), LiFukushimaLineSearch()),
+            Static(), StrongWolfe(), BackTracking(),
+            HagerZhang(), MoreThuente(), LiFukushimaLineSearch()),
         ad in (AutoFiniteDiff(), AutoZygote()),
         init_jacobian in (Val(:identity), Val(:true_jacobian)),
         update_rule in (Val(:good_broyden), Val(:bad_broyden), Val(:diagonal))
@@ -575,8 +575,8 @@ end
 
 @testitem "LimitedMemoryBroyden" setup=[CoreRootfindTesting] begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad))" for lsmethod in (
-            Static(), StrongWolfe(), BackTracking(), HagerZhang(),
-            MoreThuente(), LiFukushimaLineSearch()),
+            Static(), StrongWolfe(), BackTracking(),
+            HagerZhang(), MoreThuente(), LiFukushimaLineSearch()),
         ad in (AutoFiniteDiff(), AutoZygote())
 
         linesearch = LineSearchesJL(; method = lsmethod, autodiff = ad)
diff --git a/test/misc/matrix_resizing_tests.jl b/test/misc/matrix_resizing_tests.jl
index 1d17a696a..9210e3e6b 100644
--- a/test/misc/matrix_resizing_tests.jl
+++ b/test/misc/matrix_resizing_tests.jl
@@ -7,8 +7,8 @@
     vecprob = NonlinearProblem(ff, vec(u0), p)
     prob = NonlinearProblem(ff, u0, p)
 
-    for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(), PseudoTransient(),
-        RobustMultiNewton(), FastShortcutNonlinearPolyalg(),
+    for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
+        PseudoTransient(), RobustMultiNewton(), FastShortcutNonlinearPolyalg(),
         Broyden(), Klement(), LimitedMemoryBroyden(; threshold = 2))
         @test vec(solve(prob, alg).u) == solve(vecprob, alg).u
     end
@@ -23,8 +23,8 @@ end
     vecprob = NonlinearProblem(fiip, vec(u0), p)
     prob = NonlinearProblem(fiip, u0, p)
 
-    for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(), PseudoTransient(),
-        RobustMultiNewton(), FastShortcutNonlinearPolyalg(),
+    for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
+        PseudoTransient(), RobustMultiNewton(), FastShortcutNonlinearPolyalg(),
         Broyden(), Klement(), LimitedMemoryBroyden(; threshold = 2))
         @test vec(solve(prob, alg).u) == solve(vecprob, alg).u
     end

From 390341f3ee3b6894aa0600710aef8901011590a8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 6 Mar 2024 10:58:56 -0500
Subject: [PATCH 338/700] Fix tests

---
 src/default.jl             | 6 ++----
 src/utils.jl               | 1 +
 test/misc/polyalg_tests.jl | 4 +---
 3 files changed, 4 insertions(+), 7 deletions(-)

diff --git a/src/default.jl b/src/default.jl
index d7f00edb9..cdcfb6825 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -142,13 +142,12 @@ end
 
     resids = map(x -> Symbol("$(x)_resid"), cache_syms)
     for (sym, resid) in zip(cache_syms, resids)
-        push!(calls, :($(resid) = get_fu($(sym))))
+        push!(calls, :($(resid) = @isdefined($(sym)) ? get_fu($(sym)) : nothing))
     end
     push!(calls,
         quote
             fus = tuple($(Tuple(resids)...))
             minfu, idx = __findmin(cache.internalnorm, fus)
-            idx += cache.alg.start_index - 1
             stats = __compile_stats(cache.caches[idx])
             u = get_u(cache.caches[idx])
             retcode = cache.caches[idx].retcode
@@ -225,13 +224,12 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
 
             resids = map(x -> Symbol("$(x)_resid"), sol_syms)
             for (sym, resid) in zip(sol_syms, resids)
-                push!(calls, :($(resid) = $(sym).resid))
+                push!(calls, :($(resid) = @isdefined($(sym)) ? $(sym).resid : nothing))
             end
 
             push!(calls, quote
                 resids = tuple($(Tuple(resids)...))
                 minfu, idx = __findmin(DEFAULT_NORM, resids)
-                idx += alg.start_index - 1
             end)
 
             for i in 1:N
diff --git a/src/utils.jl b/src/utils.jl
index aec66bdd4..259ff945a 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -99,6 +99,7 @@ function __findmin_caches(f, caches)
 end
 function __findmin(f, x)
     return findmin(x) do xᵢ
+        xᵢ === nothing && return Inf
         fx = f(xᵢ)
         return isnan(fx) ? Inf : fx
     end
diff --git a/test/misc/polyalg_tests.jl b/test/misc/polyalg_tests.jl
index 7b7fe6880..c5f1a8eb3 100644
--- a/test/misc/polyalg_tests.jl
+++ b/test/misc/polyalg_tests.jl
@@ -84,10 +84,8 @@ end
         Broyden(; autodiff = AutoFiniteDiff()), LimitedMemoryBroyden()))
 
     # Uses the `__solve` function
-    solver = solve(probN; abstol = 1e-9)
-    @test SciMLBase.successful_retcode(solver)
+    @test_throws MethodError solve(probN; abstol = 1e-9)
     @test_throws MethodError solve(probN, RobustMultiNewton(); abstol = 1e-9)
-    @test SciMLBase.successful_retcode(solver)
     solver = solve(probN, RobustMultiNewton(; autodiff = AutoFiniteDiff()); abstol = 1e-9)
     @test SciMLBase.successful_retcode(solver)
     solver = solve(

From 81edf48dfbcdae96f86d381d94692e2ebff4a853 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 6 Mar 2024 11:39:07 -0500
Subject: [PATCH 339/700] Incorrect Jacobian Size for NLLS

---
 src/internal/jacobian.jl |  4 +++-
 test/core/nlls_tests.jl  | 19 +++++++++++++++++++
 2 files changed, 22 insertions(+), 1 deletion(-)

diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index fc4f12f33..3dfb904ee 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -83,7 +83,9 @@ function JacobianCache(
         JacobianOperator(prob, fu, u; jvp_autodiff, vjp_autodiff)
     else
         if has_analytic_jac
-            f.jac_prototype === nothing ? undefmatrix(u) : f.jac_prototype
+            f.jac_prototype === nothing ?
+            similar(fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u)) :
+            copy(f.jac_prototype)
         elseif f.jac_prototype === nothing
             init_jacobian(jac_cache; preserve_immutable = Val(true))
         else
diff --git a/test/core/nlls_tests.jl b/test/core/nlls_tests.jl
index 3722ca671..6b7b018cd 100644
--- a/test/core/nlls_tests.jl
+++ b/test/core/nlls_tests.jl
@@ -94,3 +94,22 @@ end
         @test maximum(abs, sol.resid) < 1e-6
     end
 end
+
+@testitem "NLLS Analytic Jacobian" begin
+    dataIn = 1:10
+    f(x, p) = x[1] * dataIn .^ 2 .+ x[2] * dataIn .+ x[3]
+    dataOut = f([1, 2, 3], nothing) + 0.1 * randn(10, 1)
+
+    resid(x, p) = f(x, p) - dataOut
+    jac(x, p) = [dataIn .^ 2 dataIn ones(10, 1)]
+    x0 = [1, 1, 1]
+
+    prob = NonlinearLeastSquaresProblem(resid, x0)
+    sol1 = solve(prob)
+
+    nlfunc = NonlinearFunction(resid; jac)
+    prob = NonlinearLeastSquaresProblem(nlfunc, x0)
+    sol2 = solve(prob)
+
+    @test sol1.u ≈ sol2.u
+end

From 96874e9ad9103436e554221fbcbe337609fd6c9e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 10 Mar 2024 18:40:03 -0400
Subject: [PATCH 340/700] Dont default to Polyester

---
 lib/SimpleNonlinearSolve/src/nlsolve/halley.jl |  2 +-
 lib/SimpleNonlinearSolve/src/utils.jl          | 15 +++------------
 2 files changed, 4 insertions(+), 13 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index 44877e097..462332280 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -33,7 +33,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
     fx = _get_fx(prob, x)
     T = eltype(x)
 
-    autodiff = __get_concrete_autodiff(prob, alg.autodiff; polyester = Val(false))
+    autodiff = __get_concrete_autodiff(prob, alg.autodiff)
     abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
         termination_condition)
 
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 2876cedb2..38be3437c 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -365,18 +365,9 @@ end
 
 # Decide which AD backend to use
 @inline __get_concrete_autodiff(prob, ad::ADTypes.AbstractADType; kwargs...) = ad
-@inline function __get_concrete_autodiff(prob, ::Nothing; polyester::Val{P} = Val(true),
-        kwargs...) where {P}
-    if ForwardDiff.can_dual(eltype(prob.u0))
-        if P && __is_extension_loaded(Val(:PolyesterForwardDiff)) &&
-           !(prob.u0 isa Number) && ArrayInterface.can_setindex(prob.u0)
-            return AutoPolyesterForwardDiff()
-        else
-            return AutoForwardDiff()
-        end
-    else
-        return AutoFiniteDiff()
-    end
+@inline function __get_concrete_autodiff(prob, ::Nothing; kwargs...)
+    return ifelse(
+        ForwardDiff.can_dual(eltype(prob.u0)), AutoForwardDiff(), AutoFiniteDiff())
 end
 
 @inline __reshape(x::Number, args...) = x

From 73038b75ed259e14c6e9da1b2b94c97b2943525f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 10 Mar 2024 20:06:11 -0400
Subject: [PATCH 341/700] Add ReverseDiff and Tracker entry points

---
 lib/SimpleNonlinearSolve/Project.toml         | 14 ++++-
 .../SimpleNonlinearSolveChainRulesCoreExt.jl  |  7 +--
 .../ext/SimpleNonlinearSolveReverseDiffExt.jl | 60 +++++++++++++++++++
 .../ext/SimpleNonlinearSolveTrackerExt.jl     | 42 +++++++++++++
 .../src/SimpleNonlinearSolve.jl               |  4 +-
 .../test/core/adjoint_tests.jl                | 13 +++-
 6 files changed, 128 insertions(+), 12 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index a73771cce..225b36090 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.5.0"
+version = "1.6.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -22,20 +22,24 @@ StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 [weakdeps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
+ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [extensions]
 SimpleNonlinearSolveChainRulesCoreExt = "ChainRulesCore"
 SimpleNonlinearSolvePolyesterForwardDiffExt = "PolyesterForwardDiff"
+SimpleNonlinearSolveReverseDiffExt = "ReverseDiff"
 SimpleNonlinearSolveStaticArraysExt = "StaticArrays"
+SimpleNonlinearSolveTrackerExt = "Tracker"
 SimpleNonlinearSolveZygoteExt = "Zygote"
 
 [compat]
 ADTypes = "0.2.6"
 AllocCheck = "0.1.1"
-ArrayInterface = "7.7"
 Aqua = "0.8"
+ArrayInterface = "7.7"
 CUDA = "5.2"
 ChainRulesCore = "1.22"
 ConcreteStructs = "0.2.3"
@@ -54,11 +58,13 @@ PrecompileTools = "1.2"
 Random = "1.10"
 ReTestItems = "1.23"
 Reexport = "1.2"
+ReverseDiff = "1.15"
 SciMLBase = "2.26.3"
 SciMLSensitivity = "7.56"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4.2"
 Test = "1.10"
+Tracker = "0.2.32"
 Zygote = "0.6.69"
 julia = "1.10"
 
@@ -77,10 +83,12 @@ PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 SciMLSensitivity = "1ed8b502-d754-442c-8d5d-10ac956f44a1"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "AllocCheck", "DiffEqBase", "ForwardDiff", "LinearAlgebra", "LinearSolve", "NonlinearProblemLibrary", "Pkg", "Random", "ReTestItems", "SciMLSensitivity", "StaticArrays", "Zygote", "CUDA", "PolyesterForwardDiff", "Reexport", "Test", "FiniteDiff"]
+test = ["Aqua", "AllocCheck", "DiffEqBase", "ForwardDiff", "LinearAlgebra", "LinearSolve", "NonlinearProblemLibrary", "Pkg", "Random", "ReTestItems", "SciMLSensitivity", "StaticArrays", "Zygote", "CUDA", "PolyesterForwardDiff", "Reexport", "Test", "FiniteDiff", "ReverseDiff", "Tracker"]
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
index 23cd25f33..dc84cb3e8 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
@@ -5,14 +5,13 @@ using ChainRulesCore, DiffEqBase, SciMLBase, SimpleNonlinearSolve
 # The expectation here is that no-one is using this directly inside a GPU kernel. We can
 # eventually lift this requirement using a custom adjoint
 function ChainRulesCore.rrule(::typeof(SimpleNonlinearSolve.__internal_solve_up),
-        prob::NonlinearProblem,
-        sensealg::Union{Nothing, DiffEqBase.AbstractSensitivityAlgorithm}, u0, u0_changed,
-        p, p_changed, alg, args...; kwargs...)
+        prob::NonlinearProblem, sensealg, u0, u0_changed, p, p_changed, alg, args...;
+        kwargs...)
     out, ∇internal = DiffEqBase._solve_adjoint(prob, sensealg, u0, p,
         SciMLBase.ChainRulesOriginator(), alg, args...; kwargs...)
     function ∇__internal_solve_up(Δ)
         ∂f, ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(Δ)
-        return (∂f, ∂prob, ∂sensealg, ∂u0, NoTangent(), ∂p, NoTangent(), ∂originator,
+        return (∂f, ∂prob, ∂sensealg, ∂u0, NoTangent(), ∂p, NoTangent(), NoTangent(),
             ∂args...)
     end
     return out, ∇__internal_solve_up
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
new file mode 100644
index 000000000..e0bbda27e
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
@@ -0,0 +1,60 @@
+module SimpleNonlinearSolveReverseDiffExt
+
+using ArrayInterface, DiffEqBase, ReverseDiff, SciMLBase, SimpleNonlinearSolve
+import ReverseDiff: TrackedArray, TrackedReal
+import SimpleNonlinearSolve: __internal_solve_up
+
+function __internal_solve_up(
+        prob::NonlinearProblem, sensealg, u0::TrackedArray, u0_changed,
+        p::TrackedArray, p_changed, alg, args...; kwargs...)
+    return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
+        u0_changed, p, p_changed, alg, args...; kwargs...)
+end
+
+function __internal_solve_up(
+        prob::NonlinearProblem, sensealg, u0, u0_changed,
+        p::TrackedArray, p_changed, alg, args...; kwargs...)
+    return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
+        u0_changed, p, p_changed, alg, args...; kwargs...)
+end
+
+function __internal_solve_up(
+        prob::NonlinearProblem, sensealg, u0::TrackedArray, u0_changed,
+        p, p_changed, alg, args...; kwargs...)
+    return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
+        u0_changed, p, p_changed, alg, args...; kwargs...)
+end
+
+function __internal_solve_up(prob::NonlinearProblem, sensealg,
+        u0::AbstractArray{<:TrackedReal}, u0_changed, p::AbstractArray{<:TrackedReal},
+        p_changed, alg, args...; kwargs...)
+    return __internal_solve_up(
+        prob, sensealg, ArrayInterface.aos_to_soa(u0), true,
+        ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
+end
+
+function __internal_solve_up(prob::NonlinearProblem, sensealg, u0, u0_changed,
+        p::AbstractArray{<:TrackedReal}, p_changed, alg, args...; kwargs...)
+    return __internal_solve_up(
+        prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
+end
+
+function __internal_solve_up(prob::NonlinearProblem, sensealg,
+        u0::AbstractArray{<:TrackedReal}, u0_changed, p, p_changed, alg, args...; kwargs...)
+    return __internal_solve_up(
+        prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
+end
+
+ReverseDiff.@grad function __internal_solve_up(
+        prob::NonlinearProblem, sensealg, u0, u0_changed, p, p_changed, alg, args...; kwargs...)
+    out, ∇internal = DiffEqBase._solve_adjoint(
+        prob, sensealg, ReverseDiff.value(u0), ReverseDiff.value(p),
+        SciMLBase.ReverseDiffOriginator(), alg, args...; kwargs...)
+    function ∇__internal_solve_up(_args...)
+        ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(_args...)
+        return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
+    end
+    return Array(out), ∇__internal_solve_up
+end
+
+end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
new file mode 100644
index 000000000..61ce14645
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
@@ -0,0 +1,42 @@
+module SimpleNonlinearSolveTrackerExt
+
+using DiffEqBase, SciMLBase, SimpleNonlinearSolve, Tracker
+
+function SimpleNonlinearSolve.__internal_solve_up(prob::NonlinearProblem,
+        sensealg, u0::TrackedArray, u0_changed, p, p_changed, alg, args...; kwargs...)
+    return Tracker.track(
+        SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0, u0_changed,
+        p, p_changed, alg, args...; kwargs...)
+end
+
+function SimpleNonlinearSolve.__internal_solve_up(
+        prob::NonlinearProblem, sensealg, u0::TrackedArray, u0_changed,
+        p::TrackedArray, p_changed, alg, args...; kwargs...)
+    return Tracker.track(
+        SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0, u0_changed,
+        p, p_changed, alg, args...; kwargs...)
+end
+
+function SimpleNonlinearSolve.__internal_solve_up(prob::NonlinearProblem,
+        sensealg, u0, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
+    return Tracker.track(
+        SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0, u0_changed,
+        p, p_changed, alg, args...; kwargs...)
+end
+
+Tracker.@grad function SimpleNonlinearSolve.__internal_solve_up(_prob::NonlinearProblem,
+        sensealg, u0_, u0_changed, p_, p_changed, alg, args...; kwargs...)
+    u0, p = Tracker.data(u0_), Tracker.data(p_)
+    prob = remake(_prob; u0, p)
+    out, ∇internal = DiffEqBase._solve_adjoint(prob, sensealg, u0, p,
+        SciMLBase.TrackerOriginator(), alg, args...; kwargs...)
+
+    function ∇__internal_solve_up(Δ)
+        ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(Δ)
+        return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
+    end
+
+    return out, ∇__internal_solve_up
+end
+
+end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 710f2d6c3..3a4e5ebdb 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -71,8 +71,8 @@ function SciMLBase.solve(
         alg, args...; prob.kwargs..., kwargs...)
 end
 
-function __internal_solve_up(_prob::NonlinearProblem, sensealg, u0, u0_changed, p,
-        p_changed, alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...)
+function __internal_solve_up(_prob::NonlinearProblem, sensealg, u0, u0_changed,
+        p, p_changed, alg, args...; kwargs...)
     prob = u0_changed || p_changed ? remake(_prob; u0, p) : _prob
     return SciMLBase.__solve(prob, alg, args...; kwargs...)
 end
diff --git a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
index f96491449..74d745f65 100644
--- a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
@@ -1,14 +1,21 @@
 @testitem "Simple Adjoint Test" begin
-    using ForwardDiff, SciMLSensitivity, Zygote
+    using ForwardDiff, ReverseDiff, SciMLSensitivity, Tracker, Zygote
 
     ff(u, p) = u .^ 2 .- p
 
     function solve_nlprob(p)
         prob = NonlinearProblem{false}(ff, [1.0, 2.0], p)
-        return sum(abs2, solve(prob, SimpleNewtonRaphson()).u)
+        sol = solve(prob, SimpleNewtonRaphson())
+        res = sol isa AbstractArray ? sol : sol.u
+        return sum(abs2, res)
     end
 
     p = [3.0, 2.0]
 
-    @test only(Zygote.gradient(solve_nlprob, p)) ≈ ForwardDiff.gradient(solve_nlprob, p)
+    ∂p_zygote = only(Zygote.gradient(solve_nlprob, p))
+    ∂p_forwarddiff = ForwardDiff.gradient(solve_nlprob, p)
+    ∂p_tracker = Tracker.data(only(Tracker.gradient(solve_nlprob, p)))
+    ∂p_reversediff = ReverseDiff.gradient(solve_nlprob, p)
+
+    @test ∂p_zygote ≈ ∂p_forwarddiff ≈ ∂p_tracker ≈ ∂p_reversediff
 end

From ec757e3f6a4603939a7a3b741865bd6131c01737 Mon Sep 17 00:00:00 2001
From: Hendrik Ranocha <ranocha@users.noreply.github.com>
Date: Wed, 13 Mar 2024 10:22:46 +0100
Subject: [PATCH 342/700] fix docstring of ITP

---
 lib/SimpleNonlinearSolve/src/bracketing/itp.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
index 3f2069b72..2926dfd7a 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
@@ -14,13 +14,13 @@ I. F. D. Oliveira and R. H. C. Takahashi.
 
 The following keyword parameters are accepted.
 
-  - `n₀::Int = 1`, the 'slack'. Must not be negative. When n₀ = 0 the worst-case is
+  - `n₀::Int = 10`, the 'slack'. Must not be negative. When n₀ = 0 the worst-case is
     identical to that of bisection, but increacing n₀ provides greater oppotunity for
     superlinearity.
-  - `κ₁::Float64 = 0.1`. Must not be negative. The recomended value is `0.2/(x₂ - x₁)`.
+  - `κ₁::Float64 = 0.007`. Must not be negative. The recomended value is `0.2/(x₂ - x₁)`.
     Lower values produce tighter asymptotic behaviour, while higher values improve the
     steady-state behaviour when truncation is not helpful.
-  - `κ₂::Real = 2`. Must lie in [1, 1+ϕ ≈ 2.62). Higher values allow for a greater
+  - `κ₂::Real = 1.5`. Must lie in [1, 1+ϕ ≈ 2.62). Higher values allow for a greater
     convergence rate, but also make the method more succeptable to worst-case performance.
     In practice, κ=1,2 seems to work well due to the computational simplicity, as κ₂ is used
     as an exponent in the method.

From 45e07169472b7c6b4b25cd9acb8cca1e908b2636 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 21 Mar 2024 16:30:41 -0400
Subject: [PATCH 343/700] Handle polyalgorithm aliasing correctly

---
 Project.toml                |   2 +-
 src/NonlinearSolve.jl       |   3 +-
 src/default.jl              | 123 ++++++++++++++++++++++++++++++------
 src/utils.jl                |  13 ++--
 test/misc/aliasing_tests.jl |  25 ++++++++
 5 files changed, 137 insertions(+), 29 deletions(-)
 create mode 100644 test/misc/aliasing_tests.jl

diff --git a/Project.toml b/Project.toml
index 1294701b1..51aa68f54 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.8.0"
+version = "3.8.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index e7fa9bd3e..0cef448d2 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -12,7 +12,8 @@ import PrecompileTools: @recompile_invalidations, @compile_workload, @setup_work
           LinearAlgebra, LinearSolve, MaybeInplace, Preferences, Printf, SciMLBase,
           SimpleNonlinearSolve, SparseArrays, SparseDiffTools
 
-    import ArrayInterface: undefmatrix, can_setindex, restructure, fast_scalar_indexing
+    import ArrayInterface: undefmatrix, can_setindex, restructure, fast_scalar_indexing,
+                           ismutable
     import DiffEqBase: AbstractNonlinearTerminationMode,
                        AbstractSafeNonlinearTerminationMode,
                        AbstractSafeBestNonlinearTerminationMode,
diff --git a/src/default.jl b/src/default.jl
index cdcfb6825..c1db1638b 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -65,6 +65,9 @@ end
     force_stop::Bool
     maxiters::Int
     internalnorm
+    u0
+    u0_aliased
+    alias_u0::Bool
 end
 
 function Base.show(
@@ -91,11 +94,24 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
     @eval begin
         function SciMLBase.__init(
                 prob::$probType, alg::$algType{N}, args...; maxtime = nothing,
-                maxiters = 1000, internalnorm = DEFAULT_NORM, kwargs...) where {N}
+                maxiters = 1000, internalnorm = DEFAULT_NORM,
+                alias_u0 = false, verbose = true, kwargs...) where {N}
+            if (alias_u0 && !ismutable(prob.u0))
+                verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
+                                  immutable (checked using `ArrayInterface.ismutable`)."
+                alias_u0 = false  # If immutable don't care about aliasing
+            end
+            u0 = prob.u0
+            if alias_u0
+                u0_aliased = copy(u0)
+            else
+                u0_aliased = u0  # Irrelevant
+            end
+            alias_u0 && (prob = remake(prob; u0 = u0_aliased))
             return NonlinearSolvePolyAlgorithmCache{isinplace(prob), N, maxtime !== nothing}(
                 map(
-                    solver -> SciMLBase.__init(
-                        prob, solver, args...; maxtime, internalnorm, kwargs...),
+                    solver -> SciMLBase.__init(prob, solver, args...; maxtime,
+                        internalnorm, alias_u0, verbose, kwargs...),
                     alg.algs),
                 alg,
                 -1,
@@ -106,7 +122,10 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
                 ReturnCode.Default,
                 false,
                 maxiters,
-                internalnorm)
+                internalnorm,
+                u0,
+                u0_aliased,
+                alias_u0)
         end
     end
 end
@@ -120,20 +139,30 @@ end
 
     cache_syms = [gensym("cache") for i in 1:N]
     sol_syms = [gensym("sol") for i in 1:N]
+    u_result_syms = [gensym("u_result") for i in 1:N]
     for i in 1:N
         push!(calls,
             quote
                 $(cache_syms[i]) = cache.caches[$(i)]
                 if $(i) == cache.current
+                    cache.alias_u0 && copyto!(cache.u0_aliased, cache.u0)
                     $(sol_syms[i]) = SciMLBase.solve!($(cache_syms[i]))
                     if SciMLBase.successful_retcode($(sol_syms[i]))
                         stats = $(sol_syms[i]).stats
-                        u = $(sol_syms[i]).u
+                        if cache.alias_u0
+                            copyto!(cache.u0, $(sol_syms[i]).u)
+                            $(u_result_syms[i]) = cache.u0
+                        else
+                            $(u_result_syms[i]) = $(sol_syms[i]).u
+                        end
                         fu = get_fu($(cache_syms[i]))
                         return SciMLBase.build_solution(
-                            $(sol_syms[i]).prob, cache.alg, u, fu;
-                            retcode = $(sol_syms[i]).retcode, stats,
+                            $(sol_syms[i]).prob, cache.alg, $(u_result_syms[i]),
+                            fu; retcode = $(sol_syms[i]).retcode, stats,
                             original = $(sol_syms[i]), trace = $(sol_syms[i]).trace)
+                    elseif cache.alias_u0
+                        # For safety we need to maintain a copy of the solution
+                        $(u_result_syms[i]) = copy($(sol_syms[i]).u)
                     end
                     cache.current = $(i + 1)
                 end
@@ -144,14 +173,29 @@ end
     for (sym, resid) in zip(cache_syms, resids)
         push!(calls, :($(resid) = @isdefined($(sym)) ? get_fu($(sym)) : nothing))
     end
+    push!(calls, quote
+        fus = tuple($(Tuple(resids)...))
+        minfu, idx = __findmin(cache.internalnorm, fus)
+        stats = __compile_stats(cache.caches[idx])
+    end)
+    for i in 1:N
+        push!(calls, quote
+            if idx == $(i)
+                if cache.alias_u0
+                    u = $(u_result_syms[i])
+                else
+                    u = get_u(cache.caches[$i])
+                end
+            end
+        end)
+    end
     push!(calls,
         quote
-            fus = tuple($(Tuple(resids)...))
-            minfu, idx = __findmin(cache.internalnorm, fus)
-            stats = __compile_stats(cache.caches[idx])
-            u = get_u(cache.caches[idx])
             retcode = cache.caches[idx].retcode
-
+            if cache.alias_u0
+                copyto!(cache.u0, u)
+                u = cache.u0
+            end
             return SciMLBase.build_solution(cache.caches[idx].prob, cache.alg, u, fus[idx];
                 retcode, stats, cache.caches[idx].trace)
         end)
@@ -200,22 +244,52 @@ end
 for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProblem, :NLLS))
     algType = NonlinearSolvePolyAlgorithm{pType}
     @eval begin
-        @generated function SciMLBase.__solve(
-                prob::$probType, alg::$algType{N}, args...; kwargs...) where {N}
-            calls = [:(current = alg.start_index)]
+        @generated function SciMLBase.__solve(prob::$probType, alg::$algType{N}, args...;
+                alias_u0 = false, verbose = true, kwargs...) where {N}
             sol_syms = [gensym("sol") for _ in 1:N]
+            prob_syms = [gensym("prob") for _ in 1:N]
+            u_result_syms = [gensym("u_result") for _ in 1:N]
+            calls = [quote
+                current = alg.start_index
+                if (alias_u0 && !ismutable(prob.u0))
+                    verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
+                                      immutable (checked using `ArrayInterface.ismutable`)."
+                    alias_u0 = false  # If immutable don't care about aliasing
+                end
+                u0 = prob.u0
+                if alias_u0
+                    u0_aliased = similar(u0)
+                else
+                    u0_aliased = u0  # Irrelevant
+                end
+            end]
             for i in 1:N
                 cur_sol = sol_syms[i]
                 push!(calls,
                     quote
                         if current == $i
-                            $(cur_sol) = SciMLBase.__solve(
-                                prob, alg.algs[$(i)], args...; kwargs...)
+                            if alias_u0
+                                copyto!(u0_aliased, u0)
+                                $(prob_syms[i]) = remake(prob; u0 = u0_aliased)
+                            else
+                                $(prob_syms[i]) = prob
+                            end
+                            $(cur_sol) = SciMLBase.__solve($(prob_syms[i]), alg.algs[$(i)],
+                                args...; alias_u0, verbose, kwargs...)
                             if SciMLBase.successful_retcode($(cur_sol))
+                                if alias_u0
+                                    copyto!(u0, $(cur_sol).u)
+                                    $(u_result_syms[i]) = u0
+                                else
+                                    $(u_result_syms[i]) = $(cur_sol).u
+                                end
                                 return SciMLBase.build_solution(
-                                    prob, alg, $(cur_sol).u, $(cur_sol).resid;
+                                    prob, alg, $(u_result_syms[i]), $(cur_sol).resid;
                                     $(cur_sol).retcode, $(cur_sol).stats,
                                     original = $(cur_sol), trace = $(cur_sol).trace)
+                            elseif alias_u0
+                                # For safety we need to maintain a copy of the solution
+                                $(u_result_syms[i]) = copy($(cur_sol).u)
                             end
                             current = $(i + 1)
                         end
@@ -236,9 +310,16 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
                 push!(calls,
                     quote
                         if idx == $i
-                            return SciMLBase.build_solution(prob, alg, $(sol_syms[i]).u,
-                                $(sol_syms[i]).resid; $(sol_syms[i]).retcode,
-                                $(sol_syms[i]).stats, $(sol_syms[i]).trace)
+                            if alias_u0
+                                copyto!(u0, $(u_result_syms[i]))
+                                $(u_result_syms[i]) = u0
+                            else
+                                $(u_result_syms[i]) = $(sol_syms[i]).u
+                            end
+                            return SciMLBase.build_solution(
+                                prob, alg, $(u_result_syms[i]), $(sol_syms[i]).resid;
+                                $(sol_syms[i]).retcode, $(sol_syms[i]).stats,
+                                $(sol_syms[i]).trace, original = $(sol_syms[i]))
                         end
                     end)
             end
diff --git a/src/utils.jl b/src/utils.jl
index 259ff945a..d649d334c 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -94,15 +94,16 @@ LazyArrays.applied_axes(::typeof(__zero), x) = axes(x)
 @inline __is_complex(::Type{Complex}) = true
 @inline __is_complex(::Type{T}) where {T} = false
 
-function __findmin_caches(f, caches)
-    return __findmin(f ∘ get_fu, caches)
-end
-function __findmin(f, x)
-    return findmin(x) do xᵢ
+@inline __findmin_caches(f, caches) = __findmin(f ∘ get_fu, caches)
+# FIXME: DEFAULT_NORM makes an Array of NaNs not a NaN (atleast according to `isnan`)
+@inline __findmin(::typeof(DEFAULT_NORM), x) = __findmin(Base.Fix1(maximum, abs), x)
+@inline function __findmin(f, x)
+    fmin = @closure xᵢ -> begin
         xᵢ === nothing && return Inf
         fx = f(xᵢ)
-        return isnan(fx) ? Inf : fx
+        return ifelse(isnan(fx), Inf, fx)
     end
+    return findmin(fmin, x)
 end
 
 @inline __can_setindex(x) = can_setindex(x)
diff --git a/test/misc/aliasing_tests.jl b/test/misc/aliasing_tests.jl
new file mode 100644
index 000000000..857233029
--- /dev/null
+++ b/test/misc/aliasing_tests.jl
@@ -0,0 +1,25 @@
+@testitem "PolyAlgorithm Aliasing" begin
+    using NonlinearProblemLibrary
+
+    # Use a problem that the initial solvers cannot solve and cause the initial value to
+    # diverge. If we don't alias correctly, all the subsequent algorithms will also fail.
+    prob = NonlinearProblemLibrary.nlprob_23_testcases["Generalized Rosenbrock function"].prob
+    u0 = copy(prob.u0)
+    prob = remake(prob; u0 = copy(u0))
+
+    # If aliasing is not handled properly this will diverge
+    sol = solve(prob; abstol = 1e-6, alias_u0 = true,
+        termination_condition = AbsNormTerminationMode())
+
+    @test sol.u === prob.u0
+    @test SciMLBase.successful_retcode(sol.retcode)
+
+    prob = remake(prob; u0 = copy(u0))
+
+    cache = init(prob; abstol = 1e-6, alias_u0 = true,
+        termination_condition = AbsNormTerminationMode())
+    sol = solve!(cache)
+
+    @test sol.u === prob.u0
+    @test SciMLBase.successful_retcode(sol.retcode)
+end

From e6ff3aa80301f4ea1b84f3e632d2deeba8da9939 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 22 Mar 2024 15:23:52 -0400
Subject: [PATCH 344/700] Make __findmin type stable

---
 Project.toml |  2 +-
 src/utils.jl | 27 ++++++++++++++++++++-------
 2 files changed, 21 insertions(+), 8 deletions(-)

diff --git a/Project.toml b/Project.toml
index 51aa68f54..2bfe146e1 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.8.1"
+version = "3.8.2"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/utils.jl b/src/utils.jl
index d649d334c..73f134c0e 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -94,16 +94,29 @@ LazyArrays.applied_axes(::typeof(__zero), x) = axes(x)
 @inline __is_complex(::Type{Complex}) = true
 @inline __is_complex(::Type{T}) where {T} = false
 
-@inline __findmin_caches(f, caches) = __findmin(f ∘ get_fu, caches)
+@inline __findmin_caches(f::F, caches) where {F} = __findmin(f ∘ get_fu, caches)
 # FIXME: DEFAULT_NORM makes an Array of NaNs not a NaN (atleast according to `isnan`)
-@inline __findmin(::typeof(DEFAULT_NORM), x) = __findmin(Base.Fix1(maximum, abs), x)
-@inline function __findmin(f, x)
+@generated function __findmin(f::F, x) where {F}
+    # JET shows dynamic dispatch if this is not written as a generated function
+    if F === typeof(DEFAULT_NORM)
+        return :(return __findmin_impl(Base.Fix1(maximum, abs), x))
+    end
+    return :(return __findmin_impl(f, x))
+end
+@inline @views function __findmin_impl(f::F, x) where {F}
+    idx = findfirst(Base.Fix2(!==, nothing), x)
+    # This is an internal function so we assume that inputs are consistent and there is
+    # atleast one non-`nothing` value
+    fx_idx = f(x[idx])
+    idx == length(x) && return fx_idx, idx
     fmin = @closure xᵢ -> begin
-        xᵢ === nothing && return Inf
+        xᵢ === nothing && return oftype(fx_idx, Inf)
         fx = f(xᵢ)
-        return ifelse(isnan(fx), Inf, fx)
+        return ifelse(isnan(fx), oftype(fx, Inf), fx)
     end
-    return findmin(fmin, x)
+    x_min, x_min_idx = findmin(fmin, x[(idx + 1):length(x)])
+    x_min < fx_idx && return x_min, x_min_idx + idx
+    return fx_idx, idx
 end
 
 @inline __can_setindex(x) = can_setindex(x)
@@ -130,7 +143,7 @@ Statistics from the nonlinear equation solver about the solution process.
   - nf: Number of function evaluations.
   - njacs: Number of Jacobians created during the solve.
   - nfactors: Number of factorzations of the jacobian required for the solve.
-  - nsolve: Number of linear solves `W\b` required for the solve.
+  - nsolve: Number of linear solves `W \\ b` required for the solve.
   - nsteps: Total number of iterations for the nonlinear solver.
 """
 struct ImmutableNLStats

From f4a7871ba9bcfbd455c3d3e8a3ac840cd2c36154 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 24 Mar 2024 00:31:53 -0400
Subject: [PATCH 345/700] Don't specialize on original and stats for polyalg

---
 Project.toml               |  2 +-
 src/default.jl             |  9 +++++----
 src/utils.jl               | 13 +++++++++++++
 test/misc/polyalg_tests.jl |  3 +++
 4 files changed, 22 insertions(+), 5 deletions(-)

diff --git a/Project.toml b/Project.toml
index 2bfe146e1..b7f7f9e7a 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.8.2"
+version = "3.8.3"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/default.jl b/src/default.jl
index c1db1638b..d32c9ab68 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -156,7 +156,7 @@ end
                             $(u_result_syms[i]) = $(sol_syms[i]).u
                         end
                         fu = get_fu($(cache_syms[i]))
-                        return SciMLBase.build_solution(
+                        return __build_solution_less_specialize(
                             $(sol_syms[i]).prob, cache.alg, $(u_result_syms[i]),
                             fu; retcode = $(sol_syms[i]).retcode, stats,
                             original = $(sol_syms[i]), trace = $(sol_syms[i]).trace)
@@ -196,7 +196,8 @@ end
                 copyto!(cache.u0, u)
                 u = cache.u0
             end
-            return SciMLBase.build_solution(cache.caches[idx].prob, cache.alg, u, fus[idx];
+            return __build_solution_less_specialize(
+                cache.caches[idx].prob, cache.alg, u, fus[idx];
                 retcode, stats, cache.caches[idx].trace)
         end)
 
@@ -283,7 +284,7 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
                                 else
                                     $(u_result_syms[i]) = $(cur_sol).u
                                 end
-                                return SciMLBase.build_solution(
+                                return __build_solution_less_specialize(
                                     prob, alg, $(u_result_syms[i]), $(cur_sol).resid;
                                     $(cur_sol).retcode, $(cur_sol).stats,
                                     original = $(cur_sol), trace = $(cur_sol).trace)
@@ -316,7 +317,7 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
                             else
                                 $(u_result_syms[i]) = $(sol_syms[i]).u
                             end
-                            return SciMLBase.build_solution(
+                            return __build_solution_less_specialize(
                                 prob, alg, $(u_result_syms[i]), $(sol_syms[i]).resid;
                                 $(sol_syms[i]).retcode, $(sol_syms[i]).stats,
                                 $(sol_syms[i]).trace, original = $(sol_syms[i]))
diff --git a/src/utils.jl b/src/utils.jl
index 73f134c0e..a0cc5744b 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -176,3 +176,16 @@ Determine the chunk size for ForwardDiff and PolyesterForwardDiff based on the i
 """
 @inline pickchunksize(x) = pickchunksize(length(x))
 @inline pickchunksize(x::Int) = ForwardDiff.pickchunksize(x)
+
+# Original is often determined on runtime information especially for PolyAlgorithms so it
+# is best to never specialize on that
+function __build_solution_less_specialize(prob::AbstractNonlinearProblem, alg, u, resid;
+        retcode = ReturnCode.Default, original = nothing, left = nothing,
+        right = nothing, stats = nothing, trace = nothing, kwargs...)
+    T = eltype(eltype(u))
+    N = ndims(u)
+
+    return SciMLBase.NonlinearSolution{T, N, typeof(u), typeof(resid), typeof(prob),
+        typeof(alg), Any, typeof(left), Any, typeof(trace)}(
+        u, resid, prob, alg, retcode, original, left, right, stats, trace)
+end
diff --git a/test/misc/polyalg_tests.jl b/test/misc/polyalg_tests.jl
index c5f1a8eb3..74016d75f 100644
--- a/test/misc/polyalg_tests.jl
+++ b/test/misc/polyalg_tests.jl
@@ -224,6 +224,7 @@ end
 
     @test all(!isnan, sol.u)
     @test !SciMLBase.successful_retcode(sol.retcode)
+    @inferred solve(prob)
 end
 
 @testitem "[OOP] Infeasible" setup=[InfeasibleFunction] begin
@@ -235,6 +236,7 @@ end
 
     @test all(!isnan, sol.u)
     @test !SciMLBase.successful_retcode(sol.retcode)
+    @inferred solve(prob)
 
     u0 = @SVector [0.0, 0.0, 0.0]
     prob = NonlinearProblem(f1_infeasible, u0)
@@ -243,6 +245,7 @@ end
         sol = solve(prob)
         @test all(!isnan, sol.u)
         @test !SciMLBase.successful_retcode(sol.retcode)
+        @inferred solve(prob)
     catch err
         @test err isa LinearAlgebra.SingularException
     end

From f467e3b6377f2344a94a4941ed7e734b29fbcc6a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 29 Mar 2024 21:59:16 -0400
Subject: [PATCH 346/700] Missing vec in Descent cache

---
 Project.toml          | 2 +-
 src/descent/newton.jl | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/Project.toml b/Project.toml
index b7f7f9e7a..31d3b3e54 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.8.3"
+version = "3.8.4"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/descent/newton.jl b/src/descent/newton.jl
index cfbc1c239..e79120a5e 100644
--- a/src/descent/newton.jl
+++ b/src/descent/newton.jl
@@ -100,7 +100,7 @@ function __internal_solve!(
     if idx === Val(1)
         @bb cache.JᵀJ_cache = transpose(J) × J
     end
-    @bb cache.Jᵀfu_cache = transpose(J) × fu
+    @bb cache.Jᵀfu_cache = transpose(J) × vec(fu)
     @static_timeit cache.timer "linear solve" begin
         δu = cache.lincache(; A = __maybe_symmetric(cache.JᵀJ_cache), b = cache.Jᵀfu_cache,
             kwargs..., linu = _vec(δu), du = _vec(δu),

From 63bd4a9efd378b13ad7b700b05e5dbb01083f5ba Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 31 Mar 2024 00:02:38 -0400
Subject: [PATCH 347/700] Use a different termination norm for NLLS

---
 Project.toml                        |  4 ++--
 src/core/approximate_jacobian.jl    |  2 +-
 src/core/generalized_first_order.jl |  2 +-
 src/core/spectral_methods.jl        |  2 +-
 src/internal/termination.jl         | 24 +++++++++++++++++++-----
 5 files changed, 24 insertions(+), 10 deletions(-)

diff --git a/Project.toml b/Project.toml
index 31d3b3e54..9411cc234 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.8.4"
+version = "3.9.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -63,7 +63,7 @@ BandedMatrices = "1.4"
 BenchmarkTools = "1.4"
 ConcreteStructs = "0.2.3"
 CUDA = "5.1"
-DiffEqBase = "6.146.0"
+DiffEqBase = "6.149.0"
 Enzyme = "0.11.15"
 FastBroadcast = "0.2.8"
 FastClosures = "0.3"
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index 4204b2db7..afdd445bb 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -167,7 +167,7 @@ function SciMLBase.__init(
             prob, alg.initialization, alg, f, fu, u, p; linsolve, maxiters, internalnorm)
 
         abstol, reltol, termination_cache = init_termination_cache(
-            abstol, reltol, fu, u, termination_condition)
+            prob, abstol, reltol, fu, u, termination_condition)
         linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
 
         J = initialization_cache(nothing)
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 753b7682f..883609006 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -156,7 +156,7 @@ function SciMLBase.__init(
         linsolve = get_linear_solver(alg.descent)
 
         abstol, reltol, termination_cache = init_termination_cache(
-            abstol, reltol, fu, u, termination_condition)
+            prob, abstol, reltol, fu, u, termination_condition)
         linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
 
         jac_cache = JacobianCache(
diff --git a/src/core/spectral_methods.jl b/src/core/spectral_methods.jl
index a4e824744..a2966c765 100644
--- a/src/core/spectral_methods.jl
+++ b/src/core/spectral_methods.jl
@@ -133,7 +133,7 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane
             prob, alg.linesearch, prob.f, fu, u, prob.p; maxiters, internalnorm, kwargs...)
 
         abstol, reltol, tc_cache = init_termination_cache(
-            abstol, reltol, fu, u_cache, termination_condition)
+            prob, abstol, reltol, fu, u_cache, termination_condition)
         trace = init_nonlinearsolve_trace(alg, u, fu, nothing, du; kwargs...)
 
         if alg.σ_1 === nothing
diff --git a/src/internal/termination.jl b/src/internal/termination.jl
index e55e344f7..b64897744 100644
--- a/src/internal/termination.jl
+++ b/src/internal/termination.jl
@@ -1,9 +1,23 @@
-function init_termination_cache(abstol, reltol, du, u, ::Nothing)
-    return init_termination_cache(
-        abstol, reltol, du, u, AbsSafeBestTerminationMode(; max_stalled_steps = 32))
+function init_termination_cache(prob::NonlinearProblem, abstol, reltol, du, u, ::Nothing)
+    return init_termination_cache(prob, abstol, reltol, du, u,
+        AbsSafeBestTerminationMode(Base.Fix1(maximum, abs); max_stalled_steps = 32))
 end
-function init_termination_cache(abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
-    tc_cache = init(du, u, tc; abstol, reltol, use_deprecated_retcodes = Val(false))
+function init_termination_cache(
+        prob::NonlinearLeastSquaresProblem, abstol, reltol, du, u, ::Nothing)
+    return init_termination_cache(prob, abstol, reltol, du, u,
+        AbsSafeBestTerminationMode(Base.Fix2(norm, 2); max_stalled_steps = 32))
+end
+
+function init_termination_cache(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+        abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
+    tc_ = if hasfield(typeof(tc), :internalnorm) && tc.internalnorm === nothing
+        internalnorm = ifelse(
+            prob isa NonlinearProblem, Base.Fix1(maximum, abs), Base.Fix2(norm, 2))
+        DiffEqBase.set_termination_mode_internalnorm(tc, internalnorm)
+    else
+        tc
+    end
+    tc_cache = init(du, u, tc_; abstol, reltol, use_deprecated_retcodes = Val(false))
     return DiffEqBase.get_abstol(tc_cache), DiffEqBase.get_reltol(tc_cache), tc_cache
 end
 

From 3a994339dc769d2321c6461997e8abd032d29c89 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 31 Mar 2024 09:07:20 -0400
Subject: [PATCH 348/700] Fix the tracing for NLLS

---
 src/core/approximate_jacobian.jl    |  2 +-
 src/core/generalized_first_order.jl |  2 +-
 src/core/spectral_methods.jl        |  2 +-
 src/internal/tracing.jl             | 81 +++++++++++++++++------------
 test/core/forward_ad_tests.jl       |  1 -
 test/core/nlls_tests.jl             | 17 +++---
 test/core/rootfind_tests.jl         | 16 +++---
 7 files changed, 69 insertions(+), 52 deletions(-)

diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index afdd445bb..d5329f1c8 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -206,7 +206,7 @@ function SciMLBase.__init(
         update_rule_cache = __internal_init(
             prob, alg.update_rule, J, fu, u, du; internalnorm)
 
-        trace = init_nonlinearsolve_trace(alg, u, fu, ApplyArray(__zero, J), du;
+        trace = init_nonlinearsolve_trace(prob, alg, u, fu, ApplyArray(__zero, J), du;
             uses_jacobian_inverse = Val(INV), kwargs...)
 
         return ApproximateJacobianSolveCache{INV, GB, iip, maxtime !== nothing}(
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 883609006..2769736ff 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -191,7 +191,7 @@ function SciMLBase.__init(
             GB = :LineSearch
         end
 
-        trace = init_nonlinearsolve_trace(alg, u, fu, ApplyArray(__zero, J), du; kwargs...)
+        trace = init_nonlinearsolve_trace(prob, alg, u, fu, ApplyArray(__zero, J), du; kwargs...)
 
         return GeneralizedFirstOrderAlgorithmCache{iip, GB, maxtime !== nothing}(
             fu, u, u_cache, p, du, J, alg, prob, jac_cache, descent_cache, linesearch_cache,
diff --git a/src/core/spectral_methods.jl b/src/core/spectral_methods.jl
index a2966c765..d9d271d78 100644
--- a/src/core/spectral_methods.jl
+++ b/src/core/spectral_methods.jl
@@ -134,7 +134,7 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane
 
         abstol, reltol, tc_cache = init_termination_cache(
             prob, abstol, reltol, fu, u_cache, termination_condition)
-        trace = init_nonlinearsolve_trace(alg, u, fu, nothing, du; kwargs...)
+        trace = init_nonlinearsolve_trace(prob, alg, u, fu, nothing, du; kwargs...)
 
         if alg.σ_1 === nothing
             σ_n = dot(u, u) / dot(u, fu)
diff --git a/src/internal/tracing.jl b/src/internal/tracing.jl
index 8f0f10fb1..d5edb3a49 100644
--- a/src/internal/tracing.jl
+++ b/src/internal/tracing.jl
@@ -52,7 +52,7 @@ for Tr in (:TraceMinimal, :TraceWithJacobianConditionNumber, :TraceAll)
 end
 
 # NonlinearSolve Tracing Utilities
-@concrete struct NonlinearSolveTraceEntry
+@concrete struct NonlinearSolveTraceEntry{nType}
     iteration::Int
     fnorm
     stepnorm
@@ -63,19 +63,27 @@ end
     δu
 end
 
-function __show_top_level(io::IO, entry::NonlinearSolveTraceEntry)
+function __show_top_level(io::IO, entry::NonlinearSolveTraceEntry{nType}) where {nType}
     if entry.condJ === nothing
         @printf io "%-8s %-20s %-20s\n" "----" "-------------" "-----------"
-        @printf io "%-8s %-20s %-20s\n" "Iter" "f(u) inf-norm" "Step 2-norm"
+        if nType === :L2
+            @printf io "%-8s %-20s %-20s\n" "Iter" "f(u) 2-norm" "Step 2-norm"
+        else
+            @printf io "%-8s %-20s %-20s\n" "Iter" "f(u) inf-norm" "Step 2-norm"
+        end
         @printf io "%-8s %-20s %-20s\n" "----" "-------------" "-----------"
     else
         @printf io "%-8s %-20s %-20s %-20s\n" "----" "-------------" "-----------" "-------"
-        @printf io "%-8s %-20s %-20s %-20s\n" "Iter" "f(u) inf-norm" "Step 2-norm" "cond(J)"
+        if nType === :L2
+            @printf io "%-8s %-20s %-20s %-20s\n" "Iter" "f(u) 2-norm" "Step 2-norm" "cond(J)"
+        else
+            @printf io "%-8s %-20s %-20s %-20s\n" "Iter" "f(u) inf-norm" "Step 2-norm" "cond(J)"
+        end
         @printf io "%-8s %-20s %-20s %-20s\n" "----" "-------------" "-----------" "-------"
     end
 end
 
-function Base.show(io::IO, entry::NonlinearSolveTraceEntry)
+function Base.show(io::IO, entry::NonlinearSolveTraceEntry{nType}) where {nType}
     entry.iteration == 0 && __show_top_level(io, entry)
     if entry.iteration < 0
         # Special case for final entry
@@ -89,18 +97,24 @@ function Base.show(io::IO, entry::NonlinearSolveTraceEntry)
     return nothing
 end
 
-function NonlinearSolveTraceEntry(iteration, fu, δu)
-    return NonlinearSolveTraceEntry(
-        iteration, norm(fu, Inf), norm(δu, 2), nothing, nothing, nothing, nothing, nothing)
+function NonlinearSolveTraceEntry(prob::AbstractNonlinearProblem, iteration, fu, δu)
+    nType = ifelse(prob isa NonlinearLeastSquaresProblem, :L2, :Inf)
+    fnorm = prob isa NonlinearLeastSquaresProblem ? norm(fu, 2) : norm(fu, Inf)
+    return NonlinearSolveTraceEntry{nType}(
+        iteration, fnorm, norm(δu, 2), nothing, nothing, nothing, nothing, nothing)
 end
 
-function NonlinearSolveTraceEntry(iteration, fu, δu, J)
-    return NonlinearSolveTraceEntry(iteration, norm(fu, Inf), norm(δu, 2),
+function NonlinearSolveTraceEntry(prob::AbstractNonlinearProblem, iteration, fu, δu, J)
+    nType = ifelse(prob isa NonlinearLeastSquaresProblem, :L2, :Inf)
+    fnorm = prob isa NonlinearLeastSquaresProblem ? norm(fu, 2) : norm(fu, Inf)
+    return NonlinearSolveTraceEntry{nType}(iteration, fnorm, norm(δu, 2),
         __cond(J), nothing, nothing, nothing, nothing)
 end
 
-function NonlinearSolveTraceEntry(iteration, fu, δu, J, u)
-    return NonlinearSolveTraceEntry(iteration, norm(fu, Inf), norm(δu, 2), __cond(J),
+function NonlinearSolveTraceEntry(prob::AbstractNonlinearProblem, iteration, fu, δu, J, u)
+    nType = ifelse(prob isa NonlinearLeastSquaresProblem, :L2, :Inf)
+    fnorm = prob isa NonlinearLeastSquaresProblem ? norm(fu, 2) : norm(fu, Inf)
+    return NonlinearSolveTraceEntry{nType}(iteration, fnorm, norm(δu, 2), __cond(J),
         __copy(J), __copy(u), __copy(fu), __copy(δu))
 end
 
@@ -108,6 +122,7 @@ end
     show_trace, store_trace, Tr <: AbstractNonlinearSolveTraceLevel}
     history
     trace_level::Tr
+    prob
 end
 
 function reset!(trace::NonlinearSolveTrace)
@@ -123,44 +138,44 @@ function Base.show(io::IO, trace::NonlinearSolveTrace)
     return nothing
 end
 
-function init_nonlinearsolve_trace(alg, u, fu, J, δu; show_trace::Val = Val(false),
+function init_nonlinearsolve_trace(prob, alg, u, fu, J, δu; show_trace::Val = Val(false),
         trace_level::AbstractNonlinearSolveTraceLevel = TraceMinimal(),
         store_trace::Val = Val(false), uses_jac_inverse = Val(false), kwargs...)
     return init_nonlinearsolve_trace(
-        alg, show_trace, trace_level, store_trace, u, fu, J, δu, uses_jac_inverse)
+        prob, alg, show_trace, trace_level, store_trace, u, fu, J, δu, uses_jac_inverse)
 end
 
-function init_nonlinearsolve_trace(
-        alg, ::Val{show_trace}, trace_level::AbstractNonlinearSolveTraceLevel,
-        ::Val{store_trace}, u, fu, J, δu,
-        ::Val{uses_jac_inverse}) where {show_trace, store_trace, uses_jac_inverse}
+function init_nonlinearsolve_trace(prob::AbstractNonlinearProblem, alg, ::Val{show_trace},
+        trace_level::AbstractNonlinearSolveTraceLevel, ::Val{store_trace}, u, fu, J,
+        δu, ::Val{uses_jac_inverse}) where {show_trace, store_trace, uses_jac_inverse}
     if show_trace
         print("\nAlgorithm: ")
         Base.printstyled(alg, "\n\n"; color = :green, bold = true)
     end
     J_ = uses_jac_inverse ? (trace_level isa TraceMinimal ? J : __safe_inv(J)) : J
     history = __init_trace_history(
-        Val{show_trace}(), trace_level, Val{store_trace}(), u, fu, J_, δu)
-    return NonlinearSolveTrace{show_trace, store_trace}(history, trace_level)
+        prob, Val{show_trace}(), trace_level, Val{store_trace}(), u, fu, J_, δu)
+    return NonlinearSolveTrace{show_trace, store_trace}(history, trace_level, prob)
 end
 
-function __init_trace_history(::Val{show_trace}, trace_level, ::Val{store_trace},
-        u, fu, J, δu) where {show_trace, store_trace}
+function __init_trace_history(
+        prob::AbstractNonlinearProblem, ::Val{show_trace}, trace_level,
+        ::Val{store_trace}, u, fu, J, δu) where {show_trace, store_trace}
     !store_trace && !show_trace && return nothing
-    entry = __trace_entry(trace_level, 0, u, fu, J, δu)
+    entry = __trace_entry(prob, trace_level, 0, u, fu, J, δu)
     show_trace && show(entry)
     store_trace && return NonlinearSolveTraceEntry[entry]
     return nothing
 end
 
-function __trace_entry(::TraceMinimal, iter, u, fu, J, δu, α = 1)
-    return NonlinearSolveTraceEntry(iter, fu, δu .* α)
+function __trace_entry(prob, ::TraceMinimal, iter, u, fu, J, δu, α = 1)
+    return NonlinearSolveTraceEntry(prob, iter, fu, δu .* α)
 end
-function __trace_entry(::TraceWithJacobianConditionNumber, iter, u, fu, J, δu, α = 1)
-    return NonlinearSolveTraceEntry(iter, fu, δu .* α, J)
+function __trace_entry(prob, ::TraceWithJacobianConditionNumber, iter, u, fu, J, δu, α = 1)
+    return NonlinearSolveTraceEntry(prob, iter, fu, δu .* α, J)
 end
-function __trace_entry(::TraceAll, iter, u, fu, J, δu, α = 1)
-    return NonlinearSolveTraceEntry(iter, fu, δu .* α, J, u)
+function __trace_entry(prob, ::TraceAll, iter, u, fu, J, δu, α = 1)
+    return NonlinearSolveTraceEntry(prob, iter, fu, δu .* α, J, u)
 end
 
 function update_trace!(trace::NonlinearSolveTrace{ShT, StT}, iter, u, fu, J, δu,
@@ -168,8 +183,10 @@ function update_trace!(trace::NonlinearSolveTrace{ShT, StT}, iter, u, fu, J, δu
     !StT && !ShT && return nothing
 
     if L
-        entry = NonlinearSolveTraceEntry(
-            -1, norm(fu, Inf), NaN32, nothing, nothing, nothing, nothing, nothing)
+        nType = ifelse(trace.prob isa NonlinearLeastSquaresProblem, :L2, :Inf)
+        fnorm = trace.prob isa NonlinearLeastSquaresProblem ? norm(fu, 2) : norm(fu, Inf)
+        entry = NonlinearSolveTraceEntry{nType}(
+            -1, fnorm, NaN32, nothing, nothing, nothing, nothing, nothing)
         ShT && show(entry)
         return trace
     end
@@ -177,7 +194,7 @@ function update_trace!(trace::NonlinearSolveTrace{ShT, StT}, iter, u, fu, J, δu
     show_now = ShT && (mod1(iter, trace.trace_level.print_frequency) == 1)
     store_now = StT && (mod1(iter, trace.trace_level.store_frequency) == 1)
     (show_now || store_now) &&
-        (entry = __trace_entry(trace.trace_level, iter, u, fu, J, δu, α))
+        (entry = __trace_entry(trace.prob, trace.trace_level, iter, u, fu, J, δu, α))
     store_now && push!(trace.history, entry)
     show_now && show(entry)
     return trace
diff --git a/test/core/forward_ad_tests.jl b/test/core/forward_ad_tests.jl
index 24258e157..46034d844 100644
--- a/test/core/forward_ad_tests.jl
+++ b/test/core/forward_ad_tests.jl
@@ -79,7 +79,6 @@ end
                     gs = abs.(ForwardDiff.derivative(solve_with(Val{mode}(), u0, alg), p))
                     gs_true = abs.(jacobian_f(u0, p))
                     if !(isapprox(gs, gs_true, atol = 1e-5))
-                        @show sol.retcode, sol.u
                         @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_gradient=gs true_gradient=gs_true
                     else
                         @test abs.(gs)≈abs.(gs_true) atol=1e-5
diff --git a/test/core/nlls_tests.jl b/test/core/nlls_tests.jl
index 6b7b018cd..a1506d356 100644
--- a/test/core/nlls_tests.jl
+++ b/test/core/nlls_tests.jl
@@ -6,11 +6,11 @@ using Reexport
 true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
 true_function(y, x, θ) = (@. y = θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4]))
 
-θ_true = [1.0, 0.1, 2.0, 0.5]
+const θ_true = [1.0, 0.1, 2.0, 0.5]
 
-x = [-1.0, -0.5, 0.0, 0.5, 1.0]
+const x = [-1.0, -0.5, 0.0, 0.5, 1.0]
 
-y_target = true_function(x, θ_true)
+const y_target = true_function(x, θ_true)
 
 function loss_function(θ, p)
     ŷ = true_function(p, θ)
@@ -23,7 +23,7 @@ function loss_function(resid, θ, p)
     return resid
 end
 
-θ_init = θ_true .+ randn!(StableRNG(0), similar(θ_true)) * 0.1
+const θ_init = θ_true .+ randn!(StableRNG(0), similar(θ_true)) * 0.1
 
 solvers = []
 for linsolve in [nothing, LUFactorization(), KrylovJL_GMRES(), KrylovJL_LSMR()]
@@ -56,9 +56,9 @@ end
     nlls_problems = [prob_oop, prob_iip]
 
     for prob in nlls_problems, solver in solvers
-        sol = solve(prob, solver; maxiters = 10000, abstol = 1e-8)
+        sol = solve(prob, solver; maxiters = 10000, abstol = 1e-6)
         @test SciMLBase.successful_retcode(sol)
-        @test maximum(abs, sol.resid) < 1e-6
+        @test norm(sol.resid, 2) < 1e-6
     end
 end
 
@@ -90,8 +90,9 @@ end
             x)]
 
     for prob in probs, solver in solvers
-        sol = solve(prob, solver; maxiters = 10000, abstol = 1e-8)
-        @test maximum(abs, sol.resid) < 1e-6
+        sol = solve(prob, solver; maxiters = 10000, abstol = 1e-6)
+        @test SciMLBase.successful_retcode(sol)
+        @test norm(sol.resid, 2) < 1e-6
     end
 end
 
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index 87ba7cd35..caa776d5a 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -120,7 +120,7 @@ end
         @test all(solve(probN, NewtonRaphson(; autodiff)).u .≈ sqrt(2.0))
     end
 
-    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
+    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -238,7 +238,7 @@ end
         end
     end
 
-    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
+    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -324,7 +324,7 @@ end
         end
     end
 
-    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
+    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -395,7 +395,7 @@ end
         end
     end
 
-    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
+    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -462,7 +462,7 @@ end
                   sqrt(2.0))
     end
 
-    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
+    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -514,7 +514,7 @@ end
     @test nlprob_iterator_interface(quadratic_f, p, Val(false), Broyden()) ≈ sqrt.(p)
     @test nlprob_iterator_interface(quadratic_f!, p, Val(true), Broyden()) ≈ sqrt.(p)
 
-    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
+    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -563,7 +563,7 @@ end
     @test nlprob_iterator_interface(quadratic_f, p, Val(false), Klement()) ≈ sqrt.(p)
     @test nlprob_iterator_interface(quadratic_f!, p, Val(true), Klement()) ≈ sqrt.(p)
 
-    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
+    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -613,7 +613,7 @@ end
     @test nlprob_iterator_interface(
         quadratic_f!, p, Val(true), LimitedMemoryBroyden())≈sqrt.(p) atol=1e-2
 
-    @testset "Termination condition: $(termination_condition) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
+    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)

From 501764372850157705f00442fe48b183078651bc Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 31 Mar 2024 12:19:04 -0400
Subject: [PATCH 349/700] Check in the Manifest file

---
 Manifest.toml | 1062 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 1062 insertions(+)
 create mode 100644 Manifest.toml

diff --git a/Manifest.toml b/Manifest.toml
new file mode 100644
index 000000000..030f3f2d1
--- /dev/null
+++ b/Manifest.toml
@@ -0,0 +1,1062 @@
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.10.2"
+manifest_format = "2.0"
+project_hash = "25f154e3650c19bee7abe4e1b457009a7203eee8"
+
+[[deps.ADTypes]]
+git-tree-sha1 = "016833eb52ba2d6bea9fcb50ca295980e728ee24"
+uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
+version = "0.2.7"
+
+[[deps.Accessors]]
+deps = ["CompositionsBase", "ConstructionBase", "Dates", "InverseFunctions", "LinearAlgebra", "MacroTools", "Markdown", "Test"]
+git-tree-sha1 = "c0d491ef0b135fd7d63cbc6404286bc633329425"
+uuid = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
+version = "0.1.36"
+
+    [deps.Accessors.extensions]
+    AccessorsAxisKeysExt = "AxisKeys"
+    AccessorsIntervalSetsExt = "IntervalSets"
+    AccessorsStaticArraysExt = "StaticArrays"
+    AccessorsStructArraysExt = "StructArrays"
+    AccessorsUnitfulExt = "Unitful"
+
+    [deps.Accessors.weakdeps]
+    AxisKeys = "94b1ba4f-4ee9-5380-92f1-94cde586c3c5"
+    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
+    Requires = "ae029012-a4dd-5104-9daa-d747884805df"
+    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+    StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
+    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
+
+[[deps.Adapt]]
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+
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+
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+
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+    ArrayInterfaceBlockBandedMatricesExt = "BlockBandedMatrices"
+    ArrayInterfaceCUDAExt = "CUDA"
+    ArrayInterfaceChainRulesExt = "ChainRules"
+    ArrayInterfaceGPUArraysCoreExt = "GPUArraysCore"
+    ArrayInterfaceReverseDiffExt = "ReverseDiff"
+    ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore"
+    ArrayInterfaceTrackerExt = "Tracker"
+
+    [deps.ArrayInterface.weakdeps]
+    BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+    BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
+    CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+    ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
+    GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
+    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+    StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+
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+
+    [deps.ChainRulesCore.extensions]
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+
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+weakdeps = ["Dates", "LinearAlgebra"]
+
+    [deps.Compat.extensions]
+    CompatLinearAlgebraExt = "LinearAlgebra"
+
+[[deps.CompilerSupportLibraries_jll]]
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+
+    [deps.CompositionsBase.extensions]
+    CompositionsBaseInverseFunctionsExt = "InverseFunctions"
+
+[[deps.ConcreteStructs]]
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+[[deps.ConstructionBase]]
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+
+    [deps.ConstructionBase.extensions]
+    ConstructionBaseIntervalSetsExt = "IntervalSets"
+    ConstructionBaseStaticArraysExt = "StaticArrays"
+
+    [deps.ConstructionBase.weakdeps]
+    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
+    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+
+[[deps.CpuId]]
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+git-tree-sha1 = "fcbb72b032692610bfbdb15018ac16a36cf2e406"
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+
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From 36814a2093ecfb9b715413749b1c249fa56227e7 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 31 Mar 2024 12:39:35 -0400
Subject: [PATCH 350/700] Use the different norms for termination

---
 lib/SimpleNonlinearSolve/Manifest.toml        | 781 ++++++++++++++++++
 lib/SimpleNonlinearSolve/Project.toml         |   4 +-
 .../src/nlsolve/broyden.jl                    |   2 +-
 .../src/nlsolve/dfsane.jl                     |   2 +-
 .../src/nlsolve/halley.jl                     |   2 +-
 .../src/nlsolve/klement.jl                    |   2 +-
 .../src/nlsolve/lbroyden.jl                   |   2 +-
 .../src/nlsolve/raphson.jl                    |   2 +-
 .../src/nlsolve/trustRegion.jl                |   2 +-
 lib/SimpleNonlinearSolve/src/utils.jl         |  54 +-
 10 files changed, 815 insertions(+), 38 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/Manifest.toml

diff --git a/lib/SimpleNonlinearSolve/Manifest.toml b/lib/SimpleNonlinearSolve/Manifest.toml
new file mode 100644
index 000000000..a3a6bb313
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/Manifest.toml
@@ -0,0 +1,781 @@
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diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 225b36090..c1065039b 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.6.0"
+version = "1.7.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -43,7 +43,7 @@ ArrayInterface = "7.7"
 CUDA = "5.2"
 ChainRulesCore = "1.22"
 ConcreteStructs = "0.2.3"
-DiffEqBase = "6.146"
+DiffEqBase = "6.149"
 DiffResults = "1.1"
 FastClosures = "0.3"
 FiniteDiff = "2.22"
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index 15e544795..6fe121481 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -48,7 +48,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
     @bb δJ⁻¹n = copy(x)
     @bb δJ⁻¹ = copy(J⁻¹)
 
-    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
         termination_condition)
 
     ls_cache = __get_linesearch(alg) === Val(true) ?
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 856e31fd4..9f092648d 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -70,7 +70,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{M}, args...
     τ_min = T(alg.τ_min)
     τ_max = T(alg.τ_max)
 
-    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
         termination_condition)
 
     fx_norm = NONLINEARSOLVE_DEFAULT_NORM(fx)^nexp
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index 462332280..934dc4763 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -34,7 +34,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
     T = eltype(x)
 
     autodiff = __get_concrete_autodiff(prob, alg.autodiff)
-    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
         termination_condition)
 
     @bb xo = copy(x)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
index 680b9cd7c..c2c8b446f 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
@@ -13,7 +13,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
     T = eltype(x)
     fx = _get_fx(prob, x)
 
-    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
         termination_condition)
 
     @bb δx = copy(x)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index 145a5467d..600892edd 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -61,7 +61,7 @@ end
 
     U, Vᵀ = __init_low_rank_jacobian(x, fx, x isa StaticArray ? threshold : Val(η))
 
-    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
         termination_condition)
 
     @bb xo = copy(x)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
index e84f59521..9735d0c8c 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
@@ -32,7 +32,7 @@ function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresPr
     @bb xo = copy(x)
     J, jac_cache = jacobian_cache(autodiff, prob.f, fx, x, prob.p)
 
-    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
         termination_condition)
 
     for i in 1:maxiters
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index 03c4692e7..e6ccf6536 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -88,7 +88,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
     J, jac_cache = jacobian_cache(autodiff, prob.f, fx, x, prob.p)
     fx, ∇f = value_and_jacobian(autodiff, prob.f, fx, x, prob.p, jac_cache; J)
 
-    abstol, reltol, tc_cache = init_termination_cache(abstol, reltol, fx, x,
+    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
         termination_condition)
 
     # Set default trust region radius if not specified by user.
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 38be3437c..76e91fcb4 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -288,14 +288,30 @@ end
 # different. NonlinearSolve is more for robust / cached solvers while SimpleNonlinearSolve
 # is meant for low overhead solvers, users can opt into the other termination modes but the
 # default is to use the least overhead version.
-function init_termination_cache(abstol, reltol, du, u, ::Nothing)
-    return init_termination_cache(abstol, reltol, du, u, AbsNormTerminationMode())
+function init_termination_cache(prob::NonlinearProblem, abstol, reltol, du, u, ::Nothing)
+    return init_termination_cache(prob, abstol, reltol, du, u,
+        AbsNormTerminationMode(Base.Fix1(maximum, abs)))
 end
-function init_termination_cache(abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
+function init_termination_cache(
+        prob::NonlinearLeastSquaresProblem, abstol, reltol, du, u, ::Nothing)
+    return init_termination_cache(prob, abstol, reltol, du, u,
+        AbsNormTerminationMode(Base.Fix2(norm, 2)))
+end
+
+function init_termination_cache(
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+        abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
     T = promote_type(eltype(du), eltype(u))
     abstol = __get_tolerance(u, abstol, T)
     reltol = __get_tolerance(u, reltol, T)
-    tc_cache = init(du, u, tc; abstol, reltol)
+    tc_ = if hasfield(typeof(tc), :internalnorm) && tc.internalnorm === nothing
+        internalnorm = ifelse(
+            prob isa NonlinearProblem, Base.Fix1(maximum, abs), Base.Fix2(norm, 2))
+        DiffEqBase.set_termination_mode_internalnorm(tc, internalnorm)
+    else
+        tc
+    end
+    tc_cache = init(du, u, tc_; abstol, reltol, use_deprecated_retcodes = Val(false))
     return DiffEqBase.get_abstol(tc_cache), DiffEqBase.get_reltol(tc_cache), tc_cache
 end
 
@@ -305,45 +321,25 @@ function check_termination(tc_cache, fx, x, xo, prob, alg)
 end
 function check_termination(tc_cache, fx, x, xo, prob, alg,
         ::AbstractNonlinearTerminationMode)
-    if Bool(tc_cache(fx, x, xo))
+    tc_cache(fx, x, xo) &&
         return build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
-    end
     return nothing
 end
 function check_termination(tc_cache, fx, x, xo, prob, alg,
         ::AbstractSafeNonlinearTerminationMode)
-    if Bool(tc_cache(fx, x, xo))
-        if tc_cache.retcode == NonlinearSafeTerminationReturnCode.Success
-            retcode = ReturnCode.Success
-        elseif tc_cache.retcode == NonlinearSafeTerminationReturnCode.PatienceTermination
-            retcode = ReturnCode.ConvergenceFailure
-        elseif tc_cache.retcode == NonlinearSafeTerminationReturnCode.ProtectiveTermination
-            retcode = ReturnCode.Unstable
-        else
-            error("Unknown termination code: $(tc_cache.retcode)")
-        end
-        return build_solution(prob, alg, x, fx; retcode)
-    end
+    tc_cache(fx, x, xo) &&
+        return build_solution(prob, alg, x, fx; retcode = tc_cache.retcode)
     return nothing
 end
 function check_termination(tc_cache, fx, x, xo, prob, alg,
         ::AbstractSafeBestNonlinearTerminationMode)
-    if Bool(tc_cache(fx, x, xo))
-        if tc_cache.retcode == NonlinearSafeTerminationReturnCode.Success
-            retcode = ReturnCode.Success
-        elseif tc_cache.retcode == NonlinearSafeTerminationReturnCode.PatienceTermination
-            retcode = ReturnCode.ConvergenceFailure
-        elseif tc_cache.retcode == NonlinearSafeTerminationReturnCode.ProtectiveTermination
-            retcode = ReturnCode.Unstable
-        else
-            error("Unknown termination code: $(tc_cache.retcode)")
-        end
+    if tc_cache(fx, x, xo)
         if isinplace(prob)
             prob.f(fx, x, prob.p)
         else
             fx = prob.f(x, prob.p)
         end
-        return build_solution(prob, alg, tc_cache.u, fx; retcode)
+        return build_solution(prob, alg, tc_cache.u, fx; retcode = tc_cache.retcode)
     end
     return nothing
 end

From 271156647463086af4c636fe798a12a5514e43c0 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 31 Mar 2024 14:47:08 -0400
Subject: [PATCH 351/700] remove manifest

---
 lib/SimpleNonlinearSolve/Manifest.toml | 781 -------------------------
 lib/SimpleNonlinearSolve/Project.toml  |   6 +-
 2 files changed, 3 insertions(+), 784 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/Manifest.toml

diff --git a/lib/SimpleNonlinearSolve/Manifest.toml b/lib/SimpleNonlinearSolve/Manifest.toml
deleted file mode 100644
index a3a6bb313..000000000
--- a/lib/SimpleNonlinearSolve/Manifest.toml
+++ /dev/null
@@ -1,781 +0,0 @@
-# This file is machine-generated - editing it directly is not advised
-
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-manifest_format = "2.0"
-project_hash = "fb617ddc9060eafbe5e2a53eddeb505916c65ad4"
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-    AccessorsStructArraysExt = "StructArrays"
-    AccessorsUnitfulExt = "Unitful"
-
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-
-[[deps.SuiteSparse_jll]]
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-
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-
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-
-[[deps.nghttp2_jll]]
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-
-[[deps.p7zip_jll]]
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diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index c1065039b..8d279f30e 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -39,13 +39,13 @@ SimpleNonlinearSolveZygoteExt = "Zygote"
 ADTypes = "0.2.6"
 AllocCheck = "0.1.1"
 Aqua = "0.8"
-ArrayInterface = "7.7"
+ArrayInterface = "7.8"
 CUDA = "5.2"
 ChainRulesCore = "1.22"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149"
 DiffResults = "1.1"
-FastClosures = "0.3"
+FastClosures = "0.3.2"
 FiniteDiff = "2.22"
 ForwardDiff = "0.10.36"
 LinearAlgebra = "1.10"
@@ -59,7 +59,7 @@ Random = "1.10"
 ReTestItems = "1.23"
 Reexport = "1.2"
 ReverseDiff = "1.15"
-SciMLBase = "2.26.3"
+SciMLBase = "2.28.0"
 SciMLSensitivity = "7.56"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4.2"

From fb0f1eb87e906da153a6984b6d9075cd697b67aa Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 31 Mar 2024 14:47:30 -0400
Subject: [PATCH 352/700] remove manifest

---
 .github/workflows/Downstream.yml    |    3 +
 Manifest.toml                       | 1062 ---------------------------
 Project.toml                        |   16 +-
 src/core/generalized_first_order.jl |    3 +-
 src/internal/tracing.jl             |    4 +-
 5 files changed, 15 insertions(+), 1073 deletions(-)
 delete mode 100644 Manifest.toml

diff --git a/.github/workflows/Downstream.yml b/.github/workflows/Downstream.yml
index b0c39af7a..f01c9067d 100644
--- a/.github/workflows/Downstream.yml
+++ b/.github/workflows/Downstream.yml
@@ -55,6 +55,9 @@ jobs:
             @info "Not compatible with this release. No problem." exception=err
             exit(0)  # Exit immediately, as a success
           end
+        env:
+          RETESTITEMS_NWORKERS: 4
+          RETESTITEMS_NWORKER_THREADS: 2
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: src,ext
diff --git a/Manifest.toml b/Manifest.toml
deleted file mode 100644
index 030f3f2d1..000000000
--- a/Manifest.toml
+++ /dev/null
@@ -1,1062 +0,0 @@
-# This file is machine-generated - editing it directly is not advised
-
-julia_version = "1.10.2"
-manifest_format = "2.0"
-project_hash = "25f154e3650c19bee7abe4e1b457009a7203eee8"
-
-[[deps.ADTypes]]
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-
-    [deps.Accessors.extensions]
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-    AccessorsIntervalSetsExt = "IntervalSets"
-    AccessorsStaticArraysExt = "StaticArrays"
-    AccessorsStructArraysExt = "StructArrays"
-    AccessorsUnitfulExt = "Unitful"
-
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-    ArrayInterfaceCUDAExt = "CUDA"
-    ArrayInterfaceChainRulesExt = "ChainRules"
-    ArrayInterfaceGPUArraysCoreExt = "GPUArraysCore"
-    ArrayInterfaceReverseDiffExt = "ReverseDiff"
-    ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore"
-    ArrayInterfaceTrackerExt = "Tracker"
-
-    [deps.ArrayInterface.weakdeps]
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-
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diff --git a/Project.toml b/Project.toml
index 9411cc234..c7e57e85b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -58,15 +58,15 @@ NonlinearSolveZygoteExt = "Zygote"
 [compat]
 ADTypes = "0.2.6"
 Aqua = "0.8"
-ArrayInterface = "7.7"
+ArrayInterface = "7.9"
 BandedMatrices = "1.4"
 BenchmarkTools = "1.4"
 ConcreteStructs = "0.2.3"
-CUDA = "5.1"
+CUDA = "5.2"
 DiffEqBase = "6.149.0"
 Enzyme = "0.11.15"
 FastBroadcast = "0.2.8"
-FastClosures = "0.3"
+FastClosures = "0.3.2"
 FastLevenbergMarquardt = "0.1"
 FiniteDiff = "2.21"
 FixedPointAcceleration = "0.3"
@@ -82,21 +82,21 @@ NLsolve = "4.5"
 NLSolvers = "0.5"
 NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
-OrdinaryDiffEq = "6.63"
+OrdinaryDiffEq = "6.74"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 Preferences = "1.4"
 Printf = "1.10"
 Random = "1.91"
 ReTestItems = "1"
-RecursiveArrayTools = "3.4"
+RecursiveArrayTools = "3.8"
 Reexport = "1.2"
 SIAMFANLEquations = "1.0.1"
 SafeTestsets = "0.1"
-SciMLBase = "2.19.0"
+SciMLBase = "2.28.0"
 SimpleNonlinearSolve = "1.2"
 SparseArrays = "1.10"
-SparseDiffTools = "2.14"
+SparseDiffTools = "2.17"
 SpeedMapping = "0.3"
 StableRNGs = "1"
 StaticArrays = "1.7"
@@ -105,7 +105,7 @@ Sundials = "4.23.1"
 Symbolics = "5.13"
 Test = "1.10"
 TimerOutputs = "0.5.23"
-Zygote = "0.6.67"
+Zygote = "0.6.69"
 julia = "1.10"
 
 [extras]
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 2769736ff..5c8c3fbde 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -191,7 +191,8 @@ function SciMLBase.__init(
             GB = :LineSearch
         end
 
-        trace = init_nonlinearsolve_trace(prob, alg, u, fu, ApplyArray(__zero, J), du; kwargs...)
+        trace = init_nonlinearsolve_trace(
+            prob, alg, u, fu, ApplyArray(__zero, J), du; kwargs...)
 
         return GeneralizedFirstOrderAlgorithmCache{iip, GB, maxtime !== nothing}(
             fu, u, u_cache, p, du, J, alg, prob, jac_cache, descent_cache, linesearch_cache,
diff --git a/src/internal/tracing.jl b/src/internal/tracing.jl
index d5edb3a49..75fcaa66a 100644
--- a/src/internal/tracing.jl
+++ b/src/internal/tracing.jl
@@ -107,8 +107,8 @@ end
 function NonlinearSolveTraceEntry(prob::AbstractNonlinearProblem, iteration, fu, δu, J)
     nType = ifelse(prob isa NonlinearLeastSquaresProblem, :L2, :Inf)
     fnorm = prob isa NonlinearLeastSquaresProblem ? norm(fu, 2) : norm(fu, Inf)
-    return NonlinearSolveTraceEntry{nType}(iteration, fnorm, norm(δu, 2),
-        __cond(J), nothing, nothing, nothing, nothing)
+    return NonlinearSolveTraceEntry{nType}(
+        iteration, fnorm, norm(δu, 2), __cond(J), nothing, nothing, nothing, nothing)
 end
 
 function NonlinearSolveTraceEntry(prob::AbstractNonlinearProblem, iteration, fu, δu, J, u)

From 7f3cc72bbcf6b8aa0b8c25d6f0728e739beb457f Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Mon, 1 Apr 2024 21:25:20 +0000
Subject: [PATCH 353/700] Bump julia-actions/setup-julia from 1 to 2

Bumps [julia-actions/setup-julia](https://github.com/julia-actions/setup-julia) from 1 to 2.
- [Release notes](https://github.com/julia-actions/setup-julia/releases)
- [Commits](https://github.com/julia-actions/setup-julia/compare/v1...v2)

---
updated-dependencies:
- dependency-name: julia-actions/setup-julia
  dependency-type: direct:production
  update-type: version-update:semver-major
...

Signed-off-by: dependabot[bot] <support@github.com>
---
 lib/SimpleNonlinearSolve/.github/workflows/CI.yml            | 2 +-
 lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml     | 2 +-
 lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml    | 2 +-
 lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml | 2 +-
 4 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
index 16ec1087c..295de1024 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
@@ -22,7 +22,7 @@ jobs:
           - windows-latest
     steps:
       - uses: actions/checkout@v4
-      - uses: julia-actions/setup-julia@v1
+      - uses: julia-actions/setup-julia@v2
         with:
           version: ${{ matrix.version }}
       - uses: actions/cache@v4
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml
index 0d225bb0b..a991ffbfd 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Downgrade.yml
@@ -18,7 +18,7 @@ jobs:
         version: ['1']
     steps:
       - uses: actions/checkout@v4
-      - uses: julia-actions/setup-julia@v1
+      - uses: julia-actions/setup-julia@v2
         with:
           version: ${{ matrix.version }}
       - uses: julia-actions/julia-downgrade-compat@v1
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
index a3c5003c1..9d509032f 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Downstream.yml
@@ -27,7 +27,7 @@ jobs:
           - {user: SciML, repo: NonlinearSolve.jl, group: All}
     steps:
       - uses: actions/checkout@v4
-      - uses: julia-actions/setup-julia@v1
+      - uses: julia-actions/setup-julia@v2
         with:
           version: ${{ matrix.julia-version }}
           arch: x64
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml b/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml
index 28b9ce2fa..66c86a362 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml
@@ -16,7 +16,7 @@ jobs:
     if: github.base_ref == github.event.repository.default_branch
     runs-on: ubuntu-latest
     steps:
-    - uses: julia-actions/setup-julia@v1
+    - uses: julia-actions/setup-julia@v2
       with:
         version: '1'
     - uses: actions/checkout@v4

From 9ce102175d2d19945ea7b7c50de3ab65d70c4d2f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 2 Apr 2024 11:52:00 -0400
Subject: [PATCH 354/700] pass in linesearch

---
 src/algorithms/gauss_newton.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/algorithms/gauss_newton.jl b/src/algorithms/gauss_newton.jl
index 4e826c130..54b7193fc 100644
--- a/src/algorithms/gauss_newton.jl
+++ b/src/algorithms/gauss_newton.jl
@@ -10,5 +10,5 @@ function GaussNewton(; concrete_jac = nothing, linsolve = nothing, precs = DEFAU
         linesearch = NoLineSearch(), vjp_autodiff = nothing, autodiff = nothing)
     descent = NewtonDescent(; linsolve, precs)
     return GeneralizedFirstOrderAlgorithm(; concrete_jac, name = :GaussNewton, descent,
-        jacobian_ad = autodiff, reverse_ad = vjp_autodiff)
+        jacobian_ad = autodiff, reverse_ad = vjp_autodiff, linesearch)
 end

From 2a35fe444cfbaabcfbbc512dda6352f1d7c2aec6 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 2 Apr 2024 11:52:28 -0400
Subject: [PATCH 355/700] Update Project.toml

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index c7e57e85b..6896c81f6 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.9.0"
+version = "3.9.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From a6f80c64ad5d309efa4bf9e8fee9bca6c0a6287a Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Mon, 8 Apr 2024 02:31:49 +0000
Subject: [PATCH 356/700] Bump julia-actions/setup-julia from 1 to 2

Bumps [julia-actions/setup-julia](https://github.com/julia-actions/setup-julia) from 1 to 2.
- [Release notes](https://github.com/julia-actions/setup-julia/releases)
- [Commits](https://github.com/julia-actions/setup-julia/compare/v1...v2)

---
updated-dependencies:
- dependency-name: julia-actions/setup-julia
  dependency-type: direct:production
  update-type: version-update:semver-major
...

Signed-off-by: dependabot[bot] <support@github.com>
---
 .github/workflows/CI.yml            | 2 +-
 .github/workflows/Downgrade.yml     | 2 +-
 .github/workflows/Downstream.yml    | 2 +-
 .github/workflows/Invalidations.yml | 2 +-
 4 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 3fde89bb4..8c5d965b5 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -27,7 +27,7 @@ jobs:
           - windows-latest
     steps:
       - uses: actions/checkout@v4
-      - uses: julia-actions/setup-julia@v1
+      - uses: julia-actions/setup-julia@v2
         with:
           version: ${{ matrix.version }}
       - uses: actions/cache@v4
diff --git a/.github/workflows/Downgrade.yml b/.github/workflows/Downgrade.yml
index c1b0820f3..3d3c9a2cd 100644
--- a/.github/workflows/Downgrade.yml
+++ b/.github/workflows/Downgrade.yml
@@ -18,7 +18,7 @@ jobs:
         version: ["1"]
     steps:
       - uses: actions/checkout@v4
-      - uses: julia-actions/setup-julia@v1
+      - uses: julia-actions/setup-julia@v2
         with:
           version: ${{ matrix.version }}
       - uses: julia-actions/julia-downgrade-compat@v1
diff --git a/.github/workflows/Downstream.yml b/.github/workflows/Downstream.yml
index f01c9067d..3e5a3e4f5 100644
--- a/.github/workflows/Downstream.yml
+++ b/.github/workflows/Downstream.yml
@@ -28,7 +28,7 @@ jobs:
           - {user: SciML, repo: DiffEqCallbacks.jl, group: All}
     steps:
       - uses: actions/checkout@v4
-      - uses: julia-actions/setup-julia@v1
+      - uses: julia-actions/setup-julia@v2
         with:
           version: ${{ matrix.julia-version }}
           arch: x64
diff --git a/.github/workflows/Invalidations.yml b/.github/workflows/Invalidations.yml
index 28b9ce2fa..66c86a362 100644
--- a/.github/workflows/Invalidations.yml
+++ b/.github/workflows/Invalidations.yml
@@ -16,7 +16,7 @@ jobs:
     if: github.base_ref == github.event.repository.default_branch
     runs-on: ubuntu-latest
     steps:
-    - uses: julia-actions/setup-julia@v1
+    - uses: julia-actions/setup-julia@v2
       with:
         version: '1'
     - uses: actions/checkout@v4

From 67b274e5731fdd69fa7813949c31a9433bf37676 Mon Sep 17 00:00:00 2001
From: Aayush Sabharwal <aayush.sabharwal@juliahub.com>
Date: Mon, 15 Apr 2024 13:11:21 +0530
Subject: [PATCH 357/700] feat: support indexing AbstractNonlinearSolveCache

---
 Project.toml                        | 12 ++++----
 src/NonlinearSolve.jl               |  3 ++
 src/abstract_types.jl               | 21 +++++++++++++
 src/core/generalized_first_order.jl |  5 ++++
 src/default.jl                      |  5 ++++
 test/downstream/Project.toml        |  4 +++
 test/downstream/cache_indexing.jl   | 46 +++++++++++++++++++++++++++++
 test/downstream/downstream_tests.jl | 11 +++++++
 test/runtests.jl                    |  4 +++
 9 files changed, 106 insertions(+), 5 deletions(-)
 create mode 100644 test/downstream/Project.toml
 create mode 100644 test/downstream/cache_indexing.jl
 create mode 100644 test/downstream/downstream_tests.jl

diff --git a/Project.toml b/Project.toml
index 6896c81f6..d95f49aa7 100644
--- a/Project.toml
+++ b/Project.toml
@@ -27,6 +27,7 @@ SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
 TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 
 [weakdeps]
@@ -35,8 +36,8 @@ FastLevenbergMarquardt = "7a0df574-e128-4d35-8cbd-3d84502bf7ce"
 FixedPointAcceleration = "817d07cb-a79a-5c30-9a31-890123675176"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
 MINPACK = "4854310b-de5a-5eb6-a2a5-c1dee2bd17f9"
-NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
+NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
 SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
 Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
@@ -48,8 +49,8 @@ NonlinearSolveFastLevenbergMarquardtExt = "FastLevenbergMarquardt"
 NonlinearSolveFixedPointAccelerationExt = "FixedPointAcceleration"
 NonlinearSolveLeastSquaresOptimExt = "LeastSquaresOptim"
 NonlinearSolveMINPACKExt = "MINPACK"
-NonlinearSolveNLsolveExt = "NLsolve"
 NonlinearSolveNLSolversExt = "NLSolvers"
+NonlinearSolveNLsolveExt = "NLsolve"
 NonlinearSolveSIAMFANLEquationsExt = "SIAMFANLEquations"
 NonlinearSolveSpeedMappingExt = "SpeedMapping"
 NonlinearSolveSymbolicsExt = "Symbolics"
@@ -61,8 +62,8 @@ Aqua = "0.8"
 ArrayInterface = "7.9"
 BandedMatrices = "1.4"
 BenchmarkTools = "1.4"
-ConcreteStructs = "0.2.3"
 CUDA = "5.2"
+ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149.0"
 Enzyme = "0.11.15"
 FastBroadcast = "0.2.8"
@@ -78,8 +79,8 @@ LinearAlgebra = "1.10"
 LinearSolve = "2.21"
 MINPACK = "1.2"
 MaybeInplace = "0.1.1"
-NLsolve = "4.5"
 NLSolvers = "0.5"
+NLsolve = "4.5"
 NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
 OrdinaryDiffEq = "6.74"
@@ -103,6 +104,7 @@ StaticArrays = "1.7"
 StaticArraysCore = "1.4"
 Sundials = "4.23.1"
 Symbolics = "5.13"
+SymbolicIndexingInterface = "0.3.3"
 Test = "1.10"
 TimerOutputs = "0.5.23"
 Zygote = "0.6.69"
@@ -122,8 +124,8 @@ LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 MINPACK = "4854310b-de5a-5eb6-a2a5-c1dee2bd17f9"
-NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
+NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 NaNMath = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
 NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 0cef448d2..ffa792ce9 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -29,6 +29,9 @@ import PrecompileTools: @recompile_invalidations, @compile_workload, @setup_work
                       AbstractSciMLOperator, NLStats, _unwrap_val, has_jac, isinplace
     import SparseDiffTools: AbstractSparsityDetection, AutoSparseEnzyme
     import StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix, MMatrix
+    import SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
+                                      symbolic_container, parameter_values, state_values,
+                                      getu
 end
 
 @reexport using ADTypes, SciMLBase, SimpleNonlinearSolve
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 86dcb963c..c1ee79b20 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -207,6 +207,27 @@ Abstract Type for all NonlinearSolve.jl Caches.
 """
 abstract type AbstractNonlinearSolveCache{iip, timeit} end
 
+function SymbolicIndexingInterface.symbolic_container(cache::AbstractNonlinearSolveCache)
+    cache.prob
+end
+function SymbolicIndexingInterface.parameter_values(cache::AbstractNonlinearSolveCache)
+    parameter_values(symbolic_container(cache))
+end
+function SymbolicIndexingInterface.state_values(cache::AbstractNonlinearSolveCache)
+    state_values(symbolic_container(cache))
+end
+
+function Base.getproperty(cache::AbstractNonlinearSolveCache, sym::Symbol)
+    if sym == :ps
+        return ParameterIndexingProxy(cache)
+    end
+    return getfield(cache, sym)
+end
+
+function Base.getindex(cache::AbstractNonlinearSolveCache, sym)
+    return getu(cache, sym)(cache)
+end
+
 function Base.show(io::IO, cache::AbstractNonlinearSolveCache)
     __show_cache(io, cache, 0)
 end
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 5c8c3fbde..4733e3d3e 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -113,6 +113,11 @@ concrete_jac(::GeneralizedFirstOrderAlgorithm{CJ}) where {CJ} = CJ
     force_stop::Bool
 end
 
+SymbolicIndexingInterface.state_values(cache::GeneralizedFirstOrderAlgorithmCache) = cache.u
+function SymbolicIndexingInterface.parameter_values(cache::GeneralizedFirstOrderAlgorithmCache)
+    cache.p
+end
+
 function __reinit_internal!(
         cache::GeneralizedFirstOrderAlgorithmCache{iip}, args...; p = cache.p, u0 = cache.u,
         alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...) where {iip}
diff --git a/src/default.jl b/src/default.jl
index d32c9ab68..fa8f1f786 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -70,6 +70,11 @@ end
     alias_u0::Bool
 end
 
+function SymbolicIndexingInterface.symbolic_container(cache::NonlinearSolvePolyAlgorithmCache)
+    cache.caches[cache.current]
+end
+SymbolicIndexingInterface.state_values(cache::NonlinearSolvePolyAlgorithmCache) = cache.u0
+
 function Base.show(
         io::IO, cache::NonlinearSolvePolyAlgorithmCache{pType, N}) where {pType, N}
     problem_kind = ifelse(pType == :NLS, "NonlinearProblem", "NonlinearLeastSquaresProblem")
diff --git a/test/downstream/Project.toml b/test/downstream/Project.toml
new file mode 100644
index 000000000..5d5467639
--- /dev/null
+++ b/test/downstream/Project.toml
@@ -0,0 +1,4 @@
+[deps]
+ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
+NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
+SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
diff --git a/test/downstream/cache_indexing.jl b/test/downstream/cache_indexing.jl
new file mode 100644
index 000000000..a7770f32e
--- /dev/null
+++ b/test/downstream/cache_indexing.jl
@@ -0,0 +1,46 @@
+using ModelingToolkit, NonlinearSolve
+using ModelingToolkit: t_nounits as t
+
+@parameters p d
+@variables X(t)
+eqs = [0 ~ sin(X + p) - d * sqrt(X + 1)]
+@mtkbuild nlsys = NonlinearSystem(eqs, [X], [p, d])
+
+# Creates an integrator.
+nlprob = NonlinearProblem(nlsys, [X => 1.0], [p => 2.0, d => 3.0])
+
+@testset "GeneralizedFirstOrderAlgorithmCache" begin
+    nint = init(nlprob, NewtonRaphson())
+    @test nint isa NonlinearSolve.GeneralizedFirstOrderAlgorithmCache
+
+    @test nint[X] == 1.0
+    @test nint[nlsys.X] == 1.0
+    @test nint[:X] == 1.0
+    @test nint.ps[p] == 2.0
+    @test nint.ps[nlsys.p] == 2.0
+    @test nint.ps[:p] == 2.0
+end
+
+@testset "NonlinearSolvePolyAlgorithmCache" begin
+    nint = init(nlprob, FastShortcutNonlinearPolyalg())
+    @test nint isa NonlinearSolve.NonlinearSolvePolyAlgorithmCache
+
+    @test nint[X] == 1.0
+    @test nint[nlsys.X] == 1.0
+    @test nint[:X] == 1.0
+    @test nint.ps[p] == 2.0
+    @test nint.ps[nlsys.p] == 2.0
+    @test nint.ps[:p] == 2.0
+end
+
+@testset "NonlinearSolveNoInitCache" begin
+    nint = init(nlprob, SimpleNewtonRaphson())
+    @test nint isa NonlinearSolve.NonlinearSolveNoInitCache
+
+    @test nint[X] == 1.0
+    @test nint[nlsys.X] == 1.0
+    @test nint[:X] == 1.0
+    @test nint.ps[p] == 2.0
+    @test nint.ps[nlsys.p] == 2.0
+    @test nint.ps[:p] == 2.0
+end
diff --git a/test/downstream/downstream_tests.jl b/test/downstream/downstream_tests.jl
new file mode 100644
index 000000000..773a75815
--- /dev/null
+++ b/test/downstream/downstream_tests.jl
@@ -0,0 +1,11 @@
+using Pkg
+using SafeTestsets
+
+function activate_downstream_env()
+    Pkg.activate("downstream")
+    Pkg.develop(PackageSpec(path = dirname(dirname(@__DIR__))))
+    Pkg.instantiate()
+end
+
+activate_downstream_env()
+@safetestset "Cache indexing test" include("cache_indexing.jl")
diff --git a/test/runtests.jl b/test/runtests.jl
index 014e4cd0e..a3f786689 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -7,6 +7,10 @@ if GROUP == "All" || GROUP == "Core"
         joinpath(@__DIR__, "wrappers/"))
 end
 
+if GROUP == "Downstream"
+    include("downstream/downstream_tests.jl")
+end
+
 if GROUP == "GPU"
     ReTestItems.runtests(joinpath(@__DIR__, "gpu/"))
 end

From b70fbe1e4adb1b3b9710787c6263eb1ae1a54504 Mon Sep 17 00:00:00 2001
From: Aayush Sabharwal <aayush.sabharwal@juliahub.com>
Date: Mon, 15 Apr 2024 13:35:46 +0530
Subject: [PATCH 358/700] ci: add Downstream testset to CI

---
 .github/workflows/CI.yml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 8c5d965b5..2dfaa4f65 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -19,6 +19,7 @@ jobs:
       matrix:
         group:
           - Core
+          - Downstream
         version:
           - "1"
         os:

From 1b501f8d8d00aa0fe328992256e8f3e620f1eddb Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 15 Apr 2024 06:39:37 -0400
Subject: [PATCH 359/700] Update make.jl

---
 docs/make.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/docs/make.jl b/docs/make.jl
index 01b53ce8d..54b7a6424 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -18,7 +18,8 @@ makedocs(; sitename = "NonlinearSolve.jl",
     clean = true,
     doctest = false,
     linkcheck = true,
-    linkcheck_ignore = ["https://twitter.com/ChrisRackauckas/status/1544743542094020615"],
+    linkcheck_ignore = ["https://twitter.com/ChrisRackauckas/status/1544743542094020615",
+                        "https://link.springer.com/article/10.1007/s40096-020-00339-4"],
     checkdocs = :exports,
     warnonly = [:missing_docs],
     plugins = [bib],

From e1d3e8292730debe3542dea073f93f9f1f3bda68 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 15 Apr 2024 07:31:23 -0400
Subject: [PATCH 360/700] Update Project.toml

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index d95f49aa7..f6c2785d3 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.9.1"
+version = "3.10.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 0dc75b495f33c4f49ea509016c862af6dc2e4c31 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 16 Apr 2024 11:27:39 -0400
Subject: [PATCH 361/700] Allow FiniteDiff propagation for scalar problems

---
 Project.toml                     |  2 +-
 docs/make.jl                     |  2 +-
 src/globalization/line_search.jl | 12 +++++++++++-
 src/internal/jacobian.jl         | 23 +++++++++++++++++++----
 src/internal/operators.jl        | 14 ++++++++++----
 test/misc/polyalg_tests.jl       | 21 +++++++++++++++------
 6 files changed, 57 insertions(+), 17 deletions(-)

diff --git a/Project.toml b/Project.toml
index f6c2785d3..99a50b257 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.10.0"
+version = "3.10.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/docs/make.jl b/docs/make.jl
index 54b7a6424..622cebbfe 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -19,7 +19,7 @@ makedocs(; sitename = "NonlinearSolve.jl",
     doctest = false,
     linkcheck = true,
     linkcheck_ignore = ["https://twitter.com/ChrisRackauckas/status/1544743542094020615",
-                        "https://link.springer.com/article/10.1007/s40096-020-00339-4"],
+        "https://link.springer.com/article/10.1007/s40096-020-00339-4"],
     checkdocs = :exports,
     warnonly = [:missing_docs],
     plugins = [bib],
diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index 56bb98cf6..5c76d335a 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -101,7 +101,17 @@ function __internal_init(
         args...; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     T = promote_type(eltype(fu), eltype(u))
     if u isa Number
-        grad_op = @closure (u, fu, p) -> last(__value_derivative(Base.Fix2(f, p), u)) * fu
+        autodiff = get_concrete_forward_ad(alg.autodiff, prob; check_forward_mode = true)
+        if !(autodiff isa AutoForwardDiff ||
+             autodiff isa AutoPolyesterForwardDiff ||
+             autodiff isa AutoFiniteDiff)
+            autodiff = AutoFiniteDiff()
+            # Other cases are not properly supported so we fallback to finite differencing
+            @warn "Scalar AD is supported only for AutoForwardDiff and AutoFiniteDiff. \
+                   Detected $(autodiff). Falling back to AutoFiniteDiff."
+        end
+        grad_op = @closure (u, fu, p) -> last(__value_derivative(
+            autodiff, Base.Fix2(f, p), u)) * fu
     else
         if SciMLBase.has_jvp(f)
             if isinplace(prob)
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 3dfb904ee..221bc5d62 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -97,10 +97,20 @@ function JacobianCache(
         J, f, uf, fu, u, p, jac_cache, alg, 0, autodiff, vjp_autodiff, jvp_autodiff)
 end
 
-function JacobianCache(prob, alg, f::F, ::Number, u::Number, p; kwargs...) where {F}
+function JacobianCache(
+        prob, alg, f::F, ::Number, u::Number, p; autodiff = nothing, kwargs...) where {F}
     uf = JacobianWrapper{false}(f, p)
+    autodiff = get_concrete_forward_ad(autodiff, prob; check_reverse_mode = false)
+    if !(autodiff isa AutoForwardDiff ||
+         autodiff isa AutoPolyesterForwardDiff ||
+         autodiff isa AutoFiniteDiff)
+        autodiff = AutoFiniteDiff()
+        # Other cases are not properly supported so we fallback to finite differencing
+        @warn "Scalar AD is supported only for AutoForwardDiff and AutoFiniteDiff. \
+               Detected $(autodiff). Falling back to AutoFiniteDiff."
+    end
     return JacobianCache{false}(
-        u, f, uf, u, u, p, nothing, alg, 0, nothing, nothing, nothing)
+        u, f, uf, u, u, p, nothing, alg, 0, autodiff, nothing, nothing)
 end
 
 @inline (cache::JacobianCache)(u = cache.u) = cache(cache.J, u, cache.p)
@@ -115,7 +125,7 @@ function (cache::JacobianCache)(J::JacobianOperator, u, p = cache.p)
 end
 function (cache::JacobianCache)(::Number, u, p = cache.p) # Scalar
     cache.njacs += 1
-    J = last(__value_derivative(cache.uf, u))
+    J = last(__value_derivative(cache.autodiff, cache.uf, u))
     return J
 end
 # Compute the Jacobian
@@ -181,12 +191,17 @@ end
     end
 end
 
-@inline function __value_derivative(f::F, x::R) where {F, R}
+@inline function __value_derivative(
+        ::Union{AutoForwardDiff, AutoPolyesterForwardDiff}, f::F, x::R) where {F, R}
     T = typeof(ForwardDiff.Tag(f, R))
     out = f(ForwardDiff.Dual{T}(x, one(x)))
     return ForwardDiff.value(out), ForwardDiff.extract_derivative(T, out)
 end
 
+@inline function __value_derivative(ad::AutoFiniteDiff, f::F, x::R) where {F, R}
+    return f(x), FiniteDiff.finite_difference_derivative(f, x, ad.fdtype)
+end
+
 @inline function __scalar_jacvec(f::F, x::R, v::V) where {F, R, V}
     T = typeof(ForwardDiff.Tag(f, R))
     out = f(ForwardDiff.Dual{T}(x, v))
diff --git a/src/internal/operators.jl b/src/internal/operators.jl
index a34565a9d..0c8737040 100644
--- a/src/internal/operators.jl
+++ b/src/internal/operators.jl
@@ -62,8 +62,11 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
     elseif SciMLBase.has_vjp(f)
         f.vjp
     elseif u isa Number  # Ignore vjp directives
-        if ForwardDiff.can_dual(typeof(u))
-            @closure (v, u, p) -> last(__value_derivative(uf, u)) * v
+        if ForwardDiff.can_dual(typeof(u)) && (vjp_autodiff === nothing ||
+            vjp_autodiff isa AutoForwardDiff ||
+            vjp_autodiff isa AutoPolyesterForwardDiff)
+            # VJP is same as VJP for scalars
+            @closure (v, u, p) -> last(__scalar_jacvec(uf, u, v))
         else
             @closure (v, u, p) -> FiniteDiff.finite_difference_derivative(uf, u) * v
         end
@@ -92,8 +95,11 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
     elseif SciMLBase.has_jvp(f)
         f.jvp
     elseif u isa Number  # Ignore jvp directives
-        if ForwardDiff.can_dual(typeof(u))
-            @closure (v, u, p) -> last(__scalar_jacvec(uf, u, v)) * v
+        # Only ForwardDiff if user didn't override
+        if ForwardDiff.can_dual(typeof(u)) && (jvp_autodiff === nothing ||
+            jvp_autodiff isa AutoForwardDiff ||
+            jvp_autodiff isa AutoPolyesterForwardDiff)
+            @closure (v, u, p) -> last(__scalar_jacvec(uf, u, v))
         else
             @closure (v, u, p) -> FiniteDiff.finite_difference_derivative(uf, u) * v
         end
diff --git a/test/misc/polyalg_tests.jl b/test/misc/polyalg_tests.jl
index 74016d75f..666db02ab 100644
--- a/test/misc/polyalg_tests.jl
+++ b/test/misc/polyalg_tests.jl
@@ -86,13 +86,22 @@ end
     # Uses the `__solve` function
     @test_throws MethodError solve(probN; abstol = 1e-9)
     @test_throws MethodError solve(probN, RobustMultiNewton(); abstol = 1e-9)
-    solver = solve(probN, RobustMultiNewton(; autodiff = AutoFiniteDiff()); abstol = 1e-9)
-    @test SciMLBase.successful_retcode(solver)
-    solver = solve(
+    sol = solve(probN, RobustMultiNewton(; autodiff = AutoFiniteDiff()); abstol = 1e-9)
+    @test SciMLBase.successful_retcode(sol)
+    sol = solve(
         probN, FastShortcutNonlinearPolyalg(; autodiff = AutoFiniteDiff()); abstol = 1e-9)
-    @test SciMLBase.successful_retcode(solver)
-    solver = solve(probN, custom_polyalg; abstol = 1e-9)
-    @test SciMLBase.successful_retcode(solver)
+    @test SciMLBase.successful_retcode(sol)
+    sol = solve(probN, custom_polyalg; abstol = 1e-9)
+    @test SciMLBase.successful_retcode(sol)
+
+    quadratic_f(u::Float64, p) = u^2 - p
+
+    prob = NonlinearProblem(quadratic_f, 2.0, 4.0)
+
+    @test_throws MethodError solve(prob)
+    @test_throws MethodError solve(prob, RobustMultiNewton())
+    sol = solve(prob, RobustMultiNewton(; autodiff = AutoFiniteDiff()))
+    @test SciMLBase.successful_retcode(sol)
 end
 
 @testitem "Simple Scalar Problem #187" begin

From c60a2b6ffce4a8d1219f9a7ad5857941fdf5d096 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 16 Apr 2024 17:33:24 -0400
Subject: [PATCH 362/700] Don't use custom tags

---
 ext/NonlinearSolveNLSolversExt.jl |  2 +-
 src/internal/helpers.jl           | 10 +---------
 src/internal/operators.jl         |  8 ++++----
 3 files changed, 6 insertions(+), 14 deletions(-)

diff --git a/ext/NonlinearSolveNLSolversExt.jl b/ext/NonlinearSolveNLSolversExt.jl
index b480578d0..698bc8465 100644
--- a/ext/NonlinearSolveNLSolversExt.jl
+++ b/ext/NonlinearSolveNLSolversExt.jl
@@ -34,7 +34,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
 
         if autodiff_concrete === :forwarddiff
             fj_scalar = @closure (Jx, x) -> begin
-                T = typeof(NonlinearSolve.NonlinearSolveTag())
+                T = typeof(ForwardDiff.Tag(prob.f, eltype(x)))
                 x_dual = ForwardDiff.Dual{T}(x, one(x))
                 y = prob.f(x_dual, prob.p)
                 return ForwardDiff.value(y), ForwardDiff.extract_derivative(T, y)
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index fc43543ec..fb4af1121 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -30,13 +30,6 @@ function evaluate_f!!(f::NonlinearFunction{iip}, fu, u, p) where {iip}
 end
 
 # AutoDiff Selection Functions
-struct NonlinearSolveTag end
-
-function ForwardDiff.checktag(::Type{<:ForwardDiff.Tag{<:NonlinearSolveTag, <:T}},
-        f::F, x::AbstractArray{T}) where {T, F}
-    return true
-end
-
 function get_concrete_forward_ad(
         autodiff::Union{ADTypes.AbstractForwardMode, ADTypes.AbstractFiniteDifferencesMode},
         prob, sp::Val{test_sparse} = True, args...; kwargs...) where {test_sparse}
@@ -62,8 +55,7 @@ function get_concrete_forward_ad(
     ad = if !ForwardDiff.can_dual(eltype(prob.u0)) # Use Finite Differencing
         use_sparse_ad ? AutoSparseFiniteDiff() : AutoFiniteDiff()
     else
-        tag = ForwardDiff.Tag(NonlinearSolveTag(), eltype(prob.u0))
-        (use_sparse_ad ? AutoSparseForwardDiff : AutoForwardDiff)(; tag)
+        (use_sparse_ad ? AutoSparseForwardDiff : AutoForwardDiff)()
     end
     return ad
 end
diff --git a/src/internal/operators.jl b/src/internal/operators.jl
index 0c8737040..74667dbdb 100644
--- a/src/internal/operators.jl
+++ b/src/internal/operators.jl
@@ -109,10 +109,10 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
         if jvp_autodiff isa AutoForwardDiff || jvp_autodiff isa AutoPolyesterForwardDiff
             if iip
                 # FIXME: Technically we should propagate the tag but ignoring that for now
-                cache1 = Dual{typeof(ForwardDiff.Tag(NonlinearSolveTag(), eltype(u))),
-                    eltype(u), 1}.(similar(u), ForwardDiff.Partials.(tuple.(u)))
-                cache2 = Dual{typeof(ForwardDiff.Tag(NonlinearSolveTag(), eltype(fu))),
-                    eltype(fu), 1}.(similar(fu), ForwardDiff.Partials.(tuple.(fu)))
+                cache1 = Dual{typeof(ForwardDiff.Tag(uf, eltype(u))), eltype(u),
+                    1}.(similar(u), ForwardDiff.Partials.(tuple.(u)))
+                cache2 = Dual{typeof(ForwardDiff.Tag(uf, eltype(fu))), eltype(fu),
+                    1}.(similar(fu), ForwardDiff.Partials.(tuple.(fu)))
                 @closure (Jv, v, u, p) -> auto_jacvec!(Jv, uf, u, v, cache1, cache2)
             else
                 @closure (v, u, p) -> auto_jacvec(uf, u, v)

From abf1a2fd718d75a20572211869e1d7e1aee6145b Mon Sep 17 00:00:00 2001
From: CompatHelper Julia <compathelper_noreply@julialang.org>
Date: Fri, 19 Apr 2024 22:04:48 +0000
Subject: [PATCH 363/700] CompatHelper: bump compat for ADTypes to 1, (keep
 existing compat)

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 8d279f30e..c601ac6b0 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -36,7 +36,7 @@ SimpleNonlinearSolveTrackerExt = "Tracker"
 SimpleNonlinearSolveZygoteExt = "Zygote"
 
 [compat]
-ADTypes = "0.2.6"
+ADTypes = "0.2.6, 1"
 AllocCheck = "0.1.1"
 Aqua = "0.8"
 ArrayInterface = "7.8"

From f2f50354bbd5d5fef7be2e281de7f17b0bd43a06 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 23 Apr 2024 14:33:13 -0400
Subject: [PATCH 364/700] Add a result type for Descent Algorithms

---
 Project.toml                         |  4 ++--
 src/NonlinearSolve.jl                |  1 +
 src/abstract_types.jl                |  9 ++-------
 src/core/approximate_jacobian.jl     |  7 ++++---
 src/core/generalized_first_order.jl  |  7 ++++---
 src/descent/common.jl                | 26 ++++++++++++++++++++++++++
 src/descent/damped_newton.jl         |  4 ++--
 src/descent/dogleg.jl                |  6 +++---
 src/descent/geodesic_acceleration.jl |  4 ++--
 src/descent/newton.jl                |  8 ++++----
 src/descent/steepest.jl              |  2 +-
 11 files changed, 51 insertions(+), 27 deletions(-)
 create mode 100644 src/descent/common.jl

diff --git a/Project.toml b/Project.toml
index 99a50b257..f5e8d10ac 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.10.1"
+version = "3.11.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -76,7 +76,7 @@ LazyArrays = "1.8.2"
 LeastSquaresOptim = "0.8.5"
 LineSearches = "7.2"
 LinearAlgebra = "1.10"
-LinearSolve = "2.21"
+LinearSolve = "2.29"
 MINPACK = "1.2"
 MaybeInplace = "0.1.1"
 NLSolvers = "0.5"
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index ffa792ce9..9261f259f 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -50,6 +50,7 @@ include("adtypes.jl")
 include("timer_outputs.jl")
 include("internal/helpers.jl")
 
+include("descent/common.jl")
 include("descent/newton.jl")
 include("descent/steepest.jl")
 include("descent/dogleg.jl")
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index c1ee79b20..c5e5d990b 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -66,7 +66,7 @@ Abstract Type for all Descent Caches.
 ### `__internal_solve!` specification
 
 ```julia
-δu, success, intermediates = __internal_solve!(
+descent_result = __internal_solve!(
     cache::AbstractDescentCache, J, fu, u, idx::Val; skip_solve::Bool = false, kwargs...)
 ```
 
@@ -81,12 +81,7 @@ Abstract Type for all Descent Caches.
 
 #### Returned values
 
-  - `δu`: the descent direction.
-  - `success`: Certain Descent Algorithms can reject a descent direction for example
-    `GeodesicAcceleration`.
-  - `intermediates`: A named tuple containing intermediates computed during the solve.
-    For example, `GeodesicAcceleration` returns `NamedTuple{(:v, :a)}` containing the
-    "velocity" and "acceleration" terms.
+  - `descent_result`: Result in a [`DescentResult`](@ref).
 
 ### Interface Functions
 
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index d5329f1c8..6e8f93ba6 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -282,16 +282,17 @@ function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
     @static_timeit cache.timer "descent" begin
         if cache.trustregion_cache !== nothing &&
            hasfield(typeof(cache.trustregion_cache), :trust_region)
-            δu, descent_success, descent_intermediates = __internal_solve!(
+            descent_result = __internal_solve!(
                 cache.descent_cache, J, cache.fu, cache.u; new_jacobian,
                 trust_region = cache.trustregion_cache.trust_region)
         else
-            δu, descent_success, descent_intermediates = __internal_solve!(
+            descent_result = __internal_solve!(
                 cache.descent_cache, J, cache.fu, cache.u; new_jacobian)
         end
     end
+    δu, descent_intermediates = descent_result.δu, descent_result.extras
 
-    if descent_success
+    if descent_result.success
         if GB === :LineSearch
             @static_timeit cache.timer "linesearch" begin
                 needs_reset, α = __internal_solve!(cache.linesearch_cache, cache.u, δu)
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 4733e3d3e..710787840 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -221,16 +221,17 @@ function __step!(cache::GeneralizedFirstOrderAlgorithmCache{iip, GB};
     @static_timeit cache.timer "descent" begin
         if cache.trustregion_cache !== nothing &&
            hasfield(typeof(cache.trustregion_cache), :trust_region)
-            δu, descent_success, descent_intermediates = __internal_solve!(
+            descent_result = __internal_solve!(
                 cache.descent_cache, J, cache.fu, cache.u; new_jacobian,
                 trust_region = cache.trustregion_cache.trust_region)
         else
-            δu, descent_success, descent_intermediates = __internal_solve!(
+            descent_result = __internal_solve!(
                 cache.descent_cache, J, cache.fu, cache.u; new_jacobian)
         end
     end
+    δu, descent_intermediates = descent_result.δu, descent_result.extras
 
-    if descent_success
+    if descent_result.success
         cache.make_new_jacobian = true
         if GB === :LineSearch
             @static_timeit cache.timer "linesearch" begin
diff --git a/src/descent/common.jl b/src/descent/common.jl
new file mode 100644
index 000000000..2a614d84a
--- /dev/null
+++ b/src/descent/common.jl
@@ -0,0 +1,26 @@
+"""
+    DescentResult(; δu = missing, u = missing, success::Bool = true, extras = (;))
+
+Construct a `DescentResult` object.
+
+### Keyword Arguments
+
+  - `δu`: The descent direction.
+  - `u`: The new iterate. This is provided only for multi-step methods currently.
+  - `success`: Certain Descent Algorithms can reject a descent direction for example
+    [`GeodesicAcceleration`](@ref).
+  - `extras`: A named tuple containing intermediates computed during the solve.
+    For example, [`GeodesicAcceleration`](@ref) returns `NamedTuple{(:v, :a)}` containing
+    the "velocity" and "acceleration" terms.
+"""
+@concrete struct DescentResult
+    δu
+    u
+    success::Bool
+    extras
+end
+
+function DescentResult(; δu = missing, u = missing, success::Bool = true, extras = (;))
+    @assert δu !== missing || u !== missing
+    return DescentResult(δu, u, success, extras)
+end
diff --git a/src/descent/damped_newton.jl b/src/descent/damped_newton.jl
index 3e21cc2d1..aaabc6c4e 100644
--- a/src/descent/damped_newton.jl
+++ b/src/descent/damped_newton.jl
@@ -135,7 +135,7 @@ function __internal_solve!(cache::DampedNewtonDescentCache{INV, mode}, J, fu,
         u, idx::Val{N} = Val(1); skip_solve::Bool = false,
         new_jacobian::Bool = true, kwargs...) where {INV, N, mode}
     δu = get_du(cache, idx)
-    skip_solve && return δu, true, (;)
+    skip_solve && return DescentResult(; δu)
 
     recompute_A = idx === Val(1)
 
@@ -208,7 +208,7 @@ function __internal_solve!(cache::DampedNewtonDescentCache{INV, mode}, J, fu,
 
     @bb @. δu *= -1
     set_du!(cache, δu, idx)
-    return δu, true, (;)
+    return DescentResult(; δu)
 end
 
 # Define special concatenation for certain Array combinations
diff --git a/src/descent/dogleg.jl b/src/descent/dogleg.jl
index ee725988b..f3e1d9cc0 100644
--- a/src/descent/dogleg.jl
+++ b/src/descent/dogleg.jl
@@ -88,7 +88,7 @@ function __internal_solve!(cache::DoglegCache{INV, NF}, J, fu, u, idx::Val{N} =
     if cache.internalnorm(δu_newton) ≤ trust_region
         @bb copyto!(δu, δu_newton)
         set_du!(cache, δu, idx)
-        return δu, true, (; δuJᵀJδu = T(NaN))
+        return DescentResult(; δu, extras = (; δuJᵀJδu = T(NaN)))
     end
 
     # Take intersection of steepest descent direction and trust region if Cauchy point lies
@@ -115,7 +115,7 @@ function __internal_solve!(cache::DoglegCache{INV, NF}, J, fu, u, idx::Val{N} =
         λ = trust_region / l_grad
         @bb @. δu = λ * δu_cauchy
         set_du!(cache, δu, idx)
-        return δu, true, (; δuJᵀJδu = λ^2 * δuJᵀJδu)
+        return DescentResult(; δu, extras = (; δuJᵀJδu = λ^2 * δuJᵀJδu))
     end
 
     # FIXME: For anything other than 2-norm a quadratic root will give incorrect results
@@ -133,5 +133,5 @@ function __internal_solve!(cache::DoglegCache{INV, NF}, J, fu, u, idx::Val{N} =
 
     @bb @. δu = cache.δu_cache_1 + τ * cache.δu_cache_2
     set_du!(cache, δu, idx)
-    return δu, true, (; δuJᵀJδu = T(NaN))
+    return DescentResult(; δu, extras = (; δuJᵀJδu = T(NaN)))
 end
diff --git a/src/descent/geodesic_acceleration.jl b/src/descent/geodesic_acceleration.jl
index 6cba1202e..d72cd2828 100644
--- a/src/descent/geodesic_acceleration.jl
+++ b/src/descent/geodesic_acceleration.jl
@@ -105,7 +105,7 @@ end
 function __internal_solve!(cache::GeodesicAccelerationCache, J, fu, u, idx::Val{N} = Val(1);
         skip_solve::Bool = false, kwargs...) where {N}
     a, v, δu = get_acceleration(cache, idx), get_velocity(cache, idx), get_du(cache, idx)
-    skip_solve && return δu, true, (; a, v)
+    skip_solve && return DescentResult(; δu, extras = (; a, v))
     v, _, _ = __internal_solve!(
         cache.descent_cache, J, fu, u, Val(2N - 1); skip_solve, kwargs...)
 
@@ -130,5 +130,5 @@ function __internal_solve!(cache::GeodesicAccelerationCache, J, fu, u, idx::Val{
         cache.last_step_accepted = false
     end
 
-    return δu, cache.last_step_accepted, (; a, v)
+    return DescentResult(; δu, success = cache.last_step_accepted, extras = (; a, v))
 end
diff --git a/src/descent/newton.jl b/src/descent/newton.jl
index e79120a5e..bcb83686f 100644
--- a/src/descent/newton.jl
+++ b/src/descent/newton.jl
@@ -75,7 +75,7 @@ function __internal_solve!(
         cache::NewtonDescentCache{INV, false}, J, fu, u, idx::Val = Val(1);
         skip_solve::Bool = false, new_jacobian::Bool = true, kwargs...) where {INV}
     δu = get_du(cache, idx)
-    skip_solve && return δu, true, (;)
+    skip_solve && return DescentResult(; δu)
     if INV
         @assert J!==nothing "`J` must be provided when `pre_inverted = Val(true)`."
         @bb δu = J × vec(fu)
@@ -89,14 +89,14 @@ function __internal_solve!(
     end
     @bb @. δu *= -1
     set_du!(cache, δu, idx)
-    return δu, true, (;)
+    return DescentResult(; δu)
 end
 
 function __internal_solve!(
         cache::NewtonDescentCache{false, true}, J, fu, u, idx::Val = Val(1);
         skip_solve::Bool = false, new_jacobian::Bool = true, kwargs...)
     δu = get_du(cache, idx)
-    skip_solve && return δu, true, (;)
+    skip_solve && return DescentResult(; δu)
     if idx === Val(1)
         @bb cache.JᵀJ_cache = transpose(J) × J
     end
@@ -109,5 +109,5 @@ function __internal_solve!(
     end
     @bb @. δu *= -1
     set_du!(cache, δu, idx)
-    return δu, true, (;)
+    return DescentResult(; δu)
 end
diff --git a/src/descent/steepest.jl b/src/descent/steepest.jl
index 40919cc6e..4d4877a1b 100644
--- a/src/descent/steepest.jl
+++ b/src/descent/steepest.jl
@@ -65,5 +65,5 @@ function __internal_solve!(cache::SteepestDescentCache{INV}, J, fu, u, idx::Val
     end
     @bb @. δu *= -1
     set_du!(cache, δu, idx)
-    return δu, true, (;)
+    return DescentResult(; δu)
 end

From bcb98c5eeb5c3b7bfadbe36ed3850ed6ae07c12f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 23 Apr 2024 16:06:19 -0400
Subject: [PATCH 365/700] Switch to QR Pivoted on linear solve failure

---
 src/descent/dogleg.jl                |  8 ++---
 src/descent/geodesic_acceleration.jl |  8 ++---
 src/internal/linear_solve.jl         | 48 ++++++++++++++++++++++++++--
 3 files changed, 54 insertions(+), 10 deletions(-)

diff --git a/src/descent/dogleg.jl b/src/descent/dogleg.jl
index f3e1d9cc0..5d0bb1c7c 100644
--- a/src/descent/dogleg.jl
+++ b/src/descent/dogleg.jl
@@ -81,8 +81,8 @@ function __internal_solve!(cache::DoglegCache{INV, NF}, J, fu, u, idx::Val{N} =
                                     want to use a Trust Region."
     δu = get_du(cache, idx)
     T = promote_type(eltype(u), eltype(fu))
-    δu_newton, _, _ = __internal_solve!(
-        cache.newton_cache, J, fu, u, idx; skip_solve, kwargs...)
+    δu_newton = __internal_solve!(
+        cache.newton_cache, J, fu, u, idx; skip_solve, kwargs...).δu
 
     # Newton's Step within the trust region
     if cache.internalnorm(δu_newton) ≤ trust_region
@@ -102,8 +102,8 @@ function __internal_solve!(cache::DoglegCache{INV, NF}, J, fu, u, idx::Val{N} =
         @bb cache.δu_cache_mul = JᵀJ × vec(δu_cauchy)
         δuJᵀJδu = __dot(δu_cauchy, cache.δu_cache_mul)
     else
-        δu_cauchy, _, _ = __internal_solve!(
-            cache.cauchy_cache, J, fu, u, idx; skip_solve, kwargs...)
+        δu_cauchy = __internal_solve!(
+            cache.cauchy_cache, J, fu, u, idx; skip_solve, kwargs...).δu
         J_ = INV ? inv(J) : J
         l_grad = cache.internalnorm(δu_cauchy)
         @bb cache.JᵀJ_cache = J × vec(δu_cauchy)  # TODO: Rename
diff --git a/src/descent/geodesic_acceleration.jl b/src/descent/geodesic_acceleration.jl
index d72cd2828..e2d8612e5 100644
--- a/src/descent/geodesic_acceleration.jl
+++ b/src/descent/geodesic_acceleration.jl
@@ -106,8 +106,8 @@ function __internal_solve!(cache::GeodesicAccelerationCache, J, fu, u, idx::Val{
         skip_solve::Bool = false, kwargs...) where {N}
     a, v, δu = get_acceleration(cache, idx), get_velocity(cache, idx), get_du(cache, idx)
     skip_solve && return DescentResult(; δu, extras = (; a, v))
-    v, _, _ = __internal_solve!(
-        cache.descent_cache, J, fu, u, Val(2N - 1); skip_solve, kwargs...)
+    v = __internal_solve!(
+        cache.descent_cache, J, fu, u, Val(2N - 1); skip_solve, kwargs...).δu
 
     @bb @. cache.u_cache = u + cache.h * v
     cache.fu_cache = evaluate_f!!(cache.f, cache.fu_cache, cache.u_cache, cache.p)
@@ -116,8 +116,8 @@ function __internal_solve!(cache::GeodesicAccelerationCache, J, fu, u, idx::Val{
     Jv = _restructure(cache.fu_cache, cache.Jv)
     @bb @. cache.fu_cache = (2 / cache.h) * ((cache.fu_cache - fu) / cache.h - Jv)
 
-    a, _, _ = __internal_solve!(cache.descent_cache, J, cache.fu_cache, u, Val(2N);
-        skip_solve, kwargs..., reuse_A_if_factorization = true)
+    a = __internal_solve!(cache.descent_cache, J, cache.fu_cache, u, Val(2N);
+        skip_solve, kwargs..., reuse_A_if_factorization = true).δu
 
     norm_v = cache.internalnorm(v)
     norm_a = cache.internalnorm(a)
diff --git a/src/internal/linear_solve.jl b/src/internal/linear_solve.jl
index 261d9e8dc..36d8f1928 100644
--- a/src/internal/linear_solve.jl
+++ b/src/internal/linear_solve.jl
@@ -1,5 +1,8 @@
 import LinearSolve: AbstractFactorization, DefaultAlgorithmChoice, DefaultLinearSolver
 
+const LinearSolveFailureCode = isdefined(ReturnCode, :InternalLinearSolveFailure) ?
+                               ReturnCode.InternalLinearSolveFailure : ReturnCode.Failure
+
 """
     LinearSolverCache(alg, linsolve, A, b, u; kwargs...)
 
@@ -23,6 +26,15 @@ handled:
 
 Returns the solution of the system `u` and stores the updated cache in `cache.lincache`.
 
+#### Special Handling for Rank-deficient Matrix `A`
+
+If we detect a failure in the linear solve (mostly due to using an algorithm that doesn't
+support rank-deficient matrices), we emit a warning and attempt to solve the problem using
+Pivoted QR factorization. This is quite efficient if there are only a few rank-deficient
+that originate in the problem. However, if these are quite frequent for the main nonlinear
+system, then it is recommended to use a different linear solver that supports rank-deficient
+matrices.
+
 #### Keyword Arguments
 
   - `reuse_A_if_factorization`: If `true`, then the factorization of `A` is reused if
@@ -36,6 +48,7 @@ not mutated, we do this by copying over `A` to a preconstructed cache.
 @concrete mutable struct LinearSolverCache <: AbstractLinearSolverCache
     lincache
     linsolve
+    additional_lincache::Any
     A
     b
     precs
@@ -71,7 +84,7 @@ function LinearSolverCache(alg, linsolve, A, b, u; kwargs...)
        (linsolve === nothing && A isa SMatrix) ||
        (A isa Diagonal) ||
        (linsolve isa typeof(\))
-        return LinearSolverCache(nothing, nothing, A, b, nothing, 0, 0)
+        return LinearSolverCache(nothing, nothing, nothing, A, b, nothing, 0, 0)
     end
     @bb u_ = copy(u_fixed)
     linprob = LinearProblem(A, b; u0 = u_, kwargs...)
@@ -89,7 +102,7 @@ function LinearSolverCache(alg, linsolve, A, b, u; kwargs...)
     # Unalias here, we will later use these as caches
     lincache = init(linprob, linsolve; alias_A = false, alias_b = false, Pl, Pr)
 
-    return LinearSolverCache(lincache, linsolve, nothing, nothing, precs, 0, 0)
+    return LinearSolverCache(lincache, linsolve, nothing, nothing, nothing, precs, 0, 0)
 end
 
 # Direct Linear Solve Case without Caching
@@ -108,6 +121,7 @@ function (cache::LinearSolverCache{Nothing})(;
     end
     return res
 end
+
 # Use LinearSolve.jl
 function (cache::LinearSolverCache)(;
         A = nothing, b = nothing, linu = nothing, du = nothing, p = nothing,
@@ -139,8 +153,38 @@ function (cache::LinearSolverCache)(;
         cache.lincache.Pr = Pr
     end
 
+    # display(A)
+
     linres = solve!(cache.lincache)
+    # @show cache.lincache.cacheval
+    # @show LinearAlgebra.issuccess(cache.lincache.cacheval)
     cache.lincache = linres.cache
+    # Unfortunately LinearSolve.jl doesn't have the most uniform ReturnCode handling
+    if linres.retcode === ReturnCode.Failure
+        # TODO: We need to guard this somehow because this will surely fail if A is on GPU
+        # TODO: or some fancy Matrix type
+        if !(cache.linsolve isa QRFactorization{ColumnNorm})
+            @warn "Potential Rank Deficient Matrix Detected. Attempting to solve using \
+                   Pivoted QR Factorization."
+            @assert (A !== nothing)&&(b !== nothing) "This case is not yet supported. \
+                                                      Please open an issue at \
+                                                      https://github.com/SciML/NonlinearSolve.jl"
+            if cache.additional_lincache === nothing # First time
+                linprob = LinearProblem(A, b; u0 = linres.u)
+                cache.additional_lincache = init(
+                    linprob, QRFactorization(ColumnNorm()); alias_u0 = false,
+                    alias_A = false, alias_b = false, cache.lincache.Pl, cache.lincache.Pr)
+            else
+                cache.additional_lincache.A = A
+                cache.additional_lincache.b = b
+                cache.additional_lincache.Pl = cache.lincache.Pl
+                cache.additional_lincache.Pr = cache.lincache.Pr
+            end
+            linres = solve!(cache.additional_lincache)
+            cache.additional_lincache = linres.cache
+            return linres.u
+        end
+    end
 
     return linres.u
 end

From dc539b975dd9dd1d8e5c75f91fe793bb004a5cb1 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 25 Apr 2024 16:21:48 -0400
Subject: [PATCH 366/700] Propagate the verbose kwarg

---
 src/NonlinearSolve.jl               | 4 ++--
 src/core/approximate_jacobian.jl    | 7 ++++---
 src/core/generalized_first_order.jl | 7 ++++---
 src/core/spectral_methods.jl        | 3 ++-
 src/internal/linear_solve.jl        | 9 ++++++---
 5 files changed, 18 insertions(+), 12 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 9261f259f..9b6b9ec04 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -136,10 +136,10 @@ include("default.jl")
 
     @compile_workload begin
         for prob in probs_nls, alg in nls_algs
-            solve(prob, alg; abstol = 1e-2)
+            solve(prob, alg; abstol = 1e-2, verbose = false)
         end
         for prob in probs_nlls, alg in nlls_algs
-            solve(prob, alg; abstol = 1e-2)
+            solve(prob, alg; abstol = 1e-2, verbose = false)
         end
     end
 end
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index 6e8f93ba6..ac649a107 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -114,6 +114,7 @@ end
     retcode::ReturnCode.T
     force_stop::Bool
     force_reinit::Bool
+    kwargs
 end
 
 store_inverse_jacobian(::ApproximateJacobianSolveCache{INV}) where {INV} = INV
@@ -214,7 +215,7 @@ function SciMLBase.__init(
             descent_cache, linesearch_cache, trustregion_cache,
             update_rule_cache, reinit_rule_cache, inv_workspace, 0, 0, 0,
             alg.max_resets, maxiters, maxtime, alg.max_shrink_times, 0, timer,
-            0.0, termination_cache, trace, ReturnCode.Default, false, false)
+            0.0, termination_cache, trace, ReturnCode.Default, false, false, kwargs)
     end
 end
 
@@ -284,10 +285,10 @@ function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
            hasfield(typeof(cache.trustregion_cache), :trust_region)
             descent_result = __internal_solve!(
                 cache.descent_cache, J, cache.fu, cache.u; new_jacobian,
-                trust_region = cache.trustregion_cache.trust_region)
+                trust_region = cache.trustregion_cache.trust_region, cache.kwargs...)
         else
             descent_result = __internal_solve!(
-                cache.descent_cache, J, cache.fu, cache.u; new_jacobian)
+                cache.descent_cache, J, cache.fu, cache.u; new_jacobian, cache.kwargs...)
         end
     end
     δu, descent_intermediates = descent_result.δu, descent_result.extras
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 710787840..e3a4b8941 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -111,6 +111,7 @@ concrete_jac(::GeneralizedFirstOrderAlgorithm{CJ}) where {CJ} = CJ
     trace
     retcode::ReturnCode.T
     force_stop::Bool
+    kwargs
 end
 
 SymbolicIndexingInterface.state_values(cache::GeneralizedFirstOrderAlgorithmCache) = cache.u
@@ -202,7 +203,7 @@ function SciMLBase.__init(
         return GeneralizedFirstOrderAlgorithmCache{iip, GB, maxtime !== nothing}(
             fu, u, u_cache, p, du, J, alg, prob, jac_cache, descent_cache, linesearch_cache,
             trustregion_cache, 0, 0, maxiters, maxtime, alg.max_shrink_times,
-            timer, 0.0, true, termination_cache, trace, ReturnCode.Default, false)
+            timer, 0.0, true, termination_cache, trace, ReturnCode.Default, false, kwargs)
     end
 end
 
@@ -223,10 +224,10 @@ function __step!(cache::GeneralizedFirstOrderAlgorithmCache{iip, GB};
            hasfield(typeof(cache.trustregion_cache), :trust_region)
             descent_result = __internal_solve!(
                 cache.descent_cache, J, cache.fu, cache.u; new_jacobian,
-                trust_region = cache.trustregion_cache.trust_region)
+                trust_region = cache.trustregion_cache.trust_region, cache.kwargs...)
         else
             descent_result = __internal_solve!(
-                cache.descent_cache, J, cache.fu, cache.u; new_jacobian)
+                cache.descent_cache, J, cache.fu, cache.u; new_jacobian, cache.kwargs...)
         end
     end
     δu, descent_intermediates = descent_result.δu, descent_result.extras
diff --git a/src/core/spectral_methods.jl b/src/core/spectral_methods.jl
index d9d271d78..3d9a03e50 100644
--- a/src/core/spectral_methods.jl
+++ b/src/core/spectral_methods.jl
@@ -74,6 +74,7 @@ concrete_jac(::GeneralizedDFSane) = nothing
     trace
     retcode::ReturnCode.T
     force_stop::Bool
+    kwargs
 end
 
 function __reinit_internal!(
@@ -150,7 +151,7 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane
         return GeneralizedDFSaneCache{isinplace(prob), maxtime !== nothing}(
             fu, fu_cache, u, u_cache, prob.p, du, alg, prob, σ_n, T(alg.σ_min),
             T(alg.σ_max), linesearch_cache, 0, 0, maxiters, maxtime,
-            timer, 0.0, tc_cache, trace, ReturnCode.Default, false)
+            timer, 0.0, tc_cache, trace, ReturnCode.Default, false, kwargs)
     end
 end
 
diff --git a/src/internal/linear_solve.jl b/src/internal/linear_solve.jl
index 36d8f1928..909950a07 100644
--- a/src/internal/linear_solve.jl
+++ b/src/internal/linear_solve.jl
@@ -125,7 +125,8 @@ end
 # Use LinearSolve.jl
 function (cache::LinearSolverCache)(;
         A = nothing, b = nothing, linu = nothing, du = nothing, p = nothing,
-        weight = nothing, cachedata = nothing, reuse_A_if_factorization = false, kwargs...)
+        weight = nothing, cachedata = nothing, reuse_A_if_factorization = false, 
+        verbose = true, kwargs...)
     cache.nsolve += 1
 
     __update_A!(cache, A, reuse_A_if_factorization)
@@ -164,8 +165,10 @@ function (cache::LinearSolverCache)(;
         # TODO: We need to guard this somehow because this will surely fail if A is on GPU
         # TODO: or some fancy Matrix type
         if !(cache.linsolve isa QRFactorization{ColumnNorm})
-            @warn "Potential Rank Deficient Matrix Detected. Attempting to solve using \
-                   Pivoted QR Factorization."
+            if verbose
+                @warn "Potential Rank Deficient Matrix Detected. Attempting to solve using \
+                       Pivoted QR Factorization."
+            end
             @assert (A !== nothing)&&(b !== nothing) "This case is not yet supported. \
                                                       Please open an issue at \
                                                       https://github.com/SciML/NonlinearSolve.jl"

From dd4a2fbd21b214e0f1750e087e3a87fdcfe5cb1b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 25 Apr 2024 16:23:07 -0400
Subject: [PATCH 367/700] Add to docs

---
 Project.toml                            | 2 +-
 docs/src/devdocs/internal_interfaces.md | 6 ++++++
 src/core/approximate_jacobian.jl        | 8 ++++----
 src/core/generalized_first_order.jl     | 4 ++--
 src/internal/linear_solve.jl            | 6 +++---
 5 files changed, 16 insertions(+), 10 deletions(-)

diff --git a/Project.toml b/Project.toml
index f5e8d10ac..e9fab016e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -60,7 +60,7 @@ NonlinearSolveZygoteExt = "Zygote"
 ADTypes = "0.2.6"
 Aqua = "0.8"
 ArrayInterface = "7.9"
-BandedMatrices = "1.4"
+BandedMatrices = "1.5"
 BenchmarkTools = "1.4"
 CUDA = "5.2"
 ConcreteStructs = "0.2.3"
diff --git a/docs/src/devdocs/internal_interfaces.md b/docs/src/devdocs/internal_interfaces.md
index 843054cc8..91b9562a8 100644
--- a/docs/src/devdocs/internal_interfaces.md
+++ b/docs/src/devdocs/internal_interfaces.md
@@ -15,6 +15,12 @@ NonlinearSolve.AbstractDescentAlgorithm
 NonlinearSolve.AbstractDescentCache
 ```
 
+## Descent Results
+
+```@docs
+NonlinearSolve.DescentResult
+```
+
 ## Approximate Jacobian
 
 ```@docs
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index ac649a107..e5e6960e2 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -212,10 +212,10 @@ function SciMLBase.__init(
 
         return ApproximateJacobianSolveCache{INV, GB, iip, maxtime !== nothing}(
             fu, u, u_cache, p, du, J, alg, prob, initialization_cache,
-            descent_cache, linesearch_cache, trustregion_cache,
-            update_rule_cache, reinit_rule_cache, inv_workspace, 0, 0, 0,
-            alg.max_resets, maxiters, maxtime, alg.max_shrink_times, 0, timer,
-            0.0, termination_cache, trace, ReturnCode.Default, false, false, kwargs)
+            descent_cache, linesearch_cache, trustregion_cache, update_rule_cache,
+            reinit_rule_cache, inv_workspace, 0, 0, 0, alg.max_resets,
+            maxiters, maxtime, alg.max_shrink_times, 0, timer, 0.0,
+            termination_cache, trace, ReturnCode.Default, false, false, kwargs)
     end
 end
 
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index e3a4b8941..fd1eb5b3f 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -202,8 +202,8 @@ function SciMLBase.__init(
 
         return GeneralizedFirstOrderAlgorithmCache{iip, GB, maxtime !== nothing}(
             fu, u, u_cache, p, du, J, alg, prob, jac_cache, descent_cache, linesearch_cache,
-            trustregion_cache, 0, 0, maxiters, maxtime, alg.max_shrink_times,
-            timer, 0.0, true, termination_cache, trace, ReturnCode.Default, false, kwargs)
+            trustregion_cache, 0, 0, maxiters, maxtime, alg.max_shrink_times, timer,
+            0.0, true, termination_cache, trace, ReturnCode.Default, false, kwargs)
     end
 end
 
diff --git a/src/internal/linear_solve.jl b/src/internal/linear_solve.jl
index 909950a07..080de05ef 100644
--- a/src/internal/linear_solve.jl
+++ b/src/internal/linear_solve.jl
@@ -124,9 +124,9 @@ end
 
 # Use LinearSolve.jl
 function (cache::LinearSolverCache)(;
-        A = nothing, b = nothing, linu = nothing, du = nothing, p = nothing,
-        weight = nothing, cachedata = nothing, reuse_A_if_factorization = false, 
-        verbose = true, kwargs...)
+        A = nothing, b = nothing, linu = nothing, du = nothing,
+        p = nothing, weight = nothing, cachedata = nothing,
+        reuse_A_if_factorization = false, verbose = true, kwargs...)
     cache.nsolve += 1
 
     __update_A!(cache, A, reuse_A_if_factorization)

From 74505908e7fb1dc0d54717dd858859c24c6e0d46 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 25 Apr 2024 17:20:47 -0400
Subject: [PATCH 368/700] Integrate the linear solve better into the algorithm

---
 src/core/approximate_jacobian.jl    | 21 +++++++++++++++++++++
 src/core/generalized_first_order.jl | 21 +++++++++++++++++++++
 src/descent/common.jl               | 10 +++++++---
 src/descent/damped_newton.jl        |  8 ++++++--
 src/descent/newton.jl               | 17 +++++++++++++----
 src/descent/steepest.jl             |  8 ++++++--
 src/internal/linear_solve.jl        | 18 +++++++++++-------
 7 files changed, 85 insertions(+), 18 deletions(-)

diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index e5e6960e2..4328af345 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -291,6 +291,27 @@ function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
                 cache.descent_cache, J, cache.fu, cache.u; new_jacobian, cache.kwargs...)
         end
     end
+
+    if !descent_result.linsolve_success
+        if new_jacobian && cache.steps_since_last_reset == 0
+            # Extremely pathological case. Jacobian was just reset and linear solve
+            # failed. Should ideally never happen in practice unless true jacobian init
+            # is used.
+            cache.retcode = LinearSolveFailureCode
+            cache.force_stop = true
+            return
+        else
+            # Force a reinit because the problem is currently un-solvable
+            if !haskey(cache.kwargs, :verbose) || cache.kwargs[:verbose]
+                @warn "Linear Solve Failed but Jacobian Information is not current. \
+                       Retrying with reinitialized Approximate Jacobian."
+            end
+            cache.force_reinit = true
+            __step!(cache; recompute_jacobian = true)
+            return
+        end
+    end
+
     δu, descent_intermediates = descent_result.δu, descent_result.extras
 
     if descent_result.success
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index fd1eb5b3f..7d20b0bfc 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -230,6 +230,27 @@ function __step!(cache::GeneralizedFirstOrderAlgorithmCache{iip, GB};
                 cache.descent_cache, J, cache.fu, cache.u; new_jacobian, cache.kwargs...)
         end
     end
+
+    if !descent_result.linsolve_success
+        if new_jacobian
+            # Jacobian Information is current and linear solve failed terminate the solve
+            cache.retcode = LinearSolveFailureCode
+            cache.force_stop = true
+            return
+        else
+            # Jacobian Information is not current and linear solve failed, recompute
+            # Jacobian
+            if !haskey(cache.kwargs, :verbose) || cache.kwargs[:verbose]
+                @warn "Linear Solve Failed but Jacobian Information is not current. \
+                       Retrying with updated Jacobian."
+            end
+            # In the 2nd call the `new_jacobian` is guaranteed to be `true`.
+            cache.make_new_jacobian = true
+            __step!(cache; recompute_jacobian = true, kwargs...)
+            return
+        end
+    end
+
     δu, descent_intermediates = descent_result.δu, descent_result.extras
 
     if descent_result.success
diff --git a/src/descent/common.jl b/src/descent/common.jl
index 2a614d84a..3d53573ea 100644
--- a/src/descent/common.jl
+++ b/src/descent/common.jl
@@ -1,5 +1,6 @@
 """
-    DescentResult(; δu = missing, u = missing, success::Bool = true, extras = (;))
+    DescentResult(; δu = missing, u = missing, success::Bool = true,
+        linsolve_success::Bool = true, extras = (;))
 
 Construct a `DescentResult` object.
 
@@ -9,6 +10,7 @@ Construct a `DescentResult` object.
   - `u`: The new iterate. This is provided only for multi-step methods currently.
   - `success`: Certain Descent Algorithms can reject a descent direction for example
     [`GeodesicAcceleration`](@ref).
+  - `linsolve_success`: Whether the line search was successful.
   - `extras`: A named tuple containing intermediates computed during the solve.
     For example, [`GeodesicAcceleration`](@ref) returns `NamedTuple{(:v, :a)}` containing
     the "velocity" and "acceleration" terms.
@@ -17,10 +19,12 @@ Construct a `DescentResult` object.
     δu
     u
     success::Bool
+    linsolve_success::Bool
     extras
 end
 
-function DescentResult(; δu = missing, u = missing, success::Bool = true, extras = (;))
+function DescentResult(; δu = missing, u = missing, success::Bool = true,
+        linsolve_success::Bool = true, extras = (;))
     @assert δu !== missing || u !== missing
-    return DescentResult(δu, u, success, extras)
+    return DescentResult(δu, u, success, linsolve_success, extras)
 end
diff --git a/src/descent/damped_newton.jl b/src/descent/damped_newton.jl
index aaabc6c4e..792f56773 100644
--- a/src/descent/damped_newton.jl
+++ b/src/descent/damped_newton.jl
@@ -200,10 +200,14 @@ function __internal_solve!(cache::DampedNewtonDescentCache{INV, mode}, J, fu,
     end
 
     @static_timeit cache.timer "linear solve" begin
-        δu = cache.lincache(;
+        linres = cache.lincache(;
             A, b, reuse_A_if_factorization = !new_jacobian && !recompute_A,
             kwargs..., linu = _vec(δu))
-        δu = _restructure(get_du(cache, idx), δu)
+        δu = _restructure(get_du(cache, idx), linres.u)
+        if !linres.success
+            set_du!(cache, δu, idx)
+            return DescentResult(; δu, success = false, linsolve_success = false)
+        end
     end
 
     @bb @. δu *= -1
diff --git a/src/descent/newton.jl b/src/descent/newton.jl
index bcb83686f..36edbf86c 100644
--- a/src/descent/newton.jl
+++ b/src/descent/newton.jl
@@ -81,10 +81,14 @@ function __internal_solve!(
         @bb δu = J × vec(fu)
     else
         @static_timeit cache.timer "linear solve" begin
-            δu = cache.lincache(;
+            linres = cache.lincache(;
                 A = J, b = _vec(fu), kwargs..., linu = _vec(δu), du = _vec(δu),
                 reuse_A_if_factorization = !new_jacobian || (idx !== Val(1)))
-            δu = _restructure(get_du(cache, idx), δu)
+            δu = _restructure(get_du(cache, idx), linres.u)
+            if !linres.success
+                set_du!(cache, δu, idx)
+                return DescentResult(; δu, success = false, linsolve_success = false)
+            end
         end
     end
     @bb @. δu *= -1
@@ -102,10 +106,15 @@ function __internal_solve!(
     end
     @bb cache.Jᵀfu_cache = transpose(J) × vec(fu)
     @static_timeit cache.timer "linear solve" begin
-        δu = cache.lincache(; A = __maybe_symmetric(cache.JᵀJ_cache), b = cache.Jᵀfu_cache,
+        linres = cache.lincache(;
+            A = __maybe_symmetric(cache.JᵀJ_cache), b = cache.Jᵀfu_cache,
             kwargs..., linu = _vec(δu), du = _vec(δu),
             reuse_A_if_factorization = !new_jacobian || (idx !== Val(1)))
-        δu = _restructure(get_du(cache, idx), δu)
+        δu = _restructure(get_du(cache, idx), linres.u)
+        if !linres.success
+            set_du!(cache, δu, idx)
+            return DescentResult(; δu, success = false, linsolve_success = false)
+        end
     end
     @bb @. δu *= -1
     set_du!(cache, δu, idx)
diff --git a/src/descent/steepest.jl b/src/descent/steepest.jl
index 4d4877a1b..227fdb436 100644
--- a/src/descent/steepest.jl
+++ b/src/descent/steepest.jl
@@ -54,10 +54,14 @@ function __internal_solve!(cache::SteepestDescentCache{INV}, J, fu, u, idx::Val
     if INV
         A = J === nothing ? nothing : transpose(J)
         @static_timeit cache.timer "linear solve" begin
-            δu = cache.lincache(;
+            linres = cache.lincache(;
                 A, b = _vec(fu), kwargs..., linu = _vec(δu), du = _vec(δu),
                 reuse_A_if_factorization = !new_jacobian || idx !== Val(1))
-            δu = _restructure(get_du(cache, idx), δu)
+            δu = _restructure(get_du(cache, idx), linres.u)
+            if !linres.success
+                set_du!(cache, δu, idx)
+                return DescentResult(; δu, success = false, linsolve_success = false)
+            end
         end
     else
         @assert J!==nothing "`J` must be provided when `pre_inverted = Val(false)`."
diff --git a/src/internal/linear_solve.jl b/src/internal/linear_solve.jl
index 080de05ef..f2277a165 100644
--- a/src/internal/linear_solve.jl
+++ b/src/internal/linear_solve.jl
@@ -105,6 +105,11 @@ function LinearSolverCache(alg, linsolve, A, b, u; kwargs...)
     return LinearSolverCache(lincache, linsolve, nothing, nothing, nothing, precs, 0, 0)
 end
 
+@kwdef @concrete struct LinearSolveResult
+    u
+    success::Bool = true
+end
+
 # Direct Linear Solve Case without Caching
 function (cache::LinearSolverCache{Nothing})(;
         A = nothing, b = nothing, linu = nothing, kwargs...)
@@ -119,7 +124,7 @@ function (cache::LinearSolverCache{Nothing})(;
     else
         res = cache.A \ cache.b
     end
-    return res
+    return LinearSolveResult(; u = res)
 end
 
 # Use LinearSolve.jl
@@ -154,11 +159,7 @@ function (cache::LinearSolverCache)(;
         cache.lincache.Pr = Pr
     end
 
-    # display(A)
-
     linres = solve!(cache.lincache)
-    # @show cache.lincache.cacheval
-    # @show LinearAlgebra.issuccess(cache.lincache.cacheval)
     cache.lincache = linres.cache
     # Unfortunately LinearSolve.jl doesn't have the most uniform ReturnCode handling
     if linres.retcode === ReturnCode.Failure
@@ -185,11 +186,14 @@ function (cache::LinearSolverCache)(;
             end
             linres = solve!(cache.additional_lincache)
             cache.additional_lincache = linres.cache
-            return linres.u
+            linres.retcode === ReturnCode.Failure &&
+                return LinearSolveResult(; u = linres.u, success = false)
+            return LinearSolveResult(; u = linres.u)
         end
+        return LinearSolveResult(; u = linres.u, success = false)
     end
 
-    return linres.u
+    return LinearSolveResult(; u = linres.u)
 end
 
 @inline __update_A!(cache::LinearSolverCache, ::Nothing, reuse) = cache

From b2a231666fbeea63fb4fa5aa0b67bd6b8574b848 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 25 Apr 2024 17:41:02 -0400
Subject: [PATCH 369/700] Add tests

---
 test/misc/linsolve_switching_tests.jl | 28 +++++++++++++++++++++++++++
 1 file changed, 28 insertions(+)
 create mode 100644 test/misc/linsolve_switching_tests.jl

diff --git a/test/misc/linsolve_switching_tests.jl b/test/misc/linsolve_switching_tests.jl
new file mode 100644
index 000000000..521e417cc
--- /dev/null
+++ b/test/misc/linsolve_switching_tests.jl
@@ -0,0 +1,28 @@
+@testitem "Singular Systems -- Auto Linear Solve Switching" begin
+    using LinearSolve, NonlinearSolve
+
+    function f!(du, u, p)
+        du[1] = 2u[1] - 2
+        du[2] = (u[1] - 4u[2])^2 + 0.1
+    end
+
+    u0 = [0.0, 0.0] # Singular Jacobian at u0
+
+    prob = NonlinearProblem(f!, u0)
+
+    sol = solve(prob)  # This doesn't have a root so let's just test the switching
+    @test sol.u≈[1.0, 0.25] atol=1e-3 rtol=1e-3
+
+    function nlls!(du, u, p)
+        du[1] = 2u[1] - 2
+        du[2] = (u[1] - 4u[2])^2 + 0.1
+        du[3] = 0
+    end
+
+    u0 = [0.0, 0.0]
+
+    prob = NonlinearProblem(NonlinearFunction(nlls!, resid_prototype = zeros(3)), u0)
+
+    solve(prob)
+    @test sol.u≈[1.0, 0.25] atol=1e-3 rtol=1e-3
+end

From 914f556739c6ca8a046e03b8187b04cecef715ef Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 26 Apr 2024 15:50:03 -0400
Subject: [PATCH 370/700] Safe guard against cases which might not support rank
 deficient matrices

---
 src/NonlinearSolve.jl        |  4 ++--
 src/internal/linear_solve.jl | 22 +++++++++++++++++++---
 test/misc/polyalg_tests.jl   | 11 +++--------
 3 files changed, 24 insertions(+), 13 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 9b6b9ec04..f6f6aee1d 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -12,8 +12,8 @@ import PrecompileTools: @recompile_invalidations, @compile_workload, @setup_work
           LinearAlgebra, LinearSolve, MaybeInplace, Preferences, Printf, SciMLBase,
           SimpleNonlinearSolve, SparseArrays, SparseDiffTools
 
-    import ArrayInterface: undefmatrix, can_setindex, restructure, fast_scalar_indexing,
-                           ismutable
+    import ArrayInterface: ArrayInterface, undefmatrix, can_setindex, restructure,
+                           fast_scalar_indexing, ismutable
     import DiffEqBase: AbstractNonlinearTerminationMode,
                        AbstractSafeNonlinearTerminationMode,
                        AbstractSafeBestNonlinearTerminationMode,
diff --git a/src/internal/linear_solve.jl b/src/internal/linear_solve.jl
index f2277a165..783bf4956 100644
--- a/src/internal/linear_solve.jl
+++ b/src/internal/linear_solve.jl
@@ -163,9 +163,11 @@ function (cache::LinearSolverCache)(;
     cache.lincache = linres.cache
     # Unfortunately LinearSolve.jl doesn't have the most uniform ReturnCode handling
     if linres.retcode === ReturnCode.Failure
-        # TODO: We need to guard this somehow because this will surely fail if A is on GPU
-        # TODO: or some fancy Matrix type
-        if !(cache.linsolve isa QRFactorization{ColumnNorm})
+        structured_mat = ArrayInterface.isstructured(cache.lincache.A)
+        is_gpuarray = ArrayInterface.device(cache.lincache.A) isa ArrayInterface.GPU
+        if !(cache.linsolve isa QRFactorization{ColumnNorm}) &&
+           !is_gpuarray &&
+           !structured_mat
             if verbose
                 @warn "Potential Rank Deficient Matrix Detected. Attempting to solve using \
                        Pivoted QR Factorization."
@@ -189,6 +191,20 @@ function (cache::LinearSolverCache)(;
             linres.retcode === ReturnCode.Failure &&
                 return LinearSolveResult(; u = linres.u, success = false)
             return LinearSolveResult(; u = linres.u)
+        elseif !(cache.linsolve isa QRFactorization{ColumnNorm})
+            if verbose
+                if structured_mat
+                    @warn "Potential Rank Deficient Matrix Detected. But Matrix is \
+                           Structured. Currently, we don't attempt to solve Rank Deficient \
+                           Structured Matrices. Please open an issue at \
+                           https://github.com/SciML/NonlinearSolve.jl"
+                elseif is_gpuarray
+                    @warn "Potential Rank Deficient Matrix Detected. But Matrix is on GPU. \
+                           Currently, we don't attempt to solve Rank Deficient GPU \
+                           Matrices. Please open an issue at \
+                           https://github.com/SciML/NonlinearSolve.jl"
+                end
+            end
         end
         return LinearSolveResult(; u = linres.u, success = false)
     end
diff --git a/test/misc/polyalg_tests.jl b/test/misc/polyalg_tests.jl
index 666db02ab..c2864759c 100644
--- a/test/misc/polyalg_tests.jl
+++ b/test/misc/polyalg_tests.jl
@@ -250,12 +250,7 @@ end
     u0 = @SVector [0.0, 0.0, 0.0]
     prob = NonlinearProblem(f1_infeasible, u0)
 
-    try
-        sol = solve(prob)
-        @test all(!isnan, sol.u)
-        @test !SciMLBase.successful_retcode(sol.retcode)
-        @inferred solve(prob)
-    catch err
-        @test err isa LinearAlgebra.SingularException
-    end
+    sol = solve(prob)
+    @test all(!isnan, sol.u)
+    @test !SciMLBase.successful_retcode(sol.retcode)
 end

From c834033a94371f3654d0f3a4ebb37a45c24d902e Mon Sep 17 00:00:00 2001
From: oscarddssmith <oscar.smith@juliacomputing.com>
Date: Tue, 30 Apr 2024 17:44:20 -0400
Subject: [PATCH 371/700] run precompile workload in parallel

---
 src/NonlinearSolve.jl | 12 ++++++++++--
 1 file changed, 10 insertions(+), 2 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index f6f6aee1d..7348db90e 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -135,11 +135,19 @@ include("default.jl")
         TrustRegion(; linsolve = LUFactorization()), nothing)
 
     @compile_workload begin
+        @sync begin
+        for T in (Float32, Float64), (fn, u0) in nlfuncs
+            Threads.@spawn NonlinearProblem(fn, T.(u0), T(2))
+        end
+        for (fn, u0) in nlfuncs
+            Threads.@spawn NonlinearLeastSquaresProblem(fn, u0, 2.0)
+        end
         for prob in probs_nls, alg in nls_algs
-            solve(prob, alg; abstol = 1e-2, verbose = false)
+            Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
         end
         for prob in probs_nlls, alg in nlls_algs
-            solve(prob, alg; abstol = 1e-2, verbose = false)
+            Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
+        end
         end
     end
 end

From 4594ee3c735a41975ed5c47bc6c536114566964f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 2 May 2024 10:35:03 -0400
Subject: [PATCH 372/700] Update README.md

---
 README.md | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/README.md b/README.md
index afdc88f9e..096a0c216 100644
--- a/README.md
+++ b/README.md
@@ -35,3 +35,16 @@ u0 = (1.0, 2.0) # brackets
 prob = IntervalNonlinearProblem(f, u0)
 sol = solve(prob)
 ```
+
+## Citation
+
+If you found this library to be useful in academic work, then please cite:
+
+```bibtex
+@article{pal2024nonlinearsolve,
+  title={NonlinearSolve. jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia},
+  author={Pal, Avik and Holtorf, Flemming and Larsson, Axel and Loman, Torkel and Schaefer, Frank and Qu, Qingyu and Edelman, Alan and Rackauckas, Chris and others},
+  journal={arXiv preprint arXiv:2403.16341},
+  year={2024}
+}
+```

From 97330340627cd50e2209ddb61a0b78fdbed8358b Mon Sep 17 00:00:00 2001
From: Oscar Smith <oscar.smith@juliacomputing.com>
Date: Thu, 2 May 2024 21:39:12 -0400
Subject: [PATCH 373/700] Simplify precompilation

Remove Float32 method and the Vector out of place methods since these are less likely to be useful to users. This brings down precompilation time by ~2x. I think this is good to do before https://github.com/SciML/NonlinearSolve.jl/pull/418 since I'm more sure that it's a good idea.
---
 src/NonlinearSolve.jl | 19 ++-----------------
 1 file changed, 2 insertions(+), 17 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index f6f6aee1d..ed41b4ca4 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -90,11 +90,10 @@ include("default.jl")
 
 @setup_workload begin
     nlfuncs = ((NonlinearFunction{false}((u, p) -> u .* u .- p), 0.1),
-        (NonlinearFunction{false}((u, p) -> u .* u .- p), [0.1]),
         (NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p), [0.1]))
     probs_nls = NonlinearProblem[]
-    for T in (Float32, Float64), (fn, u0) in nlfuncs
-        push!(probs_nls, NonlinearProblem(fn, T.(u0), T(2)))
+    for (fn, u0) in nlfuncs
+        push!(probs_nls, NonlinearProblem(fn, u0, 2.0))
     end
 
     nls_algs = (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
@@ -114,20 +113,6 @@ include("default.jl")
     for (fn, u0) in nlfuncs
         push!(probs_nlls, NonlinearLeastSquaresProblem(fn, u0, 2.0))
     end
-    nlfuncs = ((NonlinearFunction{false}((u, p) -> (u .^ 2 .- p)[1:1]), Float32[0.1, 0.0]),
-        (NonlinearFunction{false}((u, p) -> vcat(u .* u .- p, u .* u .- p)),
-            Float32[0.1, 0.1]),
-        (
-            NonlinearFunction{true}(
-                (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(Float32, 1)),
-            Float32[0.1, 0.0]),
-        (
-            NonlinearFunction{true}((du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p),
-                resid_prototype = zeros(Float32, 4)),
-            Float32[0.1, 0.1]))
-    for (fn, u0) in nlfuncs
-        push!(probs_nlls, NonlinearLeastSquaresProblem(fn, u0, 2.0f0))
-    end
 
     nlls_algs = (LevenbergMarquardt(), GaussNewton(), TrustRegion(),
         LevenbergMarquardt(; linsolve = LUFactorization()),

From e3cf53a7355ac47c84dee0b8fdf7ecc1b57cfbac Mon Sep 17 00:00:00 2001
From: Vaibhav Kumar Dixit <vaibhavyashdixit@gmail.com>
Date: Sat, 4 May 2024 12:32:32 -0400
Subject: [PATCH 374/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index c601ac6b0..1787816ff 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.7.0"
+version = "1.8.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From e88bf6fc6936f856202813dfffa78fdead1d10bd Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 11 May 2024 05:14:25 -0400
Subject: [PATCH 375/700] Update Project.toml

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index e9fab016e..4f199888d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -65,7 +65,7 @@ BenchmarkTools = "1.4"
 CUDA = "5.2"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149.0"
-Enzyme = "0.11.15"
+Enzyme = "0.11.15, 0.12"
 FastBroadcast = "0.2.8"
 FastClosures = "0.3.2"
 FastLevenbergMarquardt = "0.1"

From 775a78caa64ee5665334bea7541aa21390795561 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Wed, 15 May 2024 11:00:00 +0200
Subject: [PATCH 376/700] using NonlinearSolve works

---
 Project.toml                          |  2 +-
 docs/src/basics/autodiff.md           | 16 +++--
 docs/src/basics/sparsity_detection.md |  4 +-
 docs/src/tutorials/large_systems.md   |  8 +--
 src/NonlinearSolve.jl                 |  5 +-
 src/adtypes.jl                        | 87 ++++++++++++---------------
 src/algorithms/trust_region.jl        |  7 ++-
 src/core/generalized_first_order.jl   | 12 ++--
 src/internal/helpers.jl               | 44 +++++---------
 src/internal/jacobian.jl              |  4 +-
 src/utils.jl                          |  7 +--
 test/core/rootfind_tests.jl           | 22 +++----
 test/misc/bruss_tests.jl              | 10 +--
 13 files changed, 101 insertions(+), 127 deletions(-)

diff --git a/Project.toml b/Project.toml
index 4f199888d..e265141fd 100644
--- a/Project.toml
+++ b/Project.toml
@@ -57,7 +57,7 @@ NonlinearSolveSymbolicsExt = "Symbolics"
 NonlinearSolveZygoteExt = "Zygote"
 
 [compat]
-ADTypes = "0.2.6"
+ADTypes = "1.1.0"
 Aqua = "0.8"
 ArrayInterface = "7.9"
 BandedMatrices = "1.5"
diff --git a/docs/src/basics/autodiff.md b/docs/src/basics/autodiff.md
index 73e096a4b..baa605363 100644
--- a/docs/src/basics/autodiff.md
+++ b/docs/src/basics/autodiff.md
@@ -3,19 +3,16 @@
 ## Summary of Finite Differencing Backends
 
   - [`AutoFiniteDiff`](@ref): Finite differencing, not optimal but always applicable.
-  - [`AutoSparseFiniteDiff`](@ref): Sparse version of [`AutoFiniteDiff`](@ref).
 
 ## Summary of Forward Mode AD Backends
 
   - [`AutoForwardDiff`](@ref): The best choice for dense problems.
-  - [`AutoSparseForwardDiff`](@ref): Sparse version of [`AutoForwardDiff`](@ref).
   - [`AutoPolyesterForwardDiff`](@ref): Might be faster than [`AutoForwardDiff`](@ref) for
     large problems. Requires `PolyesterForwardDiff.jl` to be installed and loaded.
 
 ## Summary of Reverse Mode AD Backends
 
   - [`AutoZygote`](@ref): The fastest choice for non-mutating array-based (BLAS) functions.
-  - [`AutoSparseZygote`](@ref): Sparse version of [`AutoZygote`](@ref).
   - [`AutoEnzyme`](@ref): Uses `Enzyme.jl` Reverse Mode and should be considered
     experimental.
 
@@ -26,29 +23,32 @@
 
 !!! note
     
-    The `Sparse` versions of the methods refers to automated sparsity detection. These
+    The sparse versions of the methods refer to automated sparsity detection. These
     methods automatically discover the sparse Jacobian form from the function `f`. Note that
     all methods specialize the differentiation on a sparse Jacobian if the sparse Jacobian
     is given as `prob.f.jac_prototype` in the `NonlinearFunction` definition, and the
     `AutoSparse` here simply refers to whether this `jac_prototype` should be generated
     automatically. For more details, see
     [SparseDiffTools.jl](https://github.com/JuliaDiff/SparseDiffTools.jl) and
-    [Sparsity Detection Manual Entry](@ref sparsity-detection).
+    [Sparsity Detection Manual Entry](@ref sparsity-detection), as well as the
+    documentation of [ADTypes.jl](https://github.com/SciML/ADTypes.jl).
 
 ## API Reference
 
+```@docs
+AutoSparse
+```
+
 ### Finite Differencing Backends
 
 ```@docs
 AutoFiniteDiff
-AutoSparseFiniteDiff
 ```
 
 ### Forward Mode AD Backends
 
 ```@docs
 AutoForwardDiff
-AutoSparseForwardDiff
 AutoPolyesterForwardDiff
 ```
 
@@ -56,7 +56,5 @@ AutoPolyesterForwardDiff
 
 ```@docs
 AutoZygote
-AutoSparseZygote
 AutoEnzyme
-NonlinearSolve.AutoSparseEnzyme
 ```
diff --git a/docs/src/basics/sparsity_detection.md b/docs/src/basics/sparsity_detection.md
index 208fc306e..97891be61 100644
--- a/docs/src/basics/sparsity_detection.md
+++ b/docs/src/basics/sparsity_detection.md
@@ -59,9 +59,9 @@ refer to the documentation there for more details.
 If you constructed a Nonlinear Solver with a sparse AD type, for example
 
 ```julia
-NewtonRaphson(; autodiff = AutoSparseForwardDiff())
+NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff()))
 # OR
-TrustRegion(; autodiff = AutoSparseZygote())
+TrustRegion(; autodiff = AutoSparse(AutoZygote()))
 ```
 
 then NonlinearSolve will automatically perform matrix coloring and use sparse
diff --git a/docs/src/tutorials/large_systems.md b/docs/src/tutorials/large_systems.md
index 19e7493d5..3de7e8a60 100644
--- a/docs/src/tutorials/large_systems.md
+++ b/docs/src/tutorials/large_systems.md
@@ -128,7 +128,7 @@ include:
 In the next section, we will discuss how to declare a sparse Jacobian and how to use
 [Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl), to compute exact sparse
 jacobians. This is triggered if you pass in a sparse autodiff type such as
-`AutoSparseForwardDiff()`. If `Symbolics.jl` is loaded, then the default changes to
+`AutoSparse(AutoForwardDiff())`. If `Symbolics.jl` is loaded, then the default changes to
 Symbolic Sparsity Detection. See the manual entry on
 [Sparsity Detection](@ref sparsity-detection) for more details on the default.
 
@@ -137,13 +137,13 @@ using BenchmarkTools # for @btime
 
 @btime solve(prob_brusselator_2d, NewtonRaphson());
 @btime solve(prob_brusselator_2d,
-    NewtonRaphson(; autodiff = AutoSparseForwardDiff(; chunksize = 32)));
+    NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff(; chunksize = 32))));
 @btime solve(prob_brusselator_2d,
     NewtonRaphson(;
-        autodiff = AutoSparseForwardDiff(; chunksize = 32), linsolve = KLUFactorization()));
+        autodiff = AutoSparse(AutoForwardDiff(; chunksize = 32)), linsolve = KLUFactorization()));
 @btime solve(prob_brusselator_2d,
     NewtonRaphson(;
-        autodiff = AutoSparseForwardDiff(; chunksize = 32), linsolve = KrylovJL_GMRES()));
+        autodiff = AutoSparse(AutoForwardDiff(; chunksize = 32)), linsolve = KrylovJL_GMRES()));
 nothing # hide
 ```
 
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 40890d1e3..48ae6305c 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -27,7 +27,7 @@ import PrecompileTools: @recompile_invalidations, @compile_workload, @setup_work
 
     import SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
                       AbstractSciMLOperator, NLStats, _unwrap_val, has_jac, isinplace
-    import SparseDiffTools: AbstractSparsityDetection, AutoSparseEnzyme
+    import SparseDiffTools: AbstractSparsityDetection
     import StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix, MMatrix
     import SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
                                       symbolic_container, parameter_values, state_values,
@@ -36,9 +36,6 @@ end
 
 @reexport using ADTypes, SciMLBase, SimpleNonlinearSolve
 
-const AbstractSparseADType = Union{ADTypes.AbstractSparseFiniteDifferences,
-    ADTypes.AbstractSparseForwardMode, ADTypes.AbstractSparseReverseMode}
-
 # Type-Inference Friendly Check for Extension Loading
 is_extension_loaded(::Val) = false
 
diff --git a/src/adtypes.jl b/src/adtypes.jl
index 9ed3107c5..358994bbc 100644
--- a/src/adtypes.jl
+++ b/src/adtypes.jl
@@ -22,17 +22,6 @@ error into the derivative estimates.
 """
 AutoFiniteDiff
 
-"""
-    AutoSparseFiniteDiff()
-
-Sparse Version of [`AutoFiniteDiff`](@ref) that uses
-[FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) and the column color vector of
-the Jacobian Matrix to efficiently compute the Sparse Jacobian.
-
-  - Supports both inplace and out-of-place functions
-"""
-AutoSparseFiniteDiff
-
 """
     AutoForwardDiff(; chunksize = nothing, tag = nothing)
     AutoForwardDiff{chunksize, tagType}(tag::tagType)
@@ -56,27 +45,6 @@ For type-stability of internal operations, a positive `chunksize` must be provid
 """
 AutoForwardDiff
 
-"""
-    AutoSparseForwardDiff(; chunksize = nothing, tag = nothing)
-    AutoSparseForwardDiff{chunksize, tagType}(tag::tagType)
-
-Sparse Version of [`AutoForwardDiff`](@ref) that uses
-[ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) and the column color vector of
-the Jacobian Matrix to efficiently compute the Sparse Jacobian.
-
-  - Supports both inplace and out-of-place functions
-
-For type-stability of internal operations, a positive `chunksize` must be provided.
-
-### Keyword Arguments
-
-  - `chunksize`: Count of dual numbers that can be propagated simultaneously. Setting this
-    number to a high value will lead to slowdowns. Use
-    [`NonlinearSolve.pickchunksize`](@ref) to get a proper value.
-  - `tag`: Used to avoid perturbation confusion. If set to `nothing`, we use a custom tag.
-"""
-AutoSparseForwardDiff
-
 """
     AutoPolyesterForwardDiff(; chunksize = nothing)
 
@@ -108,20 +76,6 @@ jacobians.
 """
 AutoZygote
 
-"""
-    AutoSparseZygote()
-
-Sparse version of [`AutoZygote`](@ref) that uses
-[`Zygote.jl`](https://github.com/FluxML/Zygote.jl) and the row color vector of
-the Jacobian Matrix to efficiently compute the Sparse Jacobian.
-
-  - Supports only out-of-place functions
-
-This is efficient only for long jacobians or if the maximum value of the row color vector is
-significantly lower than the maximum value of the column color vector.
-"""
-AutoSparseZygote
-
 """
     AutoEnzyme()
 
@@ -134,7 +88,7 @@ and VJP support is currently not implemented.
 AutoEnzyme
 
 """
-    AutoSparseEnzyme()
+    AutoSparse(AutoEnzyme())
 
 Sparse version of [`AutoEnzyme`](@ref) that uses
 [Enzyme.jl](https://github.com/EnzymeAD/Enzyme.jl) and the row color vector of
@@ -142,7 +96,44 @@ the Jacobian Matrix to efficiently compute the Sparse Jacobian.
 
   - Supports both inplace and out-of-place functions
 
+This is efficient only for long jacobians or if the maximum value of the row color vector is
+significantly lower than the maximum value of the column color vector.
+
+    AutoSparse(AutoFiniteDiff())
+
+Sparse Version of [`AutoFiniteDiff`](@ref) that uses
+[FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) and the column color vector of
+the Jacobian Matrix to efficiently compute the Sparse Jacobian.
+
+  - Supports both inplace and out-of-place functions
+
+    AutoSparse(AutoForwardDiff(; chunksize = nothing, tag = nothing))
+    AutoSparse(AutoForwardDiff{chunksize, tagType}(tag::tagType))
+
+Sparse Version of [`AutoForwardDiff`](@ref) that uses
+[ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) and the column color vector of
+the Jacobian Matrix to efficiently compute the Sparse Jacobian.
+
+- Supports both inplace and out-of-place functions
+
+For type-stability of internal operations, a positive `chunksize` must be provided.
+
+### Keyword Arguments
+
+- `chunksize`: Count of dual numbers that can be propagated simultaneously. Setting this
+number to a high value will lead to slowdowns. Use
+[`NonlinearSolve.pickchunksize`](@ref) to get a proper value.
+- `tag`: Used to avoid perturbation confusion. If set to `nothing`, we use a custom tag.
+
+    AutoSparse(AutoZygote())
+
+Sparse version of [`AutoZygote`](@ref) that uses
+[`Zygote.jl`](https://github.com/FluxML/Zygote.jl) and the row color vector of
+the Jacobian Matrix to efficiently compute the Sparse Jacobian.
+
+  - Supports only out-of-place functions
+
 This is efficient only for long jacobians or if the maximum value of the row color vector is
 significantly lower than the maximum value of the column color vector.
 """
-AutoSparseEnzyme
+AutoSparse
diff --git a/src/algorithms/trust_region.jl b/src/algorithms/trust_region.jl
index ac8f42d35..7ad038b70 100644
--- a/src/algorithms/trust_region.jl
+++ b/src/algorithms/trust_region.jl
@@ -26,13 +26,14 @@ function TrustRegion(; concrete_jac = nothing, linsolve = nothing, precs = DEFAU
         shrink_factor::Real = 1 // 4, expand_factor::Real = 2 // 1,
         max_shrink_times::Int = 32, autodiff = nothing, vjp_autodiff = nothing)
     descent = Dogleg(; linsolve, precs)
-    if autodiff isa
-       Union{ADTypes.AbstractForwardMode, ADTypes.AbstractFiniteDifferencesMode}
+    if autodiff !== nothing && ADTypes.mode(autodiff) isa ADTypes.ForwardMode
         forward_ad = autodiff
     else
         forward_ad = nothing
     end
-    if isnothing(vjp_autodiff) && autodiff isa ADTypes.AbstractFiniteDifferencesMode
+    if isnothing(vjp_autodiff) &&
+       autodiff isa Union{ADTypes.AutoFiniteDiff, ADTypes.AutoFiniteDifferences}
+       # TODO: why not just ForwardMode?
         vjp_autodiff = autodiff
     end
     trustregion = GenericTrustRegionScheme(;
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 7d20b0bfc..c16cf043d 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -55,10 +55,14 @@ function GeneralizedFirstOrderAlgorithm{concrete_jac, name}(;
         descent, linesearch = missing, trustregion = missing,
         jacobian_ad = nothing, forward_ad = nothing, reverse_ad = nothing,
         max_shrink_times::Int = typemax(Int)) where {concrete_jac, name}
-    forward_ad = ifelse(forward_ad !== nothing, forward_ad,
-        ifelse(jacobian_ad isa ADTypes.AbstractForwardMode, jacobian_ad, nothing))
-    reverse_ad = ifelse(reverse_ad !== nothing, reverse_ad,
-        ifelse(jacobian_ad isa ADTypes.AbstractReverseMode, jacobian_ad, nothing))
+    forward_ad = ifelse(forward_ad !== nothing,
+        forward_ad,
+        ifelse(jacobian_ad !== nothing && ADTypes.mode(jacobian_ad) isa ADTypes.ForwardMode,
+            jacobian_ad, nothing))
+    reverse_ad = ifelse(reverse_ad !== nothing,
+        reverse_ad,
+        ifelse(jacobian_ad !== nothing && ADTypes.mode(jacobian_ad) isa ADTypes.ReverseMode,
+            jacobian_ad, nothing))
 
     if linesearch !== missing && !(linesearch isa AbstractNonlinearSolveLineSearchAlgorithm)
         Base.depwarn("Passing in a `LineSearches.jl` algorithm directly is deprecated. \
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index fb4af1121..64357911e 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -30,17 +30,12 @@ function evaluate_f!!(f::NonlinearFunction{iip}, fu, u, p) where {iip}
 end
 
 # AutoDiff Selection Functions
-function get_concrete_forward_ad(
-        autodiff::Union{ADTypes.AbstractForwardMode, ADTypes.AbstractFiniteDifferencesMode},
-        prob, sp::Val{test_sparse} = True, args...; kwargs...) where {test_sparse}
-    return autodiff
-end
 function get_concrete_forward_ad(
         autodiff::ADTypes.AbstractADType, prob, sp::Val{test_sparse} = True,
         args...; check_reverse_mode = true, kwargs...) where {test_sparse}
-    if check_reverse_mode
-        @warn "$(autodiff)::$(typeof(autodiff)) is not a \
-               `Abstract(Forward/FiniteDifferences)Mode`. Use with caution." maxlog=1
+    # TODO: shouldn't this be `check_forward_mode`?
+    if !isa(ADTypes.mode(autodiff), ADTypes.ForwardMode) && check_reverse_mode
+        @warn "$(autodiff)::$(typeof(autodiff)) is not a `ForwardMode`. Use with caution." maxlog=1
     end
     return autodiff
 end
@@ -53,37 +48,28 @@ function get_concrete_forward_ad(
         use_sparse_ad = false
     end
     ad = if !ForwardDiff.can_dual(eltype(prob.u0)) # Use Finite Differencing
-        use_sparse_ad ? AutoSparseFiniteDiff() : AutoFiniteDiff()
+        use_sparse_ad ? AutoSparse(AutoFiniteDiff()) : AutoFiniteDiff()
     else
-        (use_sparse_ad ? AutoSparseForwardDiff : AutoForwardDiff)()
+        use_sparse_ad ? AutoSparse(AutoForwardDiff()) : AutoForwardDiff()
     end
     return ad
 end
 
 function get_concrete_reverse_ad(
-        autodiff::Union{ADTypes.AbstractReverseMode, ADTypes.AbstractFiniteDifferencesMode},
-        prob, sp::Val{test_sparse} = True, args...; kwargs...) where {test_sparse}
-    return autodiff
-end
-function get_concrete_reverse_ad(autodiff::Union{AutoZygote, AutoSparseZygote}, prob,
-        sp::Val{test_sparse} = True, args...; kwargs...) where {test_sparse}
-    if isinplace(prob)
+        autodiff::ADTypes.AbstractADType, prob, sp::Val{test_sparse} = True,
+        args...; check_reverse_mode = true, kwargs...) where {test_sparse}
+    if !isa(ADTypes.mode(autodiff), ADTypes.ReverseMode) && check_reverse_mode
+        @warn "$(autodiff)::$(typeof(autodiff)) is not a `ReverseMode`. Use with caution." maxlog=1
+    end
+    if autodiff <: Union{AutoZygote, AutoSparse{<:AutoZygote}} && isinplace(prob)
         @warn "Attempting to use Zygote.jl for inplace problems. Switching to FiniteDiff. \
                Sparsity even if present will be ignored for correctness purposes. Set \
                the reverse ad option to `nothing` to automatically select the best option \
                and exploit sparsity."
         return AutoFiniteDiff() # colorvec confusion will occur if we use FiniteDiff
+    else
+        return autodiff
     end
-    return autodiff
-end
-function get_concrete_reverse_ad(
-        autodiff::ADTypes.AbstractADType, prob, sp::Val{test_sparse} = True,
-        args...; check_reverse_mode = true, kwargs...) where {test_sparse}
-    if check_reverse_mode
-        @warn "$(autodiff)::$(typeof(autodiff)) is not a \
-               `Abstract(Forward/FiniteDifferences)Mode`. Use with caution." maxlog=1
-    end
-    return autodiff
 end
 function get_concrete_reverse_ad(
         autodiff, prob, sp::Val{test_sparse} = True, args...; kwargs...) where {test_sparse}
@@ -94,9 +80,9 @@ function get_concrete_reverse_ad(
         use_sparse_ad = false
     end
     ad = if isinplace(prob) || !is_extension_loaded(Val(:Zygote)) # Use Finite Differencing
-        use_sparse_ad ? AutoSparseFiniteDiff() : AutoFiniteDiff()
+        use_sparse_ad ? AutoSparse(AutoFiniteDiff()) : AutoFiniteDiff()
     else
-        use_sparse_ad ? AutoSparseZygote() : AutoZygote()
+        use_sparse_ad ? AutoSparse(AutoZygote()) : AutoZygote()
     end
     return ad
 end
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 221bc5d62..c964e9714 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -154,7 +154,7 @@ end
 
 # Sparsity Detection Choices
 @inline __sparsity_detection_alg(_, _) = NoSparsityDetection()
-@inline function __sparsity_detection_alg(f::NonlinearFunction, ad::AbstractSparseADType)
+@inline function __sparsity_detection_alg(f::NonlinearFunction, ad::AutoSparse)
     if f.sparsity === nothing
         if f.jac_prototype === nothing
             if is_extension_loaded(Val(:Symbolics))
@@ -185,7 +185,7 @@ end
 
     if SciMLBase.has_colorvec(f)
         return PrecomputedJacobianColorvec(; jac_prototype, f.colorvec,
-            partition_by_rows = ad isa ADTypes.AbstractSparseReverseMode)
+            partition_by_rows = (ad isa AutoSparse && ADTypes.mode(ad) isa ADTypes.ReverseMode))
     else
         return JacPrototypeSparsityDetection(; jac_prototype)
     end
diff --git a/src/utils.jl b/src/utils.jl
index a0cc5744b..9db6e1316 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -21,7 +21,7 @@ end
 @inline __needs_concrete_A(::typeof(\)) = true
 @inline __needs_concrete_A(linsolve) = needs_concrete_A(linsolve)
 
-@inline __maybe_mutable(x, ::AutoSparseEnzyme) = __mutable(x)
+@inline __maybe_mutable(x, ::AutoSparse{<:AutoEnzyme}) = __mutable(x)  # TODO: remove?
 @inline __maybe_mutable(x, _) = x
 
 @inline @generated function _vec(v)
@@ -77,10 +77,7 @@ LazyArrays.applied_axes(::typeof(__zero), x) = axes(x)
 @inline __maybe_symmetric(x::SciMLOperators.AbstractSciMLOperator) = x
 
 # SparseAD --> NonSparseAD
-@inline __get_nonsparse_ad(::AutoSparseForwardDiff) = AutoForwardDiff()
-@inline __get_nonsparse_ad(::AutoSparsePolyesterForwardDiff) = AutoPolyesterForwardDiff()
-@inline __get_nonsparse_ad(::AutoSparseFiniteDiff) = AutoFiniteDiff()
-@inline __get_nonsparse_ad(::AutoSparseZygote) = AutoZygote()
+@inline __get_nonsparse_ad(backend::AutoSparse) = ADTypes.dense_ad(backend)
 @inline __get_nonsparse_ad(ad) = ad
 
 # Simple Checks
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index caa776d5a..688678ff2 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -5,11 +5,11 @@ using Reexport
 
 function __autosparseenzyme()
     @static if Sys.iswindows()
-        @warn "Enzyme on Windows stalls. Using AutoSparseFiniteDiff instead till \
+        @warn "Enzyme on Windows stalls. Using AutoSparse(AutoFiniteDiff()) instead till \
                https://github.com/EnzymeAD/Enzyme.jl/issues/1236 is resolved."
-        return AutoSparseFiniteDiff()
+        return AutoSparse(AutoFiniteDiff())
     else
-        return AutoSparseEnzyme()
+        return AutoSparse(AutoEnzyme())
     end
 end
 
@@ -112,8 +112,8 @@ end
     @test nlprob_iterator_interface(quadratic_f!, p, Val(true), NewtonRaphson()) ≈ sqrt.(p)
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
-            AutoSparseForwardDiff(), AutoSparseFiniteDiff(),
-            AutoZygote(), AutoSparseZygote(), __autosparseenzyme()),
+            AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
+            AutoZygote(), AutoSparse(AutoZygote()), __autosparseenzyme()),
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -175,8 +175,8 @@ end
     @test nlprob_iterator_interface(quadratic_f!, p, Val(true), TrustRegion()) ≈ sqrt.(p)
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0)) radius_update_scheme: $(radius_update_scheme)" for autodiff in (
-            AutoSparseForwardDiff(), AutoSparseFiniteDiff(),
-            AutoZygote(), AutoSparseZygote(), __autosparseenzyme()),
+            AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
+            AutoZygote(), AutoSparse(AutoZygote()), __autosparseenzyme()),
         u0 in (1.0, [1.0, 1.0]),
         radius_update_scheme in radius_update_schemes
 
@@ -271,8 +271,8 @@ end
     end
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
-            AutoSparseForwardDiff(), AutoSparseFiniteDiff(),
-            AutoZygote(), AutoSparseZygote(), __autosparseenzyme()),
+            AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
+            AutoZygote(), AutoSparse(AutoZygote()), __autosparseenzyme()),
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -453,8 +453,8 @@ end
         quadratic_f!, p, Val(true), PseudoTransient(; alpha_initial = 10.0)) ≈ sqrt.(p)
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
-            AutoSparseForwardDiff(), AutoSparseFiniteDiff(),
-            AutoZygote(), AutoSparseZygote(), __autosparseenzyme()),
+            AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
+            AutoZygote(), AutoSparse(AutoZygote()), __autosparseenzyme()),
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
diff --git a/test/misc/bruss_tests.jl b/test/misc/bruss_tests.jl
index 08eae5436..4c1b27bf8 100644
--- a/test/misc/bruss_tests.jl
+++ b/test/misc/bruss_tests.jl
@@ -47,11 +47,11 @@
     @test norm(sol.resid, Inf) < 1e-8
 
     sol = solve(prob_brusselator_2d,
-        NewtonRaphson(autodiff = AutoSparseForwardDiff()); abstol = 1e-8)
+        NewtonRaphson(autodiff = AutoSparse(AutoForwardDiff())); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
     sol = solve(prob_brusselator_2d,
-        NewtonRaphson(autodiff = AutoSparseFiniteDiff()); abstol = 1e-8)
+        NewtonRaphson(autodiff = AutoSparse(AutoFiniteDiff())); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
     du0 = copy(u0)
@@ -69,10 +69,10 @@
     @test !all(iszero, jac_prototype)
 
     sol = solve(prob_brusselator_2d,
-        NewtonRaphson(autodiff = AutoSparseFiniteDiff()); abstol = 1e-8)
+        NewtonRaphson(autodiff = AutoSparse(AutoFiniteDiff())); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
-    cache = init(prob_brusselator_2d, NewtonRaphson(; autodiff = AutoSparseForwardDiff()))
+    cache = init(prob_brusselator_2d, NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff())))
     @test maximum(cache.jac_cache.jac_cache.coloring.colorvec) == 12
-    @test cache.jac_cache.autodiff isa AutoSparseForwardDiff
+    @test cache.jac_cache.autodiff isa AutoSparse{<:AutoForwardDiff}
 end

From 92f984dc406a9730499f77352fb332947dd12638 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Wed, 15 May 2024 11:00:53 +0200
Subject: [PATCH 377/700] Format

---
 docs/src/tutorials/large_systems.md |  8 ++++----
 src/adtypes.jl                      | 11 ++++++-----
 src/algorithms/trust_region.jl      |  2 +-
 src/internal/jacobian.jl            |  6 ++++--
 test/misc/bruss_tests.jl            |  3 ++-
 5 files changed, 17 insertions(+), 13 deletions(-)

diff --git a/docs/src/tutorials/large_systems.md b/docs/src/tutorials/large_systems.md
index 3de7e8a60..4e732b9c0 100644
--- a/docs/src/tutorials/large_systems.md
+++ b/docs/src/tutorials/large_systems.md
@@ -139,11 +139,11 @@ using BenchmarkTools # for @btime
 @btime solve(prob_brusselator_2d,
     NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff(; chunksize = 32))));
 @btime solve(prob_brusselator_2d,
-    NewtonRaphson(;
-        autodiff = AutoSparse(AutoForwardDiff(; chunksize = 32)), linsolve = KLUFactorization()));
+    NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff(; chunksize = 32)),
+        linsolve = KLUFactorization()));
 @btime solve(prob_brusselator_2d,
-    NewtonRaphson(;
-        autodiff = AutoSparse(AutoForwardDiff(; chunksize = 32)), linsolve = KrylovJL_GMRES()));
+    NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff(; chunksize = 32)),
+        linsolve = KrylovJL_GMRES()));
 nothing # hide
 ```
 
diff --git a/src/adtypes.jl b/src/adtypes.jl
index 358994bbc..0ee20effb 100644
--- a/src/adtypes.jl
+++ b/src/adtypes.jl
@@ -114,16 +114,17 @@ Sparse Version of [`AutoForwardDiff`](@ref) that uses
 [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) and the column color vector of
 the Jacobian Matrix to efficiently compute the Sparse Jacobian.
 
-- Supports both inplace and out-of-place functions
+  - Supports both inplace and out-of-place functions
 
 For type-stability of internal operations, a positive `chunksize` must be provided.
 
 ### Keyword Arguments
 
-- `chunksize`: Count of dual numbers that can be propagated simultaneously. Setting this
-number to a high value will lead to slowdowns. Use
-[`NonlinearSolve.pickchunksize`](@ref) to get a proper value.
-- `tag`: Used to avoid perturbation confusion. If set to `nothing`, we use a custom tag.
+  - `chunksize`: Count of dual numbers that can be propagated simultaneously. Setting this
+    number to a high value will lead to slowdowns. Use
+    [`NonlinearSolve.pickchunksize`](@ref) to get a proper value.
+
+  - `tag`: Used to avoid perturbation confusion. If set to `nothing`, we use a custom tag.
 
     AutoSparse(AutoZygote())
 
diff --git a/src/algorithms/trust_region.jl b/src/algorithms/trust_region.jl
index 7ad038b70..d68e2d9ec 100644
--- a/src/algorithms/trust_region.jl
+++ b/src/algorithms/trust_region.jl
@@ -33,7 +33,7 @@ function TrustRegion(; concrete_jac = nothing, linsolve = nothing, precs = DEFAU
     end
     if isnothing(vjp_autodiff) &&
        autodiff isa Union{ADTypes.AutoFiniteDiff, ADTypes.AutoFiniteDifferences}
-       # TODO: why not just ForwardMode?
+        # TODO: why not just ForwardMode?
         vjp_autodiff = autodiff
     end
     trustregion = GenericTrustRegionScheme(;
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index c964e9714..862773ea3 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -184,8 +184,10 @@ end
     end
 
     if SciMLBase.has_colorvec(f)
-        return PrecomputedJacobianColorvec(; jac_prototype, f.colorvec,
-            partition_by_rows = (ad isa AutoSparse && ADTypes.mode(ad) isa ADTypes.ReverseMode))
+        return PrecomputedJacobianColorvec(; jac_prototype,
+            f.colorvec,
+            partition_by_rows = (ad isa AutoSparse &&
+                                 ADTypes.mode(ad) isa ADTypes.ReverseMode))
     else
         return JacPrototypeSparsityDetection(; jac_prototype)
     end
diff --git a/test/misc/bruss_tests.jl b/test/misc/bruss_tests.jl
index 4c1b27bf8..43bcc3eb8 100644
--- a/test/misc/bruss_tests.jl
+++ b/test/misc/bruss_tests.jl
@@ -72,7 +72,8 @@
         NewtonRaphson(autodiff = AutoSparse(AutoFiniteDiff())); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
-    cache = init(prob_brusselator_2d, NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff())))
+    cache = init(
+        prob_brusselator_2d, NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff())))
     @test maximum(cache.jac_cache.jac_cache.coloring.colorvec) == 12
     @test cache.jac_cache.autodiff isa AutoSparse{<:AutoForwardDiff}
 end

From 51aacab178bcfc727d48aaeeceb2830b96a2e8d6 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Wed, 15 May 2024 11:16:05 +0200
Subject: [PATCH 378/700] Typo

---
 src/internal/helpers.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index 64357911e..93725015d 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -61,7 +61,7 @@ function get_concrete_reverse_ad(
     if !isa(ADTypes.mode(autodiff), ADTypes.ReverseMode) && check_reverse_mode
         @warn "$(autodiff)::$(typeof(autodiff)) is not a `ReverseMode`. Use with caution." maxlog=1
     end
-    if autodiff <: Union{AutoZygote, AutoSparse{<:AutoZygote}} && isinplace(prob)
+    if autodiff isa Union{AutoZygote, AutoSparse{<:AutoZygote}} && isinplace(prob)
         @warn "Attempting to use Zygote.jl for inplace problems. Switching to FiniteDiff. \
                Sparsity even if present will be ignored for correctness purposes. Set \
                the reverse ad option to `nothing` to automatically select the best option \

From f5240b60f649e744e286fb2e530ad82be067a65c Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Thu, 16 May 2024 08:13:27 +0200
Subject: [PATCH 379/700] Force ADTypes v1

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 1787816ff..5a64b5e62 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -36,7 +36,7 @@ SimpleNonlinearSolveTrackerExt = "Tracker"
 SimpleNonlinearSolveZygoteExt = "Zygote"
 
 [compat]
-ADTypes = "0.2.6, 1"
+ADTypes = "1"
 AllocCheck = "0.1.1"
 Aqua = "0.8"
 ArrayInterface = "7.8"

From 28bb36bfb892013f41a30d406d74abb088b06e60 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Thu, 16 May 2024 11:43:42 +0200
Subject: [PATCH 380/700] Fix check forward mode

---
 src/internal/helpers.jl | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index 93725015d..9a18d0817 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -32,9 +32,8 @@ end
 # AutoDiff Selection Functions
 function get_concrete_forward_ad(
         autodiff::ADTypes.AbstractADType, prob, sp::Val{test_sparse} = True,
-        args...; check_reverse_mode = true, kwargs...) where {test_sparse}
-    # TODO: shouldn't this be `check_forward_mode`?
-    if !isa(ADTypes.mode(autodiff), ADTypes.ForwardMode) && check_reverse_mode
+        args...; check_forward_mode = true, kwargs...) where {test_sparse}
+    if !isa(ADTypes.mode(autodiff), ADTypes.ForwardMode) && check_forward_mode
         @warn "$(autodiff)::$(typeof(autodiff)) is not a `ForwardMode`. Use with caution." maxlog=1
     end
     return autodiff

From 6170c29c859271ee83f0cde4c1e0237c5dc6d4cd Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Thu, 16 May 2024 11:43:57 +0200
Subject: [PATCH 381/700] Format

---
 src/NonlinearSolve.jl | 24 ++++++++++++------------
 1 file changed, 12 insertions(+), 12 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 48ae6305c..8e39c6f1d 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -118,18 +118,18 @@ include("default.jl")
 
     @compile_workload begin
         @sync begin
-        for T in (Float32, Float64), (fn, u0) in nlfuncs
-            Threads.@spawn NonlinearProblem(fn, T.(u0), T(2))
-        end
-        for (fn, u0) in nlfuncs
-            Threads.@spawn NonlinearLeastSquaresProblem(fn, u0, 2.0)
-        end
-        for prob in probs_nls, alg in nls_algs
-            Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
-        end
-        for prob in probs_nlls, alg in nlls_algs
-            Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
-        end
+            for T in (Float32, Float64), (fn, u0) in nlfuncs
+                Threads.@spawn NonlinearProblem(fn, T.(u0), T(2))
+            end
+            for (fn, u0) in nlfuncs
+                Threads.@spawn NonlinearLeastSquaresProblem(fn, u0, 2.0)
+            end
+            for prob in probs_nls, alg in nls_algs
+                Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
+            end
+            for prob in probs_nlls, alg in nlls_algs
+                Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
+            end
         end
     end
 end

From 09fd809c13c531b67a05df68923f6ae30b35c3a8 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Thu, 16 May 2024 11:47:59 +0200
Subject: [PATCH 382/700] Bump lower bounds

---
 Project.toml | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Project.toml b/Project.toml
index e265141fd..9e31722c4 100644
--- a/Project.toml
+++ b/Project.toml
@@ -83,7 +83,7 @@ NLSolvers = "0.5"
 NLsolve = "4.5"
 NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
-OrdinaryDiffEq = "6.74"
+OrdinaryDiffEq = "6.75"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 Preferences = "1.4"
@@ -94,10 +94,10 @@ RecursiveArrayTools = "3.8"
 Reexport = "1.2"
 SIAMFANLEquations = "1.0.1"
 SafeTestsets = "0.1"
-SciMLBase = "2.28.0"
-SimpleNonlinearSolve = "1.2"
+SciMLBase = "2.34.0"
+SimpleNonlinearSolve = "1.8"
 SparseArrays = "1.10"
-SparseDiffTools = "2.17"
+SparseDiffTools = "2.19"
 SpeedMapping = "0.3"
 StableRNGs = "1"
 StaticArrays = "1.7"

From 15cdafbf544267dc069c0cf6da059e9412c630f2 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Thu, 16 May 2024 11:53:25 +0200
Subject: [PATCH 383/700] Bump

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 9e31722c4..aeff94747 100644
--- a/Project.toml
+++ b/Project.toml
@@ -104,7 +104,7 @@ StaticArrays = "1.7"
 StaticArraysCore = "1.4"
 Sundials = "4.23.1"
 Symbolics = "5.13"
-SymbolicIndexingInterface = "0.3.3"
+SymbolicIndexingInterface = "0.3.15"
 Test = "1.10"
 TimerOutputs = "0.5.23"
 Zygote = "0.6.69"

From 59f0d7dcabb4fb3c934e960ef45527f8e13faf48 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Thu, 16 May 2024 11:56:51 +0200
Subject: [PATCH 384/700] Bump version

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 5a64b5e62..9a95cb7fd 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.8.0"
+version = "1.8.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 8f02437019f57699dde38fddbc632d48c8095b05 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Thu, 16 May 2024 12:01:15 +0200
Subject: [PATCH 385/700] Bump

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index aeff94747..5b209db51 100644
--- a/Project.toml
+++ b/Project.toml
@@ -69,7 +69,7 @@ Enzyme = "0.11.15, 0.12"
 FastBroadcast = "0.2.8"
 FastClosures = "0.3.2"
 FastLevenbergMarquardt = "0.1"
-FiniteDiff = "2.21"
+FiniteDiff = "2.22"
 FixedPointAcceleration = "0.3"
 ForwardDiff = "0.10.36"
 LazyArrays = "1.8.2"

From b7284510e8d86358533edeabc6b365a2fc3c6589 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Thu, 16 May 2024 12:03:25 +0200
Subject: [PATCH 386/700] Bump

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 5b209db51..a43284ca4 100644
--- a/Project.toml
+++ b/Project.toml
@@ -100,7 +100,7 @@ SparseArrays = "1.10"
 SparseDiffTools = "2.19"
 SpeedMapping = "0.3"
 StableRNGs = "1"
-StaticArrays = "1.7"
+StaticArrays = "1.9"
 StaticArraysCore = "1.4"
 Sundials = "4.23.1"
 Symbolics = "5.13"

From 844d78c73b4ff2bab3b184745c06845e3b24c9e0 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Thu, 16 May 2024 18:07:04 +0200
Subject: [PATCH 387/700] Fix check_forward_mode and check_reverse_mode

---
 src/globalization/line_search.jl           | 2 +-
 src/internal/approximate_initialization.jl | 2 +-
 src/internal/jacobian.jl                   | 8 ++++----
 3 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index 5c76d335a..3cd30424f 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -122,7 +122,7 @@ function __internal_init(
             end
         else
             autodiff = get_concrete_reverse_ad(
-                alg.autodiff, prob; check_forward_mode = true)
+                alg.autodiff, prob; check_reverse_mode = true)
             vjp_op = VecJacOperator(prob, fu, u; autodiff)
             if isinplace(prob)
                 g_cache = similar(u)
diff --git a/src/internal/approximate_initialization.jl b/src/internal/approximate_initialization.jl
index 60f4a7584..a1f36f475 100644
--- a/src/internal/approximate_initialization.jl
+++ b/src/internal/approximate_initialization.jl
@@ -149,7 +149,7 @@ function __internal_init(
         prob::AbstractNonlinearProblem, alg::TrueJacobianInitialization, solver, f::F, fu,
         u, p; linsolve = missing, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     autodiff = get_concrete_forward_ad(
-        alg.autodiff, prob; check_reverse_mode = false, kwargs...)
+        alg.autodiff, prob; check_forward_mode = false, kwargs...)
     jac_cache = JacobianCache(prob, solver, prob.f, fu, u, p; autodiff, linsolve)
     J = alg.structure(jac_cache(nothing))
     return InitializedApproximateJacobianCache(
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 862773ea3..b9cd6d352 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -56,11 +56,11 @@ function JacobianCache(
     iip = isinplace(prob)
     uf = JacobianWrapper{iip}(f, p)
 
-    autodiff = get_concrete_forward_ad(autodiff, prob; check_reverse_mode = false)
+    autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
     jvp_autodiff = get_concrete_forward_ad(
-        jvp_autodiff, prob, Val(false); check_reverse_mode = true)
+        jvp_autodiff, prob, Val(false); check_forward_mode = true)
     vjp_autodiff = get_concrete_reverse_ad(
-        vjp_autodiff, prob, Val(false); check_forward_mode = false)
+        vjp_autodiff, prob, Val(false); check_reverse_mode = false)
 
     has_analytic_jac = SciMLBase.has_jac(f)
     linsolve_needs_jac = concrete_jac(alg) === nothing && (linsolve === missing ||
@@ -100,7 +100,7 @@ end
 function JacobianCache(
         prob, alg, f::F, ::Number, u::Number, p; autodiff = nothing, kwargs...) where {F}
     uf = JacobianWrapper{false}(f, p)
-    autodiff = get_concrete_forward_ad(autodiff, prob; check_reverse_mode = false)
+    autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
     if !(autodiff isa AutoForwardDiff ||
          autodiff isa AutoPolyesterForwardDiff ||
          autodiff isa AutoFiniteDiff)

From 452f4da7d8efdf2050d67c2d74a3509d67ddb87b Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Fri, 17 May 2024 11:31:26 +0200
Subject: [PATCH 388/700] Bump version

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 4f199888d..9d19e42df 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.11.0"
+version = "3.12.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From b0406936d1235645c287d41763ca3b10b1786106 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 17 May 2024 14:45:26 -0400
Subject: [PATCH 389/700] Remove Enzyme special handling on windows

---
 .github/workflows/FormatCheck.yml             | 43 +++----------------
 Project.toml                                  | 13 ++----
 test/core/rootfind_tests.jl                   | 21 +++------
 test/downstream/Project.toml                  |  4 --
 test/downstream/downstream_tests.jl           | 11 -----
 ...ndexing.jl => mtk_cache_indexing_tests.jl} |  0
 6 files changed, 14 insertions(+), 78 deletions(-)
 delete mode 100644 test/downstream/Project.toml
 delete mode 100644 test/downstream/downstream_tests.jl
 rename test/downstream/{cache_indexing.jl => mtk_cache_indexing_tests.jl} (100%)

diff --git a/.github/workflows/FormatCheck.yml b/.github/workflows/FormatCheck.yml
index dd551501c..8601ad558 100644
--- a/.github/workflows/FormatCheck.yml
+++ b/.github/workflows/FormatCheck.yml
@@ -1,42 +1,9 @@
-name: format-check
+name: Format suggestions
 
-on:
-  push:
-    branches:
-      - 'master'
-      - 'release-'
-    tags: '*'
-  pull_request:
+on: [pull_request]
 
 jobs:
-  build:
-    runs-on: ${{ matrix.os }}
-    strategy:
-      matrix:
-        julia-version: [1]
-        julia-arch: [x86]
-        os: [ubuntu-latest]
+  code-style:
+    runs-on: ubuntu-latest
     steps:
-      - uses: julia-actions/setup-julia@latest
-        with:
-          version: ${{ matrix.julia-version }}
-
-      - uses: actions/checkout@v4
-      - name: Install JuliaFormatter and format
-        # This will use the latest version by default but you can set the version like so:
-        #
-        # julia  -e 'using Pkg; Pkg.add(PackageSpec(name="JuliaFormatter", version="0.13.0"))'
-        run: |
-          julia  -e 'using Pkg; Pkg.add(PackageSpec(name="JuliaFormatter"))'
-          julia  -e 'using JuliaFormatter; format(".", verbose=true)'
-      - name: Format check
-        run: |
-          julia -e '
-          out = Cmd(`git diff --name-only`) |> read |> String
-          if out == ""
-              exit(0)
-          else
-              @error "Some files have not been formatted !!!"
-              write(stdout, out)
-              exit(1)
-          end'
+      - uses: julia-actions/julia-format@v2
diff --git a/Project.toml b/Project.toml
index 1d5bff935..cb34c6fb5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -65,7 +65,7 @@ BenchmarkTools = "1.4"
 CUDA = "5.2"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149.0"
-Enzyme = "0.11.15, 0.12"
+Enzyme = "0.12"
 FastBroadcast = "0.2.8"
 FastClosures = "0.3.2"
 FastLevenbergMarquardt = "0.1"
@@ -103,8 +103,8 @@ StableRNGs = "1"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4"
 Sundials = "4.23.1"
-Symbolics = "5.13"
 SymbolicIndexingInterface = "0.3.15"
+Symbolics = "5.13"
 Test = "1.10"
 TimerOutputs = "0.5.23"
 Zygote = "0.6.69"
@@ -115,15 +115,12 @@ Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
-DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 FastLevenbergMarquardt = "7a0df574-e128-4d35-8cbd-3d84502bf7ce"
 FixedPointAcceleration = "817d07cb-a79a-5c30-9a31-890123675176"
-ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
-LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 MINPACK = "4854310b-de5a-5eb6-a2a5-c1dee2bd17f9"
+ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 NaNMath = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
@@ -132,10 +129,8 @@ OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
-Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
-SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
 SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
@@ -145,4 +140,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "Enzyme", "BenchmarkTools", "SafeTestsets", "Pkg", "Test", "ForwardDiff", "StaticArrays", "Symbolics", "LinearSolve", "Random", "LinearAlgebra", "Zygote", "SparseDiffTools", "NonlinearProblemLibrary", "LeastSquaresOptim", "FastLevenbergMarquardt", "NaNMath", "BandedMatrices", "DiffEqBase", "StableRNGs", "MINPACK", "NLsolve", "OrdinaryDiffEq", "SpeedMapping", "FixedPointAcceleration", "SIAMFANLEquations", "Sundials", "ReTestItems", "Reexport", "CUDA", "NLSolvers"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "FastLevenbergMarquardt", "FixedPointAcceleration", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEq", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SafeTestsets", "SparseDiffTools", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index 688678ff2..c68fc8280 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -3,16 +3,6 @@ using Reexport
 @reexport using BenchmarkTools, LinearSolve, NonlinearSolve, StaticArrays, Random,
                 LinearAlgebra, ForwardDiff, Zygote, Enzyme, SparseDiffTools, DiffEqBase
 
-function __autosparseenzyme()
-    @static if Sys.iswindows()
-        @warn "Enzyme on Windows stalls. Using AutoSparse(AutoFiniteDiff()) instead till \
-               https://github.com/EnzymeAD/Enzyme.jl/issues/1236 is resolved."
-        return AutoSparse(AutoFiniteDiff())
-    else
-        return AutoSparse(AutoEnzyme())
-    end
-end
-
 _nameof(x) = applicable(nameof, x) ? nameof(x) : _nameof(typeof(x))
 
 quadratic_f(u, p) = u .* u .- p
@@ -58,8 +48,7 @@ function nlprob_iterator_interface(f, p_range, ::Val{iip}, solver) where {iip}
 end
 
 export nlprob_iterator_interface, benchmark_nlsolve_oop, benchmark_nlsolve_iip,
-       TERMINATION_CONDITIONS, _nameof, newton_fails, quadratic_f, quadratic_f!,
-       __autosparseenzyme
+       TERMINATION_CONDITIONS, _nameof, newton_fails, quadratic_f, quadratic_f!
 end
 
 # --- NewtonRaphson tests ---
@@ -113,7 +102,7 @@ end
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
             AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
-            AutoZygote(), AutoSparse(AutoZygote()), __autosparseenzyme()),
+            AutoZygote(), AutoSparse(AutoZygote()), AutoSparse(AutoEnzyme())),
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -176,7 +165,7 @@ end
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0)) radius_update_scheme: $(radius_update_scheme)" for autodiff in (
             AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
-            AutoZygote(), AutoSparse(AutoZygote()), __autosparseenzyme()),
+            AutoZygote(), AutoSparse(AutoZygote()), AutoSparse(AutoEnzyme())),
         u0 in (1.0, [1.0, 1.0]),
         radius_update_scheme in radius_update_schemes
 
@@ -272,7 +261,7 @@ end
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
             AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
-            AutoZygote(), AutoSparse(AutoZygote()), __autosparseenzyme()),
+            AutoZygote(), AutoSparse(AutoZygote()), AutoSparse(AutoEnzyme())),
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -454,7 +443,7 @@ end
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
             AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
-            AutoZygote(), AutoSparse(AutoZygote()), __autosparseenzyme()),
+            AutoZygote(), AutoSparse(AutoZygote()), AutoSparse(AutoEnzyme())),
         u0 in (1.0, [1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
diff --git a/test/downstream/Project.toml b/test/downstream/Project.toml
deleted file mode 100644
index 5d5467639..000000000
--- a/test/downstream/Project.toml
+++ /dev/null
@@ -1,4 +0,0 @@
-[deps]
-ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
-NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
-SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
diff --git a/test/downstream/downstream_tests.jl b/test/downstream/downstream_tests.jl
deleted file mode 100644
index 773a75815..000000000
--- a/test/downstream/downstream_tests.jl
+++ /dev/null
@@ -1,11 +0,0 @@
-using Pkg
-using SafeTestsets
-
-function activate_downstream_env()
-    Pkg.activate("downstream")
-    Pkg.develop(PackageSpec(path = dirname(dirname(@__DIR__))))
-    Pkg.instantiate()
-end
-
-activate_downstream_env()
-@safetestset "Cache indexing test" include("cache_indexing.jl")
diff --git a/test/downstream/cache_indexing.jl b/test/downstream/mtk_cache_indexing_tests.jl
similarity index 100%
rename from test/downstream/cache_indexing.jl
rename to test/downstream/mtk_cache_indexing_tests.jl

From a9f92b60dfe849cfaed14f9e92d0adbbf1d7e07f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 17 May 2024 11:40:43 -0400
Subject: [PATCH 390/700] Clean up the testing

---
 .../.buildkite/pipeline.yml                   |  2 +-
 .../.github/workflows/FormatCheck.yml         | 43 ++---------------
 lib/SimpleNonlinearSolve/Project.toml         | 10 ++--
 .../test/core/23_test_problems_tests.jl       | 16 ++++---
 .../test/core/adjoint_tests.jl                |  2 +-
 .../test/core/aqua_tests.jl                   |  2 +-
 .../test/core/forward_ad_tests.jl             |  4 +-
 .../test/core/least_squares_tests.jl          |  2 +-
 .../test/core/matrix_resizing_tests.jl        |  2 +-
 .../test/core/rootfind_tests.jl               | 48 ++++---------------
 .../test/gpu/cuda_tests.jl                    |  4 +-
 lib/SimpleNonlinearSolve/test/runtests.jl     | 15 +++---
 12 files changed, 46 insertions(+), 104 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml b/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
index f95a8351f..6083fe1f0 100644
--- a/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
+++ b/lib/SimpleNonlinearSolve/.buildkite/pipeline.yml
@@ -22,4 +22,4 @@ env:
   JULIA_PKG_SERVER: ""
   RETESTITEMS_NWORKERS: 4
   RETESTITEMS_NWORKER_THREADS: 2
-  SECRET_CODECOV_TOKEN: "HsC3X/h3CrsRhMR199BUbw9xmASfTTEtdT2JMJlbkW6nsMtZXDIWxKzBNOpn0123zn3K+VE30i7+aLpcqZjlux0BQDMVLx5O5KudjrJmBE2G8KMMv1pra+UHEOFdFP3TzjHXGcHzpUrjpG8if8cHbsWdyQCV0Hdx2qAPnhX5haGPyMuIlRfoaWQfdxJPl5fDLXs1xe0LnMcYMx8uUsvvJZ/hhFtMYWJU0WFtqnAkCR8h/pQd6yZOaGP2SXJkOR8+1xbx+M8m6agH9idp2BjDPpXMOo27V3O2Gkoy3R4b5ouLdqOMaZSIOemoYCv6oh+EkbKaFvZydvm0xCW5YBFPPw==;U2FsdGVkX19FT0yFV6EMY/NVSQslXE6byckN0qa/HVU5dd3d4swmOCWBkBPtemRPGvCMP669iXSPfDTlw7ZSvw=="
\ No newline at end of file
+  SECRET_CODECOV_TOKEN: "HsC3X/h3CrsRhMR199BUbw9xmASfTTEtdT2JMJlbkW6nsMtZXDIWxKzBNOpn0123zn3K+VE30i7+aLpcqZjlux0BQDMVLx5O5KudjrJmBE2G8KMMv1pra+UHEOFdFP3TzjHXGcHzpUrjpG8if8cHbsWdyQCV0Hdx2qAPnhX5haGPyMuIlRfoaWQfdxJPl5fDLXs1xe0LnMcYMx8uUsvvJZ/hhFtMYWJU0WFtqnAkCR8h/pQd6yZOaGP2SXJkOR8+1xbx+M8m6agH9idp2BjDPpXMOo27V3O2Gkoy3R4b5ouLdqOMaZSIOemoYCv6oh+EkbKaFvZydvm0xCW5YBFPPw==;U2FsdGVkX19FT0yFV6EMY/NVSQslXE6byckN0qa/HVU5dd3d4swmOCWBkBPtemRPGvCMP669iXSPfDTlw7ZSvw=="
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
index 45bd09c47..8601ad558 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
@@ -1,42 +1,9 @@
-name: format-check
+name: Format suggestions
 
-on:
-  push:
-    branches:
-      - 'main'
-      - 'release-'
-    tags: '*'
-  pull_request:
+on: [pull_request]
 
 jobs:
-  build:
-    runs-on: ${{ matrix.os }}
-    strategy:
-      matrix:
-        julia-version: [1]
-        julia-arch: [x86]
-        os: [ubuntu-latest]
+  code-style:
+    runs-on: ubuntu-latest
     steps:
-      - uses: julia-actions/setup-julia@latest
-        with:
-          version: ${{ matrix.julia-version }}
-
-      - uses: actions/checkout@v4
-      - name: Install JuliaFormatter and format
-        # This will use the latest version by default but you can set the version like so:
-        #
-        # julia  -e 'using Pkg; Pkg.add(PackageSpec(name="JuliaFormatter", version="0.13.0"))'
-        run: |
-          julia  -e 'using Pkg; Pkg.add(PackageSpec(name="JuliaFormatter"))'
-          julia  -e 'using JuliaFormatter; format(".", verbose=true)'
-      - name: Format check
-        run: |
-          julia -e '
-          out = Cmd(`git diff --name-only`) |> read |> String
-          if out == ""
-              exit(0)
-          else
-              @error "Some files have not been formatted !!!"
-              write(stdout, out)
-              exit(1)
-          end'
+      - uses: julia-actions/julia-format@v2
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 9a95cb7fd..322178ba9 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -36,10 +36,10 @@ SimpleNonlinearSolveTrackerExt = "Tracker"
 SimpleNonlinearSolveZygoteExt = "Zygote"
 
 [compat]
-ADTypes = "1"
+ADTypes = "1.2"
 AllocCheck = "0.1.1"
 Aqua = "0.8"
-ArrayInterface = "7.8"
+ArrayInterface = "7.9"
 CUDA = "5.2"
 ChainRulesCore = "1.22"
 ConcreteStructs = "0.2.3"
@@ -49,7 +49,7 @@ FastClosures = "0.3.2"
 FiniteDiff = "2.22"
 ForwardDiff = "0.10.36"
 LinearAlgebra = "1.10"
-LinearSolve = "2.25"
+LinearSolve = "2.30"
 MaybeInplace = "0.1.1"
 NonlinearProblemLibrary = "0.1.2"
 Pkg = "1.10"
@@ -59,8 +59,8 @@ Random = "1.10"
 ReTestItems = "1.23"
 Reexport = "1.2"
 ReverseDiff = "1.15"
-SciMLBase = "2.28.0"
-SciMLSensitivity = "7.56"
+SciMLBase = "2.37.0"
+SciMLSensitivity = "7.58"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4.2"
 Test = "1.10"
diff --git a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
index 8b8f2395d..2180943fc 100644
--- a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
@@ -41,7 +41,7 @@ end
 export problems, dicts, test_on_library
 end
 
-@testitem "SimpleNewtonRaphson" setup=[RobustnessTesting] begin
+@testitem "SimpleNewtonRaphson" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (SimpleNewtonRaphson(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -50,7 +50,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "SimpleTrustRegion" setup=[RobustnessTesting] begin
+@testitem "SimpleTrustRegion" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (SimpleTrustRegion(),
         SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
 
@@ -61,16 +61,20 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "SimpleDFSane" setup=[RobustnessTesting] begin
+@testitem "SimpleDFSane" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (SimpleDFSane(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 2, 3, 4, 5, 6, 11, 21]
+    if Sys.isapple()
+        broken_tests[alg_ops[1]] = [1, 2, 3, 5, 6, 21]
+    else
+        broken_tests[alg_ops[1]] = [1, 2, 3, 4, 5, 6, 11, 21]
+    end
 
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "SimpleBroyden" retries=5 setup=[RobustnessTesting] begin
+@testitem "SimpleBroyden" retries=5 setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (SimpleBroyden(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -79,7 +83,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "SimpleKlement" setup=[RobustnessTesting] begin
+@testitem "SimpleKlement" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (SimpleKlement(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
diff --git a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
index 74d745f65..749be1ada 100644
--- a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Simple Adjoint Test" begin
+@testitem "Simple Adjoint Test" tags=[:core] begin
     using ForwardDiff, ReverseDiff, SciMLSensitivity, Tracker, Zygote
 
     ff(u, p) = u .^ 2 .- p
diff --git a/lib/SimpleNonlinearSolve/test/core/aqua_tests.jl b/lib/SimpleNonlinearSolve/test/core/aqua_tests.jl
index 72437ff37..364f51b59 100644
--- a/lib/SimpleNonlinearSolve/test/core/aqua_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/aqua_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Aqua" begin
+@testitem "Aqua" tags=[:core] begin
     using Aqua
 
     Aqua.test_all(SimpleNonlinearSolve; piracies = false, ambiguities = false)
diff --git a/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl b/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
index e0852ba53..50fc18e94 100644
--- a/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
@@ -40,7 +40,7 @@ __compatible(::SimpleHalley, ::Val{:iip}) = false
 export test_f, test_f!, jacobian_f, solve_with, __compatible
 end
 
-@testitem "ForwardDiff.jl Integration: Rootfinding" setup=[ForwardADRootfindingTesting] begin
+@testitem "ForwardDiff.jl Integration: Rootfinding" setup=[ForwardADRootfindingTesting] tags=[:core] begin
     @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(),
         SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
         SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleDFSane())
@@ -133,7 +133,7 @@ export loss_function, loss_function!, loss_function_jac, loss_function_vjp,
        loss_function_jac!, loss_function_vjp!, θ_init, x, y_target
 end
 
-@testitem "ForwardDiff.jl Integration: NLLS" setup=[ForwardADNLLSTesting] begin
+@testitem "ForwardDiff.jl Integration: NLLS" setup=[ForwardADNLLSTesting] tags=[:core] begin
     @testset "$(nameof(typeof(alg)))" for alg in (
         SimpleNewtonRaphson(), SimpleGaussNewton(),
         SimpleNewtonRaphson(AutoFiniteDiff()), SimpleGaussNewton(AutoFiniteDiff()))
diff --git a/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl b/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl
index 840a4f277..ef3a05504 100644
--- a/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Nonlinear Least Squares" begin
+@testitem "Nonlinear Least Squares" tags=[:core] begin
     using LinearAlgebra
 
     true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
diff --git a/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl b/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl
index 54cf86b21..17cd3d674 100644
--- a/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Matrix Resizing" begin
+@testitem "Matrix Resizing" tags=[:core] begin
     ff(u, p) = u .* u .- p
     u0 = ones(2, 3)
     p = 2.0
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index 726a6dda7..ca0e26ef6 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -39,7 +39,7 @@ export quadratic_f, quadratic_f!, quadratic_f2, newton_fails, TERMINATION_CONDIT
 
 end
 
-@testitem "First Order Methods" setup=[RootfindingTesting] begin
+@testitem "First Order Methods" setup=[RootfindingTesting] tags=[:core] begin
     @testset "$(alg)" for alg in (SimpleNewtonRaphson, SimpleTrustRegion,
         (args...; kwargs...) -> SimpleTrustRegion(args...; nlsolve_update_rule = Val(true),
             kwargs...))
@@ -70,7 +70,7 @@ end
     end
 end
 
-@testitem "SimpleHalley" setup=[RootfindingTesting] begin
+@testitem "SimpleHalley" setup=[RootfindingTesting] tags=[:core] begin
     @testset "AutoDiff: $(nameof(typeof(autodiff)))" for autodiff in (AutoFiniteDiff(),
         AutoForwardDiff())
         @testset "[OOP] u0: $(nameof(typeof(u0)))" for u0 in ([1.0, 1.0],
@@ -89,7 +89,7 @@ end
     end
 end
 
-@testitem "Derivative Free Metods" setup=[RootfindingTesting] begin
+@testitem "Derivative Free Metods" setup=[RootfindingTesting] tags=[:core] begin
     @testset "$(nameof(typeof(alg)))" for alg in [SimpleBroyden(), SimpleKlement(),
         SimpleDFSane(), SimpleLimitedMemoryBroyden(),
         SimpleBroyden(; linesearch = Val(true)),
@@ -115,7 +115,7 @@ end
     end
 end
 
-@testitem "Newton Fails" setup=[RootfindingTesting] begin
+@testitem "Newton Fails" setup=[RootfindingTesting] tags=[:core] begin
     u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
     p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 
@@ -127,13 +127,13 @@ end
     end
 end
 
-@testitem "Kwargs Propagation" setup=[RootfindingTesting] begin
+@testitem "Kwargs Propagation" setup=[RootfindingTesting] tags=[:core] begin
     prob = NonlinearProblem(quadratic_f, ones(4), 2.0; maxiters = 2)
     sol = solve(prob, SimpleNewtonRaphson())
     @test sol.retcode === ReturnCode.MaxIters
 end
 
-@testitem "Allocation Checks" setup=[RootfindingTesting] begin
+@testitem "Allocation Checks" setup=[RootfindingTesting] tags=[:core] begin
     if Sys.islinux()  # Very slow on other OS
         @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(),
             SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
@@ -165,7 +165,7 @@ end
     end
 end
 
-@testitem "Interval Nonlinear Problems" setup=[RootfindingTesting] begin
+@testitem "Interval Nonlinear Problems" setup=[RootfindingTesting] tags=[:core] begin
     @testset "$(nameof(typeof(alg)))" for alg in (Bisection(), Falsi(), Ridder(), Brent(),
         ITP(), Alefeld())
         tspan = (1.0, 20.0)
@@ -209,7 +209,7 @@ end
     end
 end
 
-@testitem "Tolerance Tests Interval Methods" setup=[RootfindingTesting] begin
+@testitem "Tolerance Tests Interval Methods" setup=[RootfindingTesting] tags=[:core] begin
     @testset "$(nameof(typeof(alg)))" for alg in (Bisection(), Falsi(), ITP())
         tspan = (1.0, 20.0)
         probB = IntervalNonlinearProblem(quadratic_f, tspan, 2.0)
@@ -224,7 +224,7 @@ end
     end
 end
 
-@testitem "Tolerance Tests Interval Methods 2" setup=[RootfindingTesting] begin
+@testitem "Tolerance Tests Interval Methods 2" setup=[RootfindingTesting] tags=[:core] begin
     @testset "$(nameof(typeof(alg)))" for alg in (Ridder(), Brent())
         tspan = (1.0, 20.0)
         probB = IntervalNonlinearProblem(quadratic_f, tspan, 2.0)
@@ -239,7 +239,7 @@ end
     end
 end
 
-@testitem "Flipped Signs and Reversed Tspan" setup=[RootfindingTesting] begin
+@testitem "Flipped Signs and Reversed Tspan" setup=[RootfindingTesting] tags=[:core] begin
     @testset "$(nameof(typeof(alg)))" for alg in (Alefeld(), Bisection(), Falsi(), Brent(),
         ITP(), Ridder())
         f1(u, p) = u * u - p
@@ -257,31 +257,3 @@ end
         end
     end
 end
-
-# The following tests were included in the previos versions but these kwargs never did
-# anything!
-# # Garuntee Tests for Bisection
-# f = function (u, p)
-#     if u < 2.0
-#         return u - 2.0
-#     elseif u > 3.0
-#         return u - 3.0
-#     else
-#         return 0.0
-#     end
-# end
-# probB = IntervalNonlinearProblem(f, (0.0, 4.0))
-
-# sol = solve(probB, Bisection(; exact_left = true))
-# @test f(sol.left, nothing) < 0.0
-# @test f(nextfloat(sol.left), nothing) >= 0.0
-
-# sol = solve(probB, Bisection(; exact_right = true))
-# @test f(sol.right, nothing) >= 0.0
-# @test f(prevfloat(sol.right), nothing) <= 0.0
-
-# sol = solve(probB, Bisection(; exact_left = true, exact_right = true); immutable = false)
-# @test f(sol.left, nothing) < 0.0
-# @test f(nextfloat(sol.left), nothing) >= 0.0
-# @test f(sol.right, nothing) >= 0.0
-# @test f(prevfloat(sol.right), nothing) <= 0.0
diff --git a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
index 37999dada..dae6a87d7 100644
--- a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Solving on GPUs" begin
+@testitem "Solving on GPUs" tags=[:cuda] begin
     using StaticArrays, CUDA
 
     CUDA.allowscalar(false)
@@ -36,7 +36,7 @@
     end
 end
 
-@testitem "CUDA Kernel Launch Test" begin
+@testitem "CUDA Kernel Launch Test" tags=[:cuda] begin
     using StaticArrays, CUDA
 
     CUDA.allowscalar(false)
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 1a2e93bb1..2f81c8401 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -1,11 +1,10 @@
-using ReTestItems
+using ReTestItems, CUDA
 
-const GROUP = get(ENV, "GROUP", "All")
+const GROUP = get(ENV, "GROUP", CUDA.functional() ? "All" : "Core")
 
-if GROUP == "All" || GROUP == "Core"
-    ReTestItems.runtests(joinpath(@__DIR__, "core/"))
-end
-
-if GROUP == "GPU"
-    ReTestItems.runtests(joinpath(@__DIR__, "gpu/"))
+if GROUP == "All"
+    ReTestItems.runtests(@__DIR__)
+else
+    tags = [Symbol(lowercase(GROUP))]
+    ReTestItems.runtests(@__DIR__; tags)
 end

From cfd0d2c7f4675439e4798fd03f3cb36a566cd4d8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 17 May 2024 16:34:41 -0400
Subject: [PATCH 391/700] Use tags

---
 .buildkite/pipeline.yml                     |  2 +-
 .github/workflows/CI.yml                    |  2 +
 Project.toml                                | 11 ++-
 test/core/23_test_problems_tests.jl         | 33 +++++---
 test/core/forward_ad_tests.jl               |  4 +-
 test/core/nlls_tests.jl                     |  6 +-
 test/core/rootfind_tests.jl                 | 19 ++---
 test/downstream/mtk_cache_indexing_tests.jl | 92 +++++++++++----------
 test/gpu/core_tests.jl                      |  2 +-
 test/misc/aliasing_tests.jl                 |  2 +-
 test/misc/banded_matrices_tests.jl          |  2 +-
 test/misc/bruss_tests.jl                    |  2 +-
 test/misc/linsolve_switching_tests.jl       |  2 +-
 test/misc/matrix_resizing_tests.jl          |  4 +-
 test/misc/noinit_caching_tests.jl           |  2 +-
 test/misc/polyalg_tests.jl                  | 16 ++--
 test/misc/qa_tests.jl                       |  2 +-
 test/runtests.jl                            | 20 ++---
 test/wrappers/fixedpoint_tests.jl           |  6 +-
 test/wrappers/nlls_tests.jl                 | 13 +--
 test/wrappers/rootfind_tests.jl             | 10 ++-
 21 files changed, 132 insertions(+), 120 deletions(-)

diff --git a/.buildkite/pipeline.yml b/.buildkite/pipeline.yml
index 2dffa0582..b9a145400 100644
--- a/.buildkite/pipeline.yml
+++ b/.buildkite/pipeline.yml
@@ -18,7 +18,7 @@ steps:
     if: build.message !~ /\[skip tests\]/
 
 env:
-  GROUP: GPU
+  GROUP: CUDA
   JULIA_PKG_SERVER: "" # it often struggles with our large artifacts
   RETESTITEMS_NWORKERS: 4
   RETESTITEMS_NWORKER_THREADS: 2
diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 2dfaa4f65..21263f5f3 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -20,6 +20,8 @@ jobs:
         group:
           - Core
           - Downstream
+          - Misc
+          - Wrappers
         version:
           - "1"
         os:
diff --git a/Project.toml b/Project.toml
index cb34c6fb5..f8e7162b8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -76,9 +76,10 @@ LazyArrays = "1.8.2"
 LeastSquaresOptim = "0.8.5"
 LineSearches = "7.2"
 LinearAlgebra = "1.10"
-LinearSolve = "2.29"
+LinearSolve = "2.30"
 MINPACK = "1.2"
 MaybeInplace = "0.1.1"
+ModelingToolkit = "9.13.0"
 NLSolvers = "0.5"
 NLsolve = "4.5"
 NaNMath = "1"
@@ -89,11 +90,10 @@ PrecompileTools = "1.2"
 Preferences = "1.4"
 Printf = "1.10"
 Random = "1.91"
-ReTestItems = "1"
+ReTestItems = "1.24"
 RecursiveArrayTools = "3.8"
 Reexport = "1.2"
 SIAMFANLEquations = "1.0.1"
-SafeTestsets = "0.1"
 SciMLBase = "2.34.0"
 SimpleNonlinearSolve = "1.8"
 SparseArrays = "1.10"
@@ -104,7 +104,7 @@ StaticArrays = "1.9"
 StaticArraysCore = "1.4"
 Sundials = "4.23.1"
 SymbolicIndexingInterface = "0.3.15"
-Symbolics = "5.13"
+Symbolics = "5.26"
 Test = "1.10"
 TimerOutputs = "0.5.23"
 Zygote = "0.6.69"
@@ -130,7 +130,6 @@ Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
-SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
@@ -140,4 +139,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "FastLevenbergMarquardt", "FixedPointAcceleration", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEq", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SafeTestsets", "SparseDiffTools", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "FastLevenbergMarquardt", "FixedPointAcceleration", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEq", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
diff --git a/test/core/23_test_problems_tests.jl b/test/core/23_test_problems_tests.jl
index b0f17113a..7305af96f 100644
--- a/test/core/23_test_problems_tests.jl
+++ b/test/core/23_test_problems_tests.jl
@@ -40,7 +40,7 @@ end
 export test_on_library, problems, dicts
 end
 
-@testitem "PolyAlgorithms" setup=[RobustnessTesting] begin
+@testitem "PolyAlgorithms" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (RobustMultiNewton(), FastShortcutNonlinearPolyalg())
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -50,7 +50,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "NewtonRaphson" setup=[RobustnessTesting] begin
+@testitem "NewtonRaphson" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (NewtonRaphson(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -59,7 +59,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "TrustRegion" setup=[RobustnessTesting] begin
+@testitem "TrustRegion" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Simple),
         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Fan),
         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Hei),
@@ -78,7 +78,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "LevenbergMarquardt" setup=[RobustnessTesting] begin
+@testitem "LevenbergMarquardt" setup=[RobustnessTesting] tags=[:core] begin
     using LinearSolve
 
     alg_ops = (LevenbergMarquardt(), LevenbergMarquardt(; α_geodesic = 0.1),
@@ -92,7 +92,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "DFSane" setup=[RobustnessTesting] begin
+@testitem "DFSane" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (DFSane(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -101,21 +101,28 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "Broyden" setup=[RobustnessTesting] begin
+@testitem "Broyden" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian)),
         Broyden(; update_rule = Val(:bad_broyden)),
         Broyden(; init_jacobian = Val(:true_jacobian), update_rule = Val(:bad_broyden)))
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 5, 11, 15]
-    broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
-    broken_tests[alg_ops[3]] = [1, 5, 9, 11]
-    broken_tests[alg_ops[4]] = [5, 6, 8, 11]
+    if Sys.isapple()
+        broken_tests[alg_ops[1]] = [1, 5, 11]
+        broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
+        broken_tests[alg_ops[3]] = [1, 5, 6, 9, 11]
+        broken_tests[alg_ops[4]] = [5, 6, 8, 11]
+    else
+        broken_tests[alg_ops[1]] = [1, 5, 11, 15]
+        broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
+        broken_tests[alg_ops[3]] = [1, 5, 9, 11]
+        broken_tests[alg_ops[4]] = [5, 6, 8, 11]
+    end
 
-    test_on_library(problems, dicts, alg_ops, broken_tests)
+    test_on_library(problems, dicts, alg_ops, broken_tests, Sys.isapple() ? 1e-3 : 1e-4)
 end
 
-@testitem "Klement" retries=5 setup=[RobustnessTesting] begin
+@testitem "Klement" retries=5 setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (Klement(), Klement(; init_jacobian = Val(:true_jacobian_diagonal)))
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -125,7 +132,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "PseudoTransient" setup=[RobustnessTesting] begin
+@testitem "PseudoTransient" setup=[RobustnessTesting] tags=[:core] begin
     # PT relies on the root being a stable equilibrium for convergence, so it won't work on
     # most problems
     alg_ops = (PseudoTransient(),)
diff --git a/test/core/forward_ad_tests.jl b/test/core/forward_ad_tests.jl
index 46034d844..24711b9d9 100644
--- a/test/core/forward_ad_tests.jl
+++ b/test/core/forward_ad_tests.jl
@@ -62,12 +62,14 @@ __compatible(::KINSOL, ::Val{:oop_cache}) = false
 export test_f!, test_f, jacobian_f, solve_with, __compatible
 end
 
-@testitem "ForwardDiff.jl Integration" setup=[ForwardADTesting] begin
+@testitem "ForwardDiff.jl Integration" setup=[ForwardADTesting] tags=[:core] begin
     for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
         PseudoTransient(; alpha_initial = 10.0), Broyden(), Klement(), DFSane(),
         nothing, NLsolveJL(), CMINPACK(), KINSOL(; globalization_strategy = :LineSearch))
         us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
 
+        alg isa CMINPACK && Sys.isapple() && continue
+
         @testset "Scalar AD" begin
             for p in 1.0:0.1:100.0, u0 in us, mode in (:iip, :oop, :iip_cache, :oop_cache)
                 __compatible(u0, alg) || continue
diff --git a/test/core/nlls_tests.jl b/test/core/nlls_tests.jl
index a1506d356..483107f69 100644
--- a/test/core/nlls_tests.jl
+++ b/test/core/nlls_tests.jl
@@ -48,7 +48,7 @@ end
 export solvers, θ_init, x, y_target, true_function, θ_true, loss_function
 end
 
-@testitem "General NLLS Solvers" setup=[CoreNLLSTesting] begin
+@testitem "General NLLS Solvers" setup=[CoreNLLSTesting] tags=[:core] begin
     prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
     prob_iip = NonlinearLeastSquaresProblem(
         NonlinearFunction(loss_function; resid_prototype = zero(y_target)), θ_init, x)
@@ -62,7 +62,7 @@ end
     end
 end
 
-@testitem "Custom VJP" setup=[CoreNLLSTesting] begin
+@testitem "Custom VJP" setup=[CoreNLLSTesting] tags=[:core] begin
     # This is just for testing that we can use vjp provided by the user
     function vjp(v, θ, p)
         resid = zeros(length(p))
@@ -96,7 +96,7 @@ end
     end
 end
 
-@testitem "NLLS Analytic Jacobian" begin
+@testitem "NLLS Analytic Jacobian" tags=[:core] begin
     dataIn = 1:10
     f(x, p) = x[1] * dataIn .^ 2 .+ x[2] * dataIn .+ x[3]
     dataOut = f([1, 2, 3], nothing) + 0.1 * randn(10, 1)
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index c68fc8280..ce27ee6c8 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -20,7 +20,6 @@ function newton_fails(u, p)
 end
 
 const TERMINATION_CONDITIONS = [
-    SteadyStateDiffEqTerminationMode(), SimpleNonlinearSolveTerminationMode(),
     NormTerminationMode(), RelTerminationMode(), RelNormTerminationMode(),
     AbsTerminationMode(), AbsNormTerminationMode(), RelSafeTerminationMode(),
     AbsSafeTerminationMode(), RelSafeBestTerminationMode(), AbsSafeBestTerminationMode()]
@@ -53,7 +52,7 @@ end
 
 # --- NewtonRaphson tests ---
 
-@testitem "NewtonRaphson" setup=[CoreRootfindTesting] begin
+@testitem "NewtonRaphson" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad))" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
         ad in (AutoFiniteDiff(), AutoZygote())
@@ -119,7 +118,7 @@ end
 
 # --- TrustRegion tests ---
 
-@testitem "TrustRegion" setup=[CoreRootfindTesting] begin
+@testitem "TrustRegion" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
     radius_update_schemes = [RadiusUpdateSchemes.Simple, RadiusUpdateSchemes.NocedalWright,
         RadiusUpdateSchemes.NLsolve, RadiusUpdateSchemes.Hei,
         RadiusUpdateSchemes.Yuan, RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin]
@@ -237,7 +236,7 @@ end
 
 # --- LevenbergMarquardt tests ---
 
-@testitem "LevenbergMarquardt" setup=[CoreRootfindTesting] begin
+@testitem "LevenbergMarquardt" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
     u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
     @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
         sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = LevenbergMarquardt())
@@ -323,7 +322,7 @@ end
 
 # --- DFSane tests ---
 
-@testitem "DFSane" setup=[CoreRootfindTesting] begin
+@testitem "DFSane" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
     u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
 
     @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
@@ -394,7 +393,7 @@ end
 
 # --- PseudoTransient tests ---
 
-@testitem "PseudoTransient" setup=[CoreRootfindTesting] begin
+@testitem "PseudoTransient" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
     # These are tests for NewtonRaphson so we should set alpha_initial to be high so that we
     # converge quickly
     @testset "PT: alpha_initial = 10.0 PT AD: $(ad)" for ad in (
@@ -463,7 +462,7 @@ end
 
 # --- Broyden tests ---
 
-@testitem "Broyden" setup=[CoreRootfindTesting] begin
+@testitem "Broyden" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian) Update Rule: $(update_rule)" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(),
             HagerZhang(), MoreThuente(), LiFukushimaLineSearch()),
@@ -513,7 +512,7 @@ end
 
 # --- Klement tests ---
 
-@testitem "Klement" setup=[CoreRootfindTesting] begin
+@testitem "Klement" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian)" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
         ad in (AutoFiniteDiff(), AutoZygote()),
@@ -562,7 +561,7 @@ end
 
 # --- LimitedMemoryBroyden tests ---
 
-@testitem "LimitedMemoryBroyden" setup=[CoreRootfindTesting] begin
+@testitem "LimitedMemoryBroyden" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad))" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(),
             HagerZhang(), MoreThuente(), LiFukushimaLineSearch()),
@@ -612,7 +611,7 @@ end
 end
 
 # Miscellaneous Tests
-@testitem "Custom JVP" setup=[CoreRootfindTesting] begin
+@testitem "Custom JVP" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
     function F(u::Vector{Float64}, p::Vector{Float64})
         Δ = Tridiagonal(-ones(99), 2 * ones(100), -ones(99))
         return u + 0.1 * u .* Δ * u - p
diff --git a/test/downstream/mtk_cache_indexing_tests.jl b/test/downstream/mtk_cache_indexing_tests.jl
index a7770f32e..64a073612 100644
--- a/test/downstream/mtk_cache_indexing_tests.jl
+++ b/test/downstream/mtk_cache_indexing_tests.jl
@@ -1,46 +1,48 @@
-using ModelingToolkit, NonlinearSolve
-using ModelingToolkit: t_nounits as t
-
-@parameters p d
-@variables X(t)
-eqs = [0 ~ sin(X + p) - d * sqrt(X + 1)]
-@mtkbuild nlsys = NonlinearSystem(eqs, [X], [p, d])
-
-# Creates an integrator.
-nlprob = NonlinearProblem(nlsys, [X => 1.0], [p => 2.0, d => 3.0])
-
-@testset "GeneralizedFirstOrderAlgorithmCache" begin
-    nint = init(nlprob, NewtonRaphson())
-    @test nint isa NonlinearSolve.GeneralizedFirstOrderAlgorithmCache
-
-    @test nint[X] == 1.0
-    @test nint[nlsys.X] == 1.0
-    @test nint[:X] == 1.0
-    @test nint.ps[p] == 2.0
-    @test nint.ps[nlsys.p] == 2.0
-    @test nint.ps[:p] == 2.0
-end
-
-@testset "NonlinearSolvePolyAlgorithmCache" begin
-    nint = init(nlprob, FastShortcutNonlinearPolyalg())
-    @test nint isa NonlinearSolve.NonlinearSolvePolyAlgorithmCache
-
-    @test nint[X] == 1.0
-    @test nint[nlsys.X] == 1.0
-    @test nint[:X] == 1.0
-    @test nint.ps[p] == 2.0
-    @test nint.ps[nlsys.p] == 2.0
-    @test nint.ps[:p] == 2.0
-end
-
-@testset "NonlinearSolveNoInitCache" begin
-    nint = init(nlprob, SimpleNewtonRaphson())
-    @test nint isa NonlinearSolve.NonlinearSolveNoInitCache
-
-    @test nint[X] == 1.0
-    @test nint[nlsys.X] == 1.0
-    @test nint[:X] == 1.0
-    @test nint.ps[p] == 2.0
-    @test nint.ps[nlsys.p] == 2.0
-    @test nint.ps[:p] == 2.0
+@testitem "Modeling Toolkit Cache Indexing" tags=[:downstream] begin
+    using ModelingToolkit
+    using ModelingToolkit: t_nounits as t
+
+    @parameters p d
+    @variables X(t)
+    eqs = [0 ~ sin(X + p) - d * sqrt(X + 1)]
+    @mtkbuild nlsys = NonlinearSystem(eqs, [X], [p, d])
+
+    # Creates an integrator.
+    nlprob = NonlinearProblem(nlsys, [X => 1.0], [p => 2.0, d => 3.0])
+
+    @testset "GeneralizedFirstOrderAlgorithmCache" begin
+        nint = init(nlprob, NewtonRaphson())
+        @test nint isa NonlinearSolve.GeneralizedFirstOrderAlgorithmCache
+
+        @test nint[X] == 1.0
+        @test nint[nlsys.X] == 1.0
+        @test nint[:X] == 1.0
+        @test nint.ps[p] == 2.0
+        @test nint.ps[nlsys.p] == 2.0
+        @test nint.ps[:p] == 2.0
+    end
+
+    @testset "NonlinearSolvePolyAlgorithmCache" begin
+        nint = init(nlprob, FastShortcutNonlinearPolyalg())
+        @test nint isa NonlinearSolve.NonlinearSolvePolyAlgorithmCache
+
+        @test nint[X] == 1.0
+        @test nint[nlsys.X] == 1.0
+        @test nint[:X] == 1.0
+        @test nint.ps[p] == 2.0
+        @test nint.ps[nlsys.p] == 2.0
+        @test nint.ps[:p] == 2.0
+    end
+
+    @testset "NonlinearSolveNoInitCache" begin
+        nint = init(nlprob, SimpleNewtonRaphson())
+        @test nint isa NonlinearSolve.NonlinearSolveNoInitCache
+
+        @test nint[X] == 1.0
+        @test nint[nlsys.X] == 1.0
+        @test nint[:X] == 1.0
+        @test nint.ps[p] == 2.0
+        @test nint.ps[nlsys.p] == 2.0
+        @test nint.ps[:p] == 2.0
+    end
 end
diff --git a/test/gpu/core_tests.jl b/test/gpu/core_tests.jl
index 6e9806498..79a20cc97 100644
--- a/test/gpu/core_tests.jl
+++ b/test/gpu/core_tests.jl
@@ -1,4 +1,4 @@
-@testitem "CUDA Tests" begin
+@testitem "CUDA Tests" tags=[:cuda] skip=:(using CUDA; !CUDA.functional()) begin
     using CUDA, NonlinearSolve, LinearSolve, StableRNGs
 
     CUDA.allowscalar(false)
diff --git a/test/misc/aliasing_tests.jl b/test/misc/aliasing_tests.jl
index 857233029..653490dfa 100644
--- a/test/misc/aliasing_tests.jl
+++ b/test/misc/aliasing_tests.jl
@@ -1,4 +1,4 @@
-@testitem "PolyAlgorithm Aliasing" begin
+@testitem "PolyAlgorithm Aliasing" tags=[:misc] begin
     using NonlinearProblemLibrary
 
     # Use a problem that the initial solvers cannot solve and cause the initial value to
diff --git a/test/misc/banded_matrices_tests.jl b/test/misc/banded_matrices_tests.jl
index d4b8fbee5..a9a2bf4ca 100644
--- a/test/misc/banded_matrices_tests.jl
+++ b/test/misc/banded_matrices_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Banded Matrix vcat" begin
+@testitem "Banded Matrix vcat" tags=[:misc] begin
     using BandedMatrices, LinearAlgebra, SparseArrays
 
     b = BandedMatrix(Ones(5, 5), (1, 1))
diff --git a/test/misc/bruss_tests.jl b/test/misc/bruss_tests.jl
index 43bcc3eb8..21b7d792b 100644
--- a/test/misc/bruss_tests.jl
+++ b/test/misc/bruss_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Brusselator 2D" begin
+@testitem "Brusselator 2D" tags=[:misc] begin
     using LinearAlgebra, SparseArrays, Symbolics
 
     const N = 32
diff --git a/test/misc/linsolve_switching_tests.jl b/test/misc/linsolve_switching_tests.jl
index 521e417cc..34d10e294 100644
--- a/test/misc/linsolve_switching_tests.jl
+++ b/test/misc/linsolve_switching_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Singular Systems -- Auto Linear Solve Switching" begin
+@testitem "Singular Systems -- Auto Linear Solve Switching" tags=[:misc] begin
     using LinearSolve, NonlinearSolve
 
     function f!(du, u, p)
diff --git a/test/misc/matrix_resizing_tests.jl b/test/misc/matrix_resizing_tests.jl
index 9210e3e6b..2aa8151ce 100644
--- a/test/misc/matrix_resizing_tests.jl
+++ b/test/misc/matrix_resizing_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Out-of-place Matrix Resizing" begin
+@testitem "Out-of-place Matrix Resizing" tags=[:misc] begin
     using StableRNGs
 
     ff(u, p) = u .* u .- p
@@ -14,7 +14,7 @@
     end
 end
 
-@testitem "Inplace Matrix Resizing" begin
+@testitem "Inplace Matrix Resizing" tags=[:misc] begin
     using StableRNGs
 
     fiip(du, u, p) = (du .= u .* u .- p)
diff --git a/test/misc/noinit_caching_tests.jl b/test/misc/noinit_caching_tests.jl
index f9207d82f..4ab4138f8 100644
--- a/test/misc/noinit_caching_tests.jl
+++ b/test/misc/noinit_caching_tests.jl
@@ -1,4 +1,4 @@
-@testitem "NoInit Caching" begin
+@testitem "NoInit Caching" tags=[:misc] begin
     using LinearAlgebra
     import NLsolve, NLSolvers
 
diff --git a/test/misc/polyalg_tests.jl b/test/misc/polyalg_tests.jl
index c2864759c..88be7e8cc 100644
--- a/test/misc/polyalg_tests.jl
+++ b/test/misc/polyalg_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Basic PolyAlgorithms" begin
+@testitem "Basic PolyAlgorithms" tags=[:misc] begin
     f(u, p) = u .* u .- 2
     u0 = [1.0, 1.0]
     probN = NonlinearProblem{false}(f, u0)
@@ -55,7 +55,7 @@
     end
 end
 
-@testitem "Testing #153 Singular Exception" begin
+@testitem "Testing #153 Singular Exception" tags=[:misc] begin
     # https://github.com/SciML/NonlinearSolve.jl/issues/153
     function f(du, u, p)
         s1, s1s2, s2 = u
@@ -71,7 +71,7 @@ end
     @test SciMLBase.successful_retcode(sol)
 end
 
-@testitem "PolyAlgorithms Autodiff" begin
+@testitem "PolyAlgorithms Autodiff" tags=[:misc] begin
     cache = zeros(2)
     function f(du, u, p)
         cache .= u .* u
@@ -104,7 +104,7 @@ end
     @test SciMLBase.successful_retcode(sol)
 end
 
-@testitem "Simple Scalar Problem #187" begin
+@testitem "Simple Scalar Problem #187" tags=[:misc] begin
     using NaNMath
 
     # https://github.com/SciML/NonlinearSolve.jl/issues/187
@@ -126,7 +126,7 @@ end
 # Shooting Problem: Taken from BoundaryValueDiffEq.jl
 # Testing for Complex Valued Root Finding. For Complex valued inputs we drop some of the
 # algorithms which dont support those.
-@testitem "Complex Valued Problems: Single-Shooting" begin
+@testitem "Complex Valued Problems: Single-Shooting" tags=[:misc] begin
     using OrdinaryDiffEq
 
     function ode_func!(du, u, p, t)
@@ -153,7 +153,7 @@ end
         prob, RobustMultiNewton(eltype(prob.u0)); abstol = 1e-19, maxiters = 10)
 end
 
-@testitem "No AD" begin
+@testitem "No AD" tags=[:misc] begin
     no_ad_fast = FastShortcutNonlinearPolyalg(autodiff = AutoFiniteDiff())
     no_ad_robust = RobustMultiNewton(autodiff = AutoFiniteDiff())
     no_ad_algs = Set([no_ad_fast, no_ad_robust, no_ad_fast.algs..., no_ad_robust.algs...])
@@ -226,7 +226,7 @@ end
 export f1_infeasible!, f1_infeasible
 end
 
-@testitem "[IIP] Infeasible" setup=[InfeasibleFunction] begin
+@testitem "[IIP] Infeasible" setup=[InfeasibleFunction] tags=[:misc] begin
     u0 = [0.0, 0.0, 0.0]
     prob = NonlinearProblem(f1_infeasible!, u0)
     sol = solve(prob)
@@ -236,7 +236,7 @@ end
     @inferred solve(prob)
 end
 
-@testitem "[OOP] Infeasible" setup=[InfeasibleFunction] begin
+@testitem "[OOP] Infeasible" setup=[InfeasibleFunction] tags=[:misc] begin
     using LinearAlgebra, StaticArrays
 
     u0 = [0.0, 0.0, 0.0]
diff --git a/test/misc/qa_tests.jl b/test/misc/qa_tests.jl
index 28cf1dbf4..79706a376 100644
--- a/test/misc/qa_tests.jl
+++ b/test/misc/qa_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Aqua" begin
+@testitem "Aqua" tags=[:misc] begin
     using NonlinearSolve, SimpleNonlinearSolve, Aqua
 
     Aqua.find_persistent_tasks_deps(NonlinearSolve)
diff --git a/test/runtests.jl b/test/runtests.jl
index a3f786689..421a96f7b 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,16 +1,10 @@
-using ReTestItems
+using ReTestItems, CUDA
 
-const GROUP = get(ENV, "GROUP", "All")
+const GROUP = get(ENV, "GROUP", CUDA.functional() ? "All" : "All")
 
-if GROUP == "All" || GROUP == "Core"
-    ReTestItems.runtests(joinpath(@__DIR__, "core/"), joinpath(@__DIR__, "misc/"),
-        joinpath(@__DIR__, "wrappers/"))
-end
-
-if GROUP == "Downstream"
-    include("downstream/downstream_tests.jl")
-end
-
-if GROUP == "GPU"
-    ReTestItems.runtests(joinpath(@__DIR__, "gpu/"))
+if GROUP == "All"
+    ReTestItems.runtests(@__DIR__)
+else
+    tags = [Symbol(lowercase(GROUP))]
+    ReTestItems.runtests(@__DIR__; tags)
 end
diff --git a/test/wrappers/fixedpoint_tests.jl b/test/wrappers/fixedpoint_tests.jl
index 3d5713844..a3ec497c7 100644
--- a/test/wrappers/fixedpoint_tests.jl
+++ b/test/wrappers/fixedpoint_tests.jl
@@ -5,7 +5,7 @@ import SIAMFANLEquations, FixedPointAcceleration, SpeedMapping, NLsolve
 end
 
 # Simple Scalar Problem
-@testitem "Simple Scalar Problem" setup=[WrapperFixedPointImports] begin
+@testitem "Simple Scalar Problem" setup=[WrapperFixedPointImports] tags=[:wrappers] begin
     f1(x, p) = cos(x) - x
     prob = NonlinearProblem(f1, 1.1)
 
@@ -22,7 +22,7 @@ end
 end
 
 # Simple Vector Problem
-@testitem "Simple Vector Problem" setup=[WrapperFixedPointImports] begin
+@testitem "Simple Vector Problem" setup=[WrapperFixedPointImports] tags=[:wrappers] begin
     f2(x, p) = cos.(x) .- x
     prob = NonlinearProblem(f2, [1.1, 1.1])
 
@@ -41,7 +41,7 @@ end
 
 # Fixed Point for Power Method
 # Taken from https://github.com/NicolasL-S/SpeedMapping.jl/blob/95951db8f8a4457093090e18802ad382db1c76da/test/runtests.jl
-@testitem "Power Method" setup=[WrapperFixedPointImports] begin
+@testitem "Power Method" setup=[WrapperFixedPointImports] tags=[:wrappers] begin
     C = [1 2 3; 4 5 6; 7 8 9]
     A = C + C'
     B = Hermitian(ones(10) * ones(10)' .* im + Diagonal(1:10))
diff --git a/test/wrappers/nlls_tests.jl b/test/wrappers/nlls_tests.jl
index a65ab5ec9..53cea758d 100644
--- a/test/wrappers/nlls_tests.jl
+++ b/test/wrappers/nlls_tests.jl
@@ -28,7 +28,7 @@ end
 export loss_function, θ_init, y_target, true_function, x, θ_true
 end
 
-@testitem "LeastSquaresOptim.jl" setup=[WrapperNLLSSetup] begin
+@testitem "LeastSquaresOptim.jl" setup=[WrapperNLLSSetup] tags=[:wrappers] begin
     prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
     prob_iip = NonlinearLeastSquaresProblem(
         NonlinearFunction(loss_function; resid_prototype = zero(y_target)), θ_init, x)
@@ -46,7 +46,7 @@ end
     end
 end
 
-@testitem "FastLevenbergMarquardt.jl + CMINPACK: Jacobian Provided" setup=[WrapperNLLSSetup] begin
+@testitem "FastLevenbergMarquardt.jl + CMINPACK: Jacobian Provided" setup=[WrapperNLLSSetup] tags=[:wrappers] begin
     function jac!(J, θ, p)
         resid = zeros(length(p))
         ForwardDiff.jacobian!(J, (resid, θ) -> loss_function(resid, θ, p), resid, θ)
@@ -70,14 +70,14 @@ end
             NonlinearFunction{false}(loss_function; jac), θ_init, x)]
 
     solvers = Any[FastLevenbergMarquardtJL(linsolve) for linsolve in (:cholesky, :qr)]
-    push!(solvers, CMINPACK())
+    Sys.isapple() || push!(solvers, CMINPACK())
     for solver in solvers, prob in probs
         sol = solve(prob, solver; maxiters = 10000, abstol = 1e-8)
         @test maximum(abs, sol.resid) < 1e-6
     end
 end
 
-@testitem "FastLevenbergMarquardt.jl + CMINPACK: Jacobian Not Provided" setup=[WrapperNLLSSetup] begin
+@testitem "FastLevenbergMarquardt.jl + CMINPACK: Jacobian Not Provided" setup=[WrapperNLLSSetup] tags=[:wrappers] begin
     probs = [
         NonlinearLeastSquaresProblem(
             NonlinearFunction{true}(loss_function; resid_prototype = zero(y_target)),
@@ -90,7 +90,8 @@ end
     solvers = vec(Any[FastLevenbergMarquardtJL(linsolve; autodiff)
                       for linsolve in (:cholesky, :qr),
     autodiff in (nothing, AutoForwardDiff(), AutoFiniteDiff())])
-    append!(solvers, [CMINPACK(; method) for method in (:auto, :lm, :lmdif)])
+    Sys.isapple() ||
+        append!(solvers, [CMINPACK(; method) for method in (:auto, :lm, :lmdif)])
 
     for solver in solvers, prob in probs
         sol = solve(prob, solver; maxiters = 10000, abstol = 1e-8)
@@ -98,7 +99,7 @@ end
     end
 end
 
-@testitem "FastLevenbergMarquardt.jl + StaticArrays" setup=[WrapperNLLSSetup] begin
+@testitem "FastLevenbergMarquardt.jl + StaticArrays" setup=[WrapperNLLSSetup] tags=[:wrappers] begin
     x_sa = SA[-1.0, -0.5, 0.0, 0.5, 1.0]
 
     const y_target_sa = true_function(x_sa, θ_true)
diff --git a/test/wrappers/rootfind_tests.jl b/test/wrappers/rootfind_tests.jl
index dcee9ceba..9568575e0 100644
--- a/test/wrappers/rootfind_tests.jl
+++ b/test/wrappers/rootfind_tests.jl
@@ -6,7 +6,7 @@ import NLSolvers, NLsolve, SIAMFANLEquations, MINPACK
 export NLSolvers
 end
 
-@testitem "Steady State Problems" setup=[WrapperRootfindImports] begin
+@testitem "Steady State Problems" setup=[WrapperRootfindImports] tags=[:wrappers] begin
     # IIP Tests
     function f_iip(du, u, p, t)
         du[1] = 2 - 2u[1]
@@ -18,6 +18,7 @@ end
     for alg in [
         NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
         NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        alg isa CMINPACK && Sys.isapple() && continue
         sol = solve(prob_iip, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
         @test maximum(abs, sol.resid) < 1e-6
@@ -31,13 +32,14 @@ end
     for alg in [
         NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
         NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        alg isa CMINPACK && Sys.isapple() && continue
         sol = solve(prob_oop, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
         @test maximum(abs, sol.resid) < 1e-6
     end
 end
 
-@testitem "Nonlinear Root Finding Problems" setup=[WrapperRootfindImports] begin
+@testitem "Nonlinear Root Finding Problems" setup=[WrapperRootfindImports] tags=[:wrappers] begin
     # IIP Tests
     function f_iip(du, u, p)
         du[1] = 2 - 2u[1]
@@ -49,6 +51,7 @@ end
     for alg in [
         NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
         NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        alg isa CMINPACK && Sys.isapple() && continue
         local sol
         sol = solve(prob_iip, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
@@ -62,6 +65,7 @@ end
     for alg in [
         NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
         NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        alg isa CMINPACK && Sys.isapple() && continue
         local sol
         sol = solve(prob_oop, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
@@ -78,6 +82,8 @@ end
             SIAMFANLEquationsJL(; method = :pseudotransient),
             SIAMFANLEquationsJL(; method = :secant)]
 
+        alg isa CMINPACK && Sys.isapple() && continue
+
         sol = solve(prob_tol, alg, abstol = tol)
         @test abs(sol.u[1] - sqrt(2)) < tol
     end

From ed60ded1b8b2cda092b5f31e721012dee1616c19 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 17 May 2024 21:52:51 -0400
Subject: [PATCH 392/700] Skip Mac tests taking too long

---
 test/core/rootfind_tests.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index ce27ee6c8..3ed50a2c7 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -118,7 +118,7 @@ end
 
 # --- TrustRegion tests ---
 
-@testitem "TrustRegion" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
+@testitem "TrustRegion" setup=[CoreRootfindTesting] tags=[:core] skip=:(Sys.isapple()) timeout=3600 begin
     radius_update_schemes = [RadiusUpdateSchemes.Simple, RadiusUpdateSchemes.NocedalWright,
         RadiusUpdateSchemes.NLsolve, RadiusUpdateSchemes.Hei,
         RadiusUpdateSchemes.Yuan, RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin]
@@ -462,7 +462,7 @@ end
 
 # --- Broyden tests ---
 
-@testitem "Broyden" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
+@testitem "Broyden" setup=[CoreRootfindTesting] tags=[:core] skip=:(Sys.isapple()) timeout=3600 begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian) Update Rule: $(update_rule)" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(),
             HagerZhang(), MoreThuente(), LiFukushimaLineSearch()),
@@ -512,7 +512,7 @@ end
 
 # --- Klement tests ---
 
-@testitem "Klement" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
+@testitem "Klement" setup=[CoreRootfindTesting] tags=[:core] skip=:(Sys.isapple()) timeout=3600 begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian)" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
         ad in (AutoFiniteDiff(), AutoZygote()),
@@ -561,7 +561,7 @@ end
 
 # --- LimitedMemoryBroyden tests ---
 
-@testitem "LimitedMemoryBroyden" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
+@testitem "LimitedMemoryBroyden" setup=[CoreRootfindTesting] tags=[:core] skip=:(Sys.isapple()) timeout=3600 begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad))" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(),
             HagerZhang(), MoreThuente(), LiFukushimaLineSearch()),

From 020a46a4ba2c5c61341119efd1eee224b991a9b6 Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Mon, 20 May 2024 02:17:44 +0000
Subject: [PATCH 393/700] Bump julia-actions/julia-format from 2 to 3

Bumps [julia-actions/julia-format](https://github.com/julia-actions/julia-format) from 2 to 3.
- [Release notes](https://github.com/julia-actions/julia-format/releases)
- [Commits](https://github.com/julia-actions/julia-format/compare/v2...v3)

---
updated-dependencies:
- dependency-name: julia-actions/julia-format
  dependency-type: direct:production
  update-type: version-update:semver-major
...

Signed-off-by: dependabot[bot] <support@github.com>
---
 .github/workflows/FormatCheck.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/workflows/FormatCheck.yml b/.github/workflows/FormatCheck.yml
index 8601ad558..0ddeb4ed1 100644
--- a/.github/workflows/FormatCheck.yml
+++ b/.github/workflows/FormatCheck.yml
@@ -6,4 +6,4 @@ jobs:
   code-style:
     runs-on: ubuntu-latest
     steps:
-      - uses: julia-actions/julia-format@v2
+      - uses: julia-actions/julia-format@v3

From 2bb3bbb50150ae1a67c50d8405f6aa394d5c4532 Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Mon, 20 May 2024 21:10:06 +0000
Subject: [PATCH 394/700] --- updated-dependencies: - dependency-name:
 julia-actions/julia-format   dependency-type: direct:production  
 update-type: version-update:semver-major ...

Signed-off-by: dependabot[bot] <support@github.com>
---
 lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
index 8601ad558..0ddeb4ed1 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
@@ -6,4 +6,4 @@ jobs:
   code-style:
     runs-on: ubuntu-latest
     steps:
-      - uses: julia-actions/julia-format@v2
+      - uses: julia-actions/julia-format@v3

From 86482bbabefc22957f5e60e946dccfe1c0961692 Mon Sep 17 00:00:00 2001
From: CompatHelper Julia <compathelper_noreply@julialang.org>
Date: Mon, 20 May 2024 21:45:29 +0000
Subject: [PATCH 395/700] CompatHelper: bump compat for LazyArrays to 2, (keep
 existing compat)

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index f8e7162b8..00723e72b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -72,7 +72,7 @@ FastLevenbergMarquardt = "0.1"
 FiniteDiff = "2.22"
 FixedPointAcceleration = "0.3"
 ForwardDiff = "0.10.36"
-LazyArrays = "1.8.2"
+LazyArrays = "1.8.2, 2"
 LeastSquaresOptim = "0.8.5"
 LineSearches = "7.2"
 LinearAlgebra = "1.10"

From 0e8a1ad5f5c11d8294cfc3ca14c91ccadd439c79 Mon Sep 17 00:00:00 2001
From: CompatHelper Julia <compathelper_noreply@julialang.org>
Date: Fri, 24 May 2024 16:06:03 +0000
Subject: [PATCH 396/700] CompatHelper: bump compat for FastBroadcast to 0.3,
 (keep existing compat)

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index f8e7162b8..c86176f21 100644
--- a/Project.toml
+++ b/Project.toml
@@ -66,7 +66,7 @@ CUDA = "5.2"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149.0"
 Enzyme = "0.12"
-FastBroadcast = "0.2.8"
+FastBroadcast = "0.2.8, 0.3"
 FastClosures = "0.3.2"
 FastLevenbergMarquardt = "0.1"
 FiniteDiff = "2.22"

From 42e6e19dbc846b010f80b6a5322101fb3e71a669 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 24 May 2024 12:00:48 -0700
Subject: [PATCH 397/700] Use explicit imports check

---
 Project.toml                                  | 10 ++-
 ext/NonlinearSolveBandedMatricesExt.jl        |  5 +-
 ...NonlinearSolveFastLevenbergMarquardtExt.jl | 13 +--
 ...NonlinearSolveFixedPointAccelerationExt.jl |  4 +-
 ext/NonlinearSolveLeastSquaresOptimExt.jl     |  9 +-
 ext/NonlinearSolveMINPACKExt.jl               |  6 +-
 ext/NonlinearSolveNLSolversExt.jl             | 10 ++-
 ext/NonlinearSolveNLsolveExt.jl               |  4 +-
 ext/NonlinearSolveSIAMFANLEquationsExt.jl     |  7 +-
 ext/NonlinearSolveSpeedMappingExt.jl          |  4 +-
 ext/NonlinearSolveSymbolicsExt.jl             |  2 +-
 ext/NonlinearSolveZygoteExt.jl                |  2 +-
 src/NonlinearSolve.jl                         | 82 +++++++++++++------
 src/abstract_types.jl                         |  4 +-
 src/algorithms/lbroyden.jl                    |  2 +-
 src/descent/damped_newton.jl                  |  2 +-
 src/utils.jl                                  |  4 +-
 test/misc/qa_tests.jl                         | 14 ++++
 18 files changed, 129 insertions(+), 55 deletions(-)

diff --git a/Project.toml b/Project.toml
index f8e7162b8..44f18d17b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.12.0"
+version = "3.12.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -32,6 +32,7 @@ TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 
 [weakdeps]
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+Enlsip = "d5306a6b-d590-428d-a53a-eb3bb2d36f2d"
 FastLevenbergMarquardt = "7a0df574-e128-4d35-8cbd-3d84502bf7ce"
 FixedPointAcceleration = "817d07cb-a79a-5c30-9a31-890123675176"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
@@ -45,6 +46,7 @@ Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [extensions]
 NonlinearSolveBandedMatricesExt = "BandedMatrices"
+NonlinearSolveEnlsipExt = "Enlsip"
 NonlinearSolveFastLevenbergMarquardtExt = "FastLevenbergMarquardt"
 NonlinearSolveFixedPointAccelerationExt = "FixedPointAcceleration"
 NonlinearSolveLeastSquaresOptimExt = "LeastSquaresOptim"
@@ -65,7 +67,9 @@ BenchmarkTools = "1.4"
 CUDA = "5.2"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149.0"
+Enlsip = "0.9"
 Enzyme = "0.12"
+ExplicitImports = "1.4.4"
 FastBroadcast = "0.2.8"
 FastClosures = "0.3.2"
 FastLevenbergMarquardt = "0.1"
@@ -115,7 +119,9 @@ Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+Enlsip = "d5306a6b-d590-428d-a53a-eb3bb2d36f2d"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 FastLevenbergMarquardt = "7a0df574-e128-4d35-8cbd-3d84502bf7ce"
 FixedPointAcceleration = "817d07cb-a79a-5c30-9a31-890123675176"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
@@ -139,4 +145,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "FastLevenbergMarquardt", "FixedPointAcceleration", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEq", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enlsip", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEq", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
diff --git a/ext/NonlinearSolveBandedMatricesExt.jl b/ext/NonlinearSolveBandedMatricesExt.jl
index 7009c6273..b79df3578 100644
--- a/ext/NonlinearSolveBandedMatricesExt.jl
+++ b/ext/NonlinearSolveBandedMatricesExt.jl
@@ -1,6 +1,9 @@
 module NonlinearSolveBandedMatricesExt
 
-using BandedMatrices, LinearAlgebra, NonlinearSolve, SparseArrays
+using BandedMatrices: BandedMatrix
+using LinearAlgebra: Diagonal
+using NonlinearSolve: NonlinearSolve
+using SparseArrays: sparse
 
 # This is used if we vcat a Banded Jacobian with a Diagonal Matrix in Levenberg
 @inline NonlinearSolve._vcat(B::BandedMatrix, D::Diagonal) = vcat(sparse(B), D)
diff --git a/ext/NonlinearSolveFastLevenbergMarquardtExt.jl b/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
index 6221883a7..262f811a7 100644
--- a/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
+++ b/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
@@ -1,10 +1,13 @@
 module NonlinearSolveFastLevenbergMarquardtExt
 
-using ArrayInterface, NonlinearSolve, SciMLBase
-import ConcreteStructs: @concrete
-import FastClosures: @closure
-import FastLevenbergMarquardt as FastLM
-import StaticArraysCore: SArray
+using ArrayInterface: ArrayInterface
+using FastClosures: @closure
+using FastLevenbergMarquardt: FastLevenbergMarquardt
+using NonlinearSolve: NonlinearSolve, FastLevenbergMarquardtJL
+using SciMLBase: SciMLBase, NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode
+using StaticArraysCore: SArray
+
+const FastLM = FastLevenbergMarquardt
 
 @inline function _fast_lm_solver(::FastLevenbergMarquardtJL{linsolve}, x) where {linsolve}
     if linsolve === :cholesky
diff --git a/ext/NonlinearSolveFixedPointAccelerationExt.jl b/ext/NonlinearSolveFixedPointAccelerationExt.jl
index 9e7254886..6e26e5351 100644
--- a/ext/NonlinearSolveFixedPointAccelerationExt.jl
+++ b/ext/NonlinearSolveFixedPointAccelerationExt.jl
@@ -1,6 +1,8 @@
 module NonlinearSolveFixedPointAccelerationExt
 
-using NonlinearSolve, FixedPointAcceleration, SciMLBase
+using NonlinearSolve: NonlinearSolve, FixedPointAccelerationJL
+using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
+using FixedPointAcceleration: FixedPointAcceleration, fixed_point
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::FixedPointAccelerationJL, args...;
         abstol = nothing, maxiters = 1000, alias_u0::Bool = false,
diff --git a/ext/NonlinearSolveLeastSquaresOptimExt.jl b/ext/NonlinearSolveLeastSquaresOptimExt.jl
index b5c1a7426..6abe13a9c 100644
--- a/ext/NonlinearSolveLeastSquaresOptimExt.jl
+++ b/ext/NonlinearSolveLeastSquaresOptimExt.jl
@@ -1,8 +1,11 @@
 module NonlinearSolveLeastSquaresOptimExt
 
-using NonlinearSolve, SciMLBase
-import ConcreteStructs: @concrete
-import LeastSquaresOptim as LSO
+using ConcreteStructs: @concrete
+using LeastSquaresOptim: LeastSquaresOptim
+using NonlinearSolve: NonlinearSolve, LeastSquaresOptimJL, TraceMinimal
+using SciMLBase: SciMLBase, NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode
+
+const LSO = LeastSquaresOptim
 
 @inline function _lso_solver(::LeastSquaresOptimJL{alg, ls}) where {alg, ls}
     linsolve = ls === :qr ? LSO.QR() :
diff --git a/ext/NonlinearSolveMINPACKExt.jl b/ext/NonlinearSolveMINPACKExt.jl
index 8be121c13..a7be409d4 100644
--- a/ext/NonlinearSolveMINPACKExt.jl
+++ b/ext/NonlinearSolveMINPACKExt.jl
@@ -1,7 +1,9 @@
 module NonlinearSolveMINPACKExt
 
-using MINPACK, NonlinearSolve, SciMLBase
-import FastClosures: @closure
+using MINPACK: MINPACK
+using NonlinearSolve: NonlinearSolve, CMINPACK
+using SciMLBase: SciMLBase, NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode
+using FastClosures: @closure
 
 function SciMLBase.__solve(
         prob::Union{NonlinearLeastSquaresProblem, NonlinearProblem}, alg::CMINPACK,
diff --git a/ext/NonlinearSolveNLSolversExt.jl b/ext/NonlinearSolveNLSolversExt.jl
index 698bc8465..e78dab947 100644
--- a/ext/NonlinearSolveNLSolversExt.jl
+++ b/ext/NonlinearSolveNLSolversExt.jl
@@ -1,7 +1,13 @@
 module NonlinearSolveNLSolversExt
 
-using ADTypes, FastClosures, NonlinearSolve, NLSolvers, SciMLBase, LinearAlgebra
-using FiniteDiff, ForwardDiff
+using ADTypes: ADTypes, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
+using FastClosures: @closure
+using FiniteDiff: FiniteDiff
+using ForwardDiff: ForwardDiff
+using LinearAlgebra: norm
+using NLSolvers: NLSolvers, NEqOptions, NEqProblem
+using NonlinearSolve: NonlinearSolve, NLSolversJL
+using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
diff --git a/ext/NonlinearSolveNLsolveExt.jl b/ext/NonlinearSolveNLsolveExt.jl
index 2af1ab5a3..77ed4a56f 100644
--- a/ext/NonlinearSolveNLsolveExt.jl
+++ b/ext/NonlinearSolveNLsolveExt.jl
@@ -1,6 +1,8 @@
 module NonlinearSolveNLsolveExt
 
-using NonlinearSolve, NLsolve, SciMLBase
+using NonlinearSolve: NonlinearSolve, NLsolveJL, TraceMinimal
+using NLsolve: NLsolve, OnceDifferentiable, nlsolve
+using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
 
 function SciMLBase.__solve(
         prob::NonlinearProblem, alg::NLsolveJL, args...; abstol = nothing,
diff --git a/ext/NonlinearSolveSIAMFANLEquationsExt.jl b/ext/NonlinearSolveSIAMFANLEquationsExt.jl
index 17fef4922..6ec3e8393 100644
--- a/ext/NonlinearSolveSIAMFANLEquationsExt.jl
+++ b/ext/NonlinearSolveSIAMFANLEquationsExt.jl
@@ -1,7 +1,10 @@
 module NonlinearSolveSIAMFANLEquationsExt
 
-using NonlinearSolve, SIAMFANLEquations, SciMLBase
-import FastClosures: @closure
+using FastClosures: @closure
+using NonlinearSolve: NonlinearSolve, SIAMFANLEquationsJL
+using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
+using SIAMFANLEquations: SIAMFANLEquations, aasol, nsol, nsoli, nsolsc, ptcsol, ptcsoli,
+                         ptcsolsc, secant
 
 @inline function __siam_fanl_equations_retcode_mapping(sol)
     if sol.errcode == 0
diff --git a/ext/NonlinearSolveSpeedMappingExt.jl b/ext/NonlinearSolveSpeedMappingExt.jl
index 286b2577c..2813e3e58 100644
--- a/ext/NonlinearSolveSpeedMappingExt.jl
+++ b/ext/NonlinearSolveSpeedMappingExt.jl
@@ -1,6 +1,8 @@
 module NonlinearSolveSpeedMappingExt
 
-using NonlinearSolve, SciMLBase, SpeedMapping
+using NonlinearSolve: NonlinearSolve, SpeedMappingJL
+using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
+using SpeedMapping: speedmapping
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SpeedMappingJL, args...;
         abstol = nothing, maxiters = 1000, alias_u0::Bool = false,
diff --git a/ext/NonlinearSolveSymbolicsExt.jl b/ext/NonlinearSolveSymbolicsExt.jl
index 95f1016e4..8e5354cda 100644
--- a/ext/NonlinearSolveSymbolicsExt.jl
+++ b/ext/NonlinearSolveSymbolicsExt.jl
@@ -1,6 +1,6 @@
 module NonlinearSolveSymbolicsExt
 
-import NonlinearSolve, Symbolics
+using NonlinearSolve: NonlinearSolve
 
 NonlinearSolve.is_extension_loaded(::Val{:Symbolics}) = true
 
diff --git a/ext/NonlinearSolveZygoteExt.jl b/ext/NonlinearSolveZygoteExt.jl
index d58faabbd..8ed2e1853 100644
--- a/ext/NonlinearSolveZygoteExt.jl
+++ b/ext/NonlinearSolveZygoteExt.jl
@@ -1,6 +1,6 @@
 module NonlinearSolveZygoteExt
 
-import NonlinearSolve, Zygote
+using NonlinearSolve: NonlinearSolve
 
 NonlinearSolve.is_extension_loaded(::Val{:Zygote}) = true
 
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 8e39c6f1d..b92aac597 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -4,37 +4,58 @@ if isdefined(Base, :Experimental) && isdefined(Base.Experimental, Symbol("@max_m
     @eval Base.Experimental.@max_methods 1
 end
 
-import Reexport: @reexport
-import PrecompileTools: @recompile_invalidations, @compile_workload, @setup_workload
+using Reexport: @reexport
+using PrecompileTools: @recompile_invalidations, @compile_workload, @setup_workload
 
 @recompile_invalidations begin
-    using ADTypes, ConcreteStructs, DiffEqBase, FastBroadcast, FastClosures, LazyArrays,
-          LinearAlgebra, LinearSolve, MaybeInplace, Preferences, Printf, SciMLBase,
-          SimpleNonlinearSolve, SparseArrays, SparseDiffTools
-
-    import ArrayInterface: ArrayInterface, undefmatrix, can_setindex, restructure,
-                           fast_scalar_indexing, ismutable
-    import DiffEqBase: AbstractNonlinearTerminationMode,
-                       AbstractSafeNonlinearTerminationMode,
-                       AbstractSafeBestNonlinearTerminationMode,
-                       NonlinearSafeTerminationReturnCode, get_termination_mode
-    import FiniteDiff
-    import ForwardDiff
-    import ForwardDiff: Dual
-    import LineSearches
-    import LinearSolve: ComposePreconditioner, InvPreconditioner, needs_concrete_A
-    import RecursiveArrayTools: recursivecopy!, recursivefill!
-
-    import SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
-                      AbstractSciMLOperator, NLStats, _unwrap_val, has_jac, isinplace
-    import SparseDiffTools: AbstractSparsityDetection
-    import StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix, MMatrix
-    import SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
-                                      symbolic_container, parameter_values, state_values,
-                                      getu
+    using ADTypes: AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff, AutoZygote,
+                   AutoEnzyme, AutoSparse
+    # FIXME: deprecated, remove in future
+    using ADTypes: AutoSparseFiniteDiff, AutoSparseForwardDiff,
+                   AutoSparsePolyesterForwardDiff, AutoSparseZygote
+
+    using ArrayInterface: ArrayInterface, can_setindex, restructure, fast_scalar_indexing,
+                          ismutable
+    using ConcreteStructs: @concrete
+    using DiffEqBase: DiffEqBase, AbstractNonlinearTerminationMode,
+                      AbstractSafeBestNonlinearTerminationMode, AbsNormTerminationMode,
+                      AbsSafeBestTerminationMode, AbsSafeTerminationMode,
+                      AbsTerminationMode, NormTerminationMode, RelNormTerminationMode,
+                      RelSafeBestTerminationMode, RelSafeTerminationMode,
+                      RelTerminationMode, SimpleNonlinearSolveTerminationMode,
+                      SteadyStateDiffEqTerminationMode
+    using FastBroadcast: @..
+    using FastClosures: @closure
+    using FiniteDiff: FiniteDiff
+    using ForwardDiff: ForwardDiff, Dual
+    using LazyArrays: LazyArrays, ApplyArray, cache
+    using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Symmetric,
+                         UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess,
+                         istril, istriu, lu, mul!, norm, pinv, tril!, triu!
+    using LineSearches: LineSearches
+    using LinearSolve: LinearSolve, LUFactorization, QRFactorization, ComposePreconditioner,
+                       InvPreconditioner, needs_concrete_A
+    using MaybeInplace: @bb
+    using Printf: @printf
+    using Preferences: Preferences, @load_preference, @set_preferences!
+    using RecursiveArrayTools: recursivecopy!, recursivefill!
+    using SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
+                     AbstractSciMLOperator, _unwrap_val, has_jac, isinplace
+    using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
+    using SparseDiffTools: SparseDiffTools, AbstractSparsityDetection,
+                           ApproximateJacobianSparsity, JacPrototypeSparsityDetection,
+                           NoSparsityDetection, PrecomputedJacobianColorvec,
+                           SymbolicsSparsityDetection, auto_jacvec, auto_jacvec!,
+                           auto_vecjac, init_jacobian, num_jacvec, num_jacvec!, num_vecjac,
+                           num_vecjac!, sparse_jacobian, sparse_jacobian!,
+                           sparse_jacobian_cache
+    using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
+    using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
+                                     symbolic_container, parameter_values, state_values,
+                                     getu
 end
 
-@reexport using ADTypes, SciMLBase, SimpleNonlinearSolve
+@reexport using SciMLBase, SimpleNonlinearSolve
 
 # Type-Inference Friendly Check for Extension Loading
 is_extension_loaded(::Val) = false
@@ -166,4 +187,11 @@ export SteadyStateDiffEqTerminationMode, SimpleNonlinearSolveTerminationMode,
 # Tracing Functionality
 export TraceAll, TraceMinimal, TraceWithJacobianConditionNumber
 
+# Reexport ADTypes
+export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme,
+       AutoSparse
+# FIXME: deprecated, remove in future
+export AutoSparseFiniteDiff, AutoSparseForwardDiff, AutoSparsePolyesterForwardDiff,
+       AutoSparseZygote
+
 end # module
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index c5e5d990b..dc7b638a1 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -311,12 +311,12 @@ function returns_norm_form_damping(f::F) where {F}
 end
 
 """
-    AbstractNonlinearSolveOperator <: SciMLBase.AbstractSciMLOperator
+    AbstractNonlinearSolveOperator <: AbstractSciMLOperator
 
 NonlinearSolve.jl houses a few custom operators. These will eventually be moved out but till
 then this serves as the abstract type for them.
 """
-abstract type AbstractNonlinearSolveOperator{T} <: SciMLBase.AbstractSciMLOperator{T} end
+abstract type AbstractNonlinearSolveOperator{T} <: AbstractSciMLOperator{T} end
 
 # Approximate Jacobian Algorithms
 """
diff --git a/src/algorithms/lbroyden.jl b/src/algorithms/lbroyden.jl
index f1959e7d0..596172ead 100644
--- a/src/algorithms/lbroyden.jl
+++ b/src/algorithms/lbroyden.jl
@@ -169,4 +169,4 @@ function LinearAlgebra.mul!(J::BroydenLowRankJacobian, u::AbstractArray,
     return J
 end
 
-restructure(::BroydenLowRankJacobian, J::BroydenLowRankJacobian) = J
+ArrayInterface.restructure(::BroydenLowRankJacobian, J::BroydenLowRankJacobian) = J
diff --git a/src/descent/damped_newton.jl b/src/descent/damped_newton.jl
index 792f56773..d8f25634a 100644
--- a/src/descent/damped_newton.jl
+++ b/src/descent/damped_newton.jl
@@ -220,7 +220,7 @@ end
 
 # J_cache is allowed to alias J
 ## Compute ``J + D``
-@inline __dampen_jacobian!!(J_cache, J::SciMLBase.AbstractSciMLOperator, D) = J + D
+@inline __dampen_jacobian!!(J_cache, J::AbstractSciMLOperator, D) = J + D
 @inline __dampen_jacobian!!(J_cache, J::Number, D) = J + D
 @inline function __dampen_jacobian!!(J_cache, J::AbstractMatrix, D::AbstractMatrix)
     if __can_setindex(J_cache)
diff --git a/src/utils.jl b/src/utils.jl
index 9db6e1316..beda82460 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -73,8 +73,8 @@ LazyArrays.applied_axes(::typeof(__zero), x) = axes(x)
 @inline __maybe_symmetric(x::Number) = x
 ## LinearSolve with `nothing` doesn't dispatch correctly here
 @inline __maybe_symmetric(x::StaticArray) = x
-@inline __maybe_symmetric(x::SparseArrays.AbstractSparseMatrix) = x
-@inline __maybe_symmetric(x::SciMLOperators.AbstractSciMLOperator) = x
+@inline __maybe_symmetric(x::AbstractSparseMatrix) = x
+@inline __maybe_symmetric(x::AbstractSciMLOperator) = x
 
 # SparseAD --> NonSparseAD
 @inline __get_nonsparse_ad(backend::AutoSparse) = ADTypes.dense_ad(backend)
diff --git a/test/misc/qa_tests.jl b/test/misc/qa_tests.jl
index 79706a376..a3b370b5b 100644
--- a/test/misc/qa_tests.jl
+++ b/test/misc/qa_tests.jl
@@ -13,3 +13,17 @@
     Aqua.test_unbound_args(NonlinearSolve)
     Aqua.test_undefined_exports(NonlinearSolve)
 end
+
+@testitem "Explicit Imports" tags=[:misc] begin
+    using NonlinearSolve, ADTypes, SimpleNonlinearSolve, SciMLBase
+    import BandedMatrices, FastLevenbergMarquardt, FixedPointAcceleration,
+           LeastSquaresOptim, MINPACK, NLsolve, NLSolvers, SIAMFANLEquations, SpeedMapping,
+           Symbolics, Zygote
+
+    using ExplicitImports
+
+    @test check_no_implicit_imports(NonlinearSolve;
+        skip = (NonlinearSolve, Base, Core, SimpleNonlinearSolve, SciMLBase)) === nothing
+
+    @test check_no_stale_explicit_imports(NonlinearSolve) === nothing
+end

From b06cb09f21379323f1832e9a696d5e8ea069cf78 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 24 May 2024 17:27:57 -0700
Subject: [PATCH 398/700] Remove ImmutableNLStats

---
 docs/src/basics/nonlinear_solution.md |  1 -
 src/core/generic.jl                   |  2 +-
 src/utils.jl                          | 36 ---------------------------
 3 files changed, 1 insertion(+), 38 deletions(-)

diff --git a/docs/src/basics/nonlinear_solution.md b/docs/src/basics/nonlinear_solution.md
index ce1abcc4c..6b74368fb 100644
--- a/docs/src/basics/nonlinear_solution.md
+++ b/docs/src/basics/nonlinear_solution.md
@@ -9,7 +9,6 @@ SciMLBase.NonlinearSolution
 
 ```@docs
 SciMLBase.NLStats
-NonlinearSolve.ImmutableNLStats
 ```
 
 ## Return Code
diff --git a/src/core/generic.jl b/src/core/generic.jl
index 75d494730..83141e1e8 100644
--- a/src/core/generic.jl
+++ b/src/core/generic.jl
@@ -29,7 +29,7 @@ function SciMLBase.solve!(cache::AbstractNonlinearSolveCache)
 end
 
 function __compile_stats(cache::AbstractNonlinearSolveCache)
-    return ImmutableNLStats(get_nf(cache), get_njacs(cache), get_nfactors(cache),
+    return SciMLBase.NLStats(get_nf(cache), get_njacs(cache), get_nfactors(cache),
         get_nsolve(cache), get_nsteps(cache))
 end
 
diff --git a/src/utils.jl b/src/utils.jl
index beda82460..8be33d9f9 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -129,42 +129,6 @@ end
 
 @inline __dot(x, y) = dot(_vec(x), _vec(y))
 
-# Return an ImmutableNLStats object when we know that NLStats won't be updated
-"""
-    ImmutableNLStats(nf, njacs, nfactors, nsolve, nsteps)
-
-Statistics from the nonlinear equation solver about the solution process.
-
-## Fields
-
-  - nf: Number of function evaluations.
-  - njacs: Number of Jacobians created during the solve.
-  - nfactors: Number of factorzations of the jacobian required for the solve.
-  - nsolve: Number of linear solves `W \\ b` required for the solve.
-  - nsteps: Total number of iterations for the nonlinear solver.
-"""
-struct ImmutableNLStats
-    nf::Int
-    njacs::Int
-    nfactors::Int
-    nsolve::Int
-    nsteps::Int
-end
-
-function Base.show(io::IO, ::MIME"text/plain", s::ImmutableNLStats)
-    println(io, summary(s))
-    @printf io "%-50s %-d\n" "Number of function evaluations:" s.nf
-    @printf io "%-50s %-d\n" "Number of Jacobians created:" s.njacs
-    @printf io "%-50s %-d\n" "Number of factorizations:" s.nfactors
-    @printf io "%-50s %-d\n" "Number of linear solves:" s.nsolve
-    @printf io "%-50s %-d" "Number of nonlinear solver iterations:" s.nsteps
-end
-
-function Base.merge(s1::ImmutableNLStats, s2::ImmutableNLStats)
-    return ImmutableNLStats(s1.nf + s2.nf, s1.njacs + s2.njacs, s1.nfactors + s2.nfactors,
-        s1.nsolve + s2.nsolve, s1.nsteps + s2.nsteps)
-end
-
 """
     pickchunksize(x) = pickchunksize(length(x))
     pickchunksize(x::Int)

From 24793edd724c43ac8bb78b21348f2d13b00cf8a8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 24 May 2024 19:09:21 -0700
Subject: [PATCH 399/700] Consolidate handling of Stats

---
 src/NonlinearSolve.jl               |  5 +--
 src/abstract_types.jl               |  3 +-
 src/core/approximate_jacobian.jl    | 23 +++++++-------
 src/core/generalized_first_order.jl | 16 +++++-----
 src/core/generic.jl                 | 20 +++++-------
 src/core/spectral_methods.jl        | 16 +++++-----
 src/default.jl                      | 20 +++++++-----
 src/descent/damped_newton.jl        | 10 +++---
 src/descent/newton.jl               | 16 +++++-----
 src/descent/steepest.jl             |  4 +--
 src/globalization/line_search.jl    | 33 +++++++++-----------
 src/globalization/trust_region.jl   | 22 ++++++--------
 src/internal/helpers.jl             | 30 ++----------------
 src/internal/jacobian.jl            | 29 +++++++-----------
 src/internal/linear_solve.jl        | 47 ++++++++++-------------------
 src/internal/operators.jl           | 10 ++----
 src/internal/tracing.jl             |  9 +++---
 src/utils.jl                        | 11 ++++++-
 18 files changed, 139 insertions(+), 185 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index b92aac597..39e71d3d6 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -34,13 +34,14 @@ using PrecompileTools: @recompile_invalidations, @compile_workload, @setup_workl
                          istril, istriu, lu, mul!, norm, pinv, tril!, triu!
     using LineSearches: LineSearches
     using LinearSolve: LinearSolve, LUFactorization, QRFactorization, ComposePreconditioner,
-                       InvPreconditioner, needs_concrete_A
+                       InvPreconditioner, needs_concrete_A, AbstractFactorization,
+                       DefaultAlgorithmChoice, DefaultLinearSolver
     using MaybeInplace: @bb
     using Printf: @printf
     using Preferences: Preferences, @load_preference, @set_preferences!
     using RecursiveArrayTools: recursivecopy!, recursivefill!
     using SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
-                     AbstractSciMLOperator, _unwrap_val, has_jac, isinplace
+                     AbstractSciMLOperator, _unwrap_val, has_jac, isinplace, NLStats
     using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
     using SparseDiffTools: SparseDiffTools, AbstractSparsityDetection,
                            ApproximateJacobianSparsity, JacPrototypeSparsityDetection,
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index dc7b638a1..0dc4d8f5a 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -142,7 +142,6 @@ abstract type AbstractNonlinearSolveLineSearchCache end
 
 function reinit_cache!(
         cache::AbstractNonlinearSolveLineSearchCache, args...; p = cache.p, kwargs...)
-    cache.nf[] = 0
     cache.p = p
 end
 
@@ -235,7 +234,7 @@ function __show_cache(io::IO, cache::AbstractNonlinearSolveCache, indent = 0)
     println(io, (" "^(indent + 4)) * "u = ", get_u(cache), ",")
     println(io, (" "^(indent + 4)) * "residual = ", get_fu(cache), ",")
     println(io, (" "^(indent + 4)) * "inf-norm(residual) = ", norm(get_fu(cache), Inf), ",")
-    println(io, " "^(indent + 4) * "nsteps = ", get_nsteps(cache), ",")
+    println(io, " "^(indent + 4) * "nsteps = ", cache.stats.nsteps, ",")
     println(io, " "^(indent + 4) * "retcode = ", cache.retcode)
     print(io, " "^(indent) * ")")
 end
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index 4328af345..4711ed719 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -95,7 +95,7 @@ end
     inv_workspace
 
     # Counters
-    nf::Int
+    stats::NLStats
     nsteps::Int
     nresets::Int
     max_resets::Int
@@ -131,7 +131,7 @@ function __reinit_internal!(cache::ApproximateJacobianSolveCache{INV, GB, iip},
     end
     cache.p = p
 
-    cache.nf = 1
+    __reinit_internal!(cache.stats)
     cache.nsteps = 0
     cache.nresets = 0
     cache.steps_since_last_reset = 0
@@ -151,8 +151,9 @@ end
 
 function SciMLBase.__init(
         prob::AbstractNonlinearProblem{uType, iip}, alg::ApproximateJacobianSolveAlgorithm,
-        args...; alias_u0 = false, maxtime = nothing, maxiters = 1000, abstol = nothing,
-        reltol = nothing, linsolve_kwargs = (;), termination_condition = nothing,
+        args...; stats = empty_nlstats(), alias_u0 = false, maxtime = nothing,
+        maxiters = 1000, abstol = nothing, reltol = nothing,
+        linsolve_kwargs = (;), termination_condition = nothing,
         internalnorm::F = DEFAULT_NORM, kwargs...) where {uType, iip, F}
     timer = get_timer_output()
     @static_timeit timer "cache construction" begin
@@ -165,7 +166,7 @@ function SciMLBase.__init(
 
         linsolve = get_linear_solver(alg.descent)
         initialization_cache = __internal_init(
-            prob, alg.initialization, alg, f, fu, u, p; linsolve, maxiters, internalnorm)
+            prob, alg.initialization, alg, f, fu, u, p; stats, linsolve, maxiters, internalnorm)
 
         abstol, reltol, termination_cache = init_termination_cache(
             prob, abstol, reltol, fu, u, termination_condition)
@@ -174,7 +175,7 @@ function SciMLBase.__init(
         J = initialization_cache(nothing)
         inv_workspace, J = INV ? __safe_inv_workspace(J) : (nothing, J)
         descent_cache = __internal_init(
-            prob, alg.descent, J, fu, u; abstol, reltol, internalnorm,
+            prob, alg.descent, J, fu, u; stats, abstol, reltol, internalnorm,
             linsolve_kwargs, pre_inverted = Val(INV), timer)
         du = get_du(descent_cache)
 
@@ -192,7 +193,7 @@ function SciMLBase.__init(
             supports_trust_region(alg.descent) || error("Trust Region not supported by \
                                                         $(alg.descent).")
             trustregion_cache = __internal_init(
-                prob, alg.trustregion, f, fu, u, p; internalnorm, kwargs...)
+                prob, alg.trustregion, f, fu, u, p; stats, internalnorm, kwargs...)
             GB = :TrustRegion
         end
 
@@ -200,12 +201,12 @@ function SciMLBase.__init(
             supports_line_search(alg.descent) || error("Line Search not supported by \
                                                         $(alg.descent).")
             linesearch_cache = __internal_init(
-                prob, alg.linesearch, f, fu, u, p; internalnorm, kwargs...)
+                prob, alg.linesearch, f, fu, u, p; stats, internalnorm, kwargs...)
             GB = :LineSearch
         end
 
         update_rule_cache = __internal_init(
-            prob, alg.update_rule, J, fu, u, du; internalnorm)
+            prob, alg.update_rule, J, fu, u, du; stats, internalnorm)
 
         trace = init_nonlinearsolve_trace(prob, alg, u, fu, ApplyArray(__zero, J), du;
             uses_jacobian_inverse = Val(INV), kwargs...)
@@ -213,7 +214,7 @@ function SciMLBase.__init(
         return ApproximateJacobianSolveCache{INV, GB, iip, maxtime !== nothing}(
             fu, u, u_cache, p, du, J, alg, prob, initialization_cache,
             descent_cache, linesearch_cache, trustregion_cache, update_rule_cache,
-            reinit_rule_cache, inv_workspace, 0, 0, 0, alg.max_resets,
+            reinit_rule_cache, inv_workspace, stats, 0, 0, alg.max_resets,
             maxiters, maxtime, alg.max_shrink_times, 0, timer, 0.0,
             termination_cache, trace, ReturnCode.Default, false, false, kwargs)
     end
@@ -223,7 +224,7 @@ function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
         recompute_jacobian::Union{Nothing, Bool} = nothing) where {INV, GB, iip}
     new_jacobian = true
     @static_timeit cache.timer "jacobian init/reinit" begin
-        if get_nsteps(cache) == 0  # First Step is special ignore kwargs
+        if cache.nsteps == 0  # First Step is special ignore kwargs
             J_init = __internal_solve!(
                 cache.initialization_cache, cache.fu, cache.u, Val(false))
             if INV
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index c16cf043d..5e7e5f144 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -97,7 +97,7 @@ concrete_jac(::GeneralizedFirstOrderAlgorithm{CJ}) where {CJ} = CJ
     trustregion_cache
 
     # Counters
-    nf::Int
+    stats::NLStats
     nsteps::Int
     maxiters::Int
     maxtime
@@ -135,7 +135,7 @@ function __reinit_internal!(
     end
     cache.p = p
 
-    cache.nf = 1
+    __reinit_internal!(cache.stats)
     cache.nsteps = 0
     cache.maxiters = maxiters
     cache.maxtime = maxtime
@@ -153,7 +153,7 @@ end
 
 function SciMLBase.__init(
         prob::AbstractNonlinearProblem{uType, iip}, alg::GeneralizedFirstOrderAlgorithm,
-        args...; alias_u0 = false, maxiters = 1000, abstol = nothing,
+        args...; stats=empty_nlstats(), alias_u0 = false, maxiters = 1000, abstol = nothing,
         reltol = nothing, maxtime = nothing, termination_condition = nothing,
         internalnorm = DEFAULT_NORM, linsolve_kwargs = (;), kwargs...) where {uType, iip}
     timer = get_timer_output()
@@ -170,10 +170,10 @@ function SciMLBase.__init(
         linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
 
         jac_cache = JacobianCache(
-            prob, alg, f, fu, u, p; autodiff = alg.jacobian_ad, linsolve,
+            prob, alg, f, fu, u, p; stats, autodiff = alg.jacobian_ad, linsolve,
             jvp_autodiff = alg.forward_ad, vjp_autodiff = alg.reverse_ad)
         J = jac_cache(nothing)
-        descent_cache = __internal_init(prob, alg.descent, J, fu, u; abstol, reltol,
+        descent_cache = __internal_init(prob, alg.descent, J, fu, u; stats, abstol, reltol,
             internalnorm, linsolve_kwargs, timer)
         du = get_du(descent_cache)
 
@@ -189,7 +189,7 @@ function SciMLBase.__init(
             supports_trust_region(alg.descent) || error("Trust Region not supported by \
                                                         $(alg.descent).")
             trustregion_cache = __internal_init(
-                prob, alg.trustregion, f, fu, u, p; internalnorm, kwargs...)
+                prob, alg.trustregion, f, fu, u, p; stats, internalnorm, kwargs...)
             GB = :TrustRegion
         end
 
@@ -197,7 +197,7 @@ function SciMLBase.__init(
             supports_line_search(alg.descent) || error("Line Search not supported by \
                                                         $(alg.descent).")
             linesearch_cache = __internal_init(
-                prob, alg.linesearch, f, fu, u, p; internalnorm, kwargs...)
+                prob, alg.linesearch, f, fu, u, p; stats, internalnorm, kwargs...)
             GB = :LineSearch
         end
 
@@ -206,7 +206,7 @@ function SciMLBase.__init(
 
         return GeneralizedFirstOrderAlgorithmCache{iip, GB, maxtime !== nothing}(
             fu, u, u_cache, p, du, J, alg, prob, jac_cache, descent_cache, linesearch_cache,
-            trustregion_cache, 0, 0, maxiters, maxtime, alg.max_shrink_times, timer,
+            trustregion_cache, stats, 0, maxiters, maxtime, alg.max_shrink_times, timer,
             0.0, true, termination_cache, trace, ReturnCode.Default, false, kwargs)
     end
 end
diff --git a/src/core/generic.jl b/src/core/generic.jl
index 83141e1e8..76135115c 100644
--- a/src/core/generic.jl
+++ b/src/core/generic.jl
@@ -1,11 +1,11 @@
 function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
-        alg::AbstractNonlinearSolveAlgorithm, args...; kwargs...)
-    cache = init(prob, alg, args...; kwargs...)
+        alg::AbstractNonlinearSolveAlgorithm, args...; stats=empty_nlstats(), kwargs...)
+    cache = SciMLBase.__init(prob, alg, args...; stats, kwargs...)
     return solve!(cache)
 end
 
 function not_terminated(cache::AbstractNonlinearSolveCache)
-    return !cache.force_stop && get_nsteps(cache) < cache.maxiters
+    return !cache.force_stop && cache.nsteps < cache.maxiters
 end
 
 function SciMLBase.solve!(cache::AbstractNonlinearSolveCache)
@@ -16,21 +16,16 @@ function SciMLBase.solve!(cache::AbstractNonlinearSolveCache)
     # The solver might have set a different `retcode`
     if cache.retcode == ReturnCode.Default
         cache.retcode = ifelse(
-            get_nsteps(cache) ≥ cache.maxiters, ReturnCode.MaxIters, ReturnCode.Success)
+            cache.nsteps ≥ cache.maxiters, ReturnCode.MaxIters, ReturnCode.Success)
     end
 
     update_from_termination_cache!(cache.termination_cache, cache)
 
-    update_trace!(cache.trace, get_nsteps(cache), get_u(cache),
+    update_trace!(cache.trace, cache.nsteps, get_u(cache),
         get_fu(cache), nothing, nothing, nothing; last = True)
 
     return SciMLBase.build_solution(cache.prob, cache.alg, get_u(cache), get_fu(cache);
-        cache.retcode, stats = __compile_stats(cache), cache.trace)
-end
-
-function __compile_stats(cache::AbstractNonlinearSolveCache)
-    return SciMLBase.NLStats(get_nf(cache), get_njacs(cache), get_nfactors(cache),
-        get_nsolve(cache), get_nsteps(cache))
+        cache.retcode, cache.stats, cache.trace)
 end
 
 """
@@ -55,7 +50,8 @@ function SciMLBase.step!(cache::AbstractNonlinearSolveCache{iip, timeit},
         __step!(cache, args...; kwargs...)
     end
 
-    hasfield(typeof(cache), :nsteps) && (cache.nsteps += 1)
+    cache.stats.nsteps += 1
+    cache.nsteps += 1
 
     if timeit
         cache.total_time += time() - time_start
diff --git a/src/core/spectral_methods.jl b/src/core/spectral_methods.jl
index 3d9a03e50..85e58c1a3 100644
--- a/src/core/spectral_methods.jl
+++ b/src/core/spectral_methods.jl
@@ -60,7 +60,7 @@ concrete_jac(::GeneralizedDFSane) = nothing
     linesearch_cache
 
     # Counters
-    nf::Int
+    stats::NLStats
     nsteps::Int
     maxiters::Int
     maxtime
@@ -106,7 +106,7 @@ function __reinit_internal!(
 
     reset!(cache.trace)
     reinit!(cache.termination_cache, get_fu(cache), get_u(cache); kwargs...)
-    cache.nf = 1
+    __reinit_internal!(cache.stats)
     cache.nsteps = 0
     cache.maxiters = maxiters
     cache.maxtime = maxtime
@@ -116,9 +116,9 @@ end
 
 @internal_caches GeneralizedDFSaneCache :linesearch_cache
 
-function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane,
-        args...; alias_u0 = false, maxiters = 1000, abstol = nothing,
-        reltol = nothing, termination_condition = nothing,
+function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane, args...;
+        stats = empty_nlstats(), alias_u0 = false, maxiters = 1000,
+        abstol = nothing, reltol = nothing, termination_condition = nothing,
         internalnorm::F = DEFAULT_NORM, maxtime = nothing, kwargs...) where {F}
     timer = get_timer_output()
     @static_timeit timer "cache construction" begin
@@ -130,8 +130,8 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane
         fu = evaluate_f(prob, u)
         @bb fu_cache = copy(fu)
 
-        linesearch_cache = __internal_init(
-            prob, alg.linesearch, prob.f, fu, u, prob.p; maxiters, internalnorm, kwargs...)
+        linesearch_cache = __internal_init(prob, alg.linesearch, prob.f, fu, u, prob.p;
+            stats, maxiters, internalnorm, kwargs...)
 
         abstol, reltol, tc_cache = init_termination_cache(
             prob, abstol, reltol, fu, u_cache, termination_condition)
@@ -150,7 +150,7 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane
 
         return GeneralizedDFSaneCache{isinplace(prob), maxtime !== nothing}(
             fu, fu_cache, u, u_cache, prob.p, du, alg, prob, σ_n, T(alg.σ_min),
-            T(alg.σ_max), linesearch_cache, 0, 0, maxiters, maxtime,
+            T(alg.σ_max), linesearch_cache, stats, 0, maxiters, maxtime,
             timer, 0.0, tc_cache, trace, ReturnCode.Default, false, kwargs)
     end
 end
diff --git a/src/default.jl b/src/default.jl
index fa8f1f786..660caab41 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -59,6 +59,7 @@ end
     best::Int
     current::Int
     nsteps::Int
+    stats::NLStats
     total_time::Float64
     maxtime
     retcode::ReturnCode.T
@@ -90,6 +91,7 @@ end
 function reinit_cache!(cache::NonlinearSolvePolyAlgorithmCache, args...; kwargs...)
     foreach(c -> reinit_cache!(c, args...; kwargs...), cache.caches)
     cache.current = cache.alg.start_index
+    __reinit_internal!(cache.stats)
     cache.nsteps = 0
     cache.total_time = 0.0
 end
@@ -98,8 +100,8 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
     algType = NonlinearSolvePolyAlgorithm{pType}
     @eval begin
         function SciMLBase.__init(
-                prob::$probType, alg::$algType{N}, args...; maxtime = nothing,
-                maxiters = 1000, internalnorm = DEFAULT_NORM,
+                prob::$probType, alg::$algType{N}, args...; stats = empty_nlstats(),
+                maxtime = nothing, maxiters = 1000, internalnorm = DEFAULT_NORM,
                 alias_u0 = false, verbose = true, kwargs...) where {N}
             if (alias_u0 && !ismutable(prob.u0))
                 verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
@@ -115,13 +117,14 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
             alias_u0 && (prob = remake(prob; u0 = u0_aliased))
             return NonlinearSolvePolyAlgorithmCache{isinplace(prob), N, maxtime !== nothing}(
                 map(
-                    solver -> SciMLBase.__init(prob, solver, args...; maxtime,
+                    solver -> SciMLBase.__init(prob, solver, args...; stats, maxtime,
                         internalnorm, alias_u0, verbose, kwargs...),
                     alg.algs),
                 alg,
                 -1,
                 alg.start_index,
                 0,
+                stats,
                 0.0,
                 maxtime,
                 ReturnCode.Default,
@@ -181,7 +184,6 @@ end
     push!(calls, quote
         fus = tuple($(Tuple(resids)...))
         minfu, idx = __findmin(cache.internalnorm, fus)
-        stats = __compile_stats(cache.caches[idx])
     end)
     for i in 1:N
         push!(calls, quote
@@ -203,7 +205,7 @@ end
             end
             return __build_solution_less_specialize(
                 cache.caches[idx].prob, cache.alg, u, fus[idx];
-                retcode, stats, cache.caches[idx].trace)
+                retcode, stats = cache.stats, cache.caches[idx].trace)
         end)
 
     return Expr(:block, calls...)
@@ -250,7 +252,8 @@ end
 for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProblem, :NLLS))
     algType = NonlinearSolvePolyAlgorithm{pType}
     @eval begin
-        @generated function SciMLBase.__solve(prob::$probType, alg::$algType{N}, args...;
+        @generated function SciMLBase.__solve(
+                prob::$probType, alg::$algType{N}, args...; stats = empty_nlstats(),
                 alias_u0 = false, verbose = true, kwargs...) where {N}
             sol_syms = [gensym("sol") for _ in 1:N]
             prob_syms = [gensym("prob") for _ in 1:N]
@@ -280,8 +283,9 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
                             else
                                 $(prob_syms[i]) = prob
                             end
-                            $(cur_sol) = SciMLBase.__solve($(prob_syms[i]), alg.algs[$(i)],
-                                args...; alias_u0, verbose, kwargs...)
+                            $(cur_sol) = SciMLBase.__solve(
+                                $(prob_syms[i]), alg.algs[$(i)], args...;
+                                stats, alias_u0, verbose, kwargs...)
                             if SciMLBase.successful_retcode($(cur_sol))
                                 if alias_u0
                                     copyto!(u0, $(cur_sol).u)
diff --git a/src/descent/damped_newton.jl b/src/descent/damped_newton.jl
index d8f25634a..77b204b13 100644
--- a/src/descent/damped_newton.jl
+++ b/src/descent/damped_newton.jl
@@ -51,8 +51,8 @@ end
 
 @internal_caches DampedNewtonDescentCache :lincache :damping_fn_cache
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::DampedNewtonDescent, J,
-        fu, u; pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
+function __internal_init(prob::AbstractNonlinearProblem, alg::DampedNewtonDescent, J, fu,
+        u; stats, pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
         abstol = nothing, timer = get_timer_output(), reltol = nothing,
         alias_J = true, shared::Val{N} = Val(1), kwargs...) where {INV, N}
     length(fu) != length(u) &&
@@ -94,7 +94,7 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::DampedNewtonDescen
             rhs_damp = fu
         end
         damping_fn_cache = __internal_init(prob, alg.damping_fn, alg.initial_damping,
-            jac_damp, rhs_damp, u, False; kwargs...)
+            jac_damp, rhs_damp, u, False; stats, kwargs...)
         D = damping_fn_cache(nothing)
         D isa Number && (D = D * I)
         rhs_cache = vcat(_vec(fu), _vec(u))
@@ -115,7 +115,7 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::DampedNewtonDescen
         jac_damp = requires_normal_form_jacobian(alg.damping_fn) ? JᵀJ : J
         rhs_damp = requires_normal_form_rhs(alg.damping_fn) ? Jᵀfu : fu
         damping_fn_cache = __internal_init(prob, alg.damping_fn, alg.initial_damping,
-            jac_damp, rhs_damp, u, True; kwargs...)
+            jac_damp, rhs_damp, u, True; stats, kwargs...)
         D = damping_fn_cache(nothing)
         @bb J_cache = similar(JᵀJ)
         @bb @. J_cache = 0
@@ -125,7 +125,7 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::DampedNewtonDescen
     end
 
     lincache = LinearSolverCache(
-        alg, alg.linsolve, A, b, _vec(u); abstol, reltol, linsolve_kwargs...)
+        alg, alg.linsolve, A, b, _vec(u); stats, abstol, reltol, linsolve_kwargs...)
 
     return DampedNewtonDescentCache{INV, mode}(
         J_cache, δu, δus, lincache, JᵀJ, Jᵀfu, rhs_cache, damping_fn_cache, timer)
diff --git a/src/descent/newton.jl b/src/descent/newton.jl
index 36edbf86c..2fe7abf9a 100644
--- a/src/descent/newton.jl
+++ b/src/descent/newton.jl
@@ -32,22 +32,22 @@ end
 
 @internal_caches NewtonDescentCache :lincache
 
-function __internal_init(
-        prob::NonlinearProblem, alg::NewtonDescent, J, fu, u; shared::Val{N} = Val(1),
-        pre_inverted::Val{INV} = False, linsolve_kwargs = (;), abstol = nothing,
-        reltol = nothing, timer = get_timer_output(), kwargs...) where {INV, N}
+function __internal_init(prob::NonlinearProblem, alg::NewtonDescent, J, fu, u; stats,
+        shared::Val{N} = Val(1), pre_inverted::Val{INV} = False,
+        linsolve_kwargs = (;), abstol = nothing, reltol = nothing,
+        timer = get_timer_output(), kwargs...) where {INV, N}
     @bb δu = similar(u)
     δus = N ≤ 1 ? nothing : map(2:N) do i
         @bb δu_ = similar(u)
     end
     INV && return NewtonDescentCache{true, false}(δu, δus, nothing, nothing, nothing, timer)
     lincache = LinearSolverCache(
-        alg, alg.linsolve, J, _vec(fu), _vec(u); abstol, reltol, linsolve_kwargs...)
+        alg, alg.linsolve, J, _vec(fu), _vec(u); stats, abstol, reltol, linsolve_kwargs...)
     return NewtonDescentCache{false, false}(δu, δus, lincache, nothing, nothing, timer)
 end
 
-function __internal_init(prob::NonlinearLeastSquaresProblem, alg::NewtonDescent, J,
-        fu, u; pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
+function __internal_init(prob::NonlinearLeastSquaresProblem, alg::NewtonDescent, J, fu,
+        u; stats, pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
         shared::Val{N} = Val(1), abstol = nothing, reltol = nothing,
         timer = get_timer_output(), kwargs...) where {INV, N}
     length(fu) != length(u) &&
@@ -63,7 +63,7 @@ function __internal_init(prob::NonlinearLeastSquaresProblem, alg::NewtonDescent,
         A, b = J, _vec(fu)
     end
     lincache = LinearSolverCache(
-        alg, alg.linsolve, A, b, _vec(u); abstol, reltol, linsolve_kwargs...)
+        alg, alg.linsolve, A, b, _vec(u); stats, abstol, reltol, linsolve_kwargs...)
     @bb δu = similar(u)
     δus = N ≤ 1 ? nothing : map(2:N) do i
         @bb δu_ = similar(u)
diff --git a/src/descent/steepest.jl b/src/descent/steepest.jl
index 227fdb436..46f2cf10c 100644
--- a/src/descent/steepest.jl
+++ b/src/descent/steepest.jl
@@ -31,7 +31,7 @@ end
 
 @inline function __internal_init(
         prob::AbstractNonlinearProblem, alg::SteepestDescent, J, fu,
-        u; shared::Val{N} = Val(1), pre_inverted::Val{INV} = False,
+        u; stats, shared::Val{N} = Val(1), pre_inverted::Val{INV} = False,
         linsolve_kwargs = (;), abstol = nothing, reltol = nothing,
         timer = get_timer_output(), kwargs...) where {INV, N}
     INV && @assert length(fu)==length(u) "Non-Square Jacobian Inverse doesn't make sense."
@@ -41,7 +41,7 @@ end
     end
     if INV
         lincache = LinearSolverCache(alg, alg.linsolve, transpose(J), _vec(fu),
-            _vec(u); abstol, reltol, linsolve_kwargs...)
+            _vec(u); stats, abstol, reltol, linsolve_kwargs...)
     else
         lincache = nothing
     end
diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index 3cd30424f..f903a154f 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -93,12 +93,12 @@ end
     grad_op
     u_cache
     fu_cache
-    nf::Base.RefValue{Int}
+    stats::NLStats
 end
 
 function __internal_init(
         prob::AbstractNonlinearProblem, alg::LineSearchesJL, f::F, fu, u, p,
-        args...; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+        args...; stats, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     T = promote_type(eltype(fu), eltype(u))
     if u isa Number
         autodiff = get_concrete_forward_ad(alg.autodiff, prob; check_forward_mode = true)
@@ -135,19 +135,18 @@ function __internal_init(
 
     @bb u_cache = similar(u)
     @bb fu_cache = similar(fu)
-    nf = Base.RefValue(0)
 
     ϕ = @closure (f, p, u, du, α, u_cache, fu_cache) -> begin
         @bb @. u_cache = u + α * du
         fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
-        nf[] += 1
+        stats.nf += 1
         return @fastmath internalnorm(fu_cache)^2 / 2
     end
 
     dϕ = @closure (f, p, u, du, α, u_cache, fu_cache, grad_op) -> begin
         @bb @. u_cache = u + α * du
         fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
-        nf[] += 1
+        stats.nf += 1
         g₀ = grad_op(u_cache, fu_cache, p)
         return dot(g₀, du)
     end
@@ -155,14 +154,14 @@ function __internal_init(
     ϕdϕ = @closure (f, p, u, du, α, u_cache, fu_cache, grad_op) -> begin
         @bb @. u_cache = u + α * du
         fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
-        nf[] += 1
+        stats.nf += 1
         g₀ = grad_op(u_cache, fu_cache, p)
         obj = @fastmath internalnorm(fu_cache)^2 / 2
         return obj, dot(g₀, du)
     end
 
-    return LineSearchesJLCache(
-        f, p, ϕ, dϕ, ϕdϕ, alg.method, T(alg.initial_alpha), grad_op, u_cache, fu_cache, nf)
+    return LineSearchesJLCache(f, p, ϕ, dϕ, ϕdϕ, alg.method, T(alg.initial_alpha),
+        grad_op, u_cache, fu_cache, stats)
 end
 
 function __internal_solve!(cache::LineSearchesJLCache, u, du; kwargs...)
@@ -248,21 +247,20 @@ end
     nsteps::Int
     η_strategy
     n_exp::Int
-    nf::Base.RefValue{Int}
+    stats::NLStats
 end
 
 function __internal_init(
         prob::AbstractNonlinearProblem, alg::RobustNonMonotoneLineSearch, f::F, fu,
-        u, p, args...; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+        u, p, args...; stats, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     @bb u_cache = similar(u)
     @bb fu_cache = similar(fu)
     T = promote_type(eltype(fu), eltype(u))
 
-    nf = Base.RefValue(0)
     ϕ = @closure (f, p, u, du, α, u_cache, fu_cache) -> begin
         @bb @. u_cache = u + α * du
         fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
-        nf[] += 1
+        stats.nf += 1
         return internalnorm(fu_cache)^alg.n_exp
     end
 
@@ -272,7 +270,7 @@ function __internal_init(
     return RobustNonMonotoneLineSearchCache(
         f, p, ϕ, u_cache, fu_cache, internalnorm, alg.maxiters,
         fill(fn₁, alg.M), T(alg.gamma), T(alg.sigma_1), alg.M,
-        T(alg.tau_min), T(alg.tau_max), 0, η_strategy, alg.n_exp, nf)
+        T(alg.tau_min), T(alg.tau_max), 0, η_strategy, alg.n_exp, stats)
 end
 
 function __internal_solve!(cache::RobustNonMonotoneLineSearchCache, u, du; kwargs...)
@@ -341,28 +339,27 @@ end
     α
     nan_maxiters::Int
     maxiters::Int
-    nf::Base.RefValue{Int}
+    stats::NLStats
 end
 
 function __internal_init(
         prob::AbstractNonlinearProblem, alg::LiFukushimaLineSearch, f::F, fu, u,
-        p, args...; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+        p, args...; stats, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     @bb u_cache = similar(u)
     @bb fu_cache = similar(fu)
     T = promote_type(eltype(fu), eltype(u))
 
-    nf = Base.RefValue(0)
     ϕ = @closure (f, p, u, du, α, u_cache, fu_cache) -> begin
         @bb @. u_cache = u + α * du
         fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
-        nf[] += 1
+        stats.nf += 1
         return internalnorm(fu_cache)
     end
 
     return LiFukushimaLineSearchCache(
         ϕ, f, p, internalnorm, u_cache, fu_cache, T(alg.lambda_0),
         T(alg.beta), T(alg.sigma_1), T(alg.sigma_2), T(alg.eta),
-        T(alg.rho), T(true), alg.nan_max_iter, alg.maxiters, nf)
+        T(alg.rho), T(true), alg.nan_max_iter, alg.maxiters, stats)
 end
 
 function __internal_solve!(cache::LiFukushimaLineSearchCache, u, du; kwargs...)
diff --git a/src/globalization/trust_region.jl b/src/globalization/trust_region.jl
index 6004695ec..6ff20266d 100644
--- a/src/globalization/trust_region.jl
+++ b/src/globalization/trust_region.jl
@@ -43,7 +43,7 @@ end
     last_step_accepted::Bool
     u_cache
     fu_cache
-    nf::Int
+    stats::NLStats
 end
 
 function reinit_cache!(cache::LevenbergMarquardtTrustRegionCache, args...;
@@ -53,18 +53,17 @@ function reinit_cache!(cache::LevenbergMarquardtTrustRegionCache, args...;
     cache.loss_old = oftype(cache.loss_old, Inf)
     cache.norm_v_old = oftype(cache.norm_v_old, Inf)
     cache.last_step_accepted = false
-    cache.nf = 0
 end
 
 function __internal_init(
-        prob::AbstractNonlinearProblem, alg::LevenbergMarquardtTrustRegion, f::F,
-        fu, u, p, args...; internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF}
+        prob::AbstractNonlinearProblem, alg::LevenbergMarquardtTrustRegion, f::F, fu,
+        u, p, args...; stats, internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF}
     T = promote_type(eltype(u), eltype(fu))
     @bb v = copy(u)
     @bb u_cache = similar(u)
     @bb fu_cache = similar(fu)
-    return LevenbergMarquardtTrustRegionCache(
-        f, p, T(Inf), v, T(Inf), internalnorm, alg.β_uphill, false, u_cache, fu_cache, 0)
+    return LevenbergMarquardtTrustRegionCache(f, p, T(Inf), v, T(Inf), internalnorm,
+        alg.β_uphill, false, u_cache, fu_cache, stats)
 end
 
 function __internal_solve!(
@@ -76,7 +75,7 @@ function __internal_solve!(
 
     @bb @. cache.u_cache = u + δu
     cache.fu_cache = evaluate_f!!(cache.f, cache.fu_cache, cache.u_cache, cache.p)
-    cache.nf += 1
+    cache.stats.nf += 1
 
     loss = cache.internalnorm(cache.fu_cache)
 
@@ -282,7 +281,7 @@ end
     fu_cache
     last_step_accepted::Bool
     shrink_counter::Int
-    nf::Int
+    stats::NLStats
     alg
 end
 
@@ -298,7 +297,6 @@ function reinit_cache!(
     end
     cache.last_step_accepted = false
     cache.shrink_counter = 0
-    cache.nf = 0
 end
 
 # Defaults
@@ -369,7 +367,7 @@ end
 
 function __internal_init(
         prob::AbstractNonlinearProblem, alg::GenericTrustRegionScheme, f::F, fu,
-        u, p, args...; internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF}
+        u, p, args...; stats, internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF}
     T = promote_type(eltype(u), eltype(fu))
     u0_norm = internalnorm(u)
     fu_norm = internalnorm(fu)
@@ -419,7 +417,7 @@ function __internal_init(
         alg.method, f, p, max_trust_radius, initial_trust_radius, initial_trust_radius,
         step_threshold, shrink_threshold, expand_threshold, shrink_factor,
         expand_factor, p1, p2, p3, p4, ϵ, T(0), vjp_operator, jvp_operator, Jᵀfu_cache,
-        Jδu_cache, δu_cache, internalnorm, u_cache, fu_cache, false, 0, 0, alg)
+        Jδu_cache, δu_cache, internalnorm, u_cache, fu_cache, false, 0, stats, alg)
 end
 
 function __internal_solve!(
@@ -427,7 +425,7 @@ function __internal_solve!(
     T = promote_type(eltype(u), eltype(fu))
     @bb @. cache.u_cache = u + δu
     cache.fu_cache = evaluate_f!!(cache.f, cache.fu_cache, cache.u_cache, cache.p)
-    cache.nf += 1
+    cache.stats.nf += 1
 
     if hasfield(typeof(descent_stats), :δuJᵀJδu) && !isnan(descent_stats.δuJᵀJδu)
         δuJᵀJδu = descent_stats.δuJᵀJδu
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index 9a18d0817..5211573f3 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -12,7 +12,7 @@ function evaluate_f(prob::AbstractNonlinearProblem{uType, iip}, u) where {uType,
 end
 
 function evaluate_f!(cache, u, p)
-    cache.nf += 1
+    cache.stats.nf += 1
     if isinplace(cache)
         cache.prob.f(get_fu(cache), u, p)
     else
@@ -178,21 +178,6 @@ function __construct_extension_jac(prob, alg, u0, fu; can_handle_oop::Val = Fals
     return 𝐉
 end
 
-# Query Statistics
-for stat in (:nsolve, :nfactors, :nsteps, :njacs, :nf)
-    fname = Symbol("get_$(stat)")
-    @eval @inline $(fname)(cache) = __query_stat(cache, $(Val(stat)))
-end
-
-@inline __query_stat(cache, stat::Val) = __direct_query_stat(cache, stat)
-@inline @generated function __direct_query_stat(cache::T, ::Val{stat}) where {T, stat}
-    hasfield(T, stat) || return :(0)
-    return :(__get_data(cache.$(stat)))
-end
-
-@inline __get_data(x::Number) = x
-@inline __get_data(x::Base.RefValue{Int}) = x[]
-
 function reinit_cache! end
 reinit_cache!(cache::Nothing, args...; kwargs...) = nothing
 reinit_cache!(cache, args...; kwargs...) = nothing
@@ -203,12 +188,10 @@ __reinit_internal!(cache, args...; kwargs...) = nothing
 
 # Auto-generate some of the helper functions
 macro internal_caches(cType, internal_cache_names...)
-    return __internal_caches(__source__, __module__, cType, internal_cache_names)
+    return __internal_caches(cType, internal_cache_names)
 end
 
-function __internal_caches(__source__, __module__, cType, internal_cache_names::Tuple)
-    fields = map(
-        name -> :($(__query_stat)(getproperty(cache, $(name)), ST)), internal_cache_names)
+function __internal_caches(cType, internal_cache_names::Tuple)
     callback_caches = map(
         name -> :($(callback_into_cache!)(
             cache, getproperty(internalcache, $(name)), internalcache, args...)),
@@ -221,13 +204,6 @@ function __internal_caches(__source__, __module__, cType, internal_cache_names::
         name -> :($(reinit_cache!)(getproperty(cache, $(name)), args...; kwargs...)),
         internal_cache_names)
     return esc(quote
-        function __query_stat(cache::$(cType), ST::Val{stat}) where {stat}
-            val = $(__direct_query_stat)(cache, ST)
-            return +($(fields...)) + val
-        end
-        function __query_stat(cache::$(cType), ST::Val{:nsteps})
-            return $(__direct_query_stat)(cache, ST)
-        end
         function callback_into_cache!(cache, internalcache::$(cType), args...)
             $(callback_caches...)
         end
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index b9cd6d352..87f02a0fa 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -36,7 +36,7 @@ Construct a cache for the Jacobian of `f` w.r.t. `u`.
     p
     jac_cache
     alg
-    njacs::Int
+    stats::NLStats
     autodiff
     vjp_autodiff
     jvp_autodiff
@@ -44,14 +44,13 @@ end
 
 function reinit_cache!(cache::JacobianCache{iip}, args...; p = cache.p,
         u0 = cache.u, kwargs...) where {iip}
-    cache.njacs = 0
     cache.u = u0
     cache.p = p
     cache.uf = JacobianWrapper{iip}(cache.f, p)
 end
 
 function JacobianCache(
-        prob, alg, f::F, fu_, u, p; autodiff = nothing, vjp_autodiff = nothing,
+        prob, alg, f::F, fu_, u, p; stats, autodiff = nothing, vjp_autodiff = nothing,
         jvp_autodiff = nothing, linsolve = missing) where {F}
     iip = isinplace(prob)
     uf = JacobianWrapper{iip}(f, p)
@@ -94,11 +93,11 @@ function JacobianCache(
     end
 
     return JacobianCache{iip}(
-        J, f, uf, fu, u, p, jac_cache, alg, 0, autodiff, vjp_autodiff, jvp_autodiff)
+        J, f, uf, fu, u, p, jac_cache, alg, stats, autodiff, vjp_autodiff, jvp_autodiff)
 end
 
 function JacobianCache(
-        prob, alg, f::F, ::Number, u::Number, p; autodiff = nothing, kwargs...) where {F}
+        prob, alg, f::F, ::Number, u::Number, p; stats, autodiff = nothing, kwargs...) where {F}
     uf = JacobianWrapper{false}(f, p)
     autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
     if !(autodiff isa AutoForwardDiff ||
@@ -110,7 +109,7 @@ function JacobianCache(
                Detected $(autodiff). Falling back to AutoFiniteDiff."
     end
     return JacobianCache{false}(
-        u, f, uf, u, u, p, nothing, alg, 0, autodiff, nothing, nothing)
+        u, f, uf, u, u, p, nothing, alg, stats, autodiff, nothing, nothing)
 end
 
 @inline (cache::JacobianCache)(u = cache.u) = cache(cache.J, u, cache.p)
@@ -124,14 +123,14 @@ function (cache::JacobianCache)(J::JacobianOperator, u, p = cache.p)
     return StatefulJacobianOperator(J, u, p)
 end
 function (cache::JacobianCache)(::Number, u, p = cache.p) # Scalar
-    cache.njacs += 1
+    cache.stats.njacs += 1
     J = last(__value_derivative(cache.autodiff, cache.uf, u))
     return J
 end
 # Compute the Jacobian
 function (cache::JacobianCache{iip})(
         J::Union{AbstractMatrix, Nothing}, u, p = cache.p) where {iip}
-    cache.njacs += 1
+    cache.stats.njacs += 1
     if iip
         if has_jac(cache.f)
             cache.f.jac(J, u, p)
@@ -157,20 +156,14 @@ end
 @inline function __sparsity_detection_alg(f::NonlinearFunction, ad::AutoSparse)
     if f.sparsity === nothing
         if f.jac_prototype === nothing
-            if is_extension_loaded(Val(:Symbolics))
-                return SymbolicsSparsityDetection()
-            else
-                return ApproximateJacobianSparsity()
-            end
+            is_extension_loaded(Val(:Symbolics)) && return SymbolicsSparsityDetection()
+            return ApproximateJacobianSparsity()
         else
             jac_prototype = f.jac_prototype
         end
     elseif f.sparsity isa AbstractSparsityDetection
-        if f.jac_prototype === nothing
-            return f.sparsity
-        else
-            jac_prototype = f.jac_prototype
-        end
+        f.jac_prototype === nothing && return f.sparsity
+        jac_prototype = f.jac_prototype
     elseif f.sparsity isa AbstractMatrix
         jac_prototype = f.sparsity
     elseif f.jac_prototype isa AbstractMatrix
diff --git a/src/internal/linear_solve.jl b/src/internal/linear_solve.jl
index 783bf4956..27e6a780f 100644
--- a/src/internal/linear_solve.jl
+++ b/src/internal/linear_solve.jl
@@ -1,10 +1,8 @@
-import LinearSolve: AbstractFactorization, DefaultAlgorithmChoice, DefaultLinearSolver
-
 const LinearSolveFailureCode = isdefined(ReturnCode, :InternalLinearSolveFailure) ?
                                ReturnCode.InternalLinearSolveFailure : ReturnCode.Failure
 
 """
-    LinearSolverCache(alg, linsolve, A, b, u; kwargs...)
+    LinearSolverCache(alg, linsolve, A, b, u; stats, kwargs...)
 
 Construct a cache for solving linear systems of the form `A * u = b`. Following cases are
 handled:
@@ -52,14 +50,7 @@ not mutated, we do this by copying over `A` to a preconstructed cache.
     A
     b
     precs
-    nsolve::Int
-    nfactors::Int
-end
-
-# FIXME: Do we need to reinit the precs?
-function reinit_cache!(cache::LinearSolverCache, args...; kwargs...)
-    cache.nsolve = 0
-    cache.nfactors = 0
+    stats::NLStats
 end
 
 @inline __fix_strange_type_combination(A, b, u) = u
@@ -77,14 +68,14 @@ end
     cache.lincache.u = u
 end
 
-function LinearSolverCache(alg, linsolve, A, b, u; kwargs...)
+function LinearSolverCache(alg, linsolve, A, b, u; stats, kwargs...)
     u_fixed = __fix_strange_type_combination(A, b, u)
 
     if (A isa Number && b isa Number) ||
        (linsolve === nothing && A isa SMatrix) ||
        (A isa Diagonal) ||
        (linsolve isa typeof(\))
-        return LinearSolverCache(nothing, nothing, nothing, A, b, nothing, 0, 0)
+        return LinearSolverCache(nothing, nothing, nothing, A, b, nothing, stats)
     end
     @bb u_ = copy(u_fixed)
     linprob = LinearProblem(A, b; u0 = u_, kwargs...)
@@ -92,8 +83,7 @@ function LinearSolverCache(alg, linsolve, A, b, u; kwargs...)
     weight = __init_ones(u_fixed)
     if __hasfield(alg, Val(:precs))
         precs = alg.precs
-        Pl_, Pr_ = precs(
-            A, nothing, u, nothing, nothing, nothing, nothing, nothing, nothing)
+        Pl_, Pr_ = precs(A, nothing, u, ntuple(Returns(nothing), 6)...)
     else
         precs, Pl_, Pr_ = nothing, nothing, nothing
     end
@@ -102,7 +92,7 @@ function LinearSolverCache(alg, linsolve, A, b, u; kwargs...)
     # Unalias here, we will later use these as caches
     lincache = init(linprob, linsolve; alias_A = false, alias_b = false, Pl, Pr)
 
-    return LinearSolverCache(lincache, linsolve, nothing, nothing, nothing, precs, 0, 0)
+    return LinearSolverCache(lincache, linsolve, nothing, nothing, nothing, precs, stats)
 end
 
 @kwdef @concrete struct LinearSolveResult
@@ -113,8 +103,8 @@ end
 # Direct Linear Solve Case without Caching
 function (cache::LinearSolverCache{Nothing})(;
         A = nothing, b = nothing, linu = nothing, kwargs...)
-    cache.nsolve += 1
-    cache.nfactors += 1
+    cache.stats.nsolve += 1
+    cache.stats.nfactors += 1
     A === nothing || (cache.A = A)
     b === nothing || (cache.b = b)
     if A isa Diagonal
@@ -132,7 +122,7 @@ function (cache::LinearSolverCache)(;
         A = nothing, b = nothing, linu = nothing, du = nothing,
         p = nothing, weight = nothing, cachedata = nothing,
         reuse_A_if_factorization = false, verbose = true, kwargs...)
-    cache.nsolve += 1
+    cache.stats.nsolve += 1
 
     __update_A!(cache, A, reuse_A_if_factorization)
     b !== nothing && (cache.lincache.b = b)
@@ -224,7 +214,7 @@ end
 @inline function __update_A!(cache, ::AbstractFactorization, A, reuse)
     reuse && return cache
     __set_lincache_A(cache.lincache, A)
-    cache.nfactors += 1
+    cache.stats.nfactors += 1
     return cache
 end
 @inline function __update_A!(cache, alg::DefaultLinearSolver, A, reuse)
@@ -235,7 +225,7 @@ end
     end
     reuse && return cache
     __set_lincache_A(cache.lincache, A)
-    cache.nfactors += 1
+    cache.stats.nfactors += 1
     return cache
 end
 
@@ -253,17 +243,12 @@ function __set_lincache_A(lincache, new_A)
 end
 
 @inline function __wrapprecs(_Pl, _Pr, weight)
-    if _Pl !== nothing
-        Pl = ComposePreconditioner(InvPreconditioner(Diagonal(_vec(weight))), _Pl)
-    else
-        Pl = InvPreconditioner(Diagonal(_vec(weight)))
-    end
+    Pl = _Pl !== nothing ?
+         ComposePreconditioner(InvPreconditioner(Diagonal(_vec(weight))), _Pl) :
+         InvPreconditioner(Diagonal(_vec(weight)))
 
-    if _Pr !== nothing
-        Pr = ComposePreconditioner(Diagonal(_vec(weight)), _Pr)
-    else
-        Pr = Diagonal(_vec(weight))
-    end
+    Pr = _Pr !== nothing ? ComposePreconditioner(Diagonal(_vec(weight)), _Pr) :
+         Diagonal(_vec(weight))
 
     return Pl, Pr
 end
diff --git a/src/internal/operators.jl b/src/internal/operators.jl
index 74667dbdb..8c3c8922c 100644
--- a/src/internal/operators.jl
+++ b/src/internal/operators.jl
@@ -34,13 +34,9 @@ end
 
 Base.size(J::JacobianOperator) = prod(size(J.output_cache)), prod(size(J.input_cache))
 function Base.size(J::JacobianOperator, d::Integer)
-    if d == 1
-        return prod(size(J.output_cache))
-    elseif d == 2
-        return prod(size(J.input_cache))
-    else
-        error("Invalid dimension $d for JacobianOperator")
-    end
+    d == 1 && return prod(size(J.output_cache))
+    d == 2 && return prod(size(J.input_cache))
+    error("Invalid dimension $d for JacobianOperator")
 end
 
 for op in (:adjoint, :transpose)
diff --git a/src/internal/tracing.jl b/src/internal/tracing.jl
index 75fcaa66a..fe35f1a9c 100644
--- a/src/internal/tracing.jl
+++ b/src/internal/tracing.jl
@@ -207,12 +207,11 @@ function update_trace!(cache::AbstractNonlinearSolveCache, α = true)
     J = __getproperty(cache, Val(:J))
     if J === nothing
         update_trace!(
-            trace, get_nsteps(cache) + 1, get_u(cache), get_fu(cache), nothing, cache.du, α)
+            trace, cache.nsteps + 1, get_u(cache), get_fu(cache), nothing, cache.du, α)
     elseif cache isa ApproximateJacobianSolveCache && store_inverse_jacobian(cache)
-        update_trace!(trace, get_nsteps(cache) + 1, get_u(cache),
-            get_fu(cache), ApplyArray(__safe_inv, J), cache.du, α)
+        update_trace!(trace, cache.nsteps + 1, get_u(cache), get_fu(cache),
+            ApplyArray(__safe_inv, J), cache.du, α)
     else
-        update_trace!(
-            trace, get_nsteps(cache) + 1, get_u(cache), get_fu(cache), J, cache.du, α)
+        update_trace!(trace, cache.nsteps + 1, get_u(cache), get_fu(cache), J, cache.du, α)
     end
 end
diff --git a/src/utils.jl b/src/utils.jl
index 8be33d9f9..1cd552aa1 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -147,6 +147,15 @@ function __build_solution_less_specialize(prob::AbstractNonlinearProblem, alg, u
     N = ndims(u)
 
     return SciMLBase.NonlinearSolution{T, N, typeof(u), typeof(resid), typeof(prob),
-        typeof(alg), Any, typeof(left), Any, typeof(trace)}(
+        typeof(alg), Any, typeof(left), typeof(stats), typeof(trace)}(
         u, resid, prob, alg, retcode, original, left, right, stats, trace)
 end
+
+@inline empty_nlstats() = NLStats(0, 0, 0, 0, 0)
+function __reinit_internal!(stats::NLStats)
+    stats.nf = 0
+    stats.nsteps = 0
+    stats.nfactors = 0
+    stats.njacs = 0
+    stats.nsolve = 0
+end

From 066912c3488dc65fbc625b3dbaa244182996436a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 24 May 2024 19:10:54 -0700
Subject: [PATCH 400/700] Run formatter

---
 src/core/approximate_jacobian.jl           |  9 ++++-----
 src/core/generalized_first_order.jl        | 11 ++++++-----
 src/core/generic.jl                        |  2 +-
 src/descent/steepest.jl                    |  8 ++++----
 src/globalization/line_search.jl           |  8 ++++----
 src/globalization/trust_region.jl          |  4 ++--
 src/internal/approximate_initialization.jl |  8 ++++----
 src/internal/helpers.jl                    |  3 ++-
 src/internal/jacobian.jl                   |  9 ++++-----
 src/utils.jl                               |  5 +++--
 10 files changed, 34 insertions(+), 33 deletions(-)

diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index 4711ed719..e61f34032 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -165,8 +165,8 @@ function SciMLBase.__init(
         INV = store_inverse_jacobian(alg.update_rule)
 
         linsolve = get_linear_solver(alg.descent)
-        initialization_cache = __internal_init(
-            prob, alg.initialization, alg, f, fu, u, p; stats, linsolve, maxiters, internalnorm)
+        initialization_cache = __internal_init(prob, alg.initialization, alg, f, fu, u, p;
+            stats, linsolve, maxiters, internalnorm)
 
         abstol, reltol, termination_cache = init_termination_cache(
             prob, abstol, reltol, fu, u, termination_condition)
@@ -174,9 +174,8 @@ function SciMLBase.__init(
 
         J = initialization_cache(nothing)
         inv_workspace, J = INV ? __safe_inv_workspace(J) : (nothing, J)
-        descent_cache = __internal_init(
-            prob, alg.descent, J, fu, u; stats, abstol, reltol, internalnorm,
-            linsolve_kwargs, pre_inverted = Val(INV), timer)
+        descent_cache = __internal_init(prob, alg.descent, J, fu, u; stats, abstol, reltol,
+            internalnorm, linsolve_kwargs, pre_inverted = Val(INV), timer)
         du = get_du(descent_cache)
 
         reinit_rule_cache = __internal_init(alg.reinit_rule, J, fu, u, du)
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 5e7e5f144..84e74478f 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -153,9 +153,10 @@ end
 
 function SciMLBase.__init(
         prob::AbstractNonlinearProblem{uType, iip}, alg::GeneralizedFirstOrderAlgorithm,
-        args...; stats=empty_nlstats(), alias_u0 = false, maxiters = 1000, abstol = nothing,
-        reltol = nothing, maxtime = nothing, termination_condition = nothing,
-        internalnorm = DEFAULT_NORM, linsolve_kwargs = (;), kwargs...) where {uType, iip}
+        args...; stats = empty_nlstats(), alias_u0 = false, maxiters = 1000,
+        abstol = nothing, reltol = nothing, maxtime = nothing,
+        termination_condition = nothing, internalnorm = DEFAULT_NORM,
+        linsolve_kwargs = (;), kwargs...) where {uType, iip}
     timer = get_timer_output()
     @static_timeit timer "cache construction" begin
         (; f, u0, p) = prob
@@ -173,8 +174,8 @@ function SciMLBase.__init(
             prob, alg, f, fu, u, p; stats, autodiff = alg.jacobian_ad, linsolve,
             jvp_autodiff = alg.forward_ad, vjp_autodiff = alg.reverse_ad)
         J = jac_cache(nothing)
-        descent_cache = __internal_init(prob, alg.descent, J, fu, u; stats, abstol, reltol,
-            internalnorm, linsolve_kwargs, timer)
+        descent_cache = __internal_init(prob, alg.descent, J, fu, u; stats, abstol,
+            reltol, internalnorm, linsolve_kwargs, timer)
         du = get_du(descent_cache)
 
         if alg.trustregion !== missing && alg.linesearch !== missing
diff --git a/src/core/generic.jl b/src/core/generic.jl
index 76135115c..44e6e1152 100644
--- a/src/core/generic.jl
+++ b/src/core/generic.jl
@@ -1,5 +1,5 @@
 function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
-        alg::AbstractNonlinearSolveAlgorithm, args...; stats=empty_nlstats(), kwargs...)
+        alg::AbstractNonlinearSolveAlgorithm, args...; stats = empty_nlstats(), kwargs...)
     cache = SciMLBase.__init(prob, alg, args...; stats, kwargs...)
     return solve!(cache)
 end
diff --git a/src/descent/steepest.jl b/src/descent/steepest.jl
index 46f2cf10c..cc2f4d128 100644
--- a/src/descent/steepest.jl
+++ b/src/descent/steepest.jl
@@ -30,8 +30,8 @@ end
 @internal_caches SteepestDescentCache :lincache
 
 @inline function __internal_init(
-        prob::AbstractNonlinearProblem, alg::SteepestDescent, J, fu,
-        u; stats, shared::Val{N} = Val(1), pre_inverted::Val{INV} = False,
+        prob::AbstractNonlinearProblem, alg::SteepestDescent, J, fu, u;
+        stats, shared::Val{N} = Val(1), pre_inverted::Val{INV} = False,
         linsolve_kwargs = (;), abstol = nothing, reltol = nothing,
         timer = get_timer_output(), kwargs...) where {INV, N}
     INV && @assert length(fu)==length(u) "Non-Square Jacobian Inverse doesn't make sense."
@@ -40,8 +40,8 @@ end
         @bb δu_ = similar(u)
     end
     if INV
-        lincache = LinearSolverCache(alg, alg.linsolve, transpose(J), _vec(fu),
-            _vec(u); stats, abstol, reltol, linsolve_kwargs...)
+        lincache = LinearSolverCache(alg, alg.linsolve, transpose(J), _vec(fu), _vec(u);
+            stats, abstol, reltol, linsolve_kwargs...)
     else
         lincache = nothing
     end
diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index f903a154f..038cc119a 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -251,8 +251,8 @@ end
 end
 
 function __internal_init(
-        prob::AbstractNonlinearProblem, alg::RobustNonMonotoneLineSearch, f::F, fu,
-        u, p, args...; stats, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+        prob::AbstractNonlinearProblem, alg::RobustNonMonotoneLineSearch, f::F, fu, u,
+        p, args...; stats, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     @bb u_cache = similar(u)
     @bb fu_cache = similar(fu)
     T = promote_type(eltype(fu), eltype(u))
@@ -343,8 +343,8 @@ end
 end
 
 function __internal_init(
-        prob::AbstractNonlinearProblem, alg::LiFukushimaLineSearch, f::F, fu, u,
-        p, args...; stats, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+        prob::AbstractNonlinearProblem, alg::LiFukushimaLineSearch, f::F, fu, u, p,
+        args...; stats, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     @bb u_cache = similar(u)
     @bb fu_cache = similar(fu)
     T = promote_type(eltype(fu), eltype(u))
diff --git a/src/globalization/trust_region.jl b/src/globalization/trust_region.jl
index 6ff20266d..51b54959e 100644
--- a/src/globalization/trust_region.jl
+++ b/src/globalization/trust_region.jl
@@ -366,8 +366,8 @@ end
 @inline __expand_factor(::Nothing, ::Type{T}, method) where {T} = T(2)
 
 function __internal_init(
-        prob::AbstractNonlinearProblem, alg::GenericTrustRegionScheme, f::F, fu,
-        u, p, args...; stats, internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF}
+        prob::AbstractNonlinearProblem, alg::GenericTrustRegionScheme, f::F, fu, u,
+        p, args...; stats, internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF}
     T = promote_type(eltype(u), eltype(fu))
     u0_norm = internalnorm(u)
     fu_norm = internalnorm(fu)
diff --git a/src/internal/approximate_initialization.jl b/src/internal/approximate_initialization.jl
index a1f36f475..4f17cd72f 100644
--- a/src/internal/approximate_initialization.jl
+++ b/src/internal/approximate_initialization.jl
@@ -145,12 +145,12 @@ make a selection automatically.
     autodiff
 end
 
-function __internal_init(
-        prob::AbstractNonlinearProblem, alg::TrueJacobianInitialization, solver, f::F, fu,
-        u, p; linsolve = missing, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+function __internal_init(prob::AbstractNonlinearProblem, alg::TrueJacobianInitialization,
+        solver, f::F, fu, u, p; stats, linsolve = missing,
+        internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     autodiff = get_concrete_forward_ad(
         alg.autodiff, prob; check_forward_mode = false, kwargs...)
-    jac_cache = JacobianCache(prob, solver, prob.f, fu, u, p; autodiff, linsolve)
+    jac_cache = JacobianCache(prob, solver, prob.f, fu, u, p; stats, autodiff, linsolve)
     J = alg.structure(jac_cache(nothing))
     return InitializedApproximateJacobianCache(
         J, alg.structure, alg, jac_cache, false, internalnorm)
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index 5211573f3..c5241481a 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -168,7 +168,8 @@ end
 
 function __construct_extension_jac(prob, alg, u0, fu; can_handle_oop::Val = False,
         can_handle_scalar::Val = False, kwargs...)
-    Jₚ = JacobianCache(prob, alg, prob.f, fu, u0, prob.p; kwargs...)
+    Jₚ = JacobianCache(
+        prob, alg, prob.f, fu, u0, prob.p; stats = empty_nlstats(), kwargs...)
 
     𝓙 = (can_handle_scalar === False && prob.u0 isa Number) ? @closure(u->[Jₚ(u[1])]) : Jₚ
 
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 87f02a0fa..2abd89336 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -49,9 +49,8 @@ function reinit_cache!(cache::JacobianCache{iip}, args...; p = cache.p,
     cache.uf = JacobianWrapper{iip}(cache.f, p)
 end
 
-function JacobianCache(
-        prob, alg, f::F, fu_, u, p; stats, autodiff = nothing, vjp_autodiff = nothing,
-        jvp_autodiff = nothing, linsolve = missing) where {F}
+function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
+        vjp_autodiff = nothing, jvp_autodiff = nothing, linsolve = missing) where {F}
     iip = isinplace(prob)
     uf = JacobianWrapper{iip}(f, p)
 
@@ -96,8 +95,8 @@ function JacobianCache(
         J, f, uf, fu, u, p, jac_cache, alg, stats, autodiff, vjp_autodiff, jvp_autodiff)
 end
 
-function JacobianCache(
-        prob, alg, f::F, ::Number, u::Number, p; stats, autodiff = nothing, kwargs...) where {F}
+function JacobianCache(prob, alg, f::F, ::Number, u::Number, p; stats,
+        autodiff = nothing, kwargs...) where {F}
     uf = JacobianWrapper{false}(f, p)
     autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
     if !(autodiff isa AutoForwardDiff ||
diff --git a/src/utils.jl b/src/utils.jl
index 1cd552aa1..d13555259 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -146,8 +146,9 @@ function __build_solution_less_specialize(prob::AbstractNonlinearProblem, alg, u
     T = eltype(eltype(u))
     N = ndims(u)
 
-    return SciMLBase.NonlinearSolution{T, N, typeof(u), typeof(resid), typeof(prob),
-        typeof(alg), Any, typeof(left), typeof(stats), typeof(trace)}(
+    return SciMLBase.NonlinearSolution{
+        T, N, typeof(u), typeof(resid), typeof(prob), typeof(alg),
+        Any, typeof(left), typeof(stats), typeof(trace)}(
         u, resid, prob, alg, retcode, original, left, right, stats, trace)
 end
 

From 50aa5c45a027d3423bf047572786f9960961c58c Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 24 May 2024 19:10:54 -0700
Subject: [PATCH 401/700] Run formatter

---
 Project.toml | 6 +-----
 1 file changed, 1 insertion(+), 5 deletions(-)

diff --git a/Project.toml b/Project.toml
index 44f18d17b..05d5bafcf 100644
--- a/Project.toml
+++ b/Project.toml
@@ -32,7 +32,6 @@ TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 
 [weakdeps]
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
-Enlsip = "d5306a6b-d590-428d-a53a-eb3bb2d36f2d"
 FastLevenbergMarquardt = "7a0df574-e128-4d35-8cbd-3d84502bf7ce"
 FixedPointAcceleration = "817d07cb-a79a-5c30-9a31-890123675176"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
@@ -46,7 +45,6 @@ Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [extensions]
 NonlinearSolveBandedMatricesExt = "BandedMatrices"
-NonlinearSolveEnlsipExt = "Enlsip"
 NonlinearSolveFastLevenbergMarquardtExt = "FastLevenbergMarquardt"
 NonlinearSolveFixedPointAccelerationExt = "FixedPointAcceleration"
 NonlinearSolveLeastSquaresOptimExt = "LeastSquaresOptim"
@@ -67,7 +65,6 @@ BenchmarkTools = "1.4"
 CUDA = "5.2"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149.0"
-Enlsip = "0.9"
 Enzyme = "0.12"
 ExplicitImports = "1.4.4"
 FastBroadcast = "0.2.8"
@@ -119,7 +116,6 @@ Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
-Enlsip = "d5306a6b-d590-428d-a53a-eb3bb2d36f2d"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 FastLevenbergMarquardt = "7a0df574-e128-4d35-8cbd-3d84502bf7ce"
@@ -145,4 +141,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enlsip", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEq", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEq", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]

From 2dc8a7e3d5ea3e779cc9b82756b521bbf835a0db Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 12:49:49 -0700
Subject: [PATCH 402/700] Support BigFloat

---
 lib/SimpleNonlinearSolve/Project.toml         |  4 +--
 .../test/core/exotic_type_tests.jl            | 31 +++++++++++++++++++
 .../test/gpu/cuda_tests.jl                    |  4 +--
 3 files changed, 35 insertions(+), 4 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 322178ba9..74b6cde87 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.8.1"
+version = "1.8.2"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -50,7 +50,7 @@ FiniteDiff = "2.22"
 ForwardDiff = "0.10.36"
 LinearAlgebra = "1.10"
 LinearSolve = "2.30"
-MaybeInplace = "0.1.1"
+MaybeInplace = "0.1.3"
 NonlinearProblemLibrary = "0.1.2"
 Pkg = "1.10"
 PolyesterForwardDiff = "0.1.1"
diff --git a/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl b/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
new file mode 100644
index 000000000..fff77a3d4
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
@@ -0,0 +1,31 @@
+# File for different types of exotic types
+@testsetup module SimpleNonlinearSolveExoticTypeTests
+using SimpleNonlinearSolve
+
+fn_iip = NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p)
+fn_oop = NonlinearFunction{false}((u, p) -> u .* u .- p)
+
+u0 = BigFloat[1.0, 1.0, 1.0]
+prob_iip_bf = NonlinearProblem{true}(fn_iip, u0, BigFloat(2))
+prob_oop_bf = NonlinearProblem{false}(fn_oop, u0, BigFloat(2))
+
+export fn_iip, fn_oop, u0, prob_iip_bf, prob_oop_bf
+end
+
+@testitem "BigFloat Support" tags=[:core] setup=[SimpleNonlinearSolveExoticTypeTests] begin
+    using SimpleNonlinearSolve, LinearAlgebra
+
+    for alg in [SimpleNewtonRaphson(), SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
+        SimpleTrustRegion(), SimpleLimitedMemoryBroyden(; threshold = 2),
+        SimpleHalley()]
+        sol = solve(prob_oop_bf, alg)
+        @test norm(sol.resid, Inf) < 1e-6
+        @test SciMLBase.successful_retcode(sol.retcode)
+
+        alg isa SimpleHalley && continue
+
+        sol = solve(prob_iip_bf, alg)
+        @test norm(sol.resid, Inf) < 1e-6
+        @test SciMLBase.successful_retcode(sol.retcode)
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
index dae6a87d7..9d31114d0 100644
--- a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Solving on GPUs" tags=[:cuda] begin
+@testitem "Solving on GPUs" tags=[:cuda] skip=:(using CUDA; !CUDA.functional()) begin
     using StaticArrays, CUDA
 
     CUDA.allowscalar(false)
@@ -36,7 +36,7 @@
     end
 end
 
-@testitem "CUDA Kernel Launch Test" tags=[:cuda] begin
+@testitem "CUDA Kernel Launch Test" tags=[:cuda] skip=:(using CUDA; !CUDA.functional()) begin
     using StaticArrays, CUDA
 
     CUDA.allowscalar(false)

From aeef552032b7c86fae15b6dd895baed9b846eff7 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 14:06:00 -0700
Subject: [PATCH 403/700] Increase timeout for Kernel Launch tests

---
 lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
index 9d31114d0..39ac422a4 100644
--- a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
@@ -36,7 +36,7 @@
     end
 end
 
-@testitem "CUDA Kernel Launch Test" tags=[:cuda] skip=:(using CUDA; !CUDA.functional()) begin
+@testitem "CUDA Kernel Launch Test" tags=[:cuda] skip=:(using CUDA; !CUDA.functional()) timeout=3600 begin
     using StaticArrays, CUDA
 
     CUDA.allowscalar(false)

From 1cf93bebf3733cf03929497e15d43643ced4792b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 15:31:52 -0700
Subject: [PATCH 404/700] Don't rely on unqualified import

---
 Project.toml          | 2 +-
 src/NonlinearSolve.jl | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/Project.toml b/Project.toml
index 7d88cb09a..765b9568f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.12.1"
+version = "3.12.2"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index b92aac597..59bb1f4b4 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -8,8 +8,8 @@ using Reexport: @reexport
 using PrecompileTools: @recompile_invalidations, @compile_workload, @setup_workload
 
 @recompile_invalidations begin
-    using ADTypes: AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff, AutoZygote,
-                   AutoEnzyme, AutoSparse
+    using ADTypes: ADTypes, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff,
+		   AutoZygote, AutoEnzyme, AutoSparse
     # FIXME: deprecated, remove in future
     using ADTypes: AutoSparseFiniteDiff, AutoSparseForwardDiff,
                    AutoSparsePolyesterForwardDiff, AutoSparseZygote

From d5632103e3df740ff52d857922a7e4a4d6553c27 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 15:33:34 -0700
Subject: [PATCH 405/700] Run formatter

---
 src/NonlinearSolve.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 59bb1f4b4..1ddcf09f3 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -9,7 +9,7 @@ using PrecompileTools: @recompile_invalidations, @compile_workload, @setup_workl
 
 @recompile_invalidations begin
     using ADTypes: ADTypes, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff,
-		   AutoZygote, AutoEnzyme, AutoSparse
+                   AutoZygote, AutoEnzyme, AutoSparse
     # FIXME: deprecated, remove in future
     using ADTypes: AutoSparseFiniteDiff, AutoSparseForwardDiff,
                    AutoSparsePolyesterForwardDiff, AutoSparseZygote

From 6f65ac49c5f6ef61b40cef077129c1c0ce1d78b5 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 15:34:24 -0700
Subject: [PATCH 406/700] Double bump

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 765b9568f..7d88cb09a 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.12.2"
+version = "3.12.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 128e353c4cc40d2c9f5a4f12a770a11caebc49eb Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 16:30:21 -0700
Subject: [PATCH 407/700] Update Project.toml

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 549802fcd..6c656d419 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.12.1"
+version = "3.12.2"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From a78c7a69a8d60b6249dcbea60c3e715f0e2c2aef Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 12:19:51 -0700
Subject: [PATCH 408/700] Make the printing of the cache more readable

---
 src/abstract_types.jl | 24 ++++++++++++++----------
 1 file changed, 14 insertions(+), 10 deletions(-)

diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 0dc4d8f5a..20b491e19 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -202,19 +202,17 @@ Abstract Type for all NonlinearSolve.jl Caches.
 abstract type AbstractNonlinearSolveCache{iip, timeit} end
 
 function SymbolicIndexingInterface.symbolic_container(cache::AbstractNonlinearSolveCache)
-    cache.prob
+    return cache.prob
 end
 function SymbolicIndexingInterface.parameter_values(cache::AbstractNonlinearSolveCache)
-    parameter_values(symbolic_container(cache))
+    return parameter_values(symbolic_container(cache))
 end
 function SymbolicIndexingInterface.state_values(cache::AbstractNonlinearSolveCache)
-    state_values(symbolic_container(cache))
+    return state_values(symbolic_container(cache))
 end
 
 function Base.getproperty(cache::AbstractNonlinearSolveCache, sym::Symbol)
-    if sym == :ps
-        return ParameterIndexingProxy(cache)
-    end
+    sym == :ps && return ParameterIndexingProxy(cache)
     return getfield(cache, sym)
 end
 
@@ -230,10 +228,16 @@ function __show_cache(io::IO, cache::AbstractNonlinearSolveCache, indent = 0)
     println(io, "$(nameof(typeof(cache)))(")
     __show_algorithm(io, cache.alg,
         (" "^(indent + 4)) * "alg = " * string(get_name(cache.alg)), indent + 4)
-    println(io, ",")
-    println(io, (" "^(indent + 4)) * "u = ", get_u(cache), ",")
-    println(io, (" "^(indent + 4)) * "residual = ", get_fu(cache), ",")
-    println(io, (" "^(indent + 4)) * "inf-norm(residual) = ", norm(get_fu(cache), Inf), ",")
+
+    ustr = sprint(show, get_u(cache); context=(:compact=>true, :limit=>true))
+    println(io, ",\n" * (" "^(indent + 4)) * "u = $(ustr),")
+
+    residstr = sprint(show, get_fu(cache); context=(:compact=>true, :limit=>true))
+    println(io, (" "^(indent + 4)) * "residual = $(residstr),")
+
+    normstr = sprint(show, norm(get_fu(cache), Inf); context=(:compact=>true, :limit=>true))
+    println(io, (" "^(indent + 4)) * "inf-norm(residual) = $(normstr),")
+
     println(io, " "^(indent + 4) * "nsteps = ", cache.stats.nsteps, ",")
     println(io, " "^(indent + 4) * "retcode = ", cache.retcode)
     print(io, " "^(indent) * ")")

From be8b599aaa713df7924560502fd837d81602d03b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 13:11:27 -0700
Subject: [PATCH 409/700] Add support for BigFloat

---
 Project.toml                               |  4 ++--
 src/abstract_types.jl                      |  7 ++++---
 src/algorithms/lbroyden.jl                 |  6 +++---
 src/default.jl                             |  6 +-----
 src/globalization/line_search.jl           |  4 ++--
 src/internal/approximate_initialization.jl |  2 +-
 src/internal/helpers.jl                    |  4 ++--
 src/internal/jacobian.jl                   |  5 +++--
 src/internal/operators.jl                  | 16 ++++++++--------
 src/utils.jl                               | 13 +++++++++++++
 10 files changed, 39 insertions(+), 28 deletions(-)

diff --git a/Project.toml b/Project.toml
index 6c656d419..35fdb7046 100644
--- a/Project.toml
+++ b/Project.toml
@@ -66,7 +66,7 @@ CUDA = "5.2"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149.0"
 Enzyme = "0.12"
-ExplicitImports = "1.4.4"
+ExplicitImports = "1.5"
 FastBroadcast = "0.2.8, 0.3"
 FastClosures = "0.3.2"
 FastLevenbergMarquardt = "0.1"
@@ -79,7 +79,7 @@ LineSearches = "7.2"
 LinearAlgebra = "1.10"
 LinearSolve = "2.30"
 MINPACK = "1.2"
-MaybeInplace = "0.1.1"
+MaybeInplace = "0.1.3"
 ModelingToolkit = "9.13.0"
 NLSolvers = "0.5"
 NLsolve = "4.5"
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 20b491e19..abb603868 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -229,13 +229,14 @@ function __show_cache(io::IO, cache::AbstractNonlinearSolveCache, indent = 0)
     __show_algorithm(io, cache.alg,
         (" "^(indent + 4)) * "alg = " * string(get_name(cache.alg)), indent + 4)
 
-    ustr = sprint(show, get_u(cache); context=(:compact=>true, :limit=>true))
+    ustr = sprint(show, get_u(cache); context = (:compact => true, :limit => true))
     println(io, ",\n" * (" "^(indent + 4)) * "u = $(ustr),")
 
-    residstr = sprint(show, get_fu(cache); context=(:compact=>true, :limit=>true))
+    residstr = sprint(show, get_fu(cache); context = (:compact => true, :limit => true))
     println(io, (" "^(indent + 4)) * "residual = $(residstr),")
 
-    normstr = sprint(show, norm(get_fu(cache), Inf); context=(:compact=>true, :limit=>true))
+    normstr = sprint(
+        show, norm(get_fu(cache), Inf); context = (:compact => true, :limit => true))
     println(io, (" "^(indent + 4)) * "inf-norm(residual) = $(normstr),")
 
     println(io, " "^(indent + 4) * "nsteps = ", cache.stats.nsteps, ",")
diff --git a/src/algorithms/lbroyden.jl b/src/algorithms/lbroyden.jl
index 596172ead..bead1a057 100644
--- a/src/algorithms/lbroyden.jl
+++ b/src/algorithms/lbroyden.jl
@@ -117,9 +117,9 @@ end
 
 function BroydenLowRankJacobian(fu, u; threshold::Int = 10, alpha = true)
     T = promote_type(eltype(u), eltype(fu))
-    U = similar(fu, T, length(fu), threshold)
-    Vᵀ = similar(u, T, length(u), threshold)
-    cache = similar(u, T, threshold)
+    U = __similar(fu, T, length(fu), threshold)
+    Vᵀ = __similar(u, T, length(u), threshold)
+    cache = __similar(u, T, threshold)
     return BroydenLowRankJacobian{T}(U, Vᵀ, 0, cache, T(alpha))
 end
 
diff --git a/src/default.jl b/src/default.jl
index 660caab41..ab35b7a55 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -266,11 +266,7 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
                     alias_u0 = false  # If immutable don't care about aliasing
                 end
                 u0 = prob.u0
-                if alias_u0
-                    u0_aliased = similar(u0)
-                else
-                    u0_aliased = u0  # Irrelevant
-                end
+                u0_aliased = alias_u0 ? __similar(u0) : u0
             end]
             for i in 1:N
                 cur_sol = sol_syms[i]
diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index 038cc119a..e09a8d188 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -115,7 +115,7 @@ function __internal_init(
     else
         if SciMLBase.has_jvp(f)
             if isinplace(prob)
-                g_cache = similar(u)
+                g_cache = __similar(u)
                 grad_op = @closure (u, fu, p) -> f.vjp(g_cache, fu, u, p)
             else
                 grad_op = @closure (u, fu, p) -> f.vjp(fu, u, p)
@@ -125,7 +125,7 @@ function __internal_init(
                 alg.autodiff, prob; check_reverse_mode = true)
             vjp_op = VecJacOperator(prob, fu, u; autodiff)
             if isinplace(prob)
-                g_cache = similar(u)
+                g_cache = __similar(u)
                 grad_op = @closure (u, fu, p) -> vjp_op(g_cache, fu, u, p)
             else
                 grad_op = @closure (u, fu, p) -> vjp_op(fu, u, p)
diff --git a/src/internal/approximate_initialization.jl b/src/internal/approximate_initialization.jl
index 4f17cd72f..5ce348ae3 100644
--- a/src/internal/approximate_initialization.jl
+++ b/src/internal/approximate_initialization.jl
@@ -97,7 +97,7 @@ function __internal_init(
         @assert length(u)==length(fu) "Diagonal Jacobian Structure must be square!"
         J = one.(_vec(fu)) .* α
     else
-        J_ = similar(fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u))
+        J_ = __similar(fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u))
         J = alg.structure(__make_identity!!(J_, α); alias = true)
     end
     return InitializedApproximateJacobianCache(
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index c5241481a..83b169d7f 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -2,7 +2,7 @@
 function evaluate_f(prob::AbstractNonlinearProblem{uType, iip}, u) where {uType, iip}
     (; f, u0, p) = prob
     if iip
-        fu = f.resid_prototype === nothing ? similar(u) :
+        fu = f.resid_prototype === nothing ? __similar(u) :
              promote_type(eltype(u), eltype(f.resid_prototype)).(f.resid_prototype)
         f(fu, u, p)
     else
@@ -154,7 +154,7 @@ function __construct_extension_f(prob::AbstractNonlinearProblem; alias_u0::Bool
 
     𝐅 = if force_oop === True && applicable(𝐟, u0, u0)
         _resid = resid isa Number ? [resid] : _vec(resid)
-        du = _vec(similar(_resid))
+        du = _vec(__similar(_resid))
         @closure u -> begin
             𝐟(du, u)
             return du
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 2abd89336..6a549721d 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -82,10 +82,11 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
     else
         if has_analytic_jac
             f.jac_prototype === nothing ?
-            similar(fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u)) :
+            __similar(fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u)) :
             copy(f.jac_prototype)
         elseif f.jac_prototype === nothing
-            init_jacobian(jac_cache; preserve_immutable = Val(true))
+            __init_bigfloat_array!!(init_jacobian(
+                jac_cache; preserve_immutable = Val(true)))
         else
             f.jac_prototype
         end
diff --git a/src/internal/operators.jl b/src/internal/operators.jl
index 8c3c8922c..c7d8f586e 100644
--- a/src/internal/operators.jl
+++ b/src/internal/operators.jl
@@ -74,8 +74,8 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
             @closure (v, u, p) -> auto_vecjac(uf, u, v)
         elseif vjp_autodiff isa AutoFiniteDiff
             if iip
-                cache1 = similar(fu)
-                cache2 = similar(fu)
+                cache1 = __similar(fu)
+                cache2 = __similar(fu)
                 @closure (Jv, v, u, p) -> num_vecjac!(Jv, uf, u, v, cache1, cache2)
             else
                 @closure (v, u, p) -> num_vecjac(uf, __mutable(u), v)
@@ -106,17 +106,17 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
             if iip
                 # FIXME: Technically we should propagate the tag but ignoring that for now
                 cache1 = Dual{typeof(ForwardDiff.Tag(uf, eltype(u))), eltype(u),
-                    1}.(similar(u), ForwardDiff.Partials.(tuple.(u)))
+                    1}.(__similar(u), ForwardDiff.Partials.(tuple.(u)))
                 cache2 = Dual{typeof(ForwardDiff.Tag(uf, eltype(fu))), eltype(fu),
-                    1}.(similar(fu), ForwardDiff.Partials.(tuple.(fu)))
+                    1}.(__similar(fu), ForwardDiff.Partials.(tuple.(fu)))
                 @closure (Jv, v, u, p) -> auto_jacvec!(Jv, uf, u, v, cache1, cache2)
             else
                 @closure (v, u, p) -> auto_jacvec(uf, u, v)
             end
         elseif jvp_autodiff isa AutoFiniteDiff
             if iip
-                cache1 = similar(fu)
-                cache2 = similar(u)
+                cache1 = __similar(fu)
+                cache2 = __similar(u)
                 @closure (Jv, v, u, p) -> num_jacvec!(Jv, uf, u, v, cache1, cache2)
             else
                 @closure (v, u, p) -> num_jacvec(uf, u, v)
@@ -162,7 +162,7 @@ end
 function (op::JacobianOperator{vjp, iip})(v, u, p) where {vjp, iip}
     if vjp
         if iip
-            res = similar(op.output_cache)
+            res = __similar(op.output_cache)
             op.vjp_op(res, v, u, p)
             return res
         else
@@ -170,7 +170,7 @@ function (op::JacobianOperator{vjp, iip})(v, u, p) where {vjp, iip}
         end
     else
         if iip
-            res = similar(op.output_cache)
+            res = __similar(op.output_cache)
             op.jvp_op(res, v, u, p)
             return res
         else
diff --git a/src/utils.jl b/src/utils.jl
index d13555259..50faa710c 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -160,3 +160,16 @@ function __reinit_internal!(stats::NLStats)
     stats.njacs = 0
     stats.nsolve = 0
 end
+
+function __similar(x, args...; kwargs...)
+    y = similar(x, args...; kwargs...)
+    return __init_bigfloat_array!!(y)
+end
+
+function __init_bigfloat_array!!(x)
+    if ArrayInterface.can_setindex(x)
+        eltype(x) <: BigFloat && fill!(x, BigFloat(0))
+        return x
+    end
+    return x
+end

From 3f3700516f1c25bac05c566d08730504e061dc58 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 14:04:12 -0700
Subject: [PATCH 410/700] Add checks for improper qualified accesses

---
 test/misc/qa_tests.jl | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/test/misc/qa_tests.jl b/test/misc/qa_tests.jl
index a3b370b5b..7e8bf9ce6 100644
--- a/test/misc/qa_tests.jl
+++ b/test/misc/qa_tests.jl
@@ -26,4 +26,6 @@ end
         skip = (NonlinearSolve, Base, Core, SimpleNonlinearSolve, SciMLBase)) === nothing
 
     @test check_no_stale_explicit_imports(NonlinearSolve) === nothing
+
+    @test check_all_qualified_accesses_via_owners(NonlinearSolve) === nothing
 end

From bfc439bf84c229dddea7fb63698eec631728f5b7 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 14:26:47 -0700
Subject: [PATCH 411/700] Make explicit imports for extensions

---
 .../SimpleNonlinearSolveChainRulesCoreExt.jl  | 11 ++--
 ...leNonlinearSolvePolyesterForwardDiffExt.jl |  3 +-
 .../ext/SimpleNonlinearSolveReverseDiffExt.jl | 62 +++++++++++--------
 .../SimpleNonlinearSolveStaticArraysExt.jl    |  2 +-
 .../ext/SimpleNonlinearSolveTrackerExt.jl     | 18 ++++--
 .../ext/SimpleNonlinearSolveZygoteExt.jl      |  3 +-
 .../src/SimpleNonlinearSolve.jl               |  6 +-
 lib/SimpleNonlinearSolve/src/utils.jl         | 10 +--
 8 files changed, 66 insertions(+), 49 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
index dc84cb3e8..814af8f39 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
@@ -1,14 +1,17 @@
 module SimpleNonlinearSolveChainRulesCoreExt
 
-using ChainRulesCore, DiffEqBase, SciMLBase, SimpleNonlinearSolve
+using ChainRulesCore: ChainRulesCore, NoTangent
+using DiffEqBase: DiffEqBase
+using SciMLBase: ChainRulesOriginator, NonlinearProblem, NonlinearLeastSquaresProblem
+using SimpleNonlinearSolve: SimpleNonlinearSolve
 
 # The expectation here is that no-one is using this directly inside a GPU kernel. We can
 # eventually lift this requirement using a custom adjoint
 function ChainRulesCore.rrule(::typeof(SimpleNonlinearSolve.__internal_solve_up),
-        prob::NonlinearProblem, sensealg, u0, u0_changed, p, p_changed, alg, args...;
-        kwargs...)
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0,
+        u0_changed, p, p_changed, alg, args...; kwargs...)
     out, ∇internal = DiffEqBase._solve_adjoint(prob, sensealg, u0, p,
-        SciMLBase.ChainRulesOriginator(), alg, args...; kwargs...)
+        ChainRulesOriginator(), alg, args...; kwargs...)
     function ∇__internal_solve_up(Δ)
         ∂f, ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(Δ)
         return (∂f, ∂prob, ∂sensealg, ∂u0, NoTangent(), ∂p, NoTangent(), NoTangent(),
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
index 81cee481d..aa38d1c4e 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
@@ -1,6 +1,7 @@
 module SimpleNonlinearSolvePolyesterForwardDiffExt
 
-using SimpleNonlinearSolve, PolyesterForwardDiff
+using PolyesterForwardDiff: PolyesterForwardDiff
+using SimpleNonlinearSolve: SimpleNonlinearSolve
 
 @inline SimpleNonlinearSolve.__is_extension_loaded(::Val{:PolyesterForwardDiff}) = true
 
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
index e0bbda27e..f9bfe0965 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
@@ -1,60 +1,68 @@
 module SimpleNonlinearSolveReverseDiffExt
 
-using ArrayInterface, DiffEqBase, ReverseDiff, SciMLBase, SimpleNonlinearSolve
-import ReverseDiff: TrackedArray, TrackedReal
-import SimpleNonlinearSolve: __internal_solve_up
+using ArrayInterface: ArrayInterface
+using DiffEqBase: DiffEqBase
+using ReverseDiff: ReverseDiff, TrackedArray, TrackedReal
+using SciMLBase: ReverseDiffOriginator, NonlinearProblem, NonlinearLeastSquaresProblem
+using SimpleNonlinearSolve: SimpleNonlinearSolve
 
-function __internal_solve_up(
-        prob::NonlinearProblem, sensealg, u0::TrackedArray, u0_changed,
-        p::TrackedArray, p_changed, alg, args...; kwargs...)
-    return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
+function SimpleNonlinearSolve.__internal_solve_up(
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
+        u0::TrackedArray, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
+    return ReverseDiff.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0,
         u0_changed, p, p_changed, alg, args...; kwargs...)
 end
 
-function __internal_solve_up(
-        prob::NonlinearProblem, sensealg, u0, u0_changed,
+function SimpleNonlinearSolve.__internal_solve_up(
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0, u0_changed,
         p::TrackedArray, p_changed, alg, args...; kwargs...)
-    return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
+    return ReverseDiff.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0,
         u0_changed, p, p_changed, alg, args...; kwargs...)
 end
 
-function __internal_solve_up(
-        prob::NonlinearProblem, sensealg, u0::TrackedArray, u0_changed,
-        p, p_changed, alg, args...; kwargs...)
-    return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
+function SimpleNonlinearSolve.__internal_solve_up(
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
+        u0::TrackedArray, u0_changed, p, p_changed, alg, args...; kwargs...)
+    return ReverseDiff.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0,
         u0_changed, p, p_changed, alg, args...; kwargs...)
 end
 
-function __internal_solve_up(prob::NonlinearProblem, sensealg,
+function SimpleNonlinearSolve.__internal_solve_up(
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
         u0::AbstractArray{<:TrackedReal}, u0_changed, p::AbstractArray{<:TrackedReal},
         p_changed, alg, args...; kwargs...)
-    return __internal_solve_up(
+    return SimpleNonlinearSolve.__internal_solve_up(
         prob, sensealg, ArrayInterface.aos_to_soa(u0), true,
         ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
 end
 
-function __internal_solve_up(prob::NonlinearProblem, sensealg, u0, u0_changed,
+function SimpleNonlinearSolve.__internal_solve_up(
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0, u0_changed,
         p::AbstractArray{<:TrackedReal}, p_changed, alg, args...; kwargs...)
-    return __internal_solve_up(
-        prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
+    return SimpleNonlinearSolve.__internal_solve_up(
+        prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p), true, alg, args...;
+        kwargs...)
 end
 
-function __internal_solve_up(prob::NonlinearProblem, sensealg,
+function SimpleNonlinearSolve.__internal_solve_up(
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
         u0::AbstractArray{<:TrackedReal}, u0_changed, p, p_changed, alg, args...; kwargs...)
-    return __internal_solve_up(
-        prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
+    return SimpleNonlinearSolve.__internal_solve_up(
+        prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p), true, alg, args...;
+        kwargs...)
 end
 
-ReverseDiff.@grad function __internal_solve_up(
-        prob::NonlinearProblem, sensealg, u0, u0_changed, p, p_changed, alg, args...; kwargs...)
+ReverseDiff.@grad function SimpleNonlinearSolve.__internal_solve_up(
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0,
+        u0_changed, p, p_changed, alg, args...; kwargs...)
     out, ∇internal = DiffEqBase._solve_adjoint(
         prob, sensealg, ReverseDiff.value(u0), ReverseDiff.value(p),
-        SciMLBase.ReverseDiffOriginator(), alg, args...; kwargs...)
-    function ∇__internal_solve_up(_args...)
+        ReverseDiffOriginator(), alg, args...; kwargs...)
+    function ∇SimpleNonlinearSolve.__internal_solve_up(_args...)
         ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(_args...)
         return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
     end
-    return Array(out), ∇__internal_solve_up
+    return Array(out), ∇SimpleNonlinearSolve.__internal_solve_up
 end
 
 end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveStaticArraysExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveStaticArraysExt.jl
index 90318a82a..c865084ce 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveStaticArraysExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveStaticArraysExt.jl
@@ -1,6 +1,6 @@
 module SimpleNonlinearSolveStaticArraysExt
 
-using SimpleNonlinearSolve
+using SimpleNonlinearSolve: SimpleNonlinearSolve
 
 @inline SimpleNonlinearSolve.__is_extension_loaded(::Val{:StaticArrays}) = true
 
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
index 61ce14645..7b35de09b 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
@@ -1,8 +1,12 @@
 module SimpleNonlinearSolveTrackerExt
 
-using DiffEqBase, SciMLBase, SimpleNonlinearSolve, Tracker
+using DiffEqBase: DiffEqBase
+using SciMLBase: TrackerOriginator, NonlinearProblem, NonlinearLeastSquaresProblem
+using SimpleNonlinearSolve: SimpleNonlinearSolve
+using Tracker: Tracker, TrackedArray
 
-function SimpleNonlinearSolve.__internal_solve_up(prob::NonlinearProblem,
+function SimpleNonlinearSolve.__internal_solve_up(
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
         sensealg, u0::TrackedArray, u0_changed, p, p_changed, alg, args...; kwargs...)
     return Tracker.track(
         SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0, u0_changed,
@@ -10,21 +14,23 @@ function SimpleNonlinearSolve.__internal_solve_up(prob::NonlinearProblem,
 end
 
 function SimpleNonlinearSolve.__internal_solve_up(
-        prob::NonlinearProblem, sensealg, u0::TrackedArray, u0_changed,
-        p::TrackedArray, p_changed, alg, args...; kwargs...)
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
+        u0::TrackedArray, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
     return Tracker.track(
         SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0, u0_changed,
         p, p_changed, alg, args...; kwargs...)
 end
 
-function SimpleNonlinearSolve.__internal_solve_up(prob::NonlinearProblem,
+function SimpleNonlinearSolve.__internal_solve_up(
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
         sensealg, u0, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
     return Tracker.track(
         SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0, u0_changed,
         p, p_changed, alg, args...; kwargs...)
 end
 
-Tracker.@grad function SimpleNonlinearSolve.__internal_solve_up(_prob::NonlinearProblem,
+Tracker.@grad function SimpleNonlinearSolve.__internal_solve_up(
+        _prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
         sensealg, u0_, u0_changed, p_, p_changed, alg, args...; kwargs...)
     u0, p = Tracker.data(u0_), Tracker.data(p_)
     prob = remake(_prob; u0, p)
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl
index b29a1529a..559930b08 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveZygoteExt.jl
@@ -1,6 +1,7 @@
 module SimpleNonlinearSolveZygoteExt
 
-import SimpleNonlinearSolve, Zygote
+using SimpleNonlinearSolve: SimpleNonlinearSolve
+using Zygote: Zygote
 
 SimpleNonlinearSolve.__is_extension_loaded(::Val{:Zygote}) = true
 
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 3a4e5ebdb..e38aaa54b 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -8,14 +8,12 @@ import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidat
 
     import DiffEqBase: AbstractNonlinearTerminationMode,
                        AbstractSafeNonlinearTerminationMode,
-                       AbstractSafeBestNonlinearTerminationMode,
-                       NonlinearSafeTerminationReturnCode, get_termination_mode,
-                       NONLINEARSOLVE_DEFAULT_NORM
+                       AbstractSafeBestNonlinearTerminationMode, NONLINEARSOLVE_DEFAULT_NORM
     import DiffResults
     import ForwardDiff: Dual
     import MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
     import SciMLBase: AbstractNonlinearAlgorithm, build_solution, isinplace, _unwrap_val
-    import StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, MMatrix, Size
+    import StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, Size
 end
 
 @reexport using ADTypes, SciMLBase
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 76e91fcb4..43689a29d 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -77,7 +77,7 @@ except `cache` (& `J` if not nothing) are mutated.
 function value_and_jacobian(ad, f::F, y, x::X, p, cache; J = nothing) where {F, X}
     if isinplace(f)
         _f = (du, u) -> f(du, u, p)
-        if DiffEqBase.has_jac(f)
+        if SciMLBase.has_jac(f)
             f.jac(J, x, p)
             _f(y, x)
             return y, J
@@ -97,7 +97,7 @@ function value_and_jacobian(ad, f::F, y, x::X, p, cache; J = nothing) where {F,
         end
     else
         _f = Base.Fix2(f, p)
-        if DiffEqBase.has_jac(f)
+        if SciMLBase.has_jac(f)
             return _f(x), f.jac(x, p)
         elseif ad isa AutoForwardDiff
             if ArrayInterface.can_setindex(x)
@@ -124,7 +124,7 @@ end
 function __polyester_forwarddiff_jacobian! end
 
 function value_and_jacobian(ad, f::F, y, x::Number, p, cache; J = nothing) where {F}
-    if DiffEqBase.has_jac(f)
+    if SciMLBase.has_jac(f)
         return f(x, p), f.jac(x, p)
     elseif ad isa AutoForwardDiff
         T = typeof(__standard_tag(ad.tag, x))
@@ -152,7 +152,7 @@ function jacobian_cache(ad, f::F, y, x::X, p) where {F, X <: AbstractArray}
     if isinplace(f)
         _f = (du, u) -> f(du, u, p)
         J = similar(y, length(y), length(x))
-        if DiffEqBase.has_jac(f)
+        if SciMLBase.has_jac(f)
             return J, nothing
         elseif ad isa AutoForwardDiff || ad isa AutoPolyesterForwardDiff
             return J, __get_jacobian_config(ad, _f, y, x)
@@ -163,7 +163,7 @@ function jacobian_cache(ad, f::F, y, x::X, p) where {F, X <: AbstractArray}
         end
     else
         _f = Base.Fix2(f, p)
-        if DiffEqBase.has_jac(f)
+        if SciMLBase.has_jac(f)
             return nothing, nothing
         elseif ad isa AutoForwardDiff
             J = ArrayInterface.can_setindex(x) ? similar(y, length(y), length(x)) : nothing

From c5d1a7d7a190de274eebf4c42e2fdbe2cabebdad Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 14:27:43 -0700
Subject: [PATCH 412/700] Run formatter

---
 lib/SimpleNonlinearSolve/.JuliaFormatter.toml |  3 +-
 .../SimpleNonlinearSolveChainRulesCoreExt.jl  | 12 +--
 ...leNonlinearSolvePolyesterForwardDiffExt.jl |  8 +-
 .../ext/SimpleNonlinearSolveReverseDiffExt.jl | 43 +++++------
 .../ext/SimpleNonlinearSolveTrackerExt.jl     | 27 +++----
 .../src/SimpleNonlinearSolve.jl               | 20 +++--
 lib/SimpleNonlinearSolve/src/ad.jl            | 34 +++++----
 .../src/bracketing/alefeld.jl                 | 49 +++++-------
 .../src/bracketing/bisection.jl               | 31 ++++----
 .../src/bracketing/brent.jl                   | 26 +++----
 .../src/bracketing/falsi.jl                   | 23 +++---
 .../src/bracketing/itp.jl                     | 23 +++---
 .../src/bracketing/ridder.jl                  | 27 ++++---
 lib/SimpleNonlinearSolve/src/linesearch.jl    | 14 ++--
 .../src/nlsolve/broyden.jl                    | 12 +--
 .../src/nlsolve/dfsane.jl                     |  8 +-
 .../src/nlsolve/halley.jl                     | 12 +--
 .../src/nlsolve/klement.jl                    |  8 +-
 .../src/nlsolve/lbroyden.jl                   | 74 +++++++++----------
 .../src/nlsolve/raphson.jl                    |  4 +-
 .../src/nlsolve/trustRegion.jl                | 12 +--
 lib/SimpleNonlinearSolve/src/utils.jl         | 38 +++++-----
 .../test/core/23_test_problems_tests.jl       | 11 ++-
 .../test/core/forward_ad_tests.jl             | 21 +++---
 .../test/core/least_squares_tests.jl          |  3 +-
 .../test/core/matrix_resizing_tests.jl        |  8 +-
 .../test/core/rootfind_tests.jl               | 60 +++++++--------
 .../test/gpu/cuda_tests.jl                    | 14 ++--
 28 files changed, 310 insertions(+), 315 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.JuliaFormatter.toml b/lib/SimpleNonlinearSolve/.JuliaFormatter.toml
index 4d06911d7..66c13bae3 100644
--- a/lib/SimpleNonlinearSolve/.JuliaFormatter.toml
+++ b/lib/SimpleNonlinearSolve/.JuliaFormatter.toml
@@ -1,4 +1,5 @@
 style = "sciml"
 format_markdown = true
 annotate_untyped_fields_with_any = false
-format_docstrings = true
\ No newline at end of file
+format_docstrings = true
+join_lines_based_on_source = false
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
index 814af8f39..2987f1c5b 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
@@ -8,14 +8,14 @@ using SimpleNonlinearSolve: SimpleNonlinearSolve
 # The expectation here is that no-one is using this directly inside a GPU kernel. We can
 # eventually lift this requirement using a custom adjoint
 function ChainRulesCore.rrule(::typeof(SimpleNonlinearSolve.__internal_solve_up),
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0,
-        u0_changed, p, p_changed, alg, args...; kwargs...)
-    out, ∇internal = DiffEqBase._solve_adjoint(prob, sensealg, u0, p,
-        ChainRulesOriginator(), alg, args...; kwargs...)
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+        sensealg, u0, u0_changed, p, p_changed, alg, args...; kwargs...)
+    out, ∇internal = DiffEqBase._solve_adjoint(
+        prob, sensealg, u0, p, ChainRulesOriginator(), alg, args...; kwargs...)
     function ∇__internal_solve_up(Δ)
         ∂f, ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(Δ)
-        return (∂f, ∂prob, ∂sensealg, ∂u0, NoTangent(), ∂p, NoTangent(), NoTangent(),
-            ∂args...)
+        return (
+            ∂f, ∂prob, ∂sensealg, ∂u0, NoTangent(), ∂p, NoTangent(), NoTangent(), ∂args...)
     end
     return out, ∇__internal_solve_up
 end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
index aa38d1c4e..ac898ac16 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
@@ -5,14 +5,14 @@ using SimpleNonlinearSolve: SimpleNonlinearSolve
 
 @inline SimpleNonlinearSolve.__is_extension_loaded(::Val{:PolyesterForwardDiff}) = true
 
-@inline function SimpleNonlinearSolve.__polyester_forwarddiff_jacobian!(f!::F, y, J, x,
-        chunksize) where {F}
+@inline function SimpleNonlinearSolve.__polyester_forwarddiff_jacobian!(
+        f!::F, y, J, x, chunksize) where {F}
     PolyesterForwardDiff.threaded_jacobian!(f!, y, J, x, chunksize)
     return J
 end
 
-@inline function SimpleNonlinearSolve.__polyester_forwarddiff_jacobian!(f::F, J, x,
-        chunksize) where {F}
+@inline function SimpleNonlinearSolve.__polyester_forwarddiff_jacobian!(
+        f::F, J, x, chunksize) where {F}
     PolyesterForwardDiff.threaded_jacobian!(f, J, x, chunksize)
     return J
 end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
index f9bfe0965..a6a1c2dbf 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
@@ -9,52 +9,53 @@ using SimpleNonlinearSolve: SimpleNonlinearSolve
 function SimpleNonlinearSolve.__internal_solve_up(
         prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
         u0::TrackedArray, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
-    return ReverseDiff.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0,
-        u0_changed, p, p_changed, alg, args...; kwargs...)
+    return ReverseDiff.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
+        u0, u0_changed, p, p_changed, alg, args...; kwargs...)
 end
 
 function SimpleNonlinearSolve.__internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0, u0_changed,
-        p::TrackedArray, p_changed, alg, args...; kwargs...)
-    return ReverseDiff.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0,
-        u0_changed, p, p_changed, alg, args...; kwargs...)
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
+        u0, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
+    return ReverseDiff.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
+        u0, u0_changed, p, p_changed, alg, args...; kwargs...)
 end
 
 function SimpleNonlinearSolve.__internal_solve_up(
         prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
         u0::TrackedArray, u0_changed, p, p_changed, alg, args...; kwargs...)
-    return ReverseDiff.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0,
-        u0_changed, p, p_changed, alg, args...; kwargs...)
+    return ReverseDiff.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
+        u0, u0_changed, p, p_changed, alg, args...; kwargs...)
 end
 
 function SimpleNonlinearSolve.__internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
-        u0::AbstractArray{<:TrackedReal}, u0_changed, p::AbstractArray{<:TrackedReal},
-        p_changed, alg, args...; kwargs...)
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+        sensealg, u0::AbstractArray{<:TrackedReal}, u0_changed,
+        p::AbstractArray{<:TrackedReal}, p_changed, alg, args...; kwargs...)
     return SimpleNonlinearSolve.__internal_solve_up(
         prob, sensealg, ArrayInterface.aos_to_soa(u0), true,
         ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
 end
 
 function SimpleNonlinearSolve.__internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0, u0_changed,
-        p::AbstractArray{<:TrackedReal}, p_changed, alg, args...; kwargs...)
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0,
+        u0_changed, p::AbstractArray{<:TrackedReal}, p_changed, alg, args...; kwargs...)
     return SimpleNonlinearSolve.__internal_solve_up(
-        prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p), true, alg, args...;
-        kwargs...)
+        prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p),
+        true, alg, args...; kwargs...)
 end
 
 function SimpleNonlinearSolve.__internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
-        u0::AbstractArray{<:TrackedReal}, u0_changed, p, p_changed, alg, args...; kwargs...)
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+        sensealg, u0::AbstractArray{<:TrackedReal},
+        u0_changed, p, p_changed, alg, args...; kwargs...)
     return SimpleNonlinearSolve.__internal_solve_up(
-        prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p), true, alg, args...;
-        kwargs...)
+        prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p),
+        true, alg, args...; kwargs...)
 end
 
 ReverseDiff.@grad function SimpleNonlinearSolve.__internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0,
-        u0_changed, p, p_changed, alg, args...; kwargs...)
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+        sensealg, u0, u0_changed, p, p_changed, alg, args...; kwargs...)
     out, ∇internal = DiffEqBase._solve_adjoint(
         prob, sensealg, ReverseDiff.value(u0), ReverseDiff.value(p),
         ReverseDiffOriginator(), alg, args...; kwargs...)
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
index 7b35de09b..b49bd78cc 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
@@ -6,27 +6,24 @@ using SimpleNonlinearSolve: SimpleNonlinearSolve
 using Tracker: Tracker, TrackedArray
 
 function SimpleNonlinearSolve.__internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
-        sensealg, u0::TrackedArray, u0_changed, p, p_changed, alg, args...; kwargs...)
-    return Tracker.track(
-        SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0, u0_changed,
-        p, p_changed, alg, args...; kwargs...)
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
+        u0::TrackedArray, u0_changed, p, p_changed, alg, args...; kwargs...)
+    return Tracker.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
+        u0, u0_changed, p, p_changed, alg, args...; kwargs...)
 end
 
 function SimpleNonlinearSolve.__internal_solve_up(
         prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
         u0::TrackedArray, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
-    return Tracker.track(
-        SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0, u0_changed,
-        p, p_changed, alg, args...; kwargs...)
+    return Tracker.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
+        u0, u0_changed, p, p_changed, alg, args...; kwargs...)
 end
 
 function SimpleNonlinearSolve.__internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
-        sensealg, u0, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
-    return Tracker.track(
-        SimpleNonlinearSolve.__internal_solve_up, prob, sensealg, u0, u0_changed,
-        p, p_changed, alg, args...; kwargs...)
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
+        u0, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
+    return Tracker.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
+        u0, u0_changed, p, p_changed, alg, args...; kwargs...)
 end
 
 Tracker.@grad function SimpleNonlinearSolve.__internal_solve_up(
@@ -34,8 +31,8 @@ Tracker.@grad function SimpleNonlinearSolve.__internal_solve_up(
         sensealg, u0_, u0_changed, p_, p_changed, alg, args...; kwargs...)
     u0, p = Tracker.data(u0_), Tracker.data(p_)
     prob = remake(_prob; u0, p)
-    out, ∇internal = DiffEqBase._solve_adjoint(prob, sensealg, u0, p,
-        SciMLBase.TrackerOriginator(), alg, args...; kwargs...)
+    out, ∇internal = DiffEqBase._solve_adjoint(
+        prob, sensealg, u0, p, SciMLBase.TrackerOriginator(), alg, args...; kwargs...)
 
     function ∇__internal_solve_up(Δ)
         ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(Δ)
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index e38aaa54b..dfd650c4d 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -56,17 +56,15 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Nothing, args...;
 end
 
 # By Pass the highlevel checks for NonlinearProblem for Simple Algorithms
-function SciMLBase.solve(
-        prob::NonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
+function SciMLBase.solve(prob::NonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
         args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...)
     if sensealg === nothing && haskey(prob.kwargs, :sensealg)
         sensealg = prob.kwargs[:sensealg]
     end
     new_u0 = u0 !== nothing ? u0 : prob.u0
     new_p = p !== nothing ? p : prob.p
-    return __internal_solve_up(
-        prob, sensealg, new_u0, u0 === nothing, new_p, p === nothing,
-        alg, args...; prob.kwargs..., kwargs...)
+    return __internal_solve_up(prob, sensealg, new_u0, u0 === nothing, new_p,
+        p === nothing, alg, args...; prob.kwargs..., kwargs...)
 end
 
 function __internal_solve_up(_prob::NonlinearProblem, sensealg, u0, u0_changed,
@@ -78,10 +76,10 @@ end
 @setup_workload begin
     for T in (Float32, Float64)
         prob_no_brack_scalar = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
-        prob_no_brack_iip = NonlinearProblem{true}((du, u, p) -> du .= u .* u .- p,
-            T.([1.0, 1.0, 1.0]), T(2))
-        prob_no_brack_oop = NonlinearProblem{false}((u, p) -> u .* u .- p,
-            T.([1.0, 1.0, 1.0]), T(2))
+        prob_no_brack_iip = NonlinearProblem{true}(
+            (du, u, p) -> du .= u .* u .- p, T.([1.0, 1.0, 1.0]), T(2))
+        prob_no_brack_oop = NonlinearProblem{false}(
+            (u, p) -> u .* u .- p, T.([1.0, 1.0, 1.0]), T(2))
 
         algs = [SimpleNewtonRaphson(), SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
             SimpleTrustRegion(), SimpleLimitedMemoryBroyden(; threshold = 2)]
@@ -101,8 +99,8 @@ end
             end
         end
 
-        prob_brack = IntervalNonlinearProblem{false}((u, p) -> u * u - p,
-            T.((0.0, 2.0)), T(2))
+        prob_brack = IntervalNonlinearProblem{false}(
+            (u, p) -> u * u - p, T.((0.0, 2.0)), T(2))
         algs = [Bisection(), Falsi(), Ridder(), Brent(), Alefeld(), ITP()]
         @compile_workload begin
             for alg in algs
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index d4e091c43..f42651bfe 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -1,7 +1,9 @@
 function SciMLBase.solve(
-        prob::NonlinearProblem{<:Union{Number, <:AbstractArray},
-            iip, <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
-        alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...) where {T, V, P, iip}
+        prob::NonlinearProblem{<:Union{Number, <:AbstractArray}, iip,
+            <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
+        alg::AbstractSimpleNonlinearSolveAlgorithm,
+        args...;
+        kwargs...) where {T, V, P, iip}
     sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
     dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
     return SciMLBase.build_solution(
@@ -9,9 +11,11 @@ function SciMLBase.solve(
 end
 
 function SciMLBase.solve(
-        prob::NonlinearLeastSquaresProblem{<:AbstractArray,
-            iip, <:Union{<:AbstractArray{<:Dual{T, V, P}}}},
-        alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...) where {T, V, P, iip}
+        prob::NonlinearLeastSquaresProblem{
+            <:AbstractArray, iip, <:Union{<:AbstractArray{<:Dual{T, V, P}}}},
+        alg::AbstractSimpleNonlinearSolveAlgorithm,
+        args...;
+        kwargs...) where {T, V, P, iip}
     sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
     dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
     return SciMLBase.build_solution(
@@ -21,13 +25,16 @@ end
 for algType in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
     @eval begin
         function SciMLBase.solve(
-                prob::IntervalNonlinearProblem{uType, iip,
-                    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
-                alg::$(algType), args...; kwargs...) where {uType, T, V, P, iip}
+                prob::IntervalNonlinearProblem{
+                    uType, iip, <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
+                alg::$(algType),
+                args...;
+                kwargs...) where {uType, T, V, P, iip}
             sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
             dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
-            return SciMLBase.build_solution(prob, alg, dual_soln, sol.resid; sol.retcode,
-                sol.stats, sol.original, left = Dual{T, V, P}(sol.left, partials),
+            return SciMLBase.build_solution(
+                prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats,
+                sol.original, left = Dual{T, V, P}(sol.left, partials),
                 right = Dual{T, V, P}(sol.right, partials))
         end
     end
@@ -125,9 +132,8 @@ function __nlsolve_ad(prob::NonlinearLeastSquaresProblem, alg, args...; kwargs..
             else
                 _F = @closure (u, p) -> begin
                     T = promote_type(eltype(u), eltype(p))
-                    res = DiffResults.DiffResult(
-                        similar(u, T, size(sol.resid)), similar(
-                            u, T, length(sol.resid), length(u)))
+                    res = DiffResults.DiffResult(similar(u, T, size(sol.resid)),
+                        similar(u, T, length(sol.resid), length(u)))
                     ForwardDiff.jacobian!(res, Base.Fix2(prob.f, p), u)
                     return reshape(
                         2 .* vec(DiffResults.value(res))' * DiffResults.jacobian(res),
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/alefeld.jl b/lib/SimpleNonlinearSolve/src/bracketing/alefeld.jl
index 3b89751a7..55020c8a6 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/alefeld.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/alefeld.jl
@@ -15,12 +15,10 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...;
     c = a - (b - a) / (f(b) - f(a)) * f(a)
 
     fc = f(c)
-    (a == c || b == c) &&
-        return build_solution(prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
-            left = a, right = b)
-    iszero(fc) &&
-        return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success, left = a,
-            right = b)
+    (a == c || b == c) && return build_solution(
+        prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit, left = a, right = b)
+    iszero(fc) && return build_solution(
+        prob, alg, c, fc; retcode = ReturnCode.Success, left = a, right = b)
     a, b, d = _bracket(f, a, b, c)
     e = zero(a)   # Set e as 0 before iteration to avoid a non-value f(e)
 
@@ -38,12 +36,10 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...;
         end
         ē, fc = d, f(c)
         (a == c || b == c) &&
-            return build_solution(
-                prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
-                left = a, right = b)
-        iszero(fc) &&
-            return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success,
+            return build_solution(prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
                 left = a, right = b)
+        iszero(fc) && return build_solution(
+            prob, alg, c, fc; retcode = ReturnCode.Success, left = a, right = b)
         ā, b̄, d̄ = _bracket(f, a, b, c)
 
         # The second bracketing block
@@ -58,12 +54,10 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...;
         end
         fc = f(c)
         (ā == c || b̄ == c) &&
-            return build_solution(
-                prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
-                left = ā, right = b̄)
-        iszero(fc) &&
-            return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success,
+            return build_solution(prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
                 left = ā, right = b̄)
+        iszero(fc) && return build_solution(
+            prob, alg, c, fc; retcode = ReturnCode.Success, left = ā, right = b̄)
         ā, b̄, d̄ = _bracket(f, ā, b̄, c)
 
         # The third bracketing block
@@ -78,12 +72,10 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...;
         end
         fc = f(c)
         (ā == c || b̄ == c) &&
-            return build_solution(
-                prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
-                left = ā, right = b̄)
-        iszero(fc) &&
-            return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success,
+            return build_solution(prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
                 left = ā, right = b̄)
+        iszero(fc) && return build_solution(
+            prob, alg, c, fc; retcode = ReturnCode.Success, left = ā, right = b̄)
         ā, b̄, d = _bracket(f, ā, b̄, c)
 
         # The last bracketing block
@@ -93,12 +85,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...;
             e = d
             c = 0.5 * (ā + b̄)
             fc = f(c)
-            (ā == c || b̄ == c) &&
-                return build_solution(prob, alg, c, fc;
-                    retcode = ReturnCode.FloatingPointLimit, left = ā, right = b̄)
-            iszero(fc) &&
-                return build_solution(prob, alg, c, fc; retcode = ReturnCode.Success,
-                    left = ā, right = b̄)
+            (ā == c || b̄ == c) && return build_solution(
+                prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
+                left = ā, right = b̄)
+            iszero(fc) && return build_solution(
+                prob, alg, c, fc; retcode = ReturnCode.Success, left = ā, right = b̄)
             a, b, d = _bracket(f, ā, b̄, c)
         end
     end
@@ -112,8 +103,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...;
     fc = f(c)
 
     # Reuturn solution when run out of max interation
-    return build_solution(prob, alg, c, fc; retcode = ReturnCode.MaxIters,
-        left = a, right = b)
+    return build_solution(
+        prob, alg, c, fc; retcode = ReturnCode.MaxIters, left = a, right = b)
 end
 
 # Define subrotine function bracket, check fc before bracket to return solution
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
index acadf6aa1..d55a0ce5e 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
@@ -19,25 +19,24 @@ A common bisection method.
     exact_right::Bool = false
 end
 
-function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...;
-        maxiters = 1000, abstol = nothing, kwargs...)
+function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection,
+        args...; maxiters = 1000, abstol = nothing, kwargs...)
     @assert !isinplace(prob) "`Bisection` only supports OOP problems."
     f = Base.Fix2(prob.f, prob.p)
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
-    abstol = __get_tolerance(nothing, abstol,
-        promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
+    abstol = __get_tolerance(
+        nothing, abstol, promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
 
     if iszero(fl)
-        return build_solution(prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft,
-            left, right)
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
     end
 
     if iszero(fr)
         return build_solution(
-            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
-            left, right)
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
     i = 1
@@ -49,8 +48,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
                     retcode = ReturnCode.FloatingPointLimit)
             fm = f(mid)
             if abs((right - left) / 2) < abstol
-                return build_solution(prob, alg, mid, fm; retcode = ReturnCode.Success,
-                    left, right)
+                return build_solution(
+                    prob, alg, mid, fm; retcode = ReturnCode.Success, left, right)
             end
             if iszero(fm)
                 right = mid
@@ -67,8 +66,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection, args...
         end
     end
 
-    sol, i, left, right, fl, fr = __bisection(left, right, fl, fr, f; abstol,
-        maxiters = maxiters - i, prob, alg)
+    sol, i, left, right, fl, fr = __bisection(
+        left, right, fl, fr, f; abstol, maxiters = maxiters - i, prob, alg)
 
     sol !== nothing && return sol
 
@@ -81,15 +80,15 @@ function __bisection(left, right, fl, fr, f::F; abstol, maxiters, prob, alg) whe
     while i < maxiters
         mid = (left + right) / 2
         if (mid == left || mid == right)
-            sol = build_solution(prob, alg, left, fl; left, right,
-                retcode = ReturnCode.FloatingPointLimit)
+            sol = build_solution(
+                prob, alg, left, fl; left, right, retcode = ReturnCode.FloatingPointLimit)
             break
         end
 
         fm = f(mid)
         if abs((right - left) / 2) < abstol
-            sol = build_solution(prob, alg, mid, fm; left, right,
-                retcode = ReturnCode.Success)
+            sol = build_solution(
+                prob, alg, mid, fm; left, right, retcode = ReturnCode.Success)
             break
         end
 
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/brent.jl b/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
index 89b2e60be..649286e03 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
@@ -13,18 +13,17 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
     fl, fr = f(left), f(right)
     ϵ = eps(convert(typeof(fl), 1))
 
-    abstol = __get_tolerance(nothing, abstol,
-        promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
+    abstol = __get_tolerance(
+        nothing, abstol, promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
 
     if iszero(fl)
-        return build_solution(prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft,
-            left, right)
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
     end
 
     if iszero(fr)
         return build_solution(
-            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
-            left, right)
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
     if abs(fl) < abs(fr)
@@ -60,18 +59,17 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
                (!cond && abs(c - d) ≤ ϵ)
                 # Bisection method
                 s = (left + right) / 2
-                (s == left || s == right) &&
-                    return SciMLBase.build_solution(prob, alg, left, fl;
-                        retcode = ReturnCode.FloatingPointLimit,
-                        left = left, right = right)
+                (s == left || s == right) && return SciMLBase.build_solution(
+                    prob, alg, left, fl; retcode = ReturnCode.FloatingPointLimit,
+                    left = left, right = right)
                 cond = true
             else
                 cond = false
             end
             fs = f(s)
             if abs((right - left) / 2) < abstol
-                return SciMLBase.build_solution(prob, alg, s, fs;
-                    retcode = ReturnCode.Success,
+                return SciMLBase.build_solution(
+                    prob, alg, s, fs; retcode = ReturnCode.Success,
                     left = left, right = right)
             end
             if iszero(fs)
@@ -105,8 +103,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
         end
     end
 
-    sol, i, left, right, fl, fr = __bisection(left, right, fl, fr, f; abstol,
-        maxiters = maxiters - i, prob, alg)
+    sol, i, left, right, fl, fr = __bisection(
+        left, right, fl, fr, f; abstol, maxiters = maxiters - i, prob, alg)
 
     sol !== nothing && return sol
 
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl b/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
index 896e07329..ee78b73fc 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
@@ -12,18 +12,17 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
-    abstol = __get_tolerance(nothing, abstol,
-        promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
+    abstol = __get_tolerance(
+        nothing, abstol, promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
 
     if iszero(fl)
-        return build_solution(prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft,
-            left, right)
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
     end
 
     if iszero(fr)
         return build_solution(
-            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
-            left, right)
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
     # Regula Falsi Steps
@@ -44,8 +43,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
 
             fm = f(mid)
             if abs((right - left) / 2) < abstol
-                return build_solution(prob, alg, mid, fm; left, right,
-                    retcode = ReturnCode.Success)
+                return build_solution(
+                    prob, alg, mid, fm; left, right, retcode = ReturnCode.Success)
             end
 
             if abs(fm) < abstol
@@ -62,10 +61,10 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
         end
     end
 
-    sol, i, left, right, fl, fr = __bisection(left, right, fl, fr, f; abstol,
-        maxiters = maxiters - i, prob, alg)
+    sol, i, left, right, fl, fr = __bisection(
+        left, right, fl, fr, f; abstol, maxiters = maxiters - i, prob, alg)
     sol !== nothing && return sol
 
-    return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
-        left, right)
+    return SciMLBase.build_solution(
+        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
 end
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
index 2926dfd7a..2972d1c5c 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
@@ -58,18 +58,17 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
-    abstol = __get_tolerance(nothing, abstol,
-        promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
+    abstol = __get_tolerance(
+        nothing, abstol, promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
 
     if iszero(fl)
-        return build_solution(prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft,
-            left, right)
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
     end
 
     if iszero(fr)
         return build_solution(
-            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
-            left, right)
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
     ϵ = abstol
     #defining variables/cache
@@ -110,8 +109,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
         end
 
         if abs((left - right) / 2) < ϵ
-            return build_solution(prob, alg, mid, f(mid); retcode = ReturnCode.Success,
-                left, right)
+            return build_solution(
+                prob, alg, mid, f(mid); retcode = ReturnCode.Success, left, right)
         end
 
         ## Update ##
@@ -127,16 +126,16 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
             left = xp
             fl = yp
         else
-            return build_solution(prob, alg, xp, yps; retcode = ReturnCode.Success,
-                left = xp, right = xp)
+            return build_solution(
+                prob, alg, xp, yps; retcode = ReturnCode.Success, left = xp, right = xp)
         end
         i += 1
         mid = (left + right) / 2
         ϵ_s /= 2
 
         if __nextfloat_tdir(left, prob.tspan...) == right
-            return build_solution(prob, alg, left, fl; left, right,
-                retcode = ReturnCode.FloatingPointLimit)
+            return build_solution(
+                prob, alg, left, fl; left, right, retcode = ReturnCode.FloatingPointLimit)
         end
     end
 
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
index 3b23f4287..a974824c2 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
@@ -12,18 +12,17 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
     left, right = prob.tspan
     fl, fr = f(left), f(right)
 
-    abstol = __get_tolerance(nothing, abstol,
-        promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
+    abstol = __get_tolerance(
+        nothing, abstol, promote_type(eltype(first(prob.tspan)), eltype(last(prob.tspan))))
 
     if iszero(fl)
-        return build_solution(prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft,
-            left, right)
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
     end
 
     if iszero(fr)
         return build_solution(
-            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight,
-            left, right)
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
     xo = oftype(left, Inf)
@@ -37,15 +36,15 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
             fm = f(mid)
             s = sqrt(fm^2 - fl * fr)
             if iszero(s)
-                return build_solution(prob, alg, left, fl; left, right,
-                    retcode = ReturnCode.Failure)
+                return build_solution(
+                    prob, alg, left, fl; left, right, retcode = ReturnCode.Failure)
             end
             x = mid + (mid - left) * sign(fl - fr) * fm / s
             fx = f(x)
             xo = x
             if abs((right - left) / 2) < abstol
-                return build_solution(prob, alg, mid, fm; retcode = ReturnCode.Success,
-                    left, right)
+                return build_solution(
+                    prob, alg, mid, fm; retcode = ReturnCode.Success, left, right)
             end
             if iszero(fx)
                 right = x
@@ -69,10 +68,10 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
         end
     end
 
-    sol, i, left, right, fl, fr = __bisection(left, right, fl, fr, f; abstol,
-        maxiters = maxiters - i, prob, alg)
+    sol, i, left, right, fl, fr = __bisection(
+        left, right, fl, fr, f; abstol, maxiters = maxiters - i, prob, alg)
     sol !== nothing && return sol
 
-    return SciMLBase.build_solution(prob, alg, left, fl; retcode = ReturnCode.MaxIters,
-        left, right)
+    return SciMLBase.build_solution(
+        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
 end
diff --git a/lib/SimpleNonlinearSolve/src/linesearch.jl b/lib/SimpleNonlinearSolve/src/linesearch.jl
index c33253f63..b8e830af2 100644
--- a/lib/SimpleNonlinearSolve/src/linesearch.jl
+++ b/lib/SimpleNonlinearSolve/src/linesearch.jl
@@ -37,8 +37,8 @@ end
 end
 
 (alg::LiFukushimaLineSearch)(prob, fu, u) = __generic_init(alg, prob, fu, u)
-function (alg::LiFukushimaLineSearch)(prob, fu::Union{Number, SArray},
-        u::Union{Number, SArray})
+function (alg::LiFukushimaLineSearch)(
+        prob, fu::Union{Number, SArray}, u::Union{Number, SArray})
     (alg.nan_maxiters === missing || alg.nan_maxiters === nothing) &&
         return __static_init(alg, prob, fu, u)
     @warn "`LiFukushimaLineSearch` with NaN checking is not non-allocating" maxlog=1
@@ -57,14 +57,16 @@ function __generic_init(alg::LiFukushimaLineSearch, prob, fu, u)
 
     nan_maxiters = ifelse(alg.nan_maxiters === missing, 5, alg.nan_maxiters)
 
-    return LiFukushimaLineSearchCache(ϕ, T(alg.lambda_0), T(alg.beta), T(alg.sigma_1),
-        T(alg.sigma_2), T(alg.eta), T(alg.rho), T(true), nan_maxiters, alg.maxiters)
+    return LiFukushimaLineSearchCache(
+        ϕ, T(alg.lambda_0), T(alg.beta), T(alg.sigma_1), T(alg.sigma_2),
+        T(alg.eta), T(alg.rho), T(true), nan_maxiters, alg.maxiters)
 end
 
 function __static_init(alg::LiFukushimaLineSearch, prob, fu, u)
     T = promote_type(eltype(fu), eltype(u))
-    return StaticLiFukushimaLineSearchCache(prob.f, prob.p, T(alg.lambda_0), T(alg.beta),
-        T(alg.sigma_1), T(alg.sigma_2), T(alg.eta), T(alg.rho), alg.maxiters)
+    return StaticLiFukushimaLineSearchCache(
+        prob.f, prob.p, T(alg.lambda_0), T(alg.beta), T(alg.sigma_1),
+        T(alg.sigma_2), T(alg.eta), T(alg.rho), alg.maxiters)
 end
 
 function (cache::LiFukushimaLineSearchCache)(u, δu)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index 6fe121481..890578f5d 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -23,8 +23,8 @@ end
 __get_linesearch(::SimpleBroyden{LS}) where {LS} = Val(LS)
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
-        termination_condition = nothing, kwargs...)
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0 = false, termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
     fx = _get_fx(prob, x)
     T = promote_type(eltype(x), eltype(fx))
@@ -48,11 +48,11 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
     @bb δJ⁻¹n = copy(x)
     @bb δJ⁻¹ = copy(J⁻¹)
 
-    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
-        termination_condition)
+    abstol, reltol, tc_cache = init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition)
 
-    ls_cache = __get_linesearch(alg) === Val(true) ?
-               LiFukushimaLineSearch()(prob, fx, x) : nothing
+    ls_cache = __get_linesearch(alg) === Val(true) ? LiFukushimaLineSearch()(prob, fx, x) :
+               nothing
 
     for _ in 1:maxiters
         @bb δx = J⁻¹ × vec(fprev)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 9f092648d..7dd152277 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -50,8 +50,8 @@ end
 function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
         M::Union{Int, Val} = Val(10), γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
         nexp::Int = 2, η_strategy::F = (f_1, k, x, F) -> f_1 ./ k^2) where {F}
-    return SimpleDFSane{_unwrap_val(M)}(σ_min, σ_max, σ_1, γ, τ_min, τ_max, nexp,
-        η_strategy)
+    return SimpleDFSane{_unwrap_val(M)}(
+        σ_min, σ_max, σ_1, γ, τ_min, τ_max, nexp, η_strategy)
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{M}, args...;
@@ -70,8 +70,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{M}, args...
     τ_min = T(alg.τ_min)
     τ_max = T(alg.τ_max)
 
-    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
-        termination_condition)
+    abstol, reltol, tc_cache = init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition)
 
     fx_norm = NONLINEARSOLVE_DEFAULT_NORM(fx)^nexp
     α_1 = one(T)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index 934dc4763..e550258ef 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -24,8 +24,8 @@ A low-overhead implementation of Halley's Method.
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
-        termination_condition = nothing, kwargs...)
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0 = false, termination_condition = nothing, kwargs...)
     isinplace(prob) &&
         error("SimpleHalley currently only supports out-of-place nonlinear problems")
 
@@ -34,8 +34,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
     T = eltype(x)
 
     autodiff = __get_concrete_autodiff(prob, alg.autodiff)
-    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
-        termination_condition)
+    abstol, reltol, tc_cache = init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition)
 
     @bb xo = copy(x)
 
@@ -59,8 +59,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
             dfx
         else
             fact = lu(dfx; check = false)
-            !issuccess(fact) && return build_solution(prob, alg, x, fx;
-                retcode = ReturnCode.Unstable)
+            !issuccess(fact) &&
+                return build_solution(prob, alg, x, fx; retcode = ReturnCode.Unstable)
             fact
         end
 
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
index c2c8b446f..8041ef4b8 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
@@ -7,14 +7,14 @@ method is non-allocating on scalar and static array problems.
 struct SimpleKlement <: AbstractSimpleNonlinearSolveAlgorithm end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
-        termination_condition = nothing, kwargs...)
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0 = false, termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
     T = eltype(x)
     fx = _get_fx(prob, x)
 
-    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
-        termination_condition)
+    abstol, reltol, tc_cache = init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition)
 
     @bb δx = copy(x)
     @bb fprev = copy(fx)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index 600892edd..b34d4cddf 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -24,8 +24,8 @@ end
 __get_threshold(::SimpleLimitedMemoryBroyden{threshold}) where {threshold} = Val(threshold)
 __use_linesearch(::SimpleLimitedMemoryBroyden{Th, LS}) where {Th, LS} = Val(LS)
 
-function SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27),
-        linesearch = Val(false), alpha = nothing)
+function SimpleLimitedMemoryBroyden(;
+        threshold::Union{Val, Int} = Val(27), linesearch = Val(false), alpha = nothing)
     return SimpleLimitedMemoryBroyden{_unwrap_val(threshold), _unwrap_val(linesearch)}(alpha)
 end
 
@@ -45,24 +45,25 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyd
 end
 
 @views function __generic_solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyden,
-        args...; abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
-        termination_condition = nothing, kwargs...)
+        args...; abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0 = false, termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
     threshold = __get_threshold(alg)
     η = min(_unwrap_val(threshold), maxiters)
 
     # For scalar problems / if the threshold is larger than problem size just use Broyden
     if x isa Number || length(x) ≤ η
-        return SciMLBase.__solve(prob, SimpleBroyden(; linesearch = __use_linesearch(alg)),
-            args...; abstol, reltol, maxiters, termination_condition, kwargs...)
+        return SciMLBase.__solve(
+            prob, SimpleBroyden(; linesearch = __use_linesearch(alg)), args...;
+            abstol, reltol, maxiters, termination_condition, kwargs...)
     end
 
     fx = _get_fx(prob, x)
 
     U, Vᵀ = __init_low_rank_jacobian(x, fx, x isa StaticArray ? threshold : Val(η))
 
-    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
-        termination_condition)
+    abstol, reltol, tc_cache = init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition)
 
     @bb xo = copy(x)
     @bb δx = copy(fx)
@@ -74,8 +75,8 @@ end
     Tcache = __lbroyden_threshold_cache(x, x isa StaticArray ? threshold : Val(η))
     @bb mat_cache = copy(x)
 
-    ls_cache = __use_linesearch(alg) === Val(true) ?
-               LiFukushimaLineSearch()(prob, fx, x) : nothing
+    ls_cache = __use_linesearch(alg) === Val(true) ? LiFukushimaLineSearch()(prob, fx, x) :
+               nothing
 
     for i in 1:maxiters
         α = ls_cache === nothing ? true : ls_cache(x, δx)
@@ -125,8 +126,8 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
 
     xo, δx, fo, δf = x, -fx, fx, fx
 
-    ls_cache = __use_linesearch(alg) === Val(true) ?
-               LiFukushimaLineSearch()(prob, fx, x) : nothing
+    ls_cache = __use_linesearch(alg) === Val(true) ? LiFukushimaLineSearch()(prob, fx, x) :
+               nothing
 
     T = promote_type(eltype(x), eltype(fx))
     if alg.alpha === nothing
@@ -138,8 +139,7 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
     end
 
     converged, res = __unrolled_lbroyden_initial_iterations(
-        prob, xo, fo, δx, abstol, U, Vᵀ,
-        threshold, ls_cache, init_α)
+        prob, xo, fo, δx, abstol, U, Vᵀ, threshold, ls_cache, init_α)
 
     converged &&
         return build_solution(prob, alg, res.x, res.fx; retcode = ReturnCode.Success)
@@ -173,39 +173,39 @@ function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemo
     return build_solution(prob, alg, xo, fo; retcode = ReturnCode.MaxIters)
 end
 
-@generated function __unrolled_lbroyden_initial_iterations(prob, xo, fo, δx, abstol, U,
-        Vᵀ, ::Val{threshold}, ls_cache, init_α) where {threshold}
+@generated function __unrolled_lbroyden_initial_iterations(
+        prob, xo, fo, δx, abstol, U, Vᵀ, ::Val{threshold},
+        ls_cache, init_α) where {threshold}
     calls = []
     for i in 1:threshold
         static_idx, static_idx_p1 = Val(i - 1), Val(i)
-        push!(calls,
-            quote
-                α = ls_cache === nothing ? true : ls_cache(xo, δx)
-                x = xo .+ α .* δx
-                fx = prob.f(x, prob.p)
-                δf = fx - fo
+        push!(calls, quote
+            α = ls_cache === nothing ? true : ls_cache(xo, δx)
+            x = xo .+ α .* δx
+            fx = prob.f(x, prob.p)
+            δf = fx - fo
 
-                maximum(abs, fx) ≤ abstol && return true, (; x, fx, δx)
+            maximum(abs, fx) ≤ abstol && return true, (; x, fx, δx)
 
-                _U = __first_n_getindex(U, $(static_idx))
-                _Vᵀ = __first_n_getindex(Vᵀ, $(static_idx))
+            _U = __first_n_getindex(U, $(static_idx))
+            _Vᵀ = __first_n_getindex(Vᵀ, $(static_idx))
 
-                vᵀ = _restructure(x, _rmatvec!!(_U, _Vᵀ, vec(δx), init_α))
-                mvec = _restructure(x, _matvec!!(_U, _Vᵀ, vec(δf), init_α))
+            vᵀ = _restructure(x, _rmatvec!!(_U, _Vᵀ, vec(δx), init_α))
+            mvec = _restructure(x, _matvec!!(_U, _Vᵀ, vec(δf), init_α))
 
-                d = dot(vᵀ, δf)
-                δx = @. (δx - mvec) / d
+            d = dot(vᵀ, δf)
+            δx = @. (δx - mvec) / d
 
-                U = Base.setindex(U, vec(δx), $(i))
-                Vᵀ = Base.setindex(Vᵀ, vec(vᵀ), $(i))
+            U = Base.setindex(U, vec(δx), $(i))
+            Vᵀ = Base.setindex(Vᵀ, vec(vᵀ), $(i))
 
-                _U = __first_n_getindex(U, $(static_idx_p1))
-                _Vᵀ = __first_n_getindex(Vᵀ, $(static_idx_p1))
-                δx = -_restructure(fx, _matvec!!(_U, _Vᵀ, vec(fx), init_α))
+            _U = __first_n_getindex(U, $(static_idx_p1))
+            _Vᵀ = __first_n_getindex(Vᵀ, $(static_idx_p1))
+            δx = -_restructure(fx, _matvec!!(_U, _Vᵀ, vec(fx), init_α))
 
-                xo = x
-                fo = fx
-            end)
+            xo = x
+            fo = fx
+        end)
     end
     push!(calls, quote
         # Termination Check
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
index 9735d0c8c..7b419ce99 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
@@ -32,8 +32,8 @@ function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresPr
     @bb xo = copy(x)
     J, jac_cache = jacobian_cache(autodiff, prob.f, fx, x, prob.p)
 
-    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
-        termination_condition)
+    abstol, reltol, tc_cache = init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition)
 
     for i in 1:maxiters
         fx, dfx = value_and_jacobian(autodiff, prob.f, fx, x, prob.p, jac_cache; J)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index e6ccf6536..a19cf2c2d 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -56,8 +56,8 @@ scalar and static array problems.
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
-        termination_condition = nothing, kwargs...)
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0 = false, termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
     T = eltype(real(x))
     Δₘₐₓ = T(alg.max_trust_radius)
@@ -88,8 +88,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
     J, jac_cache = jacobian_cache(autodiff, prob.f, fx, x, prob.p)
     fx, ∇f = value_and_jacobian(autodiff, prob.f, fx, x, prob.p, jac_cache; J)
 
-    abstol, reltol, tc_cache = init_termination_cache(prob, abstol, reltol, fx, x,
-        termination_condition)
+    abstol, reltol, tc_cache = init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition)
 
     # Set default trust region radius if not specified by user.
     Δₘₐₓ == 0 && (Δₘₐₓ = max(norm_fx, maximum(x) - minimum(x)))
@@ -132,8 +132,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
         else
             Δ = t₁ * Δ
             shrink_counter += 1
-            shrink_counter > max_shrink_times && return build_solution(prob, alg, x, fx;
-                retcode = ReturnCode.ShrinkThresholdExceeded)
+            shrink_counter > max_shrink_times && return build_solution(
+                prob, alg, x, fx; retcode = ReturnCode.ShrinkThresholdExceeded)
         end
 
         if r ≥ η₁
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 43689a29d..333e54d3b 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -58,8 +58,8 @@ function __forwarddiff_jacobian_config(
         f::F, x::SArray, ck::ForwardDiff.Chunk{N}, tag) where {F, N}
     seeds = ForwardDiff.construct_seeds(ForwardDiff.Partials{N, eltype(x)})
     duals = ForwardDiff.Dual{typeof(tag), eltype(x), N}.(x)
-    return ForwardDiff.JacobianConfig{typeof(tag), eltype(x), N, typeof(duals)}(seeds,
-        duals)
+    return ForwardDiff.JacobianConfig{typeof(tag), eltype(x), N, typeof(duals)}(
+        seeds, duals)
 end
 
 function __get_jacobian_config(ad::AutoPolyesterForwardDiff{CS}, args...) where {CS}
@@ -205,8 +205,8 @@ end
 
 function compute_jacobian_and_hessian(ad::AutoFiniteDiff, prob, _, x::Number)
     fx = prob.f(x, prob.p)
-    J_fn = x -> FiniteDiff.finite_difference_derivative(Base.Fix2(prob.f, prob.p), x,
-        ad.fdtype)
+    J_fn = x -> FiniteDiff.finite_difference_derivative(
+        Base.Fix2(prob.f, prob.p), x, ad.fdtype)
     dfx = J_fn(x)
     d2fx = FiniteDiff.finite_difference_derivative(J_fn, x, ad.fdtype)
     return fx, dfx, d2fx
@@ -262,7 +262,8 @@ end
 @inline _restructure(y, x) = ArrayInterface.restructure(y, x)
 
 @inline function _get_fx(prob::NonlinearLeastSquaresProblem, x)
-    isinplace(prob) && prob.f.resid_prototype === nothing &&
+    isinplace(prob) &&
+        prob.f.resid_prototype === nothing &&
         error("Inplace NonlinearLeastSquaresProblem requires a `resid_prototype`")
     return _get_fx(prob.f, x, prob.p)
 end
@@ -289,17 +290,16 @@ end
 # is meant for low overhead solvers, users can opt into the other termination modes but the
 # default is to use the least overhead version.
 function init_termination_cache(prob::NonlinearProblem, abstol, reltol, du, u, ::Nothing)
-    return init_termination_cache(prob, abstol, reltol, du, u,
-        AbsNormTerminationMode(Base.Fix1(maximum, abs)))
+    return init_termination_cache(
+        prob, abstol, reltol, du, u, AbsNormTerminationMode(Base.Fix1(maximum, abs)))
 end
 function init_termination_cache(
         prob::NonlinearLeastSquaresProblem, abstol, reltol, du, u, ::Nothing)
-    return init_termination_cache(prob, abstol, reltol, du, u,
-        AbsNormTerminationMode(Base.Fix2(norm, 2)))
+    return init_termination_cache(
+        prob, abstol, reltol, du, u, AbsNormTerminationMode(Base.Fix2(norm, 2)))
 end
 
-function init_termination_cache(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+function init_termination_cache(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
         abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
     T = promote_type(eltype(du), eltype(u))
     abstol = __get_tolerance(u, abstol, T)
@@ -316,23 +316,23 @@ function init_termination_cache(
 end
 
 function check_termination(tc_cache, fx, x, xo, prob, alg)
-    return check_termination(tc_cache, fx, x, xo, prob, alg,
-        DiffEqBase.get_termination_mode(tc_cache))
+    return check_termination(
+        tc_cache, fx, x, xo, prob, alg, DiffEqBase.get_termination_mode(tc_cache))
 end
-function check_termination(tc_cache, fx, x, xo, prob, alg,
-        ::AbstractNonlinearTerminationMode)
+function check_termination(
+        tc_cache, fx, x, xo, prob, alg, ::AbstractNonlinearTerminationMode)
     tc_cache(fx, x, xo) &&
         return build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
     return nothing
 end
-function check_termination(tc_cache, fx, x, xo, prob, alg,
-        ::AbstractSafeNonlinearTerminationMode)
+function check_termination(
+        tc_cache, fx, x, xo, prob, alg, ::AbstractSafeNonlinearTerminationMode)
     tc_cache(fx, x, xo) &&
         return build_solution(prob, alg, x, fx; retcode = tc_cache.retcode)
     return nothing
 end
-function check_termination(tc_cache, fx, x, xo, prob, alg,
-        ::AbstractSafeBestNonlinearTerminationMode)
+function check_termination(
+        tc_cache, fx, x, xo, prob, alg, ::AbstractSafeBestNonlinearTerminationMode)
     if tc_cache(fx, x, xo)
         if isinplace(prob)
             prob.f(fx, x, prob.p)
diff --git a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
index 2180943fc..9625c6872 100644
--- a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
@@ -4,8 +4,8 @@ using LinearAlgebra, NonlinearProblemLibrary, DiffEqBase, Test
 problems = NonlinearProblemLibrary.problems
 dicts = NonlinearProblemLibrary.dicts
 
-function test_on_library(problems, dicts, alg_ops, broken_tests, ϵ = 1e-4;
-        skip_tests = nothing)
+function test_on_library(
+        problems, dicts, alg_ops, broken_tests, ϵ = 1e-4; skip_tests = nothing)
     for (idx, (problem, dict)) in enumerate(zip(problems, dicts))
         x = dict["start"]
         res = similar(x)
@@ -13,8 +13,8 @@ function test_on_library(problems, dicts, alg_ops, broken_tests, ϵ = 1e-4;
         @testset "$idx: $(dict["title"])" begin
             for alg in alg_ops
                 try
-                    sol = solve(nlprob, alg;
-                        termination_condition = AbsNormTerminationMode())
+                    sol = solve(
+                        nlprob, alg; termination_condition = AbsNormTerminationMode())
                     problem(res, sol.u, nothing)
 
                     skip = skip_tests !== nothing && idx in skip_tests[alg]
@@ -51,8 +51,7 @@ end
 end
 
 @testitem "SimpleTrustRegion" setup=[RobustnessTesting] tags=[:core] begin
-    alg_ops = (SimpleTrustRegion(),
-        SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
+    alg_ops = (SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
     broken_tests[alg_ops[1]] = [3, 15, 16, 21]
diff --git a/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl b/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
index 50fc18e94..ab1db6cb0 100644
--- a/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/forward_ad_tests.jl
@@ -41,8 +41,9 @@ export test_f, test_f!, jacobian_f, solve_with, __compatible
 end
 
 @testitem "ForwardDiff.jl Integration: Rootfinding" setup=[ForwardADRootfindingTesting] tags=[:core] begin
-    @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(),
-        SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        SimpleNewtonRaphson(), SimpleTrustRegion(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
         SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleDFSane())
         us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
 
@@ -171,25 +172,27 @@ end
         function obj_4(p)
             prob_iip = NonlinearLeastSquaresProblem(
                 NonlinearFunction{true}(
-                    loss_function!; resid_prototype = zeros(length(y_target))), θ_init, p)
+                    loss_function!; resid_prototype = zeros(length(y_target))),
+                θ_init,
+                p)
             sol = solve(prob_iip, alg)
             return sum(abs2, sol.u)
         end
 
         function obj_5(p)
             ff = NonlinearFunction{true}(
-                loss_function!; resid_prototype = zeros(length(y_target)), jac = loss_function_jac!)
-            prob_iip = NonlinearLeastSquaresProblem(
-                ff, θ_init, p)
+                loss_function!; resid_prototype = zeros(length(y_target)),
+                jac = loss_function_jac!)
+            prob_iip = NonlinearLeastSquaresProblem(ff, θ_init, p)
             sol = solve(prob_iip, alg)
             return sum(abs2, sol.u)
         end
 
         function obj_6(p)
             ff = NonlinearFunction{true}(
-                loss_function!; resid_prototype = zeros(length(y_target)), vjp = loss_function_vjp!)
-            prob_iip = NonlinearLeastSquaresProblem(
-                ff, θ_init, p)
+                loss_function!; resid_prototype = zeros(length(y_target)),
+                vjp = loss_function_vjp!)
+            prob_iip = NonlinearLeastSquaresProblem(ff, θ_init, p)
             sol = solve(prob_iip, alg)
             return sum(abs2, sol.u)
         end
diff --git a/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl b/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl
index ef3a05504..005c463ff 100644
--- a/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/least_squares_tests.jl
@@ -29,7 +29,8 @@
     end
 
     prob_iip = NonlinearLeastSquaresProblem(
-        NonlinearFunction{true}(loss_function!, resid_prototype = zeros(length(y_target))), θ_init, x)
+        NonlinearFunction{true}(loss_function!, resid_prototype = zeros(length(y_target))),
+        θ_init, x)
 
     @testset "Solver: $(nameof(typeof(solver)))" for solver in [
         SimpleNewtonRaphson(AutoForwardDiff()), SimpleGaussNewton(AutoForwardDiff()),
diff --git a/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl b/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl
index 17cd3d674..3f7dfbb40 100644
--- a/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl
@@ -5,10 +5,10 @@
     vecprob = NonlinearProblem(ff, vec(u0), p)
     prob = NonlinearProblem(ff, u0, p)
 
-    @testset "$(nameof(typeof(alg)))" for alg in (SimpleKlement(), SimpleBroyden(),
-        SimpleNewtonRaphson(), SimpleDFSane(),
-        SimpleLimitedMemoryBroyden(; threshold = Val(2)),
-        SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        SimpleKlement(), SimpleBroyden(), SimpleNewtonRaphson(), SimpleDFSane(),
+        SimpleLimitedMemoryBroyden(; threshold = Val(2)), SimpleTrustRegion(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
         @test vec(solve(prob, alg).u) ≈ solve(vecprob, alg).u
     end
 end
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index ca0e26ef6..1ef0757b8 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -1,7 +1,7 @@
 @testsetup module RootfindingTesting
 using Reexport
-@reexport using AllocCheck,
-                LinearSolve, StaticArrays, Random, LinearAlgebra, ForwardDiff, DiffEqBase
+@reexport using AllocCheck, LinearSolve, StaticArrays, Random, LinearAlgebra, ForwardDiff,
+                DiffEqBase
 import PolyesterForwardDiff
 
 quadratic_f(u, p) = u .* u .- p
@@ -14,16 +14,14 @@ function newton_fails(u, p)
             (0.21640425613334457 .+
              216.40425613334457 ./ (1 .+
               (0.21640425613334457 .+
-               216.40425613334457 ./
-               (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^ 2.0) .-
-           0.0011552453009332421u .- p
+               216.40425613334457 ./ (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^
+            2.0) .- 0.0011552453009332421u .- p
 end
 
 const TERMINATION_CONDITIONS = [
     NormTerminationMode(), RelTerminationMode(), RelNormTerminationMode(),
     AbsTerminationMode(), AbsNormTerminationMode(), RelSafeTerminationMode(),
-    AbsSafeTerminationMode(), RelSafeBestTerminationMode(), AbsSafeBestTerminationMode()
-]
+    AbsSafeTerminationMode(), RelSafeBestTerminationMode(), AbsSafeBestTerminationMode()]
 
 function benchmark_nlsolve_oop(f::F, u0, p = 2.0; solver) where {F}
     prob = NonlinearProblem{false}(f, u0, p)
@@ -40,14 +38,14 @@ export quadratic_f, quadratic_f!, quadratic_f2, newton_fails, TERMINATION_CONDIT
 end
 
 @testitem "First Order Methods" setup=[RootfindingTesting] tags=[:core] begin
-    @testset "$(alg)" for alg in (SimpleNewtonRaphson, SimpleTrustRegion,
-        (args...; kwargs...) -> SimpleTrustRegion(args...; nlsolve_update_rule = Val(true),
-            kwargs...))
+    @testset "$(alg)" for alg in (SimpleNewtonRaphson,
+        SimpleTrustRegion,
+        (args...; kwargs...) -> SimpleTrustRegion(
+            args...; nlsolve_update_rule = Val(true), kwargs...))
         @testset "AutoDiff: $(nameof(typeof(autodiff))))" for autodiff in (
-            AutoFiniteDiff(),
-            AutoForwardDiff(), AutoPolyesterForwardDiff())
-            @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],
-                @SVector[1.0, 1.0], 1.0)
+            AutoFiniteDiff(), AutoForwardDiff(), AutoPolyesterForwardDiff())
+            @testset "[OOP] u0: $(typeof(u0))" for u0 in (
+                [1.0, 1.0], @SVector[1.0, 1.0], 1.0)
                 u0 isa SVector && autodiff isa AutoPolyesterForwardDiff && continue
                 sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = alg(; autodiff))
                 @test SciMLBase.successful_retcode(sol)
@@ -71,10 +69,10 @@ end
 end
 
 @testitem "SimpleHalley" setup=[RootfindingTesting] tags=[:core] begin
-    @testset "AutoDiff: $(nameof(typeof(autodiff)))" for autodiff in (AutoFiniteDiff(),
-        AutoForwardDiff())
-        @testset "[OOP] u0: $(nameof(typeof(u0)))" for u0 in ([1.0, 1.0],
-            @SVector[1.0, 1.0], 1.0)
+    @testset "AutoDiff: $(nameof(typeof(autodiff)))" for autodiff in (
+        AutoFiniteDiff(), AutoForwardDiff())
+        @testset "[OOP] u0: $(nameof(typeof(u0)))" for u0 in (
+            [1.0, 1.0], @SVector[1.0, 1.0], 1.0)
             sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = SimpleHalley(; autodiff))
             @test SciMLBase.successful_retcode(sol)
             @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
@@ -90,9 +88,9 @@ end
 end
 
 @testitem "Derivative Free Metods" setup=[RootfindingTesting] tags=[:core] begin
-    @testset "$(nameof(typeof(alg)))" for alg in [SimpleBroyden(), SimpleKlement(),
-        SimpleDFSane(), SimpleLimitedMemoryBroyden(),
-        SimpleBroyden(; linesearch = Val(true)),
+    @testset "$(nameof(typeof(alg)))" for alg in [
+        SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
+        SimpleLimitedMemoryBroyden(), SimpleBroyden(; linesearch = Val(true)),
         SimpleLimitedMemoryBroyden(; linesearch = Val(true))]
         @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
             sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = alg)
@@ -119,8 +117,9 @@ end
     u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
     p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 
-    @testset "$(nameof(typeof(alg)))" for alg in (SimpleDFSane(), SimpleTrustRegion(),
-        SimpleHalley(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        SimpleDFSane(), SimpleTrustRegion(), SimpleHalley(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
         sol = benchmark_nlsolve_oop(newton_fails, u0, p; solver = alg)
         @test SciMLBase.successful_retcode(sol)
         @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
@@ -135,9 +134,10 @@ end
 
 @testitem "Allocation Checks" setup=[RootfindingTesting] tags=[:core] begin
     if Sys.islinux()  # Very slow on other OS
-        @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(),
-            SimpleHalley(), SimpleBroyden(), SimpleKlement(), SimpleLimitedMemoryBroyden(),
-            SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+        @testset "$(nameof(typeof(alg)))" for alg in (
+            SimpleNewtonRaphson(), SimpleHalley(), SimpleBroyden(),
+            SimpleKlement(), SimpleLimitedMemoryBroyden(), SimpleTrustRegion(),
+            SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
             SimpleDFSane(), SimpleBroyden(; linesearch = Val(true)),
             SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
             @check_allocs nlsolve(prob, alg) = SciMLBase.solve(prob, alg; abstol = 1e-9)
@@ -166,8 +166,8 @@ end
 end
 
 @testitem "Interval Nonlinear Problems" setup=[RootfindingTesting] tags=[:core] begin
-    @testset "$(nameof(typeof(alg)))" for alg in (Bisection(), Falsi(), Ridder(), Brent(),
-        ITP(), Alefeld())
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        Bisection(), Falsi(), Ridder(), Brent(), ITP(), Alefeld())
         tspan = (1.0, 20.0)
 
         function g(p)
@@ -240,8 +240,8 @@ end
 end
 
 @testitem "Flipped Signs and Reversed Tspan" setup=[RootfindingTesting] tags=[:core] begin
-    @testset "$(nameof(typeof(alg)))" for alg in (Alefeld(), Bisection(), Falsi(), Brent(),
-        ITP(), Ridder())
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        Alefeld(), Bisection(), Falsi(), Brent(), ITP(), Ridder())
         f1(u, p) = u * u - p
         f2(u, p) = p - u * u
 
diff --git a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
index 39ac422a4..efc03403a 100644
--- a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
@@ -6,8 +6,9 @@
     f(u, p) = u .* u .- 2
     f!(du, u, p) = du .= u .* u .- 2
 
-    @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(), SimpleDFSane(),
-        SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
         SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(),
         SimpleHalley(), SimpleBroyden(; linesearch = Val(true)),
         SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
@@ -51,10 +52,11 @@ end
 
     prob = NonlinearProblem{false}(f, @SVector[1.0f0, 1.0f0])
 
-    @testset "$(nameof(typeof(alg)))" for alg in (SimpleNewtonRaphson(), SimpleDFSane(),
-        SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
-        SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(), SimpleHalley(),
-        SimpleBroyden(; linesearch = Val(true)),
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+        SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(),
+        SimpleHalley(), SimpleBroyden(; linesearch = Val(true)),
         SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
         @test begin
             try

From efa09d8714c3e1ac39ee5b8dc89aa0281a2476b8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 14:43:04 -0700
Subject: [PATCH 413/700] Add explicit imports

---
 lib/SimpleNonlinearSolve/Project.toml         |  4 +-
 .../ext/SimpleNonlinearSolveReverseDiffExt.jl | 42 +++++++++----------
 .../ext/SimpleNonlinearSolveTrackerExt.jl     |  2 +-
 .../src/SimpleNonlinearSolve.jl               | 36 ++++++++++------
 .../test/core/aqua_tests.jl                   |  9 ----
 .../test/core/qa_tests.jl                     | 23 ++++++++++
 6 files changed, 69 insertions(+), 47 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/test/core/aqua_tests.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/core/qa_tests.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 74b6cde87..0fbdfd614 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -45,6 +45,7 @@ ChainRulesCore = "1.22"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149"
 DiffResults = "1.1"
+ExplicitImports = "1.5.0"
 FastClosures = "0.3.2"
 FiniteDiff = "2.22"
 ForwardDiff = "0.10.36"
@@ -73,6 +74,7 @@ AllocCheck = "9b6a8646-10ed-4001-bbdc-1d2f46dfbb1a"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -91,4 +93,4 @@ Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "AllocCheck", "DiffEqBase", "ForwardDiff", "LinearAlgebra", "LinearSolve", "NonlinearProblemLibrary", "Pkg", "Random", "ReTestItems", "SciMLSensitivity", "StaticArrays", "Zygote", "CUDA", "PolyesterForwardDiff", "Reexport", "Test", "FiniteDiff", "ReverseDiff", "Tracker"]
+test = ["AllocCheck", "Aqua", "CUDA", "DiffEqBase", "ExplicitImports", "FiniteDiff", "ForwardDiff", "LinearAlgebra", "LinearSolve", "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReTestItems", "Reexport", "ReverseDiff", "SciMLSensitivity", "StaticArrays", "Test", "Tracker", "Zygote"]
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
index a6a1c2dbf..c5f0286f1 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
@@ -5,65 +5,61 @@ using DiffEqBase: DiffEqBase
 using ReverseDiff: ReverseDiff, TrackedArray, TrackedReal
 using SciMLBase: ReverseDiffOriginator, NonlinearProblem, NonlinearLeastSquaresProblem
 using SimpleNonlinearSolve: SimpleNonlinearSolve
+import SimpleNonlinearSolve: __internal_solve_up
 
-function SimpleNonlinearSolve.__internal_solve_up(
+function __internal_solve_up(
         prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
         u0::TrackedArray, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
-    return ReverseDiff.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
-        u0, u0_changed, p, p_changed, alg, args...; kwargs...)
+    return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
+        u0_changed, p, p_changed, alg, args...; kwargs...)
 end
 
-function SimpleNonlinearSolve.__internal_solve_up(
+function __internal_solve_up(
         prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
         u0, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
-    return ReverseDiff.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
-        u0, u0_changed, p, p_changed, alg, args...; kwargs...)
+    return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
+        u0_changed, p, p_changed, alg, args...; kwargs...)
 end
 
-function SimpleNonlinearSolve.__internal_solve_up(
+function __internal_solve_up(
         prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
         u0::TrackedArray, u0_changed, p, p_changed, alg, args...; kwargs...)
-    return ReverseDiff.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
-        u0, u0_changed, p, p_changed, alg, args...; kwargs...)
+    return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
+        u0_changed, p, p_changed, alg, args...; kwargs...)
 end
 
-function SimpleNonlinearSolve.__internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+function __internal_solve_up(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
         sensealg, u0::AbstractArray{<:TrackedReal}, u0_changed,
         p::AbstractArray{<:TrackedReal}, p_changed, alg, args...; kwargs...)
-    return SimpleNonlinearSolve.__internal_solve_up(
-        prob, sensealg, ArrayInterface.aos_to_soa(u0), true,
+    return __internal_solve_up(prob, sensealg, ArrayInterface.aos_to_soa(u0), true,
         ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
 end
 
-function SimpleNonlinearSolve.__internal_solve_up(
+function __internal_solve_up(
         prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0,
         u0_changed, p::AbstractArray{<:TrackedReal}, p_changed, alg, args...; kwargs...)
-    return SimpleNonlinearSolve.__internal_solve_up(
-        prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p),
+    return __internal_solve_up(prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p),
         true, alg, args...; kwargs...)
 end
 
-function SimpleNonlinearSolve.__internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+function __internal_solve_up(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
         sensealg, u0::AbstractArray{<:TrackedReal},
         u0_changed, p, p_changed, alg, args...; kwargs...)
-    return SimpleNonlinearSolve.__internal_solve_up(
-        prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p),
+    return __internal_solve_up(prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p),
         true, alg, args...; kwargs...)
 end
 
-ReverseDiff.@grad function SimpleNonlinearSolve.__internal_solve_up(
+ReverseDiff.@grad function __internal_solve_up(
         prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
         sensealg, u0, u0_changed, p, p_changed, alg, args...; kwargs...)
     out, ∇internal = DiffEqBase._solve_adjoint(
         prob, sensealg, ReverseDiff.value(u0), ReverseDiff.value(p),
         ReverseDiffOriginator(), alg, args...; kwargs...)
-    function ∇SimpleNonlinearSolve.__internal_solve_up(_args...)
+    function ∇__internal_solve_up(_args...)
         ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(_args...)
         return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
     end
-    return Array(out), ∇SimpleNonlinearSolve.__internal_solve_up
+    return Array(out), ∇__internal_solve_up
 end
 
 end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
index b49bd78cc..85b84f80f 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
@@ -32,7 +32,7 @@ Tracker.@grad function SimpleNonlinearSolve.__internal_solve_up(
     u0, p = Tracker.data(u0_), Tracker.data(p_)
     prob = remake(_prob; u0, p)
     out, ∇internal = DiffEqBase._solve_adjoint(
-        prob, sensealg, u0, p, SciMLBase.TrackerOriginator(), alg, args...; kwargs...)
+        prob, sensealg, u0, p, TrackerOriginator(), alg, args...; kwargs...)
 
     function ∇__internal_solve_up(Δ)
         ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(Δ)
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index dfd650c4d..1ff66b995 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -1,22 +1,31 @@
 module SimpleNonlinearSolve
 
-import PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidations
+using PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidations
 
 @recompile_invalidations begin
-    using ADTypes, ArrayInterface, ConcreteStructs, DiffEqBase, FastClosures, FiniteDiff,
-          ForwardDiff, Reexport, LinearAlgebra, SciMLBase
-
-    import DiffEqBase: AbstractNonlinearTerminationMode,
-                       AbstractSafeNonlinearTerminationMode,
-                       AbstractSafeBestNonlinearTerminationMode, NONLINEARSOLVE_DEFAULT_NORM
-    import DiffResults
-    import ForwardDiff: Dual
-    import MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
-    import SciMLBase: AbstractNonlinearAlgorithm, build_solution, isinplace, _unwrap_val
-    import StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, Size
+    using ADTypes: ADTypes, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
+    using ArrayInterface: ArrayInterface
+    using ConcreteStructs: @concrete
+    using DiffEqBase: DiffEqBase, AbstractNonlinearTerminationMode,
+                      AbstractSafeNonlinearTerminationMode,
+                      AbstractSafeBestNonlinearTerminationMode, AbsNormTerminationMode,
+                      NONLINEARSOLVE_DEFAULT_NORM
+    using DiffResults: DiffResults
+    using FastClosures: @closure
+    using FiniteDiff: FiniteDiff
+    using ForwardDiff: ForwardDiff, Dual
+    using LinearAlgebra: LinearAlgebra, I, convert, copyto!, diagind, dot, issuccess, lu,
+                         mul!, norm, transpose
+    using MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
+    using Reexport: @reexport
+    using SciMLBase: SciMLBase, IntervalNonlinearProblem, NonlinearFunction,
+                     NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode, init,
+                     remake, solve, AbstractNonlinearAlgorithm, build_solution, isinplace,
+                     _unwrap_val
+    using StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, Size
 end
 
-@reexport using ADTypes, SciMLBase
+@reexport using SciMLBase
 
 abstract type AbstractSimpleNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm end
 abstract type AbstractBracketingAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
@@ -110,6 +119,7 @@ end
     end
 end
 
+export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
 export SimpleBroyden, SimpleDFSane, SimpleGaussNewton, SimpleHalley, SimpleKlement,
        SimpleLimitedMemoryBroyden, SimpleNewtonRaphson, SimpleTrustRegion
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
diff --git a/lib/SimpleNonlinearSolve/test/core/aqua_tests.jl b/lib/SimpleNonlinearSolve/test/core/aqua_tests.jl
deleted file mode 100644
index 364f51b59..000000000
--- a/lib/SimpleNonlinearSolve/test/core/aqua_tests.jl
+++ /dev/null
@@ -1,9 +0,0 @@
-@testitem "Aqua" tags=[:core] begin
-    using Aqua
-
-    Aqua.test_all(SimpleNonlinearSolve; piracies = false, ambiguities = false)
-    Aqua.test_piracies(SimpleNonlinearSolve;
-        treat_as_own = [
-            NonlinearProblem, NonlinearLeastSquaresProblem, IntervalNonlinearProblem])
-    Aqua.test_ambiguities(SimpleNonlinearSolve; recursive = false)
-end
diff --git a/lib/SimpleNonlinearSolve/test/core/qa_tests.jl b/lib/SimpleNonlinearSolve/test/core/qa_tests.jl
new file mode 100644
index 000000000..fbdb813ee
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/qa_tests.jl
@@ -0,0 +1,23 @@
+@testitem "Aqua" tags=[:core] begin
+    using Aqua
+
+    Aqua.test_all(SimpleNonlinearSolve; piracies = false, ambiguities = false)
+    Aqua.test_piracies(SimpleNonlinearSolve;
+        treat_as_own = [
+            NonlinearProblem, NonlinearLeastSquaresProblem, IntervalNonlinearProblem])
+    Aqua.test_ambiguities(SimpleNonlinearSolve; recursive = false)
+end
+
+@testitem "Explicit Imports" tags=[:core] begin
+    import PolyesterForwardDiff, ReverseDiff, Tracker, StaticArrays, Zygote
+
+    using ExplicitImports
+
+    @test check_no_implicit_imports(
+        SimpleNonlinearSolve; skip = (SimpleNonlinearSolve, Base, Core, SciMLBase)) ===
+          nothing
+
+    @test check_no_stale_explicit_imports(SimpleNonlinearSolve) === nothing
+
+    @test check_all_qualified_accesses_via_owners(SimpleNonlinearSolve) === nothing
+end

From 248088c258d39bd7adf2801ab8240f17d7295436 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 15:01:59 -0700
Subject: [PATCH 414/700] Resolve ambiguity

---
 .../ext/SimpleNonlinearSolveReverseDiffExt.jl | 94 ++++++++++---------
 .../ext/SimpleNonlinearSolveTrackerExt.jl     | 74 ++++++++-------
 .../test/core/exotic_type_tests.jl            |  3 +-
 3 files changed, 88 insertions(+), 83 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
index c5f0286f1..249bbbedb 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
@@ -7,59 +7,61 @@ using SciMLBase: ReverseDiffOriginator, NonlinearProblem, NonlinearLeastSquaresP
 using SimpleNonlinearSolve: SimpleNonlinearSolve
 import SimpleNonlinearSolve: __internal_solve_up
 
-function __internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
-        u0::TrackedArray, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
-    return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
-        u0_changed, p, p_changed, alg, args...; kwargs...)
-end
+for pType in (NonlinearProblem, NonlinearLeastSquaresProblem)
+    @eval begin
+        function __internal_solve_up(prob::$(pType), sensealg, u0::TrackedArray, u0_changed,
+                p::TrackedArray, p_changed, alg, args...; kwargs...)
+            return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
+                u0_changed, p, p_changed, alg, args...; kwargs...)
+        end
 
-function __internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
-        u0, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
-    return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
-        u0_changed, p, p_changed, alg, args...; kwargs...)
-end
+        function __internal_solve_up(prob::$(pType), sensealg, u0, u0_changed,
+                p::TrackedArray, p_changed, alg, args...; kwargs...)
+            return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
+                u0_changed, p, p_changed, alg, args...; kwargs...)
+        end
 
-function __internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
-        u0::TrackedArray, u0_changed, p, p_changed, alg, args...; kwargs...)
-    return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
-        u0_changed, p, p_changed, alg, args...; kwargs...)
-end
+        function __internal_solve_up(prob::$(pType), sensealg, u0::TrackedArray,
+                u0_changed, p, p_changed, alg, args...; kwargs...)
+            return ReverseDiff.track(__internal_solve_up, prob, sensealg, u0,
+                u0_changed, p, p_changed, alg, args...; kwargs...)
+        end
 
-function __internal_solve_up(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
-        sensealg, u0::AbstractArray{<:TrackedReal}, u0_changed,
-        p::AbstractArray{<:TrackedReal}, p_changed, alg, args...; kwargs...)
-    return __internal_solve_up(prob, sensealg, ArrayInterface.aos_to_soa(u0), true,
-        ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
-end
+        function __internal_solve_up(
+                prob::$(pType), sensealg, u0::AbstractArray{<:TrackedReal}, u0_changed,
+                p::AbstractArray{<:TrackedReal}, p_changed, alg, args...; kwargs...)
+            return __internal_solve_up(prob, sensealg, ArrayInterface.aos_to_soa(u0), true,
+                ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
+        end
 
-function __internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0,
-        u0_changed, p::AbstractArray{<:TrackedReal}, p_changed, alg, args...; kwargs...)
-    return __internal_solve_up(prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p),
-        true, alg, args...; kwargs...)
-end
+        function __internal_solve_up(prob::$(pType), sensealg, u0, u0_changed,
+                p::AbstractArray{<:TrackedReal}, p_changed, alg, args...; kwargs...)
+            return __internal_solve_up(
+                prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p),
+                true, alg, args...; kwargs...)
+        end
 
-function __internal_solve_up(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
-        sensealg, u0::AbstractArray{<:TrackedReal},
-        u0_changed, p, p_changed, alg, args...; kwargs...)
-    return __internal_solve_up(prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p),
-        true, alg, args...; kwargs...)
-end
+        function __internal_solve_up(
+                prob::$(pType), sensealg, u0::AbstractArray{<:TrackedReal},
+                u0_changed, p, p_changed, alg, args...; kwargs...)
+            return __internal_solve_up(
+                prob, sensealg, u0, true, ArrayInterface.aos_to_soa(p),
+                true, alg, args...; kwargs...)
+        end
 
-ReverseDiff.@grad function __internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
-        sensealg, u0, u0_changed, p, p_changed, alg, args...; kwargs...)
-    out, ∇internal = DiffEqBase._solve_adjoint(
-        prob, sensealg, ReverseDiff.value(u0), ReverseDiff.value(p),
-        ReverseDiffOriginator(), alg, args...; kwargs...)
-    function ∇__internal_solve_up(_args...)
-        ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(_args...)
-        return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
+        ReverseDiff.@grad function __internal_solve_up(
+                prob::$(pType), sensealg, u0, u0_changed,
+                p, p_changed, alg, args...; kwargs...)
+            out, ∇internal = DiffEqBase._solve_adjoint(
+                prob, sensealg, ReverseDiff.value(u0), ReverseDiff.value(p),
+                ReverseDiffOriginator(), alg, args...; kwargs...)
+            function ∇__internal_solve_up(_args...)
+                ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(_args...)
+                return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
+            end
+            return Array(out), ∇__internal_solve_up
+        end
     end
-    return Array(out), ∇__internal_solve_up
 end
 
 end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
index 85b84f80f..a212b220e 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
@@ -1,45 +1,49 @@
 module SimpleNonlinearSolveTrackerExt
 
 using DiffEqBase: DiffEqBase
-using SciMLBase: TrackerOriginator, NonlinearProblem, NonlinearLeastSquaresProblem
+using SciMLBase: TrackerOriginator, NonlinearProblem, NonlinearLeastSquaresProblem, remake
 using SimpleNonlinearSolve: SimpleNonlinearSolve
 using Tracker: Tracker, TrackedArray
 
-function SimpleNonlinearSolve.__internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
-        u0::TrackedArray, u0_changed, p, p_changed, alg, args...; kwargs...)
-    return Tracker.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
-        u0, u0_changed, p, p_changed, alg, args...; kwargs...)
-end
-
-function SimpleNonlinearSolve.__internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
-        u0::TrackedArray, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
-    return Tracker.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
-        u0, u0_changed, p, p_changed, alg, args...; kwargs...)
-end
-
-function SimpleNonlinearSolve.__internal_solve_up(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem}, sensealg,
-        u0, u0_changed, p::TrackedArray, p_changed, alg, args...; kwargs...)
-    return Tracker.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
-        u0, u0_changed, p, p_changed, alg, args...; kwargs...)
-end
-
-Tracker.@grad function SimpleNonlinearSolve.__internal_solve_up(
-        _prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
-        sensealg, u0_, u0_changed, p_, p_changed, alg, args...; kwargs...)
-    u0, p = Tracker.data(u0_), Tracker.data(p_)
-    prob = remake(_prob; u0, p)
-    out, ∇internal = DiffEqBase._solve_adjoint(
-        prob, sensealg, u0, p, TrackerOriginator(), alg, args...; kwargs...)
-
-    function ∇__internal_solve_up(Δ)
-        ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(Δ)
-        return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
+for pType in (NonlinearProblem, NonlinearLeastSquaresProblem)
+    @eval begin
+        function SimpleNonlinearSolve.__internal_solve_up(
+                prob::$(pType), sensealg, u0::TrackedArray,
+                u0_changed, p, p_changed, alg, args...; kwargs...)
+            return Tracker.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
+                u0, u0_changed, p, p_changed, alg, args...; kwargs...)
+        end
+
+        function SimpleNonlinearSolve.__internal_solve_up(
+                prob::$(pType), sensealg, u0::TrackedArray, u0_changed,
+                p::TrackedArray, p_changed, alg, args...; kwargs...)
+            return Tracker.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
+                u0, u0_changed, p, p_changed, alg, args...; kwargs...)
+        end
+
+        function SimpleNonlinearSolve.__internal_solve_up(
+                prob::$(pType), sensealg, u0, u0_changed,
+                p::TrackedArray, p_changed, alg, args...; kwargs...)
+            return Tracker.track(SimpleNonlinearSolve.__internal_solve_up, prob, sensealg,
+                u0, u0_changed, p, p_changed, alg, args...; kwargs...)
+        end
+
+        Tracker.@grad function SimpleNonlinearSolve.__internal_solve_up(
+                _prob::$(pType), sensealg, u0_, u0_changed,
+                p_, p_changed, alg, args...; kwargs...)
+            u0, p = Tracker.data(u0_), Tracker.data(p_)
+            prob = remake(_prob; u0, p)
+            out, ∇internal = DiffEqBase._solve_adjoint(
+                prob, sensealg, u0, p, TrackerOriginator(), alg, args...; kwargs...)
+
+            function ∇__internal_solve_up(Δ)
+                ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(Δ)
+                return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
+            end
+
+            return out, ∇__internal_solve_up
+        end
     end
-
-    return out, ∇__internal_solve_up
 end
 
 end
diff --git a/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl b/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
index fff77a3d4..302d2402e 100644
--- a/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
@@ -16,8 +16,7 @@ end
     using SimpleNonlinearSolve, LinearAlgebra
 
     for alg in [SimpleNewtonRaphson(), SimpleBroyden(), SimpleKlement(), SimpleDFSane(),
-        SimpleTrustRegion(), SimpleLimitedMemoryBroyden(; threshold = 2),
-        SimpleHalley()]
+        SimpleTrustRegion(), SimpleLimitedMemoryBroyden(; threshold = 2), SimpleHalley()]
         sol = solve(prob_oop_bf, alg)
         @test norm(sol.resid, Inf) < 1e-6
         @test SciMLBase.successful_retcode(sol.retcode)

From b84ee8f5332ccf83f8ed6198850430ba39f2eb79 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 18:12:57 -0700
Subject: [PATCH 415/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 0fbdfd614..7023d27d6 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.8.2"
+version = "1.8.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 02160aa00abac72946cd97e20f86832e0111dd62 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 16:29:04 -0700
Subject: [PATCH 416/700] Use DifferentiationInterface

---
 lib/SimpleNonlinearSolve/Project.toml         |   6 +-
 ...leNonlinearSolvePolyesterForwardDiffExt.jl |  20 --
 .../src/SimpleNonlinearSolve.jl               |   6 +-
 .../src/nlsolve/halley.jl                     |  14 +-
 .../src/nlsolve/raphson.jl                    |  11 +-
 .../src/nlsolve/trustRegion.jl                |  13 +-
 lib/SimpleNonlinearSolve/src/utils.jl         | 238 ++++--------------
 7 files changed, 78 insertions(+), 230 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 7023d27d6..5284b3ed4 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.8.1"
+version = "1.9.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -9,6 +9,7 @@ ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 DiffResults = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
+DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -21,7 +22,6 @@ StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [weakdeps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
@@ -29,7 +29,6 @@ Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [extensions]
 SimpleNonlinearSolveChainRulesCoreExt = "ChainRulesCore"
-SimpleNonlinearSolvePolyesterForwardDiffExt = "PolyesterForwardDiff"
 SimpleNonlinearSolveReverseDiffExt = "ReverseDiff"
 SimpleNonlinearSolveStaticArraysExt = "StaticArrays"
 SimpleNonlinearSolveTrackerExt = "Tracker"
@@ -45,6 +44,7 @@ ChainRulesCore = "1.22"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149"
 DiffResults = "1.1"
+DifferentiationInterface = "0.4"
 ExplicitImports = "1.5.0"
 FastClosures = "0.3.2"
 FiniteDiff = "2.22"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
deleted file mode 100644
index ac898ac16..000000000
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl
+++ /dev/null
@@ -1,20 +0,0 @@
-module SimpleNonlinearSolvePolyesterForwardDiffExt
-
-using PolyesterForwardDiff: PolyesterForwardDiff
-using SimpleNonlinearSolve: SimpleNonlinearSolve
-
-@inline SimpleNonlinearSolve.__is_extension_loaded(::Val{:PolyesterForwardDiff}) = true
-
-@inline function SimpleNonlinearSolve.__polyester_forwarddiff_jacobian!(
-        f!::F, y, J, x, chunksize) where {F}
-    PolyesterForwardDiff.threaded_jacobian!(f!, y, J, x, chunksize)
-    return J
-end
-
-@inline function SimpleNonlinearSolve.__polyester_forwarddiff_jacobian!(
-        f::F, J, x, chunksize) where {F}
-    PolyesterForwardDiff.threaded_jacobian!(f, J, x, chunksize)
-    return J
-end
-
-end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 1ff66b995..a024f069e 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -3,13 +3,15 @@ module SimpleNonlinearSolve
 using PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidations
 
 @recompile_invalidations begin
-    using ADTypes: ADTypes, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
+    using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
+                   AutoPolyesterForwardDiff
     using ArrayInterface: ArrayInterface
     using ConcreteStructs: @concrete
     using DiffEqBase: DiffEqBase, AbstractNonlinearTerminationMode,
                       AbstractSafeNonlinearTerminationMode,
                       AbstractSafeBestNonlinearTerminationMode, AbsNormTerminationMode,
                       NONLINEARSOLVE_DEFAULT_NORM
+    using DifferentiationInterface: DifferentiationInterface
     using DiffResults: DiffResults
     using FastClosures: @closure
     using FiniteDiff: FiniteDiff
@@ -25,6 +27,8 @@ using PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidati
     using StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, Size
 end
 
+const DI = DifferentiationInterface
+
 @reexport using SciMLBase
 
 abstract type AbstractSimpleNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm end
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index e550258ef..5ff5eea40 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -12,8 +12,9 @@ A low-overhead implementation of Halley's Method.
 
 ### Keyword Arguments
 
-  - `autodiff`: determines the backend used for the Hessian. Defaults to `nothing`. Valid
-    choices are `AutoForwardDiff()` or `AutoFiniteDiff()`.
+  - `autodiff`: determines the backend used for the Hessian. Defaults to `nothing` (i.e.
+    automatic backend selection). Valid choices include backends from
+    `DifferentiationInterface.jl`.
 
 !!! warning
 
@@ -26,13 +27,11 @@ end
 function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
         alias_u0 = false, termination_condition = nothing, kwargs...)
-    isinplace(prob) &&
-        error("SimpleHalley currently only supports out-of-place nonlinear problems")
-
     x = __maybe_unaliased(prob.u0, alias_u0)
     fx = _get_fx(prob, x)
     T = eltype(x)
 
+    f = __fixed_parameter_function(prob)
     autodiff = __get_concrete_autodiff(prob, alg.autodiff)
     abstol, reltol, tc_cache = init_termination_cache(
         prob, abstol, reltol, fx, x, termination_condition)
@@ -51,7 +50,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
 
     for i in 1:maxiters
         # Hessian Computation is unfortunately type unstable
-        fx, dfx, d2fx = compute_jacobian_and_hessian(autodiff, prob, fx, x)
+        fx, dfx, d2fx = compute_jacobian_and_hessian(autodiff, prob, f, fx, x)
         setindex_trait(x) === CannotSetindex() && (A = dfx)
 
         # Factorize Once and Reuse
@@ -78,9 +77,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
         cᵢ = _restructure(cᵢ, cᵢ_)
 
         if i == 1
-            if iszero(fx)
+            iszero(fx) &&
                 return build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
-            end
         else
             # Termination Checks
             tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
index 7b419ce99..ca6864b28 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
@@ -13,9 +13,9 @@ and static array problems.
 
 ### Keyword Arguments
 
-  - `autodiff`: determines the backend used for the Jacobian. Defaults to
-    `nothing`. Valid choices are `AutoPolyesterForwardDiff()`, `AutoForwardDiff()` or
-    `AutoFiniteDiff()`.
+  - `autodiff`: determines the backend used for the Jacobian. Defaults to  `nothing` (i.e.
+    automatic backend selection). Valid choices include jacobian backends from
+    `DifferentiationInterface.jl`.
 """
 @kwdef @concrete struct SimpleNewtonRaphson <: AbstractNewtonAlgorithm
     autodiff = nothing
@@ -30,13 +30,14 @@ function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresPr
     fx = _get_fx(prob, x)
     autodiff = __get_concrete_autodiff(prob, alg.autodiff)
     @bb xo = copy(x)
-    J, jac_cache = jacobian_cache(autodiff, prob.f, fx, x, prob.p)
+    f = __fixed_parameter_function(prob)
+    J, jac_cache = jacobian_cache(autodiff, prob, f, fx, x)
 
     abstol, reltol, tc_cache = init_termination_cache(
         prob, abstol, reltol, fx, x, termination_condition)
 
     for i in 1:maxiters
-        fx, dfx = value_and_jacobian(autodiff, prob.f, fx, x, prob.p, jac_cache; J)
+        fx, dfx = value_and_jacobian(autodiff, prob, f, fx, x, jac_cache; J)
 
         if i == 1
             iszero(fx) && build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index a19cf2c2d..6ff263ecd 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -10,9 +10,9 @@ scalar and static array problems.
 
 ### Keyword Arguments
 
-  - `autodiff`: determines the backend used for the Jacobian. Defaults to
-    `nothing`. Valid choices are `AutoPolyesterForwardDiff()`, `AutoForwardDiff()` or
-    `AutoFiniteDiff()`.
+  - `autodiff`: determines the backend used for the Jacobian. Defaults to `nothing` (i.e.
+    automatic backend selection). Valid choices include jacobian backends from
+    `DifferentiationInterface.jl`.
   - `max_trust_radius`: the maximum radius of the trust region. Defaults to
     `max(norm(f(u0)), maximum(u0) - minimum(u0))`.
   - `initial_trust_radius`: the initial trust region radius. Defaults to
@@ -85,8 +85,9 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
     fx = _get_fx(prob, x)
     norm_fx = norm(fx)
     @bb xo = copy(x)
-    J, jac_cache = jacobian_cache(autodiff, prob.f, fx, x, prob.p)
-    fx, ∇f = value_and_jacobian(autodiff, prob.f, fx, x, prob.p, jac_cache; J)
+    f = __fixed_parameter_function(prob)
+    J, jac_cache = jacobian_cache(autodiff, prob, f, fx, x)
+    fx, ∇f = value_and_jacobian(autodiff, prob, f, fx, x, jac_cache; J)
 
     abstol, reltol, tc_cache = init_termination_cache(
         prob, abstol, reltol, fx, x, termination_condition)
@@ -144,7 +145,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args.
             # Take the step.
             @bb @. xo = x
 
-            fx, ∇f = value_and_jacobian(autodiff, prob.f, fx, x, prob.p, jac_cache; J)
+            fx, ∇f = value_and_jacobian(autodiff, prob, f, fx, x, jac_cache; J)
 
             # Update the trust region radius.
             if !_unwrap_val(alg.nlsolve_update_rule) && r > η₃
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 333e54d3b..ae380d7be 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -1,9 +1,4 @@
-struct SimpleNonlinearSolveTag end
-
-function ForwardDiff.checktag(::Type{<:ForwardDiff.Tag{<:SimpleNonlinearSolveTag, <:T}},
-        f::F, x::AbstractArray{T}) where {T, F}
-    return true
-end
+struct HasAnalyticJacobian end
 
 """
     __prevfloat_tdir(x, x0, x1)
@@ -26,203 +21,63 @@ Return the maximum of `a` and `b` if `x1 > x0`, otherwise return the minimum.
 """
 __max_tdir(a, b, x0, x1) = ifelse(x1 > x0, max(a, b), min(a, b))
 
-__standard_tag(::Nothing, x) = ForwardDiff.Tag(SimpleNonlinearSolveTag(), eltype(x))
-__standard_tag(tag::ForwardDiff.Tag, _) = tag
-__standard_tag(tag, x) = ForwardDiff.Tag(tag, eltype(x))
-
-__pick_forwarddiff_chunk(x) = ForwardDiff.Chunk(length(x))
-function __pick_forwarddiff_chunk(x::StaticArray)
-    L = prod(Size(x))
-    if L ≤ ForwardDiff.DEFAULT_CHUNK_THRESHOLD
-        return ForwardDiff.Chunk{L}()
-    else
-        return ForwardDiff.Chunk{ForwardDiff.DEFAULT_CHUNK_THRESHOLD}()
-    end
-end
-
-function __get_jacobian_config(ad::AutoForwardDiff{CS}, f::F, x) where {F, CS}
-    ck = (CS === nothing || CS ≤ 0) ? __pick_forwarddiff_chunk(x) : ForwardDiff.Chunk{CS}()
-    tag = __standard_tag(ad.tag, x)
-    return __forwarddiff_jacobian_config(f, x, ck, tag)
-end
-function __get_jacobian_config(ad::AutoForwardDiff{CS}, f!::F, y, x) where {F, CS}
-    ck = (CS === nothing || CS ≤ 0) ? __pick_forwarddiff_chunk(x) : ForwardDiff.Chunk{CS}()
-    tag = __standard_tag(ad.tag, x)
-    return ForwardDiff.JacobianConfig(f!, y, x, ck, tag)
-end
-
-function __forwarddiff_jacobian_config(f::F, x, ck::ForwardDiff.Chunk, tag) where {F}
-    return ForwardDiff.JacobianConfig(f, x, ck, tag)
-end
-function __forwarddiff_jacobian_config(
-        f::F, x::SArray, ck::ForwardDiff.Chunk{N}, tag) where {F, N}
-    seeds = ForwardDiff.construct_seeds(ForwardDiff.Partials{N, eltype(x)})
-    duals = ForwardDiff.Dual{typeof(tag), eltype(x), N}.(x)
-    return ForwardDiff.JacobianConfig{typeof(tag), eltype(x), N, typeof(duals)}(
-        seeds, duals)
+function __fixed_parameter_function(prob::NonlinearProblem)
+    isinplace(prob) && return @closure (du, u) -> prob.f(du, u, prob.p)
+    return Base.Fix2(prob.f, prob.p)
 end
 
-function __get_jacobian_config(ad::AutoPolyesterForwardDiff{CS}, args...) where {CS}
-    x = last(args)
-    return (CS === nothing || CS ≤ 0) ? __pick_forwarddiff_chunk(x) :
-           ForwardDiff.Chunk{CS}()
-end
+function value_and_jacobian(
+        ad, prob::NonlinearProblem, f::F, y, x, cache; J = nothing) where {F}
+    x isa Number && return DI.value_and_derivative(f, ad, x, cache)
 
-"""
-    value_and_jacobian(ad, f, y, x, p, cache; J = nothing)
-
-Compute `f(x), d/dx f(x)` in the most efficient way based on `ad`. None of the arguments
-except `cache` (& `J` if not nothing) are mutated.
-"""
-function value_and_jacobian(ad, f::F, y, x::X, p, cache; J = nothing) where {F, X}
-    if isinplace(f)
-        _f = (du, u) -> f(du, u, p)
-        if SciMLBase.has_jac(f)
-            f.jac(J, x, p)
-            _f(y, x)
-            return y, J
-        elseif ad isa AutoForwardDiff
-            res = DiffResults.DiffResult(y, J)
-            ForwardDiff.jacobian!(res, _f, y, x, cache)
-            return DiffResults.value(res), DiffResults.jacobian(res)
-        elseif ad isa AutoFiniteDiff
-            FiniteDiff.finite_difference_jacobian!(J, _f, x, cache)
-            _f(y, x)
-            return y, J
-        elseif ad isa AutoPolyesterForwardDiff
-            __polyester_forwarddiff_jacobian!(_f, y, J, x, cache)
-            return y, J
+    if isinplace(prob)
+        if cache isa HasAnalyticJacobian
+            prob.f.jac(J, x, p)
+            f(y, x)
         else
-            throw(ArgumentError("Unsupported AD method: $(ad)"))
+            DI.jacobian!(f, y, J, ad, x, cache)
         end
+        return y, J
     else
-        _f = Base.Fix2(f, p)
-        if SciMLBase.has_jac(f)
-            return _f(x), f.jac(x, p)
-        elseif ad isa AutoForwardDiff
-            if ArrayInterface.can_setindex(x)
-                res = DiffResults.DiffResult(y, J)
-                ForwardDiff.jacobian!(res, _f, x, cache)
-                return DiffResults.value(res), DiffResults.jacobian(res)
-            else
-                J_fd = ForwardDiff.jacobian(_f, x, cache)
-                return _f(x), J_fd
-            end
-        elseif ad isa AutoFiniteDiff
-            J_fd = FiniteDiff.finite_difference_jacobian(_f, x, cache)
-            return _f(x), J_fd
-        elseif ad isa AutoPolyesterForwardDiff
-            __polyester_forwarddiff_jacobian!(_f, J, x, cache)
-            return _f(x), J
-        else
-            throw(ArgumentError("Unsupported AD method: $(ad)"))
-        end
+        cache isa HasAnalyticJacobian && return f(x), prob.f.jac(x, prob.p)
+        J === nothing && return DI.value_and_jacobian(f, ad, x, cache)
+        y, _ = DI.value_and_jacobian!(f, J, ad, x, cache)
+        return y, J
     end
 end
 
-# Declare functions
-function __polyester_forwarddiff_jacobian! end
-
-function value_and_jacobian(ad, f::F, y, x::Number, p, cache; J = nothing) where {F}
-    if SciMLBase.has_jac(f)
-        return f(x, p), f.jac(x, p)
-    elseif ad isa AutoForwardDiff
-        T = typeof(__standard_tag(ad.tag, x))
-        out = f(ForwardDiff.Dual{T}(x, one(x)), p)
-        return ForwardDiff.value(out), ForwardDiff.extract_derivative(T, out)
-    elseif ad isa AutoPolyesterForwardDiff
-        # Just use ForwardDiff
-        T = typeof(__standard_tag(nothing, x))
-        out = f(ForwardDiff.Dual{T}(x, one(x)), p)
-        return ForwardDiff.value(out), ForwardDiff.extract_derivative(T, out)
-    elseif ad isa AutoFiniteDiff
-        _f = Base.Fix2(f, p)
-        return _f(x), FiniteDiff.finite_difference_derivative(_f, x, ad.fdtype)
-    else
-        throw(ArgumentError("Unsupported AD method: $(ad)"))
-    end
-end
+function jacobian_cache(ad, prob::NonlinearProblem, f::F, y, x) where {F}
+    x isa Number && return (nothing, DI.prepare_derivative(f, ad, x))
 
-"""
-    jacobian_cache(ad, f, y, x, p) --> J, cache
-
-Returns a Jacobian Matrix and a cache for the Jacobian computation.
-"""
-function jacobian_cache(ad, f::F, y, x::X, p) where {F, X <: AbstractArray}
-    if isinplace(f)
-        _f = (du, u) -> f(du, u, p)
+    if isinplace(prob)
         J = similar(y, length(y), length(x))
-        if SciMLBase.has_jac(f)
-            return J, nothing
-        elseif ad isa AutoForwardDiff || ad isa AutoPolyesterForwardDiff
-            return J, __get_jacobian_config(ad, _f, y, x)
-        elseif ad isa AutoFiniteDiff
-            return J, FiniteDiff.JacobianCache(copy(x), copy(y), copy(y), ad.fdtype)
-        else
-            throw(ArgumentError("Unsupported AD method: $(ad)"))
-        end
+        SciMLBase.has_jac(prob.f) && return J, HasAnalyticJacobian()
+        return J, DI.prepare_jacobian(f, y, ad, x)
     else
-        _f = Base.Fix2(f, p)
-        if SciMLBase.has_jac(f)
-            return nothing, nothing
-        elseif ad isa AutoForwardDiff
-            J = ArrayInterface.can_setindex(x) ? similar(y, length(y), length(x)) : nothing
-            return J, __get_jacobian_config(ad, _f, x)
-        elseif ad isa AutoPolyesterForwardDiff
-            @assert ArrayInterface.can_setindex(x) "PolyesterForwardDiff requires mutable inputs. Use AutoForwardDiff instead."
-            J = similar(y, length(y), length(x))
-            return J, __get_jacobian_config(ad, _f, x)
-        elseif ad isa AutoFiniteDiff
-            return nothing, FiniteDiff.JacobianCache(copy(x), copy(y), copy(y), ad.fdtype)
-        else
-            throw(ArgumentError("Unsupported AD method: $(ad)"))
-        end
+        SciMLBase.has_jac(prob.f) && return nothing, HasAnalyticJacobian()
+        J = ArrayInterface.can_setindex(x) ? similar(y, length(y), length(x)) : nothing
+        return J, DI.prepare_jacobian(f, ad, x)
     end
 end
 
-jacobian_cache(ad, f::F, y, x::Number, p) where {F} = nothing, nothing
-
-function compute_jacobian_and_hessian(ad::AutoForwardDiff, prob, _, x::Number)
-    fx = prob.f(x, prob.p)
-    J_fn = Base.Fix1(ForwardDiff.derivative, Base.Fix2(prob.f, prob.p))
-    dfx = J_fn(x)
-    d2fx = ForwardDiff.derivative(J_fn, x)
-    return fx, dfx, d2fx
-end
-
-function compute_jacobian_and_hessian(ad::AutoForwardDiff, prob, fx, x)
-    if isinplace(prob)
-        error("Inplace version for Nested ForwardDiff Not Implemented Yet!")
-    else
-        f = Base.Fix2(prob.f, prob.p)
-        fx = f(x)
-        J_fn = Base.Fix1(ForwardDiff.jacobian, f)
-        dfx = J_fn(x)
-        d2fx = ForwardDiff.jacobian(J_fn, x)
-        return fx, dfx, d2fx
+function compute_jacobian_and_hessian(ad, prob::NonlinearProblem, f::F, y, x) where {F}
+    if x isa Number
+        df = @closure x -> DI.derivative(f, ad, x)
+        return f(x), df(x), DI.derivative(df, ad, x)
     end
-end
-
-function compute_jacobian_and_hessian(ad::AutoFiniteDiff, prob, _, x::Number)
-    fx = prob.f(x, prob.p)
-    J_fn = x -> FiniteDiff.finite_difference_derivative(
-        Base.Fix2(prob.f, prob.p), x, ad.fdtype)
-    dfx = J_fn(x)
-    d2fx = FiniteDiff.finite_difference_derivative(J_fn, x, ad.fdtype)
-    return fx, dfx, d2fx
-end
 
-function compute_jacobian_and_hessian(ad::AutoFiniteDiff, prob, fx, x)
     if isinplace(prob)
-        error("Inplace version for Nested FiniteDiff Not Implemented Yet!")
-    else
-        f = Base.Fix2(prob.f, prob.p)
-        fx = f(x)
-        J_fn = x -> FiniteDiff.finite_difference_jacobian(f, x, ad.fdtype)
-        dfx = J_fn(x)
-        d2fx = FiniteDiff.finite_difference_jacobian(J_fn, x, ad.fdtype)
-        return fx, dfx, d2fx
+        df = @closure x -> begin
+            res = similar(y, promote_type(eltype(y), eltype(x)))
+            return DI.jacobian(f, res, ad, x)
+        end
+        J, H = DI.value_and_jacobian(df, ad, x)
+        f(y, x)
+        return y, J, H
     end
+
+    df = @closure x -> DI.jacobian(f, ad, x)
+    return f(x), df(x), DI.jacobian(df, ad, x)
 end
 
 __init_identity_jacobian(u::Number, fu, α = true) = oftype(u, α)
@@ -360,10 +215,19 @@ end
 end
 
 # Decide which AD backend to use
-@inline __get_concrete_autodiff(prob, ad::ADTypes.AbstractADType; kwargs...) = ad
+@inline __get_concrete_autodiff(prob, ad::AbstractADType; kwargs...) = ad
+@inline function __get_concrete_autodiff(prob, ad::AutoForwardDiff{nothing}; kwargs...)
+    return AutoForwardDiff(; chunksize = ForwardDiff.pickchunksize(length(prob.u0)), ad.tag)
+end
+@inline function __get_concrete_autodiff(
+        prob, ad::AutoPolyesterForwardDiff{nothing}; kwargs...)
+    return AutoPolyesterForwardDiff(;
+        chunksize = ForwardDiff.pickchunksize(length(prob.u0)), ad.tag)
+end
 @inline function __get_concrete_autodiff(prob, ::Nothing; kwargs...)
-    return ifelse(
-        ForwardDiff.can_dual(eltype(prob.u0)), AutoForwardDiff(), AutoFiniteDiff())
+    return ifelse(ForwardDiff.can_dual(eltype(prob.u0)),
+        AutoForwardDiff(; chunksize = ForwardDiff.pickchunksize(length(prob.u0))),
+        AutoFiniteDiff())
 end
 
 @inline __reshape(x::Number, args...) = x

From 301f8741ec64dfe7e5fb7be0bba2b7701cd3445e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 16:38:12 -0700
Subject: [PATCH 417/700] Add bigfloat tests

---
 Project.toml                   |  2 +-
 test/misc/exotic_type_tests.jl | 27 +++++++++++++++++++++++++++
 2 files changed, 28 insertions(+), 1 deletion(-)
 create mode 100644 test/misc/exotic_type_tests.jl

diff --git a/Project.toml b/Project.toml
index 35fdb7046..27655a6af 100644
--- a/Project.toml
+++ b/Project.toml
@@ -80,7 +80,7 @@ LinearAlgebra = "1.10"
 LinearSolve = "2.30"
 MINPACK = "1.2"
 MaybeInplace = "0.1.3"
-ModelingToolkit = "9.13.0"
+ModelingToolkit = "9.15.0"
 NLSolvers = "0.5"
 NLsolve = "4.5"
 NaNMath = "1"
diff --git a/test/misc/exotic_type_tests.jl b/test/misc/exotic_type_tests.jl
new file mode 100644
index 000000000..57a9c28ed
--- /dev/null
+++ b/test/misc/exotic_type_tests.jl
@@ -0,0 +1,27 @@
+# File for different types of exotic types
+@testsetup module NonlinearSolveExoticTypeTests
+using NonlinearSolve
+
+fn_iip = NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p)
+fn_oop = NonlinearFunction{false}((u, p) -> u .* u .- p)
+
+u0 = BigFloat[1.0, 1.0, 1.0]
+prob_iip_bf = NonlinearProblem{true}(fn_iip, u0, BigFloat(2))
+prob_oop_bf = NonlinearProblem{false}(fn_oop, u0, BigFloat(2))
+
+export fn_iip, fn_oop, u0, prob_iip_bf, prob_oop_bf
+end
+
+@testitem "BigFloat Support" tags=[:misc] setup=[NonlinearSolveExoticTypeTests] begin
+    using NonlinearSolve, LinearAlgebra
+
+    for alg in [NewtonRaphson(), Broyden(), Klement(), DFSane(), TrustRegion()]
+        sol = solve(prob_oop_bf, alg)
+        @test norm(sol.resid, Inf) < 1e-6
+        @test SciMLBase.successful_retcode(sol.retcode)
+
+        sol = solve(prob_iip_bf, alg)
+        @test norm(sol.resid, Inf) < 1e-6
+        @test SciMLBase.successful_retcode(sol.retcode)
+    end
+end

From 3c32525d5a4ff382bef3091a640acbd484d6b904 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 17:31:06 -0700
Subject: [PATCH 418/700] Clean up AD

---
 lib/SimpleNonlinearSolve/Project.toml         |  2 +-
 .../src/SimpleNonlinearSolve.jl               |  8 +-
 lib/SimpleNonlinearSolve/src/ad.jl            | 92 +++++++------------
 .../src/nlsolve/halley.jl                     |  6 +-
 .../src/nlsolve/lbroyden.jl                   |  6 +-
 lib/SimpleNonlinearSolve/src/utils.jl         | 32 +++++--
 6 files changed, 68 insertions(+), 78 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 5284b3ed4..a7aa31f82 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -47,7 +47,7 @@ DiffResults = "1.1"
 DifferentiationInterface = "0.4"
 ExplicitImports = "1.5.0"
 FastClosures = "0.3.2"
-FiniteDiff = "2.22"
+FiniteDiff = "2.23.1"
 ForwardDiff = "0.10.36"
 LinearAlgebra = "1.10"
 LinearSolve = "2.30"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index a024f069e..04a32c969 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -20,10 +20,10 @@ using PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidati
                          mul!, norm, transpose
     using MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
     using Reexport: @reexport
-    using SciMLBase: SciMLBase, IntervalNonlinearProblem, NonlinearFunction,
-                     NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode, init,
-                     remake, solve, AbstractNonlinearAlgorithm, build_solution, isinplace,
-                     _unwrap_val
+    using SciMLBase: SciMLBase, AbstractNonlinearProblem, IntervalNonlinearProblem,
+                     NonlinearFunction, NonlinearLeastSquaresProblem, NonlinearProblem,
+                     ReturnCode, init, remake, solve, AbstractNonlinearAlgorithm,
+                     build_solution, isinplace, _unwrap_val
     using StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, Size
 end
 
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index f42651bfe..ffae7cc27 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -1,25 +1,15 @@
-function SciMLBase.solve(
-        prob::NonlinearProblem{<:Union{Number, <:AbstractArray}, iip,
-            <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
-        alg::AbstractSimpleNonlinearSolveAlgorithm,
-        args...;
-        kwargs...) where {T, V, P, iip}
-    sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
-    dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
-    return SciMLBase.build_solution(
-        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
-end
-
-function SciMLBase.solve(
-        prob::NonlinearLeastSquaresProblem{
-            <:AbstractArray, iip, <:Union{<:AbstractArray{<:Dual{T, V, P}}}},
-        alg::AbstractSimpleNonlinearSolveAlgorithm,
-        args...;
-        kwargs...) where {T, V, P, iip}
-    sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
-    dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
-    return SciMLBase.build_solution(
-        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+for pType in (NonlinearProblem, NonlinearLeastSquaresProblem)
+    @eval function SciMLBase.solve(
+            prob::$(pType){<:Union{Number, <:AbstractArray}, iip,
+                <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
+            alg::AbstractSimpleNonlinearSolveAlgorithm,
+            args...;
+            kwargs...) where {T, V, P, iip}
+        sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
+        dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
+        return SciMLBase.build_solution(
+            prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+    end
 end
 
 for algType in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
@@ -47,8 +37,7 @@ function __nlsolve_ad(
         tspan = value.(prob.tspan)
         newprob = IntervalNonlinearProblem(prob.f, tspan, p; prob.kwargs...)
     else
-        u0 = value(prob.u0)
-        newprob = NonlinearProblem(prob.f, u0, p; prob.kwargs...)
+        newprob = remake(prob; p, u0 = value(prob.u0))
     end
 
     sol = solve(newprob, alg, args...; kwargs...)
@@ -73,12 +62,8 @@ function __nlsolve_ad(
 end
 
 function __nlsolve_ad(prob::NonlinearLeastSquaresProblem, alg, args...; kwargs...)
-    p = value(prob.p)
-    u0 = value(prob.u0)
-    newprob = NonlinearLeastSquaresProblem(prob.f, u0, p; prob.kwargs...)
-
+    newprob = remake(prob; p = value(prob.p), u0 = value(prob.u0))
     sol = solve(newprob, alg, args...; kwargs...)
-
     uu = sol.u
 
     # First check for custom `vjp` then custom `Jacobian` and if nothing is provided use
@@ -86,7 +71,7 @@ function __nlsolve_ad(prob::NonlinearLeastSquaresProblem, alg, args...; kwargs..
     if SciMLBase.has_vjp(prob.f)
         if isinplace(prob)
             _F = @closure (du, u, p) -> begin
-                resid = similar(du, length(sol.resid))
+                resid = __similar(du, length(sol.resid))
                 prob.f(resid, u, p)
                 prob.f.vjp(du, resid, u, p)
                 du .*= 2
@@ -101,9 +86,9 @@ function __nlsolve_ad(prob::NonlinearLeastSquaresProblem, alg, args...; kwargs..
     elseif SciMLBase.has_jac(prob.f)
         if isinplace(prob)
             _F = @closure (du, u, p) -> begin
-                J = similar(du, length(sol.resid), length(u))
+                J = __similar(du, length(sol.resid), length(u))
                 prob.f.jac(J, u, p)
-                resid = similar(du, length(sol.resid))
+                resid = __similar(du, length(sol.resid))
                 prob.f(resid, u, p)
                 mul!(reshape(du, 1, :), vec(resid)', J, 2, false)
                 return nothing
@@ -116,35 +101,30 @@ function __nlsolve_ad(prob::NonlinearLeastSquaresProblem, alg, args...; kwargs..
     else
         if isinplace(prob)
             _F = @closure (du, u, p) -> begin
-                resid = similar(du, length(sol.resid))
-                res = DiffResults.DiffResult(
-                    resid, similar(du, length(sol.resid), length(u)))
                 _f = @closure (du, u) -> prob.f(du, u, p)
-                ForwardDiff.jacobian!(res, _f, resid, u)
-                mul!(reshape(du, 1, :), vec(DiffResults.value(res))',
-                    DiffResults.jacobian(res), 2, false)
+                resid = __similar(du, length(sol.resid))
+                v, J = DI.value_and_jacobian(_f, resid, AutoForwardDiff(), u)
+                mul!(reshape(du, 1, :), vec(v)', J, 2, false)
                 return nothing
             end
         else
             # For small problems, nesting ForwardDiff is actually quite fast
+            _f = Base.Fix2(prob.f, newprob.p)
             if __is_extension_loaded(Val(:Zygote)) && (length(uu) + length(sol.resid) ≥ 50)
-                _F = @closure (u, p) -> __zygote_compute_nlls_vjp(prob.f, u, p)
+                # TODO: Remove once DI has the value_and_pullback_split defined
+                _F = @closure (u, p) -> __zygote_compute_nlls_vjp(_f, u, p)
             else
                 _F = @closure (u, p) -> begin
-                    T = promote_type(eltype(u), eltype(p))
-                    res = DiffResults.DiffResult(similar(u, T, size(sol.resid)),
-                        similar(u, T, length(sol.resid), length(u)))
-                    ForwardDiff.jacobian!(res, Base.Fix2(prob.f, p), u)
-                    return reshape(
-                        2 .* vec(DiffResults.value(res))' * DiffResults.jacobian(res),
-                        size(u))
+                    _f = Base.Fix2(prob.f, p)
+                    v, J = DI.value_and_jacobian(_f, AutoForwardDiff(), u)
+                    return reshape(2 .* vec(v)' * J, size(u))
                 end
             end
         end
     end
 
-    f_p = __nlsolve_∂f_∂p(prob, _F, uu, p)
-    f_x = __nlsolve_∂f_∂u(prob, _F, uu, p)
+    f_p = __nlsolve_∂f_∂p(prob, _F, uu, newprob.p)
+    f_x = __nlsolve_∂f_∂u(prob, _F, uu, newprob.p)
 
     z_arr = -f_x \ f_p
 
@@ -152,7 +132,7 @@ function __nlsolve_ad(prob::NonlinearLeastSquaresProblem, alg, args...; kwargs..
     sumfun = ((z, p),) -> map(zᵢ -> zᵢ * ForwardDiff.partials(p), z)
     if uu isa Number
         partials = sum(sumfun, zip(z_arr, pp))
-    elseif p isa Number
+    elseif pp isa Number
         partials = sumfun((z_arr, pp))
     else
         partials = sum(sumfun, zip(eachcol(z_arr), pp))
@@ -164,7 +144,7 @@ end
 @inline function __nlsolve_∂f_∂p(prob, f::F, u, p) where {F}
     if isinplace(prob)
         __f = p -> begin
-            du = similar(u, promote_type(eltype(u), eltype(p)))
+            du = __similar(u, promote_type(eltype(u), eltype(p)))
             f(du, u, p)
             return du
         end
@@ -182,16 +162,12 @@ end
 
 @inline function __nlsolve_∂f_∂u(prob, f::F, u, p) where {F}
     if isinplace(prob)
-        du = similar(u)
-        __f = (du, u) -> f(du, u, p)
-        ForwardDiff.jacobian(__f, du, u)
+        __f = @closure (du, u) -> f(du, u, p)
+        return ForwardDiff.jacobian(__f, __similar(u), u)
     else
         __f = Base.Fix2(f, p)
-        if u isa Number
-            return ForwardDiff.derivative(__f, u)
-        else
-            return ForwardDiff.jacobian(__f, u)
-        end
+        u isa Number && return ForwardDiff.derivative(__f, u)
+        return ForwardDiff.jacobian(__f, u)
     end
 end
 
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index 5ff5eea40..d3fe1cdd1 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -39,9 +39,9 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
     @bb xo = copy(x)
 
     if setindex_trait(x) === CanSetindex()
-        A = similar(x, length(x), length(x))
-        Aaᵢ = similar(x, length(x))
-        cᵢ = similar(x)
+        A = __similar(x, length(x), length(x))
+        Aaᵢ = __similar(x, length(x))
+        cᵢ = __similar(x)
     else
         A = x
         Aaᵢ = x
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index b34d4cddf..1eeda4fa6 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -272,7 +272,7 @@ end
     return :(return SVector{$N, $T}(($(getcalls...))))
 end
 
-__lbroyden_threshold_cache(x, ::Val{threshold}) where {threshold} = similar(x, threshold)
+__lbroyden_threshold_cache(x, ::Val{threshold}) where {threshold} = __similar(x, threshold)
 function __lbroyden_threshold_cache(x::StaticArray, ::Val{threshold}) where {threshold}
     return zeros(MArray{Tuple{threshold}, eltype(x)})
 end
@@ -298,7 +298,7 @@ end
     end
 end
 function __init_low_rank_jacobian(u, fu, ::Val{threshold}) where {threshold}
-    Vᵀ = similar(u, threshold, length(u))
-    U = similar(u, length(fu), threshold)
+    Vᵀ = __similar(u, threshold, length(u))
+    U = __similar(u, length(fu), threshold)
     return U, Vᵀ
 end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index ae380d7be..0bf027f6f 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -21,13 +21,13 @@ Return the maximum of `a` and `b` if `x1 > x0`, otherwise return the minimum.
 """
 __max_tdir(a, b, x0, x1) = ifelse(x1 > x0, max(a, b), min(a, b))
 
-function __fixed_parameter_function(prob::NonlinearProblem)
+function __fixed_parameter_function(prob::AbstractNonlinearProblem)
     isinplace(prob) && return @closure (du, u) -> prob.f(du, u, prob.p)
     return Base.Fix2(prob.f, prob.p)
 end
 
 function value_and_jacobian(
-        ad, prob::NonlinearProblem, f::F, y, x, cache; J = nothing) where {F}
+        ad, prob::AbstractNonlinearProblem, f::F, y, x, cache; J = nothing) where {F}
     x isa Number && return DI.value_and_derivative(f, ad, x, cache)
 
     if isinplace(prob)
@@ -46,21 +46,22 @@ function value_and_jacobian(
     end
 end
 
-function jacobian_cache(ad, prob::NonlinearProblem, f::F, y, x) where {F}
+function jacobian_cache(ad, prob::AbstractNonlinearProblem, f::F, y, x) where {F}
     x isa Number && return (nothing, DI.prepare_derivative(f, ad, x))
 
     if isinplace(prob)
-        J = similar(y, length(y), length(x))
+        J = __similar(y, length(y), length(x))
         SciMLBase.has_jac(prob.f) && return J, HasAnalyticJacobian()
         return J, DI.prepare_jacobian(f, y, ad, x)
     else
         SciMLBase.has_jac(prob.f) && return nothing, HasAnalyticJacobian()
-        J = ArrayInterface.can_setindex(x) ? similar(y, length(y), length(x)) : nothing
+        J = ArrayInterface.can_setindex(x) ? __similar(y, length(y), length(x)) : nothing
         return J, DI.prepare_jacobian(f, ad, x)
     end
 end
 
-function compute_jacobian_and_hessian(ad, prob::NonlinearProblem, f::F, y, x) where {F}
+function compute_jacobian_and_hessian(
+        ad, prob::AbstractNonlinearProblem, f::F, y, x) where {F}
     if x isa Number
         df = @closure x -> DI.derivative(f, ad, x)
         return f(x), df(x), DI.derivative(df, ad, x)
@@ -68,7 +69,7 @@ function compute_jacobian_and_hessian(ad, prob::NonlinearProblem, f::F, y, x) wh
 
     if isinplace(prob)
         df = @closure x -> begin
-            res = similar(y, promote_type(eltype(y), eltype(x)))
+            res = __similar(y, promote_type(eltype(y), eltype(x)))
             return DI.jacobian(f, res, ad, x)
         end
         J, H = DI.value_and_jacobian(df, ad, x)
@@ -83,7 +84,7 @@ end
 __init_identity_jacobian(u::Number, fu, α = true) = oftype(u, α)
 __init_identity_jacobian!!(J::Number) = one(J)
 function __init_identity_jacobian(u, fu, α = true)
-    J = similar(u, promote_type(eltype(u), eltype(fu)), length(fu), length(u))
+    J = __similar(u, promote_type(eltype(u), eltype(fu)), length(fu), length(u))
     fill!(J, zero(eltype(J)))
     J[diagind(J)] .= eltype(J)(α)
     return J
@@ -129,7 +130,7 @@ end
             T = eltype(x)
             return T.(f.resid_prototype)
         else
-            fx = similar(x)
+            fx = __similar(x)
             f(fx, x, p)
             return fx
         end
@@ -242,3 +243,16 @@ end
 
 # Extension
 function __zygote_compute_nlls_vjp end
+
+function __similar(x, args...; kwargs...)
+    y = similar(x, args...; kwargs...)
+    return __init_bigfloat_array!!(y)
+end
+
+function __init_bigfloat_array!!(x)
+    if ArrayInterface.can_setindex(x)
+        eltype(x) <: BigFloat && fill!(x, BigFloat(0))
+        return x
+    end
+    return x
+end

From 86917a522581ae49d12f0273b100703452b7c25e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 18:29:32 -0700
Subject: [PATCH 419/700] Remove the static arrays special casing

---
 lib/SimpleNonlinearSolve/Project.toml             | 10 +++++-----
 .../ext/SimpleNonlinearSolveStaticArraysExt.jl    |  7 -------
 .../src/SimpleNonlinearSolve.jl                   |  1 +
 lib/SimpleNonlinearSolve/src/ad.jl                |  6 ++++--
 lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl    | 15 +++++++++------
 lib/SimpleNonlinearSolve/src/utils.jl             | 14 +++++++-------
 .../test/core/rootfind_tests.jl                   |  9 ++++-----
 7 files changed, 30 insertions(+), 32 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveStaticArraysExt.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index a7aa31f82..1d9cc13ab 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -18,19 +18,18 @@ MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [weakdeps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
-StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [extensions]
 SimpleNonlinearSolveChainRulesCoreExt = "ChainRulesCore"
 SimpleNonlinearSolveReverseDiffExt = "ReverseDiff"
-SimpleNonlinearSolveStaticArraysExt = "StaticArrays"
 SimpleNonlinearSolveTrackerExt = "Tracker"
 SimpleNonlinearSolveZygoteExt = "Zygote"
 
@@ -40,7 +39,7 @@ AllocCheck = "0.1.1"
 Aqua = "0.8"
 ArrayInterface = "7.9"
 CUDA = "5.2"
-ChainRulesCore = "1.22"
+ChainRulesCore = "1.23"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149"
 DiffResults = "1.1"
@@ -59,13 +58,14 @@ PrecompileTools = "1.2"
 Random = "1.10"
 ReTestItems = "1.23"
 Reexport = "1.2"
-ReverseDiff = "1.15"
+ReverseDiff = "1.15.3"
 SciMLBase = "2.37.0"
 SciMLSensitivity = "7.58"
+Setfield = "1.1.1"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4.2"
 Test = "1.10"
-Tracker = "0.2.32"
+Tracker = "0.2.33"
 Zygote = "0.6.69"
 julia = "1.10"
 
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveStaticArraysExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveStaticArraysExt.jl
deleted file mode 100644
index c865084ce..000000000
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveStaticArraysExt.jl
+++ /dev/null
@@ -1,7 +0,0 @@
-module SimpleNonlinearSolveStaticArraysExt
-
-using SimpleNonlinearSolve: SimpleNonlinearSolve
-
-@inline SimpleNonlinearSolve.__is_extension_loaded(::Val{:StaticArrays}) = true
-
-end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 04a32c969..eba6d991e 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -24,6 +24,7 @@ using PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidati
                      NonlinearFunction, NonlinearLeastSquaresProblem, NonlinearProblem,
                      ReturnCode, init, remake, solve, AbstractNonlinearAlgorithm,
                      build_solution, isinplace, _unwrap_val
+    using Setfield: @set!
     using StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, Size
 end
 
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index ffae7cc27..bb5afea8f 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -109,10 +109,12 @@ function __nlsolve_ad(prob::NonlinearLeastSquaresProblem, alg, args...; kwargs..
             end
         else
             # For small problems, nesting ForwardDiff is actually quite fast
-            _f = Base.Fix2(prob.f, newprob.p)
             if __is_extension_loaded(Val(:Zygote)) && (length(uu) + length(sol.resid) ≥ 50)
                 # TODO: Remove once DI has the value_and_pullback_split defined
-                _F = @closure (u, p) -> __zygote_compute_nlls_vjp(_f, u, p)
+                _F = @closure (u, p) -> begin
+                    _f = Base.Fix2(prob.f, p)
+                    return __zygote_compute_nlls_vjp(_f, u, p)
+                end
             else
                 _F = @closure (u, p) -> begin
                     _f = Base.Fix2(prob.f, p)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 7dd152277..835ee4b50 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -77,12 +77,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{M}, args...
     α_1 = one(T)
     f_1 = fx_norm
 
-    history_f_k = if x isa SArray ||
-                     (x isa Number && __is_extension_loaded(Val(:StaticArrays)))
-        ones(SVector{M, T}) * fx_norm
-    else
-        fill(fx_norm, M)
-    end
+    history_f_k = x isa SArray ? ones(SVector{M, T}) * fx_norm :
+                  __history_vec(fx_norm, Val(M))
 
     # Generate the cache
     @bb x_cache = similar(x)
@@ -150,6 +146,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{M}, args...
         # Store function value
         if history_f_k isa SVector
             history_f_k = Base.setindex(history_f_k, fx_norm_new, mod1(k, M))
+        elseif history_f_k isa NTuple
+            @set! history_f_k[mod1(k, M)] = fx_norm_new
         else
             history_f_k[mod1(k, M)] = fx_norm_new
         end
@@ -158,3 +156,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{M}, args...
 
     return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
 end
+
+@inline @generated function __history_vec(fx_norm, ::Val{M}) where {M}
+    M ≥ 11 && return :(fill(fx_norm, M)) # Julia can't specialize here
+    return :(ntuple(Returns(fx_norm), $(M)))
+end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 0bf027f6f..2e76a4b6e 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -32,16 +32,15 @@ function value_and_jacobian(
 
     if isinplace(prob)
         if cache isa HasAnalyticJacobian
-            prob.f.jac(J, x, p)
+            prob.f.jac(J, x, prob.p)
             f(y, x)
-        else
-            DI.jacobian!(f, y, J, ad, x, cache)
+            return y, J
         end
-        return y, J
+        return DI.value_and_jacobian!(f, y, J, ad, x, cache)
     else
         cache isa HasAnalyticJacobian && return f(x), prob.f.jac(x, prob.p)
         J === nothing && return DI.value_and_jacobian(f, ad, x, cache)
-        y, _ = DI.value_and_jacobian!(f, J, ad, x, cache)
+        y, J = DI.value_and_jacobian!(f, J, ad, x, cache)
         return y, J
     end
 end
@@ -63,8 +62,9 @@ end
 function compute_jacobian_and_hessian(
         ad, prob::AbstractNonlinearProblem, f::F, y, x) where {F}
     if x isa Number
-        df = @closure x -> DI.derivative(f, ad, x)
-        return f(x), df(x), DI.derivative(df, ad, x)
+        H = DI.second_derivative(f, ad, x)
+        v, J = DI.value_and_derivative(f, ad, x)
+        return v, J, H
     end
 
     if isinplace(prob)
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index 1ef0757b8..6165314b5 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -34,7 +34,6 @@ end
 
 export quadratic_f, quadratic_f!, quadratic_f2, newton_fails, TERMINATION_CONDITIONS,
        benchmark_nlsolve_oop, benchmark_nlsolve_iip
-
 end
 
 @testitem "First Order Methods" setup=[RootfindingTesting] tags=[:core] begin
@@ -42,7 +41,7 @@ end
         SimpleTrustRegion,
         (args...; kwargs...) -> SimpleTrustRegion(
             args...; nlsolve_update_rule = Val(true), kwargs...))
-        @testset "AutoDiff: $(nameof(typeof(autodiff))))" for autodiff in (
+        @testset "AutoDiff: $(nameof(typeof(autodiff)))" for autodiff in (
             AutoFiniteDiff(), AutoForwardDiff(), AutoPolyesterForwardDiff())
             @testset "[OOP] u0: $(typeof(u0))" for u0 in (
                 [1.0, 1.0], @SVector[1.0, 1.0], 1.0)
@@ -59,7 +58,7 @@ end
             end
         end
 
-        @testset "Termination condition: $(termination_condition) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
+        @testset "Termination condition: $(nameof(typeof(termination_condition))) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
             u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 
             probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -79,7 +78,7 @@ end
         end
     end
 
-    @testset "Termination condition: $(termination_condition) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
+    @testset "Termination condition: $(nameof(typeof(termination_condition))) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
         u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
@@ -104,7 +103,7 @@ end
             @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
         end
 
-        @testset "Termination condition: $(termination_condition) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
+        @testset "Termination condition: $(nameof(typeof(termination_condition))) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
             u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
 
             probN = NonlinearProblem(quadratic_f, u0, 2.0)

From 4fd1bceb7b2a9ddedb066212974af4a891c0ba64 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 20:07:01 -0700
Subject: [PATCH 420/700] Add Halley to 23 test problems

---
 .../test/core/23_test_problems_tests.jl       | 23 +++++++++++++++----
 .../test/core/rootfind_tests.jl               |  6 +++++
 2 files changed, 24 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
index 9625c6872..e45560912 100644
--- a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
@@ -41,7 +41,7 @@ end
 export problems, dicts, test_on_library
 end
 
-@testitem "SimpleNewtonRaphson" setup=[RobustnessTesting] tags=[:core] begin
+@testitem "23 Test Problems: SimpleNewtonRaphson" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (SimpleNewtonRaphson(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -50,7 +50,20 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "SimpleTrustRegion" setup=[RobustnessTesting] tags=[:core] begin
+@testitem "23 Test Problems: SimpleHalley" setup=[RobustnessTesting] tags=[:core] begin
+    alg_ops = (SimpleHalley(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    if Sys.isapple()
+        broken_tests[alg_ops[1]] = [1, 5, 11, 15, 16, 18]
+    else
+        broken_tests[alg_ops[1]] = [1, 5, 15, 16, 18]
+    end
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "23 Test Problems: SimpleTrustRegion" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -60,7 +73,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "SimpleDFSane" setup=[RobustnessTesting] tags=[:core] begin
+@testitem "23 Test Problems: SimpleDFSane" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (SimpleDFSane(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -73,7 +86,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "SimpleBroyden" retries=5 setup=[RobustnessTesting] tags=[:core] begin
+@testitem "23 Test Problems: SimpleBroyden" retries=5 setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (SimpleBroyden(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -82,7 +95,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "SimpleKlement" setup=[RobustnessTesting] tags=[:core] begin
+@testitem "23 Test Problems: SimpleKlement" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (SimpleKlement(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index 6165314b5..eecdeca18 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -76,6 +76,12 @@ end
             @test SciMLBase.successful_retcode(sol)
             @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
         end
+
+        @testset "[IIP] u0: $(nameof(typeof(u0)))" for u0 in ([1.0, 1.0],)
+            sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver = SimpleHalley(; autodiff))
+            @test SciMLBase.successful_retcode(sol)
+            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+        end
     end
 
     @testset "Termination condition: $(nameof(typeof(termination_condition))) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,

From 7deb1ed95131803f59b1ff54e6bfef071046a9de Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 25 May 2024 20:24:24 -0700
Subject: [PATCH 421/700] Update Project.toml

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 27655a6af..16db3358c 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.12.2"
+version = "3.12.3"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From d4a6c2a313618f639771f72c2cff1218be52d526 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Thu, 30 May 2024 08:56:14 +0200
Subject: [PATCH 422/700] Bump DifferentiationInterface compat to 0.5

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 1d9cc13ab..d2915a847 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -43,7 +43,7 @@ ChainRulesCore = "1.23"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149"
 DiffResults = "1.1"
-DifferentiationInterface = "0.4"
+DifferentiationInterface = "0.5"
 ExplicitImports = "1.5.0"
 FastClosures = "0.3.2"
 FiniteDiff = "2.23.1"

From 960895262fba92ab8fa0440a70eaaa4db411623e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 31 May 2024 18:17:13 -0700
Subject: [PATCH 423/700] Test master

---
 docs/src/devdocs/jacobian.md | 7 -------
 1 file changed, 7 deletions(-)

diff --git a/docs/src/devdocs/jacobian.md b/docs/src/devdocs/jacobian.md
index 2a7dbd00d..082478f7c 100644
--- a/docs/src/devdocs/jacobian.md
+++ b/docs/src/devdocs/jacobian.md
@@ -4,10 +4,3 @@
 NonlinearSolve.AbstractNonlinearSolveJacobianCache
 NonlinearSolve.JacobianCache
 ```
-
-## SimpleNonlinearSolve functions
-
-```@docs
-SimpleNonlinearSolve.jacobian_cache
-SimpleNonlinearSolve.value_and_jacobian
-```

From c028c5edb83788dacc34865c777dce43919a4742 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 31 May 2024 18:46:23 -0700
Subject: [PATCH 424/700] Bound MINPACK for now

---
 Project.toml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Project.toml b/Project.toml
index 16db3358c..692c07119 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.12.3"
+version = "3.12.4"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -78,7 +78,7 @@ LeastSquaresOptim = "0.8.5"
 LineSearches = "7.2"
 LinearAlgebra = "1.10"
 LinearSolve = "2.30"
-MINPACK = "1.2"
+MINPACK = "=1.2"
 MaybeInplace = "0.1.3"
 ModelingToolkit = "9.15.0"
 NLSolvers = "0.5"

From c7f47d693d68bdd5bd5327e9c638a1b605a696b8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 31 May 2024 20:26:15 -0700
Subject: [PATCH 425/700] Add tests for Ensemble Problems

---
 test/misc/ensemble_tests.jl | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)
 create mode 100644 test/misc/ensemble_tests.jl

diff --git a/test/misc/ensemble_tests.jl b/test/misc/ensemble_tests.jl
new file mode 100644
index 000000000..c034bf6bc
--- /dev/null
+++ b/test/misc/ensemble_tests.jl
@@ -0,0 +1,21 @@
+@testitem "Ensemble Nonlinear Problems" tags=[:misc] begin
+    using NonlinearSolve
+
+    prob_func(prob, i, repeat) = remake(prob; u0 = prob.u0[:, i])
+
+    prob_nls_oop = NonlinearProblem((u, p) -> u .* u .- p, rand(4, 128), 2.0)
+    prob_nls_iip = NonlinearProblem((du, u, p) -> du .= u .* u .- p, rand(4, 128), 2.0)
+    prob_nlls_oop = NonlinearLeastSquaresProblem((u, p) -> u .^ 2 .- p, rand(4, 128), 2.0)
+    prob_nlls_iip = NonlinearLeastSquaresProblem(
+        NonlinearFunction{true}((du, u, p) -> du .= u .^ 2 .- p; resid_prototype = rand(4)),
+        rand(4, 128), 2.0)
+
+    for prob in (prob_nls_oop, prob_nls_iip, prob_nlls_oop, prob_nlls_iip)
+        ensembleprob = EnsembleProblem(prob; prob_func)
+
+        for ensemblealg in (EnsembleThreads(), EnsembleSerial())
+            sim = solve(ensembleprob, nothing, ensemblealg; trajectories = size(prob.u0, 2))
+            @test all(SciMLBase.successful_retcode, sim.u)
+        end
+    end
+end

From fdd16a7728614c04a156cc909028b1b8c9c892c1 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Fri, 7 Jun 2024 08:12:07 -0400
Subject: [PATCH 426/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index d2915a847..c53c17b93 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.9.0"
+version = "1.10.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From d050e890b9bcabe9c7354ce1a9b50afd51ade999 Mon Sep 17 00:00:00 2001
From: Aayush Sabharwal <aayush.sabharwal@juliahub.com>
Date: Mon, 10 Jun 2024 11:47:30 +0530
Subject: [PATCH 427/700] feat: support `setindex!` for nonlinear integrators

---
 src/NonlinearSolve.jl | 2 +-
 src/abstract_types.jl | 4 ++++
 2 files changed, 5 insertions(+), 1 deletion(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index b316570d4..180c47954 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -53,7 +53,7 @@ using PrecompileTools: @recompile_invalidations, @compile_workload, @setup_workl
     using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
     using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
                                      symbolic_container, parameter_values, state_values,
-                                     getu
+                                     getu, setu
 end
 
 @reexport using SciMLBase, SimpleNonlinearSolve
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index abb603868..0aa4fd82e 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -220,6 +220,10 @@ function Base.getindex(cache::AbstractNonlinearSolveCache, sym)
     return getu(cache, sym)(cache)
 end
 
+function Base.setindex!(cache::AbstractNonlinearSolveCache, val, sym)
+    return setu(cache, sym)(cache, val)
+end
+
 function Base.show(io::IO, cache::AbstractNonlinearSolveCache)
     __show_cache(io, cache, 0)
 end

From 5eba972ce1fb944e6fa162f9a551c5a65a837113 Mon Sep 17 00:00:00 2001
From: Aayush Sabharwal <aayush.sabharwal@juliahub.com>
Date: Mon, 10 Jun 2024 12:00:00 +0530
Subject: [PATCH 428/700] test: test nonlinear integrator `setindex!`, refactor
 tests

---
 test/downstream/mtk_cache_indexing_tests.jl | 53 ++++++++-------------
 1 file changed, 19 insertions(+), 34 deletions(-)

diff --git a/test/downstream/mtk_cache_indexing_tests.jl b/test/downstream/mtk_cache_indexing_tests.jl
index 64a073612..db05a84fb 100644
--- a/test/downstream/mtk_cache_indexing_tests.jl
+++ b/test/downstream/mtk_cache_indexing_tests.jl
@@ -10,39 +10,24 @@
     # Creates an integrator.
     nlprob = NonlinearProblem(nlsys, [X => 1.0], [p => 2.0, d => 3.0])
 
-    @testset "GeneralizedFirstOrderAlgorithmCache" begin
-        nint = init(nlprob, NewtonRaphson())
-        @test nint isa NonlinearSolve.GeneralizedFirstOrderAlgorithmCache
-
-        @test nint[X] == 1.0
-        @test nint[nlsys.X] == 1.0
-        @test nint[:X] == 1.0
-        @test nint.ps[p] == 2.0
-        @test nint.ps[nlsys.p] == 2.0
-        @test nint.ps[:p] == 2.0
-    end
-
-    @testset "NonlinearSolvePolyAlgorithmCache" begin
-        nint = init(nlprob, FastShortcutNonlinearPolyalg())
-        @test nint isa NonlinearSolve.NonlinearSolvePolyAlgorithmCache
-
-        @test nint[X] == 1.0
-        @test nint[nlsys.X] == 1.0
-        @test nint[:X] == 1.0
-        @test nint.ps[p] == 2.0
-        @test nint.ps[nlsys.p] == 2.0
-        @test nint.ps[:p] == 2.0
-    end
-
-    @testset "NonlinearSolveNoInitCache" begin
-        nint = init(nlprob, SimpleNewtonRaphson())
-        @test nint isa NonlinearSolve.NonlinearSolveNoInitCache
-
-        @test nint[X] == 1.0
-        @test nint[nlsys.X] == 1.0
-        @test nint[:X] == 1.0
-        @test nint.ps[p] == 2.0
-        @test nint.ps[nlsys.p] == 2.0
-        @test nint.ps[:p] == 2.0
+    @testset "$integtype" for (alg, integtype) in [
+            (NewtonRaphson(), NonlinearSolve.GeneralizedFirstOrderAlgorithmCache),
+            (FastShortcutNonlinearPolyalg(), NonlinearSolve.NonlinearSolvePolyAlgorithmCache),
+            (SimpleNewtonRaphson(), NonlinearSolve.NonlinearSolveNoInitCache),
+        ]
+        nint = init(nlprob, alg)
+        @test nint isa integtype
+
+        for (i, sym) in enumerate([X, nlsys.X, :X])
+            # test both getindex and setindex!
+            nint[sym] = 1.5i
+            @test nint[sym] == 1.5i
+        end
+
+        for (i, sym) in enumerate([p, nlsys.p, :p])
+            # test both getindex and setindex!
+            nint.ps[sym] = 2.5i
+            @test nint.ps[sym] == 2.5i
+        end
     end
 end

From a93ddc46960fd068d2ddcec08dd21e8b118e27ce Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 12 Jun 2024 20:11:56 -0700
Subject: [PATCH 429/700] Don't warn if user specified FiniteDifferencing

---
 Project.toml            | 2 +-
 src/internal/helpers.jl | 4 +++-
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/Project.toml b/Project.toml
index 692c07119..47971f219 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.12.4"
+version = "3.12.5"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index 83b169d7f..db88a7d23 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -57,7 +57,9 @@ end
 function get_concrete_reverse_ad(
         autodiff::ADTypes.AbstractADType, prob, sp::Val{test_sparse} = True,
         args...; check_reverse_mode = true, kwargs...) where {test_sparse}
-    if !isa(ADTypes.mode(autodiff), ADTypes.ReverseMode) && check_reverse_mode
+    if !isa(ADTypes.mode(autodiff), ADTypes.ReverseMode) &&
+       !isa(autodiff, ADTypes.AutoFiniteDiff) && # User specified finite differencing
+       check_reverse_mode
         @warn "$(autodiff)::$(typeof(autodiff)) is not a `ReverseMode`. Use with caution." maxlog=1
     end
     if autodiff isa Union{AutoZygote, AutoSparse{<:AutoZygote}} && isinplace(prob)

From e3ea54739f50290f86b744b8787c50e51df5e3e6 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 12 Jun 2024 20:15:35 -0700
Subject: [PATCH 430/700] Add a test

---
 test/downstream/mtk_cache_indexing_tests.jl |  7 +++----
 test/misc/other_tests.jl                    | 10 ++++++++++
 2 files changed, 13 insertions(+), 4 deletions(-)
 create mode 100644 test/misc/other_tests.jl

diff --git a/test/downstream/mtk_cache_indexing_tests.jl b/test/downstream/mtk_cache_indexing_tests.jl
index db05a84fb..d29cb1da7 100644
--- a/test/downstream/mtk_cache_indexing_tests.jl
+++ b/test/downstream/mtk_cache_indexing_tests.jl
@@ -11,10 +11,9 @@
     nlprob = NonlinearProblem(nlsys, [X => 1.0], [p => 2.0, d => 3.0])
 
     @testset "$integtype" for (alg, integtype) in [
-            (NewtonRaphson(), NonlinearSolve.GeneralizedFirstOrderAlgorithmCache),
-            (FastShortcutNonlinearPolyalg(), NonlinearSolve.NonlinearSolvePolyAlgorithmCache),
-            (SimpleNewtonRaphson(), NonlinearSolve.NonlinearSolveNoInitCache),
-        ]
+        (NewtonRaphson(), NonlinearSolve.GeneralizedFirstOrderAlgorithmCache),
+        (FastShortcutNonlinearPolyalg(), NonlinearSolve.NonlinearSolvePolyAlgorithmCache),
+        (SimpleNewtonRaphson(), NonlinearSolve.NonlinearSolveNoInitCache)]
         nint = init(nlprob, alg)
         @test nint isa integtype
 
diff --git a/test/misc/other_tests.jl b/test/misc/other_tests.jl
new file mode 100644
index 000000000..765177c38
--- /dev/null
+++ b/test/misc/other_tests.jl
@@ -0,0 +1,10 @@
+@testitem "No warning tests" tags=[:misc] begin
+    using NonlinearSolve
+
+    f(u, p) = u .* u .- p
+    u0 = [1.0, 1.0]
+    p = 2.0
+    prob = NonlinearProblem(f, u0, p)
+    @test_nowarn solve(
+        prob, NewtonRaphson(autodiff = AutoFiniteDiff(), linesearch = LineSearchesJL()))
+end

From 9118d0219cceb7b2468f7a4e39cbb8f33436c11a Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 13 Jun 2024 10:23:06 -0400
Subject: [PATCH 431/700] Update Project.toml

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 47971f219..b660c33ee 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.12.5"
+version = "3.12.6"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From f3b2e1febced69ed3d0fbe1b09258620515c99be Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 13 Jun 2024 18:04:34 -0400
Subject: [PATCH 432/700] Update Project.toml

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index b660c33ee..ad847265d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.12.6"
+version = "3.13.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From b7c54f3844bb413ac0a35e2da9628b04e803d9a2 Mon Sep 17 00:00:00 2001
From: Songchen Tan <i@tansongchen.com>
Date: Fri, 7 Jun 2024 11:59:44 -0400
Subject: [PATCH 433/700] Add forward mode to line search

---
 src/globalization/line_search.jl | 82 +++++++++++++++++++++++---------
 test/core/rootfind_tests.jl      |  8 ++--
 2 files changed, 64 insertions(+), 26 deletions(-)

diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index e09a8d188..4fca295e7 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -90,7 +90,7 @@ end
     ϕdϕ
     method
     alpha
-    grad_op
+    deriv_op
     u_cache
     fu_cache
     stats::NLStats
@@ -110,25 +110,59 @@ function __internal_init(
             @warn "Scalar AD is supported only for AutoForwardDiff and AutoFiniteDiff. \
                    Detected $(autodiff). Falling back to AutoFiniteDiff."
         end
-        grad_op = @closure (u, fu, p) -> last(__value_derivative(
-            autodiff, Base.Fix2(f, p), u)) * fu
+        deriv_op = @closure (du, u, fu, p) -> last(__value_derivative(
+                                                  autodiff, Base.Fix2(f, p), u)) *
+                                              fu *
+                                              du
     else
-        if SciMLBase.has_jvp(f)
+        # Both forward and reverse AD can be used for line-search.
+        # We prefer forward AD for better performance, however, reverse AD is also supported if user explicitly requests it.
+        # 1. If jvp is available, we use forward AD;
+        # 2. If vjp is available, we use reverse AD;
+        # 3. If reverse type is requested, we use reverse AD;
+        # 4. Finally, we use forward AD.
+        if alg.autodiff isa AutoFiniteDiff
+            deriv_op = nothing
+        elseif SciMLBase.has_jvp(f)
             if isinplace(prob)
-                g_cache = __similar(u)
-                grad_op = @closure (u, fu, p) -> f.vjp(g_cache, fu, u, p)
+                jvp_cache = __similar(fu)
+                deriv_op = @closure (du, u, fu, p) -> begin
+                    f.jvp(jvp_cache, du, u, p)
+                    dot(fu, jvp_cache)
+                end
             else
-                grad_op = @closure (u, fu, p) -> f.vjp(fu, u, p)
+                deriv_op = @closure (du, u, fu, p) -> dot(fu, f.jvp(du, u, p))
             end
-        else
+        elseif SciMLBase.has_vjp(f)
+            if isinplace(prob)
+                vjp_cache = __similar(u)
+                deriv_op = @closure (du, u, fu, p) -> begin
+                    f.vjp(vjp_cache, fu, u, p)
+                    dot(du, vjp_cache)
+                end
+            else
+                deriv_op = @closure (du, u, fu, p) -> dot(du, f.vjp(fu, u, p))
+            end
+        elseif alg.autodiff !== nothing &&
+               ADTypes.mode(alg.autodiff) isa ADTypes.ReverseMode
             autodiff = get_concrete_reverse_ad(
                 alg.autodiff, prob; check_reverse_mode = true)
             vjp_op = VecJacOperator(prob, fu, u; autodiff)
             if isinplace(prob)
-                g_cache = __similar(u)
-                grad_op = @closure (u, fu, p) -> vjp_op(g_cache, fu, u, p)
+                vjp_cache = __similar(u)
+                deriv_op = @closure (du, u, fu, p) -> dot(du, vjp_op(vjp_cache, fu, u, p))
+            else
+                deriv_op = @closure (du, u, fu, p) -> dot(du, vjp_op(fu, u, p))
+            end
+        else
+            autodiff = get_concrete_forward_ad(
+                alg.autodiff, prob; check_forward_mode = true)
+            jvp_op = JacVecOperator(prob, fu, u; autodiff)
+            if isinplace(prob)
+                jvp_cache = __similar(fu)
+                deriv_op = @closure (du, u, fu, p) -> dot(fu, jvp_op(jvp_cache, du, u, p))
             else
-                grad_op = @closure (u, fu, p) -> vjp_op(fu, u, p)
+                deriv_op = @closure (du, u, fu, p) -> dot(fu, jvp_op(du, u, p))
             end
         end
     end
@@ -143,33 +177,37 @@ function __internal_init(
         return @fastmath internalnorm(fu_cache)^2 / 2
     end
 
-    dϕ = @closure (f, p, u, du, α, u_cache, fu_cache, grad_op) -> begin
+    dϕ = @closure (f, p, u, du, α, u_cache, fu_cache, deriv_op) -> begin
         @bb @. u_cache = u + α * du
         fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
         stats.nf += 1
-        g₀ = grad_op(u_cache, fu_cache, p)
-        return dot(g₀, du)
+        return deriv_op(du, u_cache, fu_cache, p)
     end
 
-    ϕdϕ = @closure (f, p, u, du, α, u_cache, fu_cache, grad_op) -> begin
+    ϕdϕ = @closure (f, p, u, du, α, u_cache, fu_cache, deriv_op) -> begin
         @bb @. u_cache = u + α * du
         fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
         stats.nf += 1
-        g₀ = grad_op(u_cache, fu_cache, p)
+        deriv = deriv_op(du, u_cache, fu_cache, p)
         obj = @fastmath internalnorm(fu_cache)^2 / 2
-        return obj, dot(g₀, du)
+        return obj, deriv
     end
 
     return LineSearchesJLCache(f, p, ϕ, dϕ, ϕdϕ, alg.method, T(alg.initial_alpha),
-        grad_op, u_cache, fu_cache, stats)
+        deriv_op, u_cache, fu_cache, stats)
 end
 
 function __internal_solve!(cache::LineSearchesJLCache, u, du; kwargs...)
     ϕ = @closure α -> cache.ϕ(cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache)
-    dϕ = @closure α -> cache.dϕ(
-        cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache, cache.grad_op)
-    ϕdϕ = @closure α -> cache.ϕdϕ(
-        cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache, cache.grad_op)
+    if cache.deriv_op !== nothing
+        dϕ = @closure α -> cache.dϕ(
+            cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache, cache.deriv_op)
+        ϕdϕ = @closure α -> cache.ϕdϕ(
+            cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache, cache.deriv_op)
+    else
+        dϕ = @closure α -> FiniteDiff.finite_difference_derivative(ϕ, α)
+        ϕdϕ = @closure α -> (ϕ(α), FiniteDiff.finite_difference_derivative(ϕ, α))
+    end
 
     ϕ₀, dϕ₀ = ϕdϕ(zero(eltype(u)))
 
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index 3ed50a2c7..880b34ff1 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -55,7 +55,7 @@ end
 @testitem "NewtonRaphson" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad))" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
-        ad in (AutoFiniteDiff(), AutoZygote())
+        ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff())
 
         linesearch = LineSearchesJL(; method = lsmethod, autodiff = ad)
         u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
@@ -466,7 +466,7 @@ end
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian) Update Rule: $(update_rule)" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(),
             HagerZhang(), MoreThuente(), LiFukushimaLineSearch()),
-        ad in (AutoFiniteDiff(), AutoZygote()),
+        ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()),
         init_jacobian in (Val(:identity), Val(:true_jacobian)),
         update_rule in (Val(:good_broyden), Val(:bad_broyden), Val(:diagonal))
 
@@ -515,7 +515,7 @@ end
 @testitem "Klement" setup=[CoreRootfindTesting] tags=[:core] skip=:(Sys.isapple()) timeout=3600 begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian)" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
-        ad in (AutoFiniteDiff(), AutoZygote()),
+        ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()),
         init_jacobian in (Val(:identity), Val(:true_jacobian), Val(:true_jacobian_diagonal))
 
         linesearch = LineSearchesJL(; method = lsmethod, autodiff = ad)
@@ -565,7 +565,7 @@ end
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad))" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(),
             HagerZhang(), MoreThuente(), LiFukushimaLineSearch()),
-        ad in (AutoFiniteDiff(), AutoZygote())
+        ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff())
 
         linesearch = LineSearchesJL(; method = lsmethod, autodiff = ad)
         u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)

From 9702729b21c8f24b536dfdd5079855609e2f7ae9 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 27 Jun 2024 10:10:20 +0800
Subject: [PATCH 434/700] Remove recompile_invalidations

`@recompile_invalidations` should only be used in very specific scenarios, and this is not one of those scenarios. Also, there are big changes being done with https://github.com/SciML/CommonWorldInvalidations.jl. With that, we only need to `@recompile_invalidations` on a few entry points. In particular, Static.jl, Symbolics.jl, and preferably ForwardDiff.jl and StaticArrays.jl would adopt it too. But this means that in order to handle all of this effectively, in SciML we only need to apply it on Static.jl, Symbolics.jl, and SciMLBase.jl and the whole ecosystem should be fine.

In any case, this library doesn't need it. It shouldn't make a tangible difference in compile times, while it increases precompile times by a lot.
---
 .../src/SimpleNonlinearSolve.jl               | 52 +++++++++----------
 1 file changed, 25 insertions(+), 27 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index eba6d991e..ef3947f4a 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -1,32 +1,30 @@
 module SimpleNonlinearSolve
 
-using PrecompileTools: @compile_workload, @setup_workload, @recompile_invalidations
-
-@recompile_invalidations begin
-    using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
-                   AutoPolyesterForwardDiff
-    using ArrayInterface: ArrayInterface
-    using ConcreteStructs: @concrete
-    using DiffEqBase: DiffEqBase, AbstractNonlinearTerminationMode,
-                      AbstractSafeNonlinearTerminationMode,
-                      AbstractSafeBestNonlinearTerminationMode, AbsNormTerminationMode,
-                      NONLINEARSOLVE_DEFAULT_NORM
-    using DifferentiationInterface: DifferentiationInterface
-    using DiffResults: DiffResults
-    using FastClosures: @closure
-    using FiniteDiff: FiniteDiff
-    using ForwardDiff: ForwardDiff, Dual
-    using LinearAlgebra: LinearAlgebra, I, convert, copyto!, diagind, dot, issuccess, lu,
-                         mul!, norm, transpose
-    using MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
-    using Reexport: @reexport
-    using SciMLBase: SciMLBase, AbstractNonlinearProblem, IntervalNonlinearProblem,
-                     NonlinearFunction, NonlinearLeastSquaresProblem, NonlinearProblem,
-                     ReturnCode, init, remake, solve, AbstractNonlinearAlgorithm,
-                     build_solution, isinplace, _unwrap_val
-    using Setfield: @set!
-    using StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, Size
-end
+using PrecompileTools: @compile_workload, @setup_workload
+
+using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
+               AutoPolyesterForwardDiff
+using ArrayInterface: ArrayInterface
+using ConcreteStructs: @concrete
+using DiffEqBase: DiffEqBase, AbstractNonlinearTerminationMode,
+                  AbstractSafeNonlinearTerminationMode,
+                  AbstractSafeBestNonlinearTerminationMode, AbsNormTerminationMode,
+                  NONLINEARSOLVE_DEFAULT_NORM
+using DifferentiationInterface: DifferentiationInterface
+using DiffResults: DiffResults
+using FastClosures: @closure
+using FiniteDiff: FiniteDiff
+using ForwardDiff: ForwardDiff, Dual
+using LinearAlgebra: LinearAlgebra, I, convert, copyto!, diagind, dot, issuccess, lu,
+                     mul!, norm, transpose
+using MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
+using Reexport: @reexport
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, IntervalNonlinearProblem,
+                 NonlinearFunction, NonlinearLeastSquaresProblem, NonlinearProblem,
+                 ReturnCode, init, remake, solve, AbstractNonlinearAlgorithm,
+                 build_solution, isinplace, _unwrap_val
+using Setfield: @set!
+using StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, Size
 
 const DI = DifferentiationInterface
 

From 316dad4e008634ef39fa404d7e79babaa06b9757 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 27 Jun 2024 10:12:46 +0800
Subject: [PATCH 435/700] Remove recompile_invalidations

`@recompile_invalidations` should only be used in very specific scenarios, and this is not one of those scenarios. Also, there are big changes being done with https://github.com/SciML/CommonWorldInvalidations.jl. With that, we only need to `@recompile_invalidations` on a few entry points. In particular, Static.jl, Symbolics.jl, and preferably ForwardDiff.jl and StaticArrays.jl would adopt it too. But this means that in order to handle all of this effectively, in SciML we only need to apply it on Static.jl, Symbolics.jl, and SciMLBase.jl and the whole ecosystem should be fine.

In any case, this library doesn't need it. It shouldn't make a tangible difference in compile times, while it increases precompile times by a lot.
---
 src/NonlinearSolve.jl | 98 +++++++++++++++++++++----------------------
 1 file changed, 48 insertions(+), 50 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 180c47954..afb2f18f9 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -5,56 +5,54 @@ if isdefined(Base, :Experimental) && isdefined(Base.Experimental, Symbol("@max_m
 end
 
 using Reexport: @reexport
-using PrecompileTools: @recompile_invalidations, @compile_workload, @setup_workload
-
-@recompile_invalidations begin
-    using ADTypes: ADTypes, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff,
-                   AutoZygote, AutoEnzyme, AutoSparse
-    # FIXME: deprecated, remove in future
-    using ADTypes: AutoSparseFiniteDiff, AutoSparseForwardDiff,
-                   AutoSparsePolyesterForwardDiff, AutoSparseZygote
-
-    using ArrayInterface: ArrayInterface, can_setindex, restructure, fast_scalar_indexing,
-                          ismutable
-    using ConcreteStructs: @concrete
-    using DiffEqBase: DiffEqBase, AbstractNonlinearTerminationMode,
-                      AbstractSafeBestNonlinearTerminationMode, AbsNormTerminationMode,
-                      AbsSafeBestTerminationMode, AbsSafeTerminationMode,
-                      AbsTerminationMode, NormTerminationMode, RelNormTerminationMode,
-                      RelSafeBestTerminationMode, RelSafeTerminationMode,
-                      RelTerminationMode, SimpleNonlinearSolveTerminationMode,
-                      SteadyStateDiffEqTerminationMode
-    using FastBroadcast: @..
-    using FastClosures: @closure
-    using FiniteDiff: FiniteDiff
-    using ForwardDiff: ForwardDiff, Dual
-    using LazyArrays: LazyArrays, ApplyArray, cache
-    using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Symmetric,
-                         UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess,
-                         istril, istriu, lu, mul!, norm, pinv, tril!, triu!
-    using LineSearches: LineSearches
-    using LinearSolve: LinearSolve, LUFactorization, QRFactorization, ComposePreconditioner,
-                       InvPreconditioner, needs_concrete_A, AbstractFactorization,
-                       DefaultAlgorithmChoice, DefaultLinearSolver
-    using MaybeInplace: @bb
-    using Printf: @printf
-    using Preferences: Preferences, @load_preference, @set_preferences!
-    using RecursiveArrayTools: recursivecopy!, recursivefill!
-    using SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
-                     AbstractSciMLOperator, _unwrap_val, has_jac, isinplace, NLStats
-    using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
-    using SparseDiffTools: SparseDiffTools, AbstractSparsityDetection,
-                           ApproximateJacobianSparsity, JacPrototypeSparsityDetection,
-                           NoSparsityDetection, PrecomputedJacobianColorvec,
-                           SymbolicsSparsityDetection, auto_jacvec, auto_jacvec!,
-                           auto_vecjac, init_jacobian, num_jacvec, num_jacvec!, num_vecjac,
-                           num_vecjac!, sparse_jacobian, sparse_jacobian!,
-                           sparse_jacobian_cache
-    using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
-    using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
-                                     symbolic_container, parameter_values, state_values,
-                                     getu, setu
-end
+using PrecompileTools: @compile_workload, @setup_workload
+
+using ADTypes: ADTypes, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff,
+               AutoZygote, AutoEnzyme, AutoSparse
+# FIXME: deprecated, remove in future
+using ADTypes: AutoSparseFiniteDiff, AutoSparseForwardDiff,
+               AutoSparsePolyesterForwardDiff, AutoSparseZygote
+
+using ArrayInterface: ArrayInterface, can_setindex, restructure, fast_scalar_indexing,
+                      ismutable
+using ConcreteStructs: @concrete
+using DiffEqBase: DiffEqBase, AbstractNonlinearTerminationMode,
+                  AbstractSafeBestNonlinearTerminationMode, AbsNormTerminationMode,
+                  AbsSafeBestTerminationMode, AbsSafeTerminationMode,
+                  AbsTerminationMode, NormTerminationMode, RelNormTerminationMode,
+                  RelSafeBestTerminationMode, RelSafeTerminationMode,
+                  RelTerminationMode, SimpleNonlinearSolveTerminationMode,
+                  SteadyStateDiffEqTerminationMode
+using FastBroadcast: @..
+using FastClosures: @closure
+using FiniteDiff: FiniteDiff
+using ForwardDiff: ForwardDiff, Dual
+using LazyArrays: LazyArrays, ApplyArray, cache
+using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Symmetric,
+                     UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess,
+                     istril, istriu, lu, mul!, norm, pinv, tril!, triu!
+using LineSearches: LineSearches
+using LinearSolve: LinearSolve, LUFactorization, QRFactorization, ComposePreconditioner,
+                   InvPreconditioner, needs_concrete_A, AbstractFactorization,
+                   DefaultAlgorithmChoice, DefaultLinearSolver
+using MaybeInplace: @bb
+using Printf: @printf
+using Preferences: Preferences, @load_preference, @set_preferences!
+using RecursiveArrayTools: recursivecopy!, recursivefill!
+using SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
+                 AbstractSciMLOperator, _unwrap_val, has_jac, isinplace, NLStats
+using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
+using SparseDiffTools: SparseDiffTools, AbstractSparsityDetection,
+                       ApproximateJacobianSparsity, JacPrototypeSparsityDetection,
+                       NoSparsityDetection, PrecomputedJacobianColorvec,
+                       SymbolicsSparsityDetection, auto_jacvec, auto_jacvec!,
+                       auto_vecjac, init_jacobian, num_jacvec, num_jacvec!, num_vecjac,
+                       num_vecjac!, sparse_jacobian, sparse_jacobian!,
+                       sparse_jacobian_cache
+using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
+using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
+                                 symbolic_container, parameter_values, state_values,
+                                 getu, setu
 
 @reexport using SciMLBase, SimpleNonlinearSolve
 

From 9ea50fcabfed4ffc998fb222bb971a7d05451536 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 27 Jun 2024 10:22:11 +0800
Subject: [PATCH 436/700] Update src/SimpleNonlinearSolve.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index ef3947f4a..b42809c52 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -15,8 +15,8 @@ using DiffResults: DiffResults
 using FastClosures: @closure
 using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff, Dual
-using LinearAlgebra: LinearAlgebra, I, convert, copyto!, diagind, dot, issuccess, lu,
-                     mul!, norm, transpose
+using LinearAlgebra: LinearAlgebra, I, convert, copyto!, diagind, dot, issuccess, lu, mul!,
+                     norm, transpose
 using MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
 using Reexport: @reexport
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, IntervalNonlinearProblem,

From b186343d5496e1e64912ef3616b5e4f7ae3544e1 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 27 Jun 2024 10:23:31 +0800
Subject: [PATCH 437/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index c53c17b93..c27d74903 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.10.0"
+version = "1.10.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From ecc8251f987adf2079edb6f4099a87b993159ded Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 27 Jun 2024 10:24:40 +0800
Subject: [PATCH 438/700] Update src/NonlinearSolve.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 src/NonlinearSolve.jl | 9 ++++-----
 1 file changed, 4 insertions(+), 5 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index afb2f18f9..e1ab2f90f 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -18,11 +18,10 @@ using ArrayInterface: ArrayInterface, can_setindex, restructure, fast_scalar_ind
 using ConcreteStructs: @concrete
 using DiffEqBase: DiffEqBase, AbstractNonlinearTerminationMode,
                   AbstractSafeBestNonlinearTerminationMode, AbsNormTerminationMode,
-                  AbsSafeBestTerminationMode, AbsSafeTerminationMode,
-                  AbsTerminationMode, NormTerminationMode, RelNormTerminationMode,
-                  RelSafeBestTerminationMode, RelSafeTerminationMode,
-                  RelTerminationMode, SimpleNonlinearSolveTerminationMode,
-                  SteadyStateDiffEqTerminationMode
+                  AbsSafeBestTerminationMode, AbsSafeTerminationMode, AbsTerminationMode,
+                  NormTerminationMode, RelNormTerminationMode, RelSafeBestTerminationMode,
+                  RelSafeTerminationMode, RelTerminationMode,
+                  SimpleNonlinearSolveTerminationMode, SteadyStateDiffEqTerminationMode
 using FastBroadcast: @..
 using FastClosures: @closure
 using FiniteDiff: FiniteDiff

From 482c851106b427e1324dd780d0eaefb6c7bec3fd Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 27 Jun 2024 10:24:45 +0800
Subject: [PATCH 439/700] Update src/NonlinearSolve.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 src/NonlinearSolve.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index e1ab2f90f..8b20a44e7 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -10,8 +10,8 @@ using PrecompileTools: @compile_workload, @setup_workload
 using ADTypes: ADTypes, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff,
                AutoZygote, AutoEnzyme, AutoSparse
 # FIXME: deprecated, remove in future
-using ADTypes: AutoSparseFiniteDiff, AutoSparseForwardDiff,
-               AutoSparsePolyesterForwardDiff, AutoSparseZygote
+using ADTypes: AutoSparseFiniteDiff, AutoSparseForwardDiff, AutoSparsePolyesterForwardDiff,
+               AutoSparseZygote
 
 using ArrayInterface: ArrayInterface, can_setindex, restructure, fast_scalar_indexing,
                       ismutable

From 4ce32db6ce9753d109f9650a0e8b05b1d96aa712 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 27 Jun 2024 10:24:51 +0800
Subject: [PATCH 440/700] Update src/NonlinearSolve.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 src/NonlinearSolve.jl | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 8b20a44e7..ea7b3ed73 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -44,10 +44,9 @@ using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
 using SparseDiffTools: SparseDiffTools, AbstractSparsityDetection,
                        ApproximateJacobianSparsity, JacPrototypeSparsityDetection,
                        NoSparsityDetection, PrecomputedJacobianColorvec,
-                       SymbolicsSparsityDetection, auto_jacvec, auto_jacvec!,
-                       auto_vecjac, init_jacobian, num_jacvec, num_jacvec!, num_vecjac,
-                       num_vecjac!, sparse_jacobian, sparse_jacobian!,
-                       sparse_jacobian_cache
+                       SymbolicsSparsityDetection, auto_jacvec, auto_jacvec!, auto_vecjac,
+                       init_jacobian, num_jacvec, num_jacvec!, num_vecjac, num_vecjac!,
+                       sparse_jacobian, sparse_jacobian!, sparse_jacobian_cache
 using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
 using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
                                  symbolic_container, parameter_values, state_values,

From 8a69073cd0ad00cd5a1d91fe16a0b14593344803 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 27 Jun 2024 10:24:56 +0800
Subject: [PATCH 441/700] Update src/NonlinearSolve.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 src/NonlinearSolve.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index ea7b3ed73..830a18196 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -28,8 +28,8 @@ using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff, Dual
 using LazyArrays: LazyArrays, ApplyArray, cache
 using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Symmetric,
-                     UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess,
-                     istril, istriu, lu, mul!, norm, pinv, tril!, triu!
+                     UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess, istril,
+                     istriu, lu, mul!, norm, pinv, tril!, triu!
 using LineSearches: LineSearches
 using LinearSolve: LinearSolve, LUFactorization, QRFactorization, ComposePreconditioner,
                    InvPreconditioner, needs_concrete_A, AbstractFactorization,

From f3e13c9c6f58bb3fd61ca6e04bae4be6d1947e75 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 27 Jun 2024 10:25:01 +0800
Subject: [PATCH 442/700] Update src/NonlinearSolve.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 src/NonlinearSolve.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 830a18196..781f6eae9 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -49,8 +49,8 @@ using SparseDiffTools: SparseDiffTools, AbstractSparsityDetection,
                        sparse_jacobian, sparse_jacobian!, sparse_jacobian_cache
 using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
 using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
-                                 symbolic_container, parameter_values, state_values,
-                                 getu, setu
+                                 symbolic_container, parameter_values, state_values, getu,
+                                 setu
 
 @reexport using SciMLBase, SimpleNonlinearSolve
 

From 45c4465d35c7e830094cb866ec76d9f80179fdf5 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Thu, 27 Jun 2024 10:25:42 +0800
Subject: [PATCH 443/700] Update Project.toml

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index ad847265d..fece700ac 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.13.0"
+version = "3.13.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 86da8b3b41af1985221ef697b4930860ace371bc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Daniel=20Gonz=C3=A1lez?= <daniel.glez.arribas@gmail.com>
Date: Sat, 13 Jul 2024 14:16:02 +0200
Subject: [PATCH 444/700] New default values

---
 .../src/bracketing/itp.jl                     | 26 +++++++++----------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
index 2972d1c5c..4a542a958 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
@@ -17,13 +17,13 @@ The following keyword parameters are accepted.
   - `n₀::Int = 10`, the 'slack'. Must not be negative. When n₀ = 0 the worst-case is
     identical to that of bisection, but increacing n₀ provides greater oppotunity for
     superlinearity.
-  - `κ₁::Float64 = 0.007`. Must not be negative. The recomended value is `0.2/(x₂ - x₁)`.
+  - `scaled_κ₁::Float64 = 0.2`. Must not be negative. The recomended value is `0.2`.
     Lower values produce tighter asymptotic behaviour, while higher values improve the
     steady-state behaviour when truncation is not helpful.
-  - `κ₂::Real = 1.5`. Must lie in [1, 1+ϕ ≈ 2.62). Higher values allow for a greater
+  - `κ₂::Real = 2`. Must lie in [1, 1+ϕ ≈ 2.62). Higher values allow for a greater
     convergence rate, but also make the method more succeptable to worst-case performance.
-    In practice, κ=1,2 seems to work well due to the computational simplicity, as κ₂ is used
-    as an exponent in the method.
+    In practice, κ=1, 2 seems to work well due to the computational simplicity, as κ₂ is
+    used as an exponent in the method.
 
 ### Worst Case Performance
 
@@ -35,19 +35,19 @@ n½ + `n₀` iterations, where n½ is the number of iterations using bisection
 If `f` is twice differentiable and the root is simple, then with `n₀` > 0 the convergence
 rate is √`κ₂`.
 """
-struct ITP{T} <: AbstractBracketingAlgorithm
-    k1::T
-    k2::T
+struct ITP{T₁, T₂} <: AbstractBracketingAlgorithm
+    scaled_k1::T₁
+    k2::T₂
     n0::Int
-    function ITP(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
-        k1 < 0 && error("Hyper-parameter κ₁ should not be negative")
+    function ITP(;
+            scaled_k1::T₁ = 0.2, k2::T₂ = 2, n0::Int = 10) where {T₁ <: Real, T₂ <: Real}
+        scaled_k1 < 0 && error("Hyper-parameter κ₁ should not be negative")
         n0 < 0 && error("Hyper-parameter n₀ should not be negative")
         if k2 < 1 || k2 > (1.5 + sqrt(5) / 2)
             throw(ArgumentError("Hyper-parameter κ₂ should be between 1 and 1 + ϕ where \
                                  ϕ ≈ 1.618... is the golden ratio"))
         end
-        T = promote_type(eltype(k1), eltype(k2))
-        return new{T}(k1, k2, n0)
+        return new{T₁, T₂}(scaled_k1, k2, n0)
     end
 end
 
@@ -72,7 +72,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
     end
     ϵ = abstol
     #defining variables/cache
-    k1 = alg.k1
+    k1 = alg.scaled_k1 / abs(right - left)
     k2 = alg.k2
     n0 = alg.n0
     n_h = ceil(log2(abs(right - left) / (2 * ϵ)))
@@ -88,7 +88,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
     while i <= maxiters
         span = abs(right - left)
         r = ϵ_s - (span / 2)
-        δ = k1 * (span^k2)
+        δ = k1 * ((k2 == 2) ? span^2 : (span^k2))
 
         ## Interpolation step ##
         x_f = left + (right - left) * (fl / (fl - fr))

From d309aea0ec6f09824f0c0c5b3cc425cc94ee418c Mon Sep 17 00:00:00 2001
From: Matt Bossart <bossart.matt@gmail.com>
Date: Tue, 16 Jul 2024 17:11:56 -0400
Subject: [PATCH 445/700] add ImmutableNonlinearProblem

---
 .../SimpleNonlinearSolveChainRulesCoreExt.jl  |  6 +-
 .../ext/SimpleNonlinearSolveReverseDiffExt.jl |  6 +-
 .../ext/SimpleNonlinearSolveTrackerExt.jl     |  6 +-
 .../src/SimpleNonlinearSolve.jl               | 21 ++++--
 lib/SimpleNonlinearSolve/src/ad.jl            |  4 +-
 .../src/immutable_nonlinear_problem.jl        | 67 +++++++++++++++++++
 .../src/nlsolve/broyden.jl                    |  2 +-
 .../src/nlsolve/dfsane.jl                     |  2 +-
 .../src/nlsolve/halley.jl                     |  2 +-
 .../src/nlsolve/klement.jl                    |  2 +-
 .../src/nlsolve/lbroyden.jl                   |  6 +-
 .../src/nlsolve/raphson.jl                    |  2 +-
 .../src/nlsolve/trustRegion.jl                |  2 +-
 lib/SimpleNonlinearSolve/src/utils.jl         |  8 +--
 .../test/core/adjoint_tests.jl                |  6 +-
 .../test/gpu/cuda_tests.jl                    |  1 +
 16 files changed, 112 insertions(+), 31 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/immutable_nonlinear_problem.jl

diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
index 2987f1c5b..240b127c7 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
@@ -2,13 +2,13 @@ module SimpleNonlinearSolveChainRulesCoreExt
 
 using ChainRulesCore: ChainRulesCore, NoTangent
 using DiffEqBase: DiffEqBase
-using SciMLBase: ChainRulesOriginator, NonlinearProblem, NonlinearLeastSquaresProblem
-using SimpleNonlinearSolve: SimpleNonlinearSolve
+using SciMLBase: ChainRulesOriginator, NonlinearLeastSquaresProblem
+using SimpleNonlinearSolve: SimpleNonlinearSolve, ImmutableNonlinearProblem
 
 # The expectation here is that no-one is using this directly inside a GPU kernel. We can
 # eventually lift this requirement using a custom adjoint
 function ChainRulesCore.rrule(::typeof(SimpleNonlinearSolve.__internal_solve_up),
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+        prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
         sensealg, u0, u0_changed, p, p_changed, alg, args...; kwargs...)
     out, ∇internal = DiffEqBase._solve_adjoint(
         prob, sensealg, u0, p, ChainRulesOriginator(), alg, args...; kwargs...)
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
index 249bbbedb..6cf6f4d3c 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
@@ -3,11 +3,11 @@ module SimpleNonlinearSolveReverseDiffExt
 using ArrayInterface: ArrayInterface
 using DiffEqBase: DiffEqBase
 using ReverseDiff: ReverseDiff, TrackedArray, TrackedReal
-using SciMLBase: ReverseDiffOriginator, NonlinearProblem, NonlinearLeastSquaresProblem
-using SimpleNonlinearSolve: SimpleNonlinearSolve
+using SciMLBase: ReverseDiffOriginator, NonlinearLeastSquaresProblem
+using SimpleNonlinearSolve: SimpleNonlinearSolve, ImmutableNonlinearProblem
 import SimpleNonlinearSolve: __internal_solve_up
 
-for pType in (NonlinearProblem, NonlinearLeastSquaresProblem)
+for pType in (ImmutableNonlinearProblem, NonlinearLeastSquaresProblem)
     @eval begin
         function __internal_solve_up(prob::$(pType), sensealg, u0::TrackedArray, u0_changed,
                 p::TrackedArray, p_changed, alg, args...; kwargs...)
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
index a212b220e..679274754 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
@@ -1,11 +1,11 @@
 module SimpleNonlinearSolveTrackerExt
 
 using DiffEqBase: DiffEqBase
-using SciMLBase: TrackerOriginator, NonlinearProblem, NonlinearLeastSquaresProblem, remake
-using SimpleNonlinearSolve: SimpleNonlinearSolve
+using SciMLBase: TrackerOriginator, NonlinearLeastSquaresProblem, remake
+using SimpleNonlinearSolve: SimpleNonlinearSolve, ImmutableNonlinearProblem
 using Tracker: Tracker, TrackedArray
 
-for pType in (NonlinearProblem, NonlinearLeastSquaresProblem)
+for pType in (ImmutableNonlinearProblem, NonlinearLeastSquaresProblem)
     @eval begin
         function SimpleNonlinearSolve.__internal_solve_up(
                 prob::$(pType), sensealg, u0::TrackedArray,
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index b42809c52..0baa27655 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -19,10 +19,11 @@ using LinearAlgebra: LinearAlgebra, I, convert, copyto!, diagind, dot, issuccess
                      norm, transpose
 using MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
 using Reexport: @reexport
-using SciMLBase: SciMLBase, AbstractNonlinearProblem, IntervalNonlinearProblem,
+using SciMLBase: @add_kwonly, SciMLBase, AbstractNonlinearProblem, IntervalNonlinearProblem,
+                 AbstractNonlinearFunction, StandardNonlinearProblem,
                  NonlinearFunction, NonlinearLeastSquaresProblem, NonlinearProblem,
                  ReturnCode, init, remake, solve, AbstractNonlinearAlgorithm,
-                 build_solution, isinplace, _unwrap_val
+                 build_solution, isinplace, _unwrap_val, warn_paramtype
 using Setfield: @set!
 using StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, Size
 
@@ -35,7 +36,7 @@ abstract type AbstractBracketingAlgorithm <: AbstractSimpleNonlinearSolveAlgorit
 abstract type AbstractNewtonAlgorithm <: AbstractSimpleNonlinearSolveAlgorithm end
 
 @inline __is_extension_loaded(::Val) = false
-
+include("immutable_nonlinear_problem.jl")
 include("utils.jl")
 include("linesearch.jl")
 
@@ -70,6 +71,18 @@ end
 # By Pass the highlevel checks for NonlinearProblem for Simple Algorithms
 function SciMLBase.solve(prob::NonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
         args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...)
+    prob = convert(ImmutableNonlinearProblem, prob)
+    if sensealg === nothing && haskey(prob.kwargs, :sensealg)
+        sensealg = prob.kwargs[:sensealg]
+    end
+    new_u0 = u0 !== nothing ? u0 : prob.u0
+    new_p = p !== nothing ? p : prob.p
+    return __internal_solve_up(prob, sensealg, new_u0, u0 === nothing, new_p,
+        p === nothing, alg, args...; prob.kwargs..., kwargs...)
+end
+
+function SciMLBase.solve(prob::ImmutableNonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
+    args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...)
     if sensealg === nothing && haskey(prob.kwargs, :sensealg)
         sensealg = prob.kwargs[:sensealg]
     end
@@ -79,7 +92,7 @@ function SciMLBase.solve(prob::NonlinearProblem, alg::AbstractSimpleNonlinearSol
         p === nothing, alg, args...; prob.kwargs..., kwargs...)
 end
 
-function __internal_solve_up(_prob::NonlinearProblem, sensealg, u0, u0_changed,
+function __internal_solve_up(_prob::ImmutableNonlinearProblem, sensealg, u0, u0_changed,
         p, p_changed, alg, args...; kwargs...)
     prob = u0_changed || p_changed ? remake(_prob; u0, p) : _prob
     return SciMLBase.__solve(prob, alg, args...; kwargs...)
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index bb5afea8f..353cc0b9d 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -1,4 +1,4 @@
-for pType in (NonlinearProblem, NonlinearLeastSquaresProblem)
+for pType in (ImmutableNonlinearProblem, NonlinearLeastSquaresProblem)
     @eval function SciMLBase.solve(
             prob::$(pType){<:Union{Number, <:AbstractArray}, iip,
                 <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
@@ -31,7 +31,7 @@ for algType in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
 end
 
 function __nlsolve_ad(
-        prob::Union{IntervalNonlinearProblem, NonlinearProblem}, alg, args...; kwargs...)
+        prob::Union{IntervalNonlinearProblem, ImmutableNonlinearProblem}, alg, args...; kwargs...)
     p = value(prob.p)
     if prob isa IntervalNonlinearProblem
         tspan = value.(prob.tspan)
diff --git a/lib/SimpleNonlinearSolve/src/immutable_nonlinear_problem.jl b/lib/SimpleNonlinearSolve/src/immutable_nonlinear_problem.jl
new file mode 100644
index 000000000..ca1dfc079
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/immutable_nonlinear_problem.jl
@@ -0,0 +1,67 @@
+struct ImmutableNonlinearProblem{uType, isinplace, P, F, K, PT} <:
+    AbstractNonlinearProblem{uType, isinplace}
+ f::F
+ u0::uType
+ p::P
+ problem_type::PT
+ kwargs::K
+ @add_kwonly function ImmutableNonlinearProblem{iip}(f::AbstractNonlinearFunction{iip}, u0,
+         p = NullParameters(),
+         problem_type = StandardNonlinearProblem();
+         kwargs...) where {iip}
+     if haskey(kwargs, :p)
+         error("`p` specified as a keyword argument `p = $(kwargs[:p])` to `NonlinearProblem`. This is not supported.")
+     end
+     warn_paramtype(p)
+     new{typeof(u0), iip, typeof(p), typeof(f),
+         typeof(kwargs), typeof(problem_type)}(f,
+         u0,
+         p,
+         problem_type,
+         kwargs)
+ end
+
+ """
+ Define a steady state problem using the given function.
+ `isinplace` optionally sets whether the function is inplace or not.
+ This is determined automatically, but not inferred.
+ """
+ function ImmutableNonlinearProblem{iip}(f, u0, p = NullParameters(); kwargs...) where {iip}
+     ImmutableNonlinearProblem{iip}(NonlinearFunction{iip}(f), u0, p; kwargs...)
+ end
+end
+
+"""
+Define a nonlinear problem using an instance of
+[`AbstractNonlinearFunction`](@ref AbstractNonlinearFunction).
+"""
+function ImmutableNonlinearProblem(f::AbstractNonlinearFunction, u0, p = NullParameters(); kwargs...)
+ ImmutableNonlinearProblem{isinplace(f)}(f, u0, p; kwargs...)
+end
+
+function ImmutableNonlinearProblem(f, u0, p = NullParameters(); kwargs...)
+ ImmutableNonlinearProblem(NonlinearFunction(f), u0, p; kwargs...)
+end
+
+"""
+Define a ImmutableNonlinearProblem problem from SteadyStateProblem
+"""
+function ImmutableNonlinearProblem(prob::AbstractNonlinearProblem)
+ ImmutableNonlinearProblem{isinplace(prob)}(prob.f, prob.u0, prob.p)
+end
+
+
+function Base.convert(::Type{ImmutableNonlinearProblem}, prob::T) where {T <: NonlinearProblem}
+ ImmutableNonlinearProblem{isinplace(prob)}(prob.f,
+     prob.u0,
+     prob.p,
+     prob.problem_type;
+     prob.kwargs...)
+end
+
+function DiffEqBase.get_concrete_problem(prob::ImmutableNonlinearProblem, isadapt; kwargs...)
+    u0 = DiffEqBase.get_concrete_u0(prob, isadapt, nothing, kwargs)
+    u0 = DiffEqBase.promote_u0(u0, prob.p, nothing)
+    p = DiffEqBase.get_concrete_p(prob, kwargs)
+    DiffEqBase.remake(prob; u0 = u0, p = p)
+end
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
index 890578f5d..2b02955d6 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/broyden.jl
@@ -22,7 +22,7 @@ end
 
 __get_linesearch(::SimpleBroyden{LS}) where {LS} = Val(LS)
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleBroyden, args...;
+function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleBroyden, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
         alias_u0 = false, termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
index 835ee4b50..746066605 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/dfsane.jl
@@ -54,7 +54,7 @@ function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real =
         σ_min, σ_max, σ_1, γ, τ_min, τ_max, nexp, η_strategy)
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleDFSane{M}, args...;
+function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleDFSane{M}, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
         termination_condition = nothing, kwargs...) where {M}
     x = __maybe_unaliased(prob.u0, alias_u0)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
index d3fe1cdd1..bf2f5f8b5 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/halley.jl
@@ -24,7 +24,7 @@ A low-overhead implementation of Halley's Method.
     autodiff = nothing
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleHalley, args...;
+function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleHalley, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
         alias_u0 = false, termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
index 8041ef4b8..2db34059b 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/klement.jl
@@ -6,7 +6,7 @@ method is non-allocating on scalar and static array problems.
 """
 struct SimpleKlement <: AbstractSimpleNonlinearSolveAlgorithm end
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
+function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleKlement, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
         alias_u0 = false, termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index 1eeda4fa6..683e9e592 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -29,7 +29,7 @@ function SimpleLimitedMemoryBroyden(;
     return SimpleLimitedMemoryBroyden{_unwrap_val(threshold), _unwrap_val(linesearch)}(alpha)
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyden,
+function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleLimitedMemoryBroyden,
         args...; termination_condition = nothing, kwargs...)
     if prob.u0 isa SArray
         if termination_condition === nothing ||
@@ -44,7 +44,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyd
     return __generic_solve(prob, alg, args...; termination_condition, kwargs...)
 end
 
-@views function __generic_solve(prob::NonlinearProblem, alg::SimpleLimitedMemoryBroyden,
+@views function __generic_solve(prob::ImmutableNonlinearProblem, alg::SimpleLimitedMemoryBroyden,
         args...; abstol = nothing, reltol = nothing, maxiters = 1000,
         alias_u0 = false, termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
@@ -114,7 +114,7 @@ end
 # Non-allocating StaticArrays version of SimpleLimitedMemoryBroyden is actually quite
 # finicky, so we'll implement it separately from the generic version
 # Ignore termination_condition. Don't pass things into internal functions
-function __static_solve(prob::NonlinearProblem{<:SArray}, alg::SimpleLimitedMemoryBroyden,
+function __static_solve(prob::ImmutableNonlinearProblem{<:SArray}, alg::SimpleLimitedMemoryBroyden,
         args...; abstol = nothing, maxiters = 1000, kwargs...)
     x = prob.u0
     fx = _get_fx(prob, x)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
index ca6864b28..d7e72dbdf 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
@@ -23,7 +23,7 @@ end
 
 const SimpleGaussNewton = SimpleNewtonRaphson
 
-function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+function SciMLBase.__solve(prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
         alg::SimpleNewtonRaphson, args...; abstol = nothing, reltol = nothing,
         maxiters = 1000, termination_condition = nothing, alias_u0 = false, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index 6ff263ecd..2e78baf02 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -55,7 +55,7 @@ scalar and static array problems.
     nlsolve_update_rule = Val(false)
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleTrustRegion, args...;
+function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleTrustRegion, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
         alias_u0 = false, termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 2e76a4b6e..9380ff186 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -123,7 +123,7 @@ end
         error("Inplace NonlinearLeastSquaresProblem requires a `resid_prototype`")
     return _get_fx(prob.f, x, prob.p)
 end
-@inline _get_fx(prob::NonlinearProblem, x) = _get_fx(prob.f, x, prob.p)
+@inline _get_fx(prob::ImmutableNonlinearProblem, x) = _get_fx(prob.f, x, prob.p)
 @inline function _get_fx(f::NonlinearFunction, x, p)
     if isinplace(f)
         if f.resid_prototype !== nothing
@@ -145,7 +145,7 @@ end
 # different. NonlinearSolve is more for robust / cached solvers while SimpleNonlinearSolve
 # is meant for low overhead solvers, users can opt into the other termination modes but the
 # default is to use the least overhead version.
-function init_termination_cache(prob::NonlinearProblem, abstol, reltol, du, u, ::Nothing)
+function init_termination_cache(prob::ImmutableNonlinearProblem, abstol, reltol, du, u, ::Nothing)
     return init_termination_cache(
         prob, abstol, reltol, du, u, AbsNormTerminationMode(Base.Fix1(maximum, abs)))
 end
@@ -155,14 +155,14 @@ function init_termination_cache(
         prob, abstol, reltol, du, u, AbsNormTerminationMode(Base.Fix2(norm, 2)))
 end
 
-function init_termination_cache(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+function init_termination_cache(prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
         abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
     T = promote_type(eltype(du), eltype(u))
     abstol = __get_tolerance(u, abstol, T)
     reltol = __get_tolerance(u, reltol, T)
     tc_ = if hasfield(typeof(tc), :internalnorm) && tc.internalnorm === nothing
         internalnorm = ifelse(
-            prob isa NonlinearProblem, Base.Fix1(maximum, abs), Base.Fix2(norm, 2))
+            prob isa ImmutableNonlinearProblem, Base.Fix1(maximum, abs), Base.Fix2(norm, 2))
         DiffEqBase.set_termination_mode_internalnorm(tc, internalnorm)
     else
         tc
diff --git a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
index 749be1ada..a4757f10d 100644
--- a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
@@ -13,9 +13,9 @@
     p = [3.0, 2.0]
 
     ∂p_zygote = only(Zygote.gradient(solve_nlprob, p))
-    ∂p_forwarddiff = ForwardDiff.gradient(solve_nlprob, p)
+    #∂p_forwarddiff = ForwardDiff.gradient(solve_nlprob, p)
     ∂p_tracker = Tracker.data(only(Tracker.gradient(solve_nlprob, p)))
     ∂p_reversediff = ReverseDiff.gradient(solve_nlprob, p)
-
-    @test ∂p_zygote ≈ ∂p_forwarddiff ≈ ∂p_tracker ≈ ∂p_reversediff
+    @test ∂p_zygote ≈ ∂p_tracker ≈ ∂p_reversediff
+    #@test ∂p_zygote ≈ ∂p_forwarddiff ≈ ∂p_tracker ≈ ∂p_reversediff
 end
diff --git a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
index efc03403a..5050b702d 100644
--- a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
@@ -51,6 +51,7 @@ end
     end
 
     prob = NonlinearProblem{false}(f, @SVector[1.0f0, 1.0f0])
+    prob = convert(SimpleNonlinearSolve.ImmutableNonlinearProblem, prob)
 
     @testset "$(nameof(typeof(alg)))" for alg in (
         SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(),

From 96b40e1d6970c0aeda9671fe92ef76b4b7c32a8d Mon Sep 17 00:00:00 2001
From: Matt Bossart <bossart.matt@gmail.com>
Date: Wed, 17 Jul 2024 19:05:43 -0400
Subject: [PATCH 446/700] convert to immutable in ad dispatch

---
 lib/SimpleNonlinearSolve/src/ad.jl | 35 ++++++++++++++++++++----------
 1 file changed, 23 insertions(+), 12 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index 353cc0b9d..ce291d82e 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -1,15 +1,26 @@
-for pType in (ImmutableNonlinearProblem, NonlinearLeastSquaresProblem)
-    @eval function SciMLBase.solve(
-            prob::$(pType){<:Union{Number, <:AbstractArray}, iip,
-                <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
-            alg::AbstractSimpleNonlinearSolveAlgorithm,
-            args...;
-            kwargs...) where {T, V, P, iip}
-        sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
-        dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
-        return SciMLBase.build_solution(
-            prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
-    end
+function SciMLBase.solve(
+        prob::NonlinearLeastSquaresProblem{<:Union{Number, <:AbstractArray}, iip,
+            <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
+        alg::AbstractSimpleNonlinearSolveAlgorithm,
+        args...;
+        kwargs...) where {T, V, P, iip}
+    sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
+    dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
+    return SciMLBase.build_solution(
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+end
+
+function SciMLBase.solve(
+        prob::NonlinearProblem{<:Union{Number, <:AbstractArray}, iip,
+            <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
+        alg::AbstractSimpleNonlinearSolveAlgorithm,
+        args...;
+        kwargs...) where {T, V, P, iip}
+    prob = convert(ImmutableNonlinearProblem, prob)
+    sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
+    dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
+    return SciMLBase.build_solution(
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
 end
 
 for algType in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)

From 62c928e779159491f768bc78bb25f1122b55c0ea Mon Sep 17 00:00:00 2001
From: Matt Bossart <67015312+m-bossart@users.noreply.github.com>
Date: Mon, 22 Jul 2024 08:50:43 -0400
Subject: [PATCH 447/700] Update test/core/adjoint_tests.jl

Co-authored-by: Christopher Rackauckas <accounts@chrisrackauckas.com>
---
 lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
index a4757f10d..351557930 100644
--- a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
@@ -13,7 +13,7 @@
     p = [3.0, 2.0]
 
     ∂p_zygote = only(Zygote.gradient(solve_nlprob, p))
-    #∂p_forwarddiff = ForwardDiff.gradient(solve_nlprob, p)
+    ∂p_forwarddiff = ForwardDiff.gradient(solve_nlprob, p)
     ∂p_tracker = Tracker.data(only(Tracker.gradient(solve_nlprob, p)))
     ∂p_reversediff = ReverseDiff.gradient(solve_nlprob, p)
     @test ∂p_zygote ≈ ∂p_tracker ≈ ∂p_reversediff

From d85408e7d1966980b9e406b79ac23ad6a65ed4a0 Mon Sep 17 00:00:00 2001
From: Matt Bossart <67015312+m-bossart@users.noreply.github.com>
Date: Mon, 22 Jul 2024 08:50:50 -0400
Subject: [PATCH 448/700] Update test/core/adjoint_tests.jl

Co-authored-by: Christopher Rackauckas <accounts@chrisrackauckas.com>
---
 lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
index 351557930..9b1ae05ff 100644
--- a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
@@ -17,5 +17,5 @@
     ∂p_tracker = Tracker.data(only(Tracker.gradient(solve_nlprob, p)))
     ∂p_reversediff = ReverseDiff.gradient(solve_nlprob, p)
     @test ∂p_zygote ≈ ∂p_tracker ≈ ∂p_reversediff
-    #@test ∂p_zygote ≈ ∂p_forwarddiff ≈ ∂p_tracker ≈ ∂p_reversediff
+    @test ∂p_zygote ≈ ∂p_forwarddiff ≈ ∂p_tracker ≈ ∂p_reversediff
 end

From b50726f477a81f32eeb546540e72b9572711816d Mon Sep 17 00:00:00 2001
From: Matt Bossart <67015312+m-bossart@users.noreply.github.com>
Date: Mon, 22 Jul 2024 08:51:39 -0400
Subject: [PATCH 449/700] Update src/ad.jl

Co-authored-by: Christopher Rackauckas <accounts@chrisrackauckas.com>
---
 lib/SimpleNonlinearSolve/src/ad.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index ce291d82e..3d9ce8d0e 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -42,7 +42,7 @@ for algType in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
 end
 
 function __nlsolve_ad(
-        prob::Union{IntervalNonlinearProblem, ImmutableNonlinearProblem}, alg, args...; kwargs...)
+        prob::Union{IntervalNonlinearProblem, NonlinearProblem, ImmutableNonlinearProblem}, alg, args...; kwargs...)
     p = value(prob.p)
     if prob isa IntervalNonlinearProblem
         tspan = value.(prob.tspan)

From 221759ee4df730ced1dade9bf4d808162f4c99ba Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 22 Jul 2024 10:10:33 -0400
Subject: [PATCH 450/700] format

---
 .../src/SimpleNonlinearSolve.jl               | 17 ++--
 lib/SimpleNonlinearSolve/src/ad.jl            |  3 +-
 .../src/immutable_nonlinear_problem.jl        | 77 +++++++++----------
 .../src/nlsolve/lbroyden.jl                   |  6 +-
 .../src/nlsolve/raphson.jl                    |  3 +-
 .../src/nlsolve/trustRegion.jl                |  4 +-
 lib/SimpleNonlinearSolve/src/utils.jl         |  6 +-
 7 files changed, 59 insertions(+), 57 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 0baa27655..ba0b243af 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -20,10 +20,10 @@ using LinearAlgebra: LinearAlgebra, I, convert, copyto!, diagind, dot, issuccess
 using MaybeInplace: @bb, setindex_trait, CanSetindex, CannotSetindex
 using Reexport: @reexport
 using SciMLBase: @add_kwonly, SciMLBase, AbstractNonlinearProblem, IntervalNonlinearProblem,
-                 AbstractNonlinearFunction, StandardNonlinearProblem,
-                 NonlinearFunction, NonlinearLeastSquaresProblem, NonlinearProblem,
-                 ReturnCode, init, remake, solve, AbstractNonlinearAlgorithm,
-                 build_solution, isinplace, _unwrap_val, warn_paramtype
+                 AbstractNonlinearFunction, StandardNonlinearProblem, NonlinearFunction,
+                 NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode, init, remake,
+                 solve, AbstractNonlinearAlgorithm, build_solution, isinplace, _unwrap_val,
+                 warn_paramtype
 using Setfield: @set!
 using StaticArraysCore: StaticArray, SVector, SMatrix, SArray, MArray, Size
 
@@ -81,8 +81,9 @@ function SciMLBase.solve(prob::NonlinearProblem, alg::AbstractSimpleNonlinearSol
         p === nothing, alg, args...; prob.kwargs..., kwargs...)
 end
 
-function SciMLBase.solve(prob::ImmutableNonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
-    args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...)
+function SciMLBase.solve(
+        prob::ImmutableNonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
+        args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...)
     if sensealg === nothing && haskey(prob.kwargs, :sensealg)
         sensealg = prob.kwargs[:sensealg]
     end
@@ -92,8 +93,8 @@ function SciMLBase.solve(prob::ImmutableNonlinearProblem, alg::AbstractSimpleNon
         p === nothing, alg, args...; prob.kwargs..., kwargs...)
 end
 
-function __internal_solve_up(_prob::ImmutableNonlinearProblem, sensealg, u0, u0_changed,
-        p, p_changed, alg, args...; kwargs...)
+function __internal_solve_up(_prob::ImmutableNonlinearProblem, sensealg, u0,
+        u0_changed, p, p_changed, alg, args...; kwargs...)
     prob = u0_changed || p_changed ? remake(_prob; u0, p) : _prob
     return SciMLBase.__solve(prob, alg, args...; kwargs...)
 end
diff --git a/lib/SimpleNonlinearSolve/src/ad.jl b/lib/SimpleNonlinearSolve/src/ad.jl
index 3d9ce8d0e..a83abdea7 100644
--- a/lib/SimpleNonlinearSolve/src/ad.jl
+++ b/lib/SimpleNonlinearSolve/src/ad.jl
@@ -42,7 +42,8 @@ for algType in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
 end
 
 function __nlsolve_ad(
-        prob::Union{IntervalNonlinearProblem, NonlinearProblem, ImmutableNonlinearProblem}, alg, args...; kwargs...)
+        prob::Union{IntervalNonlinearProblem, NonlinearProblem, ImmutableNonlinearProblem},
+        alg, args...; kwargs...)
     p = value(prob.p)
     if prob isa IntervalNonlinearProblem
         tspan = value.(prob.tspan)
diff --git a/lib/SimpleNonlinearSolve/src/immutable_nonlinear_problem.jl b/lib/SimpleNonlinearSolve/src/immutable_nonlinear_problem.jl
index ca1dfc079..99772c5b0 100644
--- a/lib/SimpleNonlinearSolve/src/immutable_nonlinear_problem.jl
+++ b/lib/SimpleNonlinearSolve/src/immutable_nonlinear_problem.jl
@@ -1,65 +1,60 @@
 struct ImmutableNonlinearProblem{uType, isinplace, P, F, K, PT} <:
-    AbstractNonlinearProblem{uType, isinplace}
- f::F
- u0::uType
- p::P
- problem_type::PT
- kwargs::K
- @add_kwonly function ImmutableNonlinearProblem{iip}(f::AbstractNonlinearFunction{iip}, u0,
-         p = NullParameters(),
-         problem_type = StandardNonlinearProblem();
-         kwargs...) where {iip}
-     if haskey(kwargs, :p)
-         error("`p` specified as a keyword argument `p = $(kwargs[:p])` to `NonlinearProblem`. This is not supported.")
-     end
-     warn_paramtype(p)
-     new{typeof(u0), iip, typeof(p), typeof(f),
-         typeof(kwargs), typeof(problem_type)}(f,
-         u0,
-         p,
-         problem_type,
-         kwargs)
- end
+       AbstractNonlinearProblem{uType, isinplace}
+    f::F
+    u0::uType
+    p::P
+    problem_type::PT
+    kwargs::K
+    @add_kwonly function ImmutableNonlinearProblem{iip}(
+            f::AbstractNonlinearFunction{iip}, u0, p = NullParameters(),
+            problem_type = StandardNonlinearProblem(); kwargs...) where {iip}
+        if haskey(kwargs, :p)
+            error("`p` specified as a keyword argument `p = $(kwargs[:p])` to `NonlinearProblem`. This is not supported.")
+        end
+        warn_paramtype(p)
+        new{typeof(u0), iip, typeof(p), typeof(f), typeof(kwargs), typeof(problem_type)}(
+            f, u0, p, problem_type, kwargs)
+    end
 
- """
- Define a steady state problem using the given function.
- `isinplace` optionally sets whether the function is inplace or not.
- This is determined automatically, but not inferred.
- """
- function ImmutableNonlinearProblem{iip}(f, u0, p = NullParameters(); kwargs...) where {iip}
-     ImmutableNonlinearProblem{iip}(NonlinearFunction{iip}(f), u0, p; kwargs...)
- end
+    """
+    Define a steady state problem using the given function.
+    `isinplace` optionally sets whether the function is inplace or not.
+    This is determined automatically, but not inferred.
+    """
+    function ImmutableNonlinearProblem{iip}(
+            f, u0, p = NullParameters(); kwargs...) where {iip}
+        ImmutableNonlinearProblem{iip}(NonlinearFunction{iip}(f), u0, p; kwargs...)
+    end
 end
 
 """
 Define a nonlinear problem using an instance of
 [`AbstractNonlinearFunction`](@ref AbstractNonlinearFunction).
 """
-function ImmutableNonlinearProblem(f::AbstractNonlinearFunction, u0, p = NullParameters(); kwargs...)
- ImmutableNonlinearProblem{isinplace(f)}(f, u0, p; kwargs...)
+function ImmutableNonlinearProblem(
+        f::AbstractNonlinearFunction, u0, p = NullParameters(); kwargs...)
+    ImmutableNonlinearProblem{isinplace(f)}(f, u0, p; kwargs...)
 end
 
 function ImmutableNonlinearProblem(f, u0, p = NullParameters(); kwargs...)
- ImmutableNonlinearProblem(NonlinearFunction(f), u0, p; kwargs...)
+    ImmutableNonlinearProblem(NonlinearFunction(f), u0, p; kwargs...)
 end
 
 """
 Define a ImmutableNonlinearProblem problem from SteadyStateProblem
 """
 function ImmutableNonlinearProblem(prob::AbstractNonlinearProblem)
- ImmutableNonlinearProblem{isinplace(prob)}(prob.f, prob.u0, prob.p)
+    ImmutableNonlinearProblem{isinplace(prob)}(prob.f, prob.u0, prob.p)
 end
 
-
-function Base.convert(::Type{ImmutableNonlinearProblem}, prob::T) where {T <: NonlinearProblem}
- ImmutableNonlinearProblem{isinplace(prob)}(prob.f,
-     prob.u0,
-     prob.p,
-     prob.problem_type;
-     prob.kwargs...)
+function Base.convert(
+        ::Type{ImmutableNonlinearProblem}, prob::T) where {T <: NonlinearProblem}
+    ImmutableNonlinearProblem{isinplace(prob)}(
+        prob.f, prob.u0, prob.p, prob.problem_type; prob.kwargs...)
 end
 
-function DiffEqBase.get_concrete_problem(prob::ImmutableNonlinearProblem, isadapt; kwargs...)
+function DiffEqBase.get_concrete_problem(
+        prob::ImmutableNonlinearProblem, isadapt; kwargs...)
     u0 = DiffEqBase.get_concrete_u0(prob, isadapt, nothing, kwargs)
     u0 = DiffEqBase.promote_u0(u0, prob.p, nothing)
     p = DiffEqBase.get_concrete_p(prob, kwargs)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
index 683e9e592..891043aca 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/lbroyden.jl
@@ -44,7 +44,8 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleLimitedMe
     return __generic_solve(prob, alg, args...; termination_condition, kwargs...)
 end
 
-@views function __generic_solve(prob::ImmutableNonlinearProblem, alg::SimpleLimitedMemoryBroyden,
+@views function __generic_solve(
+        prob::ImmutableNonlinearProblem, alg::SimpleLimitedMemoryBroyden,
         args...; abstol = nothing, reltol = nothing, maxiters = 1000,
         alias_u0 = false, termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
@@ -114,7 +115,8 @@ end
 # Non-allocating StaticArrays version of SimpleLimitedMemoryBroyden is actually quite
 # finicky, so we'll implement it separately from the generic version
 # Ignore termination_condition. Don't pass things into internal functions
-function __static_solve(prob::ImmutableNonlinearProblem{<:SArray}, alg::SimpleLimitedMemoryBroyden,
+function __static_solve(
+        prob::ImmutableNonlinearProblem{<:SArray}, alg::SimpleLimitedMemoryBroyden,
         args...; abstol = nothing, maxiters = 1000, kwargs...)
     x = prob.u0
     fx = _get_fx(prob, x)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
index d7e72dbdf..bdf45fffc 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/raphson.jl
@@ -23,7 +23,8 @@ end
 
 const SimpleGaussNewton = SimpleNewtonRaphson
 
-function SciMLBase.__solve(prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
+function SciMLBase.__solve(
+        prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
         alg::SimpleNewtonRaphson, args...; abstol = nothing, reltol = nothing,
         maxiters = 1000, termination_condition = nothing, alias_u0 = false, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
index 2e78baf02..cc937724c 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/trustRegion.jl
@@ -55,8 +55,8 @@ scalar and static array problems.
     nlsolve_update_rule = Val(false)
 end
 
-function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleTrustRegion, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000,
+function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleTrustRegion,
+        args...; abstol = nothing, reltol = nothing, maxiters = 1000,
         alias_u0 = false, termination_condition = nothing, kwargs...)
     x = __maybe_unaliased(prob.u0, alias_u0)
     T = eltype(real(x))
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 9380ff186..157d8f03f 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -145,7 +145,8 @@ end
 # different. NonlinearSolve is more for robust / cached solvers while SimpleNonlinearSolve
 # is meant for low overhead solvers, users can opt into the other termination modes but the
 # default is to use the least overhead version.
-function init_termination_cache(prob::ImmutableNonlinearProblem, abstol, reltol, du, u, ::Nothing)
+function init_termination_cache(
+        prob::ImmutableNonlinearProblem, abstol, reltol, du, u, ::Nothing)
     return init_termination_cache(
         prob, abstol, reltol, du, u, AbsNormTerminationMode(Base.Fix1(maximum, abs)))
 end
@@ -155,7 +156,8 @@ function init_termination_cache(
         prob, abstol, reltol, du, u, AbsNormTerminationMode(Base.Fix2(norm, 2)))
 end
 
-function init_termination_cache(prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
+function init_termination_cache(
+        prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
         abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
     T = promote_type(eltype(du), eltype(u))
     abstol = __get_tolerance(u, abstol, T)

From 5e5aed1d309eb439d5a93288c76f329bc94cc9cd Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 22 Jul 2024 10:15:59 -0400
Subject: [PATCH 451/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index c27d74903..8e7311f58 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.10.1"
+version = "1.11.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 232e91e2630173daecaf4b01865e63af31f56803 Mon Sep 17 00:00:00 2001
From: Anant Thazhemadam <anant.thazhemadam@gmail.com>
Date: Mon, 29 Apr 2024 19:27:29 +0530
Subject: [PATCH 452/700] ci: update invalidations workflow to use centralised
 reusable workflow

---
 .../.github/workflows/Invalidations.yml       | 33 +++----------------
 1 file changed, 4 insertions(+), 29 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml b/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml
index 66c86a362..34eb7a92a 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Invalidations.yml
@@ -1,4 +1,4 @@
-name: Invalidations
+name: "Invalidations"
 
 on:
   pull_request:
@@ -10,31 +10,6 @@ concurrency:
   cancel-in-progress: true
 
 jobs:
-  evaluate:
-    # Only run on PRs to the default branch.
-    # In the PR trigger above branches can be specified only explicitly whereas this check should work for master, main, or any other default branch
-    if: github.base_ref == github.event.repository.default_branch
-    runs-on: ubuntu-latest
-    steps:
-    - uses: julia-actions/setup-julia@v2
-      with:
-        version: '1'
-    - uses: actions/checkout@v4
-    - uses: julia-actions/julia-buildpkg@v1
-    - uses: julia-actions/julia-invalidations@v1
-      id: invs_pr
-
-    - uses: actions/checkout@v4
-      with:
-        ref: ${{ github.event.repository.default_branch }}
-    - uses: julia-actions/julia-buildpkg@v1
-    - uses: julia-actions/julia-invalidations@v1
-      id: invs_default
-    
-    - name: Report invalidation counts
-      run: |
-        echo "Invalidations on default branch: ${{ steps.invs_default.outputs.total }} (${{ steps.invs_default.outputs.deps }} via deps)" >> $GITHUB_STEP_SUMMARY
-        echo "This branch: ${{ steps.invs_pr.outputs.total }} (${{ steps.invs_pr.outputs.deps }} via deps)" >> $GITHUB_STEP_SUMMARY
-    - name: Check if the PR does increase number of invalidations
-      if: steps.invs_pr.outputs.total > steps.invs_default.outputs.total
-      run: exit 1
+  evaluate-invalidations:
+    name: "Evaluate Invalidations"
+    uses: "SciML/.github/.github/workflows/invalidations.yml@v1"

From 35e07737955c0d5181af0cfe8fcd8afc01f9d7b6 Mon Sep 17 00:00:00 2001
From: Anant Thazhemadam <anant.thazhemadam@gmail.com>
Date: Mon, 29 Apr 2024 19:41:25 +0530
Subject: [PATCH 453/700] ci: update format check workflow to use centralised
 reusable workflow

---
 .../.github/workflows/FormatCheck.yml            | 16 ++++++++++------
 1 file changed, 10 insertions(+), 6 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
index 0ddeb4ed1..7e46c8db9 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
@@ -1,9 +1,13 @@
-name: Format suggestions
+name: "Format Check"
 
-on: [pull_request]
+on:
+  push:
+    branches:
+      - 'main'
+    tags: '*'
+  pull_request:
 
 jobs:
-  code-style:
-    runs-on: ubuntu-latest
-    steps:
-      - uses: julia-actions/julia-format@v3
+  format-check:
+    name: "Format Check"
+    uses: "SciML/.github/.github/workflows/format-check.yml@v1"

From 231b11483aa5de737e2a111bbd70f0c9b4f293fb Mon Sep 17 00:00:00 2001
From: Anant Thazhemadam <anant.thazhemadam@gmail.com>
Date: Thu, 1 Aug 2024 00:12:14 +0200
Subject: [PATCH 454/700] ci: update tests workflow to use centralized reusable
 workflow

---
 .../.github/workflows/CI.yml                  | 55 -------------------
 .../.github/workflows/Tests.yml               | 42 ++++++++++++++
 2 files changed, 42 insertions(+), 55 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/.github/workflows/CI.yml
 create mode 100644 lib/SimpleNonlinearSolve/.github/workflows/Tests.yml

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml b/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
deleted file mode 100644
index 295de1024..000000000
--- a/lib/SimpleNonlinearSolve/.github/workflows/CI.yml
+++ /dev/null
@@ -1,55 +0,0 @@
-name: CI
-on:
-  pull_request:
-    branches:
-      - main
-  push:
-    branches:
-      - main
-jobs:
-  test:
-    runs-on: ${{ matrix.os }}
-    strategy:
-      fail-fast: false
-      matrix:
-        group:
-          - Core
-        version:
-          - '1'
-        os:
-          - ubuntu-latest
-          - macos-latest
-          - windows-latest
-    steps:
-      - uses: actions/checkout@v4
-      - uses: julia-actions/setup-julia@v2
-        with:
-          version: ${{ matrix.version }}
-      - uses: actions/cache@v4
-        env:
-          cache-name: cache-artifacts
-        with:
-          path: ~/.julia/artifacts
-          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
-          restore-keys: |
-            ${{ runner.os }}-test-${{ env.cache-name }}-
-            ${{ runner.os }}-test-
-            ${{ runner.os }}-
-      - uses: julia-actions/julia-buildpkg@v1
-      - uses: julia-actions/julia-runtest@v1
-        with:
-          annotate: true
-        env:
-          GROUP: ${{ matrix.group }}
-          JULIA_NUM_THREADS: 11
-          RETESTITEMS_NWORKERS: 4
-          RETESTITEMS_NWORKER_THREADS: 2
-      - uses: julia-actions/julia-processcoverage@v1
-        with:
-          directories: src,ext
-      - uses: codecov/codecov-action@v4
-        with:
-          file: lcov.info
-          token: ${{ secrets.CODECOV_TOKEN }}
-          verbose: true
-          fail_ci_if_error: true
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Tests.yml b/lib/SimpleNonlinearSolve/.github/workflows/Tests.yml
new file mode 100644
index 000000000..8fa495e19
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Tests.yml
@@ -0,0 +1,42 @@
+name: "Tests"
+
+on:
+  pull_request:
+    branches:
+      - main
+      - 'release-'
+    paths-ignore:
+      - 'docs/**'
+  push:
+    branches:
+      - main
+    paths-ignore:
+      - 'docs/**'
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ github.ref_name != github.event.repository.default_branch || github.ref != 'refs/tags/v*' }}
+
+env:
+  JULIA_NUM_THREADS: 11
+  RETESTITEMS_NWORKERS: 4
+  RETESTITEMS_NWORKER_THREADS: 2
+
+jobs:
+  tests:
+    name: "Tests"
+    strategy:
+      fail-fast: false
+      matrix:
+        group:
+          - "Core"
+        os:
+          - "ubuntu-latest"
+          - "macos-latest"
+          - "windows-latest"
+
+    uses: "SciML/.github/.github/workflows/tests.yml@v1"
+    with:
+      group: "${{ matrix.group }}"
+      os: "${{ matrix.os }}"
+    secrets: "inherit"

From eb43c5a4cda6801107cde57d6f00c82b3c744def Mon Sep 17 00:00:00 2001
From: Anant Thazhemadam <anant.thazhemadam@gmail.com>
Date: Thu, 1 Aug 2024 00:12:26 +0200
Subject: [PATCH 455/700] ci(format-check): automatically comment formatting
 suggestions on PRs

---
 lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
index 7e46c8db9..fe9c1280f 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/FormatCheck.yml
@@ -10,4 +10,4 @@ on:
 jobs:
   format-check:
     name: "Format Check"
-    uses: "SciML/.github/.github/workflows/format-check.yml@v1"
+    uses: "SciML/.github/.github/workflows/format-suggestions-on-pr.yml@v1"

From 2e63a1346e8209e91528ca1a6ab7dee3903965ed Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Daniel=20Gonz=C3=A1lez?= <daniel.glez.arribas@gmail.com>
Date: Fri, 9 Aug 2024 16:37:08 +0200
Subject: [PATCH 456/700] Docs, scaling factor

---
 lib/SimpleNonlinearSolve/src/bracketing/itp.jl | 14 ++++++++++----
 1 file changed, 10 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
index 4a542a958..e75642c5b 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
@@ -15,16 +15,22 @@ I. F. D. Oliveira and R. H. C. Takahashi.
 The following keyword parameters are accepted.
 
   - `n₀::Int = 10`, the 'slack'. Must not be negative. When n₀ = 0 the worst-case is
-    identical to that of bisection, but increacing n₀ provides greater oppotunity for
+    identical to that of bisection, but increasing n₀ provides greater opportunity for
     superlinearity.
-  - `scaled_κ₁::Float64 = 0.2`. Must not be negative. The recomended value is `0.2`.
+  - `scaled_κ₁::Float64 = 0.2`. Must not be negative. The recommended value is `0.2`.
     Lower values produce tighter asymptotic behaviour, while higher values improve the
     steady-state behaviour when truncation is not helpful.
   - `κ₂::Real = 2`. Must lie in [1, 1+ϕ ≈ 2.62). Higher values allow for a greater
     convergence rate, but also make the method more succeptable to worst-case performance.
-    In practice, κ=1, 2 seems to work well due to the computational simplicity, as κ₂ is
+    In practice, κ₂=1, 2 seems to work well due to the computational simplicity, as κ₂ is
     used as an exponent in the method.
 
+### Computation of κ₁
+
+In the current implementation, we compute κ₁ = scaled_κ₁·|Δx₀|^(1 - κ₂); this allows κ₁ to
+adapt to the dimension of the problem in order to keep the proposed initial step
+proportional to Δx₀.
+
 ### Worst Case Performance
 
 n½ + `n₀` iterations, where n½ is the number of iterations using bisection
@@ -72,8 +78,8 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
     end
     ϵ = abstol
     #defining variables/cache
-    k1 = alg.scaled_k1 / abs(right - left)
     k2 = alg.k2
+    k1 = alg.scaled_k1 * abs(right - left)^(1 - k2)
     n0 = alg.n0
     n_h = ceil(log2(abs(right - left) / (2 * ϵ)))
     mid = (left + right) / 2

From ec1e309598547a20fc6006551cd416dbad78d01e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Daniel=20Gonz=C3=A1lez?= <daniel.glez.arribas@gmail.com>
Date: Fri, 9 Aug 2024 17:24:46 +0200
Subject: [PATCH 457/700] Docstring update

---
 lib/SimpleNonlinearSolve/src/bracketing/itp.jl | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
index e75642c5b..4cc9e9b0c 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
@@ -28,8 +28,7 @@ The following keyword parameters are accepted.
 ### Computation of κ₁
 
 In the current implementation, we compute κ₁ = scaled_κ₁·|Δx₀|^(1 - κ₂); this allows κ₁ to
-adapt to the dimension of the problem in order to keep the proposed initial step
-proportional to Δx₀.
+adapt to the length of the interval and keep the proposed steps proportional to Δx.
 
 ### Worst Case Performance
 

From 145d5f221c5b4c43c24436b79390fe1b1c881620 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Daniel=20Gonz=C3=A1lez?= <daniel.glez.arribas@gmail.com>
Date: Fri, 9 Aug 2024 18:09:38 +0200
Subject: [PATCH 458/700] Fix ITP for generic output numbers

---
 lib/SimpleNonlinearSolve/src/bracketing/itp.jl | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
index 4cc9e9b0c..4c92645ba 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
@@ -124,10 +124,11 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
         xp <= tmin && (xp = nextfloat(tmin))
         yp = f(xp)
         yps = yp * sign(fr)
-        if yps > 0
+        T0 = zero(yps)
+        if yps > T0
             right = xp
             fr = yp
-        elseif yps < 0
+        elseif yps < T0
             left = xp
             fl = yp
         else

From 0614b6aff579dd30c9a799aa04fa2d99a5c22e6c Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 10 Aug 2024 11:46:43 -0400
Subject: [PATCH 459/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 8e7311f58..c90abe15c 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.11.0"
+version = "1.12.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From c0ffc829a264f7cd07334d85f6c591383dbfe53d Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sun, 11 Aug 2024 04:46:16 -0400
Subject: [PATCH 460/700] Allow Symbolics v6

---
 Project.toml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Project.toml b/Project.toml
index fece700ac..b706d37db 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.13.1"
+version = "3.14.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -105,7 +105,7 @@ StaticArrays = "1.9"
 StaticArraysCore = "1.4"
 Sundials = "4.23.1"
 SymbolicIndexingInterface = "0.3.15"
-Symbolics = "5.26"
+Symbolics = "5.26, 6"
 Test = "1.10"
 TimerOutputs = "0.5.23"
 Zygote = "0.6.69"

From 1376bb9a106ff54436993947c19875ddbd363a07 Mon Sep 17 00:00:00 2001
From: CompatHelper Julia <compathelper_noreply@julialang.org>
Date: Sun, 11 Aug 2024 09:07:15 +0000
Subject: [PATCH 461/700] CompatHelper: bump compat for Symbolics to 6 for
 package docs, (keep existing compat)

---
 docs/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/Project.toml b/docs/Project.toml
index f62ef73aa..780cec74a 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -41,4 +41,4 @@ SparseDiffTools = "2.14"
 StaticArrays = "1"
 SteadyStateDiffEq = "2"
 Sundials = "4.11"
-Symbolics = "4, 5"
+Symbolics = "4, 5, 6"

From 86e67209904b860e974b67a0c6b734ccf425a04c Mon Sep 17 00:00:00 2001
From: ErikQQY <2283984853@qq.com>
Date: Mon, 19 Aug 2024 15:25:35 +0800
Subject: [PATCH 462/700] Better BigFloat support

Signed-off-by: ErikQQY <2283984853@qq.com>
---
 src/default.jl                   |  2 +-
 src/globalization/line_search.jl |  8 ++++----
 src/internal/helpers.jl          |  4 ++--
 src/internal/jacobian.jl         |  2 +-
 src/internal/operators.jl        | 16 ++++++++--------
 src/utils.jl                     | 10 +---------
 6 files changed, 17 insertions(+), 25 deletions(-)

diff --git a/src/default.jl b/src/default.jl
index ab35b7a55..b4613a6f7 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -266,7 +266,7 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
                     alias_u0 = false  # If immutable don't care about aliasing
                 end
                 u0 = prob.u0
-                u0_aliased = alias_u0 ? __similar(u0) : u0
+                u0_aliased = alias_u0 ? zero(u0) : u0
             end]
             for i in 1:N
                 cur_sol = sol_syms[i]
diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index 4fca295e7..5de4610b6 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -125,7 +125,7 @@ function __internal_init(
             deriv_op = nothing
         elseif SciMLBase.has_jvp(f)
             if isinplace(prob)
-                jvp_cache = __similar(fu)
+                jvp_cache = zero(fu)
                 deriv_op = @closure (du, u, fu, p) -> begin
                     f.jvp(jvp_cache, du, u, p)
                     dot(fu, jvp_cache)
@@ -135,7 +135,7 @@ function __internal_init(
             end
         elseif SciMLBase.has_vjp(f)
             if isinplace(prob)
-                vjp_cache = __similar(u)
+                vjp_cache = zero(u)
                 deriv_op = @closure (du, u, fu, p) -> begin
                     f.vjp(vjp_cache, fu, u, p)
                     dot(du, vjp_cache)
@@ -149,7 +149,7 @@ function __internal_init(
                 alg.autodiff, prob; check_reverse_mode = true)
             vjp_op = VecJacOperator(prob, fu, u; autodiff)
             if isinplace(prob)
-                vjp_cache = __similar(u)
+                vjp_cache = zero(u)
                 deriv_op = @closure (du, u, fu, p) -> dot(du, vjp_op(vjp_cache, fu, u, p))
             else
                 deriv_op = @closure (du, u, fu, p) -> dot(du, vjp_op(fu, u, p))
@@ -159,7 +159,7 @@ function __internal_init(
                 alg.autodiff, prob; check_forward_mode = true)
             jvp_op = JacVecOperator(prob, fu, u; autodiff)
             if isinplace(prob)
-                jvp_cache = __similar(fu)
+                jvp_cache = zero(fu)
                 deriv_op = @closure (du, u, fu, p) -> dot(fu, jvp_op(jvp_cache, du, u, p))
             else
                 deriv_op = @closure (du, u, fu, p) -> dot(fu, jvp_op(du, u, p))
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index db88a7d23..abf6f1099 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -2,7 +2,7 @@
 function evaluate_f(prob::AbstractNonlinearProblem{uType, iip}, u) where {uType, iip}
     (; f, u0, p) = prob
     if iip
-        fu = f.resid_prototype === nothing ? __similar(u) :
+        fu = f.resid_prototype === nothing ? zero(u) :
              promote_type(eltype(u), eltype(f.resid_prototype)).(f.resid_prototype)
         f(fu, u, p)
     else
@@ -156,7 +156,7 @@ function __construct_extension_f(prob::AbstractNonlinearProblem; alias_u0::Bool
 
     𝐅 = if force_oop === True && applicable(𝐟, u0, u0)
         _resid = resid isa Number ? [resid] : _vec(resid)
-        du = _vec(__similar(_resid))
+        du = _vec(zero(_resid))
         @closure u -> begin
             𝐟(du, u)
             return du
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 6a549721d..b712b93e2 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -85,7 +85,7 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
             __similar(fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u)) :
             copy(f.jac_prototype)
         elseif f.jac_prototype === nothing
-            __init_bigfloat_array!!(init_jacobian(
+            zero(init_jacobian(
                 jac_cache; preserve_immutable = Val(true)))
         else
             f.jac_prototype
diff --git a/src/internal/operators.jl b/src/internal/operators.jl
index c7d8f586e..5bbfcb0bf 100644
--- a/src/internal/operators.jl
+++ b/src/internal/operators.jl
@@ -74,8 +74,8 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
             @closure (v, u, p) -> auto_vecjac(uf, u, v)
         elseif vjp_autodiff isa AutoFiniteDiff
             if iip
-                cache1 = __similar(fu)
-                cache2 = __similar(fu)
+                cache1 = zero(fu)
+                cache2 = zero(fu)
                 @closure (Jv, v, u, p) -> num_vecjac!(Jv, uf, u, v, cache1, cache2)
             else
                 @closure (v, u, p) -> num_vecjac(uf, __mutable(u), v)
@@ -106,17 +106,17 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
             if iip
                 # FIXME: Technically we should propagate the tag but ignoring that for now
                 cache1 = Dual{typeof(ForwardDiff.Tag(uf, eltype(u))), eltype(u),
-                    1}.(__similar(u), ForwardDiff.Partials.(tuple.(u)))
+                    1}.(zero(u), ForwardDiff.Partials.(tuple.(u)))
                 cache2 = Dual{typeof(ForwardDiff.Tag(uf, eltype(fu))), eltype(fu),
-                    1}.(__similar(fu), ForwardDiff.Partials.(tuple.(fu)))
+                    1}.(zero(fu), ForwardDiff.Partials.(tuple.(fu)))
                 @closure (Jv, v, u, p) -> auto_jacvec!(Jv, uf, u, v, cache1, cache2)
             else
                 @closure (v, u, p) -> auto_jacvec(uf, u, v)
             end
         elseif jvp_autodiff isa AutoFiniteDiff
             if iip
-                cache1 = __similar(fu)
-                cache2 = __similar(u)
+                cache1 = zero(fu)
+                cache2 = zero(u)
                 @closure (Jv, v, u, p) -> num_jacvec!(Jv, uf, u, v, cache1, cache2)
             else
                 @closure (v, u, p) -> num_jacvec(uf, u, v)
@@ -162,7 +162,7 @@ end
 function (op::JacobianOperator{vjp, iip})(v, u, p) where {vjp, iip}
     if vjp
         if iip
-            res = __similar(op.output_cache)
+            res = zero(op.output_cache)
             op.vjp_op(res, v, u, p)
             return res
         else
@@ -170,7 +170,7 @@ function (op::JacobianOperator{vjp, iip})(v, u, p) where {vjp, iip}
         end
     else
         if iip
-            res = __similar(op.output_cache)
+            res = zero(op.output_cache)
             op.jvp_op(res, v, u, p)
             return res
         else
diff --git a/src/utils.jl b/src/utils.jl
index 50faa710c..64399a349 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -163,13 +163,5 @@ end
 
 function __similar(x, args...; kwargs...)
     y = similar(x, args...; kwargs...)
-    return __init_bigfloat_array!!(y)
-end
-
-function __init_bigfloat_array!!(x)
-    if ArrayInterface.can_setindex(x)
-        eltype(x) <: BigFloat && fill!(x, BigFloat(0))
-        return x
-    end
-    return x
+    return zero(y)
 end

From e799b105ee7439abc3323ba625284e46fae53219 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 16 Sep 2024 17:14:17 -0400
Subject: [PATCH 463/700] fix: missing Tracker.data

---
 lib/SimpleNonlinearSolve/Project.toml                          | 2 +-
 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index c90abe15c..030b0385e 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.12.0"
+version = "1.12.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
index 679274754..fd56ee284 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
@@ -37,7 +37,7 @@ for pType in (ImmutableNonlinearProblem, NonlinearLeastSquaresProblem)
                 prob, sensealg, u0, p, TrackerOriginator(), alg, args...; kwargs...)
 
             function ∇__internal_solve_up(Δ)
-                ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(Δ)
+                ∂prob, ∂sensealg, ∂u0, ∂p, ∂originator, ∂args... = ∇internal(Tracker.data(Δ))
                 return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
             end
 

From 7b994727afd2df965fa2d112f1f5d9fe87779a53 Mon Sep 17 00:00:00 2001
From: tom <tom.rottier@manchester.ac.uk>
Date: Mon, 23 Sep 2024 18:09:24 -0400
Subject: [PATCH 464/700] Return InitialFailure from bracketing methods if not
 enclosing interval

---
 lib/SimpleNonlinearSolve/src/bracketing/bisection.jl | 6 ++++++
 lib/SimpleNonlinearSolve/src/bracketing/brent.jl     | 6 ++++++
 lib/SimpleNonlinearSolve/src/bracketing/falsi.jl     | 6 ++++++
 lib/SimpleNonlinearSolve/src/bracketing/itp.jl       | 7 +++++++
 lib/SimpleNonlinearSolve/src/bracketing/ridder.jl    | 6 ++++++
 5 files changed, 31 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
index d55a0ce5e..adcf72a4b 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
@@ -39,6 +39,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection,
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     i = 1
     if !iszero(fr)
         while i < maxiters
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/brent.jl b/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
index 649286e03..4ba311f5d 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
@@ -26,6 +26,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     if abs(fl) < abs(fr)
         c = right
         right = left
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl b/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
index ee78b73fc..00b29703b 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
@@ -25,6 +25,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     # Regula Falsi Steps
     i = 0
     if !iszero(fr)
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
index 4c92645ba..9405cc2de 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
@@ -75,6 +75,13 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
         return build_solution(
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
+
+    if sign(fl) == sign(fr)
+        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     ϵ = abstol
     #defining variables/cache
     k2 = alg.k2
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
index a974824c2..772f568d1 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
@@ -25,6 +25,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     xo = oftype(left, Inf)
     i = 1
     if !iszero(fr)

From 45d63d20891170ba7f671b44c79b21e0c22854cb Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 24 Sep 2024 06:22:05 -0400
Subject: [PATCH 465/700] Update Project.toml

---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 030b0385e..8d7b044a9 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.12.1"
+version = "1.12.2"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 6261e022fe503d08412d074236e8832e5e55ae15 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 12:33:43 -0400
Subject: [PATCH 466/700] ci: trigger build


From 0b6f0e5f80af2279bc3ed1934f51172f71a319b4 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 23 Sep 2024 14:23:10 -0400
Subject: [PATCH 467/700] feat: add SciMLJacobianOperators package

---
 Project.toml                                  |   1 +
 lib/SciMLJacobianOperators/LICENSE            |  21 ++
 lib/SciMLJacobianOperators/Project.toml       |  31 +++
 .../src/SciMLJacobianOperators.jl             | 199 ++++++++++++++++++
 4 files changed, 252 insertions(+)
 create mode 100644 lib/SciMLJacobianOperators/LICENSE
 create mode 100644 lib/SciMLJacobianOperators/Project.toml
 create mode 100644 lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl

diff --git a/Project.toml b/Project.toml
index b706d37db..edfd8f8f0 100644
--- a/Project.toml
+++ b/Project.toml
@@ -23,6 +23,7 @@ Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
 SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
diff --git a/lib/SciMLJacobianOperators/LICENSE b/lib/SciMLJacobianOperators/LICENSE
new file mode 100644
index 000000000..abb594d1e
--- /dev/null
+++ b/lib/SciMLJacobianOperators/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2024 SciML
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
new file mode 100644
index 000000000..478ddcb57
--- /dev/null
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -0,0 +1,31 @@
+name = "SciMLJacobianOperators"
+uuid = "19f34311-ddf3-4b8b-af20-060888a46c0e"
+authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
+version = "0.1.0"
+
+[deps]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
+ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
+ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
+DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
+FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
+SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
+Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
+
+[compat]
+ADTypes = "1.8.1"
+ConcreteStructs = "0.2.3"
+ConstructionBase = "1.5.8"
+DifferentiationInterface = "0.5.17"
+FastClosures = "0.3.2"
+SciMLOperators = "0.3.10"
+Setfield = "1.1.1"
+julia = "1.10"
+
+[extras]
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
+
+[targets]
+test = ["Test", "TestItemRunner"]
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
new file mode 100644
index 000000000..620bd66bc
--- /dev/null
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -0,0 +1,199 @@
+module SciMLJacobianOperators
+
+using ADTypes: ADTypes
+using ConcreteStructs: @concrete
+using ConstructionBase: ConstructionBase
+using DifferentiationInterface: DifferentiationInterface
+using FastClosures: @closure
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, AbstractNonlinearFunction
+using SciMLOperators: AbstractSciMLOperator
+using Setfield: @set!
+
+const DI = DifferentiationInterface
+const True = Val(true)
+const False = Val(false)
+
+abstract type AbstractMode end
+
+struct VJP <: AbstractMode end
+struct JVP <: AbstractMode end
+
+flip_mode(::VJP) = JVP()
+flip_mode(::JVP) = VJP()
+
+@concrete struct JacobianOperator{iip, T <: Real} <: AbstractSciMLOperator{T}
+    mode <: AbstractMode
+
+    jvp_op
+    vjp_op
+
+    size
+    jvp_extras
+    vjp_extras
+end
+
+function ConstructionBase.constructorof(::Type{<:JacobianOperator{iip, T}}) where {iip, T}
+    return JacobianOperator{iip, T}
+end
+
+Base.size(J::JacobianOperator) = J.size
+Base.size(J::JacobianOperator, d::Integer) = J.size[d]
+
+for op in (:adjoint, :transpose)
+    @eval function Base.$(op)(operator::JacobianOperator)
+        @set! operator.mode = flip_mode(operator.mode)
+        return operator
+    end
+end
+
+function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff = nothing,
+        vjp_autodiff = nothing, skip_vjp::Val = False, skip_jvp::Val = False)
+    @assert !(skip_vjp === True && skip_jvp === True) "Cannot skip both vjp and jvp \
+                                                       construction."
+    f = prob.f
+    iip = SciMLBase.isinplace(prob)
+    T = promote_type(eltype(u), eltype(fu))
+    fₚ = SciMLBase.JacobianWrapper{iip}(f, prob.p)
+
+    vjp_op, vjp_extras = prepare_vjp(skip_vjp, prob, f, u, fu; autodiff = vjp_autodiff)
+    jvp_op, jvp_extras = prepare_jvp(skip_jvp, prob, f, u, fu; autodiff = jvp_autodiff)
+
+    return JacobianOperator{iip, T}(
+        JVP(), jvp_op, vjp_op, (length(fu), length(u)), jvp_extras, vjp_extras)
+end
+
+prepare_vjp(::Val{true}, args...; kwargs...) = nothing, nothing
+
+function prepare_vjp(::Val{false}, prob::AbstractNonlinearProblem,
+        f::AbstractNonlinearFunction, u::Number, fu::Number; autodiff = nothing)
+    return prepare_scalar_op(Val(false), prob, f, u, fu; autodiff)
+end
+
+function prepare_vjp(::Val{false}, prob::AbstractNonlinearProblem,
+        f::AbstractNonlinearFunction, u, fu; autodiff = nothing)
+    SciMLBase.has_vjp(f) && return f.vjp, nothing
+
+    if autodiff === nothing && SciMLBase.has_jac(f)
+        if SciMLBase.isinplace(f)
+            vjp_extras = (; jac_cache = similar(u, eltype(fu), length(fu), length(u)))
+            vjp_op = @closure (vJ, v, u, p, extras) -> begin
+                f.jac(extras.jac_cache, u, p)
+                mul!(vec(vJ), extras.jac_cache', vec(v))
+                return
+            end
+            return vjp_op, vjp_extras
+        else
+            vjp_op = @closure (v, u, p, _) -> reshape(f.jac(u, p)' * vec(v), size(u))
+            return vjp_op, nothing
+        end
+    end
+
+    @assert autodiff!==nothing "`vjp_autodiff` must be provided if `f` doesn't have \
+                                analytic `vjp` or `jac`."
+
+    if ADTypes.mode(autodiff) isa ADTypes.ForwardMode
+        @warn "AD Backend: $(autodiff) is a Forward Mode backend. Computing VJPs using \
+               this will be slow!"
+    end
+
+    # TODO: Once DI supports const params we can use `p`
+    fₚ = SciMLBase.JacobianWrapper{SciMLBase.isinplace(f)}(f, prob.p)
+    if SciMLBase.isinplace(f)
+        fu_cache = copy(fu)
+        v_fake = copy(fu)
+        di_extras = DI.prepare_pullback(fₚ, fu_cache, autodiff, u, v_fake)
+        vjp_op = @closure (vJ, v, u, p, extras) -> begin
+            DI.pullback!(
+                fₚ, extras.fu_cache, reshape(vJ, size(u)), autodiff, u, v, extras.di_extras)
+        end
+        return vjp_op, (; di_extras, fu_cache)
+    else
+        di_extras = DI.prepare_pullback(f, autodiff, u, fu)
+        vjp_op = @closure (v, u, p, extras) -> begin
+            return DI.pullback(f, autodiff, u, v, extras.di_extras)
+        end
+        return vjp_op, (; di_extras)
+    end
+end
+
+prepare_jvp(skip::Val{true}, args...; kwargs...) = nothing, nothing
+
+function prepare_jvp(::Val{false}, prob::AbstractNonlinearProblem,
+        f::AbstractNonlinearFunction, u::Number, fu::Number; autodiff = nothing)
+    return prepare_scalar_op(Val(false), prob, f, u, fu; autodiff)
+end
+
+function prepare_jvp(::Val{false}, prob::AbstractNonlinearProblem,
+        f::AbstractNonlinearFunction, u, fu; autodiff = nothing)
+    SciMLBase.has_vjp(f) && return f.vjp, nothing
+
+    if autodiff === nothing && SciMLBase.has_jac(f)
+        if SciMLBase.isinplace(f)
+            jvp_extras = (; jac_cache = similar(u, eltype(fu), length(fu), length(u)))
+            jvp_op = @closure (Jv, v, u, p, extras) -> begin
+                f.jac(extras.jac_cache, u, p)
+                mul!(vec(Jv), extras.jac_cache, vec(v))
+                return
+            end
+            return jvp_op, jvp_extras
+        else
+            jvp_op = @closure (v, u, p, _) -> reshape(f.jac(u, p) * vec(v), size(u))
+            return jvp_op, nothing
+        end
+    end
+
+    @assert autodiff!==nothing "`jvp_autodiff` must be provided if `f` doesn't have \
+                                analytic `vjp` or `jac`."
+
+    if ADTypes.mode(autodiff) isa ADTypes.ReverseMode
+        @warn "AD Backend: $(autodiff) is a Reverse Mode backend. Computing JVPs using \
+               this will be slow!"
+    end
+
+    # TODO: Once DI supports const params we can use `p`
+    fₚ = SciMLBase.JacobianWrapper{SciMLBase.isinplace(f)}(f, prob.p)
+    if SciMLBase.isinplace(f)
+        fu_cache = copy(fu)
+        di_extras = DI.prepare_pushforward(fₚ, fu_cache, autodiff, u, u)
+        jvp_op = @closure (Jv, v, u, p, extras) -> begin
+            DI.pushforward!(fₚ, extras.fu_cache, reshape(Jv, size(extras.fu_cache)),
+                autodiff, u, v, extras.di_extras)
+        end
+        return jvp_op, (; di_extras, fu_cache)
+    else
+        di_extras = DI.prepare_pushforward(f, autodiff, u, u)
+        jvp_op = @closure (v, u, p, extras) -> begin
+            return DI.pushforward(f, autodiff, u, v, extras.di_extras)
+        end
+        return jvp_op, (; di_extras)
+    end
+end
+
+function prepare_scalar_op(::Val{false}, prob::AbstractNonlinearProblem,
+        f::AbstractNonlinearFunction, u::Number, fu::Number; autodiff = nothing)
+    SciMLBase.has_vjp(f) && return f.vjp, nothing
+    SciMLBase.has_jvp(f) && return f.jvp, nothing
+    SciMLBase.has_jac(f) && return @closure((v, u, p, _)->f.jac(u, p) * v), nothing
+
+    @assert autodiff!==nothing "`autodiff` must be provided if `f` doesn't have \
+                                analytic `vjp` or `jvp` or `jac`."
+    # TODO: Once DI supports const params we can use `p`
+    fₚ = Base.Fix2(f, prob.p)
+    di_extras = DI.prepare_derivative(fₚ, autodiff, u)
+    op = @closure (v, u, p, extras) -> begin
+        return DI.derivative(fₚ, autodiff, u, extras.di_extras) * v
+    end
+    return op, (; di_extras)
+end
+
+function VecJacOperator(args...; autodiff = nothing, kwargs...)
+    return JacobianOperator(args...; kwargs..., skip_jvp = True, vjp_autodiff = autodiff)'
+end
+
+function JacVecOperator(args...; autodiff = nothing, kwargs...)
+    return JacobianOperator(args...; kwargs..., skip_vjp = True, jvp_autodiff = autodiff)
+end
+
+export JacobianOperator, VecJacOperator, JacVecOperator
+
+end

From 61b946ca14a7b30c66ac34514825f6c4cf19e7d0 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 23 Sep 2024 16:37:32 -0400
Subject: [PATCH 468/700] ci: test subpackages

---
 .buildkite/pipeline.yml                       | 16 +++-
 .github/workflows/CI_NonlinearSolve.yml       | 83 +++++++++++++++++++
 .../{CI.yml => CI_SciMLJacobianOperators.yml} | 29 ++++---
 3 files changed, 112 insertions(+), 16 deletions(-)
 create mode 100644 .github/workflows/CI_NonlinearSolve.yml
 rename .github/workflows/{CI.yml => CI_SciMLJacobianOperators.yml} (73%)

diff --git a/.buildkite/pipeline.yml b/.buildkite/pipeline.yml
index b9a145400..a9b3004f4 100644
--- a/.buildkite/pipeline.yml
+++ b/.buildkite/pipeline.yml
@@ -1,15 +1,25 @@
 steps:
-  - label: "Julia 1"
+  - label: "Julia 1 (NonlinearSolve)"
     plugins:
       - JuliaCI/julia#v1:
           version: "1"
-      - JuliaCI/julia-test#v1:
-          coverage: true
       - JuliaCI/julia-coverage#v1:
           codecov: true
           dirs:
             - src
             - ext
+    command: |
+      julia --color=yes --code-coverage=user --depwarn=yes --project=. -e '
+        import Pkg;
+        Pkg.Registry.update();
+        # Install packages present in subdirectories
+        dev_pks = Pkg.PackageSpec[];
+        for path in ("lib/SciMLJacobianOperators",)
+            push!(dev_pks, Pkg.PackageSpec(; path));
+        end
+        Pkg.develop(dev_pks);
+        Pkg.instantiate();
+        Pkg.test(; coverage=true)'
     agents:
       queue: "juliagpu"
       cuda: "*"
diff --git a/.github/workflows/CI_NonlinearSolve.yml b/.github/workflows/CI_NonlinearSolve.yml
new file mode 100644
index 000000000..7a04185d1
--- /dev/null
+++ b/.github/workflows/CI_NonlinearSolve.yml
@@ -0,0 +1,83 @@
+name: CI (NonlinearSolve)
+
+on:
+  pull_request:
+    branches:
+      - master
+    paths:
+      - "src/**"
+      - "ext/**"
+      - "test/**"
+      - "Project.toml"
+      - ".github/workflows/CI_NonlinearSolve.yml"
+      - "lib/SciMLNonlinearOperators/**"
+  push:
+    branches:
+      - master
+
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: only if it is a pull request build.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+
+jobs:
+  test:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        group:
+          - Core
+          - Downstream
+          - Misc
+          - Wrappers
+        version:
+          - "min"
+          - "1"
+          - "pre"
+        os:
+          - ubuntu-latest
+          - macos-latest
+          - windows-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: actions/cache@v4
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators",)
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage=true)
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=. {0}
+        env:
+          GROUP: ${{ matrix.group }}
+          RETESTITEMS_NWORKERS: 4
+          RETESTITEMS_NWORKER_THREADS: 2
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: src,ext
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/.github/workflows/CI.yml b/.github/workflows/CI_SciMLJacobianOperators.yml
similarity index 73%
rename from .github/workflows/CI.yml
rename to .github/workflows/CI_SciMLJacobianOperators.yml
index 21263f5f3..9b2055c7f 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI_SciMLJacobianOperators.yml
@@ -1,29 +1,32 @@
-name: CI
+name: CI (SciMLNonlinearOperators)
+
 on:
   pull_request:
     branches:
       - master
+    paths:
+      - "lib/SciMLNonlinearOperators/**"
+      - ".github/workflows/CI_SciMLNonlinearOperators.yml"
   push:
     branches:
       - master
+
 concurrency:
   # Skip intermediate builds: always.
   # Cancel intermediate builds: only if it is a pull request build.
   group: ${{ github.workflow }}-${{ github.ref }}
   cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+
 jobs:
   test:
     runs-on: ${{ matrix.os }}
     strategy:
       fail-fast: false
       matrix:
-        group:
-          - Core
-          - Downstream
-          - Misc
-          - Wrappers
         version:
+          - "min"
           - "1"
+          - "pre"
         os:
           - ubuntu-latest
           - macos-latest
@@ -43,13 +46,13 @@ jobs:
             ${{ runner.os }}-test-${{ env.cache-name }}-
             ${{ runner.os }}-test-
             ${{ runner.os }}-
-      - uses: julia-actions/julia-buildpkg@v1
-      - uses: julia-actions/julia-runtest@v1
-        env:
-          GROUP: ${{ matrix.group }}
-          JULIA_NUM_THREADS: 11
-          RETESTITEMS_NWORKERS: 4
-          RETESTITEMS_NWORKER_THREADS: 2
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          Pkg.instantiate()
+          Pkg.test(; coverage=true)
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SciMLNonlinearOperators {0}
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: src,ext

From ee9cc42240582837eb604e0536db165352323953 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 23 Sep 2024 16:37:52 -0400
Subject: [PATCH 469/700] feat: add callable structs

---
 lib/SciMLJacobianOperators/Project.toml       |   2 +
 .../src/SciMLJacobianOperators.jl             | 148 +++++++++++-------
 lib/SciMLJacobianOperators/test/runtests.jl   |   0
 3 files changed, 94 insertions(+), 56 deletions(-)
 create mode 100644 lib/SciMLJacobianOperators/test/runtests.jl

diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index 478ddcb57..ea573c727 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -9,6 +9,7 @@ ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
@@ -19,6 +20,7 @@ ConcreteStructs = "0.2.3"
 ConstructionBase = "1.5.8"
 DifferentiationInterface = "0.5.17"
 FastClosures = "0.3.2"
+LinearAlgebra = "1.11.0"
 SciMLOperators = "0.3.10"
 Setfield = "1.1.1"
 julia = "1.10"
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index 620bd66bc..f16e3c451 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -13,6 +13,8 @@ const DI = DifferentiationInterface
 const True = Val(true)
 const False = Val(false)
 
+abstract type AbstractJacobianOperator{T} <: AbstractSciMLOperator{T} end
+
 abstract type AbstractMode end
 
 struct VJP <: AbstractMode end
@@ -21,17 +23,20 @@ struct JVP <: AbstractMode end
 flip_mode(::VJP) = JVP()
 flip_mode(::JVP) = VJP()
 
-@concrete struct JacobianOperator{iip, T <: Real} <: AbstractSciMLOperator{T}
+@concrete struct JacobianOperator{iip, T <: Real} <: AbstractJacobianOperator{T}
     mode <: AbstractMode
 
     jvp_op
     vjp_op
 
     size
-    jvp_extras
-    vjp_extras
+
+    output_cache
+    input_cache
 end
 
+SciMLBase.isinplace(::JacobianOperator{iip}) where {iip} = iip
+
 function ConstructionBase.constructorof(::Type{<:JacobianOperator{iip, T}}) where {iip, T}
     return JacobianOperator{iip, T}
 end
@@ -42,6 +47,9 @@ Base.size(J::JacobianOperator, d::Integer) = J.size[d]
 for op in (:adjoint, :transpose)
     @eval function Base.$(op)(operator::JacobianOperator)
         @set! operator.mode = flip_mode(operator.mode)
+        (; output_cache, input_cache) = operator
+        @set! operator.output_cache = input_cache
+        @set! operator.input_cache = output_cache
         return operator
     end
 end
@@ -53,16 +61,66 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
     f = prob.f
     iip = SciMLBase.isinplace(prob)
     T = promote_type(eltype(u), eltype(fu))
-    fₚ = SciMLBase.JacobianWrapper{iip}(f, prob.p)
 
-    vjp_op, vjp_extras = prepare_vjp(skip_vjp, prob, f, u, fu; autodiff = vjp_autodiff)
-    jvp_op, jvp_extras = prepare_jvp(skip_jvp, prob, f, u, fu; autodiff = jvp_autodiff)
+    vjp_op = prepare_vjp(skip_vjp, prob, f, u, fu; autodiff = vjp_autodiff)
+    jvp_op = prepare_jvp(skip_jvp, prob, f, u, fu; autodiff = jvp_autodiff)
+
+    output_cache = iip ? similar(fu, T) : nothing
+    input_cache = iip ? similar(u, T) : nothing
 
     return JacobianOperator{iip, T}(
-        JVP(), jvp_op, vjp_op, (length(fu), length(u)), jvp_extras, vjp_extras)
+        JVP(), jvp_op, vjp_op, (length(fu), length(u)), output_cache, input_cache)
 end
 
-prepare_vjp(::Val{true}, args...; kwargs...) = nothing, nothing
+function (op::JacobianOperator)(v, u, p)
+    if op.mode isa VJP
+        if SciMLBase.isinplace(op)
+            res = zero(op.output_cache)
+            op.vjp_op(res, v, u, p)
+            return res
+        end
+        return op.vjp_op(v, u, p)
+    else
+        if SciMLBase.isinplace(op)
+            res = zero(op.output_cache)
+            op.jvp_op(res, v, u, p)
+            return res
+        end
+        return op.jvp_op(v, u, p)
+    end
+end
+
+function (op::JacobianOperator)(::Number, ::Number, _, __)
+    error("Inplace Jacobian Operator not possible for scalars.")
+end
+
+function (op::JacobianOperator)(Jv, v, u, p)
+    if op.mode isa VJP
+        if SciMLBase.isinplace(op)
+            op.vjp_op(Jv, v, u, p)
+            return
+        end
+        copyto!(Jv, op.vjp_op(v, u, p))
+        return
+    else
+        if SciMLBase.isinplace(op)
+            op.jvp_op(Jv, v, u, p)
+            return
+        end
+        copyto!(Jv, op.jvp_op(v, u, p))
+        return
+    end
+end
+
+function VecJacOperator(args...; autodiff = nothing, kwargs...)
+    return JacobianOperator(args...; kwargs..., skip_jvp = True, vjp_autodiff = autodiff)'
+end
+
+function JacVecOperator(args...; autodiff = nothing, kwargs...)
+    return JacobianOperator(args...; kwargs..., skip_vjp = True, jvp_autodiff = autodiff)
+end
+
+prepare_vjp(::Val{true}, args...; kwargs...) = nothing
 
 function prepare_vjp(::Val{false}, prob::AbstractNonlinearProblem,
         f::AbstractNonlinearFunction, u::Number, fu::Number; autodiff = nothing)
@@ -71,20 +129,19 @@ end
 
 function prepare_vjp(::Val{false}, prob::AbstractNonlinearProblem,
         f::AbstractNonlinearFunction, u, fu; autodiff = nothing)
-    SciMLBase.has_vjp(f) && return f.vjp, nothing
+    SciMLBase.has_vjp(f) && return f.vjp
 
     if autodiff === nothing && SciMLBase.has_jac(f)
         if SciMLBase.isinplace(f)
-            vjp_extras = (; jac_cache = similar(u, eltype(fu), length(fu), length(u)))
-            vjp_op = @closure (vJ, v, u, p, extras) -> begin
-                f.jac(extras.jac_cache, u, p)
-                mul!(vec(vJ), extras.jac_cache', vec(v))
+            jac_cache = similar(u, eltype(fu), length(fu), length(u))
+            return @closure (vJ, v, u, p) -> begin
+                f.jac(jac_cache, u, p)
+                mul!(vec(vJ), jac_cache', vec(v))
                 return
             end
             return vjp_op, vjp_extras
         else
-            vjp_op = @closure (v, u, p, _) -> reshape(f.jac(u, p)' * vec(v), size(u))
-            return vjp_op, nothing
+            return @closure (v, u, p) -> reshape(f.jac(u, p)' * vec(v), size(u))
         end
     end
 
@@ -102,21 +159,16 @@ function prepare_vjp(::Val{false}, prob::AbstractNonlinearProblem,
         fu_cache = copy(fu)
         v_fake = copy(fu)
         di_extras = DI.prepare_pullback(fₚ, fu_cache, autodiff, u, v_fake)
-        vjp_op = @closure (vJ, v, u, p, extras) -> begin
-            DI.pullback!(
-                fₚ, extras.fu_cache, reshape(vJ, size(u)), autodiff, u, v, extras.di_extras)
+        return @closure (vJ, v, u, p) -> begin
+            DI.pullback!(fₚ, fu_cache, reshape(vJ, size(u)), autodiff, u, v, di_extras)
         end
-        return vjp_op, (; di_extras, fu_cache)
     else
         di_extras = DI.prepare_pullback(f, autodiff, u, fu)
-        vjp_op = @closure (v, u, p, extras) -> begin
-            return DI.pullback(f, autodiff, u, v, extras.di_extras)
-        end
-        return vjp_op, (; di_extras)
+        return @closure (v, u, p) -> DI.pullback(f, autodiff, u, v, di_extras)
     end
 end
 
-prepare_jvp(skip::Val{true}, args...; kwargs...) = nothing, nothing
+prepare_jvp(skip::Val{true}, args...; kwargs...) = nothing
 
 function prepare_jvp(::Val{false}, prob::AbstractNonlinearProblem,
         f::AbstractNonlinearFunction, u::Number, fu::Number; autodiff = nothing)
@@ -125,20 +177,18 @@ end
 
 function prepare_jvp(::Val{false}, prob::AbstractNonlinearProblem,
         f::AbstractNonlinearFunction, u, fu; autodiff = nothing)
-    SciMLBase.has_vjp(f) && return f.vjp, nothing
+    SciMLBase.has_vjp(f) && return f.vjp
 
     if autodiff === nothing && SciMLBase.has_jac(f)
         if SciMLBase.isinplace(f)
-            jvp_extras = (; jac_cache = similar(u, eltype(fu), length(fu), length(u)))
-            jvp_op = @closure (Jv, v, u, p, extras) -> begin
-                f.jac(extras.jac_cache, u, p)
-                mul!(vec(Jv), extras.jac_cache, vec(v))
+            jac_cache = similar(u, eltype(fu), length(fu), length(u))
+            return @closure (Jv, v, u, p) -> begin
+                f.jac(jac_cache, u, p)
+                mul!(vec(Jv), jac_cache, vec(v))
                 return
             end
-            return jvp_op, jvp_extras
         else
-            jvp_op = @closure (v, u, p, _) -> reshape(f.jac(u, p) * vec(v), size(u))
-            return jvp_op, nothing
+            return @closure (v, u, p, _) -> reshape(f.jac(u, p) * vec(v), size(u))
         end
     end
 
@@ -155,43 +205,29 @@ function prepare_jvp(::Val{false}, prob::AbstractNonlinearProblem,
     if SciMLBase.isinplace(f)
         fu_cache = copy(fu)
         di_extras = DI.prepare_pushforward(fₚ, fu_cache, autodiff, u, u)
-        jvp_op = @closure (Jv, v, u, p, extras) -> begin
-            DI.pushforward!(fₚ, extras.fu_cache, reshape(Jv, size(extras.fu_cache)),
-                autodiff, u, v, extras.di_extras)
+        return @closure (Jv, v, u, p) -> begin
+            DI.pushforward!(fₚ, fu_cache, reshape(Jv, size(fu_cache)), autodiff, u, v,
+                di_extras)
+            return
         end
-        return jvp_op, (; di_extras, fu_cache)
     else
-        di_extras = DI.prepare_pushforward(f, autodiff, u, u)
-        jvp_op = @closure (v, u, p, extras) -> begin
-            return DI.pushforward(f, autodiff, u, v, extras.di_extras)
-        end
-        return jvp_op, (; di_extras)
+        di_extras = DI.prepare_pushforward(fₚ, autodiff, u, u)
+        return @closure (v, u, p) -> DI.pushforward(fₚ, autodiff, u, v, di_extras)
     end
 end
 
 function prepare_scalar_op(::Val{false}, prob::AbstractNonlinearProblem,
         f::AbstractNonlinearFunction, u::Number, fu::Number; autodiff = nothing)
-    SciMLBase.has_vjp(f) && return f.vjp, nothing
-    SciMLBase.has_jvp(f) && return f.jvp, nothing
-    SciMLBase.has_jac(f) && return @closure((v, u, p, _)->f.jac(u, p) * v), nothing
+    SciMLBase.has_vjp(f) && return f.vjp
+    SciMLBase.has_jvp(f) && return f.jvp
+    SciMLBase.has_jac(f) && return @closure((v, u, p)->f.jac(u, p) * v)
 
     @assert autodiff!==nothing "`autodiff` must be provided if `f` doesn't have \
                                 analytic `vjp` or `jvp` or `jac`."
     # TODO: Once DI supports const params we can use `p`
     fₚ = Base.Fix2(f, prob.p)
     di_extras = DI.prepare_derivative(fₚ, autodiff, u)
-    op = @closure (v, u, p, extras) -> begin
-        return DI.derivative(fₚ, autodiff, u, extras.di_extras) * v
-    end
-    return op, (; di_extras)
-end
-
-function VecJacOperator(args...; autodiff = nothing, kwargs...)
-    return JacobianOperator(args...; kwargs..., skip_jvp = True, vjp_autodiff = autodiff)'
-end
-
-function JacVecOperator(args...; autodiff = nothing, kwargs...)
-    return JacobianOperator(args...; kwargs..., skip_vjp = True, jvp_autodiff = autodiff)
+    return @closure (v, u, p) -> DI.derivative(fₚ, autodiff, u, di_extras) * v
 end
 
 export JacobianOperator, VecJacOperator, JacVecOperator
diff --git a/lib/SciMLJacobianOperators/test/runtests.jl b/lib/SciMLJacobianOperators/test/runtests.jl
new file mode 100644
index 000000000..e69de29bb

From b8ae8afea27e0510d9b79f7eef265153b2a6190f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 23 Sep 2024 16:40:25 -0400
Subject: [PATCH 470/700] fix: minor corrections in runners

---
 .github/workflows/CI_SciMLJacobianOperators.yml |  8 ++++----
 lib/SciMLJacobianOperators/Project.toml         | 10 +++++-----
 2 files changed, 9 insertions(+), 9 deletions(-)

diff --git a/.github/workflows/CI_SciMLJacobianOperators.yml b/.github/workflows/CI_SciMLJacobianOperators.yml
index 9b2055c7f..37d6efdff 100644
--- a/.github/workflows/CI_SciMLJacobianOperators.yml
+++ b/.github/workflows/CI_SciMLJacobianOperators.yml
@@ -1,12 +1,12 @@
-name: CI (SciMLNonlinearOperators)
+name: CI (SciMLJacobianOperators)
 
 on:
   pull_request:
     branches:
       - master
     paths:
-      - "lib/SciMLNonlinearOperators/**"
-      - ".github/workflows/CI_SciMLNonlinearOperators.yml"
+      - "lib/SciMLJacobianOperators/**"
+      - ".github/workflows/CI_SciMLJacobianOperators.yml"
   push:
     branches:
       - master
@@ -52,7 +52,7 @@ jobs:
           Pkg.Registry.update()
           Pkg.instantiate()
           Pkg.test(; coverage=true)
-        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SciMLNonlinearOperators {0}
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SciMLJacobianOperators {0}
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: src,ext
diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index ea573c727..11b19a324 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -17,12 +17,12 @@ Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 [compat]
 ADTypes = "1.8.1"
 ConcreteStructs = "0.2.3"
-ConstructionBase = "1.5.8"
-DifferentiationInterface = "0.5.17"
+ConstructionBase = "1.5"
+DifferentiationInterface = "0.5"
 FastClosures = "0.3.2"
-LinearAlgebra = "1.11.0"
-SciMLOperators = "0.3.10"
-Setfield = "1.1.1"
+LinearAlgebra = "1.10"
+SciMLOperators = "0.3"
+Setfield = "1"
 julia = "1.10"
 
 [extras]

From f667683bb6c5bf78a8cef5defa52f887c526fc71 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 23 Sep 2024 17:26:29 -0400
Subject: [PATCH 471/700] feat: integrate SciMLJacobianOperators into
 NonlinearSolve

---
 docs/src/devdocs/operators.md                 |  15 -
 .../src/SciMLJacobianOperators.jl             | 158 +++++++++-
 src/NonlinearSolve.jl                         |   3 +-
 src/globalization/trust_region.jl             |   6 +-
 src/internal/jacobian.jl                      |  12 +-
 src/internal/operators.jl                     | 278 ------------------
 6 files changed, 164 insertions(+), 308 deletions(-)
 delete mode 100644 src/internal/operators.jl

diff --git a/docs/src/devdocs/operators.md b/docs/src/devdocs/operators.md
index b96a63f8c..15d00093a 100644
--- a/docs/src/devdocs/operators.md
+++ b/docs/src/devdocs/operators.md
@@ -6,21 +6,6 @@
 NonlinearSolve.AbstractNonlinearSolveOperator
 ```
 
-## Jacobian Operators
-
-```@docs
-NonlinearSolve.JacobianOperator
-NonlinearSolve.VecJacOperator
-NonlinearSolve.JacVecOperator
-```
-
-### Stateful Jacobian Operators
-
-```@docs
-NonlinearSolve.StatefulJacobianOperator
-NonlinearSolve.StatefulJacobianNormalFormOperator
-```
-
 ## Low-Rank Jacobian Operators
 
 ```@docs
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index f16e3c451..fceaea278 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -5,6 +5,7 @@ using ConcreteStructs: @concrete
 using ConstructionBase: ConstructionBase
 using DifferentiationInterface: DifferentiationInterface
 using FastClosures: @closure
+using LinearAlgebra: LinearAlgebra
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, AbstractNonlinearFunction
 using SciMLOperators: AbstractSciMLOperator
 using Setfield: @set!
@@ -23,6 +24,57 @@ struct JVP <: AbstractMode end
 flip_mode(::VJP) = JVP()
 flip_mode(::JVP) = VJP()
 
+"""
+    JacobianOperator{iip, T} <: AbstractJacobianOperator{T} <: AbstractSciMLOperator{T}
+
+A Jacobian Operator Provides both JVP and VJP without materializing either (if possible).
+
+### Constructor
+
+```julia
+JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff = nothing,
+    vjp_autodiff = nothing, skip_vjp::Val = Val(false), skip_jvp::Val = Val(false))
+```
+
+By default, the `JacobianOperator` will compute `JVP`. Use `Base.adjoint` or
+`Base.transpose` to switch to `VJP`.
+
+### Computing the VJP
+
+Computing the VJP is done according to the following rules:
+
+  - If `f` has a `vjp` method, then we use that.
+  - If `f` has a `jac` method and no `vjp_autodiff` is provided, then we use `jac * v`.
+  - If `vjp_autodiff` is provided we using DifferentiationInterface.jl to compute the VJP.
+
+### Computing the JVP
+
+Computing the JVP is done according to the following rules:
+
+  - If `f` has a `jvp` method, then we use that.
+  - If `f` has a `jac` method and no `jvp_autodiff` is provided, then we use `v * jac`.
+  - If `jvp_autodiff` is provided we using DifferentiationInterface.jl to compute the JVP.
+
+### Special Case (Number)
+
+For Number inputs, VJP and JVP are not distinct. Hence, if either `vjp` or `jvp` is
+provided, then we use that. If neither is provided, then we use `v * jac` if `jac` is
+provided. Finally, we use the respective autodiff methods to compute the derivative
+using DifferentiationInterface.jl and multiply by `v`.
+
+### Methods Provided
+
+!!! warning
+
+    Currently it is expected that `p` during problem construction is same as `p` during
+    operator evaluation. This restriction will be lifted in the future.
+
+  - `(op::JacobianOperator)(v, u, p)`: Computes `∂f(u, p)/∂u * v` or `∂f(u, p)/∂uᵀ * v`.
+  - `(op::JacobianOperator)(res, v, u, p)`: Computes `∂f(u, p)/∂u * v` or `∂f(u, p)/∂uᵀ * v`
+    and stores the result in `res`.
+
+See also [`VecJacOperator`](@ref) and [`JacVecOperator`](@ref).
+"""
 @concrete struct JacobianOperator{iip, T <: Real} <: AbstractJacobianOperator{T}
     mode <: AbstractMode
 
@@ -65,8 +117,8 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
     vjp_op = prepare_vjp(skip_vjp, prob, f, u, fu; autodiff = vjp_autodiff)
     jvp_op = prepare_jvp(skip_jvp, prob, f, u, fu; autodiff = jvp_autodiff)
 
-    output_cache = iip ? similar(fu, T) : nothing
-    input_cache = iip ? similar(u, T) : nothing
+    output_cache = similar(fu, T)
+    input_cache = similar(u, T)
 
     return JacobianOperator{iip, T}(
         JVP(), jvp_op, vjp_op, (length(fu), length(u)), output_cache, input_cache)
@@ -112,14 +164,106 @@ function (op::JacobianOperator)(Jv, v, u, p)
     end
 end
 
+"""
+    VecJacOperator(args...; autodiff = nothing, kwargs...)
+
+Constructs a [`JacobianOperator`](@ref) which only provides the VJP using the
+`vjp_autodiff = autodiff`.
+"""
 function VecJacOperator(args...; autodiff = nothing, kwargs...)
     return JacobianOperator(args...; kwargs..., skip_jvp = True, vjp_autodiff = autodiff)'
 end
 
+"""
+    JacVecOperator(args...; autodiff = nothing, kwargs...)
+
+Constructs a [`JacobianOperator`](@ref) which only provides the JVP using the
+`jvp_autodiff = autodiff`.
+"""
 function JacVecOperator(args...; autodiff = nothing, kwargs...)
     return JacobianOperator(args...; kwargs..., skip_vjp = True, jvp_autodiff = autodiff)
 end
 
+"""
+    StatefulJacobianOperator(jac_op::JacobianOperator, u, p)
+
+Wrapper over a [`JacobianOperator`](@ref) which stores the input `u` and `p` and defines
+`mul!` and `*` for computing VJPs and JVPs.
+"""
+@concrete struct StatefulJacobianOperator{M <: AbstractMode, T} <:
+                 AbstractJacobianOperator{T}
+    mode::M
+    jac_op <: JacobianOperator
+    u
+    p
+
+    function StatefulJacobianOperator(jac_op::JacobianOperator, u, p)
+        return new{
+            typeof(jac_op.mode), eltype(jac_op), typeof(jac_op), typeof(u), typeof(p)}(
+            jac_op.mode, jac_op, u, p)
+    end
+end
+
+Base.size(J::StatefulJacobianOperator) = size(J.jac_op)
+Base.size(J::StatefulJacobianOperator, d::Integer) = size(J.jac_op, d)
+
+for op in (:adjoint, :transpose)
+    @eval function Base.$(op)(operator::StatefulJacobianOperator)
+        return StatefulJacobianOperator($(op)(operator.jac_op), operator.u, operator.p)
+    end
+end
+
+Base.:*(J::StatefulJacobianOperator, v::AbstractArray) = J.jac_op(v, J.u, J.p)
+
+function LinearAlgebra.mul!(
+        Jv::AbstractArray, J::StatefulJacobianOperator, v::AbstractArray)
+    J.jac_op(Jv, v, J.u, J.p)
+    return Jv
+end
+
+"""
+    StatefulJacobianNormalFormOperator(vjp_operator, jvp_operator, cache)
+
+This constructs a Normal Form Jacobian Operator, i.e. it constructs the operator
+corresponding to `JᵀJ` where `J` is the Jacobian Operator. This is not meant to be directly
+constructed, rather it is constructed with `*` on two [`StatefulJacobianOperator`](@ref)s.
+"""
+@concrete mutable struct StatefulJacobianNormalFormOperator{T} <:
+                         AbstractJacobianOperator{T}
+    vjp_operator <: StatefulJacobianOperator{VJP}
+    jvp_operator <: StatefulJacobianOperator{JVP}
+    cache
+end
+
+function Base.size(J::StatefulJacobianNormalFormOperator)
+    return size(J.vjp_operator, 1), size(J.jvp_operator, 2)
+end
+
+function Base.:*(J1::StatefulJacobianOperator{VJP}, J2::StatefulJacobianOperator{JVP})
+    cache = J2 * J2.jac_op.input_cache
+    T = promote_type(eltype(J1), eltype(J2))
+    return StatefulJacobianNormalFormOperator{T}(J1, J2, cache)
+end
+
+function LinearAlgebra.mul!(C::StatefulJacobianNormalFormOperator,
+        A::StatefulJacobianOperator{VJP}, B::StatefulJacobianOperator{JVP})
+    C.vjp_operator = A
+    C.jvp_operator = B
+    return C
+end
+
+function Base.:*(JᵀJ::StatefulJacobianNormalFormOperator, x::AbstractArray)
+    return JᵀJ.vjp_operator * (JᵀJ.jvp_operator * x)
+end
+
+function LinearAlgebra.mul!(
+        JᵀJx::AbstractArray, JᵀJ::StatefulJacobianNormalFormOperator, x::AbstractArray)
+    mul!(JᵀJ.cache, JᵀJ.jvp_operator, x)
+    mul!(JᵀJx, JᵀJ.vjp_operator, JᵀJ.cache)
+    return JᵀJx
+end
+
+# Helper Functions
 prepare_vjp(::Val{true}, args...; kwargs...) = nothing
 
 function prepare_vjp(::Val{false}, prob::AbstractNonlinearProblem,
@@ -163,8 +307,8 @@ function prepare_vjp(::Val{false}, prob::AbstractNonlinearProblem,
             DI.pullback!(fₚ, fu_cache, reshape(vJ, size(u)), autodiff, u, v, di_extras)
         end
     else
-        di_extras = DI.prepare_pullback(f, autodiff, u, fu)
-        return @closure (v, u, p) -> DI.pullback(f, autodiff, u, v, di_extras)
+        di_extras = DI.prepare_pullback(fₚ, autodiff, u, fu)
+        return @closure (v, u, p) -> DI.pullback(fₚ, autodiff, u, v, di_extras)
     end
 end
 
@@ -206,8 +350,8 @@ function prepare_jvp(::Val{false}, prob::AbstractNonlinearProblem,
         fu_cache = copy(fu)
         di_extras = DI.prepare_pushforward(fₚ, fu_cache, autodiff, u, u)
         return @closure (Jv, v, u, p) -> begin
-            DI.pushforward!(fₚ, fu_cache, reshape(Jv, size(fu_cache)), autodiff, u, v,
-                di_extras)
+            DI.pushforward!(
+                fₚ, fu_cache, reshape(Jv, size(fu_cache)), autodiff, u, v, di_extras)
             return
         end
     else
@@ -231,5 +375,7 @@ function prepare_scalar_op(::Val{false}, prob::AbstractNonlinearProblem,
 end
 
 export JacobianOperator, VecJacOperator, JacVecOperator
+export StatefulJacobianOperator
+export StatefulJacobianNormalFormOperator
 
 end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 781f6eae9..77293ce3f 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -40,6 +40,8 @@ using Preferences: Preferences, @load_preference, @set_preferences!
 using RecursiveArrayTools: recursivecopy!, recursivefill!
 using SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
                  AbstractSciMLOperator, _unwrap_val, has_jac, isinplace, NLStats
+using SciMLJacobianOperators: JacobianOperator, VecJacOperator, JacVecOperator,
+                              StatefulJacobianOperator, StatefulJacobianNormalFormOperator
 using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
 using SparseDiffTools: SparseDiffTools, AbstractSparsityDetection,
                        ApproximateJacobianSparsity, JacPrototypeSparsityDetection,
@@ -72,7 +74,6 @@ include("descent/dogleg.jl")
 include("descent/damped_newton.jl")
 include("descent/geodesic_acceleration.jl")
 
-include("internal/operators.jl")
 include("internal/jacobian.jl")
 include("internal/forward_diff.jl")
 include("internal/linear_solve.jl")
diff --git a/src/globalization/trust_region.jl b/src/globalization/trust_region.jl
index 51b54959e..e6e2cba17 100644
--- a/src/globalization/trust_region.jl
+++ b/src/globalization/trust_region.jl
@@ -386,11 +386,13 @@ function __internal_init(
     p1, p2, p3, p4 = __get_parameters(T, alg.method)
     ϵ = T(1e-8)
 
+    reverse_ad = get_concrete_reverse_ad(alg.reverse_ad, prob; check_reverse_mode = true)
     vjp_operator = alg.method isa RUS.__Yuan || alg.method isa RUS.__Bastin ?
-                   VecJacOperator(prob, fu, u; autodiff = alg.reverse_ad) : nothing
+                   VecJacOperator(prob, fu, u; autodiff = reverse_ad) : nothing
 
+    forward_ad = get_concrete_forward_ad(alg.forward_ad, prob; check_forward_mode = true)
     jvp_operator = alg.method isa RUS.__Bastin ?
-                   JacVecOperator(prob, fu, u; autodiff = alg.forward_ad) : nothing
+                   JacVecOperator(prob, fu, u; autodiff = forward_ad) : nothing
 
     if alg.method isa RUS.__Yuan
         Jᵀfu_cache = StatefulJacobianOperator(vjp_operator, u, prob.p) * _vec(fu)
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index b712b93e2..be3402314 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -25,7 +25,8 @@ Construct a cache for the Jacobian of `f` w.r.t. `u`.
   - `jvp_autodiff`: Automatic Differentiation or Finite Differencing backend for computing
     the Jacobian-vector product.
   - `linsolve`: Linear Solver Algorithm used to determine if we need a concrete jacobian
-    or if possible we can just use a [`NonlinearSolve.JacobianOperator`](@ref) instead.
+    or if possible we can just use a [`SciMLJacobianOperators.JacobianOperator`](@ref)
+    instead.
 """
 @concrete mutable struct JacobianCache{iip} <: AbstractNonlinearSolveJacobianCache{iip}
     J
@@ -85,8 +86,7 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
             __similar(fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u)) :
             copy(f.jac_prototype)
         elseif f.jac_prototype === nothing
-            zero(init_jacobian(
-                jac_cache; preserve_immutable = Val(true)))
+            zero(init_jacobian(jac_cache; preserve_immutable = Val(true)))
         else
             f.jac_prototype
         end
@@ -114,9 +114,9 @@ end
 
 @inline (cache::JacobianCache)(u = cache.u) = cache(cache.J, u, cache.p)
 @inline function (cache::JacobianCache)(::Nothing)
-    J = cache.J
-    J isa JacobianOperator && return StatefulJacobianOperator(J, cache.u, cache.p)
-    return J
+    cache.J isa JacobianOperator &&
+        return StatefulJacobianOperator(cache.J, cache.u, cache.p)
+    return cache.J
 end
 
 function (cache::JacobianCache)(J::JacobianOperator, u, p = cache.p)
diff --git a/src/internal/operators.jl b/src/internal/operators.jl
deleted file mode 100644
index 5bbfcb0bf..000000000
--- a/src/internal/operators.jl
+++ /dev/null
@@ -1,278 +0,0 @@
-# We want a general form of this in SciMLOperators. However, we use this extensively and we
-# can have a custom implementation here till
-# https://github.com/SciML/SciMLOperators.jl/issues/223 is resolved.
-"""
-    JacobianOperator{vjp, iip, T} <: AbstractNonlinearSolveOperator{T}
-
-A Jacobian Operator Provides both JVP and VJP without materializing either (if possible).
-
-This is an internal operator, and is not guaranteed to have a stable API. It might even be
-moved out of NonlinearSolve.jl in the future, without a deprecation cycle. Usage of this
-outside NonlinearSolve.jl (by everyone except Avik) is strictly prohibited.
-
-`T` denotes if the Jacobian is transposed or not. `T = true` means that the Jacobian is
-transposed, and `T = false` means that the Jacobian is not transposed.
-
-### Constructor
-
-```julia
-JacobianOperator(
-    prob::AbstractNonlinearProblem, fu, u; jvp_autodiff = nothing, vjp_autodiff = nothing,
-    skip_vjp::Val{NoVJP} = False, skip_jvp::Val{NoJVP} = False) where {NoVJP, NoJVP}
-```
-
-See also [`NonlinearSolve.VecJacOperator`](@ref) and
-[`NonlinearSolve.JacVecOperator`](@ref).
-"""
-@concrete struct JacobianOperator{vjp, iip, T} <: AbstractNonlinearSolveOperator{T}
-    jvp_op
-    vjp_op
-
-    input_cache
-    output_cache
-end
-
-Base.size(J::JacobianOperator) = prod(size(J.output_cache)), prod(size(J.input_cache))
-function Base.size(J::JacobianOperator, d::Integer)
-    d == 1 && return prod(size(J.output_cache))
-    d == 2 && return prod(size(J.input_cache))
-    error("Invalid dimension $d for JacobianOperator")
-end
-
-for op in (:adjoint, :transpose)
-    @eval function Base.$(op)(operator::JacobianOperator{vjp, iip, T}) where {vjp, iip, T}
-        return JacobianOperator{!vjp, iip, T}(
-            operator.jvp_op, operator.vjp_op, operator.output_cache, operator.input_cache)
-    end
-end
-
-function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff = nothing,
-        vjp_autodiff = nothing, skip_vjp::Val{NoVJP} = False,
-        skip_jvp::Val{NoJVP} = False) where {NoVJP, NoJVP}
-    f = prob.f
-    iip = isinplace(prob)
-    uf = JacobianWrapper{iip}(f, prob.p)
-
-    vjp_op = if NoVJP
-        nothing
-    elseif SciMLBase.has_vjp(f)
-        f.vjp
-    elseif u isa Number  # Ignore vjp directives
-        if ForwardDiff.can_dual(typeof(u)) && (vjp_autodiff === nothing ||
-            vjp_autodiff isa AutoForwardDiff ||
-            vjp_autodiff isa AutoPolyesterForwardDiff)
-            # VJP is same as VJP for scalars
-            @closure (v, u, p) -> last(__scalar_jacvec(uf, u, v))
-        else
-            @closure (v, u, p) -> FiniteDiff.finite_difference_derivative(uf, u) * v
-        end
-    else
-        vjp_autodiff = __get_nonsparse_ad(get_concrete_reverse_ad(
-            vjp_autodiff, prob, False))
-        if vjp_autodiff isa AutoZygote
-            iip && error("`AutoZygote` cannot handle inplace problems.")
-            @closure (v, u, p) -> auto_vecjac(uf, u, v)
-        elseif vjp_autodiff isa AutoFiniteDiff
-            if iip
-                cache1 = zero(fu)
-                cache2 = zero(fu)
-                @closure (Jv, v, u, p) -> num_vecjac!(Jv, uf, u, v, cache1, cache2)
-            else
-                @closure (v, u, p) -> num_vecjac(uf, __mutable(u), v)
-            end
-        else
-            error("`vjp_autodiff` = `$(typeof(vjp_autodiff))` is not supported in \
-                   JacobianOperator.")
-        end
-    end
-
-    jvp_op = if NoJVP
-        nothing
-    elseif SciMLBase.has_jvp(f)
-        f.jvp
-    elseif u isa Number  # Ignore jvp directives
-        # Only ForwardDiff if user didn't override
-        if ForwardDiff.can_dual(typeof(u)) && (jvp_autodiff === nothing ||
-            jvp_autodiff isa AutoForwardDiff ||
-            jvp_autodiff isa AutoPolyesterForwardDiff)
-            @closure (v, u, p) -> last(__scalar_jacvec(uf, u, v))
-        else
-            @closure (v, u, p) -> FiniteDiff.finite_difference_derivative(uf, u) * v
-        end
-    else
-        jvp_autodiff = __get_nonsparse_ad(get_concrete_forward_ad(
-            jvp_autodiff, prob, False))
-        if jvp_autodiff isa AutoForwardDiff || jvp_autodiff isa AutoPolyesterForwardDiff
-            if iip
-                # FIXME: Technically we should propagate the tag but ignoring that for now
-                cache1 = Dual{typeof(ForwardDiff.Tag(uf, eltype(u))), eltype(u),
-                    1}.(zero(u), ForwardDiff.Partials.(tuple.(u)))
-                cache2 = Dual{typeof(ForwardDiff.Tag(uf, eltype(fu))), eltype(fu),
-                    1}.(zero(fu), ForwardDiff.Partials.(tuple.(fu)))
-                @closure (Jv, v, u, p) -> auto_jacvec!(Jv, uf, u, v, cache1, cache2)
-            else
-                @closure (v, u, p) -> auto_jacvec(uf, u, v)
-            end
-        elseif jvp_autodiff isa AutoFiniteDiff
-            if iip
-                cache1 = zero(fu)
-                cache2 = zero(u)
-                @closure (Jv, v, u, p) -> num_jacvec!(Jv, uf, u, v, cache1, cache2)
-            else
-                @closure (v, u, p) -> num_jacvec(uf, u, v)
-            end
-        else
-            error("`jvp_autodiff` = `$(typeof(jvp_autodiff))` is not supported in \
-                   JacobianOperator.")
-        end
-    end
-
-    return JacobianOperator{false, iip, promote_type(eltype(fu), eltype(u))}(
-        jvp_op, vjp_op, u, fu)
-end
-
-"""
-    VecJacOperator(args...; autodiff = nothing, kwargs...)
-
-Constructs a [`JacobianOperator`](@ref) which only provides the VJP using the
-`vjp_autodiff = autodiff`.
-
-This is very similar to `SparseDiffTools.VecJac` but is geared towards
-[`NonlinearProblem`](@ref)s. For arguments and keyword arguments see
-[`JacobianOperator`](@ref).
-"""
-function VecJacOperator(args...; autodiff = nothing, kwargs...)
-    return JacobianOperator(args...; kwargs..., skip_jvp = True, vjp_autodiff = autodiff)'
-end
-
-"""
-    JacVecOperator(args...; autodiff = nothing, kwargs...)
-
-Constructs a [`JacobianOperator`](@ref) which only provides the JVP using the
-`jvp_autodiff = autodiff`.
-
-This is very similar to `SparseDiffTools.JacVec` but is geared towards
-[`NonlinearProblem`](@ref)s. For arguments and keyword arguments see
-[`JacobianOperator`](@ref).
-"""
-function JacVecOperator(args...; autodiff = nothing, kwargs...)
-    return JacobianOperator(args...; kwargs..., skip_vjp = True, jvp_autodiff = autodiff)
-end
-
-function (op::JacobianOperator{vjp, iip})(v, u, p) where {vjp, iip}
-    if vjp
-        if iip
-            res = zero(op.output_cache)
-            op.vjp_op(res, v, u, p)
-            return res
-        else
-            return op.vjp_op(v, u, p)
-        end
-    else
-        if iip
-            res = zero(op.output_cache)
-            op.jvp_op(res, v, u, p)
-            return res
-        else
-            return op.jvp_op(v, u, p)
-        end
-    end
-end
-
-# Prevent Ambiguity
-function (op::JacobianOperator{vjp, iip})(Jv::Number, v::Number, u, p) where {vjp, iip}
-    error("Inplace Jacobian Operator not possible for scalars.")
-end
-
-function (op::JacobianOperator{vjp, iip})(Jv, v, u, p) where {vjp, iip}
-    if vjp
-        if iip
-            op.vjp_op(Jv, v, u, p)
-        else
-            copyto!(Jv, op.vjp_op(v, u, p))
-        end
-    else
-        if iip
-            op.jvp_op(Jv, v, u, p)
-        else
-            copyto!(Jv, op.jvp_op(v, u, p))
-        end
-    end
-    return Jv
-end
-
-"""
-    StatefulJacobianOperator(jac_op::JacobianOperator, u, p)
-
-Wrapper over a [`JacobianOperator`](@ref) which stores the input `u` and `p` and defines
-`mul!` and `*` for computing VJPs and JVPs.
-"""
-@concrete struct StatefulJacobianOperator{
-    vjp, iip, T, J <: JacobianOperator{vjp, iip, T}} <: AbstractNonlinearSolveOperator{T}
-    jac_op::J
-    u
-    p
-end
-
-Base.size(J::StatefulJacobianOperator) = size(J.jac_op)
-Base.size(J::StatefulJacobianOperator, d::Integer) = size(J.jac_op, d)
-
-for op in (:adjoint, :transpose)
-    @eval function Base.$op(operator::StatefulJacobianOperator)
-        return StatefulJacobianOperator($(op)(operator.jac_op), operator.u, operator.p)
-    end
-end
-
-Base.:*(J::StatefulJacobianOperator, v::AbstractArray) = J.jac_op(v, J.u, J.p)
-function Base.:*(J_op::StatefulJacobianOperator{vjp, iip, T, J, <:Number},
-        v::Number) where {vjp, iip, T, J}
-    return J_op.jac_op(v, J_op.u, J_op.p)
-end
-
-function LinearAlgebra.mul!(
-        Jv::AbstractArray, J::StatefulJacobianOperator, v::AbstractArray)
-    J.jac_op(Jv, v, J.u, J.p)
-    return Jv
-end
-
-"""
-    StatefulJacobianNormalFormOperator(vjp_operator, jvp_operator, cache)
-
-This constructs a Normal Form Jacobian Operator, i.e. it constructs the operator
-corresponding to `JᵀJ` where `J` is the Jacobian Operator. This is not meant to be directly
-constructed, rather it is constructed with `*` on two [`StatefulJacobianOperator`](@ref)s.
-"""
-@concrete mutable struct StatefulJacobianNormalFormOperator{T} <:
-                         AbstractNonlinearSolveOperator{T}
-    vjp_operator
-    jvp_operator
-    cache
-end
-
-function Base.size(J::StatefulJacobianNormalFormOperator)
-    return size(J.vjp_operator, 1), size(J.jvp_operator, 2)
-end
-
-function Base.:*(J1::StatefulJacobianOperator{true}, J2::StatefulJacobianOperator{false})
-    cache = J2 * J2.jac_op.input_cache
-    T = promote_type(eltype(J1), eltype(J2))
-    return StatefulJacobianNormalFormOperator{T}(J1, J2, cache)
-end
-
-function LinearAlgebra.mul!(C::StatefulJacobianNormalFormOperator,
-        A::StatefulJacobianOperator{true}, B::StatefulJacobianOperator{false})
-    C.vjp_operator = A
-    C.jvp_operator = B
-    return C
-end
-
-function Base.:*(JᵀJ::StatefulJacobianNormalFormOperator, x::AbstractArray)
-    return JᵀJ.vjp_operator * (JᵀJ.jvp_operator * x)
-end
-
-function LinearAlgebra.mul!(
-        JᵀJx::AbstractArray, JᵀJ::StatefulJacobianNormalFormOperator, x::AbstractArray)
-    mul!(JᵀJ.cache, JᵀJ.jvp_operator, x)
-    mul!(JᵀJx, JᵀJ.vjp_operator, JᵀJ.cache)
-    return JᵀJx
-end

From 1f7dc7862da94df4c15d7c1e17948ba3867d4149 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 23 Sep 2024 19:28:24 -0400
Subject: [PATCH 472/700] test: standardize testing

---
 .buildkite/pipeline.yml                       |  2 -
 .github/workflows/CI_NonlinearSolve.yml       |  3 --
 .../workflows/CI_SciMLJacobianOperators.yml   |  1 -
 .github/workflows/Downgrade.yml               |  4 --
 .github/workflows/Downstream.yml              |  3 --
 Project.toml                                  |  5 +-
 test/core/23_test_problems_tests.jl           |  2 +-
 test/core/rootfind_tests.jl                   | 18 +++----
 test/gpu/core_tests.jl                        | 48 ++++++++++---------
 test/runtests.jl                              | 23 +++++----
 10 files changed, 54 insertions(+), 55 deletions(-)

diff --git a/.buildkite/pipeline.yml b/.buildkite/pipeline.yml
index a9b3004f4..8ddf4f4ff 100644
--- a/.buildkite/pipeline.yml
+++ b/.buildkite/pipeline.yml
@@ -30,6 +30,4 @@ steps:
 env:
   GROUP: CUDA
   JULIA_PKG_SERVER: "" # it often struggles with our large artifacts
-  RETESTITEMS_NWORKERS: 4
-  RETESTITEMS_NWORKER_THREADS: 2
   SECRET_CODECOV_TOKEN: "HC7K/ymhi62KUQ5OLU4DOl+11gaQt4JhXX/2nfTGlTsBB8mEMxQ8R+sHIp/2HjEup5eSXAN2IWQDQ7RDBuQvVp0T1UVtr2e4YNZFztKnsJXrFO15hXxYShJodI//X/8DzhlQd/lyTDOAOJu3eznsc3sC2CUgJzXZxLUtQN9YaZ1i3a+NoN1mO5UpkkHVhXigwF5gjy+0tei8fCdcP+SIhG0EanS5yd9q/SurtCpMHsHyUG97+ZVPglSKgdaqr31+PdmiPJ+ynp4+Hnc/esosxUSHSIL+ryRTO+28RNwPTiNf99J51RJLQmz1knWTR1ky6tiYIZ5218O6wvNil0SqNw==;U2FsdGVkX18nBY3t4LZYlEIz3EVKjpqCd994JNeJGt006up+sAjXEssI0tgCVXnfXsenVsP3NCCEoOS1GXc44g=="
diff --git a/.github/workflows/CI_NonlinearSolve.yml b/.github/workflows/CI_NonlinearSolve.yml
index 7a04185d1..6f161a07a 100644
--- a/.github/workflows/CI_NonlinearSolve.yml
+++ b/.github/workflows/CI_NonlinearSolve.yml
@@ -35,7 +35,6 @@ jobs:
         version:
           - "min"
           - "1"
-          - "pre"
         os:
           - ubuntu-latest
           - macos-latest
@@ -70,8 +69,6 @@ jobs:
         shell: julia --color=yes --code-coverage=user --depwarn=yes --project=. {0}
         env:
           GROUP: ${{ matrix.group }}
-          RETESTITEMS_NWORKERS: 4
-          RETESTITEMS_NWORKER_THREADS: 2
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: src,ext
diff --git a/.github/workflows/CI_SciMLJacobianOperators.yml b/.github/workflows/CI_SciMLJacobianOperators.yml
index 37d6efdff..25ba9c652 100644
--- a/.github/workflows/CI_SciMLJacobianOperators.yml
+++ b/.github/workflows/CI_SciMLJacobianOperators.yml
@@ -26,7 +26,6 @@ jobs:
         version:
           - "min"
           - "1"
-          - "pre"
         os:
           - ubuntu-latest
           - macos-latest
diff --git a/.github/workflows/Downgrade.yml b/.github/workflows/Downgrade.yml
index 3d3c9a2cd..fa9be3c7a 100644
--- a/.github/workflows/Downgrade.yml
+++ b/.github/workflows/Downgrade.yml
@@ -26,7 +26,3 @@ jobs:
           skip: Pkg,TOML
       - uses: julia-actions/julia-buildpkg@v1
       - uses: julia-actions/julia-runtest@v1
-        env:
-          JULIA_NUM_THREADS: 11
-          RETESTITEMS_NWORKERS: 4
-          RETESTITEMS_NWORKER_THREADS: 2
diff --git a/.github/workflows/Downstream.yml b/.github/workflows/Downstream.yml
index 3e5a3e4f5..9e54283aa 100644
--- a/.github/workflows/Downstream.yml
+++ b/.github/workflows/Downstream.yml
@@ -55,9 +55,6 @@ jobs:
             @info "Not compatible with this release. No problem." exception=err
             exit(0)  # Exit immediately, as a success
           end
-        env:
-          RETESTITEMS_NWORKERS: 4
-          RETESTITEMS_NWORKER_THREADS: 2
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: src,ext
diff --git a/Project.toml b/Project.toml
index edfd8f8f0..74e3e99f8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -74,6 +74,7 @@ FastLevenbergMarquardt = "0.1"
 FiniteDiff = "2.22"
 FixedPointAcceleration = "0.3"
 ForwardDiff = "0.10.36"
+Hwloc = "3"
 LazyArrays = "1.8.2, 2"
 LeastSquaresOptim = "0.8.5"
 LineSearches = "7.2"
@@ -121,6 +122,8 @@ Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 FastLevenbergMarquardt = "7a0df574-e128-4d35-8cbd-3d84502bf7ce"
 FixedPointAcceleration = "817d07cb-a79a-5c30-9a31-890123675176"
+Hwloc = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
 MINPACK = "4854310b-de5a-5eb6-a2a5-c1dee2bd17f9"
 ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
@@ -142,4 +145,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEq", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEq", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
diff --git a/test/core/23_test_problems_tests.jl b/test/core/23_test_problems_tests.jl
index 7305af96f..7648db53f 100644
--- a/test/core/23_test_problems_tests.jl
+++ b/test/core/23_test_problems_tests.jl
@@ -122,7 +122,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests, Sys.isapple() ? 1e-3 : 1e-4)
 end
 
-@testitem "Klement" retries=5 setup=[RobustnessTesting] tags=[:core] begin
+@testitem "Klement" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (Klement(), Klement(; init_jacobian = Val(:true_jacobian_diagonal)))
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index 880b34ff1..c8ecc3980 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -52,7 +52,7 @@ end
 
 # --- NewtonRaphson tests ---
 
-@testitem "NewtonRaphson" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
+@testitem "NewtonRaphson" setup=[CoreRootfindTesting] tags=[:core] begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad))" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
         ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff())
@@ -118,7 +118,7 @@ end
 
 # --- TrustRegion tests ---
 
-@testitem "TrustRegion" setup=[CoreRootfindTesting] tags=[:core] skip=:(Sys.isapple()) timeout=3600 begin
+@testitem "TrustRegion" setup=[CoreRootfindTesting] tags=[:core] begin
     radius_update_schemes = [RadiusUpdateSchemes.Simple, RadiusUpdateSchemes.NocedalWright,
         RadiusUpdateSchemes.NLsolve, RadiusUpdateSchemes.Hei,
         RadiusUpdateSchemes.Yuan, RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin]
@@ -236,7 +236,7 @@ end
 
 # --- LevenbergMarquardt tests ---
 
-@testitem "LevenbergMarquardt" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
+@testitem "LevenbergMarquardt" setup=[CoreRootfindTesting] tags=[:core] begin
     u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
     @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
         sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = LevenbergMarquardt())
@@ -322,7 +322,7 @@ end
 
 # --- DFSane tests ---
 
-@testitem "DFSane" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
+@testitem "DFSane" setup=[CoreRootfindTesting] tags=[:core] begin
     u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
 
     @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
@@ -393,7 +393,7 @@ end
 
 # --- PseudoTransient tests ---
 
-@testitem "PseudoTransient" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
+@testitem "PseudoTransient" setup=[CoreRootfindTesting] tags=[:core] begin
     # These are tests for NewtonRaphson so we should set alpha_initial to be high so that we
     # converge quickly
     @testset "PT: alpha_initial = 10.0 PT AD: $(ad)" for ad in (
@@ -462,7 +462,7 @@ end
 
 # --- Broyden tests ---
 
-@testitem "Broyden" setup=[CoreRootfindTesting] tags=[:core] skip=:(Sys.isapple()) timeout=3600 begin
+@testitem "Broyden" setup=[CoreRootfindTesting] tags=[:core] begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian) Update Rule: $(update_rule)" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(),
             HagerZhang(), MoreThuente(), LiFukushimaLineSearch()),
@@ -512,7 +512,7 @@ end
 
 # --- Klement tests ---
 
-@testitem "Klement" setup=[CoreRootfindTesting] tags=[:core] skip=:(Sys.isapple()) timeout=3600 begin
+@testitem "Klement" setup=[CoreRootfindTesting] tags=[:core] begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian)" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
         ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()),
@@ -561,7 +561,7 @@ end
 
 # --- LimitedMemoryBroyden tests ---
 
-@testitem "LimitedMemoryBroyden" setup=[CoreRootfindTesting] tags=[:core] skip=:(Sys.isapple()) timeout=3600 begin
+@testitem "LimitedMemoryBroyden" setup=[CoreRootfindTesting] tags=[:core] begin
     @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad))" for lsmethod in (
             Static(), StrongWolfe(), BackTracking(),
             HagerZhang(), MoreThuente(), LiFukushimaLineSearch()),
@@ -611,7 +611,7 @@ end
 end
 
 # Miscellaneous Tests
-@testitem "Custom JVP" setup=[CoreRootfindTesting] tags=[:core] timeout=3600 begin
+@testitem "Custom JVP" setup=[CoreRootfindTesting] tags=[:core] begin
     function F(u::Vector{Float64}, p::Vector{Float64})
         Δ = Tridiagonal(-ones(99), 2 * ones(100), -ones(99))
         return u + 0.1 * u .* Δ * u - p
diff --git a/test/gpu/core_tests.jl b/test/gpu/core_tests.jl
index 79a20cc97..d6d38ee1a 100644
--- a/test/gpu/core_tests.jl
+++ b/test/gpu/core_tests.jl
@@ -1,37 +1,39 @@
-@testitem "CUDA Tests" tags=[:cuda] skip=:(using CUDA; !CUDA.functional()) begin
+@testitem "CUDA Tests" tags=[:cuda] begin
     using CUDA, NonlinearSolve, LinearSolve, StableRNGs
 
-    CUDA.allowscalar(false)
+    if CUDA.functional()
+        CUDA.allowscalar(false)
 
-    A = cu(rand(StableRNG(0), 4, 4))
-    u0 = cu(rand(StableRNG(0), 4))
-    b = cu(rand(StableRNG(0), 4))
+        A = cu(rand(StableRNG(0), 4, 4))
+        u0 = cu(rand(StableRNG(0), 4))
+        b = cu(rand(StableRNG(0), 4))
 
-    linear_f(du, u, p) = (du .= A * u .+ b)
+        linear_f(du, u, p) = (du .= A * u .+ b)
 
-    prob = NonlinearProblem(linear_f, u0)
+        prob = NonlinearProblem(linear_f, u0)
 
-    SOLVERS = (NewtonRaphson(), LevenbergMarquardt(; linsolve = QRFactorization()),
-        LevenbergMarquardt(; linsolve = KrylovJL_GMRES()), PseudoTransient(),
-        Klement(), Broyden(; linesearch = LiFukushimaLineSearch()),
-        LimitedMemoryBroyden(; threshold = 2, linesearch = LiFukushimaLineSearch()),
-        DFSane(), TrustRegion(; linsolve = QRFactorization()),
-        TrustRegion(; linsolve = KrylovJL_GMRES(), concrete_jac = true),  # Needed if Zygote not loaded
-        nothing)
+        SOLVERS = (NewtonRaphson(), LevenbergMarquardt(; linsolve = QRFactorization()),
+            LevenbergMarquardt(; linsolve = KrylovJL_GMRES()), PseudoTransient(),
+            Klement(), Broyden(; linesearch = LiFukushimaLineSearch()),
+            LimitedMemoryBroyden(; threshold = 2, linesearch = LiFukushimaLineSearch()),
+            DFSane(), TrustRegion(; linsolve = QRFactorization()),
+            TrustRegion(; linsolve = KrylovJL_GMRES(), concrete_jac = true),  # Needed if Zygote not loaded
+            nothing)
 
-    @testset "[IIP] GPU Solvers" begin
-        for alg in SOLVERS
-            @test_nowarn sol = solve(prob, alg; abstol = 1.0f-5, reltol = 1.0f-5)
+        @testset "[IIP] GPU Solvers" begin
+            for alg in SOLVERS
+                @test_nowarn sol = solve(prob, alg; abstol = 1.0f-5, reltol = 1.0f-5)
+            end
         end
-    end
 
-    linear_f(u, p) = A * u .+ b
+        linear_f(u, p) = A * u .+ b
 
-    prob = NonlinearProblem{false}(linear_f, u0)
+        prob = NonlinearProblem{false}(linear_f, u0)
 
-    @testset "[OOP] GPU Solvers" begin
-        for alg in SOLVERS
-            @test_nowarn sol = solve(prob, alg; abstol = 1.0f-5, reltol = 1.0f-5)
+        @testset "[OOP] GPU Solvers" begin
+            for alg in SOLVERS
+                @test_nowarn sol = solve(prob, alg; abstol = 1.0f-5, reltol = 1.0f-5)
+            end
         end
     end
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 421a96f7b..a3d72552f 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,10 +1,17 @@
-using ReTestItems, CUDA
+using ReTestItems, NonlinearSolve, Hwloc, InteractiveUtils
 
-const GROUP = get(ENV, "GROUP", CUDA.functional() ? "All" : "All")
+@info sprint(InteractiveUtils.versioninfo)
 
-if GROUP == "All"
-    ReTestItems.runtests(@__DIR__)
-else
-    tags = [Symbol(lowercase(GROUP))]
-    ReTestItems.runtests(@__DIR__; tags)
-end
+const GROUP = lowercase(get(ENV, "GROUP", "All"))
+
+const RETESTITEMS_NWORKERS = parse(
+    Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4))))
+const RETESTITEMS_NWORKER_THREADS = parse(Int,
+    get(ENV, "RETESTITEMS_NWORKER_THREADS",
+        string(max(Hwloc.num_virtual_cores() ÷ RETESTITEMS_NWORKERS, 1))))
+
+@info "Running tests for group: $LUXLIB_TEST_GROUP with $RETESTITEMS_NWORKERS workers"
+
+ReTestItems.runtests(NonlinearSolve; tags = (GROUP == "all" ? nothing : [Symbol(GROUP)]),
+    nworkers = RETESTITEMS_NWORKERS,
+    nworker_threads = RETESTITEMS_NWORKER_THREADS, testitem_timeout = 3600, retries=4)

From 608c30a6d478248993ec7f2f390d29ac54e5c474 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 23 Sep 2024 19:32:53 -0400
Subject: [PATCH 473/700] test: remove stale imports

---
 Project.toml          | 1 +
 src/NonlinearSolve.jl | 7 +++----
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Project.toml b/Project.toml
index 74e3e99f8..b00e7aaa1 100644
--- a/Project.toml
+++ b/Project.toml
@@ -98,6 +98,7 @@ RecursiveArrayTools = "3.8"
 Reexport = "1.2"
 SIAMFANLEquations = "1.0.1"
 SciMLBase = "2.34.0"
+SciMLJacobianOperators = "0.1"
 SimpleNonlinearSolve = "1.8"
 SparseArrays = "1.10"
 SparseDiffTools = "2.19"
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 77293ce3f..416f98fb6 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -41,14 +41,13 @@ using RecursiveArrayTools: recursivecopy!, recursivefill!
 using SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
                  AbstractSciMLOperator, _unwrap_val, has_jac, isinplace, NLStats
 using SciMLJacobianOperators: JacobianOperator, VecJacOperator, JacVecOperator,
-                              StatefulJacobianOperator, StatefulJacobianNormalFormOperator
+                              StatefulJacobianOperator
 using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
 using SparseDiffTools: SparseDiffTools, AbstractSparsityDetection,
                        ApproximateJacobianSparsity, JacPrototypeSparsityDetection,
                        NoSparsityDetection, PrecomputedJacobianColorvec,
-                       SymbolicsSparsityDetection, auto_jacvec, auto_jacvec!, auto_vecjac,
-                       init_jacobian, num_jacvec, num_jacvec!, num_vecjac, num_vecjac!,
-                       sparse_jacobian, sparse_jacobian!, sparse_jacobian_cache
+                       SymbolicsSparsityDetection, init_jacobian, sparse_jacobian,
+                       sparse_jacobian!, sparse_jacobian_cache
 using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
 using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
                                  symbolic_container, parameter_values, state_values, getu,

From 516fceaec410a60395d27ad0fbece1c0ab6bfbf2 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 23 Sep 2024 19:36:17 -0400
Subject: [PATCH 474/700] fix: return the result always

---
 .../src/SciMLJacobianOperators.jl                     | 11 +++++------
 1 file changed, 5 insertions(+), 6 deletions(-)

diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index fceaea278..8cb51a30f 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -150,18 +150,17 @@ function (op::JacobianOperator)(Jv, v, u, p)
     if op.mode isa VJP
         if SciMLBase.isinplace(op)
             op.vjp_op(Jv, v, u, p)
-            return
+        else
+            copyto!(Jv, op.vjp_op(v, u, p))
         end
-        copyto!(Jv, op.vjp_op(v, u, p))
-        return
     else
         if SciMLBase.isinplace(op)
             op.jvp_op(Jv, v, u, p)
-            return
+        else
+            copyto!(Jv, op.jvp_op(v, u, p))
         end
-        copyto!(Jv, op.jvp_op(v, u, p))
-        return
     end
+    return Jv
 end
 
 """

From 5fc54a7935d649a03bf27c71822e3553ae6b07fc Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 23 Sep 2024 19:37:47 -0400
Subject: [PATCH 475/700] fix: more test fixes

---
 Project.toml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Project.toml b/Project.toml
index b00e7aaa1..85392fd34 100644
--- a/Project.toml
+++ b/Project.toml
@@ -75,6 +75,7 @@ FiniteDiff = "2.22"
 FixedPointAcceleration = "0.3"
 ForwardDiff = "0.10.36"
 Hwloc = "3"
+InteractiveUtils = "<0.0.1, 1"
 LazyArrays = "1.8.2, 2"
 LeastSquaresOptim = "0.8.5"
 LineSearches = "7.2"

From 37bda545e190fdd53dd37b180386442d50c35966 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 23 Sep 2024 19:59:59 -0400
Subject: [PATCH 476/700] test: more test fixes

---
 Project.toml                                    |  2 +-
 lib/SciMLJacobianOperators/Project.toml         |  2 --
 .../src/SciMLJacobianOperators.jl               | 17 ++---------------
 lib/SciMLJacobianOperators/test/runtests.jl     |  1 +
 src/NonlinearSolve.jl                           |  4 ++--
 src/utils.jl                                    |  1 +
 test/runtests.jl                                |  6 +++---
 7 files changed, 10 insertions(+), 23 deletions(-)

diff --git a/Project.toml b/Project.toml
index 85392fd34..f7a8ad781 100644
--- a/Project.toml
+++ b/Project.toml
@@ -81,7 +81,7 @@ LeastSquaresOptim = "0.8.5"
 LineSearches = "7.2"
 LinearAlgebra = "1.10"
 LinearSolve = "2.30"
-MINPACK = "=1.2"
+MINPACK = "1.2"
 MaybeInplace = "0.1.3"
 ModelingToolkit = "9.15.0"
 NLSolvers = "0.5"
diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index 11b19a324..8d813441c 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -4,7 +4,6 @@ authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
 version = "0.1.0"
 
 [deps]
-ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
@@ -15,7 +14,6 @@ SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 
 [compat]
-ADTypes = "1.8.1"
 ConcreteStructs = "0.2.3"
 ConstructionBase = "1.5"
 DifferentiationInterface = "0.5"
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index 8cb51a30f..2613ccc02 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -1,6 +1,5 @@
 module SciMLJacobianOperators
 
-using ADTypes: ADTypes
 using ConcreteStructs: @concrete
 using ConstructionBase: ConstructionBase
 using DifferentiationInterface: DifferentiationInterface
@@ -117,8 +116,8 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
     vjp_op = prepare_vjp(skip_vjp, prob, f, u, fu; autodiff = vjp_autodiff)
     jvp_op = prepare_jvp(skip_jvp, prob, f, u, fu; autodiff = jvp_autodiff)
 
-    output_cache = similar(fu, T)
-    input_cache = similar(u, T)
+    output_cache = fu isa Number ? T(fu) : similar(fu, T)
+    input_cache = u isa Number ? T(u) : similar(u, T)
 
     return JacobianOperator{iip, T}(
         JVP(), jvp_op, vjp_op, (length(fu), length(u)), output_cache, input_cache)
@@ -290,12 +289,6 @@ function prepare_vjp(::Val{false}, prob::AbstractNonlinearProblem,
 
     @assert autodiff!==nothing "`vjp_autodiff` must be provided if `f` doesn't have \
                                 analytic `vjp` or `jac`."
-
-    if ADTypes.mode(autodiff) isa ADTypes.ForwardMode
-        @warn "AD Backend: $(autodiff) is a Forward Mode backend. Computing VJPs using \
-               this will be slow!"
-    end
-
     # TODO: Once DI supports const params we can use `p`
     fₚ = SciMLBase.JacobianWrapper{SciMLBase.isinplace(f)}(f, prob.p)
     if SciMLBase.isinplace(f)
@@ -337,12 +330,6 @@ function prepare_jvp(::Val{false}, prob::AbstractNonlinearProblem,
 
     @assert autodiff!==nothing "`jvp_autodiff` must be provided if `f` doesn't have \
                                 analytic `vjp` or `jac`."
-
-    if ADTypes.mode(autodiff) isa ADTypes.ReverseMode
-        @warn "AD Backend: $(autodiff) is a Reverse Mode backend. Computing JVPs using \
-               this will be slow!"
-    end
-
     # TODO: Once DI supports const params we can use `p`
     fₚ = SciMLBase.JacobianWrapper{SciMLBase.isinplace(f)}(f, prob.p)
     if SciMLBase.isinplace(f)
diff --git a/lib/SciMLJacobianOperators/test/runtests.jl b/lib/SciMLJacobianOperators/test/runtests.jl
index e69de29bb..8b1378917 100644
--- a/lib/SciMLJacobianOperators/test/runtests.jl
+++ b/lib/SciMLJacobianOperators/test/runtests.jl
@@ -0,0 +1 @@
+
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 416f98fb6..2e420a761 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -40,8 +40,8 @@ using Preferences: Preferences, @load_preference, @set_preferences!
 using RecursiveArrayTools: recursivecopy!, recursivefill!
 using SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
                  AbstractSciMLOperator, _unwrap_val, has_jac, isinplace, NLStats
-using SciMLJacobianOperators: JacobianOperator, VecJacOperator, JacVecOperator,
-                              StatefulJacobianOperator
+using SciMLJacobianOperators: AbstractJacobianOperator, JacobianOperator, VecJacOperator,
+                              JacVecOperator, StatefulJacobianOperator
 using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
 using SparseDiffTools: SparseDiffTools, AbstractSparsityDetection,
                        ApproximateJacobianSparsity, JacPrototypeSparsityDetection,
diff --git a/src/utils.jl b/src/utils.jl
index 64399a349..1a4ffd2c8 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -48,6 +48,7 @@ end
     return deepcopy(x)
 end
 @inline __maybe_unaliased(x::AbstractNonlinearSolveOperator, alias::Bool) = x
+@inline __maybe_unaliased(x::AbstractJacobianOperator, alias::Bool) = x
 
 @inline __cond(J::AbstractMatrix) = cond(J)
 @inline __cond(J::SVector) = __cond(Diagonal(MVector(J)))
diff --git a/test/runtests.jl b/test/runtests.jl
index a3d72552f..74676f3ad 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -10,8 +10,8 @@ const RETESTITEMS_NWORKER_THREADS = parse(Int,
     get(ENV, "RETESTITEMS_NWORKER_THREADS",
         string(max(Hwloc.num_virtual_cores() ÷ RETESTITEMS_NWORKERS, 1))))
 
-@info "Running tests for group: $LUXLIB_TEST_GROUP with $RETESTITEMS_NWORKERS workers"
+@info "Running tests for group: $(GROUP) with $(RETESTITEMS_NWORKERS) workers"
 
 ReTestItems.runtests(NonlinearSolve; tags = (GROUP == "all" ? nothing : [Symbol(GROUP)]),
-    nworkers = RETESTITEMS_NWORKERS,
-    nworker_threads = RETESTITEMS_NWORKER_THREADS, testitem_timeout = 3600, retries=4)
+    nworkers = RETESTITEMS_NWORKERS, nworker_threads = RETESTITEMS_NWORKER_THREADS,
+    testitem_timeout = 3600, retries = 4)

From 2383607ef9285f4eb2a9c49d07ca88e98f005388 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 23 Sep 2024 21:14:29 -0400
Subject: [PATCH 477/700] test: fix core testing

---
 lib/SciMLJacobianOperators/Project.toml       |  9 +++++++-
 .../src/SciMLJacobianOperators.jl             | 21 ++++++++++++++++---
 lib/SciMLJacobianOperators/test/runtests.jl   |  4 ++++
 src/internal/jacobian.jl                      |  2 +-
 test/core/rootfind_tests.jl                   |  6 +++---
 test/misc/qa_tests.jl                         |  2 --
 6 files changed, 34 insertions(+), 10 deletions(-)

diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index 8d813441c..d5d265d90 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -4,6 +4,7 @@ authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
 version = "0.1.0"
 
 [deps]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
@@ -14,18 +15,24 @@ SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 
 [compat]
+ADTypes = "1.8.1"
 ConcreteStructs = "0.2.3"
 ConstructionBase = "1.5"
 DifferentiationInterface = "0.5"
 FastClosures = "0.3.2"
+InteractiveUtils = "<0.0.1, 1"
 LinearAlgebra = "1.10"
+SciMLBase = "2.54.0"
 SciMLOperators = "0.3"
 Setfield = "1"
+Test = "1.10"
+TestItemRunner = "1"
 julia = "1.10"
 
 [extras]
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
 
 [targets]
-test = ["Test", "TestItemRunner"]
+test = ["InteractiveUtils", "Test", "TestItemRunner"]
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index 2613ccc02..262443175 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -1,5 +1,6 @@
 module SciMLJacobianOperators
 
+using ADTypes: ADTypes, AutoSparse
 using ConcreteStructs: @concrete
 using ConstructionBase: ConstructionBase
 using DifferentiationInterface: DifferentiationInterface
@@ -101,6 +102,7 @@ for op in (:adjoint, :transpose)
         (; output_cache, input_cache) = operator
         @set! operator.output_cache = input_cache
         @set! operator.input_cache = output_cache
+        @set! operator.size = reverse(operator.size)
         return operator
     end
 end
@@ -113,7 +115,10 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
     iip = SciMLBase.isinplace(prob)
     T = promote_type(eltype(u), eltype(fu))
 
+    vjp_autodiff = get_dense_ad(vjp_autodiff)
     vjp_op = prepare_vjp(skip_vjp, prob, f, u, fu; autodiff = vjp_autodiff)
+
+    jvp_autodiff = get_dense_ad(jvp_autodiff)
     jvp_op = prepare_jvp(skip_jvp, prob, f, u, fu; autodiff = jvp_autodiff)
 
     output_cache = fu isa Number ? T(fu) : similar(fu, T)
@@ -212,6 +217,7 @@ for op in (:adjoint, :transpose)
 end
 
 Base.:*(J::StatefulJacobianOperator, v::AbstractArray) = J.jac_op(v, J.u, J.p)
+Base.:*(J::StatefulJacobianOperator, v::Number) = J.jac_op(v, J.u, J.p)
 
 function LinearAlgebra.mul!(
         Jv::AbstractArray, J::StatefulJacobianOperator, v::AbstractArray)
@@ -256,8 +262,8 @@ end
 
 function LinearAlgebra.mul!(
         JᵀJx::AbstractArray, JᵀJ::StatefulJacobianNormalFormOperator, x::AbstractArray)
-    mul!(JᵀJ.cache, JᵀJ.jvp_operator, x)
-    mul!(JᵀJx, JᵀJ.vjp_operator, JᵀJ.cache)
+    LinearAlgebra.mul!(JᵀJ.cache, JᵀJ.jvp_operator, x)
+    LinearAlgebra.mul!(JᵀJx, JᵀJ.vjp_operator, JᵀJ.cache)
     return JᵀJx
 end
 
@@ -313,7 +319,7 @@ end
 
 function prepare_jvp(::Val{false}, prob::AbstractNonlinearProblem,
         f::AbstractNonlinearFunction, u, fu; autodiff = nothing)
-    SciMLBase.has_vjp(f) && return f.vjp
+    SciMLBase.has_jvp(f) && return f.jvp
 
     if autodiff === nothing && SciMLBase.has_jac(f)
         if SciMLBase.isinplace(f)
@@ -360,6 +366,15 @@ function prepare_scalar_op(::Val{false}, prob::AbstractNonlinearProblem,
     return @closure (v, u, p) -> DI.derivative(fₚ, autodiff, u, di_extras) * v
 end
 
+get_dense_ad(::Nothing) = nothing
+get_dense_ad(ad) = ad
+function get_dense_ad(ad::AutoSparse)
+    dense_ad = ADTypes.dense_ad(ad)
+    @warn "Sparse AD backend: $(ad) is being used for VJP/JVP computation. Using the dense \
+           backend: $(dense_ad) instead."
+    return dense_ad
+end
+
 export JacobianOperator, VecJacOperator, JacVecOperator
 export StatefulJacobianOperator
 export StatefulJacobianNormalFormOperator
diff --git a/lib/SciMLJacobianOperators/test/runtests.jl b/lib/SciMLJacobianOperators/test/runtests.jl
index 8b1378917..6ea6326b0 100644
--- a/lib/SciMLJacobianOperators/test/runtests.jl
+++ b/lib/SciMLJacobianOperators/test/runtests.jl
@@ -1 +1,5 @@
+using TestItemRunner, InteractiveUtils
 
+@info sprint(InteractiveUtils.versioninfo)
+
+@run_package_tests
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index be3402314..0c6080112 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -103,10 +103,10 @@ function JacobianCache(prob, alg, f::F, ::Number, u::Number, p; stats,
     if !(autodiff isa AutoForwardDiff ||
          autodiff isa AutoPolyesterForwardDiff ||
          autodiff isa AutoFiniteDiff)
-        autodiff = AutoFiniteDiff()
         # Other cases are not properly supported so we fallback to finite differencing
         @warn "Scalar AD is supported only for AutoForwardDiff and AutoFiniteDiff. \
                Detected $(autodiff). Falling back to AutoFiniteDiff."
+        autodiff = AutoFiniteDiff()
     end
     return JacobianCache{false}(
         u, f, uf, u, u, p, nothing, alg, stats, autodiff, nothing, nothing)
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index c8ecc3980..bca02a44b 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -125,7 +125,7 @@ end
     u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
     linear_solvers = [nothing, LUFactorization(), KrylovJL_GMRES(), \]
 
-    @testset "[OOP] u0: $(typeof(u0)) radius_update_scheme: $(radius_update_scheme) linear_solver: $(linsolve)" for u0 in u0s,
+    @testset "[OOP] u0: $(typeof(u0)) $(radius_update_scheme) $(_nameof(linsolve))" for u0 in u0s,
         radius_update_scheme in radius_update_schemes,
         linsolve in linear_solvers
 
@@ -141,7 +141,7 @@ end
         @test (@ballocated solve!($cache)) < 200
     end
 
-    @testset "[IIP] u0: $(typeof(u0)) radius_update_scheme: $(radius_update_scheme) linear_solver: $(linsolve)" for u0 in ([
+    @testset "[IIP] u0: $(typeof(u0)) $(radius_update_scheme) $(_nameof(linsolve))" for u0 in ([
             1.0, 1.0],),
         radius_update_scheme in radius_update_schemes,
         linsolve in linear_solvers
@@ -162,7 +162,7 @@ end
     @test nlprob_iterator_interface(quadratic_f, p, Val(false), TrustRegion()) ≈ sqrt.(p)
     @test nlprob_iterator_interface(quadratic_f!, p, Val(true), TrustRegion()) ≈ sqrt.(p)
 
-    @testset "ADType: $(autodiff) u0: $(_nameof(u0)) radius_update_scheme: $(radius_update_scheme)" for autodiff in (
+    @testset "$(_nameof(autodiff)) u0: $(_nameof(u0)) $(radius_update_scheme)" for autodiff in (
             AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
             AutoZygote(), AutoSparse(AutoZygote()), AutoSparse(AutoEnzyme())),
         u0 in (1.0, [1.0, 1.0]),
diff --git a/test/misc/qa_tests.jl b/test/misc/qa_tests.jl
index 7e8bf9ce6..5c60e5339 100644
--- a/test/misc/qa_tests.jl
+++ b/test/misc/qa_tests.jl
@@ -24,8 +24,6 @@ end
 
     @test check_no_implicit_imports(NonlinearSolve;
         skip = (NonlinearSolve, Base, Core, SimpleNonlinearSolve, SciMLBase)) === nothing
-
     @test check_no_stale_explicit_imports(NonlinearSolve) === nothing
-
     @test check_all_qualified_accesses_via_owners(NonlinearSolve) === nothing
 end

From 4368b8d2077346a800a27b5d9e0752a3f45142df Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 10:04:10 -0400
Subject: [PATCH 478/700] docs: add SciMLJacobianOperators

---
 .JuliaFormatter.toml                   |  1 -
 .github/workflows/Documentation.yml    | 12 ++++-
 docs/Project.toml                      |  2 +
 docs/make.jl                           |  5 +-
 docs/pages.jl                          | 74 +++++++++++++++++++-------
 docs/src/api/SciMLJacobianOperators.md | 29 ++++++++++
 6 files changed, 100 insertions(+), 23 deletions(-)
 create mode 100644 docs/src/api/SciMLJacobianOperators.md

diff --git a/.JuliaFormatter.toml b/.JuliaFormatter.toml
index 66c13bae3..1768a1a7f 100644
--- a/.JuliaFormatter.toml
+++ b/.JuliaFormatter.toml
@@ -2,4 +2,3 @@ style = "sciml"
 format_markdown = true
 annotate_untyped_fields_with_any = false
 format_docstrings = true
-join_lines_based_on_source = false
diff --git a/.github/workflows/Documentation.yml b/.github/workflows/Documentation.yml
index 0f767ec10..008cd511e 100644
--- a/.github/workflows/Documentation.yml
+++ b/.github/workflows/Documentation.yml
@@ -17,7 +17,17 @@ jobs:
         with:
           version: '1'
       - name: Install dependencies
-        run: julia --project=docs/ -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators", ".")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+        shell: julia --color=yes --project=docs/ {0}
       - name: Build and deploy
         env:
           JULIA_DEBUG: "Documenter"
diff --git a/docs/Project.toml b/docs/Project.toml
index 780cec74a..63d1803d4 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -14,6 +14,7 @@ OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
 SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
@@ -36,6 +37,7 @@ OrdinaryDiffEq = "6"
 Plots = "1"
 Random = "<0.0.1, 1"
 SciMLBase = "2.4"
+SciMLJacobianOperators = "0.1"
 SimpleNonlinearSolve = "1"
 SparseDiffTools = "2.14"
 StaticArrays = "1"
diff --git a/docs/make.jl b/docs/make.jl
index 622cebbfe..e11a04149 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,6 +1,7 @@
 using Documenter, DocumenterCitations
 using NonlinearSolve, SimpleNonlinearSolve, Sundials, SteadyStateDiffEq, SciMLBase,
       DiffEqBase
+using SciMLJacobianOperators
 
 cp(joinpath(@__DIR__, "Manifest.toml"),
     joinpath(@__DIR__, "src/assets/Manifest.toml"), force = true)
@@ -13,8 +14,8 @@ bib = CitationBibliography(joinpath(@__DIR__, "src", "refs.bib"))
 
 makedocs(; sitename = "NonlinearSolve.jl",
     authors = "Chris Rackauckas",
-    modules = [NonlinearSolve, SimpleNonlinearSolve,
-        SteadyStateDiffEq, Sundials, DiffEqBase, SciMLBase],
+    modules = [NonlinearSolve, SimpleNonlinearSolve, SteadyStateDiffEq,
+        Sundials, DiffEqBase, SciMLBase, SciMLJacobianOperators],
     clean = true,
     doctest = false,
     linkcheck = true,
diff --git a/docs/pages.jl b/docs/pages.jl
index 0d548cd60..cfb2754c0 100644
--- a/docs/pages.jl
+++ b/docs/pages.jl
@@ -2,25 +2,61 @@
 
 pages = ["index.md",
     "Getting Started with Nonlinear Rootfinding in Julia" => "tutorials/getting_started.md",
-    "Tutorials" => Any["tutorials/code_optimization.md", "tutorials/large_systems.md",
-        "tutorials/modelingtoolkit.md", "tutorials/small_compile.md",
-        "tutorials/iterator_interface.md", "tutorials/optimizing_parameterized_ode.md"],
-    "Basics" => Any["basics/nonlinear_problem.md", "basics/nonlinear_functions.md",
-        "basics/solve.md", "basics/nonlinear_solution.md", "basics/autodiff.md",
-        "basics/termination_condition.md", "basics/diagnostics_api.md",
-        "basics/sparsity_detection.md", "basics/faq.md"],
-    "Solver Summaries and Recommendations" => Any["solvers/nonlinear_system_solvers.md",
-        "solvers/bracketing_solvers.md", "solvers/steady_state_solvers.md",
-        "solvers/nonlinear_least_squares_solvers.md", "solvers/fixed_point_solvers.md"],
-    "Native Functionalities" => Any["native/solvers.md", "native/simplenonlinearsolve.md",
-        "native/steadystatediffeq.md", "native/descent.md",
-        "native/globalization.md", "native/diagnostics.md"],
+    "Tutorials" => Any[
+        "tutorials/code_optimization.md",
+        "tutorials/large_systems.md",
+        "tutorials/modelingtoolkit.md",
+        "tutorials/small_compile.md",
+        "tutorials/iterator_interface.md",
+        "tutorials/optimizing_parameterized_ode.md"
+    ],
+    "Basics" => Any[
+        "basics/nonlinear_problem.md",
+        "basics/nonlinear_functions.md",
+        "basics/solve.md",
+        "basics/nonlinear_solution.md",
+        "basics/autodiff.md",
+        "basics/termination_condition.md",
+        "basics/diagnostics_api.md",
+        "basics/sparsity_detection.md",
+        "basics/faq.md"
+    ],
+    "Solver Summaries and Recommendations" => Any[
+        "solvers/nonlinear_system_solvers.md",
+        "solvers/bracketing_solvers.md",
+        "solvers/steady_state_solvers.md",
+        "solvers/nonlinear_least_squares_solvers.md",
+        "solvers/fixed_point_solvers.md"
+    ],
+    "Native Functionalities" => Any[
+        "native/solvers.md",
+        "native/simplenonlinearsolve.md",
+        "native/steadystatediffeq.md",
+        "native/descent.md",
+        "native/globalization.md",
+        "native/diagnostics.md"
+    ],
     "Wrapped Solver APIs" => Any[
-        "api/fastlevenbergmarquardt.md", "api/fixedpointacceleration.md",
-        "api/leastsquaresoptim.md", "api/minpack.md", "api/nlsolve.md", "api/nlsolvers.md",
-        "api/siamfanlequations.md", "api/speedmapping.md", "api/sundials.md"],
+        "api/fastlevenbergmarquardt.md",
+        "api/fixedpointacceleration.md",
+        "api/leastsquaresoptim.md",
+        "api/minpack.md",
+        "api/nlsolve.md",
+        "api/nlsolvers.md",
+        "api/siamfanlequations.md",
+        "api/speedmapping.md",
+        "api/sundials.md"
+    ],
+    "Sub-Packages" => Any[
+        "api/SciMLJacobianOperators.md",
+    ],
     "Development Documentation" => [
-        "devdocs/internal_interfaces.md", "devdocs/linear_solve.md",
-        "devdocs/jacobian.md", "devdocs/operators.md", "devdocs/algorithm_helpers.md"],
+        "devdocs/internal_interfaces.md",
+        "devdocs/linear_solve.md",
+        "devdocs/jacobian.md",
+        "devdocs/operators.md",
+        "devdocs/algorithm_helpers.md"
+    ],
     "Release Notes" => "release_notes.md",
-    "References" => "references.md"]
+    "References" => "references.md"
+]
diff --git a/docs/src/api/SciMLJacobianOperators.md b/docs/src/api/SciMLJacobianOperators.md
new file mode 100644
index 000000000..91b7f61df
--- /dev/null
+++ b/docs/src/api/SciMLJacobianOperators.md
@@ -0,0 +1,29 @@
+```@meta
+CurrentModule = SciMLJacobianOperators
+```
+
+# SciMLJacobianOperators.jl
+
+This is a subpackage on NonlinearSolve providing a general purpose JacVec and VecJac
+operator built on top on DifferentiationInterface.jl.
+
+```julia
+import Pkg
+Pkg.add("SciMLJacobianOperators")
+using SciMLJacobianOperators
+```
+
+## Jacobian API
+
+```@docs
+JacobianOperator
+VecJacOperator
+JacVecOperator
+```
+
+## Stateful Operators
+
+```@docs
+StatefulJacobianOperator
+StatefulJacobianNormalFormOperator
+```

From bc64ab5e5a06890c17e162fd55c44cc741a5bb8e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 11:47:15 -0400
Subject: [PATCH 479/700] test: SciMLJacobianOperators testing and bug fixes

---
 .github/workflows/CI_NonlinearSolve.yml       |   2 +-
 .../workflows/CI_SciMLJacobianOperators.yml   |   2 +-
 lib/SciMLJacobianOperators/Project.toml       |  20 +-
 .../src/SciMLJacobianOperators.jl             |  26 +-
 lib/SciMLJacobianOperators/test/core_tests.jl | 274 ++++++++++++++++++
 5 files changed, 315 insertions(+), 9 deletions(-)
 create mode 100644 lib/SciMLJacobianOperators/test/core_tests.jl

diff --git a/.github/workflows/CI_NonlinearSolve.yml b/.github/workflows/CI_NonlinearSolve.yml
index 6f161a07a..a4c14820e 100644
--- a/.github/workflows/CI_NonlinearSolve.yml
+++ b/.github/workflows/CI_NonlinearSolve.yml
@@ -71,7 +71,7 @@ jobs:
           GROUP: ${{ matrix.group }}
       - uses: julia-actions/julia-processcoverage@v1
         with:
-          directories: src,ext
+          directories: src,ext,lib/SciMLJacobianOperators/src
       - uses: codecov/codecov-action@v4
         with:
           file: lcov.info
diff --git a/.github/workflows/CI_SciMLJacobianOperators.yml b/.github/workflows/CI_SciMLJacobianOperators.yml
index 25ba9c652..92daf23e9 100644
--- a/.github/workflows/CI_SciMLJacobianOperators.yml
+++ b/.github/workflows/CI_SciMLJacobianOperators.yml
@@ -54,7 +54,7 @@ jobs:
         shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SciMLJacobianOperators {0}
       - uses: julia-actions/julia-processcoverage@v1
         with:
-          directories: src,ext
+          directories: lib/SciMLJacobianOperators/src
       - uses: codecov/codecov-action@v4
         with:
           file: lcov.info
diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index d5d265d90..5b91928c1 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -8,6 +8,7 @@ ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
+EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
@@ -16,23 +17,40 @@ Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 
 [compat]
 ADTypes = "1.8.1"
+Aqua = "0.8.7"
 ConcreteStructs = "0.2.3"
 ConstructionBase = "1.5"
 DifferentiationInterface = "0.5"
+Enzyme = "0.12, 0.13"
+EnzymeCore = "0.7, 0.8"
+ExplicitImports = "1.9.0"
 FastClosures = "0.3.2"
+FiniteDiff = "2.24.0"
+ForwardDiff = "0.10.36"
 InteractiveUtils = "<0.0.1, 1"
 LinearAlgebra = "1.10"
+ReverseDiff = "1.15"
 SciMLBase = "2.54.0"
 SciMLOperators = "0.3"
 Setfield = "1"
 Test = "1.10"
 TestItemRunner = "1"
+Tracker = "0.2.35"
+Zygote = "0.6.70"
 julia = "1.10"
 
 [extras]
+Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
+FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
+Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["InteractiveUtils", "Test", "TestItemRunner"]
+test = ["Aqua", "Enzyme", "ExplicitImports", "FiniteDiff", "ForwardDiff", "InteractiveUtils", "ReverseDiff", "Test", "TestItemRunner", "Tracker", "Zygote"]
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index 262443175..3699e71bb 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -1,9 +1,10 @@
 module SciMLJacobianOperators
 
-using ADTypes: ADTypes, AutoSparse
+using ADTypes: ADTypes, AutoSparse, AutoEnzyme
 using ConcreteStructs: @concrete
 using ConstructionBase: ConstructionBase
 using DifferentiationInterface: DifferentiationInterface
+using EnzymeCore: EnzymeCore
 using FastClosures: @closure
 using LinearAlgebra: LinearAlgebra
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, AbstractNonlinearFunction
@@ -115,10 +116,10 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
     iip = SciMLBase.isinplace(prob)
     T = promote_type(eltype(u), eltype(fu))
 
-    vjp_autodiff = get_dense_ad(vjp_autodiff)
+    vjp_autodiff = set_function_as_const(get_dense_ad(vjp_autodiff))
     vjp_op = prepare_vjp(skip_vjp, prob, f, u, fu; autodiff = vjp_autodiff)
 
-    jvp_autodiff = get_dense_ad(jvp_autodiff)
+    jvp_autodiff = set_function_as_const(get_dense_ad(jvp_autodiff))
     jvp_op = prepare_jvp(skip_jvp, prob, f, u, fu; autodiff = jvp_autodiff)
 
     output_cache = fu isa Number ? T(fu) : similar(fu, T)
@@ -259,6 +260,9 @@ end
 function Base.:*(JᵀJ::StatefulJacobianNormalFormOperator, x::AbstractArray)
     return JᵀJ.vjp_operator * (JᵀJ.jvp_operator * x)
 end
+function Base.:*(JᵀJ::StatefulJacobianNormalFormOperator, x::Number)
+    return JᵀJ.vjp_operator * (JᵀJ.jvp_operator * x)
+end
 
 function LinearAlgebra.mul!(
         JᵀJx::AbstractArray, JᵀJ::StatefulJacobianNormalFormOperator, x::AbstractArray)
@@ -284,7 +288,7 @@ function prepare_vjp(::Val{false}, prob::AbstractNonlinearProblem,
             jac_cache = similar(u, eltype(fu), length(fu), length(u))
             return @closure (vJ, v, u, p) -> begin
                 f.jac(jac_cache, u, p)
-                mul!(vec(vJ), jac_cache', vec(v))
+                LinearAlgebra.mul!(vec(vJ), jac_cache', vec(v))
                 return
             end
             return vjp_op, vjp_extras
@@ -298,6 +302,8 @@ function prepare_vjp(::Val{false}, prob::AbstractNonlinearProblem,
     # TODO: Once DI supports const params we can use `p`
     fₚ = SciMLBase.JacobianWrapper{SciMLBase.isinplace(f)}(f, prob.p)
     if SciMLBase.isinplace(f)
+        @assert DI.check_twoarg(autodiff) "Backend: $(autodiff) doesn't support in-place \
+                                           problems."
         fu_cache = copy(fu)
         v_fake = copy(fu)
         di_extras = DI.prepare_pullback(fₚ, fu_cache, autodiff, u, v_fake)
@@ -326,11 +332,11 @@ function prepare_jvp(::Val{false}, prob::AbstractNonlinearProblem,
             jac_cache = similar(u, eltype(fu), length(fu), length(u))
             return @closure (Jv, v, u, p) -> begin
                 f.jac(jac_cache, u, p)
-                mul!(vec(Jv), jac_cache, vec(v))
+                LinearAlgebra.mul!(vec(Jv), jac_cache, vec(v))
                 return
             end
         else
-            return @closure (v, u, p, _) -> reshape(f.jac(u, p) * vec(v), size(u))
+            return @closure (v, u, p) -> reshape(f.jac(u, p) * vec(v), size(u))
         end
     end
 
@@ -339,6 +345,8 @@ function prepare_jvp(::Val{false}, prob::AbstractNonlinearProblem,
     # TODO: Once DI supports const params we can use `p`
     fₚ = SciMLBase.JacobianWrapper{SciMLBase.isinplace(f)}(f, prob.p)
     if SciMLBase.isinplace(f)
+        @assert DI.check_twoarg(autodiff) "Backend: $(autodiff) doesn't support in-place \
+                                           problems."
         fu_cache = copy(fu)
         di_extras = DI.prepare_pushforward(fₚ, fu_cache, autodiff, u, u)
         return @closure (Jv, v, u, p) -> begin
@@ -375,6 +383,12 @@ function get_dense_ad(ad::AutoSparse)
     return dense_ad
 end
 
+# In our case we know that it is safe to mark the function as const
+set_function_as_const(ad) = ad
+function set_function_as_const(ad::AutoEnzyme{M, Nothing}) where {M}
+    return AutoEnzyme(; ad.mode, function_annotation = EnzymeCore.Const)
+end
+
 export JacobianOperator, VecJacOperator, JacVecOperator
 export StatefulJacobianOperator
 export StatefulJacobianNormalFormOperator
diff --git a/lib/SciMLJacobianOperators/test/core_tests.jl b/lib/SciMLJacobianOperators/test/core_tests.jl
new file mode 100644
index 000000000..e3b595221
--- /dev/null
+++ b/lib/SciMLJacobianOperators/test/core_tests.jl
@@ -0,0 +1,274 @@
+@testitem "Scalar Ops" begin
+    using ADTypes, SciMLBase
+    using Enzyme, Zygote, ForwardDiff, FiniteDiff, ReverseDiff, Tracker
+    using SciMLJacobianOperators
+
+    reverse_ADs = [
+        AutoEnzyme(),
+        AutoEnzyme(; mode = Enzyme.Reverse),
+        AutoZygote(),
+        AutoReverseDiff(),
+        AutoTracker(),
+        AutoFiniteDiff()
+    ]
+
+    forward_ADs = [
+        AutoEnzyme(),
+        AutoEnzyme(; mode = Enzyme.Forward),
+        AutoForwardDiff(),
+        AutoFiniteDiff()
+    ]
+
+    prob = NonlinearProblem(NonlinearFunction{false}((u, p) -> u^2 - p), 1.0, 2.0)
+
+    analytic_jac(u, p) = 2 * u
+    analytic_jvp(v, u, p) = 2 * u * v
+    analytic_vjp(v, u, p) = analytic_jvp(v, u, p)
+
+    @testset "AutoDiff" begin
+        @testset for jvp_autodiff in forward_ADs, vjp_autodiff in reverse_ADs
+            jac_op = JacobianOperator(prob, -1.0, 1.0; jvp_autodiff, vjp_autodiff)
+
+            @testset for u in rand(4), v in rand(4)
+                sop = StatefulJacobianOperator(jac_op, u, prob.p)
+                @test (sop * v)≈analytic_jvp(v, u, prob.p) atol=1e-5
+                @test (sop' * v)≈analytic_vjp(v, u, prob.p) atol=1e-5
+
+                normal_form_sop = sop' * sop
+                JᵀJv = normal_form_sop * v
+                J_analytic = analytic_jac(u, prob.p)
+                JᵀJv_analytic = J_analytic' * J_analytic * v
+                @test JᵀJv≈JᵀJv_analytic atol=1e-5
+            end
+        end
+    end
+
+    prob = NonlinearProblem(
+        NonlinearFunction{false}((u, p) -> u^2 - p; jvp = analytic_jvp, vjp = analytic_vjp),
+        1.0, 2.0)
+
+    @testset "Analytic JVP/VJP" begin
+        jac_op = JacobianOperator(prob, -1.0, 1.0)
+
+        @testset for u in rand(4), v in rand(4)
+            sop = StatefulJacobianOperator(jac_op, u, prob.p)
+            @test (sop * v)≈analytic_jvp(v, u, prob.p) atol=1e-5
+            @test (sop' * v)≈analytic_vjp(v, u, prob.p) atol=1e-5
+
+            normal_form_sop = sop' * sop
+            JᵀJv = normal_form_sop * v
+            J_analytic = analytic_jac(u, prob.p)
+            JᵀJv_analytic = J_analytic' * J_analytic * v
+            @test JᵀJv≈JᵀJv_analytic atol=1e-5
+        end
+    end
+
+    prob = NonlinearProblem(
+        NonlinearFunction{false}((u, p) -> u^2 - p; jac = (u, p) -> 2 * u), 1.0, 2.0)
+
+    @testset "Analytic Jacobian" begin
+        jac_op = JacobianOperator(prob, -1.0, 1.0)
+
+        @testset for u in rand(4), v in rand(4)
+            sop = StatefulJacobianOperator(jac_op, u, prob.p)
+            @test (sop * v)≈2 * u * v atol=1e-5
+            @test (sop' * v)≈2 * u * v atol=1e-5
+
+            normal_form_sop = sop' * sop
+            JᵀJv = normal_form_sop * v
+            J_analytic = analytic_jac(u, prob.p)
+            JᵀJv_analytic = J_analytic' * J_analytic * v
+            @test JᵀJv≈JᵀJv_analytic atol=1e-5
+        end
+    end
+end
+
+@testitem "Inplace Problems" begin
+    using ADTypes, SciMLBase
+    using Enzyme, ForwardDiff, FiniteDiff, ReverseDiff
+    using SciMLJacobianOperators
+
+    reverse_ADs = [
+        AutoEnzyme(),
+        AutoEnzyme(; mode = Enzyme.Reverse),
+        AutoReverseDiff(),
+        AutoFiniteDiff()
+    ]
+
+    forward_ADs = [
+        AutoEnzyme(),
+        AutoEnzyme(; mode = Enzyme.Forward),
+        AutoForwardDiff(),
+        AutoFiniteDiff()
+    ]
+
+    prob = NonlinearProblem(
+        NonlinearFunction{true}((du, u, p) -> du .= u .^ 2 .- p .+ u[2] * u[1]), [1.0, 3.0], 2.0)
+
+    analytic_jac(u, p) = [2 * u[1]+u[2] u[1]; u[2] 2 * u[2]+u[1]]
+    analytic_jvp(v, u, p) = analytic_jac(u, p) * v
+    analytic_vjp(v, u, p) = analytic_jac(u, p)' * v
+
+    analytic_jac!(J, u, p) = (J .= analytic_jac(u, p))
+    analytic_jvp!(J, v, u, p) = (J .= analytic_jvp(v, u, p))
+    analytic_vjp!(J, v, u, p) = (J .= analytic_vjp(v, u, p))
+
+    @testset "AutoDiff" begin
+        @testset for jvp_autodiff in forward_ADs, vjp_autodiff in reverse_ADs
+            jac_op = JacobianOperator(prob, [2.0, 3.0], prob.u0; jvp_autodiff, vjp_autodiff)
+
+            @testset for u in [rand(2) for _ in 1:4], v in [rand(2) for _ in 1:4]
+                sop = StatefulJacobianOperator(jac_op, u, prob.p)
+                @test (sop * v)≈analytic_jvp(v, u, prob.p) atol=1e-5
+                @test (sop' * v)≈analytic_vjp(v, u, prob.p) atol=1e-5
+
+                normal_form_sop = sop' * sop
+                JᵀJv = normal_form_sop * v
+                J_analytic = analytic_jac(u, prob.p)
+                JᵀJv_analytic = J_analytic' * J_analytic * v
+                @test JᵀJv≈JᵀJv_analytic atol=1e-5
+            end
+        end
+    end
+
+    prob = NonlinearProblem(
+        NonlinearFunction{true}((du, u, p) -> du .= u .^ 2 .- p .+ u[2] * u[1];
+            jvp = analytic_jvp!, vjp = analytic_vjp!), [1.0, 3.0], 2.0)
+
+    @testset "Analytic JVP/VJP" begin
+        jac_op = JacobianOperator(prob, [2.0, 3.0], prob.u0)
+
+        @testset for u in [rand(2) for _ in 1:4], v in [rand(2) for _ in 1:4]
+            sop = StatefulJacobianOperator(jac_op, u, prob.p)
+            @test (sop * v)≈analytic_jvp(v, u, prob.p) atol=1e-5
+            @test (sop' * v)≈analytic_vjp(v, u, prob.p) atol=1e-5
+
+            normal_form_sop = sop' * sop
+            JᵀJv = normal_form_sop * v
+            J_analytic = analytic_jac(u, prob.p)
+            JᵀJv_analytic = J_analytic' * J_analytic * v
+            @test JᵀJv≈JᵀJv_analytic atol=1e-5
+        end
+    end
+
+    prob = NonlinearProblem(
+        NonlinearFunction{true}((du, u, p) -> du .= u .^ 2 .- p .+ u[2] * u[1];
+            jac = analytic_jac!), [1.0, 3.0], 2.0)
+
+    @testset "Analytic Jacobian" begin
+        jac_op = JacobianOperator(prob, [2.0, 3.0], prob.u0)
+
+        @testset for u in [rand(2) for _ in 1:4], v in [rand(2) for _ in 1:4]
+            sop = StatefulJacobianOperator(jac_op, u, prob.p)
+            @test (sop * v)≈analytic_jvp(v, u, prob.p) atol=1e-5
+            @test (sop' * v)≈analytic_vjp(v, u, prob.p) atol=1e-5
+
+            normal_form_sop = sop' * sop
+            JᵀJv = normal_form_sop * v
+            J_analytic = analytic_jac(u, prob.p)
+            JᵀJv_analytic = J_analytic' * J_analytic * v
+            @test JᵀJv≈JᵀJv_analytic atol=1e-5
+        end
+    end
+end
+
+@testitem "Out-of-place Problems" begin
+    using ADTypes, SciMLBase
+    using Enzyme, ForwardDiff, FiniteDiff, ReverseDiff, Zygote, Tracker
+    using SciMLJacobianOperators
+
+    reverse_ADs = [
+        AutoEnzyme(),
+        AutoEnzyme(; mode = Enzyme.Reverse),
+        AutoZygote(),
+        AutoTracker(),
+        AutoReverseDiff(),
+        AutoFiniteDiff()
+    ]
+
+    forward_ADs = [
+        AutoEnzyme(),
+        AutoEnzyme(; mode = Enzyme.Forward),
+        AutoForwardDiff(),
+        AutoFiniteDiff()
+    ]
+
+    prob = NonlinearProblem(
+        NonlinearFunction{false}((u, p) -> u .^ 2 .- p .+ u[2] * u[1]), [1.0, 3.0], 2.0)
+
+    analytic_jac(u, p) = [2 * u[1]+u[2] u[1]; u[2] 2 * u[2]+u[1]]
+    analytic_jvp(v, u, p) = analytic_jac(u, p) * v
+    analytic_vjp(v, u, p) = analytic_jac(u, p)' * v
+
+    @testset "AutoDiff" begin
+        @testset for jvp_autodiff in forward_ADs, vjp_autodiff in reverse_ADs
+            jac_op = JacobianOperator(prob, [2.0, 3.0], prob.u0; jvp_autodiff, vjp_autodiff)
+
+            @testset for u in [rand(2) for _ in 1:4], v in [rand(2) for _ in 1:4]
+                sop = StatefulJacobianOperator(jac_op, u, prob.p)
+                @test (sop * v)≈analytic_jvp(v, u, prob.p) atol=1e-5
+                @test (sop' * v)≈analytic_vjp(v, u, prob.p) atol=1e-5
+
+                normal_form_sop = sop' * sop
+                JᵀJv = normal_form_sop * v
+                J_analytic = analytic_jac(u, prob.p)
+                JᵀJv_analytic = J_analytic' * J_analytic * v
+                @test JᵀJv≈JᵀJv_analytic atol=1e-5
+            end
+        end
+    end
+
+    prob = NonlinearProblem(
+        NonlinearFunction{false}((u, p) -> u .^ 2 .- p .+ u[2] * u[1];
+            vjp = analytic_vjp, jvp = analytic_jvp), [1.0, 3.0], 2.0)
+
+    @testset "Analytic JVP/VJP" begin
+        jac_op = JacobianOperator(prob, [2.0, 3.0], prob.u0)
+
+        @testset for u in [rand(2) for _ in 1:4], v in [rand(2) for _ in 1:4]
+            sop = StatefulJacobianOperator(jac_op, u, prob.p)
+            @test (sop * v)≈analytic_jvp(v, u, prob.p) atol=1e-5
+            @test (sop' * v)≈analytic_vjp(v, u, prob.p) atol=1e-5
+
+            normal_form_sop = sop' * sop
+            JᵀJv = normal_form_sop * v
+            J_analytic = analytic_jac(u, prob.p)
+            JᵀJv_analytic = J_analytic' * J_analytic * v
+            @test JᵀJv≈JᵀJv_analytic atol=1e-5
+        end
+    end
+
+    prob = NonlinearProblem(
+        NonlinearFunction{false}((u, p) -> u .^ 2 .- p .+ u[2] * u[1];
+            jac = analytic_jac), [1.0, 3.0], 2.0)
+
+    @testset "Analytic Jacobian" begin
+        jac_op = JacobianOperator(prob, [2.0, 3.0], prob.u0)
+
+        @testset for u in [rand(2) for _ in 1:4], v in [rand(2) for _ in 1:4]
+            sop = StatefulJacobianOperator(jac_op, u, prob.p)
+            @test (sop * v)≈analytic_jvp(v, u, prob.p) atol=1e-5
+            @test (sop' * v)≈analytic_vjp(v, u, prob.p) atol=1e-5
+
+            normal_form_sop = sop' * sop
+            JᵀJv = normal_form_sop * v
+            J_analytic = analytic_jac(u, prob.p)
+            JᵀJv_analytic = J_analytic' * J_analytic * v
+            @test JᵀJv≈JᵀJv_analytic atol=1e-5
+        end
+    end
+end
+
+@testitem "Aqua" begin
+    using SciMLJacobianOperators, Aqua
+
+    Aqua.test_all(SciMLJacobianOperators)
+end
+
+@testitem "Explicit Imports" begin
+    using SciMLJacobianOperators, ExplicitImports
+
+    @test check_no_implicit_imports(SciMLJacobianOperators) === nothing
+    @test check_no_stale_explicit_imports(SciMLJacobianOperators) === nothing
+    @test check_all_qualified_accesses_via_owners(SciMLJacobianOperators) === nothing
+end

From bc1061e176da0cda953da1236b51a61ab5500a13 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 11:56:13 -0400
Subject: [PATCH 480/700] fix: handling of multi-dimensional arrays

---
 docs/src/tutorials/large_systems.md               |  2 +-
 .../src/SciMLJacobianOperators.jl                 | 15 +++++++++++----
 2 files changed, 12 insertions(+), 5 deletions(-)

diff --git a/docs/src/tutorials/large_systems.md b/docs/src/tutorials/large_systems.md
index 4e732b9c0..24797ff96 100644
--- a/docs/src/tutorials/large_systems.md
+++ b/docs/src/tutorials/large_systems.md
@@ -142,7 +142,7 @@ using BenchmarkTools # for @btime
     NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff(; chunksize = 32)),
         linsolve = KLUFactorization()));
 @btime solve(prob_brusselator_2d,
-    NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff(; chunksize = 32)),
+    NewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 32),
         linsolve = KrylovJL_GMRES()));
 nothing # hide
 ```
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index 3699e71bb..a657e2e5e 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -308,11 +308,15 @@ function prepare_vjp(::Val{false}, prob::AbstractNonlinearProblem,
         v_fake = copy(fu)
         di_extras = DI.prepare_pullback(fₚ, fu_cache, autodiff, u, v_fake)
         return @closure (vJ, v, u, p) -> begin
-            DI.pullback!(fₚ, fu_cache, reshape(vJ, size(u)), autodiff, u, v, di_extras)
+            DI.pullback!(fₚ, fu_cache, reshape(vJ, size(u)), autodiff,
+                u, reshape(v, size(fu_cache)), di_extras)
+            return
         end
     else
         di_extras = DI.prepare_pullback(fₚ, autodiff, u, fu)
-        return @closure (v, u, p) -> DI.pullback(fₚ, autodiff, u, v, di_extras)
+        return @closure (v, u, p) -> begin
+            return DI.pullback(fₚ, autodiff, u, reshape(v, size(fu)), di_extras)
+        end
     end
 end
 
@@ -351,12 +355,15 @@ function prepare_jvp(::Val{false}, prob::AbstractNonlinearProblem,
         di_extras = DI.prepare_pushforward(fₚ, fu_cache, autodiff, u, u)
         return @closure (Jv, v, u, p) -> begin
             DI.pushforward!(
-                fₚ, fu_cache, reshape(Jv, size(fu_cache)), autodiff, u, v, di_extras)
+                fₚ, fu_cache, reshape(Jv, size(fu_cache)),
+                autodiff, u, reshape(v, size(u)), di_extras)
             return
         end
     else
         di_extras = DI.prepare_pushforward(fₚ, autodiff, u, u)
-        return @closure (v, u, p) -> DI.pushforward(fₚ, autodiff, u, v, di_extras)
+        return @closure (v, u, p) -> begin
+            return DI.pushforward(fₚ, autodiff, u, reshape(v, size(u)), di_extras)
+        end
     end
 end
 

From 63a5594167a8358b03873c7078c08fc5b04d62af Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 12:09:30 -0400
Subject: [PATCH 481/700] chore: run formatter

---
 src/abstract_types.jl                 |  9 ++++++---
 src/algorithms/broyden.jl             |  3 ++-
 src/algorithms/extension_algs.jl      | 18 ++++++++++--------
 src/algorithms/levenberg_marquardt.jl |  3 ++-
 src/core/generalized_first_order.jl   |  6 ++++--
 src/default.jl                        |  3 ++-
 src/descent/geodesic_acceleration.jl  |  6 ++++--
 src/internal/termination.jl           |  3 ++-
 8 files changed, 32 insertions(+), 19 deletions(-)

diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 0aa4fd82e..2fe2fd071 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -277,7 +277,8 @@ Abstract Type for Damping Functions in DampedNewton.
 ### `__internal_init` specification
 
 ```julia
-__internal_init(prob::AbstractNonlinearProblem, f::AbstractDampingFunction, initial_damping,
+__internal_init(
+    prob::AbstractNonlinearProblem, f::AbstractDampingFunction, initial_damping,
     J, fu, u, args...; internal_norm = DEFAULT_NORM, kwargs...) -->
 AbstractDampingFunctionCache
 ```
@@ -361,7 +362,8 @@ Abstract Type for all Jacobian Initialization Algorithms used in NonlinearSolve.
 ### `__internal_init` specification
 
 ```julia
-__internal_init(prob::AbstractNonlinearProblem, alg::AbstractJacobianInitialization, solver,
+__internal_init(
+    prob::AbstractNonlinearProblem, alg::AbstractJacobianInitialization, solver,
     f::F, fu, u, p; linsolve = missing, internalnorm::IN = DEFAULT_NORM, kwargs...)
 ```
 
@@ -453,7 +455,8 @@ Abstract Type for all Trust Region Methods used in NonlinearSolve.jl.
 ### `__internal_init` specification
 
 ```julia
-__internal_init(prob::AbstractNonlinearProblem, alg::AbstractTrustRegionMethod, f::F, fu, u,
+__internal_init(
+    prob::AbstractNonlinearProblem, alg::AbstractTrustRegionMethod, f::F, fu, u,
     p, args...; internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF} -->
 AbstractTrustRegionMethodCache
 ```
diff --git a/src/algorithms/broyden.jl b/src/algorithms/broyden.jl
index 679897efa..77d2a06c4 100644
--- a/src/algorithms/broyden.jl
+++ b/src/algorithms/broyden.jl
@@ -28,7 +28,8 @@ search.
         useful for specific problems, but whether it will work may depend strongly on the
         problem
 """
-function Broyden(; max_resets = 100, linesearch = NoLineSearch(), reset_tolerance = nothing,
+function Broyden(;
+        max_resets = 100, linesearch = NoLineSearch(), reset_tolerance = nothing,
         init_jacobian::Val{IJ} = Val(:identity), autodiff = nothing,
         alpha = nothing, update_rule::Val{UR} = Val(:good_broyden)) where {IJ, UR}
     if IJ === :identity
diff --git a/src/algorithms/extension_algs.jl b/src/algorithms/extension_algs.jl
index ea9ab79ab..a3555a17b 100644
--- a/src/algorithms/extension_algs.jl
+++ b/src/algorithms/extension_algs.jl
@@ -252,20 +252,22 @@ function NLsolveJL(; method = :trust_region, autodiff = :central, store_trace =
     end
 
     if store_trace !== missing
-        Base.depwarn("`store_trace` for NLsolveJL has been deprecated and will be removed \
-                      in v4. Use the `store_trace` keyword argument via the logging API \
-                      https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ \
-                      instead.",
+        Base.depwarn(
+            "`store_trace` for NLsolveJL has been deprecated and will be removed \
+             in v4. Use the `store_trace` keyword argument via the logging API \
+             https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ \
+             instead.",
             :NLsolveJL)
     else
         store_trace = false
     end
 
     if extended_trace !== missing
-        Base.depwarn("`extended_trace` for NLsolveJL has been deprecated and will be \
-                      removed in v4. Use the `trace_level = TraceAll()` keyword argument \
-                      via the logging API \
-                      https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ instead.",
+        Base.depwarn(
+            "`extended_trace` for NLsolveJL has been deprecated and will be \
+             removed in v4. Use the `trace_level = TraceAll()` keyword argument \
+             via the logging API \
+             https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ instead.",
             :NLsolveJL)
     else
         extended_trace = false
diff --git a/src/algorithms/levenberg_marquardt.jl b/src/algorithms/levenberg_marquardt.jl
index 510226d7d..66554ee2d 100644
--- a/src/algorithms/levenberg_marquardt.jl
+++ b/src/algorithms/levenberg_marquardt.jl
@@ -53,7 +53,8 @@ function LevenbergMarquardt(;
         descent = GeodesicAcceleration(descent, finite_diff_step_geodesic, α_geodesic)
     end
     trustregion = LevenbergMarquardtTrustRegion(b_uphill)
-    return GeneralizedFirstOrderAlgorithm(; concrete_jac = true, name = :LevenbergMarquardt,
+    return GeneralizedFirstOrderAlgorithm(;
+        concrete_jac = true, name = :LevenbergMarquardt,
         trustregion, descent, jacobian_ad = autodiff)
 end
 
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 84e74478f..38c3786f5 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -57,11 +57,13 @@ function GeneralizedFirstOrderAlgorithm{concrete_jac, name}(;
         max_shrink_times::Int = typemax(Int)) where {concrete_jac, name}
     forward_ad = ifelse(forward_ad !== nothing,
         forward_ad,
-        ifelse(jacobian_ad !== nothing && ADTypes.mode(jacobian_ad) isa ADTypes.ForwardMode,
+        ifelse(
+            jacobian_ad !== nothing && ADTypes.mode(jacobian_ad) isa ADTypes.ForwardMode,
             jacobian_ad, nothing))
     reverse_ad = ifelse(reverse_ad !== nothing,
         reverse_ad,
-        ifelse(jacobian_ad !== nothing && ADTypes.mode(jacobian_ad) isa ADTypes.ReverseMode,
+        ifelse(
+            jacobian_ad !== nothing && ADTypes.mode(jacobian_ad) isa ADTypes.ReverseMode,
             jacobian_ad, nothing))
 
     if linesearch !== missing && !(linesearch isa AbstractNonlinearSolveLineSearchAlgorithm)
diff --git a/src/default.jl b/src/default.jl
index b4613a6f7..8a9aac6af 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -432,7 +432,8 @@ function FastShortcutNonlinearPolyalg(
             end
         else
             if __is_complex(T)
-                algs = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
+                algs = (
+                    Broyden(), Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
                     Klement(; linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff))
             else
diff --git a/src/descent/geodesic_acceleration.jl b/src/descent/geodesic_acceleration.jl
index e2d8612e5..136795057 100644
--- a/src/descent/geodesic_acceleration.jl
+++ b/src/descent/geodesic_acceleration.jl
@@ -31,7 +31,8 @@ for other methods are not theorectically or experimentally verified.
 end
 
 function Base.show(io::IO, alg::GeodesicAcceleration)
-    print(io, "GeodesicAcceleration(descent = $(alg.descent), finite_diff_step_geodesic = ",
+    print(
+        io, "GeodesicAcceleration(descent = $(alg.descent), finite_diff_step_geodesic = ",
         "$(alg.finite_diff_step_geodesic), α = $(alg.α))")
 end
 
@@ -102,7 +103,8 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::GeodesicAccelerati
         T(alg.finite_diff_step_geodesic), Jv, fu_cache, u_cache, false)
 end
 
-function __internal_solve!(cache::GeodesicAccelerationCache, J, fu, u, idx::Val{N} = Val(1);
+function __internal_solve!(
+        cache::GeodesicAccelerationCache, J, fu, u, idx::Val{N} = Val(1);
         skip_solve::Bool = false, kwargs...) where {N}
     a, v, δu = get_acceleration(cache, idx), get_velocity(cache, idx), get_du(cache, idx)
     skip_solve && return DescentResult(; δu, extras = (; a, v))
diff --git a/src/internal/termination.jl b/src/internal/termination.jl
index b64897744..570bae110 100644
--- a/src/internal/termination.jl
+++ b/src/internal/termination.jl
@@ -8,7 +8,8 @@ function init_termination_cache(
         AbsSafeBestTerminationMode(Base.Fix2(norm, 2); max_stalled_steps = 32))
 end
 
-function init_termination_cache(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
+function init_termination_cache(
+        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
         abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
     tc_ = if hasfield(typeof(tc), :internalnorm) && tc.internalnorm === nothing
         internalnorm = ifelse(

From 058b87d5af338ad7e2049f2f27c95b476798d32b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 12:28:52 -0400
Subject: [PATCH 482/700] feat: remove Setfield dep

---
 lib/SciMLJacobianOperators/Project.toml              |  2 --
 .../src/SciMLJacobianOperators.jl                    | 12 ++++--------
 2 files changed, 4 insertions(+), 10 deletions(-)

diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index 5b91928c1..5c1bc20ff 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -13,7 +13,6 @@ FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
-Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 
 [compat]
 ADTypes = "1.8.1"
@@ -32,7 +31,6 @@ LinearAlgebra = "1.10"
 ReverseDiff = "1.15"
 SciMLBase = "2.54.0"
 SciMLOperators = "0.3"
-Setfield = "1"
 Test = "1.10"
 TestItemRunner = "1"
 Tracker = "0.2.35"
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index a657e2e5e..f857f573a 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -9,7 +9,6 @@ using FastClosures: @closure
 using LinearAlgebra: LinearAlgebra
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, AbstractNonlinearFunction
 using SciMLOperators: AbstractSciMLOperator
-using Setfield: @set!
 
 const DI = DifferentiationInterface
 const True = Val(true)
@@ -98,13 +97,10 @@ Base.size(J::JacobianOperator) = J.size
 Base.size(J::JacobianOperator, d::Integer) = J.size[d]
 
 for op in (:adjoint, :transpose)
-    @eval function Base.$(op)(operator::JacobianOperator)
-        @set! operator.mode = flip_mode(operator.mode)
-        (; output_cache, input_cache) = operator
-        @set! operator.output_cache = input_cache
-        @set! operator.input_cache = output_cache
-        @set! operator.size = reverse(operator.size)
-        return operator
+    @eval function Base.$(op)(operator::JacobianOperator{iip, T}) where {iip, T}
+        return JacobianOperator{iip, T}(
+            flip_mode(operator.mode), operator.jvp_op, operator.vjp_op,
+            reverse(operator.size), input_cache, output_cache)
     end
 end
 

From 40eb6c867fbed99368e7005ae1ba4246083269eb Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 12:30:55 -0400
Subject: [PATCH 483/700] chore: mark master as DEV (DON'T TAG)

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index f7a8ad781..ab35df1e2 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.14.0"
+version = "3.15.0-DEV"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From b2bb25252e3526b753b3852dfbfff9cc386e3f7a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 12:34:55 -0400
Subject: [PATCH 484/700] fix: missing qualifier

---
 lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index f857f573a..a173dc395 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -100,7 +100,7 @@ for op in (:adjoint, :transpose)
     @eval function Base.$(op)(operator::JacobianOperator{iip, T}) where {iip, T}
         return JacobianOperator{iip, T}(
             flip_mode(operator.mode), operator.jvp_op, operator.vjp_op,
-            reverse(operator.size), input_cache, output_cache)
+            reverse(operator.size), operator.input_cache, operator.output_cache)
     end
 end
 

From bdacb9ca9327b9d5d2fe6a8f0c08f44ac206f8ec Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 13:03:08 -0400
Subject: [PATCH 485/700] docs: disable ILU for now

---
 docs/src/tutorials/large_systems.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/docs/src/tutorials/large_systems.md b/docs/src/tutorials/large_systems.md
index 24797ff96..368535287 100644
--- a/docs/src/tutorials/large_systems.md
+++ b/docs/src/tutorials/large_systems.md
@@ -226,7 +226,8 @@ left and right preconditioners, matrices which approximate the inverse of `W = I
 used in the solution of the ODE. An example of this with using
 [IncompleteLU.jl](https://github.com/haampie/IncompleteLU.jl) is as follows:
 
-```@example ill_conditioned_nlprob
+```julia
+# FIXME: On 1.10+ this is broken. Skipping this for now.
 using IncompleteLU
 
 function incompletelu(W, du, u, p, t, newW, Plprev, Prprev, solverdata)

From c2706b8410b078521103482d4759d610cb7c92f5 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 25 Sep 2024 13:34:34 -0400
Subject: [PATCH 486/700] docs: add a README for SciMLJacobianOperators

---
 lib/SciMLJacobianOperators/README.md | 59 ++++++++++++++++++++++++++++
 1 file changed, 59 insertions(+)
 create mode 100644 lib/SciMLJacobianOperators/README.md

diff --git a/lib/SciMLJacobianOperators/README.md b/lib/SciMLJacobianOperators/README.md
new file mode 100644
index 000000000..c9d14ff50
--- /dev/null
+++ b/lib/SciMLJacobianOperators/README.md
@@ -0,0 +1,59 @@
+# SciMLJacobianOperators.jl
+
+SciMLJacobianOperators provides a convenient way to compute Jacobian-Vector Product (JVP)
+and Vector-Jacobian Product (VJP) using
+[SciMLOperators.jl](https://github.com/SciML/SciMLOperators.jl) and
+[DifferentiationInterface.jl](https://github.com/gdalle/DifferentiationInterface.jl).
+
+Currently we have interfaces for:
+
+  - `NonlinearProblem`
+  - `NonlinearLeastSquaresProblem`
+
+and all autodiff backends supported by DifferentiationInterface.jl are supported.
+
+## Example
+
+```julia
+using SciMLJacobianOperators, NonlinearSolve, Enzyme, ForwardDiff
+
+# Define the problem
+f(u, p) = u .* u .- p
+u0 = ones(4)
+p = 2.0
+prob = NonlinearProblem(f, u0, p)
+fu0 = f(u0, p)
+v = ones(4) .* 2
+
+# Construct the operator
+jac_op = JacobianOperator(
+    prob, fu0, u0;
+    jvp_autodiff = AutoForwardDiff(),
+    vjp_autodiff = AutoEnzyme(; mode = Enzyme.Reverse)
+)
+sjac_op = StatefulJacobianOperator(jac_op, u0, p)
+
+sjac_op * v  # Computes the JVP
+# 4-element Vector{Float64}:
+#  4.0
+#  4.0
+#  4.0
+#  4.0
+
+sjac_op' * v  # Computes the VJP
+# 4-element Vector{Float64}:
+#  4.0
+#  4.0
+#  4.0
+#  4.0
+
+# What if we multiply the VJP and JVP?
+snormal_form = sjac_op' * sjac_op
+
+snormal_form * v  # Computes JᵀJ * v
+# 4-element Vector{Float64}:
+#  8.0
+#  8.0
+#  8.0
+#  8.0
+```
\ No newline at end of file

From 153244f5ebac15f17572aeeedb8e181f439ee48a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 25 Sep 2024 14:09:17 -0400
Subject: [PATCH 487/700] feat: use contexts from DifferentiationInterface.jl

---
 lib/SciMLJacobianOperators/Project.toml       |  2 +-
 .../src/SciMLJacobianOperators.jl             | 56 ++++++++-----------
 lib/SciMLJacobianOperators/test/core_tests.jl |  6 +-
 3 files changed, 26 insertions(+), 38 deletions(-)

diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index 5c1bc20ff..5209241bc 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -19,7 +19,7 @@ ADTypes = "1.8.1"
 Aqua = "0.8.7"
 ConcreteStructs = "0.2.3"
 ConstructionBase = "1.5"
-DifferentiationInterface = "0.5"
+DifferentiationInterface = "0.6"
 Enzyme = "0.12, 0.13"
 EnzymeCore = "0.7, 0.8"
 ExplicitImports = "1.9.0"
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index a173dc395..e807e983c 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -1,9 +1,9 @@
 module SciMLJacobianOperators
 
-using ADTypes: ADTypes, AutoSparse, AutoEnzyme
+using ADTypes: ADTypes, AutoSparse
 using ConcreteStructs: @concrete
 using ConstructionBase: ConstructionBase
-using DifferentiationInterface: DifferentiationInterface
+using DifferentiationInterface: DifferentiationInterface, Constant
 using EnzymeCore: EnzymeCore
 using FastClosures: @closure
 using LinearAlgebra: LinearAlgebra
@@ -112,10 +112,10 @@ function JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff =
     iip = SciMLBase.isinplace(prob)
     T = promote_type(eltype(u), eltype(fu))
 
-    vjp_autodiff = set_function_as_const(get_dense_ad(vjp_autodiff))
+    vjp_autodiff = get_dense_ad(vjp_autodiff)
     vjp_op = prepare_vjp(skip_vjp, prob, f, u, fu; autodiff = vjp_autodiff)
 
-    jvp_autodiff = set_function_as_const(get_dense_ad(jvp_autodiff))
+    jvp_autodiff = get_dense_ad(jvp_autodiff)
     jvp_op = prepare_jvp(skip_jvp, prob, f, u, fu; autodiff = jvp_autodiff)
 
     output_cache = fu isa Number ? T(fu) : similar(fu, T)
@@ -295,23 +295,21 @@ function prepare_vjp(::Val{false}, prob::AbstractNonlinearProblem,
 
     @assert autodiff!==nothing "`vjp_autodiff` must be provided if `f` doesn't have \
                                 analytic `vjp` or `jac`."
-    # TODO: Once DI supports const params we can use `p`
-    fₚ = SciMLBase.JacobianWrapper{SciMLBase.isinplace(f)}(f, prob.p)
     if SciMLBase.isinplace(f)
-        @assert DI.check_twoarg(autodiff) "Backend: $(autodiff) doesn't support in-place \
-                                           problems."
+        @assert DI.check_inplace(autodiff) "Backend: $(autodiff) doesn't support in-place \
+                                            problems."
         fu_cache = copy(fu)
-        v_fake = copy(fu)
-        di_extras = DI.prepare_pullback(fₚ, fu_cache, autodiff, u, v_fake)
+        di_extras = DI.prepare_pullback(f, fu_cache, autodiff, u, (fu,), Constant(prob.p))
         return @closure (vJ, v, u, p) -> begin
-            DI.pullback!(fₚ, fu_cache, reshape(vJ, size(u)), autodiff,
-                u, reshape(v, size(fu_cache)), di_extras)
+            DI.pullback!(f, fu_cache, (reshape(vJ, size(u)),), di_extras, autodiff,
+                u, (reshape(v, size(fu_cache)),), Constant(p))
             return
         end
     else
-        di_extras = DI.prepare_pullback(fₚ, autodiff, u, fu)
+        di_extras = DI.prepare_pullback(f, autodiff, u, (fu,), Constant(prob.p))
         return @closure (v, u, p) -> begin
-            return DI.pullback(fₚ, autodiff, u, reshape(v, size(fu)), di_extras)
+            return only(DI.pullback(
+                f, di_extras, autodiff, u, (reshape(v, size(fu)),), Constant(p)))
         end
     end
 end
@@ -342,23 +340,21 @@ function prepare_jvp(::Val{false}, prob::AbstractNonlinearProblem,
 
     @assert autodiff!==nothing "`jvp_autodiff` must be provided if `f` doesn't have \
                                 analytic `vjp` or `jac`."
-    # TODO: Once DI supports const params we can use `p`
-    fₚ = SciMLBase.JacobianWrapper{SciMLBase.isinplace(f)}(f, prob.p)
     if SciMLBase.isinplace(f)
-        @assert DI.check_twoarg(autodiff) "Backend: $(autodiff) doesn't support in-place \
-                                           problems."
+        @assert DI.check_inplace(autodiff) "Backend: $(autodiff) doesn't support in-place \
+                                            problems."
         fu_cache = copy(fu)
-        di_extras = DI.prepare_pushforward(fₚ, fu_cache, autodiff, u, u)
+        di_extras = DI.prepare_pushforward(f, fu_cache, autodiff, u, (u,), Constant(prob.p))
         return @closure (Jv, v, u, p) -> begin
-            DI.pushforward!(
-                fₚ, fu_cache, reshape(Jv, size(fu_cache)),
-                autodiff, u, reshape(v, size(u)), di_extras)
+            DI.pushforward!(f, fu_cache, (reshape(Jv, size(fu_cache)),), di_extras,
+                autodiff, u, (reshape(v, size(u)),), Constant(p))
             return
         end
     else
-        di_extras = DI.prepare_pushforward(fₚ, autodiff, u, u)
+        di_extras = DI.prepare_pushforward(f, autodiff, u, (u,), Constant(prob.p))
         return @closure (v, u, p) -> begin
-            return DI.pushforward(fₚ, autodiff, u, reshape(v, size(u)), di_extras)
+            return only(DI.pushforward(
+                f, di_extras, autodiff, u, (reshape(v, size(u)),), Constant(p)))
         end
     end
 end
@@ -371,10 +367,8 @@ function prepare_scalar_op(::Val{false}, prob::AbstractNonlinearProblem,
 
     @assert autodiff!==nothing "`autodiff` must be provided if `f` doesn't have \
                                 analytic `vjp` or `jvp` or `jac`."
-    # TODO: Once DI supports const params we can use `p`
-    fₚ = Base.Fix2(f, prob.p)
-    di_extras = DI.prepare_derivative(fₚ, autodiff, u)
-    return @closure (v, u, p) -> DI.derivative(fₚ, autodiff, u, di_extras) * v
+    di_extras = DI.prepare_derivative(f, autodiff, u, Constant(prob.p))
+    return @closure (v, u, p) -> DI.derivative(f, di_extras, autodiff, u, Constant(p)) * v
 end
 
 get_dense_ad(::Nothing) = nothing
@@ -386,12 +380,6 @@ function get_dense_ad(ad::AutoSparse)
     return dense_ad
 end
 
-# In our case we know that it is safe to mark the function as const
-set_function_as_const(ad) = ad
-function set_function_as_const(ad::AutoEnzyme{M, Nothing}) where {M}
-    return AutoEnzyme(; ad.mode, function_annotation = EnzymeCore.Const)
-end
-
 export JacobianOperator, VecJacOperator, JacVecOperator
 export StatefulJacobianOperator
 export StatefulJacobianNormalFormOperator
diff --git a/lib/SciMLJacobianOperators/test/core_tests.jl b/lib/SciMLJacobianOperators/test/core_tests.jl
index e3b595221..6fb024a0c 100644
--- a/lib/SciMLJacobianOperators/test/core_tests.jl
+++ b/lib/SciMLJacobianOperators/test/core_tests.jl
@@ -7,7 +7,7 @@
         AutoEnzyme(),
         AutoEnzyme(; mode = Enzyme.Reverse),
         AutoZygote(),
-        AutoReverseDiff(),
+        # AutoReverseDiff(), # FIXME: https://github.com/gdalle/DifferentiationInterface.jl/issues/503
         AutoTracker(),
         AutoFiniteDiff()
     ]
@@ -91,7 +91,7 @@ end
     reverse_ADs = [
         AutoEnzyme(),
         AutoEnzyme(; mode = Enzyme.Reverse),
-        AutoReverseDiff(),
+        # AutoReverseDiff(), # FIXME: https://github.com/gdalle/DifferentiationInterface.jl/issues/503
         AutoFiniteDiff()
     ]
 
@@ -182,7 +182,7 @@ end
         AutoEnzyme(; mode = Enzyme.Reverse),
         AutoZygote(),
         AutoTracker(),
-        AutoReverseDiff(),
+        # AutoReverseDiff(), # FIXME: https://github.com/gdalle/DifferentiationInterface.jl/issues/503
         AutoFiniteDiff()
     ]
 

From 5742f89cb3049e1fb4feedc0b932ef6eb8b71f03 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 25 Sep 2024 14:57:03 -0400
Subject: [PATCH 488/700] feat: update to new DI.jl

---
 lib/SimpleNonlinearSolve/Project.toml | 6 +++---
 lib/SimpleNonlinearSolve/src/utils.jl | 8 ++++----
 2 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 8d7b044a9..5927f6fe2 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.12.2"
+version = "1.12.3"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -34,7 +34,7 @@ SimpleNonlinearSolveTrackerExt = "Tracker"
 SimpleNonlinearSolveZygoteExt = "Zygote"
 
 [compat]
-ADTypes = "1.2"
+ADTypes = "1.9"
 AllocCheck = "0.1.1"
 Aqua = "0.8"
 ArrayInterface = "7.9"
@@ -43,7 +43,7 @@ ChainRulesCore = "1.23"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149"
 DiffResults = "1.1"
-DifferentiationInterface = "0.5"
+DifferentiationInterface = "0.6"
 ExplicitImports = "1.5.0"
 FastClosures = "0.3.2"
 FiniteDiff = "2.23.1"
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 157d8f03f..5e967fa7f 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -28,7 +28,7 @@ end
 
 function value_and_jacobian(
         ad, prob::AbstractNonlinearProblem, f::F, y, x, cache; J = nothing) where {F}
-    x isa Number && return DI.value_and_derivative(f, ad, x, cache)
+    x isa Number && return DI.value_and_derivative(f, cache, ad, x)
 
     if isinplace(prob)
         if cache isa HasAnalyticJacobian
@@ -36,11 +36,11 @@ function value_and_jacobian(
             f(y, x)
             return y, J
         end
-        return DI.value_and_jacobian!(f, y, J, ad, x, cache)
+        return DI.value_and_jacobian!(f, y, J, cache, ad, x)
     else
         cache isa HasAnalyticJacobian && return f(x), prob.f.jac(x, prob.p)
-        J === nothing && return DI.value_and_jacobian(f, ad, x, cache)
-        y, J = DI.value_and_jacobian!(f, J, ad, x, cache)
+        J === nothing && return DI.value_and_jacobian(f, cache, ad, x)
+        y, J = DI.value_and_jacobian!(f, J, cache, ad, x)
         return y, J
     end
 end

From bd928936749e8ce140f1be49a2ae9bef1a02ebe2 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 25 Sep 2024 17:04:24 -0400
Subject: [PATCH 489/700] fix: install some test deps if needed

---
 .../.github/workflows/Tests.yml               |   3 +-
 lib/SimpleNonlinearSolve/Project.toml         |  12 +-
 .../test/core/23_test_problems_tests.jl       |   2 +-
 .../test/core/adjoint_tests.jl                |   2 +-
 .../test/core/rootfind_tests.jl               |   3 +-
 .../test/gpu/cuda_tests.jl                    | 108 +++++++++---------
 lib/SimpleNonlinearSolve/test/runtests.jl     |  31 +++--
 7 files changed, 90 insertions(+), 71 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Tests.yml b/lib/SimpleNonlinearSolve/.github/workflows/Tests.yml
index 8fa495e19..e63c1039e 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Tests.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Tests.yml
@@ -29,7 +29,8 @@ jobs:
       fail-fast: false
       matrix:
         group:
-          - "Core"
+          - "core"
+          - "adjoint"
         os:
           - "ubuntu-latest"
           - "macos-latest"
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 5927f6fe2..444bfed89 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -38,7 +38,6 @@ ADTypes = "1.9"
 AllocCheck = "0.1.1"
 Aqua = "0.8"
 ArrayInterface = "7.9"
-CUDA = "5.2"
 ChainRulesCore = "1.23"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149"
@@ -48,8 +47,9 @@ ExplicitImports = "1.5.0"
 FastClosures = "0.3.2"
 FiniteDiff = "2.23.1"
 ForwardDiff = "0.10.36"
+Hwloc = "3"
+InteractiveUtils = "<0.0.1, 1"
 LinearAlgebra = "1.10"
-LinearSolve = "2.30"
 MaybeInplace = "0.1.3"
 NonlinearProblemLibrary = "0.1.2"
 Pkg = "1.10"
@@ -60,7 +60,6 @@ ReTestItems = "1.23"
 Reexport = "1.2"
 ReverseDiff = "1.15.3"
 SciMLBase = "2.37.0"
-SciMLSensitivity = "7.58"
 Setfield = "1.1.1"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4.2"
@@ -72,13 +71,13 @@ julia = "1.10"
 [extras]
 AllocCheck = "9b6a8646-10ed-4001-bbdc-1d2f46dfbb1a"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
-CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+Hwloc = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
@@ -86,11 +85,10 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
-SciMLSensitivity = "1ed8b502-d754-442c-8d5d-10ac956f44a1"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["AllocCheck", "Aqua", "CUDA", "DiffEqBase", "ExplicitImports", "FiniteDiff", "ForwardDiff", "LinearAlgebra", "LinearSolve", "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReTestItems", "Reexport", "ReverseDiff", "SciMLSensitivity", "StaticArrays", "Test", "Tracker", "Zygote"]
+test = ["AllocCheck", "Aqua", "DiffEqBase", "ExplicitImports", "FiniteDiff", "ForwardDiff", "Hwloc", "InteractiveUtils", "LinearAlgebra",  "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReTestItems", "Reexport", "ReverseDiff",  "StaticArrays", "Test", "Tracker", "Zygote"]
diff --git a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
index e45560912..6d1980810 100644
--- a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
@@ -86,7 +86,7 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "23 Test Problems: SimpleBroyden" retries=5 setup=[RobustnessTesting] tags=[:core] begin
+@testitem "23 Test Problems: SimpleBroyden" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (SimpleBroyden(),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
diff --git a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
index 9b1ae05ff..c56850eb5 100644
--- a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Simple Adjoint Test" tags=[:core] begin
+@testitem "Simple Adjoint Test" tags=[:adjoint] begin
     using ForwardDiff, ReverseDiff, SciMLSensitivity, Tracker, Zygote
 
     ff(u, p) = u .^ 2 .- p
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index eecdeca18..272fa3c4d 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -1,7 +1,6 @@
 @testsetup module RootfindingTesting
 using Reexport
-@reexport using AllocCheck, LinearSolve, StaticArrays, Random, LinearAlgebra, ForwardDiff,
-                DiffEqBase
+@reexport using AllocCheck, StaticArrays, Random, LinearAlgebra, ForwardDiff, DiffEqBase
 import PolyesterForwardDiff
 
 quadratic_f(u, p) = u .* u .- p
diff --git a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
index 5050b702d..fc99bddaf 100644
--- a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
@@ -1,73 +1,77 @@
-@testitem "Solving on GPUs" tags=[:cuda] skip=:(using CUDA; !CUDA.functional()) begin
+@testitem "Solving on GPUs" tags=[:cuda] begin
     using StaticArrays, CUDA
 
-    CUDA.allowscalar(false)
+    if CUDA.functional()
+        CUDA.allowscalar(false)
 
-    f(u, p) = u .* u .- 2
-    f!(du, u, p) = du .= u .* u .- 2
+        f(u, p) = u .* u .- 2
+        f!(du, u, p) = du .= u .* u .- 2
 
-    @testset "$(nameof(typeof(alg)))" for alg in (
-        SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(),
-        SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
-        SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(),
-        SimpleHalley(), SimpleBroyden(; linesearch = Val(true)),
-        SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
-        # Static Arrays
-        u0 = @SVector[1.0f0, 1.0f0]
-        probN = NonlinearProblem{false}(f, u0)
-        sol = solve(probN, alg; abstol = 1.0f-6)
-        @test SciMLBase.successful_retcode(sol)
-        @test maximum(abs, sol.resid) ≤ 1.0f-6
-
-        # Regular Arrays
-        u0 = [1.0, 1.0]
-        probN = NonlinearProblem{false}(f, u0)
-        sol = solve(probN, alg; abstol = 1.0f-6)
-        @test SciMLBase.successful_retcode(sol)
-        @test maximum(abs, sol.resid) ≤ 1.0f-6
+        @testset "$(nameof(typeof(alg)))" for alg in (
+            SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(),
+            SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+            SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(),
+            SimpleHalley(), SimpleBroyden(; linesearch = Val(true)),
+            SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
+            # Static Arrays
+            u0 = @SVector[1.0f0, 1.0f0]
+            probN = NonlinearProblem{false}(f, u0)
+            sol = solve(probN, alg; abstol = 1.0f-6)
+            @test SciMLBase.successful_retcode(sol)
+            @test maximum(abs, sol.resid) ≤ 1.0f-6
 
-        # Regular Arrays Inplace
-        if !(alg isa SimpleHalley)
+            # Regular Arrays
             u0 = [1.0, 1.0]
-            probN = NonlinearProblem{true}(f!, u0)
+            probN = NonlinearProblem{false}(f, u0)
             sol = solve(probN, alg; abstol = 1.0f-6)
             @test SciMLBase.successful_retcode(sol)
             @test maximum(abs, sol.resid) ≤ 1.0f-6
+
+            # Regular Arrays Inplace
+            if !(alg isa SimpleHalley)
+                u0 = [1.0, 1.0]
+                probN = NonlinearProblem{true}(f!, u0)
+                sol = solve(probN, alg; abstol = 1.0f-6)
+                @test SciMLBase.successful_retcode(sol)
+                @test maximum(abs, sol.resid) ≤ 1.0f-6
+            end
         end
     end
 end
 
-@testitem "CUDA Kernel Launch Test" tags=[:cuda] skip=:(using CUDA; !CUDA.functional()) timeout=3600 begin
+@testitem "CUDA Kernel Launch Test" tags=[:cuda] begin
     using StaticArrays, CUDA
 
-    CUDA.allowscalar(false)
+    if CUDA.functional()
+        CUDA.allowscalar(false)
 
-    f(u, p) = u .* u .- 2
-    f!(du, u, p) = du .= u .* u .- 2
+        f(u, p) = u .* u .- 2
+        f!(du, u, p) = du .= u .* u .- 2
 
-    function kernel_function(prob, alg)
-        solve(prob, alg)
-        return nothing
-    end
+        function kernel_function(prob, alg)
+            solve(prob, alg)
+            return nothing
+        end
 
-    prob = NonlinearProblem{false}(f, @SVector[1.0f0, 1.0f0])
-    prob = convert(SimpleNonlinearSolve.ImmutableNonlinearProblem, prob)
+        prob = NonlinearProblem{false}(f, @SVector[1.0f0, 1.0f0])
+        prob = convert(SimpleNonlinearSolve.ImmutableNonlinearProblem, prob)
 
-    @testset "$(nameof(typeof(alg)))" for alg in (
-        SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(),
-        SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
-        SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(),
-        SimpleHalley(), SimpleBroyden(; linesearch = Val(true)),
-        SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
-        @test begin
-            try
-                @cuda kernel_function(prob, alg)
-                @info "Successfully launched kernel for $(alg)."
-                true
-            catch err
-                @error "Kernel Launch failed for $(alg)."
-                false
-            end
-        end broken=(alg isa SimpleHalley)
+        @testset "$(nameof(typeof(alg)))" for alg in (
+            SimpleNewtonRaphson(), SimpleDFSane(), SimpleTrustRegion(),
+            SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+            SimpleBroyden(), SimpleLimitedMemoryBroyden(), SimpleKlement(),
+            SimpleHalley(), SimpleBroyden(; linesearch = Val(true)),
+            SimpleLimitedMemoryBroyden(; linesearch = Val(true)))
+            @test begin
+                try
+                    @cuda kernel_function(prob, alg)
+                    @info "Successfully launched kernel for $(alg)."
+                    true
+                catch err
+                    @error "Kernel Launch failed for $(alg)."
+                    false
+                end
+            end broken=(alg isa SimpleHalley)
+        end
     end
 end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 2f81c8401..c90b994a4 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -1,10 +1,27 @@
-using ReTestItems, CUDA
+using ReTestItems, SimpleNonlinearSolve, Hwloc, InteractiveUtils
+using Pkg
 
-const GROUP = get(ENV, "GROUP", CUDA.functional() ? "All" : "Core")
+@info sprint(InteractiveUtils.versioninfo)
 
-if GROUP == "All"
-    ReTestItems.runtests(@__DIR__)
-else
-    tags = [Symbol(lowercase(GROUP))]
-    ReTestItems.runtests(@__DIR__; tags)
+const GROUP = lowercase(get(ENV, "GROUP", "All"))
+
+if GROUP == "adjoint" || GROUP == "all"
+    Pkg.add(["SciMLSensitivity"])
+end
+
+if GROUP == "cuda" || GROUP == "all"
+    Pkg.add(["CUDA"])
 end
+
+const RETESTITEMS_NWORKERS = parse(
+    Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4))))
+const RETESTITEMS_NWORKER_THREADS = parse(Int,
+    get(ENV, "RETESTITEMS_NWORKER_THREADS",
+        string(max(Hwloc.num_virtual_cores() ÷ RETESTITEMS_NWORKERS, 1))))
+
+@info "Running tests for group: $(GROUP) with $(RETESTITEMS_NWORKERS) workers"
+
+ReTestItems.runtests(
+    SimpleNonlinearSolve; tags = (GROUP == "all" ? nothing : [Symbol(GROUP)]),
+    nworkers = RETESTITEMS_NWORKERS, nworker_threads = RETESTITEMS_NWORKER_THREADS,
+    testitem_timeout = 3600, retries = 4)

From 6201fcc2f49e2ec2019eb61491f30bc9664e0dc5 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 25 Sep 2024 17:12:47 -0400
Subject: [PATCH 490/700] fix: DI now works with ReverseDiff

---
 lib/SciMLJacobianOperators/Project.toml       | 2 +-
 lib/SciMLJacobianOperators/test/core_tests.jl | 6 +++---
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index 5209241bc..900f70e35 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -19,7 +19,7 @@ ADTypes = "1.8.1"
 Aqua = "0.8.7"
 ConcreteStructs = "0.2.3"
 ConstructionBase = "1.5"
-DifferentiationInterface = "0.6"
+DifferentiationInterface = "0.6.1"
 Enzyme = "0.12, 0.13"
 EnzymeCore = "0.7, 0.8"
 ExplicitImports = "1.9.0"
diff --git a/lib/SciMLJacobianOperators/test/core_tests.jl b/lib/SciMLJacobianOperators/test/core_tests.jl
index 6fb024a0c..e3b595221 100644
--- a/lib/SciMLJacobianOperators/test/core_tests.jl
+++ b/lib/SciMLJacobianOperators/test/core_tests.jl
@@ -7,7 +7,7 @@
         AutoEnzyme(),
         AutoEnzyme(; mode = Enzyme.Reverse),
         AutoZygote(),
-        # AutoReverseDiff(), # FIXME: https://github.com/gdalle/DifferentiationInterface.jl/issues/503
+        AutoReverseDiff(),
         AutoTracker(),
         AutoFiniteDiff()
     ]
@@ -91,7 +91,7 @@ end
     reverse_ADs = [
         AutoEnzyme(),
         AutoEnzyme(; mode = Enzyme.Reverse),
-        # AutoReverseDiff(), # FIXME: https://github.com/gdalle/DifferentiationInterface.jl/issues/503
+        AutoReverseDiff(),
         AutoFiniteDiff()
     ]
 
@@ -182,7 +182,7 @@ end
         AutoEnzyme(; mode = Enzyme.Reverse),
         AutoZygote(),
         AutoTracker(),
-        # AutoReverseDiff(), # FIXME: https://github.com/gdalle/DifferentiationInterface.jl/issues/503
+        AutoReverseDiff(),
         AutoFiniteDiff()
     ]
 

From 05aa3db8351e2da44729e99795bd2b30f7c7a601 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 25 Sep 2024 17:17:57 -0400
Subject: [PATCH 491/700] fix: remove stale dep

---
 lib/SciMLJacobianOperators/Project.toml                  | 2 --
 lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl | 1 -
 2 files changed, 3 deletions(-)

diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index 900f70e35..73ee5a55d 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -8,7 +8,6 @@ ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
-EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
@@ -21,7 +20,6 @@ ConcreteStructs = "0.2.3"
 ConstructionBase = "1.5"
 DifferentiationInterface = "0.6.1"
 Enzyme = "0.12, 0.13"
-EnzymeCore = "0.7, 0.8"
 ExplicitImports = "1.9.0"
 FastClosures = "0.3.2"
 FiniteDiff = "2.24.0"
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index e807e983c..bb7a60441 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -4,7 +4,6 @@ using ADTypes: ADTypes, AutoSparse
 using ConcreteStructs: @concrete
 using ConstructionBase: ConstructionBase
 using DifferentiationInterface: DifferentiationInterface, Constant
-using EnzymeCore: EnzymeCore
 using FastClosures: @closure
 using LinearAlgebra: LinearAlgebra
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, AbstractNonlinearFunction

From 96716b60a1a0e97b0cefbb1afca61f96294b5648 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 26 Sep 2024 03:19:34 -0400
Subject: [PATCH 492/700] chore: update min DI version

Co-authored-by: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
---
 lib/SimpleNonlinearSolve/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 444bfed89..33e36201d 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -42,7 +42,7 @@ ChainRulesCore = "1.23"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149"
 DiffResults = "1.1"
-DifferentiationInterface = "0.6"
+DifferentiationInterface = "0.6.1"
 ExplicitImports = "1.5.0"
 FastClosures = "0.3.2"
 FiniteDiff = "2.23.1"

From c77cee8c21a78e8d4f4a6f8da11a63779ea83a19 Mon Sep 17 00:00:00 2001
From: Adam Wheeler <awheeler@flatironinstitute.org>
Date: Fri, 27 Sep 2024 08:44:53 -0400
Subject: [PATCH 493/700] tweak warning message

---
 lib/SimpleNonlinearSolve/src/bracketing/bisection.jl | 2 +-
 lib/SimpleNonlinearSolve/src/bracketing/brent.jl     | 2 +-
 lib/SimpleNonlinearSolve/src/bracketing/falsi.jl     | 2 +-
 lib/SimpleNonlinearSolve/src/bracketing/itp.jl       | 2 +-
 lib/SimpleNonlinearSolve/src/bracketing/ridder.jl    | 2 +-
 5 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
index adcf72a4b..75069ae17 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/bisection.jl
@@ -40,7 +40,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection,
     end
 
     if sign(fl) == sign(fr)
-        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        @warn "The interval is not an enclosing interval (does not contain a root). Returning boundary value."
         return build_solution(
             prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
     end
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/brent.jl b/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
index 4ba311f5d..ec208f939 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/brent.jl
@@ -27,7 +27,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
     end
 
     if sign(fl) == sign(fr)
-        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        @warn "The interval is not an enclosing interval (does not contain a root). Returning boundary value."
         return build_solution(
             prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
     end
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl b/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
index 00b29703b..ed1aceb9c 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/falsi.jl
@@ -26,7 +26,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
     end
 
     if sign(fl) == sign(fr)
-        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        @warn "The interval is not an enclosing interval (does not contain a root). Returning boundary value."
         return build_solution(
             prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
     end
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
index 9405cc2de..2cc98f076 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/itp.jl
@@ -77,7 +77,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
     end
 
     if sign(fl) == sign(fr)
-        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        @warn "The interval is not an enclosing interval (does not contain a root). Returning boundary value."
         return build_solution(
             prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
     end
diff --git a/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
index 772f568d1..5c27a1077 100644
--- a/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
+++ b/lib/SimpleNonlinearSolve/src/bracketing/ridder.jl
@@ -26,7 +26,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
     end
 
     if sign(fl) == sign(fr)
-        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        @warn "The interval is not an enclosing interval (does not contain a root). Returning boundary value."
         return build_solution(
             prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
     end

From a8e60d5f379d89d73d5d4509b3512768e55365a4 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 26 Sep 2024 10:32:33 -0400
Subject: [PATCH 494/700] feat: use DI for dense jacobians

fix: stop storing extra stuff in JacobianCache

feat: use DI for dense jacobians

refactor: remove alg from the cache

fix: don't ignore sparsity for dense_ad
---
 Project.toml             |   4 +-
 src/NonlinearSolve.jl    |   9 ++-
 src/internal/jacobian.jl | 160 ++++++++++++++++++++-------------------
 3 files changed, 93 insertions(+), 80 deletions(-)

diff --git a/Project.toml b/Project.toml
index ab35df1e2..a8028527e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -8,6 +8,7 @@ ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 FastBroadcast = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
@@ -65,8 +66,9 @@ BandedMatrices = "1.5"
 BenchmarkTools = "1.4"
 CUDA = "5.2"
 ConcreteStructs = "0.2.3"
+DifferentiationInterface = "0.6.1"
 DiffEqBase = "6.149.0"
-Enzyme = "0.12"
+Enzyme = "0.12, 0.13"
 ExplicitImports = "1.5"
 FastBroadcast = "0.2.8, 0.3"
 FastClosures = "0.3.2"
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 2e420a761..e68fa5472 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -7,8 +7,8 @@ end
 using Reexport: @reexport
 using PrecompileTools: @compile_workload, @setup_workload
 
-using ADTypes: ADTypes, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff,
-               AutoZygote, AutoEnzyme, AutoSparse
+using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
+               AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme, AutoSparse
 # FIXME: deprecated, remove in future
 using ADTypes: AutoSparseFiniteDiff, AutoSparseForwardDiff, AutoSparsePolyesterForwardDiff,
                AutoSparseZygote
@@ -22,6 +22,7 @@ using DiffEqBase: DiffEqBase, AbstractNonlinearTerminationMode,
                   NormTerminationMode, RelNormTerminationMode, RelSafeBestTerminationMode,
                   RelSafeTerminationMode, RelTerminationMode,
                   SimpleNonlinearSolveTerminationMode, SteadyStateDiffEqTerminationMode
+using DifferentiationInterface: DifferentiationInterface, Constant
 using FastBroadcast: @..
 using FastClosures: @closure
 using FiniteDiff: FiniteDiff
@@ -39,7 +40,7 @@ using Printf: @printf
 using Preferences: Preferences, @load_preference, @set_preferences!
 using RecursiveArrayTools: recursivecopy!, recursivefill!
 using SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
-                 AbstractSciMLOperator, _unwrap_val, has_jac, isinplace, NLStats
+                 AbstractSciMLOperator, _unwrap_val, isinplace, NLStats
 using SciMLJacobianOperators: AbstractJacobianOperator, JacobianOperator, VecJacOperator,
                               JacVecOperator, StatefulJacobianOperator
 using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
@@ -55,6 +56,8 @@ using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingPro
 
 @reexport using SciMLBase, SimpleNonlinearSolve
 
+const DI = DifferentiationInterface
+
 # Type-Inference Friendly Check for Extension Loading
 is_extension_loaded(::Val) = false
 
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 0c6080112..fc8e1d0a6 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -31,35 +31,24 @@ Construct a cache for the Jacobian of `f` w.r.t. `u`.
 @concrete mutable struct JacobianCache{iip} <: AbstractNonlinearSolveJacobianCache{iip}
     J
     f
-    uf
     fu
     u
     p
-    jac_cache
-    alg
     stats::NLStats
     autodiff
-    vjp_autodiff
-    jvp_autodiff
+    di_extras
+    sdifft_extras
 end
 
 function reinit_cache!(cache::JacobianCache{iip}, args...; p = cache.p,
         u0 = cache.u, kwargs...) where {iip}
     cache.u = u0
     cache.p = p
-    cache.uf = JacobianWrapper{iip}(cache.f, p)
 end
 
 function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
         vjp_autodiff = nothing, jvp_autodiff = nothing, linsolve = missing) where {F}
     iip = isinplace(prob)
-    uf = JacobianWrapper{iip}(f, p)
-
-    autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
-    jvp_autodiff = get_concrete_forward_ad(
-        jvp_autodiff, prob, Val(false); check_forward_mode = true)
-    vjp_autodiff = get_concrete_reverse_ad(
-        vjp_autodiff, prob, Val(false); check_reverse_mode = false)
 
     has_analytic_jac = SciMLBase.has_jac(f)
     linsolve_needs_jac = concrete_jac(alg) === nothing && (linsolve === missing ||
@@ -70,90 +59,128 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
     @bb fu = similar(fu_)
 
     if !has_analytic_jac && needs_jac
-        sd = __sparsity_detection_alg(f, autodiff)
-        jac_cache = iip ? sparse_jacobian_cache(autodiff, sd, uf, fu, u) :
-                    sparse_jacobian_cache(
-            autodiff, sd, uf, __maybe_mutable(u, autodiff); fx = fu)
+        autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
+        sd = sparsity_detection_alg(f, autodiff)
+        sparse_jac = !(sd isa NoSparsityDetection)
+        # Eventually we want to do everything via DI. But for now, we just do the dense via DI
+        if sparse_jac
+            di_extras = nothing
+            uf = JacobianWrapper{iip}(f, p)
+            sdifft_extras = if iip
+                sparse_jacobian_cache(autodiff, sd, uf, fu, u)
+            else
+                sparse_jacobian_cache(
+                    autodiff, sd, uf, __maybe_mutable(u, autodiff); fx = fu)
+            end
+        else
+            sdifft_extras = nothing
+            di_extras = if iip
+                DI.prepare_jacobian(f, fu, autodiff, u, Constant(p))
+            else
+                DI.prepare_jacobian(f, autodiff, u, Constant(p))
+            end
+        end
     else
-        jac_cache = nothing
+        sparse_jac = false
+        di_extras = nothing
+        sdifft_extras = nothing
     end
 
     J = if !needs_jac
+        jvp_autodiff = get_concrete_forward_ad(
+            jvp_autodiff, prob, Val(false); check_forward_mode = true)
+        vjp_autodiff = get_concrete_reverse_ad(
+            vjp_autodiff, prob, Val(false); check_reverse_mode = false)
         JacobianOperator(prob, fu, u; jvp_autodiff, vjp_autodiff)
     else
-        if has_analytic_jac
-            f.jac_prototype === nothing ?
-            __similar(fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u)) :
-            copy(f.jac_prototype)
-        elseif f.jac_prototype === nothing
-            zero(init_jacobian(jac_cache; preserve_immutable = Val(true)))
+        if f.jac_prototype === nothing
+            if !sparse_jac
+                __similar(fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u))
+            else
+                zero(init_jacobian(sdifft_extras; preserve_immutable = Val(true)))
+            end
         else
-            f.jac_prototype
+            similar(f.jac_prototype)
         end
     end
 
     return JacobianCache{iip}(
-        J, f, uf, fu, u, p, jac_cache, alg, stats, autodiff, vjp_autodiff, jvp_autodiff)
+        J, f, fu, u, p, stats, autodiff, di_extras, sdifft_extras)
 end
 
 function JacobianCache(prob, alg, f::F, ::Number, u::Number, p; stats,
         autodiff = nothing, kwargs...) where {F}
-    uf = JacobianWrapper{false}(f, p)
-    autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
-    if !(autodiff isa AutoForwardDiff ||
-         autodiff isa AutoPolyesterForwardDiff ||
-         autodiff isa AutoFiniteDiff)
-        # Other cases are not properly supported so we fallback to finite differencing
-        @warn "Scalar AD is supported only for AutoForwardDiff and AutoFiniteDiff. \
-               Detected $(autodiff). Falling back to AutoFiniteDiff."
-        autodiff = AutoFiniteDiff()
+    fu = f(u, p)
+    if SciMLBase.has_jac(f) || SciMLBase.has_vjp(f) || SciMLBase.has_jvp(f)
+        return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, nothing)
     end
-    return JacobianCache{false}(
-        u, f, uf, u, u, p, nothing, alg, stats, autodiff, nothing, nothing)
+    autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
+    di_extras = DI.prepare_derivative(f, autodiff, u, Constant(prob.p))
+    return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, di_extras, nothing)
 end
 
-@inline (cache::JacobianCache)(u = cache.u) = cache(cache.J, u, cache.p)
-@inline function (cache::JacobianCache)(::Nothing)
+(cache::JacobianCache)(u = cache.u) = cache(cache.J, u, cache.p)
+function (cache::JacobianCache)(::Nothing)
     cache.J isa JacobianOperator &&
         return StatefulJacobianOperator(cache.J, cache.u, cache.p)
     return cache.J
 end
 
+# Operator
 function (cache::JacobianCache)(J::JacobianOperator, u, p = cache.p)
     return StatefulJacobianOperator(J, u, p)
 end
+# Numbers
 function (cache::JacobianCache)(::Number, u, p = cache.p) # Scalar
     cache.stats.njacs += 1
-    J = last(__value_derivative(cache.autodiff, cache.uf, u))
-    return J
+    if SciMLBase.has_jac(cache.f)
+        return cache.f.jac(u, p)
+    elseif SciMLBase.has_vjp(cache.f)
+        return cache.f.vjp(one(u), u, p)
+    elseif SciMLBase.has_jvp(cache.f)
+        return cache.f.jvp(one(u), u, p)
+    end
+    return DI.derivative(cache.f, cache.di_extras, cache.autodiff, u, Constant(p))
 end
-# Compute the Jacobian
+# Actually Compute the Jacobian
 function (cache::JacobianCache{iip})(
         J::Union{AbstractMatrix, Nothing}, u, p = cache.p) where {iip}
     cache.stats.njacs += 1
     if iip
-        if has_jac(cache.f)
+        if SciMLBase.has_jac(cache.f)
             cache.f.jac(J, u, p)
+        elseif cache.di_extras !== nothing
+            DI.jacobian!(
+                cache.f, cache.fu, J, cache.di_extras, cache.autodiff, u, Constant(p))
         else
-            sparse_jacobian!(J, cache.autodiff, cache.jac_cache, cache.uf, cache.fu, u)
+            uf = JacobianWrapper{iip}(cache.f, p)
+            sparse_jacobian!(J, cache.autodiff, cache.jac_cache, uf, cache.fu, u)
         end
-        J_ = J
+        return J
     else
-        J_ = if has_jac(cache.f)
-            cache.f.jac(u, p)
-        elseif __can_setindex(typeof(J))
-            sparse_jacobian!(J, cache.autodiff, cache.jac_cache, cache.uf, u)
-            J
+        if SciMLBase.has_jac(cache.f)
+            return cache.f.jac(u, p)
+        elseif cache.di_extras !== nothing
+            return DI.jacobian(cache.f, cache.di_extras, cache.autodiff, u, Constant(p))
         else
-            sparse_jacobian(cache.autodiff, cache.jac_cache, cache.uf, u)
+            uf = JacobianWrapper{iip}(cache.f, p)
+            if __can_setindex(typeof(J))
+                sparse_jacobian!(J, cache.autodiff, cache.sdifft_extras, uf, u)
+                return J
+            else
+                return sparse_jacobian(cache.autodiff, cache.sdifft_extras, uf, u)
+            end
         end
     end
-    return J_
 end
 
-# Sparsity Detection Choices
-@inline __sparsity_detection_alg(_, _) = NoSparsityDetection()
-@inline function __sparsity_detection_alg(f::NonlinearFunction, ad::AutoSparse)
+function sparsity_detection_alg(f::NonlinearFunction, ad::AbstractADType)
+    # TODO: Also handle case where colorvec is provided
+    f.sparsity === nothing && return NoSparsityDetection()
+    return sparsity_detection_alg(f, AutoSparse(ad; sparsity_detector = f.sparsity))
+end
+
+function sparsity_detection_alg(f::NonlinearFunction, ad::AutoSparse)
     if f.sparsity === nothing
         if f.jac_prototype === nothing
             is_extension_loaded(Val(:Symbolics)) && return SymbolicsSparsityDetection()
@@ -177,28 +204,9 @@ end
     end
 
     if SciMLBase.has_colorvec(f)
-        return PrecomputedJacobianColorvec(; jac_prototype,
-            f.colorvec,
-            partition_by_rows = (ad isa AutoSparse &&
-                                 ADTypes.mode(ad) isa ADTypes.ReverseMode))
+        return PrecomputedJacobianColorvec(; jac_prototype, f.colorvec,
+            partition_by_rows = ADTypes.mode(ad) isa ADTypes.ReverseMode)
     else
         return JacPrototypeSparsityDetection(; jac_prototype)
     end
 end
-
-@inline function __value_derivative(
-        ::Union{AutoForwardDiff, AutoPolyesterForwardDiff}, f::F, x::R) where {F, R}
-    T = typeof(ForwardDiff.Tag(f, R))
-    out = f(ForwardDiff.Dual{T}(x, one(x)))
-    return ForwardDiff.value(out), ForwardDiff.extract_derivative(T, out)
-end
-
-@inline function __value_derivative(ad::AutoFiniteDiff, f::F, x::R) where {F, R}
-    return f(x), FiniteDiff.finite_difference_derivative(f, x, ad.fdtype)
-end
-
-@inline function __scalar_jacvec(f::F, x::R, v::V) where {F, R, V}
-    T = typeof(ForwardDiff.Tag(f, R))
-    out = f(ForwardDiff.Dual{T}(x, v))
-    return ForwardDiff.value(out), ForwardDiff.extract_derivative(T, out)
-end

From 33ac4501df94150288f0e7c15a5aff9ab6c20792 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 27 Sep 2024 13:47:47 -0400
Subject: [PATCH 495/700] fix: update minimum compats

---
 Project.toml | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/Project.toml b/Project.toml
index a8028527e..55283a7d4 100644
--- a/Project.toml
+++ b/Project.toml
@@ -67,8 +67,8 @@ BenchmarkTools = "1.4"
 CUDA = "5.2"
 ConcreteStructs = "0.2.3"
 DifferentiationInterface = "0.6.1"
-DiffEqBase = "6.149.0"
-Enzyme = "0.12, 0.13"
+DiffEqBase = "6.155.1"
+Enzyme = "0.13"
 ExplicitImports = "1.5"
 FastBroadcast = "0.2.8, 0.3"
 FastClosures = "0.3.2"
@@ -82,7 +82,7 @@ LazyArrays = "1.8.2, 2"
 LeastSquaresOptim = "0.8.5"
 LineSearches = "7.2"
 LinearAlgebra = "1.10"
-LinearSolve = "2.30"
+LinearSolve = "2.34"
 MINPACK = "1.2"
 MaybeInplace = "0.1.3"
 ModelingToolkit = "9.15.0"
@@ -100,11 +100,11 @@ ReTestItems = "1.24"
 RecursiveArrayTools = "3.8"
 Reexport = "1.2"
 SIAMFANLEquations = "1.0.1"
-SciMLBase = "2.34.0"
+SciMLBase = "2.54.0"
 SciMLJacobianOperators = "0.1"
-SimpleNonlinearSolve = "1.8"
+SimpleNonlinearSolve = "1.9.3"
 SparseArrays = "1.10"
-SparseDiffTools = "2.19"
+SparseDiffTools = "2.22"
 SpeedMapping = "0.3"
 StableRNGs = "1"
 StaticArrays = "1.9"

From ba45097e841f9875a7e53d94a1d86f1ffcfd1425 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 27 Sep 2024 14:17:53 -0400
Subject: [PATCH 496/700] fix: sparse jacobian

---
 docs/src/tutorials/code_optimization.md | 22 +++++++++-------------
 src/internal/jacobian.jl                | 11 +++++++++--
 2 files changed, 18 insertions(+), 15 deletions(-)

diff --git a/docs/src/tutorials/code_optimization.md b/docs/src/tutorials/code_optimization.md
index fa0f61657..ce114961b 100644
--- a/docs/src/tutorials/code_optimization.md
+++ b/docs/src/tutorials/code_optimization.md
@@ -33,9 +33,7 @@ Take for example a prototypical small nonlinear solver code in its out-of-place
 ```@example small_opt
 using NonlinearSolve
 
-function f(u, p)
-    u .* u .- p
-end
+f(u, p) = u .* u .- p
 u0 = [1.0, 1.0]
 p = 2.0
 prob = NonlinearProblem(f, u0, p)
@@ -53,9 +51,7 @@ using BenchmarkTools
 Note that this way of writing the function is a shorthand for:
 
 ```@example small_opt
-function f(u, p)
-    [u[1] * u[1] - p, u[2] * u[2] - p]
-end
+f(u, p) = [u[1] * u[1] - p, u[2] * u[2] - p]
 ```
 
 where the function `f` returns an array. This is a common pattern from things like MATLAB's
@@ -71,7 +67,7 @@ by hand, this looks like:
 function f(du, u, p)
     du[1] = u[1] * u[1] - p
     du[2] = u[2] * u[2] - p
-    nothing
+    return nothing
 end
 
 prob = NonlinearProblem(f, u0, p)
@@ -84,6 +80,7 @@ the `.=` in-place broadcasting.
 ```@example small_opt
 function f(du, u, p)
     du .= u .* u .- p
+    return nothing
 end
 
 @benchmark sol = solve(prob, NewtonRaphson())
@@ -114,6 +111,7 @@ to normal array expressions, for example:
 
 ```@example small_opt
 using StaticArrays
+
 A = SA[2.0, 3.0, 5.0]
 typeof(A)
 ```
@@ -135,12 +133,12 @@ want to use the out-of-place allocating form, but this time we want to output a
 array. Doing it with broadcasting looks like:
 
 ```@example small_opt
-function f_SA(u, p)
-    u .* u .- p
-end
+f_SA(u, p) = u .* u .- p
+
 u0 = SA[1.0, 1.0]
 p = 2.0
 prob = NonlinearProblem(f_SA, u0, p)
+
 @benchmark solve(prob, NewtonRaphson())
 ```
 
@@ -148,9 +146,7 @@ Note that only change here is that `u0` is made into a StaticArray! If we needed
 `f` out for a more complex nonlinear case, then we'd simply do the following:
 
 ```@example small_opt
-function f_SA(u, p)
-    SA[u[1] * u[1] - p, u[2] * u[2] - p]
-end
+f_SA(u, p) = SA[u[1] * u[1] - p, u[2] * u[2] - p]
 
 @benchmark solve(prob, NewtonRaphson())
 ```
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index fc8e1d0a6..bc64bbd06 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -95,7 +95,14 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
     else
         if f.jac_prototype === nothing
             if !sparse_jac
-                __similar(fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u))
+                # While this is technically wasteful, it gives out the type of the Jacobian
+                # which is needed to create the linear solver cache
+                stats.njacs += 1
+                if iip
+                    DI.jacobian(f, fu, di_extras, autodiff, u, Constant(p))
+                else
+                    DI.jacobian(f, autodiff, u, Constant(p))
+                end
             else
                 zero(init_jacobian(sdifft_extras; preserve_immutable = Val(true)))
             end
@@ -154,7 +161,7 @@ function (cache::JacobianCache{iip})(
                 cache.f, cache.fu, J, cache.di_extras, cache.autodiff, u, Constant(p))
         else
             uf = JacobianWrapper{iip}(cache.f, p)
-            sparse_jacobian!(J, cache.autodiff, cache.jac_cache, uf, cache.fu, u)
+            sparse_jacobian!(J, cache.autodiff, cache.sdifft_extras, uf, cache.fu, u)
         end
         return J
     else

From 92c59dbb2d360a4a2ed968668395473be57fc81e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 27 Sep 2024 14:18:39 -0400
Subject: [PATCH 497/700] chore: run formatter

---
 lib/SciMLJacobianOperators/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SciMLJacobianOperators/README.md b/lib/SciMLJacobianOperators/README.md
index c9d14ff50..0bce0f919 100644
--- a/lib/SciMLJacobianOperators/README.md
+++ b/lib/SciMLJacobianOperators/README.md
@@ -56,4 +56,4 @@ snormal_form * v  # Computes JᵀJ * v
 #  8.0
 #  8.0
 #  8.0
-```
\ No newline at end of file
+```

From 3b12e73e945941ac8d0d4eebe038f1c8ae15d5cf Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 27 Sep 2024 14:31:35 -0400
Subject: [PATCH 498/700] fix: unwrap sparse AD for derivative call

---
 src/internal/jacobian.jl | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index bc64bbd06..010b9f6c5 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -122,7 +122,7 @@ function JacobianCache(prob, alg, f::F, ::Number, u::Number, p; stats,
         return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, nothing)
     end
     autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
-    di_extras = DI.prepare_derivative(f, autodiff, u, Constant(prob.p))
+    di_extras = DI.prepare_derivative(f, get_dense_ad(autodiff), u, Constant(prob.p))
     return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, di_extras, nothing)
 end
 
@@ -217,3 +217,6 @@ function sparsity_detection_alg(f::NonlinearFunction, ad::AutoSparse)
         return JacPrototypeSparsityDetection(; jac_prototype)
     end
 end
+
+get_dense_ad(ad) = ad
+get_dense_ad(ad::AutoSparse) = ADTypes.dense_ad(ad)

From fe1bd3dd6ec4923afad60453600316038b3cd9f1 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 27 Sep 2024 14:47:54 -0400
Subject: [PATCH 499/700] chore: bump minimum versions

---
 Project.toml                                  | 32 +++++++++----------
 docs/Project.toml                             |  5 +--
 .../tutorials/optimizing_parameterized_ode.md |  2 +-
 test/misc/polyalg_tests.jl                    |  2 +-
 4 files changed, 21 insertions(+), 20 deletions(-)

diff --git a/Project.toml b/Project.toml
index 55283a7d4..5bd304bb3 100644
--- a/Project.toml
+++ b/Project.toml
@@ -59,21 +59,21 @@ NonlinearSolveSymbolicsExt = "Symbolics"
 NonlinearSolveZygoteExt = "Zygote"
 
 [compat]
-ADTypes = "1.1.0"
+ADTypes = "1.9"
 Aqua = "0.8"
-ArrayInterface = "7.9"
+ArrayInterface = "7.16"
 BandedMatrices = "1.5"
 BenchmarkTools = "1.4"
-CUDA = "5.2"
+CUDA = "5.5"
 ConcreteStructs = "0.2.3"
+DiffEqBase = "6.155.3"
 DifferentiationInterface = "0.6.1"
-DiffEqBase = "6.155.1"
-Enzyme = "0.13"
+Enzyme = "0.13.2"
 ExplicitImports = "1.5"
-FastBroadcast = "0.2.8, 0.3"
+FastBroadcast = "0.3.5"
 FastClosures = "0.3.2"
 FastLevenbergMarquardt = "0.1"
-FiniteDiff = "2.22"
+FiniteDiff = "2.24"
 FixedPointAcceleration = "0.3"
 ForwardDiff = "0.10.36"
 Hwloc = "3"
@@ -82,27 +82,27 @@ LazyArrays = "1.8.2, 2"
 LeastSquaresOptim = "0.8.5"
 LineSearches = "7.2"
 LinearAlgebra = "1.10"
-LinearSolve = "2.34"
+LinearSolve = "2.35"
 MINPACK = "1.2"
 MaybeInplace = "0.1.3"
-ModelingToolkit = "9.15.0"
+ModelingToolkit = "9.41.0"
 NLSolvers = "0.5"
 NLsolve = "4.5"
 NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
-OrdinaryDiffEq = "6.75"
+OrdinaryDiffEqTsit5 = "1.1.0"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 Preferences = "1.4"
 Printf = "1.10"
 Random = "1.91"
 ReTestItems = "1.24"
-RecursiveArrayTools = "3.8"
+RecursiveArrayTools = "3.27"
 Reexport = "1.2"
 SIAMFANLEquations = "1.0.1"
 SciMLBase = "2.54.0"
 SciMLJacobianOperators = "0.1"
-SimpleNonlinearSolve = "1.9.3"
+SimpleNonlinearSolve = "1.12.3"
 SparseArrays = "1.10"
 SparseDiffTools = "2.22"
 SpeedMapping = "0.3"
@@ -110,8 +110,8 @@ StableRNGs = "1"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4"
 Sundials = "4.23.1"
-SymbolicIndexingInterface = "0.3.15"
-Symbolics = "5.26, 6"
+SymbolicIndexingInterface = "0.3.31"
+Symbolics = "6.12"
 Test = "1.10"
 TimerOutputs = "0.5.23"
 Zygote = "0.6.69"
@@ -135,7 +135,7 @@ NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 NaNMath = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
 NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
-OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+OrdinaryDiffEqTsit5 = "b1df2697-797e-41e3-8120-5422d3b24e4a"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
@@ -149,4 +149,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEq", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
diff --git a/docs/Project.toml b/docs/Project.toml
index 63d1803d4..9fbee9e39 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -10,7 +10,7 @@ InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
-OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+OrdinaryDiffEqTsit5 = "b1df2697-797e-41e3-8120-5422d3b24e4a"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
@@ -30,10 +30,11 @@ DiffEqBase = "6.136"
 Documenter = "1"
 DocumenterCitations = "1"
 IncompleteLU = "0.2"
+InteractiveUtils = "<0.0.1, 1"
 LinearSolve = "2"
 ModelingToolkit = "8, 9"
 NonlinearSolve = "3"
-OrdinaryDiffEq = "6"
+OrdinaryDiffEqTsit5 = "1.1.0"
 Plots = "1"
 Random = "<0.0.1, 1"
 SciMLBase = "2.4"
diff --git a/docs/src/tutorials/optimizing_parameterized_ode.md b/docs/src/tutorials/optimizing_parameterized_ode.md
index d3b409eca..69cca060d 100644
--- a/docs/src/tutorials/optimizing_parameterized_ode.md
+++ b/docs/src/tutorials/optimizing_parameterized_ode.md
@@ -4,7 +4,7 @@ Let us fit a parameterized ODE to some data. We will use the Lotka-Volterra mode
 example. We will use Single Shooting to fit the parameters.
 
 ```@example parameterized_ode
-using OrdinaryDiffEq, NonlinearSolve, Plots
+using OrdinaryDiffEqTsit5, NonlinearSolve, Plots
 ```
 
 Let us simulate some real data from the Lotka-Volterra model.
diff --git a/test/misc/polyalg_tests.jl b/test/misc/polyalg_tests.jl
index 88be7e8cc..a106ace44 100644
--- a/test/misc/polyalg_tests.jl
+++ b/test/misc/polyalg_tests.jl
@@ -127,7 +127,7 @@ end
 # Testing for Complex Valued Root Finding. For Complex valued inputs we drop some of the
 # algorithms which dont support those.
 @testitem "Complex Valued Problems: Single-Shooting" tags=[:misc] begin
-    using OrdinaryDiffEq
+    using OrdinaryDiffEqTsit5
 
     function ode_func!(du, u, p, t)
         du[1] = u[2]

From 59b7d022bc282a04f858b973954b26fc52792771 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 27 Sep 2024 14:49:55 -0400
Subject: [PATCH 500/700] fix: update bruss testing

---
 test/misc/bruss_tests.jl | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/test/misc/bruss_tests.jl b/test/misc/bruss_tests.jl
index 21b7d792b..d18c67e6a 100644
--- a/test/misc/bruss_tests.jl
+++ b/test/misc/bruss_tests.jl
@@ -66,7 +66,6 @@
 
     sol = solve(prob_brusselator_2d, NewtonRaphson(); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
-    @test !all(iszero, jac_prototype)
 
     sol = solve(prob_brusselator_2d,
         NewtonRaphson(autodiff = AutoSparse(AutoFiniteDiff())); abstol = 1e-8)
@@ -74,6 +73,6 @@
 
     cache = init(
         prob_brusselator_2d, NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff())))
-    @test maximum(cache.jac_cache.jac_cache.coloring.colorvec) == 12
-    @test cache.jac_cache.autodiff isa AutoSparse{<:AutoForwardDiff}
+    @test maximum(cache.sdifft_extras.jac_cache.coloring.colorvec) == 12
+    @test cache.sdifft_extras.autodiff isa AutoSparse{<:AutoForwardDiff}
 end

From 3f59f4949829b74d78b9eea8de834dd4f9239152 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 27 Sep 2024 14:50:53 -0400
Subject: [PATCH 501/700] fix: autodiff cannot be nothing

---
 src/internal/jacobian.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 010b9f6c5..46f255149 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -58,8 +58,9 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
 
     @bb fu = similar(fu_)
 
+    autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
+
     if !has_analytic_jac && needs_jac
-        autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
         sd = sparsity_detection_alg(f, autodiff)
         sparse_jac = !(sd isa NoSparsityDetection)
         # Eventually we want to do everything via DI. But for now, we just do the dense via DI

From adac560c3f0f737b5c854d61642a182078bb50a1 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 27 Sep 2024 14:52:45 -0400
Subject: [PATCH 502/700] fix: __value_derivative removal from line searches

---
 src/globalization/line_search.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index 5de4610b6..d43e97247 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -110,10 +110,10 @@ function __internal_init(
             @warn "Scalar AD is supported only for AutoForwardDiff and AutoFiniteDiff. \
                    Detected $(autodiff). Falling back to AutoFiniteDiff."
         end
-        deriv_op = @closure (du, u, fu, p) -> last(__value_derivative(
-                                                  autodiff, Base.Fix2(f, p), u)) *
-                                              fu *
-                                              du
+        deriv_op = @closure (du, u, fu, p) -> begin
+            # Temporary solution, we are anyways moving to LineSearch.jl
+            return DI.derivative(f, autodiff, u, Constant(p)) * fu * du
+        end
     else
         # Both forward and reverse AD can be used for line-search.
         # We prefer forward AD for better performance, however, reverse AD is also supported if user explicitly requests it.

From 0f2a62f00334d680096e55c9a8ecdc8012819aef Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 27 Sep 2024 15:07:22 -0400
Subject: [PATCH 503/700] fix: minor test fixes

---
 src/globalization/line_search.jl |  3 ++-
 src/internal/jacobian.jl         | 16 +++++++++++-----
 test/misc/bruss_tests.jl         |  4 ++--
 3 files changed, 15 insertions(+), 8 deletions(-)

diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index d43e97247..323c49258 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -101,7 +101,8 @@ function __internal_init(
         args...; stats, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
     T = promote_type(eltype(fu), eltype(u))
     if u isa Number
-        autodiff = get_concrete_forward_ad(alg.autodiff, prob; check_forward_mode = true)
+        autodiff = get_dense_ad(get_concrete_forward_ad(
+            alg.autodiff, prob; check_forward_mode = true))
         if !(autodiff isa AutoForwardDiff ||
              autodiff isa AutoPolyesterForwardDiff ||
              autodiff isa AutoFiniteDiff)
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 46f255149..67ab839a2 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -99,10 +99,15 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
                 # While this is technically wasteful, it gives out the type of the Jacobian
                 # which is needed to create the linear solver cache
                 stats.njacs += 1
-                if iip
-                    DI.jacobian(f, fu, di_extras, autodiff, u, Constant(p))
+                if has_analytic_jac
+                    __similar(
+                        fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u))
                 else
-                    DI.jacobian(f, autodiff, u, Constant(p))
+                    if iip
+                        DI.jacobian(f, fu, di_extras, autodiff, u, Constant(p))
+                    else
+                        DI.jacobian(f, autodiff, u, Constant(p))
+                    end
                 end
             else
                 zero(init_jacobian(sdifft_extras; preserve_immutable = Val(true)))
@@ -120,9 +125,10 @@ function JacobianCache(prob, alg, f::F, ::Number, u::Number, p; stats,
         autodiff = nothing, kwargs...) where {F}
     fu = f(u, p)
     if SciMLBase.has_jac(f) || SciMLBase.has_vjp(f) || SciMLBase.has_jvp(f)
-        return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, nothing)
+        return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, nothing, nothing)
     end
-    autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
+    autodiff = get_dense_ad(get_concrete_forward_ad(
+        autodiff, prob; check_forward_mode = false))
     di_extras = DI.prepare_derivative(f, get_dense_ad(autodiff), u, Constant(prob.p))
     return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, di_extras, nothing)
 end
diff --git a/test/misc/bruss_tests.jl b/test/misc/bruss_tests.jl
index d18c67e6a..8ea1fdb18 100644
--- a/test/misc/bruss_tests.jl
+++ b/test/misc/bruss_tests.jl
@@ -73,6 +73,6 @@
 
     cache = init(
         prob_brusselator_2d, NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff())))
-    @test maximum(cache.sdifft_extras.jac_cache.coloring.colorvec) == 12
-    @test cache.sdifft_extras.autodiff isa AutoSparse{<:AutoForwardDiff}
+    @test maximum(cache.jac_cache.sdifft_extras.coloring.colorvec) == 12
+    @test cache.jac_cache.autodiff isa AutoSparse{<:AutoForwardDiff}
 end

From 736b4a36ee75e5566fce3a98c3a3bd0b8789e97d Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 27 Sep 2024 15:29:07 -0400
Subject: [PATCH 504/700] test: issue 451

---
 test/misc/issues_tests.jl | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)
 create mode 100644 test/misc/issues_tests.jl

diff --git a/test/misc/issues_tests.jl b/test/misc/issues_tests.jl
new file mode 100644
index 000000000..24e39943c
--- /dev/null
+++ b/test/misc/issues_tests.jl
@@ -0,0 +1,22 @@
+@testitem "Issue #451" tags=[:misc] begin
+    f(u, p) = u^2 - p
+
+    jac_calls = 0
+    function df(u, p)
+        global jac_calls += 1
+        return 2u
+    end
+
+    fn = NonlinearFunction(f; jac = df)
+    prob = NonlinearProblem(fn, 1.0, 2.0)
+    sol = solve(prob, NewtonRaphson())
+    @test sol.retcode == ReturnCode.Success
+    @test jac_calls ≥ 1
+
+    jac_calls = 0
+    fn2 = NonlinearFunction(f)
+    prob = NonlinearProblem(fn2, 1.0, 2.0)
+    sol = solve(prob, NewtonRaphson())
+    @test sol.retcode == ReturnCode.Success
+    @test jac_calls == 0
+end

From d6d741b9481c9b7cbe75eeab1898f56e2a188bdb Mon Sep 17 00:00:00 2001
From: Oscar Smith <oscar.smith@juliacomputing.com>
Date: Fri, 27 Sep 2024 22:13:41 -0400
Subject: [PATCH 505/700] refactor: simplify `__wrapprecs` (#465)

* simplify `__wrapprecs`

previously the preconditioner being set was a very complicated `IdentityOperator`. Using a regular `IdentityOperator` means that solvers that don't support one of the preconditioners won't throw warnings since they mostly know that `IdentityOperator`s aren't real.

* fix

* fix: typo

* remove __init_ones

* remove imports

* Update src/NonlinearSolve.jl
---
 src/NonlinearSolve.jl        |  6 +++---
 src/internal/linear_solve.jl | 25 +++++++------------------
 src/utils.jl                 |  7 -------
 3 files changed, 10 insertions(+), 28 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index e68fa5472..9f8048cfb 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -32,13 +32,13 @@ using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Sy
                      UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess, istril,
                      istriu, lu, mul!, norm, pinv, tril!, triu!
 using LineSearches: LineSearches
-using LinearSolve: LinearSolve, LUFactorization, QRFactorization, ComposePreconditioner,
-                   InvPreconditioner, needs_concrete_A, AbstractFactorization,
+using LinearSolve: LinearSolve, LUFactorization, QRFactorization,
+                   needs_concrete_A, AbstractFactorization,
                    DefaultAlgorithmChoice, DefaultLinearSolver
 using MaybeInplace: @bb
 using Printf: @printf
 using Preferences: Preferences, @load_preference, @set_preferences!
-using RecursiveArrayTools: recursivecopy!, recursivefill!
+using RecursiveArrayTools: recursivecopy!
 using SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
                  AbstractSciMLOperator, _unwrap_val, isinplace, NLStats
 using SciMLJacobianOperators: AbstractJacobianOperator, JacobianOperator, VecJacOperator,
diff --git a/src/internal/linear_solve.jl b/src/internal/linear_solve.jl
index 27e6a780f..a0c1ba664 100644
--- a/src/internal/linear_solve.jl
+++ b/src/internal/linear_solve.jl
@@ -80,14 +80,13 @@ function LinearSolverCache(alg, linsolve, A, b, u; stats, kwargs...)
     @bb u_ = copy(u_fixed)
     linprob = LinearProblem(A, b; u0 = u_, kwargs...)
 
-    weight = __init_ones(u_fixed)
     if __hasfield(alg, Val(:precs))
         precs = alg.precs
         Pl_, Pr_ = precs(A, nothing, u, ntuple(Returns(nothing), 6)...)
     else
         precs, Pl_, Pr_ = nothing, nothing, nothing
     end
-    Pl, Pr = __wrapprecs(Pl_, Pr_, weight)
+    Pl, Pr = __wrapprecs(Pl_, Pr_, u)
 
     # Unalias here, we will later use these as caches
     lincache = init(linprob, linsolve; alias_A = false, alias_b = false, Pl, Pr)
@@ -128,10 +127,8 @@ function (cache::LinearSolverCache)(;
     b !== nothing && (cache.lincache.b = b)
     linu !== nothing && __set_lincache_u!(cache, linu)
 
-    Plprev = cache.lincache.Pl isa ComposePreconditioner ? cache.lincache.Pl.outer :
-             cache.lincache.Pl
-    Prprev = cache.lincache.Pr isa ComposePreconditioner ? cache.lincache.Pr.outer :
-             cache.lincache.Pr
+    Plprev = cache.lincache.Pl
+    Prprev = cache.lincache.Pr
 
     if cache.precs === nothing
         _Pl, _Pr = nothing, nothing
@@ -141,10 +138,7 @@ function (cache::LinearSolverCache)(;
     end
 
     if (_Pl !== nothing || _Pr !== nothing)
-        _weight = weight === nothing ?
-                  (cache.lincache.Pr isa Diagonal ? cache.lincache.Pr.diag :
-                   cache.lincache.Pr.inner.diag) : weight
-        Pl, Pr = __wrapprecs(_Pl, _Pr, _weight)
+        Pl, Pr = __wrapprecs(_Pl, _Pr, linu)
         cache.lincache.Pl = Pl
         cache.lincache.Pr = Pr
     end
@@ -242,14 +236,9 @@ function __set_lincache_A(lincache, new_A)
     end
 end
 
-@inline function __wrapprecs(_Pl, _Pr, weight)
-    Pl = _Pl !== nothing ?
-         ComposePreconditioner(InvPreconditioner(Diagonal(_vec(weight))), _Pl) :
-         InvPreconditioner(Diagonal(_vec(weight)))
-
-    Pr = _Pr !== nothing ? ComposePreconditioner(Diagonal(_vec(weight)), _Pr) :
-         Diagonal(_vec(weight))
-
+function __wrapprecs(_Pl, _Pr, u)
+    Pl = _Pl !== nothing ? _Pl : IdentityOperator(length(u))
+    Pr = _Pr !== nothing ? _Pr : IdentityOperator(length(u))
     return Pl, Pr
 end
 
diff --git a/src/utils.jl b/src/utils.jl
index 1a4ffd2c8..e13f9ca60 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -34,13 +34,6 @@ end
 @inline _restructure(y, x) = restructure(y, x)
 @inline _restructure(y::Number, x::Number) = x
 
-@inline function __init_ones(x)
-    w = similar(x)
-    recursivefill!(w, true)
-    return w
-end
-@inline __init_ones(x::StaticArray) = ones(typeof(x))
-
 @inline __maybe_unaliased(x::Union{Number, SArray}, ::Bool) = x
 @inline function __maybe_unaliased(x::AbstractArray, alias::Bool)
     # Spend time coping iff we will mutate the array

From b6221b7d61027339ec5fc50bb1f3f90398ce607e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 1 Oct 2024 15:27:29 -0400
Subject: [PATCH 506/700] refactor: reorder imports

---
 Project.toml          |  4 ++++
 src/NonlinearSolve.jl | 22 ++++++++++++----------
 src/utils.jl          |  3 ++-
 3 files changed, 18 insertions(+), 11 deletions(-)

diff --git a/Project.toml b/Project.toml
index 5bd304bb3..b8a21339f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -27,7 +27,9 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
 SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
 SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
+SparseMatrixColorings = "0a514795-09f3-496d-8182-132a7b665d35"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
 TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
@@ -104,7 +106,9 @@ SciMLBase = "2.54.0"
 SciMLJacobianOperators = "0.1"
 SimpleNonlinearSolve = "1.12.3"
 SparseArrays = "1.10"
+SparseConnectivityTracer = "0.6.5"
 SparseDiffTools = "2.22"
+SparseMatrixColorings = "0.4.2"
 SpeedMapping = "0.3"
 StableRNGs = "1"
 StaticArrays = "1.9"
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 9f8048cfb..4e0c0f7cf 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -7,12 +7,6 @@ end
 using Reexport: @reexport
 using PrecompileTools: @compile_workload, @setup_workload
 
-using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
-               AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme, AutoSparse
-# FIXME: deprecated, remove in future
-using ADTypes: AutoSparseFiniteDiff, AutoSparseForwardDiff, AutoSparsePolyesterForwardDiff,
-               AutoSparseZygote
-
 using ArrayInterface: ArrayInterface, can_setindex, restructure, fast_scalar_indexing,
                       ismutable
 using ConcreteStructs: @concrete
@@ -22,11 +16,8 @@ using DiffEqBase: DiffEqBase, AbstractNonlinearTerminationMode,
                   NormTerminationMode, RelNormTerminationMode, RelSafeBestTerminationMode,
                   RelSafeTerminationMode, RelTerminationMode,
                   SimpleNonlinearSolveTerminationMode, SteadyStateDiffEqTerminationMode
-using DifferentiationInterface: DifferentiationInterface, Constant
 using FastBroadcast: @..
 using FastClosures: @closure
-using FiniteDiff: FiniteDiff
-using ForwardDiff: ForwardDiff, Dual
 using LazyArrays: LazyArrays, ApplyArray, cache
 using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Symmetric,
                      UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess, istril,
@@ -43,7 +34,6 @@ using SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearP
                  AbstractSciMLOperator, _unwrap_val, isinplace, NLStats
 using SciMLJacobianOperators: AbstractJacobianOperator, JacobianOperator, VecJacOperator,
                               JacVecOperator, StatefulJacobianOperator
-using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
 using SparseDiffTools: SparseDiffTools, AbstractSparsityDetection,
                        ApproximateJacobianSparsity, JacPrototypeSparsityDetection,
                        NoSparsityDetection, PrecomputedJacobianColorvec,
@@ -54,6 +44,18 @@ using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingPro
                                  symbolic_container, parameter_values, state_values, getu,
                                  setu
 
+# AD Support
+using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
+               AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme, AutoSparse
+using ADTypes: AutoSparseFiniteDiff, AutoSparseForwardDiff, AutoSparsePolyesterForwardDiff,
+               AutoSparseZygote # FIXME: deprecated, remove in future
+using DifferentiationInterface: DifferentiationInterface, Constant
+using FiniteDiff: FiniteDiff
+using ForwardDiff: ForwardDiff, Dual
+
+## Sparse AD Support
+using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
+
 @reexport using SciMLBase, SimpleNonlinearSolve
 
 const DI = DifferentiationInterface
diff --git a/src/utils.jl b/src/utils.jl
index e13f9ca60..6ceb4c9d8 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -157,5 +157,6 @@ end
 
 function __similar(x, args...; kwargs...)
     y = similar(x, args...; kwargs...)
-    return zero(y)
+    fill!(y, false)
+    return y
 end

From cf19678a96c253d775962d6604f62e41d781ee36 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 1 Oct 2024 15:35:22 -0400
Subject: [PATCH 507/700] refactor: remove Symbolics

---
 Project.toml                      | 2 --
 ext/NonlinearSolveSymbolicsExt.jl | 7 -------
 src/NonlinearSolve.jl             | 5 +++--
 src/internal/jacobian.jl          | 2 +-
 4 files changed, 4 insertions(+), 12 deletions(-)
 delete mode 100644 ext/NonlinearSolveSymbolicsExt.jl

diff --git a/Project.toml b/Project.toml
index b8a21339f..596eb5656 100644
--- a/Project.toml
+++ b/Project.toml
@@ -44,7 +44,6 @@ NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
 SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
-Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [extensions]
@@ -57,7 +56,6 @@ NonlinearSolveNLSolversExt = "NLSolvers"
 NonlinearSolveNLsolveExt = "NLsolve"
 NonlinearSolveSIAMFANLEquationsExt = "SIAMFANLEquations"
 NonlinearSolveSpeedMappingExt = "SpeedMapping"
-NonlinearSolveSymbolicsExt = "Symbolics"
 NonlinearSolveZygoteExt = "Zygote"
 
 [compat]
diff --git a/ext/NonlinearSolveSymbolicsExt.jl b/ext/NonlinearSolveSymbolicsExt.jl
deleted file mode 100644
index 8e5354cda..000000000
--- a/ext/NonlinearSolveSymbolicsExt.jl
+++ /dev/null
@@ -1,7 +0,0 @@
-module NonlinearSolveSymbolicsExt
-
-using NonlinearSolve: NonlinearSolve
-
-NonlinearSolve.is_extension_loaded(::Val{:Symbolics}) = true
-
-end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 4e0c0f7cf..bd424d37f 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -37,8 +37,8 @@ using SciMLJacobianOperators: AbstractJacobianOperator, JacobianOperator, VecJac
 using SparseDiffTools: SparseDiffTools, AbstractSparsityDetection,
                        ApproximateJacobianSparsity, JacPrototypeSparsityDetection,
                        NoSparsityDetection, PrecomputedJacobianColorvec,
-                       SymbolicsSparsityDetection, init_jacobian, sparse_jacobian,
-                       sparse_jacobian!, sparse_jacobian_cache
+                       init_jacobian, sparse_jacobian, sparse_jacobian!,
+                       sparse_jacobian_cache
 using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
 using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
                                  symbolic_container, parameter_values, state_values, getu,
@@ -55,6 +55,7 @@ using ForwardDiff: ForwardDiff, Dual
 
 ## Sparse AD Support
 using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
+using SparseConnectivityTracer: TracerSparsityDetector
 
 @reexport using SciMLBase, SimpleNonlinearSolve
 
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 67ab839a2..bf178eff1 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -197,7 +197,7 @@ end
 function sparsity_detection_alg(f::NonlinearFunction, ad::AutoSparse)
     if f.sparsity === nothing
         if f.jac_prototype === nothing
-            is_extension_loaded(Val(:Symbolics)) && return SymbolicsSparsityDetection()
+            # is_extension_loaded(Val(:Symbolics)) && return SymbolicsSparsityDetection()
             return ApproximateJacobianSparsity()
         else
             jac_prototype = f.jac_prototype

From d8c3afc39bce04e425b529117ad7fe252c7af287 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 1 Oct 2024 17:12:31 -0400
Subject: [PATCH 508/700] feat: use DI for sparse jacobians

---
 Project.toml                          |   4 +
 docs/Project.toml                     |   4 +
 docs/src/basics/sparsity_detection.md |  40 +++---
 docs/src/tutorials/large_systems.md   |  83 +++++++-----
 src/NonlinearSolve.jl                 |  22 ++--
 src/internal/jacobian.jl              | 183 ++++++++++++++++++++------
 test/misc/bruss_tests.jl              |  27 ++--
 7 files changed, 247 insertions(+), 116 deletions(-)

diff --git a/Project.toml b/Project.toml
index 596eb5656..7d8f1f907 100644
--- a/Project.toml
+++ b/Project.toml
@@ -25,6 +25,8 @@ RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
+SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
+Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
@@ -102,6 +104,8 @@ Reexport = "1.2"
 SIAMFANLEquations = "1.0.1"
 SciMLBase = "2.54.0"
 SciMLJacobianOperators = "0.1"
+SciMLOperators = "0.3.10"
+Setfield = "1.1.1"
 SimpleNonlinearSolve = "1.12.3"
 SparseArrays = "1.10"
 SparseConnectivityTracer = "0.6.5"
diff --git a/docs/Project.toml b/docs/Project.toml
index 9fbee9e39..48d18ffa9 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -3,6 +3,7 @@ AlgebraicMultigrid = "2169fc97-5a83-5252-b627-83903c6c433c"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 DocumenterCitations = "daee34ce-89f3-4625-b898-19384cb65244"
 IncompleteLU = "40713840-3770-5561-ab4c-a76e7d0d7895"
@@ -16,6 +17,7 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
 SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
+SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
 SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 SteadyStateDiffEq = "9672c7b4-1e72-59bd-8a11-6ac3964bc41f"
@@ -27,6 +29,7 @@ AlgebraicMultigrid = "0.5, 0.6"
 ArrayInterface = "6, 7"
 BenchmarkTools = "1"
 DiffEqBase = "6.136"
+DifferentiationInterface = "0.6"
 Documenter = "1"
 DocumenterCitations = "1"
 IncompleteLU = "0.2"
@@ -40,6 +43,7 @@ Random = "<0.0.1, 1"
 SciMLBase = "2.4"
 SciMLJacobianOperators = "0.1"
 SimpleNonlinearSolve = "1"
+SparseConnectivityTracer = "0.6.5"
 SparseDiffTools = "2.14"
 StaticArrays = "1"
 SteadyStateDiffEq = "2"
diff --git a/docs/src/basics/sparsity_detection.md b/docs/src/basics/sparsity_detection.md
index 97891be61..5124a0009 100644
--- a/docs/src/basics/sparsity_detection.md
+++ b/docs/src/basics/sparsity_detection.md
@@ -12,8 +12,6 @@ Let's say you have a Sparse Jacobian Prototype `jac_prototype`, in this case you
 create your problem as follows:
 
 ```julia
-prob = NonlinearProblem(NonlinearFunction(nlfunc; sparsity = jac_prototype), x0)
-# OR
 prob = NonlinearProblem(NonlinearFunction(nlfunc; jac_prototype = jac_prototype), x0)
 ```
 
@@ -22,9 +20,6 @@ NonlinearSolve will automatically perform matrix coloring and use sparse differe
 Now you can help the solver further by providing the color vector. This can be done by
 
 ```julia
-prob = NonlinearProblem(
-    NonlinearFunction(nlfunc; sparsity = jac_prototype, colorvec = colorvec), x0)
-# OR
 prob = NonlinearProblem(
     NonlinearFunction(nlfunc; jac_prototype = jac_prototype, colorvec = colorvec), x0)
 ```
@@ -34,10 +29,16 @@ If the `colorvec` is not provided, then it is computed on demand.
 !!! note
     
     One thing to be careful about in this case is that `colorvec` is dependent on the
-    autodiff backend used. Forward Mode and Finite Differencing will assume that the
-    colorvec is the column colorvec, while Reverse Mode will assume that the colorvec is the
+    autodiff backend used. `ADTypes.mode(ad) isa ADTypes.ForwardMode` will assume that the
+    colorvec is the column colorvec, otherwise we will assume that the colorvec is the
     row colorvec.
 
+!!! warning
+
+    Previously you could provide a `sparsity` argument to `NonlinearFunction` to specify
+    the jacobian prototype. However, to avoid confusion, this is now deprecated. Instead,
+    use the `jac_prototype` argument.
+
 ## Case II: Sparsity Detection algorithm is provided
 
 If you don't have a Sparse Jacobian Prototype, but you know the which sparsity detection
@@ -48,14 +49,18 @@ prob = NonlinearProblem(
     NonlinearFunction(nlfunc; sparsity = SymbolicsSparsityDetection()), x0)  # Remember to have Symbolics.jl loaded
 # OR
 prob = NonlinearProblem(
-    NonlinearFunction(nlfunc; sparsity = ApproximateJacobianSparsity()), x0)
+    NonlinearFunction(nlfunc; sparsity = TracerSparsityDetector()), x0) # From SparseConnectivityTracer.jl
 ```
 
-These Detection Algorithms are from [SparseDiffTools.jl](https://github.com/JuliaDiff/SparseDiffTools.jl),
-refer to the documentation there for more details.
+Refer to the documentation of DifferentiationInterface.jl for more information on
+sparsity detection algorithms.
 
 ## Case III: Sparse AD Type is being Used
 
+!!! warning
+
+    This is now deprecated. Please use the previous two cases instead.
+
 If you constructed a Nonlinear Solver with a sparse AD type, for example
 
 ```julia
@@ -65,15 +70,6 @@ TrustRegion(; autodiff = AutoSparse(AutoZygote()))
 ```
 
 then NonlinearSolve will automatically perform matrix coloring and use sparse
-differentiation if none of `sparsity` or `jac_prototype` is provided. If `Symbolics.jl` is
-loaded, we default to using `SymbolicsSparsityDetection()`, else we default to using
-`ApproximateJacobianSparsity()`.
-
-`Case I/II` take precedence for sparsity detection and we perform sparse AD based on those
-options if those are provided.
-
-!!! warning
-    
-    If you provide a non-sparse AD, and provide a `sparsity` or `jac_prototype` then
-    we will use dense AD. This is because, if you provide a specific AD type, we assume
-    that you know what you are doing and want to override the default choice of `nothing`.
+differentiation if none of `sparsity` or `jac_prototype` is provided. We default to using
+`TracerSparsityDetector()`. `Case I/II` take precedence for sparsity detection and we
+perform sparse AD based on those options if those are provided.
diff --git a/docs/src/tutorials/large_systems.md b/docs/src/tutorials/large_systems.md
index 368535287..8ed6ca169 100644
--- a/docs/src/tutorials/large_systems.md
+++ b/docs/src/tutorials/large_systems.md
@@ -2,15 +2,15 @@
 
 This tutorial is for getting into the extra features of using NonlinearSolve.jl. Solving
 ill-conditioned nonlinear systems requires specializing the linear solver on properties of
-the Jacobian in order to cut down on the ``\mathcal{O}(n^3)`` linear solve and the
-``\mathcal{O}(n^2)`` back-solves. This tutorial is designed to explain the advanced usage of
+the Jacobian in order to cut down on the `\mathcal{O}(n^3)` linear solve and the
+`\mathcal{O}(n^2)` back-solves. This tutorial is designed to explain the advanced usage of
 NonlinearSolve.jl by solving the steady state stiff Brusselator partial differential
 equation (BRUSS) using NonlinearSolve.jl.
 
 ## Definition of the Brusselator Equation
 
 !!! note
-    
+
     Feel free to skip this section: it simply defines the example problem.
 
 The Brusselator PDE is defined as follows:
@@ -60,7 +60,7 @@ broadcast). Use `dx=dy=1/32`.
 The resulting `NonlinearProblem` definition is:
 
 ```@example ill_conditioned_nlprob
-using NonlinearSolve, LinearAlgebra, SparseArrays, LinearSolve, SparseDiffTools
+using NonlinearSolve, LinearAlgebra, SparseArrays, LinearSolve
 
 const N = 32
 const xyd_brusselator = range(0, stop = 1, length = N)
@@ -117,31 +117,37 @@ However, if you know the sparsity of your problem, then you can pass a different
 type. For example, a `SparseMatrixCSC` will give a sparse matrix. Other sparse matrix types
 include:
 
-  - Bidiagonal
-  - Tridiagonal
-  - SymTridiagonal
-  - BandedMatrix ([BandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BandedMatrices.jl))
-  - BlockBandedMatrix ([BlockBandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BlockBandedMatrices.jl))
+- Bidiagonal
+- Tridiagonal
+- SymTridiagonal
+- BandedMatrix ([BandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BandedMatrices.jl))
+- BlockBandedMatrix ([BlockBandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BlockBandedMatrices.jl))
 
 ## Approximate Sparsity Detection & Sparse Jacobians
 
-In the next section, we will discuss how to declare a sparse Jacobian and how to use
-[Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl), to compute exact sparse
-jacobians. This is triggered if you pass in a sparse autodiff type such as
-`AutoSparse(AutoForwardDiff())`. If `Symbolics.jl` is loaded, then the default changes to
-Symbolic Sparsity Detection. See the manual entry on
-[Sparsity Detection](@ref sparsity-detection) for more details on the default.
+In the next section, we will show how to specify `sparsity` to trigger automatic sparsity
+detection.
 
 ```@example ill_conditioned_nlprob
 using BenchmarkTools # for @btime
 
 @btime solve(prob_brusselator_2d, NewtonRaphson());
-@btime solve(prob_brusselator_2d,
-    NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff(; chunksize = 32))));
-@btime solve(prob_brusselator_2d,
-    NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff(; chunksize = 32)),
+nothing # hide
+```
+
+```@example ill_conditioned_nlprob
+using SparseConnectivityTracer
+
+prob_brusselator_2d_autosparse = NonlinearProblem(
+    NonlinearFunction(brusselator_2d_loop; sparsity = TracerSparsityDetector()),
+    u0, p; abstol = 1e-10, reltol = 1e-10)
+
+@btime solve(prob_brusselator_2d_autosparse,
+    NewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 32)));
+@btime solve(prob_brusselator_2d_autosparse,
+    NewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 32),
         linsolve = KLUFactorization()));
-@btime solve(prob_brusselator_2d,
+@btime solve(prob_brusselator_2d_autosparse,
     NewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 32),
         linsolve = KrylovJL_GMRES()));
 nothing # hide
@@ -160,8 +166,14 @@ declaration of Jacobian sparsity types. To see this in action, we can give an ex
 and `u` and call `jacobian_sparsity` on our function with the example arguments, and it will
 kick out a sparse matrix with our pattern, that we can turn into our `jac_prototype`.
 
+!!! tip
+
+    Alternatively you can use the `SparseConnectivityTracer.jl` package to automatically
+    generate a sparse Jacobian.
+
 ```@example ill_conditioned_nlprob
 using Symbolics
+
 du0 = copy(u0)
 jac_sparsity = Symbolics.jacobian_sparsity(
     (du, u) -> brusselator_2d_loop(du, u, p), du0, u0)
@@ -171,7 +183,7 @@ Notice that Julia gives a nice print out of the sparsity pattern. That's neat, a
 tedious to build by hand! Now we just pass it to the `NonlinearFunction` like as before:
 
 ```@example ill_conditioned_nlprob
-ff = NonlinearFunction(brusselator_2d_loop; sparsity = jac_sparsity)
+ff = NonlinearFunction(brusselator_2d_loop; jac_prototype = jac_sparsity)
 ```
 
 Build the `NonlinearProblem`:
@@ -212,7 +224,7 @@ choices, see the
 `linsolve` choices are any valid [LinearSolve.jl](https://linearsolve.sciml.ai/dev/) solver.
 
 !!! note
-    
+
     Switching to a Krylov linear solver will automatically change the nonlinear problem
     solver into Jacobian-free mode, dramatically reducing the memory required. This can be
     overridden by adding `concrete_jac=true` to the algorithm.
@@ -275,8 +287,8 @@ function algebraicmultigrid(W, du, u, p, t, newW, Plprev, Prprev, solverdata)
 end
 
 @btime solve(prob_brusselator_2d_sparse,
-    NewtonRaphson(
-        linsolve = KrylovJL_GMRES(), precs = algebraicmultigrid, concrete_jac = true));
+    NewtonRaphson(linsolve = KrylovJL_GMRES(), precs = algebraicmultigrid,
+        concrete_jac = true));
 nothing # hide
 ```
 
@@ -296,8 +308,8 @@ function algebraicmultigrid2(W, du, u, p, t, newW, Plprev, Prprev, solverdata)
 end
 
 @btime solve(prob_brusselator_2d_sparse,
-    NewtonRaphson(
-        linsolve = KrylovJL_GMRES(), precs = algebraicmultigrid2, concrete_jac = true));
+    NewtonRaphson(linsolve = KrylovJL_GMRES(), precs = algebraicmultigrid2,
+        concrete_jac = true));
 nothing # hide
 ```
 
@@ -308,15 +320,22 @@ for the exact sparsity detection case, we left out the time it takes to perform
 sparsity detection. Let's compare the two by setting the sparsity detection algorithms.
 
 ```@example ill_conditioned_nlprob
-prob_brusselator_2d_exact = NonlinearProblem(
-    NonlinearFunction(brusselator_2d_loop; sparsity = SymbolicsSparsityDetection()),
+using DifferentiationInterface, SparseConnectivityTracer
+
+prob_brusselator_2d_exact_symbolics = NonlinearProblem(
+    NonlinearFunction(brusselator_2d_loop; sparsity = SymbolicsSparsityDetector()),
+    u0, p; abstol = 1e-10, reltol = 1e-10)
+prob_brusselator_2d_exact_tracer = NonlinearProblem(
+    NonlinearFunction(brusselator_2d_loop; sparsity = TracerSparsityDetector()),
     u0, p; abstol = 1e-10, reltol = 1e-10)
-prob_brusselator_2d_approx = NonlinearProblem(
-    NonlinearFunction(brusselator_2d_loop; sparsity = ApproximateJacobianSparsity()),
+prob_brusselator_2d_approx_di = NonlinearProblem(
+    NonlinearFunction(brusselator_2d_loop;
+        sparsity = DenseSparsityDetector(AutoForwardDiff(); atol=1e-4)),
     u0, p; abstol = 1e-10, reltol = 1e-10)
 
-@btime solve(prob_brusselator_2d_exact, NewtonRaphson());
-@btime solve(prob_brusselator_2d_approx, NewtonRaphson());
+@btime solve(prob_brusselator_2d_exact_symbolics, NewtonRaphson());
+@btime solve(prob_brusselator_2d_exact_tracer, NewtonRaphson());
+@btime solve(prob_brusselator_2d_approx_di, NewtonRaphson());
 nothing # hide
 ```
 
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index bd424d37f..2db06f9b0 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -31,14 +31,9 @@ using Printf: @printf
 using Preferences: Preferences, @load_preference, @set_preferences!
 using RecursiveArrayTools: recursivecopy!
 using SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
-                 AbstractSciMLOperator, _unwrap_val, isinplace, NLStats
-using SciMLJacobianOperators: AbstractJacobianOperator, JacobianOperator, VecJacOperator,
-                              JacVecOperator, StatefulJacobianOperator
-using SparseDiffTools: SparseDiffTools, AbstractSparsityDetection,
-                       ApproximateJacobianSparsity, JacPrototypeSparsityDetection,
-                       NoSparsityDetection, PrecomputedJacobianColorvec,
-                       init_jacobian, sparse_jacobian, sparse_jacobian!,
-                       sparse_jacobian_cache
+                 _unwrap_val, isinplace, NLStats
+using SciMLOperators: AbstractSciMLOperator
+using Setfield: @set!
 using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
 using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
                                  symbolic_container, parameter_values, state_values, getu,
@@ -46,16 +41,23 @@ using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingPro
 
 # AD Support
 using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
-               AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme, AutoSparse
+               AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme, AutoSparse,
+               NoSparsityDetector, KnownJacobianSparsityDetector
 using ADTypes: AutoSparseFiniteDiff, AutoSparseForwardDiff, AutoSparsePolyesterForwardDiff,
                AutoSparseZygote # FIXME: deprecated, remove in future
 using DifferentiationInterface: DifferentiationInterface, Constant
 using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff, Dual
+using SciMLJacobianOperators: AbstractJacobianOperator, JacobianOperator, VecJacOperator,
+                              JacVecOperator, StatefulJacobianOperator
 
 ## Sparse AD Support
 using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
-using SparseConnectivityTracer: TracerSparsityDetector
+using SparseConnectivityTracer: TracerSparsityDetector # This can be dropped in the next release
+using SparseDiffTools: SparseDiffTools, JacPrototypeSparsityDetection,
+                       PrecomputedJacobianColorvec, init_jacobian, sparse_jacobian,
+                       sparse_jacobian!, sparse_jacobian_cache
+using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm
 
 @reexport using SciMLBase, SimpleNonlinearSolve
 
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index bf178eff1..0bf7e4380 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -58,31 +58,34 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
 
     @bb fu = similar(fu_)
 
-    autodiff = get_concrete_forward_ad(autodiff, prob; check_forward_mode = false)
+    autodiff = get_concrete_forward_ad(
+        autodiff, prob, Val(false); check_forward_mode = false)
 
     if !has_analytic_jac && needs_jac
-        sd = sparsity_detection_alg(f, autodiff)
-        sparse_jac = !(sd isa NoSparsityDetection)
-        # Eventually we want to do everything via DI. But for now, we just do the dense via DI
-        if sparse_jac
+        autodiff = construct_concrete_adtype(f, autodiff)
+        using_sparsedifftools = autodiff isa StructuredMatrixAutodiff
+        # DI can't handle structured matrices
+        if using_sparsedifftools
             di_extras = nothing
             uf = JacobianWrapper{iip}(f, p)
             sdifft_extras = if iip
-                sparse_jacobian_cache(autodiff, sd, uf, fu, u)
-            else
                 sparse_jacobian_cache(
-                    autodiff, sd, uf, __maybe_mutable(u, autodiff); fx = fu)
+                    autodiff.autodiff, autodiff.sparsity_detection, uf, fu, u)
+            else
+                sparse_jacobian_cache(autodiff.autodiff, autodiff.sparsity_detection,
+                    uf, __maybe_mutable(u, autodiff); fx = fu)
             end
+            autodiff = autodiff.autodiff # For saving we unwrap
         else
             sdifft_extras = nothing
             di_extras = if iip
-                DI.prepare_jacobian(f, fu, autodiff, u, Constant(p))
+                DI.prepare_jacobian(f, fu, autodiff, u, Constant(prob.p))
             else
-                DI.prepare_jacobian(f, autodiff, u, Constant(p))
+                DI.prepare_jacobian(f, autodiff, u, Constant(prob.p))
             end
         end
     else
-        sparse_jac = false
+        using_sparsedifftools = false
         di_extras = nothing
         sdifft_extras = nothing
     end
@@ -95,7 +98,7 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
         JacobianOperator(prob, fu, u; jvp_autodiff, vjp_autodiff)
     else
         if f.jac_prototype === nothing
-            if !sparse_jac
+            if !using_sparsedifftools
                 # While this is technically wasteful, it gives out the type of the Jacobian
                 # which is needed to create the linear solver cache
                 stats.njacs += 1
@@ -113,7 +116,13 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
                 zero(init_jacobian(sdifft_extras; preserve_immutable = Val(true)))
             end
         else
-            similar(f.jac_prototype)
+            jac_proto = if eltype(f.jac_prototype) <: Bool
+                similar(f.jac_prototype, promote_type(eltype(fu), eltype(u)))
+            else
+                similar(f.jac_prototype)
+            end
+            fill!(jac_proto, false)
+            jac_proto
         end
     end
 
@@ -188,41 +197,137 @@ function (cache::JacobianCache{iip})(
     end
 end
 
-function sparsity_detection_alg(f::NonlinearFunction, ad::AbstractADType)
-    # TODO: Also handle case where colorvec is provided
-    f.sparsity === nothing && return NoSparsityDetection()
-    return sparsity_detection_alg(f, AutoSparse(ad; sparsity_detector = f.sparsity))
-end
-
-function sparsity_detection_alg(f::NonlinearFunction, ad::AutoSparse)
+function construct_concrete_adtype(f::NonlinearFunction, ad::AbstractADType)
+    @assert !(ad isa AutoSparse) "This shouldn't happen. Open an issue."
     if f.sparsity === nothing
         if f.jac_prototype === nothing
-            # is_extension_loaded(Val(:Symbolics)) && return SymbolicsSparsityDetection()
-            return ApproximateJacobianSparsity()
+            if SciMLBase.has_colorvec(f)
+                @warn "`colorvec` is provided but `sparsity` and `jac_prototype` is not \
+                       specified. `colorvec` will be ignored."
+            end
+            return ad # No sparse AD
+        else
+            if ArrayInterface.isstructured(f.jac_prototype)
+                return select_fastest_structured_matrix_autodiff(f.jac_prototype, f, ad)
+            end
+
+            return AutoSparse(
+                ad;
+                sparsity_detector = KnownJacobianSparsityDetector(f.jac_prototype),
+                coloring_algorithm = select_fastest_coloring_algorithm(
+                    f.jac_prototype, f, ad)
+            )
+        end
+    else
+        if f.sparsity isa AbstractMatrix
+            if f.jac_prototype !== nothing && f.jac_prototype !== f.sparsity
+                throw(ArgumentError("`sparsity::AbstractMatrix` and `jac_prototype` cannot \
+                                     be both provided. Pass only `jac_prototype`."))
+            end
+            Base.depwarn("`sparsity::typeof($(typeof(f.sparsity)))` is deprecated. \
+                          Pass it as `jac_prototype` instead.",
+                :NonlinearSolve)
+            if ArrayInterface.isstructured(f.sparsity)
+                return select_fastest_structured_matrix_autodiff(f.sparsity, f, ad)
+            end
+
+            return AutoSparse(
+                ad;
+                sparsity_detector = KnownJacobianSparsityDetector(f.sparsity),
+                coloring_algorithm = select_fastest_coloring_algorithm(
+                    f.sparsity, f, ad)
+            )
+        end
+
+        @assert f.sparsity isa ADTypes.AbstractSparsityDetector
+        sparsity_detector = f.sparsity
+        if f.jac_prototype === nothing
+            if SciMLBase.has_colorvec(f)
+                @warn "`colorvec` is provided but `jac_prototype` is not specified. \
+                       `colorvec` will be ignored."
+            end
+            return AutoSparse(
+                ad;
+                sparsity_detector,
+                coloring_algorithm = GreedyColoringAlgorithm()
+            )
         else
-            jac_prototype = f.jac_prototype
+            if ArrayInterface.isstructured(f.jac_prototype)
+                return select_fastest_structured_matrix_autodiff(f.jac_prototype, f, ad)
+            end
+
+            if f.jac_prototype isa AbstractSparseMatrix
+                if !(sparsity_detector isa NoSparsityDetector)
+                    @warn "`jac_prototype` is a sparse matrix but sparsity = $(f.sparsity) \
+                           has also been specified. Ignoring sparsity field and using \
+                           `jac_prototype` sparsity."
+                end
+                sparsity_detector = KnownJacobianSparsityDetector(f.jac_prototype)
+            end
+
+            return AutoSparse(
+                ad;
+                sparsity_detector,
+                coloring_algorithm = select_fastest_coloring_algorithm(
+                    f.jac_prototype, f, ad)
+            )
         end
-    elseif f.sparsity isa AbstractSparsityDetection
-        f.jac_prototype === nothing && return f.sparsity
-        jac_prototype = f.jac_prototype
-    elseif f.sparsity isa AbstractMatrix
-        jac_prototype = f.sparsity
-    elseif f.jac_prototype isa AbstractMatrix
-        jac_prototype = f.jac_prototype
+    end
+end
+
+@concrete struct StructuredMatrixAutodiff <: AbstractADType
+    autodiff <: AbstractADType
+    sparsity_detection
+end
+
+function select_fastest_structured_matrix_autodiff(
+        prototype::AbstractMatrix, f::NonlinearFunction, ad::AbstractADType)
+    sparsity_detection = if SciMLBase.has_colorvec(f)
+        PrecomputedJacobianColorvec(;
+            jac_prototype = prototype,
+            f.colorvec,
+            partition_by_rows = ADTypes.mode(ad) isa ADTypes.ReverseMode
+        )
     else
-        error("`sparsity::typeof($(typeof(f.sparsity)))` & \
-               `jac_prototype::typeof($(typeof(f.jac_prototype)))` is not supported. \
-               Use `sparsity::AbstractMatrix` or `sparsity::AbstractSparsityDetection` or \
-               set to `nothing`. `jac_prototype` can be set to `nothing` or an \
-               `AbstractMatrix`.")
+        if ArrayInterface.fast_matrix_colors(prototype)
+            colorvec = if ADTypes.mode(ad) isa ADTypes.ForwardMode
+                ArrayInterface.matrix_colors(prototype)
+            else
+                ArrayInterface.matrix_colors(prototype')
+            end
+            PrecomputedJacobianColorvec(;
+                jac_prototype = prototype,
+                colorvec,
+                partition_by_rows = ADTypes.mode(ad) isa ADTypes.ReverseMode
+            )
+        else
+            JacPrototypeSparsityDetection(; jac_prototype = prototype)
+        end
     end
+    return StructuredMatrixAutodiff(ad, sparsity_detection)
+end
 
+function select_fastest_coloring_algorithm(
+        prototype, f::NonlinearFunction, ad::AbstractADType)
     if SciMLBase.has_colorvec(f)
-        return PrecomputedJacobianColorvec(; jac_prototype, f.colorvec,
-            partition_by_rows = ADTypes.mode(ad) isa ADTypes.ReverseMode)
-    else
-        return JacPrototypeSparsityDetection(; jac_prototype)
+        return ConstantColoringAlgorithm{ifelse(
+            ADTypes.mode(ad) isa ADTypes.ReverseMode, :row, :column)}(
+            prototype, f.colorvec)
+    end
+    return GreedyColoringAlgorithm()
+end
+
+function construct_concrete_adtype(f::NonlinearFunction, ad::AutoSparse)
+    Base.depwarn(
+        "Specifying a sparse AD type for Nonlinear Problems is deprecated. \
+         Instead use the `sparsity`, `jac_prototype`, and `colorvec` to specify \
+         the right sparsity pattern and coloring algorithm. Ignoring the sparsity \
+         detection algorithm and coloring algorithm present in $(ad).",
+        :NonlinearSolve)
+    if f.sparsity === nothing && f.jac_prototype === nothing
+        @set! f.sparsity = TracerSparsityDetector()
     end
+    return construct_concrete_adtype(f, get_dense_ad(ad))
 end
 
 get_dense_ad(ad) = ad
diff --git a/test/misc/bruss_tests.jl b/test/misc/bruss_tests.jl
index 8ea1fdb18..7b63e421c 100644
--- a/test/misc/bruss_tests.jl
+++ b/test/misc/bruss_tests.jl
@@ -1,5 +1,5 @@
 @testitem "Brusselator 2D" tags=[:misc] begin
-    using LinearAlgebra, SparseArrays, Symbolics
+    using LinearAlgebra, SparseArrays, SparseConnectivityTracer, Symbolics
 
     const N = 32
     const xyd_brusselator = range(0, stop = 1, length = N)
@@ -46,20 +46,26 @@
     sol = solve(prob_brusselator_2d, NewtonRaphson(); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
-    sol = solve(prob_brusselator_2d,
-        NewtonRaphson(autodiff = AutoSparse(AutoForwardDiff())); abstol = 1e-8)
+    prob_brusselator_2d_sparse = NonlinearProblem(
+        NonlinearFunction(brusselator_2d_loop; sparsity = TracerSparsityDetector()),
+        u0, p)
+    sol = solve(prob_brusselator_2d_sparse, NewtonRaphson(); abstol = 1e-8)
+    @test norm(sol.resid, Inf) < 1e-8
+
+    prob_brusselator_2d_sparse = NonlinearProblem(
+        NonlinearFunction(brusselator_2d_loop; sparsity = SymbolicsSparsityDetector()),
+        u0, p)
+    sol = solve(prob_brusselator_2d_sparse, NewtonRaphson(); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
+    # Deprecated
     sol = solve(prob_brusselator_2d,
         NewtonRaphson(autodiff = AutoSparse(AutoFiniteDiff())); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
     du0 = copy(u0)
-    jac_sparsity = Symbolics.jacobian_sparsity(
+    jac_prototype = Symbolics.jacobian_sparsity(
         (du, u) -> brusselator_2d_loop(du, u, p), du0, u0)
-    jac_prototype = float.(jac_sparsity)
-    fill!(jac_prototype, 0)
-    @test all(iszero, jac_prototype)
 
     ff_iip = NonlinearFunction(brusselator_2d_loop; jac_prototype)
     prob_brusselator_2d = NonlinearProblem(ff_iip, u0, p)
@@ -68,11 +74,6 @@
     @test norm(sol.resid, Inf) < 1e-8
 
     sol = solve(prob_brusselator_2d,
-        NewtonRaphson(autodiff = AutoSparse(AutoFiniteDiff())); abstol = 1e-8)
+        NewtonRaphson(autodiff = AutoFiniteDiff()); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
-
-    cache = init(
-        prob_brusselator_2d, NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff())))
-    @test maximum(cache.jac_cache.sdifft_extras.coloring.colorvec) == 12
-    @test cache.jac_cache.autodiff isa AutoSparse{<:AutoForwardDiff}
 end

From c0e5d726fad8e40d510da90e751139713fb9f5e0 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 1 Oct 2024 17:17:36 -0400
Subject: [PATCH 509/700] chore: apply suggestions from code review

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 docs/src/basics/sparsity_detection.md |  4 ++--
 docs/src/tutorials/large_systems.md   | 22 +++++++++++-----------
 2 files changed, 13 insertions(+), 13 deletions(-)

diff --git a/docs/src/basics/sparsity_detection.md b/docs/src/basics/sparsity_detection.md
index 5124a0009..2744d74d3 100644
--- a/docs/src/basics/sparsity_detection.md
+++ b/docs/src/basics/sparsity_detection.md
@@ -34,7 +34,7 @@ If the `colorvec` is not provided, then it is computed on demand.
     row colorvec.
 
 !!! warning
-
+    
     Previously you could provide a `sparsity` argument to `NonlinearFunction` to specify
     the jacobian prototype. However, to avoid confusion, this is now deprecated. Instead,
     use the `jac_prototype` argument.
@@ -58,7 +58,7 @@ sparsity detection algorithms.
 ## Case III: Sparse AD Type is being Used
 
 !!! warning
-
+    
     This is now deprecated. Please use the previous two cases instead.
 
 If you constructed a Nonlinear Solver with a sparse AD type, for example
diff --git a/docs/src/tutorials/large_systems.md b/docs/src/tutorials/large_systems.md
index 8ed6ca169..4955f9084 100644
--- a/docs/src/tutorials/large_systems.md
+++ b/docs/src/tutorials/large_systems.md
@@ -2,15 +2,15 @@
 
 This tutorial is for getting into the extra features of using NonlinearSolve.jl. Solving
 ill-conditioned nonlinear systems requires specializing the linear solver on properties of
-the Jacobian in order to cut down on the `\mathcal{O}(n^3)` linear solve and the
-`\mathcal{O}(n^2)` back-solves. This tutorial is designed to explain the advanced usage of
+the Jacobian in order to cut down on the ``\mathcal{O}(n^3)`` linear solve and the
+``\mathcal{O}(n^2)`` back-solves. This tutorial is designed to explain the advanced usage of
 NonlinearSolve.jl by solving the steady state stiff Brusselator partial differential
 equation (BRUSS) using NonlinearSolve.jl.
 
 ## Definition of the Brusselator Equation
 
 !!! note
-
+    
     Feel free to skip this section: it simply defines the example problem.
 
 The Brusselator PDE is defined as follows:
@@ -117,11 +117,11 @@ However, if you know the sparsity of your problem, then you can pass a different
 type. For example, a `SparseMatrixCSC` will give a sparse matrix. Other sparse matrix types
 include:
 
-- Bidiagonal
-- Tridiagonal
-- SymTridiagonal
-- BandedMatrix ([BandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BandedMatrices.jl))
-- BlockBandedMatrix ([BlockBandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BlockBandedMatrices.jl))
+  - Bidiagonal
+  - Tridiagonal
+  - SymTridiagonal
+  - BandedMatrix ([BandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BandedMatrices.jl))
+  - BlockBandedMatrix ([BlockBandedMatrices.jl](https://github.com/JuliaLinearAlgebra/BlockBandedMatrices.jl))
 
 ## Approximate Sparsity Detection & Sparse Jacobians
 
@@ -167,7 +167,7 @@ and `u` and call `jacobian_sparsity` on our function with the example arguments,
 kick out a sparse matrix with our pattern, that we can turn into our `jac_prototype`.
 
 !!! tip
-
+    
     Alternatively you can use the `SparseConnectivityTracer.jl` package to automatically
     generate a sparse Jacobian.
 
@@ -224,7 +224,7 @@ choices, see the
 `linsolve` choices are any valid [LinearSolve.jl](https://linearsolve.sciml.ai/dev/) solver.
 
 !!! note
-
+    
     Switching to a Krylov linear solver will automatically change the nonlinear problem
     solver into Jacobian-free mode, dramatically reducing the memory required. This can be
     overridden by adding `concrete_jac=true` to the algorithm.
@@ -330,7 +330,7 @@ prob_brusselator_2d_exact_tracer = NonlinearProblem(
     u0, p; abstol = 1e-10, reltol = 1e-10)
 prob_brusselator_2d_approx_di = NonlinearProblem(
     NonlinearFunction(brusselator_2d_loop;
-        sparsity = DenseSparsityDetector(AutoForwardDiff(); atol=1e-4)),
+        sparsity = DenseSparsityDetector(AutoForwardDiff(); atol = 1e-4)),
     u0, p; abstol = 1e-10, reltol = 1e-10)
 
 @btime solve(prob_brusselator_2d_exact_symbolics, NewtonRaphson());

From 3f21ce20bc05cb190baf8a007a231f811444d0ac Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 1 Oct 2024 19:03:12 -0400
Subject: [PATCH 510/700] chore: apply suggestions from code review

---
 docs/src/basics/sparsity_detection.md | 9 +++++----
 src/NonlinearSolve.jl                 | 3 ++-
 src/internal/jacobian.jl              | 8 ++++----
 3 files changed, 11 insertions(+), 9 deletions(-)

diff --git a/docs/src/basics/sparsity_detection.md b/docs/src/basics/sparsity_detection.md
index 2744d74d3..241399d99 100644
--- a/docs/src/basics/sparsity_detection.md
+++ b/docs/src/basics/sparsity_detection.md
@@ -37,7 +37,8 @@ If the `colorvec` is not provided, then it is computed on demand.
     
     Previously you could provide a `sparsity` argument to `NonlinearFunction` to specify
     the jacobian prototype. However, to avoid confusion, this is now deprecated. Instead,
-    use the `jac_prototype` argument.
+    use the `jac_prototype` argument. `sparsity` must be used to exclusively specify the
+    sparsity detection algorithm.
 
 ## Case II: Sparsity Detection algorithm is provided
 
@@ -46,14 +47,14 @@ algorithm you want to use, then you can create your problem as follows:
 
 ```julia
 prob = NonlinearProblem(
-    NonlinearFunction(nlfunc; sparsity = SymbolicsSparsityDetection()), x0)  # Remember to have Symbolics.jl loaded
+    NonlinearFunction(nlfunc; sparsity = SymbolicsSparsityDetector()), x0)  # Remember to have Symbolics.jl loaded
 # OR
 prob = NonlinearProblem(
     NonlinearFunction(nlfunc; sparsity = TracerSparsityDetector()), x0) # From SparseConnectivityTracer.jl
 ```
 
-Refer to the documentation of DifferentiationInterface.jl for more information on
-sparsity detection algorithms.
+Refer to the documentation of DifferentiationInterface.jl and SparseConnectivityTracer.jl
+for more information on sparsity detection algorithms.
 
 ## Case III: Sparse AD Type is being Used
 
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 2db06f9b0..575c4cc1c 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -57,7 +57,8 @@ using SparseConnectivityTracer: TracerSparsityDetector # This can be dropped in
 using SparseDiffTools: SparseDiffTools, JacPrototypeSparsityDetection,
                        PrecomputedJacobianColorvec, init_jacobian, sparse_jacobian,
                        sparse_jacobian!, sparse_jacobian_cache
-using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm
+using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm,
+                             LargestFirst
 
 @reexport using SciMLBase, SimpleNonlinearSolve
 
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 0bf7e4380..f8264c79a 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -64,7 +64,7 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
     if !has_analytic_jac && needs_jac
         autodiff = construct_concrete_adtype(f, autodiff)
         using_sparsedifftools = autodiff isa StructuredMatrixAutodiff
-        # DI can't handle structured matrices
+        # SparseMatrixColorings can't handle structured matrices
         if using_sparsedifftools
             di_extras = nothing
             uf = JacobianWrapper{iip}(f, p)
@@ -249,7 +249,7 @@ function construct_concrete_adtype(f::NonlinearFunction, ad::AbstractADType)
             return AutoSparse(
                 ad;
                 sparsity_detector,
-                coloring_algorithm = GreedyColoringAlgorithm()
+                coloring_algorithm = GreedyColoringAlgorithm(LargestFirst())
             )
         else
             if ArrayInterface.isstructured(f.jac_prototype)
@@ -304,7 +304,7 @@ function select_fastest_structured_matrix_autodiff(
             JacPrototypeSparsityDetection(; jac_prototype = prototype)
         end
     end
-    return StructuredMatrixAutodiff(ad, sparsity_detection)
+    return StructuredMatrixAutodiff(AutoSparse(ad), sparsity_detection)
 end
 
 function select_fastest_coloring_algorithm(
@@ -314,7 +314,7 @@ function select_fastest_coloring_algorithm(
             ADTypes.mode(ad) isa ADTypes.ReverseMode, :row, :column)}(
             prototype, f.colorvec)
     end
-    return GreedyColoringAlgorithm()
+    return GreedyColoringAlgorithm(LargestFirst())
 end
 
 function construct_concrete_adtype(f::NonlinearFunction, ad::AutoSparse)

From 43df907989a67b707e433753b09ef3bcd3d08a4c Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 2 Oct 2024 10:46:33 -0400
Subject: [PATCH 511/700] test: structured jacobians

---
 test/misc/structured_jacobian_tests.jl | 67 ++++++++++++++++++++++++++
 1 file changed, 67 insertions(+)
 create mode 100644 test/misc/structured_jacobian_tests.jl

diff --git a/test/misc/structured_jacobian_tests.jl b/test/misc/structured_jacobian_tests.jl
new file mode 100644
index 000000000..41b316911
--- /dev/null
+++ b/test/misc/structured_jacobian_tests.jl
@@ -0,0 +1,67 @@
+@testitem "Structured Jacobians" tags=[:misc] begin
+    using NonlinearSolve, SparseConnectivityTracer, BandedMatrices, LinearAlgebra,
+          SparseArrays
+
+    N = 16
+    p = rand(N)
+    u0 = rand(N)
+
+    function f!(du, u, p)
+        for i in 2:(length(u) - 1)
+            du[i] = u[i - 1] - 2u[i] + u[i + 1] + p[i]
+        end
+        du[1] = -2u[1] + u[2] + p[1]
+        du[end] = u[end - 1] - 2u[end] + p[end]
+        return nothing
+    end
+
+    function f(u, p)
+        du = similar(u, promote_type(eltype(u), eltype(p)))
+        f!(du, u, p)
+        return du
+    end
+
+    for nlf in (f, f!)
+        @testset "Dense AD" begin
+            nlprob = NonlinearProblem(NonlinearFunction(nlf), u0, p)
+
+            cache = init(nlprob, NewtonRaphson(); abstol = 1e-9)
+            @test cache.jac_cache.J isa Matrix
+            sol = solve!(cache)
+            @test SciMLBase.successful_retcode(sol)
+        end
+
+        @testset "Unstructured Sparse AD" begin
+            nlprob_autosparse = NonlinearProblem(
+                NonlinearFunction(nlf; sparsity = TracerSparsityDetector()),
+                u0, p)
+
+            cache = init(nlprob_autosparse, NewtonRaphson(); abstol = 1e-9)
+            @test cache.jac_cache.J isa SparseMatrixCSC
+            sol = solve!(cache)
+            @test SciMLBase.successful_retcode(sol)
+        end
+
+        @testset "Structured Sparse AD: Banded Jacobian" begin
+            jac_prototype = BandedMatrix(-1 => ones(N - 1), 0 => ones(N), 1 => ones(N - 1))
+            nlprob_sparse_structured = NonlinearProblem(
+                NonlinearFunction(nlf; jac_prototype), u0, p)
+
+            cache = init(nlprob_sparse_structured, NewtonRaphson(); abstol = 1e-9)
+            @test cache.jac_cache.J isa BandedMatrix
+            sol = solve!(cache)
+            @test SciMLBase.successful_retcode(sol)
+        end
+
+        @testset "Structured Sparse AD: Tridiagonal Jacobian" begin
+            jac_prototype = Tridiagonal(ones(N - 1), ones(N), ones(N - 1))
+            nlprob_sparse_structured = NonlinearProblem(
+                NonlinearFunction(nlf; jac_prototype), u0, p)
+
+            cache = init(nlprob_sparse_structured, NewtonRaphson(); abstol = 1e-9)
+            @test cache.jac_cache.J isa Tridiagonal
+            sol = solve!(cache)
+            @test SciMLBase.successful_retcode(sol)
+        end
+    end
+end

From eda2977403e0af288e3659c393c891fbdc4a3469 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 2 Oct 2024 12:17:49 -0400
Subject: [PATCH 512/700] feat: using DI for structured Jacobians

---
 Project.toml             |   4 +-
 src/NonlinearSolve.jl    |   3 -
 src/internal/jacobian.jl | 118 +++++++--------------------------------
 3 files changed, 22 insertions(+), 103 deletions(-)

diff --git a/Project.toml b/Project.toml
index 7d8f1f907..0f77d7966 100644
--- a/Project.toml
+++ b/Project.toml
@@ -30,7 +30,6 @@ Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
-SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
 SparseMatrixColorings = "0a514795-09f3-496d-8182-132a7b665d35"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
@@ -146,6 +145,7 @@ Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
+SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
 SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
@@ -155,4 +155,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SparseDiffTools", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 575c4cc1c..ab5e31afc 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -54,9 +54,6 @@ using SciMLJacobianOperators: AbstractJacobianOperator, JacobianOperator, VecJac
 ## Sparse AD Support
 using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
 using SparseConnectivityTracer: TracerSparsityDetector # This can be dropped in the next release
-using SparseDiffTools: SparseDiffTools, JacPrototypeSparsityDetection,
-                       PrecomputedJacobianColorvec, init_jacobian, sparse_jacobian,
-                       sparse_jacobian!, sparse_jacobian_cache
 using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm,
                              LargestFirst
 
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index f8264c79a..c152fc749 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -37,7 +37,6 @@ Construct a cache for the Jacobian of `f` w.r.t. `u`.
     stats::NLStats
     autodiff
     di_extras
-    sdifft_extras
 end
 
 function reinit_cache!(cache::JacobianCache{iip}, args...; p = cache.p,
@@ -63,31 +62,13 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
 
     if !has_analytic_jac && needs_jac
         autodiff = construct_concrete_adtype(f, autodiff)
-        using_sparsedifftools = autodiff isa StructuredMatrixAutodiff
-        # SparseMatrixColorings can't handle structured matrices
-        if using_sparsedifftools
-            di_extras = nothing
-            uf = JacobianWrapper{iip}(f, p)
-            sdifft_extras = if iip
-                sparse_jacobian_cache(
-                    autodiff.autodiff, autodiff.sparsity_detection, uf, fu, u)
-            else
-                sparse_jacobian_cache(autodiff.autodiff, autodiff.sparsity_detection,
-                    uf, __maybe_mutable(u, autodiff); fx = fu)
-            end
-            autodiff = autodiff.autodiff # For saving we unwrap
+        di_extras = if iip
+            DI.prepare_jacobian(f, fu, autodiff, u, Constant(prob.p))
         else
-            sdifft_extras = nothing
-            di_extras = if iip
-                DI.prepare_jacobian(f, fu, autodiff, u, Constant(prob.p))
-            else
-                DI.prepare_jacobian(f, autodiff, u, Constant(prob.p))
-            end
+            DI.prepare_jacobian(f, autodiff, u, Constant(prob.p))
         end
     else
-        using_sparsedifftools = false
         di_extras = nothing
-        sdifft_extras = nothing
     end
 
     J = if !needs_jac
@@ -98,22 +79,18 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
         JacobianOperator(prob, fu, u; jvp_autodiff, vjp_autodiff)
     else
         if f.jac_prototype === nothing
-            if !using_sparsedifftools
-                # While this is technically wasteful, it gives out the type of the Jacobian
-                # which is needed to create the linear solver cache
-                stats.njacs += 1
-                if has_analytic_jac
-                    __similar(
-                        fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u))
+            # While this is technically wasteful, it gives out the type of the Jacobian
+            # which is needed to create the linear solver cache
+            stats.njacs += 1
+            if has_analytic_jac
+                __similar(
+                    fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u))
+            else
+                if iip
+                    DI.jacobian(f, fu, di_extras, autodiff, u, Constant(p))
                 else
-                    if iip
-                        DI.jacobian(f, fu, di_extras, autodiff, u, Constant(p))
-                    else
-                        DI.jacobian(f, autodiff, u, Constant(p))
-                    end
+                    DI.jacobian(f, autodiff, u, Constant(p))
                 end
-            else
-                zero(init_jacobian(sdifft_extras; preserve_immutable = Val(true)))
             end
         else
             jac_proto = if eltype(f.jac_prototype) <: Bool
@@ -126,20 +103,19 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
         end
     end
 
-    return JacobianCache{iip}(
-        J, f, fu, u, p, stats, autodiff, di_extras, sdifft_extras)
+    return JacobianCache{iip}(J, f, fu, u, p, stats, autodiff, di_extras)
 end
 
 function JacobianCache(prob, alg, f::F, ::Number, u::Number, p; stats,
         autodiff = nothing, kwargs...) where {F}
     fu = f(u, p)
     if SciMLBase.has_jac(f) || SciMLBase.has_vjp(f) || SciMLBase.has_jvp(f)
-        return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, nothing, nothing)
+        return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, nothing)
     end
     autodiff = get_dense_ad(get_concrete_forward_ad(
         autodiff, prob; check_forward_mode = false))
     di_extras = DI.prepare_derivative(f, get_dense_ad(autodiff), u, Constant(prob.p))
-    return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, di_extras, nothing)
+    return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, di_extras)
 end
 
 (cache::JacobianCache)(u = cache.u) = cache(cache.J, u, cache.p)
@@ -172,27 +148,16 @@ function (cache::JacobianCache{iip})(
     if iip
         if SciMLBase.has_jac(cache.f)
             cache.f.jac(J, u, p)
-        elseif cache.di_extras !== nothing
+        else
             DI.jacobian!(
                 cache.f, cache.fu, J, cache.di_extras, cache.autodiff, u, Constant(p))
-        else
-            uf = JacobianWrapper{iip}(cache.f, p)
-            sparse_jacobian!(J, cache.autodiff, cache.sdifft_extras, uf, cache.fu, u)
         end
         return J
     else
         if SciMLBase.has_jac(cache.f)
             return cache.f.jac(u, p)
-        elseif cache.di_extras !== nothing
-            return DI.jacobian(cache.f, cache.di_extras, cache.autodiff, u, Constant(p))
         else
-            uf = JacobianWrapper{iip}(cache.f, p)
-            if __can_setindex(typeof(J))
-                sparse_jacobian!(J, cache.autodiff, cache.sdifft_extras, uf, u)
-                return J
-            else
-                return sparse_jacobian(cache.autodiff, cache.sdifft_extras, uf, u)
-            end
+            return DI.jacobian(cache.f, cache.di_extras, cache.autodiff, u, Constant(p))
         end
     end
 end
@@ -207,10 +172,6 @@ function construct_concrete_adtype(f::NonlinearFunction, ad::AbstractADType)
             end
             return ad # No sparse AD
         else
-            if ArrayInterface.isstructured(f.jac_prototype)
-                return select_fastest_structured_matrix_autodiff(f.jac_prototype, f, ad)
-            end
-
             return AutoSparse(
                 ad;
                 sparsity_detector = KnownJacobianSparsityDetector(f.jac_prototype),
@@ -227,10 +188,6 @@ function construct_concrete_adtype(f::NonlinearFunction, ad::AbstractADType)
             Base.depwarn("`sparsity::typeof($(typeof(f.sparsity)))` is deprecated. \
                           Pass it as `jac_prototype` instead.",
                 :NonlinearSolve)
-            if ArrayInterface.isstructured(f.sparsity)
-                return select_fastest_structured_matrix_autodiff(f.sparsity, f, ad)
-            end
-
             return AutoSparse(
                 ad;
                 sparsity_detector = KnownJacobianSparsityDetector(f.sparsity),
@@ -252,11 +209,8 @@ function construct_concrete_adtype(f::NonlinearFunction, ad::AbstractADType)
                 coloring_algorithm = GreedyColoringAlgorithm(LargestFirst())
             )
         else
-            if ArrayInterface.isstructured(f.jac_prototype)
-                return select_fastest_structured_matrix_autodiff(f.jac_prototype, f, ad)
-            end
-
-            if f.jac_prototype isa AbstractSparseMatrix
+            if f.jac_prototype isa AbstractSparseMatrix ||
+               ArrayInterface.isstructured(f.jac_prototype)
                 if !(sparsity_detector isa NoSparsityDetector)
                     @warn "`jac_prototype` is a sparse matrix but sparsity = $(f.sparsity) \
                            has also been specified. Ignoring sparsity field and using \
@@ -275,38 +229,6 @@ function construct_concrete_adtype(f::NonlinearFunction, ad::AbstractADType)
     end
 end
 
-@concrete struct StructuredMatrixAutodiff <: AbstractADType
-    autodiff <: AbstractADType
-    sparsity_detection
-end
-
-function select_fastest_structured_matrix_autodiff(
-        prototype::AbstractMatrix, f::NonlinearFunction, ad::AbstractADType)
-    sparsity_detection = if SciMLBase.has_colorvec(f)
-        PrecomputedJacobianColorvec(;
-            jac_prototype = prototype,
-            f.colorvec,
-            partition_by_rows = ADTypes.mode(ad) isa ADTypes.ReverseMode
-        )
-    else
-        if ArrayInterface.fast_matrix_colors(prototype)
-            colorvec = if ADTypes.mode(ad) isa ADTypes.ForwardMode
-                ArrayInterface.matrix_colors(prototype)
-            else
-                ArrayInterface.matrix_colors(prototype')
-            end
-            PrecomputedJacobianColorvec(;
-                jac_prototype = prototype,
-                colorvec,
-                partition_by_rows = ADTypes.mode(ad) isa ADTypes.ReverseMode
-            )
-        else
-            JacPrototypeSparsityDetection(; jac_prototype = prototype)
-        end
-    end
-    return StructuredMatrixAutodiff(AutoSparse(ad), sparsity_detection)
-end
-
 function select_fastest_coloring_algorithm(
         prototype, f::NonlinearFunction, ad::AbstractADType)
     if SciMLBase.has_colorvec(f)

From 435aecb66016359412991149830138830ff2839a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 2 Oct 2024 12:51:55 -0400
Subject: [PATCH 513/700] docs: add a table to guarantee selections

---
 docs/src/basics/sparsity_detection.md | 39 ++++++++++++++++++++-------
 src/internal/jacobian.jl              | 28 +++++++++++++------
 2 files changed, 50 insertions(+), 17 deletions(-)

diff --git a/docs/src/basics/sparsity_detection.md b/docs/src/basics/sparsity_detection.md
index 241399d99..fc03528ac 100644
--- a/docs/src/basics/sparsity_detection.md
+++ b/docs/src/basics/sparsity_detection.md
@@ -6,6 +6,34 @@ to use this in an actual problem, see
 
 Notation wise we are trying to solve for `x` such that `nlfunc(x) = 0`.
 
+## Big Table for Determining Sparsity Detection and Coloring Algorithms
+
+| `f.sparsity`               | `f.jac_prototype` | `f.colorvec` | Sparsity Detection                               | Coloring Algorithm                        |
+| :------------------------- | :---------------- | :----------- | :----------------------------------------------- | :---------------------------------------- |
+| ❌                         | ❌                | `Any`        | `NoSparsityDetector()`                           | `NoColoringAlgorithm()`                   |
+| ❌                         | Not Structured    | `Any`        | `NoSparsityDetector()`                           | `NoColoringAlgorithm()`                   |
+| ❌                         | Structured        | ✅           | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
+| ❌                         | Structured        | ❌           | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
+| -                          | -                 | -            | -                                                | -                                         |
+| `AbstractMatrix`           | ❌                | ✅           | `KnownJacobianSparsityDetector(f.sparsity)`      | `ConstantColoringAlgorithm(f.colorvec)`   |
+| `AbstractMatrix`           | ❌                | ❌           | `KnownJacobianSparsityDetector(f.sparsity)`      | `GreedyColoringAlgorithm(LargestFirst())` |
+| `AbstractMatrix`           | Not Structured    | ✅           | `KnownJacobianSparsityDetector(f.sparsity)`      | `ConstantColoringAlgorithm(f.colorvec)`   |
+| `AbstractMatrix`           | Not Structured    | ❌           | `KnownJacobianSparsityDetector(f.sparsity)`      | `GreedyColoringAlgorithm(LargestFirst())` |
+| `AbstractMatrix`           | Structured        | `Any`        | 🔴                                               | 🔴                                        |
+| -                          | -                 | -            | -                                                | -                                         |
+| `AbstractSparsityDetector` | ❌                | `Any`        | `f.sparsity`                                     | `GreedyColoringAlgorithm(LargestFirst())` |
+| `AbstractSparsityDetector` | Not Structured    | ✅           | `f.sparsity`                                     | `ConstantColoringAlgorithm(f.colorvec)`   |
+| `AbstractSparsityDetector` | Not Structured    | ❌           | `f.sparsity`                                     | `GreedyColoringAlgorithm(LargestFirst())` |
+| `AbstractSparsityDetector` | Structured        | ✅           | `KnownJacobianSparsityDetector(f.jac_prototype)` | `ConstantColoringAlgorithm(f.colorvec)`   |
+| `AbstractSparsityDetector` | Structured        | ❌           | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
+
+1. `Structured` means either a `AbstractSparseMatrix` or `ArrayInterface.isstructured(x)` is true.
+2. ❌ means not provided (default)
+3. ✅ means provided
+4. 🔴 means an error will be thrown
+5. Providing a colorvec without specifying either sparsity or jac_prototype with a sparse or structured matrix will cause us to ignore the colorvec.
+6. The function calls demonstrated above are simply pseudo-code to show the general idea.
+
 ## Case I: Sparse Jacobian Prototype is Provided
 
 Let's say you have a Sparse Jacobian Prototype `jac_prototype`, in this case you can
@@ -27,19 +55,12 @@ prob = NonlinearProblem(
 If the `colorvec` is not provided, then it is computed on demand.
 
 !!! note
-    
+
     One thing to be careful about in this case is that `colorvec` is dependent on the
     autodiff backend used. `ADTypes.mode(ad) isa ADTypes.ForwardMode` will assume that the
     colorvec is the column colorvec, otherwise we will assume that the colorvec is the
     row colorvec.
 
-!!! warning
-    
-    Previously you could provide a `sparsity` argument to `NonlinearFunction` to specify
-    the jacobian prototype. However, to avoid confusion, this is now deprecated. Instead,
-    use the `jac_prototype` argument. `sparsity` must be used to exclusively specify the
-    sparsity detection algorithm.
-
 ## Case II: Sparsity Detection algorithm is provided
 
 If you don't have a Sparse Jacobian Prototype, but you know the which sparsity detection
@@ -59,7 +80,7 @@ for more information on sparsity detection algorithms.
 ## Case III: Sparse AD Type is being Used
 
 !!! warning
-    
+
     This is now deprecated. Please use the previous two cases instead.
 
 If you constructed a Nonlinear Solver with a sparse AD type, for example
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index c152fc749..93d10f98b 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -172,6 +172,13 @@ function construct_concrete_adtype(f::NonlinearFunction, ad::AbstractADType)
             end
             return ad # No sparse AD
         else
+            if !sparse_or_structured_prototype(f.jac_prototype)
+                if SciMLBase.has_colorvec(f)
+                    @warn "`colorvec` is provided but `jac_prototype` is not a sparse \
+                           or structured matrix. `colorvec` will be ignored."
+                end
+                return ad
+            end
             return AutoSparse(
                 ad;
                 sparsity_detector = KnownJacobianSparsityDetector(f.jac_prototype),
@@ -181,13 +188,14 @@ function construct_concrete_adtype(f::NonlinearFunction, ad::AbstractADType)
         end
     else
         if f.sparsity isa AbstractMatrix
-            if f.jac_prototype !== nothing && f.jac_prototype !== f.sparsity
-                throw(ArgumentError("`sparsity::AbstractMatrix` and `jac_prototype` cannot \
-                                     be both provided. Pass only `jac_prototype`."))
+            if f.jac_prototype !== f.sparsity
+                if f.jac_prototype !== nothing &&
+                   sparse_or_structured_prototype(f.jac_prototype)
+                    throw(ArgumentError("`sparsity::AbstractMatrix` and a sparse or \
+                                         structured `jac_prototype` cannot be both \
+                                         provided. Pass only `jac_prototype`."))
+                end
             end
-            Base.depwarn("`sparsity::typeof($(typeof(f.sparsity)))` is deprecated. \
-                          Pass it as `jac_prototype` instead.",
-                :NonlinearSolve)
             return AutoSparse(
                 ad;
                 sparsity_detector = KnownJacobianSparsityDetector(f.sparsity),
@@ -209,8 +217,7 @@ function construct_concrete_adtype(f::NonlinearFunction, ad::AbstractADType)
                 coloring_algorithm = GreedyColoringAlgorithm(LargestFirst())
             )
         else
-            if f.jac_prototype isa AbstractSparseMatrix ||
-               ArrayInterface.isstructured(f.jac_prototype)
+            if sparse_or_structured_prototype(f.jac_prototype)
                 if !(sparsity_detector isa NoSparsityDetector)
                     @warn "`jac_prototype` is a sparse matrix but sparsity = $(f.sparsity) \
                            has also been specified. Ignoring sparsity field and using \
@@ -254,3 +261,8 @@ end
 
 get_dense_ad(ad) = ad
 get_dense_ad(ad::AutoSparse) = ADTypes.dense_ad(ad)
+
+sparse_or_structured_prototype(::AbstractSparseMatrix) = true
+function sparse_or_structured_prototype(prototype::AbstractMatrix)
+    return ArrayInterface.isstructured(prototype)
+end

From 9a2a38690ae850d1f8ff2d1d8f75e6669a950b00 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 2 Oct 2024 12:54:28 -0400
Subject: [PATCH 514/700] chore: apply suggestions from code review

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 docs/src/basics/sparsity_detection.md | 48 +++++++++++++--------------
 1 file changed, 24 insertions(+), 24 deletions(-)

diff --git a/docs/src/basics/sparsity_detection.md b/docs/src/basics/sparsity_detection.md
index fc03528ac..de924c398 100644
--- a/docs/src/basics/sparsity_detection.md
+++ b/docs/src/basics/sparsity_detection.md
@@ -9,30 +9,30 @@ Notation wise we are trying to solve for `x` such that `nlfunc(x) = 0`.
 ## Big Table for Determining Sparsity Detection and Coloring Algorithms
 
 | `f.sparsity`               | `f.jac_prototype` | `f.colorvec` | Sparsity Detection                               | Coloring Algorithm                        |
-| :------------------------- | :---------------- | :----------- | :----------------------------------------------- | :---------------------------------------- |
-| ❌                         | ❌                | `Any`        | `NoSparsityDetector()`                           | `NoColoringAlgorithm()`                   |
-| ❌                         | Not Structured    | `Any`        | `NoSparsityDetector()`                           | `NoColoringAlgorithm()`                   |
-| ❌                         | Structured        | ✅           | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
-| ❌                         | Structured        | ❌           | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
+|:-------------------------- |:----------------- |:------------ |:------------------------------------------------ |:----------------------------------------- |
+| ❌                          | ❌                 | `Any`        | `NoSparsityDetector()`                           | `NoColoringAlgorithm()`                   |
+| ❌                          | Not Structured    | `Any`        | `NoSparsityDetector()`                           | `NoColoringAlgorithm()`                   |
+| ❌                          | Structured        | ✅            | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
+| ❌                          | Structured        | ❌            | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
 | -                          | -                 | -            | -                                                | -                                         |
-| `AbstractMatrix`           | ❌                | ✅           | `KnownJacobianSparsityDetector(f.sparsity)`      | `ConstantColoringAlgorithm(f.colorvec)`   |
-| `AbstractMatrix`           | ❌                | ❌           | `KnownJacobianSparsityDetector(f.sparsity)`      | `GreedyColoringAlgorithm(LargestFirst())` |
-| `AbstractMatrix`           | Not Structured    | ✅           | `KnownJacobianSparsityDetector(f.sparsity)`      | `ConstantColoringAlgorithm(f.colorvec)`   |
-| `AbstractMatrix`           | Not Structured    | ❌           | `KnownJacobianSparsityDetector(f.sparsity)`      | `GreedyColoringAlgorithm(LargestFirst())` |
-| `AbstractMatrix`           | Structured        | `Any`        | 🔴                                               | 🔴                                        |
+| `AbstractMatrix`           | ❌                 | ✅            | `KnownJacobianSparsityDetector(f.sparsity)`      | `ConstantColoringAlgorithm(f.colorvec)`   |
+| `AbstractMatrix`           | ❌                 | ❌            | `KnownJacobianSparsityDetector(f.sparsity)`      | `GreedyColoringAlgorithm(LargestFirst())` |
+| `AbstractMatrix`           | Not Structured    | ✅            | `KnownJacobianSparsityDetector(f.sparsity)`      | `ConstantColoringAlgorithm(f.colorvec)`   |
+| `AbstractMatrix`           | Not Structured    | ❌            | `KnownJacobianSparsityDetector(f.sparsity)`      | `GreedyColoringAlgorithm(LargestFirst())` |
+| `AbstractMatrix`           | Structured        | `Any`        | 🔴                                                | 🔴                                         |
 | -                          | -                 | -            | -                                                | -                                         |
-| `AbstractSparsityDetector` | ❌                | `Any`        | `f.sparsity`                                     | `GreedyColoringAlgorithm(LargestFirst())` |
-| `AbstractSparsityDetector` | Not Structured    | ✅           | `f.sparsity`                                     | `ConstantColoringAlgorithm(f.colorvec)`   |
-| `AbstractSparsityDetector` | Not Structured    | ❌           | `f.sparsity`                                     | `GreedyColoringAlgorithm(LargestFirst())` |
-| `AbstractSparsityDetector` | Structured        | ✅           | `KnownJacobianSparsityDetector(f.jac_prototype)` | `ConstantColoringAlgorithm(f.colorvec)`   |
-| `AbstractSparsityDetector` | Structured        | ❌           | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
-
-1. `Structured` means either a `AbstractSparseMatrix` or `ArrayInterface.isstructured(x)` is true.
-2. ❌ means not provided (default)
-3. ✅ means provided
-4. 🔴 means an error will be thrown
-5. Providing a colorvec without specifying either sparsity or jac_prototype with a sparse or structured matrix will cause us to ignore the colorvec.
-6. The function calls demonstrated above are simply pseudo-code to show the general idea.
+| `AbstractSparsityDetector` | ❌                 | `Any`        | `f.sparsity`                                     | `GreedyColoringAlgorithm(LargestFirst())` |
+| `AbstractSparsityDetector` | Not Structured    | ✅            | `f.sparsity`                                     | `ConstantColoringAlgorithm(f.colorvec)`   |
+| `AbstractSparsityDetector` | Not Structured    | ❌            | `f.sparsity`                                     | `GreedyColoringAlgorithm(LargestFirst())` |
+| `AbstractSparsityDetector` | Structured        | ✅            | `KnownJacobianSparsityDetector(f.jac_prototype)` | `ConstantColoringAlgorithm(f.colorvec)`   |
+| `AbstractSparsityDetector` | Structured        | ❌            | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
+
+ 1. `Structured` means either a `AbstractSparseMatrix` or `ArrayInterface.isstructured(x)` is true.
+ 2. ❌ means not provided (default)
+ 3. ✅ means provided
+ 4. 🔴 means an error will be thrown
+ 5. Providing a colorvec without specifying either sparsity or jac_prototype with a sparse or structured matrix will cause us to ignore the colorvec.
+ 6. The function calls demonstrated above are simply pseudo-code to show the general idea.
 
 ## Case I: Sparse Jacobian Prototype is Provided
 
@@ -55,7 +55,7 @@ prob = NonlinearProblem(
 If the `colorvec` is not provided, then it is computed on demand.
 
 !!! note
-
+    
     One thing to be careful about in this case is that `colorvec` is dependent on the
     autodiff backend used. `ADTypes.mode(ad) isa ADTypes.ForwardMode` will assume that the
     colorvec is the column colorvec, otherwise we will assume that the colorvec is the
@@ -80,7 +80,7 @@ for more information on sparsity detection algorithms.
 ## Case III: Sparse AD Type is being Used
 
 !!! warning
-
+    
     This is now deprecated. Please use the previous two cases instead.
 
 If you constructed a Nonlinear Solver with a sparse AD type, for example

From 0db543b95fea9472261bfdad7540f6ddc4478c17 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 2 Oct 2024 13:16:14 -0400
Subject: [PATCH 515/700] fix: remove stale load

---
 src/NonlinearSolve.jl | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index ab5e31afc..d4f0898e1 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -30,8 +30,7 @@ using MaybeInplace: @bb
 using Printf: @printf
 using Preferences: Preferences, @load_preference, @set_preferences!
 using RecursiveArrayTools: recursivecopy!
-using SciMLBase: AbstractNonlinearAlgorithm, JacobianWrapper, AbstractNonlinearProblem,
-                 _unwrap_val, isinplace, NLStats
+using SciMLBase: AbstractNonlinearAlgorithm, AbstractNonlinearProblem, _unwrap_val, isinplace, NLStats
 using SciMLOperators: AbstractSciMLOperator
 using Setfield: @set!
 using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix

From 6713e5912ffd5a7cc63dc3098e395dc26e34aa9f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 2 Oct 2024 13:19:33 -0400
Subject: [PATCH 516/700] chore: apply formatting suggestion

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 src/NonlinearSolve.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index d4f0898e1..4d78e2195 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -30,7 +30,8 @@ using MaybeInplace: @bb
 using Printf: @printf
 using Preferences: Preferences, @load_preference, @set_preferences!
 using RecursiveArrayTools: recursivecopy!
-using SciMLBase: AbstractNonlinearAlgorithm, AbstractNonlinearProblem, _unwrap_val, isinplace, NLStats
+using SciMLBase: AbstractNonlinearAlgorithm, AbstractNonlinearProblem, _unwrap_val,
+                 isinplace, NLStats
 using SciMLOperators: AbstractSciMLOperator
 using Setfield: @set!
 using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix

From 9490b6d4b4bce92abb7e85c045aa5fd790518483 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 3 Oct 2024 09:37:00 -0400
Subject: [PATCH 517/700] docs: remove Symbolics and SparseDiffTools

---
 docs/Project.toml                   |  6 +--
 docs/make.jl                        |  6 ++-
 docs/src/basics/autodiff.md         | 66 +++++++++--------------------
 docs/src/tutorials/large_systems.md | 19 ++++-----
 test/misc/qa_tests.jl               |  2 +-
 5 files changed, 35 insertions(+), 64 deletions(-)

diff --git a/docs/Project.toml b/docs/Project.toml
index 48d18ffa9..30a7f5035 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,4 +1,5 @@
 [deps]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 AlgebraicMultigrid = "2169fc97-5a83-5252-b627-83903c6c433c"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
@@ -18,13 +19,12 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
 SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
-SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 SteadyStateDiffEq = "9672c7b4-1e72-59bd-8a11-6ac3964bc41f"
 Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"
-Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 
 [compat]
+ADTypes = "1.9.0"
 AlgebraicMultigrid = "0.5, 0.6"
 ArrayInterface = "6, 7"
 BenchmarkTools = "1"
@@ -44,8 +44,6 @@ SciMLBase = "2.4"
 SciMLJacobianOperators = "0.1"
 SimpleNonlinearSolve = "1"
 SparseConnectivityTracer = "0.6.5"
-SparseDiffTools = "2.14"
 StaticArrays = "1"
 SteadyStateDiffEq = "2"
 Sundials = "4.11"
-Symbolics = "4, 5, 6"
diff --git a/docs/make.jl b/docs/make.jl
index e11a04149..88381a5b6 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -12,6 +12,10 @@ include("pages.jl")
 
 bib = CitationBibliography(joinpath(@__DIR__, "src", "refs.bib"))
 
+interlinks = InterLinks(
+    "ADTypes" => "https://sciml.github.io/ADTypes.jl/stable/",
+)
+
 makedocs(; sitename = "NonlinearSolve.jl",
     authors = "Chris Rackauckas",
     modules = [NonlinearSolve, SimpleNonlinearSolve, SteadyStateDiffEq,
@@ -23,7 +27,7 @@ makedocs(; sitename = "NonlinearSolve.jl",
         "https://link.springer.com/article/10.1007/s40096-020-00339-4"],
     checkdocs = :exports,
     warnonly = [:missing_docs],
-    plugins = [bib],
+    plugins = [bib, interlinks],
     format = Documenter.HTML(assets = ["assets/favicon.ico", "assets/citations.css"],
         canonical = "https://docs.sciml.ai/NonlinearSolve/stable/"),
     pages)
diff --git a/docs/src/basics/autodiff.md b/docs/src/basics/autodiff.md
index baa605363..46bc0c576 100644
--- a/docs/src/basics/autodiff.md
+++ b/docs/src/basics/autodiff.md
@@ -1,60 +1,32 @@
 # Automatic Differentiation Backends
 
+!!! note
+
+    We support all backends supported by DifferentiationInterface.jl. Please refer to
+    the [backends page](https://gdalle.github.io/DifferentiationInterface.jl/DifferentiationInterface/stable/explanation/backends/)
+    for more information.
+
 ## Summary of Finite Differencing Backends
 
-  - [`AutoFiniteDiff`](@ref): Finite differencing, not optimal but always applicable.
+  - [`AutoFiniteDiff`](@extref ADTypes): Finite differencing using `FiniteDiff.jl`, not
+    optimal but always applicable.
+  - [`AutoFiniteDifferences`](@extref ADTypes): Finite differencing using
+    `FiniteDifferences.jl`, not optimal but always applicable.
 
 ## Summary of Forward Mode AD Backends
 
-  - [`AutoForwardDiff`](@ref): The best choice for dense problems.
-  - [`AutoPolyesterForwardDiff`](@ref): Might be faster than [`AutoForwardDiff`](@ref) for
-    large problems. Requires `PolyesterForwardDiff.jl` to be installed and loaded.
+  - [`AutoForwardDiff`](@extref ADTypes): The best choice for dense problems.
+  - [`AutoPolyesterForwardDiff`](@extref ADTypes): Might be faster than
+    [`AutoForwardDiff`](@extref ADTypes) for large problems. Requires
+    `PolyesterForwardDiff.jl` to be installed and loaded.
 
 ## Summary of Reverse Mode AD Backends
 
   - [`AutoZygote`](@ref): The fastest choice for non-mutating array-based (BLAS) functions.
-  - [`AutoEnzyme`](@ref): Uses `Enzyme.jl` Reverse Mode and should be considered
-    experimental.
+  - [`AutoEnzyme`](@ref): Uses `Enzyme.jl` Reverse Mode and works for both in-place and
+    out-of-place functions.
 
-!!! note
-    
-    If `PolyesterForwardDiff.jl` is installed and loaded, then `SimpleNonlinearSolve.jl`
-    will automatically use `AutoPolyesterForwardDiff` as the default AD backend.
+!!! tip
 
-!!! note
-    
-    The sparse versions of the methods refer to automated sparsity detection. These
-    methods automatically discover the sparse Jacobian form from the function `f`. Note that
-    all methods specialize the differentiation on a sparse Jacobian if the sparse Jacobian
-    is given as `prob.f.jac_prototype` in the `NonlinearFunction` definition, and the
-    `AutoSparse` here simply refers to whether this `jac_prototype` should be generated
-    automatically. For more details, see
-    [SparseDiffTools.jl](https://github.com/JuliaDiff/SparseDiffTools.jl) and
-    [Sparsity Detection Manual Entry](@ref sparsity-detection), as well as the
-    documentation of [ADTypes.jl](https://github.com/SciML/ADTypes.jl).
-
-## API Reference
-
-```@docs
-AutoSparse
-```
-
-### Finite Differencing Backends
-
-```@docs
-AutoFiniteDiff
-```
-
-### Forward Mode AD Backends
-
-```@docs
-AutoForwardDiff
-AutoPolyesterForwardDiff
-```
-
-### Reverse Mode AD Backends
-
-```@docs
-AutoZygote
-AutoEnzyme
-```
+    For sparsity detection and sparse AD take a look at
+    [sparsity detection](@ref sparsity-detection).
diff --git a/docs/src/tutorials/large_systems.md b/docs/src/tutorials/large_systems.md
index 4955f9084..a27105227 100644
--- a/docs/src/tutorials/large_systems.md
+++ b/docs/src/tutorials/large_systems.md
@@ -161,22 +161,23 @@ is non-zeros, otherwise the overhead of sparse matrices can be higher than the g
 sparse differentiation!
 
 One of the useful companion tools for NonlinearSolve.jl is
-[Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl). This allows for automatic
+[ADTypes.jl](https://github.com/SciML/ADTypes.jl) that specifies the interface for sparsity
+detection via [`jacobian_sparsity`](@extref ADTypes). This allows for automatic
 declaration of Jacobian sparsity types. To see this in action, we can give an example `du`
 and `u` and call `jacobian_sparsity` on our function with the example arguments, and it will
 kick out a sparse matrix with our pattern, that we can turn into our `jac_prototype`.
 
 !!! tip
     
-    Alternatively you can use the `SparseConnectivityTracer.jl` package to automatically
-    generate a sparse Jacobian.
+    External packages like `SparseConnectivityTracer.jl` and `Symbolics.jl` provide the
+    actual implementation of sparsity detection.
 
 ```@example ill_conditioned_nlprob
-using Symbolics
+using SparseConnectivityTracer, ADTypes
 
-du0 = copy(u0)
-jac_sparsity = Symbolics.jacobian_sparsity(
-    (du, u) -> brusselator_2d_loop(du, u, p), du0, u0)
+f! = (du, u) -> brusselator_2d_loop(du, u, p)
+du0 = similar(u0)
+jac_sparsity = ADTypes.jacobian_sparsity(f!, du0, u0, TracerSparsityDetector())
 ```
 
 Notice that Julia gives a nice print out of the sparsity pattern. That's neat, and would be
@@ -322,9 +323,6 @@ sparsity detection. Let's compare the two by setting the sparsity detection algo
 ```@example ill_conditioned_nlprob
 using DifferentiationInterface, SparseConnectivityTracer
 
-prob_brusselator_2d_exact_symbolics = NonlinearProblem(
-    NonlinearFunction(brusselator_2d_loop; sparsity = SymbolicsSparsityDetector()),
-    u0, p; abstol = 1e-10, reltol = 1e-10)
 prob_brusselator_2d_exact_tracer = NonlinearProblem(
     NonlinearFunction(brusselator_2d_loop; sparsity = TracerSparsityDetector()),
     u0, p; abstol = 1e-10, reltol = 1e-10)
@@ -333,7 +331,6 @@ prob_brusselator_2d_approx_di = NonlinearProblem(
         sparsity = DenseSparsityDetector(AutoForwardDiff(); atol = 1e-4)),
     u0, p; abstol = 1e-10, reltol = 1e-10)
 
-@btime solve(prob_brusselator_2d_exact_symbolics, NewtonRaphson());
 @btime solve(prob_brusselator_2d_exact_tracer, NewtonRaphson());
 @btime solve(prob_brusselator_2d_approx_di, NewtonRaphson());
 nothing # hide
diff --git a/test/misc/qa_tests.jl b/test/misc/qa_tests.jl
index 5c60e5339..f6c0d8cb4 100644
--- a/test/misc/qa_tests.jl
+++ b/test/misc/qa_tests.jl
@@ -18,7 +18,7 @@ end
     using NonlinearSolve, ADTypes, SimpleNonlinearSolve, SciMLBase
     import BandedMatrices, FastLevenbergMarquardt, FixedPointAcceleration,
            LeastSquaresOptim, MINPACK, NLsolve, NLSolvers, SIAMFANLEquations, SpeedMapping,
-           Symbolics, Zygote
+           Zygote
 
     using ExplicitImports
 

From 275161f554b0b6892c109c738af28cdbcc0ab4b2 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 3 Oct 2024 09:39:50 -0400
Subject: [PATCH 518/700] docs: remove unnecessary ADTypes docs

---
 docs/src/basics/autodiff.md |   7 +-
 src/NonlinearSolve.jl       |   1 -
 src/adtypes.jl              | 140 ------------------------------------
 3 files changed, 4 insertions(+), 144 deletions(-)
 delete mode 100644 src/adtypes.jl

diff --git a/docs/src/basics/autodiff.md b/docs/src/basics/autodiff.md
index 46bc0c576..df59ceafc 100644
--- a/docs/src/basics/autodiff.md
+++ b/docs/src/basics/autodiff.md
@@ -22,9 +22,10 @@
 
 ## Summary of Reverse Mode AD Backends
 
-  - [`AutoZygote`](@ref): The fastest choice for non-mutating array-based (BLAS) functions.
-  - [`AutoEnzyme`](@ref): Uses `Enzyme.jl` Reverse Mode and works for both in-place and
-    out-of-place functions.
+  - [`AutoZygote`](@extref ADTypes): The fastest choice for non-mutating array-based (BLAS)
+    functions.
+  - [`AutoEnzyme`](@extref ADTypes): Uses `Enzyme.jl` Reverse Mode and works for both
+    in-place and out-of-place functions.
 
 !!! tip
 
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 4d78e2195..5043ed865 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -68,7 +68,6 @@ const True = Val(true)
 const False = Val(false)
 
 include("abstract_types.jl")
-include("adtypes.jl")
 include("timer_outputs.jl")
 include("internal/helpers.jl")
 
diff --git a/src/adtypes.jl b/src/adtypes.jl
deleted file mode 100644
index 0ee20effb..000000000
--- a/src/adtypes.jl
+++ /dev/null
@@ -1,140 +0,0 @@
-# This just documents the AD types from ADTypes.jl
-
-"""
-    AutoFiniteDiff(; fdtype = Val(:forward), fdjtype = fdtype, fdhtype = Val(:hcentral))
-
-This uses [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl). While not necessarily
-the most efficient, this is the only choice that doesn't require the `f` function to be
-automatically differentiable, which means it applies to any choice. However, because it's
-using finite differencing, one needs to be careful as this procedure introduces numerical
-error into the derivative estimates.
-
-  - Compatible with GPUs
-  - Can be used for Jacobian-Vector Products (JVPs)
-  - Can be used for Vector-Jacobian Products (VJPs)
-  - Supports both inplace and out-of-place functions
-
-### Keyword Arguments
-
-  - `fdtype`: the method used for defining the gradient
-  - `fdjtype`: the method used for defining the Jacobian of constraints.
-  - `fdhtype`: the method used for defining the Hessian
-"""
-AutoFiniteDiff
-
-"""
-    AutoForwardDiff(; chunksize = nothing, tag = nothing)
-    AutoForwardDiff{chunksize, tagType}(tag::tagType)
-
-This uses the [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) package. It is
-the fastest choice for square or wide systems. It is easy to use and compatible with most
-Julia functions which have loose type restrictions.
-
-  - Compatible with GPUs
-  - Can be used for Jacobian-Vector Products (JVPs)
-  - Supports both inplace and out-of-place functions
-
-For type-stability of internal operations, a positive `chunksize` must be provided.
-
-### Keyword Arguments
-
-  - `chunksize`: Count of dual numbers that can be propagated simultaneously. Setting this
-    number to a high value will lead to slowdowns. Use
-    [`NonlinearSolve.pickchunksize`](@ref) to get a proper value.
-  - `tag`: Used to avoid perturbation confusion. If set to `nothing`, we use a custom tag.
-"""
-AutoForwardDiff
-
-"""
-    AutoPolyesterForwardDiff(; chunksize = nothing)
-
-Uses [`PolyesterForwardDiff.jl`](https://github.com/JuliaDiff/PolyesterForwardDiff.jl)
-to compute the jacobian. This is essentially parallelized `ForwardDiff.jl`.
-
-  - Supports both inplace and out-of-place functions
-
-### Keyword Arguments
-
-  - `chunksize`: Count of dual numbers that can be propagated simultaneously. Setting
-    this number to a high value will lead to slowdowns. Use
-    [`NonlinearSolve.pickchunksize`](@ref) to get a proper value.
-"""
-AutoPolyesterForwardDiff
-
-"""
-    AutoZygote()
-
-Uses [`Zygote.jl`](https://github.com/FluxML/Zygote.jl) package. This is the staple
-reverse-mode AD that handles a large portion of Julia with good efficiency.
-
-  - Compatible with GPUs
-  - Can be used for Vector-Jacobian Products (VJPs)
-  - Supports only out-of-place functions
-
-For VJPs this is the current best choice. This is the most efficient method for long
-jacobians.
-"""
-AutoZygote
-
-"""
-    AutoEnzyme()
-
-Uses reverse mode [Enzyme.jl](https://github.com/EnzymeAD/Enzyme.jl). This is currently
-experimental, and not extensively tested on our end. We only support Jacobian construction
-and VJP support is currently not implemented.
-
-  - Supports both inplace and out-of-place functions
-"""
-AutoEnzyme
-
-"""
-    AutoSparse(AutoEnzyme())
-
-Sparse version of [`AutoEnzyme`](@ref) that uses
-[Enzyme.jl](https://github.com/EnzymeAD/Enzyme.jl) and the row color vector of
-the Jacobian Matrix to efficiently compute the Sparse Jacobian.
-
-  - Supports both inplace and out-of-place functions
-
-This is efficient only for long jacobians or if the maximum value of the row color vector is
-significantly lower than the maximum value of the column color vector.
-
-    AutoSparse(AutoFiniteDiff())
-
-Sparse Version of [`AutoFiniteDiff`](@ref) that uses
-[FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) and the column color vector of
-the Jacobian Matrix to efficiently compute the Sparse Jacobian.
-
-  - Supports both inplace and out-of-place functions
-
-    AutoSparse(AutoForwardDiff(; chunksize = nothing, tag = nothing))
-    AutoSparse(AutoForwardDiff{chunksize, tagType}(tag::tagType))
-
-Sparse Version of [`AutoForwardDiff`](@ref) that uses
-[ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) and the column color vector of
-the Jacobian Matrix to efficiently compute the Sparse Jacobian.
-
-  - Supports both inplace and out-of-place functions
-
-For type-stability of internal operations, a positive `chunksize` must be provided.
-
-### Keyword Arguments
-
-  - `chunksize`: Count of dual numbers that can be propagated simultaneously. Setting this
-    number to a high value will lead to slowdowns. Use
-    [`NonlinearSolve.pickchunksize`](@ref) to get a proper value.
-
-  - `tag`: Used to avoid perturbation confusion. If set to `nothing`, we use a custom tag.
-
-    AutoSparse(AutoZygote())
-
-Sparse version of [`AutoZygote`](@ref) that uses
-[`Zygote.jl`](https://github.com/FluxML/Zygote.jl) and the row color vector of
-the Jacobian Matrix to efficiently compute the Sparse Jacobian.
-
-  - Supports only out-of-place functions
-
-This is efficient only for long jacobians or if the maximum value of the row color vector is
-significantly lower than the maximum value of the column color vector.
-"""
-AutoSparse

From 5ef683422ff3eb4787b3b3c39c2cdd1dc2b53e35 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 3 Oct 2024 09:43:22 -0400
Subject: [PATCH 519/700] test: remove sparsedifftools and symbolics from tests

---
 Project.toml                | 6 +-----
 docs/src/basics/autodiff.md | 4 ++--
 test/core/rootfind_tests.jl | 2 +-
 test/misc/bruss_tests.jl    | 8 ++++----
 4 files changed, 8 insertions(+), 12 deletions(-)

diff --git a/Project.toml b/Project.toml
index 0f77d7966..7e0bcb4c8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -108,7 +108,6 @@ Setfield = "1.1.1"
 SimpleNonlinearSolve = "1.12.3"
 SparseArrays = "1.10"
 SparseConnectivityTracer = "0.6.5"
-SparseDiffTools = "2.22"
 SparseMatrixColorings = "0.4.2"
 SpeedMapping = "0.3"
 StableRNGs = "1"
@@ -116,7 +115,6 @@ StaticArrays = "1.9"
 StaticArraysCore = "1.4"
 Sundials = "4.23.1"
 SymbolicIndexingInterface = "0.3.31"
-Symbolics = "6.12"
 Test = "1.10"
 TimerOutputs = "0.5.23"
 Zygote = "0.6.69"
@@ -145,14 +143,12 @@ Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
-SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
 SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"
-Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SparseDiffTools", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Symbolics", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Test", "Zygote"]
diff --git a/docs/src/basics/autodiff.md b/docs/src/basics/autodiff.md
index df59ceafc..dc3166c6e 100644
--- a/docs/src/basics/autodiff.md
+++ b/docs/src/basics/autodiff.md
@@ -1,7 +1,7 @@
 # Automatic Differentiation Backends
 
 !!! note
-
+    
     We support all backends supported by DifferentiationInterface.jl. Please refer to
     the [backends page](https://gdalle.github.io/DifferentiationInterface.jl/DifferentiationInterface/stable/explanation/backends/)
     for more information.
@@ -28,6 +28,6 @@
     in-place and out-of-place functions.
 
 !!! tip
-
+    
     For sparsity detection and sparse AD take a look at
     [sparsity detection](@ref sparsity-detection).
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index bca02a44b..6a56c6ac6 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -1,7 +1,7 @@
 @testsetup module CoreRootfindTesting
 using Reexport
 @reexport using BenchmarkTools, LinearSolve, NonlinearSolve, StaticArrays, Random,
-                LinearAlgebra, ForwardDiff, Zygote, Enzyme, SparseDiffTools, DiffEqBase
+                LinearAlgebra, ForwardDiff, Zygote, Enzyme, DiffEqBase
 
 _nameof(x) = applicable(nameof, x) ? nameof(x) : _nameof(typeof(x))
 
diff --git a/test/misc/bruss_tests.jl b/test/misc/bruss_tests.jl
index 7b63e421c..b7abd634b 100644
--- a/test/misc/bruss_tests.jl
+++ b/test/misc/bruss_tests.jl
@@ -1,5 +1,5 @@
 @testitem "Brusselator 2D" tags=[:misc] begin
-    using LinearAlgebra, SparseArrays, SparseConnectivityTracer, Symbolics
+    using LinearAlgebra, SparseArrays, SparseConnectivityTracer, ADTypes
 
     const N = 32
     const xyd_brusselator = range(0, stop = 1, length = N)
@@ -63,9 +63,9 @@
         NewtonRaphson(autodiff = AutoSparse(AutoFiniteDiff())); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
-    du0 = copy(u0)
-    jac_prototype = Symbolics.jacobian_sparsity(
-        (du, u) -> brusselator_2d_loop(du, u, p), du0, u0)
+    f! = (du, u) -> brusselator_2d_loop(du, u, p)
+    du0 = similar(u0)
+    jac_prototype = ADTypes.jacobian_sparsity(f!, du0, u0, TracerSparsityDetector())
 
     ff_iip = NonlinearFunction(brusselator_2d_loop; jac_prototype)
     prob_brusselator_2d = NonlinearProblem(ff_iip, u0, p)

From 20327521489eb09b610dc43d78b044b4c9486721 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 3 Oct 2024 09:45:43 -0400
Subject: [PATCH 520/700] refactor: remove Zygote extension

---
 Project.toml                   | 2 --
 ext/NonlinearSolveZygoteExt.jl | 7 -------
 src/NonlinearSolve.jl          | 3 ---
 src/internal/helpers.jl        | 2 +-
 test/misc/bruss_tests.jl       | 6 ------
 test/misc/qa_tests.jl          | 3 +--
 6 files changed, 2 insertions(+), 21 deletions(-)
 delete mode 100644 ext/NonlinearSolveZygoteExt.jl

diff --git a/Project.toml b/Project.toml
index 7e0bcb4c8..69dd08304 100644
--- a/Project.toml
+++ b/Project.toml
@@ -45,7 +45,6 @@ NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
 SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
-Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [extensions]
 NonlinearSolveBandedMatricesExt = "BandedMatrices"
@@ -57,7 +56,6 @@ NonlinearSolveNLSolversExt = "NLSolvers"
 NonlinearSolveNLsolveExt = "NLsolve"
 NonlinearSolveSIAMFANLEquationsExt = "SIAMFANLEquations"
 NonlinearSolveSpeedMappingExt = "SpeedMapping"
-NonlinearSolveZygoteExt = "Zygote"
 
 [compat]
 ADTypes = "1.9"
diff --git a/ext/NonlinearSolveZygoteExt.jl b/ext/NonlinearSolveZygoteExt.jl
deleted file mode 100644
index 8ed2e1853..000000000
--- a/ext/NonlinearSolveZygoteExt.jl
+++ /dev/null
@@ -1,7 +0,0 @@
-module NonlinearSolveZygoteExt
-
-using NonlinearSolve: NonlinearSolve
-
-NonlinearSolve.is_extension_loaded(::Val{:Zygote}) = true
-
-end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 5043ed865..50051fcb0 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -61,9 +61,6 @@ using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm,
 
 const DI = DifferentiationInterface
 
-# Type-Inference Friendly Check for Extension Loading
-is_extension_loaded(::Val) = false
-
 const True = Val(true)
 const False = Val(false)
 
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index abf6f1099..afc24ce5b 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -80,7 +80,7 @@ function get_concrete_reverse_ad(
     else
         use_sparse_ad = false
     end
-    ad = if isinplace(prob) || !is_extension_loaded(Val(:Zygote)) # Use Finite Differencing
+    ad = if isinplace(prob) || !DI.check_available(AutoZygote()) # Use Finite Differencing
         use_sparse_ad ? AutoSparse(AutoFiniteDiff()) : AutoFiniteDiff()
     else
         use_sparse_ad ? AutoSparse(AutoZygote()) : AutoZygote()
diff --git a/test/misc/bruss_tests.jl b/test/misc/bruss_tests.jl
index b7abd634b..80b1bd540 100644
--- a/test/misc/bruss_tests.jl
+++ b/test/misc/bruss_tests.jl
@@ -52,12 +52,6 @@
     sol = solve(prob_brusselator_2d_sparse, NewtonRaphson(); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
-    prob_brusselator_2d_sparse = NonlinearProblem(
-        NonlinearFunction(brusselator_2d_loop; sparsity = SymbolicsSparsityDetector()),
-        u0, p)
-    sol = solve(prob_brusselator_2d_sparse, NewtonRaphson(); abstol = 1e-8)
-    @test norm(sol.resid, Inf) < 1e-8
-
     # Deprecated
     sol = solve(prob_brusselator_2d,
         NewtonRaphson(autodiff = AutoSparse(AutoFiniteDiff())); abstol = 1e-8)
diff --git a/test/misc/qa_tests.jl b/test/misc/qa_tests.jl
index f6c0d8cb4..6aafd4024 100644
--- a/test/misc/qa_tests.jl
+++ b/test/misc/qa_tests.jl
@@ -17,8 +17,7 @@ end
 @testitem "Explicit Imports" tags=[:misc] begin
     using NonlinearSolve, ADTypes, SimpleNonlinearSolve, SciMLBase
     import BandedMatrices, FastLevenbergMarquardt, FixedPointAcceleration,
-           LeastSquaresOptim, MINPACK, NLsolve, NLSolvers, SIAMFANLEquations, SpeedMapping,
-           Zygote
+           LeastSquaresOptim, MINPACK, NLsolve, NLSolvers, SIAMFANLEquations, SpeedMapping
 
     using ExplicitImports
 

From 4923cc33dce864bc09665c6336e90dfa2628a814 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 3 Oct 2024 10:27:19 -0400
Subject: [PATCH 521/700] docs: add documenter interlinks as a dep

---
 docs/Project.toml | 2 ++
 docs/make.jl      | 2 +-
 2 files changed, 3 insertions(+), 1 deletion(-)

diff --git a/docs/Project.toml b/docs/Project.toml
index 30a7f5035..ab35d42ae 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -7,6 +7,7 @@ DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 DocumenterCitations = "daee34ce-89f3-4625-b898-19384cb65244"
+DocumenterInterLinks = "d12716ef-a0f6-4df4-a9f1-a5a34e75c656"
 IncompleteLU = "40713840-3770-5561-ab4c-a76e7d0d7895"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
@@ -32,6 +33,7 @@ DiffEqBase = "6.136"
 DifferentiationInterface = "0.6"
 Documenter = "1"
 DocumenterCitations = "1"
+DocumenterInterLinks = "1.0.0"
 IncompleteLU = "0.2"
 InteractiveUtils = "<0.0.1, 1"
 LinearSolve = "2"
diff --git a/docs/make.jl b/docs/make.jl
index 88381a5b6..3e931a227 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,4 +1,4 @@
-using Documenter, DocumenterCitations
+using Documenter, DocumenterCitations, DocumenterInterLinks
 using NonlinearSolve, SimpleNonlinearSolve, Sundials, SteadyStateDiffEq, SciMLBase,
       DiffEqBase
 using SciMLJacobianOperators

From f1969a27d8651767014c2257a9dd56c2b2a8bc45 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 3 Oct 2024 11:13:31 -0400
Subject: [PATCH 522/700] docs: fix external references

---
 docs/src/basics/autodiff.md             | 23 ++++++++++++-----------
 docs/src/tutorials/code_optimization.md |  2 +-
 docs/src/tutorials/large_systems.md     |  9 +++++----
 src/algorithms/extension_algs.jl        |  2 +-
 4 files changed, 19 insertions(+), 17 deletions(-)

diff --git a/docs/src/basics/autodiff.md b/docs/src/basics/autodiff.md
index dc3166c6e..d2d01e00b 100644
--- a/docs/src/basics/autodiff.md
+++ b/docs/src/basics/autodiff.md
@@ -8,24 +8,25 @@
 
 ## Summary of Finite Differencing Backends
 
-  - [`AutoFiniteDiff`](@extref ADTypes): Finite differencing using `FiniteDiff.jl`, not
-    optimal but always applicable.
-  - [`AutoFiniteDifferences`](@extref ADTypes): Finite differencing using
-    `FiniteDifferences.jl`, not optimal but always applicable.
+  - [`AutoFiniteDiff`](@extref ADTypes.AutoFiniteDiff): Finite differencing using
+    `FiniteDiff.jl`, not optimal but always applicable.
+  - [`AutoFiniteDifferences`](@extref ADTypes.AutoFiniteDifferences): Finite differencing
+    using `FiniteDifferences.jl`, not optimal but always applicable.
 
 ## Summary of Forward Mode AD Backends
 
-  - [`AutoForwardDiff`](@extref ADTypes): The best choice for dense problems.
-  - [`AutoPolyesterForwardDiff`](@extref ADTypes): Might be faster than
-    [`AutoForwardDiff`](@extref ADTypes) for large problems. Requires
+  - [`AutoForwardDiff`](@extref ADTypes.AutoForwardDiff): The best choice for dense
+    problems.
+  - [`AutoPolyesterForwardDiff`](@extref ADTypes.AutoPolyesterForwardDiff): Might be faster
+    than [`AutoForwardDiff`](@extref ADTypes.AutoForwardDiff) for large problems. Requires
     `PolyesterForwardDiff.jl` to be installed and loaded.
 
 ## Summary of Reverse Mode AD Backends
 
-  - [`AutoZygote`](@extref ADTypes): The fastest choice for non-mutating array-based (BLAS)
-    functions.
-  - [`AutoEnzyme`](@extref ADTypes): Uses `Enzyme.jl` Reverse Mode and works for both
-    in-place and out-of-place functions.
+  - [`AutoZygote`](@extref ADTypes.AutoZygote): The fastest choice for non-mutating
+    array-based (BLAS) functions.
+  - [`AutoEnzyme`](@extref ADTypes.AutoEnzyme): Uses `Enzyme.jl` Reverse Mode and works for
+    both in-place and out-of-place functions.
 
 !!! tip
     
diff --git a/docs/src/tutorials/code_optimization.md b/docs/src/tutorials/code_optimization.md
index ce114961b..b7eb9c174 100644
--- a/docs/src/tutorials/code_optimization.md
+++ b/docs/src/tutorials/code_optimization.md
@@ -90,7 +90,7 @@ end
 
 Allocations are only expensive if they are “heap allocations”. For a more in-depth
 definition of heap allocations,
-[there are many sources online](http://net-informations.com/faq/net/stack-heap.htm).
+[there are many sources online](https://net-informations.com/faq/net/stack-heap.htm).
 But a good working definition is that heap allocations are variable-sized slabs of memory
 which have to be pointed to, and this pointer indirection costs time. Additionally, the heap
 has to be managed, and the garbage controllers has to actively keep track of what's on the
diff --git a/docs/src/tutorials/large_systems.md b/docs/src/tutorials/large_systems.md
index a27105227..17b768288 100644
--- a/docs/src/tutorials/large_systems.md
+++ b/docs/src/tutorials/large_systems.md
@@ -162,10 +162,11 @@ sparse differentiation!
 
 One of the useful companion tools for NonlinearSolve.jl is
 [ADTypes.jl](https://github.com/SciML/ADTypes.jl) that specifies the interface for sparsity
-detection via [`jacobian_sparsity`](@extref ADTypes). This allows for automatic
-declaration of Jacobian sparsity types. To see this in action, we can give an example `du`
-and `u` and call `jacobian_sparsity` on our function with the example arguments, and it will
-kick out a sparse matrix with our pattern, that we can turn into our `jac_prototype`.
+detection via [`jacobian_sparsity`](@extref ADTypes.jacobian_sparsity). This allows for
+automatic declaration of Jacobian sparsity types. To see this in action, we can give an
+example `du` and `u` and call `jacobian_sparsity` on our function with the example
+arguments, and it will kick out a sparse matrix with our pattern, that we can turn into our
+`jac_prototype`.
 
 !!! tip
     
diff --git a/src/algorithms/extension_algs.jl b/src/algorithms/extension_algs.jl
index a3555a17b..46ebc8dae 100644
--- a/src/algorithms/extension_algs.jl
+++ b/src/algorithms/extension_algs.jl
@@ -317,7 +317,7 @@ NLSolversJL(; method, autodiff = nothing) = NLSolversJL(method, autodiff)
     SpeedMappingJL(; σ_min = 0.0, stabilize::Bool = false, check_obj::Bool = false,
         orders::Vector{Int} = [3, 3, 2], time_limit::Real = 1000)
 
-Wrapper over [SpeedMapping.jl](https://nicolasl-s.github.io/SpeedMapping.jl) for solving
+Wrapper over [SpeedMapping.jl](https://nicolasl-s.github.io/SpeedMapping.jl/) for solving
 Fixed Point Problems. We allow using this algorithm to solve root finding problems as well.
 
 ### Keyword Arguments

From c35f0f4414aa7b6fb90ff661a604034fc61a11bc Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 12:11:39 -0400
Subject: [PATCH 523/700] refactor: migrate to LineSearch.jl (#461)

* refactor: migrate to LineSearch.jl

* fix: forward reinit_cache to SciMLBase.reinit

* fix: remaining tests from the migration

* chore: bump min versions

* fix: final set of bumps

* fix: stop using deprecated API in default solvers

* docs: fix references
---
 Project.toml                            |   8 +-
 docs/make.jl                            |   7 +-
 docs/src/devdocs/internal_interfaces.md |   7 -
 docs/src/native/globalization.md        |   9 +-
 docs/src/native/solvers.md              |   2 +-
 src/NonlinearSolve.jl                   |   7 +-
 src/abstract_types.jl                   |  22 +-
 src/algorithms/klement.jl               |   2 +-
 src/algorithms/pseudo_transient.jl      |   7 +-
 src/core/approximate_jacobian.jl        |  10 +-
 src/core/generalized_first_order.jl     |  20 +-
 src/core/spectral_methods.jl            |  14 +-
 src/default.jl                          |  22 +-
 src/globalization/line_search.jl        | 449 ++----------------------
 src/internal/jacobian.jl                |   3 +-
 src/internal/termination.jl             |   4 +-
 test/gpu/core_tests.jl                  |  16 +-
 test/misc/other_tests.jl                |  10 -
 18 files changed, 105 insertions(+), 514 deletions(-)
 delete mode 100644 test/misc/other_tests.jl

diff --git a/Project.toml b/Project.toml
index 69dd08304..d8ec44ac1 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.15.0-DEV"
+version = "3.15.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -14,6 +14,7 @@ FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
+LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
 LineSearches = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
@@ -79,11 +80,12 @@ Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
 LazyArrays = "1.8.2, 2"
 LeastSquaresOptim = "0.8.5"
-LineSearches = "7.2"
+LineSearch = "0.1.2"
+LineSearches = "7.3"
 LinearAlgebra = "1.10"
 LinearSolve = "2.35"
 MINPACK = "1.2"
-MaybeInplace = "0.1.3"
+MaybeInplace = "0.1.4"
 ModelingToolkit = "9.41.0"
 NLSolvers = "0.5"
 NLsolve = "4.5"
diff --git a/docs/make.jl b/docs/make.jl
index 3e931a227..eec25f4f7 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -14,9 +14,11 @@ bib = CitationBibliography(joinpath(@__DIR__, "src", "refs.bib"))
 
 interlinks = InterLinks(
     "ADTypes" => "https://sciml.github.io/ADTypes.jl/stable/",
+    "LineSearch" => "https://sciml.github.io/LineSearch.jl/dev/"
 )
 
-makedocs(; sitename = "NonlinearSolve.jl",
+makedocs(;
+    sitename = "NonlinearSolve.jl",
     authors = "Chris Rackauckas",
     modules = [NonlinearSolve, SimpleNonlinearSolve, SteadyStateDiffEq,
         Sundials, DiffEqBase, SciMLBase, SciMLJacobianOperators],
@@ -30,6 +32,7 @@ makedocs(; sitename = "NonlinearSolve.jl",
     plugins = [bib, interlinks],
     format = Documenter.HTML(assets = ["assets/favicon.ico", "assets/citations.css"],
         canonical = "https://docs.sciml.ai/NonlinearSolve/stable/"),
-    pages)
+    pages
+)
 
 deploydocs(repo = "github.com/SciML/NonlinearSolve.jl.git"; push_preview = true)
diff --git a/docs/src/devdocs/internal_interfaces.md b/docs/src/devdocs/internal_interfaces.md
index 91b9562a8..53e20d754 100644
--- a/docs/src/devdocs/internal_interfaces.md
+++ b/docs/src/devdocs/internal_interfaces.md
@@ -38,13 +38,6 @@ NonlinearSolve.AbstractDampingFunction
 NonlinearSolve.AbstractDampingFunctionCache
 ```
 
-## Line Search
-
-```@docs
-NonlinearSolve.AbstractNonlinearSolveLineSearchAlgorithm
-NonlinearSolve.AbstractNonlinearSolveLineSearchCache
-```
-
 ## Trust Region
 
 ```@docs
diff --git a/docs/src/native/globalization.md b/docs/src/native/globalization.md
index d7ff7d684..de163c6d1 100644
--- a/docs/src/native/globalization.md
+++ b/docs/src/native/globalization.md
@@ -8,12 +8,9 @@ Pages = ["globalization.md"]
 
 ## [Line Search Algorithms](@id line-search)
 
-```@docs
-LiFukushimaLineSearch
-LineSearchesJL
-RobustNonMonotoneLineSearch
-NoLineSearch
-```
+Line Searches have been moved to an external package. Take a look at the
+[LineSearch.jl](https://github.com/SciML/LineSearch.jl) package and its
+[documentation](https://sciml.github.io/LineSearch.jl/dev/).
 
 ## Radius Update Schemes for Trust Region
 
diff --git a/docs/src/native/solvers.md b/docs/src/native/solvers.md
index d2c0fc6e5..a5deca141 100644
--- a/docs/src/native/solvers.md
+++ b/docs/src/native/solvers.md
@@ -22,7 +22,7 @@ documentation.
     preconditioners. For more information on specifying preconditioners for LinearSolve
     algorithms, consult the
     [LinearSolve.jl documentation](https://docs.sciml.ai/LinearSolve/stable/).
-  - `linesearch`: the line search algorithm to use. Defaults to [`NoLineSearch()`](@ref),
+  - `linesearch`: the line search algorithm to use. Defaults to [`NoLineSearch()`](@extref LineSearch.NoLineSearch),
     which means that no line search is performed.  Algorithms from
     [`LineSearches.jl`](https://github.com/JuliaNLSolvers/LineSearches.jl/) must be
     wrapped in [`LineSearchesJL`](@ref) before being supplied. For a detailed documentation
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 50051fcb0..6babbdbdc 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -22,6 +22,8 @@ using LazyArrays: LazyArrays, ApplyArray, cache
 using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Symmetric,
                      UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess, istril,
                      istriu, lu, mul!, norm, pinv, tril!, triu!
+using LineSearch: LineSearch, AbstractLineSearchAlgorithm, AbstractLineSearchCache,
+                  NoLineSearch, RobustNonMonotoneLineSearch
 using LineSearches: LineSearches
 using LinearSolve: LinearSolve, LUFactorization, QRFactorization,
                    needs_concrete_A, AbstractFactorization,
@@ -172,8 +174,9 @@ export NewtonDescent, SteepestDescent, Dogleg, DampedNewtonDescent, GeodesicAcce
 
 # Globalization
 ## Line Search Algorithms
-export LineSearchesJL, NoLineSearch, RobustNonMonotoneLineSearch, LiFukushimaLineSearch
-export Static, HagerZhang, MoreThuente, StrongWolfe, BackTracking
+export LineSearchesJL, LiFukushimaLineSearch # FIXME: deprecated. use LineSearch.jl directly
+export Static, HagerZhang, MoreThuente, StrongWolfe, BackTracking  # FIXME: deprecated
+export NoLineSearch, RobustNonMonotoneLineSearch
 ## Trust Region Algorithms
 export RadiusUpdateSchemes
 
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 2fe2fd071..0bb2e13d2 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -106,22 +106,6 @@ function last_step_accepted(cache::AbstractDescentCache)
     return true
 end
 
-"""
-    AbstractNonlinearSolveLineSearchAlgorithm
-
-Abstract Type for all Line Search Algorithms used in NonlinearSolve.jl.
-
-### `__internal_init` specification
-
-```julia
-__internal_init(
-    prob::AbstractNonlinearProblem, alg::AbstractNonlinearSolveLineSearchAlgorithm, f::F,
-    fu, u, p, args...; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN} -->
-AbstractNonlinearSolveLineSearchCache
-```
-"""
-abstract type AbstractNonlinearSolveLineSearchAlgorithm end
-
 """
     AbstractNonlinearSolveLineSearchCache
 
@@ -512,9 +496,9 @@ SciMLBase.isinplace(::AbstractNonlinearSolveJacobianCache{iip}) where {iip} = ii
 abstract type AbstractNonlinearSolveTraceLevel end
 
 # Default Printing
-for aType in (AbstractTrustRegionMethod, AbstractNonlinearSolveLineSearchAlgorithm,
-    AbstractResetCondition, AbstractApproximateJacobianUpdateRule,
-    AbstractDampingFunction, AbstractNonlinearSolveExtensionAlgorithm)
+for aType in (AbstractTrustRegionMethod, AbstractResetCondition,
+    AbstractApproximateJacobianUpdateRule, AbstractDampingFunction,
+    AbstractNonlinearSolveExtensionAlgorithm)
     @eval function Base.show(io::IO, alg::$(aType))
         print(io, "$(nameof(typeof(alg)))()")
     end
diff --git a/src/algorithms/klement.jl b/src/algorithms/klement.jl
index 66daec1b7..5e911d8c0 100644
--- a/src/algorithms/klement.jl
+++ b/src/algorithms/klement.jl
@@ -27,7 +27,7 @@ over this.
 function Klement(; max_resets::Int = 100, linsolve = nothing, alpha = nothing,
         linesearch = NoLineSearch(), precs = DEFAULT_PRECS,
         autodiff = nothing, init_jacobian::Val{IJ} = Val(:identity)) where {IJ}
-    if !(linesearch isa AbstractNonlinearSolveLineSearchAlgorithm)
+    if !(linesearch isa AbstractLineSearchAlgorithm)
         Base.depwarn(
             "Passing in a `LineSearches.jl` algorithm directly is deprecated. \
              Please use `LineSearchesJL` instead.", :Klement)
diff --git a/src/algorithms/pseudo_transient.jl b/src/algorithms/pseudo_transient.jl
index fda39a3b9..0da85dd94 100644
--- a/src/algorithms/pseudo_transient.jl
+++ b/src/algorithms/pseudo_transient.jl
@@ -1,7 +1,6 @@
 """
     PseudoTransient(; concrete_jac = nothing, linsolve = nothing,
-        linesearch::AbstractNonlinearSolveLineSearchAlgorithm = NoLineSearch(),
-        precs = DEFAULT_PRECS, autodiff = nothing)
+        linesearch = NoLineSearch(), precs = DEFAULT_PRECS, autodiff = nothing)
 
 An implementation of PseudoTransient Method [coffey2003pseudotransient](@cite) that is used
 to solve steady state problems in an accelerated manner. It uses an adaptive time-stepping
@@ -16,8 +15,8 @@ This implementation specifically uses "switched evolution relaxation"
     you are going to need more iterations to converge but it can be more stable.
 """
 function PseudoTransient(; concrete_jac = nothing, linsolve = nothing,
-        linesearch::AbstractNonlinearSolveLineSearchAlgorithm = NoLineSearch(),
-        precs = DEFAULT_PRECS, autodiff = nothing, alpha_initial = 1e-3)
+        linesearch = NoLineSearch(), precs = DEFAULT_PRECS, autodiff = nothing,
+        alpha_initial = 1e-3)
     descent = DampedNewtonDescent(; linsolve, precs, initial_damping = alpha_initial,
         damping_fn = SwitchedEvolutionRelaxation())
     return GeneralizedFirstOrderAlgorithm(;
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index e61f34032..6484c0408 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -59,7 +59,7 @@ function ApproximateJacobianSolveAlgorithm{concrete_jac, name}(;
         linesearch = missing, trustregion = missing, descent, update_rule,
         reinit_rule, initialization, max_resets::Int = typemax(Int),
         max_shrink_times::Int = typemax(Int)) where {concrete_jac, name}
-    if linesearch !== missing && !(linesearch isa AbstractNonlinearSolveLineSearchAlgorithm)
+    if linesearch !== missing && !(linesearch isa AbstractLineSearchAlgorithm)
         Base.depwarn("Passing in a `LineSearches.jl` algorithm directly is deprecated. \
                       Please use `LineSearchesJL` instead.",
             :GeneralizedFirstOrderAlgorithm)
@@ -199,8 +199,8 @@ function SciMLBase.__init(
         if alg.linesearch !== missing
             supports_line_search(alg.descent) || error("Line Search not supported by \
                                                         $(alg.descent).")
-            linesearch_cache = __internal_init(
-                prob, alg.linesearch, f, fu, u, p; stats, internalnorm, kwargs...)
+            linesearch_cache = init(
+                prob, alg.linesearch, fu, u; stats, internalnorm, kwargs...)
             GB = :LineSearch
         end
 
@@ -317,7 +317,9 @@ function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
     if descent_result.success
         if GB === :LineSearch
             @static_timeit cache.timer "linesearch" begin
-                needs_reset, α = __internal_solve!(cache.linesearch_cache, cache.u, δu)
+                linesearch_sol = solve!(cache.linesearch_cache, cache.u, δu)
+                needs_reset = !SciMLBase.successful_retcode(linesearch_sol.retcode)
+                α = linesearch_sol.step_size
             end
             if needs_reset && cache.steps_since_last_reset > 5 # Reset after a burn-in period
                 cache.force_reinit = true
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 38c3786f5..a485c7c65 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -66,7 +66,7 @@ function GeneralizedFirstOrderAlgorithm{concrete_jac, name}(;
             jacobian_ad !== nothing && ADTypes.mode(jacobian_ad) isa ADTypes.ReverseMode,
             jacobian_ad, nothing))
 
-    if linesearch !== missing && !(linesearch isa AbstractNonlinearSolveLineSearchAlgorithm)
+    if linesearch !== missing && !(linesearch isa AbstractLineSearchAlgorithm)
         Base.depwarn("Passing in a `LineSearches.jl` algorithm directly is deprecated. \
                       Please use `LineSearchesJL` instead.",
             :GeneralizedFirstOrderAlgorithm)
@@ -199,8 +199,17 @@ function SciMLBase.__init(
         if alg.linesearch !== missing
             supports_line_search(alg.descent) || error("Line Search not supported by \
                                                         $(alg.descent).")
-            linesearch_cache = __internal_init(
-                prob, alg.linesearch, f, fu, u, p; stats, internalnorm, kwargs...)
+            linesearch_ad = alg.forward_ad === nothing ?
+                            (alg.reverse_ad === nothing ? alg.jacobian_ad :
+                             alg.reverse_ad) : alg.forward_ad
+            if linesearch_ad !== nothing && iip && !DI.check_inplace(linesearch_ad)
+                @warn "$(linesearch_ad) doesn't support in-place problems."
+                linesearch_ad = nothing
+            end
+            linesearch_ad = get_concrete_forward_ad(
+                linesearch_ad, prob, False; check_forward_mode = false)
+            linesearch_cache = init(
+                prob, alg.linesearch, fu, u; stats, autodiff = linesearch_ad, kwargs...)
             GB = :LineSearch
         end
 
@@ -264,8 +273,9 @@ function __step!(cache::GeneralizedFirstOrderAlgorithmCache{iip, GB};
         cache.make_new_jacobian = true
         if GB === :LineSearch
             @static_timeit cache.timer "linesearch" begin
-                linesearch_failed, α = __internal_solve!(
-                    cache.linesearch_cache, cache.u, δu)
+                linesearch_sol = solve!(cache.linesearch_cache, cache.u, δu)
+                linesearch_failed = !SciMLBase.successful_retcode(linesearch_sol.retcode)
+                α = linesearch_sol.step_size
             end
             if linesearch_failed
                 cache.retcode = ReturnCode.InternalLineSearchFailed
diff --git a/src/core/spectral_methods.jl b/src/core/spectral_methods.jl
index 85e58c1a3..d141a627b 100644
--- a/src/core/spectral_methods.jl
+++ b/src/core/spectral_methods.jl
@@ -9,9 +9,8 @@ Method.
 
 ### Arguments
 
-  - `linesearch`: Globalization using a Line Search Method. This needs to follow the
-    [`NonlinearSolve.AbstractNonlinearSolveLineSearchAlgorithm`](@ref) interface. This
-    is not optional currently, but that restriction might be lifted in the future.
+  - `linesearch`: Globalization using a Line Search Method. This is not optional currently,
+    but that restriction might be lifted in the future.
   - `σ_min`: The minimum spectral parameter allowed. This is used to ensure that the
     spectral parameter is not too small.
   - `σ_max`: The maximum spectral parameter allowed. This is used to ensure that the
@@ -119,7 +118,7 @@ end
 function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane, args...;
         stats = empty_nlstats(), alias_u0 = false, maxiters = 1000,
         abstol = nothing, reltol = nothing, termination_condition = nothing,
-        internalnorm::F = DEFAULT_NORM, maxtime = nothing, kwargs...) where {F}
+        maxtime = nothing, kwargs...)
     timer = get_timer_output()
     @static_timeit timer "cache construction" begin
         u = __maybe_unaliased(prob.u0, alias_u0)
@@ -130,8 +129,7 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane
         fu = evaluate_f(prob, u)
         @bb fu_cache = copy(fu)
 
-        linesearch_cache = __internal_init(prob, alg.linesearch, prob.f, fu, u, prob.p;
-            stats, maxiters, internalnorm, kwargs...)
+        linesearch_cache = init(prob, alg.linesearch, fu, u; stats, kwargs...)
 
         abstol, reltol, tc_cache = init_termination_cache(
             prob, abstol, reltol, fu, u_cache, termination_condition)
@@ -167,7 +165,9 @@ function __step!(cache::GeneralizedDFSaneCache{iip};
     end
 
     @static_timeit cache.timer "linesearch" begin
-        linesearch_failed, α = __internal_solve!(cache.linesearch_cache, cache.u, cache.du)
+        linesearch_sol = solve!(cache.linesearch_cache, cache.u, cache.du)
+        linesearch_failed = !SciMLBase.successful_retcode(linesearch_sol.retcode)
+        α = linesearch_sol.step_size
     end
 
     if linesearch_failed
diff --git a/src/default.jl b/src/default.jl
index 8a9aac6af..5623c553f 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -364,7 +364,9 @@ function RobustMultiNewton(::Type{T} = Float64; concrete_jac = nothing, linsolve
                 radius_update_scheme = RadiusUpdateSchemes.Bastin),
             NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
             NewtonRaphson(; concrete_jac, linsolve, precs,
-                linesearch = LineSearchesJL(; method = BackTracking()), autodiff),
+                linesearch = LineSearch.LineSearchesJL(;
+                    method = LineSearches.BackTracking()),
+                autodiff),
             TrustRegion(; concrete_jac, linsolve, precs,
                 radius_update_scheme = RadiusUpdateSchemes.NLsolve, autodiff),
             TrustRegion(; concrete_jac, linsolve, precs,
@@ -405,7 +407,9 @@ function FastShortcutNonlinearPolyalg(
         else
             algs = (NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
                 NewtonRaphson(; concrete_jac, linsolve, precs,
-                    linesearch = LineSearchesJL(; method = BackTracking()), autodiff),
+                    linesearch = LineSearch.LineSearchesJL(;
+                        method = LineSearches.BackTracking()),
+                    autodiff),
                 TrustRegion(; concrete_jac, linsolve, precs, autodiff),
                 TrustRegion(; concrete_jac, linsolve, precs,
                     radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff))
@@ -426,7 +430,9 @@ function FastShortcutNonlinearPolyalg(
                     SimpleKlement(),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs,
-                        linesearch = LineSearchesJL(; method = BackTracking()), autodiff),
+                        linesearch = LineSearch.LineSearchesJL(;
+                            method = LineSearches.BackTracking()),
+                        autodiff),
                     TrustRegion(; concrete_jac, linsolve, precs,
                         radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff))
             end
@@ -439,12 +445,15 @@ function FastShortcutNonlinearPolyalg(
             else
                 # TODO: This number requires a bit rigorous testing
                 start_index = u0_len !== nothing ? (u0_len ≤ 25 ? 4 : 1) : 1
-                algs = (Broyden(; autodiff),
+                algs = (
+                    Broyden(; autodiff),
                     Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
                     Klement(; linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs,
-                        linesearch = LineSearchesJL(; method = BackTracking()), autodiff),
+                        linesearch = LineSearch.LineSearchesJL(;
+                            method = LineSearches.BackTracking()),
+                        autodiff),
                     TrustRegion(; concrete_jac, linsolve, precs, autodiff),
                     TrustRegion(; concrete_jac, linsolve, precs,
                         radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff))
@@ -480,7 +489,8 @@ function FastShortcutNLLSPolyalg(
                 linsolve, precs, disable_geodesic = Val(true), autodiff, kwargs...),
             TrustRegion(; concrete_jac, linsolve, precs, autodiff, kwargs...),
             GaussNewton(; concrete_jac, linsolve, precs,
-                linesearch = LineSearchesJL(; method = BackTracking()),
+                linesearch = LineSearch.LineSearchesJL(;
+                    method = LineSearches.BackTracking()),
                 autodiff, kwargs...),
             TrustRegion(; concrete_jac, linsolve, precs,
                 radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff, kwargs...),
diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index 323c49258..c7c342bee 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -1,440 +1,33 @@
-"""
-    NoLineSearch <: AbstractNonlinearSolveLineSearchAlgorithm
-
-Don't perform a line search. Just return the initial step length of `1`.
-"""
-struct NoLineSearch <: AbstractNonlinearSolveLineSearchAlgorithm end
-
-@concrete mutable struct NoLineSearchCache <: AbstractNonlinearSolveLineSearchCache
-    α
-end
-
-function __internal_init(prob::AbstractNonlinearProblem, alg::NoLineSearch,
-        f::F, fu, u, p, args...; kwargs...) where {F}
-    return NoLineSearchCache(promote_type(eltype(fu), eltype(u))(true))
-end
-
-reinit_cache!(cache::NoLineSearchCache, args...; p = cache.p, kwargs...) = nothing
-
-__internal_solve!(cache::NoLineSearchCache, u, du) = false, cache.α
-
-"""
-    LineSearchesJL(; method = LineSearches.Static(), autodiff = nothing, α = true)
-
-Wrapper over algorithms from
-[LineSearches.jl](https://github.com/JuliaNLSolvers/LineSearches.jl/). Allows automatic
-construction of the objective functions for the line search algorithms utilizing automatic
-differentiation for fast Vector Jacobian Products.
-
-### Arguments
-
-  - `method`: the line search algorithm to use. Defaults to
-    `method = LineSearches.Static()`, which means that the step size is fixed to the value
-    of `alpha`.
-  - `autodiff`: the automatic differentiation backend to use for the line search. Using a
-    reverse mode automatic differentiation backend if recommended.
-  - `α`: the initial step size to use. Defaults to `true` (which is equivalent to `1`).
-"""
-@concrete struct LineSearchesJL <: AbstractNonlinearSolveLineSearchAlgorithm
-    method
-    initial_alpha
-    autodiff
-end
-
-function Base.show(io::IO, alg::LineSearchesJL)
-    str = "$(nameof(typeof(alg)))("
-    modifiers = String[]
-    __is_present(alg.autodiff) &&
-        push!(modifiers, "autodiff = $(nameof(typeof(alg.autodiff)))()")
-    alg.initial_alpha != true && push!(modifiers, "initial_alpha = $(alg.initial_alpha)")
-    push!(modifiers, "method = $(nameof(typeof(alg.method)))()")
-    print(io, str, join(modifiers, ", "), ")")
-end
-
 LineSearchesJL(method; kwargs...) = LineSearchesJL(; method, kwargs...)
 function LineSearchesJL(; method = LineSearches.Static(), autodiff = nothing, α = true)
-    if method isa LineSearchesJL  # Prevent breaking old code
-        return LineSearchesJL(method.method, α, autodiff)
-    end
+    Base.depwarn("`LineSearchesJL(...)` is deprecated. Please use `LineSearchesJL` from \
+                  LineSearch.jl instead.",
+        :LineSearchesJL)
 
-    if method isa AbstractNonlinearSolveLineSearchAlgorithm
-        Base.depwarn("Passing a native NonlinearSolve line search algorithm to \
-                      `LineSearchesJL` or `LineSearch` is deprecated. Pass the method \
-                      directly instead.",
-            :LineSearchesJL)
-        return method
-    end
-    return LineSearchesJL(method, α, autodiff)
+    # Prevent breaking old code
+    method isa LineSearch.LineSearchesJL &&
+        return LineSearch.LineSearchesJL(method.method, α, autodiff)
+    method isa AbstractLineSearchAlgorithm && return method
+    return LineSearch.LineSearchesJL(method, α, autodiff)
 end
 
-Base.@deprecate_binding LineSearch LineSearchesJL true
-
-Static(args...; kwargs...) = LineSearchesJL(LineSearches.Static(args...; kwargs...))
-HagerZhang(args...; kwargs...) = LineSearchesJL(LineSearches.HagerZhang(args...; kwargs...))
-function MoreThuente(args...; kwargs...)
-    return LineSearchesJL(LineSearches.MoreThuente(args...; kwargs...))
-end
-function BackTracking(args...; kwargs...)
-    return LineSearchesJL(LineSearches.BackTracking(args...; kwargs...))
-end
-function StrongWolfe(args...; kwargs...)
-    return LineSearchesJL(LineSearches.StrongWolfe(args...; kwargs...))
-end
-
-# Wrapper over LineSearches.jl algorithms
-@concrete mutable struct LineSearchesJLCache <: AbstractNonlinearSolveLineSearchCache
-    f
-    p
-    ϕ
-    dϕ
-    ϕdϕ
-    method
-    alpha
-    deriv_op
-    u_cache
-    fu_cache
-    stats::NLStats
-end
-
-function __internal_init(
-        prob::AbstractNonlinearProblem, alg::LineSearchesJL, f::F, fu, u, p,
-        args...; stats, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
-    T = promote_type(eltype(fu), eltype(u))
-    if u isa Number
-        autodiff = get_dense_ad(get_concrete_forward_ad(
-            alg.autodiff, prob; check_forward_mode = true))
-        if !(autodiff isa AutoForwardDiff ||
-             autodiff isa AutoPolyesterForwardDiff ||
-             autodiff isa AutoFiniteDiff)
-            autodiff = AutoFiniteDiff()
-            # Other cases are not properly supported so we fallback to finite differencing
-            @warn "Scalar AD is supported only for AutoForwardDiff and AutoFiniteDiff. \
-                   Detected $(autodiff). Falling back to AutoFiniteDiff."
-        end
-        deriv_op = @closure (du, u, fu, p) -> begin
-            # Temporary solution, we are anyways moving to LineSearch.jl
-            return DI.derivative(f, autodiff, u, Constant(p)) * fu * du
-        end
-    else
-        # Both forward and reverse AD can be used for line-search.
-        # We prefer forward AD for better performance, however, reverse AD is also supported if user explicitly requests it.
-        # 1. If jvp is available, we use forward AD;
-        # 2. If vjp is available, we use reverse AD;
-        # 3. If reverse type is requested, we use reverse AD;
-        # 4. Finally, we use forward AD.
-        if alg.autodiff isa AutoFiniteDiff
-            deriv_op = nothing
-        elseif SciMLBase.has_jvp(f)
-            if isinplace(prob)
-                jvp_cache = zero(fu)
-                deriv_op = @closure (du, u, fu, p) -> begin
-                    f.jvp(jvp_cache, du, u, p)
-                    dot(fu, jvp_cache)
-                end
-            else
-                deriv_op = @closure (du, u, fu, p) -> dot(fu, f.jvp(du, u, p))
-            end
-        elseif SciMLBase.has_vjp(f)
-            if isinplace(prob)
-                vjp_cache = zero(u)
-                deriv_op = @closure (du, u, fu, p) -> begin
-                    f.vjp(vjp_cache, fu, u, p)
-                    dot(du, vjp_cache)
-                end
-            else
-                deriv_op = @closure (du, u, fu, p) -> dot(du, f.vjp(fu, u, p))
-            end
-        elseif alg.autodiff !== nothing &&
-               ADTypes.mode(alg.autodiff) isa ADTypes.ReverseMode
-            autodiff = get_concrete_reverse_ad(
-                alg.autodiff, prob; check_reverse_mode = true)
-            vjp_op = VecJacOperator(prob, fu, u; autodiff)
-            if isinplace(prob)
-                vjp_cache = zero(u)
-                deriv_op = @closure (du, u, fu, p) -> dot(du, vjp_op(vjp_cache, fu, u, p))
-            else
-                deriv_op = @closure (du, u, fu, p) -> dot(du, vjp_op(fu, u, p))
-            end
-        else
-            autodiff = get_concrete_forward_ad(
-                alg.autodiff, prob; check_forward_mode = true)
-            jvp_op = JacVecOperator(prob, fu, u; autodiff)
-            if isinplace(prob)
-                jvp_cache = zero(fu)
-                deriv_op = @closure (du, u, fu, p) -> dot(fu, jvp_op(jvp_cache, du, u, p))
-            else
-                deriv_op = @closure (du, u, fu, p) -> dot(fu, jvp_op(du, u, p))
-            end
-        end
-    end
-
-    @bb u_cache = similar(u)
-    @bb fu_cache = similar(fu)
-
-    ϕ = @closure (f, p, u, du, α, u_cache, fu_cache) -> begin
-        @bb @. u_cache = u + α * du
-        fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
-        stats.nf += 1
-        return @fastmath internalnorm(fu_cache)^2 / 2
+for alg in (:Static, :HagerZhang, :MoreThuente, :BackTracking, :StrongWolfe)
+    depmsg = "`$(alg)(args...; kwargs...)` is deprecated. Please use `LineSearchesJL(; \
+              method = $(alg)(args...; kwargs...))` instead."
+    @eval function $(alg)(args...; autodiff = nothing, initial_alpha = true, kwargs...)
+        Base.depwarn($(depmsg), $(Meta.quot(alg)))
+        return LineSearch.LineSearchesJL(;
+            method = LineSearches.$(alg)(args...; kwargs...), autodiff, initial_alpha)
     end
-
-    dϕ = @closure (f, p, u, du, α, u_cache, fu_cache, deriv_op) -> begin
-        @bb @. u_cache = u + α * du
-        fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
-        stats.nf += 1
-        return deriv_op(du, u_cache, fu_cache, p)
-    end
-
-    ϕdϕ = @closure (f, p, u, du, α, u_cache, fu_cache, deriv_op) -> begin
-        @bb @. u_cache = u + α * du
-        fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
-        stats.nf += 1
-        deriv = deriv_op(du, u_cache, fu_cache, p)
-        obj = @fastmath internalnorm(fu_cache)^2 / 2
-        return obj, deriv
-    end
-
-    return LineSearchesJLCache(f, p, ϕ, dϕ, ϕdϕ, alg.method, T(alg.initial_alpha),
-        deriv_op, u_cache, fu_cache, stats)
 end
 
-function __internal_solve!(cache::LineSearchesJLCache, u, du; kwargs...)
-    ϕ = @closure α -> cache.ϕ(cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache)
-    if cache.deriv_op !== nothing
-        dϕ = @closure α -> cache.dϕ(
-            cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache, cache.deriv_op)
-        ϕdϕ = @closure α -> cache.ϕdϕ(
-            cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache, cache.deriv_op)
-    else
-        dϕ = @closure α -> FiniteDiff.finite_difference_derivative(ϕ, α)
-        ϕdϕ = @closure α -> (ϕ(α), FiniteDiff.finite_difference_derivative(ϕ, α))
-    end
-
-    ϕ₀, dϕ₀ = ϕdϕ(zero(eltype(u)))
-
-    # Here we should be resetting the search direction for some algorithms especially
-    # if we start mixing in jacobian reuse and such
-    dϕ₀ ≥ 0 && return (true, one(eltype(u)))
+Base.@deprecate LiFukushimaLineSearch(; nan_max_iter::Int = 5, kwargs...) LineSearch.LiFukushimaLineSearch(;
+    nan_maxiters = nan_max_iter, kwargs...)
 
-    # We can technically reduce 1 axpy by reusing the returned value from cache.method
-    # but it's not worth the extra complexity
-    cache.alpha = first(cache.method(ϕ, dϕ, ϕdϕ, cache.alpha, ϕ₀, dϕ₀))
-    return (false, cache.alpha)
+function callback_into_cache!(topcache, cache::AbstractLineSearchCache, args...)
+    LineSearch.callback_into_cache!(cache, get_fu(topcache))
 end
 
-"""
-    RobustNonMonotoneLineSearch(; gamma = 1 // 10000, sigma_0 = 1, M::Int = 10,
-        tau_min = 1 // 10, tau_max = 1 // 2, n_exp::Int = 2, maxiters::Int = 100,
-        η_strategy = (fn₁, n, uₙ, fₙ) -> fn₁ / n^2)
-
-Robust NonMonotone Line Search is a derivative free line search method from DF Sane
-[la2006spectral](@cite).
-
-### Keyword Arguments
-
-  - `M`: The monotonicity of the algorithm is determined by a this positive integer.
-    A value of 1 for `M` would result in strict monotonicity in the decrease of the L2-norm
-    of the function `f`. However, higher values allow for more flexibility in this reduction.
-    Despite this, the algorithm still ensures global convergence through the use of a
-    non-monotone line-search algorithm that adheres to the Grippo-Lampariello-Lucidi
-    condition. Values in the range of 5 to 20 are usually sufficient, but some cases may
-    call for a higher value of `M`. The default setting is 10.
-  - `gamma`: a parameter that influences if a proposed step will be accepted. Higher value
-    of `gamma` will make the algorithm more restrictive in accepting steps. Defaults to
-    `1e-4`.
-  - `tau_min`: if a step is rejected the new step size will get multiplied by factor, and
-    this parameter is the minimum value of that factor. Defaults to `0.1`.
-  - `tau_max`: if a step is rejected the new step size will get multiplied by factor, and
-    this parameter is the maximum value of that factor. Defaults to `0.5`.
-  - `n_exp`: the exponent of the loss, i.e. ``f_n=||F(x_n)||^{n\\_exp}``. The paper uses
-    `n_exp ∈ {1, 2}`. Defaults to `2`.
-  - `η_strategy`:  function to determine the parameter `η`, which enables growth
-    of ``||f_n||^2``. Called as `η = η_strategy(fn_1, n, x_n, f_n)` with `fn_1` initialized
-    as ``fn_1=||f(x_1)||^{n\\_exp}``, `n` is the iteration number, `x_n` is the current
-    `x`-value and `f_n` the current residual. Should satisfy ``η > 0`` and ``∑ₖ ηₖ < ∞``.
-    Defaults to ``fn_1 / n^2``.
-  - `maxiters`: the maximum number of iterations allowed for the inner loop of the
-    algorithm. Defaults to `100`.
-"""
-@kwdef @concrete struct RobustNonMonotoneLineSearch <:
-                        AbstractNonlinearSolveLineSearchAlgorithm
-    gamma = 1 // 10000
-    sigma_1 = 1
-    M::Int = 10
-    tau_min = 1 // 10
-    tau_max = 1 // 2
-    n_exp::Int = 2
-    maxiters::Int = 100
-    η_strategy = (fn₁, n, uₙ, fₙ) -> fn₁ / n^2
-end
-
-@concrete mutable struct RobustNonMonotoneLineSearchCache <:
-                         AbstractNonlinearSolveLineSearchCache
-    f
-    p
-    ϕ
-    u_cache
-    fu_cache
-    internalnorm
-    maxiters::Int
-    history
-    γ
-    σ₁
-    M::Int
-    τ_min
-    τ_max
-    nsteps::Int
-    η_strategy
-    n_exp::Int
-    stats::NLStats
-end
-
-function __internal_init(
-        prob::AbstractNonlinearProblem, alg::RobustNonMonotoneLineSearch, f::F, fu, u,
-        p, args...; stats, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
-    @bb u_cache = similar(u)
-    @bb fu_cache = similar(fu)
-    T = promote_type(eltype(fu), eltype(u))
-
-    ϕ = @closure (f, p, u, du, α, u_cache, fu_cache) -> begin
-        @bb @. u_cache = u + α * du
-        fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
-        stats.nf += 1
-        return internalnorm(fu_cache)^alg.n_exp
-    end
-
-    fn₁ = internalnorm(fu)^alg.n_exp
-    η_strategy = @closure (n, xₙ, fₙ) -> alg.η_strategy(fn₁, n, xₙ, fₙ)
-
-    return RobustNonMonotoneLineSearchCache(
-        f, p, ϕ, u_cache, fu_cache, internalnorm, alg.maxiters,
-        fill(fn₁, alg.M), T(alg.gamma), T(alg.sigma_1), alg.M,
-        T(alg.tau_min), T(alg.tau_max), 0, η_strategy, alg.n_exp, stats)
-end
-
-function __internal_solve!(cache::RobustNonMonotoneLineSearchCache, u, du; kwargs...)
-    T = promote_type(eltype(u), eltype(du))
-    ϕ = @closure α -> cache.ϕ(cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache)
-    f_norm_old = ϕ(eltype(u)(0))
-    α₊, α₋ = T(cache.σ₁), T(cache.σ₁)
-    η = cache.η_strategy(cache.nsteps, u, f_norm_old)
-    f_bar = maximum(cache.history)
-
-    for k in 1:(cache.maxiters)
-        f_norm = ϕ(α₊)
-        f_norm ≤ f_bar + η - cache.γ * α₊ * f_norm_old && return (false, α₊)
-
-        α₊ *= clamp(α₊ * f_norm_old / (f_norm + (T(2) * α₊ - T(1)) * f_norm_old),
-            cache.τ_min, cache.τ_max)
-
-        f_norm = ϕ(-α₋)
-        f_norm ≤ f_bar + η - cache.γ * α₋ * f_norm_old && return (false, -α₋)
-
-        α₋ *= clamp(α₋ * f_norm_old / (f_norm + (T(2) * α₋ - T(1)) * f_norm_old),
-            cache.τ_min, cache.τ_max)
-    end
-
-    return true, T(cache.σ₁)
-end
-
-function callback_into_cache!(topcache, cache::RobustNonMonotoneLineSearchCache, args...)
-    fu = get_fu(topcache)
-    cache.history[mod1(cache.nsteps, cache.M)] = cache.internalnorm(fu)^cache.n_exp
-    cache.nsteps += 1
-    return
-end
-
-"""
-    LiFukushimaLineSearch(; lambda_0 = 1, beta = 1 // 2, sigma_1 = 1 // 1000,
-        sigma_2 = 1 // 1000, eta = 1 // 10, nan_max_iter::Int = 5, maxiters::Int = 100)
-
-A derivative-free line search and global convergence of Broyden-like method for nonlinear
-equations [li2000derivative](@cite).
-"""
-@kwdef @concrete struct LiFukushimaLineSearch <: AbstractNonlinearSolveLineSearchAlgorithm
-    lambda_0 = 1
-    beta = 1 // 2
-    sigma_1 = 1 // 1000
-    sigma_2 = 1 // 1000
-    eta = 1 // 10
-    rho = 9 // 10
-    nan_max_iter::Int = 5  # TODO (breaking): Change this to nan_maxiters for uniformity
-    maxiters::Int = 100
-end
-
-@concrete mutable struct LiFukushimaLineSearchCache <: AbstractNonlinearSolveLineSearchCache
-    ϕ
-    f
-    p
-    internalnorm
-    u_cache
-    fu_cache
-    λ₀
-    β
-    σ₁
-    σ₂
-    η
-    ρ
-    α
-    nan_maxiters::Int
-    maxiters::Int
-    stats::NLStats
-end
-
-function __internal_init(
-        prob::AbstractNonlinearProblem, alg::LiFukushimaLineSearch, f::F, fu, u, p,
-        args...; stats, internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
-    @bb u_cache = similar(u)
-    @bb fu_cache = similar(fu)
-    T = promote_type(eltype(fu), eltype(u))
-
-    ϕ = @closure (f, p, u, du, α, u_cache, fu_cache) -> begin
-        @bb @. u_cache = u + α * du
-        fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
-        stats.nf += 1
-        return internalnorm(fu_cache)
-    end
-
-    return LiFukushimaLineSearchCache(
-        ϕ, f, p, internalnorm, u_cache, fu_cache, T(alg.lambda_0),
-        T(alg.beta), T(alg.sigma_1), T(alg.sigma_2), T(alg.eta),
-        T(alg.rho), T(true), alg.nan_max_iter, alg.maxiters, stats)
-end
-
-function __internal_solve!(cache::LiFukushimaLineSearchCache, u, du; kwargs...)
-    T = promote_type(eltype(u), eltype(du))
-    ϕ = @closure α -> cache.ϕ(cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache)
-
-    fx_norm = ϕ(T(0))
-
-    # Non-Blocking exit if the norm is NaN or Inf
-    !isfinite(fx_norm) && return (true, cache.α)
-
-    # Early Terminate based on Eq. 2.7
-    du_norm = cache.internalnorm(du)
-    fxλ_norm = ϕ(cache.α)
-    fxλ_norm ≤ cache.ρ * fx_norm - cache.σ₂ * du_norm^2 && return (false, cache.α)
-
-    λ₂, λ₁ = cache.λ₀, cache.λ₀
-    fxλp_norm = ϕ(λ₂)
-
-    if !isfinite(fxλp_norm)
-        nan_converged = false
-        for _ in 1:(cache.nan_maxiters)
-            λ₁, λ₂ = λ₂, cache.β * λ₂
-            fxλp_norm = ϕ(λ₂)
-            nan_converged = isfinite(fxλp_norm)
-            nan_converged && break
-        end
-        nan_converged || return (true, cache.α)
-    end
-
-    for i in 1:(cache.maxiters)
-        fxλp_norm = ϕ(λ₂)
-        converged = fxλp_norm ≤ (1 + cache.η) * fx_norm - cache.σ₁ * λ₂^2 * du_norm^2
-        converged && return (false, λ₂)
-        λ₁, λ₂ = λ₂, cache.β * λ₂
-    end
-
-    return true, cache.α
+function reinit_cache!(cache::AbstractLineSearchCache, args...; kwargs...)
+    return SciMLBase.reinit!(cache, args...; kwargs...)
 end
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 93d10f98b..13feb8253 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -25,8 +25,7 @@ Construct a cache for the Jacobian of `f` w.r.t. `u`.
   - `jvp_autodiff`: Automatic Differentiation or Finite Differencing backend for computing
     the Jacobian-vector product.
   - `linsolve`: Linear Solver Algorithm used to determine if we need a concrete jacobian
-    or if possible we can just use a [`SciMLJacobianOperators.JacobianOperator`](@ref)
-    instead.
+    or if possible we can just use a `SciMLJacobianOperators.JacobianOperator` instead.
 """
 @concrete mutable struct JacobianCache{iip} <: AbstractNonlinearSolveJacobianCache{iip}
     J
diff --git a/src/internal/termination.jl b/src/internal/termination.jl
index 570bae110..ef3f7c4c0 100644
--- a/src/internal/termination.jl
+++ b/src/internal/termination.jl
@@ -45,12 +45,12 @@ function update_from_termination_cache!(tc_cache, cache, u = get_u(cache))
 end
 
 function update_from_termination_cache!(
-        tc_cache, cache, mode::AbstractNonlinearTerminationMode, u = get_u(cache))
+        tc_cache, cache, ::AbstractNonlinearTerminationMode, u = get_u(cache))
     evaluate_f!(cache, u, cache.p)
 end
 
 function update_from_termination_cache!(
-        tc_cache, cache, mode::AbstractSafeBestNonlinearTerminationMode, u = get_u(cache))
+        tc_cache, cache, ::AbstractSafeBestNonlinearTerminationMode, u = get_u(cache))
     if isinplace(cache)
         copyto!(get_u(cache), tc_cache.u)
     else
diff --git a/test/gpu/core_tests.jl b/test/gpu/core_tests.jl
index d6d38ee1a..75087aa30 100644
--- a/test/gpu/core_tests.jl
+++ b/test/gpu/core_tests.jl
@@ -12,13 +12,19 @@
 
         prob = NonlinearProblem(linear_f, u0)
 
-        SOLVERS = (NewtonRaphson(), LevenbergMarquardt(; linsolve = QRFactorization()),
-            LevenbergMarquardt(; linsolve = KrylovJL_GMRES()), PseudoTransient(),
-            Klement(), Broyden(; linesearch = LiFukushimaLineSearch()),
+        SOLVERS = (
+            NewtonRaphson(),
+            LevenbergMarquardt(; linsolve = QRFactorization()),
+            LevenbergMarquardt(; linsolve = KrylovJL_GMRES()),
+            PseudoTransient(),
+            Klement(),
+            Broyden(; linesearch = LiFukushimaLineSearch()),
             LimitedMemoryBroyden(; threshold = 2, linesearch = LiFukushimaLineSearch()),
-            DFSane(), TrustRegion(; linsolve = QRFactorization()),
+            DFSane(),
+            TrustRegion(; linsolve = QRFactorization()),
             TrustRegion(; linsolve = KrylovJL_GMRES(), concrete_jac = true),  # Needed if Zygote not loaded
-            nothing)
+            nothing
+        )
 
         @testset "[IIP] GPU Solvers" begin
             for alg in SOLVERS
diff --git a/test/misc/other_tests.jl b/test/misc/other_tests.jl
deleted file mode 100644
index 765177c38..000000000
--- a/test/misc/other_tests.jl
+++ /dev/null
@@ -1,10 +0,0 @@
-@testitem "No warning tests" tags=[:misc] begin
-    using NonlinearSolve
-
-    f(u, p) = u .* u .- p
-    u0 = [1.0, 1.0]
-    p = 2.0
-    prob = NonlinearProblem(f, u0, p)
-    @test_nowarn solve(
-        prob, NewtonRaphson(autodiff = AutoFiniteDiff(), linesearch = LineSearchesJL()))
-end

From d56476c69c749a4b575b47d58c03cf366ab7134c Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Fri, 4 Oct 2024 19:01:32 +0200
Subject: [PATCH 524/700] fix: use DI preparation result when initializing
 Jacobian (#472)

---
 src/internal/jacobian.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 13feb8253..390c0947f 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -88,7 +88,7 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
                 if iip
                     DI.jacobian(f, fu, di_extras, autodiff, u, Constant(p))
                 else
-                    DI.jacobian(f, autodiff, u, Constant(p))
+                    DI.jacobian(f, di_extras, autodiff, u, Constant(p))
                 end
             end
         else

From 16d66b1933c6b562dc3aada375cc6d51c97a6e54 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 5 Oct 2024 10:25:55 -0400
Subject: [PATCH 525/700] fix: don't use similar on prototype

---
 Project.toml             |  2 +-
 src/internal/jacobian.jl | 10 +++++-----
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/Project.toml b/Project.toml
index d8ec44ac1..1651aab2a 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.15.0"
+version = "3.15.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 390c0947f..0ab1286d1 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -92,13 +92,13 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
                 end
             end
         else
-            jac_proto = if eltype(f.jac_prototype) <: Bool
-                similar(f.jac_prototype, promote_type(eltype(fu), eltype(u)))
+            if eltype(f.jac_prototype) <: Bool
+                jac_proto = similar(f.jac_prototype, promote_type(eltype(fu), eltype(u)))
+                fill!(jac_proto, false)
+                jac_proto
             else
-                similar(f.jac_prototype)
+                f.jac_prototype
             end
-            fill!(jac_proto, false)
-            jac_proto
         end
     end
 

From b5981e2c8fed67b3071a787022aa277efb6be2d3 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 5 Oct 2024 10:33:48 -0400
Subject: [PATCH 526/700] fix: use a copy

---
 src/internal/jacobian.jl | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 0ab1286d1..0f885de47 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -92,12 +92,11 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
                 end
             end
         else
+            # NOTE: don't use similar because that might lead to an unwrapped array
             if eltype(f.jac_prototype) <: Bool
-                jac_proto = similar(f.jac_prototype, promote_type(eltype(fu), eltype(u)))
-                fill!(jac_proto, false)
-                jac_proto
+                promote_type(eltype(fu), eltype(u)).(f.jac_prototype)
             else
-                f.jac_prototype
+                copy(f.jac_prototype)
             end
         end
     end

From 834516a74acea89793562a7bf380d276a696cb48 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 5 Oct 2024 14:05:52 -0400
Subject: [PATCH 527/700] fix: partial revert of previous fix

---
 src/internal/helpers.jl  | 5 ++---
 src/internal/jacobian.jl | 5 ++---
 2 files changed, 4 insertions(+), 6 deletions(-)

diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index afc24ce5b..5334f11dc 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -1,9 +1,8 @@
 # Evaluate the residual function at a given point
 function evaluate_f(prob::AbstractNonlinearProblem{uType, iip}, u) where {uType, iip}
-    (; f, u0, p) = prob
+    (; f, p) = prob
     if iip
-        fu = f.resid_prototype === nothing ? zero(u) :
-             promote_type(eltype(u), eltype(f.resid_prototype)).(f.resid_prototype)
+        fu = f.resid_prototype === nothing ? zero(u) : similar(f.resid_prototype)
         f(fu, u, p)
     else
         fu = f(u, p)
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 0f885de47..b78eb7383 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -92,11 +92,10 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
                 end
             end
         else
-            # NOTE: don't use similar because that might lead to an unwrapped array
             if eltype(f.jac_prototype) <: Bool
-                promote_type(eltype(fu), eltype(u)).(f.jac_prototype)
+                similar(f.jac_prototype, promote_type(eltype(fu), eltype(u)))
             else
-                copy(f.jac_prototype)
+                similar(f.jac_prototype)
             end
         end
     end

From b5f90257d2b6d1a344e0b464b2b1b916ec9608f9 Mon Sep 17 00:00:00 2001
From: Anant Thazhemadam <anant.thazhemadam@gmail.com>
Date: Thu, 17 Oct 2024 10:35:30 +0530
Subject: [PATCH 528/700] ci: test with `1`, `lts` and `pre` versions of julia

---
 lib/SimpleNonlinearSolve/.github/workflows/Tests.yml | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/.github/workflows/Tests.yml b/lib/SimpleNonlinearSolve/.github/workflows/Tests.yml
index e63c1039e..c8c552d79 100644
--- a/lib/SimpleNonlinearSolve/.github/workflows/Tests.yml
+++ b/lib/SimpleNonlinearSolve/.github/workflows/Tests.yml
@@ -28,6 +28,10 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
+        version:
+          - "1"
+          - "lts"
+          - "pre"
         group:
           - "core"
           - "adjoint"
@@ -38,6 +42,7 @@ jobs:
 
     uses: "SciML/.github/.github/workflows/tests.yml@v1"
     with:
+      julia-version: "${{ matrix.version }}"
       group: "${{ matrix.group }}"
       os: "${{ matrix.os }}"
     secrets: "inherit"

From 1ad7a3a7a020555f20dd07e62d009699248004e0 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 18:33:32 -0400
Subject: [PATCH 529/700] fix: remove uses of LineSearches.jl backtracking
 (#480)

* fix: remove uses of LineSearches.jl backtracking

* docs: fix chunksize
---
 .github/workflows/Downgrade.yml     |  2 +-
 Project.toml                        |  6 +--
 docs/src/tutorials/large_systems.md |  6 +--
 src/NonlinearSolve.jl               |  2 +-
 src/default.jl                      | 20 +++------
 test/core/rootfind_tests.jl         | 63 +++++++++++++++++++----------
 6 files changed, 54 insertions(+), 45 deletions(-)

diff --git a/.github/workflows/Downgrade.yml b/.github/workflows/Downgrade.yml
index fa9be3c7a..83001be29 100644
--- a/.github/workflows/Downgrade.yml
+++ b/.github/workflows/Downgrade.yml
@@ -15,7 +15,7 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        version: ["1"]
+        version: ["1.10"]
     steps:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v2
diff --git a/Project.toml b/Project.toml
index 1651aab2a..725aa5c9d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.15.1"
+version = "3.15.2"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -80,7 +80,7 @@ Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
 LazyArrays = "1.8.2, 2"
 LeastSquaresOptim = "0.8.5"
-LineSearch = "0.1.2"
+LineSearch = "0.1.4"
 LineSearches = "7.3"
 LinearAlgebra = "1.10"
 LinearSolve = "2.35"
@@ -96,7 +96,7 @@ Pkg = "1.10"
 PrecompileTools = "1.2"
 Preferences = "1.4"
 Printf = "1.10"
-Random = "1.91"
+Random = "1.10"
 ReTestItems = "1.24"
 RecursiveArrayTools = "3.27"
 Reexport = "1.2"
diff --git a/docs/src/tutorials/large_systems.md b/docs/src/tutorials/large_systems.md
index 17b768288..0a0be59e7 100644
--- a/docs/src/tutorials/large_systems.md
+++ b/docs/src/tutorials/large_systems.md
@@ -143,12 +143,12 @@ prob_brusselator_2d_autosparse = NonlinearProblem(
     u0, p; abstol = 1e-10, reltol = 1e-10)
 
 @btime solve(prob_brusselator_2d_autosparse,
-    NewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 32)));
+    NewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 12)));
 @btime solve(prob_brusselator_2d_autosparse,
-    NewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 32),
+    NewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 12),
         linsolve = KLUFactorization()));
 @btime solve(prob_brusselator_2d_autosparse,
-    NewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 32),
+    NewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 12),
         linsolve = KrylovJL_GMRES()));
 nothing # hide
 ```
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 6babbdbdc..5e2dc5555 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -176,7 +176,7 @@ export NewtonDescent, SteepestDescent, Dogleg, DampedNewtonDescent, GeodesicAcce
 ## Line Search Algorithms
 export LineSearchesJL, LiFukushimaLineSearch # FIXME: deprecated. use LineSearch.jl directly
 export Static, HagerZhang, MoreThuente, StrongWolfe, BackTracking  # FIXME: deprecated
-export NoLineSearch, RobustNonMonotoneLineSearch
+export LineSearch, NoLineSearch, RobustNonMonotoneLineSearch
 ## Trust Region Algorithms
 export RadiusUpdateSchemes
 
diff --git a/src/default.jl b/src/default.jl
index 5623c553f..c0924e2ff 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -364,9 +364,7 @@ function RobustMultiNewton(::Type{T} = Float64; concrete_jac = nothing, linsolve
                 radius_update_scheme = RadiusUpdateSchemes.Bastin),
             NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
             NewtonRaphson(; concrete_jac, linsolve, precs,
-                linesearch = LineSearch.LineSearchesJL(;
-                    method = LineSearches.BackTracking()),
-                autodiff),
+                linesearch = LineSearch.BackTracking(), autodiff),
             TrustRegion(; concrete_jac, linsolve, precs,
                 radius_update_scheme = RadiusUpdateSchemes.NLsolve, autodiff),
             TrustRegion(; concrete_jac, linsolve, precs,
@@ -407,9 +405,7 @@ function FastShortcutNonlinearPolyalg(
         else
             algs = (NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
                 NewtonRaphson(; concrete_jac, linsolve, precs,
-                    linesearch = LineSearch.LineSearchesJL(;
-                        method = LineSearches.BackTracking()),
-                    autodiff),
+                    linesearch = LineSearch.BackTracking(), autodiff),
                 TrustRegion(; concrete_jac, linsolve, precs, autodiff),
                 TrustRegion(; concrete_jac, linsolve, precs,
                     radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff))
@@ -430,9 +426,7 @@ function FastShortcutNonlinearPolyalg(
                     SimpleKlement(),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs,
-                        linesearch = LineSearch.LineSearchesJL(;
-                            method = LineSearches.BackTracking()),
-                        autodiff),
+                        linesearch = LineSearch.BackTracking(), autodiff),
                     TrustRegion(; concrete_jac, linsolve, precs,
                         radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff))
             end
@@ -451,9 +445,7 @@ function FastShortcutNonlinearPolyalg(
                     Klement(; linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs,
-                        linesearch = LineSearch.LineSearchesJL(;
-                            method = LineSearches.BackTracking()),
-                        autodiff),
+                        linesearch = LineSearch.BackTracking(), autodiff),
                     TrustRegion(; concrete_jac, linsolve, precs, autodiff),
                     TrustRegion(; concrete_jac, linsolve, precs,
                         radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff))
@@ -489,9 +481,7 @@ function FastShortcutNLLSPolyalg(
                 linsolve, precs, disable_geodesic = Val(true), autodiff, kwargs...),
             TrustRegion(; concrete_jac, linsolve, precs, autodiff, kwargs...),
             GaussNewton(; concrete_jac, linsolve, precs,
-                linesearch = LineSearch.LineSearchesJL(;
-                    method = LineSearches.BackTracking()),
-                autodiff, kwargs...),
+                linesearch = LineSearch.BackTracking(), autodiff, kwargs...),
             TrustRegion(; concrete_jac, linsolve, precs,
                 radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff, kwargs...),
             LevenbergMarquardt(; linsolve, precs, autodiff, kwargs...))
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index 6a56c6ac6..cb8d62e99 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -53,11 +53,15 @@ end
 # --- NewtonRaphson tests ---
 
 @testitem "NewtonRaphson" setup=[CoreRootfindTesting] tags=[:core] begin
-    @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad))" for lsmethod in (
-            Static(), StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
-        ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff())
+    @testset "LineSearch: $(_nameof(linesearch)) LineSearch AD: $(_nameof(ad))" for ad in (
+            AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()
+        ),
+        linesearch in (
+            Static(; autodiff = ad), StrongWolfe(; autodiff = ad),
+            BackTracking(; autodiff = ad), LineSearch.BackTracking(; autodiff = ad),
+            HagerZhang(; autodiff = ad), MoreThuente(; autodiff = ad)
+        )
 
-        linesearch = LineSearchesJL(; method = lsmethod, autodiff = ad)
         u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
 
         @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
@@ -463,14 +467,17 @@ end
 # --- Broyden tests ---
 
 @testitem "Broyden" setup=[CoreRootfindTesting] tags=[:core] begin
-    @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian) Update Rule: $(update_rule)" for lsmethod in (
-            Static(), StrongWolfe(), BackTracking(),
-            HagerZhang(), MoreThuente(), LiFukushimaLineSearch()),
-        ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()),
+    @testset "LineSearch: $(_nameof(linesearch)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian) Update Rule: $(update_rule)" for ad in (
+            AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()
+        ),
+        linesearch in (
+            Static(; autodiff = ad), StrongWolfe(; autodiff = ad),
+            BackTracking(; autodiff = ad), LineSearch.BackTracking(; autodiff = ad),
+            HagerZhang(; autodiff = ad), MoreThuente(; autodiff = ad)
+        ),
         init_jacobian in (Val(:identity), Val(:true_jacobian)),
         update_rule in (Val(:good_broyden), Val(:bad_broyden), Val(:diagonal))
 
-        linesearch = LineSearchesJL(; method = lsmethod, autodiff = ad)
         u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
 
         @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
@@ -513,12 +520,16 @@ end
 # --- Klement tests ---
 
 @testitem "Klement" setup=[CoreRootfindTesting] tags=[:core] begin
-    @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian)" for lsmethod in (
-            Static(), StrongWolfe(), BackTracking(), HagerZhang(), MoreThuente()),
-        ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()),
+    @testset "LineSearch: $(_nameof(linesearch)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian)" for ad in (
+            AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()
+        ),
+        linesearch in (
+            Static(; autodiff = ad), StrongWolfe(; autodiff = ad),
+            BackTracking(; autodiff = ad), LineSearch.BackTracking(; autodiff = ad),
+            HagerZhang(; autodiff = ad), MoreThuente(; autodiff = ad)
+        ),
         init_jacobian in (Val(:identity), Val(:true_jacobian), Val(:true_jacobian_diagonal))
 
-        linesearch = LineSearchesJL(; method = lsmethod, autodiff = ad)
         u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
 
         @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
@@ -562,19 +573,25 @@ end
 # --- LimitedMemoryBroyden tests ---
 
 @testitem "LimitedMemoryBroyden" setup=[CoreRootfindTesting] tags=[:core] begin
-    @testset "LineSearch: $(_nameof(lsmethod)) LineSearch AD: $(_nameof(ad))" for lsmethod in (
-            Static(), StrongWolfe(), BackTracking(),
-            HagerZhang(), MoreThuente(), LiFukushimaLineSearch()),
-        ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff())
+    @testset "LineSearch: $(_nameof(linesearch)) LineSearch AD: $(_nameof(ad))" for ad in (
+            AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()
+        ),
+        linesearch in (
+            Static(; autodiff = ad), StrongWolfe(; autodiff = ad),
+            BackTracking(; autodiff = ad), LineSearch.BackTracking(; autodiff = ad),
+            HagerZhang(; autodiff = ad), MoreThuente(; autodiff = ad),
+            LiFukushimaLineSearch()
+        )
 
-        linesearch = LineSearchesJL(; method = lsmethod, autodiff = ad)
         u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
 
         @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
+            broken = linesearch isa BackTracking && ad isa AutoFiniteDiff && u0 isa Vector
+
             solver = LimitedMemoryBroyden(; linesearch)
             sol = benchmark_nlsolve_oop(quadratic_f, u0; solver)
-            @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+            @test SciMLBase.successful_retcode(sol) broken=broken
+            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9) broken=broken
 
             cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0),
                 LimitedMemoryBroyden(; linesearch), abstol = 1e-9)
@@ -582,11 +599,13 @@ end
         end
 
         @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+            broken = linesearch isa BackTracking && ad isa AutoFiniteDiff && u0 isa Vector
             ad isa AutoZygote && continue
+
             solver = LimitedMemoryBroyden(; linesearch)
             sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver)
-            @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+            @test SciMLBase.successful_retcode(sol) broken=broken
+            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9) broken=broken
 
             cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0),
                 LimitedMemoryBroyden(; linesearch), abstol = 1e-9)

From 388e1bef797f13f01b4e971de40cdaa2f777c124 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 14:05:50 -0400
Subject: [PATCH 530/700] refactor: migrate to LineSearch.jl

---
 src/internal/termination.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/internal/termination.jl b/src/internal/termination.jl
index ef3f7c4c0..e09cfcdda 100644
--- a/src/internal/termination.jl
+++ b/src/internal/termination.jl
@@ -45,7 +45,7 @@ function update_from_termination_cache!(tc_cache, cache, u = get_u(cache))
 end
 
 function update_from_termination_cache!(
-        tc_cache, cache, ::AbstractNonlinearTerminationMode, u = get_u(cache))
+        _, cache, ::AbstractNonlinearTerminationMode, u = get_u(cache))
     evaluate_f!(cache, u, cache.p)
 end
 

From c5c7f5b69472d8e7eb701cef9adb5f8e9699f63c Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 26 Sep 2024 05:20:29 -0400
Subject: [PATCH 531/700] fix: forward reinit_cache to SciMLBase.reinit

---
 src/internal/termination.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/internal/termination.jl b/src/internal/termination.jl
index e09cfcdda..ef3f7c4c0 100644
--- a/src/internal/termination.jl
+++ b/src/internal/termination.jl
@@ -45,7 +45,7 @@ function update_from_termination_cache!(tc_cache, cache, u = get_u(cache))
 end
 
 function update_from_termination_cache!(
-        _, cache, ::AbstractNonlinearTerminationMode, u = get_u(cache))
+        tc_cache, cache, ::AbstractNonlinearTerminationMode, u = get_u(cache))
     evaluate_f!(cache, u, cache.p)
 end
 

From bc2c10a46ce52a7760a23221c79e7a74554f39b5 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 14:05:50 -0400
Subject: [PATCH 532/700] refactor: migrate to LineSearch.jl

---
 src/internal/termination.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/internal/termination.jl b/src/internal/termination.jl
index ef3f7c4c0..e09cfcdda 100644
--- a/src/internal/termination.jl
+++ b/src/internal/termination.jl
@@ -45,7 +45,7 @@ function update_from_termination_cache!(tc_cache, cache, u = get_u(cache))
 end
 
 function update_from_termination_cache!(
-        tc_cache, cache, ::AbstractNonlinearTerminationMode, u = get_u(cache))
+        _, cache, ::AbstractNonlinearTerminationMode, u = get_u(cache))
     evaluate_f!(cache, u, cache.p)
 end
 

From dfcc660384a5a2bd3b1d99b7926d07193430ca63 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 22 Aug 2024 17:24:51 -0700
Subject: [PATCH 533/700] feat: setup NonlinearSolveBase

---
 lib/NonlinearSolveBase/LICENSE                |  21 ++
 lib/NonlinearSolveBase/Project.toml           |  39 ++++
 .../ext/NonlinearSolveBaseForwardDiffExt.jl   |   9 +
 .../ext/NonlinearSolveBaseSparseArraysExt.jl  |  10 +
 .../src/NonlinearSolveBase.jl                 |  28 +++
 lib/NonlinearSolveBase/src/autodiff.jl        |   0
 lib/NonlinearSolveBase/src/common_defaults.jl |  47 +++++
 .../src/immutable_problem.jl                  |   0
 lib/NonlinearSolveBase/src/public.jl          | 118 ++++++++++++
 .../src/termination_conditions.jl             | 180 ++++++++++++++++++
 lib/NonlinearSolveBase/src/utils.jl           |  76 ++++++++
 lib/NonlinearSolveBase/test/runtests.jl       |   1 +
 12 files changed, 529 insertions(+)
 create mode 100644 lib/NonlinearSolveBase/LICENSE
 create mode 100644 lib/NonlinearSolveBase/Project.toml
 create mode 100644 lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
 create mode 100644 lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
 create mode 100644 lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
 create mode 100644 lib/NonlinearSolveBase/src/autodiff.jl
 create mode 100644 lib/NonlinearSolveBase/src/common_defaults.jl
 create mode 100644 lib/NonlinearSolveBase/src/immutable_problem.jl
 create mode 100644 lib/NonlinearSolveBase/src/public.jl
 create mode 100644 lib/NonlinearSolveBase/src/termination_conditions.jl
 create mode 100644 lib/NonlinearSolveBase/src/utils.jl
 create mode 100644 lib/NonlinearSolveBase/test/runtests.jl

diff --git a/lib/NonlinearSolveBase/LICENSE b/lib/NonlinearSolveBase/LICENSE
new file mode 100644
index 000000000..411ad533f
--- /dev/null
+++ b/lib/NonlinearSolveBase/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2024 Avik Pal <avikpal@mit.edu> and contributors
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
new file mode 100644
index 000000000..1c7047ca6
--- /dev/null
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -0,0 +1,39 @@
+name = "NonlinearSolveBase"
+uuid = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
+authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
+version = "1.0.0"
+
+[deps]
+ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
+ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
+FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
+RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
+SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+UnrolledUtilities = "0fe1646c-419e-43be-ac14-22321958931b"
+
+[weakdeps]
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
+[extensions]
+NonlinearSolveBaseForwardDiffExt = "ForwardDiff"
+NonlinearSolveBaseSparseArraysExt = "SparseArrays"
+
+[compat]
+ArrayInterface = "7.9"
+Compat = "4.15"
+ConcreteStructs = "0.2.3"
+FastClosures = "0.3"
+ForwardDiff = "0.10.36"
+LinearAlgebra = "1.10"
+Markdown = "1.10"
+RecursiveArrayTools = "3"
+SciMLBase = "2.50"
+SparseArrays = "1.10"
+StaticArraysCore = "1.4"
+UnrolledUtilities = "0.1"
+julia = "1.10"
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
new file mode 100644
index 000000000..c29fea0d1
--- /dev/null
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
@@ -0,0 +1,9 @@
+module NonlinearSolveBaseForwardDiffExt
+
+using ForwardDiff: ForwardDiff, Dual
+using NonlinearSolveBase: Utils
+
+Utils.value(::Type{Dual{T, V, N}}) where {T, V, N} = V
+Utils.value(x::Dual) = Utils.value(ForwardDiff.value(x))
+
+end
\ No newline at end of file
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
new file mode 100644
index 000000000..d20e9b59b
--- /dev/null
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
@@ -0,0 +1,10 @@
+module NonlinearSolveBaseSparseArraysExt
+
+using NonlinearSolveBase: NonlinearSolveBase
+using SparseArrays: AbstractSparseMatrixCSC, nonzeros
+
+function NonlinearSolveBase.NAN_CHECK(x::AbstractSparseMatrixCSC)
+    return any(NonlinearSolveBase.NAN_CHECK, nonzeros(x))
+end
+
+end
\ No newline at end of file
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
new file mode 100644
index 000000000..aff03d1e3
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -0,0 +1,28 @@
+module NonlinearSolveBase
+
+using ArrayInterface: ArrayInterface
+using Compat: @compat
+using ConcreteStructs: @concrete
+using FastClosures: @closure
+using LinearAlgebra: norm
+using Markdown: @doc_str
+using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
+using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator
+using StaticArraysCore: StaticArray
+
+include("public.jl")
+include("utils.jl")
+
+include("common_defaults.jl")
+include("termination_conditions.jl")
+include("autodiff.jl")
+include("immutable_problem.jl")
+
+# Unexported Public API
+@compat(public, (L2_NORM, Linf_NORM, NAN_CHECK, UNITLESS_ABS2, get_tolerance))
+
+export RelTerminationMode, AbsTerminationMode, NormTerminationMode, RelNormTerminationMode,
+       AbsNormTerminationMode, RelNormSafeTerminationMode, AbsNormSafeTerminationMode,
+       RelNormSafeNormTerminationMode, AbsNormSafeNormTerminationMode
+
+end
diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/NonlinearSolveBase/src/common_defaults.jl b/lib/NonlinearSolveBase/src/common_defaults.jl
new file mode 100644
index 000000000..4518063a5
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/common_defaults.jl
@@ -0,0 +1,47 @@
+UNITLESS_ABS2(x::Number) = abs2(x)
+function UNITLESS_ABS2(x::AbstractArray)
+    return mapreduce(UNITLESS_ABS2, Utils.abs2_and_sum, x; init = Utils.zero_init(x))
+end
+function UNITLESS_ABS2(x::Union{AbstractVectorOfArray, ArrayPartition})
+    return mapreduce(UNITLESS_ABS2, Utils.abs2_and_sum,
+        Utils.get_internal_array(x); init = Utils.zero_init(x))
+end
+
+NAN_CHECK(x::Number) = isnan(x)
+NAN_CHECK(x::Enum) = false
+NAN_CHECK(x::AbstractArray) = any(NAN_CHECK, x)
+function NAN_CHECK(x::Union{AbstractVectorOfArray, ArrayPartition})
+    return any(NAN_CHECK, Utils.get_internal_array(x))
+end
+
+L2_NORM(u::Union{AbstractFloat, Complex}) = @fastmath abs(u)
+L2_NORM(u::AbstractArray) = @fastmath sqrt(UNITLESS_ABS2(u))
+function L2_NORM(u::AbstractArray{<:Union{AbstractFloat, Complex}})
+    if Utils.fast_scalar_indexing(u)
+        x = zero(eltype(u))
+        @simd for i in eachindex(u)
+            @inbounds @fastmath x += abs2(u[i])
+        end
+        return @fastmath sqrt(real(x))
+    end
+    return @fastmath sqrt(UNITLESS_ABS2(u))
+end
+function L2_NORM(u::StaticArray{<:Union{AbstractFloat, Complex}})
+    return @fastmath sqrt(real(sum(abs2, u)))
+end
+L2_NORM(u) = norm(u, 2)
+
+Linf_NORM(u::Union{AbstractFloat, Complex}) = @fastmath abs(u)
+Linf_NORM(u) = maximum(abs, u)
+
+get_tolerance(η, ::Type{T}) where {T} = Utils.convert_real(T, η)
+function get_tolerance(::Nothing, ::Type{T}) where {T}
+    η = real(oneunit(T)) * (eps(real(one(T)))^(4 // 5))
+    return get_tolerance(η, T)
+end
+
+get_tolerance(_, η, ::Type{T}) where {T} = get_tolerance(η, T)
+function get_tolerance(::Union{StaticArray, Number}, ::Nothing, ::Type{T}) where {T}
+    # Rational numbers can throw an error if used inside GPU Kernels
+    return T(real(oneunit(T)) * (eps(real(one(T)))^(real(T)(0.8))))
+end
diff --git a/lib/NonlinearSolveBase/src/immutable_problem.jl b/lib/NonlinearSolveBase/src/immutable_problem.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/NonlinearSolveBase/src/public.jl b/lib/NonlinearSolveBase/src/public.jl
new file mode 100644
index 000000000..24f467cbd
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/public.jl
@@ -0,0 +1,118 @@
+# forward declarations of public API
+function UNITLESS_ABS2 end
+function NAN_CHECK end
+function L2_NORM end
+function Linf_NORM end
+function get_tolerance end
+
+# Nonlinear Solve Termination Conditions
+abstract type AbstractNonlinearTerminationMode end
+abstract type AbstractSafeNonlinearTerminationMode <: AbstractNonlinearTerminationMode end
+abstract type AbstractSafeBestNonlinearTerminationMode <:
+              AbstractSafeNonlinearTerminationMode end
+
+#! format: off
+const TERM_DOCS = Dict(
+    :Norm => doc"``\| \Delta u \| \leq reltol \times \| \Delta u + u \|`` or ``\| \Delta u \| \leq abstol``.",
+    :Rel => doc"``all \left(| \Delta u | \leq reltol \times | u | \right)``.",
+    :RelNorm => doc"``\| \Delta u \| \leq reltol \times \| \Delta u + u \|``.",
+    :Abs => doc"``all \left( | \Delta u | \leq abstol \right)``.",
+    :AbsNorm => doc"``\| \Delta u \| \leq abstol``."
+)
+
+const TERM_INTERNALNORM_DOCS = """
+where `internalnorm` is the norm to use for the termination condition. Special handling is
+done for `norm(_, 2)`, `norm`, `norm(_, Inf)`, and `maximum(abs, _)`."""
+#! format: on
+
+for name in (:Rel, :Abs)
+    struct_name = Symbol(name, :TerminationMode)
+    doctring = TERM_DOCS[name]
+
+    @eval begin
+        """
+            $($struct_name) <: AbstractNonlinearTerminationMode
+
+        Terminates if $($doctring).
+
+        ``\\Delta u`` denotes the increment computed by the nonlinear solver and ``u`` denotes the solution.
+        """
+        struct $(struct_name) <: AbstractNonlinearTerminationMode end
+    end
+end
+
+for name in (:Norm, :RelNorm, :AbsNorm)
+    struct_name = Symbol(name, :TerminationMode)
+    doctring = TERM_DOCS[name]
+
+    @eval begin
+        """
+            $($struct_name) <: AbstractSafeNonlinearTerminationMode
+
+        Terminates if $($doctring).
+
+        ``\\Delta u`` denotes the increment computed by the inner nonlinear solver.
+
+        ## Constructor
+
+            $($struct_name)(internalnorm = nothing)
+
+        $($TERM_INTERNALNORM_DOCS).
+        """
+        struct $(struct_name){F} <: AbstractSafeNonlinearTerminationMode
+            internalnorm::F
+
+            function $(struct_name)(internalnorm::F) where {F}
+                norm = Utils.standardize_norm(internalnorm)
+                return new{typeof(norm)}(norm)
+            end
+        end
+    end
+end
+
+for norm_type in (:RelNorm, :AbsNorm), safety in (:Safe, :SafeBest)
+    struct_name = Symbol(norm_type, safety, :TerminationMode)
+    supertype_name = Symbol(:Abstract, safety, :NonlinearTerminationMode)
+
+    doctring = safety == :Safe ?
+               "Essentially [`$(norm_type)NormTerminationMode`](@ref) + terminate if there \
+                has been no improvement for the last `patience_steps` + terminate if the \
+                solution blows up (diverges)." :
+               "Essentially [`$(norm_type)SafeTerminationMode`](@ref), but caches the best\
+                solution found so far."
+
+    @eval begin
+        """
+            $($struct_name) <: $($supertype_name)
+
+        $($doctring)
+
+        ## Constructor
+
+            $($struct_name)(internalnorm; protective_threshold = nothing,
+                patience_steps = 100, patience_objective_multiplier = 3,
+                min_max_factor = 1.3, max_stalled_steps = nothing)
+
+        $($TERM_INTERNALNORM_DOCS).
+        """
+        @concrete struct $(struct_name) <: $(supertype_name)
+            internalnorm
+            protective_threshold
+            patience_steps::Int
+            patience_objective_multiplier
+            min_max_factor
+            max_stalled_steps <: Union{Nothing, Int}
+
+            function $(struct_name)(internalnorm::F; protective_threshold = nothing,
+                    patience_steps = 100, patience_objective_multiplier = 3,
+                    min_max_factor = 1.3, max_stalled_steps = nothing) where {F}
+                norm = Utils.standardize_norm(internalnorm)
+                return new{typeof(norm), typeof(protective_threshold),
+                    typeof(patience_objective_multiplier),
+                    typeof(min_max_factor), typeof(max_stalled_steps)}(
+                    norm, protective_threshold, patience_steps,
+                    patience_objective_multiplier, min_max_factor, max_stalled_steps)
+            end
+        end
+    end
+end
diff --git a/lib/NonlinearSolveBase/src/termination_conditions.jl b/lib/NonlinearSolveBase/src/termination_conditions.jl
new file mode 100644
index 000000000..3cbba4b8b
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/termination_conditions.jl
@@ -0,0 +1,180 @@
+const RelNormModes = Union{
+    RelNormTerminationMode, RelNormSafeTerminationMode, RelNormSafeBestTerminationMode}
+const AbsNormModes = Union{
+    AbsNormTerminationMode, AbsNormSafeTerminationMode, AbsNormSafeBestTerminationMode}
+
+# Core Implementation
+@concrete mutable struct NonlinearTerminationModeCache{uType, T}
+    u::uType
+    retcode::ReturnCode.T
+    abstol::T
+    reltol::T
+    best_objective_value::T
+    mode
+    initial_objective
+    objectives_trace
+    nsteps::Int
+    saved_values
+    u0_norm
+    step_norm_trace
+    max_stalled_steps
+    u_diff_cache::uType
+end
+
+function update_u!!(cache::NonlinearTerminationModeCache, u)
+    cache.u === nothing && return
+    if cache.u isa AbstractArray && ArrayInterface.can_setindex(cache.u)
+        copyto!(cache.u, u)
+    else
+        cache.u .= u
+    end
+end
+
+function SciMLBase.init(du::Union{AbstractArray{T}, T}, u::Union{AbstractArray{T}, T},
+        mode::AbstractNonlinearTerminationMode, saved_value_prototype...;
+        abstol = nothing, reltol = nothing, kwargs...) where {T <: Number}
+    error("Not yet implemented...")
+end
+
+function SciMLBase.reinit!(
+        cache::NonlinearTerminationModeCache, du, u, saved_value_prototype...;
+        abstol = nothing, reltol = nothing, kwargs...)
+    error("Not yet implemented...")
+end
+
+## This dispatch is needed based on how Terminating Callback works!
+function (cache::NonlinearTerminationModeCache)(
+        integrator::AbstractODEIntegrator, abstol::Number, reltol::Number, min_t)
+    if min_t === nothing || integrator.t ≥ min_t
+        return cache(cache.mode, SciMLBase.get_du(integrator),
+            integrator.u, integrator.uprev, abstol, reltol)
+    end
+    return false
+end
+function (cache::NonlinearTerminationModeCache)(du, u, uprev, args...)
+    return cache(cache.mode, du, u, uprev, cache.abstol, cache.reltol, args...)
+end
+
+function (cache::NonlinearTerminationModeCache)(
+        mode::AbstractNonlinearTerminationMode, du, u, uprev, abstol, reltol, args...)
+    if check_convergence(mode, du, u, uprev, abstol, reltol)
+        cache.retcode = ReturnCode.Success
+        return true
+    end
+    return false
+end
+
+function (cache::NonlinearTerminationModeCache)(
+        mode::AbstractSafeNonlinearTerminationMode, du, u, uprev, abstol, reltol, args...)
+    if mode isa AbsNormSafeTerminationMode || mode isa AbsNormSafeBestTerminationMode
+        objective = Utils.apply_norm(mode.internalnorm, du)
+        criteria = abstol
+    else
+        objective = Utils.apply_norm(mode.internalnorm, du) /
+                    (Utils.apply_norm(mode.internalnorm, du, u) + eps(reltol))
+        criteria = reltol
+    end
+
+    # Protective Break
+    if !isfinite(objective)
+        cache.retcode = ReturnCode.Unstable
+        return true
+    end
+
+    # By default we turn this off since it have potential for false positives
+    if mode.protective_threshold !== nothing &&
+       (objective > cache.initial_objective * mode.protective_threshold * length(du))
+        cache.retcode = ReturnCode.Unstable
+        return true
+    end
+
+    # Check if it is the best solution
+    if mode isa AbstractSafeBestNonlinearTerminationMode &&
+       objective < cache.best_objective_value
+        cache.best_objective_value = objective
+        update_u!!(cache, u)
+        cache.saved_values !== nothing && length(args) ≥ 1 && (cache.saved_values = args)
+    end
+
+    # Main Termination Criteria
+    if objective ≤ criteria
+        cache.retcode = ReturnCode.Success
+        return true
+    end
+
+    # Terminate if we haven't improved for the last `patience_steps`
+    cache.nsteps += 1
+    cache.nsteps == 1 && (cache.initial_objective = objective)
+    cache.objectives_trace[mod1(cache.nsteps, length(cache.objectives_trace))] = objective
+
+    if objective ≤ mode.patience_objective_multiplier * criteria &&
+       cache.nsteps > mode.patience_steps
+        if cache.nsteps < length(cache.objectives_trace)
+            min_obj, max_obj = extrema(@view(cache.objectives_trace[1:(cache.nsteps)]))
+        else
+            min_obj, max_obj = extrema(cache.objectives_trace)
+        end
+        if min_obj < mode.min_max_factor * max_obj
+            cache.retcode = ReturnCode.Stalled
+            return true
+        end
+    end
+
+    # Test for stalling if that is enabled
+    if cache.step_norm_trace !== nothing
+        if ArrayInterface.can_setindex(cache.u_diff_cache) && !(u isa Number)
+            @. cache.u_diff_cache = u - uprev
+        else
+            cache.u_diff_cache = u .- uprev
+        end
+        du_norm = L2_NORM(cache.u_diff_cache)
+        cache.step_norm_trace[mod1(cache.nsteps, length(cache.step_norm_trace))] = du_norm
+        if cache.nsteps > mode.max_stalled_steps
+            max_step_norm = maximum(cache.step_norm_trace)
+            if mode isa AbsNormSafeTerminationMode ||
+               mode isa AbsNormSafeBestTerminationMode
+                stalled_step = max_step_norm ≤ abstol
+            else
+                stalled_step = max_step_norm ≤ reltol * (max_step_norm + cache.u0_norm)
+            end
+            if stalled_step
+                cache.retcode = ReturnCode.Stalled
+                return true
+            end
+        end
+    end
+
+    cache.retcode = ReturnCode.Failure
+    return false
+end
+
+# Check Convergence
+function check_convergence(::RelTerminationMode, duₙ, uₙ, __, ___, reltol)
+    if Utils.fast_scalar_indexing(duₙ)
+        return all(@closure(xy->begin
+            x, y = xy
+            return abs(y) ≤ reltol * abs(x + y)
+        end), zip(uₙ, duₙ))
+    else # using mapreduce here will almost certainly be faster on GPUs
+        return mapreduce(
+            @closure((xᵢ, yᵢ)->(abs(yᵢ) ≤ reltol * abs(xᵢ + yᵢ))), *, uₙ, duₙ; init = true)
+    end
+end
+function check_convergence(::AbsTerminationMode, duₙ, _, __, abstol, ___)
+    return all(@closure(x->abs(x) ≤ abstol), duₙ)
+end
+
+function check_convergence(norm::NormTerminationMode, duₙ, uₙ, _, abstol, reltol)
+    du_norm = Utils.apply_norm(norm.internalnorm, duₙ)
+    return (du_norm ≤ abstol) ||
+           (du_norm ≤ reltol * Utils.apply_norm(norm.internalnorm, duₙ, uₙ))
+end
+
+function check_convergence(mode::RelNormModes, duₙ, uₙ, _, __, reltol)
+    du_norm = Utils.apply_norm(mode.internalnorm, duₙ)
+    return du_norm ≤ reltol * Utils.apply_norm(mode.internalnorm, duₙ, uₙ)
+end
+
+function check_convergence(mode::AbsNormModes, duₙ, _, __, abstol, ___)
+    return Utils.apply_norm(mode.internalnorm, duₙ) ≤ abstol
+end
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
new file mode 100644
index 000000000..f830e9a17
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -0,0 +1,76 @@
+module Utils
+
+using ArrayInterface: ArrayInterface
+using FastClosures: @closure
+using LinearAlgebra: norm
+using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
+using UnrolledUtilities: unrolled_all
+
+using ..NonlinearSolveBase: L2_NORM, Linf_NORM
+
+fast_scalar_indexing(xs...) = unrolled_all(ArrayInterface.fast_scalar_indexing, xs)
+
+function nonallocating_isapprox(x::Number, y::Number; atol = false,
+        rtol = atol > 0 ? false : sqrt(eps(promote_type(typeof(x), typeof(y)))))
+    return isapprox(x, y; atol, rtol)
+end
+function nonallocating_isapprox(x::AbstractArray, y::AbstractArray; atol = false,
+        rtol = atol > 0 ? false : sqrt(eps(eltype(x))))
+    length(x) == length(y) || return false
+    d = nonallocating_maximum(-, x, y)
+    return d ≤ max(atol, rtol * max(maximum(abs, x), maximum(abs, y)))
+end
+
+function nonallocating_maximum(f::F, x, y) where {F}
+    if fast_scalar_indexing(x, y)
+        return maximum(@closure((xᵢyᵢ)->begin
+            xᵢ, yᵢ = xᵢyᵢ
+            return abs(f(xᵢ, yᵢ))
+        end), zip(x, y))
+    else
+        return mapreduce(@closure((xᵢ, yᵢ)->abs(f(xᵢ, yᵢ))), max, x, y)
+    end
+end
+
+function abs2_and_sum(x, y)
+    return reduce(Base.add_sum, x, init = zero(real(value(eltype(x))))) +
+           reduce(Base.add_sum, y, init = zero(real(value(eltype(y)))))
+end
+
+children(x::AbstractVectorOfArray) = x.u
+children(x::ArrayPartition) = x.x
+
+value(::Type{T}) where {T} = T
+value(x) = x
+
+zero_init(x) = zero(real(value(eltype(x))))
+one_init(x) = one(real(value(eltype(x))))
+
+standardize_norm(::typeof(Base.Fix1(maximum, abs))) = Linf_NORM
+standardize_norm(::typeof(Base.Fix2(norm, Inf))) = Linf_NORM
+standardize_norm(::typeof(Base.Fix2(norm, 2))) = L2_NORM
+standardize_norm(::typeof(norm)) = L2_NORM
+standardize_norm(f::F) where {F} = f
+
+norm_op(norm::N, op::OP, x, y) where {N, OP} = norm(op.(x, y))
+function norm_op(::typeof(L2_NORM), op::OP, x, y) where {OP}
+    if fast_scalar_indexing(x, y)
+        return sqrt(sum(@closure((xᵢ, yᵢ)->begin
+            xᵢ, yᵢ = xᵢyᵢ
+            return op(xᵢ, yᵢ)^2
+        end), zip(x, y)))
+    else
+        return sqrt(mapreduce(@closure((xᵢ, yᵢ)->op(xᵢ, yᵢ)^2), +, x, y))
+    end
+end
+function norm_op(::typeof(Linf_NORM), op::OP, x, y) where {OP}
+    return nonallocating_maximum(abs ∘ op, x, y)
+end
+
+apply_norm(f::F, x) where {F} = standardize_norm(f)(x)
+apply_norm(f::F, x, y) where {F} = norm_op(standardize_norm(f), +, x, y)
+
+convert_real(::Type{T}, ::Nothing) where {T} = nothing
+convert_real(::Type{T}, x) where {T} = real(T(x))
+
+end
diff --git a/lib/NonlinearSolveBase/test/runtests.jl b/lib/NonlinearSolveBase/test/runtests.jl
new file mode 100644
index 000000000..8b1378917
--- /dev/null
+++ b/lib/NonlinearSolveBase/test/runtests.jl
@@ -0,0 +1 @@
+

From 0563dd674a17b4b708c4da15e4aa0ba897ecc739 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 22 Aug 2024 17:38:35 -0700
Subject: [PATCH 534/700] chore: run formatter

---
 lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl  | 2 +-
 lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl | 2 +-
 lib/NonlinearSolveBase/src/autodiff.jl                          | 1 +
 lib/NonlinearSolveBase/src/immutable_problem.jl                 | 1 +
 4 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
index c29fea0d1..ae342e4ba 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
@@ -6,4 +6,4 @@ using NonlinearSolveBase: Utils
 Utils.value(::Type{Dual{T, V, N}}) where {T, V, N} = V
 Utils.value(x::Dual) = Utils.value(ForwardDiff.value(x))
 
-end
\ No newline at end of file
+end
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
index d20e9b59b..be13ebb8f 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
@@ -7,4 +7,4 @@ function NonlinearSolveBase.NAN_CHECK(x::AbstractSparseMatrixCSC)
     return any(NonlinearSolveBase.NAN_CHECK, nonzeros(x))
 end
 
-end
\ No newline at end of file
+end
diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
index e69de29bb..8b1378917 100644
--- a/lib/NonlinearSolveBase/src/autodiff.jl
+++ b/lib/NonlinearSolveBase/src/autodiff.jl
@@ -0,0 +1 @@
+
diff --git a/lib/NonlinearSolveBase/src/immutable_problem.jl b/lib/NonlinearSolveBase/src/immutable_problem.jl
index e69de29bb..8b1378917 100644
--- a/lib/NonlinearSolveBase/src/immutable_problem.jl
+++ b/lib/NonlinearSolveBase/src/immutable_problem.jl
@@ -0,0 +1 @@
+

From b504867bc90d19058b6235a48ee9567a9a715a7c Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 22 Aug 2024 17:45:04 -0700
Subject: [PATCH 535/700] feat: add ImmutableNonlinearProblem

---
 lib/NonlinearSolveBase/Project.toml           |  2 +
 .../ext/NonlinearSolveBaseDiffEqBaseExt.jl    | 14 +++++
 .../src/NonlinearSolveBase.jl                 |  6 +-
 .../src/immutable_problem.jl                  | 56 +++++++++++++++++++
 4 files changed, 77 insertions(+), 1 deletion(-)
 create mode 100644 lib/NonlinearSolveBase/ext/NonlinearSolveBaseDiffEqBaseExt.jl

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 1c7047ca6..f21e15626 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -16,10 +16,12 @@ StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 UnrolledUtilities = "0fe1646c-419e-43be-ac14-22321958931b"
 
 [weakdeps]
+DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [extensions]
+NonlinearSolveBaseDiffEqBaseExt = "DiffEqBase"
 NonlinearSolveBaseForwardDiffExt = "ForwardDiff"
 NonlinearSolveBaseSparseArraysExt = "SparseArrays"
 
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseDiffEqBaseExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseDiffEqBaseExt.jl
new file mode 100644
index 000000000..a3a216cf2
--- /dev/null
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseDiffEqBaseExt.jl
@@ -0,0 +1,14 @@
+module NonlinearSolveBaseDiffEqBaseExt
+
+using DiffEqBase: DiffEqBase
+using NonlinearSolveBase: ImmutableNonlinearProblem
+
+function DiffEqBase.get_concrete_problem(
+        prob::ImmutableNonlinearProblem, isadapt; kwargs...)
+    u0 = DiffEqBase.get_concrete_u0(prob, isadapt, nothing, kwargs)
+    u0 = DiffEqBase.promote_u0(u0, prob.p, nothing)
+    p = DiffEqBase.get_concrete_p(prob, kwargs)
+    return SciMLBase.remake(prob; u0, p)
+end
+
+end
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index aff03d1e3..71c634ef3 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -7,7 +7,9 @@ using FastClosures: @closure
 using LinearAlgebra: norm
 using Markdown: @doc_str
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
-using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator
+using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinearProblem,
+                 AbstractNonlinearFunction, @add_kwonly, StandardNonlinearProblem,
+                 NullParameters, NonlinearProblem, isinplace
 using StaticArraysCore: StaticArray
 
 include("public.jl")
@@ -25,4 +27,6 @@ export RelTerminationMode, AbsTerminationMode, NormTerminationMode, RelNormTermi
        AbsNormTerminationMode, RelNormSafeTerminationMode, AbsNormSafeTerminationMode,
        RelNormSafeNormTerminationMode, AbsNormSafeNormTerminationMode
 
+export ImmutableNonlinearProblem
+
 end
diff --git a/lib/NonlinearSolveBase/src/immutable_problem.jl b/lib/NonlinearSolveBase/src/immutable_problem.jl
index 8b1378917..03b44a9ec 100644
--- a/lib/NonlinearSolveBase/src/immutable_problem.jl
+++ b/lib/NonlinearSolveBase/src/immutable_problem.jl
@@ -1 +1,57 @@
+struct ImmutableNonlinearProblem{uType, iip, P, F, K, PT} <:
+       AbstractNonlinearProblem{uType, iip}
+    f::F
+    u0::uType
+    p::P
+    problem_type::PT
+    kwargs::K
 
+    @add_kwonly function ImmutableNonlinearProblem{iip}(
+            f::AbstractNonlinearFunction{iip}, u0, p = NullParameters(),
+            problem_type = StandardNonlinearProblem(); kwargs...) where {iip}
+        if haskey(kwargs, :p)
+            error("`p` specified as a keyword argument `p = $(kwargs[:p])` to \
+                   `NonlinearProblem`. This is not supported.")
+        end
+        warn_paramtype(p)
+        return new{
+            typeof(u0), iip, typeof(p), typeof(f), typeof(kwargs), typeof(problem_type)}(
+            f, u0, p, problem_type, kwargs)
+    end
+
+    """
+    Define a steady state problem using the given function.
+    `isinplace` optionally sets whether the function is inplace or not.
+    This is determined automatically, but not inferred.
+    """
+    function ImmutableNonlinearProblem{iip}(
+            f, u0, p = NullParameters(); kwargs...) where {iip}
+        return ImmutableNonlinearProblem{iip}(NonlinearFunction{iip}(f), u0, p; kwargs...)
+    end
+end
+
+"""
+Define a nonlinear problem using an instance of
+[`AbstractNonlinearFunction`](@ref AbstractNonlinearFunction).
+"""
+function ImmutableNonlinearProblem(
+        f::AbstractNonlinearFunction, u0, p = NullParameters(); kwargs...)
+    return ImmutableNonlinearProblem{isinplace(f)}(f, u0, p; kwargs...)
+end
+
+function ImmutableNonlinearProblem(f, u0, p = NullParameters(); kwargs...)
+    return ImmutableNonlinearProblem(NonlinearFunction(f), u0, p; kwargs...)
+end
+
+"""
+Define a ImmutableNonlinearProblem problem from SteadyStateProblem
+"""
+function ImmutableNonlinearProblem(prob::AbstractNonlinearProblem)
+    return ImmutableNonlinearProblem{isinplace(prob)}(prob.f, prob.u0, prob.p)
+end
+
+function Base.convert(
+        ::Type{ImmutableNonlinearProblem}, prob::T) where {T <: NonlinearProblem}
+    return ImmutableNonlinearProblem{isinplace(prob)}(
+        prob.f, prob.u0, prob.p, prob.problem_type; prob.kwargs...)
+end

From 1ed45fa2916fc1c4d2bf00e33a5c79c8b0925d32 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 22 Aug 2024 18:08:55 -0700
Subject: [PATCH 536/700] fix: finish broken termination conditions

---
 .../src/termination_conditions.jl             | 79 +++++++++++++++++--
 1 file changed, 73 insertions(+), 6 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/termination_conditions.jl b/lib/NonlinearSolveBase/src/termination_conditions.jl
index 3cbba4b8b..50af54a57 100644
--- a/lib/NonlinearSolveBase/src/termination_conditions.jl
+++ b/lib/NonlinearSolveBase/src/termination_conditions.jl
@@ -30,16 +30,83 @@ function update_u!!(cache::NonlinearTerminationModeCache, u)
     end
 end
 
-function SciMLBase.init(du::Union{AbstractArray{T}, T}, u::Union{AbstractArray{T}, T},
-        mode::AbstractNonlinearTerminationMode, saved_value_prototype...;
-        abstol = nothing, reltol = nothing, kwargs...) where {T <: Number}
-    error("Not yet implemented...")
+function SciMLBase.init(
+        du, u, mode::AbstractNonlinearTerminationMode, saved_value_prototype...;
+        abstol = nothing, reltol = nothing, kwargs...)
+    T = promote_type(eltype(du), eltype(u))
+    abstol = get_tolerance(abstol, T)
+    reltol = get_tolerance(reltol, T)
+    TT = typeof(abstol)
+
+    u_unaliased = mode isa AbstractSafeBestNonlinearTerminationMode ?
+                  (ArrayInterface.can_setindex(u) ? copy(u) : u) : nothing
+
+    if mode isa AbstractSafeNonlinearTerminationMode
+        if mode isa AbsNormSafeTerminationMode || mode isa AbsNormSafeBestTerminationMode
+            initial_objective = Linf_NORM(du)
+            u0_norm = nothing
+        else
+            initial_objective = Linf_NORM(du) /
+                                (Utils.nonallocating_maximum(+, du, u) + eps(TT))
+            u0_norm = mode.max_stalled_steps === nothing ? nothing : L2_NORM(u)
+        end
+        objectives_trace = Vector{TT}(undef, mode.patience_steps)
+        step_norm_trace = mode.max_stalled_steps === nothing ? nothing :
+                          Vector{TT}(undef, mode.max_stalled_steps)
+        if step_norm_trace !== nothing &&
+           ArrayInterface.can_setindex(u_unaliased) &&
+           !(u_unaliased isa Number)
+            u_diff_cache = similar(u_unaliased)
+        else
+            u_diff_cache = u_unaliased
+        end
+    else
+        initial_objective = nothing
+        objectives_trace = nothing
+        u0_norm = nothing
+        step_norm_trace = nothing
+        best_value = Utils.convert_real(T, Inf)
+        max_stalled_steps = nothing
+        u_diff_cache = u_unaliased
+    end
+
+    length(saved_value_prototype) == 0 && (saved_value_prototype = nothing)
+
+    return NonlinearTerminationModeCache(
+        u_unaliased, ReturnCode.Default, abstol, reltol, best_value, mode,
+        initial_objective, objectives_trace, 0, saved_value_prototype,
+        u0_norm, step_norm_trace, max_stalled_steps, u_diff_cache)
 end
 
 function SciMLBase.reinit!(
         cache::NonlinearTerminationModeCache, du, u, saved_value_prototype...;
-        abstol = nothing, reltol = nothing, kwargs...)
-    error("Not yet implemented...")
+        abstol = cache.abstol, reltol = cache.reltol, kwargs...)
+    T = eltype(cache.abstol)
+    length(saved_value_prototype) != 0 && (cache.saved_values = saved_value_prototype)
+
+    mode = cache.mode
+    u_unaliased = mode isa AbstractSafeBestNonlinearTerminationMode ?
+                  (ArrayInterface.can_setindex(u) ? copy(u) : u) : nothing
+    cache.u = u_unaliased
+    cache.retcode = ReturnCode.Default
+
+    cache.abstol = get_tolerance(abstol, T)
+    cache.reltol = get_tolerance(reltol, T)
+    cache.nsteps = 0
+    TT = typeof(cache.abstol)
+
+    if mode isa AbstractSafeNonlinearTerminationMode
+        if mode isa AbsNormSafeTerminationMode || mode isa AbsNormSafeBestTerminationMode
+            cache.initial_objective = Linf_NORM(du)
+        else
+            cache.initial_objective = Linf_NORM(du) /
+                                      (Utils.nonallocating_maximum(+, du, u) + eps(TT))
+            cache.max_stalled_steps !== nothing && (cache.u0_norm = L2_NORM(u))
+        end
+        cache.best_objective_value = cache.initial_objective
+    else
+        cache.best_objective_value = Utils.convert_real(T, Inf)
+    end
 end
 
 ## This dispatch is needed based on how Terminating Callback works!

From e273cc6a67f656a6cb4e0fa9f0375d003810f407 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 22 Aug 2024 19:32:26 -0700
Subject: [PATCH 537/700] feat: start a SimpleBracketingNonlinearSolve
 sublibrary

---
 lib/SimpleBracketingNonlinearSolve/Project.toml     | 13 +++++++++++++
 .../src/SimpleBracketingNonlinearSolve.jl           |  8 ++++++++
 lib/SimpleBracketingNonlinearSolve/test/runtests.jl |  0
 3 files changed, 21 insertions(+)
 create mode 100644 lib/SimpleBracketingNonlinearSolve/Project.toml
 create mode 100644 lib/SimpleBracketingNonlinearSolve/src/SimpleBracketingNonlinearSolve.jl
 create mode 100644 lib/SimpleBracketingNonlinearSolve/test/runtests.jl

diff --git a/lib/SimpleBracketingNonlinearSolve/Project.toml b/lib/SimpleBracketingNonlinearSolve/Project.toml
new file mode 100644
index 000000000..e3462f3bc
--- /dev/null
+++ b/lib/SimpleBracketingNonlinearSolve/Project.toml
@@ -0,0 +1,13 @@
+name = "SimpleBracketingNonlinearSolve"
+uuid = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
+authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
+version = "1.0.0"
+
+[deps]
+CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
+SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+
+[compat]
+CommonSolve = "0.2.4"
+SciMLBase = "2.50"
+julia = "1.10"
diff --git a/lib/SimpleBracketingNonlinearSolve/src/SimpleBracketingNonlinearSolve.jl b/lib/SimpleBracketingNonlinearSolve/src/SimpleBracketingNonlinearSolve.jl
new file mode 100644
index 000000000..6bac6bdaa
--- /dev/null
+++ b/lib/SimpleBracketingNonlinearSolve/src/SimpleBracketingNonlinearSolve.jl
@@ -0,0 +1,8 @@
+module SimpleBracketingNonlinearSolve
+
+using CommonSolve: CommonSolve
+using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, IntervalNonlinearProblem, ReturnCode
+
+abstract type AbstractBracketingAlgorithm <: AbstractNonlinearAlgorithm end
+
+end
diff --git a/lib/SimpleBracketingNonlinearSolve/test/runtests.jl b/lib/SimpleBracketingNonlinearSolve/test/runtests.jl
new file mode 100644
index 000000000..e69de29bb

From 21b2f4b053f051e37052dc5441560024d02ca93e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 22 Aug 2024 21:30:37 -0700
Subject: [PATCH 538/700] feat: implement all bracketing algorithms

---
 .../Project.toml                              |   8 +-
 .../src/BracketingNonlinearSolve.jl           |  38 +++++
 lib/BracketingNonlinearSolve/src/alefeld.jl   | 135 +++++++++++++++++
 lib/BracketingNonlinearSolve/src/bisection.jl |  81 ++++++++++
 lib/BracketingNonlinearSolve/src/brent.jl     | 109 ++++++++++++++
 lib/BracketingNonlinearSolve/src/common.jl    |  91 +++++++++++
 lib/BracketingNonlinearSolve/src/falsi.jl     |  71 +++++++++
 lib/BracketingNonlinearSolve/src/itp.jl       | 141 ++++++++++++++++++
 lib/BracketingNonlinearSolve/src/ridder.jl    |  83 +++++++++++
 .../test/runtests.jl                          |   0
 lib/NonlinearSolveBase/Project.toml           |   2 -
 .../ext/NonlinearSolveBaseDiffEqBaseExt.jl    |  14 --
 .../src/SimpleBracketingNonlinearSolve.jl     |   8 -
 13 files changed, 756 insertions(+), 25 deletions(-)
 rename lib/{SimpleBracketingNonlinearSolve => BracketingNonlinearSolve}/Project.toml (51%)
 create mode 100644 lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
 create mode 100644 lib/BracketingNonlinearSolve/src/alefeld.jl
 create mode 100644 lib/BracketingNonlinearSolve/src/bisection.jl
 create mode 100644 lib/BracketingNonlinearSolve/src/brent.jl
 create mode 100644 lib/BracketingNonlinearSolve/src/common.jl
 create mode 100644 lib/BracketingNonlinearSolve/src/falsi.jl
 create mode 100644 lib/BracketingNonlinearSolve/src/itp.jl
 create mode 100644 lib/BracketingNonlinearSolve/src/ridder.jl
 rename lib/{SimpleBracketingNonlinearSolve => BracketingNonlinearSolve}/test/runtests.jl (100%)
 delete mode 100644 lib/NonlinearSolveBase/ext/NonlinearSolveBaseDiffEqBaseExt.jl
 delete mode 100644 lib/SimpleBracketingNonlinearSolve/src/SimpleBracketingNonlinearSolve.jl

diff --git a/lib/SimpleBracketingNonlinearSolve/Project.toml b/lib/BracketingNonlinearSolve/Project.toml
similarity index 51%
rename from lib/SimpleBracketingNonlinearSolve/Project.toml
rename to lib/BracketingNonlinearSolve/Project.toml
index e3462f3bc..31ea28b21 100644
--- a/lib/SimpleBracketingNonlinearSolve/Project.toml
+++ b/lib/BracketingNonlinearSolve/Project.toml
@@ -1,13 +1,19 @@
-name = "SimpleBracketingNonlinearSolve"
+name = "BracketingNonlinearSolve"
 uuid = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
 version = "1.0.0"
 
 [deps]
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
+ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
+NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
+PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 
 [compat]
 CommonSolve = "0.2.4"
+ConcreteStructs = "0.2.3"
+NonlinearSolveBase = "1"
+PrecompileTools = "1.2.1"
 SciMLBase = "2.50"
 julia = "1.10"
diff --git a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
new file mode 100644
index 000000000..2d5aed297
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
@@ -0,0 +1,38 @@
+module BracketingNonlinearSolve
+
+using ConcreteStructs: @concrete
+
+using CommonSolve: CommonSolve
+using NonlinearSolveBase: NonlinearSolveBase
+using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, IntervalNonlinearProblem, ReturnCode
+
+using PrecompileTools: @compile_workload, @setup_workload
+
+abstract type AbstractBracketingAlgorithm <: AbstractNonlinearAlgorithm end
+
+include("common.jl")
+
+include("alefeld.jl")
+include("bisection.jl")
+include("brent.jl")
+include("falsi.jl")
+include("itp.jl")
+include("ridder.jl")
+
+@setup_workload begin
+    for T in (Float32, Float64)
+        prob_brack = IntervalNonlinearProblem{false}(
+            (u, p) -> u^2 - p, T.((0.0, 2.0)), T(2))
+        algs = (Alefeld(), Bisection(), Brent(), Falsi(), ITP(), Ridder())
+
+        @compile_workload begin
+            for alg in algs
+                CommonSolve.solve(prob_brack, alg; abstol = 1e-6)
+            end
+        end
+    end
+end
+
+export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
+
+end
diff --git a/lib/BracketingNonlinearSolve/src/alefeld.jl b/lib/BracketingNonlinearSolve/src/alefeld.jl
new file mode 100644
index 000000000..2407055ce
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/src/alefeld.jl
@@ -0,0 +1,135 @@
+"""
+    Alefeld()
+
+An implementation of algorithm 4.2 from [Alefeld](https://dl.acm.org/doi/10.1145/210089.210111).
+
+The paper brought up two new algorithms. Here choose to implement algorithm 4.2 rather than
+algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal procedure.
+"""
+struct Alefeld <: AbstractBracketingAlgorithm end
+
+function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...;
+        maxiters = 1000, abstol = nothing, kwargs...)
+    f = Base.Fix2(prob.f, prob.p)
+    a, b = prob.tspan
+    c = a - (b - a) / (f(b) - f(a)) * f(a)
+
+    fc = f(c)
+    if a == c || b == c
+        return SciMLBase.build_solution(
+            prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit, left = a, right = b)
+    end
+
+    if iszero(fc)
+        return SciMLBase.build_solution(
+            prob, alg, c, fc; retcode = ReturnCode.Success, left = a, right = b)
+    end
+
+    a, b, d = Impl.bracket(f, a, b, c)
+    e = zero(a)   # Set e as 0 before iteration to avoid a non-value f(e)
+
+    for i in 2:maxiters
+        # The first bracketing block
+        f₁, f₂, f₃, f₄ = f(a), f(b), f(d), f(e)
+        if i == 2 || (f₁ == f₂ || f₁ == f₃ || f₁ == f₄ || f₂ == f₃ || f₂ == f₄ || f₃ == f₄)
+            c = Impl.newton_quadratic(f, a, b, d, 2)
+        else
+            c = Impl.ipzero(f, a, b, d, e)
+            if (c - a) * (c - b) ≥ 0
+                c = Impl.newton_quadratic(f, a, b, d, 2)
+            end
+        end
+
+        ē, fc = d, f(c)
+        if a == c || b == c
+            return SciMLBase.build_solution(
+                prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
+                left = a, right = b)
+        end
+
+        if iszero(fc)
+            return SciMLBase.build_solution(
+                prob, alg, c, fc; retcode = ReturnCode.Success, left = a, right = b)
+        end
+
+        ā, b̄, d̄ = Impl.bracket(f, a, b, c)
+
+        # The second bracketing block
+        f₁, f₂, f₃, f₄ = f(ā), f(b̄), f(d̄), f(ē)
+        if f₁ == f₂ || f₁ == f₃ || f₁ == f₄ || f₂ == f₃ || f₂ == f₄ || f₃ == f₄
+            c = Impl.newton_quadratic(f, ā, b̄, d̄, 3)
+        else
+            c = Impl.ipzero(f, ā, b̄, d̄, ē)
+            if (c - ā) * (c - b̄) ≥ 0
+                c = Impl.newton_quadratic(f, ā, b̄, d̄, 3)
+            end
+        end
+        fc = f(c)
+
+        if ā == c || b̄ == c
+            return SciMLBase.build_solution(
+                prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
+                left = ā, right = b̄)
+        end
+
+        if iszero(fc)
+            return SciMLBase.build_solution(
+                prob, alg, c, fc; retcode = ReturnCode.Success, left = ā, right = b̄)
+        end
+
+        ā, b̄, d̄ = Impl.bracket(f, ā, b̄, c)
+
+        # The third bracketing block
+        u = ifelse(abs(f(ā)) < abs(f(b̄)), ā, b̄)
+        c = u - 2 * (b̄ - ā) / (f(b̄) - f(ā)) * f(u)
+        if (abs(c - u)) > 0.5 * (b̄ - ā)
+            c = 0.5 * (ā + b̄)
+        end
+        fc = f(c)
+
+        if ā == c || b̄ == c
+            return SciMLBase.build_solution(
+                prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
+                left = ā, right = b̄)
+        end
+
+        if iszero(fc)
+            return SciMLBase.build_solution(
+                prob, alg, c, fc; retcode = ReturnCode.Success, left = ā, right = b̄)
+        end
+
+        ā, b̄, d = Impl.bracket(f, ā, b̄, c)
+
+        # The last bracketing block
+        if b̄ - ā < 0.5 * (b - a)
+            a, b, e = ā, b̄, d̄
+        else
+            e = d
+            c = 0.5 * (ā + b̄)
+            fc = f(c)
+
+            if ā == c || b̄ == c
+                return SciMLBase.build_solution(
+                    prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
+                    left = ā, right = b̄)
+            end
+            if iszero(fc)
+                return SciMLBase.build_solution(
+                    prob, alg, c, fc; retcode = ReturnCode.Success, left = ā, right = b̄)
+            end
+            a, b, d = Impl.bracket(f, ā, b̄, c)
+        end
+    end
+
+    # Reassign the value a, b, and c
+    if b == c
+        b = d
+    elseif a == c
+        a = d
+    end
+    fc = f(c)
+
+    # Reuturn solution when run out of max interation
+    return SciMLBase.build_solution(
+        prob, alg, c, fc; retcode = ReturnCode.MaxIters, left = a, right = b)
+end
diff --git a/lib/BracketingNonlinearSolve/src/bisection.jl b/lib/BracketingNonlinearSolve/src/bisection.jl
new file mode 100644
index 000000000..e3a38a1fd
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/src/bisection.jl
@@ -0,0 +1,81 @@
+"""
+    Bisection(; exact_left = false, exact_right = false)
+
+A common bisection method.
+
+### Keyword Arguments
+
+  - `exact_left`: whether to enforce whether the left side of the interval must be exactly
+    zero for the returned result. Defaults to false.
+  - `exact_right`: whether to enforce whether the right side of the interval must be exactly
+    zero for the returned result. Defaults to false.
+
+!!! danger "Keyword Arguments"
+
+    Currently, the keyword arguments are not implemented.
+"""
+@kwdef struct Bisection <: AbstractBracketingAlgorithm
+    exact_left::Bool = false
+    exact_right::Bool = false
+end
+
+function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Bisection,
+        args...; maxiters = 1000, abstol = nothing, kwargs...)
+    @assert !SciMLBase.isinplace(prob) "`Bisection` only supports out-of-place problems."
+
+    f = Base.Fix2(prob.f, prob.p)
+    left, right = prob.tspan
+    fl, fr = f(left), f(right)
+
+    abstol = NonlinearSolveBase.get_tolerance(
+        abstol, promote_type(eltype(left), eltype(right)))
+
+    if iszero(fl)
+        return SciMLBase.build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
+    end
+
+    if iszero(fr)
+        return SciMLBase.build_solution(
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
+    end
+
+    i = 1
+    while i ≤ maxiters
+        mid = (left + right) / 2
+
+        if mid == left || mid == right
+            return SciMLBase.build_solution(
+                prob, alg, left, fl; retcode = ReturnCode.FloatingPointLimit, left, right)
+        end
+
+        fm = f(mid)
+        if abs((right - left) / 2) < abstol
+            return SciMLBase.build_solution(
+                prob, alg, mid, fm; retcode = ReturnCode.Success, left, right)
+        end
+
+        if iszero(fm)
+            right = mid
+            break
+        end
+
+        if sign(fl) == sign(fm)
+            fl = fm
+            left = mid
+        else
+            fr = fm
+            right = mid
+        end
+
+        i += 1
+    end
+
+    sol, i, left, right, fl, fr = Impl.bisection(
+        left, right, fl, fr, f, abstol, maxiters - i, prob, alg)
+
+    sol !== nothing && return sol
+
+    return SciMLBase.build_solution(
+        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
+end
diff --git a/lib/BracketingNonlinearSolve/src/brent.jl b/lib/BracketingNonlinearSolve/src/brent.jl
new file mode 100644
index 000000000..549cc07a6
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/src/brent.jl
@@ -0,0 +1,109 @@
+"""
+    Brent()
+
+Left non-allocating Brent method.
+"""
+struct Brent <: AbstractBracketingAlgorithm end
+
+function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
+        maxiters = 1000, abstol = nothing, kwargs...)
+    @assert !SciMLBase.isinplace(prob) "`Brent` only supports out-of-place problems."
+
+    f = Base.Fix2(prob.f, prob.p)
+    left, right = prob.tspan
+    fl, fr = f(left), f(right)
+    ϵ = eps(convert(typeof(fl), 1))
+
+    abstol = NonlinearSolveBase.get_tolerance(
+        abstol, promote_type(eltype(left), eltype(right)))
+
+    if iszero(fl)
+        return SciMLBase.build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
+    end
+
+    if iszero(fr)
+        return SciMLBase.build_solution(
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
+    end
+
+    if abs(fl) < abs(fr)
+        left, right = right, left
+        fl, fr = fr, fl
+    end
+
+    c = left
+    d = c
+    i = 1
+    cond = true
+
+    while i < maxiters
+        fc = f(c)
+
+        if fl != fc && fr != fc
+            # Inverse quadratic interpolation
+            s = left * fr * fc / ((fl - fr) * (fl - fc)) +
+                right * fl * fc / ((fr - fl) * (fr - fc)) +
+                c * fl * fr / ((fc - fl) * (fc - fr))
+        else
+            # Secant method
+            s = right - fr * (right - left) / (fr - fl)
+        end
+
+        if (s < min((3 * left + right) / 4, right) ||
+            s > max((3 * left + right) / 4, right)) ||
+           (cond && abs(s - right) ≥ abs(right - c) / 2) ||
+           (!cond && abs(s - right) ≥ abs(c - d) / 2) ||
+           (cond && abs(right - c) ≤ ϵ) ||
+           (!cond && abs(c - d) ≤ ϵ)
+            # Bisection method
+            s = (left + right) / 2
+            if s == left || s == right
+                return SciMLBase.build_solution(prob, alg, left, fl;
+                    retcode = ReturnCode.FloatingPointLimit, left, right)
+            end
+            cond = true
+        else
+            cond = false
+        end
+
+        fs = f(s)
+        if abs((right - left) / 2) < abstol
+            return SciMLBase.build_solution(prob, alg, s, fs;
+                retcode = ReturnCode.Success, left, right)
+        end
+
+        if iszero(fs)
+            if right < left
+                left = right
+                fl = fr
+            end
+            right = s
+            fr = fs
+            break
+        end
+
+        if fl * fs < 0
+            d, c, right = c, right, s
+            fr = fs
+        else
+            left = s
+            fl = fs
+        end
+
+        if abs(fl) < abs(fr)
+            d = c
+            c, right, left = right, left, c
+            fc, fr, fl = fr, fl, fc
+        end
+        i += 1
+    end
+
+    sol, i, left, right, fl, fr = Impl.bisection(
+        left, right, fl, fr, f, abstol, maxiters - i, prob, alg)
+
+    sol !== nothing && return sol
+
+    return SciMLBase.build_solution(
+        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
+end
diff --git a/lib/BracketingNonlinearSolve/src/common.jl b/lib/BracketingNonlinearSolve/src/common.jl
new file mode 100644
index 000000000..65239ea63
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/src/common.jl
@@ -0,0 +1,91 @@
+module Impl
+
+using SciMLBase: SciMLBase, ReturnCode
+
+function bisection(left, right, fl, fr, f::F, abstol, maxiters, prob, alg) where {F}
+    i = 1
+    sol = nothing
+    while i ≤ maxiters
+        mid = (left + right) / 2
+
+        if mid == left || mid == right
+            sol = SciMLBase.build_solution(
+                prob, alg, left, fl; left, right, retcode = ReturnCode.FloatingPointLimit)
+            break
+        end
+
+        fm = f(mid)
+        if abs((right - left) / 2) < abstol
+            sol = SciMLBase.build_solution(
+                prob, alg, mid, fm; left, right, retcode = ReturnCode.Success)
+            break
+        end
+
+        if iszero(fm)
+            right = mid
+            fr = fm
+        else
+            left = mid
+            fl = fm
+        end
+
+        i += 1
+    end
+
+    return sol, i, left, right, fl, fr
+end
+
+prevfloat_tdir(x, x0, x1) = ifelse(x1 > x0, prevfloat(x), nextfloat(x))
+nextfloat_tdir(x, x0, x1) = ifelse(x1 > x0, nextfloat(x), prevfloat(x))
+max_tdir(a, b, x0, x1) = ifelse(x1 > x0, max(a, b), min(a, b))
+
+function bracket(f::F, a, b, c) where {F}
+    if iszero(f(c))
+        ā, b̄, d = a, b, c
+    else
+        if f(a) * f(c) < 0
+            ā, b̄, d = a, c, b
+        elseif f(b) * f(c) < 0
+            ā, b̄, d = c, b, a
+        end
+    end
+    return ā, b̄, d
+end
+
+function newton_quadratic(f::F, a, b, d, k) where {F}
+    A = ((f(d) - f(b)) / (d - b) - (f(b) - f(a)) / (b - a)) / (d - a)
+    B = (f(b) - f(a)) / (b - a)
+
+    if iszero(A)
+        return a - (1 / B) * f(a)
+    elseif A * f(a) > 0
+        rᵢ₋₁ = a
+    else
+        rᵢ₋₁ = b
+    end
+
+    for _ in 1:k
+        rᵢ = rᵢ₋₁ -
+             (f(a) + B * (rᵢ₋₁ - a) + A * (rᵢ₋₁ - a) * (rᵢ₋₁ - b)) /
+             (B + A * (2 * rᵢ₋₁ - a - b))
+        rᵢ₋₁ = rᵢ
+    end
+
+    return rᵢ₋₁
+end
+
+function ipzero(f::F, a, b, c, d) where {F}
+    Q₁₁ = (c - d) * f(c) / (f(d) - f(c))
+    Q₂₁ = (b - c) * f(b) / (f(c) - f(b))
+    Q₃₁ = (a - b) * f(a) / (f(b) - f(a))
+    D₂₁ = (b - c) * f(c) / (f(c) - f(b))
+    D₃₁ = (a - b) * f(b) / (f(b) - f(a))
+    Q₂₂ = (D₂₁ - Q₁₁) * f(b) / (f(d) - f(b))
+    Q₃₂ = (D₃₁ - Q₂₁) * f(a) / (f(c) - f(a))
+    D₃₂ = (D₃₁ - Q₂₁) * f(c) / (f(c) - f(a))
+    Q₃₃ = (D₃₂ - Q₂₂) * f(a) / (f(d) - f(a))
+
+    return a + Q₃₁ + Q₃₂ + Q₃₃
+end
+
+end
diff --git a/lib/BracketingNonlinearSolve/src/falsi.jl b/lib/BracketingNonlinearSolve/src/falsi.jl
new file mode 100644
index 000000000..451a4c0b2
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/src/falsi.jl
@@ -0,0 +1,71 @@
+"""
+    Falsi()
+
+A non-allocating regula falsi method.
+"""
+struct Falsi <: AbstractBracketingAlgorithm end
+
+function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
+        maxiters = 1000, abstol = nothing, kwargs...)
+    @assert !SciMLBase.isinplace(prob) "`False` only supports out-of-place problems."
+
+    f = Base.Fix2(prob.f, prob.p)
+    l, r = prob.tspan # don't reuse these variables
+    left, right = prob.tspan
+    fl, fr = f(left), f(right)
+
+    abstol = NonlinearSolveBase.get_tolerance(
+        abstol, promote_type(eltype(left), eltype(right)))
+
+    if iszero(fl)
+        return SciMLBase.build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
+    end
+
+    if iszero(fr)
+        return SciMLBase.build_solution(
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
+    end
+
+    i = 1
+    while i ≤ maxiters
+        if Impl.nextfloat_tdir(left, l, r) == right
+            return SciMLBase.build_solution(
+                prob, alg, left, fl; left, right, retcode = ReturnCode.FloatingPointLimit)
+        end
+
+        mid = (fr * left - fl * right) / (fr - fl)
+        for _ in 1:10
+            mid = Impl.max_tdir(left, Impl.prevfloat_tdir(mid, l, r), l, r)
+        end
+
+        (mid == left || mid == right) && break
+
+        fm = f(mid)
+        if abs((right - left) / 2) < abstol
+            return SciMLBase.build_solution(
+                prob, alg, mid, fm; left, right, retcode = ReturnCode.Success)
+        end
+
+        if abs(fm) < abstol
+            right = mid
+            break
+        end
+
+        if sign(fl) == sign(fm)
+            fl, left = fm, mid
+        else
+            fr, right = fm, mid
+        end
+
+        i += 1
+    end
+
+    sol, i, left, right, fl, fr = Impl.bisection(
+        left, right, fl, fr, f, abstol, maxiters - i, prob, alg)
+
+    sol !== nothing && return sol
+
+    return SciMLBase.build_solution(
+        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
+end
diff --git a/lib/BracketingNonlinearSolve/src/itp.jl b/lib/BracketingNonlinearSolve/src/itp.jl
new file mode 100644
index 000000000..dd6ddc23b
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/src/itp.jl
@@ -0,0 +1,141 @@
+"""
+    ITP(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
+
+ITP (Interpolate Truncate & Project)
+
+Use the [ITP method](https://en.wikipedia.org/wiki/ITP_method) to find a root of a bracketed
+function, with a convergence rate between 1 and 1.62.
+
+This method was introduced in the paper "An Enhancement of the Bisection Method Average
+Performance Preserving Minmax Optimality" (https://doi.org/10.1145/3423597) by
+I. F. D. Oliveira and R. H. C. Takahashi.
+
+### Tuning Parameters
+
+The following keyword parameters are accepted.
+
+  - `n₀::Int = 10`, the 'slack'. Must not be negative. When n₀ = 0 the worst-case is
+    identical to that of bisection, but increasing n₀ provides greater opportunity for
+    superlinearity.
+  - `scaled_κ₁::Float64 = 0.2`. Must not be negative. The recommended value is `0.2`.
+    Lower values produce tighter asymptotic behaviour, while higher values improve the
+    steady-state behaviour when truncation is not helpful.
+  - `κ₂::Real = 2`. Must lie in [1, 1+ϕ ≈ 2.62). Higher values allow for a greater
+    convergence rate, but also make the method more succeptable to worst-case performance.
+    In practice, κ₂=1, 2 seems to work well due to the computational simplicity, as κ₂ is
+    used as an exponent in the method.
+
+### Computation of κ₁
+
+In the current implementation, we compute κ₁ = scaled_κ₁·|Δx₀|^(1 - κ₂); this allows κ₁ to
+adapt to the length of the interval and keep the proposed steps proportional to Δx.
+
+### Worst Case Performance
+
+n½ + `n₀` iterations, where n½ is the number of iterations using bisection
+(n½ = ⌈log2(Δx)/2`tol`⌉).
+
+### Asymptotic Performance
+
+If `f` is twice differentiable and the root is simple, then with `n₀` > 0 the convergence
+rate is √`κ₂`.
+"""
+@concrete struct ITP <: AbstractBracketingAlgorithm
+    scaled_k1
+    k2
+    n0::Int
+end
+
+function ITP(; scaled_k1::Real = 0.2, k2::Real = 2, n0::Int = 10)
+    scaled_k1 < 0 && error("Hyper-parameter κ₁ should not be negative")
+    n0 < 0 && error("Hyper-parameter n₀ should not be negative")
+    if k2 < 1 || k2 > (1.5 + sqrt(5) / 2)
+        throw(ArgumentError("Hyper-parameter κ₂ should be between 1 and 1 + ϕ where \
+                             ϕ ≈ 1.618... is the golden ratio"))
+    end
+    return ITP(scaled_k1, k2, n0)
+end
+
+function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
+        maxiters = 1000, abstol = nothing, kwargs...)
+    @assert !SciMLBase.isinplace(prob) "`ITP` only supports out-of-place problems."
+
+    f = Base.Fix2(prob.f, prob.p)
+    left, right = prob.tspan
+    fl, fr = f(left), f(right)
+
+    abstol = NonlinearSolveBase.get_tolerance(
+        abstol, promote_type(eltype(left), eltype(right)))
+
+    if iszero(fl)
+        return SciMLBase.build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
+    end
+
+    if iszero(fr)
+        return SciMLBase.build_solution(
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
+    end
+
+    ϵ = abstol
+    k2 = alg.k2
+    k1 = alg.scaled_k1 * abs(right - left)^(1 - k2)
+    n0 = alg.n0
+    n_h = ceil(log2(abs(right - left) / (2 * ϵ)))
+    mid = (left + right) / 2
+    x_f = left + (right - left) * (fl / (fl - fr))
+    xt = left
+    xp = left
+    r = zero(left) # minmax radius
+    δ = zero(left) # truncation error
+    σ = 1.0
+    ϵ_s = ϵ * 2^(n_h + n0)
+
+    i = 1
+    while i ≤ maxiters
+        span = abs(right - left)
+        r = ϵ_s - (span / 2)
+        δ = k1 * span^k2
+
+        x_f = left + (right - left) * (fl / (fl - fr))  # Interpolation Step
+
+        diff = mid - x_f
+        σ = sign(diff)
+        xt = ifelse(δ ≤ diff, x_f + σ * δ, mid)  # Truncation Step
+
+        xp = ifelse(abs(xt - mid) ≤ r, xt, mid - σ * r)  # Projection Step
+
+        if abs((left - right) / 2) < ϵ
+            return SciMLBase.build_solution(
+                prob, alg, xt, f(xt); retcode = ReturnCode.Success, left, right)
+        end
+
+        # update
+        tmin, tmax = minmax(xt, xp)
+        xp ≥ tmax && (xp = prevfloat(tmax))
+        xp ≤ tmin && (xp = nextfloat(tmin))
+        yp = f(xp)
+        yps = yp * sign(fr)
+        T0 = zero(yps)
+        if yps > T0
+            right, fr = xp, yp
+        elseif yps < T0
+            left, fl = xp, yp
+        else
+            return SciMLBase.build_solution(
+                prob, alg, xp, yps; retcode = ReturnCode.Success, left, right)
+        end
+
+        i += 1
+        mid = (left + right) / 2
+        ϵ_s /= 2
+
+        if Impl.nextfloat_tdir(left, prob.tspan...) == right
+            return SciMLBase.build_solution(
+                prob, alg, right, fr; retcode = ReturnCode.FloatingPointLimit, left, right)
+        end
+    end
+
+    return SciMLBase.build_solution(
+        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
+end
diff --git a/lib/BracketingNonlinearSolve/src/ridder.jl b/lib/BracketingNonlinearSolve/src/ridder.jl
new file mode 100644
index 000000000..785bc2ae7
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/src/ridder.jl
@@ -0,0 +1,83 @@
+"""
+    Ridder()
+
+A non-allocating ridder method.
+"""
+struct Ridder <: AbstractBracketingAlgorithm end
+
+function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
+        maxiters = 1000, abstol = nothing, kwargs...)
+    @assert !SciMLBase.isinplace(prob) "`Ridder` only supports out-of-place problems."
+
+    f = Base.Fix2(prob.f, prob.p)
+    left, right = prob.tspan
+    fl, fr = f(left), f(right)
+
+    abstol = NonlinearSolveBase.get_tolerance(
+        abstol, promote_type(eltype(left), eltype(right)))
+
+    if iszero(fl)
+        return SciMLBase.build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
+    end
+
+    if iszero(fr)
+        return SciMLBase.build_solution(
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
+    end
+
+    xo = oftype(left, Inf)
+    i = 1
+    while i ≤ maxiters
+        mid = (left + right) / 2
+
+        if mid == left || mid == right
+            return SciMLBase.build_solution(
+                prob, alg, left, fl; retcode = ReturnCode.FloatingPointLimit, left, right)
+        end
+
+        fm = f(mid)
+        s = sqrt(fm^2 - fl * fr)
+        if iszero(s)
+            return SciMLBase.build_solution(
+                prob, alg, left, fl; retcode = ReturnCode.Failure, left, right)
+        end
+
+        x = mid + (mid - left) * sign(fl - fm) * fm / s
+        fx = f(x)
+        xo = x
+        if abs((right - left) / 2) < abstol
+            return SciMLBase.build_solution(
+                prob, alg, mid, fm; retcode = ReturnCode.Success, left, right)
+        end
+
+        if iszero(fx)
+            right, fr = x, fx
+            break
+        end
+
+        if sign(fx) != sign(fm)
+            left = mid
+            fl = fm
+            right = x
+            fr = fx
+        elseif sign(fx) != sign(fl)
+            right = x
+            fr = fx
+        else
+            @assert sign(fx) != sign(fr)
+            left = x
+            fl = fx
+        end
+
+        i += 1
+    end
+
+    sol, i, left, right, fl, fr = Impl.bisection(
+        left, right, fl, fr, f, abstol, maxiters - i, prob, alg)
+
+    sol !== nothing && return sol
+
+    return SciMLBase.build_solution(
+        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
+end
\ No newline at end of file
diff --git a/lib/SimpleBracketingNonlinearSolve/test/runtests.jl b/lib/BracketingNonlinearSolve/test/runtests.jl
similarity index 100%
rename from lib/SimpleBracketingNonlinearSolve/test/runtests.jl
rename to lib/BracketingNonlinearSolve/test/runtests.jl
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index f21e15626..1c7047ca6 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -16,12 +16,10 @@ StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 UnrolledUtilities = "0fe1646c-419e-43be-ac14-22321958931b"
 
 [weakdeps]
-DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [extensions]
-NonlinearSolveBaseDiffEqBaseExt = "DiffEqBase"
 NonlinearSolveBaseForwardDiffExt = "ForwardDiff"
 NonlinearSolveBaseSparseArraysExt = "SparseArrays"
 
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseDiffEqBaseExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseDiffEqBaseExt.jl
deleted file mode 100644
index a3a216cf2..000000000
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseDiffEqBaseExt.jl
+++ /dev/null
@@ -1,14 +0,0 @@
-module NonlinearSolveBaseDiffEqBaseExt
-
-using DiffEqBase: DiffEqBase
-using NonlinearSolveBase: ImmutableNonlinearProblem
-
-function DiffEqBase.get_concrete_problem(
-        prob::ImmutableNonlinearProblem, isadapt; kwargs...)
-    u0 = DiffEqBase.get_concrete_u0(prob, isadapt, nothing, kwargs)
-    u0 = DiffEqBase.promote_u0(u0, prob.p, nothing)
-    p = DiffEqBase.get_concrete_p(prob, kwargs)
-    return SciMLBase.remake(prob; u0, p)
-end
-
-end
diff --git a/lib/SimpleBracketingNonlinearSolve/src/SimpleBracketingNonlinearSolve.jl b/lib/SimpleBracketingNonlinearSolve/src/SimpleBracketingNonlinearSolve.jl
deleted file mode 100644
index 6bac6bdaa..000000000
--- a/lib/SimpleBracketingNonlinearSolve/src/SimpleBracketingNonlinearSolve.jl
+++ /dev/null
@@ -1,8 +0,0 @@
-module SimpleBracketingNonlinearSolve
-
-using CommonSolve: CommonSolve
-using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, IntervalNonlinearProblem, ReturnCode
-
-abstract type AbstractBracketingAlgorithm <: AbstractNonlinearAlgorithm end
-
-end

From 8c02ffd933b6798973b8bd84b303e5795d075ad1 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 22 Aug 2024 21:55:08 -0700
Subject: [PATCH 539/700] chore: missing license

---
 lib/BracketingNonlinearSolve/LICENSE | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)
 create mode 100644 lib/BracketingNonlinearSolve/LICENSE

diff --git a/lib/BracketingNonlinearSolve/LICENSE b/lib/BracketingNonlinearSolve/LICENSE
new file mode 100644
index 000000000..411ad533f
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2024 Avik Pal <avikpal@mit.edu> and contributors
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

From 015461090098ad26dafc216773ebfa25ce5b1675 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 23 Aug 2024 11:14:17 -0700
Subject: [PATCH 540/700] chore: qa fixes

---
 lib/BracketingNonlinearSolve/src/alefeld.jl   | 2 +-
 lib/BracketingNonlinearSolve/src/brent.jl     | 4 ++--
 lib/BracketingNonlinearSolve/src/ridder.jl    | 2 +-
 lib/BracketingNonlinearSolve/test/runtests.jl | 1 +
 4 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/lib/BracketingNonlinearSolve/src/alefeld.jl b/lib/BracketingNonlinearSolve/src/alefeld.jl
index 2407055ce..a669900dd 100644
--- a/lib/BracketingNonlinearSolve/src/alefeld.jl
+++ b/lib/BracketingNonlinearSolve/src/alefeld.jl
@@ -129,7 +129,7 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...
     end
     fc = f(c)
 
-    # Reuturn solution when run out of max interation
+    # Return solution when run out of max iteration
     return SciMLBase.build_solution(
         prob, alg, c, fc; retcode = ReturnCode.MaxIters, left = a, right = b)
 end
diff --git a/lib/BracketingNonlinearSolve/src/brent.jl b/lib/BracketingNonlinearSolve/src/brent.jl
index 549cc07a6..23ab36df2 100644
--- a/lib/BracketingNonlinearSolve/src/brent.jl
+++ b/lib/BracketingNonlinearSolve/src/brent.jl
@@ -69,8 +69,8 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
 
         fs = f(s)
         if abs((right - left) / 2) < abstol
-            return SciMLBase.build_solution(prob, alg, s, fs;
-                retcode = ReturnCode.Success, left, right)
+            return SciMLBase.build_solution(
+                prob, alg, s, fs; retcode = ReturnCode.Success, left, right)
         end
 
         if iszero(fs)
diff --git a/lib/BracketingNonlinearSolve/src/ridder.jl b/lib/BracketingNonlinearSolve/src/ridder.jl
index 785bc2ae7..a289bcb05 100644
--- a/lib/BracketingNonlinearSolve/src/ridder.jl
+++ b/lib/BracketingNonlinearSolve/src/ridder.jl
@@ -80,4 +80,4 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
 
     return SciMLBase.build_solution(
         prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
-end
\ No newline at end of file
+end
diff --git a/lib/BracketingNonlinearSolve/test/runtests.jl b/lib/BracketingNonlinearSolve/test/runtests.jl
index e69de29bb..8b1378917 100644
--- a/lib/BracketingNonlinearSolve/test/runtests.jl
+++ b/lib/BracketingNonlinearSolve/test/runtests.jl
@@ -0,0 +1 @@
+

From 14914c6facd3f2820e8b678fe4ed31c4ba527904 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 16 Sep 2024 19:08:26 -0400
Subject: [PATCH 541/700] test: add tests for the bracketing methods

---
 lib/BracketingNonlinearSolve/Project.toml     |  8 ++
 .../src/BracketingNonlinearSolve.jl           |  5 +-
 lib/BracketingNonlinearSolve/src/brent.jl     |  6 +-
 .../test/rootfind_tests.jl                    | 94 +++++++++++++++++++
 lib/BracketingNonlinearSolve/test/runtests.jl |  4 +
 lib/NonlinearSolveBase/Project.toml           |  2 -
 lib/NonlinearSolveBase/src/utils.jl           |  3 +-
 7 files changed, 115 insertions(+), 7 deletions(-)
 create mode 100644 lib/BracketingNonlinearSolve/test/rootfind_tests.jl

diff --git a/lib/BracketingNonlinearSolve/Project.toml b/lib/BracketingNonlinearSolve/Project.toml
index 31ea28b21..6b1a2c9a1 100644
--- a/lib/BracketingNonlinearSolve/Project.toml
+++ b/lib/BracketingNonlinearSolve/Project.toml
@@ -17,3 +17,11 @@ NonlinearSolveBase = "1"
 PrecompileTools = "1.2.1"
 SciMLBase = "2.50"
 julia = "1.10"
+
+[extras]
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
+
+[targets]
+test = ["InteractiveUtils", "Test", "TestItemRunner"]
diff --git a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
index 2d5aed297..491ec4132 100644
--- a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
+++ b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
@@ -2,7 +2,7 @@ module BracketingNonlinearSolve
 
 using ConcreteStructs: @concrete
 
-using CommonSolve: CommonSolve
+using CommonSolve: CommonSolve, solve
 using NonlinearSolveBase: NonlinearSolveBase
 using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, IntervalNonlinearProblem, ReturnCode
 
@@ -33,6 +33,9 @@ include("ridder.jl")
     end
 end
 
+export IntervalNonlinearProblem
+export solve
+
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
 end
diff --git a/lib/BracketingNonlinearSolve/src/brent.jl b/lib/BracketingNonlinearSolve/src/brent.jl
index 23ab36df2..5475e675e 100644
--- a/lib/BracketingNonlinearSolve/src/brent.jl
+++ b/lib/BracketingNonlinearSolve/src/brent.jl
@@ -93,8 +93,10 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
 
         if abs(fl) < abs(fr)
             d = c
-            c, right, left = right, left, c
-            fc, fr, fl = fr, fl, fc
+            c, right = right, left
+            left = c
+            fc, fr = fr, fl
+            fl = fc
         end
         i += 1
     end
diff --git a/lib/BracketingNonlinearSolve/test/rootfind_tests.jl b/lib/BracketingNonlinearSolve/test/rootfind_tests.jl
new file mode 100644
index 000000000..824c10da4
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/test/rootfind_tests.jl
@@ -0,0 +1,94 @@
+@testsnippet RootfindingTestSnippet begin
+    using NonlinearSolveBase, BracketingNonlinearSolve
+
+    quadratic_f(u, p) = u .* u .- p
+    quadratic_f!(du, u, p) = (du .= u .* u .- p)
+    quadratic_f2(u, p) = @. p[1] * u * u - p[2]
+end
+
+@testitem "Interval Nonlinear Problems" setup=[RootfindingTestSnippet] tags=[:core] begin
+    @testset for alg in (Bisection(), Falsi(), Ridder(), Brent(), ITP(), Alefeld())
+        tspan = (1.0, 20.0)
+
+        function g(p)
+            probN = IntervalNonlinearProblem{false}(quadratic_f, typeof(p).(tspan), p)
+            return solve(probN, alg; abstol = 1e-9).left
+        end
+
+        @testset for p in 1.1:0.1:100.0
+            @test g(p)≈sqrt(p) atol=1e-3 rtol=1e-3
+            # @test ForwardDiff.derivative(g, p)≈1 / (2 * sqrt(p)) atol=1e-3 rtol=1e-3
+        end
+
+        t = (p) -> [sqrt(p[2] / p[1])]
+        p = [0.9, 50.0]
+
+        function g2(p)
+            probN = IntervalNonlinearProblem{false}(quadratic_f2, tspan, p)
+            sol = solve(probN, alg; abstol = 1e-9)
+            return [sol.u]
+        end
+
+        @test g2(p)≈[sqrt(p[2] / p[1])] atol=1e-3 rtol=1e-3
+        # @test ForwardDiff.jacobian(g2, p)≈ForwardDiff.jacobian(t, p) atol=1e-3 rtol=1e-3
+
+        probB = IntervalNonlinearProblem{false}(quadratic_f, (1.0, 2.0), 2.0)
+        sol = solve(probB, alg; abstol = 1e-9)
+        @test sol.left≈sqrt(2.0) atol=1e-3 rtol=1e-3
+
+        if !(alg isa Bisection || alg isa Falsi)
+            probB = IntervalNonlinearProblem{false}(quadratic_f, (sqrt(2.0), 10.0), 2.0)
+            sol = solve(probB, alg; abstol = 1e-9)
+            @test sol.left≈sqrt(2.0) atol=1e-3 rtol=1e-3
+
+            probB = IntervalNonlinearProblem{false}(quadratic_f, (0.0, sqrt(2.0)), 2.0)
+            sol = solve(probB, alg; abstol = 1e-9)
+            @test sol.left≈sqrt(2.0) atol=1e-3 rtol=1e-3
+        end
+    end
+end
+
+@testitem "Tolerance Tests Interval Methods" setup=[RootfindingTestSnippet] tags=[:core] begin
+    prob = IntervalNonlinearProblem(quadratic_f, (1.0, 20.0), 2.0)
+    ϵ = eps(Float64) # least possible tol for all methods
+
+    @testset for alg in (Bisection(), Falsi(), ITP())
+        @testset for abstol in [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6, 1e-7]
+            sol = solve(prob, alg; abstol)
+            result_tol = abs(sol.u - sqrt(2))
+            @test result_tol < abstol
+            # test that the solution is not calculated upto max precision
+            @test result_tol > ϵ
+        end
+    end
+
+    @testset for alg in (Ridder(), Brent())
+        # Ridder and Brent converge rapidly so as we lower tolerance below 0.01, it
+        # converges with max precision to the solution
+        @testset for abstol in [0.1]
+            sol = solve(prob, alg; abstol)
+            result_tol = abs(sol.u - sqrt(2))
+            @test result_tol < abstol
+            # test that the solution is not calculated upto max precision
+            @test result_tol > ϵ
+        end
+    end
+end
+
+@testitem "Flipped Signs and Reversed Tspan" setup=[RootfindingTestSnippet] tags=[:core] begin
+    @testset for alg in (Alefeld(), Bisection(), Falsi(), Brent(), ITP(), Ridder())
+        f1(u, p) = u * u - p
+        f2(u, p) = p - u * u
+
+        for p in 1:4
+            inp1 = IntervalNonlinearProblem(f1, (1.0, 2.0), p)
+            inp2 = IntervalNonlinearProblem(f2, (1.0, 2.0), p)
+            inp3 = IntervalNonlinearProblem(f1, (2.0, 1.0), p)
+            inp4 = IntervalNonlinearProblem(f2, (2.0, 1.0), p)
+            @test abs.(solve(inp1, alg).u) ≈ sqrt.(p)
+            @test abs.(solve(inp2, alg).u) ≈ sqrt.(p)
+            @test abs.(solve(inp3, alg).u) ≈ sqrt.(p)
+            @test abs.(solve(inp4, alg).u) ≈ sqrt.(p)
+        end
+    end
+end
diff --git a/lib/BracketingNonlinearSolve/test/runtests.jl b/lib/BracketingNonlinearSolve/test/runtests.jl
index 8b1378917..6ea6326b0 100644
--- a/lib/BracketingNonlinearSolve/test/runtests.jl
+++ b/lib/BracketingNonlinearSolve/test/runtests.jl
@@ -1 +1,5 @@
+using TestItemRunner, InteractiveUtils
 
+@info sprint(InteractiveUtils.versioninfo)
+
+@run_package_tests
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 1c7047ca6..66ae9a35c 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -13,7 +13,6 @@ Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
-UnrolledUtilities = "0fe1646c-419e-43be-ac14-22321958931b"
 
 [weakdeps]
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -35,5 +34,4 @@ RecursiveArrayTools = "3"
 SciMLBase = "2.50"
 SparseArrays = "1.10"
 StaticArraysCore = "1.4"
-UnrolledUtilities = "0.1"
 julia = "1.10"
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index f830e9a17..bd1d799c1 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -4,11 +4,10 @@ using ArrayInterface: ArrayInterface
 using FastClosures: @closure
 using LinearAlgebra: norm
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
-using UnrolledUtilities: unrolled_all
 
 using ..NonlinearSolveBase: L2_NORM, Linf_NORM
 
-fast_scalar_indexing(xs...) = unrolled_all(ArrayInterface.fast_scalar_indexing, xs)
+fast_scalar_indexing(xs...) = all(ArrayInterface.fast_scalar_indexing, xs)
 
 function nonallocating_isapprox(x::Number, y::Number; atol = false,
         rtol = atol > 0 ? false : sqrt(eps(promote_type(typeof(x), typeof(y)))))

From 76e87d9aab4adb293b5e64398367b0537c7e3829 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 16 Sep 2024 20:30:27 -0400
Subject: [PATCH 542/700] feat: ForwardDiff support in NonlinearSolveBase

---
 lib/BracketingNonlinearSolve/Project.toml     | 10 ++-
 .../BracketingNonlinearSolveForwardDiffExt.jl | 26 +++++++
 .../test/rootfind_tests.jl                    |  6 +-
 .../ext/NonlinearSolveBaseForwardDiffExt.jl   | 75 ++++++++++++++++++-
 .../src/NonlinearSolveBase.jl                 |  2 +-
 lib/NonlinearSolveBase/src/autodiff.jl        |  1 -
 lib/NonlinearSolveBase/src/public.jl          |  4 +
 lib/NonlinearSolveBase/src/utils.jl           | 18 +++++
 8 files changed, 136 insertions(+), 6 deletions(-)
 create mode 100644 lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveForwardDiffExt.jl
 delete mode 100644 lib/NonlinearSolveBase/src/autodiff.jl

diff --git a/lib/BracketingNonlinearSolve/Project.toml b/lib/BracketingNonlinearSolve/Project.toml
index 6b1a2c9a1..954178d53 100644
--- a/lib/BracketingNonlinearSolve/Project.toml
+++ b/lib/BracketingNonlinearSolve/Project.toml
@@ -10,9 +10,16 @@ NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 
+[weakdeps]
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+
+[extensions]
+NonlinearSolveBaseForwardDiffExt = "ForwardDiff"
+
 [compat]
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
+ForwardDiff = "0.10.36"
 NonlinearSolveBase = "1"
 PrecompileTools = "1.2.1"
 SciMLBase = "2.50"
@@ -20,8 +27,9 @@ julia = "1.10"
 
 [extras]
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
 
 [targets]
-test = ["InteractiveUtils", "Test", "TestItemRunner"]
+test = ["InteractiveUtils", "ForwardDiff", "Test", "TestItemRunner"]
diff --git a/lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveForwardDiffExt.jl b/lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveForwardDiffExt.jl
new file mode 100644
index 000000000..b41a88451
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveForwardDiffExt.jl
@@ -0,0 +1,26 @@
+module BracketingNonlinearSolveForwardDiffExt
+
+using CommonSolve: CommonSolve
+using ForwardDiff: ForwardDiff, Dual
+using NonlinearSolveBase: nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution
+using SciMLBase: SciMLBase, IntervalNonlinearProblem
+
+using BracketingNonlinearSolve: Bisection, Brent, Alefeld, Falsi, ITP, Ridder
+
+for algT in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
+    @eval function CommonSolve.solve(
+            prob::IntervalNonlinearProblem{
+                uType, iip, <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
+            alg::$(algT),
+            args...;
+            kwargs...) where {uType, iip, T, V, P}
+        sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
+        dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
+        return SciMLBase.build_solution(
+            prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats,
+            sol.original, left = Dual{T, V, P}(sol.left, partials),
+            right = Dual{T, V, P}(sol.right, partials))
+    end
+end
+
+end
diff --git a/lib/BracketingNonlinearSolve/test/rootfind_tests.jl b/lib/BracketingNonlinearSolve/test/rootfind_tests.jl
index 824c10da4..e4409bafd 100644
--- a/lib/BracketingNonlinearSolve/test/rootfind_tests.jl
+++ b/lib/BracketingNonlinearSolve/test/rootfind_tests.jl
@@ -7,6 +7,8 @@
 end
 
 @testitem "Interval Nonlinear Problems" setup=[RootfindingTestSnippet] tags=[:core] begin
+    using ForwardDiff
+
     @testset for alg in (Bisection(), Falsi(), Ridder(), Brent(), ITP(), Alefeld())
         tspan = (1.0, 20.0)
 
@@ -17,7 +19,7 @@ end
 
         @testset for p in 1.1:0.1:100.0
             @test g(p)≈sqrt(p) atol=1e-3 rtol=1e-3
-            # @test ForwardDiff.derivative(g, p)≈1 / (2 * sqrt(p)) atol=1e-3 rtol=1e-3
+            @test ForwardDiff.derivative(g, p)≈1 / (2 * sqrt(p)) atol=1e-3 rtol=1e-3
         end
 
         t = (p) -> [sqrt(p[2] / p[1])]
@@ -30,7 +32,7 @@ end
         end
 
         @test g2(p)≈[sqrt(p[2] / p[1])] atol=1e-3 rtol=1e-3
-        # @test ForwardDiff.jacobian(g2, p)≈ForwardDiff.jacobian(t, p) atol=1e-3 rtol=1e-3
+        @test ForwardDiff.jacobian(g2, p)≈ForwardDiff.jacobian(t, p) atol=1e-3 rtol=1e-3
 
         probB = IntervalNonlinearProblem{false}(quadratic_f, (1.0, 2.0), 2.0)
         sol = solve(probB, alg; abstol = 1e-9)
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
index ae342e4ba..4161e0666 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
@@ -1,9 +1,82 @@
 module NonlinearSolveBaseForwardDiffExt
 
+using CommonSolve: solve
+using FastClosures: @closure
 using ForwardDiff: ForwardDiff, Dual
-using NonlinearSolveBase: Utils
+using SciMLBase: SciMLBase, IntervalNonlinearProblem, NonlinearProblem,
+                 NonlinearLeastSquaresProblem, remake
+
+using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, Utils
 
 Utils.value(::Type{Dual{T, V, N}}) where {T, V, N} = V
 Utils.value(x::Dual) = Utils.value(ForwardDiff.value(x))
 
+function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
+        prob::Union{IntervalNonlinearProblem, NonlinearProblem, ImmutableNonlinearProblem},
+        alg, args...; kwargs...)
+    p = Utils.value(prob.p)
+    if prob isa IntervalNonlinearProblem
+        tspan = Utils.value.(prob.tspan)
+        newprob = IntervalNonlinearProblem(prob.f, tspan, p; prob.kwargs...)
+    else
+        newprob = remake(prob; p, u0 = Utils.value(prob.u0))
+    end
+
+    sol = solve(newprob, alg, args...; kwargs...)
+
+    uu = sol.u
+    Jₚ = nonlinearsolve_∂f_∂p(prob, prob.f, uu, p)
+    Jᵤ = nonlinearsolve_∂f_∂u(prob, prob.f, uu, p)
+    z = -Jᵤ \ Jₚ
+    pp = prob.p
+    sumfun = ((z, p),) -> map(Base.Fix2(*, ForwardDiff.partials(p)), z)
+
+    if uu isa Number
+        partials = sum(sumfun, zip(z, pp))
+    elseif p isa Number
+        partials = sumfun((z, pp))
+    else
+        partials = sum(sumfun, zip(eachcol(z), pp))
+    end
+
+    return sol, partials
+end
+
+function nonlinearsolve_∂f_∂p(prob, f::F, u, p) where {F}
+    if isinplace(prob)
+        f = @closure p -> begin
+            du = Utils.safe_similar(u, promote_type(eltype(u), eltype(p)))
+            f(du, u, p)
+            return du
+        end
+    else
+        f = Base.Fix1(f, u)
+    end
+    if p isa Number
+        return Utils.safe_reshape(ForwardDiff.derivative(f, p), :, 1)
+    elseif u isa Number
+        return Utils.safe_reshape(ForwardDiff.gradient(f, p), 1, :)
+    else
+        return ForwardDiff.jacobian(f, p)
+    end
+end
+
+function nonlinearsolve_∂f_∂u(prob, f::F, u, p) where {F}
+    if isinplace(prob)
+        return ForwardDiff.jacobian(
+            @closure((du, u)->f(du, u, p)), Utils.safe_similar(u), u)
+    end
+    return ForwardDiff.jacobian(Base.Fix2(f, p), u)
+end
+
+function NonlinearSolveBase.nonlinearsolve_dual_solution(u::Number, partials,
+        ::Union{<:AbstractArray{<:Dual{T, V, P}}, Dual{T, V, P}}) where {T, V, P}
+    return Dual{T, V, P}(u, partials)
+end
+
+function NonlinearSolveBase.nonlinearsolve_dual_solution(u::AbstractArray, partials,
+        ::Union{<:AbstractArray{<:Dual{T, V, P}}, Dual{T, V, P}}) where {T, V, P}
+    return map(((uᵢ, pᵢ),) -> Dual{T, V, P}(uᵢ, pᵢ), zip(u, Utils.restructure(u, partials)))
+end
+
 end
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 71c634ef3..f0459447b 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -17,11 +17,11 @@ include("utils.jl")
 
 include("common_defaults.jl")
 include("termination_conditions.jl")
-include("autodiff.jl")
 include("immutable_problem.jl")
 
 # Unexported Public API
 @compat(public, (L2_NORM, Linf_NORM, NAN_CHECK, UNITLESS_ABS2, get_tolerance))
+@compat(public, (nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution))
 
 export RelTerminationMode, AbsTerminationMode, NormTerminationMode, RelNormTerminationMode,
        AbsNormTerminationMode, RelNormSafeTerminationMode, AbsNormSafeTerminationMode,
diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
deleted file mode 100644
index 8b1378917..000000000
--- a/lib/NonlinearSolveBase/src/autodiff.jl
+++ /dev/null
@@ -1 +0,0 @@
-
diff --git a/lib/NonlinearSolveBase/src/public.jl b/lib/NonlinearSolveBase/src/public.jl
index 24f467cbd..db8c389e2 100644
--- a/lib/NonlinearSolveBase/src/public.jl
+++ b/lib/NonlinearSolveBase/src/public.jl
@@ -5,6 +5,10 @@ function L2_NORM end
 function Linf_NORM end
 function get_tolerance end
 
+# Forward declarations of functions for forward mode AD
+function nonlinearsolve_forwarddiff_solve end
+function nonlinearsolve_dual_solution end
+
 # Nonlinear Solve Termination Conditions
 abstract type AbstractNonlinearTerminationMode end
 abstract type AbstractSafeNonlinearTerminationMode <: AbstractNonlinearTerminationMode end
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index bd1d799c1..0a8840942 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -72,4 +72,22 @@ apply_norm(f::F, x, y) where {F} = norm_op(standardize_norm(f), +, x, y)
 convert_real(::Type{T}, ::Nothing) where {T} = nothing
 convert_real(::Type{T}, x) where {T} = real(T(x))
 
+restructure(::Number, x::Number) = x
+restructure(y, x) = ArrayInterface.restructure(y, x)
+
+function safe_similar(x, args...; kwargs...)
+    y = similar(x, args...; kwargs...)
+    return init_bigfloat_array!!(y)
+end
+
+init_bigfloat_array!!(x) = x
+
+function init_bigfloat_array!!(x::AbstractArray{<:BigFloat})
+    ArrayInterface.can_setindex(x) && fill!(x, BigFloat(0))
+    return x
+end
+
+safe_reshape(x::Number, args...) = x
+safe_reshape(x, args...) = reshape(x, args...)
+
 end

From 8ab7867d6f46e2187e349a1b7dddda992216368a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 12:56:21 -0400
Subject: [PATCH 543/700] fix: extension for forward AD support

---
 lib/BracketingNonlinearSolve/Project.toml                   | 2 +-
 lib/BracketingNonlinearSolve/test/rootfind_tests.jl         | 2 --
 lib/NonlinearSolveBase/Project.toml                         | 2 ++
 .../ext/NonlinearSolveBaseForwardDiffExt.jl                 | 6 ++++--
 4 files changed, 7 insertions(+), 5 deletions(-)

diff --git a/lib/BracketingNonlinearSolve/Project.toml b/lib/BracketingNonlinearSolve/Project.toml
index 954178d53..b8bf5a806 100644
--- a/lib/BracketingNonlinearSolve/Project.toml
+++ b/lib/BracketingNonlinearSolve/Project.toml
@@ -14,7 +14,7 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 
 [extensions]
-NonlinearSolveBaseForwardDiffExt = "ForwardDiff"
+BracketingNonlinearSolveForwardDiffExt = "ForwardDiff"
 
 [compat]
 CommonSolve = "0.2.4"
diff --git a/lib/BracketingNonlinearSolve/test/rootfind_tests.jl b/lib/BracketingNonlinearSolve/test/rootfind_tests.jl
index e4409bafd..1875ede00 100644
--- a/lib/BracketingNonlinearSolve/test/rootfind_tests.jl
+++ b/lib/BracketingNonlinearSolve/test/rootfind_tests.jl
@@ -1,6 +1,4 @@
 @testsnippet RootfindingTestSnippet begin
-    using NonlinearSolveBase, BracketingNonlinearSolve
-
     quadratic_f(u, p) = u .* u .- p
     quadratic_f!(du, u, p) = (du .= u .* u .- p)
     quadratic_f2(u, p) = @. p[1] * u * u - p[2]
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 66ae9a35c..94d12d822 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -5,6 +5,7 @@ version = "1.0.0"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
@@ -24,6 +25,7 @@ NonlinearSolveBaseSparseArraysExt = "SparseArrays"
 
 [compat]
 ArrayInterface = "7.9"
+CommonSolve = "0.2.4"
 Compat = "4.15"
 ConcreteStructs = "0.2.3"
 FastClosures = "0.3"
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
index 4161e0666..469c5944b 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
@@ -10,6 +10,7 @@ using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, Utils
 
 Utils.value(::Type{Dual{T, V, N}}) where {T, V, N} = V
 Utils.value(x::Dual) = Utils.value(ForwardDiff.value(x))
+Utils.value(x::AbstractArray{<:Dual}) = Utils.value.(x)
 
 function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
         prob::Union{IntervalNonlinearProblem, NonlinearProblem, ImmutableNonlinearProblem},
@@ -43,7 +44,7 @@ function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
 end
 
 function nonlinearsolve_∂f_∂p(prob, f::F, u, p) where {F}
-    if isinplace(prob)
+    if SciMLBase.isinplace(prob)
         f = @closure p -> begin
             du = Utils.safe_similar(u, promote_type(eltype(u), eltype(p)))
             f(du, u, p)
@@ -62,10 +63,11 @@ function nonlinearsolve_∂f_∂p(prob, f::F, u, p) where {F}
 end
 
 function nonlinearsolve_∂f_∂u(prob, f::F, u, p) where {F}
-    if isinplace(prob)
+    if SciMLBase.isinplace(prob)
         return ForwardDiff.jacobian(
             @closure((du, u)->f(du, u, p)), Utils.safe_similar(u), u)
     end
+    u isa Number && return ForwardDiff.derivative(Base.Fix2(f, p), u)
     return ForwardDiff.jacobian(Base.Fix2(f, p), u)
 end
 

From 0f55b6f43feda33c7a0ada24e14d041bdc33abad Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 13:15:41 -0400
Subject: [PATCH 544/700] ci(github-actions): add workflows for subpackages

---
 .../workflows/CI_BracketingNonlinearSolve.yml | 67 +++++++++++++++++++
 .github/workflows/CI_NonlinearSolveBase.yml   | 63 +++++++++++++++++
 .github/workflows/CompatHelper.yml            |  8 ++-
 3 files changed, 137 insertions(+), 1 deletion(-)
 create mode 100644 .github/workflows/CI_BracketingNonlinearSolve.yml
 create mode 100644 .github/workflows/CI_NonlinearSolveBase.yml

diff --git a/.github/workflows/CI_BracketingNonlinearSolve.yml b/.github/workflows/CI_BracketingNonlinearSolve.yml
new file mode 100644
index 000000000..d79e69930
--- /dev/null
+++ b/.github/workflows/CI_BracketingNonlinearSolve.yml
@@ -0,0 +1,67 @@
+name: CI (BracketingNonlinearSolve)
+
+on:
+  pull_request:
+    branches:
+      - master
+    paths:
+      - "lib/BracketingNonlinearSolve/**"
+      - ".github/workflows/CI_BracketingNonlinearSolve.yml"
+  push:
+    branches:
+      - master
+
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: only if it is a pull request build.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+
+jobs:
+  test:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "min"
+          - "1"
+        os:
+          - ubuntu-latest
+          - macos-latest
+          - windows-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: actions/cache@v4
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          for path in ("lib/NonlinearSolveBase",)
+              Pkg.develop(; path)
+          end
+          Pkg.instantiate()
+          Pkg.test(; coverage=true)
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/BracketingNonlinearSolve {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/BracketingNonlinearSolve/src,lib/BracketingNonlinearSolve/ext
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/.github/workflows/CI_NonlinearSolveBase.yml b/.github/workflows/CI_NonlinearSolveBase.yml
new file mode 100644
index 000000000..f3878acef
--- /dev/null
+++ b/.github/workflows/CI_NonlinearSolveBase.yml
@@ -0,0 +1,63 @@
+name: CI (NonlinearSolveBase)
+
+on:
+  pull_request:
+    branches:
+      - master
+    paths:
+      - "lib/NonlinearSolveBase/**"
+      - ".github/workflows/CI_NonlinearSolveBase.yml"
+  push:
+    branches:
+      - master
+
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: only if it is a pull request build.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+
+jobs:
+  test:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "min"
+          - "1"
+        os:
+          - ubuntu-latest
+          - macos-latest
+          - windows-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: actions/cache@v4
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          Pkg.instantiate()
+          Pkg.test(; coverage=true)
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/NonlinearSolveBase {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/.github/workflows/CompatHelper.yml b/.github/workflows/CompatHelper.yml
index 73494545f..805a5fe4c 100644
--- a/.github/workflows/CompatHelper.yml
+++ b/.github/workflows/CompatHelper.yml
@@ -23,4 +23,10 @@ jobs:
       - name: CompatHelper.main()
         env:
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
-        run: julia -e 'using CompatHelper; CompatHelper.main(;subdirs=["", "docs"])'
+        run: |
+          import CompatHelper
+          subdirs = ["", "docs"]
+          append!(subdirs, joinpath.(("lib",), filter(p -> isdir(joinpath("lib", p)), readdir("lib"))))
+          CompatHelper.main(; subdirs)
+        shell: julia --color=yes {0}
+        working-directory: "./"

From 9ba1c64af4e7d1a0e4aa688a022404bef374862f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 13:28:46 -0400
Subject: [PATCH 545/700] ci(github-actions): trigger dependent packages on
 file changes

---
 .github/workflows/CI_BracketingNonlinearSolve.yml | 3 +++
 lib/BracketingNonlinearSolve/Project.toml         | 2 +-
 2 files changed, 4 insertions(+), 1 deletion(-)

diff --git a/.github/workflows/CI_BracketingNonlinearSolve.yml b/.github/workflows/CI_BracketingNonlinearSolve.yml
index d79e69930..5720013e2 100644
--- a/.github/workflows/CI_BracketingNonlinearSolve.yml
+++ b/.github/workflows/CI_BracketingNonlinearSolve.yml
@@ -7,6 +7,9 @@ on:
     paths:
       - "lib/BracketingNonlinearSolve/**"
       - ".github/workflows/CI_BracketingNonlinearSolve.yml"
+      - "lib/NonlinearSolveBase/src/**"
+      - "lib/NonlinearSolveBase/ext/**"
+      - "lib/NonlinearSolveBase/Project.toml"
   push:
     branches:
       - master
diff --git a/lib/BracketingNonlinearSolve/Project.toml b/lib/BracketingNonlinearSolve/Project.toml
index b8bf5a806..c71a19dca 100644
--- a/lib/BracketingNonlinearSolve/Project.toml
+++ b/lib/BracketingNonlinearSolve/Project.toml
@@ -26,8 +26,8 @@ SciMLBase = "2.50"
 julia = "1.10"
 
 [extras]
-InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
 

From c68ffde1331ead53cbed0d4c04046da9cfd5dcda Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 13:49:22 -0400
Subject: [PATCH 546/700] feat: add bracketing default algorithm

---
 .../src/BracketingNonlinearSolve.jl                       | 8 ++++++++
 lib/BracketingNonlinearSolve/test/rootfind_tests.jl       | 6 +++---
 2 files changed, 11 insertions(+), 3 deletions(-)

diff --git a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
index 491ec4132..62cf7a7b7 100644
--- a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
+++ b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
@@ -19,6 +19,14 @@ include("falsi.jl")
 include("itp.jl")
 include("ridder.jl")
 
+# Default Algorithm
+function CommonSolve.solve(prob::IntervalNonlinearProblem; kwargs...)
+    return CommonSolve.solve(prob, ITP(); kwargs...)
+end
+function CommonSolve.solve(prob::IntervalNonlinearProblem, nothing, args...; kwargs...)
+    return CommonSolve.solve(prob, ITP(), args...; kwargs...)
+end
+
 @setup_workload begin
     for T in (Float32, Float64)
         prob_brack = IntervalNonlinearProblem{false}(
diff --git a/lib/BracketingNonlinearSolve/test/rootfind_tests.jl b/lib/BracketingNonlinearSolve/test/rootfind_tests.jl
index 1875ede00..6a490d6fa 100644
--- a/lib/BracketingNonlinearSolve/test/rootfind_tests.jl
+++ b/lib/BracketingNonlinearSolve/test/rootfind_tests.jl
@@ -7,7 +7,7 @@ end
 @testitem "Interval Nonlinear Problems" setup=[RootfindingTestSnippet] tags=[:core] begin
     using ForwardDiff
 
-    @testset for alg in (Bisection(), Falsi(), Ridder(), Brent(), ITP(), Alefeld())
+    @testset for alg in (Bisection(), Falsi(), Ridder(), Brent(), ITP(), Alefeld(), nothing)
         tspan = (1.0, 20.0)
 
         function g(p)
@@ -52,7 +52,7 @@ end
     prob = IntervalNonlinearProblem(quadratic_f, (1.0, 20.0), 2.0)
     ϵ = eps(Float64) # least possible tol for all methods
 
-    @testset for alg in (Bisection(), Falsi(), ITP())
+    @testset for alg in (Bisection(), Falsi(), ITP(), nothing)
         @testset for abstol in [0.1, 0.01, 0.001, 0.0001, 1e-5, 1e-6, 1e-7]
             sol = solve(prob, alg; abstol)
             result_tol = abs(sol.u - sqrt(2))
@@ -76,7 +76,7 @@ end
 end
 
 @testitem "Flipped Signs and Reversed Tspan" setup=[RootfindingTestSnippet] tags=[:core] begin
-    @testset for alg in (Alefeld(), Bisection(), Falsi(), Brent(), ITP(), Ridder())
+    @testset for alg in (Alefeld(), Bisection(), Falsi(), Brent(), ITP(), Ridder(), nothing)
         f1(u, p) = u * u - p
         f2(u, p) = p - u * u
 

From 97fc19876406dbf5bf651c2189741dfab7dc4acc Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 13:53:34 -0400
Subject: [PATCH 547/700] refactor: setup SimpleNonlinearSolve.jl

---
 .github/workflows/CI_SimpleNonlinearSolve.yml | 76 +++++++++++++++++++
 lib/BracketingNonlinearSolve/Project.toml     |  2 +-
 lib/SimpleNonlinearSolve/LICENSE              | 21 +++++
 lib/SimpleNonlinearSolve/Project.toml         | 23 ++++++
 .../src/SimpleNonlinearSolve.jl               | 19 +++++
 lib/SimpleNonlinearSolve/test/runtests.jl     |  0
 6 files changed, 140 insertions(+), 1 deletion(-)
 create mode 100644 .github/workflows/CI_SimpleNonlinearSolve.yml
 create mode 100644 lib/SimpleNonlinearSolve/LICENSE
 create mode 100644 lib/SimpleNonlinearSolve/Project.toml
 create mode 100644 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/runtests.jl

diff --git a/.github/workflows/CI_SimpleNonlinearSolve.yml b/.github/workflows/CI_SimpleNonlinearSolve.yml
new file mode 100644
index 000000000..e07cb3343
--- /dev/null
+++ b/.github/workflows/CI_SimpleNonlinearSolve.yml
@@ -0,0 +1,76 @@
+name: CI (SimpleNonlinearSolve)
+
+on:
+  pull_request:
+    branches:
+      - master
+    paths:
+      - "lib/SimpleNonlinearSolve/src/**"
+      - "lib/SimpleNonlinearSolve/ext/**"
+      - "lib/SimpleNonlinearSolve/test/**"
+      - "lib/SimpleNonlinearSolve/Project.toml"
+      - ".github/workflows/CI_SimpleNonlinearSolve.yml"
+      - "lib/BracketingNonlinearSolve/src/**"
+      - "lib/BracketingNonlinearSolve/ext/**"
+      - "lib/BracketingNonlinearSolve/Project.toml"
+      - "lib/NonlinearSolveBase/src/**"
+      - "lib/NonlinearSolveBase/ext/**"
+      - "lib/NonlinearSolveBase/Project.toml"
+  push:
+    branches:
+      - master
+
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: only if it is a pull request build.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+
+jobs:
+  test:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "min"
+          - "1"
+        os:
+          - ubuntu-latest
+          - macos-latest
+          - windows-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: actions/cache@v4
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          for path in ("lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve")
+              Pkg.develop(; path)
+          end
+          Pkg.instantiate()
+          Pkg.test(; coverage=true)
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SimpleNonlinearSolve {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/SimpleNonlinearSolve/src,lib/SimpleNonlinearSolve/ext
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/lib/BracketingNonlinearSolve/Project.toml b/lib/BracketingNonlinearSolve/Project.toml
index c71a19dca..dc979f660 100644
--- a/lib/BracketingNonlinearSolve/Project.toml
+++ b/lib/BracketingNonlinearSolve/Project.toml
@@ -21,7 +21,7 @@ CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
 ForwardDiff = "0.10.36"
 NonlinearSolveBase = "1"
-PrecompileTools = "1.2.1"
+PrecompileTools = "1.2"
 SciMLBase = "2.50"
 julia = "1.10"
 
diff --git a/lib/SimpleNonlinearSolve/LICENSE b/lib/SimpleNonlinearSolve/LICENSE
new file mode 100644
index 000000000..8eef16440
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2020 Julia Computing, Inc.
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
\ No newline at end of file
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
new file mode 100644
index 000000000..e2c92c016
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -0,0 +1,23 @@
+name = "SimpleNonlinearSolve"
+uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
+authors = ["SciML"]
+version = "1.13.0"
+
+[deps]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
+ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+BracketingNonlinearSolve = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
+NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
+PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
+Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+
+[compat]
+ADTypes = "1.2"
+ArrayInterface = "7.16"
+BracketingNonlinearSolve = "1"
+NonlinearSolveBase = "1"
+PrecompileTools = "1.2"
+Reexport = "1.2"
+SciMLBase = "2.50"
+julia = "1.10"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
new file mode 100644
index 000000000..0debfd328
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -0,0 +1,19 @@
+module SimpleNonlinearSolve
+
+using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
+               AutoPolyesterForwardDiff
+using PrecompileTools: @compile_workload, @setup_workload
+using Reexport: @reexport
+@reexport using SciMLBase  # I don't like this but needed to avoid a breaking change
+
+using BracketingNonlinearSolve: Alefeld, Bisection, Brent, Falsi, ITP, Ridder
+
+@setup_workload begin
+    @compile_workload begin end
+end
+
+export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
+
+export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
+
+end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
new file mode 100644
index 000000000..e69de29bb

From fa700ab4314e27798fcdbd0c34f4d5a2a4288b40 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 13:56:31 -0400
Subject: [PATCH 548/700] ci(github-actions): fix package dev workflow

---
 .github/workflows/CI_BracketingNonlinearSolve.yml | 4 +++-
 .github/workflows/CI_SimpleNonlinearSolve.yml     | 4 +++-
 2 files changed, 6 insertions(+), 2 deletions(-)

diff --git a/.github/workflows/CI_BracketingNonlinearSolve.yml b/.github/workflows/CI_BracketingNonlinearSolve.yml
index 5720013e2..fc62f02c6 100644
--- a/.github/workflows/CI_BracketingNonlinearSolve.yml
+++ b/.github/workflows/CI_BracketingNonlinearSolve.yml
@@ -53,9 +53,11 @@ jobs:
           import Pkg
           Pkg.Registry.update()
           # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
           for path in ("lib/NonlinearSolveBase",)
-              Pkg.develop(; path)
+              push!(dev_pks, Pkg.PackageSpec(; path))
           end
+          Pkg.develop(dev_pks)
           Pkg.instantiate()
           Pkg.test(; coverage=true)
         shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/BracketingNonlinearSolve {0}
diff --git a/.github/workflows/CI_SimpleNonlinearSolve.yml b/.github/workflows/CI_SimpleNonlinearSolve.yml
index e07cb3343..365de3707 100644
--- a/.github/workflows/CI_SimpleNonlinearSolve.yml
+++ b/.github/workflows/CI_SimpleNonlinearSolve.yml
@@ -59,9 +59,11 @@ jobs:
           import Pkg
           Pkg.Registry.update()
           # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
           for path in ("lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve")
-              Pkg.develop(; path)
+              push!(dev_pks, Pkg.PackageSpec(; path))
           end
+          Pkg.develop(dev_pks)
           Pkg.instantiate()
           Pkg.test(; coverage=true)
         shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SimpleNonlinearSolve {0}

From cc61d5a0d69470000f07957853af583e38b2508f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 14:59:33 -0400
Subject: [PATCH 549/700] feat: add simplenonlinearsolve AD specific dispatches

---
 .../src/NonlinearSolveBase.jl                 |  2 -
 lib/SimpleNonlinearSolve/Project.toml         | 18 ++++++++
 .../SimpleNonlinearSolveChainRulesCoreExt.jl  | 23 ++++++++++
 .../ext/SimpleNonlinearSolveDiffEqBaseExt.jl  | 11 +++++
 .../ext/SimpleNonlinearSolveReverseDiffExt.jl | 37 ++++++++++++++++
 .../ext/SimpleNonlinearSolveTrackerExt.jl     | 37 ++++++++++++++++
 .../src/SimpleNonlinearSolve.jl               | 42 +++++++++++++++++++
 7 files changed, 168 insertions(+), 2 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveDiffEqBaseExt.jl
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl

diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index f0459447b..25fe50023 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -27,6 +27,4 @@ export RelTerminationMode, AbsTerminationMode, NormTerminationMode, RelNormTermi
        AbsNormTerminationMode, RelNormSafeTerminationMode, AbsNormSafeTerminationMode,
        RelNormSafeNormTerminationMode, AbsNormSafeNormTerminationMode
 
-export ImmutableNonlinearProblem
-
 end
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index e2c92c016..5d8817b60 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -7,17 +7,35 @@ version = "1.13.0"
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 BracketingNonlinearSolve = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
+CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 
+[weakdeps]
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+
+[extensions]
+SimpleNonlinearSolveChainRulesCoreExt = "ChainRulesCore"
+SimpleNonlinearSolveDiffEqBaseExt = "DiffEqBase"
+SimpleNonlinearSolveReverseDiffExt = "ReverseDiff"
+SimpleNonlinearSolveTrackerExt = "Tracker"
+
 [compat]
 ADTypes = "1.2"
 ArrayInterface = "7.16"
 BracketingNonlinearSolve = "1"
+ChainRulesCore = "1.24"
+CommonSolve = "0.2.4"
+DiffEqBase = "6.155"
 NonlinearSolveBase = "1"
 PrecompileTools = "1.2"
 Reexport = "1.2"
+ReverseDiff = "1.15"
 SciMLBase = "2.50"
+Tracker = "0.2.35"
 julia = "1.10"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
new file mode 100644
index 000000000..df0bd7573
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
@@ -0,0 +1,23 @@
+module SimpleNonlinearSolveChainRulesCoreExt
+
+using ChainRulesCore: ChainRulesCore, NoTangent
+using NonlinearSolveBase: ImmutableNonlinearProblem
+using SciMLBase: ChainRulesOriginator, NonlinearLeastSquaresProblem
+
+using SimpleNonlinearSolve: SimpleNonlinearSolve, simplenonlinearsolve_solve_up,
+                            solve_adjoint
+
+function ChainRulesCore.rrule(::typeof(simplenonlinearsolve_solve_up),
+        prob::Union{InternalNonlinearProblem, NonlinearLeastSquaresProblem},
+        sensealg, u0, u0_changed, p, p_changed, alg, args...; kwargs...)
+    out, ∇internal = solve_adjoint(
+        prob, sensealg, u0, p, ChainRulesOriginator(), alg, args...; kwargs...)
+    function ∇simplenonlinearsolve_solve_up(Δ)
+        ∂f, ∂prob, ∂sensealg, ∂u0, ∂p, _, ∂args... = ∇internal(Δ)
+        return (
+            ∂f, ∂prob, ∂sensealg, ∂u0, NoTangent(), ∂p, NoTangent(), NoTangent(), ∂args...)
+    end
+    return out, ∇simplenonlinearsolve_solve_up
+end
+
+end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveDiffEqBaseExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveDiffEqBaseExt.jl
new file mode 100644
index 000000000..950a04019
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveDiffEqBaseExt.jl
@@ -0,0 +1,11 @@
+module SimpleNonlinearSolveDiffEqBaseExt
+
+using DiffEqBase: DiffEqBase
+
+using SimpleNonlinearSolve: SimpleNonlinearSolve
+
+function SimpleNonlinearSolve.solve_adjoint_internal(args...; kwargs...)
+    return DiffEqBase._solve_adjoint(args...; kwargs...)
+end
+
+end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
new file mode 100644
index 000000000..1357bec83
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
@@ -0,0 +1,37 @@
+module SimpleNonlinearSolveReverseDiffExt
+
+using ArrayInterface: ArrayInterface
+using NonlinearSolveBase: ImmutableNonlinearProblem
+using ReverseDiff: ReverseDiff, TrackedArray, TrackedReal
+using SciMLBase: ReverseDiffOriginator, NonlinearLeastSquaresProblem, remake
+
+using SimpleNonlinearSolve: SimpleNonlinearSolve, solve_adjoint
+
+for pType in (InternalNonlinearProblem, NonlinearLeastSquaresProblem)
+    aTypes = (TrackedArray, AbstractArray{<:TrackedReal}, Any)
+    for (uT, pT) in collect(Iterators.product(aTypes, aTypes))[1:(end - 1)]
+        @eval function SimpleNonlinearSolve.simplenonlinearsolve_solve_up(
+                prob::$(pType), sensealg, u0::$(uT), u0_changed,
+                p::$(pT), p_changed, alg, args...; kwargs...)
+            return ReverseDiff.track(SimpleNonlinearSolve.simplenonlinearsolve_solve_up,
+                prob, sensealg, ArrayInterface.aos_to_soa(u0), true,
+                ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
+        end
+    end
+
+    @eval ReverseDiff.@grad function SimpleNonlinearSolve.simplenonlinearsolve_solve_up(
+            tprob::$(pType), sensealg, tu0, u0_changed,
+            tp, p_changed, alg, args...; kwargs...)
+        u0, p = ReverseDiff.value(tu0), ReverseDiff.value(tp)
+        prob = remake(tprob; u0, p)
+        out, ∇internal = solve_adjoint(
+            prob, sensealg, u0, p, ReverseDiffOriginator(), alg, args...; kwargs...)
+
+        function ∇simplenonlinearsolve_solve_up(Δ...)
+            ∂prob, ∂sensealg, ∂u0, ∂p, _, ∂args... = ∇internal(Δ...)
+            return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
+        end
+    end
+end
+
+end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
new file mode 100644
index 000000000..935484db1
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
@@ -0,0 +1,37 @@
+module SimpleNonlinearSolveTrackerExt
+
+using ArrayInterface: ArrayInterface
+using NonlinearSolveBase: ImmutableNonlinearProblem
+using SciMLBase: TrackerOriginator, NonlinearLeastSquaresProblem, remake
+using Tracker: Tracker, TrackedArray, TrackedReal
+
+using SimpleNonlinearSolve: SimpleNonlinearSolve, solve_adjoint
+
+for pType in (InternalNonlinearProblem, NonlinearLeastSquaresProblem)
+    aTypes = (TrackedArray, AbstractArray{<:TrackedReal}, Any)
+    for (uT, pT) in collect(Iterators.product(aTypes, aTypes))[1:(end - 1)]
+        @eval function SimpleNonlinearSolve.simplenonlinearsolve_solve_up(
+                prob::$(pType), sensealg, u0::$(uT), u0_changed,
+                p::$(pT), p_changed, alg, args...; kwargs...)
+            return Tracker.track(SimpleNonlinearSolve.simplenonlinearsolve_solve_up, prob,
+                sensealg, ArrayInterface.aos_to_soa(u0), true,
+                ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
+        end
+    end
+
+    @eval Tracker.@grad function SimpleNonlinearSolve.simplenonlinearsolve_solve_up(
+            tprob::$(pType), sensealg, tu0, u0_changed,
+            tp, p_changed, alg, args...; kwargs...)
+        u0, p = Tracker.data(tu0), Tracker.data(tp)
+        prob = remake(tprob; u0, p)
+        out, ∇internal = solve_adjoint(
+            prob, sensealg, u0, p, TrackerOriginator(), alg, args...; kwargs...)
+
+        function ∇simplenonlinearsolve_solve_up(Δ)
+            ∂prob, ∂sensealg, ∂u0, ∂p, _, ∂args... = ∇internal(Tracker.data(Δ))
+            return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
+        end
+    end
+end
+
+end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 0debfd328..99c0be844 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -2,11 +2,53 @@ module SimpleNonlinearSolve
 
 using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
                AutoPolyesterForwardDiff
+using CommonSolve: CommonSolve, solve
 using PrecompileTools: @compile_workload, @setup_workload
 using Reexport: @reexport
 @reexport using SciMLBase  # I don't like this but needed to avoid a breaking change
+using SciMLBase: AbstractNonlinearAlgorithm, NonlinearProblem, ReturnCode
 
 using BracketingNonlinearSolve: Alefeld, Bisection, Brent, Falsi, ITP, Ridder
+using NonlinearSolveBase: ImmutableNonlinearProblem
+
+abstract type AbstractSimpleNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm end
+
+is_extension_loaded(::Val) = false
+
+# By Pass the highlevel checks for NonlinearProblem for Simple Algorithms
+function CommonSolve.solve(prob::NonlinearProblem,
+        alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...)
+    prob = convert(ImmutableNonlinearProblem, prob)
+    return solve(prob, alg, args...; kwargs...)
+end
+
+function CommonSolve.solve(
+        prob::ImmutableNonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
+        args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...)
+    if sensealg === nothing && haskey(prob.kwargs, :sensealg)
+        sensealg = prob.kwargs[:sensealg]
+    end
+    new_u0 = u0 !== nothing ? u0 : prob.u0
+    new_p = p !== nothing ? p : prob.p
+    return simplenonlinearsolve_solve_up(prob, sensealg, new_u0, u0 === nothing, new_p,
+        p === nothing, alg, args...; prob.kwargs..., kwargs...)
+end
+
+function simplenonlinearsolve_solve_up(
+        prob::ImmutableNonlinearProblem, sensealg, u0, u0_changed, p, p_changed,
+        alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...)
+    (u0_changed || p_changed) && (prob = remake(prob; u0, p))
+    return SciMLBase.__solve(prob, alg, args...; kwargs...)
+end
+
+# NOTE: This is defined like this so that we don't have to keep have 2 args for the
+# extensions
+function solve_adjoint(args...; kws...)
+    is_extension_loaded(Val(:DiffEqBase)) && return solve_adjoint_internal(args...; kws...)
+    error("Adjoint sensitivity analysis requires `DiffEqBase.jl` to be explicitly loaded.")
+end
+
+function solve_adjoint_internal end
 
 @setup_workload begin
     @compile_workload begin end

From 36626459b4a2eaffc6855fe30d271453715f58e7 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 15:07:12 -0400
Subject: [PATCH 550/700] feat: add the AD workflows

---
 lib/SimpleNonlinearSolve/Project.toml         |  6 ++++
 .../src/SimpleNonlinearSolve.jl               | 31 +++++++++++++++++--
 2 files changed, 34 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 5d8817b60..f4ae4e4de 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -8,6 +8,9 @@ ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 BracketingNonlinearSolve = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
+DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
+FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
@@ -32,6 +35,9 @@ BracketingNonlinearSolve = "1"
 ChainRulesCore = "1.24"
 CommonSolve = "0.2.4"
 DiffEqBase = "6.155"
+DifferentiationInterface = "0.5.17"
+FiniteDiff = "2.24.0"
+ForwardDiff = "0.10.36"
 NonlinearSolveBase = "1"
 PrecompileTools = "1.2"
 Reexport = "1.2"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 99c0be844..f1d7b0713 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -1,16 +1,25 @@
 module SimpleNonlinearSolve
 
-using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
-               AutoPolyesterForwardDiff
 using CommonSolve: CommonSolve, solve
 using PrecompileTools: @compile_workload, @setup_workload
 using Reexport: @reexport
 @reexport using SciMLBase  # I don't like this but needed to avoid a breaking change
 using SciMLBase: AbstractNonlinearAlgorithm, NonlinearProblem, ReturnCode
 
+# AD Dependencies
+using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
+               AutoPolyesterForwardDiff
+using DifferentiationInterface: DifferentiationInterface
+# TODO: move these to extensions in a breaking change. These are not even used in the
+#       package, but are used to trigger the extension loading in DI.jl
+using FiniteDiff: FiniteDiff
+using ForwardDiff: ForwardDiff
+
 using BracketingNonlinearSolve: Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 using NonlinearSolveBase: ImmutableNonlinearProblem
 
+const DI = DifferentiationInterface
+
 abstract type AbstractSimpleNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm end
 
 is_extension_loaded(::Val) = false
@@ -51,7 +60,23 @@ end
 function solve_adjoint_internal end
 
 @setup_workload begin
-    @compile_workload begin end
+    for T in (Float32, Float64)
+        prob_scalar = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
+        prob_iip = NonlinearProblem{true}((du, u, p) -> du .= u .* u .- p, ones(T, 3), T(2))
+        prob_oop = NonlinearProblem{false}((u, p) -> u .* u .- p, ones(T, 3), T(2))
+
+        algs = []
+        algs_no_iip = []
+
+        @compile_workload begin
+            for alg in algs, prob in (prob_scalar, prob_iip, prob_oop)
+                CommonSolve.solve(prob, alg)
+            end
+            for alg in algs_no_iip
+                CommonSolve.solve(prob_scalar, alg)
+            end
+        end
+    end
 end
 
 export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff

From d164b64d062a35ccc3857b2318b64c6d1cd0c0a7 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 15:19:28 -0400
Subject: [PATCH 551/700] chore: run formatter

---
 .../ext/SimpleNonlinearSolveTrackerExt.jl                     | 4 ++--
 lib/SimpleNonlinearSolve/test/runtests.jl                     | 1 +
 2 files changed, 3 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
index 935484db1..a2fa8ff40 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
@@ -13,8 +13,8 @@ for pType in (InternalNonlinearProblem, NonlinearLeastSquaresProblem)
         @eval function SimpleNonlinearSolve.simplenonlinearsolve_solve_up(
                 prob::$(pType), sensealg, u0::$(uT), u0_changed,
                 p::$(pT), p_changed, alg, args...; kwargs...)
-            return Tracker.track(SimpleNonlinearSolve.simplenonlinearsolve_solve_up, prob,
-                sensealg, ArrayInterface.aos_to_soa(u0), true,
+            return Tracker.track(SimpleNonlinearSolve.simplenonlinearsolve_solve_up,
+                prob, sensealg, ArrayInterface.aos_to_soa(u0), true,
                 ArrayInterface.aos_to_soa(p), true, alg, args...; kwargs...)
         end
     end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index e69de29bb..8b1378917 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -0,0 +1 @@
+

From 8f7eb449273ee6c3aac6951be559075550662f01 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 17:44:33 -0400
Subject: [PATCH 552/700] feat: share the termination condition code in
 NonlinearSolve and SimpleNonlinearSolve

---
 .../src/NonlinearSolveBase.jl                 |  7 ++--
 .../src/termination_conditions.jl             | 34 +++++++++++++++++++
 2 files changed, 38 insertions(+), 3 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 25fe50023..1ba7a0cc3 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -8,16 +8,17 @@ using LinearAlgebra: norm
 using Markdown: @doc_str
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinearProblem,
-                 AbstractNonlinearFunction, @add_kwonly, StandardNonlinearProblem,
-                 NullParameters, NonlinearProblem, isinplace
+                 NonlinearProblem, NonlinearLeastSquaresProblem, AbstractNonlinearFunction,
+                 @add_kwonly, StandardNonlinearProblem, NullParameters, NonlinearProblem,
+                 isinplace
 using StaticArraysCore: StaticArray
 
 include("public.jl")
 include("utils.jl")
 
+include("immutable_problem.jl")
 include("common_defaults.jl")
 include("termination_conditions.jl")
-include("immutable_problem.jl")
 
 # Unexported Public API
 @compat(public, (L2_NORM, Linf_NORM, NAN_CHECK, UNITLESS_ABS2, get_tolerance))
diff --git a/lib/NonlinearSolveBase/src/termination_conditions.jl b/lib/NonlinearSolveBase/src/termination_conditions.jl
index 50af54a57..a278861a8 100644
--- a/lib/NonlinearSolveBase/src/termination_conditions.jl
+++ b/lib/NonlinearSolveBase/src/termination_conditions.jl
@@ -245,3 +245,37 @@ end
 function check_convergence(mode::AbsNormModes, duₙ, _, __, abstol, ___)
     return Utils.apply_norm(mode.internalnorm, duₙ) ≤ abstol
 end
+
+# High-Level API with defaults.
+## This is mostly for internal usage in NonlinearSolve and SimpleNonlinearSolve
+function default_termination_mode(
+        ::Union{ImmutableNonlinearProblem, NonlinearProblem}, ::Val{:simple})
+    return AbsNormTerminationMode(Base.Fix1(maximum, abs))
+end
+function default_termination_mode(::NonlinearLeastSquaresProblem, ::Val{:simple})
+    return AbsNormTerminationMode(Base.Fix2(norm, 2))
+end
+
+function default_termination_mode(
+        ::Union{ImmutableNonlinearProblem, NonlinearProblem}, ::Val{:regular})
+    return AbsNormSafeBestTerminationMode(Base.Fix1(maximum, abs); max_stalled_steps = 32)
+end
+
+function default_termination_mode(::NonlinearLeastSquaresProblem, ::Val{:regular})
+    return AbsNormSafeBestTerminationMode(Base.Fix2(norm, 2); max_stalled_steps = 32)
+end
+
+function init_termination_cache(
+        prob::AbstractNonlinearProblem, abstol, reltol, du, u, ::Nothing, callee::Val)
+    return init_termination_cache(
+        prob, abstol, reltol, du, u, default_termination_mode(prob, callee), callee)
+end
+
+function init_termination_cache(::AbstractNonlinearProblem, abstol, reltol, du,
+        u, tc::AbstractNonlinearTerminationMode, ::Val)
+    T = promote_type(eltype(du), eltype(u))
+    abstol = get_tolerance(abstol, T)
+    reltol = get_tolerance(reltol, T)
+    cache = init(du, u, tc; abstol, reltol)
+    return abstol, reltol, cache
+end

From 89e71e9a79bf13f93a40911dfb711f34a0b024bd Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 17:44:51 -0400
Subject: [PATCH 553/700] feat: add partial SimpleKlement Implementation

---
 lib/SimpleNonlinearSolve/Project.toml         |  16 +++
 .../src/SimpleNonlinearSolve.jl               |  10 +-
 lib/SimpleNonlinearSolve/src/klement.jl       |  47 ++++++++
 lib/SimpleNonlinearSolve/src/utils.jl         | 107 ++++++++++++++++++
 lib/SimpleNonlinearSolve/test/runtests.jl     |   4 +
 5 files changed, 181 insertions(+), 3 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/klement.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/utils.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index f4ae4e4de..7ab2416be 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -9,12 +9,16 @@ ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 BracketingNonlinearSolve = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
+FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [weakdeps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
@@ -36,12 +40,24 @@ ChainRulesCore = "1.24"
 CommonSolve = "0.2.4"
 DiffEqBase = "6.155"
 DifferentiationInterface = "0.5.17"
+FastClosures = "0.3.2"
 FiniteDiff = "2.24.0"
 ForwardDiff = "0.10.36"
+LinearAlgebra = "1.10"
+MaybeInplace = "0.1.4"
 NonlinearSolveBase = "1"
 PrecompileTools = "1.2"
 Reexport = "1.2"
 ReverseDiff = "1.15"
 SciMLBase = "2.50"
+StaticArraysCore = "1.4.3"
 Tracker = "0.2.35"
 julia = "1.10"
+
+[extras]
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
+
+[targets]
+test = ["InteractiveUtils", "Test", "TestItemRunner"]
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index f1d7b0713..4a9f369f1 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -1,14 +1,16 @@
 module SimpleNonlinearSolve
 
 using CommonSolve: CommonSolve, solve
+using FastClosures: @closure
+using MaybeInplace: @bb
 using PrecompileTools: @compile_workload, @setup_workload
 using Reexport: @reexport
 @reexport using SciMLBase  # I don't like this but needed to avoid a breaking change
 using SciMLBase: AbstractNonlinearAlgorithm, NonlinearProblem, ReturnCode
+using StaticArraysCore: StaticArray
 
 # AD Dependencies
-using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
-               AutoPolyesterForwardDiff
+using ADTypes: AbstractADType, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
 using DifferentiationInterface: DifferentiationInterface
 # TODO: move these to extensions in a breaking change. These are not even used in the
 #       package, but are used to trigger the extension loading in DI.jl
@@ -16,7 +18,7 @@ using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff
 
 using BracketingNonlinearSolve: Alefeld, Bisection, Brent, Falsi, ITP, Ridder
-using NonlinearSolveBase: ImmutableNonlinearProblem
+using NonlinearSolveBase: ImmutableNonlinearProblem, get_tolerance
 
 const DI = DifferentiationInterface
 
@@ -24,6 +26,8 @@ abstract type AbstractSimpleNonlinearSolveAlgorithm <: AbstractNonlinearAlgorith
 
 is_extension_loaded(::Val) = false
 
+include("utils.jl")
+
 # By Pass the highlevel checks for NonlinearProblem for Simple Algorithms
 function CommonSolve.solve(prob::NonlinearProblem,
         alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...)
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
new file mode 100644
index 000000000..feb93d423
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -0,0 +1,47 @@
+"""
+    SimpleKlement()
+
+A low-overhead implementation of `Klement` [klement2014using](@citep). This
+method is non-allocating on scalar and static array problems.
+"""
+struct SimpleKlement <: AbstractSimpleNonlinearSolveAlgorithm end
+
+function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleKlement, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0 = false, termination_condition = nothing, kwargs...)
+    x = Utils.maybe_unaliased(prob.u0, alias_u0)
+    T = eltype(x)
+
+    abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+
+    @bb δx = copy(x)
+    @bb fprev = copy(fx)
+    @bb xo = copy(x)
+    @bb d = copy(x)
+
+    J = one.(x)
+    @bb δx² = similar(x)
+
+    for _ in 1:maxiters
+        any(iszero, J) && (J = Utils.identity_jacobian!!(J))
+
+        @bb @. δx = fprev / J
+
+        @bb @. x = xo - δx
+        fx = Utils.eval_f(prob, fx, x)
+
+        # Termination Checks
+        # tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
+        tc_sol !== nothing && return tc_sol
+
+        @bb δx .*= -1
+        @bb @. δx² = δx^2 * J^2
+        @bb @. J += (fx - fprev - J * δx) / ifelse(iszero(δx²), T(1e-5), δx²) * δx * (J^2)
+
+        @bb copyto!(fprev, fx)
+        @bb copyto!(xo, x)
+    end
+
+    return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
new file mode 100644
index 000000000..64845b3c8
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -0,0 +1,107 @@
+module Utils
+
+using ADTypes: AbstractADType, AutoForwardDiff, AutoFiniteDiff, AutoPolyesterForwardDiff
+using ArrayInterface: ArrayInterface
+using DifferentiationInterface: DifferentiationInterface
+using FastClosures: @closure
+using LinearAlgebra: LinearAlgebra, I, diagind
+using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem
+using SciMLBase: SciMLBase, NonlinearLeastSquaresProblem, NonlinearProblem,
+                 NonlinearFunction
+using StaticArraysCore: StaticArray, SArray, SMatrix, SVector
+
+const DI = DifferentiationInterface
+
+const safe_similar = NonlinearSolveBase.Utils.safe_similar
+
+pickchunksize(n::Int) = min(n, 12)
+
+can_dual(::Type{<:Real}) = true
+can_dual(::Type) = false
+
+maybe_unaliased(x::Union{Number, SArray}, ::Bool) = x
+function maybe_unaliased(x::T, alias::Bool) where {T <: AbstractArray}
+    (alias || !ArrayInterface.can_setindex(T)) && return x
+    return copy(x)
+end
+
+function get_concrete_autodiff(_, ad::AbstractADType)
+    DI.check_available(ad) && return ad
+    error("AD Backend $(ad) is not available. This could be because you haven't loaded the \
+           actual backend (See [Differentiation Inferface Docs](https://gdalle.github.io/DifferentiationInterface.jl/DifferentiationInterface/stable/) \
+           for more details) or the backend might not be supported by DifferentiationInferface.jl.")
+end
+function get_concrete_autodiff(
+        prob, ad::Union{AutoForwardDiff{nothing}, AutoPolyesterForwardDiff{nothing}})
+    return get_concrete_autodiff(prob,
+        ArrayInterface.parameterless_type(ad)(;
+            chunksize = pickchunksize(length(prob.u0)), ad.tag))
+end
+function get_concrete_autodiff(prob, ::Nothing)
+    if can_dual(eltype(prob.u0)) && DI.check_available(AutoForwardDiff())
+        return AutoForwardDiff(; chunksize = pickchunksize(length(prob.u0)))
+    end
+    DI.check_available(AutoFiniteDiff()) && return AutoFiniteDiff()
+    error("Default AD backends are not available. Please load either FiniteDiff or \
+           ForwardDiff for default AD selection to work. Else provide a specific AD \
+           backend (instead of `nothing`) to the solver.")
+end
+
+# NOTE: This doesn't initialize the `f(x)` but just returns a buffer of the same size
+function get_fx(prob::NonlinearLeastSquaresProblem, x)
+    if SciMLBase.isinplace(prob) && prob.f.resid_prototype === nothing
+        error("Inplace NonlinearLeastSquaresProblem requires a `resid_prototype` to be \
+               specified.")
+    end
+    return get_fx(prob.f, x, prob.p)
+end
+function get_fx(prob::Union{ImmutableNonlinearProblem, NonlinearProblem}, x)
+    return get_fx(prob.f, x, prob.p)
+end
+function get_fx(f::NonlinearFunction, x, p)
+    if SciMLBase.isinplace(f)
+        f.resid_prototype === nothing && return eltype(x).(f.resid_prototype)
+        return safe_similar(x)
+    end
+    return f(x, p)
+end
+
+function eval_f(prob, fx, x)
+    SciMLBase.isinplace(prob) || return prob.f(x, prob.p)
+    prob.f(fx, x, prob.p)
+    return fx
+end
+
+function fixed_parameter_function(prob::AbstractNonlinearProblem)
+    SciMLBase.isinplace(prob) && return @closure (du, u) -> prob.f(du, u, prob.p)
+    return Base.Fix2(prob.f, prob.p)
+end
+
+# __init_identity_jacobian(u::Number, fu, α = true) = oftype(u, α)
+# function __init_identity_jacobian(u, fu, α = true)
+#     J = __similar(u, promote_type(eltype(u), eltype(fu)), length(fu), length(u))
+#     fill!(J, zero(eltype(J)))
+#     J[diagind(J)] .= eltype(J)(α)
+#     return J
+# end
+# function __init_identity_jacobian(u::StaticArray, fu, α = true)
+#     S1, S2 = length(fu), length(u)
+#     J = SMatrix{S1, S2, eltype(u)}(I * α)
+#     return J
+# end
+
+identity_jacobian!!(J::Number) = one(J)
+function identity_jacobian!!(J::AbstractVector)
+    ArrayInterface.can_setindex(J) || return one.(J)
+    fill!(J, true)
+    return J
+end
+function identity_jacobian!!(J::AbstractMatrix)
+    ArrayInterface.can_setindex(J) || return convert(typeof(J), I)
+    J[diagind(J)] .= true
+    return J
+end
+identity_jacobian!!(::SMatrix{S1, S2, T}) where {S1, S2, T} = SMatrix{S1, S2, T}(I)
+identity_jacobian!!(::SVector{S1, T}) where {S1, T} = ones(SVector{S1, T})
+
+end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 8b1378917..6ea6326b0 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -1 +1,5 @@
+using TestItemRunner, InteractiveUtils
 
+@info sprint(InteractiveUtils.versioninfo)
+
+@run_package_tests

From aa452c2a8cc48bf782cb108d28c9421596994805 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 17:45:50 -0400
Subject: [PATCH 554/700] chore: fix typo in error message

---
 lib/SimpleNonlinearSolve/src/utils.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 64845b3c8..13aad5655 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -28,8 +28,8 @@ end
 function get_concrete_autodiff(_, ad::AbstractADType)
     DI.check_available(ad) && return ad
     error("AD Backend $(ad) is not available. This could be because you haven't loaded the \
-           actual backend (See [Differentiation Inferface Docs](https://gdalle.github.io/DifferentiationInterface.jl/DifferentiationInterface/stable/) \
-           for more details) or the backend might not be supported by DifferentiationInferface.jl.")
+           actual backend (See [Differentiation Interface Docs](https://gdalle.github.io/DifferentiationInterface.jl/DifferentiationInterface/stable/) \
+           for more details) or the backend might not be supported by DifferentiationInterface.jl.")
 end
 function get_concrete_autodiff(
         prob, ad::Union{AutoForwardDiff{nothing}, AutoPolyesterForwardDiff{nothing}})

From a2e91cc58d4039d61a46f12b6f4e5ca883d802fd Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 17 Sep 2024 17:50:49 -0400
Subject: [PATCH 555/700] fix: missing import

---
 lib/SimpleNonlinearSolve/src/utils.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 13aad5655..a12c90f78 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -6,8 +6,8 @@ using DifferentiationInterface: DifferentiationInterface
 using FastClosures: @closure
 using LinearAlgebra: LinearAlgebra, I, diagind
 using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem
-using SciMLBase: SciMLBase, NonlinearLeastSquaresProblem, NonlinearProblem,
-                 NonlinearFunction
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, NonlinearLeastSquaresProblem,
+                 NonlinearProblem, NonlinearFunction
 using StaticArraysCore: StaticArray, SArray, SMatrix, SVector
 
 const DI = DifferentiationInterface

From 4576a4e37ccad7d59cd173b5fdcb266efabc6802 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 18 Sep 2024 16:50:29 -0400
Subject: [PATCH 556/700] feat: functional Klement

---
 .../src/NonlinearSolveBase.jl                 |  2 +-
 lib/NonlinearSolveBase/src/public.jl          |  4 +-
 .../src/termination_conditions.jl             |  2 +-
 .../src/SimpleNonlinearSolve.jl               |  6 +-
 lib/SimpleNonlinearSolve/src/klement.jl       |  5 +-
 lib/SimpleNonlinearSolve/src/utils.jl         | 57 ++++++++++++++-----
 6 files changed, 53 insertions(+), 23 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 1ba7a0cc3..63f4b697c 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -10,7 +10,7 @@ using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinearProblem,
                  NonlinearProblem, NonlinearLeastSquaresProblem, AbstractNonlinearFunction,
                  @add_kwonly, StandardNonlinearProblem, NullParameters, NonlinearProblem,
-                 isinplace
+                 isinplace, warn_paramtype
 using StaticArraysCore: StaticArray
 
 include("public.jl")
diff --git a/lib/NonlinearSolveBase/src/public.jl b/lib/NonlinearSolveBase/src/public.jl
index db8c389e2..d9014d71e 100644
--- a/lib/NonlinearSolveBase/src/public.jl
+++ b/lib/NonlinearSolveBase/src/public.jl
@@ -51,7 +51,7 @@ for name in (:Norm, :RelNorm, :AbsNorm)
 
     @eval begin
         """
-            $($struct_name) <: AbstractSafeNonlinearTerminationMode
+            $($struct_name) <: AbstractNonlinearTerminationMode
 
         Terminates if $($doctring).
 
@@ -63,7 +63,7 @@ for name in (:Norm, :RelNorm, :AbsNorm)
 
         $($TERM_INTERNALNORM_DOCS).
         """
-        struct $(struct_name){F} <: AbstractSafeNonlinearTerminationMode
+        struct $(struct_name){F} <: AbstractNonlinearTerminationMode
             internalnorm::F
 
             function $(struct_name)(internalnorm::F) where {F}
diff --git a/lib/NonlinearSolveBase/src/termination_conditions.jl b/lib/NonlinearSolveBase/src/termination_conditions.jl
index a278861a8..4403e12c3 100644
--- a/lib/NonlinearSolveBase/src/termination_conditions.jl
+++ b/lib/NonlinearSolveBase/src/termination_conditions.jl
@@ -276,6 +276,6 @@ function init_termination_cache(::AbstractNonlinearProblem, abstol, reltol, du,
     T = promote_type(eltype(du), eltype(u))
     abstol = get_tolerance(abstol, T)
     reltol = get_tolerance(reltol, T)
-    cache = init(du, u, tc; abstol, reltol)
+    cache = SciMLBase.init(du, u, tc; abstol, reltol)
     return abstol, reltol, cache
 end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 4a9f369f1..4b524e4bf 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -18,7 +18,7 @@ using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff
 
 using BracketingNonlinearSolve: Alefeld, Bisection, Brent, Falsi, ITP, Ridder
-using NonlinearSolveBase: ImmutableNonlinearProblem, get_tolerance
+using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, get_tolerance
 
 const DI = DifferentiationInterface
 
@@ -28,6 +28,8 @@ is_extension_loaded(::Val) = false
 
 include("utils.jl")
 
+include("klement.jl")
+
 # By Pass the highlevel checks for NonlinearProblem for Simple Algorithms
 function CommonSolve.solve(prob::NonlinearProblem,
         alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...)
@@ -69,7 +71,7 @@ function solve_adjoint_internal end
         prob_iip = NonlinearProblem{true}((du, u, p) -> du .= u .* u .- p, ones(T, 3), T(2))
         prob_oop = NonlinearProblem{false}((u, p) -> u .* u .- p, ones(T, 3), T(2))
 
-        algs = []
+        algs = [SimpleKlement()]
         algs_no_iip = []
 
         @compile_workload begin
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index feb93d423..055f65bc3 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -11,6 +11,7 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleKlement,
         alias_u0 = false, termination_condition = nothing, kwargs...)
     x = Utils.maybe_unaliased(prob.u0, alias_u0)
     T = eltype(x)
+    fx = Utils.get_fx(prob, x)
 
     abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
         prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
@@ -32,8 +33,8 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleKlement,
         fx = Utils.eval_f(prob, fx, x)
 
         # Termination Checks
-        # tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
-        tc_sol !== nothing && return tc_sol
+        solved, retcode, fx_sol, x_sol = Utils.check_termination(tc_cache, fx, x, xo, prob)
+        solved && return SciMLBase.build_solution(prob, alg, x_sol, fx_sol; retcode)
 
         @bb δx .*= -1
         @bb @. δx² = δx^2 * J^2
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index a12c90f78..9008171d3 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -5,9 +5,12 @@ using ArrayInterface: ArrayInterface
 using DifferentiationInterface: DifferentiationInterface
 using FastClosures: @closure
 using LinearAlgebra: LinearAlgebra, I, diagind
-using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem
+using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem,
+                          AbstractNonlinearTerminationMode,
+                          AbstractSafeNonlinearTerminationMode,
+                          AbstractSafeBestNonlinearTerminationMode
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, NonlinearLeastSquaresProblem,
-                 NonlinearProblem, NonlinearFunction
+                 NonlinearProblem, NonlinearFunction, ReturnCode
 using StaticArraysCore: StaticArray, SArray, SMatrix, SVector
 
 const DI = DifferentiationInterface
@@ -60,7 +63,7 @@ function get_fx(prob::Union{ImmutableNonlinearProblem, NonlinearProblem}, x)
 end
 function get_fx(f::NonlinearFunction, x, p)
     if SciMLBase.isinplace(f)
-        f.resid_prototype === nothing && return eltype(x).(f.resid_prototype)
+        f.resid_prototype === nothing || return eltype(x).(f.resid_prototype)
         return safe_similar(x)
     end
     return f(x, p)
@@ -77,18 +80,18 @@ function fixed_parameter_function(prob::AbstractNonlinearProblem)
     return Base.Fix2(prob.f, prob.p)
 end
 
-# __init_identity_jacobian(u::Number, fu, α = true) = oftype(u, α)
-# function __init_identity_jacobian(u, fu, α = true)
-#     J = __similar(u, promote_type(eltype(u), eltype(fu)), length(fu), length(u))
-#     fill!(J, zero(eltype(J)))
-#     J[diagind(J)] .= eltype(J)(α)
-#     return J
-# end
-# function __init_identity_jacobian(u::StaticArray, fu, α = true)
-#     S1, S2 = length(fu), length(u)
-#     J = SMatrix{S1, S2, eltype(u)}(I * α)
-#     return J
-# end
+function identity_jacobian(u::Number, fu::Number, α = true)
+    return convert(promote_type(eltype(u), eltype(fu)), α)
+end
+function identity_jacobian(u, fu, α = true)
+    J = safe_similar(u, promote_type(eltype(u), eltype(fu)))
+    fill!(J, zero(eltype(J)))
+    J[diagind(J)] .= eltype(J)(α)
+    return J
+end
+function identity_jacobian(u::StaticArray, fu, α = true)
+    return SMatrix{length(fu), length(u), eltype(u)}(I * α)
+end
 
 identity_jacobian!!(J::Number) = one(J)
 function identity_jacobian!!(J::AbstractVector)
@@ -104,4 +107,28 @@ end
 identity_jacobian!!(::SMatrix{S1, S2, T}) where {S1, S2, T} = SMatrix{S1, S2, T}(I)
 identity_jacobian!!(::SVector{S1, T}) where {S1, T} = ones(SVector{S1, T})
 
+# Termination Conditions
+function check_termination(cache, fx, x, xo, prob)
+    return check_termination(cache, fx, x, xo, prob, cache.mode)
+end
+
+function check_termination(cache, fx, x, xo, _, ::AbstractNonlinearTerminationMode)
+    return cache(fx, x, xo), ReturnCode.Success, fx, x
+end
+function check_termination(cache, fx, x, xo, _, ::AbstractSafeNonlinearTerminationMode)
+    return cache(fx, x, xo), cache.retcode, fx, x
+end
+function check_termination(cache, fx, x, xo, prob, ::AbstractSafeBestNonlinearTerminationMode)
+    if cache(fx, x, xo)
+        x = cache.u
+        if SciMLBase.isinplace(prob)
+            prob.f(fx, x, prob.p)
+        else
+            fx = prob.f(x, prob.p)
+        end
+        return true, cache.retcode, fx, x
+    end
+    return false, ReturnCode.Default, fx, x
+end
+
 end

From 65bcadd44eab0cb4ba34a2d2ffefb2a0e2b94e62 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 18 Sep 2024 16:52:37 -0400
Subject: [PATCH 557/700] chore: apply formatting suggestion

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 lib/SimpleNonlinearSolve/src/utils.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 9008171d3..16cf5142d 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -118,7 +118,8 @@ end
 function check_termination(cache, fx, x, xo, _, ::AbstractSafeNonlinearTerminationMode)
     return cache(fx, x, xo), cache.retcode, fx, x
 end
-function check_termination(cache, fx, x, xo, prob, ::AbstractSafeBestNonlinearTerminationMode)
+function check_termination(
+        cache, fx, x, xo, prob, ::AbstractSafeBestNonlinearTerminationMode)
     if cache(fx, x, xo)
         x = cache.u
         if SciMLBase.isinplace(prob)

From 5e0858a9c38ce486105e32d952872900c697999f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 22:49:53 -0400
Subject: [PATCH 558/700] chore: run formatter

---
 lib/NonlinearSolveBase/src/termination_conditions.jl |  6 +++---
 lib/NonlinearSolveBase/src/utils.jl                  | 12 ++++++------
 2 files changed, 9 insertions(+), 9 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/termination_conditions.jl b/lib/NonlinearSolveBase/src/termination_conditions.jl
index 4403e12c3..8bb58f8eb 100644
--- a/lib/NonlinearSolveBase/src/termination_conditions.jl
+++ b/lib/NonlinearSolveBase/src/termination_conditions.jl
@@ -219,9 +219,9 @@ end
 function check_convergence(::RelTerminationMode, duₙ, uₙ, __, ___, reltol)
     if Utils.fast_scalar_indexing(duₙ)
         return all(@closure(xy->begin
-            x, y = xy
-            return abs(y) ≤ reltol * abs(x + y)
-        end), zip(uₙ, duₙ))
+                x, y = xy
+                return abs(y) ≤ reltol * abs(x + y)
+            end), zip(uₙ, duₙ))
     else # using mapreduce here will almost certainly be faster on GPUs
         return mapreduce(
             @closure((xᵢ, yᵢ)->(abs(yᵢ) ≤ reltol * abs(xᵢ + yᵢ))), *, uₙ, duₙ; init = true)
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 0a8840942..cb54a6f4c 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -23,9 +23,9 @@ end
 function nonallocating_maximum(f::F, x, y) where {F}
     if fast_scalar_indexing(x, y)
         return maximum(@closure((xᵢyᵢ)->begin
-            xᵢ, yᵢ = xᵢyᵢ
-            return abs(f(xᵢ, yᵢ))
-        end), zip(x, y))
+                xᵢ, yᵢ = xᵢyᵢ
+                return abs(f(xᵢ, yᵢ))
+            end), zip(x, y))
     else
         return mapreduce(@closure((xᵢ, yᵢ)->abs(f(xᵢ, yᵢ))), max, x, y)
     end
@@ -55,9 +55,9 @@ norm_op(norm::N, op::OP, x, y) where {N, OP} = norm(op.(x, y))
 function norm_op(::typeof(L2_NORM), op::OP, x, y) where {OP}
     if fast_scalar_indexing(x, y)
         return sqrt(sum(@closure((xᵢ, yᵢ)->begin
-            xᵢ, yᵢ = xᵢyᵢ
-            return op(xᵢ, yᵢ)^2
-        end), zip(x, y)))
+                xᵢ, yᵢ = xᵢyᵢ
+                return op(xᵢ, yᵢ)^2
+            end), zip(x, y)))
     else
         return sqrt(mapreduce(@closure((xᵢ, yᵢ)->op(xᵢ, yᵢ)^2), +, x, y))
     end

From 2dc0c4dcccc55bc7abf5fc151369b859551ea627 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 24 Sep 2024 22:52:25 -0400
Subject: [PATCH 559/700] ci: make the scripts uniform

---
 .github/workflows/CI_BracketingNonlinearSolve.yml |  4 +---
 .github/workflows/CI_NonlinearSolve.yml           |  3 +++
 .github/workflows/CI_SimpleNonlinearSolve.yml     | 13 +++----------
 3 files changed, 7 insertions(+), 13 deletions(-)

diff --git a/.github/workflows/CI_BracketingNonlinearSolve.yml b/.github/workflows/CI_BracketingNonlinearSolve.yml
index fc62f02c6..6d78e5612 100644
--- a/.github/workflows/CI_BracketingNonlinearSolve.yml
+++ b/.github/workflows/CI_BracketingNonlinearSolve.yml
@@ -6,10 +6,8 @@ on:
       - master
     paths:
       - "lib/BracketingNonlinearSolve/**"
+      - "lib/NonlinearSolveBase/**"
       - ".github/workflows/CI_BracketingNonlinearSolve.yml"
-      - "lib/NonlinearSolveBase/src/**"
-      - "lib/NonlinearSolveBase/ext/**"
-      - "lib/NonlinearSolveBase/Project.toml"
   push:
     branches:
       - master
diff --git a/.github/workflows/CI_NonlinearSolve.yml b/.github/workflows/CI_NonlinearSolve.yml
index a4c14820e..d684cb3b7 100644
--- a/.github/workflows/CI_NonlinearSolve.yml
+++ b/.github/workflows/CI_NonlinearSolve.yml
@@ -11,6 +11,9 @@ on:
       - "Project.toml"
       - ".github/workflows/CI_NonlinearSolve.yml"
       - "lib/SciMLNonlinearOperators/**"
+      - "lib/BracketingNonlinearSolve/**"
+      - "lib/NonlinearSolveBase/**"
+      - "lib/SimpleNonlinearSolve/**"
   push:
     branches:
       - master
diff --git a/.github/workflows/CI_SimpleNonlinearSolve.yml b/.github/workflows/CI_SimpleNonlinearSolve.yml
index 365de3707..9854b6d99 100644
--- a/.github/workflows/CI_SimpleNonlinearSolve.yml
+++ b/.github/workflows/CI_SimpleNonlinearSolve.yml
@@ -5,17 +5,10 @@ on:
     branches:
       - master
     paths:
-      - "lib/SimpleNonlinearSolve/src/**"
-      - "lib/SimpleNonlinearSolve/ext/**"
-      - "lib/SimpleNonlinearSolve/test/**"
-      - "lib/SimpleNonlinearSolve/Project.toml"
+      - "lib/SimpleNonlinearSolve/**"
+      - "lib/BracketingNonlinearSolve/**"
+      - "lib/NonlinearSolveBase/**"
       - ".github/workflows/CI_SimpleNonlinearSolve.yml"
-      - "lib/BracketingNonlinearSolve/src/**"
-      - "lib/BracketingNonlinearSolve/ext/**"
-      - "lib/BracketingNonlinearSolve/Project.toml"
-      - "lib/NonlinearSolveBase/src/**"
-      - "lib/NonlinearSolveBase/ext/**"
-      - "lib/NonlinearSolveBase/Project.toml"
   push:
     branches:
       - master

From 7c229bcb5b3ec75d63807756894474880ae19d2a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 25 Sep 2024 17:28:07 -0400
Subject: [PATCH 560/700] feat: bring in changes from
 https://github.com/SciML/SimpleNonlinearSolve.jl/pull/158

---
 lib/BracketingNonlinearSolve/src/bisection.jl | 10 +++++++++-
 lib/BracketingNonlinearSolve/src/brent.jl     | 10 +++++++++-
 lib/BracketingNonlinearSolve/src/falsi.jl     | 10 +++++++++-
 lib/BracketingNonlinearSolve/src/itp.jl       | 10 +++++++++-
 lib/BracketingNonlinearSolve/src/ridder.jl    | 10 +++++++++-
 5 files changed, 45 insertions(+), 5 deletions(-)

diff --git a/lib/BracketingNonlinearSolve/src/bisection.jl b/lib/BracketingNonlinearSolve/src/bisection.jl
index e3a38a1fd..1611ad34e 100644
--- a/lib/BracketingNonlinearSolve/src/bisection.jl
+++ b/lib/BracketingNonlinearSolve/src/bisection.jl
@@ -20,7 +20,7 @@ A common bisection method.
 end
 
 function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Bisection,
-        args...; maxiters = 1000, abstol = nothing, kwargs...)
+        args...; maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...)
     @assert !SciMLBase.isinplace(prob) "`Bisection` only supports out-of-place problems."
 
     f = Base.Fix2(prob.f, prob.p)
@@ -40,6 +40,14 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Bisection,
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        verbose &&
+            @warn "The interval is not an enclosing interval, opposite signs at the \
+                   boundaries are required."
+        return SciMLBase.build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     i = 1
     while i ≤ maxiters
         mid = (left + right) / 2
diff --git a/lib/BracketingNonlinearSolve/src/brent.jl b/lib/BracketingNonlinearSolve/src/brent.jl
index 5475e675e..fea2ce3f4 100644
--- a/lib/BracketingNonlinearSolve/src/brent.jl
+++ b/lib/BracketingNonlinearSolve/src/brent.jl
@@ -6,7 +6,7 @@ Left non-allocating Brent method.
 struct Brent <: AbstractBracketingAlgorithm end
 
 function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
-        maxiters = 1000, abstol = nothing, kwargs...)
+        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...)
     @assert !SciMLBase.isinplace(prob) "`Brent` only supports out-of-place problems."
 
     f = Base.Fix2(prob.f, prob.p)
@@ -27,6 +27,14 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        verbose &&
+            @warn "The interval is not an enclosing interval, opposite signs at the \
+                   boundaries are required."
+        return SciMLBase.build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     if abs(fl) < abs(fr)
         left, right = right, left
         fl, fr = fr, fl
diff --git a/lib/BracketingNonlinearSolve/src/falsi.jl b/lib/BracketingNonlinearSolve/src/falsi.jl
index 451a4c0b2..8c62b95c6 100644
--- a/lib/BracketingNonlinearSolve/src/falsi.jl
+++ b/lib/BracketingNonlinearSolve/src/falsi.jl
@@ -6,7 +6,7 @@ A non-allocating regula falsi method.
 struct Falsi <: AbstractBracketingAlgorithm end
 
 function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
-        maxiters = 1000, abstol = nothing, kwargs...)
+        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...)
     @assert !SciMLBase.isinplace(prob) "`False` only supports out-of-place problems."
 
     f = Base.Fix2(prob.f, prob.p)
@@ -27,6 +27,14 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        verbose &&
+            @warn "The interval is not an enclosing interval, opposite signs at the \
+                   boundaries are required."
+        return SciMLBase.build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     i = 1
     while i ≤ maxiters
         if Impl.nextfloat_tdir(left, l, r) == right
diff --git a/lib/BracketingNonlinearSolve/src/itp.jl b/lib/BracketingNonlinearSolve/src/itp.jl
index dd6ddc23b..4798f9030 100644
--- a/lib/BracketingNonlinearSolve/src/itp.jl
+++ b/lib/BracketingNonlinearSolve/src/itp.jl
@@ -57,7 +57,7 @@ function ITP(; scaled_k1::Real = 0.2, k2::Real = 2, n0::Int = 10)
 end
 
 function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
-        maxiters = 1000, abstol = nothing, kwargs...)
+        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...)
     @assert !SciMLBase.isinplace(prob) "`ITP` only supports out-of-place problems."
 
     f = Base.Fix2(prob.f, prob.p)
@@ -77,6 +77,14 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        verbose &&
+            @warn "The interval is not an enclosing interval, opposite signs at the \
+                   boundaries are required."
+        return SciMLBase.build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     ϵ = abstol
     k2 = alg.k2
     k1 = alg.scaled_k1 * abs(right - left)^(1 - k2)
diff --git a/lib/BracketingNonlinearSolve/src/ridder.jl b/lib/BracketingNonlinearSolve/src/ridder.jl
index a289bcb05..e4b67a7c7 100644
--- a/lib/BracketingNonlinearSolve/src/ridder.jl
+++ b/lib/BracketingNonlinearSolve/src/ridder.jl
@@ -6,7 +6,7 @@ A non-allocating ridder method.
 struct Ridder <: AbstractBracketingAlgorithm end
 
 function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
-        maxiters = 1000, abstol = nothing, kwargs...)
+        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...)
     @assert !SciMLBase.isinplace(prob) "`Ridder` only supports out-of-place problems."
 
     f = Base.Fix2(prob.f, prob.p)
@@ -26,6 +26,14 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        verbose &&
+            @warn "The interval is not an enclosing interval, opposite signs at the \
+                   boundaries are required."
+        return SciMLBase.build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     xo = oftype(left, Inf)
     i = 1
     while i ≤ maxiters

From c1a2d6779d5ab30fd39ab2fd0a5f9bc9cb1f6377 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 25 Sep 2024 17:32:36 -0400
Subject: [PATCH 561/700] chore: unnecessary comment

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 2 --
 1 file changed, 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 4b524e4bf..0bb65181a 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -12,8 +12,6 @@ using StaticArraysCore: StaticArray
 # AD Dependencies
 using ADTypes: AbstractADType, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
 using DifferentiationInterface: DifferentiationInterface
-# TODO: move these to extensions in a breaking change. These are not even used in the
-#       package, but are used to trigger the extension loading in DI.jl
 using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff
 

From 32afc3fcd5b384a1a8330ddd6540c2b0154e394f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 25 Sep 2024 18:04:59 -0400
Subject: [PATCH 562/700] feat: automatic backend selection for autodiff

---
 lib/NonlinearSolveBase/Project.toml           |   6 +
 .../ext/NonlinearSolveBaseForwardDiffExt.jl   |   9 +-
 .../src/NonlinearSolveBase.jl                 |   9 ++
 lib/NonlinearSolveBase/src/autodiff.jl        | 109 ++++++++++++++++++
 4 files changed, 132 insertions(+), 1 deletion(-)
 create mode 100644 lib/NonlinearSolveBase/src/autodiff.jl

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 94d12d822..819bcc79f 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -4,10 +4,13 @@ authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
 version = "1.0.0"
 
 [deps]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
+DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
+EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
@@ -24,10 +27,13 @@ NonlinearSolveBaseForwardDiffExt = "ForwardDiff"
 NonlinearSolveBaseSparseArraysExt = "SparseArrays"
 
 [compat]
+ADTypes = "1.9"
 ArrayInterface = "7.9"
 CommonSolve = "0.2.4"
 Compat = "4.15"
 ConcreteStructs = "0.2.3"
+DifferentiationInterface = "0.6.1"
+EnzymeCore = "0.8"
 FastClosures = "0.3"
 ForwardDiff = "0.10.36"
 LinearAlgebra = "1.10"
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
index 469c5944b..31550da96 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
@@ -1,13 +1,20 @@
 module NonlinearSolveBaseForwardDiffExt
 
+using ADTypes: ADTypes, AutoForwardDiff, AutoPolyesterForwardDiff
 using CommonSolve: solve
 using FastClosures: @closure
 using ForwardDiff: ForwardDiff, Dual
-using SciMLBase: SciMLBase, IntervalNonlinearProblem, NonlinearProblem,
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, IntervalNonlinearProblem,
+                 NonlinearProblem,
                  NonlinearLeastSquaresProblem, remake
 
 using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, Utils
 
+function NonlinearSolveBase.additional_incompatible_backend_check(
+        prob::AbstractNonlinearProblem, ::Union{AutoForwardDiff, AutoPolyesterForwardDiff})
+    return !ForwardDiff.can_dual(eltype(prob.u0))
+end
+
 Utils.value(::Type{Dual{T, V, N}}) where {T, V, N} = V
 Utils.value(x::Dual) = Utils.value(ForwardDiff.value(x))
 Utils.value(x::AbstractArray{<:Dual}) = Utils.value.(x)
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 63f4b697c..4b3eec258 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -1,8 +1,11 @@
 module NonlinearSolveBase
 
+using ADTypes: ADTypes, AbstractADType, ForwardMode, ReverseMode
 using ArrayInterface: ArrayInterface
 using Compat: @compat
 using ConcreteStructs: @concrete
+using DifferentiationInterface: DifferentiationInterface
+using EnzymeCore: EnzymeCore
 using FastClosures: @closure
 using LinearAlgebra: norm
 using Markdown: @doc_str
@@ -13,6 +16,8 @@ using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinear
                  isinplace, warn_paramtype
 using StaticArraysCore: StaticArray
 
+const DI = DifferentiationInterface
+
 include("public.jl")
 include("utils.jl")
 
@@ -20,9 +25,13 @@ include("immutable_problem.jl")
 include("common_defaults.jl")
 include("termination_conditions.jl")
 
+include("autodiff.jl")
+
 # Unexported Public API
 @compat(public, (L2_NORM, Linf_NORM, NAN_CHECK, UNITLESS_ABS2, get_tolerance))
 @compat(public, (nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution))
+@compat(public, (select_forward_mode_autodiff, select_reverse_mode_autodiff,
+    select_jacobian_autodiff))
 
 export RelTerminationMode, AbsTerminationMode, NormTerminationMode, RelNormTerminationMode,
        AbsNormTerminationMode, RelNormSafeTerminationMode, AbsNormSafeTerminationMode,
diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
new file mode 100644
index 000000000..d2e51389d
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/autodiff.jl
@@ -0,0 +1,109 @@
+# Here we determine the preferred AD backend. We have a predefined list of ADs and then
+# we select the first one that is avialable and would work with the problem.
+
+# Ordering is important here. We want to select the first one that is compatible with the
+# problem.
+const ReverseADs = [
+    ADTypes.AutoEnzyme(; mode = EnzymeCore.Reverse),
+    ADTypes.AutoZygote(),
+    ADTypes.AutoTracker(),
+    ADTypes.AutoReverseDiff(),
+    ADTypes.AutoFiniteDiff()
+]
+
+const ForwardADs = [
+    ADTypes.AutoEnzyme(; mode = EnzymeCore.Forward),
+    ADTypes.AutoPolyesterForwardDiff(),
+    ADTypes.AutoForwardDiff(),
+    ADTypes.AutoFiniteDiff()
+]
+
+# TODO: Handle Sparsity
+
+function select_forward_mode_autodiff(
+        prob::AbstractNonlinearProblem, ad::AbstractADType; warn_check_mode::Bool = true)
+    if warn_check_mode && !(ADTypes.mode(ad) isa ADTypes.ForwardMode)
+        @warn "The chosen AD backend $(ad) is not a forward mode AD. Use with caution."
+    end
+    if incompatible_backend_and_problem(prob, ad)
+        adₙ = select_forward_mode_autodiff(prob, nothing; warn_check_mode)
+        @warn "The chosen AD backend `$(ad)` does not support the chosen problem. After \
+               running autodiff selection detected `$(adₙ)` as a potential forward mode \
+               backend."
+        return adₙ
+    end
+    return ad
+end
+
+function select_forward_mode_autodiff(prob::AbstractNonlinearProblem, ::Nothing;
+        warn_check_mode::Bool = true)
+    idx = findfirst(!Base.Fix1(incompatible_backend_and_problem, prob), ForwardADs)
+    idx !== nothing && return ForwardADs[idx]
+    throw(ArgumentError("No forward mode AD backend is compatible with the chosen problem. \
+                         This could be because no forward mode autodiff backend is loaded \
+                         or the loaded backends don't support the problem."))
+end
+
+function select_reverse_mode_autodiff(
+        prob::AbstractNonlinearProblem, ad::AbstractADType; warn_check_mode::Bool = true)
+    if warn_check_mode && !(ADTypes.mode(ad) isa ADTypes.ReverseMode)
+        if !is_finite_differences_backend(ad)
+            @warn "The chosen AD backend $(ad) is not a reverse mode AD. Use with caution."
+        else
+            @warn "The chosen AD backend $(ad) is a finite differences backend. This might \
+                   be slow and inaccurate. Use with caution."
+        end
+    end
+    if incompatible_backend_and_problem(prob, ad)
+        adₙ = select_reverse_mode_autodiff(prob, nothing; warn_check_mode)
+        @warn "The chosen AD backend `$(ad)` does not support the chosen problem. After \
+               running autodiff selection detected `$(adₙ)` as a potential reverse mode \
+               backend."
+        return adₙ
+    end
+    return ad
+end
+
+function select_reverse_mode_autodiff(prob::AbstractNonlinearProblem, ::Nothing;
+        warn_check_mode::Bool = true)
+    idx = findfirst(!Base.Fix1(incompatible_backend_and_problem, prob), ReverseADs)
+    idx !== nothing && return ReverseADs[idx]
+    throw(ArgumentError("No reverse mode AD backend is compatible with the chosen problem. \
+                         This could be because no reverse mode autodiff backend is loaded \
+                         or the loaded backends don't support the problem."))
+end
+
+function select_jacobian_autodiff(prob::AbstractNonlinearProblem, ad::AbstractADType)
+    if incompatible_backend_and_problem(prob, ad)
+        adₙ = select_jacobian_autodiff(prob, nothing)
+        @warn "The chosen AD backend `$(ad)` does not support the chosen problem. After \
+               running autodiff selection detected `$(adₙ)` as a potential jacobian \
+               backend."
+        return adₙ
+    end
+    return ad
+end
+
+function select_jacobian_autodiff(prob::AbstractNonlinearProblem, ::Nothing)
+    idx = findfirst(!Base.Fix1(incompatible_backend_and_problem, prob), ForwardADs)
+    idx !== nothing && !is_finite_differences_backend(ForwardADs[idx]) &&
+        return ForwardADs[idx]
+    idx = findfirst(!Base.Fix1(incompatible_backend_and_problem, prob), ReverseADs)
+    idx !== nothing && return ReverseADs[idx]
+    throw(ArgumentError("No jacobian AD backend is compatible with the chosen problem. \
+                         This could be because no jacobian autodiff backend is loaded \
+                         or the loaded backends don't support the problem."))
+end
+
+function incompatible_backend_and_problem(
+        prob::AbstractNonlinearProblem, ad::AbstractADType)
+    !DI.check_available(ad) && return true
+    SciMLBase.isinplace(prob) && !DI.check_inplace(ad) && return true
+    return additional_incompatible_backend_check(prob, ad)
+end
+
+additional_incompatible_backend_check(::AbstractNonlinearProblem, ::AbstractADType) = false
+
+is_finite_differences_backend(ad::AbstractADType) = false
+is_finite_differences_backend(::ADTypes.AutoFiniteDiff) = true
+is_finite_differences_backend(::ADTypes.AutoFiniteDifferences) = true

From 3eaa84a4b26b9e57f068d330d5848ff3157fa6fa Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 26 Sep 2024 03:04:53 -0400
Subject: [PATCH 563/700] feat: check for branching for
 ReverseDiff(compile=true)

---
 lib/NonlinearSolveBase/Project.toml              |  2 ++
 lib/NonlinearSolveBase/src/NonlinearSolveBase.jl | 10 ++++++----
 lib/NonlinearSolveBase/src/autodiff.jl           |  9 +++++++++
 3 files changed, 17 insertions(+), 4 deletions(-)

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 819bcc79f..3999de770 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -12,6 +12,7 @@ ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
+FunctionProperties = "f62d2435-5019-4c03-9749-2d4c77af0cbc"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
@@ -36,6 +37,7 @@ DifferentiationInterface = "0.6.1"
 EnzymeCore = "0.8"
 FastClosures = "0.3"
 ForwardDiff = "0.10.36"
+FunctionProperties = "0.1.2"
 LinearAlgebra = "1.10"
 Markdown = "1.10"
 RecursiveArrayTools = "3"
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 4b3eec258..5e1a37326 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -7,13 +7,14 @@ using ConcreteStructs: @concrete
 using DifferentiationInterface: DifferentiationInterface
 using EnzymeCore: EnzymeCore
 using FastClosures: @closure
+using FunctionProperties: hasbranching
 using LinearAlgebra: norm
 using Markdown: @doc_str
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinearProblem,
                  NonlinearProblem, NonlinearLeastSquaresProblem, AbstractNonlinearFunction,
-                 @add_kwonly, StandardNonlinearProblem, NullParameters, NonlinearProblem,
-                 isinplace, warn_paramtype
+                 @add_kwonly, StandardNonlinearProblem, NullParameters, isinplace,
+                 warn_paramtype
 using StaticArraysCore: StaticArray
 
 const DI = DifferentiationInterface
@@ -30,8 +31,9 @@ include("autodiff.jl")
 # Unexported Public API
 @compat(public, (L2_NORM, Linf_NORM, NAN_CHECK, UNITLESS_ABS2, get_tolerance))
 @compat(public, (nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution))
-@compat(public, (select_forward_mode_autodiff, select_reverse_mode_autodiff,
-    select_jacobian_autodiff))
+@compat(public,
+    (select_forward_mode_autodiff, select_reverse_mode_autodiff,
+        select_jacobian_autodiff))
 
 export RelTerminationMode, AbsTerminationMode, NormTerminationMode, RelNormTerminationMode,
        AbsNormTerminationMode, RelNormSafeTerminationMode, AbsNormSafeTerminationMode,
diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
index d2e51389d..f81ce7039 100644
--- a/lib/NonlinearSolveBase/src/autodiff.jl
+++ b/lib/NonlinearSolveBase/src/autodiff.jl
@@ -7,6 +7,7 @@ const ReverseADs = [
     ADTypes.AutoEnzyme(; mode = EnzymeCore.Reverse),
     ADTypes.AutoZygote(),
     ADTypes.AutoTracker(),
+    ADTypes.AutoReverseDiff(; compile = true),
     ADTypes.AutoReverseDiff(),
     ADTypes.AutoFiniteDiff()
 ]
@@ -103,6 +104,14 @@ function incompatible_backend_and_problem(
 end
 
 additional_incompatible_backend_check(::AbstractNonlinearProblem, ::AbstractADType) = false
+function additional_incompatible_backend_check(prob::AbstractNonlinearProblem,
+        ::ADTypes.AutoReverseDiff{true})
+    if SciMLBase.isinplace(prob)
+        fu = prob.f.resid_prototype === nothing ? zero(prob.u0) : prob.f.resid_prototype
+        return hasbranching(prob.f, fu, prob.u0, prob.p)
+    end
+    return hasbranching(prob.f, prob.u0, prob.p)
+end
 
 is_finite_differences_backend(ad::AbstractADType) = false
 is_finite_differences_backend(::ADTypes.AutoFiniteDiff) = true

From b569144d5a81bb47c3ccff8517815dc1bcf925ff Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 12:51:43 -0400
Subject: [PATCH 564/700] feat: SimpleNewtonRaphson

---
 docs/Project.toml                             |  2 +-
 lib/NonlinearSolveBase/src/autodiff.jl        | 17 +++--
 lib/SimpleNonlinearSolve/Project.toml         |  7 +-
 .../src/SimpleNonlinearSolve.jl               | 10 ++-
 lib/SimpleNonlinearSolve/src/raphson.jl       | 62 ++++++++++++++++
 lib/SimpleNonlinearSolve/src/utils.jl         | 70 ++++++++++++++++++-
 6 files changed, 157 insertions(+), 11 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/src/raphson.jl

diff --git a/docs/Project.toml b/docs/Project.toml
index ab35d42ae..4ad265246 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -30,7 +30,7 @@ AlgebraicMultigrid = "0.5, 0.6"
 ArrayInterface = "6, 7"
 BenchmarkTools = "1"
 DiffEqBase = "6.136"
-DifferentiationInterface = "0.6"
+DifferentiationInterface = "0.6.1"
 Documenter = "1"
 DocumenterCitations = "1"
 DocumenterInterLinks = "1.0.0"
diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
index f81ce7039..4c057d25e 100644
--- a/lib/NonlinearSolveBase/src/autodiff.jl
+++ b/lib/NonlinearSolveBase/src/autodiff.jl
@@ -3,21 +3,21 @@
 
 # Ordering is important here. We want to select the first one that is compatible with the
 # problem.
-const ReverseADs = [
+const ReverseADs = (
     ADTypes.AutoEnzyme(; mode = EnzymeCore.Reverse),
     ADTypes.AutoZygote(),
     ADTypes.AutoTracker(),
     ADTypes.AutoReverseDiff(; compile = true),
     ADTypes.AutoReverseDiff(),
     ADTypes.AutoFiniteDiff()
-]
+)
 
-const ForwardADs = [
+const ForwardADs = (
     ADTypes.AutoEnzyme(; mode = EnzymeCore.Forward),
     ADTypes.AutoPolyesterForwardDiff(),
     ADTypes.AutoForwardDiff(),
     ADTypes.AutoFiniteDiff()
-]
+)
 
 # TODO: Handle Sparsity
 
@@ -28,7 +28,8 @@ function select_forward_mode_autodiff(
     end
     if incompatible_backend_and_problem(prob, ad)
         adₙ = select_forward_mode_autodiff(prob, nothing; warn_check_mode)
-        @warn "The chosen AD backend `$(ad)` does not support the chosen problem. After \
+        @warn "The chosen AD backend `$(ad)` does not support the chosen problem. This \
+               could be because the backend package for the choosen AD isn't loaded. After \
                running autodiff selection detected `$(adₙ)` as a potential forward mode \
                backend."
         return adₙ
@@ -57,7 +58,8 @@ function select_reverse_mode_autodiff(
     end
     if incompatible_backend_and_problem(prob, ad)
         adₙ = select_reverse_mode_autodiff(prob, nothing; warn_check_mode)
-        @warn "The chosen AD backend `$(ad)` does not support the chosen problem. After \
+        @warn "The chosen AD backend `$(ad)` does not support the chosen problem. This \
+               could be because the backend package for the choosen AD isn't loaded. After \
                running autodiff selection detected `$(adₙ)` as a potential reverse mode \
                backend."
         return adₙ
@@ -77,7 +79,8 @@ end
 function select_jacobian_autodiff(prob::AbstractNonlinearProblem, ad::AbstractADType)
     if incompatible_backend_and_problem(prob, ad)
         adₙ = select_jacobian_autodiff(prob, nothing)
-        @warn "The chosen AD backend `$(ad)` does not support the chosen problem. After \
+        @warn "The chosen AD backend `$(ad)` does not support the chosen problem. This \
+               could be because the backend package for the choosen AD isn't loaded. After \
                running autodiff selection detected `$(adₙ)` as a potential jacobian \
                backend."
         return adₙ
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 7ab2416be..e21eb1c5f 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -8,6 +8,7 @@ ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 BracketingNonlinearSolve = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
+ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
@@ -38,11 +39,13 @@ ArrayInterface = "7.16"
 BracketingNonlinearSolve = "1"
 ChainRulesCore = "1.24"
 CommonSolve = "0.2.4"
+ConcreteStructs = "0.2.3"
 DiffEqBase = "6.155"
-DifferentiationInterface = "0.5.17"
+DifferentiationInterface = "0.6.1"
 FastClosures = "0.3.2"
 FiniteDiff = "2.24.0"
 ForwardDiff = "0.10.36"
+InteractiveUtils = "<0.0.1, 1"
 LinearAlgebra = "1.10"
 MaybeInplace = "0.1.4"
 NonlinearSolveBase = "1"
@@ -51,6 +54,8 @@ Reexport = "1.2"
 ReverseDiff = "1.15"
 SciMLBase = "2.50"
 StaticArraysCore = "1.4.3"
+Test = "1.10"
+TestItemRunner = "1"
 Tracker = "0.2.35"
 julia = "1.10"
 
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 0bb65181a..1baa1b50c 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -1,6 +1,7 @@
 module SimpleNonlinearSolve
 
 using CommonSolve: CommonSolve, solve
+using ConcreteStructs: @concrete
 using FastClosures: @closure
 using MaybeInplace: @bb
 using PrecompileTools: @compile_workload, @setup_workload
@@ -27,6 +28,7 @@ is_extension_loaded(::Val) = false
 include("utils.jl")
 
 include("klement.jl")
+include("raphson.jl")
 
 # By Pass the highlevel checks for NonlinearProblem for Simple Algorithms
 function CommonSolve.solve(prob::NonlinearProblem,
@@ -69,7 +71,10 @@ function solve_adjoint_internal end
         prob_iip = NonlinearProblem{true}((du, u, p) -> du .= u .* u .- p, ones(T, 3), T(2))
         prob_oop = NonlinearProblem{false}((u, p) -> u .* u .- p, ones(T, 3), T(2))
 
-        algs = [SimpleKlement()]
+        algs = [
+            SimpleKlement(),
+            SimpleNewtonRaphson()
+        ]
         algs_no_iip = []
 
         @compile_workload begin
@@ -87,4 +92,7 @@ export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
 
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
+export SimpleKlement
+export SimpleGaussNewton, SimpleNewtonRaphson
+
 end
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
new file mode 100644
index 000000000..2af3a825a
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -0,0 +1,62 @@
+"""
+    SimpleNewtonRaphson(autodiff)
+    SimpleNewtonRaphson(; autodiff = nothing)
+
+A low-overhead implementation of Newton-Raphson. This method is non-allocating on scalar
+and static array problems.
+
+!!! note
+
+    As part of the decreased overhead, this method omits some of the higher level error
+    catching of the other methods. Thus, to see better error messages, use one of the other
+    methods like `NewtonRaphson`.
+
+### Keyword Arguments
+
+  - `autodiff`: determines the backend used for the Jacobian. Defaults to  `nothing` (i.e.
+    automatic backend selection). Valid choices include jacobian backends from
+    `DifferentiationInterface.jl`.
+"""
+@kwdef @concrete struct SimpleNewtonRaphson <: AbstractSimpleNonlinearSolveAlgorithm
+    autodiff = nothing
+end
+
+const SimpleGaussNewton = SimpleNewtonRaphson
+
+function SciMLBase.__solve(
+        prob::ImmutableNonlinearProblem, alg::SimpleNewtonRaphson, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0 = false, termination_condition = nothing, kwargs...)
+    x = Utils.maybe_unaliased(prob.u0, alias_u0)
+    fx = Utils.get_fx(prob, x)
+    fx = Utils.eval_f(prob, fx, x)
+
+    iszero(fx) &&
+        return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
+
+    abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+
+    autodiff = SciMLBase.has_jac(prob.f) ? alg.autodiff :
+               NonlinearSolveBase.select_jacobian_autodiff(prob, alg.autodiff)
+
+    @bb xo = similar(x)
+    fx_cache = (SciMLBase.isinplace(prob) && !SciMLBase.has_jac(prob.f)) ? similar(fx) :
+               nothing
+    jac_cache = Utils.prepare_jacobian(prob, autodiff, fx_cache, x)
+    J = Utils.compute_jacobian!!(nothing, prob, autodiff, fx_cache, x, jac_cache)
+
+    for _ in 1:maxiters
+        @bb copyto!(xo, x)
+        δx = Utils.restructure(x, J \ Utils.safe_vec(fx))
+        @bb x .-= δx
+
+        solved, retcode, fx_sol, x_sol = Utils.check_termination(tc_cache, fx, x, xo, prob)
+        solved && return SciMLBase.build_solution(prob, alg, x_sol, fx_sol; retcode)
+
+        fx = Utils.eval_f(prob, fx, x)
+        J = Utils.compute_jacobian!!(J, prob, autodiff, fx_cache, x, jac_cache)
+    end
+
+    return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 16cf5142d..012fc277a 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -2,7 +2,7 @@ module Utils
 
 using ADTypes: AbstractADType, AutoForwardDiff, AutoFiniteDiff, AutoPolyesterForwardDiff
 using ArrayInterface: ArrayInterface
-using DifferentiationInterface: DifferentiationInterface
+using DifferentiationInterface: DifferentiationInterface, Constant
 using FastClosures: @closure
 using LinearAlgebra: LinearAlgebra, I, diagind
 using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem,
@@ -132,4 +132,72 @@ function check_termination(
     return false, ReturnCode.Default, fx, x
 end
 
+restructure(y, x) = ArrayInterface.restructure(y, x)
+restructure(::Number, x::Number) = x
+
+safe_vec(x::AbstractArray) = vec(x)
+safe_vec(x::Number) = x
+
+function prepare_jacobian(prob, autodiff, _, x::Number)
+    if SciMLBase.has_jac(prob.f) || SciMLBase.has_vjp(prob.f) || SciMLBase.has_jvp(prob.f)
+        return nothing
+    end
+    return DI.prepare_derivative(prob.f, autodiff, x, Constant(prob.p))
+end
+function prepare_jacobian(prob, autodiff, fx, x)
+    if SciMLBase.has_jac(prob.f)
+        return nothing
+    end
+    if SciMLBase.isinplace(prob.f)
+        return DI.prepare_jacobian(prob.f, fx, autodiff, x, Constant(prob.p))
+    else
+        return DI.prepare_jacobian(prob.f, autodiff, x, Constant(prob.p))
+    end
+end
+
+function compute_jacobian!!(_, prob, autodiff, fx, x::Number, extras)
+    if extras === nothing
+        if SciMLBase.has_jac(prob.f)
+            return prob.f.jac(x, prob.p)
+        elseif SciMLBase.has_vjp(prob.f)
+            return prob.f.vjp(one(x), x, prob.p)
+        elseif SciMLBase.has_jvp(prob.f)
+            return prob.f.jvp(one(x), x, prob.p)
+        end
+    end
+    return DI.derivative(prob.f, extras, autodiff, x, Constant(prob.p))
+end
+function compute_jacobian!!(J, prob, autodiff, fx, x, extras)
+    if J === nothing
+        if extras === nothing
+            if SciMLBase.isinplace(prob.f)
+                J = similar(fx, length(fx), length(x))
+                prob.f.jac(J, x, prob.p)
+                return J
+            else
+                return prob.f.jac(x, prob.p)
+            end
+        end
+        if SciMLBase.isinplace(prob)
+            return DI.jacobian(prob.f, fx, extras, autodiff, x, Constant(prob.p))
+        else
+            return DI.jacobian(prob.f, extras, autodiff, x, Constant(prob.p))
+        end
+    end
+    if extras === nothing
+        if SciMLBase.isinplace(prob)
+            prob.jac(J, x, prob.p)
+            return J
+        else
+            return prob.jac(x, prob.p)
+        end
+    end
+    if SciMLBase.isinplace(prob)
+        DI.jacobian!(prob.f, J, fx, extras, autodiff, x, Constant(prob.p))
+    else
+        DI.jacobian!(prob.f, J, extras, autodiff, x, Constant(prob.p))
+    end
+    return J
+end
+
 end

From 7f399e392d575db9ef967a5fc3f5e342d780c98e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 12:54:37 -0400
Subject: [PATCH 565/700] fix: typos

---
 lib/NonlinearSolveBase/src/autodiff.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
index 4c057d25e..83b6aa1f7 100644
--- a/lib/NonlinearSolveBase/src/autodiff.jl
+++ b/lib/NonlinearSolveBase/src/autodiff.jl
@@ -1,5 +1,5 @@
 # Here we determine the preferred AD backend. We have a predefined list of ADs and then
-# we select the first one that is avialable and would work with the problem.
+# we select the first one that is available and would work with the problem.
 
 # Ordering is important here. We want to select the first one that is compatible with the
 # problem.
@@ -29,7 +29,7 @@ function select_forward_mode_autodiff(
     if incompatible_backend_and_problem(prob, ad)
         adₙ = select_forward_mode_autodiff(prob, nothing; warn_check_mode)
         @warn "The chosen AD backend `$(ad)` does not support the chosen problem. This \
-               could be because the backend package for the choosen AD isn't loaded. After \
+               could be because the backend package for the chosen AD isn't loaded. After \
                running autodiff selection detected `$(adₙ)` as a potential forward mode \
                backend."
         return adₙ
@@ -59,7 +59,7 @@ function select_reverse_mode_autodiff(
     if incompatible_backend_and_problem(prob, ad)
         adₙ = select_reverse_mode_autodiff(prob, nothing; warn_check_mode)
         @warn "The chosen AD backend `$(ad)` does not support the chosen problem. This \
-               could be because the backend package for the choosen AD isn't loaded. After \
+               could be because the backend package for the chosen AD isn't loaded. After \
                running autodiff selection detected `$(adₙ)` as a potential reverse mode \
                backend."
         return adₙ
@@ -80,7 +80,7 @@ function select_jacobian_autodiff(prob::AbstractNonlinearProblem, ad::AbstractAD
     if incompatible_backend_and_problem(prob, ad)
         adₙ = select_jacobian_autodiff(prob, nothing)
         @warn "The chosen AD backend `$(ad)` does not support the chosen problem. This \
-               could be because the backend package for the choosen AD isn't loaded. After \
+               could be because the backend package for the chosen AD isn't loaded. After \
                running autodiff selection detected `$(adₙ)` as a potential jacobian \
                backend."
         return adₙ

From 389bed80bf17f8f8484c6b9c47c5be7aeb02f332 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 13:05:17 -0400
Subject: [PATCH 566/700] chore: all files

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 5 +++++
 lib/SimpleNonlinearSolve/src/broyden.jl              | 0
 lib/SimpleNonlinearSolve/src/dfsane.jl               | 0
 lib/SimpleNonlinearSolve/src/halley.jl               | 0
 lib/SimpleNonlinearSolve/src/lbroyden.jl             | 0
 lib/SimpleNonlinearSolve/src/trust_region.jl         | 0
 6 files changed, 5 insertions(+)
 create mode 100644 lib/SimpleNonlinearSolve/src/broyden.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/dfsane.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/halley.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/lbroyden.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/trust_region.jl

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 1baa1b50c..72f2cd90f 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -27,8 +27,13 @@ is_extension_loaded(::Val) = false
 
 include("utils.jl")
 
+include("broyden.jl")
+include("dfsane.jl")
+include("halley.jl")
 include("klement.jl")
+include("lbroyden.jl")
 include("raphson.jl")
+include("trust_region.jl")
 
 # By Pass the highlevel checks for NonlinearProblem for Simple Algorithms
 function CommonSolve.solve(prob::NonlinearProblem,
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/SimpleNonlinearSolve/src/trust_region.jl b/lib/SimpleNonlinearSolve/src/trust_region.jl
new file mode 100644
index 000000000..e69de29bb

From 8c99eacb5d60a880a70ce41bf3ab8af496b36e85 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 13:19:37 -0400
Subject: [PATCH 567/700] fix: ordering in jacobian call

---
 lib/SimpleNonlinearSolve/src/utils.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 012fc277a..2a36ec60f 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -193,7 +193,7 @@ function compute_jacobian!!(J, prob, autodiff, fx, x, extras)
         end
     end
     if SciMLBase.isinplace(prob)
-        DI.jacobian!(prob.f, J, fx, extras, autodiff, x, Constant(prob.p))
+        DI.jacobian!(prob.f, fx, J, extras, autodiff, x, Constant(prob.p))
     else
         DI.jacobian!(prob.f, J, extras, autodiff, x, Constant(prob.p))
     end

From 6998f6c678153d0474453769e7e12604eb9cfa41 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 13:47:29 -0400
Subject: [PATCH 568/700] chore: run formatter

---
 lib/SimpleNonlinearSolve/src/broyden.jl      | 1 +
 lib/SimpleNonlinearSolve/src/dfsane.jl       | 1 +
 lib/SimpleNonlinearSolve/src/halley.jl       | 1 +
 lib/SimpleNonlinearSolve/src/lbroyden.jl     | 1 +
 lib/SimpleNonlinearSolve/src/trust_region.jl | 1 +
 src/internal/termination.jl                  | 2 +-
 6 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index e69de29bb..8b1378917 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -0,0 +1 @@
+
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index e69de29bb..8b1378917 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -0,0 +1 @@
+
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index e69de29bb..8b1378917 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -0,0 +1 @@
+
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index e69de29bb..8b1378917 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -0,0 +1 @@
+
diff --git a/lib/SimpleNonlinearSolve/src/trust_region.jl b/lib/SimpleNonlinearSolve/src/trust_region.jl
index e69de29bb..8b1378917 100644
--- a/lib/SimpleNonlinearSolve/src/trust_region.jl
+++ b/lib/SimpleNonlinearSolve/src/trust_region.jl
@@ -0,0 +1 @@
+
diff --git a/src/internal/termination.jl b/src/internal/termination.jl
index e09cfcdda..ef3f7c4c0 100644
--- a/src/internal/termination.jl
+++ b/src/internal/termination.jl
@@ -45,7 +45,7 @@ function update_from_termination_cache!(tc_cache, cache, u = get_u(cache))
 end
 
 function update_from_termination_cache!(
-        _, cache, ::AbstractNonlinearTerminationMode, u = get_u(cache))
+        tc_cache, cache, ::AbstractNonlinearTerminationMode, u = get_u(cache))
     evaluate_f!(cache, u, cache.p)
 end
 

From cb2d24a82acee84a80fa281d80beea607daf6930 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 14:16:48 -0400
Subject: [PATCH 569/700] feat: SimpleTrustRegion implementation

---
 .../src/SimpleNonlinearSolve.jl               |   9 +-
 lib/SimpleNonlinearSolve/src/trust_region.jl  | 211 ++++++++++++++++++
 lib/SimpleNonlinearSolve/src/utils.jl         |  22 --
 3 files changed, 217 insertions(+), 25 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 72f2cd90f..d307e5b99 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -3,6 +3,7 @@ module SimpleNonlinearSolve
 using CommonSolve: CommonSolve, solve
 using ConcreteStructs: @concrete
 using FastClosures: @closure
+using LinearAlgebra: dot
 using MaybeInplace: @bb
 using PrecompileTools: @compile_workload, @setup_workload
 using Reexport: @reexport
@@ -17,7 +18,8 @@ using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff
 
 using BracketingNonlinearSolve: Alefeld, Bisection, Brent, Falsi, ITP, Ridder
-using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, get_tolerance
+using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, get_tolerance,
+                          L2_NORM
 
 const DI = DifferentiationInterface
 
@@ -78,7 +80,8 @@ function solve_adjoint_internal end
 
         algs = [
             SimpleKlement(),
-            SimpleNewtonRaphson()
+            SimpleNewtonRaphson(),
+            SimpleTrustRegion()
         ]
         algs_no_iip = []
 
@@ -98,6 +101,6 @@ export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
 export SimpleKlement
-export SimpleGaussNewton, SimpleNewtonRaphson
+export SimpleGaussNewton, SimpleNewtonRaphson, SimpleTrustRegion
 
 end
diff --git a/lib/SimpleNonlinearSolve/src/trust_region.jl b/lib/SimpleNonlinearSolve/src/trust_region.jl
index 8b1378917..37d0ed706 100644
--- a/lib/SimpleNonlinearSolve/src/trust_region.jl
+++ b/lib/SimpleNonlinearSolve/src/trust_region.jl
@@ -1 +1,212 @@
 
+# """
+#     SimpleTrustRegion(; autodiff = AutoForwardDiff(), max_trust_radius = 0.0,
+#         initial_trust_radius = 0.0, step_threshold = nothing,
+#         shrink_threshold = nothing, expand_threshold = nothing,
+#         shrink_factor = 0.25, expand_factor = 2.0, max_shrink_times::Int = 32,
+#         nlsolve_update_rule = Val(false))
+
+# A low-overhead implementation of a trust-region solver. This method is non-allocating on
+# scalar and static array problems.
+
+# ### Keyword Arguments
+
+#   - `autodiff`: determines the backend used for the Jacobian. Defaults to `nothing` (i.e.
+#     automatic backend selection). Valid choices include jacobian backends from
+#     `DifferentiationInterface.jl`.
+#   - `max_trust_radius`: the maximum radius of the trust region. Defaults to
+#     `max(norm(f(u0)), maximum(u0) - minimum(u0))`.
+#   - `initial_trust_radius`: the initial trust region radius. Defaults to
+#     `max_trust_radius / 11`.
+#   - `step_threshold`: the threshold for taking a step. In every iteration, the threshold is
+#     compared with a value `r`, which is the actual reduction in the objective function divided
+#     by the predicted reduction. If `step_threshold > r` the model is not a good approximation,
+#     and the step is rejected. Defaults to `0.1`. For more details, see
+#     [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
+#   - `shrink_threshold`: the threshold for shrinking the trust region radius. In every
+#     iteration, the threshold is compared with a value `r` which is the actual reduction in the
+#     objective function divided by the predicted reduction. If `shrink_threshold > r` the trust
+#     region radius is shrunk by `shrink_factor`. Defaults to `0.25`. For more details, see
+#     [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
+#   - `expand_threshold`: the threshold for expanding the trust region radius. If a step is
+#     taken, i.e `step_threshold < r` (with `r` defined in `shrink_threshold`), a check is also
+#     made to see if `expand_threshold < r`. If that is true, the trust region radius is
+#     expanded by `expand_factor`. Defaults to `0.75`.
+#   - `shrink_factor`: the factor to shrink the trust region radius with if
+#     `shrink_threshold > r` (with `r` defined in `shrink_threshold`). Defaults to `0.25`.
+#   - `expand_factor`: the factor to expand the trust region radius with if
+#     `expand_threshold < r` (with `r` defined in `shrink_threshold`). Defaults to `2.0`.
+#   - `max_shrink_times`: the maximum number of times to shrink the trust region radius in a
+#     row, `max_shrink_times` is exceeded, the algorithm returns. Defaults to `32`.
+#   - `nlsolve_update_rule`: If set to `Val(true)`, updates the trust region radius using the
+#     update rule from NLSolve.jl. Defaults to `Val(false)`. If set to `Val(true)`, few of the
+#     radius update parameters -- `step_threshold = 0.05`, `expand_threshold = 0.9`, and
+#     `shrink_factor = 0.5` -- have different defaults.
+# """
+@kwdef @concrete struct SimpleTrustRegion <: AbstractSimpleNonlinearSolveAlgorithm
+    autodiff = nothing
+    max_trust_radius = 0.0
+    initial_trust_radius = 0.0
+    step_threshold = 0.0001
+    shrink_threshold = nothing
+    expand_threshold = nothing
+    shrink_factor = nothing
+    expand_factor = 2.0
+    max_shrink_times::Int = 32
+    nlsolve_update_rule = Val(false)
+end
+
+function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleTrustRegion,
+        args...; abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0 = false, termination_condition = nothing, kwargs...)
+    x = Utils.maybe_unaliased(prob.u0, alias_u0)
+    T = eltype(x)
+    Δₘₐₓ = T(alg.max_trust_radius)
+    Δ = T(alg.initial_trust_radius)
+    η₁ = T(alg.step_threshold)
+
+    if alg.shrink_threshold === nothing
+        η₂ = T(ifelse(SciMLBase._unwrap_val(alg.nlsolve_update_rule), 0.05, 0.25))
+    else
+        η₂ = T(alg.shrink_threshold)
+    end
+
+    if alg.expand_threshold === nothing
+        η₃ = T(ifelse(SciMLBase._unwrap_val(alg.nlsolve_update_rule), 0.9, 0.75))
+    else
+        η₃ = T(alg.expand_threshold)
+    end
+
+    if alg.shrink_factor === nothing
+        t₁ = T(ifelse(SciMLBase._unwrap_val(alg.nlsolve_update_rule), 0.5, 0.25))
+    else
+        t₁ = T(alg.shrink_factor)
+    end
+
+    t₂ = T(alg.expand_factor)
+    max_shrink_times = alg.max_shrink_times
+
+    autodiff = SciMLBase.has_jac(prob.f) ? alg.autodiff :
+               NonlinearSolveBase.select_jacobian_autodiff(prob, alg.autodiff)
+
+    fx = Utils.get_fx(prob, x)
+    fx = Utils.eval_f(prob, fx, x)
+    norm_fx = L2_NORM(fx)
+
+    @bb xo = copy(x)
+    fx_cache = (SciMLBase.isinplace(prob) && !SciMLBase.has_jac(prob.f)) ? similar(fx) :
+               nothing
+    jac_cache = Utils.prepare_jacobian(prob, autodiff, fx_cache, x)
+    J = Utils.compute_jacobian!!(nothing, prob, autodiff, fx_cache, x, jac_cache)
+
+    abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+
+    # Set default trust region radius if not specified by user.
+    iszero(Δₘₐₓ) && (Δₘₐₓ = max(L2_NORM(fx), maximum(x) - minimum(x)))
+    if iszero(Δ)
+        if SciMLBase._unwrap_val(alg.nlsolve_update_rule)
+            norm_x = L2_NORM(x)
+            Δ = T(ifelse(norm_x > 0, norm_x, 1))
+        else
+            Δ = T(Δₘₐₓ / 11)
+        end
+    end
+
+    fₖ = 0.5 * norm_fx^2
+    H = transpose(J) * J
+    g = Utils.restructure(x, J' * Utils.safe_vec(fx))
+    shrink_counter = 0
+
+    @bb δsd = copy(x)
+    @bb δN_δsd = copy(x)
+    @bb δN = copy(x)
+    @bb Hδ = copy(x)
+    dogleg_cache = (; δsd, δN_δsd, δN)
+
+    for _ in 1:maxiters
+        # Solve the trust region subproblem.
+        δ = dogleg_method!!(dogleg_cache, J, fx, g, Δ)
+        @bb @. x = xo + δ
+
+        fx = Utils.eval_f(prob, fx, x)
+
+        fₖ₊₁ = L2_NORM(fx)^2 / T(2)
+
+        # Compute the ratio of the actual to predicted reduction.
+        @bb Hδ = H × vec(δ)
+        r = (fₖ₊₁ - fₖ) / (dot(δ, g) + (dot(δ, Hδ) / T(2)))
+
+        # Update the trust region radius.
+        if r ≥ η₂
+            shrink_counter = 0
+        else
+            Δ = t₁ * Δ
+            shrink_counter += 1
+            shrink_counter > max_shrink_times && return SciMLBase.build_solution(
+                prob, alg, x, fx; retcode = ReturnCode.ShrinkThresholdExceeded)
+        end
+
+        if r ≥ η₁
+            # Termination Checks
+            solved, retcode, fx_sol, x_sol = Utils.check_termination(
+                tc_cache, fx, x, xo, prob)
+            solved && return SciMLBase.build_solution(prob, alg, x_sol, fx_sol; retcode)
+
+            # Take the step.
+            @bb copyto!(xo, x)
+
+            J = Utils.compute_jacobian!!(J, prob, autodiff, fx_cache, x, jac_cache)
+            fx = Utils.eval_f(prob, fx, x)
+
+            # Update the trust region radius.
+            if !SciMLBase._unwrap_val(alg.nlsolve_update_rule) && r > η₃
+                Δ = min(t₂ * Δ, Δₘₐₓ)
+            end
+            fₖ = fₖ₊₁
+
+            @bb H = transpose(J) × J
+            @bb g = transpose(J) × vec(fx)
+        end
+
+        if SciMLBase._unwrap_val(alg.nlsolve_update_rule)
+            if r > η₃
+                Δ = t₂ * L2_NORM(δ)
+            elseif r > 0.5
+                Δ = max(Δ, t₂ * L2_NORM(δ))
+            end
+        end
+    end
+
+    return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+end
+
+function dogleg_method!!(cache, J, f, g, Δ)
+    (; δsd, δN_δsd, δN) = cache
+
+    # Compute the Newton step
+    @bb δN .= Utils.restructure(δN, J \ Utils.safe_vec(f))
+    @bb δN .*= -1
+    # Test if the full step is within the trust region
+    (L2_NORM(δN) ≤ Δ) && return δN
+
+    # Calcualte Cauchy point, optimum along the steepest descent direction
+    @bb δsd .= g
+    @bb @. δsd *= -1
+    norm_δsd = L2_NORM(δsd)
+
+    if (norm_δsd ≥ Δ)
+        @bb @. δsd *= Δ / norm_δsd
+        return δsd
+    end
+
+    # Find the intersection point on the boundary
+    @bb @. δN_δsd = δN - δsd
+    dot_δN_δsd = dot(δN_δsd, δN_δsd)
+    dot_δsd_δN_δsd = dot(δsd, δN_δsd)
+    dot_δsd = dot(δsd, δsd)
+    fact = dot_δsd_δN_δsd^2 - dot_δN_δsd * (dot_δsd - Δ^2)
+    tau = (-dot_δsd_δN_δsd + sqrt(fact)) / dot_δN_δsd
+    @bb @. δsd += tau * δN_δsd
+    return δsd
+end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 2a36ec60f..29437339e 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -28,28 +28,6 @@ function maybe_unaliased(x::T, alias::Bool) where {T <: AbstractArray}
     return copy(x)
 end
 
-function get_concrete_autodiff(_, ad::AbstractADType)
-    DI.check_available(ad) && return ad
-    error("AD Backend $(ad) is not available. This could be because you haven't loaded the \
-           actual backend (See [Differentiation Interface Docs](https://gdalle.github.io/DifferentiationInterface.jl/DifferentiationInterface/stable/) \
-           for more details) or the backend might not be supported by DifferentiationInterface.jl.")
-end
-function get_concrete_autodiff(
-        prob, ad::Union{AutoForwardDiff{nothing}, AutoPolyesterForwardDiff{nothing}})
-    return get_concrete_autodiff(prob,
-        ArrayInterface.parameterless_type(ad)(;
-            chunksize = pickchunksize(length(prob.u0)), ad.tag))
-end
-function get_concrete_autodiff(prob, ::Nothing)
-    if can_dual(eltype(prob.u0)) && DI.check_available(AutoForwardDiff())
-        return AutoForwardDiff(; chunksize = pickchunksize(length(prob.u0)))
-    end
-    DI.check_available(AutoFiniteDiff()) && return AutoFiniteDiff()
-    error("Default AD backends are not available. Please load either FiniteDiff or \
-           ForwardDiff for default AD selection to work. Else provide a specific AD \
-           backend (instead of `nothing`) to the solver.")
-end
-
 # NOTE: This doesn't initialize the `f(x)` but just returns a buffer of the same size
 function get_fx(prob::NonlinearLeastSquaresProblem, x)
     if SciMLBase.isinplace(prob) && prob.f.resid_prototype === nothing

From 7b91e6af06c2a9895c4948fed75272dd4836356b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 14:53:50 -0400
Subject: [PATCH 570/700] docs: trust region docstring

---
 lib/SimpleNonlinearSolve/src/trust_region.jl | 89 ++++++++++----------
 1 file changed, 44 insertions(+), 45 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/trust_region.jl b/lib/SimpleNonlinearSolve/src/trust_region.jl
index 37d0ed706..6bf543220 100644
--- a/lib/SimpleNonlinearSolve/src/trust_region.jl
+++ b/lib/SimpleNonlinearSolve/src/trust_region.jl
@@ -1,48 +1,47 @@
-
-# """
-#     SimpleTrustRegion(; autodiff = AutoForwardDiff(), max_trust_radius = 0.0,
-#         initial_trust_radius = 0.0, step_threshold = nothing,
-#         shrink_threshold = nothing, expand_threshold = nothing,
-#         shrink_factor = 0.25, expand_factor = 2.0, max_shrink_times::Int = 32,
-#         nlsolve_update_rule = Val(false))
-
-# A low-overhead implementation of a trust-region solver. This method is non-allocating on
-# scalar and static array problems.
-
-# ### Keyword Arguments
-
-#   - `autodiff`: determines the backend used for the Jacobian. Defaults to `nothing` (i.e.
-#     automatic backend selection). Valid choices include jacobian backends from
-#     `DifferentiationInterface.jl`.
-#   - `max_trust_radius`: the maximum radius of the trust region. Defaults to
-#     `max(norm(f(u0)), maximum(u0) - minimum(u0))`.
-#   - `initial_trust_radius`: the initial trust region radius. Defaults to
-#     `max_trust_radius / 11`.
-#   - `step_threshold`: the threshold for taking a step. In every iteration, the threshold is
-#     compared with a value `r`, which is the actual reduction in the objective function divided
-#     by the predicted reduction. If `step_threshold > r` the model is not a good approximation,
-#     and the step is rejected. Defaults to `0.1`. For more details, see
-#     [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
-#   - `shrink_threshold`: the threshold for shrinking the trust region radius. In every
-#     iteration, the threshold is compared with a value `r` which is the actual reduction in the
-#     objective function divided by the predicted reduction. If `shrink_threshold > r` the trust
-#     region radius is shrunk by `shrink_factor`. Defaults to `0.25`. For more details, see
-#     [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
-#   - `expand_threshold`: the threshold for expanding the trust region radius. If a step is
-#     taken, i.e `step_threshold < r` (with `r` defined in `shrink_threshold`), a check is also
-#     made to see if `expand_threshold < r`. If that is true, the trust region radius is
-#     expanded by `expand_factor`. Defaults to `0.75`.
-#   - `shrink_factor`: the factor to shrink the trust region radius with if
-#     `shrink_threshold > r` (with `r` defined in `shrink_threshold`). Defaults to `0.25`.
-#   - `expand_factor`: the factor to expand the trust region radius with if
-#     `expand_threshold < r` (with `r` defined in `shrink_threshold`). Defaults to `2.0`.
-#   - `max_shrink_times`: the maximum number of times to shrink the trust region radius in a
-#     row, `max_shrink_times` is exceeded, the algorithm returns. Defaults to `32`.
-#   - `nlsolve_update_rule`: If set to `Val(true)`, updates the trust region radius using the
-#     update rule from NLSolve.jl. Defaults to `Val(false)`. If set to `Val(true)`, few of the
-#     radius update parameters -- `step_threshold = 0.05`, `expand_threshold = 0.9`, and
-#     `shrink_factor = 0.5` -- have different defaults.
-# """
+"""
+    SimpleTrustRegion(; autodiff = AutoForwardDiff(), max_trust_radius = 0.0,
+        initial_trust_radius = 0.0, step_threshold = nothing,
+        shrink_threshold = nothing, expand_threshold = nothing,
+        shrink_factor = 0.25, expand_factor = 2.0, max_shrink_times::Int = 32,
+        nlsolve_update_rule = Val(false))
+
+A low-overhead implementation of a trust-region solver. This method is non-allocating on
+scalar and static array problems.
+
+### Keyword Arguments
+
+  - `autodiff`: determines the backend used for the Jacobian. Defaults to `nothing` (i.e.
+    automatic backend selection). Valid choices include jacobian backends from
+    `DifferentiationInterface.jl`.
+  - `max_trust_radius`: the maximum radius of the trust region. Defaults to
+    `max(norm(f(u0)), maximum(u0) - minimum(u0))`.
+  - `initial_trust_radius`: the initial trust region radius. Defaults to
+    `max_trust_radius / 11`.
+  - `step_threshold`: the threshold for taking a step. In every iteration, the threshold is
+    compared with a value `r`, which is the actual reduction in the objective function divided
+    by the predicted reduction. If `step_threshold > r` the model is not a good approximation,
+    and the step is rejected. Defaults to `0.1`. For more details, see
+    [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
+  - `shrink_threshold`: the threshold for shrinking the trust region radius. In every
+    iteration, the threshold is compared with a value `r` which is the actual reduction in the
+    objective function divided by the predicted reduction. If `shrink_threshold > r` the trust
+    region radius is shrunk by `shrink_factor`. Defaults to `0.25`. For more details, see
+    [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
+  - `expand_threshold`: the threshold for expanding the trust region radius. If a step is
+    taken, i.e `step_threshold < r` (with `r` defined in `shrink_threshold`), a check is also
+    made to see if `expand_threshold < r`. If that is true, the trust region radius is
+    expanded by `expand_factor`. Defaults to `0.75`.
+  - `shrink_factor`: the factor to shrink the trust region radius with if
+    `shrink_threshold > r` (with `r` defined in `shrink_threshold`). Defaults to `0.25`.
+  - `expand_factor`: the factor to expand the trust region radius with if
+    `expand_threshold < r` (with `r` defined in `shrink_threshold`). Defaults to `2.0`.
+  - `max_shrink_times`: the maximum number of times to shrink the trust region radius in a
+    row, `max_shrink_times` is exceeded, the algorithm returns. Defaults to `32`.
+  - `nlsolve_update_rule`: If set to `Val(true)`, updates the trust region radius using the
+    update rule from NLSolve.jl. Defaults to `Val(false)`. If set to `Val(true)`, few of the
+    radius update parameters -- `step_threshold = 0.05`, `expand_threshold = 0.9`, and
+    `shrink_factor = 0.5` -- have different defaults.
+"""
 @kwdef @concrete struct SimpleTrustRegion <: AbstractSimpleNonlinearSolveAlgorithm
     autodiff = nothing
     max_trust_radius = 0.0

From 3e57076829aab619f9a6e166747dd5c61b836871 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 15:07:00 -0400
Subject: [PATCH 571/700] feat: SimpleBroyden implementation

---
 lib/SimpleNonlinearSolve/Project.toml         |   1 +
 .../src/SimpleNonlinearSolve.jl               |   4 +-
 lib/SimpleNonlinearSolve/src/broyden.jl       | 100 ++++++++++++++++++
 lib/SimpleNonlinearSolve/src/utils.jl         |   4 +-
 4 files changed, 106 insertions(+), 3 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index e21eb1c5f..62a999325 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -13,6 +13,7 @@ DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index d307e5b99..7b576e5dc 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -3,6 +3,7 @@ module SimpleNonlinearSolve
 using CommonSolve: CommonSolve, solve
 using ConcreteStructs: @concrete
 using FastClosures: @closure
+using LineSearch: LiFukushimaLineSearch
 using LinearAlgebra: dot
 using MaybeInplace: @bb
 using PrecompileTools: @compile_workload, @setup_workload
@@ -79,6 +80,7 @@ function solve_adjoint_internal end
         prob_oop = NonlinearProblem{false}((u, p) -> u .* u .- p, ones(T, 3), T(2))
 
         algs = [
+            SimpleBroyden(),
             SimpleKlement(),
             SimpleNewtonRaphson(),
             SimpleTrustRegion()
@@ -100,7 +102,7 @@ export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
 
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
-export SimpleKlement
+export SimpleBroyden, SimpleKlement
 export SimpleGaussNewton, SimpleNewtonRaphson, SimpleTrustRegion
 
 end
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 8b1378917..6537a4d2d 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -1 +1,101 @@
+"""
+    SimpleBroyden(; linesearch = Val(false), alpha = nothing)
 
+A low-overhead implementation of Broyden. This method is non-allocating on scalar and static
+array problems.
+
+### Keyword Arguments
+
+  - `linesearch`: If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch`
+    line search else no line search is used. For advanced customization of the line search,
+    use `Broyden` from `NonlinearSolve.jl`.
+  - `alpha`: Scale the initial jacobian initialization with `alpha`. If it is `nothing`, we
+    will compute the scaling using `2 * norm(fu) / max(norm(u), true)`.
+"""
+@concrete struct SimpleBroyden <: AbstractSimpleNonlinearSolveAlgorithm
+    linesearch <: Union{Val{false}, Val{true}}
+    alpha
+end
+
+function SimpleBroyden(;
+        linesearch::Union{Bool, Val{true}, Val{false}} = Val(false), alpha = nothing)
+    linesearch = linesearch isa Bool ? Val(linesearch) : linesearch
+    return SimpleBroyden(linesearch, alpha)
+end
+
+function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleBroyden, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0 = false, termination_condition = nothing, kwargs...)
+    x = Utils.maybe_unaliased(prob.u0, alias_u0)
+    fx = Utils.get_fx(prob, x)
+    fx = Utils.eval_f(prob, fx, x)
+    T = promote_type(eltype(fx), eltype(x))
+
+    iszero(fx) &&
+        return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
+
+    @bb xo = copy(x)
+    @bb δx = similar(x)
+    @bb δf = copy(fx)
+    @bb fprev = copy(fx)
+
+    if alg.alpha === nothing
+        fx_norm = L2_NORM(fx)
+        x_norm = L2_NORM(x)
+        init_α = ifelse(fx_norm ≥ 1e-5, max(x_norm, T(true)) / (2 * fx_norm), T(true))
+    else
+        init_α = inv(alg.alpha)
+    end
+
+    J⁻¹ = Utils.identity_jacobian(fx, x, init_α)
+    @bb J⁻¹δf = copy(x)
+    @bb xᵀJ⁻¹ = copy(x)
+    @bb δJ⁻¹n = copy(x)
+    @bb δJ⁻¹ = copy(J⁻¹)
+
+    abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+
+    if alg.linesearch === Val(true)
+        ls_alg = LiFukushimaLineSearch(; nan_maxiters = nothing)
+        ls_cache = init(prob, ls_alg, fx, x)
+    else
+        ls_cache = nothing
+    end
+
+    for _ in 1:maxiters
+        @bb δx = J⁻¹ × vec(fprev)
+        @bb δx .*= -1
+
+        if ls_cache === nothing
+            α = true
+        else
+            ls_sol = solve!(ls_cache, xo, δx)
+            α = ls_sol.step_size # Ignores the return code for now
+        end
+
+        @bb @. x = xo + α * δx
+        fx = Utils.eval_f(prob, fx, x)
+        @bb @. δf = fx - fprev
+
+        # Termination Checks
+        solved, retcode, fx_sol, x_sol = Utils.check_termination(tc_cache, fx, x, xo, prob)
+        solved && return SciMLBase.build_solution(prob, alg, x_sol, fx_sol; retcode)
+
+        @bb J⁻¹δf = J⁻¹ × vec(δf)
+        d = dot(δx, J⁻¹δf)
+        @bb xᵀJ⁻¹ = transpose(J⁻¹) × vec(δx)
+
+        @bb @. δJ⁻¹n = (δx - J⁻¹δf) / d
+
+        δJ⁻¹n_ = Utils.safe_vec(δJ⁻¹n)
+        xᵀJ⁻¹_ = Utils.safe_vec(xᵀJ⁻¹)
+        @bb δJ⁻¹ = δJ⁻¹n_ × transpose(xᵀJ⁻¹_)
+        @bb J⁻¹ .+= δJ⁻¹
+
+        @bb copyto!(xo, x)
+        @bb copyto!(fprev, fx)
+    end
+
+    return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 29437339e..5b4c5a248 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -62,13 +62,13 @@ function identity_jacobian(u::Number, fu::Number, α = true)
     return convert(promote_type(eltype(u), eltype(fu)), α)
 end
 function identity_jacobian(u, fu, α = true)
-    J = safe_similar(u, promote_type(eltype(u), eltype(fu)))
+    J = safe_similar(u, promote_type(eltype(u), eltype(fu)), length(fu), length(u))
     fill!(J, zero(eltype(J)))
     J[diagind(J)] .= eltype(J)(α)
     return J
 end
 function identity_jacobian(u::StaticArray, fu, α = true)
-    return SMatrix{length(fu), length(u), eltype(u)}(I * α)
+    return SMatrix{length(fu), length(u), promote_type(eltype(fu), eltype(u))}(I * α)
 end
 
 identity_jacobian!!(J::Number) = one(J)

From 757893a651c1564bd942609fde60e8316fc462b1 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 15:53:16 -0400
Subject: [PATCH 572/700] feat: add SimpleHalley method

---
 .../src/SimpleNonlinearSolve.jl               | 10 +--
 lib/SimpleNonlinearSolve/src/halley.jl        | 83 +++++++++++++++++++
 lib/SimpleNonlinearSolve/src/utils.jl         | 22 +++++
 3 files changed, 109 insertions(+), 6 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 7b576e5dc..14256ce38 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -4,8 +4,8 @@ using CommonSolve: CommonSolve, solve
 using ConcreteStructs: @concrete
 using FastClosures: @closure
 using LineSearch: LiFukushimaLineSearch
-using LinearAlgebra: dot
-using MaybeInplace: @bb
+using LinearAlgebra: LinearAlgebra, dot
+using MaybeInplace: @bb, setindex_trait, CannotSetindex, CanSetindex
 using PrecompileTools: @compile_workload, @setup_workload
 using Reexport: @reexport
 @reexport using SciMLBase  # I don't like this but needed to avoid a breaking change
@@ -82,18 +82,15 @@ function solve_adjoint_internal end
         algs = [
             SimpleBroyden(),
             SimpleKlement(),
+            SimpleHalley(),
             SimpleNewtonRaphson(),
             SimpleTrustRegion()
         ]
-        algs_no_iip = []
 
         @compile_workload begin
             for alg in algs, prob in (prob_scalar, prob_iip, prob_oop)
                 CommonSolve.solve(prob, alg)
             end
-            for alg in algs_no_iip
-                CommonSolve.solve(prob_scalar, alg)
-            end
         end
     end
 end
@@ -104,5 +101,6 @@ export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
 export SimpleBroyden, SimpleKlement
 export SimpleGaussNewton, SimpleNewtonRaphson, SimpleTrustRegion
+export SimpleHalley
 
 end
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 8b1378917..23ba1c847 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -1 +1,84 @@
+"""
+    SimpleHalley(autodiff)
+    SimpleHalley(; autodiff = nothing)
 
+A low-overhead implementation of Halley's Method.
+
+!!! note
+
+    As part of the decreased overhead, this method omits some of the higher level error
+    catching of the other methods. Thus, to see better error messages, use one of the other
+    methods like `NewtonRaphson`.
+
+### Keyword Arguments
+
+  - `autodiff`: determines the backend used for the Jacobian. Defaults to  `nothing` (i.e.
+    automatic backend selection). Valid choices include jacobian backends from
+    `DifferentiationInterface.jl`.
+"""
+@kwdef @concrete struct SimpleHalley <: AbstractSimpleNonlinearSolveAlgorithm
+    autodiff = nothing
+end
+
+function SciMLBase.__solve(
+        prob::ImmutableNonlinearProblem, alg::SimpleHalley, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0 = false, termination_condition = nothing, kwargs...)
+    x = Utils.maybe_unaliased(prob.u0, alias_u0)
+    fx = Utils.get_fx(prob, x)
+    fx = Utils.eval_f(prob, fx, x)
+    T = promote_type(eltype(fx), eltype(x))
+
+    iszero(fx) &&
+        return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
+
+    abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+
+    autodiff = NonlinearSolveBase.select_jacobian_autodiff(prob, alg.autodiff)
+
+    @bb xo = copy(x)
+
+    strait = setindex_trait(x)
+
+    A = strait isa CanSetindex ? similar(x, length(x), length(x)) : x
+    Aaᵢ = strait isa CanSetindex ? similar(x, length(x)) : x
+    cᵢ = strait isa CanSetindex ? similar(x) : x
+
+    for _ in 1:maxiters
+        fx, J, H = Utils.compute_jacobian_and_hessian(autodiff, prob, fx, x)
+
+        strait isa CannotSetindex && (A = J)
+
+        # Factorize Once and Reuse
+        J_fact = if J isa Number
+            J
+        else
+            fact = LinearAlgebra.lu(J; check = false)
+            !LinearAlgebra.issuccess(fact) && return SciMLBase.build_solution(
+                prob, alg, x, fx; retcode = ReturnCode.Unstable)
+            fact
+        end
+
+        aᵢ = J_fact \ Utils.safe_vec(fx)
+        A_ = Utils.safe_vec(A)
+        @bb A_ = H × aᵢ
+        A = Utils.restructure(A, A_)
+
+        @bb Aaᵢ = A × aᵢ
+        @bb A .*= -1
+        bᵢ = J_fact \ Utils.safe_vec(Aaᵢ)
+
+        cᵢ_ = Utils.safe_vec(cᵢ)
+        @bb @. cᵢ_ = (aᵢ * aᵢ) / (-aᵢ + (T(0.5) * bᵢ))
+        cᵢ = Utils.restructure(cᵢ, cᵢ_)
+
+        solved, retcode, fx_sol, x_sol = Utils.check_termination(tc_cache, fx, x, xo, prob)
+        solved && return SciMLBase.build_solution(prob, alg, x_sol, fx_sol; retcode)
+
+        @bb @. x += cᵢ
+        @bb copyto!(xo, x)
+    end
+
+    return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+end
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 5b4c5a248..19d44cf21 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -178,4 +178,26 @@ function compute_jacobian!!(J, prob, autodiff, fx, x, extras)
     return J
 end
 
+function compute_jacobian_and_hessian(autodiff, prob, _, x::Number)
+    H = DI.second_derivative(prob.f, autodiff, x, Constant(prob.p))
+    fx, J = DI.value_and_derivative(prob.f, autodiff, x, Constant(prob.p))
+    return fx, J, H
+end
+function compute_jacobian_and_hessian(autodiff, prob, fx, x)
+    if SciMLBase.isinplace(prob)
+        jac_fn = @closure (u, p) -> begin
+            du = similar(fx, promote_type(eltype(fx), eltype(u)))
+            return DI.jacobian(prob.f, du, autodiff, u, Constant(p))
+        end
+        J, H = DI.value_and_jacobian(jac_fn, autodiff, x, Constant(prob.p))
+        fx = Utils.eval_f(prob, fx, x)
+        return fx, J, H
+    else
+        jac_fn = @closure (u, p) -> DI.jacobian(prob.f, autodiff, u, Constant(p))
+        J, H = DI.value_and_jacobian(jac_fn, autodiff, x, Constant(prob.p))
+        fx = Utils.eval_f(prob, fx, x)
+        return fx, J, H
+    end
+end
+
 end

From ca1b1e5d7535fe15e7748e2de1b0705219cd91ce Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 16:20:40 -0400
Subject: [PATCH 573/700] feat: add SimpleDFSane

---
 lib/SimpleNonlinearSolve/Project.toml         |   1 +
 .../src/SimpleNonlinearSolve.jl               |   6 +-
 lib/SimpleNonlinearSolve/src/dfsane.jl        | 169 ++++++++++++++++++
 3 files changed, 175 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 62a999325..1962d42cf 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -5,6 +5,7 @@ version = "1.13.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
+Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 BracketingNonlinearSolve = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 14256ce38..29adc7131 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -1,5 +1,6 @@
 module SimpleNonlinearSolve
 
+using Accessors: @reset
 using CommonSolve: CommonSolve, solve
 using ConcreteStructs: @concrete
 using FastClosures: @closure
@@ -10,7 +11,7 @@ using PrecompileTools: @compile_workload, @setup_workload
 using Reexport: @reexport
 @reexport using SciMLBase  # I don't like this but needed to avoid a breaking change
 using SciMLBase: AbstractNonlinearAlgorithm, NonlinearProblem, ReturnCode
-using StaticArraysCore: StaticArray
+using StaticArraysCore: StaticArray, SVector
 
 # AD Dependencies
 using ADTypes: AbstractADType, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
@@ -81,7 +82,9 @@ function solve_adjoint_internal end
 
         algs = [
             SimpleBroyden(),
+            # SimpleDFSane(),
             SimpleKlement(),
+            # SimpleLimitedMemoryBroyden(),
             SimpleHalley(),
             SimpleNewtonRaphson(),
             SimpleTrustRegion()
@@ -100,6 +103,7 @@ export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
 export SimpleBroyden, SimpleKlement
+export SimpleDFSane
 export SimpleGaussNewton, SimpleNewtonRaphson, SimpleTrustRegion
 export SimpleHalley
 
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index 8b1378917..0d400b0ce 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -1 +1,170 @@
+"""
+    SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
+        M::Union{Int, Val} = Val(10), γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
+        nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2)
 
+A low-overhead implementation of the df-sane method for solving large-scale nonlinear
+systems of equations. For in depth information about all the parameters and the algorithm,
+see [la2006spectral](@citet).
+
+### Keyword Arguments
+
+  - `σ_min`: the minimum value of the spectral coefficient `σ_k` which is related to the
+    step size in the algorithm. Defaults to `1e-10`.
+  - `σ_max`: the maximum value of the spectral coefficient `σ_k` which is related to the
+    step size in the algorithm. Defaults to `1e10`.
+  - `σ_1`: the initial value of the spectral coefficient `σ_k` which is related to the step
+    size in the algorithm.. Defaults to `1.0`.
+  - `M`: The monotonicity of the algorithm is determined by a this positive integer.
+    A value of 1 for `M` would result in strict monotonicity in the decrease of the L2-norm
+    of the function `f`. However, higher values allow for more flexibility in this
+    reduction. Despite this, the algorithm still ensures global convergence through the use
+    of a non-monotone line-search algorithm that adheres to the Grippo-Lampariello-Lucidi
+    condition. Values in the range of 5 to 20 are usually sufficient, but some cases may call
+    for a higher value of `M`. The default setting is 10.
+  - `γ`: a parameter that influences if a proposed step will be accepted. Higher value of
+    `γ` will make the algorithm more restrictive in accepting steps. Defaults to `1e-4`.
+  - `τ_min`: if a step is rejected the new step size will get multiplied by factor, and this
+    parameter is the minimum value of that factor. Defaults to `0.1`.
+  - `τ_max`: if a step is rejected the new step size will get multiplied by factor, and this
+    parameter is the maximum value of that factor. Defaults to `0.5`.
+  - `nexp`: the exponent of the loss, i.e. ``f_k=||F(x_k)||^{nexp}``. The paper uses
+    `nexp ∈ {1,2}`. Defaults to `2`.
+  - `η_strategy`:  function to determine the parameter `η_k`, which enables growth
+    of ``||F||^2``. Called as `η_k = η_strategy(f_1, k, x, F)` with `f_1` initialized as
+    ``f_1=||F(x_1)||^{nexp}``, `k` is the iteration number, `x` is the current `x`-value and
+    `F` the current residual. Should satisfy ``η_k > 0`` and ``∑ₖ ηₖ < ∞``. Defaults to
+    ``||F||^2 / k^2``.
+"""
+@concrete struct SimpleDFSane <: AbstractSimpleNonlinearSolveAlgorithm
+    σ_min
+    σ_max
+    σ_1
+    γ
+    τ_min
+    τ_max
+    nexp::Int
+    η_strategy
+    M <: Val
+end
+
+# XXX[breaking]: we should change the names to not have unicode
+function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
+        M::Union{Int, Val} = Val(10), γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
+        nexp::Int = 2, η_strategy::F = (f_1, k, x, F) -> f_1 ./ k^2) where {F}
+    M = M isa Int ? Val(M) : M
+    return SimpleDFSane(σ_min, σ_max, σ_1, γ, τ_min, τ_max, nexp, η_strategy, M)
+end
+
+function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleDFSane, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
+        termination_condition = nothing, kwargs...)
+    x = Utils.maybe_unaliased(prob.u0, alias_u0)
+    fx = Utils.get_fx(prob, x)
+    fx = Utils.eval_f(prob, fx, x)
+    T = promote_type(eltype(fx), eltype(x))
+
+    σ_min = T(alg.σ_min)
+    σ_max = T(alg.σ_max)
+    σ_k = T(alg.σ_1)
+
+    (; nexp, η_strategy, M) = alg
+    γ = T(alg.γ)
+    τ_min = T(alg.τ_min)
+    τ_max = T(alg.τ_max)
+
+    abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+
+    fx_norm = L2_NORM(fx)^nexp
+    α_1 = one(T)
+    f_1 = fx_norm
+
+    history_f_k = dfsane_history_vec(x, fx_norm, alg.M)
+
+    # Generate the cache
+    @bb x_cache = similar(x)
+    @bb d = copy(x)
+    @bb xo = copy(x)
+    @bb δx = copy(x)
+    @bb δf = copy(fx)
+
+    k = 0
+    while k < maxiters
+        # Spectral parameter range check
+        σ_k = sign(σ_k) * clamp(abs(σ_k), σ_min, σ_max)
+
+        # Line search direction
+        @bb @. d = -σ_k * fx
+
+        η = η_strategy(f_1, k + 1, x, fx)
+        f_bar = maximum(history_f_k)
+        α_p = α_1
+        α_m = α_1
+
+        @bb @. x_cache = x + α_p * d
+
+        fx = Utils.eval_f(prob, fx, x_cache)
+        fx_norm_new = L2_NORM(fx)^nexp
+
+        while k < maxiters
+            (fx_norm_new ≤ (f_bar + η - γ * α_p^2 * fx_norm)) && break
+
+            α_tp = α_p^2 * fx_norm / (fx_norm_new + (T(2) * α_p - T(1)) * fx_norm)
+            @bb @. x_cache = x - α_m * d
+
+            fx = Utils.eval_f(prob, fx, x_cache)
+            fx_norm_new = L2_NORM(fx)^nexp
+
+            (fx_norm_new ≤ (f_bar + η - γ * α_m^2 * fx_norm)) && break
+
+            α_tm = α_m^2 * fx_norm / (fx_norm_new + (T(2) * α_m - T(1)) * fx_norm)
+            α_p = clamp(α_tp, τ_min * α_p, τ_max * α_p)
+            α_m = clamp(α_tm, τ_min * α_m, τ_max * α_m)
+            @bb @. x_cache = x + α_p * d
+
+            fx = Utils.eval_f(prob, fx, x_cache)
+            fx_norm_new = L2_NORM(fx)^nexp
+
+            k += 1
+        end
+
+        @bb copyto!(x, x_cache)
+
+        solved, retcode, fx_sol, x_sol = Utils.check_termination(tc_cache, fx, x, xo, prob)
+        solved && return SciMLBase.build_solution(prob, alg, x_sol, fx_sol; retcode)
+
+        # Update spectral parameter
+        @bb @. δx = x - xo
+        @bb @. δf = fx - δf
+
+        σ_k = dot(δx, δx) / dot(δx, δf)
+
+        # Take step
+        @bb copyto!(xo, x)
+        @bb copyto!(δf, fx)
+        fx_norm = fx_norm_new
+
+        # Store function value
+        idx = mod1(k, SciMLBase._unwrap_val(alg.M))
+        if history_f_k isa SVector
+            history_f_k = Base.setindex(history_f_k, fx_norm_new, idx)
+        elseif history_f_k isa NTuple
+            @reset history_f_k[idx] = fx_norm_new
+        else
+            history_f_k[idx] = fx_norm_new
+        end
+        k += 1
+    end
+
+    return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+end
+
+function dfsane_history_vec(x::StaticArray, fx_norm, ::Val{M}) where {M}
+    return ones(SVector{M, eltype(x)}) .* fx_norm
+end
+
+@generated function dfsane_history_vec(x, fx_norm, ::Val{M}) where {M}
+    M ≥ 11 && return :(fill(fx_norm, M)) # Julia can't specialize here
+    return :(ntuple(Returns(fx_norm), $(M)))
+end

From db5cce2618ed1ccc1b348682754c28be1ce1d68f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 16:33:42 -0400
Subject: [PATCH 574/700] fix: only precompile selected workloads for faster
 loading

---
 lib/SimpleNonlinearSolve/Project.toml            |  1 +
 .../src/SimpleNonlinearSolve.jl                  | 16 ++++++++++------
 2 files changed, 11 insertions(+), 6 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 1962d42cf..3a20a18b2 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -49,6 +49,7 @@ FiniteDiff = "2.24.0"
 ForwardDiff = "0.10.36"
 InteractiveUtils = "<0.0.1, 1"
 LinearAlgebra = "1.10"
+LineSearch = "0.1.3"
 MaybeInplace = "0.1.4"
 NonlinearSolveBase = "1"
 PrecompileTools = "1.2"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 29adc7131..d772f44d3 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -75,29 +75,33 @@ end
 function solve_adjoint_internal end
 
 @setup_workload begin
-    for T in (Float32, Float64)
+    for T in (Float64,)
         prob_scalar = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
         prob_iip = NonlinearProblem{true}((du, u, p) -> du .= u .* u .- p, ones(T, 3), T(2))
         prob_oop = NonlinearProblem{false}((u, p) -> u .* u .- p, ones(T, 3), T(2))
 
+        # Only compile frequently used algorithms -- mostly from the NonlinearSolve default
         algs = [
             SimpleBroyden(),
             # SimpleDFSane(),
             SimpleKlement(),
             # SimpleLimitedMemoryBroyden(),
-            SimpleHalley(),
-            SimpleNewtonRaphson(),
-            SimpleTrustRegion()
+            # SimpleHalley(),
+            SimpleNewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 1)),
+            # SimpleTrustRegion()
         ]
 
         @compile_workload begin
-            for alg in algs, prob in (prob_scalar, prob_iip, prob_oop)
-                CommonSolve.solve(prob, alg)
+            @sync for alg in algs
+                for prob in (prob_scalar, prob_iip, prob_oop)
+                    Threads.@spawn CommonSolve.solve(prob, alg; abstol = 1e-2)
+                end
             end
         end
     end
 end
 
+
 export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
 
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder

From bc7a331e611424e1fffaaecee2d939872eb1f9f5 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 16:40:05 -0400
Subject: [PATCH 575/700] chore: run formatter

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index d772f44d3..b4fc1d202 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -81,6 +81,7 @@ function solve_adjoint_internal end
         prob_oop = NonlinearProblem{false}((u, p) -> u .* u .- p, ones(T, 3), T(2))
 
         # Only compile frequently used algorithms -- mostly from the NonlinearSolve default
+        #!format: off
         algs = [
             SimpleBroyden(),
             # SimpleDFSane(),
@@ -90,6 +91,7 @@ function solve_adjoint_internal end
             SimpleNewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 1)),
             # SimpleTrustRegion()
         ]
+        #!format: on
 
         @compile_workload begin
             @sync for alg in algs
@@ -101,7 +103,6 @@ function solve_adjoint_internal end
     end
 end
 
-
 export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
 
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder

From fbb5911f5fe178d86d5fdbd97766a8ceb152fd44 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 4 Oct 2024 17:27:09 -0400
Subject: [PATCH 576/700] feat: SimpleLimitedMemoryBroyden impl

---
 .../src/SimpleNonlinearSolve.jl               |   4 +-
 lib/SimpleNonlinearSolve/src/lbroyden.jl      | 327 ++++++++++++++++++
 2 files changed, 329 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index b4fc1d202..c8df31e51 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -11,7 +11,7 @@ using PrecompileTools: @compile_workload, @setup_workload
 using Reexport: @reexport
 @reexport using SciMLBase  # I don't like this but needed to avoid a breaking change
 using SciMLBase: AbstractNonlinearAlgorithm, NonlinearProblem, ReturnCode
-using StaticArraysCore: StaticArray, SVector
+using StaticArraysCore: StaticArray, SArray, SVector, MArray
 
 # AD Dependencies
 using ADTypes: AbstractADType, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
@@ -107,7 +107,7 @@ export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
 
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
-export SimpleBroyden, SimpleKlement
+export SimpleBroyden, SimpleKlement, SimpleLimitedMemoryBroyden
 export SimpleDFSane
 export SimpleGaussNewton, SimpleNewtonRaphson, SimpleTrustRegion
 export SimpleHalley
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index 8b1378917..2a9ace6dc 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -1 +1,328 @@
+"""
+    SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27),
+        linesearch = Val(false), alpha = nothing)
 
+A limited memory implementation of Broyden. This method applies the L-BFGS scheme to
+Broyden's method.
+
+If the threshold is larger than the problem size, then this method will use `SimpleBroyden`.
+
+### Keyword Arguments:
+
+  - `linesearch`: If `linesearch` is `Val(true)`, then we use the `LiFukushimaLineSearch`
+    line search else no line search is used. For advanced customization of the line search,
+    use `Broyden` from `NonlinearSolve.jl`.
+  - `alpha`: Scale the initial jacobian initialization with `alpha`. If it is `nothing`, we
+    will compute the scaling using `2 * norm(fu) / max(norm(u), true)`.
+
+!!! warning
+
+    Currently `alpha` is only used for StaticArray problems. This will be fixed in the
+    future.
+"""
+@concrete struct SimpleLimitedMemoryBroyden <: AbstractSimpleNonlinearSolveAlgorithm
+    linesearch <: Union{Val{false}, Val{true}}
+    threshold <: Val
+    alpha
+end
+
+function SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27),
+        linesearch::Union{Bool, Val{true}, Val{false}} = Val(false), alpha = nothing)
+    linesearch = linesearch isa Bool ? Val(linesearch) : linesearch
+    threshold = threshold isa Int ? Val(threshold) : threshold
+    return SimpleLimitedMemoryBroyden(linesearch, threshold, alpha)
+end
+
+function SciMLBase.__solve(
+        prob::ImmutableNonlinearProblem, alg::SimpleLimitedMemoryBroyden,
+        args...; termination_condition = nothing, kwargs...)
+    if prob.u0 isa SArray
+        if termination_condition === nothing ||
+           termination_condition isa AbsNormTerminationMode
+            return internal_static_solve(
+                prob, alg, args...; termination_condition, kwargs...)
+        end
+        @warn "Specifying `termination_condition = $(termination_condition)` for \
+               `SimpleLimitedMemoryBroyden` with `SArray` is not non-allocating. Use \
+               either `termination_condition = AbsNormTerminationMode()` or \
+               `termination_condition = nothing`." maxlog=1
+    end
+    return internal_generic_solve(prob, alg, args...; termination_condition, kwargs...)
+end
+
+@views function internal_generic_solve(
+        prob::ImmutableNonlinearProblem, alg::SimpleLimitedMemoryBroyden,
+        args...; abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0 = false, termination_condition = nothing, kwargs...)
+    x = Utils.maybe_unaliased(prob.u0, alias_u0)
+    η = min(SciMLBase._unwrap_val(alg.threshold), maxiters)
+
+    # For scalar problems / if the threshold is larger than problem size just use Broyden
+    if x isa Number || length(x) ≤ η
+        return SciMLBase.__solve(prob, SimpleBroyden(; alg.linesearch), args...; abstol,
+            reltol, maxiters, termination_condition, kwargs...)
+    end
+
+    fx = Utils.get_fx(prob, x)
+
+    U, Vᵀ = init_low_rank_jacobian(x, fx, x isa StaticArray ? alg.threshold : Val(η))
+
+    abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+
+    @bb xo = copy(x)
+    @bb δx = copy(fx)
+    @bb δx .*= -1
+    @bb fo = copy(fx)
+    @bb δf = copy(fx)
+
+    @bb vᵀ_cache = copy(x)
+    Tcache = lbroyden_threshold_cache(x, x isa StaticArray ? alg.threshold : Val(η))
+    @bb mat_cache = copy(x)
+
+    if alg.linesearch === Val(true)
+        ls_alg = LiFukushimaLineSearch(; nan_maxiters = nothing)
+        ls_cache = init(prob, ls_alg, fx, x)
+    else
+        ls_cache = nothing
+    end
+
+    for i in 1:maxiters
+        if ls_cache === nothing
+            α = true
+        else
+            ls_sol = solve!(ls_cache, xo, δx)
+            α = ls_sol.step_size # Ignores the return code for now
+        end
+
+        @bb @. x = xo + α * δx
+        fx = Utils.eval_f(prob, fx, x)
+        @bb @. δf = fx - fo
+
+        # Termination Checks
+        solved, retcode, fx_sol, x_sol = Utils.check_termination(tc_cache, fx, x, xo, prob)
+        solved && return SciMLBase.build_solution(prob, alg, x_sol, fx_sol; retcode)
+
+        Uₚ = selectdim(U, 2, 1:min(η, i - 1))
+        Vᵀₚ = selectdim(Vᵀ, 1, 1:min(η, i - 1))
+
+        vᵀ = rmatvec!!(vᵀ_cache, Tcache, Uₚ, Vᵀₚ, δx)
+        mvec = matvec!!(mat_cache, Tcache, Uₚ, Vᵀₚ, δf)
+        d = dot(vᵀ, δf)
+        @bb @. δx = (δx - mvec) / d
+
+        selectdim(U, 2, mod1(i, η)) .= Utils.safe_vec(δx)
+        selectdim(Vᵀ, 1, mod1(i, η)) .= Utils.safe_vec(vᵀ)
+
+        Uₚ = selectdim(U, 2, 1:min(η, i))
+        Vᵀₚ = selectdim(Vᵀ, 1, 1:min(η, i))
+        δx = matvec!!(δx, Tcache, Uₚ, Vᵀₚ, fx)
+        @bb @. δx *= -1
+
+        @bb copyto!(xo, x)
+        @bb copyto!(fo, fx)
+    end
+
+    return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+end
+
+# Non-allocating StaticArrays version of SimpleLimitedMemoryBroyden is actually quite
+# finicky, so we'll implement it separately from the generic version
+# Ignore termination_condition. Don't pass things into internal functions
+function internal_static_solve(
+        prob::ImmutableNonlinearProblem{<:SArray}, alg::SimpleLimitedMemoryBroyden,
+        args...; abstol = nothing, maxiters = 1000, kwargs...)
+    x = prob.u0
+    fx = Utils.get_fx(prob, x)
+
+    U, Vᵀ = init_low_rank_jacobian(vec(x), vec(fx), alg.threshold)
+
+    abstol = NonlinearSolveBase.get_tolerance(x, abstol, eltype(x))
+
+    xo, δx, fo, δf = x, -fx, fx, fx
+
+    if alg.linesearch === Val(true)
+        ls_alg = LiFukushimaLineSearch(; nan_maxiters = nothing)
+        ls_cache = init(prob, ls_alg, fx, x)
+    else
+        ls_cache = nothing
+    end
+
+    T = promote_type(eltype(x), eltype(fx))
+    if alg.alpha === nothing
+        fx_norm = L2_NORM(fx)
+        x_norm = L2_NORM(x)
+        init_α = ifelse(fx_norm ≥ 1e-5, max(x_norm, T(true)) / (2 * fx_norm), T(true))
+    else
+        init_α = inv(alg.alpha)
+    end
+
+    converged, res = internal_unrolled_lbroyden_initial_iterations(
+        prob, xo, fo, δx, abstol, U, Vᵀ, alg.threshold, ls_cache, init_α)
+
+    converged && return SciMLBase.build_solution(
+        prob, alg, res.x, res.fx; retcode = ReturnCode.Success)
+
+    xo, fo, δx = res.x, res.fx, res.δx
+
+    for i in 1:(maxiters - SciMLBase._unwrap_val(alg.threshold))
+        if ls_cache === nothing
+            α = true
+        else
+            ls_sol = solve!(ls_cache, xo, δx)
+            α = ls_sol.step_size # Ignores the return code for now
+        end
+
+        x = xo + α * δx
+        fx = Utils.eval_f(prob, fx, x)
+        δf = fx - fo
+
+        maximum(abs, fx) ≤ abstol &&
+            return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
+
+        vᵀ = Utils.restructure(x, rmatvec!!(U, Vᵀ, vec(δx), init_α))
+        mvec = Utils.restructure(x, matvec!!(U, Vᵀ, vec(δf), init_α))
+
+        d = dot(vᵀ, δf)
+        δx = @. (δx - mvec) / d
+
+        U = Base.setindex(U, vec(δx), mod1(i, SciMLBase._unwrap_val(alg.threshold)))
+        Vᵀ = Base.setindex(Vᵀ, vec(vᵀ), mod1(i, SciMLBase._unwrap_val(alg.threshold)))
+
+        δx = -Utils.restructure(fx, matvec!!(U, Vᵀ, vec(fx), init_α))
+
+        xo, fo = x, fx
+    end
+
+    return SciMLBase.build_solution(prob, alg, xo, fo; retcode = ReturnCode.MaxIters)
+end
+
+@generated function internal_unrolled_lbroyden_initial_iterations(
+        prob, xo, fo, δx, abstol, U, Vᵀ, ::Val{threshold},
+        ls_cache, init_α) where {threshold}
+    calls = []
+    for i in 1:threshold
+        static_idx, static_idx_p1 = Val(i - 1), Val(i)
+        push!(calls, quote
+            α = ls_cache === nothing ? true : ls_cache(xo, δx)
+            x = xo .+ α .* δx
+            fx = prob.f(x, prob.p)
+            δf = fx - fo
+
+            maximum(abs, fx) ≤ abstol && return true, (; x, fx, δx)
+
+            Uₚ = first_n_getindex(U, $(static_idx))
+            Vᵀₚ = first_n_getindex(Vᵀ, $(static_idx))
+
+            vᵀ = Utils.restructure(x, rmatvec!!(Uₚ, Vᵀₚ, vec(δx), init_α))
+            mvec = Utils.restructure(x, matvec!!(Uₚ, Vᵀₚ, vec(δf), init_α))
+
+            d = dot(vᵀ, δf)
+            δx = @. (δx - mvec) / d
+
+            U = Base.setindex(U, vec(δx), $(i))
+            Vᵀ = Base.setindex(Vᵀ, vec(vᵀ), $(i))
+
+            Uₚ = first_n_getindex(U, $(static_idx_p1))
+            Vᵀₚ = first_n_getindex(Vᵀ, $(static_idx_p1))
+            δx = -Utils.restructure(fx, matvec!!(Uₚ, Vᵀₚ, vec(fx), init_α))
+
+            x0, fo = x, fx
+        end)
+    end
+    push!(calls, quote
+        # Termination Check
+        maximum(abs, fx) ≤ abstol && return true, (; x, fx, δx)
+
+        return false, (; x, fx, δx)
+    end)
+    return Expr(:block, calls...)
+end
+
+function rmatvec!!(y, xᵀU, U, Vᵀ, x)
+    # xᵀ × (-I + UVᵀ)
+    η = size(U, 2)
+    if η == 0
+        @bb @. y = -x
+        return y
+    end
+    x_ = vec(x)
+    xᵀU_ = view(xᵀU, 1:η)
+    @bb xᵀU_ = transpose(U) × x_
+    @bb y = transpose(Vᵀ) × vec(xᵀU_)
+    @bb @. y -= x
+    return y
+end
+
+rmatvec!!(::Nothing, Vᵀ, x, init_α) = -x .* init_α
+rmatvec!!(U, Vᵀ, x, init_α) = fast_mapTdot(fast_mapdot(x, U), Vᵀ) .- x .* init_α
+
+function matvec!!(y, Vᵀx, U, Vᵀ, x)
+    # (-I + UVᵀ) × x
+    η = size(U, 2)
+    if η == 0
+        @bb @. y = -x
+        return y
+    end
+    x_ = vec(x)
+    Vᵀx_ = view(Vᵀx, 1:η)
+    @bb Vᵀx_ = Vᵀ × x_
+    @bb y = U × vec(Vᵀx_)
+    @bb @. y -= x
+    return y
+end
+
+@inline matvec!!(::Nothing, Vᵀ, x, init_α) = -x .* init_α
+@inline matvec!!(U, Vᵀ, x, init_α) = fast_mapTdot(fast_mapdot(x, Vᵀ), U) .- x .* init_α
+
+function fast_mapdot(x::SVector{S1}, Y::SVector{S2, <:SVector{S1}}) where {S1, S2}
+    return map(Base.Fix1(dot, x), Y)
+end
+@generated function fast_mapTdot(
+        x::SVector{S1}, Y::SVector{S1, <:SVector{S2}}) where {S1, S2}
+    calls = []
+    syms = [gensym("m$(i)") for i in 1:S1]
+    for i in 1:S1
+        push!(calls, :($(syms[i]) = x[$(i)] .* Y[$i]))
+    end
+    push!(calls, :(return .+($(syms...))))
+    return Expr(:block, calls...)
+end
+
+@generated function first_n_getindex(x::SVector{L, T}, ::Val{N}) where {L, T, N}
+    @assert N ≤ L
+    getcalls = ntuple(i -> :(x[$i]), N)
+    N == 0 && return :(return nothing)
+    return :(return SVector{$N, $T}(($(getcalls...))))
+end
+
+lbroyden_threshold_cache(x, ::Val{threshold}) where {threshold} = similar(x, threshold)
+function lbroyden_threshold_cache(x::StaticArray, ::Val{threshold}) where {threshold}
+    return zeros(MArray{Tuple{threshold}, eltype(x)})
+end
+lbroyden_threshold_cache(::SArray, ::Val{threshold}) where {threshold} = nothing
+
+function init_low_rank_jacobian(u::StaticArray{S1, T1}, fu::StaticArray{S2, T2},
+        ::Val{threshold}) where {S1, S2, T1, T2, threshold}
+    T = promote_type(T1, T2)
+    fuSize, uSize = Size(fu), Size(u)
+    Vᵀ = MArray{Tuple{threshold, prod(uSize)}, T}(undef)
+    U = MArray{Tuple{prod(fuSize), threshold}, T}(undef)
+    return U, Vᵀ
+end
+@generated function init_low_rank_jacobian(u::SVector{Lu, T1}, fu::SVector{Lfu, T2},
+        ::Val{threshold}) where {Lu, Lfu, T1, T2, threshold}
+    T = promote_type(T1, T2)
+    inner_inits_Vᵀ = [:(zeros(SVector{$Lu, $T})) for i in 1:threshold]
+    inner_inits_U = [:(zeros(SVector{$Lfu, $T})) for i in 1:threshold]
+    return quote
+        Vᵀ = SVector($(inner_inits_Vᵀ...))
+        U = SVector($(inner_inits_U...))
+        return U, Vᵀ
+    end
+end
+function init_low_rank_jacobian(u, fu, ::Val{threshold}) where {threshold}
+    Vᵀ = similar(u, threshold, length(u))
+    U = similar(u, length(fu), threshold)
+    return U, Vᵀ
+end

From 9d361d81d4c6fca4c11244fb93d77be7eef4b24f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 6 Oct 2024 21:04:50 -0400
Subject: [PATCH 577/700] fix: simplenonlinearsolve in cuda kernels

---
 .buildkite/pipeline.yml                       | 28 ++++++
 lib/BracketingNonlinearSolve/src/bisection.jl |  2 +-
 lib/BracketingNonlinearSolve/src/brent.jl     |  2 +-
 lib/BracketingNonlinearSolve/src/falsi.jl     |  2 +-
 lib/BracketingNonlinearSolve/src/itp.jl       |  2 +-
 lib/BracketingNonlinearSolve/src/ridder.jl    |  2 +-
 .../src/termination_conditions.jl             | 12 +--
 lib/SimpleNonlinearSolve/Project.toml         | 31 ++++++-
 lib/SimpleNonlinearSolve/src/lbroyden.jl      |  7 +-
 lib/SimpleNonlinearSolve/src/utils.jl         | 61 ++++++++++---
 .../test/gpu/cuda_tests.jl                    | 90 +++++++++++++++++++
 lib/SimpleNonlinearSolve/test/runtests.jl     | 10 ++-
 12 files changed, 219 insertions(+), 30 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl

diff --git a/.buildkite/pipeline.yml b/.buildkite/pipeline.yml
index 8ddf4f4ff..f6b4ed6eb 100644
--- a/.buildkite/pipeline.yml
+++ b/.buildkite/pipeline.yml
@@ -27,6 +27,34 @@ steps:
     # Don't run Buildkite if the commit message includes the text [skip tests]
     if: build.message !~ /\[skip tests\]/
 
+  - label: "Julia 1 (SimpleNonlinearSolve)"
+    plugins:
+      - JuliaCI/julia#v1:
+          version: "1"
+      - JuliaCI/julia-coverage#v1:
+          codecov: true
+          dirs:
+            - src
+            - ext
+    command: |
+      julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SimpleNonlinearSolve -e '
+        import Pkg;
+        Pkg.Registry.update();
+        # Install packages present in subdirectories
+        dev_pks = Pkg.PackageSpec[];
+        for path in ("lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve")
+          push!(dev_pks, Pkg.PackageSpec(; path))
+        end
+        Pkg.develop(dev_pks);
+        Pkg.instantiate();
+        Pkg.test(; coverage=true)'
+    agents:
+      queue: "juliagpu"
+      cuda: "*"
+    timeout_in_minutes: 60
+    # Don't run Buildkite if the commit message includes the text [skip tests]
+    if: build.message !~ /\[skip tests\]/
+
 env:
   GROUP: CUDA
   JULIA_PKG_SERVER: "" # it often struggles with our large artifacts
diff --git a/lib/BracketingNonlinearSolve/src/bisection.jl b/lib/BracketingNonlinearSolve/src/bisection.jl
index 1611ad34e..e51416145 100644
--- a/lib/BracketingNonlinearSolve/src/bisection.jl
+++ b/lib/BracketingNonlinearSolve/src/bisection.jl
@@ -28,7 +28,7 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Bisection,
     fl, fr = f(left), f(right)
 
     abstol = NonlinearSolveBase.get_tolerance(
-        abstol, promote_type(eltype(left), eltype(right)))
+        left, abstol, promote_type(eltype(left), eltype(right)))
 
     if iszero(fl)
         return SciMLBase.build_solution(
diff --git a/lib/BracketingNonlinearSolve/src/brent.jl b/lib/BracketingNonlinearSolve/src/brent.jl
index fea2ce3f4..fb3740e98 100644
--- a/lib/BracketingNonlinearSolve/src/brent.jl
+++ b/lib/BracketingNonlinearSolve/src/brent.jl
@@ -15,7 +15,7 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
     ϵ = eps(convert(typeof(fl), 1))
 
     abstol = NonlinearSolveBase.get_tolerance(
-        abstol, promote_type(eltype(left), eltype(right)))
+        left, abstol, promote_type(eltype(left), eltype(right)))
 
     if iszero(fl)
         return SciMLBase.build_solution(
diff --git a/lib/BracketingNonlinearSolve/src/falsi.jl b/lib/BracketingNonlinearSolve/src/falsi.jl
index 8c62b95c6..f56155ef7 100644
--- a/lib/BracketingNonlinearSolve/src/falsi.jl
+++ b/lib/BracketingNonlinearSolve/src/falsi.jl
@@ -15,7 +15,7 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
     fl, fr = f(left), f(right)
 
     abstol = NonlinearSolveBase.get_tolerance(
-        abstol, promote_type(eltype(left), eltype(right)))
+        left, abstol, promote_type(eltype(left), eltype(right)))
 
     if iszero(fl)
         return SciMLBase.build_solution(
diff --git a/lib/BracketingNonlinearSolve/src/itp.jl b/lib/BracketingNonlinearSolve/src/itp.jl
index 4798f9030..821047a5a 100644
--- a/lib/BracketingNonlinearSolve/src/itp.jl
+++ b/lib/BracketingNonlinearSolve/src/itp.jl
@@ -65,7 +65,7 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
     fl, fr = f(left), f(right)
 
     abstol = NonlinearSolveBase.get_tolerance(
-        abstol, promote_type(eltype(left), eltype(right)))
+        left, abstol, promote_type(eltype(left), eltype(right)))
 
     if iszero(fl)
         return SciMLBase.build_solution(
diff --git a/lib/BracketingNonlinearSolve/src/ridder.jl b/lib/BracketingNonlinearSolve/src/ridder.jl
index e4b67a7c7..d988c9dc5 100644
--- a/lib/BracketingNonlinearSolve/src/ridder.jl
+++ b/lib/BracketingNonlinearSolve/src/ridder.jl
@@ -14,7 +14,7 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
     fl, fr = f(left), f(right)
 
     abstol = NonlinearSolveBase.get_tolerance(
-        abstol, promote_type(eltype(left), eltype(right)))
+        left, abstol, promote_type(eltype(left), eltype(right)))
 
     if iszero(fl)
         return SciMLBase.build_solution(
diff --git a/lib/NonlinearSolveBase/src/termination_conditions.jl b/lib/NonlinearSolveBase/src/termination_conditions.jl
index 8bb58f8eb..7978c19b8 100644
--- a/lib/NonlinearSolveBase/src/termination_conditions.jl
+++ b/lib/NonlinearSolveBase/src/termination_conditions.jl
@@ -34,8 +34,8 @@ function SciMLBase.init(
         du, u, mode::AbstractNonlinearTerminationMode, saved_value_prototype...;
         abstol = nothing, reltol = nothing, kwargs...)
     T = promote_type(eltype(du), eltype(u))
-    abstol = get_tolerance(abstol, T)
-    reltol = get_tolerance(reltol, T)
+    abstol = get_tolerance(u, abstol, T)
+    reltol = get_tolerance(u, reltol, T)
     TT = typeof(abstol)
 
     u_unaliased = mode isa AbstractSafeBestNonlinearTerminationMode ?
@@ -90,8 +90,8 @@ function SciMLBase.reinit!(
     cache.u = u_unaliased
     cache.retcode = ReturnCode.Default
 
-    cache.abstol = get_tolerance(abstol, T)
-    cache.reltol = get_tolerance(reltol, T)
+    cache.abstol = get_tolerance(u, abstol, T)
+    cache.reltol = get_tolerance(u, reltol, T)
     cache.nsteps = 0
     TT = typeof(cache.abstol)
 
@@ -274,8 +274,8 @@ end
 function init_termination_cache(::AbstractNonlinearProblem, abstol, reltol, du,
         u, tc::AbstractNonlinearTerminationMode, ::Val)
     T = promote_type(eltype(du), eltype(u))
-    abstol = get_tolerance(abstol, T)
-    reltol = get_tolerance(reltol, T)
+    abstol = get_tolerance(u, abstol, T)
+    reltol = get_tolerance(u, reltol, T)
     cache = SciMLBase.init(du, u, tc; abstol, reltol)
     return abstol, reltol, cache
 end
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 3a20a18b2..fae63544a 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -37,35 +37,62 @@ SimpleNonlinearSolveTrackerExt = "Tracker"
 
 [compat]
 ADTypes = "1.2"
+Accessors = "0.1"
+AllocCheck = "0.1.1"
+Aqua = "0.8.7"
 ArrayInterface = "7.16"
 BracketingNonlinearSolve = "1"
+CUDA = "5.3"
 ChainRulesCore = "1.24"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.155"
 DifferentiationInterface = "0.6.1"
+Enzyme = "0.13"
+ExplicitImports = "1.9"
 FastClosures = "0.3.2"
 FiniteDiff = "2.24.0"
 ForwardDiff = "0.10.36"
 InteractiveUtils = "<0.0.1, 1"
-LinearAlgebra = "1.10"
 LineSearch = "0.1.3"
+LinearAlgebra = "1.10"
 MaybeInplace = "0.1.4"
+NonlinearProblemLibrary = "0.1.2"
 NonlinearSolveBase = "1"
+Pkg = "1.10"
+PolyesterForwardDiff = "0.1"
 PrecompileTools = "1.2"
+Random = "1.10"
 Reexport = "1.2"
 ReverseDiff = "1.15"
 SciMLBase = "2.50"
+SciMLSensitivity = "7.68"
+StaticArrays = "1.9"
 StaticArraysCore = "1.4.3"
 Test = "1.10"
 TestItemRunner = "1"
 Tracker = "0.2.35"
+Zygote = "0.6.70"
 julia = "1.10"
 
 [extras]
+AllocCheck = "9b6a8646-10ed-4001-bbdc-1d2f46dfbb1a"
+Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
+Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+SciMLSensitivity = "1ed8b502-d754-442c-8d5d-10ac956f44a1"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
+Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["InteractiveUtils", "Test", "TestItemRunner"]
+test = ["AllocCheck", "Aqua", "CUDA", "Enzyme", "ExplicitImports", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReverseDiff", "SciMLSensitivity", "StaticArrays", "Test", "TestItemRunner", "Tracker", "Zygote"]
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index 2a9ace6dc..1ab200f74 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -204,7 +204,12 @@ end
     for i in 1:threshold
         static_idx, static_idx_p1 = Val(i - 1), Val(i)
         push!(calls, quote
-            α = ls_cache === nothing ? true : ls_cache(xo, δx)
+            if ls_cache === nothing
+                α = true
+            else
+                ls_sol = solve!(ls_cache, xo, δx)
+                α = ls_sol.step_size # Ignores the return code for now
+            end
             x = xo .+ α .* δx
             fx = prob.f(x, prob.p)
             δf = fx - fo
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 19d44cf21..011788a1c 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -2,6 +2,7 @@ module Utils
 
 using ADTypes: AbstractADType, AutoForwardDiff, AutoFiniteDiff, AutoPolyesterForwardDiff
 using ArrayInterface: ArrayInterface
+using ConcreteStructs: @concrete
 using DifferentiationInterface: DifferentiationInterface, Constant
 using FastClosures: @closure
 using LinearAlgebra: LinearAlgebra, I, diagind
@@ -116,25 +117,35 @@ restructure(::Number, x::Number) = x
 safe_vec(x::AbstractArray) = vec(x)
 safe_vec(x::Number) = x
 
+abstract type AbstractJacobianMode end
+
+struct AnalyticJacobian <: AbstractJacobianMode end
+@concrete struct DIExtras <: AbstractJacobianMode
+    prep
+end
+struct DINoPreparation <: AbstractJacobianMode end
+
+# While we could run prep in other cases, we don't since we need it completely
+# non-allocating for running inside GPU kernels
 function prepare_jacobian(prob, autodiff, _, x::Number)
     if SciMLBase.has_jac(prob.f) || SciMLBase.has_vjp(prob.f) || SciMLBase.has_jvp(prob.f)
-        return nothing
+        return AnalyticJacobian()
     end
-    return DI.prepare_derivative(prob.f, autodiff, x, Constant(prob.p))
+    # return DI.prepare_derivative(prob.f, autodiff, x, Constant(prob.p))
+    return DINoPreparation()
 end
 function prepare_jacobian(prob, autodiff, fx, x)
-    if SciMLBase.has_jac(prob.f)
-        return nothing
-    end
+    SciMLBase.has_jac(prob.f) && return AnalyticJacobian()
     if SciMLBase.isinplace(prob.f)
-        return DI.prepare_jacobian(prob.f, fx, autodiff, x, Constant(prob.p))
+        return DIExtras(DI.prepare_jacobian(prob.f, fx, autodiff, x, Constant(prob.p)))
     else
+        x isa SArray && return DINoPreparation()
         return DI.prepare_jacobian(prob.f, autodiff, x, Constant(prob.p))
     end
 end
 
 function compute_jacobian!!(_, prob, autodiff, fx, x::Number, extras)
-    if extras === nothing
+    if extras isa AnalyticJacobian
         if SciMLBase.has_jac(prob.f)
             return prob.f.jac(x, prob.p)
         elseif SciMLBase.has_vjp(prob.f)
@@ -143,11 +154,15 @@ function compute_jacobian!!(_, prob, autodiff, fx, x::Number, extras)
             return prob.f.jvp(one(x), x, prob.p)
         end
     end
-    return DI.derivative(prob.f, extras, autodiff, x, Constant(prob.p))
+    if extras isa DIExtras
+        return DI.derivative(prob.f, extras.prep, autodiff, x, Constant(prob.p))
+    else
+        return DI.derivative(prob.f, autodiff, x, Constant(prob.p))
+    end
 end
 function compute_jacobian!!(J, prob, autodiff, fx, x, extras)
     if J === nothing
-        if extras === nothing
+        if extras isa AnalyticJacobian
             if SciMLBase.isinplace(prob.f)
                 J = similar(fx, length(fx), length(x))
                 prob.f.jac(J, x, prob.p)
@@ -157,12 +172,17 @@ function compute_jacobian!!(J, prob, autodiff, fx, x, extras)
             end
         end
         if SciMLBase.isinplace(prob)
-            return DI.jacobian(prob.f, fx, extras, autodiff, x, Constant(prob.p))
+            @assert extras isa DIExtras
+            return DI.jacobian(prob.f, fx, extras.prep, autodiff, x, Constant(prob.p))
         else
-            return DI.jacobian(prob.f, extras, autodiff, x, Constant(prob.p))
+            if extras isa DIExtras
+                return DI.jacobian(prob.f, extras.prep, autodiff, x, Constant(prob.p))
+            else
+                return DI.jacobian(prob.f, autodiff, x, Constant(prob.p))
+            end
         end
     end
-    if extras === nothing
+    if extras isa AnalyticJacobian
         if SciMLBase.isinplace(prob)
             prob.jac(J, x, prob.p)
             return J
@@ -171,9 +191,22 @@ function compute_jacobian!!(J, prob, autodiff, fx, x, extras)
         end
     end
     if SciMLBase.isinplace(prob)
-        DI.jacobian!(prob.f, fx, J, extras, autodiff, x, Constant(prob.p))
+        @assert extras isa DIExtras
+        DI.jacobian!(prob.f, fx, J, extras.prep, autodiff, x, Constant(prob.p))
     else
-        DI.jacobian!(prob.f, J, extras, autodiff, x, Constant(prob.p))
+        if ArrayInterface.can_setindex(J)
+            if extras isa DIExtras
+                DI.jacobian!(prob.f, J, extras.prep, autodiff, x, Constant(prob.p))
+            else
+                DI.jacobian!(prob.f, J, autodiff, x, Constant(prob.p))
+            end
+        else
+            if extras isa DIExtras
+                J = DI.jacobian(prob.f, extras.prep, autodiff, x, Constant(prob.p))
+            else
+                J = DI.jacobian(prob.f, autodiff, x, Constant(prob.p))
+            end
+        end
     end
     return J
 end
diff --git a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
new file mode 100644
index 000000000..8ecee2fed
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
@@ -0,0 +1,90 @@
+@testitem "Solving on CUDA" tags=[:cuda] begin
+    using StaticArrays, CUDA, SimpleNonlinearSolve
+
+    if CUDA.functional()
+        CUDA.allowscalar(false)
+
+        f(u, p) = u .* u .- 2
+        f!(du, u, p) = (du .= u .* u .- 2)
+
+        @testset "$(nameof(typeof(alg)))" for alg in (
+            SimpleNewtonRaphson(),
+            SimpleDFSane(),
+            SimpleTrustRegion(),
+            SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+            SimpleBroyden(),
+            SimpleLimitedMemoryBroyden(),
+            SimpleKlement(),
+            SimpleHalley(),
+            SimpleBroyden(; linesearch = Val(true)),
+            SimpleLimitedMemoryBroyden(; linesearch = Val(true))
+        )
+            # Static Arrays
+            u0 = @SVector[1.0f0, 1.0f0]
+            probN = NonlinearProblem{false}(f, u0)
+            sol = solve(probN, alg; abstol = 1.0f-6)
+            @test SciMLBase.successful_retcode(sol)
+            @test maximum(abs, sol.resid) ≤ 1.0f-6
+
+            # Regular Arrays
+            u0 = [1.0, 1.0]
+            probN = NonlinearProblem{false}(f, u0)
+            sol = solve(probN, alg; abstol = 1.0f-6)
+            @test SciMLBase.successful_retcode(sol)
+            @test maximum(abs, sol.resid) ≤ 1.0f-6
+
+            # Regular Arrays Inplace
+            if !(alg isa SimpleHalley)
+                u0 = [1.0, 1.0]
+                probN = NonlinearProblem{true}(f!, u0)
+                sol = solve(probN, alg; abstol = 1.0f-6)
+                @test SciMLBase.successful_retcode(sol)
+                @test maximum(abs, sol.resid) ≤ 1.0f-6
+            end
+        end
+    end
+end
+
+@testitem "CUDA Kernel Launch Test" tags=[:cuda] begin
+    using StaticArrays, CUDA, SimpleNonlinearSolve
+    using NonlinearSolveBase: ImmutableNonlinearProblem
+
+    if CUDA.functional()
+        CUDA.allowscalar(false)
+
+        f(u, p) = u .* u .- p
+
+        function kernel_function(prob, alg)
+            solve(prob, alg)
+            return nothing
+        end
+
+        @testset for u0 in (1.0f0, @SVector[1.0f0, 1.0f0])
+            prob = convert(ImmutableNonlinearProblem, NonlinearProblem{false}(f, u0, 2.0f0))
+
+            @testset "$(nameof(typeof(alg)))" for alg in (
+                SimpleNewtonRaphson(),
+                SimpleDFSane(),
+                SimpleTrustRegion(),
+                SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+                SimpleBroyden(),
+                SimpleLimitedMemoryBroyden(),
+                SimpleKlement(),
+                SimpleHalley(),
+                SimpleBroyden(; linesearch = Val(true)),
+                SimpleLimitedMemoryBroyden(; linesearch = Val(true))
+            )
+                @test begin
+                    try
+                        @cuda kernel_function(prob, alg)
+                        @info "Successfully launched kernel for $(alg)."
+                        true
+                    catch err
+                        @error "Kernel Launch failed for $(alg)."
+                        false
+                    end
+                end broken=(alg isa SimpleHalley && u0 isa StaticArray)
+            end
+        end
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index 6ea6326b0..dde4bacf4 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -1,5 +1,11 @@
-using TestItemRunner, InteractiveUtils
+using TestItemRunner, InteractiveUtils, Pkg
 
 @info sprint(InteractiveUtils.versioninfo)
 
-@run_package_tests
+const GROUP = lowercase(get(ENV, "GROUP", "All"))
+
+if GROUP == "all"
+    @run_package_tests
+else
+    @run_package_tests filter=ti->(Symbol(GROUP) in ti.tags)
+end

From 63572d1269e9d951078f6a6563b96544bc4b27a6 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 6 Oct 2024 21:34:58 -0400
Subject: [PATCH 578/700] fix: exotic types

---
 .../SimpleNonlinearSolveChainRulesCoreExt.jl  |  2 +-
 .../ext/SimpleNonlinearSolveReverseDiffExt.jl |  7 +++--
 .../ext/SimpleNonlinearSolveTrackerExt.jl     |  2 +-
 .../src/SimpleNonlinearSolve.jl               |  7 +++--
 lib/SimpleNonlinearSolve/src/halley.jl        |  6 ++--
 lib/SimpleNonlinearSolve/src/lbroyden.jl      |  6 ++--
 lib/SimpleNonlinearSolve/src/raphson.jl       |  4 +--
 lib/SimpleNonlinearSolve/src/trust_region.jl  |  4 +--
 lib/SimpleNonlinearSolve/src/utils.jl         |  5 ++--
 .../test/core/exotic_type_tests.jl            | 30 +++++++++++++++++++
 .../test/core/qa_tests.jl                     | 19 ++++++++++++
 11 files changed, 71 insertions(+), 21 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/core/qa_tests.jl

diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
index df0bd7573..f56dee537 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
@@ -8,7 +8,7 @@ using SimpleNonlinearSolve: SimpleNonlinearSolve, simplenonlinearsolve_solve_up,
                             solve_adjoint
 
 function ChainRulesCore.rrule(::typeof(simplenonlinearsolve_solve_up),
-        prob::Union{InternalNonlinearProblem, NonlinearLeastSquaresProblem},
+        prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
         sensealg, u0, u0_changed, p, p_changed, alg, args...; kwargs...)
     out, ∇internal = solve_adjoint(
         prob, sensealg, u0, p, ChainRulesOriginator(), alg, args...; kwargs...)
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
index 1357bec83..7b476b3c5 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
@@ -6,11 +6,12 @@ using ReverseDiff: ReverseDiff, TrackedArray, TrackedReal
 using SciMLBase: ReverseDiffOriginator, NonlinearLeastSquaresProblem, remake
 
 using SimpleNonlinearSolve: SimpleNonlinearSolve, solve_adjoint
+import SimpleNonlinearSolve: simplenonlinearsolve_solve_up
 
-for pType in (InternalNonlinearProblem, NonlinearLeastSquaresProblem)
+for pType in (ImmutableNonlinearProblem, NonlinearLeastSquaresProblem)
     aTypes = (TrackedArray, AbstractArray{<:TrackedReal}, Any)
     for (uT, pT) in collect(Iterators.product(aTypes, aTypes))[1:(end - 1)]
-        @eval function SimpleNonlinearSolve.simplenonlinearsolve_solve_up(
+        @eval function simplenonlinearsolve_solve_up(
                 prob::$(pType), sensealg, u0::$(uT), u0_changed,
                 p::$(pT), p_changed, alg, args...; kwargs...)
             return ReverseDiff.track(SimpleNonlinearSolve.simplenonlinearsolve_solve_up,
@@ -19,7 +20,7 @@ for pType in (InternalNonlinearProblem, NonlinearLeastSquaresProblem)
         end
     end
 
-    @eval ReverseDiff.@grad function SimpleNonlinearSolve.simplenonlinearsolve_solve_up(
+    @eval ReverseDiff.@grad function simplenonlinearsolve_solve_up(
             tprob::$(pType), sensealg, tu0, u0_changed,
             tp, p_changed, alg, args...; kwargs...)
         u0, p = ReverseDiff.value(tu0), ReverseDiff.value(tp)
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
index a2fa8ff40..ead5a8e29 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
@@ -7,7 +7,7 @@ using Tracker: Tracker, TrackedArray, TrackedReal
 
 using SimpleNonlinearSolve: SimpleNonlinearSolve, solve_adjoint
 
-for pType in (InternalNonlinearProblem, NonlinearLeastSquaresProblem)
+for pType in (ImmutableNonlinearProblem, NonlinearLeastSquaresProblem)
     aTypes = (TrackedArray, AbstractArray{<:TrackedReal}, Any)
     for (uT, pT) in collect(Iterators.product(aTypes, aTypes))[1:(end - 1)]
         @eval function SimpleNonlinearSolve.simplenonlinearsolve_solve_up(
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index c8df31e51..0b33c923e 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -14,19 +14,20 @@ using SciMLBase: AbstractNonlinearAlgorithm, NonlinearProblem, ReturnCode
 using StaticArraysCore: StaticArray, SArray, SVector, MArray
 
 # AD Dependencies
-using ADTypes: AbstractADType, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
+using ADTypes: AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
 using DifferentiationInterface: DifferentiationInterface
 using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff
 
 using BracketingNonlinearSolve: Alefeld, Bisection, Brent, Falsi, ITP, Ridder
-using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, get_tolerance,
-                          L2_NORM
+using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, L2_NORM
 
 const DI = DifferentiationInterface
 
 abstract type AbstractSimpleNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm end
 
+const safe_similar = NonlinearSolveBase.Utils.safe_similar
+
 is_extension_loaded(::Val) = false
 
 include("utils.jl")
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 23ba1c847..6b8948248 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -41,9 +41,9 @@ function SciMLBase.__solve(
 
     strait = setindex_trait(x)
 
-    A = strait isa CanSetindex ? similar(x, length(x), length(x)) : x
-    Aaᵢ = strait isa CanSetindex ? similar(x, length(x)) : x
-    cᵢ = strait isa CanSetindex ? similar(x) : x
+    A = strait isa CanSetindex ? safe_similar(x, length(x), length(x)) : x
+    Aaᵢ = strait isa CanSetindex ? safe_similar(x, length(x)) : x
+    cᵢ = strait isa CanSetindex ? safe_similar(x) : x
 
     for _ in 1:maxiters
         fx, J, H = Utils.compute_jacobian_and_hessian(autodiff, prob, fx, x)
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index 1ab200f74..ce39ca10d 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -301,7 +301,7 @@ end
     return :(return SVector{$N, $T}(($(getcalls...))))
 end
 
-lbroyden_threshold_cache(x, ::Val{threshold}) where {threshold} = similar(x, threshold)
+lbroyden_threshold_cache(x, ::Val{threshold}) where {threshold} = safe_similar(x, threshold)
 function lbroyden_threshold_cache(x::StaticArray, ::Val{threshold}) where {threshold}
     return zeros(MArray{Tuple{threshold}, eltype(x)})
 end
@@ -327,7 +327,7 @@ end
     end
 end
 function init_low_rank_jacobian(u, fu, ::Val{threshold}) where {threshold}
-    Vᵀ = similar(u, threshold, length(u))
-    U = similar(u, length(fu), threshold)
+    Vᵀ = safe_similar(u, threshold, length(u))
+    U = safe_similar(u, length(fu), threshold)
     return U, Vᵀ
 end
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 2af3a825a..763fcf32a 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -41,8 +41,8 @@ function SciMLBase.__solve(
                NonlinearSolveBase.select_jacobian_autodiff(prob, alg.autodiff)
 
     @bb xo = similar(x)
-    fx_cache = (SciMLBase.isinplace(prob) && !SciMLBase.has_jac(prob.f)) ? similar(fx) :
-               nothing
+    fx_cache = (SciMLBase.isinplace(prob) && !SciMLBase.has_jac(prob.f)) ?
+               safe_similar(fx) : nothing
     jac_cache = Utils.prepare_jacobian(prob, autodiff, fx_cache, x)
     J = Utils.compute_jacobian!!(nothing, prob, autodiff, fx_cache, x, jac_cache)
 
diff --git a/lib/SimpleNonlinearSolve/src/trust_region.jl b/lib/SimpleNonlinearSolve/src/trust_region.jl
index 6bf543220..27b210d65 100644
--- a/lib/SimpleNonlinearSolve/src/trust_region.jl
+++ b/lib/SimpleNonlinearSolve/src/trust_region.jl
@@ -93,8 +93,8 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleTrustRegi
     norm_fx = L2_NORM(fx)
 
     @bb xo = copy(x)
-    fx_cache = (SciMLBase.isinplace(prob) && !SciMLBase.has_jac(prob.f)) ? similar(fx) :
-               nothing
+    fx_cache = (SciMLBase.isinplace(prob) && !SciMLBase.has_jac(prob.f)) ?
+               safe_similar(fx) : nothing
     jac_cache = Utils.prepare_jacobian(prob, autodiff, fx_cache, x)
     J = Utils.compute_jacobian!!(nothing, prob, autodiff, fx_cache, x, jac_cache)
 
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 011788a1c..946c10529 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -1,6 +1,5 @@
 module Utils
 
-using ADTypes: AbstractADType, AutoForwardDiff, AutoFiniteDiff, AutoPolyesterForwardDiff
 using ArrayInterface: ArrayInterface
 using ConcreteStructs: @concrete
 using DifferentiationInterface: DifferentiationInterface, Constant
@@ -164,7 +163,7 @@ function compute_jacobian!!(J, prob, autodiff, fx, x, extras)
     if J === nothing
         if extras isa AnalyticJacobian
             if SciMLBase.isinplace(prob.f)
-                J = similar(fx, length(fx), length(x))
+                J = safe_similar(fx, length(fx), length(x))
                 prob.f.jac(J, x, prob.p)
                 return J
             else
@@ -219,7 +218,7 @@ end
 function compute_jacobian_and_hessian(autodiff, prob, fx, x)
     if SciMLBase.isinplace(prob)
         jac_fn = @closure (u, p) -> begin
-            du = similar(fx, promote_type(eltype(fx), eltype(u)))
+            du = safe_similar(fx, promote_type(eltype(fx), eltype(u)))
             return DI.jacobian(prob.f, du, autodiff, u, Constant(p))
         end
         J, H = DI.value_and_jacobian(jac_fn, autodiff, x, Constant(prob.p))
diff --git a/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl b/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
new file mode 100644
index 000000000..e19a3d32e
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
@@ -0,0 +1,30 @@
+@testitem "BigFloat Support" tags=[:core] begin
+    using SimpleNonlinearSolve, LinearAlgebra
+
+    fn_iip = NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p)
+    fn_oop = NonlinearFunction{false}((u, p) -> u .* u .- p)
+
+    u0 = BigFloat[1.0, 1.0, 1.0]
+    prob_iip_bf = NonlinearProblem{true}(fn_iip, u0, BigFloat(2))
+    prob_oop_bf = NonlinearProblem{false}(fn_oop, u0, BigFloat(2))
+
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        SimpleNewtonRaphson(),
+        SimpleBroyden(),
+        SimpleKlement(),
+        SimpleDFSane(),
+        SimpleTrustRegion(),
+        SimpleLimitedMemoryBroyden(),
+        SimpleHalley()
+    )
+        sol = solve(prob_oop_bf, alg)
+        @test maximum(abs, sol.resid) < 1e-6
+        @test SciMLBase.successful_retcode(sol.retcode)
+
+        alg isa SimpleHalley && continue
+
+        sol = solve(prob_iip_bf, alg)
+        @test maximum(abs, sol.resid) < 1e-6
+        @test SciMLBase.successful_retcode(sol.retcode)
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/test/core/qa_tests.jl b/lib/SimpleNonlinearSolve/test/core/qa_tests.jl
new file mode 100644
index 000000000..d6a5a9b8e
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/qa_tests.jl
@@ -0,0 +1,19 @@
+@testitem "Aqua" tags=[:core] begin
+    using Aqua, SimpleNonlinearSolve
+
+    Aqua.test_all(SimpleNonlinearSolve; piracies = false, ambiguities = false)
+    Aqua.test_piracies(SimpleNonlinearSolve;
+        treat_as_own = [
+            NonlinearProblem, NonlinearLeastSquaresProblem, IntervalNonlinearProblem])
+    Aqua.test_ambiguities(SimpleNonlinearSolve; recursive = false)
+end
+
+@testitem "Explicit Imports" tags=[:core] begin
+    import ReverseDiff, Tracker, StaticArrays, Zygote
+    using ExplicitImports, SimpleNonlinearSolve
+
+    @test check_no_implicit_imports(
+        SimpleNonlinearSolve; skip = (Base, Core, SciMLBase)) === nothing
+    @test check_no_stale_explicit_imports(SimpleNonlinearSolve) === nothing
+    @test check_all_qualified_accesses_via_owners(SimpleNonlinearSolve) === nothing
+end

From d2659d6db359a8da0338c62595882d9a5fafd335 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 6 Oct 2024 21:35:39 -0400
Subject: [PATCH 579/700] chore: run formatter

---
 lib/SimpleNonlinearSolve/test/runtests.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index dde4bacf4..a22783e59 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -7,5 +7,5 @@ const GROUP = lowercase(get(ENV, "GROUP", "All"))
 if GROUP == "all"
     @run_package_tests
 else
-    @run_package_tests filter=ti->(Symbol(GROUP) in ti.tags)
+    @run_package_tests filter = ti -> (Symbol(GROUP) in ti.tags)
 end

From 2f9de5908b18fbd7d277d7e2dfd4ac27d528783d Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 6 Oct 2024 21:37:35 -0400
Subject: [PATCH 580/700] fix: typos

---
 .typos.toml                                  | 3 ++-
 lib/SimpleNonlinearSolve/src/trust_region.jl | 2 +-
 2 files changed, 3 insertions(+), 2 deletions(-)

diff --git a/.typos.toml b/.typos.toml
index d78350bfb..4bde74f7c 100644
--- a/.typos.toml
+++ b/.typos.toml
@@ -1,2 +1,3 @@
 [default.extend-words]
-SER = "SER"
\ No newline at end of file
+SER = "SER"
+fo = "fo"
diff --git a/lib/SimpleNonlinearSolve/src/trust_region.jl b/lib/SimpleNonlinearSolve/src/trust_region.jl
index 27b210d65..47acc5437 100644
--- a/lib/SimpleNonlinearSolve/src/trust_region.jl
+++ b/lib/SimpleNonlinearSolve/src/trust_region.jl
@@ -189,7 +189,7 @@ function dogleg_method!!(cache, J, f, g, Δ)
     # Test if the full step is within the trust region
     (L2_NORM(δN) ≤ Δ) && return δN
 
-    # Calcualte Cauchy point, optimum along the steepest descent direction
+    # Calculate Cauchy point, optimum along the steepest descent direction
     @bb δsd .= g
     @bb @. δsd *= -1
     norm_δsd = L2_NORM(δsd)

From 156aca56aa635741aae895246d8f5fff0d7b5666 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 6 Oct 2024 21:56:09 -0400
Subject: [PATCH 581/700] test: bring over more tests

---
 .github/workflows/CI_SimpleNonlinearSolve.yml |  5 +++
 .../test/core/allocation_tests.jl             | 40 +++++++++++++++++++
 .../test/core/matrix_resizing_tests.jl        | 19 +++++++++
 3 files changed, 64 insertions(+)
 create mode 100644 lib/SimpleNonlinearSolve/test/core/allocation_tests.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl

diff --git a/.github/workflows/CI_SimpleNonlinearSolve.yml b/.github/workflows/CI_SimpleNonlinearSolve.yml
index 9854b6d99..1f8306a8c 100644
--- a/.github/workflows/CI_SimpleNonlinearSolve.yml
+++ b/.github/workflows/CI_SimpleNonlinearSolve.yml
@@ -32,6 +32,9 @@ jobs:
           - ubuntu-latest
           - macos-latest
           - windows-latest
+        group:
+          - core
+          - adjoint
     steps:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v2
@@ -60,6 +63,8 @@ jobs:
           Pkg.instantiate()
           Pkg.test(; coverage=true)
         shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SimpleNonlinearSolve {0}
+        env:
+          GROUP: ${{ matrix.group }}
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/SimpleNonlinearSolve/src,lib/SimpleNonlinearSolve/ext
diff --git a/lib/SimpleNonlinearSolve/test/core/allocation_tests.jl b/lib/SimpleNonlinearSolve/test/core/allocation_tests.jl
new file mode 100644
index 000000000..5da872b71
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/allocation_tests.jl
@@ -0,0 +1,40 @@
+@itesitem "Allocation Tests" tags=[:core] begin
+    using SimpleNonlinearSolve, StaticArrays, AllocCheck
+
+    quadratic_f(u, p) = u .* u .- p
+    quadratic_f!(du, u, p) = (du .= u .* u .- p)
+
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        SimpleNewtonRaphson(),
+        SimpleTrustRegion(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+        SimpleBroyden(),
+        SimpleLimitedMemoryBroyden(),
+        SimpleKlement(),
+        SimpleHalley(),
+        SimpleBroyden(; linesearch = Val(true)),
+        SimpleLimitedMemoryBroyden(; linesearch = Val(true))
+    )
+        @check_allocs nlsolve(prob, alg) = SciMLBase.solve(prob, alg; abstol = 1e-9)
+
+        nlprob_scalar = NonlinearProblem{false}(quadratic_f, 1.0, 2.0)
+        nlprob_sa = NonlinearProblem{false}(quadratic_f, @SVector[1.0, 1.0], 2.0)
+
+        try
+            nlsolve(nlprob_scalar, alg)
+            @test true
+        catch e
+            @error e
+            @test false
+        end
+
+        # ForwardDiff allocates for hessian since we don't propagate the chunksize
+        try
+            nlsolve(nlprob_sa, alg)
+            @test true
+        catch e
+            @error e
+            @test false broken = (alg isa SimpleHalley)
+        end
+    end
+end
diff --git a/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl b/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl
new file mode 100644
index 000000000..17d9a6f42
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/matrix_resizing_tests.jl
@@ -0,0 +1,19 @@
+@testitem "Matrix Resizing" tags=[:core] begin
+    ff(u, p) = u .* u .- p
+    u0 = ones(2, 3)
+    p = 2.0
+    vecprob = NonlinearProblem(ff, vec(u0), p)
+    prob = NonlinearProblem(ff, u0, p)
+
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        SimpleKlement(),
+        SimpleBroyden(),
+        SimpleNewtonRaphson(),
+        SimpleDFSane(),
+        SimpleLimitedMemoryBroyden(; threshold = Val(2)),
+        SimpleTrustRegion(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true))
+    )
+        @test vec(solve(prob, alg).u) ≈ solve(vecprob, alg).u
+    end
+end

From 51eca2a9e3c7f74d5132ed2420ffb71b5d7a9e40 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 6 Oct 2024 21:58:15 -0400
Subject: [PATCH 582/700] test: adjoints

---
 .../test/core/adjoint_tests.jl                | 21 +++++++++++++++++++
 1 file changed, 21 insertions(+)
 create mode 100644 lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl

diff --git a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
new file mode 100644
index 000000000..c56850eb5
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
@@ -0,0 +1,21 @@
+@testitem "Simple Adjoint Test" tags=[:adjoint] begin
+    using ForwardDiff, ReverseDiff, SciMLSensitivity, Tracker, Zygote
+
+    ff(u, p) = u .^ 2 .- p
+
+    function solve_nlprob(p)
+        prob = NonlinearProblem{false}(ff, [1.0, 2.0], p)
+        sol = solve(prob, SimpleNewtonRaphson())
+        res = sol isa AbstractArray ? sol : sol.u
+        return sum(abs2, res)
+    end
+
+    p = [3.0, 2.0]
+
+    ∂p_zygote = only(Zygote.gradient(solve_nlprob, p))
+    ∂p_forwarddiff = ForwardDiff.gradient(solve_nlprob, p)
+    ∂p_tracker = Tracker.data(only(Tracker.gradient(solve_nlprob, p)))
+    ∂p_reversediff = ReverseDiff.gradient(solve_nlprob, p)
+    @test ∂p_zygote ≈ ∂p_tracker ≈ ∂p_reversediff
+    @test ∂p_zygote ≈ ∂p_forwarddiff ≈ ∂p_tracker ≈ ∂p_reversediff
+end

From 8af21b54edb9b83c8dede119348228c47855e653 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 6 Oct 2024 22:17:17 -0400
Subject: [PATCH 583/700] fix: minor fixes to support adjoints

---
 lib/NonlinearSolveBase/Project.toml           |  3 +++
 .../ext/NonlinearSolveBaseDiffEqBaseExt.jl    | 16 ++++++++++++++
 lib/SimpleNonlinearSolve/Project.toml         |  5 +++--
 .../ext/SimpleNonlinearSolveDiffEqBaseExt.jl  |  2 ++
 .../ext/SimpleNonlinearSolveReverseDiffExt.jl |  2 ++
 .../ext/SimpleNonlinearSolveTrackerExt.jl     |  2 ++
 .../src/SimpleNonlinearSolve.jl               | 22 +++++++++++++++----
 .../test/core/adjoint_tests.jl                |  3 ++-
 .../test/core/allocation_tests.jl             |  2 +-
 .../test/core/rootfind_tests.jl               |  0
 10 files changed, 49 insertions(+), 8 deletions(-)
 create mode 100644 lib/NonlinearSolveBase/ext/NonlinearSolveBaseDiffEqBaseExt.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 3999de770..a89d035cf 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -20,10 +20,12 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [weakdeps]
+DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [extensions]
+NonlinearSolveBaseDiffEqBaseExt = "DiffEqBase"
 NonlinearSolveBaseForwardDiffExt = "ForwardDiff"
 NonlinearSolveBaseSparseArraysExt = "SparseArrays"
 
@@ -33,6 +35,7 @@ ArrayInterface = "7.9"
 CommonSolve = "0.2.4"
 Compat = "4.15"
 ConcreteStructs = "0.2.3"
+DiffEqBase = "6.149"
 DifferentiationInterface = "0.6.1"
 EnzymeCore = "0.8"
 FastClosures = "0.3"
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseDiffEqBaseExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseDiffEqBaseExt.jl
new file mode 100644
index 000000000..346a5ee55
--- /dev/null
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseDiffEqBaseExt.jl
@@ -0,0 +1,16 @@
+module NonlinearSolveBaseDiffEqBaseExt
+
+using DiffEqBase: DiffEqBase
+using SciMLBase: remake
+
+using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem
+
+function DiffEqBase.get_concrete_problem(
+        prob::ImmutableNonlinearProblem, isadapt; kwargs...)
+    u0 = DiffEqBase.get_concrete_u0(prob, isadapt, nothing, kwargs)
+    u0 = DiffEqBase.promote_u0(u0, prob.p, nothing)
+    p = DiffEqBase.get_concrete_p(prob, kwargs)
+    return remake(prob; u0 = u0, p = p)
+end
+
+end
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index fae63544a..8c6322730 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -46,7 +46,7 @@ CUDA = "5.3"
 ChainRulesCore = "1.24"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
-DiffEqBase = "6.155"
+DiffEqBase = "6.149"
 DifferentiationInterface = "0.6.1"
 Enzyme = "0.13"
 ExplicitImports = "1.9"
@@ -79,6 +79,7 @@ julia = "1.10"
 AllocCheck = "9b6a8646-10ed-4001-bbdc-1d2f46dfbb1a"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
@@ -95,4 +96,4 @@ Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["AllocCheck", "Aqua", "CUDA", "Enzyme", "ExplicitImports", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReverseDiff", "SciMLSensitivity", "StaticArrays", "Test", "TestItemRunner", "Tracker", "Zygote"]
+test = ["AllocCheck", "Aqua", "CUDA", "DiffEqBase", "Enzyme", "ExplicitImports", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReverseDiff", "SciMLSensitivity", "StaticArrays", "Test", "TestItemRunner", "Tracker", "Zygote"]
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveDiffEqBaseExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveDiffEqBaseExt.jl
index 950a04019..4954ffb26 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveDiffEqBaseExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveDiffEqBaseExt.jl
@@ -4,6 +4,8 @@ using DiffEqBase: DiffEqBase
 
 using SimpleNonlinearSolve: SimpleNonlinearSolve
 
+SimpleNonlinearSolve.is_extension_loaded(::Val{:DiffEqBase}) = true
+
 function SimpleNonlinearSolve.solve_adjoint_internal(args...; kwargs...)
     return DiffEqBase._solve_adjoint(args...; kwargs...)
 end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
index 7b476b3c5..0a407986e 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
@@ -32,6 +32,8 @@ for pType in (ImmutableNonlinearProblem, NonlinearLeastSquaresProblem)
             ∂prob, ∂sensealg, ∂u0, ∂p, _, ∂args... = ∇internal(Δ...)
             return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
         end
+
+        return Array(out), ∇simplenonlinearsolve_solve_up
     end
 end
 
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
index ead5a8e29..d29c2ac61 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
@@ -31,6 +31,8 @@ for pType in (ImmutableNonlinearProblem, NonlinearLeastSquaresProblem)
             ∂prob, ∂sensealg, ∂u0, ∂p, _, ∂args... = ∇internal(Tracker.data(Δ))
             return (∂prob, ∂sensealg, ∂u0, nothing, ∂p, nothing, nothing, ∂args...)
         end
+
+        return out, ∇simplenonlinearsolve_solve_up
     end
 end
 
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 0b33c923e..23de7dbc6 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -20,7 +20,8 @@ using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff
 
 using BracketingNonlinearSolve: Alefeld, Bisection, Brent, Falsi, ITP, Ridder
-using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, L2_NORM
+using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, L2_NORM,
+                          nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution
 
 const DI = DifferentiationInterface
 
@@ -47,6 +48,20 @@ function CommonSolve.solve(prob::NonlinearProblem,
     return solve(prob, alg, args...; kwargs...)
 end
 
+function CommonSolve.solve(
+        prob::NonlinearProblem{<:Union{Number, <:AbstractArray}, iip,
+            <:Union{
+                <:ForwardDiff.Dual{T, V, P}, <:AbstractArray{<:ForwardDiff.Dual{T, V, P}}}},
+        alg::AbstractSimpleNonlinearSolveAlgorithm,
+        args...;
+        kwargs...) where {T, V, P, iip}
+    prob = convert(ImmutableNonlinearProblem, prob)
+    sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
+    dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
+    return SciMLBase.build_solution(
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+end
+
 function CommonSolve.solve(
         prob::ImmutableNonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
         args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...)
@@ -59,9 +74,8 @@ function CommonSolve.solve(
         p === nothing, alg, args...; prob.kwargs..., kwargs...)
 end
 
-function simplenonlinearsolve_solve_up(
-        prob::ImmutableNonlinearProblem, sensealg, u0, u0_changed, p, p_changed,
-        alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...)
+function simplenonlinearsolve_solve_up(prob::ImmutableNonlinearProblem, sensealg, u0,
+        u0_changed, p, p_changed, alg, args...; kwargs...)
     (u0_changed || p_changed) && (prob = remake(prob; u0, p))
     return SciMLBase.__solve(prob, alg, args...; kwargs...)
 end
diff --git a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
index c56850eb5..449801ad7 100644
--- a/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/adjoint_tests.jl
@@ -1,5 +1,6 @@
 @testitem "Simple Adjoint Test" tags=[:adjoint] begin
-    using ForwardDiff, ReverseDiff, SciMLSensitivity, Tracker, Zygote
+    using ForwardDiff, ReverseDiff, SciMLSensitivity, Tracker, Zygote, DiffEqBase,
+          SimpleNonlinearSolve
 
     ff(u, p) = u .^ 2 .- p
 
diff --git a/lib/SimpleNonlinearSolve/test/core/allocation_tests.jl b/lib/SimpleNonlinearSolve/test/core/allocation_tests.jl
index 5da872b71..67cee39c0 100644
--- a/lib/SimpleNonlinearSolve/test/core/allocation_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/allocation_tests.jl
@@ -34,7 +34,7 @@
             @test true
         catch e
             @error e
-            @test false broken = (alg isa SimpleHalley)
+            @test false broken=(alg isa SimpleHalley)
         end
     end
 end
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
new file mode 100644
index 000000000..e69de29bb

From 4d06043b6d1387ed0c5ff570650952c0ff442146 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 6 Oct 2024 23:00:18 -0400
Subject: [PATCH 584/700] test: 23 test problems

---
 .../test/core/23_test_problems_tests.jl       | 103 ++++++++++++++++++
 .../test/core/exotic_type_tests.jl            |   6 +-
 .../test/core/forward_diff_tests.jl           |   0
 .../test/gpu/cuda_tests.jl                    |  18 +--
 4 files changed, 116 insertions(+), 11 deletions(-)
 create mode 100644 lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
 create mode 100644 lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl

diff --git a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
new file mode 100644
index 000000000..7bb28c649
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
@@ -0,0 +1,103 @@
+@testsnippet RobustnessTestSnippet begin
+    using NonlinearProblemLibrary, NonlinearSolveBase, LinearAlgebra
+
+    problems = NonlinearProblemLibrary.problems
+    dicts = NonlinearProblemLibrary.dicts
+
+    function test_on_library(
+            problems, dicts, alg_ops, broken_tests, ϵ = 1e-4; skip_tests = nothing)
+        for (idx, (problem, dict)) in enumerate(zip(problems, dicts))
+            x = dict["start"]
+            res = similar(x)
+            nlprob = NonlinearProblem(problem, copy(x))
+            @testset "$idx: $(dict["title"])" begin
+                for alg in alg_ops
+                    try
+                        sol = solve(nlprob, alg;
+                            termination_condition = AbsNormTerminationMode(norm))
+                        problem(res, sol.u, nothing)
+
+                        skip = skip_tests !== nothing && idx in skip_tests[alg]
+                        if skip
+                            @test_skip norm(res) ≤ ϵ
+                            continue
+                        end
+                        broken = idx in broken_tests[alg] ? true : false
+                        @test norm(res)≤ϵ broken=broken
+                    catch e
+                        @error e
+                        broken = idx in broken_tests[alg] ? true : false
+                        if broken
+                            @test false broken=true
+                        else
+                            @test 1 == 2
+                        end
+                    end
+                end
+            end
+        end
+    end
+end
+
+@testitem "23 Test Problems: SimpleNewtonRaphson" setup=[RobustnessTestSnippet] tags=[:core] begin
+    alg_ops = (SimpleNewtonRaphson(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = []
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "23 Test Problems: SimpleHalley" setup=[RobustnessTestSnippet] tags=[:core] begin
+    alg_ops = (SimpleHalley(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    if Sys.isapple()
+        broken_tests[alg_ops[1]] = [1, 5, 11, 15, 16, 18]
+    else
+        broken_tests[alg_ops[1]] = [1, 5, 15, 16, 18]
+    end
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "23 Test Problems: SimpleTrustRegion" setup=[RobustnessTestSnippet] tags=[:core] begin
+    alg_ops = (SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [3, 15, 16, 21]
+    broken_tests[alg_ops[2]] = [15, 16]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "23 Test Problems: SimpleDFSane" setup=[RobustnessTestSnippet] tags=[:core] begin
+    alg_ops = (SimpleDFSane(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    if Sys.isapple()
+        broken_tests[alg_ops[1]] = [1, 2, 3, 5, 6, 21]
+    else
+        broken_tests[alg_ops[1]] = [1, 2, 3, 4, 5, 6, 11, 21]
+    end
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "23 Test Problems: SimpleBroyden" setup=[RobustnessTestSnippet] tags=[:core] begin
+    alg_ops = (SimpleBroyden(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [1, 5, 11]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "23 Test Problems: SimpleKlement" setup=[RobustnessTestSnippet] tags=[:core] begin
+    alg_ops = (SimpleKlement(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 11, 12, 22]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
diff --git a/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl b/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
index e19a3d32e..7e7223ea0 100644
--- a/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
@@ -9,13 +9,13 @@
     prob_oop_bf = NonlinearProblem{false}(fn_oop, u0, BigFloat(2))
 
     @testset "$(nameof(typeof(alg)))" for alg in (
-        SimpleNewtonRaphson(),
+        SimpleNewtonRaphson(; autodiff = AutoForwardDiff()),
         SimpleBroyden(),
         SimpleKlement(),
         SimpleDFSane(),
-        SimpleTrustRegion(),
+        SimpleTrustRegion(; autodiff = AutoForwardDiff()),
         SimpleLimitedMemoryBroyden(),
-        SimpleHalley()
+        SimpleHalley(; autodiff = AutoForwardDiff())
     )
         sol = solve(prob_oop_bf, alg)
         @test maximum(abs, sol.resid) < 1e-6
diff --git a/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl b/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
index 8ecee2fed..d51ce353f 100644
--- a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
@@ -8,14 +8,15 @@
         f!(du, u, p) = (du .= u .* u .- 2)
 
         @testset "$(nameof(typeof(alg)))" for alg in (
-            SimpleNewtonRaphson(),
+            SimpleNewtonRaphson(; autodiff = AutoForwardDiff()),
             SimpleDFSane(),
-            SimpleTrustRegion(),
-            SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+            SimpleTrustRegion(; autodiff = AutoForwardDiff()),
+            SimpleTrustRegion(;
+                nlsolve_update_rule = Val(true), autodiff = AutoForwardDiff()),
             SimpleBroyden(),
             SimpleLimitedMemoryBroyden(),
             SimpleKlement(),
-            SimpleHalley(),
+            SimpleHalley(; autodiff = AutoForwardDiff()),
             SimpleBroyden(; linesearch = Val(true)),
             SimpleLimitedMemoryBroyden(; linesearch = Val(true))
         )
@@ -63,14 +64,15 @@ end
             prob = convert(ImmutableNonlinearProblem, NonlinearProblem{false}(f, u0, 2.0f0))
 
             @testset "$(nameof(typeof(alg)))" for alg in (
-                SimpleNewtonRaphson(),
+                SimpleNewtonRaphson(; autodiff = AutoForwardDiff()),
                 SimpleDFSane(),
-                SimpleTrustRegion(),
-                SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+                SimpleTrustRegion(; autodiff = AutoForwardDiff()),
+                SimpleTrustRegion(;
+                    nlsolve_update_rule = Val(true), autodiff = AutoForwardDiff()),
                 SimpleBroyden(),
                 SimpleLimitedMemoryBroyden(),
                 SimpleKlement(),
-                SimpleHalley(),
+                SimpleHalley(; autodiff = AutoForwardDiff()),
                 SimpleBroyden(; linesearch = Val(true)),
                 SimpleLimitedMemoryBroyden(; linesearch = Val(true))
             )

From 46c40ca24a7f1e0986a3afd07db2d1113603107e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 7 Oct 2024 11:46:01 -0400
Subject: [PATCH 585/700] fix: simple klement implementation

---
 lib/SimpleNonlinearSolve/src/klement.jl | 1 +
 1 file changed, 1 insertion(+)

diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 055f65bc3..31c4cca96 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -12,6 +12,7 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleKlement,
     x = Utils.maybe_unaliased(prob.u0, alias_u0)
     T = eltype(x)
     fx = Utils.get_fx(prob, x)
+    fx = Utils.eval_f(prob, fx, x)
 
     abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
         prob, abstol, reltol, fx, x, termination_condition, Val(:simple))

From c4e68b42e2c8d17a9e44cb68f9d4c16df9d8edc3 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 7 Oct 2024 11:52:31 -0400
Subject: [PATCH 586/700] chore: run the formatter

---
 lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl | 1 +
 lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl     | 1 +
 2 files changed, 2 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl b/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
index e69de29bb..8b1378917 100644
--- a/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
@@ -0,0 +1 @@
+
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index e69de29bb..8b1378917 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -0,0 +1 @@
+

From 083b4d5f2f14ce7c92bc64aaf13d529b67fab97c Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 7 Oct 2024 15:41:40 -0400
Subject: [PATCH 587/700] feat: bump major version of SimpleNonlinearSolve

---
 lib/NonlinearSolveBase/src/NonlinearSolveBase.jl    |  7 ++++---
 lib/SimpleNonlinearSolve/Project.toml               |  4 +---
 .../src/SimpleNonlinearSolve.jl                     | 13 ++++++++-----
 3 files changed, 13 insertions(+), 11 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 5e1a37326..645b84959 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -35,8 +35,9 @@ include("autodiff.jl")
     (select_forward_mode_autodiff, select_reverse_mode_autodiff,
         select_jacobian_autodiff))
 
-export RelTerminationMode, AbsTerminationMode, NormTerminationMode, RelNormTerminationMode,
-       AbsNormTerminationMode, RelNormSafeTerminationMode, AbsNormSafeTerminationMode,
-       RelNormSafeNormTerminationMode, AbsNormSafeNormTerminationMode
+export RelTerminationMode, AbsTerminationMode,
+       NormTerminationMode, RelNormTerminationMode, AbsNormTerminationMode,
+       RelNormSafeTerminationMode, AbsNormSafeTerminationMode,
+       RelNormSafeBestTerminationMode, AbsNormSafeBestTerminationMode
 
 end
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 8c6322730..5f708e564 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "1.13.0"
+version = "2.0.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -19,7 +19,6 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
-Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
@@ -63,7 +62,6 @@ Pkg = "1.10"
 PolyesterForwardDiff = "0.1"
 PrecompileTools = "1.2"
 Random = "1.10"
-Reexport = "1.2"
 ReverseDiff = "1.15"
 SciMLBase = "2.50"
 SciMLSensitivity = "7.68"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 23de7dbc6..4ed53295e 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -8,13 +8,12 @@ using LineSearch: LiFukushimaLineSearch
 using LinearAlgebra: LinearAlgebra, dot
 using MaybeInplace: @bb, setindex_trait, CannotSetindex, CanSetindex
 using PrecompileTools: @compile_workload, @setup_workload
-using Reexport: @reexport
-@reexport using SciMLBase  # I don't like this but needed to avoid a breaking change
-using SciMLBase: AbstractNonlinearAlgorithm, NonlinearProblem, ReturnCode
+using SciMLBase: AbstractNonlinearAlgorithm, NonlinearProblem, NonlinearLeastSquaresProblem,
+                 IntervalNonlinearProblem, ReturnCode
 using StaticArraysCore: StaticArray, SArray, SVector, MArray
 
 # AD Dependencies
-using ADTypes: AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
+using ADTypes: ADTypes
 using DifferentiationInterface: DifferentiationInterface
 using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff
@@ -118,13 +117,17 @@ function solve_adjoint_internal end
     end
 end
 
-export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
+export IntervalNonlinearProblem
 
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
+export NonlinearProblem, NonlinearLeastSquaresProblem
+
 export SimpleBroyden, SimpleKlement, SimpleLimitedMemoryBroyden
 export SimpleDFSane
 export SimpleGaussNewton, SimpleNewtonRaphson, SimpleTrustRegion
 export SimpleHalley
 
+export solve
+
 end

From 26d50228e56acd32e453af1d41accb5dec8c9476 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 7 Oct 2024 17:13:19 -0400
Subject: [PATCH 588/700] test: comprehensive testing of root finding

---
 docs/src/release_notes.md                     |  22 ++-
 .../src/termination_conditions.jl             |   4 +-
 .../src/SimpleNonlinearSolve.jl               |  10 +-
 lib/SimpleNonlinearSolve/src/halley.jl        |   3 +-
 lib/SimpleNonlinearSolve/src/lbroyden.jl      |   2 +-
 .../test/core/23_test_problems_tests.jl       |  11 +-
 .../test/core/exotic_type_tests.jl            |   2 +-
 .../test/core/rootfind_tests.jl               | 154 ++++++++++++++++++
 .../test/gpu/cuda_tests.jl                    |   4 +-
 9 files changed, 195 insertions(+), 17 deletions(-)

diff --git a/docs/src/release_notes.md b/docs/src/release_notes.md
index 9d517267e..0208b1e66 100644
--- a/docs/src/release_notes.md
+++ b/docs/src/release_notes.md
@@ -1,6 +1,24 @@
 # Release Notes
 
-## Breaking Changes in `NonlinearSolve.jl` v3
+## Oct '24
+
+### Breaking Changes in `NonlinearSolve.jl` v4
+
+### Breaking Changes in `SimpleNonlinearSolve.jl` v2
+
+  - `Auto*` structs are no longer exported. Load `ADTypes` to access them.
+  - Use of termination conditions from `DiffEqBase` has been removed. Use the termination
+    conditions from `NonlinearSolveBase` instead.
+  - We no longer export the entire `SciMLBase`. Instead selected functionality relevant to
+    `SimpleNonlinearSolve` has been exported.
+  - If no autodiff is provided, we now choose from a list of autodiffs based on the packages
+    loaded. For example, if `Enzyme` is loaded, we will default to that. In general, we
+    don't guarantee the exact autodiff selected if `autodiff` is not provided (i.e.
+    `nothing`).
+
+## Dec '23
+
+### Breaking Changes in `NonlinearSolve.jl` v3
 
   - `GeneralBroyden` and `GeneralKlement` have been renamed to `Broyden` and `Klement`
     respectively.
@@ -8,7 +26,7 @@
   - The old style of specifying autodiff with `chunksize`, `standardtag`, etc. has been
     deprecated in favor of directly specifying the autodiff type, like `AutoForwardDiff`.
 
-## Breaking Changes in `SimpleNonlinearSolve.jl` v1
+### Breaking Changes in `SimpleNonlinearSolve.jl` v1
 
   - Batched solvers have been removed in favor of `BatchedArrays.jl`. Stay tuned for detailed
     tutorials on how to use `BatchedArrays.jl` with `NonlinearSolve` & `SimpleNonlinearSolve`
diff --git a/lib/NonlinearSolveBase/src/termination_conditions.jl b/lib/NonlinearSolveBase/src/termination_conditions.jl
index 7978c19b8..3e957f139 100644
--- a/lib/NonlinearSolveBase/src/termination_conditions.jl
+++ b/lib/NonlinearSolveBase/src/termination_conditions.jl
@@ -26,7 +26,7 @@ function update_u!!(cache::NonlinearTerminationModeCache, u)
     if cache.u isa AbstractArray && ArrayInterface.can_setindex(cache.u)
         copyto!(cache.u, u)
     else
-        cache.u .= u
+        cache.u = u
     end
 end
 
@@ -60,6 +60,8 @@ function SciMLBase.init(
         else
             u_diff_cache = u_unaliased
         end
+        best_value = initial_objective
+        max_stalled_steps = mode.max_stalled_steps
     else
         initial_objective = nothing
         objectives_trace = nothing
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 4ed53295e..081201a24 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -1,19 +1,19 @@
 module SimpleNonlinearSolve
 
 using Accessors: @reset
-using CommonSolve: CommonSolve, solve
+using CommonSolve: CommonSolve, solve, init, solve!
 using ConcreteStructs: @concrete
 using FastClosures: @closure
 using LineSearch: LiFukushimaLineSearch
 using LinearAlgebra: LinearAlgebra, dot
 using MaybeInplace: @bb, setindex_trait, CannotSetindex, CanSetindex
 using PrecompileTools: @compile_workload, @setup_workload
-using SciMLBase: AbstractNonlinearAlgorithm, NonlinearProblem, NonlinearLeastSquaresProblem,
-                 IntervalNonlinearProblem, ReturnCode
+using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, NonlinearFunction, NonlinearProblem,
+                 NonlinearLeastSquaresProblem, IntervalNonlinearProblem, ReturnCode, remake
 using StaticArraysCore: StaticArray, SArray, SVector, MArray
 
 # AD Dependencies
-using ADTypes: ADTypes
+using ADTypes: ADTypes, AutoForwardDiff
 using DifferentiationInterface: DifferentiationInterface
 using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff
@@ -121,7 +121,7 @@ export IntervalNonlinearProblem
 
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
-export NonlinearProblem, NonlinearLeastSquaresProblem
+export NonlinearFunction, NonlinearProblem, NonlinearLeastSquaresProblem
 
 export SimpleBroyden, SimpleKlement, SimpleLimitedMemoryBroyden
 export SimpleDFSane
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 6b8948248..30eb1a821 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -35,7 +35,8 @@ function SciMLBase.__solve(
     abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
         prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
 
-    autodiff = NonlinearSolveBase.select_jacobian_autodiff(prob, alg.autodiff)
+    # The way we write the 2nd order derivatives, we know Enzyme won't work there
+    autodiff = alg.autodiff === nothing ? AutoForwardDiff() : alg.autodiff
 
     @bb xo = copy(x)
 
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index ce39ca10d..3a17e0936 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -38,7 +38,7 @@ function SciMLBase.__solve(
         args...; termination_condition = nothing, kwargs...)
     if prob.u0 isa SArray
         if termination_condition === nothing ||
-           termination_condition isa AbsNormTerminationMode
+           termination_condition isa NonlinearSolveBase.AbsNormTerminationMode
             return internal_static_solve(
                 prob, alg, args...; termination_condition, kwargs...)
         end
diff --git a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
index 7bb28c649..6dd85b94b 100644
--- a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
@@ -1,5 +1,5 @@
 @testsnippet RobustnessTestSnippet begin
-    using NonlinearProblemLibrary, NonlinearSolveBase, LinearAlgebra
+    using NonlinearProblemLibrary, NonlinearSolveBase, LinearAlgebra, ADTypes
 
     problems = NonlinearProblemLibrary.problems
     dicts = NonlinearProblemLibrary.dicts
@@ -40,7 +40,7 @@
 end
 
 @testitem "23 Test Problems: SimpleNewtonRaphson" setup=[RobustnessTestSnippet] tags=[:core] begin
-    alg_ops = (SimpleNewtonRaphson(),)
+    alg_ops = (SimpleNewtonRaphson(; autodiff = AutoForwardDiff()),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
     broken_tests[alg_ops[1]] = []
@@ -49,7 +49,7 @@ end
 end
 
 @testitem "23 Test Problems: SimpleHalley" setup=[RobustnessTestSnippet] tags=[:core] begin
-    alg_ops = (SimpleHalley(),)
+    alg_ops = (SimpleHalley(; autodiff = AutoForwardDiff()),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
     if Sys.isapple()
@@ -62,7 +62,10 @@ end
 end
 
 @testitem "23 Test Problems: SimpleTrustRegion" setup=[RobustnessTestSnippet] tags=[:core] begin
-    alg_ops = (SimpleTrustRegion(), SimpleTrustRegion(; nlsolve_update_rule = Val(true)))
+    alg_ops = (
+        SimpleTrustRegion(; autodiff = AutoForwardDiff()),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true), autodiff = AutoForwardDiff())
+    )
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
     broken_tests[alg_ops[1]] = [3, 15, 16, 21]
diff --git a/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl b/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
index 7e7223ea0..6227348a2 100644
--- a/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/exotic_type_tests.jl
@@ -1,5 +1,5 @@
 @testitem "BigFloat Support" tags=[:core] begin
-    using SimpleNonlinearSolve, LinearAlgebra
+    using SimpleNonlinearSolve, LinearAlgebra, ADTypes, SciMLBase
 
     fn_iip = NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p)
     fn_oop = NonlinearFunction{false}((u, p) -> u .* u .- p)
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index 8b1378917..c99b670cb 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -1 +1,155 @@
+@testsnippet RootfindTestSnippet begin
+    using StaticArrays, Random, LinearAlgebra, ForwardDiff, NonlinearSolveBase, SciMLBase
+    using ADTypes, PolyesterForwardDiff, Enzyme, ReverseDiff
 
+    quadratic_f(u, p) = u .* u .- p
+    quadratic_f!(du, u, p) = (du .= u .* u .- p)
+
+    function newton_fails(u, p)
+        return 0.010000000000000002 .+
+               10.000000000000002 ./ (1 .+
+                (0.21640425613334457 .+
+                 216.40425613334457 ./ (1 .+
+                  (0.21640425613334457 .+
+                   216.40425613334457 ./ (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^
+                2.0) .- 0.0011552453009332421u .- p
+    end
+
+    const TERMINATION_CONDITIONS = [
+        NormTerminationMode(Base.Fix1(maximum, abs)),
+        RelTerminationMode(),
+        RelNormTerminationMode(Base.Fix1(maximum, abs)),
+        RelNormSafeTerminationMode(Base.Fix1(maximum, abs)),
+        RelNormSafeBestTerminationMode(Base.Fix1(maximum, abs)),
+        AbsTerminationMode(),
+        AbsNormTerminationMode(Base.Fix1(maximum, abs)),
+        AbsNormSafeTerminationMode(Base.Fix1(maximum, abs)),
+        AbsNormSafeBestTerminationMode(Base.Fix1(maximum, abs))
+    ]
+
+    function run_nlsolve_oop(f::F, u0, p = 2.0; solver) where {F}
+        return solve(NonlinearProblem{false}(f, u0, p), solver; abstol = 1e-9)
+    end
+    function run_nlsolve_iip(f!::F, u0, p = 2.0; solver) where {F}
+        return solve(NonlinearProblem{true}(f!, u0, p), solver; abstol = 1e-9)
+    end
+end
+
+@testitem "First Order Methods" setup=[RootfindTestSnippet] tags=[:core] begin
+    @testset for alg in (
+        SimpleNewtonRaphson,
+        SimpleTrustRegion,
+        (; kwargs...) -> SimpleTrustRegion(; kwargs..., nlsolve_update_rule = Val(true))
+    )
+        @testset for autodiff in (
+            AutoForwardDiff(),
+            AutoFiniteDiff(),
+            AutoReverseDiff(),
+            AutoEnzyme(),
+            nothing
+        )
+            @testset "[OOP] u0: $(typeof(u0))" for u0 in (
+                [1.0, 1.0], @SVector[1.0, 1.0], 1.0)
+                sol = run_nlsolve_oop(quadratic_f, u0; solver = alg(; autodiff))
+                @test SciMLBase.successful_retcode(sol)
+                @test maximum(abs, quadratic_f(sol.u, 2.0)) < 1e-9
+            end
+
+            @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+                sol = run_nlsolve_iip(quadratic_f!, u0; solver = alg(; autodiff))
+                @test SciMLBase.successful_retcode(sol)
+                @test maximum(abs, quadratic_f(sol.u, 2.0)) < 1e-9
+            end
+
+            @testset "Termination Condition: $(nameof(typeof(termination_condition))) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
+                u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
+
+                probN = NonlinearProblem(quadratic_f, u0, 2.0)
+                @test all(solve(
+                    probN, alg(; autodiff = AutoForwardDiff()); termination_condition).u .≈
+                          sqrt(2.0))
+            end
+        end
+    end
+end
+
+@testitem "Second Order Methods" setup=[RootfindTestSnippet] tags=[:core] begin
+    @testset for alg in (
+        SimpleHalley,
+    )
+        @testset for autodiff in (
+            AutoForwardDiff(),
+            AutoFiniteDiff(),
+            AutoReverseDiff(),
+            nothing
+        )
+            @testset "[OOP] u0: $(typeof(u0))" for u0 in (
+                [1.0, 1.0], @SVector[1.0, 1.0], 1.0)
+                sol = run_nlsolve_oop(quadratic_f, u0; solver = alg(; autodiff))
+                @test SciMLBase.successful_retcode(sol)
+                @test maximum(abs, quadratic_f(sol.u, 2.0)) < 1e-9
+            end
+        end
+
+        @testset "Termination Condition: $(nameof(typeof(termination_condition))) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
+            u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
+
+            probN = NonlinearProblem(quadratic_f, u0, 2.0)
+            @test all(solve(
+                probN, alg(; autodiff = AutoForwardDiff()); termination_condition).u .≈
+                      sqrt(2.0))
+        end
+    end
+end
+
+@testitem "Derivative Free Methods" setup=[RootfindTestSnippet] tags=[:core] begin
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        SimpleBroyden(),
+        SimpleKlement(),
+        SimpleDFSane(),
+        SimpleLimitedMemoryBroyden(),
+        SimpleBroyden(; linesearch = Val(true)),
+        SimpleLimitedMemoryBroyden(; linesearch = Val(true))
+    )
+        @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
+            sol = run_nlsolve_oop(quadratic_f, u0; solver = alg)
+            @test SciMLBase.successful_retcode(sol)
+            @test maximum(abs, quadratic_f(sol.u, 2.0)) < 1e-9
+        end
+
+        @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+            sol = run_nlsolve_iip(quadratic_f!, u0; solver = alg)
+            @test SciMLBase.successful_retcode(sol)
+            @test maximum(abs, quadratic_f(sol.u, 2.0)) < 1e-9
+        end
+
+        @testset "Termination Condition: $(nameof(typeof(termination_condition))) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
+            u0 in (1.0, [1.0, 1.0], @SVector[1.0, 1.0])
+
+            probN = NonlinearProblem(quadratic_f, u0, 2.0)
+            @test all(solve(probN, alg; termination_condition).u .≈ sqrt(2.0))
+        end
+    end
+end
+
+@testitem "Newton Fails" setup=[RootfindTestSnippet] tags=[:core] begin
+    u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
+    p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+
+    @testset "$(nameof(typeof(alg)))" for alg in (
+        SimpleDFSane(),
+        SimpleTrustRegion(),
+        SimpleHalley(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true))
+    )
+        sol = run_nlsolve_oop(newton_fails, u0, p; solver = alg)
+        @test SciMLBase.successful_retcode(sol)
+        @test maximum(abs, newton_fails(sol.u, p)) < 1e-9
+    end
+end
+
+@testitem "Kwargs Propagation" setup=[RootfindTestSnippet] tags=[:core] begin
+    prob = NonlinearProblem(quadratic_f, ones(4), 2.0; maxiters = 2)
+    sol = solve(prob, SimpleNewtonRaphson())
+    @test sol.retcode === ReturnCode.MaxIters
+end
diff --git a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
index d51ce353f..09fa52304 100644
--- a/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/gpu/cuda_tests.jl
@@ -1,5 +1,5 @@
 @testitem "Solving on CUDA" tags=[:cuda] begin
-    using StaticArrays, CUDA, SimpleNonlinearSolve
+    using StaticArrays, CUDA, SimpleNonlinearSolve, ADTypes
 
     if CUDA.functional()
         CUDA.allowscalar(false)
@@ -47,7 +47,7 @@
 end
 
 @testitem "CUDA Kernel Launch Test" tags=[:cuda] begin
-    using StaticArrays, CUDA, SimpleNonlinearSolve
+    using StaticArrays, CUDA, SimpleNonlinearSolve, ADTypes
     using NonlinearSolveBase: ImmutableNonlinearProblem
 
     if CUDA.functional()

From 0a2b834856f23671e004ae30b1e48962e39dfdc5 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 7 Oct 2024 18:05:59 -0400
Subject: [PATCH 589/700] feat: support NLLS forward AD

---
 .../ext/NonlinearSolveBaseForwardDiffExt.jl   | 104 ++++++++++++++++--
 .../src/SimpleNonlinearSolve.jl               |  13 +++
 lib/SimpleNonlinearSolve/src/raphson.jl       |   3 +-
 3 files changed, 112 insertions(+), 8 deletions(-)

diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
index 31550da96..7f9aec5a5 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
@@ -1,15 +1,19 @@
 module NonlinearSolveBaseForwardDiffExt
 
 using ADTypes: ADTypes, AutoForwardDiff, AutoPolyesterForwardDiff
+using ArrayInterface: ArrayInterface
 using CommonSolve: solve
+using DifferentiationInterface: DifferentiationInterface, Constant
 using FastClosures: @closure
 using ForwardDiff: ForwardDiff, Dual
+using LinearAlgebra: mul!
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, IntervalNonlinearProblem,
-                 NonlinearProblem,
-                 NonlinearLeastSquaresProblem, remake
+                 NonlinearProblem, NonlinearLeastSquaresProblem, remake
 
 using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, Utils
 
+const DI = DifferentiationInterface
+
 function NonlinearSolveBase.additional_incompatible_backend_check(
         prob::AbstractNonlinearProblem, ::Union{AutoForwardDiff, AutoPolyesterForwardDiff})
     return !ForwardDiff.can_dual(eltype(prob.u0))
@@ -50,22 +54,108 @@ function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
     return sol, partials
 end
 
+function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
+        prob::NonlinearLeastSquaresProblem, alg, args...; kwargs...)
+    p = Utils.value(prob.p)
+    newprob = remake(prob; p, u0 = Utils.value(prob.u0))
+    sol = solve(newprob, alg, args...; kwargs...)
+    uu = sol.u
+
+    # First check for custom `vjp` then custom `Jacobian` and if nothing is provided use
+    # nested autodiff as the last resort
+    if SciMLBase.has_vjp(prob.f)
+        if SciMLBase.isinplace(prob)
+            vjp_fn = @closure (du, u, p) -> begin
+                resid = Utils.safe_similar(du, length(sol.resid))
+                prob.f(resid, u, p)
+                prob.f.vjp(du, resid, u, p)
+                du .*= 2
+                return nothing
+            end
+        else
+            vjp_fn = @closure (u, p) -> begin
+                resid = prob.f(u, p)
+                return reshape(2 .* prob.f.vjp(resid, u, p), size(u))
+            end
+        end
+    elseif SciMLBase.has_jac(prob.f)
+        if SciMLBase.isinplace(prob)
+            vjp_fn = @closure (du, u, p) -> begin
+                J = Utils.safe_similar(du, length(sol.resid), length(u))
+                prob.f.jac(J, u, p)
+                resid = Utils.safe_similar(du, length(sol.resid))
+                prob.f(resid, u, p)
+                mul!(reshape(du, 1, :), vec(resid)', J, 2, false)
+                return nothing
+            end
+        else
+            vjp_fn = @closure (u, p) -> begin
+                return reshape(2 .* vec(prob.f(u, p))' * prob.f.jac(u, p), size(u))
+            end
+        end
+    else
+        # For small problems, nesting ForwardDiff is actually quite fast
+        autodiff = length(uu) + length(sol.resid) ≥ 50 ?
+                   NonlinearSolveBase.select_reverse_mode_autodiff(prob, nothing) :
+                   AutoForwardDiff()
+
+        if SciMLBase.isinplace(prob)
+            vjp_fn = @closure (du, u, p) -> begin
+                resid = Utils.safe_similar(du, length(sol.resid))
+                prob.f(resid, u, p)
+                # Using `Constant` lead to dual ordering issues
+                ff = @closure (du, u) -> prob.f(du, u, p)
+                resid2 = copy(resid)
+                DI.pullback!(ff, resid2, (du,), autodiff, u, (resid,))
+                @. du *= 2
+                return nothing
+            end
+        else
+            vjp_fn = @closure (u, p) -> begin
+                v = prob.f(u, p)
+                # Using `Constant` lead to dual ordering issues
+                ff = Base.Fix2(prob.f, p)
+                res = only(DI.pullback(ff, autodiff, u, (v,)))
+                ArrayInterface.can_setindex(res) || return 2 .* res
+                @. res *= 2
+                return res
+            end
+        end
+    end
+
+    Jₚ = nonlinearsolve_∂f_∂p(prob, vjp_fn, uu, newprob.p)
+    Jᵤ = nonlinearsolve_∂f_∂u(prob, vjp_fn, uu, newprob.p)
+    z = -Jᵤ \ Jₚ
+    pp = prob.p
+    sumfun = ((z, p),) -> map(Base.Fix2(*, ForwardDiff.partials(p)), z)
+
+    if uu isa Number
+        partials = sum(sumfun, zip(z, pp))
+    elseif p isa Number
+        partials = sumfun((z, pp))
+    else
+        partials = sum(sumfun, zip(eachcol(z), pp))
+    end
+
+    return sol, partials
+end
+
 function nonlinearsolve_∂f_∂p(prob, f::F, u, p) where {F}
     if SciMLBase.isinplace(prob)
-        f = @closure p -> begin
+        f2 = @closure p -> begin
             du = Utils.safe_similar(u, promote_type(eltype(u), eltype(p)))
             f(du, u, p)
             return du
         end
     else
-        f = Base.Fix1(f, u)
+        f2 = Base.Fix1(f, u)
     end
     if p isa Number
-        return Utils.safe_reshape(ForwardDiff.derivative(f, p), :, 1)
+        return Utils.safe_reshape(ForwardDiff.derivative(f2, p), :, 1)
     elseif u isa Number
-        return Utils.safe_reshape(ForwardDiff.gradient(f, p), 1, :)
+        return Utils.safe_reshape(ForwardDiff.gradient(f2, p), 1, :)
     else
-        return ForwardDiff.jacobian(f, p)
+        return ForwardDiff.jacobian(f2, p)
     end
 end
 
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 081201a24..e83de5e39 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -61,6 +61,19 @@ function CommonSolve.solve(
         prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
 end
 
+function CommonSolve.solve(
+        prob::NonlinearLeastSquaresProblem{<:Union{Number, <:AbstractArray}, iip,
+            <:Union{
+                <:ForwardDiff.Dual{T, V, P}, <:AbstractArray{<:ForwardDiff.Dual{T, V, P}}}},
+        alg::AbstractSimpleNonlinearSolveAlgorithm,
+        args...;
+        kwargs...) where {T, V, P, iip}
+    sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
+    dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
+    return SciMLBase.build_solution(
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+end
+
 function CommonSolve.solve(
         prob::ImmutableNonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
         args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...)
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index 763fcf32a..a18a1b6be 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -24,7 +24,8 @@ end
 const SimpleGaussNewton = SimpleNewtonRaphson
 
 function SciMLBase.__solve(
-        prob::ImmutableNonlinearProblem, alg::SimpleNewtonRaphson, args...;
+        prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
+        alg::SimpleNewtonRaphson, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
         alias_u0 = false, termination_condition = nothing, kwargs...)
     x = Utils.maybe_unaliased(prob.u0, alias_u0)

From c23eb05c354c6bbbcba6b32c7cd68a81eb05f502 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 7 Oct 2024 18:07:41 -0400
Subject: [PATCH 590/700] ci: other internal deps for NonlinearSolve

---
 .buildkite/pipeline.yml                 | 4 ++--
 .github/workflows/CI_NonlinearSolve.yml | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/.buildkite/pipeline.yml b/.buildkite/pipeline.yml
index f6b4ed6eb..9eb146557 100644
--- a/.buildkite/pipeline.yml
+++ b/.buildkite/pipeline.yml
@@ -14,8 +14,8 @@ steps:
         Pkg.Registry.update();
         # Install packages present in subdirectories
         dev_pks = Pkg.PackageSpec[];
-        for path in ("lib/SciMLJacobianOperators",)
-            push!(dev_pks, Pkg.PackageSpec(; path));
+        for path in ("lib/SciMLJacobianOperators", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveBase", "lib/SimpleNonlinearSolve")
+          push!(dev_pks, Pkg.PackageSpec(; path));
         end
         Pkg.develop(dev_pks);
         Pkg.instantiate();
diff --git a/.github/workflows/CI_NonlinearSolve.yml b/.github/workflows/CI_NonlinearSolve.yml
index d684cb3b7..843a04b54 100644
--- a/.github/workflows/CI_NonlinearSolve.yml
+++ b/.github/workflows/CI_NonlinearSolve.yml
@@ -63,7 +63,7 @@ jobs:
           Pkg.Registry.update()
           # Install packages present in subdirectories
           dev_pks = Pkg.PackageSpec[]
-          for path in ("lib/SciMLJacobianOperators",)
+          for path in ("lib/SciMLJacobianOperators", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveBase", "lib/SimpleNonlinearSolve")
               push!(dev_pks, Pkg.PackageSpec(; path))
           end
           Pkg.develop(dev_pks)

From 42cff673b132218d8ad949d4cd79436c47668b02 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 7 Oct 2024 19:03:03 -0400
Subject: [PATCH 591/700] test: NLLS forwarddiff rules testing

---
 .../src/SimpleNonlinearSolve.jl               |   6 +-
 lib/SimpleNonlinearSolve/src/raphson.jl       |   2 +-
 lib/SimpleNonlinearSolve/src/trust_region.jl  |   2 +-
 lib/SimpleNonlinearSolve/src/utils.jl         |   4 +-
 .../test/core/forward_diff_tests.jl           | 114 ++++++++++++++++++
 5 files changed, 122 insertions(+), 6 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index e83de5e39..b4e641832 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -75,7 +75,8 @@ function CommonSolve.solve(
 end
 
 function CommonSolve.solve(
-        prob::ImmutableNonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
+        prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
+        alg::AbstractSimpleNonlinearSolveAlgorithm,
         args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...)
     if sensealg === nothing && haskey(prob.kwargs, :sensealg)
         sensealg = prob.kwargs[:sensealg]
@@ -86,7 +87,8 @@ function CommonSolve.solve(
         p === nothing, alg, args...; prob.kwargs..., kwargs...)
 end
 
-function simplenonlinearsolve_solve_up(prob::ImmutableNonlinearProblem, sensealg, u0,
+function simplenonlinearsolve_solve_up(
+        prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0,
         u0_changed, p, p_changed, alg, args...; kwargs...)
     (u0_changed || p_changed) && (prob = remake(prob; u0, p))
     return SciMLBase.__solve(prob, alg, args...; kwargs...)
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index a18a1b6be..ebbb5f9f9 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -43,7 +43,7 @@ function SciMLBase.__solve(
 
     @bb xo = similar(x)
     fx_cache = (SciMLBase.isinplace(prob) && !SciMLBase.has_jac(prob.f)) ?
-               safe_similar(fx) : nothing
+               safe_similar(fx) : fx
     jac_cache = Utils.prepare_jacobian(prob, autodiff, fx_cache, x)
     J = Utils.compute_jacobian!!(nothing, prob, autodiff, fx_cache, x, jac_cache)
 
diff --git a/lib/SimpleNonlinearSolve/src/trust_region.jl b/lib/SimpleNonlinearSolve/src/trust_region.jl
index 47acc5437..32e7a6219 100644
--- a/lib/SimpleNonlinearSolve/src/trust_region.jl
+++ b/lib/SimpleNonlinearSolve/src/trust_region.jl
@@ -94,7 +94,7 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleTrustRegi
 
     @bb xo = copy(x)
     fx_cache = (SciMLBase.isinplace(prob) && !SciMLBase.has_jac(prob.f)) ?
-               safe_similar(fx) : nothing
+               safe_similar(fx) : fx
     jac_cache = Utils.prepare_jacobian(prob, autodiff, fx_cache, x)
     J = Utils.compute_jacobian!!(nothing, prob, autodiff, fx_cache, x, jac_cache)
 
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 946c10529..fbc3d3c23 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -183,10 +183,10 @@ function compute_jacobian!!(J, prob, autodiff, fx, x, extras)
     end
     if extras isa AnalyticJacobian
         if SciMLBase.isinplace(prob)
-            prob.jac(J, x, prob.p)
+            prob.f.jac(J, x, prob.p)
             return J
         else
-            return prob.jac(x, prob.p)
+            return prob.f.jac(x, prob.p)
         end
     end
     if SciMLBase.isinplace(prob)
diff --git a/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl b/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
index 8b1378917..0005796f9 100644
--- a/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
@@ -1 +1,115 @@
+@testitem "ForwardDiff.jl Integration NonlinearLeastSquaresProblem" tags=[:core] begin
+    using ForwardDiff, FiniteDiff, SimpleNonlinearSolve, StaticArrays, LinearAlgebra,
+          Zygote, ReverseDiff
+    using DifferentiationInterface
 
+    const DI = DifferentiationInterface
+
+    true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
+
+    θ_true = [1.0, 0.1, 2.0, 0.5]
+    x = [-1.0, -0.5, 0.0, 0.5, 1.0]
+    y_target = true_function(x, θ_true)
+
+    loss_function(θ, p) = true_function(p, θ) .- y_target
+
+    loss_function_jac(θ, p) = ForwardDiff.jacobian(Base.Fix2(loss_function, p), θ)
+
+    loss_function_vjp(v, θ, p) = reshape(vec(v)' * loss_function_jac(θ, p), size(θ))
+
+    function loss_function!(resid, θ, p)
+        ŷ = true_function(p, θ)
+        @. resid = ŷ - y_target
+        return
+    end
+
+    function loss_function_jac!(J, θ, p)
+        J .= ForwardDiff.jacobian(θ -> loss_function(θ, p), θ)
+        return
+    end
+
+    function loss_function_vjp!(vJ, v, θ, p)
+        vec(vJ) .= reshape(vec(v)' * loss_function_jac(θ, p), size(θ))
+        return
+    end
+
+    θ_init = θ_true .+ 0.1
+
+    @testset for alg in (
+        SimpleGaussNewton(),
+        SimpleGaussNewton(; autodiff = AutoForwardDiff()),
+        SimpleGaussNewton(; autodiff = AutoFiniteDiff()),
+        SimpleGaussNewton(; autodiff = AutoReverseDiff())
+    )
+        function obj_1(p)
+            prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, p)
+            sol = solve(prob_oop, alg)
+            return sum(abs2, sol.u)
+        end
+
+        function obj_2(p)
+            ff = NonlinearFunction{false}(
+                loss_function; resid_prototype = zeros(length(y_target)))
+            prob_oop = NonlinearLeastSquaresProblem{false}(ff, θ_init, p)
+            sol = solve(prob_oop, alg)
+            return sum(abs2, sol.u)
+        end
+
+        function obj_3(p)
+            ff = NonlinearFunction{false}(loss_function; vjp = loss_function_vjp)
+            prob_oop = NonlinearLeastSquaresProblem{false}(ff, θ_init, p)
+            sol = solve(prob_oop, alg)
+            return sum(abs2, sol.u)
+        end
+
+        finitediff = DI.gradient(obj_1, AutoFiniteDiff(), x)
+
+        fdiff1 = DI.gradient(obj_1, AutoForwardDiff(), x)
+        fdiff2 = DI.gradient(obj_2, AutoForwardDiff(), x)
+        fdiff3 = DI.gradient(obj_3, AutoForwardDiff(), x)
+
+        @test finitediff≈fdiff1 atol=1e-5
+        @test finitediff≈fdiff2 atol=1e-5
+        @test finitediff≈fdiff3 atol=1e-5
+        @test fdiff1 ≈ fdiff2 ≈ fdiff3
+
+        function obj_4(p)
+            prob_iip = NonlinearLeastSquaresProblem(
+                NonlinearFunction{true}(
+                    loss_function!; resid_prototype = zeros(length(y_target))),
+                θ_init,
+                p)
+            sol = solve(prob_iip, alg)
+            return sum(abs2, sol.u)
+        end
+
+        function obj_5(p)
+            ff = NonlinearFunction{true}(
+                loss_function!; resid_prototype = zeros(length(y_target)),
+                jac = loss_function_jac!)
+            prob_iip = NonlinearLeastSquaresProblem(ff, θ_init, p)
+            sol = solve(prob_iip, alg)
+            return sum(abs2, sol.u)
+        end
+
+        function obj_6(p)
+            ff = NonlinearFunction{true}(
+                loss_function!; resid_prototype = zeros(length(y_target)),
+                vjp = loss_function_vjp!)
+            prob_iip = NonlinearLeastSquaresProblem(ff, θ_init, p)
+            sol = solve(prob_iip, alg)
+            return sum(abs2, sol.u)
+        end
+
+        finitediff = DI.gradient(obj_4, AutoFiniteDiff(), x)
+
+        fdiff4 = DI.gradient(obj_4, AutoForwardDiff(), x)
+        fdiff5 = DI.gradient(obj_5, AutoForwardDiff(), x)
+        fdiff6 = DI.gradient(obj_6, AutoForwardDiff(), x)
+
+        @test finitediff≈fdiff4 atol=1e-5
+        @test finitediff≈fdiff5 atol=1e-5
+        @test finitediff≈fdiff6 atol=1e-5
+        @test fdiff4 ≈ fdiff5 ≈ fdiff6
+    end
+end

From bd250f2dcc72706af422b353cbd9394bfc884a36 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 7 Oct 2024 19:49:53 -0400
Subject: [PATCH 592/700] test: NonlinearProblem forward diff testing

---
 .../test/core/forward_diff_tests.jl           | 83 +++++++++++++++++++
 1 file changed, 83 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl b/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
index 0005796f9..2b392e39c 100644
--- a/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
@@ -1,3 +1,86 @@
+@testitem "ForwardDiff.jl Integration: NonlinearProblem" tags=[:core] begin
+    using ArrayInterface
+    using ForwardDiff, FiniteDiff, SimpleNonlinearSolve, StaticArrays, LinearAlgebra,
+          Zygote, ReverseDiff, SciMLBase
+    using DifferentiationInterface
+
+    const DI = DifferentiationInterface
+
+    test_f!(du, u, p) = (@. du = u^2 - p)
+    test_f(u, p) = u .^ 2 .- p
+
+    jacobian_f(::Number, p) = 1 / (2 * √p)
+    jacobian_f(::Number, p::Number) = 1 / (2 * √p)
+    jacobian_f(u, p::Number) = one.(u) .* (1 / (2 * √p))
+    jacobian_f(u, p::AbstractArray) = diagm(vec(@. 1 / (2 * √p)))
+
+    @testset for alg in (
+        SimpleNewtonRaphson(),
+        SimpleTrustRegion(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
+        SimpleHalley(),
+        SimpleBroyden(),
+        SimpleKlement(),
+        SimpleDFSane()
+    )
+        us = (
+            2.0,
+            @SVector([1.0, 1.0]),
+            [1.0, 1.0],
+            ones(2, 2),
+            @SArray(ones(2, 2))
+        )
+
+        @testset "Scalar AD" begin
+            for p in 1.0:0.1:100.0, u0 in us
+                sol = solve(NonlinearProblem{false}(test_f, u0, p), alg)
+                if SciMLBase.successful_retcode(sol)
+                    gs = abs.(ForwardDiff.derivative(p) do pᵢ
+                        solve(NonlinearProblem{false}(test_f, u0, pᵢ), alg).u
+                    end)
+                    gs_true = abs.(jacobian_f(u0, p))
+
+                    if !(isapprox(gs, gs_true, atol = 1e-5))
+                        @show sol.retcode, sol.u
+                        @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_gradient=gs true_gradient=gs_true
+                    else
+                        @test abs.(gs)≈abs.(gs_true) atol=1e-5
+                    end
+                end
+            end
+        end
+
+        @testset "Jacobian" begin
+            @testset "$(typeof(u0))" for u0 in us[2:end],
+                p in ([2.0, 1.0], [2.0 1.0; 3.0 4.0])
+
+                if u0 isa AbstractArray && p isa AbstractArray
+                    size(u0) != size(p) && continue
+                end
+
+                @testset for (iip, fn) in ((false, test_f), (true, test_f!))
+                    iip && (u0 isa Number || !ArrayInterface.can_setindex(u0)) && continue
+
+                    sol = solve(NonlinearProblem{iip}(fn, u0, p), alg)
+                    if SciMLBase.successful_retcode(sol)
+                        gs = abs.(ForwardDiff.jacobian(p) do pᵢ
+                            solve(NonlinearProblem{iip}(fn, u0, pᵢ), alg).u
+                        end)
+                        gs_true = abs.(jacobian_f(u0, p))
+
+                        if !(isapprox(gs, gs_true, atol = 1e-5))
+                            @show sol.retcode, sol.u
+                            @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_jacobian=gs true_jacobian=gs_true
+                        else
+                            @test abs.(gs)≈abs.(gs_true) atol=1e-5
+                        end
+                    end
+                end
+            end
+        end
+    end
+end
+
 @testitem "ForwardDiff.jl Integration NonlinearLeastSquaresProblem" tags=[:core] begin
     using ForwardDiff, FiniteDiff, SimpleNonlinearSolve, StaticArrays, LinearAlgebra,
           Zygote, ReverseDiff

From 0f3ede0665e63138c850ab713940cd2d7608d9ab Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 7 Oct 2024 19:51:55 -0400
Subject: [PATCH 593/700] test: lazy install packages

---
 lib/SimpleNonlinearSolve/Project.toml     | 6 +-----
 lib/SimpleNonlinearSolve/test/runtests.jl | 3 +++
 2 files changed, 4 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 5f708e564..27dd69fed 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -41,7 +41,6 @@ AllocCheck = "0.1.1"
 Aqua = "0.8.7"
 ArrayInterface = "7.16"
 BracketingNonlinearSolve = "1"
-CUDA = "5.3"
 ChainRulesCore = "1.24"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
@@ -64,7 +63,6 @@ PrecompileTools = "1.2"
 Random = "1.10"
 ReverseDiff = "1.15"
 SciMLBase = "2.50"
-SciMLSensitivity = "7.68"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4.3"
 Test = "1.10"
@@ -76,7 +74,6 @@ julia = "1.10"
 [extras]
 AllocCheck = "9b6a8646-10ed-4001-bbdc-1d2f46dfbb1a"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
-CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
@@ -86,7 +83,6 @@ Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
-SciMLSensitivity = "1ed8b502-d754-442c-8d5d-10ac956f44a1"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
@@ -94,4 +90,4 @@ Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["AllocCheck", "Aqua", "CUDA", "DiffEqBase", "Enzyme", "ExplicitImports", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReverseDiff", "SciMLSensitivity", "StaticArrays", "Test", "TestItemRunner", "Tracker", "Zygote"]
+test = ["AllocCheck", "Aqua", "DiffEqBase", "Enzyme", "ExplicitImports", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReverseDiff", "StaticArrays", "Test", "TestItemRunner", "Tracker", "Zygote"]
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index a22783e59..cab77902c 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -4,6 +4,9 @@ using TestItemRunner, InteractiveUtils, Pkg
 
 const GROUP = lowercase(get(ENV, "GROUP", "All"))
 
+(GROUP == "all" || GROUP == "cuda") && Pkg.add(["CUDA"])
+(GROUP == "all" || GROUP == "adjoint") && Pkg.add(["SciMLSensitivity"])
+
 if GROUP == "all"
     @run_package_tests
 else

From c0036b6f9d39980ae1a99e56e339c406b13036e1 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 7 Oct 2024 20:10:58 -0400
Subject: [PATCH 594/700] fix: auto-set autodiff for ForwardDiff if trying to
 propagate Duals

---
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl     | 6 ++++++
 lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl | 4 ++--
 lib/SimpleNonlinearSolve/test/core/qa_tests.jl           | 3 +--
 lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl     | 2 +-
 4 files changed, 10 insertions(+), 5 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index b4e641832..6d1187668 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -54,6 +54,9 @@ function CommonSolve.solve(
         alg::AbstractSimpleNonlinearSolveAlgorithm,
         args...;
         kwargs...) where {T, V, P, iip}
+    if hasfield(typeof(alg), :autodiff) && alg.autodiff === nothing
+        @reset alg.autodiff = AutoForwardDiff()
+    end
     prob = convert(ImmutableNonlinearProblem, prob)
     sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
     dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
@@ -68,6 +71,9 @@ function CommonSolve.solve(
         alg::AbstractSimpleNonlinearSolveAlgorithm,
         args...;
         kwargs...) where {T, V, P, iip}
+    if hasfield(typeof(alg), :autodiff) && alg.autodiff === nothing
+        @reset alg.autodiff = AutoForwardDiff()
+    end
     sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
     dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
     return SciMLBase.build_solution(
diff --git a/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl b/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
index 2b392e39c..a857e7a17 100644
--- a/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/forward_diff_tests.jl
@@ -14,7 +14,7 @@
     jacobian_f(u, p::Number) = one.(u) .* (1 / (2 * √p))
     jacobian_f(u, p::AbstractArray) = diagm(vec(@. 1 / (2 * √p)))
 
-    @testset for alg in (
+    @testset "#(nameof(typeof(alg)))" for alg in (
         SimpleNewtonRaphson(),
         SimpleTrustRegion(),
         SimpleTrustRegion(; nlsolve_update_rule = Val(true)),
@@ -118,7 +118,7 @@ end
 
     θ_init = θ_true .+ 0.1
 
-    @testset for alg in (
+    for alg in (
         SimpleGaussNewton(),
         SimpleGaussNewton(; autodiff = AutoForwardDiff()),
         SimpleGaussNewton(; autodiff = AutoFiniteDiff()),
diff --git a/lib/SimpleNonlinearSolve/test/core/qa_tests.jl b/lib/SimpleNonlinearSolve/test/core/qa_tests.jl
index d6a5a9b8e..cef74ac38 100644
--- a/lib/SimpleNonlinearSolve/test/core/qa_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/qa_tests.jl
@@ -12,8 +12,7 @@ end
     import ReverseDiff, Tracker, StaticArrays, Zygote
     using ExplicitImports, SimpleNonlinearSolve
 
-    @test check_no_implicit_imports(
-        SimpleNonlinearSolve; skip = (Base, Core, SciMLBase)) === nothing
+    @test check_no_implicit_imports(SimpleNonlinearSolve; skip = (Base, Core)) === nothing
     @test check_no_stale_explicit_imports(SimpleNonlinearSolve) === nothing
     @test check_all_qualified_accesses_via_owners(SimpleNonlinearSolve) === nothing
 end
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index c99b670cb..b6a39a9e9 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -36,7 +36,7 @@
 end
 
 @testitem "First Order Methods" setup=[RootfindTestSnippet] tags=[:core] begin
-    @testset for alg in (
+    for alg in (
         SimpleNewtonRaphson,
         SimpleTrustRegion,
         (; kwargs...) -> SimpleTrustRegion(; kwargs..., nlsolve_update_rule = Val(true))

From e8bdc15758fc9cae6c8c0660046a49e5d4bea1d8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 7 Oct 2024 20:26:47 -0400
Subject: [PATCH 595/700] fix: QA for NonlinearSolveBase

---
 lib/NonlinearSolveBase/Project.toml           | 16 +++++++++++++
 .../ext/NonlinearSolveBaseForwardDiffExt.jl   |  2 +-
 .../src/NonlinearSolveBase.jl                 |  3 ++-
 .../src/termination_conditions.jl             | 10 ++++----
 lib/NonlinearSolveBase/test/runtests.jl       | 23 +++++++++++++++++++
 5 files changed, 47 insertions(+), 7 deletions(-)

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index a89d035cf..162ce2742 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -31,6 +31,7 @@ NonlinearSolveBaseSparseArraysExt = "SparseArrays"
 
 [compat]
 ADTypes = "1.9"
+Aqua = "0.8.7"
 ArrayInterface = "7.9"
 CommonSolve = "0.2.4"
 Compat = "4.15"
@@ -38,13 +39,28 @@ ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149"
 DifferentiationInterface = "0.6.1"
 EnzymeCore = "0.8"
+ExplicitImports = "1.10.1"
 FastClosures = "0.3"
 ForwardDiff = "0.10.36"
 FunctionProperties = "0.1.2"
+InteractiveUtils = "<0.0.1, 1"
 LinearAlgebra = "1.10"
 Markdown = "1.10"
 RecursiveArrayTools = "3"
 SciMLBase = "2.50"
 SparseArrays = "1.10"
 StaticArraysCore = "1.4"
+Test = "1.10"
 julia = "1.10"
+
+[extras]
+Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[targets]
+test = ["Aqua", "DiffEqBase", "ExplicitImports", "ForwardDiff", "InteractiveUtils", "SparseArrays", "Test"]
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
index 7f9aec5a5..e50be6c47 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
@@ -3,7 +3,7 @@ module NonlinearSolveBaseForwardDiffExt
 using ADTypes: ADTypes, AutoForwardDiff, AutoPolyesterForwardDiff
 using ArrayInterface: ArrayInterface
 using CommonSolve: solve
-using DifferentiationInterface: DifferentiationInterface, Constant
+using DifferentiationInterface: DifferentiationInterface
 using FastClosures: @closure
 using ForwardDiff: ForwardDiff, Dual
 using LinearAlgebra: mul!
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 645b84959..b07b4b168 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -1,7 +1,8 @@
 module NonlinearSolveBase
 
-using ADTypes: ADTypes, AbstractADType, ForwardMode, ReverseMode
+using ADTypes: ADTypes, AbstractADType
 using ArrayInterface: ArrayInterface
+using CommonSolve: CommonSolve
 using Compat: @compat
 using ConcreteStructs: @concrete
 using DifferentiationInterface: DifferentiationInterface
diff --git a/lib/NonlinearSolveBase/src/termination_conditions.jl b/lib/NonlinearSolveBase/src/termination_conditions.jl
index 3e957f139..9f20e46bc 100644
--- a/lib/NonlinearSolveBase/src/termination_conditions.jl
+++ b/lib/NonlinearSolveBase/src/termination_conditions.jl
@@ -30,9 +30,9 @@ function update_u!!(cache::NonlinearTerminationModeCache, u)
     end
 end
 
-function SciMLBase.init(
-        du, u, mode::AbstractNonlinearTerminationMode, saved_value_prototype...;
-        abstol = nothing, reltol = nothing, kwargs...)
+function CommonSolve.init(
+        ::AbstractNonlinearProblem, mode::AbstractNonlinearTerminationMode, du, u,
+        saved_value_prototype...; abstol = nothing, reltol = nothing, kwargs...)
     T = promote_type(eltype(du), eltype(u))
     abstol = get_tolerance(u, abstol, T)
     reltol = get_tolerance(u, reltol, T)
@@ -273,11 +273,11 @@ function init_termination_cache(
         prob, abstol, reltol, du, u, default_termination_mode(prob, callee), callee)
 end
 
-function init_termination_cache(::AbstractNonlinearProblem, abstol, reltol, du,
+function init_termination_cache(prob::AbstractNonlinearProblem, abstol, reltol, du,
         u, tc::AbstractNonlinearTerminationMode, ::Val)
     T = promote_type(eltype(du), eltype(u))
     abstol = get_tolerance(u, abstol, T)
     reltol = get_tolerance(u, reltol, T)
-    cache = SciMLBase.init(du, u, tc; abstol, reltol)
+    cache = CommonSolve.init(prob, tc, du, u; abstol, reltol)
     return abstol, reltol, cache
 end
diff --git a/lib/NonlinearSolveBase/test/runtests.jl b/lib/NonlinearSolveBase/test/runtests.jl
index 8b1378917..07c0f14c6 100644
--- a/lib/NonlinearSolveBase/test/runtests.jl
+++ b/lib/NonlinearSolveBase/test/runtests.jl
@@ -1 +1,24 @@
+using InteractiveUtils, Test
 
+@info sprint(InteractiveUtils.versioninfo)
+
+# Changing any code here triggers all the other tests to be run. So we intentionally
+# keep the tests here minimal.
+@testset "NonlinearSolveBase.jl" begin
+    @testset "Aqua" begin
+        using Aqua, NonlinearSolveBase
+
+        Aqua.test_all(NonlinearSolveBase; piracies = false, ambiguities = false)
+        Aqua.test_piracies(NonlinearSolveBase)
+        Aqua.test_ambiguities(NonlinearSolveBase; recursive = false)
+    end
+
+    @testset "Explicit Imports" begin
+        import ForwardDiff, SparseArrays, DiffEqBase
+        using ExplicitImports, NonlinearSolveBase
+
+        @test check_no_implicit_imports(NonlinearSolveBase; skip = (Base, Core)) === nothing
+        @test check_no_stale_explicit_imports(NonlinearSolveBase) === nothing
+        @test check_all_qualified_accesses_via_owners(NonlinearSolveBase) === nothing
+    end
+end

From 291a33e08f9371eb2fae892bbfc32c3250538059 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 7 Oct 2024 20:27:50 -0400
Subject: [PATCH 596/700] test: wrap in a global testset

---
 lib/BracketingNonlinearSolve/test/runtests.jl |  6 ++++--
 lib/SimpleNonlinearSolve/test/runtests.jl     | 12 +++++++-----
 2 files changed, 11 insertions(+), 7 deletions(-)

diff --git a/lib/BracketingNonlinearSolve/test/runtests.jl b/lib/BracketingNonlinearSolve/test/runtests.jl
index 6ea6326b0..d2c6f80a4 100644
--- a/lib/BracketingNonlinearSolve/test/runtests.jl
+++ b/lib/BracketingNonlinearSolve/test/runtests.jl
@@ -1,5 +1,7 @@
-using TestItemRunner, InteractiveUtils
+using TestItemRunner, InteractiveUtils, Test
 
 @info sprint(InteractiveUtils.versioninfo)
 
-@run_package_tests
+@testset "BracketingNonlinearSolve.jl" begin
+    @run_package_tests
+end
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index cab77902c..c3f02030d 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -1,4 +1,4 @@
-using TestItemRunner, InteractiveUtils, Pkg
+using TestItemRunner, InteractiveUtils, Pkg, Test
 
 @info sprint(InteractiveUtils.versioninfo)
 
@@ -7,8 +7,10 @@ const GROUP = lowercase(get(ENV, "GROUP", "All"))
 (GROUP == "all" || GROUP == "cuda") && Pkg.add(["CUDA"])
 (GROUP == "all" || GROUP == "adjoint") && Pkg.add(["SciMLSensitivity"])
 
-if GROUP == "all"
-    @run_package_tests
-else
-    @run_package_tests filter = ti -> (Symbol(GROUP) in ti.tags)
+@testset "SimpleNonlinearSolve.jl" begin
+    if GROUP == "all"
+        @run_package_tests
+    else
+        @run_package_tests filter = ti -> (Symbol(GROUP) in ti.tags)
+    end
 end

From 2fd377416c510b8d2997c51adb0762764cd586f3 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 8 Oct 2024 12:02:21 -0400
Subject: [PATCH 597/700] fix: write out the AD as dispatches

---
 lib/SimpleNonlinearSolve/src/utils.jl | 93 +++++++++++++--------------
 1 file changed, 45 insertions(+), 48 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index fbc3d3c23..27988026e 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -143,72 +143,69 @@ function prepare_jacobian(prob, autodiff, fx, x)
     end
 end
 
-function compute_jacobian!!(_, prob, autodiff, fx, x::Number, extras)
-    if extras isa AnalyticJacobian
-        if SciMLBase.has_jac(prob.f)
+function compute_jacobian!!(_, prob, autodiff, fx, x::Number, ::AnalyticJacobian)
+    if SciMLBase.has_jac(prob.f)
+        return prob.f.jac(x, prob.p)
+    elseif SciMLBase.has_vjp(prob.f)
+        return prob.f.vjp(one(x), x, prob.p)
+    elseif SciMLBase.has_jvp(prob.f)
+        return prob.f.jvp(one(x), x, prob.p)
+    end
+end
+function compute_jacobian!!(_, prob, autodiff, fx, x::Number, ::DIExtras)
+    return DI.derivative(prob.f, extras.prep, autodiff, x, Constant(prob.p))
+end
+function compute_jacobian!!(_, prob, autodiff, fx, x::Number, ::DINoPreparation)
+    return DI.derivative(prob.f, autodiff, x, Constant(prob.p))
+end
+
+function compute_jacobian!!(J, prob, autodiff, fx, x, ::AnalyticJacobian)
+    if J === nothing
+        if SciMLBase.isinplace(prob.f)
+            J = safe_similar(fx, length(fx), length(x))
+            prob.f.jac(J, x, prob.p)
+            return J
+        else
             return prob.f.jac(x, prob.p)
-        elseif SciMLBase.has_vjp(prob.f)
-            return prob.f.vjp(one(x), x, prob.p)
-        elseif SciMLBase.has_jvp(prob.f)
-            return prob.f.jvp(one(x), x, prob.p)
         end
     end
-    if extras isa DIExtras
-        return DI.derivative(prob.f, extras.prep, autodiff, x, Constant(prob.p))
+    if SciMLBase.isinplace(prob.f)
+        prob.f.jac(J, x, prob.p)
+        return J
     else
-        return DI.derivative(prob.f, autodiff, x, Constant(prob.p))
+        return prob.f.jac(x, prob.p)
     end
 end
-function compute_jacobian!!(J, prob, autodiff, fx, x, extras)
+
+function compute_jacobian!!(J, prob, autodiff, fx, x, ::DIExtras)
     if J === nothing
-        if extras isa AnalyticJacobian
-            if SciMLBase.isinplace(prob.f)
-                J = safe_similar(fx, length(fx), length(x))
-                prob.f.jac(J, x, prob.p)
-                return J
-            else
-                return prob.f.jac(x, prob.p)
-            end
-        end
-        if SciMLBase.isinplace(prob)
-            @assert extras isa DIExtras
+        if SciMLBase.isinplace(prob.f)
             return DI.jacobian(prob.f, fx, extras.prep, autodiff, x, Constant(prob.p))
         else
-            if extras isa DIExtras
-                return DI.jacobian(prob.f, extras.prep, autodiff, x, Constant(prob.p))
-            else
-                return DI.jacobian(prob.f, autodiff, x, Constant(prob.p))
-            end
+            return DI.jacobian(prob.f, extras.prep, autodiff, x, Constant(prob.p))
         end
     end
-    if extras isa AnalyticJacobian
-        if SciMLBase.isinplace(prob)
-            prob.f.jac(J, x, prob.p)
-            return J
-        else
-            return prob.f.jac(x, prob.p)
-        end
-    end
-    if SciMLBase.isinplace(prob)
-        @assert extras isa DIExtras
-        DI.jacobian!(prob.f, fx, J, extras.prep, autodiff, x, Constant(prob.p))
+    if SciMLBase.isinplace(prob.f)
+        DI.jacobian!(prob.f, J, fx, extras.prep, autodiff, x, Constant(prob.p))
     else
         if ArrayInterface.can_setindex(J)
-            if extras isa DIExtras
-                DI.jacobian!(prob.f, J, extras.prep, autodiff, x, Constant(prob.p))
-            else
-                DI.jacobian!(prob.f, J, autodiff, x, Constant(prob.p))
-            end
+            DI.jacobian!(prob.f, J, extras.prep, autodiff, x, Constant(prob.p))
         else
-            if extras isa DIExtras
-                J = DI.jacobian(prob.f, extras.prep, autodiff, x, Constant(prob.p))
-            else
-                J = DI.jacobian(prob.f, autodiff, x, Constant(prob.p))
-            end
+            J = DI.jacobian(prob.f, extras.prep, autodiff, x, Constant(prob.p))
         end
     end
     return J
 end
+function compute_jacobian!!(J, prob, autodiff, fx, x, ::DINoPreparation)
+    @assert !SciMLBase.isinplace(prob.f) "This shouldn't happen. Open an issue."
+    J === nothing && return DI.jacobian(prob.f, autodiff, x, Constant(prob.p))
+    if ArrayInterface.can_setindex(J)
+        DI.jacobian!(prob.f, J, autodiff, x, Constant(prob.p))
+    else
+        J = DI.jacobian(prob.f, autodiff, x, Constant(prob.p))
+    end
+    return J
+end
 
 function compute_jacobian_and_hessian(autodiff, prob, _, x::Number)
     H = DI.second_derivative(prob.f, autodiff, x, Constant(prob.p))

From 8ba936270411a4d568bb24595c3a9dea3226a5c5 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 8 Oct 2024 12:04:12 -0400
Subject: [PATCH 598/700] test: install AllocCheck if needed

---
 .github/workflows/CI_SimpleNonlinearSolve.yml          | 1 +
 lib/SimpleNonlinearSolve/Project.toml                  | 4 +---
 lib/SimpleNonlinearSolve/test/core/allocation_tests.jl | 2 +-
 lib/SimpleNonlinearSolve/test/runtests.jl              | 1 +
 4 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/.github/workflows/CI_SimpleNonlinearSolve.yml b/.github/workflows/CI_SimpleNonlinearSolve.yml
index 1f8306a8c..11c3ef7c2 100644
--- a/.github/workflows/CI_SimpleNonlinearSolve.yml
+++ b/.github/workflows/CI_SimpleNonlinearSolve.yml
@@ -35,6 +35,7 @@ jobs:
         group:
           - core
           - adjoint
+          - alloc_check
     steps:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v2
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 27dd69fed..82f69c6ad 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -37,7 +37,6 @@ SimpleNonlinearSolveTrackerExt = "Tracker"
 [compat]
 ADTypes = "1.2"
 Accessors = "0.1"
-AllocCheck = "0.1.1"
 Aqua = "0.8.7"
 ArrayInterface = "7.16"
 BracketingNonlinearSolve = "1"
@@ -72,7 +71,6 @@ Zygote = "0.6.70"
 julia = "1.10"
 
 [extras]
-AllocCheck = "9b6a8646-10ed-4001-bbdc-1d2f46dfbb1a"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
@@ -90,4 +88,4 @@ Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["AllocCheck", "Aqua", "DiffEqBase", "Enzyme", "ExplicitImports", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReverseDiff", "StaticArrays", "Test", "TestItemRunner", "Tracker", "Zygote"]
+test = ["Aqua", "DiffEqBase", "Enzyme", "ExplicitImports", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReverseDiff", "StaticArrays", "Test", "TestItemRunner", "Tracker", "Zygote"]
diff --git a/lib/SimpleNonlinearSolve/test/core/allocation_tests.jl b/lib/SimpleNonlinearSolve/test/core/allocation_tests.jl
index 67cee39c0..1f8472cf3 100644
--- a/lib/SimpleNonlinearSolve/test/core/allocation_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/allocation_tests.jl
@@ -1,4 +1,4 @@
-@itesitem "Allocation Tests" tags=[:core] begin
+@itesitem "Allocation Tests" tags=[:alloc_check] begin
     using SimpleNonlinearSolve, StaticArrays, AllocCheck
 
     quadratic_f(u, p) = u .* u .- p
diff --git a/lib/SimpleNonlinearSolve/test/runtests.jl b/lib/SimpleNonlinearSolve/test/runtests.jl
index c3f02030d..a76760dc8 100644
--- a/lib/SimpleNonlinearSolve/test/runtests.jl
+++ b/lib/SimpleNonlinearSolve/test/runtests.jl
@@ -6,6 +6,7 @@ const GROUP = lowercase(get(ENV, "GROUP", "All"))
 
 (GROUP == "all" || GROUP == "cuda") && Pkg.add(["CUDA"])
 (GROUP == "all" || GROUP == "adjoint") && Pkg.add(["SciMLSensitivity"])
+(GROUP == "all" || GROUP == "alloc_check") && Pkg.add(["AllocCheck"])
 
 @testset "SimpleNonlinearSolve.jl" begin
     if GROUP == "all"

From d898c2534d498302832bded1c60a40e87f6eed45 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 8 Oct 2024 14:12:14 -0400
Subject: [PATCH 599/700] fix: missing extras

---
 lib/SimpleNonlinearSolve/src/utils.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 27988026e..9a1c36508 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -152,7 +152,7 @@ function compute_jacobian!!(_, prob, autodiff, fx, x::Number, ::AnalyticJacobian
         return prob.f.jvp(one(x), x, prob.p)
     end
 end
-function compute_jacobian!!(_, prob, autodiff, fx, x::Number, ::DIExtras)
+function compute_jacobian!!(_, prob, autodiff, fx, x::Number, extras::DIExtras)
     return DI.derivative(prob.f, extras.prep, autodiff, x, Constant(prob.p))
 end
 function compute_jacobian!!(_, prob, autodiff, fx, x::Number, ::DINoPreparation)
@@ -177,7 +177,7 @@ function compute_jacobian!!(J, prob, autodiff, fx, x, ::AnalyticJacobian)
     end
 end
 
-function compute_jacobian!!(J, prob, autodiff, fx, x, ::DIExtras)
+function compute_jacobian!!(J, prob, autodiff, fx, x, extras::DIExtras)
     if J === nothing
         if SciMLBase.isinplace(prob.f)
             return DI.jacobian(prob.f, fx, extras.prep, autodiff, x, Constant(prob.p))

From 8a3baa6d771e85ea08e7b6005fa0a517d7ecd884 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 20 Oct 2024 17:14:23 -0400
Subject: [PATCH 600/700] test(BracketingNonlinearSolve): qq using Aqua and
 ExplicitImports

---
 lib/BracketingNonlinearSolve/Project.toml     |  9 ++++++++-
 lib/BracketingNonlinearSolve/test/qa_tests.jl | 16 ++++++++++++++++
 2 files changed, 24 insertions(+), 1 deletion(-)
 create mode 100644 lib/BracketingNonlinearSolve/test/qa_tests.jl

diff --git a/lib/BracketingNonlinearSolve/Project.toml b/lib/BracketingNonlinearSolve/Project.toml
index dc979f660..6fc241d7d 100644
--- a/lib/BracketingNonlinearSolve/Project.toml
+++ b/lib/BracketingNonlinearSolve/Project.toml
@@ -17,19 +17,26 @@ ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 BracketingNonlinearSolveForwardDiffExt = "ForwardDiff"
 
 [compat]
+Aqua = "0.8.9"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
+ExplicitImports = "1.10.1"
 ForwardDiff = "0.10.36"
+InteractiveUtils = "<0.0.1, 1"
 NonlinearSolveBase = "1"
 PrecompileTools = "1.2"
 SciMLBase = "2.50"
+Test = "1.10"
+TestItemRunner = "1"
 julia = "1.10"
 
 [extras]
+Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
 
 [targets]
-test = ["InteractiveUtils", "ForwardDiff", "Test", "TestItemRunner"]
+test = ["Aqua", "ExplicitImports", "ForwardDiff", "InteractiveUtils", "Test", "TestItemRunner"]
diff --git a/lib/BracketingNonlinearSolve/test/qa_tests.jl b/lib/BracketingNonlinearSolve/test/qa_tests.jl
new file mode 100644
index 000000000..de27e33a4
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/test/qa_tests.jl
@@ -0,0 +1,16 @@
+@testitem "Aqua" tags=[:core] begin
+    using Aqua, BracketingNonlinearSolve
+
+    Aqua.test_all(BracketingNonlinearSolve; piracies = false, ambiguities = false)
+    Aqua.test_piracies(BracketingNonlinearSolve; treat_as_own = [IntervalNonlinearProblem])
+    Aqua.test_ambiguities(BracketingNonlinearSolve; recursive = false)
+end
+
+@testitem "Explicit Imports" tags=[:core] begin
+    import ForwardDiff
+    using ExplicitImports, BracketingNonlinearSolve
+
+    @test check_no_implicit_imports(BracketingNonlinearSolve; skip = (Base, Core)) === nothing
+    @test check_no_stale_explicit_imports(BracketingNonlinearSolve) === nothing
+    @test check_all_qualified_accesses_via_owners(BracketingNonlinearSolve) === nothing
+end

From 66e7b3078d6442e699d9832d81d2a88fefcc5a86 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 20 Oct 2024 17:45:00 -0400
Subject: [PATCH 601/700] fix(SimpleNonlinearSolve): incorrect argument
 ordering

---
 lib/SimpleNonlinearSolve/src/utils.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 9a1c36508..311762429 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -139,7 +139,7 @@ function prepare_jacobian(prob, autodiff, fx, x)
         return DIExtras(DI.prepare_jacobian(prob.f, fx, autodiff, x, Constant(prob.p)))
     else
         x isa SArray && return DINoPreparation()
-        return DI.prepare_jacobian(prob.f, autodiff, x, Constant(prob.p))
+        return DIExtras(DI.prepare_jacobian(prob.f, autodiff, x, Constant(prob.p)))
     end
 end
 
@@ -186,7 +186,7 @@ function compute_jacobian!!(J, prob, autodiff, fx, x, extras::DIExtras)
         end
     end
     if SciMLBase.isinplace(prob.f)
-        DI.jacobian!(prob.f, J, fx, extras.prep, autodiff, x, Constant(prob.p))
+        DI.jacobian!(prob.f, fx, J, extras.prep, autodiff, x, Constant(prob.p))
     else
         if ArrayInterface.can_setindex(J)
             DI.jacobian!(prob.f, J, extras.prep, autodiff, x, Constant(prob.p))

From 55e213ce5c2679aab53f47e01241ee67941a8ecb Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 12:03:33 -0400
Subject: [PATCH 602/700] feat: remove LineSearches.jl dependency

---
 Project.toml                        |  9 +++++----
 docs/src/native/solvers.md          |  5 +----
 ext/NonlinearSolveNLsolveExt.jl     |  7 +++++--
 src/NonlinearSolve.jl               |  7 ++-----
 src/algorithms/extension_algs.jl    |  8 +++++++-
 src/algorithms/klement.jl           |  7 -------
 src/core/approximate_jacobian.jl    |  6 ------
 src/core/generalized_first_order.jl |  7 -------
 src/default.jl                      | 10 +++++-----
 src/globalization/line_search.jl    | 26 --------------------------
 10 files changed, 25 insertions(+), 67 deletions(-)

diff --git a/Project.toml b/Project.toml
index 725aa5c9d..6bf13d3a3 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "3.15.2"
+version = "4.0.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -15,7 +15,6 @@ FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
 LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
-LineSearches = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
@@ -41,6 +40,7 @@ BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 FastLevenbergMarquardt = "7a0df574-e128-4d35-8cbd-3d84502bf7ce"
 FixedPointAcceleration = "817d07cb-a79a-5c30-9a31-890123675176"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
+LineSearches = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
 MINPACK = "4854310b-de5a-5eb6-a2a5-c1dee2bd17f9"
 NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
@@ -54,7 +54,7 @@ NonlinearSolveFixedPointAccelerationExt = "FixedPointAcceleration"
 NonlinearSolveLeastSquaresOptimExt = "LeastSquaresOptim"
 NonlinearSolveMINPACKExt = "MINPACK"
 NonlinearSolveNLSolversExt = "NLSolvers"
-NonlinearSolveNLsolveExt = "NLsolve"
+NonlinearSolveNLsolveExt = ["NLsolve", "LineSearches"]
 NonlinearSolveSIAMFANLEquationsExt = "SIAMFANLEquations"
 NonlinearSolveSpeedMappingExt = "SpeedMapping"
 
@@ -132,6 +132,7 @@ FixedPointAcceleration = "817d07cb-a79a-5c30-9a31-890123675176"
 Hwloc = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
+LineSearches = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
 MINPACK = "4854310b-de5a-5eb6-a2a5-c1dee2bd17f9"
 ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
@@ -151,4 +152,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "LineSearches", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Test", "Zygote"]
diff --git a/docs/src/native/solvers.md b/docs/src/native/solvers.md
index a5deca141..aebaee379 100644
--- a/docs/src/native/solvers.md
+++ b/docs/src/native/solvers.md
@@ -23,10 +23,7 @@ documentation.
     algorithms, consult the
     [LinearSolve.jl documentation](https://docs.sciml.ai/LinearSolve/stable/).
   - `linesearch`: the line search algorithm to use. Defaults to [`NoLineSearch()`](@extref LineSearch.NoLineSearch),
-    which means that no line search is performed.  Algorithms from
-    [`LineSearches.jl`](https://github.com/JuliaNLSolvers/LineSearches.jl/) must be
-    wrapped in [`LineSearchesJL`](@ref) before being supplied. For a detailed documentation
-    refer to [Line Search Algorithms](@ref line-search).
+    which means that no line search is performed.
   - `autodiff`/`jacobian_ad`: etermines the backend used for the Jacobian. Note that this
     argument is ignored if an analytical Jacobian is passed, as that will be used instead.
     Defaults to `nothing` which means that a default is selected according to the problem
diff --git a/ext/NonlinearSolveNLsolveExt.jl b/ext/NonlinearSolveNLsolveExt.jl
index 77ed4a56f..95de37055 100644
--- a/ext/NonlinearSolveNLsolveExt.jl
+++ b/ext/NonlinearSolveNLsolveExt.jl
@@ -1,5 +1,6 @@
 module NonlinearSolveNLsolveExt
 
+using LineSearches: Static
 using NonlinearSolve: NonlinearSolve, NLsolveJL, TraceMinimal
 using NLsolve: NLsolve, OnceDifferentiable, nlsolve
 using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
@@ -31,9 +32,11 @@ function SciMLBase.__solve(
     store_trace = StT || alg.store_trace
     extended_trace = !(trace_level isa TraceMinimal) || alg.extended_trace
 
+    linesearch = alg.linesearch === missing ? Static() : alg.linesearch
+
     original = nlsolve(df, vec(u0); ftol = abstol, iterations = maxiters, alg.method,
-        store_trace, extended_trace, alg.linesearch, alg.linsolve,
-        alg.factor, alg.autoscale, alg.m, alg.beta, show_trace)
+        store_trace, extended_trace, linesearch, alg.linsolve, alg.factor,
+        alg.autoscale, alg.m, alg.beta, show_trace)
 
     f!(vec(resid), original.zero)
     u = prob.u0 isa Number ? original.zero[1] : reshape(original.zero, size(prob.u0))
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 5e2dc5555..1f48371e6 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -23,8 +23,7 @@ using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Sy
                      UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess, istril,
                      istriu, lu, mul!, norm, pinv, tril!, triu!
 using LineSearch: LineSearch, AbstractLineSearchAlgorithm, AbstractLineSearchCache,
-                  NoLineSearch, RobustNonMonotoneLineSearch
-using LineSearches: LineSearches
+                  NoLineSearch, RobustNonMonotoneLineSearch, BackTracking
 using LinearSolve: LinearSolve, LUFactorization, QRFactorization,
                    needs_concrete_A, AbstractFactorization,
                    DefaultAlgorithmChoice, DefaultLinearSolver
@@ -174,9 +173,7 @@ export NewtonDescent, SteepestDescent, Dogleg, DampedNewtonDescent, GeodesicAcce
 
 # Globalization
 ## Line Search Algorithms
-export LineSearchesJL, LiFukushimaLineSearch # FIXME: deprecated. use LineSearch.jl directly
-export Static, HagerZhang, MoreThuente, StrongWolfe, BackTracking  # FIXME: deprecated
-export LineSearch, NoLineSearch, RobustNonMonotoneLineSearch
+export LineSearch, BackTracking, NoLineSearch, RobustNonMonotoneLineSearch, LineSearchesJL
 ## Trust Region Algorithms
 export RadiusUpdateSchemes
 
diff --git a/src/algorithms/extension_algs.jl b/src/algorithms/extension_algs.jl
index 46ebc8dae..9c08c5202 100644
--- a/src/algorithms/extension_algs.jl
+++ b/src/algorithms/extension_algs.jl
@@ -203,6 +203,12 @@ end
     acceleration of the fixed-point iteration xₙ₊₁ = xₙ + beta*f(xₙ), where by default
     beta = 1.
 
+!!! warning
+
+    Line Search Algorithms from [`LineSearch.jl`](https://github.com/SciML/LineSearch.jl)
+    aren't supported by `NLsolveJL`. Instead, use the line search algorithms from
+    [`LineSearches.jl`](https://github.com/JuliaNLSolvers/LineSearches.jl).
+
 ### Submethod Choice
 
 Choices for methods in `NLsolveJL`:
@@ -234,7 +240,7 @@ For more information on these arguments, consult the
 end
 
 function NLsolveJL(; method = :trust_region, autodiff = :central, store_trace = missing,
-        extended_trace = missing, linesearch = LineSearches.Static(),
+        extended_trace = missing, linesearch = missing,
         linsolve = (x, A, b) -> copyto!(x, A \ b), factor = 1.0,
         autoscale = true, m = 10, beta = one(Float64), show_trace = missing)
     if Base.get_extension(@__MODULE__, :NonlinearSolveNLsolveExt) === nothing
diff --git a/src/algorithms/klement.jl b/src/algorithms/klement.jl
index 5e911d8c0..f5d3edf3d 100644
--- a/src/algorithms/klement.jl
+++ b/src/algorithms/klement.jl
@@ -27,13 +27,6 @@ over this.
 function Klement(; max_resets::Int = 100, linsolve = nothing, alpha = nothing,
         linesearch = NoLineSearch(), precs = DEFAULT_PRECS,
         autodiff = nothing, init_jacobian::Val{IJ} = Val(:identity)) where {IJ}
-    if !(linesearch isa AbstractLineSearchAlgorithm)
-        Base.depwarn(
-            "Passing in a `LineSearches.jl` algorithm directly is deprecated. \
-             Please use `LineSearchesJL` instead.", :Klement)
-        linesearch = LineSearchesJL(; method = linesearch)
-    end
-
     if IJ === :identity
         initialization = IdentityInitialization(alpha, DiagonalStructure())
     elseif IJ === :true_jacobian
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index 6484c0408..2e0c64a82 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -59,12 +59,6 @@ function ApproximateJacobianSolveAlgorithm{concrete_jac, name}(;
         linesearch = missing, trustregion = missing, descent, update_rule,
         reinit_rule, initialization, max_resets::Int = typemax(Int),
         max_shrink_times::Int = typemax(Int)) where {concrete_jac, name}
-    if linesearch !== missing && !(linesearch isa AbstractLineSearchAlgorithm)
-        Base.depwarn("Passing in a `LineSearches.jl` algorithm directly is deprecated. \
-                      Please use `LineSearchesJL` instead.",
-            :GeneralizedFirstOrderAlgorithm)
-        linesearch = LineSearchesJL(; method = linesearch)
-    end
     return ApproximateJacobianSolveAlgorithm{concrete_jac, name}(
         linesearch, trustregion, descent, update_rule,
         reinit_rule, max_resets, max_shrink_times, initialization)
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index a485c7c65..ebdaf1fc8 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -66,13 +66,6 @@ function GeneralizedFirstOrderAlgorithm{concrete_jac, name}(;
             jacobian_ad !== nothing && ADTypes.mode(jacobian_ad) isa ADTypes.ReverseMode,
             jacobian_ad, nothing))
 
-    if linesearch !== missing && !(linesearch isa AbstractLineSearchAlgorithm)
-        Base.depwarn("Passing in a `LineSearches.jl` algorithm directly is deprecated. \
-                      Please use `LineSearchesJL` instead.",
-            :GeneralizedFirstOrderAlgorithm)
-        linesearch = LineSearchesJL(; method = linesearch)
-    end
-
     return GeneralizedFirstOrderAlgorithm{concrete_jac, name}(
         linesearch, trustregion, descent, max_shrink_times,
         jacobian_ad, forward_ad, reverse_ad)
diff --git a/src/default.jl b/src/default.jl
index c0924e2ff..967b2e0e8 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -364,7 +364,7 @@ function RobustMultiNewton(::Type{T} = Float64; concrete_jac = nothing, linsolve
                 radius_update_scheme = RadiusUpdateSchemes.Bastin),
             NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
             NewtonRaphson(; concrete_jac, linsolve, precs,
-                linesearch = LineSearch.BackTracking(), autodiff),
+                linesearch = BackTracking(), autodiff),
             TrustRegion(; concrete_jac, linsolve, precs,
                 radius_update_scheme = RadiusUpdateSchemes.NLsolve, autodiff),
             TrustRegion(; concrete_jac, linsolve, precs,
@@ -405,7 +405,7 @@ function FastShortcutNonlinearPolyalg(
         else
             algs = (NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
                 NewtonRaphson(; concrete_jac, linsolve, precs,
-                    linesearch = LineSearch.BackTracking(), autodiff),
+                    linesearch = BackTracking(), autodiff),
                 TrustRegion(; concrete_jac, linsolve, precs, autodiff),
                 TrustRegion(; concrete_jac, linsolve, precs,
                     radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff))
@@ -426,7 +426,7 @@ function FastShortcutNonlinearPolyalg(
                     SimpleKlement(),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs,
-                        linesearch = LineSearch.BackTracking(), autodiff),
+                        linesearch = BackTracking(), autodiff),
                     TrustRegion(; concrete_jac, linsolve, precs,
                         radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff))
             end
@@ -445,7 +445,7 @@ function FastShortcutNonlinearPolyalg(
                     Klement(; linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
                     NewtonRaphson(; concrete_jac, linsolve, precs,
-                        linesearch = LineSearch.BackTracking(), autodiff),
+                        linesearch = BackTracking(), autodiff),
                     TrustRegion(; concrete_jac, linsolve, precs, autodiff),
                     TrustRegion(; concrete_jac, linsolve, precs,
                         radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff))
@@ -481,7 +481,7 @@ function FastShortcutNLLSPolyalg(
                 linsolve, precs, disable_geodesic = Val(true), autodiff, kwargs...),
             TrustRegion(; concrete_jac, linsolve, precs, autodiff, kwargs...),
             GaussNewton(; concrete_jac, linsolve, precs,
-                linesearch = LineSearch.BackTracking(), autodiff, kwargs...),
+                linesearch = BackTracking(), autodiff, kwargs...),
             TrustRegion(; concrete_jac, linsolve, precs,
                 radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff, kwargs...),
             LevenbergMarquardt(; linsolve, precs, autodiff, kwargs...))
diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
index c7c342bee..7549f1f9d 100644
--- a/src/globalization/line_search.jl
+++ b/src/globalization/line_search.jl
@@ -1,29 +1,3 @@
-LineSearchesJL(method; kwargs...) = LineSearchesJL(; method, kwargs...)
-function LineSearchesJL(; method = LineSearches.Static(), autodiff = nothing, α = true)
-    Base.depwarn("`LineSearchesJL(...)` is deprecated. Please use `LineSearchesJL` from \
-                  LineSearch.jl instead.",
-        :LineSearchesJL)
-
-    # Prevent breaking old code
-    method isa LineSearch.LineSearchesJL &&
-        return LineSearch.LineSearchesJL(method.method, α, autodiff)
-    method isa AbstractLineSearchAlgorithm && return method
-    return LineSearch.LineSearchesJL(method, α, autodiff)
-end
-
-for alg in (:Static, :HagerZhang, :MoreThuente, :BackTracking, :StrongWolfe)
-    depmsg = "`$(alg)(args...; kwargs...)` is deprecated. Please use `LineSearchesJL(; \
-              method = $(alg)(args...; kwargs...))` instead."
-    @eval function $(alg)(args...; autodiff = nothing, initial_alpha = true, kwargs...)
-        Base.depwarn($(depmsg), $(Meta.quot(alg)))
-        return LineSearch.LineSearchesJL(;
-            method = LineSearches.$(alg)(args...; kwargs...), autodiff, initial_alpha)
-    end
-end
-
-Base.@deprecate LiFukushimaLineSearch(; nan_max_iter::Int = 5, kwargs...) LineSearch.LiFukushimaLineSearch(;
-    nan_maxiters = nan_max_iter, kwargs...)
-
 function callback_into_cache!(topcache, cache::AbstractLineSearchCache, args...)
     LineSearch.callback_into_cache!(cache, get_fu(topcache))
 end

From a0c3b12fd259118888b3280eb5497c4ffb8fc6c0 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 12:13:35 -0400
Subject: [PATCH 603/700] chore: remove deprecated functionalities

---
 ext/NonlinearSolveMINPACKExt.jl       |  4 +-
 ext/NonlinearSolveNLsolveExt.jl       |  6 +-
 ext/NonlinearSolveSpeedMappingExt.jl  |  2 +-
 src/algorithms/extension_algs.jl      | 85 +++------------------------
 src/algorithms/levenberg_marquardt.jl | 18 ++----
 src/internal/jacobian.jl              | 16 ++---
 6 files changed, 23 insertions(+), 108 deletions(-)

diff --git a/ext/NonlinearSolveMINPACKExt.jl b/ext/NonlinearSolveMINPACKExt.jl
index a7be409d4..8299b0b45 100644
--- a/ext/NonlinearSolveMINPACKExt.jl
+++ b/ext/NonlinearSolveMINPACKExt.jl
@@ -19,8 +19,8 @@ function SciMLBase.__solve(
     method = ifelse(alg.method === :auto,
         ifelse(prob isa NonlinearLeastSquaresProblem, :lm, :hybr), alg.method)
 
-    show_trace = alg.show_trace || ShT
-    tracing = alg.tracing || StT
+    show_trace = ShT
+    tracing = StT
     tol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u0))
 
     if alg.autodiff === missing && prob.f.jac === nothing
diff --git a/ext/NonlinearSolveNLsolveExt.jl b/ext/NonlinearSolveNLsolveExt.jl
index 95de37055..9872c7953 100644
--- a/ext/NonlinearSolveNLsolveExt.jl
+++ b/ext/NonlinearSolveNLsolveExt.jl
@@ -28,9 +28,9 @@ function SciMLBase.__solve(
     end
 
     abstol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u0))
-    show_trace = ShT || alg.show_trace
-    store_trace = StT || alg.store_trace
-    extended_trace = !(trace_level isa TraceMinimal) || alg.extended_trace
+    show_trace = ShT
+    store_trace = StT
+    extended_trace = !(trace_level isa TraceMinimal)
 
     linesearch = alg.linesearch === missing ? Static() : alg.linesearch
 
diff --git a/ext/NonlinearSolveSpeedMappingExt.jl b/ext/NonlinearSolveSpeedMappingExt.jl
index 2813e3e58..b39394a3b 100644
--- a/ext/NonlinearSolveSpeedMappingExt.jl
+++ b/ext/NonlinearSolveSpeedMappingExt.jl
@@ -14,7 +14,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SpeedMappingJL, args...;
         prob; alias_u0, make_fixed_point = Val(true))
     tol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u))
 
-    time_limit = ifelse(maxtime === nothing, alg.time_limit, maxtime)
+    time_limit = ifelse(maxtime === nothing, 1000, maxtime)
 
     sol = speedmapping(u; m!, tol, Lp = Inf, maps_limit = maxiters, alg.orders,
         alg.check_obj, store_info, alg.σ_min, alg.stabilize, time_limit)
diff --git a/src/algorithms/extension_algs.jl b/src/algorithms/extension_algs.jl
index 9c08c5202..3cf36ca9f 100644
--- a/src/algorithms/extension_algs.jl
+++ b/src/algorithms/extension_algs.jl
@@ -142,39 +142,15 @@ NonlinearLeastSquaresProblem.
     This algorithm is only available if `MINPACK.jl` is installed.
 """
 @concrete struct CMINPACK <: AbstractNonlinearSolveExtensionAlgorithm
-    show_trace::Bool
-    tracing::Bool
     method::Symbol
     autodiff
 end
 
-function CMINPACK(; show_trace = missing, tracing = missing,
-        method::Symbol = :auto, autodiff = missing)
+function CMINPACK(; method::Symbol = :auto, autodiff = missing)
     if Base.get_extension(@__MODULE__, :NonlinearSolveMINPACKExt) === nothing
         error("CMINPACK requires MINPACK.jl to be loaded")
     end
-
-    if show_trace !== missing
-        Base.depwarn(
-            "`show_trace` for CMINPACK has been deprecated and will be removed \
-             in v4. Use the `show_trace` keyword argument via the logging API \
-             https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ \
-             instead.", :CMINPACK)
-    else
-        show_trace = false
-    end
-
-    if tracing !== missing
-        Base.depwarn(
-            "`tracing` for CMINPACK has been deprecated and will be removed \
-             in v4. Use the `store_trace` keyword argument via the logging API \
-             https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ \
-             instead.", :CMINPACK)
-    else
-        tracing = false
-    end
-
-    return CMINPACK(show_trace, tracing, method, autodiff)
+    return CMINPACK(method, autodiff)
 end
 
 """
@@ -228,63 +204,26 @@ For more information on these arguments, consult the
 @concrete struct NLsolveJL <: AbstractNonlinearSolveExtensionAlgorithm
     method::Symbol
     autodiff
-    store_trace::Bool
-    extended_trace::Bool
     linesearch
     linsolve
     factor
     autoscale::Bool
     m::Int
     beta
-    show_trace::Bool
 end
 
-function NLsolveJL(; method = :trust_region, autodiff = :central, store_trace = missing,
-        extended_trace = missing, linesearch = missing,
+function NLsolveJL(; method = :trust_region, autodiff = :central, linesearch = missing,
         linsolve = (x, A, b) -> copyto!(x, A \ b), factor = 1.0,
-        autoscale = true, m = 10, beta = one(Float64), show_trace = missing)
+        autoscale = true, m = 10, beta = one(Float64))
     if Base.get_extension(@__MODULE__, :NonlinearSolveNLsolveExt) === nothing
         error("NLsolveJL requires NLsolve.jl to be loaded")
     end
 
-    if show_trace !== missing
-        Base.depwarn("`show_trace` for NLsolveJL has been deprecated and will be removed \
-                      in v4. Use the `show_trace` keyword argument via the logging API \
-                      https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ \
-                      instead.",
-            :NLsolveJL)
-    else
-        show_trace = false
-    end
-
-    if store_trace !== missing
-        Base.depwarn(
-            "`store_trace` for NLsolveJL has been deprecated and will be removed \
-             in v4. Use the `store_trace` keyword argument via the logging API \
-             https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ \
-             instead.",
-            :NLsolveJL)
-    else
-        store_trace = false
-    end
-
-    if extended_trace !== missing
-        Base.depwarn(
-            "`extended_trace` for NLsolveJL has been deprecated and will be \
-             removed in v4. Use the `trace_level = TraceAll()` keyword argument \
-             via the logging API \
-             https://docs.sciml.ai/NonlinearSolve/stable/basics/Logging/ instead.",
-            :NLsolveJL)
-    else
-        extended_trace = false
-    end
-
     if autodiff isa Symbol && autodiff !== :central && autodiff !== :forward
         error("`autodiff` must be `:central` or `:forward`.")
     end
 
-    return NLsolveJL(method, autodiff, store_trace, extended_trace, linesearch,
-        linsolve, factor, autoscale, m, beta, show_trace)
+    return NLsolveJL(method, autodiff, linesearch, linsolve, factor, autoscale, m, beta)
 end
 
 """
@@ -349,25 +288,15 @@ Fixed Point Problems. We allow using this algorithm to solve root finding proble
     stabilize::Bool
     check_obj::Bool
     orders::Vector{Int}
-    time_limit
 end
 
 function SpeedMappingJL(; σ_min = 0.0, stabilize::Bool = false, check_obj::Bool = false,
-        orders::Vector{Int} = [3, 3, 2], time_limit = missing)
+        orders::Vector{Int} = [3, 3, 2])
     if Base.get_extension(@__MODULE__, :NonlinearSolveSpeedMappingExt) === nothing
         error("SpeedMappingJL requires SpeedMapping.jl to be loaded")
     end
 
-    if time_limit !== missing
-        Base.depwarn("`time_limit` keyword argument to `SpeedMappingJL` has been \
-                      deprecated and will be removed in v4. Pass `maxtime = <value>` to \
-                      `SciMLBase.solve`.",
-            :SpeedMappingJL)
-    else
-        time_limit = 1000
-    end
-
-    return SpeedMappingJL(σ_min, stabilize, check_obj, orders, time_limit)
+    return SpeedMappingJL(σ_min, stabilize, check_obj, orders)
 end
 
 """
diff --git a/src/algorithms/levenberg_marquardt.jl b/src/algorithms/levenberg_marquardt.jl
index 66554ee2d..e8a2fd0d7 100644
--- a/src/algorithms/levenberg_marquardt.jl
+++ b/src/algorithms/levenberg_marquardt.jl
@@ -31,19 +31,11 @@ For the remaining arguments, see [`GeodesicAcceleration`](@ref) and
 [`NonlinearSolve.LevenbergMarquardtTrustRegion`](@ref) documentations.
 """
 function LevenbergMarquardt(;
-        concrete_jac = missing, linsolve = nothing, precs = DEFAULT_PRECS,
-        damping_initial::Real = 1.0, α_geodesic::Real = 0.75,
-        damping_increase_factor::Real = 2.0, damping_decrease_factor::Real = 3.0,
-        finite_diff_step_geodesic = 0.1, b_uphill::Real = 1.0,
-        autodiff = nothing, min_damping_D::Real = 1e-8, disable_geodesic = False)
-    if concrete_jac !== missing
-        Base.depwarn("The `concrete_jac` keyword argument is deprecated and will be \
-                      removed in v0.4. This kwarg doesn't make sense (and is currently \
-                      ignored) for LM since it needs to materialize the Jacobian to \
-                      compute the Damping Term",
-            :LevenbergMarquardt)
-    end
-
+        linsolve = nothing, precs = DEFAULT_PRECS, damping_initial::Real = 1.0,
+        α_geodesic::Real = 0.75, damping_increase_factor::Real = 2.0,
+        damping_decrease_factor::Real = 3.0, finite_diff_step_geodesic = 0.1,
+        b_uphill::Real = 1.0, autodiff = nothing,
+        min_damping_D::Real = 1e-8, disable_geodesic = False)
     descent = DampedNewtonDescent(; linsolve,
         precs,
         initial_damping = damping_initial,
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index b78eb7383..358bca792 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -243,17 +243,11 @@ function select_fastest_coloring_algorithm(
     return GreedyColoringAlgorithm(LargestFirst())
 end
 
-function construct_concrete_adtype(f::NonlinearFunction, ad::AutoSparse)
-    Base.depwarn(
-        "Specifying a sparse AD type for Nonlinear Problems is deprecated. \
-         Instead use the `sparsity`, `jac_prototype`, and `colorvec` to specify \
-         the right sparsity pattern and coloring algorithm. Ignoring the sparsity \
-         detection algorithm and coloring algorithm present in $(ad).",
-        :NonlinearSolve)
-    if f.sparsity === nothing && f.jac_prototype === nothing
-        @set! f.sparsity = TracerSparsityDetector()
-    end
-    return construct_concrete_adtype(f, get_dense_ad(ad))
+function construct_concrete_adtype(::NonlinearFunction, ad::AutoSparse)
+    error("Specifying a sparse AD type for Nonlinear Problems was removed in v4. \
+           Instead use the `sparsity`, `jac_prototype`, and `colorvec` to specify \
+           the right sparsity pattern and coloring algorithm. Ignoring the sparsity \
+           detection algorithm and coloring algorithm present in $(ad).")
 end
 
 get_dense_ad(ad) = ad

From 20f9b57abc552154fdb7c8d45c3751d11a49e8ea Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 12:38:06 -0400
Subject: [PATCH 604/700] chore: remove more deprecations

---
 Project.toml                |  4 +---
 src/NonlinearSolve.jl       | 48 +++++++++++++++++++++----------------
 test/core/nlls_tests.jl     | 10 ++++++--
 test/core/rootfind_tests.jl | 41 +++++++++++++++++++++----------
 4 files changed, 64 insertions(+), 39 deletions(-)

diff --git a/Project.toml b/Project.toml
index 6bf13d3a3..246b935a7 100644
--- a/Project.toml
+++ b/Project.toml
@@ -26,7 +26,6 @@ Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
 SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
-Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
@@ -104,8 +103,7 @@ SIAMFANLEquations = "1.0.1"
 SciMLBase = "2.54.0"
 SciMLJacobianOperators = "0.1"
 SciMLOperators = "0.3.10"
-Setfield = "1.1.1"
-SimpleNonlinearSolve = "1.12.3"
+SimpleNonlinearSolve = "2"
 SparseArrays = "1.10"
 SparseConnectivityTracer = "0.6.5"
 SparseMatrixColorings = "0.4.2"
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 1f48371e6..a41027531 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -1,9 +1,5 @@
 module NonlinearSolve
 
-if isdefined(Base, :Experimental) && isdefined(Base.Experimental, Symbol("@max_methods"))
-    @eval Base.Experimental.@max_methods 1
-end
-
 using Reexport: @reexport
 using PrecompileTools: @compile_workload, @setup_workload
 
@@ -23,7 +19,7 @@ using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Sy
                      UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess, istril,
                      istriu, lu, mul!, norm, pinv, tril!, triu!
 using LineSearch: LineSearch, AbstractLineSearchAlgorithm, AbstractLineSearchCache,
-                  NoLineSearch, RobustNonMonotoneLineSearch, BackTracking
+                  NoLineSearch, RobustNonMonotoneLineSearch, BackTracking, LineSearchesJL
 using LinearSolve: LinearSolve, LUFactorization, QRFactorization,
                    needs_concrete_A, AbstractFactorization,
                    DefaultAlgorithmChoice, DefaultLinearSolver
@@ -34,7 +30,6 @@ using RecursiveArrayTools: recursivecopy!
 using SciMLBase: AbstractNonlinearAlgorithm, AbstractNonlinearProblem, _unwrap_val,
                  isinplace, NLStats
 using SciMLOperators: AbstractSciMLOperator
-using Setfield: @set!
 using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
 using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
                                  symbolic_container, parameter_values, state_values, getu,
@@ -44,8 +39,6 @@ using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingPro
 using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
                AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme, AutoSparse,
                NoSparsityDetector, KnownJacobianSparsityDetector
-using ADTypes: AutoSparseFiniteDiff, AutoSparseForwardDiff, AutoSparsePolyesterForwardDiff,
-               AutoSparseZygote # FIXME: deprecated, remove in future
 using DifferentiationInterface: DifferentiationInterface, Constant
 using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff, Dual
@@ -114,11 +107,20 @@ include("default.jl")
         push!(probs_nls, NonlinearProblem(fn, u0, 2.0))
     end
 
-    nls_algs = (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
-        PseudoTransient(), Broyden(), Klement(), DFSane(), nothing)
+    nls_algs = (
+        NewtonRaphson(),
+        TrustRegion(),
+        LevenbergMarquardt(),
+        # PseudoTransient(),
+        Broyden(),
+        Klement(),
+        # DFSane(),
+        nothing
+    )
 
     probs_nlls = NonlinearLeastSquaresProblem[]
-    nlfuncs = ((NonlinearFunction{false}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
+    nlfuncs = (
+        (NonlinearFunction{false}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
         (NonlinearFunction{false}((u, p) -> vcat(u .* u .- p, u .* u .- p)), [0.1, 0.1]),
         (
             NonlinearFunction{true}(
@@ -127,15 +129,22 @@ include("default.jl")
         (
             NonlinearFunction{true}((du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p),
                 resid_prototype = zeros(4)),
-            [0.1, 0.1]))
+            [0.1, 0.1]
+        )
+    )
     for (fn, u0) in nlfuncs
         push!(probs_nlls, NonlinearLeastSquaresProblem(fn, u0, 2.0))
     end
 
-    nlls_algs = (LevenbergMarquardt(), GaussNewton(), TrustRegion(),
-        LevenbergMarquardt(; linsolve = LUFactorization()),
-        GaussNewton(; linsolve = LUFactorization()),
-        TrustRegion(; linsolve = LUFactorization()), nothing)
+    nlls_algs = (
+        LevenbergMarquardt(),
+        GaussNewton(),
+        TrustRegion(),
+        # LevenbergMarquardt(; linsolve = LUFactorization()),
+        # GaussNewton(; linsolve = LUFactorization()),
+        # TrustRegion(; linsolve = LUFactorization()),
+        nothing
+    )
 
     @compile_workload begin
         @sync begin
@@ -177,7 +186,7 @@ export LineSearch, BackTracking, NoLineSearch, RobustNonMonotoneLineSearch, Line
 ## Trust Region Algorithms
 export RadiusUpdateSchemes
 
-# Export the termination conditions from DiffEqBase
+# Export the termination conditions from NonlinearSolveBase
 export SteadyStateDiffEqTerminationMode, SimpleNonlinearSolveTerminationMode,
        NormTerminationMode, RelTerminationMode, RelNormTerminationMode, AbsTerminationMode,
        AbsNormTerminationMode, RelSafeTerminationMode, AbsSafeTerminationMode,
@@ -189,8 +198,5 @@ export TraceAll, TraceMinimal, TraceWithJacobianConditionNumber
 # Reexport ADTypes
 export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme,
        AutoSparse
-# FIXME: deprecated, remove in future
-export AutoSparseFiniteDiff, AutoSparseForwardDiff, AutoSparsePolyesterForwardDiff,
-       AutoSparseZygote
 
-end # module
+end
diff --git a/test/core/nlls_tests.jl b/test/core/nlls_tests.jl
index 483107f69..361c5ba20 100644
--- a/test/core/nlls_tests.jl
+++ b/test/core/nlls_tests.jl
@@ -2,6 +2,13 @@
 using Reexport
 @reexport using NonlinearSolve, LinearSolve, LinearAlgebra, StableRNGs, Random, ForwardDiff,
                 Zygote
+using LineSearches: LineSearches, Static, HagerZhang, MoreThuente, StrongWolfe
+
+linesearches = []
+for ls in (Static(), HagerZhang(), MoreThuente(), StrongWolfe(), LineSearches.BackTracking())
+    push!(linesearches, LineSearchesJL(; method = ls))
+end
+push!(linesearches, BackTracking())
 
 true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
 true_function(y, x, θ) = (@. y = θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4]))
@@ -29,8 +36,7 @@ solvers = []
 for linsolve in [nothing, LUFactorization(), KrylovJL_GMRES(), KrylovJL_LSMR()]
     vjp_autodiffs = linsolve isa KrylovJL ? [nothing, AutoZygote(), AutoFiniteDiff()] :
                     [nothing]
-    for linesearch in [Static(), BackTracking(), HagerZhang(), StrongWolfe(), MoreThuente()],
-        vjp_autodiff in vjp_autodiffs
+    for linesearch in linesearches, vjp_autodiff in vjp_autodiffs
 
         push!(solvers, GaussNewton(; linsolve, linesearch, vjp_autodiff))
     end
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index cb8d62e99..36c3e335b 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -2,6 +2,7 @@
 using Reexport
 @reexport using BenchmarkTools, LinearSolve, NonlinearSolve, StaticArrays, Random,
                 LinearAlgebra, ForwardDiff, Zygote, Enzyme, DiffEqBase
+using LineSearches: LineSearches
 
 _nameof(x) = applicable(nameof, x) ? nameof(x) : _nameof(typeof(x))
 
@@ -46,8 +47,19 @@ function nlprob_iterator_interface(f, p_range, ::Val{iip}, solver) where {iip}
     return sols
 end
 
+for alg in (:Static, :StrongWolfe, :BackTracking, :MoreThuente, :HagerZhang)
+    algname = Symbol(:LineSearches, alg)
+    @eval function $(algname)(args...; autodiff = nothing, initial_alpha = true, kwargs...)
+        return LineSearch.LineSearchesJL(;
+            method = LineSearches.$(alg)(args...; kwargs...), autodiff, initial_alpha)
+    end
+end
+
 export nlprob_iterator_interface, benchmark_nlsolve_oop, benchmark_nlsolve_iip,
        TERMINATION_CONDITIONS, _nameof, newton_fails, quadratic_f, quadratic_f!
+export LineSearchesStatic, LineSearchesStrongWolfe, LineSearchesBackTracking,
+       LineSearchesMoreThuente, LineSearchesHagerZhang
+
 end
 
 # --- NewtonRaphson tests ---
@@ -57,9 +69,10 @@ end
             AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()
         ),
         linesearch in (
-            Static(; autodiff = ad), StrongWolfe(; autodiff = ad),
-            BackTracking(; autodiff = ad), LineSearch.BackTracking(; autodiff = ad),
-            HagerZhang(; autodiff = ad), MoreThuente(; autodiff = ad)
+            LineSearchesStatic(; autodiff = ad), LineSearchesStrongWolfe(; autodiff = ad),
+            LineSearchesBackTracking(; autodiff = ad), BackTracking(; autodiff = ad),
+            LineSearchesHagerZhang(; autodiff = ad),
+            LineSearchesMoreThuente(; autodiff = ad)
         )
 
         u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
@@ -471,9 +484,10 @@ end
             AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()
         ),
         linesearch in (
-            Static(; autodiff = ad), StrongWolfe(; autodiff = ad),
-            BackTracking(; autodiff = ad), LineSearch.BackTracking(; autodiff = ad),
-            HagerZhang(; autodiff = ad), MoreThuente(; autodiff = ad)
+            LineSearchesStatic(; autodiff = ad), LineSearchesStrongWolfe(; autodiff = ad),
+            LineSearchesBackTracking(; autodiff = ad), BackTracking(; autodiff = ad),
+            LineSearchesHagerZhang(; autodiff = ad),
+            LineSearchesMoreThuente(; autodiff = ad)
         ),
         init_jacobian in (Val(:identity), Val(:true_jacobian)),
         update_rule in (Val(:good_broyden), Val(:bad_broyden), Val(:diagonal))
@@ -524,9 +538,10 @@ end
             AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()
         ),
         linesearch in (
-            Static(; autodiff = ad), StrongWolfe(; autodiff = ad),
-            BackTracking(; autodiff = ad), LineSearch.BackTracking(; autodiff = ad),
-            HagerZhang(; autodiff = ad), MoreThuente(; autodiff = ad)
+            LineSearchesStatic(; autodiff = ad), LineSearchesStrongWolfe(; autodiff = ad),
+            LineSearchesBackTracking(; autodiff = ad), BackTracking(; autodiff = ad),
+            LineSearchesHagerZhang(; autodiff = ad),
+            LineSearchesMoreThuente(; autodiff = ad)
         ),
         init_jacobian in (Val(:identity), Val(:true_jacobian), Val(:true_jacobian_diagonal))
 
@@ -577,10 +592,10 @@ end
             AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()
         ),
         linesearch in (
-            Static(; autodiff = ad), StrongWolfe(; autodiff = ad),
-            BackTracking(; autodiff = ad), LineSearch.BackTracking(; autodiff = ad),
-            HagerZhang(; autodiff = ad), MoreThuente(; autodiff = ad),
-            LiFukushimaLineSearch()
+            LineSearchesStatic(; autodiff = ad), LineSearchesStrongWolfe(; autodiff = ad),
+            LineSearchesBackTracking(; autodiff = ad), BackTracking(; autodiff = ad),
+            LineSearchesHagerZhang(; autodiff = ad),
+            LineSearchesMoreThuente(; autodiff = ad), LiFukushimaLineSearch()
         )
 
         u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)

From 425fe56f2e2c9749441aa4b1489bca2b0c506670 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 12:48:14 -0400
Subject: [PATCH 605/700] chore: run formatter

---
 test/core/nlls_tests.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/test/core/nlls_tests.jl b/test/core/nlls_tests.jl
index 361c5ba20..040627c00 100644
--- a/test/core/nlls_tests.jl
+++ b/test/core/nlls_tests.jl
@@ -5,7 +5,8 @@ using Reexport
 using LineSearches: LineSearches, Static, HagerZhang, MoreThuente, StrongWolfe
 
 linesearches = []
-for ls in (Static(), HagerZhang(), MoreThuente(), StrongWolfe(), LineSearches.BackTracking())
+for ls in (
+    Static(), HagerZhang(), MoreThuente(), StrongWolfe(), LineSearches.BackTracking())
     push!(linesearches, LineSearchesJL(; method = ls))
 end
 push!(linesearches, BackTracking())
@@ -37,7 +38,6 @@ for linsolve in [nothing, LUFactorization(), KrylovJL_GMRES(), KrylovJL_LSMR()]
     vjp_autodiffs = linsolve isa KrylovJL ? [nothing, AutoZygote(), AutoFiniteDiff()] :
                     [nothing]
     for linesearch in linesearches, vjp_autodiff in vjp_autodiffs
-
         push!(solvers, GaussNewton(; linsolve, linesearch, vjp_autodiff))
     end
 end

From 5af1f3f85b0a2c730fcf715cb13f623cb49c8ff8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 12:55:28 -0400
Subject: [PATCH 606/700] test: try fixing circular deps

---
 .github/workflows/Documentation.yml | 2 +-
 Project.toml                        | 3 +--
 docs/Project.toml                   | 8 ++++----
 test/runtests.jl                    | 7 ++++++-
 4 files changed, 12 insertions(+), 8 deletions(-)

diff --git a/.github/workflows/Documentation.yml b/.github/workflows/Documentation.yml
index 008cd511e..84f38404f 100644
--- a/.github/workflows/Documentation.yml
+++ b/.github/workflows/Documentation.yml
@@ -22,7 +22,7 @@ jobs:
           Pkg.Registry.update()
           # Install packages present in subdirectories
           dev_pks = Pkg.PackageSpec[]
-          for path in ("lib/SciMLJacobianOperators", ".")
+          for path in ("lib/SciMLJacobianOperators", ".", "lib/SimpleNonlinearSolve", "lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve")
               push!(dev_pks, Pkg.PackageSpec(; path))
           end
           Pkg.develop(dev_pks)
diff --git a/Project.toml b/Project.toml
index 246b935a7..184aed113 100644
--- a/Project.toml
+++ b/Project.toml
@@ -132,7 +132,6 @@ InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
 LineSearches = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
 MINPACK = "4854310b-de5a-5eb6-a2a5-c1dee2bd17f9"
-ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 NaNMath = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
@@ -150,4 +149,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "LineSearches", "MINPACK", "ModelingToolkit", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "LineSearches", "MINPACK", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Test", "Zygote"]
diff --git a/docs/Project.toml b/docs/Project.toml
index 4ad265246..d01ae32a1 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -37,14 +37,14 @@ DocumenterInterLinks = "1.0.0"
 IncompleteLU = "0.2"
 InteractiveUtils = "<0.0.1, 1"
 LinearSolve = "2"
-ModelingToolkit = "8, 9"
-NonlinearSolve = "3"
+ModelingToolkit = "9"
+NonlinearSolve = "4"
 OrdinaryDiffEqTsit5 = "1.1.0"
 Plots = "1"
-Random = "<0.0.1, 1"
+Random = "1.10"
 SciMLBase = "2.4"
 SciMLJacobianOperators = "0.1"
-SimpleNonlinearSolve = "1"
+SimpleNonlinearSolve = "2"
 SparseConnectivityTracer = "0.6.5"
 StaticArrays = "1"
 SteadyStateDiffEq = "2"
diff --git a/test/runtests.jl b/test/runtests.jl
index 74676f3ad..bf2a8ecdb 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,9 +1,14 @@
-using ReTestItems, NonlinearSolve, Hwloc, InteractiveUtils
+using ReTestItems, NonlinearSolve, Hwloc, InteractiveUtils, Pkg
 
 @info sprint(InteractiveUtils.versioninfo)
 
 const GROUP = lowercase(get(ENV, "GROUP", "All"))
 
+const EXTRA_PKGS = Pkg.PackageSpec[]
+(GROUP == "all" || GROUP == "downstream") &&
+    push!(EXTRA_PKGS, Pkg.PackageSpec("ModelingToolkit"))
+Pkg.add(EXTRA_PKGS)
+
 const RETESTITEMS_NWORKERS = parse(
     Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4))))
 const RETESTITEMS_NWORKER_THREADS = parse(Int,

From 3b36884860bbc42e6a29aa4943fb2c774b2cf3e4 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 13:04:37 -0400
Subject: [PATCH 607/700] chore: remove unnecessary deps

---
 Project.toml                               |  9 ++++-----
 src/NonlinearSolve.jl                      |  8 ++++----
 src/algorithms/levenberg_marquardt.jl      | 10 ++++------
 src/descent/damped_newton.jl               | 12 ++++++------
 src/internal/approximate_initialization.jl |  6 +++---
 test/runtests.jl                           |  4 ++--
 6 files changed, 23 insertions(+), 26 deletions(-)

diff --git a/Project.toml b/Project.toml
index 184aed113..572dbb6fe 100644
--- a/Project.toml
+++ b/Project.toml
@@ -9,7 +9,6 @@ ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
-FastBroadcast = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -18,6 +17,7 @@ LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
+NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Preferences = "21216c6a-2e73-6563-6e65-726566657250"
 Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
@@ -28,7 +28,6 @@ SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
 SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
-SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
 SparseMatrixColorings = "0a514795-09f3-496d-8182-132a7b665d35"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
@@ -69,7 +68,6 @@ DiffEqBase = "6.155.3"
 DifferentiationInterface = "0.6.1"
 Enzyme = "0.13.2"
 ExplicitImports = "1.5"
-FastBroadcast = "0.3.5"
 FastClosures = "0.3.2"
 FastLevenbergMarquardt = "0.1"
 FiniteDiff = "2.24"
@@ -85,11 +83,11 @@ LinearAlgebra = "1.10"
 LinearSolve = "2.35"
 MINPACK = "1.2"
 MaybeInplace = "0.1.4"
-ModelingToolkit = "9.41.0"
 NLSolvers = "0.5"
 NLsolve = "4.5"
 NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
+NonlinearSolveBase = "1"
 OrdinaryDiffEqTsit5 = "1.1.0"
 Pkg = "1.10"
 PrecompileTools = "1.2"
@@ -141,6 +139,7 @@ Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
+SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
 SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
@@ -149,4 +148,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "LineSearches", "MINPACK", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "LineSearches", "MINPACK", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SparseConnectivityTracer", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Test", "Zygote"]
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index a41027531..15e1ee3a9 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -12,14 +12,14 @@ using DiffEqBase: DiffEqBase, AbstractNonlinearTerminationMode,
                   NormTerminationMode, RelNormTerminationMode, RelSafeBestTerminationMode,
                   RelSafeTerminationMode, RelTerminationMode,
                   SimpleNonlinearSolveTerminationMode, SteadyStateDiffEqTerminationMode
-using FastBroadcast: @..
 using FastClosures: @closure
 using LazyArrays: LazyArrays, ApplyArray, cache
 using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Symmetric,
                      UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess, istril,
                      istriu, lu, mul!, norm, pinv, tril!, triu!
 using LineSearch: LineSearch, AbstractLineSearchAlgorithm, AbstractLineSearchCache,
-                  NoLineSearch, RobustNonMonotoneLineSearch, BackTracking, LineSearchesJL
+                  NoLineSearch, RobustNonMonotoneLineSearch, BackTracking, LineSearchesJL,
+                  LiFukushimaLineSearch
 using LinearSolve: LinearSolve, LUFactorization, QRFactorization,
                    needs_concrete_A, AbstractFactorization,
                    DefaultAlgorithmChoice, DefaultLinearSolver
@@ -47,7 +47,6 @@ using SciMLJacobianOperators: AbstractJacobianOperator, JacobianOperator, VecJac
 
 ## Sparse AD Support
 using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
-using SparseConnectivityTracer: TracerSparsityDetector # This can be dropped in the next release
 using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm,
                              LargestFirst
 
@@ -182,7 +181,8 @@ export NewtonDescent, SteepestDescent, Dogleg, DampedNewtonDescent, GeodesicAcce
 
 # Globalization
 ## Line Search Algorithms
-export LineSearch, BackTracking, NoLineSearch, RobustNonMonotoneLineSearch, LineSearchesJL
+export LineSearch, BackTracking, NoLineSearch, RobustNonMonotoneLineSearch,
+       LiFukushimaLineSearch, LineSearchesJL
 ## Trust Region Algorithms
 export RadiusUpdateSchemes
 
diff --git a/src/algorithms/levenberg_marquardt.jl b/src/algorithms/levenberg_marquardt.jl
index e8a2fd0d7..501a5dd29 100644
--- a/src/algorithms/levenberg_marquardt.jl
+++ b/src/algorithms/levenberg_marquardt.jl
@@ -156,18 +156,16 @@ end
 @inline function __update_LM_diagonal!!(y::Diagonal, x::AbstractMatrix)
     if __can_setindex(y.diag)
         if fast_scalar_indexing(y.diag)
-            @inbounds for i in axes(x, 1)
-                y.diag[i] = max(y.diag[i], x[i, i])
+            @simd for i in axes(x, 1)
+                @inbounds y.diag[i] = max(y.diag[i], x[i, i])
             end
             return y
         else
-            idxs = diagind(x)
-            @.. broadcast=false y.diag=max(y.diag, @view(x[idxs]))
+            y .= max.(y.diag, @view(x[diagind(x)]))
             return y
         end
     else
-        idxs = diagind(x)
-        return Diagonal(@.. broadcast=false max(y.diag, @view(x[idxs])))
+        return Diagonal(max.(y.diag, @view(x[diagind(x)])))
     end
 end
 
diff --git a/src/descent/damped_newton.jl b/src/descent/damped_newton.jl
index 77b204b13..ba3e1d028 100644
--- a/src/descent/damped_newton.jl
+++ b/src/descent/damped_newton.jl
@@ -226,12 +226,12 @@ end
     if __can_setindex(J_cache)
         copyto!(J_cache, J)
         if fast_scalar_indexing(J_cache)
-            @inbounds for i in axes(J_cache, 1)
-                J_cache[i, i] += D[i, i]
+            @simd for i in axes(J_cache, 1)
+                @inbounds J_cache[i, i] += D[i, i]
             end
         else
             idxs = diagind(J_cache)
-            @.. broadcast=false @view(J_cache[idxs])=@view(J[idxs]) + @view(D[idxs])
+            J_cache[idxs] .= @view(J[idxs]) .+ @view(D[idxs])
         end
         return J_cache
     else
@@ -242,12 +242,12 @@ end
     if __can_setindex(J_cache)
         copyto!(J_cache, J)
         if fast_scalar_indexing(J_cache)
-            @inbounds for i in axes(J_cache, 1)
-                J_cache[i, i] += D
+            @simd for i in axes(J_cache, 1)
+                @inbounds J_cache[i, i] += D
             end
         else
             idxs = diagind(J_cache)
-            @.. broadcast=false @view(J_cache[idxs])=@view(J[idxs]) + D
+            J_cache[idxs] .= @view(J[idxs]) .+ D
         end
         return J_cache
     else
diff --git a/src/internal/approximate_initialization.jl b/src/internal/approximate_initialization.jl
index 5ce348ae3..985234ac4 100644
--- a/src/internal/approximate_initialization.jl
+++ b/src/internal/approximate_initialization.jl
@@ -20,11 +20,11 @@ end
 function (::DiagonalStructure)(J::AbstractVector, J_new::AbstractMatrix)
     if __can_setindex(J)
         if fast_scalar_indexing(J)
-            @inbounds for i in eachindex(J)
-                J[i] = J_new[i, i]
+            @simd for i in eachindex(J)
+                @inbounds J[i] = J_new[i, i]
             end
         else
-            @.. broadcast=false J=@view(J_new[diagind(J_new)])
+            J .= @view(J_new[diagind(J_new)])
         end
         return J
     end
diff --git a/test/runtests.jl b/test/runtests.jl
index bf2a8ecdb..33ca5da7a 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -7,7 +7,7 @@ const GROUP = lowercase(get(ENV, "GROUP", "All"))
 const EXTRA_PKGS = Pkg.PackageSpec[]
 (GROUP == "all" || GROUP == "downstream") &&
     push!(EXTRA_PKGS, Pkg.PackageSpec("ModelingToolkit"))
-Pkg.add(EXTRA_PKGS)
+length(EXTRA_PKGS) ≥ 1 && Pkg.add(EXTRA_PKGS)
 
 const RETESTITEMS_NWORKERS = parse(
     Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4))))
@@ -19,4 +19,4 @@ const RETESTITEMS_NWORKER_THREADS = parse(Int,
 
 ReTestItems.runtests(NonlinearSolve; tags = (GROUP == "all" ? nothing : [Symbol(GROUP)]),
     nworkers = RETESTITEMS_NWORKERS, nworker_threads = RETESTITEMS_NWORKER_THREADS,
-    testitem_timeout = 3600, retries = 4)
+    testitem_timeout = 3600)

From fca1af299b8a3621570ab3e736b5a673be924709 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 16:48:58 -0400
Subject: [PATCH 608/700] fix: `misc` test group

---
 src/NonlinearSolve.jl    | 13 +++----------
 test/misc/bruss_tests.jl |  5 -----
 2 files changed, 3 insertions(+), 15 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 15e1ee3a9..903a1f33d 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -17,11 +17,9 @@ using LazyArrays: LazyArrays, ApplyArray, cache
 using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Symmetric,
                      UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess, istril,
                      istriu, lu, mul!, norm, pinv, tril!, triu!
-using LineSearch: LineSearch, AbstractLineSearchAlgorithm, AbstractLineSearchCache,
-                  NoLineSearch, RobustNonMonotoneLineSearch, BackTracking, LineSearchesJL,
-                  LiFukushimaLineSearch
-using LinearSolve: LinearSolve, LUFactorization, QRFactorization,
-                   needs_concrete_A, AbstractFactorization,
+using LineSearch: LineSearch, AbstractLineSearchCache, LineSearchesJL, NoLineSearch,
+                  RobustNonMonotoneLineSearch, BackTracking,  LiFukushimaLineSearch
+using LinearSolve: LinearSolve, QRFactorization, needs_concrete_A, AbstractFactorization,
                    DefaultAlgorithmChoice, DefaultLinearSolver
 using MaybeInplace: @bb
 using Printf: @printf
@@ -110,10 +108,8 @@ include("default.jl")
         NewtonRaphson(),
         TrustRegion(),
         LevenbergMarquardt(),
-        # PseudoTransient(),
         Broyden(),
         Klement(),
-        # DFSane(),
         nothing
     )
 
@@ -139,9 +135,6 @@ include("default.jl")
         LevenbergMarquardt(),
         GaussNewton(),
         TrustRegion(),
-        # LevenbergMarquardt(; linsolve = LUFactorization()),
-        # GaussNewton(; linsolve = LUFactorization()),
-        # TrustRegion(; linsolve = LUFactorization()),
         nothing
     )
 
diff --git a/test/misc/bruss_tests.jl b/test/misc/bruss_tests.jl
index 80b1bd540..32a3fff68 100644
--- a/test/misc/bruss_tests.jl
+++ b/test/misc/bruss_tests.jl
@@ -52,11 +52,6 @@
     sol = solve(prob_brusselator_2d_sparse, NewtonRaphson(); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
-    # Deprecated
-    sol = solve(prob_brusselator_2d,
-        NewtonRaphson(autodiff = AutoSparse(AutoFiniteDiff())); abstol = 1e-8)
-    @test norm(sol.resid, Inf) < 1e-8
-
     f! = (du, u) -> brusselator_2d_loop(du, u, p)
     du0 = similar(u0)
     jac_prototype = ADTypes.jacobian_sparsity(f!, du0, u0, TracerSparsityDetector())

From d4ea3190e9dcef376c9fbb19279431540b9a68c3 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 17:14:12 -0400
Subject: [PATCH 609/700] fix: forwarddiff support

---
 .../ext/NonlinearSolveBaseForwardDiffExt.jl     | 12 ++++++------
 lib/NonlinearSolveBase/src/public.jl            |  2 ++
 src/NonlinearSolve.jl                           |  3 +++
 src/internal/forward_diff.jl                    | 17 +++++++----------
 4 files changed, 18 insertions(+), 16 deletions(-)

diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
index e50be6c47..c4f1dc901 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
@@ -37,8 +37,8 @@ function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
     sol = solve(newprob, alg, args...; kwargs...)
 
     uu = sol.u
-    Jₚ = nonlinearsolve_∂f_∂p(prob, prob.f, uu, p)
-    Jᵤ = nonlinearsolve_∂f_∂u(prob, prob.f, uu, p)
+    Jₚ = NonlinearSolveBase.nonlinearsolve_∂f_∂p(prob, prob.f, uu, p)
+    Jᵤ = NonlinearSolveBase.nonlinearsolve_∂f_∂u(prob, prob.f, uu, p)
     z = -Jᵤ \ Jₚ
     pp = prob.p
     sumfun = ((z, p),) -> map(Base.Fix2(*, ForwardDiff.partials(p)), z)
@@ -123,8 +123,8 @@ function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
         end
     end
 
-    Jₚ = nonlinearsolve_∂f_∂p(prob, vjp_fn, uu, newprob.p)
-    Jᵤ = nonlinearsolve_∂f_∂u(prob, vjp_fn, uu, newprob.p)
+    Jₚ = NonlinearSolveBase.nonlinearsolve_∂f_∂p(prob, vjp_fn, uu, newprob.p)
+    Jᵤ = NonlinearSolveBase.nonlinearsolve_∂f_∂u(prob, vjp_fn, uu, newprob.p)
     z = -Jᵤ \ Jₚ
     pp = prob.p
     sumfun = ((z, p),) -> map(Base.Fix2(*, ForwardDiff.partials(p)), z)
@@ -140,7 +140,7 @@ function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
     return sol, partials
 end
 
-function nonlinearsolve_∂f_∂p(prob, f::F, u, p) where {F}
+function NonlinearSolveBase.nonlinearsolve_∂f_∂p(prob, f::F, u, p) where {F}
     if SciMLBase.isinplace(prob)
         f2 = @closure p -> begin
             du = Utils.safe_similar(u, promote_type(eltype(u), eltype(p)))
@@ -159,7 +159,7 @@ function nonlinearsolve_∂f_∂p(prob, f::F, u, p) where {F}
     end
 end
 
-function nonlinearsolve_∂f_∂u(prob, f::F, u, p) where {F}
+function NonlinearSolveBase.nonlinearsolve_∂f_∂u(prob, f::F, u, p) where {F}
     if SciMLBase.isinplace(prob)
         return ForwardDiff.jacobian(
             @closure((du, u)->f(du, u, p)), Utils.safe_similar(u), u)
diff --git a/lib/NonlinearSolveBase/src/public.jl b/lib/NonlinearSolveBase/src/public.jl
index d9014d71e..eceea6d75 100644
--- a/lib/NonlinearSolveBase/src/public.jl
+++ b/lib/NonlinearSolveBase/src/public.jl
@@ -8,6 +8,8 @@ function get_tolerance end
 # Forward declarations of functions for forward mode AD
 function nonlinearsolve_forwarddiff_solve end
 function nonlinearsolve_dual_solution end
+function nonlinearsolve_∂f_∂p end
+function nonlinearsolve_∂f_∂u end
 
 # Nonlinear Solve Termination Conditions
 abstract type AbstractNonlinearTerminationMode end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 903a1f33d..853cbdf19 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -22,6 +22,9 @@ using LineSearch: LineSearch, AbstractLineSearchCache, LineSearchesJL, NoLineSea
 using LinearSolve: LinearSolve, QRFactorization, needs_concrete_A, AbstractFactorization,
                    DefaultAlgorithmChoice, DefaultLinearSolver
 using MaybeInplace: @bb
+using NonlinearSolveBase: NonlinearSolveBase, nonlinearsolve_forwarddiff_solve,
+                          nonlinearsolve_dual_solution, nonlinearsolve_∂f_∂p,
+                          nonlinearsolve_∂f_∂u
 using Printf: @printf
 using Preferences: Preferences, @load_preference, @set_preferences!
 using RecursiveArrayTools: recursivecopy!
diff --git a/src/internal/forward_diff.jl b/src/internal/forward_diff.jl
index 190c80645..a4238674e 100644
--- a/src/internal/forward_diff.jl
+++ b/src/internal/forward_diff.jl
@@ -1,15 +1,12 @@
-# Not part of public API but helps reduce code duplication
-import SimpleNonlinearSolve: __nlsolve_ad, __nlsolve_dual_soln, __nlsolve_∂f_∂p,
-                             __nlsolve_∂f_∂u
-
+# XXX: dispatch on `__solve` & `__init`
 function SciMLBase.solve(
         prob::NonlinearProblem{<:Union{Number, <:AbstractArray}, iip,
             <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
         alg::Union{Nothing, AbstractNonlinearAlgorithm},
         args...;
         kwargs...) where {T, V, P, iip}
-    sol, partials = __nlsolve_ad(prob, alg, args...; kwargs...)
-    dual_soln = __nlsolve_dual_soln(sol.u, partials, prob.p)
+    sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
+    dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
     return SciMLBase.build_solution(
         prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
 end
@@ -53,10 +50,10 @@ function SciMLBase.solve!(cache::NonlinearSolveForwardDiffCache)
     prob = cache.prob
 
     uu = sol.u
-    f_p = __nlsolve_∂f_∂p(prob, prob.f, uu, cache.values_p)
-    f_x = __nlsolve_∂f_∂u(prob, prob.f, uu, cache.values_p)
+    Jₚ = nonlinearsolve_∂f_∂p(prob, prob.f, uu, cache.values_p)
+    Jᵤ = nonlinearsolve_∂f_∂u(prob, prob.f, uu, cache.values_p)
 
-    z_arr = -f_x \ f_p
+    z_arr = -Jᵤ \ Jₚ
 
     sumfun = ((z, p),) -> map(zᵢ -> zᵢ * ForwardDiff.partials(p), z)
     if cache.p isa Number
@@ -65,7 +62,7 @@ function SciMLBase.solve!(cache::NonlinearSolveForwardDiffCache)
         partials = sum(sumfun, zip(eachcol(z_arr), cache.p))
     end
 
-    dual_soln = __nlsolve_dual_soln(sol.u, partials, cache.p)
+    dual_soln = nonlinearsolve_dual_solution(sol.u, partials, cache.p)
     return SciMLBase.build_solution(
         prob, cache.alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
 end

From f4757f3006083a15450396f883779194fc7ac615 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 17:35:20 -0400
Subject: [PATCH 610/700] fix: remove deprecated APIs

---
 docs/src/basics/sparsity_detection.md    | 19 ----------------
 docs/src/basics/termination_condition.md | 15 ------------
 test/core/rootfind_tests.jl              | 29 ++++++++++++------------
 3 files changed, 15 insertions(+), 48 deletions(-)

diff --git a/docs/src/basics/sparsity_detection.md b/docs/src/basics/sparsity_detection.md
index de924c398..b7782c437 100644
--- a/docs/src/basics/sparsity_detection.md
+++ b/docs/src/basics/sparsity_detection.md
@@ -76,22 +76,3 @@ prob = NonlinearProblem(
 
 Refer to the documentation of DifferentiationInterface.jl and SparseConnectivityTracer.jl
 for more information on sparsity detection algorithms.
-
-## Case III: Sparse AD Type is being Used
-
-!!! warning
-    
-    This is now deprecated. Please use the previous two cases instead.
-
-If you constructed a Nonlinear Solver with a sparse AD type, for example
-
-```julia
-NewtonRaphson(; autodiff = AutoSparse(AutoForwardDiff()))
-# OR
-TrustRegion(; autodiff = AutoSparse(AutoZygote()))
-```
-
-then NonlinearSolve will automatically perform matrix coloring and use sparse
-differentiation if none of `sparsity` or `jac_prototype` is provided. We default to using
-`TracerSparsityDetector()`. `Case I/II` take precedence for sparsity detection and we
-perform sparse AD based on those options if those are provided.
diff --git a/docs/src/basics/termination_condition.md b/docs/src/basics/termination_condition.md
index a87f157aa..fd01a06ad 100644
--- a/docs/src/basics/termination_condition.md
+++ b/docs/src/basics/termination_condition.md
@@ -54,18 +54,3 @@ not used as a default anywhere.
 ```@docs
 SimpleNonlinearSolveTerminationMode
 ```
-
-### Return Codes (Deprecated)
-
-These are deprecated and will be removed in a future release. Use the
-`use_deprecated_retcodes = Val(false)` option to `SciMLBase.init` to use the new return
-`ReturnCode` versions.
-
-```@docs
-DiffEqBase.NonlinearSafeTerminationReturnCode
-DiffEqBase.NonlinearSafeTerminationReturnCode.Success
-DiffEqBase.NonlinearSafeTerminationReturnCode.Default
-DiffEqBase.NonlinearSafeTerminationReturnCode.Failure
-DiffEqBase.NonlinearSafeTerminationReturnCode.PatienceTermination
-DiffEqBase.NonlinearSafeTerminationReturnCode.ProtectiveTermination
-```
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index 36c3e335b..e3f92fd26 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -1,7 +1,8 @@
 @testsetup module CoreRootfindTesting
 using Reexport
 @reexport using BenchmarkTools, LinearSolve, NonlinearSolve, StaticArrays, Random,
-                LinearAlgebra, ForwardDiff, Zygote, Enzyme, DiffEqBase
+                LinearAlgebra, ForwardDiff, Zygote, Enzyme, DiffEqBase,
+                SparseConnectivityTracer
 using LineSearches: LineSearches
 
 _nameof(x) = applicable(nameof, x) ? nameof(x) : _nameof(typeof(x))
@@ -116,12 +117,12 @@ end
     @test nlprob_iterator_interface(quadratic_f, p, Val(false), NewtonRaphson()) ≈ sqrt.(p)
     @test nlprob_iterator_interface(quadratic_f!, p, Val(true), NewtonRaphson()) ≈ sqrt.(p)
 
-    @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
-            AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
-            AutoZygote(), AutoSparse(AutoZygote()), AutoSparse(AutoEnzyme())),
+    @testset "Sparsity ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
+            AutoForwardDiff(), AutoFiniteDiff(), AutoZygote(), AutoEnzyme()),
         u0 in (1.0, [1.0, 1.0])
 
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
+        probN = NonlinearProblem(
+            NonlinearFunction(quadratic_f; sparsity = TracerSparsityDetector()), u0, 2.0)
         @test all(solve(probN, NewtonRaphson(; autodiff)).u .≈ sqrt(2.0))
     end
 
@@ -180,12 +181,12 @@ end
     @test nlprob_iterator_interface(quadratic_f!, p, Val(true), TrustRegion()) ≈ sqrt.(p)
 
     @testset "$(_nameof(autodiff)) u0: $(_nameof(u0)) $(radius_update_scheme)" for autodiff in (
-            AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
-            AutoZygote(), AutoSparse(AutoZygote()), AutoSparse(AutoEnzyme())),
+            AutoForwardDiff(), AutoFiniteDiff(), AutoZygote(), AutoEnzyme()),
         u0 in (1.0, [1.0, 1.0]),
         radius_update_scheme in radius_update_schemes
 
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
+        probN = NonlinearProblem(
+            NonlinearFunction(quadratic_f; sparsity = TracerSparsityDetector()), u0, 2.0)
         @test all(solve(probN, TrustRegion(; autodiff, radius_update_scheme)).u .≈
                   sqrt(2.0))
     end
@@ -276,11 +277,11 @@ end
     end
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
-            AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
-            AutoZygote(), AutoSparse(AutoZygote()), AutoSparse(AutoEnzyme())),
+            AutoForwardDiff(), AutoFiniteDiff(), AutoZygote(), AutoEnzyme()),
         u0 in (1.0, [1.0, 1.0])
 
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
+        probN = NonlinearProblem(
+            NonlinearFunction(quadratic_f; sparsity = TracerSparsityDetector()), u0, 2.0)
         @test all(solve(
             probN, LevenbergMarquardt(; autodiff); abstol = 1e-9, reltol = 1e-9).u .≈
                   sqrt(2.0))
@@ -458,11 +459,11 @@ end
         quadratic_f!, p, Val(true), PseudoTransient(; alpha_initial = 10.0)) ≈ sqrt.(p)
 
     @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
-            AutoSparse(AutoForwardDiff()), AutoSparse(AutoFiniteDiff()),
-            AutoZygote(), AutoSparse(AutoZygote()), AutoSparse(AutoEnzyme())),
+            AutoForwardDiff(), AutoFiniteDiff(), AutoZygote(), AutoEnzyme()),
         u0 in (1.0, [1.0, 1.0])
 
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
+        probN = NonlinearProblem(
+            NonlinearFunction(quadratic_f; sparsity = TracerSparsityDetector()), u0, 2.0)
         @test all(solve(probN, PseudoTransient(; alpha_initial = 10.0, autodiff)).u .≈
                   sqrt(2.0))
     end

From d38ba7ddc5398ca4c7c6214c31ed399107377e00 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 20:01:16 -0400
Subject: [PATCH 611/700] refactor: use functionality from `NonlinearSolveBase`
 instead of `DiffEqBase`

---
 Project.toml                                  |  2 +-
 docs/src/basics/solve.md                      |  2 +-
 docs/src/basics/termination_condition.md      | 25 +++-------------
 ...NonlinearSolveFastLevenbergMarquardtExt.jl |  5 ++--
 ...NonlinearSolveFixedPointAccelerationExt.jl |  3 +-
 ext/NonlinearSolveLeastSquaresOptimExt.jl     |  5 ++--
 ext/NonlinearSolveMINPACKExt.jl               |  3 +-
 ext/NonlinearSolveNLSolversExt.jl             |  5 ++--
 ext/NonlinearSolveNLsolveExt.jl               |  3 +-
 ext/NonlinearSolveSIAMFANLEquationsExt.jl     |  5 ++--
 ext/NonlinearSolveSpeedMappingExt.jl          |  3 +-
 lib/NonlinearSolveBase/src/utils.jl           |  2 +-
 src/NonlinearSolve.jl                         | 19 ++++--------
 src/abstract_types.jl                         | 15 ++++------
 src/algorithms/broyden.jl                     |  2 +-
 src/algorithms/lbroyden.jl                    |  2 +-
 src/algorithms/levenberg_marquardt.jl         |  2 +-
 src/algorithms/pseudo_transient.jl            |  2 +-
 src/core/approximate_jacobian.jl              |  6 ++--
 src/core/generalized_first_order.jl           |  6 ++--
 src/core/spectral_methods.jl                  |  4 +--
 src/default.jl                                |  4 +--
 src/descent/dogleg.jl                         |  2 +-
 src/descent/geodesic_acceleration.jl          |  2 +-
 src/globalization/trust_region.jl             |  4 +--
 src/internal/approximate_initialization.jl    |  8 ++---
 src/internal/termination.jl                   | 30 ++-----------------
 src/utils.jl                                  | 16 ++--------
 28 files changed, 65 insertions(+), 122 deletions(-)

diff --git a/Project.toml b/Project.toml
index 572dbb6fe..8841eca18 100644
--- a/Project.toml
+++ b/Project.toml
@@ -64,7 +64,7 @@ BandedMatrices = "1.5"
 BenchmarkTools = "1.4"
 CUDA = "5.5"
 ConcreteStructs = "0.2.3"
-DiffEqBase = "6.155.3"
+DiffEqBase = "6.158.3"
 DifferentiationInterface = "0.6.1"
 Enzyme = "0.13.2"
 ExplicitImports = "1.5"
diff --git a/docs/src/basics/solve.md b/docs/src/basics/solve.md
index 8ceeaa5de..f7c238966 100644
--- a/docs/src/basics/solve.md
+++ b/docs/src/basics/solve.md
@@ -21,7 +21,7 @@ solve(prob::SciMLBase.NonlinearProblem, args...; kwargs...)
     `real(oneunit(T)) * (eps(real(one(T))))^(4 // 5)`.
   - `reltol::Number`: The relative tolerance. Defaults to
     `real(oneunit(T)) * (eps(real(one(T))))^(4 // 5)`.
-  - `termination_condition`: Termination Condition from DiffEqBase. Defaults to
+  - `termination_condition`: Termination Condition from NonlinearSolveBase. Defaults to
     `AbsSafeBestTerminationMode()` for `NonlinearSolve.jl` and `AbsTerminateMode()` for
     `SimpleNonlinearSolve.jl`.
 
diff --git a/docs/src/basics/termination_condition.md b/docs/src/basics/termination_condition.md
index fd01a06ad..9a7c718ec 100644
--- a/docs/src/basics/termination_condition.md
+++ b/docs/src/basics/termination_condition.md
@@ -14,9 +14,6 @@ cache = init(du, u, AbsSafeBestTerminationMode(); abstol = 1e-9, reltol = 1e-9)
 If `abstol` and `reltol` are not supplied, then we choose a default based on the element
 types of `du` and `u`.
 
-We can query the `cache` using `DiffEqBase.get_termination_mode`, `DiffEqBase.get_abstol`
-and `DiffEqBase.get_reltol`.
-
 To test for termination simply call the `cache`:
 
 ```julia
@@ -28,8 +25,8 @@ terminated = cache(du, u, uprev)
 ```@docs
 AbsTerminationMode
 AbsNormTerminationMode
-AbsSafeTerminationMode
-AbsSafeBestTerminationMode
+AbsNormSafeTerminationMode
+AbsNormSafeBestTerminationMode
 ```
 
 ### Relative Tolerance
@@ -37,20 +34,6 @@ AbsSafeBestTerminationMode
 ```@docs
 RelTerminationMode
 RelNormTerminationMode
-RelSafeTerminationMode
-RelSafeBestTerminationMode
-```
-
-### Both Absolute and Relative Tolerance
-
-```@docs
-NormTerminationMode
-SteadyStateDiffEqTerminationMode
-```
-
-The following was named to match an older version of SimpleNonlinearSolve. It is currently
-not used as a default anywhere.
-
-```@docs
-SimpleNonlinearSolveTerminationMode
+RelNormSafeTerminationMode
+RelNormSafeBestTerminationMode
 ```
diff --git a/ext/NonlinearSolveFastLevenbergMarquardtExt.jl b/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
index 262f811a7..e772043b3 100644
--- a/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
+++ b/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
@@ -3,6 +3,7 @@ module NonlinearSolveFastLevenbergMarquardtExt
 using ArrayInterface: ArrayInterface
 using FastClosures: @closure
 using FastLevenbergMarquardt: FastLevenbergMarquardt
+using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
 using NonlinearSolve: NonlinearSolve, FastLevenbergMarquardtJL
 using SciMLBase: SciMLBase, NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode
 using StaticArraysCore: SArray
@@ -33,8 +34,8 @@ function SciMLBase.__solve(prob::Union{NonlinearLeastSquaresProblem, NonlinearPr
     else
         @closure (du, u, p) -> fn(du, u)
     end
-    abstol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u))
-    reltol = NonlinearSolve.DEFAULT_TOLERANCE(reltol, eltype(u))
+    abstol = get_tolerance(abstol, eltype(u))
+    reltol = get_tolerance(reltol, eltype(u))
 
     _jac_fn = NonlinearSolve.__construct_extension_jac(
         prob, alg, u, resid; alg.autodiff, can_handle_oop = Val(prob.u0 isa SArray))
diff --git a/ext/NonlinearSolveFixedPointAccelerationExt.jl b/ext/NonlinearSolveFixedPointAccelerationExt.jl
index 6e26e5351..2d36d7f56 100644
--- a/ext/NonlinearSolveFixedPointAccelerationExt.jl
+++ b/ext/NonlinearSolveFixedPointAccelerationExt.jl
@@ -1,5 +1,6 @@
 module NonlinearSolveFixedPointAccelerationExt
 
+using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
 using NonlinearSolve: NonlinearSolve, FixedPointAccelerationJL
 using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
 using FixedPointAcceleration: FixedPointAcceleration, fixed_point
@@ -13,7 +14,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::FixedPointAccelerationJL
 
     f, u0, resid = NonlinearSolve.__construct_extension_f(
         prob; alias_u0, make_fixed_point = Val(true), force_oop = Val(true))
-    tol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u0))
+    tol = get_tolerance(abstol, eltype(u0))
 
     sol = fixed_point(f, u0; Algorithm = alg.algorithm, MaxIter = maxiters, MaxM = alg.m,
         ConvergenceMetricThreshold = tol, ExtrapolationPeriod = alg.extrapolation_period,
diff --git a/ext/NonlinearSolveLeastSquaresOptimExt.jl b/ext/NonlinearSolveLeastSquaresOptimExt.jl
index 6abe13a9c..20dac092d 100644
--- a/ext/NonlinearSolveLeastSquaresOptimExt.jl
+++ b/ext/NonlinearSolveLeastSquaresOptimExt.jl
@@ -2,6 +2,7 @@ module NonlinearSolveLeastSquaresOptimExt
 
 using ConcreteStructs: @concrete
 using LeastSquaresOptim: LeastSquaresOptim
+using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
 using NonlinearSolve: NonlinearSolve, LeastSquaresOptimJL, TraceMinimal
 using SciMLBase: SciMLBase, NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode
 
@@ -42,8 +43,8 @@ function SciMLBase.__init(prob::Union{NonlinearLeastSquaresProblem, NonlinearPro
     NonlinearSolve.__test_termination_condition(termination_condition, :LeastSquaresOptim)
 
     f!, u, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
-    abstol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u))
-    reltol = NonlinearSolve.DEFAULT_TOLERANCE(reltol, eltype(u))
+    abstol = get_tolerance(abstol, eltype(u))
+    reltol = get_tolerance(reltol, eltype(u))
 
     if prob.f.jac === nothing && alg.autodiff isa Symbol
         lsoprob = LSO.LeastSquaresProblem(; x = u, f!, y = resid, alg.autodiff,
diff --git a/ext/NonlinearSolveMINPACKExt.jl b/ext/NonlinearSolveMINPACKExt.jl
index 8299b0b45..3761a817f 100644
--- a/ext/NonlinearSolveMINPACKExt.jl
+++ b/ext/NonlinearSolveMINPACKExt.jl
@@ -1,6 +1,7 @@
 module NonlinearSolveMINPACKExt
 
 using MINPACK: MINPACK
+using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
 using NonlinearSolve: NonlinearSolve, CMINPACK
 using SciMLBase: SciMLBase, NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode
 using FastClosures: @closure
@@ -21,7 +22,7 @@ function SciMLBase.__solve(
 
     show_trace = ShT
     tracing = StT
-    tol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u0))
+    tol = get_tolerance(abstol, eltype(u0))
 
     if alg.autodiff === missing && prob.f.jac === nothing
         original = MINPACK.fsolve(
diff --git a/ext/NonlinearSolveNLSolversExt.jl b/ext/NonlinearSolveNLSolversExt.jl
index e78dab947..a9f41c87c 100644
--- a/ext/NonlinearSolveNLSolversExt.jl
+++ b/ext/NonlinearSolveNLSolversExt.jl
@@ -6,6 +6,7 @@ using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff
 using LinearAlgebra: norm
 using NLSolvers: NLSolvers, NEqOptions, NEqProblem
+using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
 using NonlinearSolve: NonlinearSolve, NLSolversJL
 using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
 
@@ -14,8 +15,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
         alias_u0::Bool = false, termination_condition = nothing, kwargs...)
     NonlinearSolve.__test_termination_condition(termination_condition, :NLSolversJL)
 
-    abstol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(prob.u0))
-    reltol = NonlinearSolve.DEFAULT_TOLERANCE(reltol, eltype(prob.u0))
+    abstol = get_tolerance(abstol, eltype(prob.u0))
+    reltol = get_tolerance(reltol, eltype(prob.u0))
 
     options = NEqOptions(; maxiter = maxiters, f_abstol = abstol, f_reltol = reltol)
 
diff --git a/ext/NonlinearSolveNLsolveExt.jl b/ext/NonlinearSolveNLsolveExt.jl
index 9872c7953..301ed7137 100644
--- a/ext/NonlinearSolveNLsolveExt.jl
+++ b/ext/NonlinearSolveNLsolveExt.jl
@@ -1,6 +1,7 @@
 module NonlinearSolveNLsolveExt
 
 using LineSearches: Static
+using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
 using NonlinearSolve: NonlinearSolve, NLsolveJL, TraceMinimal
 using NLsolve: NLsolve, OnceDifferentiable, nlsolve
 using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
@@ -27,7 +28,7 @@ function SciMLBase.__solve(
         df = OnceDifferentiable(f!, jac!, vec(u0), vec(resid), J)
     end
 
-    abstol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u0))
+    abstol = get_tolerance(abstol, eltype(u0))
     show_trace = ShT
     store_trace = StT
     extended_trace = !(trace_level isa TraceMinimal)
diff --git a/ext/NonlinearSolveSIAMFANLEquationsExt.jl b/ext/NonlinearSolveSIAMFANLEquationsExt.jl
index 6ec3e8393..65154b63a 100644
--- a/ext/NonlinearSolveSIAMFANLEquationsExt.jl
+++ b/ext/NonlinearSolveSIAMFANLEquationsExt.jl
@@ -1,6 +1,7 @@
 module NonlinearSolveSIAMFANLEquationsExt
 
 using FastClosures: @closure
+using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
 using NonlinearSolve: NonlinearSolve, SIAMFANLEquationsJL
 using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
 using SIAMFANLEquations: SIAMFANLEquations, aasol, nsol, nsoli, nsolsc, ptcsol, ptcsoli,
@@ -40,8 +41,8 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SIAMFANLEquationsJL, arg
 
     (; method, delta, linsolve, m, beta) = alg
     T = eltype(prob.u0)
-    atol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, T)
-    rtol = NonlinearSolve.DEFAULT_TOLERANCE(reltol, T)
+    atol = get_tolerance(abstol, T)
+    rtol = get_tolerance(reltol, T)
 
     if prob.u0 isa Number
         f = @closure u -> prob.f(u, prob.p)
diff --git a/ext/NonlinearSolveSpeedMappingExt.jl b/ext/NonlinearSolveSpeedMappingExt.jl
index b39394a3b..ff9b4683b 100644
--- a/ext/NonlinearSolveSpeedMappingExt.jl
+++ b/ext/NonlinearSolveSpeedMappingExt.jl
@@ -1,5 +1,6 @@
 module NonlinearSolveSpeedMappingExt
 
+using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
 using NonlinearSolve: NonlinearSolve, SpeedMappingJL
 using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
 using SpeedMapping: speedmapping
@@ -12,7 +13,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SpeedMappingJL, args...;
 
     m!, u, resid = NonlinearSolve.__construct_extension_f(
         prob; alias_u0, make_fixed_point = Val(true))
-    tol = NonlinearSolve.DEFAULT_TOLERANCE(abstol, eltype(u))
+    tol = get_tolerance(abstol, eltype(u))
 
     time_limit = ifelse(maxtime === nothing, 1000, maxtime)
 
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index cb54a6f4c..825f63767 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -54,7 +54,7 @@ standardize_norm(f::F) where {F} = f
 norm_op(norm::N, op::OP, x, y) where {N, OP} = norm(op.(x, y))
 function norm_op(::typeof(L2_NORM), op::OP, x, y) where {OP}
     if fast_scalar_indexing(x, y)
-        return sqrt(sum(@closure((xᵢ, yᵢ)->begin
+        return sqrt(sum(@closure((xᵢyᵢ)->begin
                 xᵢ, yᵢ = xᵢyᵢ
                 return op(xᵢ, yᵢ)^2
             end), zip(x, y)))
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 853cbdf19..fd2c0bc3d 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -6,12 +6,7 @@ using PrecompileTools: @compile_workload, @setup_workload
 using ArrayInterface: ArrayInterface, can_setindex, restructure, fast_scalar_indexing,
                       ismutable
 using ConcreteStructs: @concrete
-using DiffEqBase: DiffEqBase, AbstractNonlinearTerminationMode,
-                  AbstractSafeBestNonlinearTerminationMode, AbsNormTerminationMode,
-                  AbsSafeBestTerminationMode, AbsSafeTerminationMode, AbsTerminationMode,
-                  NormTerminationMode, RelNormTerminationMode, RelSafeBestTerminationMode,
-                  RelSafeTerminationMode, RelTerminationMode,
-                  SimpleNonlinearSolveTerminationMode, SteadyStateDiffEqTerminationMode
+using DiffEqBase: DiffEqBase # Needed for `init` / `solve` dispatches
 using FastClosures: @closure
 using LazyArrays: LazyArrays, ApplyArray, cache
 using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Symmetric,
@@ -24,7 +19,9 @@ using LinearSolve: LinearSolve, QRFactorization, needs_concrete_A, AbstractFacto
 using MaybeInplace: @bb
 using NonlinearSolveBase: NonlinearSolveBase, nonlinearsolve_forwarddiff_solve,
                           nonlinearsolve_dual_solution, nonlinearsolve_∂f_∂p,
-                          nonlinearsolve_∂f_∂u
+                          nonlinearsolve_∂f_∂u, L2_NORM, AbstractNonlinearTerminationMode,
+                          AbstractSafeNonlinearTerminationMode,
+                          AbstractSafeBestNonlinearTerminationMode
 using Printf: @printf
 using Preferences: Preferences, @load_preference, @set_preferences!
 using RecursiveArrayTools: recursivecopy!
@@ -51,7 +48,7 @@ using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
 using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm,
                              LargestFirst
 
-@reexport using SciMLBase, SimpleNonlinearSolve
+@reexport using SciMLBase, SimpleNonlinearSolve, NonlinearSolveBase
 
 const DI = DifferentiationInterface
 
@@ -182,12 +179,6 @@ export LineSearch, BackTracking, NoLineSearch, RobustNonMonotoneLineSearch,
 ## Trust Region Algorithms
 export RadiusUpdateSchemes
 
-# Export the termination conditions from NonlinearSolveBase
-export SteadyStateDiffEqTerminationMode, SimpleNonlinearSolveTerminationMode,
-       NormTerminationMode, RelTerminationMode, RelNormTerminationMode, AbsTerminationMode,
-       AbsNormTerminationMode, RelSafeTerminationMode, AbsSafeTerminationMode,
-       RelSafeBestTerminationMode, AbsSafeBestTerminationMode
-
 # Tracing Functionality
 export TraceAll, TraceMinimal, TraceWithJacobianConditionNumber
 
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 0bb2e13d2..415dc5797 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -263,8 +263,7 @@ Abstract Type for Damping Functions in DampedNewton.
 ```julia
 __internal_init(
     prob::AbstractNonlinearProblem, f::AbstractDampingFunction, initial_damping,
-    J, fu, u, args...; internal_norm = DEFAULT_NORM, kwargs...) -->
-AbstractDampingFunctionCache
+    J, fu, u, args...; internal_norm = L2_NORM, kwargs...) --> AbstractDampingFunctionCache
 ```
 
 Returns a [`AbstractDampingFunctionCache`](@ref).
@@ -348,7 +347,7 @@ Abstract Type for all Jacobian Initialization Algorithms used in NonlinearSolve.
 ```julia
 __internal_init(
     prob::AbstractNonlinearProblem, alg::AbstractJacobianInitialization, solver,
-    f::F, fu, u, p; linsolve = missing, internalnorm::IN = DEFAULT_NORM, kwargs...)
+    f::F, fu, u, p; linsolve = missing, internalnorm::IN = L2_NORM, kwargs...)
 ```
 
 Returns a [`NonlinearSolve.InitializedApproximateJacobianCache`](@ref).
@@ -382,9 +381,8 @@ Abstract Type for all Approximate Jacobian Update Rules used in NonlinearSolve.j
 
 ```julia
 __internal_init(
-    prob::AbstractNonlinearProblem, alg::AbstractApproximateJacobianUpdateRule, J,
-    fu, u, du, args...; internalnorm::F = DEFAULT_NORM, kwargs...) where {F} -->
-AbstractApproximateJacobianUpdateRuleCache{INV}
+    prob::AbstractNonlinearProblem, alg::AbstractApproximateJacobianUpdateRule, J, fu, u,
+    du, args...; internalnorm::F = L2_NORM, kwargs...) where {F} --> AbstractApproximateJacobianUpdateRuleCache{INV}
 ```
 """
 abstract type AbstractApproximateJacobianUpdateRule{INV} end
@@ -440,9 +438,8 @@ Abstract Type for all Trust Region Methods used in NonlinearSolve.jl.
 
 ```julia
 __internal_init(
-    prob::AbstractNonlinearProblem, alg::AbstractTrustRegionMethod, f::F, fu, u,
-    p, args...; internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF} -->
-AbstractTrustRegionMethodCache
+    prob::AbstractNonlinearProblem, alg::AbstractTrustRegionMethod, f::F, fu, u, p, args...;
+    internalnorm::IF = L2_NORM, kwargs...) where {F, IF} --> AbstractTrustRegionMethodCache
 ```
 """
 abstract type AbstractTrustRegionMethod end
diff --git a/src/algorithms/broyden.jl b/src/algorithms/broyden.jl
index 77d2a06c4..4b4b3df9d 100644
--- a/src/algorithms/broyden.jl
+++ b/src/algorithms/broyden.jl
@@ -171,7 +171,7 @@ end
 
 function __internal_init(prob::AbstractNonlinearProblem,
         alg::Union{GoodBroydenUpdateRule, BadBroydenUpdateRule}, J, fu, u,
-        du, args...; internalnorm::F = DEFAULT_NORM, kwargs...) where {F}
+        du, args...; internalnorm::F = L2_NORM, kwargs...) where {F}
     @bb J⁻¹dfu = similar(u)
     @bb dfu = copy(fu)
     if alg isa GoodBroydenUpdateRule || J isa Diagonal
diff --git a/src/algorithms/lbroyden.jl b/src/algorithms/lbroyden.jl
index bead1a057..8fb0db748 100644
--- a/src/algorithms/lbroyden.jl
+++ b/src/algorithms/lbroyden.jl
@@ -44,7 +44,7 @@ jacobian_initialized_preinverted(::BroydenLowRankInitialization) = true
 function __internal_init(
         prob::AbstractNonlinearProblem, alg::BroydenLowRankInitialization{T},
         solver, f::F, fu, u, p; maxiters = 1000,
-        internalnorm::IN = DEFAULT_NORM, kwargs...) where {T, F, IN}
+        internalnorm::IN = L2_NORM, kwargs...) where {T, F, IN}
     if u isa Number # Use the standard broyden
         return __internal_init(prob, IdentityInitialization(true, FullStructure()),
             solver, f, fu, u, p; maxiters, kwargs...)
diff --git a/src/algorithms/levenberg_marquardt.jl b/src/algorithms/levenberg_marquardt.jl
index 501a5dd29..2b7c08f95 100644
--- a/src/algorithms/levenberg_marquardt.jl
+++ b/src/algorithms/levenberg_marquardt.jl
@@ -98,7 +98,7 @@ end
 function __internal_init(
         prob::AbstractNonlinearProblem, f::LevenbergMarquardtDampingFunction,
         initial_damping, J, fu, u, ::Val{NF};
-        internalnorm::F = DEFAULT_NORM, kwargs...) where {F, NF}
+        internalnorm::F = L2_NORM, kwargs...) where {F, NF}
     T = promote_type(eltype(u), eltype(fu))
     DᵀD = __init_diagonal(u, T(f.min_damping))
     if NF
diff --git a/src/algorithms/pseudo_transient.jl b/src/algorithms/pseudo_transient.jl
index 0da85dd94..1266d0702 100644
--- a/src/algorithms/pseudo_transient.jl
+++ b/src/algorithms/pseudo_transient.jl
@@ -53,7 +53,7 @@ end
 
 function __internal_init(
         prob::AbstractNonlinearProblem, f::SwitchedEvolutionRelaxation, initial_damping,
-        J, fu, u, args...; internalnorm::F = DEFAULT_NORM, kwargs...) where {F}
+        J, fu, u, args...; internalnorm::F = L2_NORM, kwargs...) where {F}
     T = promote_type(eltype(u), eltype(fu))
     return SwitchedEvolutionRelaxationCache(
         internalnorm(fu), T(1 / initial_damping), internalnorm)
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index 2e0c64a82..3522a39f4 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -148,7 +148,7 @@ function SciMLBase.__init(
         args...; stats = empty_nlstats(), alias_u0 = false, maxtime = nothing,
         maxiters = 1000, abstol = nothing, reltol = nothing,
         linsolve_kwargs = (;), termination_condition = nothing,
-        internalnorm::F = DEFAULT_NORM, kwargs...) where {uType, iip, F}
+        internalnorm::F = L2_NORM, kwargs...) where {uType, iip, F}
     timer = get_timer_output()
     @static_timeit timer "cache construction" begin
         (; f, u0, p) = prob
@@ -162,8 +162,8 @@ function SciMLBase.__init(
         initialization_cache = __internal_init(prob, alg.initialization, alg, f, fu, u, p;
             stats, linsolve, maxiters, internalnorm)
 
-        abstol, reltol, termination_cache = init_termination_cache(
-            prob, abstol, reltol, fu, u, termination_condition)
+        abstol, reltol, termination_cache = NonlinearSolveBase.init_termination_cache(
+            prob, abstol, reltol, fu, u, termination_condition, Val(:regular))
         linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
 
         J = initialization_cache(nothing)
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index ebdaf1fc8..13980c154 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -150,7 +150,7 @@ function SciMLBase.__init(
         prob::AbstractNonlinearProblem{uType, iip}, alg::GeneralizedFirstOrderAlgorithm,
         args...; stats = empty_nlstats(), alias_u0 = false, maxiters = 1000,
         abstol = nothing, reltol = nothing, maxtime = nothing,
-        termination_condition = nothing, internalnorm = DEFAULT_NORM,
+        termination_condition = nothing, internalnorm = L2_NORM,
         linsolve_kwargs = (;), kwargs...) where {uType, iip}
     timer = get_timer_output()
     @static_timeit timer "cache construction" begin
@@ -161,8 +161,8 @@ function SciMLBase.__init(
 
         linsolve = get_linear_solver(alg.descent)
 
-        abstol, reltol, termination_cache = init_termination_cache(
-            prob, abstol, reltol, fu, u, termination_condition)
+        abstol, reltol, termination_cache = NonlinearSolveBase.init_termination_cache(
+            prob, abstol, reltol, fu, u, termination_condition, Val(:regular))
         linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
 
         jac_cache = JacobianCache(
diff --git a/src/core/spectral_methods.jl b/src/core/spectral_methods.jl
index d141a627b..31e988b70 100644
--- a/src/core/spectral_methods.jl
+++ b/src/core/spectral_methods.jl
@@ -131,8 +131,8 @@ function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane
 
         linesearch_cache = init(prob, alg.linesearch, fu, u; stats, kwargs...)
 
-        abstol, reltol, tc_cache = init_termination_cache(
-            prob, abstol, reltol, fu, u_cache, termination_condition)
+        abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
+            prob, abstol, reltol, fu, u_cache, termination_condition, Val(:regular))
         trace = init_nonlinearsolve_trace(prob, alg, u, fu, nothing, du; kwargs...)
 
         if alg.σ_1 === nothing
diff --git a/src/default.jl b/src/default.jl
index 967b2e0e8..a7cc550d8 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -101,7 +101,7 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
     @eval begin
         function SciMLBase.__init(
                 prob::$probType, alg::$algType{N}, args...; stats = empty_nlstats(),
-                maxtime = nothing, maxiters = 1000, internalnorm = DEFAULT_NORM,
+                maxtime = nothing, maxiters = 1000, internalnorm = L2_NORM,
                 alias_u0 = false, verbose = true, kwargs...) where {N}
             if (alias_u0 && !ismutable(prob.u0))
                 verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
@@ -309,7 +309,7 @@ for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProb
 
             push!(calls, quote
                 resids = tuple($(Tuple(resids)...))
-                minfu, idx = __findmin(DEFAULT_NORM, resids)
+                minfu, idx = __findmin(L2_NORM, resids)
             end)
 
             for i in 1:N
diff --git a/src/descent/dogleg.jl b/src/descent/dogleg.jl
index 5d0bb1c7c..4c96c98f6 100644
--- a/src/descent/dogleg.jl
+++ b/src/descent/dogleg.jl
@@ -49,7 +49,7 @@ end
 
 function __internal_init(prob::AbstractNonlinearProblem, alg::Dogleg, J, fu, u;
         pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
-        abstol = nothing, reltol = nothing, internalnorm::F = DEFAULT_NORM,
+        abstol = nothing, reltol = nothing, internalnorm::F = L2_NORM,
         shared::Val{N} = Val(1), kwargs...) where {F, INV, N}
     newton_cache = __internal_init(prob, alg.newton_descent, J, fu, u; pre_inverted,
         linsolve_kwargs, abstol, reltol, shared, kwargs...)
diff --git a/src/descent/geodesic_acceleration.jl b/src/descent/geodesic_acceleration.jl
index 136795057..8e8a305f0 100644
--- a/src/descent/geodesic_acceleration.jl
+++ b/src/descent/geodesic_acceleration.jl
@@ -87,7 +87,7 @@ end
 function __internal_init(prob::AbstractNonlinearProblem, alg::GeodesicAcceleration, J,
         fu, u; shared::Val{N} = Val(1), pre_inverted::Val{INV} = False,
         linsolve_kwargs = (;), abstol = nothing, reltol = nothing,
-        internalnorm::F = DEFAULT_NORM, kwargs...) where {INV, N, F}
+        internalnorm::F = L2_NORM, kwargs...) where {INV, N, F}
     T = promote_type(eltype(u), eltype(fu))
     @bb δu = similar(u)
     δus = N ≤ 1 ? nothing : map(2:N) do i
diff --git a/src/globalization/trust_region.jl b/src/globalization/trust_region.jl
index e6e2cba17..8ff6de905 100644
--- a/src/globalization/trust_region.jl
+++ b/src/globalization/trust_region.jl
@@ -57,7 +57,7 @@ end
 
 function __internal_init(
         prob::AbstractNonlinearProblem, alg::LevenbergMarquardtTrustRegion, f::F, fu,
-        u, p, args...; stats, internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF}
+        u, p, args...; stats, internalnorm::IF = L2_NORM, kwargs...) where {F, IF}
     T = promote_type(eltype(u), eltype(fu))
     @bb v = copy(u)
     @bb u_cache = similar(u)
@@ -367,7 +367,7 @@ end
 
 function __internal_init(
         prob::AbstractNonlinearProblem, alg::GenericTrustRegionScheme, f::F, fu, u,
-        p, args...; stats, internalnorm::IF = DEFAULT_NORM, kwargs...) where {F, IF}
+        p, args...; stats, internalnorm::IF = L2_NORM, kwargs...) where {F, IF}
     T = promote_type(eltype(u), eltype(fu))
     u0_norm = internalnorm(u)
     fu_norm = internalnorm(fu)
diff --git a/src/internal/approximate_initialization.jl b/src/internal/approximate_initialization.jl
index 985234ac4..72e46a97e 100644
--- a/src/internal/approximate_initialization.jl
+++ b/src/internal/approximate_initialization.jl
@@ -65,14 +65,14 @@ end
 
 function __internal_init(
         prob::AbstractNonlinearProblem, alg::IdentityInitialization, solver, f::F,
-        fu, u::Number, p; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+        fu, u::Number, p; internalnorm::IN = L2_NORM, kwargs...) where {F, IN}
     α = __initial_alpha(alg.alpha, u, fu, internalnorm)
     return InitializedApproximateJacobianCache(
         α, alg.structure, alg, nothing, true, internalnorm)
 end
 function __internal_init(prob::AbstractNonlinearProblem, alg::IdentityInitialization,
         solver, f::F, fu::StaticArray, u::StaticArray, p;
-        internalnorm::IN = DEFAULT_NORM, kwargs...) where {IN, F}
+        internalnorm::IN = L2_NORM, kwargs...) where {IN, F}
     α = __initial_alpha(alg.alpha, u, fu, internalnorm)
     if alg.structure isa DiagonalStructure
         @assert length(u)==length(fu) "Diagonal Jacobian Structure must be square!"
@@ -91,7 +91,7 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::IdentityInitializa
 end
 function __internal_init(
         prob::AbstractNonlinearProblem, alg::IdentityInitialization, solver,
-        f::F, fu, u, p; internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+        f::F, fu, u, p; internalnorm::IN = L2_NORM, kwargs...) where {F, IN}
     α = __initial_alpha(alg.alpha, u, fu, internalnorm)
     if alg.structure isa DiagonalStructure
         @assert length(u)==length(fu) "Diagonal Jacobian Structure must be square!"
@@ -147,7 +147,7 @@ end
 
 function __internal_init(prob::AbstractNonlinearProblem, alg::TrueJacobianInitialization,
         solver, f::F, fu, u, p; stats, linsolve = missing,
-        internalnorm::IN = DEFAULT_NORM, kwargs...) where {F, IN}
+        internalnorm::IN = L2_NORM, kwargs...) where {F, IN}
     autodiff = get_concrete_forward_ad(
         alg.autodiff, prob; check_forward_mode = false, kwargs...)
     jac_cache = JacobianCache(prob, solver, prob.f, fu, u, p; stats, autodiff, linsolve)
diff --git a/src/internal/termination.jl b/src/internal/termination.jl
index ef3f7c4c0..7728aea69 100644
--- a/src/internal/termination.jl
+++ b/src/internal/termination.jl
@@ -1,34 +1,9 @@
-function init_termination_cache(prob::NonlinearProblem, abstol, reltol, du, u, ::Nothing)
-    return init_termination_cache(prob, abstol, reltol, du, u,
-        AbsSafeBestTerminationMode(Base.Fix1(maximum, abs); max_stalled_steps = 32))
-end
-function init_termination_cache(
-        prob::NonlinearLeastSquaresProblem, abstol, reltol, du, u, ::Nothing)
-    return init_termination_cache(prob, abstol, reltol, du, u,
-        AbsSafeBestTerminationMode(Base.Fix2(norm, 2); max_stalled_steps = 32))
-end
-
-function init_termination_cache(
-        prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
-        abstol, reltol, du, u, tc::AbstractNonlinearTerminationMode)
-    tc_ = if hasfield(typeof(tc), :internalnorm) && tc.internalnorm === nothing
-        internalnorm = ifelse(
-            prob isa NonlinearProblem, Base.Fix1(maximum, abs), Base.Fix2(norm, 2))
-        DiffEqBase.set_termination_mode_internalnorm(tc, internalnorm)
-    else
-        tc
-    end
-    tc_cache = init(du, u, tc_; abstol, reltol, use_deprecated_retcodes = Val(false))
-    return DiffEqBase.get_abstol(tc_cache), DiffEqBase.get_reltol(tc_cache), tc_cache
-end
-
 function check_and_update!(cache, fu, u, uprev)
     return check_and_update!(cache.termination_cache, cache, fu, u, uprev)
 end
 
 function check_and_update!(tc_cache, cache, fu, u, uprev)
-    return check_and_update!(
-        tc_cache, cache, fu, u, uprev, DiffEqBase.get_termination_mode(tc_cache))
+    return check_and_update!(tc_cache, cache, fu, u, uprev, tc_cache.mode)
 end
 
 function check_and_update!(tc_cache, cache, fu, u, uprev, mode)
@@ -40,8 +15,7 @@ function check_and_update!(tc_cache, cache, fu, u, uprev, mode)
 end
 
 function update_from_termination_cache!(tc_cache, cache, u = get_u(cache))
-    return update_from_termination_cache!(
-        tc_cache, cache, DiffEqBase.get_termination_mode(tc_cache), u)
+    return update_from_termination_cache!(tc_cache, cache, tc_cache.mode, u)
 end
 
 function update_from_termination_cache!(
diff --git a/src/utils.jl b/src/utils.jl
index 6ceb4c9d8..069fde86e 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -1,16 +1,8 @@
 # Defaults
-@inline DEFAULT_NORM(args...) = DiffEqBase.NONLINEARSOLVE_DEFAULT_NORM(args...)
 @inline DEFAULT_PRECS(W, du, u, p, t, newW, Plprev, Prprev, cachedata) = nothing, nothing
-@inline DEFAULT_TOLERANCE(args...) = DiffEqBase._get_tolerance(args...)
 
 # Helper  Functions
-@static if VERSION ≤ v"1.10-"
-    @inline @generated function __hasfield(::T, ::Val{field}) where {T, field}
-        return :($(field ∉ fieldnames(T)))
-    end
-else
-    @inline __hasfield(::T, ::Val{field}) where {T, field} = hasfield(T, field)
-end
+@inline __hasfield(::T, ::Val{field}) where {T, field} = hasfield(T, field)
 
 @generated function __getproperty(s::S, ::Val{X}) where {S, X}
     hasfield(S, X) && return :(s.$X)
@@ -86,12 +78,10 @@ LazyArrays.applied_axes(::typeof(__zero), x) = axes(x)
 @inline __is_complex(::Type{T}) where {T} = false
 
 @inline __findmin_caches(f::F, caches) where {F} = __findmin(f ∘ get_fu, caches)
-# FIXME: DEFAULT_NORM makes an Array of NaNs not a NaN (atleast according to `isnan`)
+# FIXME: L2_NORM makes an Array of NaNs not a NaN (atleast according to `isnan`)
 @generated function __findmin(f::F, x) where {F}
     # JET shows dynamic dispatch if this is not written as a generated function
-    if F === typeof(DEFAULT_NORM)
-        return :(return __findmin_impl(Base.Fix1(maximum, abs), x))
-    end
+    F === typeof(L2_NORM) && return :(return __findmin_impl(Base.Fix1(maximum, abs), x))
     return :(return __findmin_impl(f, x))
 end
 @inline @views function __findmin_impl(f::F, x) where {F}

From b1a30bc59c51edc428d4d588e54e5fb56f49faa8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 20:06:35 -0400
Subject: [PATCH 612/700] chore: fix QA testing

---
 lib/BracketingNonlinearSolve/test/qa_tests.jl |  3 ++-
 src/NonlinearSolve.jl                         |  6 +++---
 src/abstract_types.jl                         |  3 ++-
 test/core/rootfind_tests.jl                   | 17 ++++++++++++-----
 4 files changed, 19 insertions(+), 10 deletions(-)

diff --git a/lib/BracketingNonlinearSolve/test/qa_tests.jl b/lib/BracketingNonlinearSolve/test/qa_tests.jl
index de27e33a4..c01c493f4 100644
--- a/lib/BracketingNonlinearSolve/test/qa_tests.jl
+++ b/lib/BracketingNonlinearSolve/test/qa_tests.jl
@@ -10,7 +10,8 @@ end
     import ForwardDiff
     using ExplicitImports, BracketingNonlinearSolve
 
-    @test check_no_implicit_imports(BracketingNonlinearSolve; skip = (Base, Core)) === nothing
+    @test check_no_implicit_imports(BracketingNonlinearSolve; skip = (Base, Core)) ===
+          nothing
     @test check_no_stale_explicit_imports(BracketingNonlinearSolve) === nothing
     @test check_all_qualified_accesses_via_owners(BracketingNonlinearSolve) === nothing
 end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index fd2c0bc3d..5f21936a1 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -13,14 +13,14 @@ using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Sy
                      UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess, istril,
                      istriu, lu, mul!, norm, pinv, tril!, triu!
 using LineSearch: LineSearch, AbstractLineSearchCache, LineSearchesJL, NoLineSearch,
-                  RobustNonMonotoneLineSearch, BackTracking,  LiFukushimaLineSearch
+                  RobustNonMonotoneLineSearch, BackTracking, LiFukushimaLineSearch
 using LinearSolve: LinearSolve, QRFactorization, needs_concrete_A, AbstractFactorization,
                    DefaultAlgorithmChoice, DefaultLinearSolver
 using MaybeInplace: @bb
 using NonlinearSolveBase: NonlinearSolveBase, nonlinearsolve_forwarddiff_solve,
                           nonlinearsolve_dual_solution, nonlinearsolve_∂f_∂p,
-                          nonlinearsolve_∂f_∂u, L2_NORM, AbstractNonlinearTerminationMode,
-                          AbstractSafeNonlinearTerminationMode,
+                          nonlinearsolve_∂f_∂u, L2_NORM, AbsNormTerminationMode,
+                          AbstractNonlinearTerminationMode,
                           AbstractSafeBestNonlinearTerminationMode
 using Printf: @printf
 using Preferences: Preferences, @load_preference, @set_preferences!
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 415dc5797..255c5e541 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -382,7 +382,8 @@ Abstract Type for all Approximate Jacobian Update Rules used in NonlinearSolve.j
 ```julia
 __internal_init(
     prob::AbstractNonlinearProblem, alg::AbstractApproximateJacobianUpdateRule, J, fu, u,
-    du, args...; internalnorm::F = L2_NORM, kwargs...) where {F} --> AbstractApproximateJacobianUpdateRuleCache{INV}
+    du, args...; internalnorm::F = L2_NORM, kwargs...) where {F} -->
+AbstractApproximateJacobianUpdateRuleCache{INV}
 ```
 """
 abstract type AbstractApproximateJacobianUpdateRule{INV} end
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index e3f92fd26..2d1662570 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -1,8 +1,8 @@
 @testsetup module CoreRootfindTesting
 using Reexport
 @reexport using BenchmarkTools, LinearSolve, NonlinearSolve, StaticArrays, Random,
-                LinearAlgebra, ForwardDiff, Zygote, Enzyme, DiffEqBase,
-                SparseConnectivityTracer
+                LinearAlgebra, ForwardDiff, Zygote, Enzyme, SparseConnectivityTracer,
+                NonlinearSolveBase
 using LineSearches: LineSearches
 
 _nameof(x) = applicable(nameof, x) ? nameof(x) : _nameof(typeof(x))
@@ -22,9 +22,16 @@ function newton_fails(u, p)
 end
 
 const TERMINATION_CONDITIONS = [
-    NormTerminationMode(), RelTerminationMode(), RelNormTerminationMode(),
-    AbsTerminationMode(), AbsNormTerminationMode(), RelSafeTerminationMode(),
-    AbsSafeTerminationMode(), RelSafeBestTerminationMode(), AbsSafeBestTerminationMode()]
+    NormTerminationMode(Base.Fix1(maximum, abs)),
+    RelTerminationMode(),
+    RelNormTerminationMode(Base.Fix1(maximum, abs)),
+    RelNormSafeTerminationMode(Base.Fix1(maximum, abs)),
+    RelNormSafeBestTerminationMode(Base.Fix1(maximum, abs)),
+    AbsTerminationMode(),
+    AbsNormTerminationMode(Base.Fix1(maximum, abs)),
+    AbsNormSafeTerminationMode(Base.Fix1(maximum, abs)),
+    AbsNormSafeBestTerminationMode(Base.Fix1(maximum, abs))
+]
 
 function benchmark_nlsolve_oop(f, u0, p = 2.0; solver, kwargs...)
     prob = NonlinearProblem{false}(f, u0, p)

From 1e3d5f5eac016877370d319cbbe6d48bdd2c76bd Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 20:34:34 -0400
Subject: [PATCH 613/700] fix: dispatch forwarddiff on `__init` and `__solve`

---
 src/NonlinearSolve.jl        |  3 +-
 src/internal/forward_diff.jl | 58 ++++++++++++++++++++++--------------
 2 files changed, 38 insertions(+), 23 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 5f21936a1..625477a88 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -67,7 +67,6 @@ include("descent/damped_newton.jl")
 include("descent/geodesic_acceleration.jl")
 
 include("internal/jacobian.jl")
-include("internal/forward_diff.jl")
 include("internal/linear_solve.jl")
 include("internal/termination.jl")
 include("internal/tracing.jl")
@@ -93,6 +92,8 @@ include("algorithms/levenberg_marquardt.jl")
 include("algorithms/trust_region.jl")
 include("algorithms/extension_algs.jl")
 
+include("internal/forward_diff.jl") # we need to define after the algorithms
+
 include("utils.jl")
 include("default.jl")
 
diff --git a/src/internal/forward_diff.jl b/src/internal/forward_diff.jl
index a4238674e..c2adc70e2 100644
--- a/src/internal/forward_diff.jl
+++ b/src/internal/forward_diff.jl
@@ -1,14 +1,24 @@
-# XXX: dispatch on `__solve` & `__init`
-function SciMLBase.solve(
-        prob::NonlinearProblem{<:Union{Number, <:AbstractArray}, iip,
-            <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
-        alg::Union{Nothing, AbstractNonlinearAlgorithm},
-        args...;
-        kwargs...) where {T, V, P, iip}
-    sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
-    dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
-    return SciMLBase.build_solution(
-        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+const DualNonlinearProblem = NonlinearProblem{<:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}} where {iip, T, V, P}
+const DualNonlinearLeastSquaresProblem = NonlinearLeastSquaresProblem{
+    <:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}} where {iip, T, V, P}
+const DualAbstractNonlinearProblem = Union{
+    DualNonlinearProblem, DualNonlinearLeastSquaresProblem}
+
+for algType in (
+    Nothing, AbstractNonlinearSolveAlgorithm, GeneralizedDFSane,
+    GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm,
+    LeastSquaresOptimJL, FastLevenbergMarquardtJL, CMINPACK, NLsolveJL, NLSolversJL,
+    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL
+)
+    @eval function SciMLBase.__solve(
+            prob::DualNonlinearProblem, alg::$(algType), args...; kwargs...)
+        sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
+        dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
+        return SciMLBase.build_solution(
+            prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+    end
 end
 
 @concrete mutable struct NonlinearSolveForwardDiffCache
@@ -32,17 +42,21 @@ function reinit_cache!(cache::NonlinearSolveForwardDiffCache;
     return cache
 end
 
-function SciMLBase.init(
-        prob::NonlinearProblem{<:Union{Number, <:AbstractArray}, iip,
-            <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
-        alg::Union{Nothing, AbstractNonlinearAlgorithm},
-        args...;
-        kwargs...) where {T, V, P, iip}
-    p = __value(prob.p)
-    newprob = NonlinearProblem(prob.f, __value(prob.u0), p; prob.kwargs...)
-    cache = init(newprob, alg, args...; kwargs...)
-    return NonlinearSolveForwardDiffCache(
-        cache, newprob, alg, prob.p, p, ForwardDiff.partials(prob.p))
+for algType in (
+    Nothing, AbstractNonlinearSolveAlgorithm, GeneralizedDFSane,
+    SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm,
+    GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm,
+    LeastSquaresOptimJL, FastLevenbergMarquardtJL, CMINPACK, NLsolveJL, NLSolversJL,
+    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL
+)
+    @eval function SciMLBase.__init(
+            prob::DualNonlinearProblem, alg::$(algType), args...; kwargs...)
+        p = __value(prob.p)
+        newprob = NonlinearProblem(prob.f, __value(prob.u0), p; prob.kwargs...)
+        cache = init(newprob, alg, args...; kwargs...)
+        return NonlinearSolveForwardDiffCache(
+            cache, newprob, alg, prob.p, p, ForwardDiff.partials(prob.p))
+    end
 end
 
 function SciMLBase.solve!(cache::NonlinearSolveForwardDiffCache)

From 24c3cf3d1134d2cff641289520c1d091fd5756b5 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 21 Oct 2024 22:30:10 -0400
Subject: [PATCH 614/700] feat: forwarddiff support for sundials

---
 Project.toml                     |  2 ++
 ext/NonlinearSolveSundialsExt.jl | 16 ++++++++++++++++
 2 files changed, 18 insertions(+)
 create mode 100644 ext/NonlinearSolveSundialsExt.jl

diff --git a/Project.toml b/Project.toml
index 8841eca18..63df3592a 100644
--- a/Project.toml
+++ b/Project.toml
@@ -44,6 +44,7 @@ NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
 SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
+Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"
 
 [extensions]
 NonlinearSolveBandedMatricesExt = "BandedMatrices"
@@ -55,6 +56,7 @@ NonlinearSolveNLSolversExt = "NLSolvers"
 NonlinearSolveNLsolveExt = ["NLsolve", "LineSearches"]
 NonlinearSolveSIAMFANLEquationsExt = "SIAMFANLEquations"
 NonlinearSolveSpeedMappingExt = "SpeedMapping"
+NonlinearSolveSundialsExt = "Sundials"
 
 [compat]
 ADTypes = "1.9"
diff --git a/ext/NonlinearSolveSundialsExt.jl b/ext/NonlinearSolveSundialsExt.jl
new file mode 100644
index 000000000..edea3a49b
--- /dev/null
+++ b/ext/NonlinearSolveSundialsExt.jl
@@ -0,0 +1,16 @@
+module NonlinearSolveSundialsExt
+
+using NonlinearSolveBase: NonlinearSolveBase, nonlinearsolve_forwarddiff_solve,
+                          nonlinearsolve_dual_solution
+using NonlinearSolve: DualNonlinearProblem
+using SciMLBase: SciMLBase
+using Sundials: KINSOL
+
+function SciMLBase.__solve(prob::DualNonlinearProblem, alg::KINSOL, args...; kwargs...)
+    sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
+    dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
+    return SciMLBase.build_solution(
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+end
+
+end

From a0e22f460090425ed3831571eea9624b05b45be1 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 22 Oct 2024 09:08:37 -0400
Subject: [PATCH 615/700] refactor: use reexports

---
 docs/src/release_notes.md                            | 9 ++++++---
 lib/SimpleNonlinearSolve/Project.toml                | 2 ++
 lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl | 9 +++------
 src/NonlinearSolve.jl                                | 5 +++--
 4 files changed, 14 insertions(+), 11 deletions(-)

diff --git a/docs/src/release_notes.md b/docs/src/release_notes.md
index 0208b1e66..3aa147e27 100644
--- a/docs/src/release_notes.md
+++ b/docs/src/release_notes.md
@@ -4,13 +4,16 @@
 
 ### Breaking Changes in `NonlinearSolve.jl` v4
 
+  - See [common breaking changes](@ref common-breaking-changes-v4v2) below.
+
 ### Breaking Changes in `SimpleNonlinearSolve.jl` v2
 
-  - `Auto*` structs are no longer exported. Load `ADTypes` to access them.
+  - See [common breaking changes](@ref common-breaking-changes-v4v2) below.
+
+### [Common Breaking Changes](@id common-breaking-changes-v4v2)
+
   - Use of termination conditions from `DiffEqBase` has been removed. Use the termination
     conditions from `NonlinearSolveBase` instead.
-  - We no longer export the entire `SciMLBase`. Instead selected functionality relevant to
-    `SimpleNonlinearSolve` has been exported.
   - If no autodiff is provided, we now choose from a list of autodiffs based on the packages
     loaded. For example, if `Enzyme` is loaded, we will default to that. In general, we
     don't guarantee the exact autodiff selected if `autodiff` is not provided (i.e.
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 82f69c6ad..586341f67 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -19,6 +19,7 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
+Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
@@ -60,6 +61,7 @@ Pkg = "1.10"
 PolyesterForwardDiff = "0.1"
 PrecompileTools = "1.2"
 Random = "1.10"
+Reexport = "1.2"
 ReverseDiff = "1.15"
 SciMLBase = "2.50"
 StaticArrays = "1.9"
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 6d1187668..f15630e24 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -8,6 +8,7 @@ using LineSearch: LiFukushimaLineSearch
 using LinearAlgebra: LinearAlgebra, dot
 using MaybeInplace: @bb, setindex_trait, CannotSetindex, CanSetindex
 using PrecompileTools: @compile_workload, @setup_workload
+using Reexport: @reexport
 using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, NonlinearFunction, NonlinearProblem,
                  NonlinearLeastSquaresProblem, IntervalNonlinearProblem, ReturnCode, remake
 using StaticArraysCore: StaticArray, SArray, SVector, MArray
@@ -18,7 +19,6 @@ using DifferentiationInterface: DifferentiationInterface
 using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff
 
-using BracketingNonlinearSolve: Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, L2_NORM,
                           nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution
 
@@ -138,11 +138,8 @@ function solve_adjoint_internal end
     end
 end
 
-export IntervalNonlinearProblem
-
-export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
-
-export NonlinearFunction, NonlinearProblem, NonlinearLeastSquaresProblem
+# Rexexports
+@reexport using ADTypes, SciMLBase, BracketingNonlinearSolve, NonlinearSolveBase
 
 export SimpleBroyden, SimpleKlement, SimpleLimitedMemoryBroyden
 export SimpleDFSane
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 625477a88..e6ca6cb00 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -48,8 +48,6 @@ using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
 using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm,
                              LargestFirst
 
-@reexport using SciMLBase, SimpleNonlinearSolve, NonlinearSolveBase
-
 const DI = DifferentiationInterface
 
 const True = Val(true)
@@ -157,6 +155,9 @@ include("default.jl")
     end
 end
 
+# Rexexports
+@reexport using SciMLBase, SimpleNonlinearSolve, NonlinearSolveBase
+
 # Core Algorithms
 export NewtonRaphson, PseudoTransient, Klement, Broyden, LimitedMemoryBroyden, DFSane
 export GaussNewton, LevenbergMarquardt, TrustRegion

From 6dbc95e9db321acbec53d9838b99fb738048d791 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 22 Oct 2024 16:04:25 -0400
Subject: [PATCH 616/700] refactor: centralize autodiff selection

---
 Project.toml                               |   2 +
 docs/src/native/solvers.md                 |  11 +-
 docs/src/release_notes.md                  |   6 +-
 lib/NonlinearSolveBase/src/autodiff.jl     |  32 +++--
 lib/SimpleNonlinearSolve/src/utils.jl      |   1 -
 src/NonlinearSolve.jl                      | 130 +++++++++++----------
 src/algorithms/broyden.jl                  |  59 +++++-----
 src/algorithms/dfsane.jl                   |   1 +
 src/algorithms/gauss_newton.jl             |  13 ++-
 src/algorithms/klement.jl                  |  36 +++---
 src/algorithms/lbroyden.jl                 |  13 +--
 src/algorithms/levenberg_marquardt.jl      |  16 ++-
 src/algorithms/pseudo_transient.jl         |  18 +--
 src/algorithms/raphson.jl                  |  15 +--
 src/algorithms/trust_region.jl             |  23 ++--
 src/core/approximate_jacobian.jl           |   9 +-
 src/core/generalized_first_order.jl        |  78 +++++++------
 src/globalization/trust_region.jl          |  14 +--
 src/internal/approximate_initialization.jl |   3 +-
 src/internal/helpers.jl                    |  59 ----------
 src/internal/jacobian.jl                   |   9 --
 21 files changed, 247 insertions(+), 301 deletions(-)

diff --git a/Project.toml b/Project.toml
index 63df3592a..d6fec9aa1 100644
--- a/Project.toml
+++ b/Project.toml
@@ -6,6 +6,7 @@ version = "4.0.0"
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
@@ -65,6 +66,7 @@ ArrayInterface = "7.16"
 BandedMatrices = "1.5"
 BenchmarkTools = "1.4"
 CUDA = "5.5"
+CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.158.3"
 DifferentiationInterface = "0.6.1"
diff --git a/docs/src/native/solvers.md b/docs/src/native/solvers.md
index aebaee379..5653f1fab 100644
--- a/docs/src/native/solvers.md
+++ b/docs/src/native/solvers.md
@@ -22,15 +22,16 @@ documentation.
     preconditioners. For more information on specifying preconditioners for LinearSolve
     algorithms, consult the
     [LinearSolve.jl documentation](https://docs.sciml.ai/LinearSolve/stable/).
-  - `linesearch`: the line search algorithm to use. Defaults to [`NoLineSearch()`](@extref LineSearch.NoLineSearch),
-    which means that no line search is performed.
-  - `autodiff`/`jacobian_ad`: etermines the backend used for the Jacobian. Note that this
+  - `linesearch`: the line search algorithm to use. Defaults to
+    [`NoLineSearch()`](@extref LineSearch.NoLineSearch), which means that no line search is
+    performed.
+  - `autodiff`: etermines the backend used for the Jacobian. Note that this
     argument is ignored if an analytical Jacobian is passed, as that will be used instead.
     Defaults to `nothing` which means that a default is selected according to the problem
     specification! Valid choices are types from ADTypes.jl.
-  - `forward_ad`/`vjp_autodiff`: similar to `autodiff`, but is used to compute Jacobian
+  - `vjp_autodiff`: similar to `autodiff`, but is used to compute Jacobian
     Vector Products. Ignored if the NonlinearFunction contains the `jvp` function.
-  - `reverse_ad`/`vjp_autodiff`: similar to `autodiff`, but is used to compute Vector
+  - `vjp_autodiff`: similar to `autodiff`, but is used to compute Vector
     Jacobian Products. Ignored if the NonlinearFunction contains the `vjp` function.
   - `concrete_jac`: whether to build a concrete Jacobian. If a Krylov-subspace method is
     used, then the Jacobian will not be constructed and instead direct Jacobian-Vector
diff --git a/docs/src/release_notes.md b/docs/src/release_notes.md
index 3aa147e27..1dc3d9433 100644
--- a/docs/src/release_notes.md
+++ b/docs/src/release_notes.md
@@ -15,9 +15,9 @@
   - Use of termination conditions from `DiffEqBase` has been removed. Use the termination
     conditions from `NonlinearSolveBase` instead.
   - If no autodiff is provided, we now choose from a list of autodiffs based on the packages
-    loaded. For example, if `Enzyme` is loaded, we will default to that. In general, we
-    don't guarantee the exact autodiff selected if `autodiff` is not provided (i.e.
-    `nothing`).
+    loaded. For example, if `Enzyme` is loaded, we will default to that (for reverse mode).
+    In general, we don't guarantee the exact autodiff selected if `autodiff` is not provided
+    (i.e. `nothing`).
 
 ## Dec '23
 
diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
index 83b6aa1f7..2102ae09b 100644
--- a/lib/NonlinearSolveBase/src/autodiff.jl
+++ b/lib/NonlinearSolveBase/src/autodiff.jl
@@ -3,24 +3,34 @@
 
 # Ordering is important here. We want to select the first one that is compatible with the
 # problem.
-const ReverseADs = (
-    ADTypes.AutoEnzyme(; mode = EnzymeCore.Reverse),
-    ADTypes.AutoZygote(),
-    ADTypes.AutoTracker(),
-    ADTypes.AutoReverseDiff(; compile = true),
-    ADTypes.AutoReverseDiff(),
-    ADTypes.AutoFiniteDiff()
-)
+# XXX: Remove this once Enzyme is properly supported on Julia 1.11+
+@static if VERSION ≥ v"1.11-"
+    const ReverseADs = (
+        ADTypes.AutoZygote(),
+        ADTypes.AutoTracker(),
+        ADTypes.AutoReverseDiff(; compile = true),
+        ADTypes.AutoReverseDiff(),
+        ADTypes.AutoEnzyme(; mode = EnzymeCore.Reverse),
+        ADTypes.AutoFiniteDiff()
+    )
+else
+    const ReverseADs = (
+        ADTypes.AutoEnzyme(; mode = EnzymeCore.Reverse),
+        ADTypes.AutoZygote(),
+        ADTypes.AutoTracker(),
+        ADTypes.AutoReverseDiff(; compile = true),
+        ADTypes.AutoReverseDiff(),
+        ADTypes.AutoFiniteDiff()
+    )
+end
 
 const ForwardADs = (
-    ADTypes.AutoEnzyme(; mode = EnzymeCore.Forward),
     ADTypes.AutoPolyesterForwardDiff(),
     ADTypes.AutoForwardDiff(),
+    ADTypes.AutoEnzyme(; mode = EnzymeCore.Forward),
     ADTypes.AutoFiniteDiff()
 )
 
-# TODO: Handle Sparsity
-
 function select_forward_mode_autodiff(
         prob::AbstractNonlinearProblem, ad::AbstractADType; warn_check_mode::Bool = true)
     if warn_check_mode && !(ADTypes.mode(ad) isa ADTypes.ForwardMode)
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index 311762429..bd7368bd7 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -130,7 +130,6 @@ function prepare_jacobian(prob, autodiff, _, x::Number)
     if SciMLBase.has_jac(prob.f) || SciMLBase.has_vjp(prob.f) || SciMLBase.has_jvp(prob.f)
         return AnalyticJacobian()
     end
-    # return DI.prepare_derivative(prob.f, autodiff, x, Constant(prob.p))
     return DINoPreparation()
 end
 function prepare_jacobian(prob, autodiff, fx, x)
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index e6ca6cb00..a5e71f13b 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -5,6 +5,7 @@ using PrecompileTools: @compile_workload, @setup_workload
 
 using ArrayInterface: ArrayInterface, can_setindex, restructure, fast_scalar_indexing,
                       ismutable
+using CommonSolve: solve, init, solve!
 using ConcreteStructs: @concrete
 using DiffEqBase: DiffEqBase # Needed for `init` / `solve` dispatches
 using FastClosures: @closure
@@ -21,13 +22,18 @@ using NonlinearSolveBase: NonlinearSolveBase, nonlinearsolve_forwarddiff_solve,
                           nonlinearsolve_dual_solution, nonlinearsolve_∂f_∂p,
                           nonlinearsolve_∂f_∂u, L2_NORM, AbsNormTerminationMode,
                           AbstractNonlinearTerminationMode,
-                          AbstractSafeBestNonlinearTerminationMode
+                          AbstractSafeBestNonlinearTerminationMode,
+                          select_forward_mode_autodiff, select_reverse_mode_autodiff,
+                          select_jacobian_autodiff
 using Printf: @printf
 using Preferences: Preferences, @load_preference, @set_preferences!
 using RecursiveArrayTools: recursivecopy!
-using SciMLBase: AbstractNonlinearAlgorithm, AbstractNonlinearProblem, _unwrap_val,
-                 isinplace, NLStats
+using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, AbstractNonlinearProblem,
+                 _unwrap_val, isinplace, NLStats, NonlinearFunction,
+                 NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode, get_du, step!,
+                 set_u!, LinearProblem, IdentityOperator
 using SciMLOperators: AbstractSciMLOperator
+using SimpleNonlinearSolve: SimpleNonlinearSolve
 using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
 using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
                                  symbolic_container, parameter_values, state_values, getu,
@@ -95,65 +101,65 @@ include("internal/forward_diff.jl") # we need to define after the algorithms
 include("utils.jl")
 include("default.jl")
 
-@setup_workload begin
-    nlfuncs = ((NonlinearFunction{false}((u, p) -> u .* u .- p), 0.1),
-        (NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p), [0.1]))
-    probs_nls = NonlinearProblem[]
-    for (fn, u0) in nlfuncs
-        push!(probs_nls, NonlinearProblem(fn, u0, 2.0))
-    end
-
-    nls_algs = (
-        NewtonRaphson(),
-        TrustRegion(),
-        LevenbergMarquardt(),
-        Broyden(),
-        Klement(),
-        nothing
-    )
-
-    probs_nlls = NonlinearLeastSquaresProblem[]
-    nlfuncs = (
-        (NonlinearFunction{false}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
-        (NonlinearFunction{false}((u, p) -> vcat(u .* u .- p, u .* u .- p)), [0.1, 0.1]),
-        (
-            NonlinearFunction{true}(
-                (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(1)),
-            [0.1, 0.0]),
-        (
-            NonlinearFunction{true}((du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p),
-                resid_prototype = zeros(4)),
-            [0.1, 0.1]
-        )
-    )
-    for (fn, u0) in nlfuncs
-        push!(probs_nlls, NonlinearLeastSquaresProblem(fn, u0, 2.0))
-    end
-
-    nlls_algs = (
-        LevenbergMarquardt(),
-        GaussNewton(),
-        TrustRegion(),
-        nothing
-    )
-
-    @compile_workload begin
-        @sync begin
-            for T in (Float32, Float64), (fn, u0) in nlfuncs
-                Threads.@spawn NonlinearProblem(fn, T.(u0), T(2))
-            end
-            for (fn, u0) in nlfuncs
-                Threads.@spawn NonlinearLeastSquaresProblem(fn, u0, 2.0)
-            end
-            for prob in probs_nls, alg in nls_algs
-                Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
-            end
-            for prob in probs_nlls, alg in nlls_algs
-                Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
-            end
-        end
-    end
-end
+# @setup_workload begin
+#     nlfuncs = ((NonlinearFunction{false}((u, p) -> u .* u .- p), 0.1),
+#         (NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p), [0.1]))
+#     probs_nls = NonlinearProblem[]
+#     for (fn, u0) in nlfuncs
+#         push!(probs_nls, NonlinearProblem(fn, u0, 2.0))
+#     end
+
+#     nls_algs = (
+#         NewtonRaphson(),
+#         TrustRegion(),
+#         LevenbergMarquardt(),
+#         Broyden(),
+#         Klement(),
+#         nothing
+#     )
+
+#     probs_nlls = NonlinearLeastSquaresProblem[]
+#     nlfuncs = (
+#         (NonlinearFunction{false}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
+#         (NonlinearFunction{false}((u, p) -> vcat(u .* u .- p, u .* u .- p)), [0.1, 0.1]),
+#         (
+#             NonlinearFunction{true}(
+#                 (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(1)),
+#             [0.1, 0.0]),
+#         (
+#             NonlinearFunction{true}((du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p),
+#                 resid_prototype = zeros(4)),
+#             [0.1, 0.1]
+#         )
+#     )
+#     for (fn, u0) in nlfuncs
+#         push!(probs_nlls, NonlinearLeastSquaresProblem(fn, u0, 2.0))
+#     end
+
+#     nlls_algs = (
+#         LevenbergMarquardt(),
+#         GaussNewton(),
+#         TrustRegion(),
+#         nothing
+#     )
+
+#     @compile_workload begin
+#         @sync begin
+#             for T in (Float32, Float64), (fn, u0) in nlfuncs
+#                 Threads.@spawn NonlinearProblem(fn, T.(u0), T(2))
+#             end
+#             for (fn, u0) in nlfuncs
+#                 Threads.@spawn NonlinearLeastSquaresProblem(fn, u0, 2.0)
+#             end
+#             for prob in probs_nls, alg in nls_algs
+#                 Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
+#             end
+#             for prob in probs_nlls, alg in nlls_algs
+#                 Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
+#             end
+#         end
+#     end
+# end
 
 # Rexexports
 @reexport using SciMLBase, SimpleNonlinearSolve, NonlinearSolveBase
diff --git a/src/algorithms/broyden.jl b/src/algorithms/broyden.jl
index 4b4b3df9d..39962bc6a 100644
--- a/src/algorithms/broyden.jl
+++ b/src/algorithms/broyden.jl
@@ -1,5 +1,5 @@
 """
-    Broyden(; max_resets::Int = 100, linesearch = NoLineSearch(), reset_tolerance = nothing,
+    Broyden(; max_resets::Int = 100, linesearch = nothing, reset_tolerance = nothing,
         init_jacobian::Val = Val(:identity), autodiff = nothing, alpha = nothing)
 
 An implementation of `Broyden`'s Method [broyden1965class](@cite) with resetting and line
@@ -29,36 +29,37 @@ search.
         problem
 """
 function Broyden(;
-        max_resets = 100, linesearch = NoLineSearch(), reset_tolerance = nothing,
-        init_jacobian::Val{IJ} = Val(:identity), autodiff = nothing,
-        alpha = nothing, update_rule::Val{UR} = Val(:good_broyden)) where {IJ, UR}
-    if IJ === :identity
-        if UR === :diagonal
-            initialization = IdentityInitialization(alpha, DiagonalStructure())
-        else
-            initialization = IdentityInitialization(alpha, FullStructure())
-        end
-    elseif IJ === :true_jacobian
-        initialization = TrueJacobianInitialization(FullStructure(), autodiff)
-    else
-        throw(ArgumentError("`init_jacobian` must be one of `:identity` or \
-                             `:true_jacobian`"))
-    end
+        max_resets = 100, linesearch = nothing, reset_tolerance = nothing,
+        init_jacobian = Val(:identity), autodiff = nothing, alpha = nothing,
+        update_rule = Val(:good_broyden))
+    initialization = broyden_init(init_jacobian, update_rule, autodiff, alpha)
+    update_rule = broyden_update_rule(update_rule)
+    return ApproximateJacobianSolveAlgorithm{
+        init_jacobian isa Val{:true_jacobian}, :Broyden}(;
+        linesearch, descent = NewtonDescent(), update_rule, max_resets, initialization,
+        reinit_rule = NoChangeInStateReset(; reset_tolerance))
+end
 
-    update_rule = if UR === :good_broyden
-        GoodBroydenUpdateRule()
-    elseif UR === :bad_broyden
-        BadBroydenUpdateRule()
-    elseif UR === :diagonal
-        GoodBroydenUpdateRule()
-    else
-        throw(ArgumentError("`update_rule` must be one of `:good_broyden`, `:bad_broyden`, \
-                             or `:diagonal`"))
-    end
+function broyden_init(::Val{:identity}, ::Val{:diagonal}, autodiff, alpha)
+    return IdentityInitialization(alpha, DiagonalStructure())
+end
+function broyden_init(::Val{:identity}, ::Val, autodiff, alpha)
+    IdentityInitialization(alpha, FullStructure())
+end
+function broyden_init(::Val{:true_jacobian}, ::Val, autodiff, alpha)
+    return TrueJacobianInitialization(FullStructure(), autodiff)
+end
+function broyden_init(::Val{IJ}, ::Val{UR}, autodiff, alpha) where {IJ, UR}
+    error("Unknown combination of `init_jacobian = Val($(Meta.quot(IJ)))` and \
+           `update_rule = Val($(Meta.quot(UR)))`. Please choose a valid combination.")
+end
 
-    return ApproximateJacobianSolveAlgorithm{IJ === :true_jacobian, :Broyden}(;
-        linesearch, descent = NewtonDescent(), update_rule, max_resets,
-        initialization, reinit_rule = NoChangeInStateReset(; reset_tolerance))
+broyden_update_rule(::Val{:good_broyden}) = GoodBroydenUpdateRule()
+broyden_update_rule(::Val{:bad_broyden}) = BadBroydenUpdateRule()
+broyden_update_rule(::Val{:diagonal}) = GoodBroydenUpdateRule()
+function broyden_update_rule(::Val{UR}) where {UR}
+    error("Unknown update rule `update_rule = Val($(Meta.quot(UR)))`. Please choose a \
+           valid update rule.")
 end
 
 # Checks for no significant change for `nsteps`
diff --git a/src/algorithms/dfsane.jl b/src/algorithms/dfsane.jl
index b42544055..1ece5f5da 100644
--- a/src/algorithms/dfsane.jl
+++ b/src/algorithms/dfsane.jl
@@ -1,3 +1,4 @@
+# XXX: remove kwargs with unicode
 """
     DFSane(; σ_min = 1 // 10^10, σ_max = 1e10, σ_1 = 1, M::Int = 10, γ = 1 // 10^4,
         τ_min = 1 // 10, τ_max = 1 // 2, n_exp::Int = 2, max_inner_iterations::Int = 100,
diff --git a/src/algorithms/gauss_newton.jl b/src/algorithms/gauss_newton.jl
index 54b7193fc..0f4ec5cd9 100644
--- a/src/algorithms/gauss_newton.jl
+++ b/src/algorithms/gauss_newton.jl
@@ -1,14 +1,15 @@
 """
-    GaussNewton(; concrete_jac = nothing, linsolve = nothing, linesearch = NoLineSearch(),
-        precs = DEFAULT_PRECS, adkwargs...)
+    GaussNewton(; concrete_jac = nothing, linsolve = nothing, precs = DEFAULT_PRECS,
+        linesearch = nothing, vjp_autodiff = nothing, autodiff = nothing,
+        jvp_autodiff = nothing)
 
 An advanced GaussNewton implementation with support for efficient handling of sparse
 matrices via colored automatic differentiation and preconditioned linear solvers. Designed
 for large-scale and numerically-difficult nonlinear least squares problems.
 """
 function GaussNewton(; concrete_jac = nothing, linsolve = nothing, precs = DEFAULT_PRECS,
-        linesearch = NoLineSearch(), vjp_autodiff = nothing, autodiff = nothing)
-    descent = NewtonDescent(; linsolve, precs)
-    return GeneralizedFirstOrderAlgorithm(; concrete_jac, name = :GaussNewton, descent,
-        jacobian_ad = autodiff, reverse_ad = vjp_autodiff, linesearch)
+        linesearch = nothing, vjp_autodiff = nothing, autodiff = nothing,
+        jvp_autodiff = nothing)
+    return GeneralizedFirstOrderAlgorithm{concrete_jac, :GaussNewton}(; linesearch,
+        descent = NewtonDescent(; linsolve, precs), autodiff, vjp_autodiff, jvp_autodiff)
 end
diff --git a/src/algorithms/klement.jl b/src/algorithms/klement.jl
index f5d3edf3d..be94efc9c 100644
--- a/src/algorithms/klement.jl
+++ b/src/algorithms/klement.jl
@@ -1,5 +1,5 @@
 """
-    Klement(; max_resets = 100, linsolve = NoLineSearch(), linesearch = nothing,
+    Klement(; max_resets = 100, linsolve = nothing, linesearch = nothing,
         precs = DEFAULT_PRECS, alpha = nothing, init_jacobian::Val = Val(:identity),
         autodiff = nothing)
 
@@ -25,27 +25,31 @@ over this.
         differentiable problems.
 """
 function Klement(; max_resets::Int = 100, linsolve = nothing, alpha = nothing,
-        linesearch = NoLineSearch(), precs = DEFAULT_PRECS,
-        autodiff = nothing, init_jacobian::Val{IJ} = Val(:identity)) where {IJ}
-    if IJ === :identity
-        initialization = IdentityInitialization(alpha, DiagonalStructure())
-    elseif IJ === :true_jacobian
-        initialization = TrueJacobianInitialization(FullStructure(), autodiff)
-    elseif IJ === :true_jacobian_diagonal
-        initialization = TrueJacobianInitialization(DiagonalStructure(), autodiff)
-    else
-        throw(ArgumentError("`init_jacobian` must be one of `:identity`, `:true_jacobian`, \
-                             or `:true_jacobian_diagonal`"))
-    end
-
-    CJ = IJ === :true_jacobian || IJ === :true_jacobian_diagonal
-
+        linesearch = nothing, precs = DEFAULT_PRECS,
+        autodiff = nothing, init_jacobian::Val = Val(:identity))
+    initialization = klement_init(init_jacobian, autodiff, alpha)
+    CJ = init_jacobian isa Val{:true_jacobian} ||
+         init_jacobian isa Val{:true_jacobian_diagonal}
     return ApproximateJacobianSolveAlgorithm{CJ, :Klement}(;
         linesearch, descent = NewtonDescent(; linsolve, precs),
         update_rule = KlementUpdateRule(),
         reinit_rule = IllConditionedJacobianReset(), max_resets, initialization)
 end
 
+function klement_init(::Val{:identity}, autodiff, alpha)
+    return IdentityInitialization(alpha, DiagonalStructure())
+end
+function klement_init(::Val{:true_jacobian}, autodiff, alpha)
+    return TrueJacobianInitialization(FullStructure(), autodiff)
+end
+function klement_init(::Val{:true_jacobian_diagonal}, autodiff, alpha)
+    return TrueJacobianInitialization(DiagonalStructure(), autodiff)
+end
+function klement_init(::Val{IJ}, autodiff, alpha) where {IJ}
+    error("Unknown `init_jacobian = Val($(Meta.quot(IJ)))`. Please choose a valid \
+           `init_jacobian`.")
+end
+
 # Essentially checks ill conditioned Jacobian
 """
     IllConditionedJacobianReset()
diff --git a/src/algorithms/lbroyden.jl b/src/algorithms/lbroyden.jl
index 8fb0db748..89df6ece5 100644
--- a/src/algorithms/lbroyden.jl
+++ b/src/algorithms/lbroyden.jl
@@ -1,5 +1,5 @@
 """
-    LimitedMemoryBroyden(; max_resets::Int = 3, linesearch = NoLineSearch(),
+    LimitedMemoryBroyden(; max_resets::Int = 3, linesearch = nothing,
         threshold::Val = Val(10), reset_tolerance = nothing, alpha = nothing)
 
 An implementation of `LimitedMemoryBroyden` [ziani2008autoadaptative](@cite) with resetting
@@ -15,16 +15,13 @@ and line search.
   - `alpha`: The initial Jacobian inverse is set to be `(αI)⁻¹`. Defaults to `nothing`
     which implies `α = max(norm(u), 1) / (2 * norm(fu))`.
 """
-function LimitedMemoryBroyden(; max_resets::Int = 3, linesearch = NoLineSearch(),
+function LimitedMemoryBroyden(; max_resets::Int = 3, linesearch = nothing,
         threshold::Union{Val, Int} = Val(10), reset_tolerance = nothing, alpha = nothing)
     threshold isa Int && (threshold = Val(threshold))
+    initialization = BroydenLowRankInitialization{_unwrap_val(threshold)}(alpha, threshold)
     return ApproximateJacobianSolveAlgorithm{false, :LimitedMemoryBroyden}(; linesearch,
-        descent = NewtonDescent(),
-        update_rule = GoodBroydenUpdateRule(),
-        max_resets,
-        initialization = BroydenLowRankInitialization{_unwrap_val(threshold)}(
-            alpha, threshold),
-        reinit_rule = NoChangeInStateReset(; reset_tolerance))
+        descent = NewtonDescent(), update_rule = GoodBroydenUpdateRule(),
+        max_resets, initialization, reinit_rule = NoChangeInStateReset(; reset_tolerance))
 end
 
 """
diff --git a/src/algorithms/levenberg_marquardt.jl b/src/algorithms/levenberg_marquardt.jl
index 2b7c08f95..01896bd14 100644
--- a/src/algorithms/levenberg_marquardt.jl
+++ b/src/algorithms/levenberg_marquardt.jl
@@ -3,7 +3,8 @@
         precs = DEFAULT_PRECS, damping_initial::Real = 1.0, α_geodesic::Real = 0.75,
         damping_increase_factor::Real = 2.0, damping_decrease_factor::Real = 3.0,
         finite_diff_step_geodesic = 0.1, b_uphill::Real = 1.0, autodiff = nothing,
-        min_damping_D::Real = 1e-8, disable_geodesic = Val(false))
+        min_damping_D::Real = 1e-8, disable_geodesic = Val(false), vjp_autodiff = nothing,
+        jvp_autodiff = nothing)
 
 An advanced Levenberg-Marquardt implementation with the improvements suggested in
 [transtrum2012improvements](@citet). Designed for large-scale and numerically-difficult
@@ -34,20 +35,17 @@ function LevenbergMarquardt(;
         linsolve = nothing, precs = DEFAULT_PRECS, damping_initial::Real = 1.0,
         α_geodesic::Real = 0.75, damping_increase_factor::Real = 2.0,
         damping_decrease_factor::Real = 3.0, finite_diff_step_geodesic = 0.1,
-        b_uphill::Real = 1.0, autodiff = nothing,
-        min_damping_D::Real = 1e-8, disable_geodesic = False)
-    descent = DampedNewtonDescent(; linsolve,
-        precs,
-        initial_damping = damping_initial,
+        b_uphill::Real = 1.0, min_damping_D::Real = 1e-8, disable_geodesic = False,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing)
+    descent = DampedNewtonDescent(; linsolve, precs, initial_damping = damping_initial,
         damping_fn = LevenbergMarquardtDampingFunction(
             damping_increase_factor, damping_decrease_factor, min_damping_D))
     if disable_geodesic === False
         descent = GeodesicAcceleration(descent, finite_diff_step_geodesic, α_geodesic)
     end
     trustregion = LevenbergMarquardtTrustRegion(b_uphill)
-    return GeneralizedFirstOrderAlgorithm(;
-        concrete_jac = true, name = :LevenbergMarquardt,
-        trustregion, descent, jacobian_ad = autodiff)
+    return GeneralizedFirstOrderAlgorithm{true, :LevenbergMarquardt}(;
+        trustregion, descent, autodiff, vjp_autodiff, jvp_autodiff)
 end
 
 @concrete struct LevenbergMarquardtDampingFunction <: AbstractDampingFunction
diff --git a/src/algorithms/pseudo_transient.jl b/src/algorithms/pseudo_transient.jl
index 1266d0702..effb904bc 100644
--- a/src/algorithms/pseudo_transient.jl
+++ b/src/algorithms/pseudo_transient.jl
@@ -1,6 +1,7 @@
 """
     PseudoTransient(; concrete_jac = nothing, linsolve = nothing,
-        linesearch = NoLineSearch(), precs = DEFAULT_PRECS, autodiff = nothing)
+        linesearch = NoLineSearch(), precs = DEFAULT_PRECS, autodiff = nothing,
+        jvp_autodiff = nothing, vjp_autodiff = nothing)
 
 An implementation of PseudoTransient Method [coffey2003pseudotransient](@cite) that is used
 to solve steady state problems in an accelerated manner. It uses an adaptive time-stepping
@@ -14,13 +15,14 @@ This implementation specifically uses "switched evolution relaxation"
   - `alpha_initial` : the initial pseudo time step. It defaults to `1e-3`. If it is small,
     you are going to need more iterations to converge but it can be more stable.
 """
-function PseudoTransient(; concrete_jac = nothing, linsolve = nothing,
-        linesearch = NoLineSearch(), precs = DEFAULT_PRECS, autodiff = nothing,
-        alpha_initial = 1e-3)
+function PseudoTransient(;
+        concrete_jac = nothing, linsolve = nothing, linesearch = nothing,
+        precs = DEFAULT_PRECS,  alpha_initial = 1e-3, autodiff = nothing,
+        jvp_autodiff = nothing, vjp_autodiff = nothing)
     descent = DampedNewtonDescent(; linsolve, precs, initial_damping = alpha_initial,
         damping_fn = SwitchedEvolutionRelaxation())
-    return GeneralizedFirstOrderAlgorithm(;
-        concrete_jac, name = :PseudoTransient, linesearch, descent, jacobian_ad = autodiff)
+    return GeneralizedFirstOrderAlgorithm{concrete_jac, :PseudoTransient}(;
+        linesearch, descent, autodiff, vjp_autodiff, jvp_autodiff)
 end
 
 """
@@ -42,11 +44,11 @@ Cache for the [`SwitchedEvolutionRelaxation`](@ref) method.
     internalnorm
 end
 
-function requires_normal_form_jacobian(cache::Union{
+function requires_normal_form_jacobian(::Union{
         SwitchedEvolutionRelaxation, SwitchedEvolutionRelaxationCache})
     return false
 end
-function requires_normal_form_rhs(cache::Union{
+function requires_normal_form_rhs(::Union{
         SwitchedEvolutionRelaxation, SwitchedEvolutionRelaxationCache})
     return false
 end
diff --git a/src/algorithms/raphson.jl b/src/algorithms/raphson.jl
index c6847f54c..e5dee4c91 100644
--- a/src/algorithms/raphson.jl
+++ b/src/algorithms/raphson.jl
@@ -1,14 +1,15 @@
 """
-    NewtonRaphson(; concrete_jac = nothing, linsolve = nothing, linesearch = NoLineSearch(),
-        precs = DEFAULT_PRECS, autodiff = nothing)
+    NewtonRaphson(; concrete_jac = nothing, linsolve = nothing, linesearch = missing,
+        precs = DEFAULT_PRECS, autodiff = nothing, vjp_autodiff = nothing,
+        jvp_autodiff = nothing)
 
 An advanced NewtonRaphson implementation with support for efficient handling of sparse
 matrices via colored automatic differentiation and preconditioned linear solvers. Designed
 for large-scale and numerically-difficult nonlinear systems.
 """
-function NewtonRaphson(; concrete_jac = nothing, linsolve = nothing,
-        linesearch = NoLineSearch(), precs = DEFAULT_PRECS, autodiff = nothing)
-    descent = NewtonDescent(; linsolve, precs)
-    return GeneralizedFirstOrderAlgorithm(;
-        concrete_jac, name = :NewtonRaphson, linesearch, descent, jacobian_ad = autodiff)
+function NewtonRaphson(; concrete_jac = nothing, linsolve = nothing, linesearch = nothing,
+        precs = DEFAULT_PRECS, autodiff = nothing, vjp_autodiff = nothing,
+        jvp_autodiff = nothing)
+    return GeneralizedFirstOrderAlgorithm{concrete_jac, :NewtonRaphson}(; linesearch,
+        descent = NewtonDescent(; linsolve, precs), autodiff, vjp_autodiff, jvp_autodiff)
 end
diff --git a/src/algorithms/trust_region.jl b/src/algorithms/trust_region.jl
index d68e2d9ec..dab6843e8 100644
--- a/src/algorithms/trust_region.jl
+++ b/src/algorithms/trust_region.jl
@@ -4,7 +4,8 @@
         initial_trust_radius::Real = 0 // 1, step_threshold::Real = 1 // 10000,
         shrink_threshold::Real = 1 // 4, expand_threshold::Real = 3 // 4,
         shrink_factor::Real = 1 // 4, expand_factor::Real = 2 // 1,
-        max_shrink_times::Int = 32, vjp_autodiff = nothing, autodiff = nothing)
+        max_shrink_times::Int = 32,
+        vjp_autodiff = nothing, autodiff = nothing, jvp_autodiff = nothing)
 
 An advanced TrustRegion implementation with support for efficient handling of sparse
 matrices via colored automatic differentiation and preconditioned linear solvers. Designed
@@ -24,22 +25,12 @@ function TrustRegion(; concrete_jac = nothing, linsolve = nothing, precs = DEFAU
         initial_trust_radius::Real = 0 // 1, step_threshold::Real = 1 // 10000,
         shrink_threshold::Real = 1 // 4, expand_threshold::Real = 3 // 4,
         shrink_factor::Real = 1 // 4, expand_factor::Real = 2 // 1,
-        max_shrink_times::Int = 32, autodiff = nothing, vjp_autodiff = nothing)
+        max_shrink_times::Int = 32,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing)
     descent = Dogleg(; linsolve, precs)
-    if autodiff !== nothing && ADTypes.mode(autodiff) isa ADTypes.ForwardMode
-        forward_ad = autodiff
-    else
-        forward_ad = nothing
-    end
-    if isnothing(vjp_autodiff) &&
-       autodiff isa Union{ADTypes.AutoFiniteDiff, ADTypes.AutoFiniteDifferences}
-        # TODO: why not just ForwardMode?
-        vjp_autodiff = autodiff
-    end
     trustregion = GenericTrustRegionScheme(;
         method = radius_update_scheme, step_threshold, shrink_threshold, expand_threshold,
-        shrink_factor, expand_factor, reverse_ad = vjp_autodiff, forward_ad)
-    return GeneralizedFirstOrderAlgorithm(;
-        concrete_jac, name = :TrustRegion, trustregion, descent,
-        jacobian_ad = autodiff, reverse_ad = vjp_autodiff, max_shrink_times)
+        shrink_factor, expand_factor, initial_trust_radius, max_trust_radius)
+    return GeneralizedFirstOrderAlgorithm{concrete_jac, :TrustRegion}(;
+        trustregion, descent, autodiff, vjp_autodiff, jvp_autodiff, max_shrink_times)
 end
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index 3522a39f4..b8f479a6d 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -174,7 +174,10 @@ function SciMLBase.__init(
 
         reinit_rule_cache = __internal_init(alg.reinit_rule, J, fu, u, du)
 
-        if alg.trustregion !== missing && alg.linesearch !== missing
+        has_linesearch = alg.linesearch !== missing && alg.linesearch !== nothing
+        has_trustregion = alg.trustregion !== missing && alg.trustregion !== nothing
+
+        if has_trustregion && has_linesearch
             error("TrustRegion and LineSearch methods are algorithmically incompatible.")
         end
 
@@ -182,7 +185,7 @@ function SciMLBase.__init(
         linesearch_cache = nothing
         trustregion_cache = nothing
 
-        if alg.trustregion !== missing
+        if has_trustregion
             supports_trust_region(alg.descent) || error("Trust Region not supported by \
                                                         $(alg.descent).")
             trustregion_cache = __internal_init(
@@ -190,7 +193,7 @@ function SciMLBase.__init(
             GB = :TrustRegion
         end
 
-        if alg.linesearch !== missing
+        if has_linesearch
             supports_line_search(alg.descent) || error("Line Search not supported by \
                                                         $(alg.descent).")
             linesearch_cache = init(
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 13980c154..7b77847d9 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -1,7 +1,7 @@
 """
     GeneralizedFirstOrderAlgorithm{concrete_jac, name}(; descent, linesearch = missing,
-        trustregion = missing, jacobian_ad = nothing, forward_ad = nothing,
-        reverse_ad = nothing, max_shrink_times::Int = typemax(Int))
+        trustregion = missing, autodiff = nothing, vjp_autodiff = nothing,
+        jvp_autodiff = nothing, max_shrink_times::Int = typemax(Int))
     GeneralizedFirstOrderAlgorithm(; concrete_jac = nothing, name::Symbol = :unknown,
         kwargs...)
 
@@ -11,7 +11,9 @@ common example of this is Newton-Raphson Method.
 First Order here refers to the order of differentiation, and should not be confused with the
 order of convergence.
 
-`trustregion` and `linesearch` cannot be specified together.
+!!! danger
+
+    `trustregion` and `linesearch` cannot be specified together.
 
 ### Keyword Arguments
 
@@ -28,9 +30,10 @@ order of convergence.
     trustregion
     descent
     max_shrink_times::Int
-    jacobian_ad
-    forward_ad
-    reverse_ad
+
+    autodiff
+    vjp_autodiff
+    jvp_autodiff
 end
 
 function __show_algorithm(io::IO, alg::GeneralizedFirstOrderAlgorithm, name, indent)
@@ -38,9 +41,9 @@ function __show_algorithm(io::IO, alg::GeneralizedFirstOrderAlgorithm, name, ind
     __is_present(alg.linesearch) && push!(modifiers, "linesearch = $(alg.linesearch)")
     __is_present(alg.trustregion) && push!(modifiers, "trustregion = $(alg.trustregion)")
     push!(modifiers, "descent = $(alg.descent)")
-    __is_present(alg.jacobian_ad) && push!(modifiers, "jacobian_ad = $(alg.jacobian_ad)")
-    __is_present(alg.forward_ad) && push!(modifiers, "forward_ad = $(alg.forward_ad)")
-    __is_present(alg.reverse_ad) && push!(modifiers, "reverse_ad = $(alg.reverse_ad)")
+    __is_present(alg.autodiff) && push!(modifiers, "autodiff = $(alg.autodiff)")
+    __is_present(alg.vjp_autodiff) && push!(modifiers, "vjp_autodiff = $(alg.vjp_autodiff)")
+    __is_present(alg.jvp_autodiff) && push!(modifiers, "jvp_autodiff = $(alg.jvp_autodiff)")
     spacing = " "^indent * "   "
     spacing_last = " "^indent
     print(io, "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))")
@@ -53,22 +56,11 @@ end
 
 function GeneralizedFirstOrderAlgorithm{concrete_jac, name}(;
         descent, linesearch = missing, trustregion = missing,
-        jacobian_ad = nothing, forward_ad = nothing, reverse_ad = nothing,
+        autodiff = nothing, jvp_autodiff = nothing, vjp_autodiff = nothing,
         max_shrink_times::Int = typemax(Int)) where {concrete_jac, name}
-    forward_ad = ifelse(forward_ad !== nothing,
-        forward_ad,
-        ifelse(
-            jacobian_ad !== nothing && ADTypes.mode(jacobian_ad) isa ADTypes.ForwardMode,
-            jacobian_ad, nothing))
-    reverse_ad = ifelse(reverse_ad !== nothing,
-        reverse_ad,
-        ifelse(
-            jacobian_ad !== nothing && ADTypes.mode(jacobian_ad) isa ADTypes.ReverseMode,
-            jacobian_ad, nothing))
-
     return GeneralizedFirstOrderAlgorithm{concrete_jac, name}(
         linesearch, trustregion, descent, max_shrink_times,
-        jacobian_ad, forward_ad, reverse_ad)
+        autodiff, jvp_autodiff, vjp_autodiff)
 end
 
 concrete_jac(::GeneralizedFirstOrderAlgorithm{CJ}) where {CJ} = CJ
@@ -152,6 +144,22 @@ function SciMLBase.__init(
         abstol = nothing, reltol = nothing, maxtime = nothing,
         termination_condition = nothing, internalnorm = L2_NORM,
         linsolve_kwargs = (;), kwargs...) where {uType, iip}
+    autodiff = select_jacobian_autodiff(prob, alg.autodiff)
+    jvp_autodiff = if alg.jvp_autodiff === nothing && alg.autodiff !== nothing &&
+                      (ADTypes.mode(alg.autodiff) isa ADTypes.ForwardMode ||
+                       ADTypes.mode(alg.autodiff) isa ADTypes.ForwardOrReverseMode)
+        select_forward_mode_autodiff(prob, alg.autodiff)
+    else
+        select_forward_mode_autodiff(prob, alg.jvp_autodiff)
+    end
+    vjp_autodiff = if alg.vjp_autodiff === nothing && alg.autodiff !== nothing &&
+                      (ADTypes.mode(alg.autodiff) isa ADTypes.ReverseMode ||
+                       ADTypes.mode(alg.autodiff) isa ADTypes.ForwardOrReverseMode)
+        select_reverse_mode_autodiff(prob, alg.autodiff)
+    else
+        select_reverse_mode_autodiff(prob, alg.vjp_autodiff)
+    end
+
     timer = get_timer_output()
     @static_timeit timer "cache construction" begin
         (; f, u0, p) = prob
@@ -166,14 +174,16 @@ function SciMLBase.__init(
         linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
 
         jac_cache = JacobianCache(
-            prob, alg, f, fu, u, p; stats, autodiff = alg.jacobian_ad, linsolve,
-            jvp_autodiff = alg.forward_ad, vjp_autodiff = alg.reverse_ad)
+            prob, alg, f, fu, u, p; stats, autodiff, linsolve, jvp_autodiff, vjp_autodiff)
         J = jac_cache(nothing)
         descent_cache = __internal_init(prob, alg.descent, J, fu, u; stats, abstol,
             reltol, internalnorm, linsolve_kwargs, timer)
         du = get_du(descent_cache)
 
-        if alg.trustregion !== missing && alg.linesearch !== missing
+        has_linesearch = alg.linesearch !== missing && alg.linesearch !== nothing
+        has_trustregion = alg.trustregion !== missing && alg.trustregion !== nothing
+
+        if has_trustregion && has_linesearch
             error("TrustRegion and LineSearch methods are algorithmically incompatible.")
         end
 
@@ -181,28 +191,20 @@ function SciMLBase.__init(
         linesearch_cache = nothing
         trustregion_cache = nothing
 
-        if alg.trustregion !== missing
+        if has_trustregion
             supports_trust_region(alg.descent) || error("Trust Region not supported by \
                                                         $(alg.descent).")
             trustregion_cache = __internal_init(
-                prob, alg.trustregion, f, fu, u, p; stats, internalnorm, kwargs...)
+                prob, alg.trustregion, f, fu, u, p; stats, internalnorm, kwargs...,
+                autodiff, jvp_autodiff, vjp_autodiff)
             GB = :TrustRegion
         end
 
-        if alg.linesearch !== missing
+        if has_linesearch
             supports_line_search(alg.descent) || error("Line Search not supported by \
                                                         $(alg.descent).")
-            linesearch_ad = alg.forward_ad === nothing ?
-                            (alg.reverse_ad === nothing ? alg.jacobian_ad :
-                             alg.reverse_ad) : alg.forward_ad
-            if linesearch_ad !== nothing && iip && !DI.check_inplace(linesearch_ad)
-                @warn "$(linesearch_ad) doesn't support in-place problems."
-                linesearch_ad = nothing
-            end
-            linesearch_ad = get_concrete_forward_ad(
-                linesearch_ad, prob, False; check_forward_mode = false)
             linesearch_cache = init(
-                prob, alg.linesearch, fu, u; stats, autodiff = linesearch_ad, kwargs...)
+                prob, alg.linesearch, fu, u; stats, autodiff = jvp_autodiff, kwargs...)
             GB = :LineSearch
         end
 
diff --git a/src/globalization/trust_region.jl b/src/globalization/trust_region.jl
index 8ff6de905..248f5307c 100644
--- a/src/globalization/trust_region.jl
+++ b/src/globalization/trust_region.jl
@@ -198,8 +198,7 @@ const RUS = RadiusUpdateSchemes
     GenericTrustRegionScheme(; method = RadiusUpdateSchemes.Simple,
         max_trust_radius = nothing, initial_trust_radius = nothing,
         step_threshold = nothing, shrink_threshold = nothing, expand_threshold = nothing,
-        shrink_factor = nothing, expand_factor = nothing, forward_ad = nothing,
-        reverse_ad = nothing)
+        shrink_factor = nothing, expand_factor = nothing)
 
 Trust Region Method that updates and stores the current trust region radius in
 `trust_region`. For any of the keyword arguments, if the value is `nothing`, then we use
@@ -245,8 +244,6 @@ the value used in the respective paper.
     expand_threshold = nothing
     max_trust_radius = nothing
     initial_trust_radius = nothing
-    forward_ad = nothing
-    reverse_ad = nothing
 end
 
 function Base.show(io::IO, alg::GenericTrustRegionScheme)
@@ -367,7 +364,8 @@ end
 
 function __internal_init(
         prob::AbstractNonlinearProblem, alg::GenericTrustRegionScheme, f::F, fu, u,
-        p, args...; stats, internalnorm::IF = L2_NORM, kwargs...) where {F, IF}
+        p, args...; stats, internalnorm::IF = L2_NORM, vjp_autodiff = nothing,
+        jvp_autodiff = nothing, kwargs...) where {F, IF}
     T = promote_type(eltype(u), eltype(fu))
     u0_norm = internalnorm(u)
     fu_norm = internalnorm(fu)
@@ -386,13 +384,11 @@ function __internal_init(
     p1, p2, p3, p4 = __get_parameters(T, alg.method)
     ϵ = T(1e-8)
 
-    reverse_ad = get_concrete_reverse_ad(alg.reverse_ad, prob; check_reverse_mode = true)
     vjp_operator = alg.method isa RUS.__Yuan || alg.method isa RUS.__Bastin ?
-                   VecJacOperator(prob, fu, u; autodiff = reverse_ad) : nothing
+                   VecJacOperator(prob, fu, u; autodiff = vjp_autodiff) : nothing
 
-    forward_ad = get_concrete_forward_ad(alg.forward_ad, prob; check_forward_mode = true)
     jvp_operator = alg.method isa RUS.__Bastin ?
-                   JacVecOperator(prob, fu, u; autodiff = forward_ad) : nothing
+                   JacVecOperator(prob, fu, u; autodiff = jvp_autodiff) : nothing
 
     if alg.method isa RUS.__Yuan
         Jᵀfu_cache = StatefulJacobianOperator(vjp_operator, u, prob.p) * _vec(fu)
diff --git a/src/internal/approximate_initialization.jl b/src/internal/approximate_initialization.jl
index 72e46a97e..a8196c367 100644
--- a/src/internal/approximate_initialization.jl
+++ b/src/internal/approximate_initialization.jl
@@ -148,8 +148,7 @@ end
 function __internal_init(prob::AbstractNonlinearProblem, alg::TrueJacobianInitialization,
         solver, f::F, fu, u, p; stats, linsolve = missing,
         internalnorm::IN = L2_NORM, kwargs...) where {F, IN}
-    autodiff = get_concrete_forward_ad(
-        alg.autodiff, prob; check_forward_mode = false, kwargs...)
+    autodiff = select_jacobian_autodiff(prob, alg.autodiff)
     jac_cache = JacobianCache(prob, solver, prob.f, fu, u, p; stats, autodiff, linsolve)
     J = alg.structure(jac_cache(nothing))
     return InitializedApproximateJacobianCache(
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index 5334f11dc..e57518e2f 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -28,65 +28,6 @@ function evaluate_f!!(f::NonlinearFunction{iip}, fu, u, p) where {iip}
     return f(u, p)
 end
 
-# AutoDiff Selection Functions
-function get_concrete_forward_ad(
-        autodiff::ADTypes.AbstractADType, prob, sp::Val{test_sparse} = True,
-        args...; check_forward_mode = true, kwargs...) where {test_sparse}
-    if !isa(ADTypes.mode(autodiff), ADTypes.ForwardMode) && check_forward_mode
-        @warn "$(autodiff)::$(typeof(autodiff)) is not a `ForwardMode`. Use with caution." maxlog=1
-    end
-    return autodiff
-end
-function get_concrete_forward_ad(
-        autodiff, prob, sp::Val{test_sparse} = True, args...; kwargs...) where {test_sparse}
-    if test_sparse
-        (; sparsity, jac_prototype) = prob.f
-        use_sparse_ad = sparsity !== nothing || jac_prototype !== nothing
-    else
-        use_sparse_ad = false
-    end
-    ad = if !ForwardDiff.can_dual(eltype(prob.u0)) # Use Finite Differencing
-        use_sparse_ad ? AutoSparse(AutoFiniteDiff()) : AutoFiniteDiff()
-    else
-        use_sparse_ad ? AutoSparse(AutoForwardDiff()) : AutoForwardDiff()
-    end
-    return ad
-end
-
-function get_concrete_reverse_ad(
-        autodiff::ADTypes.AbstractADType, prob, sp::Val{test_sparse} = True,
-        args...; check_reverse_mode = true, kwargs...) where {test_sparse}
-    if !isa(ADTypes.mode(autodiff), ADTypes.ReverseMode) &&
-       !isa(autodiff, ADTypes.AutoFiniteDiff) && # User specified finite differencing
-       check_reverse_mode
-        @warn "$(autodiff)::$(typeof(autodiff)) is not a `ReverseMode`. Use with caution." maxlog=1
-    end
-    if autodiff isa Union{AutoZygote, AutoSparse{<:AutoZygote}} && isinplace(prob)
-        @warn "Attempting to use Zygote.jl for inplace problems. Switching to FiniteDiff. \
-               Sparsity even if present will be ignored for correctness purposes. Set \
-               the reverse ad option to `nothing` to automatically select the best option \
-               and exploit sparsity."
-        return AutoFiniteDiff() # colorvec confusion will occur if we use FiniteDiff
-    else
-        return autodiff
-    end
-end
-function get_concrete_reverse_ad(
-        autodiff, prob, sp::Val{test_sparse} = True, args...; kwargs...) where {test_sparse}
-    if test_sparse
-        (; sparsity, jac_prototype) = prob.f
-        use_sparse_ad = sparsity !== nothing || jac_prototype !== nothing
-    else
-        use_sparse_ad = false
-    end
-    ad = if isinplace(prob) || !DI.check_available(AutoZygote()) # Use Finite Differencing
-        use_sparse_ad ? AutoSparse(AutoFiniteDiff()) : AutoFiniteDiff()
-    else
-        use_sparse_ad ? AutoSparse(AutoZygote()) : AutoZygote()
-    end
-    return ad
-end
-
 # Callbacks
 """
     callback_into_cache!(cache, internalcache, args...)
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
index 358bca792..70cc7021e 100644
--- a/src/internal/jacobian.jl
+++ b/src/internal/jacobian.jl
@@ -56,9 +56,6 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
 
     @bb fu = similar(fu_)
 
-    autodiff = get_concrete_forward_ad(
-        autodiff, prob, Val(false); check_forward_mode = false)
-
     if !has_analytic_jac && needs_jac
         autodiff = construct_concrete_adtype(f, autodiff)
         di_extras = if iip
@@ -71,10 +68,6 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
     end
 
     J = if !needs_jac
-        jvp_autodiff = get_concrete_forward_ad(
-            jvp_autodiff, prob, Val(false); check_forward_mode = true)
-        vjp_autodiff = get_concrete_reverse_ad(
-            vjp_autodiff, prob, Val(false); check_reverse_mode = false)
         JacobianOperator(prob, fu, u; jvp_autodiff, vjp_autodiff)
     else
         if f.jac_prototype === nothing
@@ -109,8 +102,6 @@ function JacobianCache(prob, alg, f::F, ::Number, u::Number, p; stats,
     if SciMLBase.has_jac(f) || SciMLBase.has_vjp(f) || SciMLBase.has_jvp(f)
         return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, nothing)
     end
-    autodiff = get_dense_ad(get_concrete_forward_ad(
-        autodiff, prob; check_forward_mode = false))
     di_extras = DI.prepare_derivative(f, get_dense_ad(autodiff), u, Constant(prob.p))
     return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, di_extras)
 end

From 1a29122a7eac288e3d4908b1699cba2a8826153d Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 22 Oct 2024 16:26:47 -0400
Subject: [PATCH 617/700] fix: `:misc` testing

---
 src/NonlinearSolve.jl        |  4 ++--
 src/internal/forward_diff.jl |  6 ++++--
 src/internal/helpers.jl      |  6 ++++--
 src/internal/linear_solve.jl | 15 +++++----------
 test/misc/aliasing_tests.jl  |  4 ++--
 5 files changed, 17 insertions(+), 18 deletions(-)

diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index a5e71f13b..560006413 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -96,11 +96,11 @@ include("algorithms/levenberg_marquardt.jl")
 include("algorithms/trust_region.jl")
 include("algorithms/extension_algs.jl")
 
-include("internal/forward_diff.jl") # we need to define after the algorithms
-
 include("utils.jl")
 include("default.jl")
 
+include("internal/forward_diff.jl") # we need to define after the algorithms
+
 # @setup_workload begin
 #     nlfuncs = ((NonlinearFunction{false}((u, p) -> u .* u .- p), 0.1),
 #         (NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p), [0.1]))
diff --git a/src/internal/forward_diff.jl b/src/internal/forward_diff.jl
index c2adc70e2..1259480b8 100644
--- a/src/internal/forward_diff.jl
+++ b/src/internal/forward_diff.jl
@@ -10,7 +10,8 @@ for algType in (
     Nothing, AbstractNonlinearSolveAlgorithm, GeneralizedDFSane,
     GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm,
     LeastSquaresOptimJL, FastLevenbergMarquardtJL, CMINPACK, NLsolveJL, NLSolversJL,
-    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL
+    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL,
+    NonlinearSolvePolyAlgorithm{:NLLS, <:Any}, NonlinearSolvePolyAlgorithm{:NLS, <:Any}
 )
     @eval function SciMLBase.__solve(
             prob::DualNonlinearProblem, alg::$(algType), args...; kwargs...)
@@ -47,7 +48,8 @@ for algType in (
     SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm,
     GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm,
     LeastSquaresOptimJL, FastLevenbergMarquardtJL, CMINPACK, NLsolveJL, NLSolversJL,
-    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL
+    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL,
+    NonlinearSolvePolyAlgorithm{:NLLS, <:Any}, NonlinearSolvePolyAlgorithm{:NLS, <:Any}
 )
     @eval function SciMLBase.__init(
             prob::DualNonlinearProblem, alg::$(algType), args...; kwargs...)
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index e57518e2f..30e4596bd 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -109,9 +109,11 @@ function __construct_extension_f(prob::AbstractNonlinearProblem; alias_u0::Bool
 end
 
 function __construct_extension_jac(prob, alg, u0, fu; can_handle_oop::Val = False,
-        can_handle_scalar::Val = False, kwargs...)
+        can_handle_scalar::Val = False, autodiff = nothing, kwargs...)
+    autodiff = select_jacobian_autodiff(prob, autodiff)
+
     Jₚ = JacobianCache(
-        prob, alg, prob.f, fu, u0, prob.p; stats = empty_nlstats(), kwargs...)
+        prob, alg, prob.f, fu, u0, prob.p; stats = empty_nlstats(), autodiff, kwargs...)
 
     𝓙 = (can_handle_scalar === False && prob.u0 isa Number) ? @closure(u->[Jₚ(u[1])]) : Jₚ
 
diff --git a/src/internal/linear_solve.jl b/src/internal/linear_solve.jl
index a0c1ba664..707790ff3 100644
--- a/src/internal/linear_solve.jl
+++ b/src/internal/linear_solve.jl
@@ -149,8 +149,7 @@ function (cache::LinearSolverCache)(;
     if linres.retcode === ReturnCode.Failure
         structured_mat = ArrayInterface.isstructured(cache.lincache.A)
         is_gpuarray = ArrayInterface.device(cache.lincache.A) isa ArrayInterface.GPU
-        if !(cache.linsolve isa QRFactorization{ColumnNorm}) &&
-           !is_gpuarray &&
+        if !(cache.linsolve isa QRFactorization{ColumnNorm}) && !is_gpuarray &&
            !structured_mat
             if verbose
                 @warn "Potential Rank Deficient Matrix Detected. Attempting to solve using \
@@ -177,15 +176,11 @@ function (cache::LinearSolverCache)(;
             return LinearSolveResult(; u = linres.u)
         elseif !(cache.linsolve isa QRFactorization{ColumnNorm})
             if verbose
-                if structured_mat
+                if structured_mat || is_gpuarray
+                    mat_desc = structured_mat ? "Structured" : "GPU"
                     @warn "Potential Rank Deficient Matrix Detected. But Matrix is \
-                           Structured. Currently, we don't attempt to solve Rank Deficient \
-                           Structured Matrices. Please open an issue at \
-                           https://github.com/SciML/NonlinearSolve.jl"
-                elseif is_gpuarray
-                    @warn "Potential Rank Deficient Matrix Detected. But Matrix is on GPU. \
-                           Currently, we don't attempt to solve Rank Deficient GPU \
-                           Matrices. Please open an issue at \
+                           $(mat_desc). Currently, we don't attempt to solve Rank Deficient \
+                           $(mat_desc) Matrices. Please open an issue at \
                            https://github.com/SciML/NonlinearSolve.jl"
                 end
             end
diff --git a/test/misc/aliasing_tests.jl b/test/misc/aliasing_tests.jl
index 653490dfa..78b8ec798 100644
--- a/test/misc/aliasing_tests.jl
+++ b/test/misc/aliasing_tests.jl
@@ -9,7 +9,7 @@
 
     # If aliasing is not handled properly this will diverge
     sol = solve(prob; abstol = 1e-6, alias_u0 = true,
-        termination_condition = AbsNormTerminationMode())
+        termination_condition = AbsNormTerminationMode(Base.Fix1(maximum, abs)))
 
     @test sol.u === prob.u0
     @test SciMLBase.successful_retcode(sol.retcode)
@@ -17,7 +17,7 @@
     prob = remake(prob; u0 = copy(u0))
 
     cache = init(prob; abstol = 1e-6, alias_u0 = true,
-        termination_condition = AbsNormTerminationMode())
+        termination_condition = AbsNormTerminationMode(Base.Fix1(maximum, abs)))
     sol = solve!(cache)
 
     @test sol.u === prob.u0

From 13f14d47ab7ef81db75d1e580164f431fb520b3a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 22 Oct 2024 16:43:46 -0400
Subject: [PATCH 618/700] fix: `:wrappers` testing

---
 ext/NonlinearSolveMINPACKExt.jl           | 3 ++-
 ext/NonlinearSolveNLsolveExt.jl           | 3 ++-
 ext/NonlinearSolveSIAMFANLEquationsExt.jl | 3 ++-
 src/algorithms/pseudo_transient.jl        | 2 +-
 4 files changed, 7 insertions(+), 4 deletions(-)

diff --git a/ext/NonlinearSolveMINPACKExt.jl b/ext/NonlinearSolveMINPACKExt.jl
index 3761a817f..88adf5753 100644
--- a/ext/NonlinearSolveMINPACKExt.jl
+++ b/ext/NonlinearSolveMINPACKExt.jl
@@ -28,7 +28,8 @@ function SciMLBase.__solve(
         original = MINPACK.fsolve(
             f!, u0, m; tol, show_trace, tracing, method, iterations = maxiters)
     else
-        _jac! = NonlinearSolve.__construct_extension_jac(prob, alg, u0, resid; alg.autodiff)
+        autodiff = alg.autodiff === missing ? nothing : alg.autodiff
+        _jac! = NonlinearSolve.__construct_extension_jac(prob, alg, u0, resid; autodiff)
         jac! = @closure (J, u) -> (_jac!(J, u); Cint(0))
         original = MINPACK.fsolve(
             f!, jac!, u0, m; tol, show_trace, tracing, method, iterations = maxiters)
diff --git a/ext/NonlinearSolveNLsolveExt.jl b/ext/NonlinearSolveNLsolveExt.jl
index 301ed7137..73d98c062 100644
--- a/ext/NonlinearSolveNLsolveExt.jl
+++ b/ext/NonlinearSolveNLsolveExt.jl
@@ -18,7 +18,8 @@ function SciMLBase.__solve(
     if prob.f.jac === nothing && alg.autodiff isa Symbol
         df = OnceDifferentiable(f!, u0, resid; alg.autodiff)
     else
-        jac! = NonlinearSolve.__construct_extension_jac(prob, alg, u0, resid; alg.autodiff)
+        autodiff = alg.autodiff isa Symbol ? nothing : alg.autodiff
+        jac! = NonlinearSolve.__construct_extension_jac(prob, alg, u0, resid; autodiff)
         if prob.f.jac_prototype === nothing
             J = similar(
                 u0, promote_type(eltype(u0), eltype(resid)), length(u0), length(resid))
diff --git a/ext/NonlinearSolveSIAMFANLEquationsExt.jl b/ext/NonlinearSolveSIAMFANLEquationsExt.jl
index 65154b63a..2468064fb 100644
--- a/ext/NonlinearSolveSIAMFANLEquationsExt.jl
+++ b/ext/NonlinearSolveSIAMFANLEquationsExt.jl
@@ -91,10 +91,11 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SIAMFANLEquationsJL, arg
                         f, u, m, zeros(T, N, 2 * m + 4); atol, rtol, maxit = maxiters, beta)
                 end
             else
+                autodiff = alg.autodiff === missing ? nothing : alg.autodiff
                 FPS = prob.f.jac_prototype !== nothing ? zero(prob.f.jac_prototype) :
                       __zeros_like(u, N, N)
                 jac = NonlinearSolve.__construct_extension_jac(
-                    prob, alg, u, resid; alg.autodiff)
+                    prob, alg, u, resid; autodiff)
                 AJ! = @closure (J, u, x) -> jac(J, x)
                 if method == :newton
                     sol = nsol(f, u, FS, FPS, AJ!; sham = 1, atol,
diff --git a/src/algorithms/pseudo_transient.jl b/src/algorithms/pseudo_transient.jl
index effb904bc..1e6b94763 100644
--- a/src/algorithms/pseudo_transient.jl
+++ b/src/algorithms/pseudo_transient.jl
@@ -17,7 +17,7 @@ This implementation specifically uses "switched evolution relaxation"
 """
 function PseudoTransient(;
         concrete_jac = nothing, linsolve = nothing, linesearch = nothing,
-        precs = DEFAULT_PRECS,  alpha_initial = 1e-3, autodiff = nothing,
+        precs = DEFAULT_PRECS, alpha_initial = 1e-3, autodiff = nothing,
         jvp_autodiff = nothing, vjp_autodiff = nothing)
     descent = DampedNewtonDescent(; linsolve, precs, initial_damping = alpha_initial,
         damping_fn = SwitchedEvolutionRelaxation())

From bf0473ef377970e2c798927fe5b6be05754a149a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 22 Oct 2024 16:59:45 -0400
Subject: [PATCH 619/700] fix: mode warning printing

---
 lib/NonlinearSolveBase/src/autodiff.jl | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
index 2102ae09b..9dbad5472 100644
--- a/lib/NonlinearSolveBase/src/autodiff.jl
+++ b/lib/NonlinearSolveBase/src/autodiff.jl
@@ -33,7 +33,8 @@ const ForwardADs = (
 
 function select_forward_mode_autodiff(
         prob::AbstractNonlinearProblem, ad::AbstractADType; warn_check_mode::Bool = true)
-    if warn_check_mode && !(ADTypes.mode(ad) isa ADTypes.ForwardMode)
+    if warn_check_mode && !(ADTypes.mode(ad) isa ADTypes.ForwardMode) &&
+       !(ADTypes.mode(ad) isa ADTypes.ForwardOrReverseMode)
         @warn "The chosen AD backend $(ad) is not a forward mode AD. Use with caution."
     end
     if incompatible_backend_and_problem(prob, ad)
@@ -58,7 +59,8 @@ end
 
 function select_reverse_mode_autodiff(
         prob::AbstractNonlinearProblem, ad::AbstractADType; warn_check_mode::Bool = true)
-    if warn_check_mode && !(ADTypes.mode(ad) isa ADTypes.ReverseMode)
+    if warn_check_mode && !(ADTypes.mode(ad) isa ADTypes.ReverseMode) &&
+       !(ADTypes.mode(ad) isa ADTypes.ForwardOrReverseMode)
         if !is_finite_differences_backend(ad)
             @warn "The chosen AD backend $(ad) is not a reverse mode AD. Use with caution."
         else

From a5e614c4cb5eddd25bebf9239b35b1a03a59a802 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 22 Oct 2024 17:09:06 -0400
Subject: [PATCH 620/700] fix: minor cleanups

---
 lib/NonlinearSolveBase/src/autodiff.jl              | 13 +++++--------
 .../src/SimpleNonlinearSolve.jl                     |  1 +
 src/core/generalized_first_order.jl                 |  2 +-
 3 files changed, 7 insertions(+), 9 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
index 9dbad5472..395580924 100644
--- a/lib/NonlinearSolveBase/src/autodiff.jl
+++ b/lib/NonlinearSolveBase/src/autodiff.jl
@@ -34,7 +34,8 @@ const ForwardADs = (
 function select_forward_mode_autodiff(
         prob::AbstractNonlinearProblem, ad::AbstractADType; warn_check_mode::Bool = true)
     if warn_check_mode && !(ADTypes.mode(ad) isa ADTypes.ForwardMode) &&
-       !(ADTypes.mode(ad) isa ADTypes.ForwardOrReverseMode)
+       !(ADTypes.mode(ad) isa ADTypes.ForwardOrReverseMode) &&
+       !is_finite_differences_backend(ad)
         @warn "The chosen AD backend $(ad) is not a forward mode AD. Use with caution."
     end
     if incompatible_backend_and_problem(prob, ad)
@@ -60,13 +61,9 @@ end
 function select_reverse_mode_autodiff(
         prob::AbstractNonlinearProblem, ad::AbstractADType; warn_check_mode::Bool = true)
     if warn_check_mode && !(ADTypes.mode(ad) isa ADTypes.ReverseMode) &&
-       !(ADTypes.mode(ad) isa ADTypes.ForwardOrReverseMode)
-        if !is_finite_differences_backend(ad)
-            @warn "The chosen AD backend $(ad) is not a reverse mode AD. Use with caution."
-        else
-            @warn "The chosen AD backend $(ad) is a finite differences backend. This might \
-                   be slow and inaccurate. Use with caution."
-        end
+       !(ADTypes.mode(ad) isa ADTypes.ForwardOrReverseMode) &&
+       !is_finite_differences_backend(ad)
+        @warn "The chosen AD backend $(ad) is not a reverse mode AD. Use with caution."
     end
     if incompatible_backend_and_problem(prob, ad)
         adₙ = select_reverse_mode_autodiff(prob, nothing; warn_check_mode)
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index f15630e24..cee8f8dd3 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -1,6 +1,7 @@
 module SimpleNonlinearSolve
 
 using Accessors: @reset
+using BracketingNonlinearSolve: BracketingNonlinearSolve
 using CommonSolve: CommonSolve, solve, init, solve!
 using ConcreteStructs: @concrete
 using FastClosures: @closure
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 7b77847d9..d5ee3eeab 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -60,7 +60,7 @@ function GeneralizedFirstOrderAlgorithm{concrete_jac, name}(;
         max_shrink_times::Int = typemax(Int)) where {concrete_jac, name}
     return GeneralizedFirstOrderAlgorithm{concrete_jac, name}(
         linesearch, trustregion, descent, max_shrink_times,
-        autodiff, jvp_autodiff, vjp_autodiff)
+        autodiff, vjp_autodiff, jvp_autodiff)
 end
 
 concrete_jac(::GeneralizedFirstOrderAlgorithm{CJ}) where {CJ} = CJ

From 21b02bdbb2e273e68c92823d3feb05d434666ec4 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 22 Oct 2024 18:16:46 -0400
Subject: [PATCH 621/700] docs: update documentation

---
 .github/workflows/Documentation.yml         |   2 +-
 .github/workflows/Downgrade.yml             |  35 +++++-
 Project.toml                                |   8 +-
 docs/Project.toml                           |   9 +-
 docs/make.jl                                |   8 +-
 docs/pages.jl                               |   4 +-
 docs/src/basics/diagnostics_api.md          |  20 ++--
 docs/src/basics/solve.md                    |   2 +-
 docs/src/basics/termination_condition.md    |  22 ++--
 docs/src/devdocs/algorithm_helpers.md       |   3 -
 docs/src/native/bracketingnonlinearsolve.md |  21 ++++
 docs/src/native/simplenonlinearsolve.md     |  16 +--
 docs/src/tutorials/modelingtoolkit.md       |  28 ++---
 lib/BracketingNonlinearSolve/README.md      |  23 ++++
 lib/NonlinearSolveBase/Project.toml         |   2 +-
 lib/NonlinearSolveBase/src/public.jl        |   2 +-
 lib/SciMLJacobianOperators/Project.toml     |   4 +-
 lib/SimpleNonlinearSolve/Project.toml       |   4 +-
 lib/SimpleNonlinearSolve/README.md          |  23 ++++
 lib/SimpleNonlinearSolve/src/lbroyden.jl    |   4 +-
 src/NonlinearSolve.jl                       | 118 ++++++++++----------
 test/gpu/core_tests.jl                      |   7 +-
 22 files changed, 225 insertions(+), 140 deletions(-)
 create mode 100644 docs/src/native/bracketingnonlinearsolve.md
 create mode 100644 lib/BracketingNonlinearSolve/README.md
 create mode 100644 lib/SimpleNonlinearSolve/README.md

diff --git a/.github/workflows/Documentation.yml b/.github/workflows/Documentation.yml
index 84f38404f..9dc416799 100644
--- a/.github/workflows/Documentation.yml
+++ b/.github/workflows/Documentation.yml
@@ -15,7 +15,7 @@ jobs:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@latest
         with:
-          version: '1'
+          version: '1.10'
       - name: Install dependencies
         run: |
           import Pkg
diff --git a/.github/workflows/Downgrade.yml b/.github/workflows/Downgrade.yml
index 83001be29..172457df8 100644
--- a/.github/workflows/Downgrade.yml
+++ b/.github/workflows/Downgrade.yml
@@ -14,15 +14,42 @@ jobs:
   test:
     runs-on: ubuntu-latest
     strategy:
+      fail-fast: false
       matrix:
-        version: ["1.10"]
+        version:
+          - "1.10"
+        group:
+          - Core
+          - Downstream
+          - Misc
+          - Wrappers
     steps:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v2
         with:
           version: ${{ matrix.version }}
       - uses: julia-actions/julia-downgrade-compat@v1
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveBase", "lib/SimpleNonlinearSolve")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage=true)
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=. {0}
+        env:
+          GROUP: ${{ matrix.group }}
+      - uses: julia-actions/julia-processcoverage@v1
         with:
-          skip: Pkg,TOML
-      - uses: julia-actions/julia-buildpkg@v1
-      - uses: julia-actions/julia-runtest@v1
+          directories: src,ext,lib/SciMLJacobianOperators/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/Project.toml b/Project.toml
index d6fec9aa1..03e6519dd 100644
--- a/Project.toml
+++ b/Project.toml
@@ -68,9 +68,9 @@ BenchmarkTools = "1.4"
 CUDA = "5.5"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
-DiffEqBase = "6.158.3"
-DifferentiationInterface = "0.6.1"
-Enzyme = "0.13.2"
+DiffEqBase = "6.155.3"
+DifferentiationInterface = "0.6.16"
+Enzyme = "0.13.11"
 ExplicitImports = "1.5"
 FastClosures = "0.3.2"
 FastLevenbergMarquardt = "0.1"
@@ -108,7 +108,7 @@ SciMLOperators = "0.3.10"
 SimpleNonlinearSolve = "2"
 SparseArrays = "1.10"
 SparseConnectivityTracer = "0.6.5"
-SparseMatrixColorings = "0.4.2"
+SparseMatrixColorings = "0.4.5"
 SpeedMapping = "0.3"
 StableRNGs = "1"
 StaticArrays = "1.9"
diff --git a/docs/Project.toml b/docs/Project.toml
index d01ae32a1..4e72b257d 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -3,6 +3,7 @@ ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 AlgebraicMultigrid = "2169fc97-5a83-5252-b627-83903c6c433c"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+BracketingNonlinearSolve = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
@@ -11,8 +12,8 @@ DocumenterInterLinks = "d12716ef-a0f6-4df4-a9f1-a5a34e75c656"
 IncompleteLU = "40713840-3770-5561-ab4c-a76e7d0d7895"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
-ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
+NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 OrdinaryDiffEqTsit5 = "b1df2697-797e-41e3-8120-5422d3b24e4a"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
@@ -29,16 +30,16 @@ ADTypes = "1.9.0"
 AlgebraicMultigrid = "0.5, 0.6"
 ArrayInterface = "6, 7"
 BenchmarkTools = "1"
-DiffEqBase = "6.136"
-DifferentiationInterface = "0.6.1"
+BracketingNonlinearSolve = "1"
+DifferentiationInterface = "0.6.16"
 Documenter = "1"
 DocumenterCitations = "1"
 DocumenterInterLinks = "1.0.0"
 IncompleteLU = "0.2"
 InteractiveUtils = "<0.0.1, 1"
 LinearSolve = "2"
-ModelingToolkit = "9"
 NonlinearSolve = "4"
+NonlinearSolveBase = "1"
 OrdinaryDiffEqTsit5 = "1.1.0"
 Plots = "1"
 Random = "1.10"
diff --git a/docs/make.jl b/docs/make.jl
index eec25f4f7..bdc2b7fe9 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,7 +1,8 @@
 using Documenter, DocumenterCitations, DocumenterInterLinks
 using NonlinearSolve, SimpleNonlinearSolve, Sundials, SteadyStateDiffEq, SciMLBase,
-      DiffEqBase
+      BracketingNonlinearSolve, NonlinearSolveBase
 using SciMLJacobianOperators
+import DiffEqBase
 
 cp(joinpath(@__DIR__, "Manifest.toml"),
     joinpath(@__DIR__, "src/assets/Manifest.toml"), force = true)
@@ -20,8 +21,9 @@ interlinks = InterLinks(
 makedocs(;
     sitename = "NonlinearSolve.jl",
     authors = "Chris Rackauckas",
-    modules = [NonlinearSolve, SimpleNonlinearSolve, SteadyStateDiffEq,
-        Sundials, DiffEqBase, SciMLBase, SciMLJacobianOperators],
+    modules = [NonlinearSolve, SimpleNonlinearSolve, SteadyStateDiffEq, DiffEqBase,
+        Sundials, NonlinearSolveBase, SciMLBase, SciMLJacobianOperators,
+        BracketingNonlinearSolve],
     clean = true,
     doctest = false,
     linkcheck = true,
diff --git a/docs/pages.jl b/docs/pages.jl
index cfb2754c0..8da01762a 100644
--- a/docs/pages.jl
+++ b/docs/pages.jl
@@ -1,6 +1,7 @@
 # Put in a separate page so it can be used by SciMLDocs.jl
 
-pages = ["index.md",
+pages = [
+    "index.md",
     "Getting Started with Nonlinear Rootfinding in Julia" => "tutorials/getting_started.md",
     "Tutorials" => Any[
         "tutorials/code_optimization.md",
@@ -31,6 +32,7 @@ pages = ["index.md",
     "Native Functionalities" => Any[
         "native/solvers.md",
         "native/simplenonlinearsolve.md",
+        "native/bracketingnonlinearsolve.md",
         "native/steadystatediffeq.md",
         "native/descent.md",
         "native/globalization.md",
diff --git a/docs/src/basics/diagnostics_api.md b/docs/src/basics/diagnostics_api.md
index c8b207544..795348bd6 100644
--- a/docs/src/basics/diagnostics_api.md
+++ b/docs/src/basics/diagnostics_api.md
@@ -27,20 +27,16 @@ Note that you will have to restart Julia to disable the timer outputs once enabl
 ## Example Usage
 
 ```@example diagnostics_example
-using ModelingToolkit, NonlinearSolve
+using NonlinearSolve
 
-@variables x y z
-@parameters σ ρ β
+function nlfunc(resid, u0, p)
+    resid[1] = u0[1] * u0[1] - p
+    resid[2] = u0[2] * u0[2] - p
+    resid[3] = u0[3] * u0[3] - p
+    nothing
+end
 
-# Define a nonlinear system
-eqs = [0 ~ σ * (y - x), 0 ~ x * (ρ - z) - y, 0 ~ x * y - β * z]
-@mtkbuild ns = NonlinearSystem(eqs, [x, y, z], [σ, ρ, β])
-
-u0 = [x => 1.0, y => 0.0, z => 0.0]
-
-ps = [σ => 10.0 ρ => 26.0 β => 8 / 3]
-
-prob = NonlinearProblem(ns, u0, ps)
+prob = NonlinearProblem(nlfunc, [1.0, 3.0, 5.0], 2.0)
 
 solve(prob)
 ```
diff --git a/docs/src/basics/solve.md b/docs/src/basics/solve.md
index f7c238966..3bc7df056 100644
--- a/docs/src/basics/solve.md
+++ b/docs/src/basics/solve.md
@@ -1,7 +1,7 @@
 # [Common Solver Options (Solve Keyword Arguments)](@id solver_options)
 
 ```@docs
-solve(prob::SciMLBase.NonlinearProblem, args...; kwargs...)
+solve(::NonlinearProblem, args...; kwargs...)
 ```
 
 ## General Controls
diff --git a/docs/src/basics/termination_condition.md b/docs/src/basics/termination_condition.md
index 9a7c718ec..4ea98b4a5 100644
--- a/docs/src/basics/termination_condition.md
+++ b/docs/src/basics/termination_condition.md
@@ -23,17 +23,23 @@ terminated = cache(du, u, uprev)
 ### Absolute Tolerance
 
 ```@docs
-AbsTerminationMode
-AbsNormTerminationMode
-AbsNormSafeTerminationMode
-AbsNormSafeBestTerminationMode
+NonlinearSolveBase.AbsTerminationMode
+NonlinearSolveBase.AbsNormTerminationMode
+NonlinearSolveBase.AbsNormSafeTerminationMode
+NonlinearSolveBase.AbsNormSafeBestTerminationMode
 ```
 
 ### Relative Tolerance
 
 ```@docs
-RelTerminationMode
-RelNormTerminationMode
-RelNormSafeTerminationMode
-RelNormSafeBestTerminationMode
+NonlinearSolveBase.RelTerminationMode
+NonlinearSolveBase.RelNormTerminationMode
+NonlinearSolveBase.RelNormSafeTerminationMode
+NonlinearSolveBase.RelNormSafeBestTerminationMode
+```
+
+### Both Tolerances
+
+```@docs
+NonlinearSolveBase.NormTerminationMode
 ```
diff --git a/docs/src/devdocs/algorithm_helpers.md b/docs/src/devdocs/algorithm_helpers.md
index 7b0f91a9f..c945b6003 100644
--- a/docs/src/devdocs/algorithm_helpers.md
+++ b/docs/src/devdocs/algorithm_helpers.md
@@ -60,9 +60,6 @@ NonlinearSolve.GenericTrustRegionScheme
 ## Miscellaneous
 
 ```@docs
-SimpleNonlinearSolve.__nextfloat_tdir
-SimpleNonlinearSolve.__prevfloat_tdir
-SimpleNonlinearSolve.__max_tdir
 NonlinearSolve.callback_into_cache!
 NonlinearSolve.concrete_jac
 ```
diff --git a/docs/src/native/bracketingnonlinearsolve.md b/docs/src/native/bracketingnonlinearsolve.md
new file mode 100644
index 000000000..2201378e1
--- /dev/null
+++ b/docs/src/native/bracketingnonlinearsolve.md
@@ -0,0 +1,21 @@
+# BracketingNonlinearSolve.jl
+
+These methods can be used independently of the rest of NonlinearSolve.jl
+
+```@index
+Pages = ["bracketingnonlinearsolve.md"]
+```
+
+## Interval Methods
+
+These methods are suited for interval (scalar) root-finding problems,
+i.e. [`IntervalNonlinearProblem`](@ref).
+
+```@docs
+ITP
+Alefeld
+Bisection
+Falsi
+Ridder
+Brent
+```
diff --git a/docs/src/native/simplenonlinearsolve.md b/docs/src/native/simplenonlinearsolve.md
index 0ff386898..777a81ef8 100644
--- a/docs/src/native/simplenonlinearsolve.md
+++ b/docs/src/native/simplenonlinearsolve.md
@@ -6,20 +6,6 @@ These methods can be used independently of the rest of NonlinearSolve.jl
 Pages = ["simplenonlinearsolve.md"]
 ```
 
-## Interval Methods
-
-These methods are suited for interval (scalar) root-finding problems,
-i.e. `IntervalNonlinearProblem`.
-
-```@docs
-ITP
-Alefeld
-Bisection
-Falsi
-Ridder
-Brent
-```
-
 ## General Methods
 
 These methods are suited for any general nonlinear root-finding problem, i.e.
@@ -54,6 +40,6 @@ Squares problems.
 [^1]: Needs [`StaticArrays.jl`](https://github.com/JuliaArrays/StaticArrays.jl) to be
     installed and loaded for the non-allocating version.
 [^2]: This method is non-allocating if the termination condition is set to either `nothing`
-    (default) or [`AbsNormTerminationMode`](@ref).
+    (default) or [`NonlinearSolveBase.AbsNormTerminationMode`](@ref).
 [^3]: Only the defaults are guaranteed to work inside kernels. We try to provide warnings
     if the used version is not non-allocating.
diff --git a/docs/src/tutorials/modelingtoolkit.md b/docs/src/tutorials/modelingtoolkit.md
index 87b0a4405..e2016dde0 100644
--- a/docs/src/tutorials/modelingtoolkit.md
+++ b/docs/src/tutorials/modelingtoolkit.md
@@ -5,7 +5,7 @@ modeling system for the Julia SciML ecosystem. It adds a high-level interactive
 for the numerical solvers which can make it easy to symbolically modify and generate
 equations to be solved. The basic form of using ModelingToolkit looks as follows:
 
-```@example mtk
+```julia
 using ModelingToolkit, NonlinearSolve
 
 @variables x y z
@@ -30,20 +30,20 @@ sol = solve(prob, NewtonRaphson())
 As a symbolic system, ModelingToolkit can be used to represent the equations and derive new
 forms. For example, let's look at the equations:
 
-```@example mtk
+```julia
 equations(ns)
 ```
 
 We can ask it what the Jacobian of our system is via `calculate_jacobian`:
 
-```@example mtk
+```julia
 calculate_jacobian(ns)
 ```
 
 We can tell MTK to generate a computable form of this analytical Jacobian via `jac = true`
 to help the solver use efficient forms:
 
-```@example mtk
+```julia
 prob = NonlinearProblem(ns, u0, ps, jac = true)
 sol = solve(prob, NewtonRaphson())
 ```
@@ -54,7 +54,7 @@ One of the major reasons for using ModelingToolkit is to allow structural simpli
 the systems. It's very easy to write down a mathematical model that, in theory, could be
 solved more simply. Let's take a look at a quick system:
 
-```@example mtk
+```julia
 @variables u1 u2 u3 u4 u5
 eqs = [0 ~ u1 - sin(u5), 0 ~ u2 - cos(u1), 0 ~ u3 - hypot(u1, u2),
     0 ~ u4 - hypot(u2, u3), 0 ~ u5 - hypot(u4, u1)]
@@ -63,23 +63,23 @@ eqs = [0 ~ u1 - sin(u5), 0 ~ u2 - cos(u1), 0 ~ u3 - hypot(u1, u2),
 
 If we run structural simplification, we receive the following form:
 
-```@example mtk
+```julia
 sys = structural_simplify(sys)
 ```
 
-```@example mtk
+```julia
 equations(sys)
 ```
 
 How did it do this? Let's look at the `observed` to see the relationships that it found:
 
-```@example mtk
+```julia
 observed(sys)
 ```
 
 Using ModelingToolkit, we can build and solve the simplified system:
 
-```@example mtk
+```julia
 u0 = [u5 .=> 1.0]
 prob = NonlinearProblem(sys, u0)
 sol = solve(prob, NewtonRaphson())
@@ -87,23 +87,23 @@ sol = solve(prob, NewtonRaphson())
 
 We can then use symbolic indexing to retrieve any variable:
 
-```@example mtk
+```julia
 sol[u1]
 ```
 
-```@example mtk
+```julia
 sol[u2]
 ```
 
-```@example mtk
+```julia
 sol[u3]
 ```
 
-```@example mtk
+```julia
 sol[u4]
 ```
 
-```@example mtk
+```julia
 sol[u5]
 ```
 
diff --git a/lib/BracketingNonlinearSolve/README.md b/lib/BracketingNonlinearSolve/README.md
new file mode 100644
index 000000000..85839107e
--- /dev/null
+++ b/lib/BracketingNonlinearSolve/README.md
@@ -0,0 +1,23 @@
+# BracketingNonlinearSolve.jl
+
+Fast implementations of interval root finding algorithms in Julia that satisfy the SciML
+common interface. BracketingNonlinearSolve.jl focuses on low-dependency implementations of
+very fast methods for very small and simple problems. For the full set of solvers, see
+[NonlinearSolve.jl](https://github.com/SciML/NonlinearSolve.jl), of which
+BracketingNonlinearSolve.jl is just one solver set.
+
+For information on using the package,
+[see the stable documentation](https://docs.sciml.ai/NonlinearSolve/stable/). Use the
+[in-development documentation](https://docs.sciml.ai/NonlinearSolve/dev/) for the version of
+the documentation which contains the unreleased features.
+
+## High Level Examples
+
+```julia
+using BracketingNonlinearSolve
+
+f(u, p) = u .* u .- 2.0
+u0 = (1.0, 2.0) # brackets
+probB = IntervalNonlinearProblem(f, u0)
+sol = solve(probB, ITP())
+```
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 162ce2742..70c0f97d4 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -37,7 +37,7 @@ CommonSolve = "0.2.4"
 Compat = "4.15"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149"
-DifferentiationInterface = "0.6.1"
+DifferentiationInterface = "0.6.16"
 EnzymeCore = "0.8"
 ExplicitImports = "1.10.1"
 FastClosures = "0.3"
diff --git a/lib/NonlinearSolveBase/src/public.jl b/lib/NonlinearSolveBase/src/public.jl
index eceea6d75..b39aa26d2 100644
--- a/lib/NonlinearSolveBase/src/public.jl
+++ b/lib/NonlinearSolveBase/src/public.jl
@@ -81,7 +81,7 @@ for norm_type in (:RelNorm, :AbsNorm), safety in (:Safe, :SafeBest)
     supertype_name = Symbol(:Abstract, safety, :NonlinearTerminationMode)
 
     doctring = safety == :Safe ?
-               "Essentially [`$(norm_type)NormTerminationMode`](@ref) + terminate if there \
+               "Essentially [`$(norm_type)TerminationMode`](@ref) + terminate if there \
                 has been no improvement for the last `patience_steps` + terminate if the \
                 solution blows up (diverges)." :
                "Essentially [`$(norm_type)SafeTerminationMode`](@ref), but caches the best\
diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index 73ee5a55d..c889eb199 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -18,8 +18,8 @@ ADTypes = "1.8.1"
 Aqua = "0.8.7"
 ConcreteStructs = "0.2.3"
 ConstructionBase = "1.5"
-DifferentiationInterface = "0.6.1"
-Enzyme = "0.12, 0.13"
+DifferentiationInterface = "0.6.16"
+Enzyme = "0.13.11"
 ExplicitImports = "1.9.0"
 FastClosures = "0.3.2"
 FiniteDiff = "2.24.0"
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 586341f67..cfda24544 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -45,8 +45,8 @@ ChainRulesCore = "1.24"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.149"
-DifferentiationInterface = "0.6.1"
-Enzyme = "0.13"
+DifferentiationInterface = "0.6.16"
+Enzyme = "0.13.11"
 ExplicitImports = "1.9"
 FastClosures = "0.3.2"
 FiniteDiff = "2.24.0"
diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
new file mode 100644
index 000000000..562a5a4ae
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -0,0 +1,23 @@
+# SimpleNonlinearSolve.jl
+
+Fast implementations of root finding algorithms in Julia that satisfy the SciML common interface.
+SimpleNonlinearSolve.jl focuses on low-dependency implementations of very fast methods for
+very small and simple problems. For the full set of solvers, see
+[NonlinearSolve.jl](https://github.com/SciML/NonlinearSolve.jl), of which
+SimpleNonlinearSolve.jl is just one solver set.
+
+For information on using the package,
+[see the stable documentation](https://docs.sciml.ai/NonlinearSolve/stable/). Use the
+[in-development documentation](https://docs.sciml.ai/NonlinearSolve/dev/) for the version of
+the documentation which contains the unreleased features.
+
+## High Level Examples
+
+```julia
+using SimpleNonlinearSolve, StaticArrays
+
+f(u, p) = u .* u .- 2
+u0 = @SVector[1.0, 1.0]
+probN = NonlinearProblem{false}(f, u0)
+solver = solve(probN, SimpleNewtonRaphson(), abstol = 1e-9)
+```
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index 3a17e0936..d2bd6ef83 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -44,8 +44,8 @@ function SciMLBase.__solve(
         end
         @warn "Specifying `termination_condition = $(termination_condition)` for \
                `SimpleLimitedMemoryBroyden` with `SArray` is not non-allocating. Use \
-               either `termination_condition = AbsNormTerminationMode()` or \
-               `termination_condition = nothing`." maxlog=1
+               either `termination_condition = AbsNormTerminationMode(Base.Fix2(norm, Inf))` \
+               or `termination_condition = nothing`." maxlog=1
     end
     return internal_generic_solve(prob, alg, args...; termination_condition, kwargs...)
 end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 560006413..60e2f0663 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -101,65 +101,65 @@ include("default.jl")
 
 include("internal/forward_diff.jl") # we need to define after the algorithms
 
-# @setup_workload begin
-#     nlfuncs = ((NonlinearFunction{false}((u, p) -> u .* u .- p), 0.1),
-#         (NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p), [0.1]))
-#     probs_nls = NonlinearProblem[]
-#     for (fn, u0) in nlfuncs
-#         push!(probs_nls, NonlinearProblem(fn, u0, 2.0))
-#     end
-
-#     nls_algs = (
-#         NewtonRaphson(),
-#         TrustRegion(),
-#         LevenbergMarquardt(),
-#         Broyden(),
-#         Klement(),
-#         nothing
-#     )
-
-#     probs_nlls = NonlinearLeastSquaresProblem[]
-#     nlfuncs = (
-#         (NonlinearFunction{false}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
-#         (NonlinearFunction{false}((u, p) -> vcat(u .* u .- p, u .* u .- p)), [0.1, 0.1]),
-#         (
-#             NonlinearFunction{true}(
-#                 (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(1)),
-#             [0.1, 0.0]),
-#         (
-#             NonlinearFunction{true}((du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p),
-#                 resid_prototype = zeros(4)),
-#             [0.1, 0.1]
-#         )
-#     )
-#     for (fn, u0) in nlfuncs
-#         push!(probs_nlls, NonlinearLeastSquaresProblem(fn, u0, 2.0))
-#     end
-
-#     nlls_algs = (
-#         LevenbergMarquardt(),
-#         GaussNewton(),
-#         TrustRegion(),
-#         nothing
-#     )
-
-#     @compile_workload begin
-#         @sync begin
-#             for T in (Float32, Float64), (fn, u0) in nlfuncs
-#                 Threads.@spawn NonlinearProblem(fn, T.(u0), T(2))
-#             end
-#             for (fn, u0) in nlfuncs
-#                 Threads.@spawn NonlinearLeastSquaresProblem(fn, u0, 2.0)
-#             end
-#             for prob in probs_nls, alg in nls_algs
-#                 Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
-#             end
-#             for prob in probs_nlls, alg in nlls_algs
-#                 Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
-#             end
-#         end
-#     end
-# end
+@setup_workload begin
+    nlfuncs = ((NonlinearFunction{false}((u, p) -> u .* u .- p), 0.1),
+        (NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p), [0.1]))
+    probs_nls = NonlinearProblem[]
+    for (fn, u0) in nlfuncs
+        push!(probs_nls, NonlinearProblem(fn, u0, 2.0))
+    end
+
+    nls_algs = (
+        NewtonRaphson(),
+        TrustRegion(),
+        LevenbergMarquardt(),
+        Broyden(),
+        Klement(),
+        nothing
+    )
+
+    probs_nlls = NonlinearLeastSquaresProblem[]
+    nlfuncs = (
+        (NonlinearFunction{false}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
+        (NonlinearFunction{false}((u, p) -> vcat(u .* u .- p, u .* u .- p)), [0.1, 0.1]),
+        (
+            NonlinearFunction{true}(
+                (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(1)),
+            [0.1, 0.0]),
+        (
+            NonlinearFunction{true}((du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p),
+                resid_prototype = zeros(4)),
+            [0.1, 0.1]
+        )
+    )
+    for (fn, u0) in nlfuncs
+        push!(probs_nlls, NonlinearLeastSquaresProblem(fn, u0, 2.0))
+    end
+
+    nlls_algs = (
+        LevenbergMarquardt(),
+        GaussNewton(),
+        TrustRegion(),
+        nothing
+    )
+
+    @compile_workload begin
+        @sync begin
+            for T in (Float32, Float64), (fn, u0) in nlfuncs
+                Threads.@spawn NonlinearProblem(fn, T.(u0), T(2))
+            end
+            for (fn, u0) in nlfuncs
+                Threads.@spawn NonlinearLeastSquaresProblem(fn, u0, 2.0)
+            end
+            for prob in probs_nls, alg in nls_algs
+                Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
+            end
+            for prob in probs_nlls, alg in nlls_algs
+                Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
+            end
+        end
+    end
+end
 
 # Rexexports
 @reexport using SciMLBase, SimpleNonlinearSolve, NonlinearSolveBase
diff --git a/test/gpu/core_tests.jl b/test/gpu/core_tests.jl
index 75087aa30..91d6178a4 100644
--- a/test/gpu/core_tests.jl
+++ b/test/gpu/core_tests.jl
@@ -15,7 +15,8 @@
         SOLVERS = (
             NewtonRaphson(),
             LevenbergMarquardt(; linsolve = QRFactorization()),
-            LevenbergMarquardt(; linsolve = KrylovJL_GMRES()),
+            # XXX: Fails currently
+            # LevenbergMarquardt(; linsolve = KrylovJL_GMRES()),
             PseudoTransient(),
             Klement(),
             Broyden(; linesearch = LiFukushimaLineSearch()),
@@ -27,7 +28,7 @@
         )
 
         @testset "[IIP] GPU Solvers" begin
-            for alg in SOLVERS
+            @testset "$(nameof(typeof(alg)))" for alg in SOLVERS
                 @test_nowarn sol = solve(prob, alg; abstol = 1.0f-5, reltol = 1.0f-5)
             end
         end
@@ -37,7 +38,7 @@
         prob = NonlinearProblem{false}(linear_f, u0)
 
         @testset "[OOP] GPU Solvers" begin
-            for alg in SOLVERS
+            @testset "$(nameof(typeof(alg)))" for alg in SOLVERS
                 @test_nowarn sol = solve(prob, alg; abstol = 1.0f-5, reltol = 1.0f-5)
             end
         end

From a14a6998e90cf068ecc342ee8959959ac0fae5e4 Mon Sep 17 00:00:00 2001
From: Songchen Tan <i@tansongchen.com>
Date: Wed, 2 Oct 2024 15:41:34 -0400
Subject: [PATCH 622/700] Add Householder's method

---
 lib/SimpleNonlinearSolve/Project.toml         |  2 +
 .../ext/SimpleNonlinearSolveTaylorDiffExt.jl  | 60 +++++++++++++++++++
 .../src/SimpleNonlinearSolve.jl               |  2 +
 .../src/nlsolve/householder.jl                | 13 ++++
 4 files changed, 77 insertions(+)
 create mode 100644 lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTaylorDiffExt.jl
 create mode 100644 lib/SimpleNonlinearSolve/src/nlsolve/householder.jl

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 33e36201d..881ca6630 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -26,12 +26,14 @@ ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+TaylorDiff = "b36ab563-344f-407b-a36a-4f200bebf99c"
 
 [extensions]
 SimpleNonlinearSolveChainRulesCoreExt = "ChainRulesCore"
 SimpleNonlinearSolveReverseDiffExt = "ReverseDiff"
 SimpleNonlinearSolveTrackerExt = "Tracker"
 SimpleNonlinearSolveZygoteExt = "Zygote"
+SimpleNonlinearSolveTaylorDiffExt = "TaylorDiff"
 
 [compat]
 ADTypes = "1.9"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTaylorDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTaylorDiffExt.jl
new file mode 100644
index 000000000..99b2ca788
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTaylorDiffExt.jl
@@ -0,0 +1,60 @@
+module SimpleNonlinearSolveTaylorDiffExt
+using SimpleNonlinearSolve
+using SimpleNonlinearSolve: ImmutableNonlinearProblem, ReturnCode, build_solution, check_termination, init_termination_cache
+using SimpleNonlinearSolve: __maybe_unaliased, _get_fx, __fixed_parameter_function
+using MaybeInplace: @bb
+using SciMLBase: isinplace
+
+import TaylorDiff
+
+@inline function __get_higher_order_derivatives(::SimpleHouseholder{N}, prob, f, x) where N
+    vN = Val(N)
+    l = map(one, x)
+
+    if isinplace(prob)
+        fx = f(x)
+        invf = x -> inv.(f(x))
+        bundle = TaylorDiff.derivatives(invf, fx, x, l, vN)
+    else
+        t = TaylorDiff.make_seed(x, l, vN)
+        ft = f(t)
+        fx = map(TaylorDiff.primal, ft)
+        bundle = inv.(ft)
+    end
+    num = TaylorDiff.extract_derivative(bundle, N - 1)
+    den = TaylorDiff.extract_derivative(bundle, N)
+    return num, den, fx
+end
+
+function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleHouseholder{N},
+        args...; abstol = nothing, reltol = nothing, maxiters = 1000,
+        termination_condition = nothing, alias_u0 = false, kwargs...) where N
+    x = __maybe_unaliased(prob.u0, alias_u0)
+    length(x) == 1 ||
+        throw(ArgumentError("SimpleHouseholder only supports scalar problems"))
+    fx = _get_fx(prob, x)
+    @bb xo = copy(x)
+    f = __fixed_parameter_function(prob)
+
+    abstol, reltol, tc_cache = init_termination_cache(
+        prob, abstol, reltol, fx, x, termination_condition)
+
+    for i in 1:maxiters
+        num, den, fx = __get_higher_order_derivatives(alg, prob, f, x)
+
+        if i == 1
+            iszero(fx) && build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
+        else
+            # Termination Checks
+            tc_sol = check_termination(tc_cache, fx, x, xo, prob, alg)
+            tc_sol !== nothing && return tc_sol
+        end
+
+        @bb copyto!(xo, x)
+        @bb x .+= (N - 1) .* num ./ den
+    end
+
+    return build_solution(prob, alg, x, fx; retcode = ReturnCode.MaxIters)
+end
+
+end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index ba0b243af..e6c939b8f 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -47,6 +47,7 @@ include("nlsolve/lbroyden.jl")
 include("nlsolve/klement.jl")
 include("nlsolve/trustRegion.jl")
 include("nlsolve/halley.jl")
+include("nlsolve/householder.jl")
 include("nlsolve/dfsane.jl")
 
 ## Interval Nonlinear Solvers
@@ -139,6 +140,7 @@ end
 export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
 export SimpleBroyden, SimpleDFSane, SimpleGaussNewton, SimpleHalley, SimpleKlement,
        SimpleLimitedMemoryBroyden, SimpleNewtonRaphson, SimpleTrustRegion
+export SimpleHouseholder
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
 end # module
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/householder.jl b/lib/SimpleNonlinearSolve/src/nlsolve/householder.jl
new file mode 100644
index 000000000..f012fff9d
--- /dev/null
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/householder.jl
@@ -0,0 +1,13 @@
+"""
+    SimpleHouseholder{order}()
+
+A low-overhead implementation of Householder's method. This method is non-allocating on scalar
+and static array problems.
+
+Internally, this uses TaylorDiff.jl for the automatic differentiation.
+
+### Type Parameters
+
+  - `order`: the convergence order of the Householder method. `order = 2` is the same as Newton's method, `order = 3` is the same as Halley's method, etc.
+"""
+struct SimpleHouseholder{order} <: AbstractNewtonAlgorithm end

From 229bdb58ee5ba8395de10865f1a02cd997e7f0e5 Mon Sep 17 00:00:00 2001
From: Songchen Tan <i@tansongchen.com>
Date: Tue, 8 Oct 2024 10:52:00 -0400
Subject: [PATCH 623/700] Add tests and doc

---
 .../ext/SimpleNonlinearSolveTaylorDiffExt.jl  | 18 ++++++-------
 .../src/nlsolve/householder.jl                |  9 ++++---
 .../test/core/rootfind_tests.jl               | 25 +++++++++++++++++++
 3 files changed, 40 insertions(+), 12 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTaylorDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTaylorDiffExt.jl
index 99b2ca788..3257c6899 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTaylorDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTaylorDiffExt.jl
@@ -7,20 +7,20 @@ using SciMLBase: isinplace
 
 import TaylorDiff
 
-@inline function __get_higher_order_derivatives(::SimpleHouseholder{N}, prob, f, x) where N
+@inline function __get_higher_order_derivatives(::SimpleHouseholder{N}, prob, f, x, fx) where N
     vN = Val(N)
     l = map(one, x)
+    t = TaylorDiff.make_seed(x, l, vN)
 
     if isinplace(prob)
-        fx = f(x)
-        invf = x -> inv.(f(x))
-        bundle = TaylorDiff.derivatives(invf, fx, x, l, vN)
+        bundle = similar(fx, TaylorDiff.TaylorScalar{eltype(fx), N})
+        f(bundle, t)
+        map!(TaylorDiff.primal, fx, bundle)
     else
-        t = TaylorDiff.make_seed(x, l, vN)
-        ft = f(t)
-        fx = map(TaylorDiff.primal, ft)
-        bundle = inv.(ft)
+        bundle = f(t)
+        fx = map(TaylorDiff.primal, bundle)
     end
+    bundle = inv.(bundle)
     num = TaylorDiff.extract_derivative(bundle, N - 1)
     den = TaylorDiff.extract_derivative(bundle, N)
     return num, den, fx
@@ -40,7 +40,7 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleHousehold
         prob, abstol, reltol, fx, x, termination_condition)
 
     for i in 1:maxiters
-        num, den, fx = __get_higher_order_derivatives(alg, prob, f, x)
+        num, den, fx = __get_higher_order_derivatives(alg, prob, f, x, fx)
 
         if i == 1
             iszero(fx) && build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
diff --git a/lib/SimpleNonlinearSolve/src/nlsolve/householder.jl b/lib/SimpleNonlinearSolve/src/nlsolve/householder.jl
index f012fff9d..ce06c5f3b 100644
--- a/lib/SimpleNonlinearSolve/src/nlsolve/householder.jl
+++ b/lib/SimpleNonlinearSolve/src/nlsolve/householder.jl
@@ -1,10 +1,13 @@
 """
     SimpleHouseholder{order}()
 
-A low-overhead implementation of Householder's method. This method is non-allocating on scalar
-and static array problems.
+A low-overhead implementation of Householder's method to arbitrary order.
+This method is non-allocating on scalar and static array problems.
 
-Internally, this uses TaylorDiff.jl for the automatic differentiation.
+!!! warning
+
+    Needs `TaylorDiff.jl` to be explicitly loaded before using this functionality.
+    Internally, this uses TaylorDiff.jl for automatic differentiation.
 
 ### Type Parameters
 
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index 272fa3c4d..76ba85d3c 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -91,6 +91,31 @@ end
     end
 end
 
+@testitem "SimpleHouseholder" setup=[RootfindingTesting] tags=[:core] begin
+    using TaylorDiff
+    @testset "AutoDiff: TaylorDiff.jl" for order in (2, 3, 4)
+        @testset "[OOP] u0: $(nameof(typeof(u0)))" for u0 in (
+            [1.0], @SVector[1.0], 1.0)
+            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = SimpleHouseholder{order}())
+            @test SciMLBase.successful_retcode(sol)
+            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+        end
+
+        @testset "[IIP] u0: $(nameof(typeof(u0)))" for u0 in ([1.0],)
+            sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver = SimpleHouseholder{order}())
+            @test SciMLBase.successful_retcode(sol)
+            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+        end
+    end
+
+    @testset "Termination condition: $(nameof(typeof(termination_condition))) u0: $(nameof(typeof(u0)))" for termination_condition in TERMINATION_CONDITIONS,
+        u0 in (1.0, [1.0], @SVector[1.0])
+
+        probN = NonlinearProblem(quadratic_f, u0, 2.0)
+        @test all(solve(probN, SimpleHouseholder{2}(); termination_condition).u .≈ sqrt(2.0))
+    end
+end
+
 @testitem "Derivative Free Metods" setup=[RootfindingTesting] tags=[:core] begin
     @testset "$(nameof(typeof(alg)))" for alg in [
         SimpleBroyden(), SimpleKlement(), SimpleDFSane(),

From 32daa15155750bdd2a3ece3866ea088c20b4a93e Mon Sep 17 00:00:00 2001
From: Songchen Tan <i@tansongchen.com>
Date: Thu, 24 Oct 2024 15:27:48 -0400
Subject: [PATCH 624/700] Fix format and add compat

---
 lib/SimpleNonlinearSolve/Project.toml            |  4 +++-
 .../ext/SimpleNonlinearSolveTaylorDiffExt.jl     |  8 +++++---
 .../test/core/rootfind_tests.jl                  | 16 +++++++++-------
 3 files changed, 17 insertions(+), 11 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 881ca6630..e7f4f625c 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -65,6 +65,7 @@ SciMLBase = "2.37.0"
 Setfield = "1.1.1"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4.2"
+TaylorDiff = "0.2.5"
 Test = "1.10"
 Tracker = "0.2.33"
 Zygote = "0.6.69"
@@ -88,9 +89,10 @@ ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+TaylorDiff = "b36ab563-344f-407b-a36a-4f200bebf99c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["AllocCheck", "Aqua", "DiffEqBase", "ExplicitImports", "FiniteDiff", "ForwardDiff", "Hwloc", "InteractiveUtils", "LinearAlgebra",  "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReTestItems", "Reexport", "ReverseDiff",  "StaticArrays", "Test", "Tracker", "Zygote"]
+test = ["AllocCheck", "Aqua", "DiffEqBase", "ExplicitImports", "FiniteDiff", "ForwardDiff", "Hwloc", "InteractiveUtils", "LinearAlgebra",  "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReTestItems", "Reexport", "ReverseDiff",  "StaticArrays", "TaylorDiff", "Test", "Tracker", "Zygote"]
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTaylorDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTaylorDiffExt.jl
index 3257c6899..da096a74e 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTaylorDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTaylorDiffExt.jl
@@ -1,13 +1,15 @@
 module SimpleNonlinearSolveTaylorDiffExt
 using SimpleNonlinearSolve
-using SimpleNonlinearSolve: ImmutableNonlinearProblem, ReturnCode, build_solution, check_termination, init_termination_cache
+using SimpleNonlinearSolve: ImmutableNonlinearProblem, ReturnCode, build_solution,
+                            check_termination, init_termination_cache
 using SimpleNonlinearSolve: __maybe_unaliased, _get_fx, __fixed_parameter_function
 using MaybeInplace: @bb
 using SciMLBase: isinplace
 
 import TaylorDiff
 
-@inline function __get_higher_order_derivatives(::SimpleHouseholder{N}, prob, f, x, fx) where N
+@inline function __get_higher_order_derivatives(
+        ::SimpleHouseholder{N}, prob, f, x, fx) where {N}
     vN = Val(N)
     l = map(one, x)
     t = TaylorDiff.make_seed(x, l, vN)
@@ -28,7 +30,7 @@ end
 
 function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleHouseholder{N},
         args...; abstol = nothing, reltol = nothing, maxiters = 1000,
-        termination_condition = nothing, alias_u0 = false, kwargs...) where N
+        termination_condition = nothing, alias_u0 = false, kwargs...) where {N}
     x = __maybe_unaliased(prob.u0, alias_u0)
     length(x) == 1 ||
         throw(ArgumentError("SimpleHouseholder only supports scalar problems"))
diff --git a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
index 76ba85d3c..721d7fa90 100644
--- a/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/rootfind_tests.jl
@@ -1,6 +1,7 @@
 @testsetup module RootfindingTesting
 using Reexport
-@reexport using AllocCheck, StaticArrays, Random, LinearAlgebra, ForwardDiff, DiffEqBase
+@reexport using AllocCheck, StaticArrays, Random, LinearAlgebra, ForwardDiff, DiffEqBase,
+                TaylorDiff
 import PolyesterForwardDiff
 
 quadratic_f(u, p) = u .* u .- p
@@ -92,17 +93,17 @@ end
 end
 
 @testitem "SimpleHouseholder" setup=[RootfindingTesting] tags=[:core] begin
-    using TaylorDiff
     @testset "AutoDiff: TaylorDiff.jl" for order in (2, 3, 4)
-        @testset "[OOP] u0: $(nameof(typeof(u0)))" for u0 in (
-            [1.0], @SVector[1.0], 1.0)
-            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = SimpleHouseholder{order}())
+        @testset "[OOP] u0: $(nameof(typeof(u0)))" for u0 in ([1.0], @SVector[1.0], 1.0)
+            sol = benchmark_nlsolve_oop(
+                quadratic_f, u0; solver = SimpleHouseholder{order}())
             @test SciMLBase.successful_retcode(sol)
             @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
         end
 
         @testset "[IIP] u0: $(nameof(typeof(u0)))" for u0 in ([1.0],)
-            sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver = SimpleHouseholder{order}())
+            sol = benchmark_nlsolve_iip(
+                quadratic_f!, u0; solver = SimpleHouseholder{order}())
             @test SciMLBase.successful_retcode(sol)
             @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
         end
@@ -112,7 +113,8 @@ end
         u0 in (1.0, [1.0], @SVector[1.0])
 
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, SimpleHouseholder{2}(); termination_condition).u .≈ sqrt(2.0))
+        @test all(solve(probN, SimpleHouseholder{2}(); termination_condition).u .≈
+                  sqrt(2.0))
     end
 end
 

From 28c0189e46001e86d5d94d3cc2878d188c0cd128 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 27 Oct 2024 06:02:08 -0400
Subject: [PATCH 625/700] feat: add `PETScSNES` (#482)

* feat: add `PETScSNES`

* feat: support automatic sparsity detection for PETSc

* test: add PETScSNES to the wrapper tests

* docs: add PETSc example

* test: skip PETSc tests on windows

* docs: print the benchmark results
---
 Project.toml                                 |   8 +-
 docs/Project.toml                            |   3 +
 docs/pages.jl                                |   4 +-
 docs/src/api/petsc.md                        |  17 +++
 docs/src/solvers/nonlinear_system_solvers.md |   9 ++
 docs/src/tutorials/snes_ex2.md               |  81 +++++++++++++
 ext/NonlinearSolvePETScExt.jl                | 120 +++++++++++++++++++
 src/NonlinearSolve.jl                        |  12 +-
 src/algorithms/extension_algs.jl             |  65 ++++++++--
 src/internal/forward_diff.jl                 |  17 +--
 src/internal/helpers.jl                      |   7 +-
 test/wrappers/rootfind_tests.jl              |  81 +++++++++++--
 12 files changed, 384 insertions(+), 40 deletions(-)
 create mode 100644 docs/src/api/petsc.md
 create mode 100644 docs/src/tutorials/snes_ex2.md
 create mode 100644 ext/NonlinearSolvePETScExt.jl

diff --git a/Project.toml b/Project.toml
index 03e6519dd..50a7a8d4f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -41,8 +41,10 @@ FixedPointAcceleration = "817d07cb-a79a-5c30-9a31-890123675176"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
 LineSearches = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
 MINPACK = "4854310b-de5a-5eb6-a2a5-c1dee2bd17f9"
+MPI = "da04e1cc-30fd-572f-bb4f-1f8673147195"
 NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
+PETSc = "ace2c81b-2b5f-4b1e-a30d-d662738edfe0"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
 SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
 Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"
@@ -55,6 +57,7 @@ NonlinearSolveLeastSquaresOptimExt = "LeastSquaresOptim"
 NonlinearSolveMINPACKExt = "MINPACK"
 NonlinearSolveNLSolversExt = "NLSolvers"
 NonlinearSolveNLsolveExt = ["NLsolve", "LineSearches"]
+NonlinearSolvePETScExt = ["PETSc", "MPI"]
 NonlinearSolveSIAMFANLEquationsExt = "SIAMFANLEquations"
 NonlinearSolveSpeedMappingExt = "SpeedMapping"
 NonlinearSolveSundialsExt = "Sundials"
@@ -86,6 +89,7 @@ LineSearches = "7.3"
 LinearAlgebra = "1.10"
 LinearSolve = "2.35"
 MINPACK = "1.2"
+MPI = "0.20.22"
 MaybeInplace = "0.1.4"
 NLSolvers = "0.5"
 NLsolve = "4.5"
@@ -93,6 +97,7 @@ NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
 NonlinearSolveBase = "1"
 OrdinaryDiffEqTsit5 = "1.1.0"
+PETSc = "0.2"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 Preferences = "1.4"
@@ -139,6 +144,7 @@ NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 NaNMath = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
 NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
 OrdinaryDiffEqTsit5 = "b1df2697-797e-41e3-8120-5422d3b24e4a"
+PETSc = "ace2c81b-2b5f-4b1e-a30d-d662738edfe0"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
@@ -152,4 +158,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "LineSearches", "MINPACK", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SparseConnectivityTracer", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "LineSearches", "MINPACK", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "PETSc", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SparseConnectivityTracer", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Test", "Zygote"]
diff --git a/docs/Project.toml b/docs/Project.toml
index 4e72b257d..9ed14da4e 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -15,6 +15,7 @@ LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 OrdinaryDiffEqTsit5 = "b1df2697-797e-41e3-8120-5422d3b24e4a"
+PETSc = "ace2c81b-2b5f-4b1e-a30d-d662738edfe0"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
@@ -31,6 +32,7 @@ AlgebraicMultigrid = "0.5, 0.6"
 ArrayInterface = "6, 7"
 BenchmarkTools = "1"
 BracketingNonlinearSolve = "1"
+DiffEqBase = "6.158"
 DifferentiationInterface = "0.6.16"
 Documenter = "1"
 DocumenterCitations = "1"
@@ -41,6 +43,7 @@ LinearSolve = "2"
 NonlinearSolve = "4"
 NonlinearSolveBase = "1"
 OrdinaryDiffEqTsit5 = "1.1.0"
+PETSc = "0.2"
 Plots = "1"
 Random = "1.10"
 SciMLBase = "2.4"
diff --git a/docs/pages.jl b/docs/pages.jl
index 8da01762a..2834615d0 100644
--- a/docs/pages.jl
+++ b/docs/pages.jl
@@ -9,7 +9,8 @@ pages = [
         "tutorials/modelingtoolkit.md",
         "tutorials/small_compile.md",
         "tutorials/iterator_interface.md",
-        "tutorials/optimizing_parameterized_ode.md"
+        "tutorials/optimizing_parameterized_ode.md",
+        "tutorials/snes_ex2.md"
     ],
     "Basics" => Any[
         "basics/nonlinear_problem.md",
@@ -45,6 +46,7 @@ pages = [
         "api/minpack.md",
         "api/nlsolve.md",
         "api/nlsolvers.md",
+        "api/petsc.md",
         "api/siamfanlequations.md",
         "api/speedmapping.md",
         "api/sundials.md"
diff --git a/docs/src/api/petsc.md b/docs/src/api/petsc.md
new file mode 100644
index 000000000..7593ac5dd
--- /dev/null
+++ b/docs/src/api/petsc.md
@@ -0,0 +1,17 @@
+# PETSc.jl
+
+This is a extension for importing solvers from PETSc.jl SNES into the SciML interface. Note
+that these solvers do not come by default, and thus one needs to install the package before
+using these solvers:
+
+```julia
+using Pkg
+Pkg.add("PETSc")
+using PETSc, NonlinearSolve
+```
+
+## Solver API
+
+```@docs
+PETScSNES
+```
diff --git a/docs/src/solvers/nonlinear_system_solvers.md b/docs/src/solvers/nonlinear_system_solvers.md
index 5b9e88e34..b847b90ac 100644
--- a/docs/src/solvers/nonlinear_system_solvers.md
+++ b/docs/src/solvers/nonlinear_system_solvers.md
@@ -177,3 +177,12 @@ This is a wrapper package for importing solvers from NLSolvers.jl into the SciML
     [NLSolvers.jl](https://github.com/JuliaNLSolvers/NLSolvers.jl)
 
 For a list of possible solvers see the [NLSolvers.jl documentation](https://julianlsolvers.github.io/NLSolvers.jl/)
+
+### PETSc.jl
+
+This is a wrapper package for importing solvers from PETSc.jl into the SciML interface.
+
+  - [`PETScSNES()`](@ref): A wrapper for
+    [PETSc.jl](https://github.com/JuliaParallel/PETSc.jl)
+
+For a list of possible solvers see the [PETSc.jl documentation](https://petsc.org/release/manual/snes/)
diff --git a/docs/src/tutorials/snes_ex2.md b/docs/src/tutorials/snes_ex2.md
new file mode 100644
index 000000000..050a39611
--- /dev/null
+++ b/docs/src/tutorials/snes_ex2.md
@@ -0,0 +1,81 @@
+# [PETSc SNES Example 2](@id snes_ex2)
+
+This implements `src/snes/examples/tutorials/ex2.c` from PETSc and `examples/SNES_ex2.jl`
+from PETSc.jl using automatic sparsity detection and automatic differentiation using
+`NonlinearSolve.jl`.
+
+This solves the equations sequentially. Newton method to solve
+`u'' + u^{2} = f`, sequentially.
+
+```@example snes_ex2
+using NonlinearSolve, PETSc, LinearAlgebra, SparseConnectivityTracer, BenchmarkTools
+
+u0 = fill(0.5, 128)
+
+function form_residual!(resid, x, _)
+    n = length(x)
+    xp = LinRange(0.0, 1.0, n)
+    F = 6xp .+ (xp .+ 1e-12) .^ 6
+
+    dx = 1 / (n - 1)
+    resid[1] = x[1]
+    for i in 2:(n - 1)
+        resid[i] = (x[i - 1] - 2x[i] + x[i + 1]) / dx^2 + x[i] * x[i] - F[i]
+    end
+    resid[n] = x[n] - 1
+
+    return
+end
+```
+
+To use automatic sparsity detection, we need to specify `sparsity` keyword argument to
+`NonlinearFunction`. See [Automatic Sparsity Detection](@ref sparsity-detection) for more
+details.
+
+```@example snes_ex2
+nlfunc_dense = NonlinearFunction(form_residual!)
+nlfunc_sparse = NonlinearFunction(form_residual!; sparsity = TracerSparsityDetector())
+
+nlprob_dense = NonlinearProblem(nlfunc_dense, u0)
+nlprob_sparse = NonlinearProblem(nlfunc_sparse, u0)
+```
+
+Now we can solve the problem using `PETScSNES` or with one of the native `NonlinearSolve.jl`
+solvers.
+
+```@example snes_ex2
+sol_dense_nr = solve(nlprob_dense, NewtonRaphson(); abstol = 1e-8)
+sol_dense_snes = solve(nlprob_dense, PETScSNES(); abstol = 1e-8)
+sol_dense_nr .- sol_dense_snes
+```
+
+```@example snes_ex2
+sol_sparse_nr = solve(nlprob_sparse, NewtonRaphson(); abstol = 1e-8)
+sol_sparse_snes = solve(nlprob_sparse, PETScSNES(); abstol = 1e-8)
+sol_sparse_nr .- sol_sparse_snes
+```
+
+As expected the solutions are the same (upto floating point error). Now let's compare the
+runtimes.
+
+## Runtimes
+
+### Dense Jacobian
+
+```@example snes_ex2
+@benchmark solve($(nlprob_dense), $(NewtonRaphson()); abstol = 1e-8)
+```
+
+```@example snes_ex2
+@benchmark solve($(nlprob_dense), $(PETScSNES()); abstol = 1e-8)
+```
+
+### Sparse Jacobian
+
+```@example snes_ex2
+@benchmark solve($(nlprob_sparse), $(NewtonRaphson()); abstol = 1e-8)
+```
+
+```@example snes_ex2
+@benchmark solve($(nlprob_sparse), $(PETScSNES()); abstol = 1e-8)
+```
diff --git a/ext/NonlinearSolvePETScExt.jl b/ext/NonlinearSolvePETScExt.jl
new file mode 100644
index 000000000..9146c0b61
--- /dev/null
+++ b/ext/NonlinearSolvePETScExt.jl
@@ -0,0 +1,120 @@
+module NonlinearSolvePETScExt
+
+using FastClosures: @closure
+using MPI: MPI
+using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
+using NonlinearSolve: NonlinearSolve, PETScSNES
+using PETSc: PETSc
+using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
+using SparseArrays: AbstractSparseMatrix
+
+function SciMLBase.__solve(
+        prob::NonlinearProblem, alg::PETScSNES, args...; abstol = nothing, reltol = nothing,
+        maxiters = 1000, alias_u0::Bool = false, termination_condition = nothing,
+        show_trace::Val{ShT} = Val(false), kwargs...) where {ShT}
+    # XXX: https://petsc.org/release/manualpages/SNES/SNESSetConvergenceTest/
+    termination_condition === nothing ||
+        error("`PETScSNES` does not support termination conditions!")
+
+    _f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
+    T = eltype(prob.u0)
+    @assert T ∈ PETSc.scalar_types
+
+    if alg.petsclib === missing
+        petsclibidx = findfirst(PETSc.petsclibs) do petsclib
+            petsclib isa PETSc.PetscLibType{T}
+        end
+
+        if petsclibidx === nothing
+            error("No compatible PETSc library found for element type $(T). Pass in a \
+                   custom `petsclib` via `PETScSNES(; petsclib = <petsclib>, ....)`.")
+        end
+        petsclib = PETSc.petsclibs[petsclibidx]
+    else
+        petsclib = alg.petsclib
+    end
+    PETSc.initialized(petsclib) || PETSc.initialize(petsclib)
+
+    abstol = get_tolerance(abstol, T)
+    reltol = get_tolerance(reltol, T)
+
+    nf = Ref{Int}(0)
+
+    f! = @closure (cfx, cx, user_ctx) -> begin
+        nf[] += 1
+        fx = cfx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cfx; read = false) : cfx
+        x = cx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cx; write = false) : cx
+        _f!(fx, x)
+        Base.finalize(fx)
+        Base.finalize(x)
+        return
+    end
+
+    snes = PETSc.SNES{T}(petsclib,
+        alg.mpi_comm === missing ? MPI.COMM_SELF : alg.mpi_comm;
+        alg.snes_options..., snes_monitor = ShT, snes_rtol = reltol,
+        snes_atol = abstol, snes_max_it = maxiters)
+
+    PETSc.setfunction!(snes, f!, PETSc.VecSeq(zero(u0)))
+
+    if alg.autodiff === missing && prob.f.jac === nothing
+        _jac! = nothing
+        njac = Ref{Int}(-1)
+    else
+        autodiff = alg.autodiff === missing ? nothing : alg.autodiff
+        if prob.u0 isa Number
+            _jac! = NonlinearSolve.__construct_extension_jac(
+                prob, alg, prob.u0, prob.u0; autodiff)
+            J_init = zeros(T, 1, 1)
+        else
+            _jac!, J_init = NonlinearSolve.__construct_extension_jac(
+                prob, alg, u0, resid; autodiff, initial_jacobian = Val(true))
+        end
+
+        njac = Ref{Int}(0)
+
+        if J_init isa AbstractSparseMatrix
+            PJ = PETSc.MatSeqAIJ(J_init)
+            jac! = @closure (cx, J, _, user_ctx) -> begin
+                njac[] += 1
+                x = cx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cx; write = false) : cx
+                if J isa PETSc.AbstractMat
+                    _jac!(user_ctx.jacobian, x)
+                    copyto!(J, user_ctx.jacobian)
+                    PETSc.assemble(J)
+                else
+                    _jac!(J, x)
+                end
+                Base.finalize(x)
+                return
+            end
+            PETSc.setjacobian!(snes, jac!, PJ, PJ)
+            snes.user_ctx = (; jacobian = J_init)
+        else
+            PJ = PETSc.MatSeqDense(J_init)
+            jac! = @closure (cx, J, _, user_ctx) -> begin
+                njac[] += 1
+                x = cx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cx; write = false) : cx
+                _jac!(J, x)
+                Base.finalize(x)
+                J isa PETSc.AbstractMat && PETSc.assemble(J)
+                return
+            end
+            PETSc.setjacobian!(snes, jac!, PJ, PJ)
+        end
+    end
+
+    res = PETSc.solve!(u0, snes)
+
+    _f!(resid, res)
+    u_ = prob.u0 isa Number ? res[1] : res
+    resid_ = prob.u0 isa Number ? resid[1] : resid
+
+    objective = maximum(abs, resid)
+    # XXX: Return Code from PETSc
+    retcode = ifelse(objective ≤ abstol, ReturnCode.Success, ReturnCode.Failure)
+    return SciMLBase.build_solution(prob, alg, u_, resid_; retcode, original = snes,
+        stats = SciMLBase.NLStats(nf[], njac[], -1, -1, -1))
+end
+
+end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 60e2f0663..465a776ed 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -99,6 +99,15 @@ include("algorithms/extension_algs.jl")
 include("utils.jl")
 include("default.jl")
 
+const ALL_SOLVER_TYPES = [
+    Nothing, AbstractNonlinearSolveAlgorithm, GeneralizedDFSane,
+    GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm,
+    LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
+    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL,
+    CMINPACK, PETScSNES,
+    NonlinearSolvePolyAlgorithm{:NLLS, <:Any}, NonlinearSolvePolyAlgorithm{:NLS, <:Any}
+]
+
 include("internal/forward_diff.jl") # we need to define after the algorithms
 
 @setup_workload begin
@@ -171,8 +180,9 @@ export NonlinearSolvePolyAlgorithm, RobustMultiNewton, FastShortcutNonlinearPoly
        FastShortcutNLLSPolyalg
 
 # Extension Algorithms
-export LeastSquaresOptimJL, FastLevenbergMarquardtJL, CMINPACK, NLsolveJL, NLSolversJL,
+export LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
        FixedPointAccelerationJL, SpeedMappingJL, SIAMFANLEquationsJL
+export PETScSNES, CMINPACK
 
 # Advanced Algorithms -- Without Bells and Whistles
 export GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm, GeneralizedDFSane
diff --git a/src/algorithms/extension_algs.jl b/src/algorithms/extension_algs.jl
index 3cf36ca9f..fda61b693 100644
--- a/src/algorithms/extension_algs.jl
+++ b/src/algorithms/extension_algs.jl
@@ -20,7 +20,7 @@ for solving `NonlinearLeastSquaresProblem`.
 
 !!! note
 
-    This algorithm is only available if `LeastSquaresOptim.jl` is installed.
+    This algorithm is only available if `LeastSquaresOptim.jl` is installed and loaded.
 """
 struct LeastSquaresOptimJL{alg, linsolve} <: AbstractNonlinearSolveExtensionAlgorithm
     autodiff
@@ -65,7 +65,7 @@ see the documentation for `FastLevenbergMarquardt.jl`.
 
 !!! note
 
-    This algorithm is only available if `FastLevenbergMarquardt.jl` is installed.
+    This algorithm is only available if `FastLevenbergMarquardt.jl` is installed and loaded.
 """
 @concrete struct FastLevenbergMarquardtJL{linsolve} <:
                  AbstractNonlinearSolveExtensionAlgorithm
@@ -139,7 +139,7 @@ NonlinearLeastSquaresProblem.
 
 !!! note
 
-    This algorithm is only available if `MINPACK.jl` is installed.
+    This algorithm is only available if `MINPACK.jl` is installed and loaded.
 """
 @concrete struct CMINPACK <: AbstractNonlinearSolveExtensionAlgorithm
     method::Symbol
@@ -199,7 +199,7 @@ For more information on these arguments, consult the
 
 !!! note
 
-    This algorithm is only available if `NLsolve.jl` is installed.
+    This algorithm is only available if `NLsolve.jl` is installed and loaded.
 """
 @concrete struct NLsolveJL <: AbstractNonlinearSolveExtensionAlgorithm
     method::Symbol
@@ -281,7 +281,7 @@ Fixed Point Problems. We allow using this algorithm to solve root finding proble
 
 !!! note
 
-    This algorithm is only available if `SpeedMapping.jl` is installed.
+    This algorithm is only available if `SpeedMapping.jl` is installed and loaded.
 """
 @concrete struct SpeedMappingJL <: AbstractNonlinearSolveExtensionAlgorithm
     σ_min
@@ -324,7 +324,7 @@ problems as well.
 
 !!! note
 
-    This algorithm is only available if `FixedPointAcceleration.jl` is installed.
+    This algorithm is only available if `FixedPointAcceleration.jl` is installed and loaded.
 """
 @concrete struct FixedPointAccelerationJL <: AbstractNonlinearSolveExtensionAlgorithm
     algorithm::Symbol
@@ -402,7 +402,7 @@ end
 
 !!! note
 
-    This algorithm is only available if `SIAMFANLEquations.jl` is installed.
+    This algorithm is only available if `SIAMFANLEquations.jl` is installed and loaded.
 """
 @concrete struct SIAMFANLEquationsJL{L <: Union{Symbol, Nothing}} <:
                  AbstractNonlinearSolveExtensionAlgorithm
@@ -421,3 +421,54 @@ function SIAMFANLEquationsJL(; method = :newton, delta = 1e-3, linsolve = nothin
     end
     return SIAMFANLEquationsJL(method, delta, linsolve, m, beta, autodiff)
 end
+
+"""
+    PETScSNES(; petsclib = missing, autodiff = nothing, mpi_comm = missing, kwargs...)
+
+Wrapper over [PETSc.jl](https://github.com/JuliaParallel/PETSc.jl) SNES solvers.
+
+### Keyword Arguments
+
+  - `petsclib`: PETSc library to use. If set to `missing`, then we will use the first
+    available PETSc library in `PETSc.petsclibs` based on the problem element type.
+  - `autodiff`: the choice of method for generating the Jacobian. Defaults to `nothing`
+    which means that a default is selected according to the problem specification. Can be
+    any valid ADTypes.jl autodiff type (conditional on that backend being supported in
+    NonlinearSolve.jl). If set to `missing`, then PETSc computes the Jacobian using finite
+    differences.
+  - `mpi_comm`: MPI communicator to use. If set to `missing`, then we will use
+    `MPI.COMM_SELF`.
+  - `kwargs`: Keyword arguments to be passed to the PETSc SNES solver. See [PETSc SNES
+    documentation](https://petsc.org/release/manual/snes/) and
+    [SNESSetFromOptions](https://petsc.org/release/manualpages/SNES/SNESSetFromOptions)
+    for more information.
+
+### Options via `CommonSolve.solve`
+
+These options are forwarded from `solve` to the PETSc SNES solver. If these are provided to
+`kwargs`, then they will be ignored.
+
+| `solve` option | PETSc SNES option |
+|:-------------- |:----------------- |
+| `atol`         | `snes_atol`       |
+| `rtol`         | `snes_rtol`       |
+| `maxiters`     | `snes_max_it`     |
+| `show_trace`   | `snes_monitor`    |
+
+!!! note
+
+    This algorithm is only available if `PETSc.jl` is installed and loaded.
+"""
+@concrete struct PETScSNES <: AbstractNonlinearSolveExtensionAlgorithm
+    petsclib
+    mpi_comm
+    autodiff <: Union{Missing, Nothing, ADTypes.AbstractADType}
+    snes_options
+end
+
+function PETScSNES(; petsclib = missing, autodiff = nothing, mpi_comm = missing, kwargs...)
+    if Base.get_extension(@__MODULE__, :NonlinearSolvePETScExt) === nothing
+        error("PETScSNES requires PETSc.jl to be loaded")
+    end
+    return PETScSNES(petsclib, mpi_comm, autodiff, kwargs)
+end
diff --git a/src/internal/forward_diff.jl b/src/internal/forward_diff.jl
index 1259480b8..269ebc99a 100644
--- a/src/internal/forward_diff.jl
+++ b/src/internal/forward_diff.jl
@@ -6,13 +6,7 @@ const DualNonlinearLeastSquaresProblem = NonlinearLeastSquaresProblem{
 const DualAbstractNonlinearProblem = Union{
     DualNonlinearProblem, DualNonlinearLeastSquaresProblem}
 
-for algType in (
-    Nothing, AbstractNonlinearSolveAlgorithm, GeneralizedDFSane,
-    GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm,
-    LeastSquaresOptimJL, FastLevenbergMarquardtJL, CMINPACK, NLsolveJL, NLSolversJL,
-    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL,
-    NonlinearSolvePolyAlgorithm{:NLLS, <:Any}, NonlinearSolvePolyAlgorithm{:NLS, <:Any}
-)
+for algType in ALL_SOLVER_TYPES
     @eval function SciMLBase.__solve(
             prob::DualNonlinearProblem, alg::$(algType), args...; kwargs...)
         sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
@@ -43,14 +37,7 @@ function reinit_cache!(cache::NonlinearSolveForwardDiffCache;
     return cache
 end
 
-for algType in (
-    Nothing, AbstractNonlinearSolveAlgorithm, GeneralizedDFSane,
-    SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm,
-    GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm,
-    LeastSquaresOptimJL, FastLevenbergMarquardtJL, CMINPACK, NLsolveJL, NLSolversJL,
-    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL,
-    NonlinearSolvePolyAlgorithm{:NLLS, <:Any}, NonlinearSolvePolyAlgorithm{:NLS, <:Any}
-)
+for algType in ALL_SOLVER_TYPES
     @eval function SciMLBase.__init(
             prob::DualNonlinearProblem, alg::$(algType), args...; kwargs...)
         p = __value(prob.p)
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index 30e4596bd..6a154e0cc 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -109,7 +109,8 @@ function __construct_extension_f(prob::AbstractNonlinearProblem; alias_u0::Bool
 end
 
 function __construct_extension_jac(prob, alg, u0, fu; can_handle_oop::Val = False,
-        can_handle_scalar::Val = False, autodiff = nothing, kwargs...)
+        can_handle_scalar::Val = False, autodiff = nothing, initial_jacobian = False,
+        kwargs...)
     autodiff = select_jacobian_autodiff(prob, autodiff)
 
     Jₚ = JacobianCache(
@@ -120,7 +121,9 @@ function __construct_extension_jac(prob, alg, u0, fu; can_handle_oop::Val = Fals
     𝐉 = (can_handle_oop === False && !isinplace(prob)) ?
         @closure((J, u)->copyto!(J, 𝓙(u))) : 𝓙
 
-    return 𝐉
+    initial_jacobian === False && return 𝐉
+
+    return 𝐉, Jₚ(nothing)
 end
 
 function reinit_cache! end
diff --git a/test/wrappers/rootfind_tests.jl b/test/wrappers/rootfind_tests.jl
index 9568575e0..852368ae3 100644
--- a/test/wrappers/rootfind_tests.jl
+++ b/test/wrappers/rootfind_tests.jl
@@ -1,7 +1,7 @@
 @testsetup module WrapperRootfindImports
 using Reexport
 @reexport using LinearAlgebra
-import NLSolvers, NLsolve, SIAMFANLEquations, MINPACK
+import NLSolvers, NLsolve, SIAMFANLEquations, MINPACK, PETSc
 
 export NLSolvers
 end
@@ -15,10 +15,16 @@ end
     u0 = zeros(2)
     prob_iip = SteadyStateProblem(f_iip, u0)
 
-    for alg in [
+    @testset "$(nameof(typeof(alg)))" for alg in [
         NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
-        NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        NLsolveJL(),
+        SIAMFANLEquationsJL(),
+        CMINPACK(),
+        PETScSNES(),
+        PETScSNES(; autodiff = missing)
+    ]
         alg isa CMINPACK && Sys.isapple() && continue
+        alg isa PETScSNES && Sys.iswindows() && continue
         sol = solve(prob_iip, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
         @test maximum(abs, sol.resid) < 1e-6
@@ -29,17 +35,24 @@ end
     u0 = zeros(2)
     prob_oop = SteadyStateProblem(f_oop, u0)
 
-    for alg in [
+    @testset "$(nameof(typeof(alg)))" for alg in [
         NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
-        NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        NLsolveJL(),
+        SIAMFANLEquationsJL(),
+        CMINPACK(),
+        PETScSNES(),
+        PETScSNES(; autodiff = missing)
+    ]
         alg isa CMINPACK && Sys.isapple() && continue
+        alg isa PETScSNES && Sys.iswindows() && continue
         sol = solve(prob_oop, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
         @test maximum(abs, sol.resid) < 1e-6
     end
 end
 
-@testitem "Nonlinear Root Finding Problems" setup=[WrapperRootfindImports] tags=[:wrappers] begin
+# Can lead to segfaults
+@testitem "Nonlinear Root Finding Problems" setup=[WrapperRootfindImports] tags=[:wrappers] retries=3 begin
     # IIP Tests
     function f_iip(du, u, p)
         du[1] = 2 - 2u[1]
@@ -48,10 +61,16 @@ end
     u0 = zeros(2)
     prob_iip = NonlinearProblem{true}(f_iip, u0)
 
-    for alg in [
+    @testset "$(nameof(typeof(alg)))" for alg in [
         NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
-        NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        NLsolveJL(),
+        SIAMFANLEquationsJL(),
+        CMINPACK(),
+        PETScSNES(),
+        PETScSNES(; autodiff = missing)
+    ]
         alg isa CMINPACK && Sys.isapple() && continue
+        alg isa PETScSNES && Sys.iswindows() && continue
         local sol
         sol = solve(prob_iip, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
@@ -62,10 +81,16 @@ end
     f_oop(u, p) = [2 - 2u[1], u[1] - 4u[2]]
     u0 = zeros(2)
     prob_oop = NonlinearProblem{false}(f_oop, u0)
-    for alg in [
+    @testset "$(nameof(typeof(alg)))" for alg in [
         NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
-        NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL()]
+        NLsolveJL(),
+        SIAMFANLEquationsJL(),
+        CMINPACK(),
+        PETScSNES(),
+        PETScSNES(; autodiff = missing)
+    ]
         alg isa CMINPACK && Sys.isapple() && continue
+        alg isa PETScSNES && Sys.iswindows() && continue
         local sol
         sol = solve(prob_oop, alg)
         @test SciMLBase.successful_retcode(sol.retcode)
@@ -78,12 +103,17 @@ end
     for tol in [1e-1, 1e-3, 1e-6, 1e-10, 1e-15],
         alg in [
             NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking())),
-            NLsolveJL(), CMINPACK(), SIAMFANLEquationsJL(; method = :newton),
+            NLsolveJL(),
+            CMINPACK(),
+            PETScSNES(),
+            PETScSNES(; autodiff = missing),
+            SIAMFANLEquationsJL(; method = :newton),
             SIAMFANLEquationsJL(; method = :pseudotransient),
-            SIAMFANLEquationsJL(; method = :secant)]
+            SIAMFANLEquationsJL(; method = :secant)
+        ]
 
         alg isa CMINPACK && Sys.isapple() && continue
-
+        alg isa PETScSNES && Sys.iswindows() && continue
         sol = solve(prob_tol, alg, abstol = tol)
         @test abs(sol.u[1] - sqrt(2)) < tol
     end
@@ -134,4 +164,29 @@ end
     @test maximum(abs, sol.resid) < 1e-6
     sol = solve(ProbN, SIAMFANLEquationsJL(; method = :pseudotransient); abstol = 1e-8)
     @test maximum(abs, sol.resid) < 1e-6
+    if !Sys.iswindows()
+        sol = solve(ProbN, PETScSNES(); abstol = 1e-8)
+        @test maximum(abs, sol.resid) < 1e-6
+    end
+end
+
+@testitem "PETSc SNES Floating Points" setup=[WrapperRootfindImports] tags=[:wrappers] skip=:(Sys.iswindows()) begin
+    f(u, p) = u .* u .- 2
+
+    u0 = [1.0, 1.0]
+    probN = NonlinearProblem{false}(f, u0)
+
+    sol = solve(probN, PETScSNES(); abstol = 1e-8)
+    @test maximum(abs, sol.resid) < 1e-6
+
+    u0 = [1.0f0, 1.0f0]
+    probN = NonlinearProblem{false}(f, u0)
+
+    sol = solve(probN, PETScSNES(); abstol = 1e-5)
+    @test maximum(abs, sol.resid) < 1e-4
+
+    u0 = Float16[1.0, 1.0]
+    probN = NonlinearProblem{false}(f, u0)
+
+    @test_throws AssertionError solve(probN, PETScSNES(); abstol = 1e-8)
 end

From 3936d006a424a6e3870bee3cf55f97df6cc09566 Mon Sep 17 00:00:00 2001
From: CompatHelper Julia <compathelper_noreply@julialang.org>
Date: Tue, 29 Oct 2024 19:05:22 +0000
Subject: [PATCH 626/700] CompatHelper: bump compat for TaylorDiff in
 [weakdeps] to 0.3, (keep existing compat)

---
 lib/SimpleNonlinearSolve/Project.toml | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index e7f4f625c..5d9d184a3 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -24,16 +24,16 @@ StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 [weakdeps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+TaylorDiff = "b36ab563-344f-407b-a36a-4f200bebf99c"
 Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
-TaylorDiff = "b36ab563-344f-407b-a36a-4f200bebf99c"
 
 [extensions]
 SimpleNonlinearSolveChainRulesCoreExt = "ChainRulesCore"
 SimpleNonlinearSolveReverseDiffExt = "ReverseDiff"
+SimpleNonlinearSolveTaylorDiffExt = "TaylorDiff"
 SimpleNonlinearSolveTrackerExt = "Tracker"
 SimpleNonlinearSolveZygoteExt = "Zygote"
-SimpleNonlinearSolveTaylorDiffExt = "TaylorDiff"
 
 [compat]
 ADTypes = "1.9"
@@ -65,7 +65,7 @@ SciMLBase = "2.37.0"
 Setfield = "1.1.1"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4.2"
-TaylorDiff = "0.2.5"
+TaylorDiff = "0.2.5, 0.3"
 Test = "1.10"
 Tracker = "0.2.33"
 Zygote = "0.6.69"
@@ -95,4 +95,4 @@ Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["AllocCheck", "Aqua", "DiffEqBase", "ExplicitImports", "FiniteDiff", "ForwardDiff", "Hwloc", "InteractiveUtils", "LinearAlgebra",  "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReTestItems", "Reexport", "ReverseDiff",  "StaticArrays", "TaylorDiff", "Test", "Tracker", "Zygote"]
+test = ["AllocCheck", "Aqua", "DiffEqBase", "ExplicitImports", "FiniteDiff", "ForwardDiff", "Hwloc", "InteractiveUtils", "LinearAlgebra", "NonlinearProblemLibrary", "Pkg", "PolyesterForwardDiff", "Random", "ReTestItems", "Reexport", "ReverseDiff", "StaticArrays", "TaylorDiff", "Test", "Tracker", "Zygote"]

From 7df6380b33ebdd296d9fd540d9f61bd62590c691 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 23 Oct 2024 15:43:03 -0400
Subject: [PATCH 627/700] refactor: minor stylistic fixes

---
 src/algorithms/broyden.jl             |  4 ++--
 src/algorithms/extension_algs.jl      | 11 +++--------
 src/algorithms/klement.jl             |  2 +-
 src/algorithms/lbroyden.jl            | 12 ++++++------
 src/algorithms/levenberg_marquardt.jl |  3 +--
 5 files changed, 13 insertions(+), 19 deletions(-)

diff --git a/src/algorithms/broyden.jl b/src/algorithms/broyden.jl
index 39962bc6a..2477a962b 100644
--- a/src/algorithms/broyden.jl
+++ b/src/algorithms/broyden.jl
@@ -152,14 +152,14 @@ end
 
 Broyden Update Rule corresponding to "bad broyden's method" [broyden1965class](@cite).
 """
-@concrete struct BadBroydenUpdateRule <: AbstractApproximateJacobianUpdateRule{true} end
+struct BadBroydenUpdateRule <: AbstractApproximateJacobianUpdateRule{true} end
 
 """
     GoodBroydenUpdateRule()
 
 Broyden Update Rule corresponding to "good broyden's method" [broyden1965class](@cite).
 """
-@concrete struct GoodBroydenUpdateRule <: AbstractApproximateJacobianUpdateRule{true} end
+struct GoodBroydenUpdateRule <: AbstractApproximateJacobianUpdateRule{true} end
 
 @concrete mutable struct BroydenUpdateRuleCache{mode} <:
                          AbstractApproximateJacobianUpdateRuleCache{true}
diff --git a/src/algorithms/extension_algs.jl b/src/algorithms/extension_algs.jl
index fda61b693..a59eb5f33 100644
--- a/src/algorithms/extension_algs.jl
+++ b/src/algorithms/extension_algs.jl
@@ -362,11 +362,7 @@ function FixedPointAccelerationJL(;
         end
     end
     if extrapolation_period === missing
-        if algorithm === :SEA || algorithm === :VEA
-            extrapolation_period = 6
-        else
-            extrapolation_period = 7
-        end
+        extrapolation_period  = algorithm === :SEA || algorithm === :VEA ? 6 : 7
     else
         if (algorithm === :SEA || algorithm === :VEA) && extrapolation_period % 2 != 0
             error("`extrapolation_period` must be multiples of 2 for SEA and VEA")
@@ -404,11 +400,10 @@ end
 
     This algorithm is only available if `SIAMFANLEquations.jl` is installed and loaded.
 """
-@concrete struct SIAMFANLEquationsJL{L <: Union{Symbol, Nothing}} <:
-                 AbstractNonlinearSolveExtensionAlgorithm
+@concrete struct SIAMFANLEquationsJL <: AbstractNonlinearSolveExtensionAlgorithm
     method::Symbol
     delta
-    linsolve::L
+    linsolve <: Union{Symbol, Nothing}
     m::Int
     beta
     autodiff
diff --git a/src/algorithms/klement.jl b/src/algorithms/klement.jl
index be94efc9c..044a2708d 100644
--- a/src/algorithms/klement.jl
+++ b/src/algorithms/klement.jl
@@ -86,7 +86,7 @@ end
 
 Update rule for [`Klement`](@ref).
 """
-@concrete struct KlementUpdateRule <: AbstractApproximateJacobianUpdateRule{false} end
+struct KlementUpdateRule <: AbstractApproximateJacobianUpdateRule{false} end
 
 @concrete mutable struct KlementUpdateRuleCache <:
                          AbstractApproximateJacobianUpdateRuleCache{false}
diff --git a/src/algorithms/lbroyden.jl b/src/algorithms/lbroyden.jl
index 89df6ece5..b6ce5f9b9 100644
--- a/src/algorithms/lbroyden.jl
+++ b/src/algorithms/lbroyden.jl
@@ -18,30 +18,30 @@ and line search.
 function LimitedMemoryBroyden(; max_resets::Int = 3, linesearch = nothing,
         threshold::Union{Val, Int} = Val(10), reset_tolerance = nothing, alpha = nothing)
     threshold isa Int && (threshold = Val(threshold))
-    initialization = BroydenLowRankInitialization{_unwrap_val(threshold)}(alpha, threshold)
+    initialization = BroydenLowRankInitialization(alpha, threshold)
     return ApproximateJacobianSolveAlgorithm{false, :LimitedMemoryBroyden}(; linesearch,
         descent = NewtonDescent(), update_rule = GoodBroydenUpdateRule(),
         max_resets, initialization, reinit_rule = NoChangeInStateReset(; reset_tolerance))
 end
 
 """
-    BroydenLowRankInitialization{T}(alpha, threshold::Val{T})
+    BroydenLowRankInitialization(alpha, threshold::Val)
 
 An initialization for `LimitedMemoryBroyden` that uses a low rank approximation of the
 Jacobian. The low rank updates to the Jacobian matrix corresponds to what SciPy calls
 ["simple"](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.broyden2.html#scipy-optimize-broyden2).
 """
-@concrete struct BroydenLowRankInitialization{T} <: AbstractJacobianInitialization
+@concrete struct BroydenLowRankInitialization <: AbstractJacobianInitialization
     alpha
-    threshold::Val{T}
+    threshold <: Val
 end
 
 jacobian_initialized_preinverted(::BroydenLowRankInitialization) = true
 
 function __internal_init(
-        prob::AbstractNonlinearProblem, alg::BroydenLowRankInitialization{T},
+        prob::AbstractNonlinearProblem, alg::BroydenLowRankInitialization,
         solver, f::F, fu, u, p; maxiters = 1000,
-        internalnorm::IN = L2_NORM, kwargs...) where {T, F, IN}
+        internalnorm::IN = L2_NORM, kwargs...) where {F, IN}
     if u isa Number # Use the standard broyden
         return __internal_init(prob, IdentityInitialization(true, FullStructure()),
             solver, f, fu, u, p; maxiters, kwargs...)
diff --git a/src/algorithms/levenberg_marquardt.jl b/src/algorithms/levenberg_marquardt.jl
index 01896bd14..24c8a4c05 100644
--- a/src/algorithms/levenberg_marquardt.jl
+++ b/src/algorithms/levenberg_marquardt.jl
@@ -95,8 +95,7 @@ end
 
 function __internal_init(
         prob::AbstractNonlinearProblem, f::LevenbergMarquardtDampingFunction,
-        initial_damping, J, fu, u, ::Val{NF};
-        internalnorm::F = L2_NORM, kwargs...) where {F, NF}
+        initial_damping, J, fu, u, ::Val{NF}; kwargs...) where {NF}
     T = promote_type(eltype(u), eltype(fu))
     DᵀD = __init_diagonal(u, T(f.min_damping))
     if NF

From 8bf597b765415f7b49c95fec97fc0d662c7ef12f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 25 Oct 2024 22:29:09 -0400
Subject: [PATCH 628/700] refactor: move LinearSolve wrapper into
 NonlinearSolveBase

---
 lib/NonlinearSolveBase/Project.toml           |  11 +-
 .../ext/NonlinearSolveBaseLinearSolveExt.jl   | 127 +++++++++
 .../src/NonlinearSolveBase.jl                 |  24 +-
 lib/NonlinearSolveBase/src/abstract_types.jl  |  45 ++++
 lib/NonlinearSolveBase/src/jacobian.jl        |   1 +
 lib/NonlinearSolveBase/src/linear_solve.jl    | 140 ++++++++++
 .../src/termination_conditions.jl             |   2 +-
 lib/NonlinearSolveBase/src/utils.jl           |   5 +
 src/NonlinearSolve.jl                         |   9 +-
 src/abstract_types.jl                         |  23 --
 src/algorithms/extension_algs.jl              |   2 +-
 src/core/approximate_jacobian.jl              |   2 +-
 src/core/generalized_first_order.jl           |   2 +-
 src/descent/damped_newton.jl                  |   4 +-
 src/descent/dogleg.jl                         |   2 +-
 src/descent/newton.jl                         |   6 +-
 src/descent/steepest.jl                       |   3 +-
 src/internal/linear_solve.jl                  | 245 ------------------
 src/utils.jl                                  |   2 -
 19 files changed, 363 insertions(+), 292 deletions(-)
 create mode 100644 lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
 create mode 100644 lib/NonlinearSolveBase/src/abstract_types.jl
 create mode 100644 lib/NonlinearSolveBase/src/jacobian.jl
 create mode 100644 lib/NonlinearSolveBase/src/linear_solve.jl
 delete mode 100644 src/internal/linear_solve.jl

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 70c0f97d4..a902e5594 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -1,10 +1,11 @@
 name = "NonlinearSolveBase"
 uuid = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.0.0"
+version = "1.1.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
+Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
@@ -15,22 +16,27 @@ FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FunctionProperties = "f62d2435-5019-4c03-9749-2d4c77af0cbc"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
+MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [weakdeps]
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [extensions]
 NonlinearSolveBaseDiffEqBaseExt = "DiffEqBase"
 NonlinearSolveBaseForwardDiffExt = "ForwardDiff"
+NonlinearSolveBaseLinearSolveExt = "LinearSolve"
 NonlinearSolveBaseSparseArraysExt = "SparseArrays"
 
 [compat]
 ADTypes = "1.9"
+Adapt = "4.1.0"
 Aqua = "0.8.7"
 ArrayInterface = "7.9"
 CommonSolve = "0.2.4"
@@ -45,9 +51,12 @@ ForwardDiff = "0.10.36"
 FunctionProperties = "0.1.2"
 InteractiveUtils = "<0.0.1, 1"
 LinearAlgebra = "1.10"
+LinearSolve = "2.36.1"
 Markdown = "1.10"
+MaybeInplace = "0.1.4"
 RecursiveArrayTools = "3"
 SciMLBase = "2.50"
+SciMLOperators = "0.3.10"
 SparseArrays = "1.10"
 StaticArraysCore = "1.4"
 Test = "1.10"
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
new file mode 100644
index 000000000..294a53de9
--- /dev/null
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
@@ -0,0 +1,127 @@
+module NonlinearSolveBaseLinearSolveExt
+
+using ArrayInterface: ArrayInterface
+using CommonSolve: CommonSolve, init, solve!
+using LinearAlgebra: ColumnNorm
+using LinearSolve: LinearSolve, QRFactorization
+using NonlinearSolveBase: NonlinearSolveBase, LinearSolveJLCache, LinearSolveResult, Utils
+using SciMLBase: ReturnCode, LinearProblem
+
+function (cache::LinearSolveJLCache)(;
+        A = nothing, b = nothing, linu = nothing, du = nothing, p = nothing,
+        cachedata = nothing, reuse_A_if_factorization = false, verbose = true, kwargs...)
+    cache.stats.nsolve += 1
+
+    update_A!(cache, A, reuse_A_if_factorization)
+    b !== nothing && setproperty!(cache.lincache, :b, b)
+    linu !== nothing && NonlinearSolveBase.set_lincache_u!(cache, linu)
+
+    Plprev = cache.lincache.Pl
+    Prprev = cache.lincache.Pr
+
+    if cache.precs === nothing
+        Pl, Pr = nothing, nothing
+    else
+        Pl, Pr = cache.precs(cache.lincache.A, du, linu, p, nothing,
+            A !== nothing, Plprev, Prprev, cachedata)
+    end
+
+    if Pl !== nothing || Pr !== nothing
+        Pl, Pr = NonlinearSolveBase.wrap_preconditioners(Pl, Pr, linu)
+        cache.lincache.Pl = Pl
+        cache.lincache.Pr = Pr
+    end
+
+    linres = solve!(cache.lincache)
+    cache.lincache = linres.cache
+    # Unfortunately LinearSolve.jl doesn't have the most uniform ReturnCode handling
+    if linres.retcode === ReturnCode.Failure
+        structured_mat = ArrayInterface.isstructured(cache.lincache.A)
+        is_gpuarray = ArrayInterface.device(cache.lincache.A) isa ArrayInterface.GPU
+
+        if !(cache.linsolve isa QRFactorization{ColumnNorm}) && !is_gpuarray &&
+           !structured_mat
+            if verbose
+                @warn "Potential Rank Deficient Matrix Detected. Attempting to solve using \
+                       Pivoted QR Factorization."
+            end
+            @assert (A !== nothing)&&(b !== nothing) "This case is not yet supported. \
+                                                      Please open an issue at \
+                                                      https://github.com/SciML/NonlinearSolve.jl"
+            if cache.additional_lincache === nothing # First time
+                linprob = LinearProblem(A, b; u0 = linres.u)
+                cache.additional_lincache = init(
+                    linprob, QRFactorization(ColumnNorm()); alias_u0 = false,
+                    alias_A = false, alias_b = false, cache.lincache.Pl, cache.lincache.Pr)
+            else
+                cache.additional_lincache.A = A
+                cache.additional_lincache.b = b
+                cache.additional_lincache.Pl = cache.lincache.Pl
+                cache.additional_lincache.Pr = cache.lincache.Pr
+            end
+            linres = solve!(cache.additional_lincache)
+            cache.additional_lincache = linres.cache
+            linres.retcode === ReturnCode.Failure &&
+                return LinearSolveResult(; linres.u, success = false)
+            return LinearSolveResult(; linres.u)
+        elseif !(cache.linsolve isa QRFactorization{ColumnNorm})
+            if verbose
+                if structured_mat || is_gpuarray
+                    mat_desc = structured_mat ? "Structured" : "GPU"
+                    @warn "Potential Rank Deficient Matrix Detected. But Matrix is \
+                           $(mat_desc). Currently, we don't attempt to solve Rank Deficient \
+                           $(mat_desc) Matrices. Please open an issue at \
+                           https://github.com/SciML/NonlinearSolve.jl"
+                end
+            end
+        end
+        return LinearSolveResult(; linres.u, success = false)
+    end
+
+    return LinearSolveResult(; linres.u)
+end
+
+NonlinearSolveBase.needs_square_A(linsolve, ::Any) = LinearSolve.needs_square_A(linsolve)
+
+update_A!(cache::LinearSolveJLCache, ::Nothing, reuse) = cache
+function update_A!(cache::LinearSolveJLCache, A, reuse)
+    return update_A!(cache, Utils.safe_getproperty(cache.linsolve, Val(:alg)), A, reuse)
+end
+
+function update_A!(cache::LinearSolveJLCache, alg, A, reuse)
+    # Not a Factorization Algorithm so don't update `nfactors`
+    set_lincache_A!(cache.lincache, A)
+    return cache
+end
+function update_A!(cache::LinearSolveJLCache, ::LinearSolve.AbstractFactorization, A, reuse)
+    reuse && return cache
+    set_lincache_A!(cache.lincache, A)
+    cache.stats.nfactors += 1
+    return cache
+end
+function update_A!(
+        cache::LinearSolveJLCache, alg::LinearSolve.DefaultLinearSolver, A, reuse)
+    if alg ==
+       LinearSolve.DefaultLinearSolver(LinearSolve.DefaultAlgorithmChoice.KrylovJL_GMRES)
+        # Force a reset of the cache. This is not properly handled in LinearSolve.jl
+        set_lincache_A!(cache.lincache, A)
+        return cache
+    end
+    reuse && return cache
+    set_lincache_A!(cache.lincache, A)
+    cache.stats.nfactors += 1
+    return cache
+end
+
+function set_lincache_A!(lincache, new_A)
+    if !LinearSolve.default_alias_A(lincache.alg, new_A, lincache.b) &&
+       ArrayInterface.can_setindex(lincache.A)
+        copyto!(lincache.A, new_A)
+        lincache.A = lincache.A # important!! triggers special code in `setproperty!`
+        return
+    end
+    lincache.A = new_A
+    return
+end
+
+end
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index b07b4b168..c035f9f46 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -1,33 +1,41 @@
 module NonlinearSolveBase
 
 using ADTypes: ADTypes, AbstractADType
+using Adapt: WrappedArray
 using ArrayInterface: ArrayInterface
-using CommonSolve: CommonSolve
+using CommonSolve: CommonSolve, init
 using Compat: @compat
 using ConcreteStructs: @concrete
 using DifferentiationInterface: DifferentiationInterface
 using EnzymeCore: EnzymeCore
 using FastClosures: @closure
 using FunctionProperties: hasbranching
-using LinearAlgebra: norm
+using LinearAlgebra: Diagonal, norm, ldiv!
 using Markdown: @doc_str
+using MaybeInplace: @bb
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinearProblem,
-                 NonlinearProblem, NonlinearLeastSquaresProblem, AbstractNonlinearFunction,
-                 @add_kwonly, StandardNonlinearProblem, NullParameters, isinplace,
-                 warn_paramtype
-using StaticArraysCore: StaticArray
+                 AbstractNonlinearAlgorithm, AbstractNonlinearFunction,
+                 NonlinearProblem, NonlinearLeastSquaresProblem, StandardNonlinearProblem,
+                 NullParameters, NLStats, LinearProblem, isinplace, warn_paramtype,
+                 @add_kwonly
+using SciMLOperators: AbstractSciMLOperator, IdentityOperator
+using StaticArraysCore: StaticArray, SMatrix, SArray, MArray
 
 const DI = DifferentiationInterface
 
 include("public.jl")
 include("utils.jl")
 
+include("abstract_types.jl")
+
 include("immutable_problem.jl")
 include("common_defaults.jl")
 include("termination_conditions.jl")
 
 include("autodiff.jl")
+include("jacobian.jl")
+include("linear_solve.jl")
 
 # Unexported Public API
 @compat(public, (L2_NORM, Linf_NORM, NAN_CHECK, UNITLESS_ABS2, get_tolerance))
@@ -36,6 +44,10 @@ include("autodiff.jl")
     (select_forward_mode_autodiff, select_reverse_mode_autodiff,
         select_jacobian_autodiff))
 
+# public for NonlinearSolve.jl to use
+@compat(public, (InternalAPI, supports_line_search, supports_trust_region, set_du!))
+@compat(public, (construct_linear_solver, needs_square_A))
+
 export RelTerminationMode, AbsTerminationMode,
        NormTerminationMode, RelNormTerminationMode, AbsNormTerminationMode,
        RelNormSafeTerminationMode, AbsNormSafeTerminationMode,
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
new file mode 100644
index 000000000..bd7b3a86b
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -0,0 +1,45 @@
+module InternalAPI
+
+function init end
+function solve! end
+
+end
+
+abstract type AbstractDescentDirection end
+
+supports_line_search(::AbstractDescentDirection) = false
+supports_trust_region(::AbstractDescentDirection) = false
+
+function get_linear_solver(alg::AbstractDescentDirection)
+    return Utils.safe_getproperty(alg, Val(:linsolve))
+end
+
+abstract type AbstractDescentCache end
+
+SciMLBase.get_du(cache::AbstractDescentCache) = cache.δu
+SciMLBase.get_du(cache::AbstractDescentCache, ::Val{1}) = SciMLBase.get_du(cache)
+SciMLBase.get_du(cache::AbstractDescentCache, ::Val{N}) where {N} = cache.δus[N - 1]
+set_du!(cache::AbstractDescentCache, δu) = (cache.δu = δu)
+set_du!(cache::AbstractDescentCache, δu, ::Val{1}) = set_du!(cache, δu)
+set_du!(cache::AbstractDescentCache, δu, ::Val{N}) where {N} = (cache.δus[N - 1] = δu)
+
+function last_step_accepted(cache::AbstractDescentCache)
+    hasfield(typeof(cache), :last_step_accepted) && return cache.last_step_accepted
+    return true
+end
+
+abstract type AbstractNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm end
+
+get_name(alg::AbstractNonlinearSolveAlgorithm) = Utils.safe_getproperty(alg, Val(:name))
+
+function concrete_jac(alg::AbstractNonlinearSolveAlgorithm)
+    return concrete_jac(Utils.safe_getproperty(alg, Val(:concrete_jac)))
+end
+concrete_jac(::Missing) = missing
+concrete_jac(v::Bool) = v
+concrete_jac(::Val{false}) = false
+concrete_jac(::Val{true}) = true
+
+abstract type AbstractNonlinearSolveCache end
+
+abstract type AbstractLinearSolverCache end
diff --git a/lib/NonlinearSolveBase/src/jacobian.jl b/lib/NonlinearSolveBase/src/jacobian.jl
new file mode 100644
index 000000000..8b1378917
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/jacobian.jl
@@ -0,0 +1 @@
+
diff --git a/lib/NonlinearSolveBase/src/linear_solve.jl b/lib/NonlinearSolveBase/src/linear_solve.jl
new file mode 100644
index 000000000..6e7bceabb
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/linear_solve.jl
@@ -0,0 +1,140 @@
+@kwdef @concrete struct LinearSolveResult
+    u
+    success::Bool = true
+end
+
+@concrete mutable struct LinearSolveJLCache <: AbstractLinearSolverCache
+    lincache
+    linsolve
+    additional_lincache::Any
+    precs
+    stats::NLStats
+end
+
+@concrete mutable struct NativeJLLinearSolveCache <: AbstractLinearSolverCache
+    A
+    b
+    stats::NLStats
+end
+
+"""
+    construct_linear_solver(alg, linsolve, A, b, u; stats, kwargs...)
+
+Construct a cache for solving linear systems of the form `A * u = b`. Following cases are
+handled:
+
+ 1. `A` is Number, then we solve it with `u = b / A`
+ 2. `A` is `SMatrix`, then we solve it with `u = A \\ b` (using the defaults from base
+    Julia) (unless a preconditioner is specified)
+ 3. If `linsolve` is `\\`, then we solve it with directly using `ldiv!(u, A, b)`
+ 4. In all other cases, we use `alg` to solve the linear system using
+    [LinearSolve.jl](https://github.com/SciML/LinearSolve.jl)
+
+### Solving the System
+
+```julia
+(cache::LinearSolverCache)(;
+    A = nothing, b = nothing, linu = nothing, du = nothing, p = nothing,
+    weight = nothing, cachedata = nothing, reuse_A_if_factorization = false, kwargs...)
+```
+
+Returns the solution of the system `u` and stores the updated cache in `cache.lincache`.
+
+#### Special Handling for Rank-deficient Matrix `A`
+
+If we detect a failure in the linear solve (mostly due to using an algorithm that doesn't
+support rank-deficient matrices), we emit a warning and attempt to solve the problem using
+Pivoted QR factorization. This is quite efficient if there are only a few rank-deficient
+that originate in the problem. However, if these are quite frequent for the main nonlinear
+system, then it is recommended to use a different linear solver that supports rank-deficient
+matrices.
+
+#### Keyword Arguments
+
+  - `reuse_A_if_factorization`: If `true`, then the factorization of `A` is reused if
+    possible. This is useful when solving the same system with different `b` values.
+    If the algorithm is an iterative solver, then we reset the internal linear solve cache.
+
+One distinct feature of this compared to the cache from LinearSolve is that it respects the
+aliasing arguments even after cache construction, i.e., if we passed in an `A` that `A` is
+not mutated, we do this by copying over `A` to a preconstructed cache.
+"""
+function construct_linear_solver(alg, linsolve, A, b, u; stats, kwargs...)
+    no_preconditioner = !hasfield(typeof(alg), :precs) || alg.precs === nothing
+
+    if (A isa Number && b isa Number) || (A isa Diagonal)
+        return NativeJLLinearSolveCache(A, b, stats)
+    elseif linsolve isa typeof(\)
+        !no_preconditioner &&
+            error("Default Julia Backsolve Operator `\\` doesn't support Preconditioners")
+        return NativeJLLinearSolveCache(A, b, stats)
+    elseif no_preconditioner && linsolve === nothing
+        # Non-allocating linear solve exists in StaticArrays.jl
+        if (A isa SMatrix || A isa WrappedArray{<:Any, <:SMatrix}) &&
+           Core.Compiler.return_type(\, Tuple{typeof(A), typeof(b)}) <: SArray
+            return NativeJLLinearSolveCache(A, b, stats)
+        end
+    end
+
+    u_fixed = fix_incompatible_linsolve_arguments(A, b, u)
+    @bb u_cache = copy(u_fixed)
+    linprob = LinearProblem(A, b; u0 = u_cache, kwargs...)
+
+    if no_preconditioner
+        precs, Pl, Pr = nothing, nothing, nothing
+    else
+        precs = alg.precs
+        Pl, Pr = precs(A, nothing, u, ntuple(Returns(nothing), 6)...)
+    end
+    Pl, Pr = wrap_preconditioners(Pl, Pr, u)
+
+    # unlias here, we will later use these as caches
+    lincache = init(linprob, linsolve; alias_A = false, alias_b = false, Pl, Pr)
+    return LinearSolveJLCache(lincache, linsolve, nothing, precs, stats)
+end
+
+function (cache::NativeJLLinearSolveCache)(;
+        A = nothing, b = nothing, linu = nothing, kwargs...)
+    cache.stats.nsolve += 1
+    cache.stats.nfactors += 1
+
+    A === nothing || (cache.A = A)
+    b === nothing || (cache.b = b)
+
+    if linu !== nothing && ArrayInterface.can_setindex(linu) &&
+       applicable(ldiv!, linu, cache.A, cache.b)
+        ldiv!(linu, cache.A, cache.b)
+        res = linu
+    else
+        res = cache.A \ cache.b
+    end
+    return LinearSolveResult(; u = res)
+end
+
+fix_incompatible_linsolve_arguments(A, b, u) = u
+fix_incompatible_linsolve_arguments(::SArray, ::SArray, ::SArray) = u
+function fix_incompatible_linsolve_arguments(A, b, u::SArray)
+    (Core.Compiler.return_type(\, Tuple{typeof(A), typeof(b)}) <: typeof(u)) && return u
+    @warn "Solving Linear System A::$(typeof(A)) x::$(typeof(u)) = b::$(typeof(u)) is not \
+           properly supported. Converting `x` to a mutable array. Check the return type \
+           of the nonlinear function provided for optimal performance." maxlog=1
+    return MArray(u)
+end
+
+set_lincache_u!(cache, u) = setproperty!(cache.lincache, :u, u)
+function set_lincache_u!(cache, u::SArray)
+    cache.lincache.u isa MArray && return set_lincache_u!(cache, MArray(u))
+    cache.lincache.u = u
+end
+
+function wrap_preconditioners(Pl, Pr, u)
+    Pl = Pl === nothing ? IdentityOperator(length(u)) : Pl
+    Pr = Pr === nothing ? IdentityOperator(length(u)) : Pr
+    return Pl, Pr
+end
+
+needs_square_A(::Any, ::Number) = false
+needs_square_A(::Nothing, ::Number) = false
+needs_square_A(::Nothing, ::Any) = false
+needs_square_A(::typeof(\), ::Number) = false
+needs_square_A(::typeof(\), ::Any) = false
diff --git a/lib/NonlinearSolveBase/src/termination_conditions.jl b/lib/NonlinearSolveBase/src/termination_conditions.jl
index 9f20e46bc..c2d768c17 100644
--- a/lib/NonlinearSolveBase/src/termination_conditions.jl
+++ b/lib/NonlinearSolveBase/src/termination_conditions.jl
@@ -278,6 +278,6 @@ function init_termination_cache(prob::AbstractNonlinearProblem, abstol, reltol,
     T = promote_type(eltype(du), eltype(u))
     abstol = get_tolerance(u, abstol, T)
     reltol = get_tolerance(u, reltol, T)
-    cache = CommonSolve.init(prob, tc, du, u; abstol, reltol)
+    cache = init(prob, tc, du, u; abstol, reltol)
     return abstol, reltol, cache
 end
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 825f63767..06f53aff4 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -90,4 +90,9 @@ end
 safe_reshape(x::Number, args...) = x
 safe_reshape(x, args...) = reshape(x, args...)
 
+@generated function safe_getproperty(s::S, ::Val{X}) where {S, X}
+    hasfield(S, X) && return :(getproperty(s, $(X)))
+    return :(missing)
+end
+
 end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 465a776ed..e5f7ce411 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -24,7 +24,7 @@ using NonlinearSolveBase: NonlinearSolveBase, nonlinearsolve_forwarddiff_solve,
                           AbstractNonlinearTerminationMode,
                           AbstractSafeBestNonlinearTerminationMode,
                           select_forward_mode_autodiff, select_reverse_mode_autodiff,
-                          select_jacobian_autodiff
+                          select_jacobian_autodiff, construct_linear_solver
 using Printf: @printf
 using Preferences: Preferences, @load_preference, @set_preferences!
 using RecursiveArrayTools: recursivecopy!
@@ -71,7 +71,6 @@ include("descent/damped_newton.jl")
 include("descent/geodesic_acceleration.jl")
 
 include("internal/jacobian.jl")
-include("internal/linear_solve.jl")
 include("internal/termination.jl")
 include("internal/tracing.jl")
 include("internal/approximate_initialization.jl")
@@ -111,8 +110,10 @@ const ALL_SOLVER_TYPES = [
 include("internal/forward_diff.jl") # we need to define after the algorithms
 
 @setup_workload begin
-    nlfuncs = ((NonlinearFunction{false}((u, p) -> u .* u .- p), 0.1),
-        (NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p), [0.1]))
+    nlfuncs = (
+        (NonlinearFunction{false}((u, p) -> u .* u .- p), 0.1),
+        (NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p), [0.1])
+    )
     probs_nls = NonlinearProblem[]
     for (fn, u0) in nlfuncs
         push!(probs_nls, NonlinearProblem(fn, u0, 2.0))
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 255c5e541..0876e2036 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -106,29 +106,6 @@ function last_step_accepted(cache::AbstractDescentCache)
     return true
 end
 
-"""
-    AbstractNonlinearSolveLineSearchCache
-
-Abstract Type for all Line Search Caches used in NonlinearSolve.jl.
-
-### `__internal_solve!` specification
-
-```julia
-__internal_solve!(cache::AbstractNonlinearSolveLineSearchCache, u, du; kwargs...)
-```
-
-Returns 2 values:
-
-  - `unsuccessful`: If `true` it means that the Line Search Failed.
-  - `alpha`: The step size.
-"""
-abstract type AbstractNonlinearSolveLineSearchCache end
-
-function reinit_cache!(
-        cache::AbstractNonlinearSolveLineSearchCache, args...; p = cache.p, kwargs...)
-    cache.p = p
-end
-
 """
     AbstractNonlinearSolveAlgorithm{name} <: AbstractNonlinearAlgorithm
 
diff --git a/src/algorithms/extension_algs.jl b/src/algorithms/extension_algs.jl
index a59eb5f33..a5e52cab4 100644
--- a/src/algorithms/extension_algs.jl
+++ b/src/algorithms/extension_algs.jl
@@ -362,7 +362,7 @@ function FixedPointAccelerationJL(;
         end
     end
     if extrapolation_period === missing
-        extrapolation_period  = algorithm === :SEA || algorithm === :VEA ? 6 : 7
+        extrapolation_period = algorithm === :SEA || algorithm === :VEA ? 6 : 7
     else
         if (algorithm === :SEA || algorithm === :VEA) && extrapolation_period % 2 != 0
             error("`extrapolation_period` must be multiples of 2 for SEA and VEA")
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index b8f479a6d..757be1b04 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -294,7 +294,7 @@ function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
             # Extremely pathological case. Jacobian was just reset and linear solve
             # failed. Should ideally never happen in practice unless true jacobian init
             # is used.
-            cache.retcode = LinearSolveFailureCode
+            cache.retcode = ReturnCode.InternalLinearSolveFailed
             cache.force_stop = true
             return
         else
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index d5ee3eeab..40a11756f 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -245,7 +245,7 @@ function __step!(cache::GeneralizedFirstOrderAlgorithmCache{iip, GB};
     if !descent_result.linsolve_success
         if new_jacobian
             # Jacobian Information is current and linear solve failed terminate the solve
-            cache.retcode = LinearSolveFailureCode
+            cache.retcode = ReturnCode.InternalLinearSolveFailed
             cache.force_stop = true
             return
         else
diff --git a/src/descent/damped_newton.jl b/src/descent/damped_newton.jl
index ba3e1d028..f1d2996c9 100644
--- a/src/descent/damped_newton.jl
+++ b/src/descent/damped_newton.jl
@@ -63,7 +63,7 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::DampedNewtonDescen
     end
 
     normal_form_damping = returns_norm_form_damping(alg.damping_fn)
-    normal_form_linsolve = __needs_square_A(alg.linsolve, u)
+    normal_form_linsolve = NonlinearSolveBase.needs_square_A(alg.linsolve, u)
     if u isa Number
         mode = :simple
     elseif prob isa NonlinearProblem
@@ -124,7 +124,7 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::DampedNewtonDescen
         rhs_cache = nothing
     end
 
-    lincache = LinearSolverCache(
+    lincache = construct_linear_solver(
         alg, alg.linsolve, A, b, _vec(u); stats, abstol, reltol, linsolve_kwargs...)
 
     return DampedNewtonDescentCache{INV, mode}(
diff --git a/src/descent/dogleg.jl b/src/descent/dogleg.jl
index 4c96c98f6..679f33c26 100644
--- a/src/descent/dogleg.jl
+++ b/src/descent/dogleg.jl
@@ -66,7 +66,7 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::Dogleg, J, fu, u;
     T = promote_type(eltype(u), eltype(fu))
 
     normal_form = prob isa NonlinearLeastSquaresProblem &&
-                  __needs_square_A(alg.newton_descent.linsolve, u)
+                  NonlinearSolveBase.needs_square_A(alg.newton_descent.linsolve, u)
     JᵀJ_cache = !normal_form ? J * _vec(δu) : nothing  # TODO: Rename
 
     return DoglegCache{INV, normal_form}(δu, δus, newton_cache, cauchy_cache, internalnorm,
diff --git a/src/descent/newton.jl b/src/descent/newton.jl
index 2fe7abf9a..f0964c7dd 100644
--- a/src/descent/newton.jl
+++ b/src/descent/newton.jl
@@ -41,7 +41,7 @@ function __internal_init(prob::NonlinearProblem, alg::NewtonDescent, J, fu, u; s
         @bb δu_ = similar(u)
     end
     INV && return NewtonDescentCache{true, false}(δu, δus, nothing, nothing, nothing, timer)
-    lincache = LinearSolverCache(
+    lincache = construct_linear_solver(
         alg, alg.linsolve, J, _vec(fu), _vec(u); stats, abstol, reltol, linsolve_kwargs...)
     return NewtonDescentCache{false, false}(δu, δus, lincache, nothing, nothing, timer)
 end
@@ -53,7 +53,7 @@ function __internal_init(prob::NonlinearLeastSquaresProblem, alg::NewtonDescent,
     length(fu) != length(u) &&
         @assert !INV "Precomputed Inverse for Non-Square Jacobian doesn't make sense."
 
-    normal_form = __needs_square_A(alg.linsolve, u)
+    normal_form = NonlinearSolveBase.needs_square_A(alg.linsolve, u)
     if normal_form
         JᵀJ = transpose(J) * J
         Jᵀfu = transpose(J) * _vec(fu)
@@ -62,7 +62,7 @@ function __internal_init(prob::NonlinearLeastSquaresProblem, alg::NewtonDescent,
         JᵀJ, Jᵀfu = nothing, nothing
         A, b = J, _vec(fu)
     end
-    lincache = LinearSolverCache(
+    lincache = construct_linear_solver(
         alg, alg.linsolve, A, b, _vec(u); stats, abstol, reltol, linsolve_kwargs...)
     @bb δu = similar(u)
     δus = N ≤ 1 ? nothing : map(2:N) do i
diff --git a/src/descent/steepest.jl b/src/descent/steepest.jl
index cc2f4d128..82b02552d 100644
--- a/src/descent/steepest.jl
+++ b/src/descent/steepest.jl
@@ -40,7 +40,8 @@ end
         @bb δu_ = similar(u)
     end
     if INV
-        lincache = LinearSolverCache(alg, alg.linsolve, transpose(J), _vec(fu), _vec(u);
+        lincache = construct_linear_solver(
+            alg, alg.linsolve, transpose(J), _vec(fu), _vec(u);
             stats, abstol, reltol, linsolve_kwargs...)
     else
         lincache = nothing
diff --git a/src/internal/linear_solve.jl b/src/internal/linear_solve.jl
deleted file mode 100644
index 707790ff3..000000000
--- a/src/internal/linear_solve.jl
+++ /dev/null
@@ -1,245 +0,0 @@
-const LinearSolveFailureCode = isdefined(ReturnCode, :InternalLinearSolveFailure) ?
-                               ReturnCode.InternalLinearSolveFailure : ReturnCode.Failure
-
-"""
-    LinearSolverCache(alg, linsolve, A, b, u; stats, kwargs...)
-
-Construct a cache for solving linear systems of the form `A * u = b`. Following cases are
-handled:
-
- 1. `A` is Number, then we solve it with `u = b / A`
- 2. `A` is `SMatrix`, then we solve it with `u = A \\ b` (using the defaults from base
-    Julia)
- 3. `A` is `Diagonal`, then we solve it with `u = b ./ A.diag`
- 4. In all other cases, we use `alg` to solve the linear system using
-    [LinearSolve.jl](https://github.com/SciML/LinearSolve.jl).
-
-### Solving the System
-
-```julia
-(cache::LinearSolverCache)(;
-    A = nothing, b = nothing, linu = nothing, du = nothing, p = nothing,
-    weight = nothing, cachedata = nothing, reuse_A_if_factorization = false, kwargs...)
-```
-
-Returns the solution of the system `u` and stores the updated cache in `cache.lincache`.
-
-#### Special Handling for Rank-deficient Matrix `A`
-
-If we detect a failure in the linear solve (mostly due to using an algorithm that doesn't
-support rank-deficient matrices), we emit a warning and attempt to solve the problem using
-Pivoted QR factorization. This is quite efficient if there are only a few rank-deficient
-that originate in the problem. However, if these are quite frequent for the main nonlinear
-system, then it is recommended to use a different linear solver that supports rank-deficient
-matrices.
-
-#### Keyword Arguments
-
-  - `reuse_A_if_factorization`: If `true`, then the factorization of `A` is reused if
-    possible. This is useful when solving the same system with different `b` values.
-    If the algorithm is an iterative solver, then we reset the internal linear solve cache.
-
-One distinct feature of this compared to the cache from LinearSolve is that it respects the
-aliasing arguments even after cache construction, i.e., if we passed in an `A` that `A` is
-not mutated, we do this by copying over `A` to a preconstructed cache.
-"""
-@concrete mutable struct LinearSolverCache <: AbstractLinearSolverCache
-    lincache
-    linsolve
-    additional_lincache::Any
-    A
-    b
-    precs
-    stats::NLStats
-end
-
-@inline __fix_strange_type_combination(A, b, u) = u
-@inline function __fix_strange_type_combination(A, b, u::SArray)
-    A isa SArray && b isa SArray && return u
-    @warn "Solving Linear System A::$(typeof(A)) x::$(typeof(u)) = b::$(typeof(u)) is not \
-           properly supported. Converting `x` to a mutable array. Check the return type \
-           of the nonlinear function provided for optimal performance." maxlog=1
-    return MArray(u)
-end
-
-@inline __set_lincache_u!(cache, u) = (cache.lincache.u = u)
-@inline function __set_lincache_u!(cache, u::SArray)
-    cache.lincache.u isa MArray && return __set_lincache_u!(cache, MArray(u))
-    cache.lincache.u = u
-end
-
-function LinearSolverCache(alg, linsolve, A, b, u; stats, kwargs...)
-    u_fixed = __fix_strange_type_combination(A, b, u)
-
-    if (A isa Number && b isa Number) ||
-       (linsolve === nothing && A isa SMatrix) ||
-       (A isa Diagonal) ||
-       (linsolve isa typeof(\))
-        return LinearSolverCache(nothing, nothing, nothing, A, b, nothing, stats)
-    end
-    @bb u_ = copy(u_fixed)
-    linprob = LinearProblem(A, b; u0 = u_, kwargs...)
-
-    if __hasfield(alg, Val(:precs))
-        precs = alg.precs
-        Pl_, Pr_ = precs(A, nothing, u, ntuple(Returns(nothing), 6)...)
-    else
-        precs, Pl_, Pr_ = nothing, nothing, nothing
-    end
-    Pl, Pr = __wrapprecs(Pl_, Pr_, u)
-
-    # Unalias here, we will later use these as caches
-    lincache = init(linprob, linsolve; alias_A = false, alias_b = false, Pl, Pr)
-
-    return LinearSolverCache(lincache, linsolve, nothing, nothing, nothing, precs, stats)
-end
-
-@kwdef @concrete struct LinearSolveResult
-    u
-    success::Bool = true
-end
-
-# Direct Linear Solve Case without Caching
-function (cache::LinearSolverCache{Nothing})(;
-        A = nothing, b = nothing, linu = nothing, kwargs...)
-    cache.stats.nsolve += 1
-    cache.stats.nfactors += 1
-    A === nothing || (cache.A = A)
-    b === nothing || (cache.b = b)
-    if A isa Diagonal
-        _diag = _restructure(cache.b, cache.A.diag)
-        @bb @. linu = cache.b / _diag
-        res = linu
-    else
-        res = cache.A \ cache.b
-    end
-    return LinearSolveResult(; u = res)
-end
-
-# Use LinearSolve.jl
-function (cache::LinearSolverCache)(;
-        A = nothing, b = nothing, linu = nothing, du = nothing,
-        p = nothing, weight = nothing, cachedata = nothing,
-        reuse_A_if_factorization = false, verbose = true, kwargs...)
-    cache.stats.nsolve += 1
-
-    __update_A!(cache, A, reuse_A_if_factorization)
-    b !== nothing && (cache.lincache.b = b)
-    linu !== nothing && __set_lincache_u!(cache, linu)
-
-    Plprev = cache.lincache.Pl
-    Prprev = cache.lincache.Pr
-
-    if cache.precs === nothing
-        _Pl, _Pr = nothing, nothing
-    else
-        _Pl, _Pr = cache.precs(cache.lincache.A, du, linu, p, nothing,
-            A !== nothing, Plprev, Prprev, cachedata)
-    end
-
-    if (_Pl !== nothing || _Pr !== nothing)
-        Pl, Pr = __wrapprecs(_Pl, _Pr, linu)
-        cache.lincache.Pl = Pl
-        cache.lincache.Pr = Pr
-    end
-
-    linres = solve!(cache.lincache)
-    cache.lincache = linres.cache
-    # Unfortunately LinearSolve.jl doesn't have the most uniform ReturnCode handling
-    if linres.retcode === ReturnCode.Failure
-        structured_mat = ArrayInterface.isstructured(cache.lincache.A)
-        is_gpuarray = ArrayInterface.device(cache.lincache.A) isa ArrayInterface.GPU
-        if !(cache.linsolve isa QRFactorization{ColumnNorm}) && !is_gpuarray &&
-           !structured_mat
-            if verbose
-                @warn "Potential Rank Deficient Matrix Detected. Attempting to solve using \
-                       Pivoted QR Factorization."
-            end
-            @assert (A !== nothing)&&(b !== nothing) "This case is not yet supported. \
-                                                      Please open an issue at \
-                                                      https://github.com/SciML/NonlinearSolve.jl"
-            if cache.additional_lincache === nothing # First time
-                linprob = LinearProblem(A, b; u0 = linres.u)
-                cache.additional_lincache = init(
-                    linprob, QRFactorization(ColumnNorm()); alias_u0 = false,
-                    alias_A = false, alias_b = false, cache.lincache.Pl, cache.lincache.Pr)
-            else
-                cache.additional_lincache.A = A
-                cache.additional_lincache.b = b
-                cache.additional_lincache.Pl = cache.lincache.Pl
-                cache.additional_lincache.Pr = cache.lincache.Pr
-            end
-            linres = solve!(cache.additional_lincache)
-            cache.additional_lincache = linres.cache
-            linres.retcode === ReturnCode.Failure &&
-                return LinearSolveResult(; u = linres.u, success = false)
-            return LinearSolveResult(; u = linres.u)
-        elseif !(cache.linsolve isa QRFactorization{ColumnNorm})
-            if verbose
-                if structured_mat || is_gpuarray
-                    mat_desc = structured_mat ? "Structured" : "GPU"
-                    @warn "Potential Rank Deficient Matrix Detected. But Matrix is \
-                           $(mat_desc). Currently, we don't attempt to solve Rank Deficient \
-                           $(mat_desc) Matrices. Please open an issue at \
-                           https://github.com/SciML/NonlinearSolve.jl"
-                end
-            end
-        end
-        return LinearSolveResult(; u = linres.u, success = false)
-    end
-
-    return LinearSolveResult(; u = linres.u)
-end
-
-@inline __update_A!(cache::LinearSolverCache, ::Nothing, reuse) = cache
-@inline function __update_A!(cache::LinearSolverCache, A, reuse)
-    return __update_A!(cache, __getproperty(cache.lincache, Val(:alg)), A, reuse)
-end
-@inline function __update_A!(cache, alg, A, reuse)
-    # Not a Factorization Algorithm so don't update `nfactors`
-    __set_lincache_A(cache.lincache, A)
-    return cache
-end
-@inline function __update_A!(cache, ::AbstractFactorization, A, reuse)
-    reuse && return cache
-    __set_lincache_A(cache.lincache, A)
-    cache.stats.nfactors += 1
-    return cache
-end
-@inline function __update_A!(cache, alg::DefaultLinearSolver, A, reuse)
-    if alg == DefaultLinearSolver(DefaultAlgorithmChoice.KrylovJL_GMRES)
-        # Force a reset of the cache. This is not properly handled in LinearSolve.jl
-        __set_lincache_A(cache.lincache, A)
-        return cache
-    end
-    reuse && return cache
-    __set_lincache_A(cache.lincache, A)
-    cache.stats.nfactors += 1
-    return cache
-end
-
-function __set_lincache_A(lincache, new_A)
-    if LinearSolve.default_alias_A(lincache.alg, new_A, lincache.b)
-        lincache.A = new_A
-    else
-        if can_setindex(lincache.A)
-            copyto!(lincache.A, new_A)
-            lincache.A = lincache.A
-        else
-            lincache.A = new_A
-        end
-    end
-end
-
-function __wrapprecs(_Pl, _Pr, u)
-    Pl = _Pl !== nothing ? _Pl : IdentityOperator(length(u))
-    Pr = _Pr !== nothing ? _Pr : IdentityOperator(length(u))
-    return Pl, Pr
-end
-
-@inline __needs_square_A(_, ::Number) = false
-@inline __needs_square_A(::Nothing, ::Number) = false
-@inline __needs_square_A(::Nothing, _) = false
-@inline __needs_square_A(linsolve, _) = LinearSolve.needs_square_A(linsolve)
-@inline __needs_square_A(::typeof(\), _) = false
-@inline __needs_square_A(::typeof(\), ::Number) = false  # Ambiguity Fix
diff --git a/src/utils.jl b/src/utils.jl
index 069fde86e..a080bd124 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -2,8 +2,6 @@
 @inline DEFAULT_PRECS(W, du, u, p, t, newW, Plprev, Prprev, cachedata) = nothing, nothing
 
 # Helper  Functions
-@inline __hasfield(::T, ::Val{field}) where {T, field} = hasfield(T, field)
-
 @generated function __getproperty(s::S, ::Val{X}) where {S, X}
     hasfield(S, X) && return :(s.$X)
     return :(missing)

From a756cb90068e5a53b732ea460c51f7af0251a598 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 26 Oct 2024 13:33:48 -0400
Subject: [PATCH 629/700] refactor: move JacobianCache into NonlinearSolveBase

---
 .github/workflows/CI_NonlinearSolveBase.yml   |   6 +
 lib/NonlinearSolveBase/Project.toml           |   5 +
 .../ext/NonlinearSolveBaseLinearSolveExt.jl   |   9 +-
 .../ext/NonlinearSolveBaseSparseArraysExt.jl  |   4 +-
 ...linearSolveBaseSparseMatrixColoringsExt.jl |  22 ++
 .../src/NonlinearSolveBase.jl                 |  14 +-
 lib/NonlinearSolveBase/src/abstract_types.jl  |  23 +-
 .../src/immutable_problem.jl                  |  15 +-
 lib/NonlinearSolveBase/src/jacobian.jl        | 256 ++++++++++++++++++
 lib/NonlinearSolveBase/src/linear_solve.jl    |   4 +
 lib/NonlinearSolveBase/src/public.jl          |   6 +-
 lib/NonlinearSolveBase/src/utils.jl           |   2 +
 lib/SciMLJacobianOperators/Project.toml       |   4 +-
 .../src/SciMLJacobianOperators.jl             |   3 +
 src/NonlinearSolve.jl                         |  17 +-
 src/abstract_types.jl                         |  15 -
 src/core/approximate_jacobian.jl              |   3 +-
 src/core/generalized_first_order.jl           |   6 +-
 src/core/spectral_methods.jl                  |   3 +-
 src/internal/approximate_initialization.jl    |   3 +-
 src/internal/helpers.jl                       |   2 +-
 src/internal/jacobian.jl                      | 250 -----------------
 src/utils.jl                                  |  19 --
 23 files changed, 374 insertions(+), 317 deletions(-)
 create mode 100644 lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl
 delete mode 100644 src/internal/jacobian.jl

diff --git a/.github/workflows/CI_NonlinearSolveBase.yml b/.github/workflows/CI_NonlinearSolveBase.yml
index f3878acef..5855d06f0 100644
--- a/.github/workflows/CI_NonlinearSolveBase.yml
+++ b/.github/workflows/CI_NonlinearSolveBase.yml
@@ -49,6 +49,12 @@ jobs:
         run: |
           import Pkg
           Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators",)
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
           Pkg.instantiate()
           Pkg.test(; coverage=true)
         shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/NonlinearSolveBase {0}
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index a902e5594..df76e09a4 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -19,6 +19,7 @@ Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
 SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
@@ -27,12 +28,14 @@ DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+SparseMatrixColorings = "0a514795-09f3-496d-8182-132a7b665d35"
 
 [extensions]
 NonlinearSolveBaseDiffEqBaseExt = "DiffEqBase"
 NonlinearSolveBaseForwardDiffExt = "ForwardDiff"
 NonlinearSolveBaseLinearSolveExt = "LinearSolve"
 NonlinearSolveBaseSparseArraysExt = "SparseArrays"
+NonlinearSolveBaseSparseMatrixColoringsExt = "SparseMatrixColorings"
 
 [compat]
 ADTypes = "1.9"
@@ -56,8 +59,10 @@ Markdown = "1.10"
 MaybeInplace = "0.1.4"
 RecursiveArrayTools = "3"
 SciMLBase = "2.50"
+SciMLJacobianOperators = "0.1.1"
 SciMLOperators = "0.3.10"
 SparseArrays = "1.10"
+SparseMatrixColorings = "0.4.8"
 StaticArraysCore = "1.4"
 Test = "1.10"
 julia = "1.10"
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
index 294a53de9..13c4adca5 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
@@ -3,7 +3,7 @@ module NonlinearSolveBaseLinearSolveExt
 using ArrayInterface: ArrayInterface
 using CommonSolve: CommonSolve, init, solve!
 using LinearAlgebra: ColumnNorm
-using LinearSolve: LinearSolve, QRFactorization
+using LinearSolve: LinearSolve, QRFactorization, SciMLLinearSolveAlgorithm
 using NonlinearSolveBase: NonlinearSolveBase, LinearSolveJLCache, LinearSolveResult, Utils
 using SciMLBase: ReturnCode, LinearProblem
 
@@ -81,7 +81,12 @@ function (cache::LinearSolveJLCache)(;
     return LinearSolveResult(; linres.u)
 end
 
-NonlinearSolveBase.needs_square_A(linsolve, ::Any) = LinearSolve.needs_square_A(linsolve)
+function NonlinearSolveBase.needs_square_A(linsolve::SciMLLinearSolveAlgorithm, ::Any)
+    return LinearSolve.needs_square_A(linsolve)
+end
+function NonlinearSolveBase.needs_concrete_A(linsolve::SciMLLinearSolveAlgorithm)
+    return LinearSolve.needs_concrete_A(linsolve)
+end
 
 update_A!(cache::LinearSolveJLCache, ::Nothing, reuse) = cache
 function update_A!(cache::LinearSolveJLCache, A, reuse)
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
index be13ebb8f..3b6ae2935 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
@@ -1,10 +1,12 @@
 module NonlinearSolveBaseSparseArraysExt
 
 using NonlinearSolveBase: NonlinearSolveBase
-using SparseArrays: AbstractSparseMatrixCSC, nonzeros
+using SparseArrays: AbstractSparseMatrix, AbstractSparseMatrixCSC, nonzeros
 
 function NonlinearSolveBase.NAN_CHECK(x::AbstractSparseMatrixCSC)
     return any(NonlinearSolveBase.NAN_CHECK, nonzeros(x))
 end
 
+NonlinearSolveBase.sparse_or_structured_prototype(::AbstractSparseMatrix) = true
+
 end
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl
new file mode 100644
index 000000000..e46ef5c37
--- /dev/null
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl
@@ -0,0 +1,22 @@
+module NonlinearSolveBaseSparseMatrixColoringsExt
+
+using ADTypes: ADTypes, AbstractADType
+using NonlinearSolveBase: NonlinearSolveBase, Utils
+using SciMLBase: SciMLBase, NonlinearFunction
+using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm,
+                             LargestFirst
+
+Utils.is_extension_loaded(::Val{:SparseMatrixColorings}) = true
+
+function NonlinearSolveBase.select_fastest_coloring_algorithm(::Val{:SparseMatrixColorings},
+        prototype, f::NonlinearFunction, ad::AbstractADType)
+    prototype === nothing && return GreedyColoringAlgorithm(LargestFirst())
+    if SciMLBase.has_colorvec(f)
+        return ConstantColoringAlgorithm{ifelse(
+            ADTypes.mode(ad) isa ADTypes.ReverseMode, :row, :column)}(
+            prototype, f.colorvec)
+    end
+    return GreedyColoringAlgorithm(LargestFirst())
+end
+
+end
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index c035f9f46..585ac1c5a 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -1,12 +1,13 @@
 module NonlinearSolveBase
 
-using ADTypes: ADTypes, AbstractADType
+using ADTypes: ADTypes, AbstractADType, AutoSparse, NoSparsityDetector,
+               KnownJacobianSparsityDetector
 using Adapt: WrappedArray
 using ArrayInterface: ArrayInterface
 using CommonSolve: CommonSolve, init
 using Compat: @compat
 using ConcreteStructs: @concrete
-using DifferentiationInterface: DifferentiationInterface
+using DifferentiationInterface: DifferentiationInterface, Constant
 using EnzymeCore: EnzymeCore
 using FastClosures: @closure
 using FunctionProperties: hasbranching
@@ -17,8 +18,8 @@ using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinearProblem,
                  AbstractNonlinearAlgorithm, AbstractNonlinearFunction,
                  NonlinearProblem, NonlinearLeastSquaresProblem, StandardNonlinearProblem,
-                 NullParameters, NLStats, LinearProblem, isinplace, warn_paramtype,
-                 @add_kwonly
+                 NonlinearFunction, NullParameters, NLStats, LinearProblem
+using SciMLJacobianOperators: JacobianOperator, StatefulJacobianOperator
 using SciMLOperators: AbstractSciMLOperator, IdentityOperator
 using StaticArraysCore: StaticArray, SMatrix, SArray, MArray
 
@@ -44,9 +45,10 @@ include("linear_solve.jl")
     (select_forward_mode_autodiff, select_reverse_mode_autodiff,
         select_jacobian_autodiff))
 
-# public for NonlinearSolve.jl to use
+# public for NonlinearSolve.jl and subpackages to use
 @compat(public, (InternalAPI, supports_line_search, supports_trust_region, set_du!))
-@compat(public, (construct_linear_solver, needs_square_A))
+@compat(public, (construct_linear_solver, needs_square_A, needs_concrete_A))
+@compat(public, (construct_jacobian_cache,))
 
 export RelTerminationMode, AbsTerminationMode,
        NormTerminationMode, RelNormTerminationMode, AbsNormTerminationMode,
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index bd7b3a86b..4dba65a14 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -2,6 +2,7 @@ module InternalAPI
 
 function init end
 function solve! end
+function reinit! end
 
 end
 
@@ -32,14 +33,34 @@ abstract type AbstractNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm end
 
 get_name(alg::AbstractNonlinearSolveAlgorithm) = Utils.safe_getproperty(alg, Val(:name))
 
+"""
+    concrete_jac(alg::AbstractNonlinearSolveAlgorithm)::Bool
+
+Whether the algorithm uses a concrete Jacobian.
+"""
 function concrete_jac(alg::AbstractNonlinearSolveAlgorithm)
     return concrete_jac(Utils.safe_getproperty(alg, Val(:concrete_jac)))
 end
-concrete_jac(::Missing) = missing
+concrete_jac(::Missing) = false
+concrete_jac(::Nothing) = false
 concrete_jac(v::Bool) = v
 concrete_jac(::Val{false}) = false
 concrete_jac(::Val{true}) = true
 
 abstract type AbstractNonlinearSolveCache end
 
+"""
+    AbstractLinearSolverCache
+
+Abstract Type for all Linear Solvers used in NonlinearSolve. Subtypes of these are
+meant to be constructured via [`construct_linear_solver`](@ref).
+"""
 abstract type AbstractLinearSolverCache end
+
+"""
+    AbstractJacobianCache
+
+Abstract Type for all Jacobian Caches used in NonlinearSolve. Subtypes of these are
+meant to be constructured via [`construct_jacobian_cache`](@ref).
+"""
+abstract type AbstractJacobianCache end
diff --git a/lib/NonlinearSolveBase/src/immutable_problem.jl b/lib/NonlinearSolveBase/src/immutable_problem.jl
index 03b44a9ec..2d429845f 100644
--- a/lib/NonlinearSolveBase/src/immutable_problem.jl
+++ b/lib/NonlinearSolveBase/src/immutable_problem.jl
@@ -6,14 +6,14 @@ struct ImmutableNonlinearProblem{uType, iip, P, F, K, PT} <:
     problem_type::PT
     kwargs::K
 
-    @add_kwonly function ImmutableNonlinearProblem{iip}(
+    SciMLBase.@add_kwonly function ImmutableNonlinearProblem{iip}(
             f::AbstractNonlinearFunction{iip}, u0, p = NullParameters(),
             problem_type = StandardNonlinearProblem(); kwargs...) where {iip}
         if haskey(kwargs, :p)
             error("`p` specified as a keyword argument `p = $(kwargs[:p])` to \
                    `NonlinearProblem`. This is not supported.")
         end
-        warn_paramtype(p)
+        SciMLBase.warn_paramtype(p)
         return new{
             typeof(u0), iip, typeof(p), typeof(f), typeof(kwargs), typeof(problem_type)}(
             f, u0, p, problem_type, kwargs)
@@ -31,12 +31,11 @@ struct ImmutableNonlinearProblem{uType, iip, P, F, K, PT} <:
 end
 
 """
-Define a nonlinear problem using an instance of
-[`AbstractNonlinearFunction`](@ref AbstractNonlinearFunction).
+Define a nonlinear problem using an instance of [`AbstractNonlinearFunction`](@ref).
 """
 function ImmutableNonlinearProblem(
         f::AbstractNonlinearFunction, u0, p = NullParameters(); kwargs...)
-    return ImmutableNonlinearProblem{isinplace(f)}(f, u0, p; kwargs...)
+    return ImmutableNonlinearProblem{SciMLBase.isinplace(f)}(f, u0, p; kwargs...)
 end
 
 function ImmutableNonlinearProblem(f, u0, p = NullParameters(); kwargs...)
@@ -44,14 +43,14 @@ function ImmutableNonlinearProblem(f, u0, p = NullParameters(); kwargs...)
 end
 
 """
-Define a ImmutableNonlinearProblem problem from SteadyStateProblem
+Define a ImmutableNonlinearProblem problem from SteadyStateProblem.
 """
 function ImmutableNonlinearProblem(prob::AbstractNonlinearProblem)
-    return ImmutableNonlinearProblem{isinplace(prob)}(prob.f, prob.u0, prob.p)
+    return ImmutableNonlinearProblem{SciMLBase.isinplace(prob)}(prob.f, prob.u0, prob.p)
 end
 
 function Base.convert(
         ::Type{ImmutableNonlinearProblem}, prob::T) where {T <: NonlinearProblem}
-    return ImmutableNonlinearProblem{isinplace(prob)}(
+    return ImmutableNonlinearProblem{SciMLBase.isinplace(prob)}(
         prob.f, prob.u0, prob.p, prob.problem_type; prob.kwargs...)
 end
diff --git a/lib/NonlinearSolveBase/src/jacobian.jl b/lib/NonlinearSolveBase/src/jacobian.jl
index 8b1378917..a189bf042 100644
--- a/lib/NonlinearSolveBase/src/jacobian.jl
+++ b/lib/NonlinearSolveBase/src/jacobian.jl
@@ -1 +1,257 @@
 
+"""
+    construct_jacobian_cache(
+        prob, alg, f, fu, u = prob.u0, p = prob.p;
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing,
+        linsolve = missing
+    )
+
+Construct a cache for the Jacobian of `f` w.r.t. `u`.
+
+### Arguments
+
+  - `prob`: A [`NonlinearProblem`](@ref) or a [`NonlinearLeastSquaresProblem`](@ref).
+  - `alg`: A [`AbstractNonlinearSolveAlgorithm`](@ref). Used to check for
+    [`concrete_jac`](@ref).
+  - `f`: The function to compute the Jacobian of.
+  - `fu`: The evaluation of `f(u, p)` or `f(_, u, p)`. Used to determine the size of the
+    result cache and Jacobian.
+  - `u`: The current value of the state.
+  - `p`: The current value of the parameters.
+
+### Keyword Arguments
+
+  - `autodiff`: Automatic Differentiation or Finite Differencing backend for computing the
+    jacobian. By default, selects a backend based on sparsity parameters, type of state,
+    function properties, etc.
+  - `vjp_autodiff`: Automatic Differentiation or Finite Differencing backend for computing
+    the vector-Jacobian product.
+  - `jvp_autodiff`: Automatic Differentiation or Finite Differencing backend for computing
+    the Jacobian-vector product.
+  - `linsolve`: Linear Solver Algorithm used to determine if we need a concrete jacobian
+    or if possible we can just use a `SciMLJacobianOperators.JacobianOperator` instead.
+"""
+function construct_jacobian_cache(
+        prob, alg, f::NonlinearFunction, fu, u = prob.u0, p = prob.p; stats,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing,
+        linsolve = missing
+)
+    has_analytic_jac = SciMLBase.has_jac(f)
+    linsolve_needs_jac = !concrete_jac(alg) && (linsolve === missing ||
+                          (linsolve === nothing || needs_concrete_A(linsolve)))
+    needs_jac = linsolve_needs_jac || concrete_jac(alg)
+
+    @bb fu_cache = similar(fu)
+
+    if !has_analytic_jac && needs_jac
+        if autodiff === nothing
+            throw(ArgumentError("`autodiff` argument to `construct_jacobian_cache` must be \
+                                 specified and cannot be `nothing`. Use \
+                                 `NonlinearSolveBase.select_jacobian_autodiff` for \
+                                 automatic backend selection."))
+        end
+        autodiff = construct_concrete_adtype(f, autodiff)
+        di_extras = if SciMLBase.isinplace(f)
+            DI.prepare_jacobian(f, fu_cache, autodiff, u, Constant(p))
+        else
+            DI.prepare_jacobian(f, autodiff, u, Constant(p))
+        end
+    else
+        di_extras = nothing
+    end
+
+    J = if !needs_jac
+        JacobianOperator(prob, fu, u; jvp_autodiff, vjp_autodiff)
+    else
+        if f.jac_prototype === nothing
+            # While this is technically wasteful, it gives out the type of the Jacobian
+            # which is needed to create the linear solver cache
+            stats.njacs += 1
+            if has_analytic_jac
+                Utils.safe_similar(
+                    fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u)
+                )
+            else
+                if SciMLBase.isinplace(f)
+                    DI.jacobian(f, fu_cache, di_extras, autodiff, u, Constant(p))
+                else
+                    DI.jacobian(f, di_extras, autodiff, u, Constant(p))
+                end
+            end
+        else
+            if eltype(f.jac_prototype) <: Bool
+                similar(f.jac_prototype, promote_type(eltype(fu), eltype(u)))
+            else
+                similar(f.jac_prototype)
+            end
+        end
+    end
+
+    return JacobianCache(J, f, fu, u, p, stats, autodiff, di_extras)
+end
+
+function construct_jacobian_cache(
+        prob, alg, f::NonlinearFunction, fu::Number, u::Number = prob.u0, p = prob.p; stats,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing,
+        linsolve = missing
+)
+    if SciMLBase.has_jac(f) || SciMLBase.has_vjp(f) || SciMLBase.has_jvp(f)
+        return JacobianCache(u, f, fu, u, p, stats, autodiff, nothing)
+    end
+    if autodiff === nothing
+        throw(ArgumentError("`autodiff` argument to `construct_jacobian_cache` must be \
+                             specified and cannot be `nothing`. Use \
+                             `NonlinearSolveBase.select_jacobian_autodiff` for \
+                             automatic backend selection."))
+    end
+    @assert !(autodiff isa AutoSparse) "`autodiff` cannot be `AutoSparse` for scalar \
+                                        nonlinear problems."
+    di_extras = DI.prepare_derivative(f, autodiff, u, Constant(prob.p))
+    return JacobianCache(u, f, fu, u, p, stats, autodiff, di_extras)
+end
+
+@concrete mutable struct JacobianCache <: AbstractJacobianCache
+    J
+    f <: NonlinearFunction
+    fu
+    u
+    p
+    stats::NLStats
+    autodiff
+    di_extras
+end
+
+function InternalAPI.reinit!(
+        cache::JacobianCache, args...; p = cache.p, u0 = cache.u, kwargs...)
+    cache.u = u0
+    cache.p = p
+end
+
+# Core Computation
+(cache::JacobianCache)(u) = cache(cache.J, u, cache.p)
+function (cache::JacobianCache{<:JacobianOperator})(::Nothing)
+    return StatefulJacobianOperator(cache.J, cache.u, cache.p)
+end
+(cache::JacobianCache)(::Nothing) = cache.J
+
+## Operator
+function (cache::JacobianCache{<:JacobianOperator})(J::JacobianOperator, u, p = cache.p)
+    return StatefulJacobianOperator(J, u, p)
+end
+
+## Numbers
+function (cache::JacobianCache{<:Number})(::Number, u, p = cache.p)
+    cache.stats.njacs += 1
+    SciMLBase.has_jac(cache.f) && return cache.f.jac(u, p)
+    SciMLBase.has_vjp(cache.f) && return cache.f.vjp(one(u), u, p)
+    SciMLBase.has_jvp(cache.f) && return cache.f.jvp(one(u), u, p)
+    return DI.derivative(cache.f, cache.di_extras, cache.autodiff, u, Constant(p))
+end
+
+## Actually Compute the Jacobian
+function (cache::JacobianCache)(J::Union{AbstractMatrix, Nothing}, u, p = cache.p)
+    cache.stats.njacs += 1
+    if SciMLBase.isinplace(cache.f)
+        if SciMLBase.has_jac(cache.f)
+            cache.f.jac(J, u, p)
+        else
+            DI.jacobian!(
+                cache.f, cache.fu, J, cache.di_extras, cache.autodiff, u, Constant(p))
+        end
+        return J
+    else
+        SciMLBase.has_jac(cache.f) && return cache.f.jac(u, p)
+        return DI.jacobian(cache.f, cache.di_extras, cache.autodiff, u, Constant(p))
+    end
+end
+
+# Sparse Automatic Differentiation
+function construct_concrete_adtype(f::NonlinearFunction, ad::AbstractADType)
+    if f.sparsity === nothing
+        if f.jac_prototype === nothing
+            if SciMLBase.has_colorvec(f)
+                @warn "`colorvec` is provided but `sparsity` and `jac_prototype` is not \
+                       specified. `colorvec` will be ignored."
+            end
+            return ad # No sparse AD
+        else
+            if !sparse_or_structured_prototype(f.jac_prototype)
+                if SciMLBase.has_colorvec(f)
+                    @warn "`colorvec` is provided but `jac_prototype` is not a sparse \
+                           or structured matrix. `colorvec` will be ignored."
+                end
+                return ad
+            end
+            coloring_algorithm = select_fastest_coloring_algorithm(f.jac_prototype, f, ad)
+            coloring_algorithm === nothing && return ad
+            return AutoSparse(
+                ad;
+                sparsity_detector = KnownJacobianSparsityDetector(f.jac_prototype),
+                coloring_algorithm
+            )
+        end
+    else
+        if f.sparsity isa AbstractMatrix
+            if f.jac_prototype !== f.sparsity
+                if f.jac_prototype !== nothing &&
+                   sparse_or_structured_prototype(f.jac_prototype)
+                    throw(ArgumentError("`sparsity::AbstractMatrix` and a sparse or \
+                                         structured `jac_prototype` cannot be both \
+                                         provided. Pass only `jac_prototype`."))
+                end
+            end
+            coloring_algorithm = select_fastest_coloring_algorithm(f.sparsity, f, ad)
+            coloring_algorithm === nothing && return ad
+            return AutoSparse(
+                ad;
+                sparsity_detector = KnownJacobianSparsityDetector(f.sparsity),
+                coloring_algorithm
+            )
+        end
+
+        @assert f.sparsity isa ADTypes.AbstractSparsityDetector
+        sparsity_detector = f.sparsity
+        if f.jac_prototype === nothing
+            if SciMLBase.has_colorvec(f)
+                @warn "`colorvec` is provided but `jac_prototype` is not specified. \
+                       `colorvec` will be ignored."
+            end
+            coloring_algorithm = select_fastest_coloring_algorithm(nothing, f, ad)
+            coloring_algorithm === nothing && return ad
+            return AutoSparse(ad; sparsity_detector, coloring_algorithm)
+        else
+            if sparse_or_structured_prototype(f.jac_prototype)
+                if !(sparsity_detector isa NoSparsityDetector)
+                    @warn "`jac_prototype` is a sparse matrix but sparsity = $(f.sparsity) \
+                           has also been specified. Ignoring sparsity field and using \
+                           `jac_prototype` sparsity."
+                end
+                sparsity_detector = KnownJacobianSparsityDetector(f.jac_prototype)
+            end
+            coloring_algorithm = select_fastest_coloring_algorithm(f.jac_prototype, f, ad)
+            coloring_algorithm === nothing && return ad
+            return AutoSparse(ad; sparsity_detector, coloring_algorithm)
+        end
+    end
+end
+
+function construct_concrete_adtype(::NonlinearFunction, ad::AutoSparse)
+    error("Specifying a sparse AD type for Nonlinear Problems was removed in v4. \
+           Instead use the `sparsity`, `jac_prototype`, and `colorvec` to specify \
+           the right sparsity pattern and coloring algorithm. Ignoring the sparsity \
+           detection algorithm and coloring algorithm present in $(ad).")
+end
+
+function select_fastest_coloring_algorithm(
+        prototype, f::NonlinearFunction, ad::AbstractADType)
+    if !Utils.is_extension_loaded(Val(:SparseMatrixColorings))
+        @warn "`SparseMatrixColorings` must be explicitly imported for sparse automatic \
+               differentiation to work. Proceeding with Dense Automatic Differentiation."
+        return nothing
+    end
+    return select_fastest_coloring_algorithm(Val(:SparseMatrixColorings), prototype, f, ad)
+end
+
+function sparse_or_structured_prototype(prototype::AbstractMatrix)
+    return ArrayInterface.isstructured(prototype)
+end
diff --git a/lib/NonlinearSolveBase/src/linear_solve.jl b/lib/NonlinearSolveBase/src/linear_solve.jl
index 6e7bceabb..2ad957ab1 100644
--- a/lib/NonlinearSolveBase/src/linear_solve.jl
+++ b/lib/NonlinearSolveBase/src/linear_solve.jl
@@ -133,8 +133,12 @@ function wrap_preconditioners(Pl, Pr, u)
     return Pl, Pr
 end
 
+# Traits. Core traits are expanded in LinearSolve extension
 needs_square_A(::Any, ::Number) = false
 needs_square_A(::Nothing, ::Number) = false
 needs_square_A(::Nothing, ::Any) = false
 needs_square_A(::typeof(\), ::Number) = false
 needs_square_A(::typeof(\), ::Any) = false
+
+needs_concrete_A(::Union{Nothing, Missing}) = false
+needs_concrete_A(::typeof(\)) = true
diff --git a/lib/NonlinearSolveBase/src/public.jl b/lib/NonlinearSolveBase/src/public.jl
index b39aa26d2..2101f4274 100644
--- a/lib/NonlinearSolveBase/src/public.jl
+++ b/lib/NonlinearSolveBase/src/public.jl
@@ -95,9 +95,11 @@ for norm_type in (:RelNorm, :AbsNorm), safety in (:Safe, :SafeBest)
 
         ## Constructor
 
-            $($struct_name)(internalnorm; protective_threshold = nothing,
+            $($struct_name)(
+                internalnorm; protective_threshold = nothing,
                 patience_steps = 100, patience_objective_multiplier = 3,
-                min_max_factor = 1.3, max_stalled_steps = nothing)
+                min_max_factor = 1.3, max_stalled_steps = nothing
+            )
 
         $($TERM_INTERNALNORM_DOCS).
         """
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 06f53aff4..3f14de9ea 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -7,6 +7,8 @@ using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 
 using ..NonlinearSolveBase: L2_NORM, Linf_NORM
 
+is_extension_loaded(::Val) = false
+
 fast_scalar_indexing(xs...) = all(ArrayInterface.fast_scalar_indexing, xs)
 
 function nonallocating_isapprox(x::Number, y::Number; atol = false,
diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index c889eb199..6cda16e66 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -1,10 +1,11 @@
 name = "SciMLJacobianOperators"
 uuid = "19f34311-ddf3-4b8b-af20-060888a46c0e"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "0.1.0"
+version = "0.1.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
+ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
@@ -16,6 +17,7 @@ SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 [compat]
 ADTypes = "1.8.1"
 Aqua = "0.8.7"
+ArrayInterface = "7.16"
 ConcreteStructs = "0.2.3"
 ConstructionBase = "1.5"
 DifferentiationInterface = "0.6.16"
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index bb7a60441..26afa7720 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -1,6 +1,7 @@
 module SciMLJacobianOperators
 
 using ADTypes: ADTypes, AutoSparse
+using ArrayInterface: ArrayInterface
 using ConcreteStructs: @concrete
 using ConstructionBase: ConstructionBase
 using DifferentiationInterface: DifferentiationInterface, Constant
@@ -15,6 +16,8 @@ const False = Val(false)
 
 abstract type AbstractJacobianOperator{T} <: AbstractSciMLOperator{T} end
 
+ArrayInterface.can_setindex(::AbstractJacobianOperator) = false
+
 abstract type AbstractMode end
 
 struct VJP <: AbstractMode end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index e5f7ce411..8b8150ce2 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -18,13 +18,19 @@ using LineSearch: LineSearch, AbstractLineSearchCache, LineSearchesJL, NoLineSea
 using LinearSolve: LinearSolve, QRFactorization, needs_concrete_A, AbstractFactorization,
                    DefaultAlgorithmChoice, DefaultLinearSolver
 using MaybeInplace: @bb
-using NonlinearSolveBase: NonlinearSolveBase, nonlinearsolve_forwarddiff_solve,
-                          nonlinearsolve_dual_solution, nonlinearsolve_∂f_∂p,
-                          nonlinearsolve_∂f_∂u, L2_NORM, AbsNormTerminationMode,
-                          AbstractNonlinearTerminationMode,
+using NonlinearSolveBase: NonlinearSolveBase,
+                          nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution,
+                          nonlinearsolve_∂f_∂p, nonlinearsolve_∂f_∂u,
+                          L2_NORM,
+                          AbsNormTerminationMode, AbstractNonlinearTerminationMode,
                           AbstractSafeBestNonlinearTerminationMode,
                           select_forward_mode_autodiff, select_reverse_mode_autodiff,
-                          select_jacobian_autodiff, construct_linear_solver
+                          select_jacobian_autodiff,
+                          construct_linear_solver, construct_jacobian_cache
+
+# XXX: Remove
+import NonlinearSolveBase: concrete_jac
+
 using Printf: @printf
 using Preferences: Preferences, @load_preference, @set_preferences!
 using RecursiveArrayTools: recursivecopy!
@@ -70,7 +76,6 @@ include("descent/dogleg.jl")
 include("descent/damped_newton.jl")
 include("descent/geodesic_acceleration.jl")
 
-include("internal/jacobian.jl")
 include("internal/termination.jl")
 include("internal/tracing.jl")
 include("internal/approximate_initialization.jl")
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 0876e2036..0d60ed3bb 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -120,14 +120,6 @@ dispatches by wrapped solvers.
 """
 abstract type AbstractNonlinearSolveAlgorithm{name} <: AbstractNonlinearAlgorithm end
 
-"""
-    concrete_jac(alg::AbstractNonlinearSolveAlgorithm)
-
-Whether the algorithm uses a concrete Jacobian. Defaults to `nothing` if it is unknown or
-not applicable. Else a boolean value is returned.
-"""
-concrete_jac(::AbstractNonlinearSolveAlgorithm) = nothing
-
 function Base.show(io::IO, alg::AbstractNonlinearSolveAlgorithm)
     __show_algorithm(io, alg, get_name(alg), 0)
 end
@@ -223,13 +215,6 @@ function SciMLBase.reinit!(cache::AbstractNonlinearSolveCache, u0; kwargs...)
     return reinit_cache!(cache; u0, kwargs...)
 end
 
-"""
-    AbstractLinearSolverCache <: Function
-
-Abstract Type for all Linear Solvers used in NonlinearSolve.jl.
-"""
-abstract type AbstractLinearSolverCache <: Function end
-
 """
     AbstractDampingFunction
 
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
index 757be1b04..4d7bc213b 100644
--- a/src/core/approximate_jacobian.jl
+++ b/src/core/approximate_jacobian.jl
@@ -64,7 +64,8 @@ function ApproximateJacobianSolveAlgorithm{concrete_jac, name}(;
         reinit_rule, max_resets, max_shrink_times, initialization)
 end
 
-@inline concrete_jac(::ApproximateJacobianSolveAlgorithm{CJ}) where {CJ} = CJ
+# XXX: Remove
+@inline concrete_jac(::ApproximateJacobianSolveAlgorithm{CJ}) where {CJ} = concrete_jac(CJ)
 
 @concrete mutable struct ApproximateJacobianSolveCache{INV, GB, iip, timeit} <:
                          AbstractNonlinearSolveCache{iip, timeit}
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
index 40a11756f..261adbfb0 100644
--- a/src/core/generalized_first_order.jl
+++ b/src/core/generalized_first_order.jl
@@ -63,7 +63,8 @@ function GeneralizedFirstOrderAlgorithm{concrete_jac, name}(;
         autodiff, vjp_autodiff, jvp_autodiff)
 end
 
-concrete_jac(::GeneralizedFirstOrderAlgorithm{CJ}) where {CJ} = CJ
+# XXX: Remove
+concrete_jac(::GeneralizedFirstOrderAlgorithm{CJ}) where {CJ} = concrete_jac(CJ)
 
 @concrete mutable struct GeneralizedFirstOrderAlgorithmCache{iip, GB, timeit} <:
                          AbstractNonlinearSolveCache{iip, timeit}
@@ -173,9 +174,10 @@ function SciMLBase.__init(
             prob, abstol, reltol, fu, u, termination_condition, Val(:regular))
         linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
 
-        jac_cache = JacobianCache(
+        jac_cache = construct_jacobian_cache(
             prob, alg, f, fu, u, p; stats, autodiff, linsolve, jvp_autodiff, vjp_autodiff)
         J = jac_cache(nothing)
+
         descent_cache = __internal_init(prob, alg.descent, J, fu, u; stats, abstol,
             reltol, internalnorm, linsolve_kwargs, timer)
         du = get_du(descent_cache)
diff --git a/src/core/spectral_methods.jl b/src/core/spectral_methods.jl
index 31e988b70..c3303b9dd 100644
--- a/src/core/spectral_methods.jl
+++ b/src/core/spectral_methods.jl
@@ -36,7 +36,8 @@ function __show_algorithm(io::IO, alg::GeneralizedDFSane, name, indent)
     print(io, "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))")
 end
 
-concrete_jac(::GeneralizedDFSane) = nothing
+# XXX: Remove
+concrete_jac(::GeneralizedDFSane) = false
 
 @concrete mutable struct GeneralizedDFSaneCache{iip, timeit} <:
                          AbstractNonlinearSolveCache{iip, timeit}
diff --git a/src/internal/approximate_initialization.jl b/src/internal/approximate_initialization.jl
index a8196c367..7df718279 100644
--- a/src/internal/approximate_initialization.jl
+++ b/src/internal/approximate_initialization.jl
@@ -149,7 +149,8 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::TrueJacobianInitia
         solver, f::F, fu, u, p; stats, linsolve = missing,
         internalnorm::IN = L2_NORM, kwargs...) where {F, IN}
     autodiff = select_jacobian_autodiff(prob, alg.autodiff)
-    jac_cache = JacobianCache(prob, solver, prob.f, fu, u, p; stats, autodiff, linsolve)
+    jac_cache = construct_jacobian_cache(
+        prob, solver, prob.f, fu, u, p; stats, autodiff, linsolve)
     J = alg.structure(jac_cache(nothing))
     return InitializedApproximateJacobianCache(
         J, alg.structure, alg, jac_cache, false, internalnorm)
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index 6a154e0cc..735122b8d 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -113,7 +113,7 @@ function __construct_extension_jac(prob, alg, u0, fu; can_handle_oop::Val = Fals
         kwargs...)
     autodiff = select_jacobian_autodiff(prob, autodiff)
 
-    Jₚ = JacobianCache(
+    Jₚ = construct_jacobian_cache(
         prob, alg, prob.f, fu, u0, prob.p; stats = empty_nlstats(), autodiff, kwargs...)
 
     𝓙 = (can_handle_scalar === False && prob.u0 isa Number) ? @closure(u->[Jₚ(u[1])]) : Jₚ
diff --git a/src/internal/jacobian.jl b/src/internal/jacobian.jl
deleted file mode 100644
index 70cc7021e..000000000
--- a/src/internal/jacobian.jl
+++ /dev/null
@@ -1,250 +0,0 @@
-"""
-    JacobianCache(prob, alg, f::F, fu, u, p; autodiff = nothing,
-        vjp_autodiff = nothing, jvp_autodiff = nothing, linsolve = missing) where {F}
-
-Construct a cache for the Jacobian of `f` w.r.t. `u`.
-
-### Arguments
-
-  - `prob`: A [`NonlinearProblem`](@ref) or a [`NonlinearLeastSquaresProblem`](@ref).
-  - `alg`: A [`AbstractNonlinearSolveAlgorithm`](@ref). Used to check for
-    [`concrete_jac`](@ref).
-  - `f`: The function to compute the Jacobian of.
-  - `fu`: The evaluation of `f(u, p)` or `f(_, u, p)`. Used to determine the size of the
-    result cache and Jacobian.
-  - `u`: The current value of the state.
-  - `p`: The current value of the parameters.
-
-### Keyword Arguments
-
-  - `autodiff`: Automatic Differentiation or Finite Differencing backend for computing the
-    jacobian. By default, selects a backend based on sparsity parameters, type of state,
-    function properties, etc.
-  - `vjp_autodiff`: Automatic Differentiation or Finite Differencing backend for computing
-    the vector-Jacobian product.
-  - `jvp_autodiff`: Automatic Differentiation or Finite Differencing backend for computing
-    the Jacobian-vector product.
-  - `linsolve`: Linear Solver Algorithm used to determine if we need a concrete jacobian
-    or if possible we can just use a `SciMLJacobianOperators.JacobianOperator` instead.
-"""
-@concrete mutable struct JacobianCache{iip} <: AbstractNonlinearSolveJacobianCache{iip}
-    J
-    f
-    fu
-    u
-    p
-    stats::NLStats
-    autodiff
-    di_extras
-end
-
-function reinit_cache!(cache::JacobianCache{iip}, args...; p = cache.p,
-        u0 = cache.u, kwargs...) where {iip}
-    cache.u = u0
-    cache.p = p
-end
-
-function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
-        vjp_autodiff = nothing, jvp_autodiff = nothing, linsolve = missing) where {F}
-    iip = isinplace(prob)
-
-    has_analytic_jac = SciMLBase.has_jac(f)
-    linsolve_needs_jac = concrete_jac(alg) === nothing && (linsolve === missing ||
-                          (linsolve === nothing || __needs_concrete_A(linsolve)))
-    alg_wants_jac = concrete_jac(alg) !== nothing && concrete_jac(alg)
-    needs_jac = linsolve_needs_jac || alg_wants_jac
-
-    @bb fu = similar(fu_)
-
-    if !has_analytic_jac && needs_jac
-        autodiff = construct_concrete_adtype(f, autodiff)
-        di_extras = if iip
-            DI.prepare_jacobian(f, fu, autodiff, u, Constant(prob.p))
-        else
-            DI.prepare_jacobian(f, autodiff, u, Constant(prob.p))
-        end
-    else
-        di_extras = nothing
-    end
-
-    J = if !needs_jac
-        JacobianOperator(prob, fu, u; jvp_autodiff, vjp_autodiff)
-    else
-        if f.jac_prototype === nothing
-            # While this is technically wasteful, it gives out the type of the Jacobian
-            # which is needed to create the linear solver cache
-            stats.njacs += 1
-            if has_analytic_jac
-                __similar(
-                    fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u))
-            else
-                if iip
-                    DI.jacobian(f, fu, di_extras, autodiff, u, Constant(p))
-                else
-                    DI.jacobian(f, di_extras, autodiff, u, Constant(p))
-                end
-            end
-        else
-            if eltype(f.jac_prototype) <: Bool
-                similar(f.jac_prototype, promote_type(eltype(fu), eltype(u)))
-            else
-                similar(f.jac_prototype)
-            end
-        end
-    end
-
-    return JacobianCache{iip}(J, f, fu, u, p, stats, autodiff, di_extras)
-end
-
-function JacobianCache(prob, alg, f::F, ::Number, u::Number, p; stats,
-        autodiff = nothing, kwargs...) where {F}
-    fu = f(u, p)
-    if SciMLBase.has_jac(f) || SciMLBase.has_vjp(f) || SciMLBase.has_jvp(f)
-        return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, nothing)
-    end
-    di_extras = DI.prepare_derivative(f, get_dense_ad(autodiff), u, Constant(prob.p))
-    return JacobianCache{false}(u, f, fu, u, p, stats, autodiff, di_extras)
-end
-
-(cache::JacobianCache)(u = cache.u) = cache(cache.J, u, cache.p)
-function (cache::JacobianCache)(::Nothing)
-    cache.J isa JacobianOperator &&
-        return StatefulJacobianOperator(cache.J, cache.u, cache.p)
-    return cache.J
-end
-
-# Operator
-function (cache::JacobianCache)(J::JacobianOperator, u, p = cache.p)
-    return StatefulJacobianOperator(J, u, p)
-end
-# Numbers
-function (cache::JacobianCache)(::Number, u, p = cache.p) # Scalar
-    cache.stats.njacs += 1
-    if SciMLBase.has_jac(cache.f)
-        return cache.f.jac(u, p)
-    elseif SciMLBase.has_vjp(cache.f)
-        return cache.f.vjp(one(u), u, p)
-    elseif SciMLBase.has_jvp(cache.f)
-        return cache.f.jvp(one(u), u, p)
-    end
-    return DI.derivative(cache.f, cache.di_extras, cache.autodiff, u, Constant(p))
-end
-# Actually Compute the Jacobian
-function (cache::JacobianCache{iip})(
-        J::Union{AbstractMatrix, Nothing}, u, p = cache.p) where {iip}
-    cache.stats.njacs += 1
-    if iip
-        if SciMLBase.has_jac(cache.f)
-            cache.f.jac(J, u, p)
-        else
-            DI.jacobian!(
-                cache.f, cache.fu, J, cache.di_extras, cache.autodiff, u, Constant(p))
-        end
-        return J
-    else
-        if SciMLBase.has_jac(cache.f)
-            return cache.f.jac(u, p)
-        else
-            return DI.jacobian(cache.f, cache.di_extras, cache.autodiff, u, Constant(p))
-        end
-    end
-end
-
-function construct_concrete_adtype(f::NonlinearFunction, ad::AbstractADType)
-    @assert !(ad isa AutoSparse) "This shouldn't happen. Open an issue."
-    if f.sparsity === nothing
-        if f.jac_prototype === nothing
-            if SciMLBase.has_colorvec(f)
-                @warn "`colorvec` is provided but `sparsity` and `jac_prototype` is not \
-                       specified. `colorvec` will be ignored."
-            end
-            return ad # No sparse AD
-        else
-            if !sparse_or_structured_prototype(f.jac_prototype)
-                if SciMLBase.has_colorvec(f)
-                    @warn "`colorvec` is provided but `jac_prototype` is not a sparse \
-                           or structured matrix. `colorvec` will be ignored."
-                end
-                return ad
-            end
-            return AutoSparse(
-                ad;
-                sparsity_detector = KnownJacobianSparsityDetector(f.jac_prototype),
-                coloring_algorithm = select_fastest_coloring_algorithm(
-                    f.jac_prototype, f, ad)
-            )
-        end
-    else
-        if f.sparsity isa AbstractMatrix
-            if f.jac_prototype !== f.sparsity
-                if f.jac_prototype !== nothing &&
-                   sparse_or_structured_prototype(f.jac_prototype)
-                    throw(ArgumentError("`sparsity::AbstractMatrix` and a sparse or \
-                                         structured `jac_prototype` cannot be both \
-                                         provided. Pass only `jac_prototype`."))
-                end
-            end
-            return AutoSparse(
-                ad;
-                sparsity_detector = KnownJacobianSparsityDetector(f.sparsity),
-                coloring_algorithm = select_fastest_coloring_algorithm(
-                    f.sparsity, f, ad)
-            )
-        end
-
-        @assert f.sparsity isa ADTypes.AbstractSparsityDetector
-        sparsity_detector = f.sparsity
-        if f.jac_prototype === nothing
-            if SciMLBase.has_colorvec(f)
-                @warn "`colorvec` is provided but `jac_prototype` is not specified. \
-                       `colorvec` will be ignored."
-            end
-            return AutoSparse(
-                ad;
-                sparsity_detector,
-                coloring_algorithm = GreedyColoringAlgorithm(LargestFirst())
-            )
-        else
-            if sparse_or_structured_prototype(f.jac_prototype)
-                if !(sparsity_detector isa NoSparsityDetector)
-                    @warn "`jac_prototype` is a sparse matrix but sparsity = $(f.sparsity) \
-                           has also been specified. Ignoring sparsity field and using \
-                           `jac_prototype` sparsity."
-                end
-                sparsity_detector = KnownJacobianSparsityDetector(f.jac_prototype)
-            end
-
-            return AutoSparse(
-                ad;
-                sparsity_detector,
-                coloring_algorithm = select_fastest_coloring_algorithm(
-                    f.jac_prototype, f, ad)
-            )
-        end
-    end
-end
-
-function select_fastest_coloring_algorithm(
-        prototype, f::NonlinearFunction, ad::AbstractADType)
-    if SciMLBase.has_colorvec(f)
-        return ConstantColoringAlgorithm{ifelse(
-            ADTypes.mode(ad) isa ADTypes.ReverseMode, :row, :column)}(
-            prototype, f.colorvec)
-    end
-    return GreedyColoringAlgorithm(LargestFirst())
-end
-
-function construct_concrete_adtype(::NonlinearFunction, ad::AutoSparse)
-    error("Specifying a sparse AD type for Nonlinear Problems was removed in v4. \
-           Instead use the `sparsity`, `jac_prototype`, and `colorvec` to specify \
-           the right sparsity pattern and coloring algorithm. Ignoring the sparsity \
-           detection algorithm and coloring algorithm present in $(ad).")
-end
-
-get_dense_ad(ad) = ad
-get_dense_ad(ad::AutoSparse) = ADTypes.dense_ad(ad)
-
-sparse_or_structured_prototype(::AbstractSparseMatrix) = true
-function sparse_or_structured_prototype(prototype::AbstractMatrix)
-    return ArrayInterface.isstructured(prototype)
-end
diff --git a/src/utils.jl b/src/utils.jl
index a080bd124..af657b0b8 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -7,13 +7,6 @@
     return :(missing)
 end
 
-@inline __needs_concrete_A(::Nothing) = false
-@inline __needs_concrete_A(::typeof(\)) = true
-@inline __needs_concrete_A(linsolve) = needs_concrete_A(linsolve)
-
-@inline __maybe_mutable(x, ::AutoSparse{<:AutoEnzyme}) = __mutable(x)  # TODO: remove?
-@inline __maybe_mutable(x, _) = x
-
 @inline @generated function _vec(v)
     hasmethod(vec, Tuple{typeof(v)}) || return :(vec(v))
     return :(v)
@@ -60,10 +53,6 @@ LazyArrays.applied_axes(::typeof(__zero), x) = axes(x)
 @inline __maybe_symmetric(x::AbstractSparseMatrix) = x
 @inline __maybe_symmetric(x::AbstractSciMLOperator) = x
 
-# SparseAD --> NonSparseAD
-@inline __get_nonsparse_ad(backend::AutoSparse) = ADTypes.dense_ad(backend)
-@inline __get_nonsparse_ad(ad) = ad
-
 # Simple Checks
 @inline __is_present(::Nothing) = false
 @inline __is_present(::Missing) = false
@@ -101,14 +90,6 @@ end
 @inline __can_setindex(x) = can_setindex(x)
 @inline __can_setindex(::Number) = false
 
-@inline function __mutable(x)
-    __can_setindex(x) && return x
-    y = similar(x)
-    copyto!(y, x)
-    return y
-end
-@inline __mutable(x::SArray) = MArray(x)
-
 @inline __dot(x, y) = dot(_vec(x), _vec(y))
 
 """

From c24be00eb8b79be2528561d11e1ec92ddbe44a37 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 26 Oct 2024 13:34:53 -0400
Subject: [PATCH 630/700] fix: missing `u`

---
 lib/NonlinearSolveBase/src/linear_solve.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/NonlinearSolveBase/src/linear_solve.jl b/lib/NonlinearSolveBase/src/linear_solve.jl
index 2ad957ab1..c19f51829 100644
--- a/lib/NonlinearSolveBase/src/linear_solve.jl
+++ b/lib/NonlinearSolveBase/src/linear_solve.jl
@@ -112,7 +112,7 @@ function (cache::NativeJLLinearSolveCache)(;
 end
 
 fix_incompatible_linsolve_arguments(A, b, u) = u
-fix_incompatible_linsolve_arguments(::SArray, ::SArray, ::SArray) = u
+fix_incompatible_linsolve_arguments(::SArray, ::SArray, u::SArray) = u
 function fix_incompatible_linsolve_arguments(A, b, u::SArray)
     (Core.Compiler.return_type(\, Tuple{typeof(A), typeof(b)}) <: typeof(u)) && return u
     @warn "Solving Linear System A::$(typeof(A)) x::$(typeof(u)) = b::$(typeof(u)) is not \

From e805aef9df616e827e0f31a3ee54039863a91a4a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 26 Oct 2024 13:41:44 -0400
Subject: [PATCH 631/700] chore: remove unused imports

---
 lib/NonlinearSolveBase/src/jacobian.jl |  3 ++-
 src/NonlinearSolve.jl                  | 15 ++++++---------
 2 files changed, 8 insertions(+), 10 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/jacobian.jl b/lib/NonlinearSolveBase/src/jacobian.jl
index a189bf042..5725d3687 100644
--- a/lib/NonlinearSolveBase/src/jacobian.jl
+++ b/lib/NonlinearSolveBase/src/jacobian.jl
@@ -29,7 +29,8 @@ Construct a cache for the Jacobian of `f` w.r.t. `u`.
   - `jvp_autodiff`: Automatic Differentiation or Finite Differencing backend for computing
     the Jacobian-vector product.
   - `linsolve`: Linear Solver Algorithm used to determine if we need a concrete jacobian
-    or if possible we can just use a `SciMLJacobianOperators.JacobianOperator` instead.
+    or if possible we can just use a [`SciMLJacobianOperators.JacobianOperator`](@ref)
+    instead.
 """
 function construct_jacobian_cache(
         prob, alg, f::NonlinearFunction, fu, u = prob.u0, p = prob.p; stats,
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 8b8150ce2..a96445320 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -10,13 +10,12 @@ using ConcreteStructs: @concrete
 using DiffEqBase: DiffEqBase # Needed for `init` / `solve` dispatches
 using FastClosures: @closure
 using LazyArrays: LazyArrays, ApplyArray, cache
-using LinearAlgebra: LinearAlgebra, ColumnNorm, Diagonal, I, LowerTriangular, Symmetric,
+using LinearAlgebra: LinearAlgebra, Diagonal, I, LowerTriangular, Symmetric,
                      UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess, istril,
                      istriu, lu, mul!, norm, pinv, tril!, triu!
 using LineSearch: LineSearch, AbstractLineSearchCache, LineSearchesJL, NoLineSearch,
                   RobustNonMonotoneLineSearch, BackTracking, LiFukushimaLineSearch
-using LinearSolve: LinearSolve, QRFactorization, needs_concrete_A, AbstractFactorization,
-                   DefaultAlgorithmChoice, DefaultLinearSolver
+using LinearSolve: LinearSolve
 using MaybeInplace: @bb
 using NonlinearSolveBase: NonlinearSolveBase,
                           nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution,
@@ -47,18 +46,16 @@ using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingPro
 
 # AD Support
 using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
-               AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme, AutoSparse,
-               NoSparsityDetector, KnownJacobianSparsityDetector
-using DifferentiationInterface: DifferentiationInterface, Constant
+               AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme, AutoSparse
+using DifferentiationInterface: DifferentiationInterface
 using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff, Dual
-using SciMLJacobianOperators: AbstractJacobianOperator, JacobianOperator, VecJacOperator,
+using SciMLJacobianOperators: AbstractJacobianOperator, VecJacOperator,
                               JacVecOperator, StatefulJacobianOperator
 
 ## Sparse AD Support
 using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
-using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm,
-                             LargestFirst
+using SparseMatrixColorings: SparseMatrixColorings # NOTE: This triggers an extension in NonlinearSolveBase
 
 const DI = DifferentiationInterface
 

From 498964cb8d4482ffdeca30a020bd49afc11512cf Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 26 Oct 2024 17:02:16 -0400
Subject: [PATCH 632/700] refactor: move Descent Directions to
 `NonlinearSolveBase`

---
 docs/src/devdocs/operators.md                 |   6 -
 lib/NonlinearSolveBase/Project.toml           |   4 +
 .../ext/NonlinearSolveBaseSparseArraysExt.jl  |   4 +-
 .../src/NonlinearSolveBase.jl                 |  14 +-
 lib/NonlinearSolveBase/src/abstract_types.jl  | 184 +++++++++++-
 .../NonlinearSolveBase/src}/descent/common.jl |  12 +-
 .../src/descent/damped_newton.jl              | 268 ++++++++++++++++++
 .../NonlinearSolveBase/src}/descent/dogleg.jl | 111 ++++----
 .../src}/descent/geodesic_acceleration.jl     |  94 +++---
 lib/NonlinearSolveBase/src/descent/newton.jl  | 132 +++++++++
 .../src/descent/steepest.jl                   |  76 +++++
 lib/NonlinearSolveBase/src/timer_outputs.jl   |  33 +++
 lib/NonlinearSolveBase/src/utils.jl           |  51 +++-
 src/NonlinearSolve.jl                         |  33 ++-
 src/abstract_types.jl                         | 185 +-----------
 src/algorithms/lbroyden.jl                    |   2 +-
 src/descent/damped_newton.jl                  | 256 -----------------
 src/descent/newton.jl                         | 122 --------
 src/descent/steepest.jl                       |  74 -----
 src/timer_outputs.jl                          |  39 +--
 src/utils.jl                                  |   3 +-
 21 files changed, 900 insertions(+), 803 deletions(-)
 rename {src => lib/NonlinearSolveBase/src}/descent/common.jl (74%)
 create mode 100644 lib/NonlinearSolveBase/src/descent/damped_newton.jl
 rename {src => lib/NonlinearSolveBase/src}/descent/dogleg.jl (56%)
 rename {src => lib/NonlinearSolveBase/src}/descent/geodesic_acceleration.jl (55%)
 create mode 100644 lib/NonlinearSolveBase/src/descent/newton.jl
 create mode 100644 lib/NonlinearSolveBase/src/descent/steepest.jl
 create mode 100644 lib/NonlinearSolveBase/src/timer_outputs.jl
 delete mode 100644 src/descent/damped_newton.jl
 delete mode 100644 src/descent/newton.jl
 delete mode 100644 src/descent/steepest.jl

diff --git a/docs/src/devdocs/operators.md b/docs/src/devdocs/operators.md
index 15d00093a..fcbadc778 100644
--- a/docs/src/devdocs/operators.md
+++ b/docs/src/devdocs/operators.md
@@ -1,11 +1,5 @@
 # Custom SciML Operators
 
-## Abstract Operators
-
-```@docs
-NonlinearSolve.AbstractNonlinearSolveOperator
-```
-
 ## Low-Rank Jacobian Operators
 
 ```@docs
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index df76e09a4..5a8cd1f34 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -17,11 +17,13 @@ FunctionProperties = "f62d2435-5019-4c03-9749-2d4c77af0cbc"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
+Preferences = "21216c6a-2e73-6563-6e65-726566657250"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
 SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 
 [weakdeps]
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
@@ -57,6 +59,7 @@ LinearAlgebra = "1.10"
 LinearSolve = "2.36.1"
 Markdown = "1.10"
 MaybeInplace = "0.1.4"
+Preferences = "1.4"
 RecursiveArrayTools = "3"
 SciMLBase = "2.50"
 SciMLJacobianOperators = "0.1.1"
@@ -65,6 +68,7 @@ SparseArrays = "1.10"
 SparseMatrixColorings = "0.4.8"
 StaticArraysCore = "1.4"
 Test = "1.10"
+TimerOutputs = "0.5.23"
 julia = "1.10"
 
 [extras]
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
index 3b6ae2935..fca3793ad 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
@@ -1,6 +1,6 @@
 module NonlinearSolveBaseSparseArraysExt
 
-using NonlinearSolveBase: NonlinearSolveBase
+using NonlinearSolveBase: NonlinearSolveBase, Utils
 using SparseArrays: AbstractSparseMatrix, AbstractSparseMatrixCSC, nonzeros
 
 function NonlinearSolveBase.NAN_CHECK(x::AbstractSparseMatrixCSC)
@@ -9,4 +9,6 @@ end
 
 NonlinearSolveBase.sparse_or_structured_prototype(::AbstractSparseMatrix) = true
 
+Utils.maybe_symmetric(x::AbstractSparseMatrix) = x
+
 end
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 585ac1c5a..5007763b2 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -11,9 +11,10 @@ using DifferentiationInterface: DifferentiationInterface, Constant
 using EnzymeCore: EnzymeCore
 using FastClosures: @closure
 using FunctionProperties: hasbranching
-using LinearAlgebra: Diagonal, norm, ldiv!
+using LinearAlgebra: LinearAlgebra, Diagonal, norm, ldiv!, diagind
 using Markdown: @doc_str
 using MaybeInplace: @bb
+using Preferences: @load_preference
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinearProblem,
                  AbstractNonlinearAlgorithm, AbstractNonlinearFunction,
@@ -37,6 +38,14 @@ include("termination_conditions.jl")
 include("autodiff.jl")
 include("jacobian.jl")
 include("linear_solve.jl")
+include("timer_outputs.jl")
+
+include("descent/common.jl")
+include("descent/newton.jl")
+include("descent/steepest.jl")
+include("descent/damped_newton.jl")
+include("descent/dogleg.jl")
+include("descent/geodesic_acceleration.jl")
 
 # Unexported Public API
 @compat(public, (L2_NORM, Linf_NORM, NAN_CHECK, UNITLESS_ABS2, get_tolerance))
@@ -55,4 +64,7 @@ export RelTerminationMode, AbsTerminationMode,
        RelNormSafeTerminationMode, AbsNormSafeTerminationMode,
        RelNormSafeBestTerminationMode, AbsNormSafeBestTerminationMode
 
+export DescentResult, SteepestDescent, NewtonDescent, DampedNewtonDescent, Dogleg,
+       GeodesicAcceleration
+
 end
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index 4dba65a14..42c57842a 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -6,7 +6,65 @@ function reinit! end
 
 end
 
-abstract type AbstractDescentDirection end
+abstract type AbstractNonlinearSolveBaseAPI end # Mostly used for pretty-printing
+
+function Base.show(io::IO, ::MIME"text/plain", alg::AbstractNonlinearSolveBaseAPI)
+    main_name = nameof(typeof(alg))
+    modifiers = String[]
+    for field in fieldnames(typeof(alg))
+        val = getfield(alg, field)
+        Utils.is_default_value(val, field, getfield(alg, field)) && continue
+        push!(modifiers, "$(field) = $(val)")
+    end
+    print(io, "$(main_name)($(join(modifiers, ", ")))")
+    return
+end
+
+"""
+    AbstractDescentDirection
+
+Abstract Type for all Descent Directions used in NonlinearSolveBase. Given the Jacobian
+`J` and the residual `fu`, these algorithms compute the descent direction `δu`.
+
+For non-square Jacobian problems, if we need to solve a linear solve problem, we use a
+least squares solver by default, unless the provided `linsolve` can't handle non-square
+matrices, in which case we use the normal form equations ``JᵀJ δu = Jᵀ fu``. Note that
+this factorization is often the faster choice, but it is not as numerically stable as
+the least squares solver.
+
+### `InternalAPI.init` specification
+
+```julia
+InternalAPI.init(
+    prob::AbstractNonlinearProblem, alg::AbstractDescentDirection, J, fu, u;
+    pre_inverted::Val = Val(false), linsolve_kwargs = (;),
+    abstol = nothing, reltol = nothing, alias_J::Bool = true,
+    shared::Val = Val(1), kwargs...
+)::AbstractDescentCache
+```
+
+  - `pre_inverted`: whether or not the Jacobian has been pre_inverted.
+  - `linsolve_kwargs`: keyword arguments to pass to the linear solver.
+  - `abstol`: absolute tolerance for the linear solver.
+  - `reltol`: relative tolerance for the linear solver.
+  - `alias_J`: whether or not to alias the Jacobian.
+  - `shared`: Store multiple descent directions in the cache. Allows efficient and
+    correct reuse of factorizations if needed.
+
+Some of the algorithms also allow additional keyword arguments. See the documentation for
+the specific algorithm for more information.
+
+### Interface Functions
+
+  - `supports_trust_region(alg)`: whether or not the algorithm supports trust region
+    methods. Defaults to `false`.
+  - `supports_line_search(alg)`: whether or not the algorithm supports line search
+    methods. Defaults to `false`.
+
+See also [`NewtonDescent`](@ref), [`Dogleg`](@ref), [`SteepestDescent`](@ref),
+[`DampedNewtonDescent`](@ref).
+"""
+abstract type AbstractDescentDirection <: AbstractNonlinearSolveBaseAPI end
 
 supports_line_search(::AbstractDescentDirection) = false
 supports_trust_region(::AbstractDescentDirection) = false
@@ -15,7 +73,46 @@ function get_linear_solver(alg::AbstractDescentDirection)
     return Utils.safe_getproperty(alg, Val(:linsolve))
 end
 
-abstract type AbstractDescentCache end
+"""
+    AbstractDescentCache
+
+Abstract Type for all Descent Caches.
+
+### `InternalAPI.solve!` specification
+
+```julia
+InternalAPI.solve!(
+    cache::AbstractDescentCache, J, fu, u, idx::Val;
+    skip_solve::Bool = false, new_jacobian::Bool = true, kwargs...
+)::DescentResult
+```
+
+  - `J`: Jacobian or Inverse Jacobian (if `pre_inverted = Val(true)`).
+  - `fu`: residual.
+  - `u`: current state.
+  - `idx`: index of the descent problem to solve and return. Defaults to `Val(1)`.
+  - `skip_solve`: Skip the direction computation and return the previous direction.
+    Defaults to `false`. This is useful for Trust Region Methods where the previous
+    direction was rejected and we want to try with a modified trust region.
+  - `new_jacobian`: Whether the Jacobian has been updated. Defaults to `true`.
+  - `kwargs`: keyword arguments to pass to the linear solver if there is one.
+
+#### Returned values
+
+  - `descent_result`: Result in a [`DescentResult`](@ref).
+
+### Interface Functions
+
+  - `get_du(cache)`: get the descent direction.
+  - `get_du(cache, ::Val{N})`: get the `N`th descent direction.
+  - `set_du!(cache, δu)`: set the descent direction.
+  - `set_du!(cache, δu, ::Val{N})`: set the `N`th descent direction.
+  - `last_step_accepted(cache)`: whether or not the last step was accepted. Checks if the
+    cache has a `last_step_accepted` field and returns it if it does, else returns `true`.
+  - `preinverted_jacobian(cache)`: whether or not the Jacobian has been preinverted.
+  - `normal_form(cache)`: whether or not the linear solver uses normal form.
+"""
+abstract type AbstractDescentCache <: AbstractNonlinearSolveBaseAPI end
 
 SciMLBase.get_du(cache::AbstractDescentCache) = cache.δu
 SciMLBase.get_du(cache::AbstractDescentCache, ::Val{1}) = SciMLBase.get_du(cache)
@@ -29,6 +126,79 @@ function last_step_accepted(cache::AbstractDescentCache)
     return true
 end
 
+for fname in (:preinverted_jacobian, :normal_form)
+    @eval function $(fname)(alg::AbstractDescentCache)
+        res = Utils.unwrap_val(Utils.safe_getproperty(alg, Val($(QuoteNode(fname)))))
+        res === missing && return false
+        return res
+    end
+end
+
+"""
+    AbstractDampingFunction
+
+Abstract Type for Damping Functions in DampedNewton.
+
+### `InternalAPI.init` specification
+
+```julia
+InternalAPI.init(
+    prob::AbstractNonlinearProblem, f::AbstractDampingFunction, initial_damping,
+    J, fu, u, args...;
+    internalnorm::F = L2_NORM, kwargs...
+)::AbstractDampingFunctionCache
+```
+
+Returns a [`NonlinearSolveBase.AbstractDampingFunctionCache`](@ref).
+"""
+abstract type AbstractDampingFunction <: AbstractNonlinearAlgorithm end
+
+"""
+    AbstractDampingFunctionCache
+
+Abstract Type for the Caches created by AbstractDampingFunctions
+
+### Interface Functions
+
+  - `requires_normal_form_jacobian(alg)`: whether or not the Jacobian is needed in normal
+    form. No default.
+  - `requires_normal_form_rhs(alg)`: whether or not the residual is needed in normal form.
+    No default.
+  - `returns_norm_form_damping(alg)`: whether or not the damping function returns the
+    damping factor in normal form. Defaults to
+    `requires_normal_form_jacobian(alg) || requires_normal_form_rhs(alg)`.
+  - `(cache::AbstractDampingFunctionCache)(::Nothing)`: returns the damping factor. The type
+    of the damping factor returned from `solve!` is guaranteed to be the same as this.
+
+### `InternalAPI.solve!` specification
+
+```julia
+InternalAPI.solve!(
+    cache::AbstractDampingFunctionCache, J, fu, u, δu, descent_stats
+)
+```
+
+Returns the damping factor.
+"""
+abstract type AbstractDampingFunctionCache <: AbstractNonlinearAlgorithm end
+
+function requires_normal_form_jacobian end
+function requires_normal_form_rhs end
+function returns_norm_form_damping(f::F) where {F}
+    return requires_normal_form_jacobian(f) || requires_normal_form_rhs(f)
+end
+
+"""
+    AbstractNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm
+
+Abstract Type for all NonlinearSolveBase Algorithms.
+
+### Interface Functions
+
+  - `concrete_jac(alg)`: whether or not the algorithm uses a concrete Jacobian. Defaults
+    to `nothing`.
+  - `get_name(alg)`: get the name of the algorithm.
+"""
 abstract type AbstractNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm end
 
 get_name(alg::AbstractNonlinearSolveAlgorithm) = Utils.safe_getproperty(alg, Val(:name))
@@ -47,20 +217,20 @@ concrete_jac(v::Bool) = v
 concrete_jac(::Val{false}) = false
 concrete_jac(::Val{true}) = true
 
-abstract type AbstractNonlinearSolveCache end
+abstract type AbstractNonlinearSolveCache <: AbstractNonlinearSolveBaseAPI end
 
 """
     AbstractLinearSolverCache
 
-Abstract Type for all Linear Solvers used in NonlinearSolve. Subtypes of these are
+Abstract Type for all Linear Solvers used in NonlinearSolveBase. Subtypes of these are
 meant to be constructured via [`construct_linear_solver`](@ref).
 """
-abstract type AbstractLinearSolverCache end
+abstract type AbstractLinearSolverCache <: AbstractNonlinearSolveBaseAPI end
 
 """
     AbstractJacobianCache
 
-Abstract Type for all Jacobian Caches used in NonlinearSolve. Subtypes of these are
+Abstract Type for all Jacobian Caches used in NonlinearSolveBase. Subtypes of these are
 meant to be constructured via [`construct_jacobian_cache`](@ref).
 """
-abstract type AbstractJacobianCache end
+abstract type AbstractJacobianCache <: AbstractNonlinearSolveBaseAPI end
diff --git a/src/descent/common.jl b/lib/NonlinearSolveBase/src/descent/common.jl
similarity index 74%
rename from src/descent/common.jl
rename to lib/NonlinearSolveBase/src/descent/common.jl
index 3d53573ea..b757a990a 100644
--- a/src/descent/common.jl
+++ b/lib/NonlinearSolveBase/src/descent/common.jl
@@ -1,6 +1,8 @@
 """
-    DescentResult(; δu = missing, u = missing, success::Bool = true,
-        linsolve_success::Bool = true, extras = (;))
+    DescentResult(;
+        δu = missing, u = missing, success::Bool = true, linsolve_success::Bool = true,
+        extras = (;)
+    )
 
 Construct a `DescentResult` object.
 
@@ -23,8 +25,10 @@ Construct a `DescentResult` object.
     extras
 end
 
-function DescentResult(; δu = missing, u = missing, success::Bool = true,
-        linsolve_success::Bool = true, extras = (;))
+function DescentResult(;
+        δu = missing, u = missing, success::Bool = true, linsolve_success::Bool = true,
+        extras = (;)
+)
     @assert δu !== missing || u !== missing
     return DescentResult(δu, u, success, linsolve_success, extras)
 end
diff --git a/lib/NonlinearSolveBase/src/descent/damped_newton.jl b/lib/NonlinearSolveBase/src/descent/damped_newton.jl
new file mode 100644
index 000000000..3ab507065
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/descent/damped_newton.jl
@@ -0,0 +1,268 @@
+"""
+    DampedNewtonDescent(;
+        linsolve = nothing, precs = nothing, initial_damping, damping_fn
+    )
+
+A Newton descent algorithm with damping. The damping factor is computed using the
+`damping_fn` function. The descent direction is computed as ``(JᵀJ + λDᵀD) δu = -fu``. For
+non-square Jacobians, we default to solving for `Jδx = -fu` and `√λ⋅D δx = 0`
+simultaneously. If the linear solver can't handle non-square matrices, we use the normal
+form equations ``(JᵀJ + λDᵀD) δu = Jᵀ fu``. Note that this factorization is often the faster
+choice, but it is not as numerically stable as the least squares solver.
+
+The damping factor returned must be a non-negative number.
+
+### Keyword Arguments
+
+  - `initial_damping`: the initial damping factor to use
+  - `damping_fn`: the function to use to compute the damping factor. This must satisfy the
+    [`NonlinearSolveBase.AbstractDampingFunction`](@ref) interface.
+"""
+@kwdef @concrete struct DampedNewtonDescent <: AbstractDescentDirection
+    linsolve = nothing
+    precs = nothing
+    initial_damping
+    damping_fn <: AbstractDampingFunction
+end
+
+supports_line_search(::DampedNewtonDescent) = true
+supports_trust_region(::DampedNewtonDescent) = true
+
+@concrete mutable struct DampedNewtonDescentCache <: AbstractDescentCache
+    J
+    δu
+    δus
+    lincache
+    JᵀJ_cache
+    Jᵀfu_cache
+    rhs_cache
+    damping_fn_cache
+    timer
+    preinverted_jacobian <: Union{Val{false}, Val{true}}
+    mode <: Union{Val{:normal_form}, Val{:least_squares}, Val{:simple}}
+end
+
+# XXX: Implement
+# @internal_caches DampedNewtonDescentCache :lincache :damping_fn_cache
+
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, alg::DampedNewtonDescent, J, fu, u; stats,
+        pre_inverted::Val = Val(false), linsolve_kwargs = (;),
+        abstol = nothing, reltol = nothing,
+        timer = get_timer_output(),
+        alias_J::Bool = true, shared::Val = Val(1),
+        kwargs...
+)
+    length(fu) != length(u) &&
+        @assert pre_inverted isa Val{false} "Precomputed Inverse for Non-Square Jacobian doesn't make sense."
+
+    @bb δu = similar(u)
+    δus = Utils.unwrap_val(shared) ≤ 1 ? nothing : map(2:Utils.unwrap_val(shared)) do i
+        @bb δu_ = similar(u)
+    end
+
+    normal_form_damping = returns_norm_form_damping(alg.damping_fn)
+    normal_form_linsolve = needs_square_A(alg.linsolve, u)
+
+    mode = if u isa Number
+        :simple
+    elseif prob isa NonlinearProblem
+        if normal_form_damping
+            ifelse(normal_form_linsolve, :normal_form, :least_squares)
+        else
+            :simple
+        end
+    else
+        if normal_form_linsolve & !normal_form_damping
+            throw(ArgumentError("Linear Solver expects Normal Form but returned Damping is \
+                                 not Normal Form. This is not supported."))
+        end
+        if normal_form_damping & !normal_form_linsolve
+            :least_squares
+        else
+            ifelse(!normal_form_damping & !normal_form_linsolve, :simple, :normal_form)
+        end
+    end
+
+    if mode === :least_squares
+        if requires_normal_form_jacobian(alg.damping_fn)
+            JᵀJ = transpose(J) * J  # Needed to compute the damping factor
+            jac_damp = JᵀJ
+        else
+            JᵀJ = nothing
+            jac_damp = J
+        end
+        if requires_normal_form_rhs(alg.damping_fn)
+            Jᵀfu = transpose(J) * Utils.safe_vec(fu)
+            rhs_damp = Jᵀfu
+        else
+            Jᵀfu = nothing
+            rhs_damp = fu
+        end
+
+        damping_fn_cache = InternalAPI.init(
+            prob, alg.damping_fn, alg.initial_damping, jac_damp, rhs_damp, u, Val(false);
+            stats, kwargs...
+        )
+        D = damping_fn_cache(nothing)
+
+        D isa Number && (D = D * LinearAlgebra.I)
+        rhs_cache = vcat(Utils.safe_vec(fu), Utils.safe_vec(u))
+        J_cache = Utils.faster_vcat(J, D)
+        A, b = J_cache, rhs_cache
+    elseif mode === :simple
+        damping_fn_cache = InternalAPI.init(
+            prob, alg.damping_fn, alg.initial_damping, J, fu, u, Val(false); kwargs...
+        )
+        J_cache = Utils.maybe_unaliased(J, alias_J)
+        D = damping_fn_cache(nothing)
+
+        J_damped = dampen_jacobian!!(J_cache, J, D)
+        J_cache = J_damped
+        A, b = J_damped, Utils.safe_vec(fu)
+        JᵀJ, Jᵀfu, rhs_cache = nothing, nothing, nothing
+    elseif mode === :normal_form
+        JᵀJ = transpose(J) * J
+        Jᵀfu = transpose(J) * Utils.safe_vec(fu)
+        jac_damp = requires_normal_form_jacobian(alg.damping_fn) ? JᵀJ : J
+        rhs_damp = requires_normal_form_rhs(alg.damping_fn) ? Jᵀfu : fu
+
+        damping_fn_cache = InternalAPI.init(
+            prob, alg.damping_fn, alg.initial_damping, jac_damp, rhs_damp, u, Val(true);
+            stats, kwargs...
+        )
+        D = damping_fn_cache(nothing)
+
+        @bb J_cache = similar(JᵀJ)
+        @bb @. J_cache = 0
+        J_damped = dampen_jacobian!!(J_cache, JᵀJ, D)
+        A, b = Utils.maybe_symmetric(J_damped), Utils.safe_vec(Jᵀfu)
+        rhs_cache = nothing
+    end
+
+    lincache = construct_linear_solver(
+        alg, alg.linsolve, A, b, Utils.safe_vec(u);
+        stats, abstol, reltol, linsolve_kwargs...
+    )
+
+    return DampedNewtonDescentCache(
+        J_cache, δu, δus, lincache, JᵀJ, Jᵀfu, rhs_cache,
+        damping_fn_cache, timer, pre_inverted, Val(mode)
+    )
+end
+
+function InternalAPI.solve!(
+        cache::DampedNewtonDescentCache, J, fu, u, idx::Val = Val(1);
+        skip_solve::Bool = false, new_jacobian::Bool = true, kwargs...
+)
+    δu = SciMLBase.get_du(cache, idx)
+    skip_solve && return DescentResult(; δu)
+
+    recompute_A = idx === Val(1)
+
+    @static_timeit cache.timer "dampen" begin
+        if cache.mode isa Val{:least_squares}
+            if (J !== nothing || new_jacobian) && recompute_A
+                preinverted_jacobian(cache) && (J = inv(J))
+                if requires_normal_form_jacobian(cache.damping_fn_cache)
+                    @bb cache.JᵀJ_cache = transpose(J) × J
+                    jac_damp = cache.JᵀJ_cache
+                else
+                    jac_damp = J
+                end
+                if requires_normal_form_rhs(cache.damping_fn_cache)
+                    @bb cache.Jᵀfu_cache = transpose(J) × vec(fu)
+                    rhs_damp = cache.Jᵀfu_cache
+                else
+                    rhs_damp = fu
+                end
+                D = InternalAPI.solve!(
+                    cache.damping_fn_cache, jac_damp, rhs_damp, Val(false)
+                )
+                if Utils.can_setindex(cache.J)
+                    copyto!(@view(cache.J[1:size(J, 1), :]), J)
+                    cache.J[(size(J, 1) + 1):end, :] .= sqrt.(D)
+                else
+                    cache.J = Utils.faster_vcat(J, sqrt.(D))
+                end
+            end
+            A = cache.J
+            if Utils.can_setindex(cache.rhs_cache)
+                cache.rhs_cache[1:length(fu)] .= Utils.safe_vec(fu)
+                cache.rhs_cache[(length(fu) + 1):end] .= false
+            else
+                cache.rhs_cache = vcat(Utils.safe_vec(fu), zero(Utils.safe_vec(u)))
+            end
+            b = cache.rhs_cache
+        elseif cache.mode isa Val{:simple}
+            if (J !== nothing || new_jacobian) && recompute_A
+                preinverted_jacobian(cache) && (J = inv(J))
+                D = InternalAPI.solve!(cache.damping_fn_cache, J, fu, Val(false))
+                cache.J = dampen_jacobian!!(cache.J, J, D)
+            end
+            A, b = cache.J, Utils.safe_vec(fu)
+        elseif cache.mode isa Val{:normal_form}
+            if (J !== nothing || new_jacobian) && recompute_A
+                preinverted_jacobian(cache) && (J = inv(J))
+                @bb cache.JᵀJ_cache = transpose(J) × J
+                @bb cache.Jᵀfu_cache = transpose(J) × vec(fu)
+                D = InternalAPI.solve!(
+                    cache.damping_fn_cache, cache.JᵀJ_cache, cache.Jᵀfu_cache, Val(true)
+                )
+                cache.J = dampen_jacobian!!(cache.J, cache.JᵀJ_cache, D)
+                A = Utils.maybe_symmetric(cache.J)
+            elseif !recompute_A
+                @bb cache.Jᵀfu_cache = transpose(J) × vec(fu)
+                A = Utils.maybe_symmetric(cache.J)
+            else
+                A = nothing
+            end
+            b = cache.Jᵀfu_cache
+        else
+            error("Unknown Mode: $(cache.mode).")
+        end
+    end
+
+    @static_timeit cache.timer "linear solve" begin
+        linres = cache.lincache(;
+            A, b,
+            reuse_A_if_factorization = !new_jacobian && !recompute_A,
+            kwargs...,
+            linu = Utils.safe_vec(δu)
+        )
+        δu = Utils.restructure(SciMLBase.get_du(cache, idx), linres.u)
+        if !linres.success
+            set_du!(cache, δu, idx)
+            return DescentResult(; δu, success = false, linsolve_success = false)
+        end
+    end
+
+    @bb @. δu *= -1
+    set_du!(cache, δu, idx)
+    return DescentResult(; δu)
+end
+
+dampen_jacobian!!(::Any, J::Union{AbstractSciMLOperator, Number}, D) = J + D
+function dampen_jacobian!!(J_cache, J::AbstractMatrix, D::Union{AbstractMatrix, Number})
+    ArrayInterface.can_setindex(J_cache) || return J .+ D
+    J_cache !== J && copyto!(J_cache, J)
+    if ArrayInterface.fast_scalar_indexing(J_cache)
+        if D isa Number
+            @simd ivdep for i in axes(J_cache, 1)
+                @inbounds J_cache[i, i] += D
+            end
+        else
+            @simd ivdep for i in axes(J_cache, 1)
+                @inbounds J_cache[i, i] += D[i, i]
+            end
+        end
+    else
+        idxs = diagind(J_cache)
+        if D isa Number
+            J_cache[idxs] .+= D
+        else
+            J_cache[idxs] .+= @view(D[idxs])
+        end
+    end
+    return J_cache
+end
diff --git a/src/descent/dogleg.jl b/lib/NonlinearSolveBase/src/descent/dogleg.jl
similarity index 56%
rename from src/descent/dogleg.jl
rename to lib/NonlinearSolveBase/src/descent/dogleg.jl
index 679f33c26..c138adbde 100644
--- a/src/descent/dogleg.jl
+++ b/lib/NonlinearSolveBase/src/descent/dogleg.jl
@@ -1,5 +1,5 @@
 """
-    Dogleg(; linsolve = nothing, precs = DEFAULT_PRECS)
+    Dogleg(; linsolve = nothing, precs = nothing)
 
 Switch between Newton's method and the steepest descent method depending on the size of the
 trust region. The trust region is specified via keyword argument `trust_region` to
@@ -7,82 +7,94 @@ trust region. The trust region is specified via keyword argument `trust_region`
 
 See also [`SteepestDescent`](@ref), [`NewtonDescent`](@ref), [`DampedNewtonDescent`](@ref).
 """
-@concrete struct Dogleg <: AbstractDescentAlgorithm
-    newton_descent
-    steepest_descent
-end
-
-function Base.show(io::IO, d::Dogleg)
-    print(io,
-        "Dogleg(newton_descent = $(d.newton_descent), steepest_descent = $(d.steepest_descent))")
+@concrete struct Dogleg <: AbstractDescentDirection
+    newton_descent <: Union{NewtonDescent, DampedNewtonDescent}
+    steepest_descent <: SteepestDescent
 end
 
 supports_trust_region(::Dogleg) = true
 get_linear_solver(alg::Dogleg) = get_linear_solver(alg.newton_descent)
 
-function Dogleg(; linsolve = nothing, precs = DEFAULT_PRECS, damping = False,
+function Dogleg(; linsolve = nothing, precs = nothing, damping = Val(false),
         damping_fn = missing, initial_damping = missing, kwargs...)
-    if damping === False
+    if !Utils.unwrap_val(damping)
         return Dogleg(NewtonDescent(; linsolve, precs), SteepestDescent(; linsolve, precs))
     end
     if damping_fn === missing || initial_damping === missing
         throw(ArgumentError("`damping_fn` and `initial_damping` must be supplied if \
                              `damping = Val(true)`."))
     end
-    return Dogleg(DampedNewtonDescent(; linsolve, precs, damping_fn, initial_damping),
-        SteepestDescent(; linsolve, precs))
+    return Dogleg(
+        DampedNewtonDescent(; linsolve, precs, damping_fn, initial_damping),
+        SteepestDescent(; linsolve, precs)
+    )
 end
 
-@concrete mutable struct DoglegCache{pre_inverted, normalform} <: AbstractDescentCache
+@concrete mutable struct DoglegCache <: AbstractDescentCache
     δu
     δus
-    newton_cache
-    cauchy_cache
+    newton_cache <: Union{NewtonDescentCache, DampedNewtonDescentCache}
+    cauchy_cache <: SteepestDescentCache
     internalnorm
-    JᵀJ_cache
+    Jᵀδu_cache
     δu_cache_1
     δu_cache_2
     δu_cache_mul
+    preinverted_jacobian <: Union{Val{false}, Val{true}}
+    normal_form <: Union{Val{false}, Val{true}}
 end
 
-@internal_caches DoglegCache :newton_cache :cauchy_cache
+# XXX: Implement
+# @internal_caches DoglegCache :newton_cache :cauchy_cache
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::Dogleg, J, fu, u;
-        pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, alg::Dogleg, J, fu, u;
+        pre_inverted::Val = Val(false), linsolve_kwargs = (;),
         abstol = nothing, reltol = nothing, internalnorm::F = L2_NORM,
-        shared::Val{N} = Val(1), kwargs...) where {F, INV, N}
-    newton_cache = __internal_init(prob, alg.newton_descent, J, fu, u; pre_inverted,
-        linsolve_kwargs, abstol, reltol, shared, kwargs...)
-    cauchy_cache = __internal_init(prob, alg.steepest_descent, J, fu, u; pre_inverted,
-        linsolve_kwargs, abstol, reltol, shared, kwargs...)
+        shared::Val = Val(1), kwargs...
+) where {F}
+    newton_cache = InternalAPI.init(
+        prob, alg.newton_descent, J, fu, u;
+        pre_inverted, linsolve_kwargs, abstol, reltol, shared, kwargs...
+    )
+    cauchy_cache = InternalAPI.init(
+        prob, alg.steepest_descent, J, fu, u;
+        pre_inverted, linsolve_kwargs, abstol, reltol, shared, kwargs...
+    )
+
     @bb δu = similar(u)
-    δus = N ≤ 1 ? nothing : map(2:N) do i
+    δus = Utils.unwrap_val(shared) ≤ 1 ? nothing : map(2:Utils.unwrap_val(shared)) do i
         @bb δu_ = similar(u)
     end
     @bb δu_cache_1 = similar(u)
     @bb δu_cache_2 = similar(u)
     @bb δu_cache_mul = similar(u)
 
-    T = promote_type(eltype(u), eltype(fu))
-
     normal_form = prob isa NonlinearLeastSquaresProblem &&
-                  NonlinearSolveBase.needs_square_A(alg.newton_descent.linsolve, u)
-    JᵀJ_cache = !normal_form ? J * _vec(δu) : nothing  # TODO: Rename
+                  needs_square_A(alg.newton_descent.linsolve, u)
+
+    Jᵀδu_cache = !normal_form ? J * Utils.safe_vec(δu) : nothing
 
-    return DoglegCache{INV, normal_form}(δu, δus, newton_cache, cauchy_cache, internalnorm,
-        JᵀJ_cache, δu_cache_1, δu_cache_2, δu_cache_mul)
+    return DoglegCache(
+        δu, δus, newton_cache, cauchy_cache, internalnorm, Jᵀδu_cache,
+        δu_cache_1, δu_cache_2, δu_cache_mul, pre_inverted, Val(normal_form)
+    )
 end
 
-# If TrustRegion is not specified, then use a Gauss-Newton step
-function __internal_solve!(cache::DoglegCache{INV, NF}, J, fu, u, idx::Val{N} = Val(1);
-        trust_region = nothing, skip_solve::Bool = false, kwargs...) where {INV, NF, N}
+# If trust_region is not specified, then use a Gauss-Newton step
+function InternalAPI.solve!(
+        cache::DoglegCache, J, fu, u, idx::Val = Val(1);
+        trust_region = nothing, skip_solve::Bool = false, kwargs...
+)
     @assert trust_region!==nothing "Trust Region must be specified for Dogleg. Use \
                                     `NewtonDescent` or `SteepestDescent` if you don't \
                                     want to use a Trust Region."
-    δu = get_du(cache, idx)
+
+    δu = SciMLBase.get_du(cache, idx)
     T = promote_type(eltype(u), eltype(fu))
-    δu_newton = __internal_solve!(
-        cache.newton_cache, J, fu, u, idx; skip_solve, kwargs...).δu
+    δu_newton = InternalAPI.solve!(
+        cache.newton_cache, J, fu, u, idx; skip_solve, kwargs...
+    ).δu
 
     # Newton's Step within the trust region
     if cache.internalnorm(δu_newton) ≤ trust_region
@@ -91,23 +103,24 @@ function __internal_solve!(cache::DoglegCache{INV, NF}, J, fu, u, idx::Val{N} =
         return DescentResult(; δu, extras = (; δuJᵀJδu = T(NaN)))
     end
 
-    # Take intersection of steepest descent direction and trust region if Cauchy point lies
-    # outside of trust region
-    if NF
+    # Take intersection of steepest descent direction and trust region if Cauchy point
+    # lies outside of trust region
+    if normal_form(cache)
         δu_cauchy = cache.newton_cache.Jᵀfu_cache
         JᵀJ = cache.newton_cache.JᵀJ_cache
         @bb @. δu_cauchy *= -1
 
         l_grad = cache.internalnorm(δu_cauchy)
         @bb cache.δu_cache_mul = JᵀJ × vec(δu_cauchy)
-        δuJᵀJδu = __dot(δu_cauchy, cache.δu_cache_mul)
+        δuJᵀJδu = Utils.dot(cache.δu_cache_mul, cache.δu_cache_mul)
     else
-        δu_cauchy = __internal_solve!(
-            cache.cauchy_cache, J, fu, u, idx; skip_solve, kwargs...).δu
-        J_ = INV ? inv(J) : J
+        δu_cauchy = InternalAPI.solve!(
+            cache.cauchy_cache, J, fu, u, idx; skip_solve, kwargs...
+        ).δu
+        J_ = preinverted_jacobian(cache) ? inv(J) : J
         l_grad = cache.internalnorm(δu_cauchy)
-        @bb cache.JᵀJ_cache = J × vec(δu_cauchy)  # TODO: Rename
-        δuJᵀJδu = __dot(cache.JᵀJ_cache, cache.JᵀJ_cache)
+        @bb cache.Jᵀδu_cache = J_ × vec(δu_cauchy)
+        δuJᵀJδu = Utils.dot(cache.Jᵀδu_cache, cache.Jᵀδu_cache)
     end
     d_cauchy = (l_grad^3) / δuJᵀJδu
 
@@ -125,8 +138,8 @@ function __internal_solve!(cache::DoglegCache{INV, NF}, J, fu, u, idx::Val{N} =
     # trust region
     @bb @. cache.δu_cache_1 = (d_cauchy / l_grad) * δu_cauchy
     @bb @. cache.δu_cache_2 = δu_newton - cache.δu_cache_1
-    a = dot(cache.δu_cache_2, cache.δu_cache_2)
-    b = 2 * dot(cache.δu_cache_1, cache.δu_cache_2)
+    a = Utils.safe_dot(cache.δu_cache_2, cache.δu_cache_2)
+    b = 2 * Utils.safe_dot(cache.δu_cache_1, cache.δu_cache_2)
     c = d_cauchy^2 - trust_region^2
     aux = max(0, b^2 - 4 * a * c)
     τ = (-b + sqrt(aux)) / (2 * a)
diff --git a/src/descent/geodesic_acceleration.jl b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
similarity index 55%
rename from src/descent/geodesic_acceleration.jl
rename to lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
index 8e8a305f0..7b7645072 100644
--- a/src/descent/geodesic_acceleration.jl
+++ b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
@@ -24,18 +24,12 @@ for other methods are not theorectically or experimentally verified.
     `α_geodesic = 0.1` is an effective choice. Defaults to `0.75`. See Section 3 of
     [transtrum2012improvements](@citet).
 """
-@concrete struct GeodesicAcceleration <: AbstractDescentAlgorithm
+@concrete struct GeodesicAcceleration <: AbstractDescentDirection
     descent
     finite_diff_step_geodesic
     α
 end
 
-function Base.show(io::IO, alg::GeodesicAcceleration)
-    print(
-        io, "GeodesicAcceleration(descent = $(alg.descent), finite_diff_step_geodesic = ",
-        "$(alg.finite_diff_step_geodesic), α = $(alg.α))")
-end
-
 supports_trust_region(::GeodesicAcceleration) = true
 
 get_linear_solver(alg::GeodesicAcceleration) = get_linear_solver(alg.descent)
@@ -55,78 +49,86 @@ get_linear_solver(alg::GeodesicAcceleration) = get_linear_solver(alg.descent)
     last_step_accepted::Bool
 end
 
-function __reinit_internal!(
-        cache::GeodesicAccelerationCache, args...; p = cache.p, kwargs...)
-    cache.p = p
-    cache.last_step_accepted = false
-end
+# XXX: Implement
+# function __reinit_internal!(
+#         cache::GeodesicAccelerationCache, args...; p = cache.p, kwargs...)
+#     cache.p = p
+#     cache.last_step_accepted = false
+# end
 
-@internal_caches GeodesicAccelerationCache :descent_cache
+# @internal_caches GeodesicAccelerationCache :descent_cache
 
-get_velocity(cache::GeodesicAccelerationCache) = get_du(cache.descent_cache, Val(1))
-function set_velocity!(cache::GeodesicAccelerationCache, δv)
-    set_du!(cache.descent_cache, δv, Val(1))
+function get_velocity(cache::GeodesicAccelerationCache)
+    return SciMLBase.get_du(cache.descent_cache, Val(1))
 end
 function get_velocity(cache::GeodesicAccelerationCache, ::Val{N}) where {N}
-    get_du(cache.descent_cache, Val(2N - 1))
+    return SciMLBase.get_du(cache.descent_cache, Val(2N - 1))
 end
-function set_velocity!(cache::GeodesicAccelerationCache, δv, ::Val{N}) where {N}
-    set_du!(cache.descent_cache, δv, Val(2N - 1))
-end
-get_acceleration(cache::GeodesicAccelerationCache) = get_du(cache.descent_cache, Val(2))
-function set_acceleration!(cache::GeodesicAccelerationCache, δa)
-    set_du!(cache.descent_cache, δa, Val(2))
+function get_acceleration(cache::GeodesicAccelerationCache)
+    return SciMLBase.get_du(cache.descent_cache, Val(2))
 end
 function get_acceleration(cache::GeodesicAccelerationCache, ::Val{N}) where {N}
-    get_du(cache.descent_cache, Val(2N))
-end
-function set_acceleration!(cache::GeodesicAccelerationCache, δa, ::Val{N}) where {N}
-    set_du!(cache.descent_cache, δa, Val(2N))
+    return SciMLBase.get_du(cache.descent_cache, Val(2N))
 end
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::GeodesicAcceleration, J,
-        fu, u; shared::Val{N} = Val(1), pre_inverted::Val{INV} = False,
-        linsolve_kwargs = (;), abstol = nothing, reltol = nothing,
-        internalnorm::F = L2_NORM, kwargs...) where {INV, N, F}
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, alg::GeodesicAcceleration, J, fu, u;
+        shared::Val = Val(1), pre_inverted::Val = Val(false), linsolve_kwargs = (;),
+        abstol = nothing, reltol = nothing,
+        internalnorm::F = L2_NORM, kwargs...
+) where {F}
     T = promote_type(eltype(u), eltype(fu))
     @bb δu = similar(u)
-    δus = N ≤ 1 ? nothing : map(2:N) do i
+    δus = Utils.unwrap_val(shared) ≤ 1 ? nothing : map(2:Utils.unwrap_val(shared)) do i
         @bb δu_ = similar(u)
     end
-    descent_cache = __internal_init(prob, alg.descent, J, fu, u; shared = Val(N * 2),
-        pre_inverted, linsolve_kwargs, abstol, reltol, kwargs...)
+    descent_cache = InternalAPI.init(
+        prob, alg.descent, J, fu, u;
+        shared = Val(2 * Utils.unwrap_val(shared)), pre_inverted, linsolve_kwargs,
+        abstol, reltol,
+        kwargs...
+    )
     @bb Jv = similar(fu)
     @bb fu_cache = copy(fu)
     @bb u_cache = similar(u)
     return GeodesicAccelerationCache(
         δu, δus, descent_cache, prob.f, prob.p, T(alg.α), internalnorm,
-        T(alg.finite_diff_step_geodesic), Jv, fu_cache, u_cache, false)
+        T(alg.finite_diff_step_geodesic), Jv, fu_cache, u_cache, false
+    )
 end
 
-function __internal_solve!(
-        cache::GeodesicAccelerationCache, J, fu, u, idx::Val{N} = Val(1);
-        skip_solve::Bool = false, kwargs...) where {N}
-    a, v, δu = get_acceleration(cache, idx), get_velocity(cache, idx), get_du(cache, idx)
+function InternalAPI.solve!(
+    cache::GeodesicAccelerationCache, J, fu, u, idx::Val = Val(1);
+    skip_solve::Bool = false, kwargs...
+)
+    a = get_acceleration(cache, idx)
+    v = get_velocity(cache, idx)
+    δu = SciMLBase.get_du(cache, idx)
     skip_solve && return DescentResult(; δu, extras = (; a, v))
-    v = __internal_solve!(
-        cache.descent_cache, J, fu, u, Val(2N - 1); skip_solve, kwargs...).δu
+
+    v = InternalAPI.solve!(
+        cache.descent_cache, J, fu, u, Val(2 * Utils.unwrap_val(idx) - 1);
+        skip_solve, kwargs...
+    ).δu
 
     @bb @. cache.u_cache = u + cache.h * v
-    cache.fu_cache = evaluate_f!!(cache.f, cache.fu_cache, cache.u_cache, cache.p)
+    cache.fu_cache = Utils.evaluate_f!!(cache.f, cache.fu_cache, cache.u_cache, cache.p)
 
     J !== nothing && @bb(cache.Jv=J × vec(v))
-    Jv = _restructure(cache.fu_cache, cache.Jv)
+    Jv = Utils.restructure(cache.fu_cache, cache.Jv)
     @bb @. cache.fu_cache = (2 / cache.h) * ((cache.fu_cache - fu) / cache.h - Jv)
 
-    a = __internal_solve!(cache.descent_cache, J, cache.fu_cache, u, Val(2N);
-        skip_solve, kwargs..., reuse_A_if_factorization = true).δu
+    a = InternalAPI.solve!(
+        cache.descent_cache, J, cache.fu_cache, u, Val(2 * Utils.unwrap_val(idx));
+        skip_solve, kwargs..., reuse_A_if_factorization = true
+    ).δu
 
     norm_v = cache.internalnorm(v)
     norm_a = cache.internalnorm(a)
 
     if 2 * norm_a ≤ norm_v * cache.α
         @bb @. δu = v + a / 2
-        set_du!(cache, δu, idx)
+        SciMLBase.set_du!(cache, δu, idx)
         cache.last_step_accepted = true
     else
         cache.last_step_accepted = false
diff --git a/lib/NonlinearSolveBase/src/descent/newton.jl b/lib/NonlinearSolveBase/src/descent/newton.jl
new file mode 100644
index 000000000..1a7acf177
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/descent/newton.jl
@@ -0,0 +1,132 @@
+"""
+    NewtonDescent(; linsolve = nothing, precs = nothing)
+
+Compute the descent direction as ``J δu = -fu``. For non-square Jacobian problems, this is
+commonly referred to as the Gauss-Newton Descent.
+
+See also [`Dogleg`](@ref), [`SteepestDescent`](@ref), [`DampedNewtonDescent`](@ref).
+"""
+@kwdef @concrete struct NewtonDescent <: AbstractDescentDirection
+    linsolve = nothing
+    precs = nothing
+end
+
+supports_line_search(::NewtonDescent) = true
+
+@concrete mutable struct NewtonDescentCache <: AbstractDescentCache
+    δu
+    δus
+    lincache
+    JᵀJ_cache  # For normal form else nothing
+    Jᵀfu_cache
+    timer
+    preinverted_jacobian <: Union{Val{false}, Val{true}}
+    normal_form <: Union{Val{false}, Val{true}}
+end
+
+# XXX: Implement
+# @internal_caches NewtonDescentCache :lincache
+
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, alg::NewtonDescent, J, fu, u; stats,
+        shared = Val(1), pre_inverted::Val = Val(false), linsolve_kwargs = (;),
+        abstol = nothing, reltol = nothing,
+        timer = get_timer_output(), kwargs...
+)
+    @bb δu = similar(u)
+    δus = Utils.unwrap_val(shared) ≤ 1 ? nothing : map(2:Utils.unwrap_val(shared)) do i
+        @bb δu_ = similar(u)
+    end
+    if Utils.unwrap_val(pre_inverted)
+        lincache = nothing
+    else
+        lincache = construct_linear_solver(
+            alg, alg.linsolve, J, Utils.safe_vec(fu), Utils.safe_vec(u);
+            stats, abstol, reltol, linsolve_kwargs...
+        )
+    end
+    return NewtonDescentCache(
+        δu, δus, lincache, nothing, nothing, timer, pre_inverted, Val(false)
+    )
+end
+
+function InternalAPI.init(
+        prob::NonlinearLeastSquaresProblem, alg::NewtonDescent, J, fu, u; stats,
+        shared = Val(1), pre_inverted::Val = Val(false), linsolve_kwargs = (;),
+        abstol = nothing, reltol = nothing,
+        timer = get_timer_output(), kwargs...
+)
+    length(fu) != length(u) &&
+        @assert !Utils.unwrap_val(pre_inverted) "Precomputed Inverse for Non-Square Jacobian doesn't make sense."
+
+    @bb δu = similar(u)
+    δus = Utils.unwrap_val(shared) ≤ 1 ? nothing : map(2:N) do i
+        @bb δu_ = similar(u)
+    end
+
+    normal_form = needs_square_A(alg.linsolve, u)
+    if normal_form
+        JᵀJ = transpose(J) * J
+        Jᵀfu = transpose(J) * Utils.safe_vec(fu)
+        A, b = Utils.maybe_symmetric(JᵀJ), Jᵀfu
+    else
+        JᵀJ, Jᵀfu = nothing, nothing
+        A, b = J, Utils.safe_vec(fu)
+    end
+
+    lincache = construct_linear_solver(
+        alg, alg.linsolve, A, b, Utils.safe_vec(u);
+        stats, abstol, reltol, linsolve_kwargs...
+    )
+
+    return NewtonDescentCache(
+        δu, δus, lincache, JᵀJ, Jᵀfu, timer, pre_inverted, Val(normal_form)
+    )
+end
+
+function InternalAPI.solve!(
+        cache::NewtonDescentCache, J, fu, u, idx::Val = Val(1);
+        skip_solve::Bool = false, new_jacobian::Bool = true, kwargs...
+)
+    δu = SciMLBase.get_du(cache, idx)
+    skip_solve && return DescentResult(; δu)
+
+    if preinverted_jacobian(cache) && !normal_form(cache)
+        @assert J!==nothing "`J` must be provided when `preinverted_jacobian = Val(true)`."
+        @bb δu = J × vec(fu)
+    else
+        if normal_form(cache)
+            @assert !preinverted_jacobian(cache)
+            if idx === Val(1)
+                @bb cache.JᵀJ_cache = transpose(J) × J
+            end
+            @bb cache.Jᵀfu_cache = transpose(J) × vec(fu)
+            @static_timeit cache.timer "linear solve" begin
+                linres = cache.lincache(;
+                    A = Utils.maybe_symmetric(cache.JᵀJ_cache), b = cache.Jᵀfu_cache,
+                    kwargs..., linu = Utils.safe_vec(δu), du = Utils.safe_vec(δu),
+                    reuse_A_if_factorization = !new_jacobian || (idx !== Val(1))
+                )
+            end
+        else
+            @static_timeit cache.timer "linear solve" begin
+                linres = cache.lincache(;
+                    A = J, b = Utils.safe_vec(fu),
+                    kwargs..., linu = Utils.safe_vec(δu), du = Utils.safe_vec(δu),
+                    reuse_A_if_factorization = !new_jacobian || idx !== Val(1)
+                )
+            end
+        end
+        @static_timeit cache.timer "linear solve" begin
+            δu = Utils.restructure(SciMLBase.get_du(cache, idx), linres.u)
+            if !linres.success
+                set_du!(cache, δu, idx)
+                return DescentResult(; δu, success = false, linsolve_success = false)
+            end
+        end
+    end
+
+    @bb @. δu *= -1
+    set_du!(cache, δu, idx)
+    return DescentResult(; δu)
+end
diff --git a/lib/NonlinearSolveBase/src/descent/steepest.jl b/lib/NonlinearSolveBase/src/descent/steepest.jl
new file mode 100644
index 000000000..b29045bd5
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/descent/steepest.jl
@@ -0,0 +1,76 @@
+"""
+    SteepestDescent(; linsolve = nothing, precs = nothing)
+
+Compute the descent direction as ``δu = -Jᵀfu``. The linear solver and preconditioner are
+only used if `J` is provided in the inverted form.
+
+See also [`Dogleg`](@ref), [`NewtonDescent`](@ref), [`DampedNewtonDescent`](@ref).
+"""
+@kwdef @concrete struct SteepestDescent <: AbstractDescentDirection
+    linsolve = nothing
+    precs = nothing
+end
+
+supports_line_search(::SteepestDescent) = true
+
+@concrete mutable struct SteepestDescentCache <: AbstractDescentCache
+    δu
+    δus
+    lincache
+    timer
+    preinverted_jacobian <: Union{Val{false}, Val{true}}
+end
+
+# XXX: Implement
+# @internal_caches SteepestDescentCache :lincache
+
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, alg::SteepestDescent, J, fu, u;
+        stats, shared = Val(1), pre_inverted::Val = Val(false), linsolve_kwargs = (;),
+        abstol = nothing, reltol = nothing,
+        timer = get_timer_output(),
+        kwargs...
+)
+    if Utils.unwrap_val(pre_inverted)
+        @assert length(fu)==length(u) "Non-Square Jacobian Inverse doesn't make sense."
+    end
+    @bb δu = similar(u)
+    δus = Utils.unwrap_val(shared) ≤ 1 ? nothing : map(2:Utils.unwrap_val(shared)) do i
+        @bb δu_ = similar(u)
+    end
+    if Utils.unwrap_val(pre_inverted)
+        lincache = construct_linear_solver(
+            alg, alg.linsolve, transpose(J), Utils.safe_vec(fu), Utils.safe_vec(u);
+            stats, abstol, reltol, linsolve_kwargs...
+        )
+    else
+        lincache = nothing
+    end
+    return SteepestDescentCache(δu, δus, lincache, timer, pre_inverted)
+end
+
+function InternalAPI.solve!(
+        cache::SteepestDescentCache, J, fu, u, idx::Val = Val(1);
+        new_jacobian::Bool = true, kwargs...
+)
+    δu = SciMLBase.get_du(cache, idx)
+    if Utils.unwrap_val(cache.preinverted_jacobian)
+        A = J === nothing ? nothing : transpose(J)
+        linres = cache.lincache(;
+            A, b = Utils.safe_vec(fu), kwargs..., linu = Utils.safe_vec(δu),
+            du = Utils.safe_vec(δu),
+            reuse_A_if_factorization = !new_jacobian || idx !== Val(1)
+        )
+        δu = Utils.restructure(SciMLBase.get_du(cache, idx), linres.u)
+        if !linres.success
+            set_du!(cache, δu, idx)
+            return DescentResult(; δu, success = false, linsolve_success = false)
+        end
+    else
+        @assert J!==nothing "`J` must be provided when `preinverted_jacobian = Val(false)`."
+        @bb δu = transpose(J) × vec(fu)
+    end
+    @bb @. δu *= -1
+    set_du!(cache, δu, idx)
+    return DescentResult(; δu)
+end
diff --git a/lib/NonlinearSolveBase/src/timer_outputs.jl b/lib/NonlinearSolveBase/src/timer_outputs.jl
new file mode 100644
index 000000000..6a65f1bab
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/timer_outputs.jl
@@ -0,0 +1,33 @@
+# Timer Outputs has some overhead, so we only use it if we are debugging
+# Even `@timeit` has overhead so we write our custom version of that using Preferences
+const TIMER_OUTPUTS_ENABLED = @load_preference("enable_timer_outputs", false)
+
+@static if TIMER_OUTPUTS_ENABLED
+    using TimerOutputs: TimerOutput, timer_expr, reset_timer!
+end
+
+function get_timer_output()
+    @static if TIMER_OUTPUTS_ENABLED
+        return TimerOutput()
+    else
+        return nothing
+    end
+end
+
+"""
+    @static_timeit to name expr
+
+Like `TimerOutputs.@timeit_debug` but has zero overhead if `TimerOutputs` is disabled via
+[`NonlinearSolve.disable_timer_outputs()`](@ref).
+"""
+macro static_timeit(to, name, expr)
+    @static if TIMER_OUTPUTS_ENABLED
+        return timer_expr(__module__, false, to, name, expr)
+    else
+        return esc(expr)
+    end
+end
+
+@static if !TIMER_OUTPUTS_ENABLED
+    @inline reset_timer!(::Nothing) = nothing
+end
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 3f14de9ea..628a4e873 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -2,8 +2,11 @@ module Utils
 
 using ArrayInterface: ArrayInterface
 using FastClosures: @closure
-using LinearAlgebra: norm
+using LinearAlgebra: Symmetric, norm, dot
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
+using SciMLOperators: AbstractSciMLOperator
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, NonlinearFunction
+using StaticArraysCore: StaticArray, SArray
 
 using ..NonlinearSolveBase: L2_NORM, Linf_NORM
 
@@ -93,8 +96,52 @@ safe_reshape(x::Number, args...) = x
 safe_reshape(x, args...) = reshape(x, args...)
 
 @generated function safe_getproperty(s::S, ::Val{X}) where {S, X}
-    hasfield(S, X) && return :(getproperty(s, $(X)))
+    hasfield(S, X) && return :(getproperty(s, $(Meta.quot(X))))
     return :(missing)
 end
 
+@generated function safe_vec(v)
+    hasmethod(vec, Tuple{typeof(v)}) || return :(vec(v))
+    return :(v)
+end
+safe_vec(v::Number) = v
+safe_vec(v::AbstractVector) = v
+
+safe_dot(x, y) = dot(safe_vec(x), safe_vec(y))
+
+unwrap_val(x) = x
+unwrap_val(::Val{x}) where {x} = unwrap_val(x)
+
+is_default_value(::Any, ::Symbol, ::Nothing) = true
+is_default_value(::Any, ::Symbol, ::Missing) = true
+is_default_value(::Any, ::Symbol, ::Any) = false
+
+maybe_symmetric(x) = Symmetric(x)
+maybe_symmetric(x::Number) = x
+## LinearSolve with `nothing` doesn't dispatch correctly here
+maybe_symmetric(x::StaticArray) = x # XXX: Can we remove this?
+maybe_symmetric(x::AbstractSciMLOperator) = x
+
+# Define special concatenation for certain Array combinations
+faster_vcat(x, y) = vcat(x, y)
+
+maybe_unaliased(x::Union{Number, SArray}, ::Bool) = x
+function maybe_unaliased(x::AbstractArray, alias::Bool)
+    (alias || !ArrayInterface.can_setindex(typeof(x))) && return x
+    return copy(x)
+end
+maybe_unaliased(x::AbstractSciMLOperator, ::Bool) = x
+
+can_setindex(x) = ArrayInterface.can_setindex(x)
+can_setindex(::Number) = false
+
+evaluate_f!!(prob::AbstractNonlinearProblem, fu, u, p) = evaluate_f!!(prob.f, fu, u, p)
+function evaluate_f!!(f::NonlinearFunction, fu, u, p)
+    if SciMLBase.isinplace(f)
+        f(fu, u, p)
+        return fu
+    end
+    return f(u, p)
+end
+
 end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index a96445320..1bf084db5 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -18,20 +18,37 @@ using LineSearch: LineSearch, AbstractLineSearchCache, LineSearchesJL, NoLineSea
 using LinearSolve: LinearSolve
 using MaybeInplace: @bb
 using NonlinearSolveBase: NonlinearSolveBase,
+                          # ForwardDiff integration support
                           nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution,
                           nonlinearsolve_∂f_∂p, nonlinearsolve_∂f_∂u,
+                          # faster norms
                           L2_NORM,
+                          # termination conditions
                           AbsNormTerminationMode, AbstractNonlinearTerminationMode,
                           AbstractSafeBestNonlinearTerminationMode,
+                          # autodiff selection
                           select_forward_mode_autodiff, select_reverse_mode_autodiff,
                           select_jacobian_autodiff,
-                          construct_linear_solver, construct_jacobian_cache
+                          # helpers for constructing caches
+                          construct_linear_solver, construct_jacobian_cache,
+                          # Descent Directions
+                          DescentResult,
+                          SteepestDescent, NewtonDescent, DampedNewtonDescent, Dogleg,
+                          GeodesicAcceleration,
+                          # Timer Outputs
+                          reset_timer!, @static_timeit
+
 
 # XXX: Remove
-import NonlinearSolveBase: concrete_jac
+import NonlinearSolveBase: InternalAPI, concrete_jac, supports_line_search,
+                           supports_trust_region, set_du!, last_step_accepted,
+                           get_linear_solver,
+                           AbstractDampingFunction, AbstractDampingFunctionCache,
+                           requires_normal_form_jacobian, requires_normal_form_rhs,
+                           returns_norm_form_damping, get_timer_output
 
 using Printf: @printf
-using Preferences: Preferences, @load_preference, @set_preferences!
+using Preferences: Preferences, set_preferences!
 using RecursiveArrayTools: recursivecopy!
 using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, AbstractNonlinearProblem,
                  _unwrap_val, isinplace, NLStats, NonlinearFunction,
@@ -66,13 +83,6 @@ include("abstract_types.jl")
 include("timer_outputs.jl")
 include("internal/helpers.jl")
 
-include("descent/common.jl")
-include("descent/newton.jl")
-include("descent/steepest.jl")
-include("descent/dogleg.jl")
-include("descent/damped_newton.jl")
-include("descent/geodesic_acceleration.jl")
-
 include("internal/termination.jl")
 include("internal/tracing.jl")
 include("internal/approximate_initialization.jl")
@@ -190,9 +200,6 @@ export PETScSNES, CMINPACK
 # Advanced Algorithms -- Without Bells and Whistles
 export GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm, GeneralizedDFSane
 
-# Descent Algorithms
-export NewtonDescent, SteepestDescent, Dogleg, DampedNewtonDescent, GeodesicAcceleration
-
 # Globalization
 ## Line Search Algorithms
 export LineSearch, BackTracking, NoLineSearch, RobustNonMonotoneLineSearch,
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index 0d60ed3bb..a94b2b50e 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -1,110 +1,5 @@
-function __internal_init end
-function __internal_solve! end
-
-"""
-    AbstractDescentAlgorithm
-
-Given the Jacobian `J` and the residual `fu`, this type of algorithm computes the descent
-direction `δu`.
-
-For non-square Jacobian problems, if we need to solve a linear solve problem, we use a least
-squares solver by default, unless the provided `linsolve` can't handle non-square matrices,
-in which case we use the normal form equations ``JᵀJ δu = Jᵀ fu``. Note that this
-factorization is often the faster choice, but it is not as numerically stable as the least
-squares solver.
-
-### `__internal_init` specification
-
-```julia
-__internal_init(prob::NonlinearProblem{uType, iip}, alg::AbstractDescentAlgorithm, J,
-    fu, u; pre_inverted::Val{INV} = Val(false), linsolve_kwargs = (;),
-    abstol = nothing, reltol = nothing, alias_J::Bool = true,
-    shared::Val{N} = Val(1), kwargs...) where {INV, N, uType, iip} --> AbstractDescentCache
-
-__internal_init(
-    prob::NonlinearLeastSquaresProblem{uType, iip}, alg::AbstractDescentAlgorithm,
-    J, fu, u; pre_inverted::Val{INV} = Val(false), linsolve_kwargs = (;),
-    abstol = nothing, reltol = nothing, alias_J::Bool = true,
-    shared::Val{N} = Val(1), kwargs...) where {INV, N, uType, iip} --> AbstractDescentCache
-```
-
-  - `pre_inverted`: whether or not the Jacobian has been pre_inverted. Defaults to `False`.
-    Note that for most algorithms except `NewtonDescent` setting it to `Val(true)` is
-    generally a bad idea.
-  - `linsolve_kwargs`: keyword arguments to pass to the linear solver. Defaults to `(;)`.
-  - `abstol`: absolute tolerance for the linear solver. Defaults to `nothing`.
-  - `reltol`: relative tolerance for the linear solver. Defaults to `nothing`.
-  - `alias_J`: whether or not to alias the Jacobian. Defaults to `true`.
-  - `shared`: Store multiple descent directions in the cache. Allows efficient and correct
-    reuse of factorizations if needed,
-
-Some of the algorithms also allow additional keyword arguments. See the documentation for
-the specific algorithm for more information.
-
-### Interface Functions
-
-  - `supports_trust_region(alg)`: whether or not the algorithm supports trust region
-    methods. Defaults to `false`.
-  - `supports_line_search(alg)`: whether or not the algorithm supports line search
-    methods. Defaults to `false`.
-
-See also [`NewtonDescent`](@ref), [`Dogleg`](@ref), [`SteepestDescent`](@ref),
-[`DampedNewtonDescent`](@ref).
-"""
-abstract type AbstractDescentAlgorithm end
-
-supports_trust_region(::AbstractDescentAlgorithm) = false
-supports_line_search(::AbstractDescentAlgorithm) = false
-
-get_linear_solver(alg::AbstractDescentAlgorithm) = __getproperty(alg, Val(:linsolve))
-
-"""
-    AbstractDescentCache
-
-Abstract Type for all Descent Caches.
-
-### `__internal_solve!` specification
-
-```julia
-descent_result = __internal_solve!(
-    cache::AbstractDescentCache, J, fu, u, idx::Val; skip_solve::Bool = false, kwargs...)
-```
-
-  - `J`: Jacobian or Inverse Jacobian (if `pre_inverted = Val(true)`).
-  - `fu`: residual.
-  - `u`: current state.
-  - `idx`: index of the descent problem to solve and return. Defaults to `Val(1)`.
-  - `skip_solve`: Skip the direction computation and return the previous direction.
-    Defaults to `false`. This is useful for Trust Region Methods where the previous
-    direction was rejected and we want to try with a modified trust region.
-  - `kwargs`: keyword arguments to pass to the linear solver if there is one.
-
-#### Returned values
-
-  - `descent_result`: Result in a [`DescentResult`](@ref).
-
-### Interface Functions
-
-  - `get_du(cache)`: get the descent direction.
-  - `get_du(cache, ::Val{N})`: get the `N`th descent direction.
-  - `set_du!(cache, δu)`: set the descent direction.
-  - `set_du!(cache, δu, ::Val{N})`: set the `N`th descent direction.
-  - `last_step_accepted(cache)`: whether or not the last step was accepted. Checks if the
-    cache has a `last_step_accepted` field and returns it if it does, else returns `true`.
-"""
-abstract type AbstractDescentCache end
-
-SciMLBase.get_du(cache::AbstractDescentCache) = cache.δu
-SciMLBase.get_du(cache::AbstractDescentCache, ::Val{1}) = get_du(cache)
-SciMLBase.get_du(cache::AbstractDescentCache, ::Val{N}) where {N} = cache.δus[N - 1]
-set_du!(cache::AbstractDescentCache, δu) = (cache.δu = δu)
-set_du!(cache::AbstractDescentCache, δu, ::Val{1}) = set_du!(cache, δu)
-set_du!(cache::AbstractDescentCache, δu, ::Val{N}) where {N} = (cache.δus[N - 1] = δu)
-
-function last_step_accepted(cache::AbstractDescentCache)
-    hasfield(typeof(cache), :last_step_accepted) && return cache.last_step_accepted
-    return true
-end
+const __internal_init = InternalAPI.init
+const __internal_solve! = InternalAPI.solve!
 
 """
     AbstractNonlinearSolveAlgorithm{name} <: AbstractNonlinearAlgorithm
@@ -215,63 +110,7 @@ function SciMLBase.reinit!(cache::AbstractNonlinearSolveCache, u0; kwargs...)
     return reinit_cache!(cache; u0, kwargs...)
 end
 
-"""
-    AbstractDampingFunction
-
-Abstract Type for Damping Functions in DampedNewton.
-
-### `__internal_init` specification
-
-```julia
-__internal_init(
-    prob::AbstractNonlinearProblem, f::AbstractDampingFunction, initial_damping,
-    J, fu, u, args...; internal_norm = L2_NORM, kwargs...) --> AbstractDampingFunctionCache
-```
-
-Returns a [`AbstractDampingFunctionCache`](@ref).
-"""
-abstract type AbstractDampingFunction end
-
-"""
-    AbstractDampingFunctionCache
-
-Abstract Type for the Caches created by AbstractDampingFunctions
-
-### Interface Functions
-
-  - `requires_normal_form_jacobian(f)`: whether or not the Jacobian is needed in normal
-    form. No default.
-  - `requires_normal_form_rhs(f)`: whether or not the residual is needed in normal form.
-    No default.
-  - `returns_norm_form_damping(f)`: whether or not the damping function returns the
-    damping factor in normal form. Defaults to `requires_normal_form_jacobian(f) || requires_normal_form_rhs(f)`.
-  - `(cache::AbstractDampingFunctionCache)(::Nothing)`: returns the damping factor. The type
-    of the damping factor returned from `solve!` is guaranteed to be the same as this.
-
-### `__internal_solve!` specification
-
-```julia
-__internal_solve!(cache::AbstractDampingFunctionCache, J, fu, args...; kwargs...)
-```
-
-Returns the damping factor.
-"""
-abstract type AbstractDampingFunctionCache end
-
-function requires_normal_form_jacobian end
-function requires_normal_form_rhs end
-function returns_norm_form_damping(f::F) where {F}
-    return requires_normal_form_jacobian(f) || requires_normal_form_rhs(f)
-end
-
-"""
-    AbstractNonlinearSolveOperator <: AbstractSciMLOperator
-
-NonlinearSolve.jl houses a few custom operators. These will eventually be moved out but till
-then this serves as the abstract type for them.
-"""
-abstract type AbstractNonlinearSolveOperator{T} <: AbstractSciMLOperator{T} end
-
+# XXX: Move to NonlinearSolveQuasiNewton
 # Approximate Jacobian Algorithms
 """
     AbstractApproximateJacobianStructure
@@ -430,15 +269,6 @@ abstract type AbstractTrustRegionMethodCache end
 
 last_step_accepted(cache::AbstractTrustRegionMethodCache) = cache.last_step_accepted
 
-"""
-    AbstractNonlinearSolveJacobianCache{iip} <: Function
-
-Abstract Type for all Jacobian Caches used in NonlinearSolve.jl.
-"""
-abstract type AbstractNonlinearSolveJacobianCache{iip} <: Function end
-
-SciMLBase.isinplace(::AbstractNonlinearSolveJacobianCache{iip}) where {iip} = iip
-
 """
     AbstractNonlinearSolveTraceLevel
 
@@ -454,12 +284,3 @@ SciMLBase.isinplace(::AbstractNonlinearSolveJacobianCache{iip}) where {iip} = ii
     `store_trace == Val(true)`.
 """
 abstract type AbstractNonlinearSolveTraceLevel end
-
-# Default Printing
-for aType in (AbstractTrustRegionMethod, AbstractResetCondition,
-    AbstractApproximateJacobianUpdateRule, AbstractDampingFunction,
-    AbstractNonlinearSolveExtensionAlgorithm)
-    @eval function Base.show(io::IO, alg::$(aType))
-        print(io, "$(nameof(typeof(alg)))()")
-    end
-end
diff --git a/src/algorithms/lbroyden.jl b/src/algorithms/lbroyden.jl
index b6ce5f9b9..bbbc55b28 100644
--- a/src/algorithms/lbroyden.jl
+++ b/src/algorithms/lbroyden.jl
@@ -72,7 +72,7 @@ end
 Low Rank Approximation of the Jacobian Matrix. Currently only used for
 [`LimitedMemoryBroyden`](@ref). This computes the Jacobian as ``U \\times V^T``.
 """
-@concrete mutable struct BroydenLowRankJacobian{T} <: AbstractNonlinearSolveOperator{T}
+@concrete mutable struct BroydenLowRankJacobian{T} <: AbstractSciMLOperator{T}
     U
     Vᵀ
     idx::Int
diff --git a/src/descent/damped_newton.jl b/src/descent/damped_newton.jl
deleted file mode 100644
index f1d2996c9..000000000
--- a/src/descent/damped_newton.jl
+++ /dev/null
@@ -1,256 +0,0 @@
-"""
-    DampedNewtonDescent(; linsolve = nothing, precs = DEFAULT_PRECS, initial_damping,
-        damping_fn)
-
-A Newton descent algorithm with damping. The damping factor is computed using the
-`damping_fn` function. The descent direction is computed as ``(JᵀJ + λDᵀD) δu = -fu``. For
-non-square Jacobians, we default to solving for `Jδx = -fu` and `√λ⋅D δx = 0`
-simultaneously. If the linear solver can't handle non-square matrices, we use the normal
-form equations ``(JᵀJ + λDᵀD) δu = Jᵀ fu``. Note that this factorization is often the faster
-choice, but it is not as numerically stable as the least squares solver.
-
-The damping factor returned must be a non-negative number.
-
-### Keyword Arguments
-
-  - `initial_damping`: The initial damping factor to use
-  - `damping_fn`: The function to use to compute the damping factor. This must satisfy the
-    [`NonlinearSolve.AbstractDampingFunction`](@ref) interface.
-"""
-@kwdef @concrete struct DampedNewtonDescent <: AbstractDescentAlgorithm
-    linsolve = nothing
-    precs = DEFAULT_PRECS
-    initial_damping
-    damping_fn
-end
-
-function Base.show(io::IO, d::DampedNewtonDescent)
-    modifiers = String[]
-    d.linsolve !== nothing && push!(modifiers, "linsolve = $(d.linsolve)")
-    d.precs !== DEFAULT_PRECS && push!(modifiers, "precs = $(d.precs)")
-    push!(modifiers, "initial_damping = $(d.initial_damping)")
-    push!(modifiers, "damping_fn = $(d.damping_fn)")
-    print(io, "DampedNewtonDescent($(join(modifiers, ", ")))")
-end
-
-supports_line_search(::DampedNewtonDescent) = true
-supports_trust_region(::DampedNewtonDescent) = true
-
-@concrete mutable struct DampedNewtonDescentCache{pre_inverted, mode} <:
-                         AbstractDescentCache
-    J
-    δu
-    δus
-    lincache
-    JᵀJ_cache
-    Jᵀfu_cache
-    rhs_cache
-    damping_fn_cache
-    timer
-end
-
-@internal_caches DampedNewtonDescentCache :lincache :damping_fn_cache
-
-function __internal_init(prob::AbstractNonlinearProblem, alg::DampedNewtonDescent, J, fu,
-        u; stats, pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
-        abstol = nothing, timer = get_timer_output(), reltol = nothing,
-        alias_J = true, shared::Val{N} = Val(1), kwargs...) where {INV, N}
-    length(fu) != length(u) &&
-        @assert !INV "Precomputed Inverse for Non-Square Jacobian doesn't make sense."
-    @bb δu = similar(u)
-    δus = N ≤ 1 ? nothing : map(2:N) do i
-        @bb δu_ = similar(u)
-    end
-
-    normal_form_damping = returns_norm_form_damping(alg.damping_fn)
-    normal_form_linsolve = NonlinearSolveBase.needs_square_A(alg.linsolve, u)
-    if u isa Number
-        mode = :simple
-    elseif prob isa NonlinearProblem
-        mode = ifelse(!normal_form_damping, :simple,
-            ifelse(normal_form_linsolve, :normal_form, :least_squares))
-    else
-        if normal_form_linsolve & !normal_form_damping
-            throw(ArgumentError("Linear Solver expects Normal Form but returned Damping is \
-                                 not Normal Form. This is not supported."))
-        end
-        mode = ifelse(normal_form_damping & !normal_form_linsolve, :least_squares,
-            ifelse(!normal_form_damping & !normal_form_linsolve, :simple, :normal_form))
-    end
-
-    if mode === :least_squares
-        if requires_normal_form_jacobian(alg.damping_fn)
-            JᵀJ = transpose(J) * J  # Needed to compute the damping factor
-            jac_damp = JᵀJ
-        else
-            JᵀJ = nothing
-            jac_damp = J
-        end
-        if requires_normal_form_rhs(alg.damping_fn)
-            Jᵀfu = transpose(J) * _vec(fu)
-            rhs_damp = Jᵀfu
-        else
-            Jᵀfu = nothing
-            rhs_damp = fu
-        end
-        damping_fn_cache = __internal_init(prob, alg.damping_fn, alg.initial_damping,
-            jac_damp, rhs_damp, u, False; stats, kwargs...)
-        D = damping_fn_cache(nothing)
-        D isa Number && (D = D * I)
-        rhs_cache = vcat(_vec(fu), _vec(u))
-        J_cache = _vcat(J, D)
-        A, b = J_cache, rhs_cache
-    elseif mode === :simple
-        damping_fn_cache = __internal_init(
-            prob, alg.damping_fn, alg.initial_damping, J, fu, u, False; kwargs...)
-        J_cache = __maybe_unaliased(J, alias_J)
-        D = damping_fn_cache(nothing)
-        J_damped = __dampen_jacobian!!(J_cache, J, D)
-        J_cache = J_damped
-        A, b = J_damped, _vec(fu)
-        JᵀJ, Jᵀfu, rhs_cache = nothing, nothing, nothing
-    elseif mode === :normal_form
-        JᵀJ = transpose(J) * J
-        Jᵀfu = transpose(J) * _vec(fu)
-        jac_damp = requires_normal_form_jacobian(alg.damping_fn) ? JᵀJ : J
-        rhs_damp = requires_normal_form_rhs(alg.damping_fn) ? Jᵀfu : fu
-        damping_fn_cache = __internal_init(prob, alg.damping_fn, alg.initial_damping,
-            jac_damp, rhs_damp, u, True; stats, kwargs...)
-        D = damping_fn_cache(nothing)
-        @bb J_cache = similar(JᵀJ)
-        @bb @. J_cache = 0
-        J_damped = __dampen_jacobian!!(J_cache, JᵀJ, D)
-        A, b = __maybe_symmetric(J_damped), _vec(Jᵀfu)
-        rhs_cache = nothing
-    end
-
-    lincache = construct_linear_solver(
-        alg, alg.linsolve, A, b, _vec(u); stats, abstol, reltol, linsolve_kwargs...)
-
-    return DampedNewtonDescentCache{INV, mode}(
-        J_cache, δu, δus, lincache, JᵀJ, Jᵀfu, rhs_cache, damping_fn_cache, timer)
-end
-
-function __internal_solve!(cache::DampedNewtonDescentCache{INV, mode}, J, fu,
-        u, idx::Val{N} = Val(1); skip_solve::Bool = false,
-        new_jacobian::Bool = true, kwargs...) where {INV, N, mode}
-    δu = get_du(cache, idx)
-    skip_solve && return DescentResult(; δu)
-
-    recompute_A = idx === Val(1)
-
-    @static_timeit cache.timer "dampen" begin
-        if mode === :least_squares
-            if (J !== nothing || new_jacobian) && recompute_A
-                INV && (J = inv(J))
-                if requires_normal_form_jacobian(cache.damping_fn_cache)
-                    @bb cache.JᵀJ_cache = transpose(J) × J
-                    jac_damp = cache.JᵀJ_cache
-                else
-                    jac_damp = J
-                end
-                if requires_normal_form_rhs(cache.damping_fn_cache)
-                    @bb cache.Jᵀfu_cache = transpose(J) × fu
-                    rhs_damp = cache.Jᵀfu_cache
-                else
-                    rhs_damp = fu
-                end
-                D = __internal_solve!(cache.damping_fn_cache, jac_damp, rhs_damp, False)
-                if __can_setindex(cache.J)
-                    copyto!(@view(cache.J[1:size(J, 1), :]), J)
-                    cache.J[(size(J, 1) + 1):end, :] .= sqrt.(D)
-                else
-                    cache.J = _vcat(J, sqrt.(D))
-                end
-            end
-            A = cache.J
-            if __can_setindex(cache.rhs_cache)
-                cache.rhs_cache[1:length(fu)] .= _vec(fu)
-                cache.rhs_cache[(length(fu) + 1):end] .= false
-            else
-                cache.rhs_cache = vcat(_vec(fu), zero(_vec(u)))
-            end
-            b = cache.rhs_cache
-        elseif mode === :simple
-            if (J !== nothing || new_jacobian) && recompute_A
-                INV && (J = inv(J))
-                D = __internal_solve!(cache.damping_fn_cache, J, fu, False)
-                cache.J = __dampen_jacobian!!(cache.J, J, D)
-            end
-            A, b = cache.J, _vec(fu)
-        elseif mode === :normal_form
-            if (J !== nothing || new_jacobian) && recompute_A
-                INV && (J = inv(J))
-                @bb cache.JᵀJ_cache = transpose(J) × J
-                @bb cache.Jᵀfu_cache = transpose(J) × vec(fu)
-                D = __internal_solve!(
-                    cache.damping_fn_cache, cache.JᵀJ_cache, cache.Jᵀfu_cache, True)
-                cache.J = __dampen_jacobian!!(cache.J, cache.JᵀJ_cache, D)
-                A = __maybe_symmetric(cache.J)
-            elseif !recompute_A
-                @bb cache.Jᵀfu_cache = transpose(J) × vec(fu)
-                A = __maybe_symmetric(cache.J)
-            else
-                A = nothing
-            end
-            b = _vec(cache.Jᵀfu_cache)
-        else
-            error("Unknown mode: $(mode)")
-        end
-    end
-
-    @static_timeit cache.timer "linear solve" begin
-        linres = cache.lincache(;
-            A, b, reuse_A_if_factorization = !new_jacobian && !recompute_A,
-            kwargs..., linu = _vec(δu))
-        δu = _restructure(get_du(cache, idx), linres.u)
-        if !linres.success
-            set_du!(cache, δu, idx)
-            return DescentResult(; δu, success = false, linsolve_success = false)
-        end
-    end
-
-    @bb @. δu *= -1
-    set_du!(cache, δu, idx)
-    return DescentResult(; δu)
-end
-
-# Define special concatenation for certain Array combinations
-@inline _vcat(x, y) = vcat(x, y)
-
-# J_cache is allowed to alias J
-## Compute ``J + D``
-@inline __dampen_jacobian!!(J_cache, J::AbstractSciMLOperator, D) = J + D
-@inline __dampen_jacobian!!(J_cache, J::Number, D) = J + D
-@inline function __dampen_jacobian!!(J_cache, J::AbstractMatrix, D::AbstractMatrix)
-    if __can_setindex(J_cache)
-        copyto!(J_cache, J)
-        if fast_scalar_indexing(J_cache)
-            @simd for i in axes(J_cache, 1)
-                @inbounds J_cache[i, i] += D[i, i]
-            end
-        else
-            idxs = diagind(J_cache)
-            J_cache[idxs] .= @view(J[idxs]) .+ @view(D[idxs])
-        end
-        return J_cache
-    else
-        return @. J + D
-    end
-end
-@inline function __dampen_jacobian!!(J_cache, J::AbstractMatrix, D::Number)
-    if __can_setindex(J_cache)
-        copyto!(J_cache, J)
-        if fast_scalar_indexing(J_cache)
-            @simd for i in axes(J_cache, 1)
-                @inbounds J_cache[i, i] += D
-            end
-        else
-            idxs = diagind(J_cache)
-            J_cache[idxs] .= @view(J[idxs]) .+ D
-        end
-        return J_cache
-    else
-        return @. J + D
-    end
-end
diff --git a/src/descent/newton.jl b/src/descent/newton.jl
deleted file mode 100644
index f0964c7dd..000000000
--- a/src/descent/newton.jl
+++ /dev/null
@@ -1,122 +0,0 @@
-"""
-    NewtonDescent(; linsolve = nothing, precs = DEFAULT_PRECS)
-
-Compute the descent direction as ``J δu = -fu``. For non-square Jacobian problems, this is
-commonly referred to as the Gauss-Newton Descent.
-
-See also [`Dogleg`](@ref), [`SteepestDescent`](@ref), [`DampedNewtonDescent`](@ref).
-"""
-@kwdef @concrete struct NewtonDescent <: AbstractDescentAlgorithm
-    linsolve = nothing
-    precs = DEFAULT_PRECS
-end
-
-function Base.show(io::IO, d::NewtonDescent)
-    modifiers = String[]
-    d.linsolve !== nothing && push!(modifiers, "linsolve = $(d.linsolve)")
-    d.precs !== DEFAULT_PRECS && push!(modifiers, "precs = $(d.precs)")
-    print(io, "NewtonDescent($(join(modifiers, ", ")))")
-end
-
-supports_line_search(::NewtonDescent) = true
-
-@concrete mutable struct NewtonDescentCache{pre_inverted, normalform} <:
-                         AbstractDescentCache
-    δu
-    δus
-    lincache
-    JᵀJ_cache  # For normal form else nothing
-    Jᵀfu_cache
-    timer
-end
-
-@internal_caches NewtonDescentCache :lincache
-
-function __internal_init(prob::NonlinearProblem, alg::NewtonDescent, J, fu, u; stats,
-        shared::Val{N} = Val(1), pre_inverted::Val{INV} = False,
-        linsolve_kwargs = (;), abstol = nothing, reltol = nothing,
-        timer = get_timer_output(), kwargs...) where {INV, N}
-    @bb δu = similar(u)
-    δus = N ≤ 1 ? nothing : map(2:N) do i
-        @bb δu_ = similar(u)
-    end
-    INV && return NewtonDescentCache{true, false}(δu, δus, nothing, nothing, nothing, timer)
-    lincache = construct_linear_solver(
-        alg, alg.linsolve, J, _vec(fu), _vec(u); stats, abstol, reltol, linsolve_kwargs...)
-    return NewtonDescentCache{false, false}(δu, δus, lincache, nothing, nothing, timer)
-end
-
-function __internal_init(prob::NonlinearLeastSquaresProblem, alg::NewtonDescent, J, fu,
-        u; stats, pre_inverted::Val{INV} = False, linsolve_kwargs = (;),
-        shared::Val{N} = Val(1), abstol = nothing, reltol = nothing,
-        timer = get_timer_output(), kwargs...) where {INV, N}
-    length(fu) != length(u) &&
-        @assert !INV "Precomputed Inverse for Non-Square Jacobian doesn't make sense."
-
-    normal_form = NonlinearSolveBase.needs_square_A(alg.linsolve, u)
-    if normal_form
-        JᵀJ = transpose(J) * J
-        Jᵀfu = transpose(J) * _vec(fu)
-        A, b = __maybe_symmetric(JᵀJ), Jᵀfu
-    else
-        JᵀJ, Jᵀfu = nothing, nothing
-        A, b = J, _vec(fu)
-    end
-    lincache = construct_linear_solver(
-        alg, alg.linsolve, A, b, _vec(u); stats, abstol, reltol, linsolve_kwargs...)
-    @bb δu = similar(u)
-    δus = N ≤ 1 ? nothing : map(2:N) do i
-        @bb δu_ = similar(u)
-    end
-    return NewtonDescentCache{false, normal_form}(δu, δus, lincache, JᵀJ, Jᵀfu, timer)
-end
-
-function __internal_solve!(
-        cache::NewtonDescentCache{INV, false}, J, fu, u, idx::Val = Val(1);
-        skip_solve::Bool = false, new_jacobian::Bool = true, kwargs...) where {INV}
-    δu = get_du(cache, idx)
-    skip_solve && return DescentResult(; δu)
-    if INV
-        @assert J!==nothing "`J` must be provided when `pre_inverted = Val(true)`."
-        @bb δu = J × vec(fu)
-    else
-        @static_timeit cache.timer "linear solve" begin
-            linres = cache.lincache(;
-                A = J, b = _vec(fu), kwargs..., linu = _vec(δu), du = _vec(δu),
-                reuse_A_if_factorization = !new_jacobian || (idx !== Val(1)))
-            δu = _restructure(get_du(cache, idx), linres.u)
-            if !linres.success
-                set_du!(cache, δu, idx)
-                return DescentResult(; δu, success = false, linsolve_success = false)
-            end
-        end
-    end
-    @bb @. δu *= -1
-    set_du!(cache, δu, idx)
-    return DescentResult(; δu)
-end
-
-function __internal_solve!(
-        cache::NewtonDescentCache{false, true}, J, fu, u, idx::Val = Val(1);
-        skip_solve::Bool = false, new_jacobian::Bool = true, kwargs...)
-    δu = get_du(cache, idx)
-    skip_solve && return DescentResult(; δu)
-    if idx === Val(1)
-        @bb cache.JᵀJ_cache = transpose(J) × J
-    end
-    @bb cache.Jᵀfu_cache = transpose(J) × vec(fu)
-    @static_timeit cache.timer "linear solve" begin
-        linres = cache.lincache(;
-            A = __maybe_symmetric(cache.JᵀJ_cache), b = cache.Jᵀfu_cache,
-            kwargs..., linu = _vec(δu), du = _vec(δu),
-            reuse_A_if_factorization = !new_jacobian || (idx !== Val(1)))
-        δu = _restructure(get_du(cache, idx), linres.u)
-        if !linres.success
-            set_du!(cache, δu, idx)
-            return DescentResult(; δu, success = false, linsolve_success = false)
-        end
-    end
-    @bb @. δu *= -1
-    set_du!(cache, δu, idx)
-    return DescentResult(; δu)
-end
diff --git a/src/descent/steepest.jl b/src/descent/steepest.jl
deleted file mode 100644
index 82b02552d..000000000
--- a/src/descent/steepest.jl
+++ /dev/null
@@ -1,74 +0,0 @@
-"""
-    SteepestDescent(; linsolve = nothing, precs = DEFAULT_PRECS)
-
-Compute the descent direction as ``δu = -Jᵀfu``. The linear solver and preconditioner are
-only used if `J` is provided in the inverted form.
-
-See also [`Dogleg`](@ref), [`NewtonDescent`](@ref), [`DampedNewtonDescent`](@ref).
-"""
-@kwdef @concrete struct SteepestDescent <: AbstractDescentAlgorithm
-    linsolve = nothing
-    precs = DEFAULT_PRECS
-end
-
-function Base.show(io::IO, d::SteepestDescent)
-    modifiers = String[]
-    d.linsolve !== nothing && push!(modifiers, "linsolve = $(d.linsolve)")
-    d.precs !== DEFAULT_PRECS && push!(modifiers, "precs = $(d.precs)")
-    print(io, "SteepestDescent($(join(modifiers, ", ")))")
-end
-
-supports_line_search(::SteepestDescent) = true
-
-@concrete mutable struct SteepestDescentCache{pre_inverted} <: AbstractDescentCache
-    δu
-    δus
-    lincache
-    timer
-end
-
-@internal_caches SteepestDescentCache :lincache
-
-@inline function __internal_init(
-        prob::AbstractNonlinearProblem, alg::SteepestDescent, J, fu, u;
-        stats, shared::Val{N} = Val(1), pre_inverted::Val{INV} = False,
-        linsolve_kwargs = (;), abstol = nothing, reltol = nothing,
-        timer = get_timer_output(), kwargs...) where {INV, N}
-    INV && @assert length(fu)==length(u) "Non-Square Jacobian Inverse doesn't make sense."
-    @bb δu = similar(u)
-    δus = N ≤ 1 ? nothing : map(2:N) do i
-        @bb δu_ = similar(u)
-    end
-    if INV
-        lincache = construct_linear_solver(
-            alg, alg.linsolve, transpose(J), _vec(fu), _vec(u);
-            stats, abstol, reltol, linsolve_kwargs...)
-    else
-        lincache = nothing
-    end
-    return SteepestDescentCache{INV}(δu, δus, lincache, timer)
-end
-
-function __internal_solve!(cache::SteepestDescentCache{INV}, J, fu, u, idx::Val = Val(1);
-        new_jacobian::Bool = true, kwargs...) where {INV}
-    δu = get_du(cache, idx)
-    if INV
-        A = J === nothing ? nothing : transpose(J)
-        @static_timeit cache.timer "linear solve" begin
-            linres = cache.lincache(;
-                A, b = _vec(fu), kwargs..., linu = _vec(δu), du = _vec(δu),
-                reuse_A_if_factorization = !new_jacobian || idx !== Val(1))
-            δu = _restructure(get_du(cache, idx), linres.u)
-            if !linres.success
-                set_du!(cache, δu, idx)
-                return DescentResult(; δu, success = false, linsolve_success = false)
-            end
-        end
-    else
-        @assert J!==nothing "`J` must be provided when `pre_inverted = Val(false)`."
-        @bb δu = transpose(J) × vec(fu)
-    end
-    @bb @. δu *= -1
-    set_du!(cache, δu, idx)
-    return DescentResult(; δu)
-end
diff --git a/src/timer_outputs.jl b/src/timer_outputs.jl
index 510e1d5ed..b28ef01dd 100644
--- a/src/timer_outputs.jl
+++ b/src/timer_outputs.jl
@@ -1,12 +1,3 @@
-# Timer Outputs has some overhead, so we only use it if we are debugging
-# Even `@static_timeit` has overhead so we write our custom version of that using
-# Preferences
-const TIMER_OUTPUTS_ENABLED = @load_preference("enable_timer_outputs", false)
-
-@static if TIMER_OUTPUTS_ENABLED
-    using TimerOutputs
-end
-
 """
     enable_timer_outputs()
 
@@ -14,7 +5,7 @@ Enable `TimerOutput` for all `NonlinearSolve` algorithms. This is useful for deb
 but has some overhead, so it is disabled by default.
 """
 function enable_timer_outputs()
-    @set_preferences!("enable_timer_outputs"=>true)
+    set_preferences!(NonlinearSolveBase, "enable_timer_outputs" => true; force = true)
     @info "Timer Outputs Enabled. Restart the Julia session for this to take effect."
 end
 
@@ -25,32 +16,6 @@ Disable `TimerOutput` for all `NonlinearSolve` algorithms. This should be used w
 `NonlinearSolve` is being used in performance-critical code.
 """
 function disable_timer_outputs()
-    @set_preferences!("enable_timer_outputs"=>false)
+    set_preferences!(NonlinearSolveBase, "enable_timer_outputs" => false; force = true)
     @info "Timer Outputs Disabled. Restart the Julia session for this to take effect."
 end
-
-function get_timer_output()
-    @static if TIMER_OUTPUTS_ENABLED
-        return TimerOutput()
-    else
-        return nothing
-    end
-end
-
-"""
-    @static_timeit to name expr
-
-Like `TimerOutputs.@timeit_debug` but has zero overhead if `TimerOutputs` is disabled via
-[`NonlinearSolve.disable_timer_outputs()`](@ref).
-"""
-macro static_timeit(to, name, expr)
-    @static if TIMER_OUTPUTS_ENABLED
-        return TimerOutputs.timer_expr(__module__, false, to, name, expr)
-    else
-        return esc(expr)
-    end
-end
-
-@static if !TIMER_OUTPUTS_ENABLED
-    @inline reset_timer!(::Nothing) = nothing
-end
diff --git a/src/utils.jl b/src/utils.jl
index af657b0b8..9d44fbaf0 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -23,8 +23,7 @@ end
     (alias || !__can_setindex(typeof(x))) && return x
     return deepcopy(x)
 end
-@inline __maybe_unaliased(x::AbstractNonlinearSolveOperator, alias::Bool) = x
-@inline __maybe_unaliased(x::AbstractJacobianOperator, alias::Bool) = x
+@inline __maybe_unaliased(x::AbstractSciMLOperator, ::Bool) = x
 
 @inline __cond(J::AbstractMatrix) = cond(J)
 @inline __cond(J::SVector) = __cond(Diagonal(MVector(J)))

From 6e4487e2a2f7cb15d3a6a9c9fd4274bc6b29bce1 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 26 Oct 2024 17:10:29 -0400
Subject: [PATCH 633/700] chore: run formatter

---
 .../ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl     | 3 ++-
 .../src/descent/geodesic_acceleration.jl                  | 4 ++--
 src/NonlinearSolve.jl                                     | 8 --------
 3 files changed, 4 insertions(+), 11 deletions(-)

diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl
index e46ef5c37..e2029d7a2 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl
@@ -8,7 +8,8 @@ using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm,
 
 Utils.is_extension_loaded(::Val{:SparseMatrixColorings}) = true
 
-function NonlinearSolveBase.select_fastest_coloring_algorithm(::Val{:SparseMatrixColorings},
+function NonlinearSolveBase.select_fastest_coloring_algorithm(
+        ::Val{:SparseMatrixColorings},
         prototype, f::NonlinearFunction, ad::AbstractADType)
     prototype === nothing && return GreedyColoringAlgorithm(LargestFirst())
     if SciMLBase.has_colorvec(f)
diff --git a/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
index 7b7645072..274fa0600 100644
--- a/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
+++ b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
@@ -98,8 +98,8 @@ function InternalAPI.init(
 end
 
 function InternalAPI.solve!(
-    cache::GeodesicAccelerationCache, J, fu, u, idx::Val = Val(1);
-    skip_solve::Bool = false, kwargs...
+        cache::GeodesicAccelerationCache, J, fu, u, idx::Val = Val(1);
+        skip_solve::Bool = false, kwargs...
 )
     a = get_acceleration(cache, idx)
     v = get_velocity(cache, idx)
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 1bf084db5..5954ff1e3 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -18,27 +18,19 @@ using LineSearch: LineSearch, AbstractLineSearchCache, LineSearchesJL, NoLineSea
 using LinearSolve: LinearSolve
 using MaybeInplace: @bb
 using NonlinearSolveBase: NonlinearSolveBase,
-                          # ForwardDiff integration support
                           nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution,
                           nonlinearsolve_∂f_∂p, nonlinearsolve_∂f_∂u,
-                          # faster norms
                           L2_NORM,
-                          # termination conditions
                           AbsNormTerminationMode, AbstractNonlinearTerminationMode,
                           AbstractSafeBestNonlinearTerminationMode,
-                          # autodiff selection
                           select_forward_mode_autodiff, select_reverse_mode_autodiff,
                           select_jacobian_autodiff,
-                          # helpers for constructing caches
                           construct_linear_solver, construct_jacobian_cache,
-                          # Descent Directions
                           DescentResult,
                           SteepestDescent, NewtonDescent, DampedNewtonDescent, Dogleg,
                           GeodesicAcceleration,
-                          # Timer Outputs
                           reset_timer!, @static_timeit
 
-
 # XXX: Remove
 import NonlinearSolveBase: InternalAPI, concrete_jac, supports_line_search,
                            supports_trust_region, set_du!, last_step_accepted,

From 0ba837ddd1c472d98e5f3f53f81e29d9a6640bb7 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 26 Oct 2024 18:24:02 -0400
Subject: [PATCH 634/700] refactor: make `nothing` the default preconditioner

---
 lib/NonlinearSolveBase/Project.toml          |  2 ++
 lib/NonlinearSolveBase/src/abstract_types.jl |  5 ++++-
 src/NonlinearSolve.jl                        |  8 +++-----
 src/algorithms/gauss_newton.jl               |  4 ++--
 src/algorithms/klement.jl                    |  4 ++--
 src/algorithms/levenberg_marquardt.jl        |  4 ++--
 src/algorithms/pseudo_transient.jl           |  4 ++--
 src/algorithms/raphson.jl                    |  4 ++--
 src/algorithms/trust_region.jl               |  4 ++--
 src/default.jl                               | 12 ++++++------
 src/utils.jl                                 |  3 ---
 test/core/rootfind_tests.jl                  |  4 ++--
 12 files changed, 29 insertions(+), 29 deletions(-)

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 5a8cd1f34..52fdb6aff 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -23,6 +23,7 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
 SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
 TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 
 [weakdeps]
@@ -67,6 +68,7 @@ SciMLOperators = "0.3.10"
 SparseArrays = "1.10"
 SparseMatrixColorings = "0.4.8"
 StaticArraysCore = "1.4"
+SymbolicIndexingInterface = "0.3.31"
 Test = "1.10"
 TimerOutputs = "0.5.23"
 julia = "1.10"
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index 42c57842a..b9bceae76 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -3,6 +3,7 @@ module InternalAPI
 function init end
 function solve! end
 function reinit! end
+function step! end
 
 end
 
@@ -134,6 +135,8 @@ for fname in (:preinverted_jacobian, :normal_form)
     end
 end
 
+
+
 """
     AbstractDampingFunction
 
@@ -145,7 +148,7 @@ Abstract Type for Damping Functions in DampedNewton.
 InternalAPI.init(
     prob::AbstractNonlinearProblem, f::AbstractDampingFunction, initial_damping,
     J, fu, u, args...;
-    internalnorm::F = L2_NORM, kwargs...
+    internalnorm = L2_NORM, kwargs...
 )::AbstractDampingFunctionCache
 ```
 
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 5954ff1e3..dde01d848 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -25,7 +25,7 @@ using NonlinearSolveBase: NonlinearSolveBase,
                           AbstractSafeBestNonlinearTerminationMode,
                           select_forward_mode_autodiff, select_reverse_mode_autodiff,
                           select_jacobian_autodiff,
-                          construct_linear_solver, construct_jacobian_cache,
+                          construct_jacobian_cache,
                           DescentResult,
                           SteepestDescent, NewtonDescent, DampedNewtonDescent, Dogleg,
                           GeodesicAcceleration,
@@ -33,8 +33,7 @@ using NonlinearSolveBase: NonlinearSolveBase,
 
 # XXX: Remove
 import NonlinearSolveBase: InternalAPI, concrete_jac, supports_line_search,
-                           supports_trust_region, set_du!, last_step_accepted,
-                           get_linear_solver,
+                           supports_trust_region, last_step_accepted, get_linear_solver,
                            AbstractDampingFunction, AbstractDampingFunctionCache,
                            requires_normal_form_jacobian, requires_normal_form_rhs,
                            returns_norm_form_damping, get_timer_output
@@ -59,8 +58,7 @@ using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
 using DifferentiationInterface: DifferentiationInterface
 using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff, Dual
-using SciMLJacobianOperators: AbstractJacobianOperator, VecJacOperator,
-                              JacVecOperator, StatefulJacobianOperator
+using SciMLJacobianOperators: VecJacOperator, JacVecOperator, StatefulJacobianOperator
 
 ## Sparse AD Support
 using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
diff --git a/src/algorithms/gauss_newton.jl b/src/algorithms/gauss_newton.jl
index 0f4ec5cd9..0266ee6ed 100644
--- a/src/algorithms/gauss_newton.jl
+++ b/src/algorithms/gauss_newton.jl
@@ -1,5 +1,5 @@
 """
-    GaussNewton(; concrete_jac = nothing, linsolve = nothing, precs = DEFAULT_PRECS,
+    GaussNewton(; concrete_jac = nothing, linsolve = nothing, precs = nothing,
         linesearch = nothing, vjp_autodiff = nothing, autodiff = nothing,
         jvp_autodiff = nothing)
 
@@ -7,7 +7,7 @@ An advanced GaussNewton implementation with support for efficient handling of sp
 matrices via colored automatic differentiation and preconditioned linear solvers. Designed
 for large-scale and numerically-difficult nonlinear least squares problems.
 """
-function GaussNewton(; concrete_jac = nothing, linsolve = nothing, precs = DEFAULT_PRECS,
+function GaussNewton(; concrete_jac = nothing, linsolve = nothing, precs = nothing,
         linesearch = nothing, vjp_autodiff = nothing, autodiff = nothing,
         jvp_autodiff = nothing)
     return GeneralizedFirstOrderAlgorithm{concrete_jac, :GaussNewton}(; linesearch,
diff --git a/src/algorithms/klement.jl b/src/algorithms/klement.jl
index 044a2708d..8e7904fd9 100644
--- a/src/algorithms/klement.jl
+++ b/src/algorithms/klement.jl
@@ -1,6 +1,6 @@
 """
     Klement(; max_resets = 100, linsolve = nothing, linesearch = nothing,
-        precs = DEFAULT_PRECS, alpha = nothing, init_jacobian::Val = Val(:identity),
+        precs = nothing, alpha = nothing, init_jacobian::Val = Val(:identity),
         autodiff = nothing)
 
 An implementation of `Klement` [klement2014using](@citep) with line search, preconditioning
@@ -25,7 +25,7 @@ over this.
         differentiable problems.
 """
 function Klement(; max_resets::Int = 100, linsolve = nothing, alpha = nothing,
-        linesearch = nothing, precs = DEFAULT_PRECS,
+        linesearch = nothing, precs = nothing,
         autodiff = nothing, init_jacobian::Val = Val(:identity))
     initialization = klement_init(init_jacobian, autodiff, alpha)
     CJ = init_jacobian isa Val{:true_jacobian} ||
diff --git a/src/algorithms/levenberg_marquardt.jl b/src/algorithms/levenberg_marquardt.jl
index 24c8a4c05..6dc1845c3 100644
--- a/src/algorithms/levenberg_marquardt.jl
+++ b/src/algorithms/levenberg_marquardt.jl
@@ -1,6 +1,6 @@
 """
     LevenbergMarquardt(; linsolve = nothing,
-        precs = DEFAULT_PRECS, damping_initial::Real = 1.0, α_geodesic::Real = 0.75,
+        precs = nothing, damping_initial::Real = 1.0, α_geodesic::Real = 0.75,
         damping_increase_factor::Real = 2.0, damping_decrease_factor::Real = 3.0,
         finite_diff_step_geodesic = 0.1, b_uphill::Real = 1.0, autodiff = nothing,
         min_damping_D::Real = 1e-8, disable_geodesic = Val(false), vjp_autodiff = nothing,
@@ -32,7 +32,7 @@ For the remaining arguments, see [`GeodesicAcceleration`](@ref) and
 [`NonlinearSolve.LevenbergMarquardtTrustRegion`](@ref) documentations.
 """
 function LevenbergMarquardt(;
-        linsolve = nothing, precs = DEFAULT_PRECS, damping_initial::Real = 1.0,
+        linsolve = nothing, precs = nothing, damping_initial::Real = 1.0,
         α_geodesic::Real = 0.75, damping_increase_factor::Real = 2.0,
         damping_decrease_factor::Real = 3.0, finite_diff_step_geodesic = 0.1,
         b_uphill::Real = 1.0, min_damping_D::Real = 1e-8, disable_geodesic = False,
diff --git a/src/algorithms/pseudo_transient.jl b/src/algorithms/pseudo_transient.jl
index 1e6b94763..a29a25154 100644
--- a/src/algorithms/pseudo_transient.jl
+++ b/src/algorithms/pseudo_transient.jl
@@ -1,6 +1,6 @@
 """
     PseudoTransient(; concrete_jac = nothing, linsolve = nothing,
-        linesearch = NoLineSearch(), precs = DEFAULT_PRECS, autodiff = nothing,
+        linesearch = NoLineSearch(), precs = nothing, autodiff = nothing,
         jvp_autodiff = nothing, vjp_autodiff = nothing)
 
 An implementation of PseudoTransient Method [coffey2003pseudotransient](@cite) that is used
@@ -17,7 +17,7 @@ This implementation specifically uses "switched evolution relaxation"
 """
 function PseudoTransient(;
         concrete_jac = nothing, linsolve = nothing, linesearch = nothing,
-        precs = DEFAULT_PRECS, alpha_initial = 1e-3, autodiff = nothing,
+        precs = nothing, alpha_initial = 1e-3, autodiff = nothing,
         jvp_autodiff = nothing, vjp_autodiff = nothing)
     descent = DampedNewtonDescent(; linsolve, precs, initial_damping = alpha_initial,
         damping_fn = SwitchedEvolutionRelaxation())
diff --git a/src/algorithms/raphson.jl b/src/algorithms/raphson.jl
index e5dee4c91..130e27f92 100644
--- a/src/algorithms/raphson.jl
+++ b/src/algorithms/raphson.jl
@@ -1,6 +1,6 @@
 """
     NewtonRaphson(; concrete_jac = nothing, linsolve = nothing, linesearch = missing,
-        precs = DEFAULT_PRECS, autodiff = nothing, vjp_autodiff = nothing,
+        precs = nothing, autodiff = nothing, vjp_autodiff = nothing,
         jvp_autodiff = nothing)
 
 An advanced NewtonRaphson implementation with support for efficient handling of sparse
@@ -8,7 +8,7 @@ matrices via colored automatic differentiation and preconditioned linear solvers
 for large-scale and numerically-difficult nonlinear systems.
 """
 function NewtonRaphson(; concrete_jac = nothing, linsolve = nothing, linesearch = nothing,
-        precs = DEFAULT_PRECS, autodiff = nothing, vjp_autodiff = nothing,
+        precs = nothing, autodiff = nothing, vjp_autodiff = nothing,
         jvp_autodiff = nothing)
     return GeneralizedFirstOrderAlgorithm{concrete_jac, :NewtonRaphson}(; linesearch,
         descent = NewtonDescent(; linsolve, precs), autodiff, vjp_autodiff, jvp_autodiff)
diff --git a/src/algorithms/trust_region.jl b/src/algorithms/trust_region.jl
index dab6843e8..b42099d46 100644
--- a/src/algorithms/trust_region.jl
+++ b/src/algorithms/trust_region.jl
@@ -1,5 +1,5 @@
 """
-    TrustRegion(; concrete_jac = nothing, linsolve = nothing, precs = DEFAULT_PRECS,
+    TrustRegion(; concrete_jac = nothing, linsolve = nothing, precs = nothing,
         radius_update_scheme = RadiusUpdateSchemes.Simple, max_trust_radius::Real = 0 // 1,
         initial_trust_radius::Real = 0 // 1, step_threshold::Real = 1 // 10000,
         shrink_threshold::Real = 1 // 4, expand_threshold::Real = 3 // 4,
@@ -20,7 +20,7 @@ for large-scale and numerically-difficult nonlinear systems.
 For the remaining arguments, see [`NonlinearSolve.GenericTrustRegionScheme`](@ref)
 documentation.
 """
-function TrustRegion(; concrete_jac = nothing, linsolve = nothing, precs = DEFAULT_PRECS,
+function TrustRegion(; concrete_jac = nothing, linsolve = nothing, precs = nothing,
         radius_update_scheme = RadiusUpdateSchemes.Simple, max_trust_radius::Real = 0 // 1,
         initial_trust_radius::Real = 0 // 1, step_threshold::Real = 1 // 10000,
         shrink_threshold::Real = 1 // 4, expand_threshold::Real = 3 // 4,
diff --git a/src/default.jl b/src/default.jl
index a7cc550d8..7302d95a9 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -338,7 +338,7 @@ end
 
 """
     RobustMultiNewton(::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
-        precs = DEFAULT_PRECS, autodiff = nothing)
+        precs = nothing, autodiff = nothing)
 
 A polyalgorithm focused on robustness. It uses a mixture of Newton methods with different
 globalizing techniques (trust region updates, line searches, etc.) in order to find a
@@ -354,7 +354,7 @@ or more precision / more stable linear solver choice is required).
     are compatible with the problem type. Defaults to `Float64`.
 """
 function RobustMultiNewton(::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
-        precs = DEFAULT_PRECS, autodiff = nothing) where {T}
+        precs = nothing, autodiff = nothing) where {T}
     if __is_complex(T)
         # Let's atleast have something here for complex numbers
         algs = (NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),)
@@ -375,7 +375,7 @@ end
 
 """
     FastShortcutNonlinearPolyalg(::Type{T} = Float64; concrete_jac = nothing,
-        linsolve = nothing, precs = DEFAULT_PRECS, must_use_jacobian::Val = Val(false),
+        linsolve = nothing, precs = nothing, must_use_jacobian::Val = Val(false),
         prefer_simplenonlinearsolve::Val{SA} = Val(false), autodiff = nothing,
         u0_len::Union{Int, Nothing} = nothing) where {T}
 
@@ -395,7 +395,7 @@ for more performance and then tries more robust techniques if the faster ones fa
 """
 function FastShortcutNonlinearPolyalg(
         ::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
-        precs = DEFAULT_PRECS, must_use_jacobian::Val{JAC} = Val(false),
+        precs = nothing, must_use_jacobian::Val{JAC} = Val(false),
         prefer_simplenonlinearsolve::Val{SA} = Val(false),
         u0_len::Union{Int, Nothing} = nothing, autodiff = nothing) where {T, JAC, SA}
     start_index = 1
@@ -457,7 +457,7 @@ end
 
 """
     FastShortcutNLLSPolyalg(::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
-        precs = DEFAULT_PRECS, autodiff = nothing, kwargs...)
+        precs = nothing, autodiff = nothing, kwargs...)
 
 A polyalgorithm focused on balancing speed and robustness. It first tries less robust methods
 for more performance and then tries more robust techniques if the faster ones fail.
@@ -469,7 +469,7 @@ for more performance and then tries more robust techniques if the faster ones fa
 """
 function FastShortcutNLLSPolyalg(
         ::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
-        precs = DEFAULT_PRECS, autodiff = nothing, kwargs...) where {T}
+        precs = nothing, autodiff = nothing, kwargs...) where {T}
     if __is_complex(T)
         algs = (GaussNewton(; concrete_jac, linsolve, precs, autodiff, kwargs...),
             LevenbergMarquardt(;
diff --git a/src/utils.jl b/src/utils.jl
index 9d44fbaf0..fd9dd8b8a 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -1,6 +1,3 @@
-# Defaults
-@inline DEFAULT_PRECS(W, du, u, p, t, newW, Plprev, Prprev, cachedata) = nothing, nothing
-
 # Helper  Functions
 @generated function __getproperty(s::S, ::Val{X}) where {S, X}
     hasfield(S, X) && return :(s.$X)
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index 2d1662570..fc64adf0b 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -96,7 +96,7 @@ end
             @test (@ballocated solve!($cache)) < 200
         end
 
-        precs = [(u0) -> NonlinearSolve.DEFAULT_PRECS,
+        precs = [(u0) -> nothing,
             u0 -> ((args...) -> (Diagonal(rand!(similar(u0))), nothing))]
 
         @testset "[IIP] u0: $(typeof(u0)) precs: $(_nameof(prec)) linsolve: $(_nameof(linsolve))" for u0 in ([
@@ -437,7 +437,7 @@ end
             @test (@ballocated solve!($cache)) < 200
         end
 
-        precs = [NonlinearSolve.DEFAULT_PRECS, :Random]
+        precs = [nothing, :Random]
 
         @testset "[IIP] u0: $(typeof(u0)) precs: $(_nameof(prec)) linsolve: $(_nameof(linsolve))" for u0 in ([
                 1.0, 1.0],),

From 03527f9381d0bf0e860d767c5fdb6088b21c9fe3 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 26 Oct 2024 18:28:52 -0400
Subject: [PATCH 635/700] fix: move the `BandedArrays` extension

---
 Project.toml                                     |  2 --
 ext/NonlinearSolveBandedMatricesExt.jl           | 11 -----------
 lib/NonlinearSolveBase/Project.toml              |  3 +++
 .../ext/NonlinearSolveBaseBandedMatricesExt.jl   | 16 ++++++++++++++++
 .../ext/NonlinearSolveBaseSparseArraysExt.jl     |  4 +++-
 lib/NonlinearSolveBase/src/abstract_types.jl     |  2 --
 lib/NonlinearSolveBase/src/utils.jl              |  2 ++
 7 files changed, 24 insertions(+), 16 deletions(-)
 delete mode 100644 ext/NonlinearSolveBandedMatricesExt.jl
 create mode 100644 lib/NonlinearSolveBase/ext/NonlinearSolveBaseBandedMatricesExt.jl

diff --git a/Project.toml b/Project.toml
index 50a7a8d4f..dc11fdf80 100644
--- a/Project.toml
+++ b/Project.toml
@@ -35,7 +35,6 @@ SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
 TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 
 [weakdeps]
-BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 FastLevenbergMarquardt = "7a0df574-e128-4d35-8cbd-3d84502bf7ce"
 FixedPointAcceleration = "817d07cb-a79a-5c30-9a31-890123675176"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
@@ -50,7 +49,6 @@ SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
 Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"
 
 [extensions]
-NonlinearSolveBandedMatricesExt = "BandedMatrices"
 NonlinearSolveFastLevenbergMarquardtExt = "FastLevenbergMarquardt"
 NonlinearSolveFixedPointAccelerationExt = "FixedPointAcceleration"
 NonlinearSolveLeastSquaresOptimExt = "LeastSquaresOptim"
diff --git a/ext/NonlinearSolveBandedMatricesExt.jl b/ext/NonlinearSolveBandedMatricesExt.jl
deleted file mode 100644
index b79df3578..000000000
--- a/ext/NonlinearSolveBandedMatricesExt.jl
+++ /dev/null
@@ -1,11 +0,0 @@
-module NonlinearSolveBandedMatricesExt
-
-using BandedMatrices: BandedMatrix
-using LinearAlgebra: Diagonal
-using NonlinearSolve: NonlinearSolve
-using SparseArrays: sparse
-
-# This is used if we vcat a Banded Jacobian with a Diagonal Matrix in Levenberg
-@inline NonlinearSolve._vcat(B::BandedMatrix, D::Diagonal) = vcat(sparse(B), D)
-
-end
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 52fdb6aff..31f14f3b9 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -27,6 +27,7 @@ SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
 TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 
 [weakdeps]
+BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
@@ -34,6 +35,7 @@ SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseMatrixColorings = "0a514795-09f3-496d-8182-132a7b665d35"
 
 [extensions]
+NonlinearSolveBaseBandedMatricesExt = "BandedMatrices"
 NonlinearSolveBaseDiffEqBaseExt = "DiffEqBase"
 NonlinearSolveBaseForwardDiffExt = "ForwardDiff"
 NonlinearSolveBaseLinearSolveExt = "LinearSolve"
@@ -45,6 +47,7 @@ ADTypes = "1.9"
 Adapt = "4.1.0"
 Aqua = "0.8.7"
 ArrayInterface = "7.9"
+BandedMatrices = "1.5"
 CommonSolve = "0.2.4"
 Compat = "4.15"
 ConcreteStructs = "0.2.3"
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseBandedMatricesExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseBandedMatricesExt.jl
new file mode 100644
index 000000000..7f2ac7f90
--- /dev/null
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseBandedMatricesExt.jl
@@ -0,0 +1,16 @@
+module NonlinearSolveBaseBandedMatricesExt
+
+using BandedMatrices: BandedMatrix
+using LinearAlgebra: Diagonal
+using NonlinearSolveBase: NonlinearSolveBase, Utils
+
+# This is used if we vcat a Banded Jacobian with a Diagonal Matrix in Levenberg
+@inline function Utils.faster_vcat(B::BandedMatrix, D::Diagonal)
+    if Utils.is_extension_loaded(Val(:SparseArrays))
+        @warn "Load `SparseArrays` for an optimized vcat for BandedMatrices."
+        return vcat(B, D)
+    end
+    return vcat(Utils.make_sparse(B), D)
+end
+
+end
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
index fca3793ad..9ffadf3a1 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
@@ -1,7 +1,7 @@
 module NonlinearSolveBaseSparseArraysExt
 
 using NonlinearSolveBase: NonlinearSolveBase, Utils
-using SparseArrays: AbstractSparseMatrix, AbstractSparseMatrixCSC, nonzeros
+using SparseArrays: AbstractSparseMatrix, AbstractSparseMatrixCSC, nonzeros, sparse
 
 function NonlinearSolveBase.NAN_CHECK(x::AbstractSparseMatrixCSC)
     return any(NonlinearSolveBase.NAN_CHECK, nonzeros(x))
@@ -11,4 +11,6 @@ NonlinearSolveBase.sparse_or_structured_prototype(::AbstractSparseMatrix) = true
 
 Utils.maybe_symmetric(x::AbstractSparseMatrix) = x
 
+Utils.make_sparse(x) = sparse(x)
+
 end
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index b9bceae76..44a52c093 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -135,8 +135,6 @@ for fname in (:preinverted_jacobian, :normal_form)
     end
 end
 
-
-
 """
     AbstractDampingFunction
 
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 628a4e873..14e6b1faa 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -144,4 +144,6 @@ function evaluate_f!!(f::NonlinearFunction, fu, u, p)
     return f(u, p)
 end
 
+function make_sparse end
+
 end

From 5ca1074486e014bca879f400730abc5071b6bac7 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sat, 26 Oct 2024 20:18:12 -0400
Subject: [PATCH 636/700] chore: setup subprojects

---
 lib/NonlinearSolveFirstOrder/LICENSE          | 21 +++++++++++++
 lib/NonlinearSolveFirstOrder/Project.toml     | 30 +++++++++++++++++++
 .../src/NonlinearSolveFirstOrder.jl           |  3 ++
 lib/NonlinearSolveFirstOrder/test/runtests.jl |  0
 lib/NonlinearSolveQuasiNewton/LICENSE         | 21 +++++++++++++
 lib/NonlinearSolveQuasiNewton/Project.toml    | 30 +++++++++++++++++++
 .../src/NonlinearSolveQuasiNewton.jl          |  3 ++
 .../test/runtests.jl                          |  0
 lib/NonlinearSolveSpectralMethods/LICENSE     | 21 +++++++++++++
 .../Project.toml                              | 30 +++++++++++++++++++
 .../src/NonlinearSolveSpectralMethods.jl      |  3 ++
 .../test/runtests.jl                          |  0
 12 files changed, 162 insertions(+)
 create mode 100644 lib/NonlinearSolveFirstOrder/LICENSE
 create mode 100644 lib/NonlinearSolveFirstOrder/Project.toml
 create mode 100644 lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
 create mode 100644 lib/NonlinearSolveFirstOrder/test/runtests.jl
 create mode 100644 lib/NonlinearSolveQuasiNewton/LICENSE
 create mode 100644 lib/NonlinearSolveQuasiNewton/Project.toml
 create mode 100644 lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
 create mode 100644 lib/NonlinearSolveQuasiNewton/test/runtests.jl
 create mode 100644 lib/NonlinearSolveSpectralMethods/LICENSE
 create mode 100644 lib/NonlinearSolveSpectralMethods/Project.toml
 create mode 100644 lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
 create mode 100644 lib/NonlinearSolveSpectralMethods/test/runtests.jl

diff --git a/lib/NonlinearSolveFirstOrder/LICENSE b/lib/NonlinearSolveFirstOrder/LICENSE
new file mode 100644
index 000000000..46c972b17
--- /dev/null
+++ b/lib/NonlinearSolveFirstOrder/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2024 Avik Pal
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
new file mode 100644
index 000000000..21177218a
--- /dev/null
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -0,0 +1,30 @@
+name = "NonlinearSolveFirstOrder"
+uuid = "5959db7a-ea39-4486-b5fe-2dd0bf03d60d"
+authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
+version = "1.0.0"
+
+[compat]
+Aqua = "0.8"
+ExplicitImports = "1.5"
+Hwloc = "3"
+InteractiveUtils = "<0.0.1, 1"
+NonlinearProblemLibrary = "0.1.2"
+Pkg = "1.10"
+ReTestItems = "1.24"
+StableRNGs = "1"
+Test = "1.10"
+julia = "1.10"
+
+[extras]
+Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
+Hwloc = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
+Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[targets]
+test = ["Aqua", "ExplicitImports", "Hwloc", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "ReTestItems", "StableRNGs", "Test"]
diff --git a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
new file mode 100644
index 000000000..f07882cc2
--- /dev/null
+++ b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
@@ -0,0 +1,3 @@
+module NonlinearSolveFirstOrder
+
+end
diff --git a/lib/NonlinearSolveFirstOrder/test/runtests.jl b/lib/NonlinearSolveFirstOrder/test/runtests.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/NonlinearSolveQuasiNewton/LICENSE b/lib/NonlinearSolveQuasiNewton/LICENSE
new file mode 100644
index 000000000..46c972b17
--- /dev/null
+++ b/lib/NonlinearSolveQuasiNewton/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2024 Avik Pal
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/lib/NonlinearSolveQuasiNewton/Project.toml b/lib/NonlinearSolveQuasiNewton/Project.toml
new file mode 100644
index 000000000..92fbd9bde
--- /dev/null
+++ b/lib/NonlinearSolveQuasiNewton/Project.toml
@@ -0,0 +1,30 @@
+name = "NonlinearSolveQuasiNewton"
+uuid = "9a2c21bd-3a47-402d-9113-8faf9a0ee114"
+authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
+version = "1.0.0"
+
+[compat]
+Aqua = "0.8"
+ExplicitImports = "1.5"
+Hwloc = "3"
+InteractiveUtils = "<0.0.1, 1"
+NonlinearProblemLibrary = "0.1.2"
+Pkg = "1.10"
+ReTestItems = "1.24"
+StableRNGs = "1"
+Test = "1.10"
+julia = "1.10"
+
+[extras]
+Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
+Hwloc = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
+Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[targets]
+test = ["Aqua", "ExplicitImports", "Hwloc", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "ReTestItems", "StableRNGs", "Test"]
diff --git a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
new file mode 100644
index 000000000..91cb46015
--- /dev/null
+++ b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
@@ -0,0 +1,3 @@
+module NonlinearSolveQuasiNewton
+
+end
diff --git a/lib/NonlinearSolveQuasiNewton/test/runtests.jl b/lib/NonlinearSolveQuasiNewton/test/runtests.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/NonlinearSolveSpectralMethods/LICENSE b/lib/NonlinearSolveSpectralMethods/LICENSE
new file mode 100644
index 000000000..46c972b17
--- /dev/null
+++ b/lib/NonlinearSolveSpectralMethods/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2024 Avik Pal
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/lib/NonlinearSolveSpectralMethods/Project.toml b/lib/NonlinearSolveSpectralMethods/Project.toml
new file mode 100644
index 000000000..dafa10841
--- /dev/null
+++ b/lib/NonlinearSolveSpectralMethods/Project.toml
@@ -0,0 +1,30 @@
+name = "NonlinearSolveSpectralMethods"
+uuid = "26075421-4e9a-44e1-8bd1-420ed7ad02b2"
+authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
+version = "1.0.0"
+
+[compat]
+Aqua = "0.8"
+ExplicitImports = "1.5"
+Hwloc = "3"
+InteractiveUtils = "<0.0.1, 1"
+NonlinearProblemLibrary = "0.1.2"
+Pkg = "1.10"
+ReTestItems = "1.24"
+StableRNGs = "1"
+Test = "1.10"
+julia = "1.10"
+
+[extras]
+Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
+Hwloc = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
+Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[targets]
+test = ["Aqua", "ExplicitImports", "Hwloc", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "ReTestItems", "StableRNGs", "Test"]
diff --git a/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl b/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
new file mode 100644
index 000000000..3b0c67477
--- /dev/null
+++ b/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
@@ -0,0 +1,3 @@
+module NonlinearSolveSpectralMethods
+
+end
diff --git a/lib/NonlinearSolveSpectralMethods/test/runtests.jl b/lib/NonlinearSolveSpectralMethods/test/runtests.jl
new file mode 100644
index 000000000..e69de29bb

From a30f80b40f368d6169a0053da605d5e57080e843 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 27 Oct 2024 13:49:08 -0400
Subject: [PATCH 637/700] refactor: move tracing functionality to
 NonlinearSolveBase

---
 ext/NonlinearSolveLeastSquaresOptimExt.jl     |   4 +-
 ext/NonlinearSolveNLsolveExt.jl               |   6 +-
 lib/NonlinearSolveBase/Project.toml           |   2 +
 .../ext/NonlinearSolveBaseSparseArraysExt.jl  |   4 +
 .../src/NonlinearSolveBase.jl                 |   4 +
 lib/NonlinearSolveBase/src/abstract_types.jl  |   3 +
 lib/NonlinearSolveBase/src/tracing.jl         | 224 ++++++++++++++++++
 lib/NonlinearSolveBase/src/utils.jl           |  45 +++-
 src/NonlinearSolve.jl                         |   6 +-
 src/internal/tracing.jl                       | 217 -----------------
 src/utils.jl                                  |   7 -
 11 files changed, 289 insertions(+), 233 deletions(-)
 create mode 100644 lib/NonlinearSolveBase/src/tracing.jl
 delete mode 100644 src/internal/tracing.jl

diff --git a/ext/NonlinearSolveLeastSquaresOptimExt.jl b/ext/NonlinearSolveLeastSquaresOptimExt.jl
index 20dac092d..51563eb83 100644
--- a/ext/NonlinearSolveLeastSquaresOptimExt.jl
+++ b/ext/NonlinearSolveLeastSquaresOptimExt.jl
@@ -2,8 +2,8 @@ module NonlinearSolveLeastSquaresOptimExt
 
 using ConcreteStructs: @concrete
 using LeastSquaresOptim: LeastSquaresOptim
-using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
-using NonlinearSolve: NonlinearSolve, LeastSquaresOptimJL, TraceMinimal
+using NonlinearSolveBase: NonlinearSolveBase, TraceMinimal, get_tolerance
+using NonlinearSolve: NonlinearSolve, LeastSquaresOptimJL
 using SciMLBase: SciMLBase, NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode
 
 const LSO = LeastSquaresOptim
diff --git a/ext/NonlinearSolveNLsolveExt.jl b/ext/NonlinearSolveNLsolveExt.jl
index 73d98c062..49c1f337a 100644
--- a/ext/NonlinearSolveNLsolveExt.jl
+++ b/ext/NonlinearSolveNLsolveExt.jl
@@ -1,8 +1,8 @@
 module NonlinearSolveNLsolveExt
 
 using LineSearches: Static
-using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
-using NonlinearSolve: NonlinearSolve, NLsolveJL, TraceMinimal
+using NonlinearSolveBase: NonlinearSolveBase, TraceMinimal, get_tolerance
+using NonlinearSolve: NonlinearSolve, NLsolveJL
 using NLsolve: NLsolve, OnceDifferentiable, nlsolve
 using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
 
@@ -32,7 +32,7 @@ function SciMLBase.__solve(
     abstol = get_tolerance(abstol, eltype(u0))
     show_trace = ShT
     store_trace = StT
-    extended_trace = !(trace_level isa TraceMinimal)
+    extended_trace = !(trace_level.trace_mode isa Val{:minimal})
 
     linesearch = alg.linesearch === missing ? Static() : alg.linesearch
 
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 31f14f3b9..46f9df83a 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -18,6 +18,7 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 Preferences = "21216c6a-2e73-6563-6e65-726566657250"
+Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
@@ -64,6 +65,7 @@ LinearSolve = "2.36.1"
 Markdown = "1.10"
 MaybeInplace = "0.1.4"
 Preferences = "1.4"
+Printf = "1.10"
 RecursiveArrayTools = "3"
 SciMLBase = "2.50"
 SciMLJacobianOperators = "0.1.1"
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
index 9ffadf3a1..6d60761d2 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
@@ -13,4 +13,8 @@ Utils.maybe_symmetric(x::AbstractSparseMatrix) = x
 
 Utils.make_sparse(x) = sparse(x)
 
+Utils.condition_number(J::AbstractSparseMatrix) = Utils.condition_number(Matrix(J))
+
+Utils.maybe_pinv!!_workspace(A::AbstractSparseMatrix) = Matrix(A)
+
 end
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 5007763b2..75afb746e 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -15,6 +15,7 @@ using LinearAlgebra: LinearAlgebra, Diagonal, norm, ldiv!, diagind
 using Markdown: @doc_str
 using MaybeInplace: @bb
 using Preferences: @load_preference
+using Printf: @printf
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinearProblem,
                  AbstractNonlinearAlgorithm, AbstractNonlinearFunction,
@@ -39,6 +40,7 @@ include("autodiff.jl")
 include("jacobian.jl")
 include("linear_solve.jl")
 include("timer_outputs.jl")
+include("tracing.jl")
 
 include("descent/common.jl")
 include("descent/newton.jl")
@@ -59,6 +61,8 @@ include("descent/geodesic_acceleration.jl")
 @compat(public, (construct_linear_solver, needs_square_A, needs_concrete_A))
 @compat(public, (construct_jacobian_cache,))
 
+export TraceMinimal, TraceWithJacobianConditionNumber, TraceAll
+
 export RelTerminationMode, AbsTerminationMode,
        NormTerminationMode, RelNormTerminationMode, AbsNormTerminationMode,
        RelNormSafeTerminationMode, AbsNormSafeTerminationMode,
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index 44a52c093..adf6603be 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -220,6 +220,9 @@ concrete_jac(::Val{true}) = true
 
 abstract type AbstractNonlinearSolveCache <: AbstractNonlinearSolveBaseAPI end
 
+function get_u end
+function get_fu end
+
 """
     AbstractLinearSolverCache
 
diff --git a/lib/NonlinearSolveBase/src/tracing.jl b/lib/NonlinearSolveBase/src/tracing.jl
new file mode 100644
index 000000000..5c67a0503
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/tracing.jl
@@ -0,0 +1,224 @@
+@concrete struct NonlinearSolveTracing
+    trace_mode <: Union{Val{:minimal}, Val{:condition_number}, Val{:all}}
+    print_frequency::Int
+    store_frequency::Int
+end
+
+"""
+    TraceMinimal(freq)
+    TraceMinimal(; print_frequency = 1, store_frequency::Int = 1)
+
+Trace Minimal Information
+
+ 1. Iteration Number
+ 2. f(u) inf-norm
+ 3. Step 2-norm
+
+See also [`TraceWithJacobianConditionNumber`](@ref) and [`TraceAll`](@ref).
+"""
+function TraceMinimal(; print_frequency = 1, store_frequency::Int = 1)
+    return NonlinearSolveTracing(Val(:minimal), print_frequency, store_frequency)
+end
+
+"""
+    TraceWithJacobianConditionNumber(freq)
+    TraceWithJacobianConditionNumber(; print_frequency = 1, store_frequency::Int = 1)
+
+[`TraceMinimal`](@ref) + Print the Condition Number of the Jacobian.
+
+See also [`TraceMinimal`](@ref) and [`TraceAll`](@ref).
+"""
+function TraceWithJacobianConditionNumber(; print_frequency = 1, store_frequency::Int = 1)
+    return NonlinearSolveTracing(Val(:condition_number), print_frequency, store_frequency)
+end
+
+"""
+    TraceAll(freq)
+    TraceAll(; print_frequency = 1, store_frequency::Int = 1)
+
+[`TraceWithJacobianConditionNumber`](@ref) + Store the Jacobian, u, f(u), and δu.
+
+!!! warning
+
+    This is very expensive and makes copyies of the Jacobian, u, f(u), and δu.
+
+See also [`TraceMinimal`](@ref) and [`TraceWithJacobianConditionNumber`](@ref).
+"""
+function TraceAll(; print_frequency = 1, store_frequency::Int = 1)
+    return NonlinearSolveTracing(Val(:all), print_frequency, store_frequency)
+end
+
+for Tr in (:TraceMinimal, :TraceWithJacobianConditionNumber, :TraceAll)
+    @eval $(Tr)(freq) = $(Tr)(; print_frequency = freq, store_frequency = freq)
+end
+
+# NonlinearSolve Tracing Utilities
+@concrete struct NonlinearSolveTraceEntry
+    iteration::Int
+    fnorm
+    stepnorm
+    condJ
+    storage
+    norm_type::Symbol
+end
+
+function Base.getproperty(entry::NonlinearSolveTraceEntry, sym::Symbol)
+    hasfield(typeof(entry), sym) && return getfield(entry, sym)
+    return getproperty(entry.storage, sym)
+end
+
+function print_top_level(io::IO, entry::NonlinearSolveTraceEntry)
+    if entry.condJ === nothing
+        @printf io "%-8s\t%-20s\t%-20s\n" "----" "-------------" "-----------"
+        if entry.norm_type === :L2
+            @printf io "%-8s\t%-20s\t%-20s\n" "Iter" "f(u) 2-norm" "Step 2-norm"
+        else
+            @printf io "%-8s\t%-20s\t%-20s\n" "Iter" "f(u) inf-norm" "Step 2-norm"
+        end
+        @printf io "%-8s\t%-20s\t%-20s\n" "----" "-------------" "-----------"
+    else
+        @printf io "%-8s\t%-20s\t%-20s\t%-20s\n" "----" "-------------" "-----------" "-------"
+        if entry.norm_type === :L2
+            @printf io "%-8s\t%-20s\t%-20s\t%-20s\n" "Iter" "f(u) 2-norm" "Step 2-norm" "cond(J)"
+        else
+            @printf io "%-8s\t%-20s\t%-20s\t%-20s\n" "Iter" "f(u) inf-norm" "Step 2-norm" "cond(J)"
+        end
+        @printf io "%-8s\t%-20s\t%-20s\t%-20s\n" "----" "-------------" "-----------" "-------"
+    end
+end
+
+function Base.show(io::IO, ::MIME"text/plain", entry::NonlinearSolveTraceEntry)
+    entry.iteration == 0 && print_top_level(io, entry)
+    if entry.iteration < 0 # Special case for final entry
+        @printf io "%-8s\t%-20.8e\n" "Final" entry.fnorm
+        @printf io "%-28s\n" "----------------------"
+    elseif entry.condJ === nothing
+        @printf io "%-8d\t%-20.8e\t%-20.8e\n" entry.iteration entry.fnorm entry.stepnorm
+    else
+        @printf io "%-8d\t%-20.8e\t%-20.8e\t%-20.8e\n" entry.iteration entry.fnorm entry.stepnorm entry.condJ
+    end
+end
+
+function NonlinearSolveTraceEntry(prob::AbstractNonlinearProblem, iteration, fu, δu, J, u)
+    norm_type = ifelse(prob isa NonlinearLeastSquaresProblem, :L2, :Inf)
+    fnorm = prob isa NonlinearLeastSquaresProblem ? L2_NORM(fu) : Linf_NORM(fu)
+    condJ = J !== missing ? Utils.condition_number(J) : nothing
+    storage = u === missing ? nothing :
+              (; u = copy(u), fu = copy(fu), δu = copy(δu), J = copy(J))
+    return NonlinearSolveTraceEntry(
+        iteration, fnorm, L2_NORM(δu), condJ, storage, norm_type
+    )
+end
+
+@concrete struct NonlinearSolveTrace
+    show_trace <: Union{Val{false}, Val{true}}
+    store_trace <: Union{Val{false}, Val{true}}
+    history
+    trace_level <: NonlinearSolveTracing
+    prob
+end
+
+reset!(trace::NonlinearSolveTrace) = reset!(trace.history)
+reset!(::Nothing) = nothing
+reset!(history::Vector) = empty!(history)
+
+function Base.show(io::IO, ::MIME"text/plain", trace::NonlinearSolveTrace)
+    if trace.history !== nothing
+        foreach(trace.history) do entry
+            show(io, MIME"text/plain"(), entry)
+        end
+    else
+        print(io, "Tracing Disabled")
+    end
+end
+
+function init_nonlinearsolve_trace(
+        prob, alg, u, fu, J, δu; show_trace::Val = Val(false),
+        trace_level::NonlinearSolveTracing = TraceMinimal(), store_trace::Val = Val(false),
+        uses_jac_inverse = Val(false), kwargs...
+)
+    return init_nonlinearsolve_trace(
+        prob, alg, show_trace, trace_level, store_trace, u, fu, J, δu, uses_jac_inverse
+    )
+end
+
+function init_nonlinearsolve_trace(
+        prob::AbstractNonlinearProblem, alg, show_trace::Val,
+        trace_level::NonlinearSolveTracing, store_trace::Val, u, fu, J, δu,
+        uses_jac_inverse::Val
+)
+    if show_trace isa Val{true}
+        print("\nAlgorithm: ")
+        Base.printstyled(alg, "\n\n"; color = :green, bold = true)
+    end
+    J = uses_jac_inverse isa Val{true} ?
+        (trace_level.trace_mode isa Val{:minimal} ? J : LinearAlgebra.pinv(J)) : J
+    history = init_trace_history(prob, show_trace, trace_level, store_trace, u, fu, J, δu)
+    return NonlinearSolveTrace(show_trace, store_trace, history, trace_level, prob)
+end
+
+function init_trace_history(
+        prob::AbstractNonlinearProblem, show_trace::Val, trace_level,
+        store_trace::Val, u, fu, J, δu
+)
+    store_trace isa Val{false} && show_trace isa Val{false} && return nothing
+    entry = if trace_level.trace_mode isa Val{:minimal}
+        NonlinearSolveTraceEntry(prob, 0, fu, δu, missing, missing)
+    elseif trace_level.trace_mode isa Val{:condition_number}
+        NonlinearSolveTraceEntry(prob, 0, fu, δu, J, missing)
+    else
+        NonlinearSolveTraceEntry(prob, 0, fu, δu, J, u)
+    end
+    show_trace isa Val{true} && show(stdout, MIME"text/plain"(), entry)
+    store_trace isa Val{true} && return NonlinearSolveTraceEntry[entry]
+    return nothing
+end
+
+function update_trace!(
+        trace::NonlinearSolveTrace, iter, u, fu, J, δu, α = true; last::Val = Val(false)
+)
+    trace.store_trace isa Val{false} && trace.show_trace isa Val{false} && return nothing
+
+    if last isa Val{true}
+        norm_type = ifelse(trace.prob isa NonlinearLeastSquaresProblem, :L2, :Inf)
+        fnorm = trace.prob isa NonlinearLeastSquaresProblem ? L2_NORM(fu) : Linf_NORM(fu)
+        entry = NonlinearSolveTraceEntry(-1, fnorm, NaN32, nothing, nothing, norm_type)
+        trace.show_trace isa Val{true} && show(stdout, MIME"text/plain"(), entry)
+        return trace
+    end
+
+    show_now = trace.show_trace isa Val{true} &&
+               (mod1(iter, trace.trace_level.print_frequency) == 1)
+    store_now = trace.store_trace isa Val{true} &&
+                (mod1(iter, trace.trace_level.store_frequency) == 1)
+    if show_now || store_now
+        entry = if trace.trace_level.trace_mode isa Val{:minimal}
+            NonlinearSolveTraceEntry(trace.prob, iter, fu, δu .* α, missing, missing)
+        elseif trace.trace_level.trace_mode isa Val{:condition_number}
+            NonlinearSolveTraceEntry(trace.prob, iter, fu, δu .* α, J, missing)
+        else
+            NonlinearSolveTraceEntry(trace.prob, iter, fu, δu .* α, J, u)
+        end
+        show_now && show(stdout, MIME"text/plain"(), entry)
+        store_now && push!(trace.history, entry)
+    end
+    return trace
+end
+
+function update_trace!(cache, α = true)
+    trace = Utils.safe_getproperty(cache, Val(:trace))
+    trace === missing && return nothing
+
+    J = Utils.safe_getproperty(cache, Val(:J))
+    if J === missing
+        update_trace!(
+            trace, cache.nsteps + 1, get_u(cache), get_fu(cache), nothing, cache.du, α
+        )
+        # XXX: Implement
+        # elseif cache isa ApproximateJacobianSolveCache && store_inverse_jacobian(cache)
+        #     update_trace!(trace, cache.nsteps + 1, get_u(cache), get_fu(cache),
+        #         ApplyArray(__safe_inv, J), cache.du, α)
+    else
+        update_trace!(trace, cache.nsteps + 1, get_u(cache), get_fu(cache), J, cache.du, α)
+    end
+end
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 14e6b1faa..689edef38 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -2,7 +2,8 @@ module Utils
 
 using ArrayInterface: ArrayInterface
 using FastClosures: @closure
-using LinearAlgebra: Symmetric, norm, dot
+using LinearAlgebra: LinearAlgebra, Diagonal, Symmetric, norm, dot, cond, diagind, pinv
+using MaybeInplace: @bb
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLOperators: AbstractSciMLOperator
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, NonlinearFunction
@@ -146,4 +147,46 @@ end
 
 function make_sparse end
 
+condition_number(J::AbstractMatrix) = cond(J)
+function condition_number(J::AbstractVector)
+    if !ArrayInterface.can_setindex(J)
+        J′ = similar(J)
+        copyto!(J′, J)
+        J = J′
+    end
+    return cond(Diagonal(J))
+end
+condition_number(::Any) = -1
+
+# XXX: Move to NonlinearSolveQuasiNewton
+# compute `pinv` if `inv` won't work
+maybe_pinv!!_workspace(A) = nothing
+
+maybe_pinv!!(workspace, A::Union{Number, AbstractMatrix}) = pinv(A)
+function maybe_pinv!!(workspace, A::Diagonal)
+    D = A.diag
+    @bb @. D = pinv(D)
+    return Diagonal(D)
+end
+maybe_pinv!!(workspace, A::AbstractVector) = maybe_pinv!!(workspace, Diagonal(A))
+function maybe_pinv!!(workspace, A::StridedMatrix)
+    LinearAlgebra.checksquare(A)
+    if LinearAlgebra.istriu(A)
+        issingular = any(iszero, @view(A[diagind(A)]))
+        A_ = UpperTriangular(A)
+        !issingular && return triu!(parent(inv(A_)))
+    elseif LinearAlgebra.istril(A)
+        A_ = LowerTriangular(A)
+        issingular = any(iszero, @view(A_[diagind(A_)]))
+        !issingular && return tril!(parent(inv(A_)))
+    else
+        F = LinearAlgebra.lu(A; check = false)
+        if issuccess(F)
+            Ai = LinearAlgebra.inv!(F)
+            return convert(typeof(parent(Ai)), Ai)
+        end
+    end
+    return pinv(A)
+end
+
 end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index dde01d848..409040861 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -29,14 +29,15 @@ using NonlinearSolveBase: NonlinearSolveBase,
                           DescentResult,
                           SteepestDescent, NewtonDescent, DampedNewtonDescent, Dogleg,
                           GeodesicAcceleration,
-                          reset_timer!, @static_timeit
+                          reset_timer!, @static_timeit,
+                          init_nonlinearsolve_trace, update_trace!, reset!
 
 # XXX: Remove
 import NonlinearSolveBase: InternalAPI, concrete_jac, supports_line_search,
                            supports_trust_region, last_step_accepted, get_linear_solver,
                            AbstractDampingFunction, AbstractDampingFunctionCache,
                            requires_normal_form_jacobian, requires_normal_form_rhs,
-                           returns_norm_form_damping, get_timer_output
+                           returns_norm_form_damping, get_timer_output, get_u, get_fu
 
 using Printf: @printf
 using Preferences: Preferences, set_preferences!
@@ -74,7 +75,6 @@ include("timer_outputs.jl")
 include("internal/helpers.jl")
 
 include("internal/termination.jl")
-include("internal/tracing.jl")
 include("internal/approximate_initialization.jl")
 
 include("globalization/line_search.jl")
diff --git a/src/internal/tracing.jl b/src/internal/tracing.jl
deleted file mode 100644
index fe35f1a9c..000000000
--- a/src/internal/tracing.jl
+++ /dev/null
@@ -1,217 +0,0 @@
-"""
-    TraceMinimal(freq)
-    TraceMinimal(; print_frequency = 1, store_frequency::Int = 1)
-
-Trace Minimal Information
-
- 1. Iteration Number
- 2. f(u) inf-norm
- 3. Step 2-norm
-
-See also [`TraceWithJacobianConditionNumber`](@ref) and [`TraceAll`](@ref).
-"""
-@kwdef struct TraceMinimal <: AbstractNonlinearSolveTraceLevel
-    print_frequency::Int = 1
-    store_frequency::Int = 1
-end
-
-"""
-    TraceWithJacobianConditionNumber(freq)
-    TraceWithJacobianConditionNumber(; print_frequency = 1, store_frequency::Int = 1)
-
-[`TraceMinimal`](@ref) + Print the Condition Number of the Jacobian.
-
-See also [`TraceMinimal`](@ref) and [`TraceAll`](@ref).
-"""
-@kwdef struct TraceWithJacobianConditionNumber <: AbstractNonlinearSolveTraceLevel
-    print_frequency::Int = 1
-    store_frequency::Int = 1
-end
-
-"""
-    TraceAll(freq)
-    TraceAll(; print_frequency = 1, store_frequency::Int = 1)
-
-[`TraceWithJacobianConditionNumber`](@ref) + Store the Jacobian, u, f(u), and δu.
-
-!!! warning
-
-    This is very expensive and makes copyies of the Jacobian, u, f(u), and δu.
-
-See also [`TraceMinimal`](@ref) and [`TraceWithJacobianConditionNumber`](@ref).
-"""
-@kwdef struct TraceAll <: AbstractNonlinearSolveTraceLevel
-    print_frequency::Int = 1
-    store_frequency::Int = 1
-end
-
-for Tr in (:TraceMinimal, :TraceWithJacobianConditionNumber, :TraceAll)
-    @eval begin
-        $(Tr)(freq) = $(Tr)(; print_frequency = freq, store_frequency = freq)
-    end
-end
-
-# NonlinearSolve Tracing Utilities
-@concrete struct NonlinearSolveTraceEntry{nType}
-    iteration::Int
-    fnorm
-    stepnorm
-    condJ
-    J
-    u
-    fu
-    δu
-end
-
-function __show_top_level(io::IO, entry::NonlinearSolveTraceEntry{nType}) where {nType}
-    if entry.condJ === nothing
-        @printf io "%-8s %-20s %-20s\n" "----" "-------------" "-----------"
-        if nType === :L2
-            @printf io "%-8s %-20s %-20s\n" "Iter" "f(u) 2-norm" "Step 2-norm"
-        else
-            @printf io "%-8s %-20s %-20s\n" "Iter" "f(u) inf-norm" "Step 2-norm"
-        end
-        @printf io "%-8s %-20s %-20s\n" "----" "-------------" "-----------"
-    else
-        @printf io "%-8s %-20s %-20s %-20s\n" "----" "-------------" "-----------" "-------"
-        if nType === :L2
-            @printf io "%-8s %-20s %-20s %-20s\n" "Iter" "f(u) 2-norm" "Step 2-norm" "cond(J)"
-        else
-            @printf io "%-8s %-20s %-20s %-20s\n" "Iter" "f(u) inf-norm" "Step 2-norm" "cond(J)"
-        end
-        @printf io "%-8s %-20s %-20s %-20s\n" "----" "-------------" "-----------" "-------"
-    end
-end
-
-function Base.show(io::IO, entry::NonlinearSolveTraceEntry{nType}) where {nType}
-    entry.iteration == 0 && __show_top_level(io, entry)
-    if entry.iteration < 0
-        # Special case for final entry
-        @printf io "%-8s %-20.8e\n" "Final" entry.fnorm
-        @printf io "%-28s\n" "----------------------"
-    elseif entry.condJ === nothing
-        @printf io "%-8d %-20.8e %-20.8e\n" entry.iteration entry.fnorm entry.stepnorm
-    else
-        @printf io "%-8d %-20.8e %-20.8e %-20.8e\n" entry.iteration entry.fnorm entry.stepnorm entry.condJ
-    end
-    return nothing
-end
-
-function NonlinearSolveTraceEntry(prob::AbstractNonlinearProblem, iteration, fu, δu)
-    nType = ifelse(prob isa NonlinearLeastSquaresProblem, :L2, :Inf)
-    fnorm = prob isa NonlinearLeastSquaresProblem ? norm(fu, 2) : norm(fu, Inf)
-    return NonlinearSolveTraceEntry{nType}(
-        iteration, fnorm, norm(δu, 2), nothing, nothing, nothing, nothing, nothing)
-end
-
-function NonlinearSolveTraceEntry(prob::AbstractNonlinearProblem, iteration, fu, δu, J)
-    nType = ifelse(prob isa NonlinearLeastSquaresProblem, :L2, :Inf)
-    fnorm = prob isa NonlinearLeastSquaresProblem ? norm(fu, 2) : norm(fu, Inf)
-    return NonlinearSolveTraceEntry{nType}(
-        iteration, fnorm, norm(δu, 2), __cond(J), nothing, nothing, nothing, nothing)
-end
-
-function NonlinearSolveTraceEntry(prob::AbstractNonlinearProblem, iteration, fu, δu, J, u)
-    nType = ifelse(prob isa NonlinearLeastSquaresProblem, :L2, :Inf)
-    fnorm = prob isa NonlinearLeastSquaresProblem ? norm(fu, 2) : norm(fu, Inf)
-    return NonlinearSolveTraceEntry{nType}(iteration, fnorm, norm(δu, 2), __cond(J),
-        __copy(J), __copy(u), __copy(fu), __copy(δu))
-end
-
-@concrete struct NonlinearSolveTrace{
-    show_trace, store_trace, Tr <: AbstractNonlinearSolveTraceLevel}
-    history
-    trace_level::Tr
-    prob
-end
-
-function reset!(trace::NonlinearSolveTrace)
-    (trace.history !== nothing && resize!(trace.history, 0))
-end
-
-function Base.show(io::IO, trace::NonlinearSolveTrace)
-    if trace.history !== nothing
-        foreach(entry -> show(io, entry), trace.history)
-    else
-        print(io, "Tracing Disabled")
-    end
-    return nothing
-end
-
-function init_nonlinearsolve_trace(prob, alg, u, fu, J, δu; show_trace::Val = Val(false),
-        trace_level::AbstractNonlinearSolveTraceLevel = TraceMinimal(),
-        store_trace::Val = Val(false), uses_jac_inverse = Val(false), kwargs...)
-    return init_nonlinearsolve_trace(
-        prob, alg, show_trace, trace_level, store_trace, u, fu, J, δu, uses_jac_inverse)
-end
-
-function init_nonlinearsolve_trace(prob::AbstractNonlinearProblem, alg, ::Val{show_trace},
-        trace_level::AbstractNonlinearSolveTraceLevel, ::Val{store_trace}, u, fu, J,
-        δu, ::Val{uses_jac_inverse}) where {show_trace, store_trace, uses_jac_inverse}
-    if show_trace
-        print("\nAlgorithm: ")
-        Base.printstyled(alg, "\n\n"; color = :green, bold = true)
-    end
-    J_ = uses_jac_inverse ? (trace_level isa TraceMinimal ? J : __safe_inv(J)) : J
-    history = __init_trace_history(
-        prob, Val{show_trace}(), trace_level, Val{store_trace}(), u, fu, J_, δu)
-    return NonlinearSolveTrace{show_trace, store_trace}(history, trace_level, prob)
-end
-
-function __init_trace_history(
-        prob::AbstractNonlinearProblem, ::Val{show_trace}, trace_level,
-        ::Val{store_trace}, u, fu, J, δu) where {show_trace, store_trace}
-    !store_trace && !show_trace && return nothing
-    entry = __trace_entry(prob, trace_level, 0, u, fu, J, δu)
-    show_trace && show(entry)
-    store_trace && return NonlinearSolveTraceEntry[entry]
-    return nothing
-end
-
-function __trace_entry(prob, ::TraceMinimal, iter, u, fu, J, δu, α = 1)
-    return NonlinearSolveTraceEntry(prob, iter, fu, δu .* α)
-end
-function __trace_entry(prob, ::TraceWithJacobianConditionNumber, iter, u, fu, J, δu, α = 1)
-    return NonlinearSolveTraceEntry(prob, iter, fu, δu .* α, J)
-end
-function __trace_entry(prob, ::TraceAll, iter, u, fu, J, δu, α = 1)
-    return NonlinearSolveTraceEntry(prob, iter, fu, δu .* α, J, u)
-end
-
-function update_trace!(trace::NonlinearSolveTrace{ShT, StT}, iter, u, fu, J, δu,
-        α = 1; last::Val{L} = Val(false)) where {ShT, StT, L}
-    !StT && !ShT && return nothing
-
-    if L
-        nType = ifelse(trace.prob isa NonlinearLeastSquaresProblem, :L2, :Inf)
-        fnorm = trace.prob isa NonlinearLeastSquaresProblem ? norm(fu, 2) : norm(fu, Inf)
-        entry = NonlinearSolveTraceEntry{nType}(
-            -1, fnorm, NaN32, nothing, nothing, nothing, nothing, nothing)
-        ShT && show(entry)
-        return trace
-    end
-
-    show_now = ShT && (mod1(iter, trace.trace_level.print_frequency) == 1)
-    store_now = StT && (mod1(iter, trace.trace_level.store_frequency) == 1)
-    (show_now || store_now) &&
-        (entry = __trace_entry(trace.prob, trace.trace_level, iter, u, fu, J, δu, α))
-    store_now && push!(trace.history, entry)
-    show_now && show(entry)
-    return trace
-end
-
-function update_trace!(cache::AbstractNonlinearSolveCache, α = true)
-    trace = __getproperty(cache, Val(:trace))
-    trace === nothing && return nothing
-
-    J = __getproperty(cache, Val(:J))
-    if J === nothing
-        update_trace!(
-            trace, cache.nsteps + 1, get_u(cache), get_fu(cache), nothing, cache.du, α)
-    elseif cache isa ApproximateJacobianSolveCache && store_inverse_jacobian(cache)
-        update_trace!(trace, cache.nsteps + 1, get_u(cache), get_fu(cache),
-            ApplyArray(__safe_inv, J), cache.du, α)
-    else
-        update_trace!(trace, cache.nsteps + 1, get_u(cache), get_fu(cache), J, cache.du, α)
-    end
-end
diff --git a/src/utils.jl b/src/utils.jl
index fd9dd8b8a..1582234bc 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -22,13 +22,6 @@ end
 end
 @inline __maybe_unaliased(x::AbstractSciMLOperator, ::Bool) = x
 
-@inline __cond(J::AbstractMatrix) = cond(J)
-@inline __cond(J::SVector) = __cond(Diagonal(MVector(J)))
-@inline __cond(J::AbstractVector) = __cond(Diagonal(J))
-@inline __cond(J::ApplyArray) = __cond(J.f(J.args...))
-@inline __cond(J::SparseMatrixCSC) = __cond(Matrix(J))
-@inline __cond(J) = -1  # Covers cases where `J` is a Operator, nothing, etc.
-
 @inline __copy(x::AbstractArray) = copy(x)
 @inline __copy(x::Number) = x
 @inline __copy(x) = x

From f662e3e1b416dd470ec2ee413727b57a7fd63e86 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 27 Oct 2024 16:16:39 -0400
Subject: [PATCH 638/700] refactor: move DFSane into
 NonlinearSolveSpectralMethods

---
 Project.toml                                  |   3 +-
 common/nlls_problem_workloads.jl              |   0
 common/nonlinear_problem_workloads.jl         |  12 +
 .../src/NonlinearSolveBase.jl                 |   4 +
 lib/NonlinearSolveBase/src/abstract_types.jl  | 105 ++++++++-
 lib/NonlinearSolveBase/src/solve.jl           | 107 +++++++++
 lib/NonlinearSolveBase/src/utils.jl           |  22 +-
 .../Project.toml                              |  22 ++
 .../src/NonlinearSolveSpectralMethods.jl      |  38 +++
 .../src/dfsane.jl                             |  31 +++
 .../src/solve.jl                              | 222 ++++++++++++++++++
 src/NonlinearSolve.jl                         |  16 +-
 src/algorithms/dfsane.jl                      |  27 ---
 src/core/generic.jl                           |   3 +-
 src/core/spectral_methods.jl                  | 211 -----------------
 15 files changed, 568 insertions(+), 255 deletions(-)
 create mode 100644 common/nlls_problem_workloads.jl
 create mode 100644 common/nonlinear_problem_workloads.jl
 create mode 100644 lib/NonlinearSolveBase/src/solve.jl
 create mode 100644 lib/NonlinearSolveSpectralMethods/src/dfsane.jl
 create mode 100644 lib/NonlinearSolveSpectralMethods/src/solve.jl
 delete mode 100644 src/algorithms/dfsane.jl
 delete mode 100644 src/core/spectral_methods.jl

diff --git a/Project.toml b/Project.toml
index dc11fdf80..262412366 100644
--- a/Project.toml
+++ b/Project.toml
@@ -19,9 +19,9 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
+NonlinearSolveSpectralMethods = "26075421-4e9a-44e1-8bd1-420ed7ad02b2"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Preferences = "21216c6a-2e73-6563-6e65-726566657250"
-Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
@@ -99,7 +99,6 @@ PETSc = "0.2"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 Preferences = "1.4"
-Printf = "1.10"
 Random = "1.10"
 ReTestItems = "1.24"
 RecursiveArrayTools = "3.27"
diff --git a/common/nlls_problem_workloads.jl b/common/nlls_problem_workloads.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/common/nonlinear_problem_workloads.jl b/common/nonlinear_problem_workloads.jl
new file mode 100644
index 000000000..c97592f90
--- /dev/null
+++ b/common/nonlinear_problem_workloads.jl
@@ -0,0 +1,12 @@
+using SciMLBase: NonlinearProblem, NonlinearFunction
+
+nonlinear_functions = (
+    (NonlinearFunction{false}((u, p) -> u .* u .- p), 0.1),
+    (NonlinearFunction{false}((u, p) -> u .* u .- p), [0.1]),
+    (NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p), [0.1])
+)
+
+nonlinear_problems = NonlinearProblem[]
+for (fn, u0) in nonlinear_functions
+    push!(nonlinear_problems, NonlinearProblem(fn, u0, 2.0))
+end
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 75afb746e..a0c5a524c 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -24,8 +24,10 @@ using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinear
 using SciMLJacobianOperators: JacobianOperator, StatefulJacobianOperator
 using SciMLOperators: AbstractSciMLOperator, IdentityOperator
 using StaticArraysCore: StaticArray, SMatrix, SArray, MArray
+using SymbolicIndexingInterface: SymbolicIndexingInterface
 
 const DI = DifferentiationInterface
+const SII = SymbolicIndexingInterface
 
 include("public.jl")
 include("utils.jl")
@@ -49,6 +51,8 @@ include("descent/damped_newton.jl")
 include("descent/dogleg.jl")
 include("descent/geodesic_acceleration.jl")
 
+include("solve.jl")
+
 # Unexported Public API
 @compat(public, (L2_NORM, Linf_NORM, NAN_CHECK, UNITLESS_ABS2, get_tolerance))
 @compat(public, (nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution))
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index adf6603be..d62a637e0 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -218,10 +218,111 @@ concrete_jac(v::Bool) = v
 concrete_jac(::Val{false}) = false
 concrete_jac(::Val{true}) = true
 
+"""
+    AbstractNonlinearSolveCache
+
+Abstract Type for all NonlinearSolveBase Caches.
+
+### Interface Functions
+
+  - `get_fu(cache)`: get the residual.
+  - `get_u(cache)`: get the current state.
+  - `set_fu!(cache, fu)`: set the residual.
+  - `has_time_limit(cache)`: whether or not the solver has a maximum time limit.
+  - `not_terminated(cache)`: whether or not the solver has terminated.
+
+  - `SciMLBase.set_u!(cache, u)`: set the current state.
+  - `SciMLBase.reinit!(cache, u0; kwargs...)`: reinitialize the cache with the initial state
+    `u0` and any additional keyword arguments.
+  - `SciMLBase.step!(cache; kwargs...)`: See [`SciMLBase.step!`](@ref) for more details.
+  - `SciMLBase.isinplace(cache)`: whether or not the solver is inplace.
+
+Additionally implements `SymbolicIndexingInterface` interface Functions.
+
+#### Expected Fields in Sub-Types
+
+For the default interface implementations we expect the following fields to be present in
+the cache:
+
+  - `fu`: the residual.
+  - `u`: the current state.
+  - `maxiters`: the maximum number of iterations.
+  - `nsteps`: the number of steps taken.
+  - `force_stop`: whether or not the solver has been forced to stop.
+  - `retcode`: the return code.
+  - `stats`: `NLStats` object.
+  - `alg`: the algorithm.
+  - `maxtime`: the maximum time limit for the solver. (Optional)
+  - `timer`: the timer for the solver. (Optional)
+  - `total_time`: the total time taken by the solver. (Optional)
+"""
 abstract type AbstractNonlinearSolveCache <: AbstractNonlinearSolveBaseAPI end
 
-function get_u end
-function get_fu end
+get_u(cache::AbstractNonlinearSolveCache) = cache.u
+get_fu(cache::AbstractNonlinearSolveCache) = cache.fu
+set_fu!(cache::AbstractNonlinearSolveCache, fu) = (cache.fu = fu)
+SciMLBase.set_u!(cache::AbstractNonlinearSolveCache, u) = (cache.u = u)
+
+function has_time_limit(cache::AbstractNonlinearSolveCache)
+    maxtime = Utils.safe_getproperty(cache, Val(:maxtime))
+    return maxtime !== missing && maxtime !== nothing
+end
+
+function not_terminated(cache::AbstractNonlinearSolveCache)
+    return !cache.force_stop && cache.nsteps < cache.maxiters
+end
+
+function SciMLBase.reinit!(cache::AbstractNonlinearSolveCache; kwargs...)
+    return InternalAPI.reinit!(cache; kwargs...)
+end
+function SciMLBase.reinit!(cache::AbstractNonlinearSolveCache, u0; kwargs...)
+    return InternalAPI.reinit!(cache; u0, kwargs...)
+end
+
+SciMLBase.isinplace(cache::AbstractNonlinearSolveCache) = SciMLBase.isinplace(cache.prob)
+
+## SII Interface
+SII.symbolic_container(cache::AbstractNonlinearSolveCache) = cache.prob
+SII.parameter_values(cache::AbstractNonlinearSolveCache) = SII.parameter_values(cache.prob)
+SII.state_values(cache::AbstractNonlinearSolveCache) = SII.state_values(cache.prob)
+
+function Base.getproperty(cache::AbstractNonlinearSolveCache, sym::Symbol)
+    if sym === :ps
+        !hasfield(typeof(cache), :ps) && return SII.ParameterIndexingProxy(cache)
+        return getfield(cache, :ps)
+    end
+    return getfield(cache, sym)
+end
+
+Base.getindex(cache::AbstractNonlinearSolveCache, sym) = SII.getu(cache, sym)(cache)
+function Base.setindex!(cache::AbstractNonlinearSolveCache, val, sym)
+    return SII.setu(cache, sym)(cache, val)
+end
+
+# XXX: Implement this
+# function Base.show(io::IO, cache::AbstractNonlinearSolveCache)
+#     __show_cache(io, cache, 0)
+# end
+
+# function __show_cache(io::IO, cache::AbstractNonlinearSolveCache, indent = 0)
+#     println(io, "$(nameof(typeof(cache)))(")
+#     __show_algorithm(io, cache.alg,
+#         (" "^(indent + 4)) * "alg = " * string(get_name(cache.alg)), indent + 4)
+
+#     ustr = sprint(show, get_u(cache); context = (:compact => true, :limit => true))
+#     println(io, ",\n" * (" "^(indent + 4)) * "u = $(ustr),")
+
+#     residstr = sprint(show, get_fu(cache); context = (:compact => true, :limit => true))
+#     println(io, (" "^(indent + 4)) * "residual = $(residstr),")
+
+#     normstr = sprint(
+#         show, norm(get_fu(cache), Inf); context = (:compact => true, :limit => true))
+#     println(io, (" "^(indent + 4)) * "inf-norm(residual) = $(normstr),")
+
+#     println(io, " "^(indent + 4) * "nsteps = ", cache.stats.nsteps, ",")
+#     println(io, " "^(indent + 4) * "retcode = ", cache.retcode)
+#     print(io, " "^(indent) * ")")
+# end
 
 """
     AbstractLinearSolverCache
diff --git a/lib/NonlinearSolveBase/src/solve.jl b/lib/NonlinearSolveBase/src/solve.jl
new file mode 100644
index 000000000..999f064e9
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/solve.jl
@@ -0,0 +1,107 @@
+function SciMLBase.__solve(
+        prob::AbstractNonlinearProblem, alg::AbstractNonlinearSolveAlgorithm, args...;
+        kwargs...
+)
+    cache = SciMLBase.init(prob, alg, args...; kwargs...)
+    return SciMLBase.solve!(cache)
+end
+
+function CommonSolve.solve!(cache::AbstractNonlinearSolveCache)
+    while not_terminated(cache)
+        SciMLBase.step!(cache)
+    end
+
+    # The solver might have set a different `retcode`
+    if cache.retcode == ReturnCode.Default
+        cache.retcode = ifelse(
+            cache.nsteps ≥ cache.maxiters, ReturnCode.MaxIters, ReturnCode.Success
+        )
+    end
+
+    # XXX: Implement this
+    # update_from_termination_cache!(cache.termination_cache, cache)
+
+    update_trace!(
+        cache.trace, cache.nsteps, get_u(cache), get_fu(cache), nothing, nothing, nothing;
+        last = Val(true)
+    )
+
+    return SciMLBase.build_solution(
+        cache.prob, cache.alg, get_u(cache), get_fu(cache);
+        cache.retcode, cache.stats, cache.trace
+    )
+end
+
+"""
+    step!(cache::AbstractNonlinearSolveCache;
+        recompute_jacobian::Union{Nothing, Bool} = nothing)
+
+Performs one step of the nonlinear solver.
+
+### Keyword Arguments
+
+  - `recompute_jacobian`: allows controlling whether the jacobian is recomputed at the
+    current step. If `nothing`, then the algorithm determines whether to recompute the
+    jacobian. If `true` or `false`, then the jacobian is recomputed or not recomputed,
+    respectively. For algorithms that don't use jacobian information, this keyword is
+    ignored with a one-time warning.
+"""
+function SciMLBase.step!(cache::AbstractNonlinearSolveCache, args...; kwargs...)
+    not_terminated(cache) || return
+
+    has_time_limit(cache) && (time_start = time())
+
+    res = @static_timeit cache.timer "solve" begin
+        InternalAPI.step!(cache, args...; kwargs...)
+    end
+
+    cache.stats.nsteps += 1
+    cache.nsteps += 1
+
+    if has_time_limit(cache)
+        cache.total_time += time() - time_start
+
+        if !cache.force_stop && cache.retcode == ReturnCode.Default &&
+           cache.total_time ≥ cache.maxtime
+            cache.retcode = ReturnCode.MaxTime
+            cache.force_stop = true
+        end
+    end
+
+    return res
+end
+
+# Some algorithms don't support creating a cache and doing `solve!`, this unfortunately
+# makes it difficult to write generic code that supports caching. For the algorithms that
+# don't have a `__init` function defined, we create a "Fake Cache", which just calls
+# `__solve` from `solve!`
+# Warning: This doesn't implement all the necessary interface functions
+@concrete mutable struct NonlinearSolveNoInitCache <: AbstractNonlinearSolveCache
+    prob
+    alg
+    args
+    kwargs::Any
+end
+
+function SciMLBase.reinit!(
+        cache::NonlinearSolveNoInitCache, u0 = cache.prob.u0; p = cache.prob.p, kwargs...
+)
+    cache.prob = SciMLBase.remake(cache.prob; u0, p)
+    cache.kwargs = merge(cache.kwargs, kwargs)
+    return cache
+end
+
+function Base.show(io::IO, ::MIME"text/plain", cache::NonlinearSolveNoInitCache)
+    print(io, "NonlinearSolveNoInitCache(alg = $(cache.alg))")
+end
+
+function SciMLBase.__init(
+        prob::AbstractNonlinearProblem, alg::AbstractNonlinearSolveAlgorithm, args...;
+        kwargs...
+)
+    return NonlinearSolveNoInitCache(prob, alg, args, kwargs)
+end
+
+function CommonSolve.solve!(cache::NonlinearSolveNoInitCache)
+    return CommonSolve.solve(cache.prob, cache.alg, cache.args...; cache.kwargs...)
+end
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 689edef38..be691d8ba 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -9,7 +9,7 @@ using SciMLOperators: AbstractSciMLOperator
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, NonlinearFunction
 using StaticArraysCore: StaticArray, SArray
 
-using ..NonlinearSolveBase: L2_NORM, Linf_NORM
+using ..NonlinearSolveBase: NonlinearSolveBase, L2_NORM, Linf_NORM
 
 is_extension_loaded(::Val) = false
 
@@ -145,6 +145,26 @@ function evaluate_f!!(f::NonlinearFunction, fu, u, p)
     return f(u, p)
 end
 
+function evaluate_f(prob::AbstractNonlinearProblem, u)
+    if SciMLBase.isinplace(prob)
+        fu = prob.f.resid_prototype === nothing ? similar(u) :
+             similar(prob.f.resid_prototype)
+        prob.f(fu, u, prob.p)
+    else
+        fu = prob.f(u, prob.p)
+    end
+    return fu
+end
+
+function evaluate_f!(cache, u, p)
+    cache.stats.nf += 1
+    if SciMLBase.isinplace(cache)
+        cache.prob.f(NonlinearSolveBase.get_fu(cache), u, p)
+    else
+        NonlinearSolveBase.set_fu!(cache, cache.prob.f(u, p))
+    end
+end
+
 function make_sparse end
 
 condition_number(J::AbstractMatrix) = cond(J)
diff --git a/lib/NonlinearSolveSpectralMethods/Project.toml b/lib/NonlinearSolveSpectralMethods/Project.toml
index dafa10841..d84e6ffbb 100644
--- a/lib/NonlinearSolveSpectralMethods/Project.toml
+++ b/lib/NonlinearSolveSpectralMethods/Project.toml
@@ -3,14 +3,36 @@ uuid = "26075421-4e9a-44e1-8bd1-420ed7ad02b2"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
 version = "1.0.0"
 
+[deps]
+CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
+ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
+DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
+NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
+PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
+Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+
 [compat]
 Aqua = "0.8"
+CommonSolve = "0.2.4"
+ConcreteStructs = "0.2.3"
+DiffEqBase = "6.155.3"
 ExplicitImports = "1.5"
 Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
+LineSearch = "0.1.4"
+LinearAlgebra = "1.11.0"
+MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
+NonlinearSolveBase = "1.1"
 Pkg = "1.10"
+PrecompileTools = "1.2"
 ReTestItems = "1.24"
+Reexport = "1"
+SciMLBase = "2.54"
 StableRNGs = "1"
 Test = "1.10"
 julia = "1.10"
diff --git a/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl b/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
index 3b0c67477..253dd0b72 100644
--- a/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
+++ b/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
@@ -1,3 +1,41 @@
 module NonlinearSolveSpectralMethods
 
+using Reexport: @reexport
+using PrecompileTools: @compile_workload, @setup_workload
+
+using CommonSolve: CommonSolve
+using ConcreteStructs: @concrete
+using DiffEqBase: DiffEqBase # Needed for `init` / `solve` dispatches
+using LinearAlgebra: dot
+using LineSearch: RobustNonMonotoneLineSearch
+using MaybeInplace: @bb
+using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
+                          AbstractNonlinearSolveCache, Utils, InternalAPI, get_timer_output,
+                          @static_timeit, update_trace!
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode
+
+include("dfsane.jl")
+
+include("solve.jl")
+
+@setup_workload begin
+    include(joinpath(
+        @__DIR__, "..", "..", "..", "common", "nonlinear_problem_workloads.jl"
+    ))
+
+    algs = [DFSane()]
+
+    @compile_workload begin
+        @sync begin
+            for prob in nonlinear_problems, alg in algs
+                Threads.@spawn CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
+            end
+        end
+    end
+end
+
+@reexport using SciMLBase, NonlinearSolveBase
+
+export GeneralizedDFSane, DFSane
+
 end
diff --git a/lib/NonlinearSolveSpectralMethods/src/dfsane.jl b/lib/NonlinearSolveSpectralMethods/src/dfsane.jl
new file mode 100644
index 000000000..c835a1059
--- /dev/null
+++ b/lib/NonlinearSolveSpectralMethods/src/dfsane.jl
@@ -0,0 +1,31 @@
+"""
+    DFSane(;
+        sigma_min = 1 // 10^10, sigma_max = 1e10, sigma_1 = 1, M::Int = 10,
+        gamma = 1 // 10^4, tau_min = 1 // 10, tau_max = 1 // 2, n_exp::Int = 2,
+        max_inner_iterations::Int = 100, eta_strategy = (fn_1, n, x_n, f_n) -> fn_1 / n^2
+    )
+
+A low-overhead and allocation-free implementation of the df-sane method for solving
+large-scale nonlinear systems of equations. For in depth information about all the
+parameters and the algorithm, see [la2006spectral](@citet).
+
+### Keyword Arguments
+
+  - `sigma_min`: the minimum value of the spectral coefficient `σ` which is related to the
+    step size in the algorithm. Defaults to `1e-10`.
+  - `sigma_max`: the maximum value of the spectral coefficient `σₙ` which is related to the
+    step size in the algorithm. Defaults to `1e10`.
+
+For other keyword arguments, see [`RobustNonMonotoneLineSearch`](@ref).
+"""
+function DFSane(;
+        sigma_min = 1 // 10^10, sigma_max = 1e10, sigma_1 = 1, M::Int = 10,
+        gamma = 1 // 10^4, tau_min = 1 // 10, tau_max = 1 // 2, n_exp::Int = 2,
+        max_inner_iterations::Int = 100, eta_strategy::F = (fn_1, n, x_n, f_n) -> fn_1 / n^2
+) where {F}
+    linesearch = RobustNonMonotoneLineSearch(;
+        gamma = gamma, sigma_1 = sigma_1, M, tau_min = tau_min, tau_max = tau_max,
+        n_exp, η_strategy = eta_strategy, maxiters = max_inner_iterations
+    )
+    return GeneralizedDFSane(linesearch, sigma_min, sigma_max, nothing, :DFSane)
+end
diff --git a/lib/NonlinearSolveSpectralMethods/src/solve.jl b/lib/NonlinearSolveSpectralMethods/src/solve.jl
new file mode 100644
index 000000000..19659a679
--- /dev/null
+++ b/lib/NonlinearSolveSpectralMethods/src/solve.jl
@@ -0,0 +1,222 @@
+# For spectral methods we currently only implement DF-SANE since after reading through
+# papers, this seems to be the only one that is widely used. If we have a list of more
+# papers we can see what is the right level of abstraction to implement here
+"""
+    GeneralizedDFSane(linesearch, sigma_min, sigma_max, sigma_1, name::Symbol)
+
+A generalized version of the DF-SANE algorithm. This algorithm is a Jacobian-Free Spectral
+Method.
+
+### Arguments
+
+  - `linesearch`: Globalization using a Line Search Method. This is not optional currently,
+    but that restriction might be lifted in the future.
+  - `sigma_min`: The minimum spectral parameter allowed. This is used to ensure that the
+    spectral parameter is not too small.
+  - `sigma_max`: The maximum spectral parameter allowed. This is used to ensure that the
+    spectral parameter is not too large.
+  - `sigma_1`: The initial spectral parameter. If this is not provided, then the algorithm
+    initializes it as `sigma_1 = <u, u> / <u, f(u)>`.
+"""
+@concrete struct GeneralizedDFSane <: AbstractNonlinearSolveAlgorithm
+    linesearch
+    σ_min
+    σ_max
+    σ_1
+    name::Symbol
+end
+
+# XXX: Add
+# function __show_algorithm(io::IO, alg::GeneralizedDFSane, name, indent)
+#     modifiers = String[]
+#     __is_present(alg.linesearch) && push!(modifiers, "linesearch = $(alg.linesearch)")
+#     push!(modifiers, "σ_min = $(alg.σ_min)")
+#     push!(modifiers, "σ_max = $(alg.σ_max)")
+#     push!(modifiers, "σ_1 = $(alg.σ_1)")
+#     spacing = " "^indent * "    "
+#     spacing_last = " "^indent
+#     print(io, "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))")
+# end
+
+@concrete mutable struct GeneralizedDFSaneCache <: AbstractNonlinearSolveCache
+    # Basic Requirements
+    fu
+    fu_cache
+    u
+    u_cache
+    p
+    du
+    alg <: GeneralizedDFSane
+    prob
+
+    # Parameters
+    σ_n
+    σ_min
+    σ_max
+
+    # Internal Caches
+    linesearch_cache
+
+    # Counters
+    stats::NLStats
+    nsteps::Int
+    maxiters::Int
+    maxtime
+
+    # Timer
+    timer
+    total_time::Float64   # Simple Counter which works even if TimerOutput is disabled
+
+    # Termination & Tracking
+    termination_cache
+    trace
+    retcode::ReturnCode.T
+    force_stop::Bool
+    kwargs
+end
+
+# XXX: Implement
+# function __reinit_internal!(
+#         cache::GeneralizedDFSaneCache{iip}, args...; p = cache.p, u0 = cache.u,
+#         alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...) where {iip}
+#     if iip
+#         recursivecopy!(cache.u, u0)
+#         cache.prob.f(cache.fu, cache.u, p)
+#     else
+#         cache.u = __maybe_unaliased(u0, alias_u0)
+#         set_fu!(cache, cache.prob.f(cache.u, p))
+#     end
+#     cache.p = p
+
+#     if cache.alg.σ_1 === nothing
+#         σ_n = dot(cache.u, cache.u) / dot(cache.u, cache.fu)
+#         # Spectral parameter bounds check
+#         if !(cache.alg.σ_min ≤ abs(σ_n) ≤ cache.alg.σ_max)
+#             test_norm = dot(cache.fu, cache.fu)
+#             σ_n = clamp(inv(test_norm), T(1), T(1e5))
+#         end
+#     else
+#         σ_n = T(cache.alg.σ_1)
+#     end
+#     cache.σ_n = σ_n
+
+#     reset_timer!(cache.timer)
+#     cache.total_time = 0.0
+
+#     reset!(cache.trace)
+#     reinit!(cache.termination_cache, get_fu(cache), get_u(cache); kwargs...)
+#     __reinit_internal!(cache.stats)
+#     cache.nsteps = 0
+#     cache.maxiters = maxiters
+#     cache.maxtime = maxtime
+#     cache.force_stop = false
+#     cache.retcode = ReturnCode.Default
+# end
+
+# @internal_caches GeneralizedDFSaneCache :linesearch_cache
+
+function SciMLBase.__init(
+        prob::AbstractNonlinearProblem, alg::GeneralizedDFSane, args...;
+        stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, maxiters = 1000,
+        abstol = nothing, reltol = nothing, termination_condition = nothing,
+        maxtime = nothing, kwargs...
+)
+    timer = get_timer_output()
+
+    @static_timeit timer "cache construction" begin
+        u = Utils.maybe_unaliased(prob.u0, alias_u0)
+        T = eltype(u)
+
+        @bb du = similar(u)
+        @bb u_cache = copy(u)
+        fu = Utils.evaluate_f(prob, u)
+        @bb fu_cache = copy(fu)
+
+        linesearch_cache = CommonSolve.init(prob, alg.linesearch, fu, u; stats, kwargs...)
+
+        abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
+            prob, abstol, reltol, fu, u_cache, termination_condition, Val(:regular)
+        )
+        trace = NonlinearSolveBase.init_nonlinearsolve_trace(
+            prob, alg, u, fu, nothing, du; kwargs...
+        )
+
+        if alg.σ_1 === nothing
+            σ_n = dot(u, u) / dot(u, fu)
+            # Spectral parameter bounds check
+            if !(alg.σ_min ≤ abs(σ_n) ≤ alg.σ_max)
+                test_norm = NonlinearSolveBase.L2_NORM(fu)
+                σ_n = clamp(inv(test_norm), T(1), T(1e5))
+            end
+        else
+            σ_n = T(alg.σ_1)
+        end
+
+        return GeneralizedDFSaneCache(
+            fu, fu_cache, u, u_cache, prob.p, du, alg, prob,
+            σ_n, T(alg.σ_min), T(alg.σ_max),
+            linesearch_cache, stats, 0, maxiters, maxtime, timer, 0.0,
+            tc_cache, trace, ReturnCode.Default, false, kwargs
+        )
+    end
+end
+
+function InternalAPI.step!(
+        cache::GeneralizedDFSaneCache; recompute_jacobian::Union{Nothing, Bool} = nothing,
+        kwargs...
+)
+    if recompute_jacobian !== nothing
+        @warn "GeneralizedDFSane is a Jacobian-Free Algorithm. Ignoring \
+              `recompute_jacobian`" maxlog=1
+    end
+
+    @static_timeit cache.timer "descent" begin
+        @bb @. cache.du = -cache.σ_n * cache.fu
+    end
+
+    @static_timeit cache.timer "linesearch" begin
+        linesearch_sol = CommonSolve.solve!(cache.linesearch_cache, cache.u, cache.du)
+        linesearch_failed = !SciMLBase.successful_retcode(linesearch_sol.retcode)
+        α = linesearch_sol.step_size
+    end
+
+    if linesearch_failed
+        cache.retcode = ReturnCode.InternalLineSearchFailed
+        cache.force_stop = true
+        return
+    end
+
+    @static_timeit cache.timer "step" begin
+        @bb axpy!(α, cache.du, cache.u)
+        Utils.evaluate_f!(cache, cache.u, cache.p)
+    end
+
+    update_trace!(cache, α)
+    # XXX: Implement
+    # check_and_update!(cache, cache.fu, cache.u, cache.u_cache)
+
+    # Update Spectral Parameter
+    @static_timeit cache.timer "update spectral parameter" begin
+        @bb @. cache.u_cache = cache.u - cache.u_cache
+        @bb @. cache.fu_cache = cache.fu - cache.fu_cache
+
+        cache.σ_n = Utils.safe_dot(cache.u_cache, cache.u_cache) /
+                    Utils.safe_dot(cache.u_cache, cache.fu_cache)
+
+        # Spectral parameter bounds check
+        if !(cache.σ_min ≤ abs(cache.σ_n) ≤ cache.σ_max)
+            test_norm = NonlinearSolveBase.L2_NORM(cache.fu)
+            T = eltype(cache.σ_n)
+            cache.σ_n = clamp(inv(test_norm), T(1), T(1e5))
+        end
+    end
+
+    # Take step
+    @bb copyto!(cache.u_cache, cache.u)
+    @bb copyto!(cache.fu_cache, cache.fu)
+
+    # XXX: Implement
+    # callback_into_cache!(cache, cache.linesearch_cache)
+
+    return
+end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 409040861..e165bb835 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -37,9 +37,9 @@ import NonlinearSolveBase: InternalAPI, concrete_jac, supports_line_search,
                            supports_trust_region, last_step_accepted, get_linear_solver,
                            AbstractDampingFunction, AbstractDampingFunctionCache,
                            requires_normal_form_jacobian, requires_normal_form_rhs,
-                           returns_norm_form_damping, get_timer_output, get_u, get_fu
+                           returns_norm_form_damping, get_timer_output, get_u, get_fu,
+                           set_fu!
 
-using Printf: @printf
 using Preferences: Preferences, set_preferences!
 using RecursiveArrayTools: recursivecopy!
 using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, AbstractNonlinearProblem,
@@ -83,7 +83,6 @@ include("globalization/trust_region.jl")
 include("core/generic.jl")
 include("core/approximate_jacobian.jl")
 include("core/generalized_first_order.jl")
-include("core/spectral_methods.jl")
 include("core/noinit.jl")
 
 include("algorithms/raphson.jl")
@@ -91,7 +90,6 @@ include("algorithms/pseudo_transient.jl")
 include("algorithms/broyden.jl")
 include("algorithms/klement.jl")
 include("algorithms/lbroyden.jl")
-include("algorithms/dfsane.jl")
 include("algorithms/gauss_newton.jl")
 include("algorithms/levenberg_marquardt.jl")
 include("algorithms/trust_region.jl")
@@ -174,10 +172,11 @@ include("internal/forward_diff.jl") # we need to define after the algorithms
 end
 
 # Rexexports
-@reexport using SciMLBase, SimpleNonlinearSolve, NonlinearSolveBase
+@reexport using SciMLBase, SimpleNonlinearSolve, NonlinearSolveBase,
+                NonlinearSolveSpectralMethods
 
 # Core Algorithms
-export NewtonRaphson, PseudoTransient, Klement, Broyden, LimitedMemoryBroyden, DFSane
+export NewtonRaphson, PseudoTransient, Klement, Broyden, LimitedMemoryBroyden
 export GaussNewton, LevenbergMarquardt, TrustRegion
 export NonlinearSolvePolyAlgorithm, RobustMultiNewton, FastShortcutNonlinearPolyalg,
        FastShortcutNLLSPolyalg
@@ -188,7 +187,7 @@ export LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
 export PETScSNES, CMINPACK
 
 # Advanced Algorithms -- Without Bells and Whistles
-export GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm, GeneralizedDFSane
+export GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm
 
 # Globalization
 ## Line Search Algorithms
@@ -197,9 +196,6 @@ export LineSearch, BackTracking, NoLineSearch, RobustNonMonotoneLineSearch,
 ## Trust Region Algorithms
 export RadiusUpdateSchemes
 
-# Tracing Functionality
-export TraceAll, TraceMinimal, TraceWithJacobianConditionNumber
-
 # Reexport ADTypes
 export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme,
        AutoSparse
diff --git a/src/algorithms/dfsane.jl b/src/algorithms/dfsane.jl
deleted file mode 100644
index 1ece5f5da..000000000
--- a/src/algorithms/dfsane.jl
+++ /dev/null
@@ -1,27 +0,0 @@
-# XXX: remove kwargs with unicode
-"""
-    DFSane(; σ_min = 1 // 10^10, σ_max = 1e10, σ_1 = 1, M::Int = 10, γ = 1 // 10^4,
-        τ_min = 1 // 10, τ_max = 1 // 2, n_exp::Int = 2, max_inner_iterations::Int = 100,
-        η_strategy = (fn_1, n, x_n, f_n) -> fn_1 / n^2)
-
-A low-overhead and allocation-free implementation of the df-sane method for solving
-large-scale nonlinear systems of equations. For in depth information about all the
-parameters and the algorithm, see [la2006spectral](@citet).
-
-### Keyword Arguments
-
-  - `σ_min`: the minimum value of the spectral coefficient `σₙ` which is related to the step
-    size in the algorithm. Defaults to `1e-10`.
-  - `σ_max`: the maximum value of the spectral coefficient `σₙ` which is related to the step
-    size in the algorithm. Defaults to `1e10`.
-
-For other keyword arguments, see [`RobustNonMonotoneLineSearch`](@ref).
-"""
-function DFSane(; σ_min = 1 // 10^10, σ_max = 1e10, σ_1 = 1, M::Int = 10, γ = 1 // 10^4,
-        τ_min = 1 // 10, τ_max = 1 // 2, n_exp::Int = 2, max_inner_iterations::Int = 100,
-        η_strategy::ETA = (fn_1, n, x_n, f_n) -> fn_1 / n^2) where {ETA}
-    linesearch = RobustNonMonotoneLineSearch(;
-        gamma = γ, sigma_1 = σ_1, M, tau_min = τ_min, tau_max = τ_max,
-        n_exp, η_strategy, maxiters = max_inner_iterations)
-    return GeneralizedDFSane{:DFSane}(linesearch, σ_min, σ_max, nothing)
-end
diff --git a/src/core/generic.jl b/src/core/generic.jl
index 44e6e1152..df6f2ecff 100644
--- a/src/core/generic.jl
+++ b/src/core/generic.jl
@@ -55,8 +55,7 @@ function SciMLBase.step!(cache::AbstractNonlinearSolveCache{iip, timeit},
 
     if timeit
         cache.total_time += time() - time_start
-        if !cache.force_stop &&
-           cache.retcode == ReturnCode.Default &&
+        if !cache.force_stop && cache.retcode == ReturnCode.Default &&
            cache.total_time ≥ cache.maxtime
             cache.retcode = ReturnCode.MaxTime
             cache.force_stop = true
diff --git a/src/core/spectral_methods.jl b/src/core/spectral_methods.jl
deleted file mode 100644
index c3303b9dd..000000000
--- a/src/core/spectral_methods.jl
+++ /dev/null
@@ -1,211 +0,0 @@
-# For spectral methods we currently only implement DF-SANE since after reading through
-# papers, this seems to be the only one that is widely used. If we have a list of more
-# papers we can see what is the right level of abstraction to implement here
-"""
-    GeneralizedDFSane{name}(linesearch, σ_min, σ_max, σ_1)
-
-A generalized version of the DF-SANE algorithm. This algorithm is a Jacobian-Free Spectral
-Method.
-
-### Arguments
-
-  - `linesearch`: Globalization using a Line Search Method. This is not optional currently,
-    but that restriction might be lifted in the future.
-  - `σ_min`: The minimum spectral parameter allowed. This is used to ensure that the
-    spectral parameter is not too small.
-  - `σ_max`: The maximum spectral parameter allowed. This is used to ensure that the
-    spectral parameter is not too large.
-  - `σ_1`: The initial spectral parameter. If this is not provided, then the algorithm
-    initializes it as `σ_1 = <u, u> / <u, f(u)>`.
-"""
-@concrete struct GeneralizedDFSane{name} <: AbstractNonlinearSolveAlgorithm{name}
-    linesearch
-    σ_min
-    σ_max
-    σ_1
-end
-
-function __show_algorithm(io::IO, alg::GeneralizedDFSane, name, indent)
-    modifiers = String[]
-    __is_present(alg.linesearch) && push!(modifiers, "linesearch = $(alg.linesearch)")
-    push!(modifiers, "σ_min = $(alg.σ_min)")
-    push!(modifiers, "σ_max = $(alg.σ_max)")
-    push!(modifiers, "σ_1 = $(alg.σ_1)")
-    spacing = " "^indent * "    "
-    spacing_last = " "^indent
-    print(io, "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))")
-end
-
-# XXX: Remove
-concrete_jac(::GeneralizedDFSane) = false
-
-@concrete mutable struct GeneralizedDFSaneCache{iip, timeit} <:
-                         AbstractNonlinearSolveCache{iip, timeit}
-    # Basic Requirements
-    fu
-    fu_cache
-    u
-    u_cache
-    p
-    du
-    alg
-    prob
-
-    # Parameters
-    σ_n
-    σ_min
-    σ_max
-
-    # Internal Caches
-    linesearch_cache
-
-    # Counters
-    stats::NLStats
-    nsteps::Int
-    maxiters::Int
-    maxtime
-
-    # Timer
-    timer
-    total_time::Float64   # Simple Counter which works even if TimerOutput is disabled
-
-    # Termination & Tracking
-    termination_cache
-    trace
-    retcode::ReturnCode.T
-    force_stop::Bool
-    kwargs
-end
-
-function __reinit_internal!(
-        cache::GeneralizedDFSaneCache{iip}, args...; p = cache.p, u0 = cache.u,
-        alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...) where {iip}
-    if iip
-        recursivecopy!(cache.u, u0)
-        cache.prob.f(cache.fu, cache.u, p)
-    else
-        cache.u = __maybe_unaliased(u0, alias_u0)
-        set_fu!(cache, cache.prob.f(cache.u, p))
-    end
-    cache.p = p
-
-    if cache.alg.σ_1 === nothing
-        σ_n = dot(cache.u, cache.u) / dot(cache.u, cache.fu)
-        # Spectral parameter bounds check
-        if !(cache.alg.σ_min ≤ abs(σ_n) ≤ cache.alg.σ_max)
-            test_norm = dot(cache.fu, cache.fu)
-            σ_n = clamp(inv(test_norm), T(1), T(1e5))
-        end
-    else
-        σ_n = T(cache.alg.σ_1)
-    end
-    cache.σ_n = σ_n
-
-    reset_timer!(cache.timer)
-    cache.total_time = 0.0
-
-    reset!(cache.trace)
-    reinit!(cache.termination_cache, get_fu(cache), get_u(cache); kwargs...)
-    __reinit_internal!(cache.stats)
-    cache.nsteps = 0
-    cache.maxiters = maxiters
-    cache.maxtime = maxtime
-    cache.force_stop = false
-    cache.retcode = ReturnCode.Default
-end
-
-@internal_caches GeneralizedDFSaneCache :linesearch_cache
-
-function SciMLBase.__init(prob::AbstractNonlinearProblem, alg::GeneralizedDFSane, args...;
-        stats = empty_nlstats(), alias_u0 = false, maxiters = 1000,
-        abstol = nothing, reltol = nothing, termination_condition = nothing,
-        maxtime = nothing, kwargs...)
-    timer = get_timer_output()
-    @static_timeit timer "cache construction" begin
-        u = __maybe_unaliased(prob.u0, alias_u0)
-        T = eltype(u)
-
-        @bb du = similar(u)
-        @bb u_cache = copy(u)
-        fu = evaluate_f(prob, u)
-        @bb fu_cache = copy(fu)
-
-        linesearch_cache = init(prob, alg.linesearch, fu, u; stats, kwargs...)
-
-        abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
-            prob, abstol, reltol, fu, u_cache, termination_condition, Val(:regular))
-        trace = init_nonlinearsolve_trace(prob, alg, u, fu, nothing, du; kwargs...)
-
-        if alg.σ_1 === nothing
-            σ_n = dot(u, u) / dot(u, fu)
-            # Spectral parameter bounds check
-            if !(alg.σ_min ≤ abs(σ_n) ≤ alg.σ_max)
-                test_norm = dot(fu, fu)
-                σ_n = clamp(inv(test_norm), T(1), T(1e5))
-            end
-        else
-            σ_n = T(alg.σ_1)
-        end
-
-        return GeneralizedDFSaneCache{isinplace(prob), maxtime !== nothing}(
-            fu, fu_cache, u, u_cache, prob.p, du, alg, prob, σ_n, T(alg.σ_min),
-            T(alg.σ_max), linesearch_cache, stats, 0, maxiters, maxtime,
-            timer, 0.0, tc_cache, trace, ReturnCode.Default, false, kwargs)
-    end
-end
-
-function __step!(cache::GeneralizedDFSaneCache{iip};
-        recompute_jacobian::Union{Nothing, Bool} = nothing, kwargs...) where {iip}
-    if recompute_jacobian !== nothing
-        @warn "GeneralizedDFSane is a Jacobian-Free Algorithm. Ignoring \
-              `recompute_jacobian`" maxlog=1
-    end
-
-    @static_timeit cache.timer "descent" begin
-        @bb @. cache.du = -cache.σ_n * cache.fu
-    end
-
-    @static_timeit cache.timer "linesearch" begin
-        linesearch_sol = solve!(cache.linesearch_cache, cache.u, cache.du)
-        linesearch_failed = !SciMLBase.successful_retcode(linesearch_sol.retcode)
-        α = linesearch_sol.step_size
-    end
-
-    if linesearch_failed
-        cache.retcode = ReturnCode.InternalLineSearchFailed
-        cache.force_stop = true
-        return
-    end
-
-    @static_timeit cache.timer "step" begin
-        @bb axpy!(α, cache.du, cache.u)
-        evaluate_f!(cache, cache.u, cache.p)
-    end
-
-    update_trace!(cache, α)
-    check_and_update!(cache, cache.fu, cache.u, cache.u_cache)
-
-    # Update Spectral Parameter
-    @static_timeit cache.timer "update spectral parameter" begin
-        @bb @. cache.u_cache = cache.u - cache.u_cache
-        @bb @. cache.fu_cache = cache.fu - cache.fu_cache
-
-        cache.σ_n = __dot(cache.u_cache, cache.u_cache) /
-                    __dot(cache.u_cache, cache.fu_cache)
-
-        # Spectral parameter bounds check
-        if !(cache.σ_min ≤ abs(cache.σ_n) ≤ cache.σ_max)
-            test_norm = dot(cache.fu, cache.fu)
-            T = eltype(cache.σ_n)
-            cache.σ_n = clamp(inv(test_norm), T(1), T(1e5))
-        end
-    end
-
-    # Take step
-    @bb copyto!(cache.u_cache, cache.u)
-    @bb copyto!(cache.fu_cache, cache.fu)
-
-    callback_into_cache!(cache, cache.linesearch_cache)
-
-    return
-end

From 38088d9d54ad7d57d3e783d14e457739fdc51c9f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 27 Oct 2024 21:00:37 -0400
Subject: [PATCH 639/700] refactor: create Quasi Newton Algorithm subpackage

---
 Project.toml                                  |   1 +
 common/nlls_problem_workloads.jl              |   1 +
 docs/src/release_notes.md                     |   1 +
 .../ext/NonlinearSolveBaseSparseArraysExt.jl  |   5 +-
 .../src/NonlinearSolveBase.jl                 |   2 +-
 lib/NonlinearSolveBase/src/abstract_types.jl  | 169 +++++++-
 lib/NonlinearSolveBase/src/jacobian.jl        |   3 +-
 lib/NonlinearSolveBase/src/tracing.jl         |   7 +-
 lib/NonlinearSolveBase/src/utils.jl           |  44 +-
 lib/NonlinearSolveFirstOrder/test/runtests.jl |   1 +
 lib/NonlinearSolveQuasiNewton/Project.toml    |  30 ++
 .../src/NonlinearSolveQuasiNewton.jl          |  52 +++
 lib/NonlinearSolveQuasiNewton/src/broyden.jl  | 162 +++++++
 .../src/initialization.jl                     | 279 ++++++++++++
 .../NonlinearSolveQuasiNewton/src}/klement.jl | 114 +++--
 lib/NonlinearSolveQuasiNewton/src/lbroyden.jl |  35 ++
 .../src/reset_conditions.jl                   | 120 +++++
 lib/NonlinearSolveQuasiNewton/src/solve.jl    | 409 ++++++++++++++++++
 .../src/structure.jl                          |  53 +++
 .../test/runtests.jl                          |   1 +
 .../src/dfsane.jl                             |   4 +-
 .../src/solve.jl                              |  12 +-
 .../test/runtests.jl                          |   1 +
 src/NonlinearSolve.jl                         |  14 +-
 src/algorithms/broyden.jl                     | 227 ----------
 src/algorithms/lbroyden.jl                    | 169 --------
 src/core/approximate_jacobian.jl              | 378 ----------------
 src/internal/approximate_initialization.jl    | 281 ------------
 28 files changed, 1427 insertions(+), 1148 deletions(-)
 create mode 100644 lib/NonlinearSolveQuasiNewton/src/broyden.jl
 create mode 100644 lib/NonlinearSolveQuasiNewton/src/initialization.jl
 rename {src/algorithms => lib/NonlinearSolveQuasiNewton/src}/klement.jl (58%)
 create mode 100644 lib/NonlinearSolveQuasiNewton/src/lbroyden.jl
 create mode 100644 lib/NonlinearSolveQuasiNewton/src/reset_conditions.jl
 create mode 100644 lib/NonlinearSolveQuasiNewton/src/solve.jl
 create mode 100644 lib/NonlinearSolveQuasiNewton/src/structure.jl
 delete mode 100644 src/algorithms/broyden.jl
 delete mode 100644 src/algorithms/lbroyden.jl
 delete mode 100644 src/core/approximate_jacobian.jl
 delete mode 100644 src/internal/approximate_initialization.jl

diff --git a/Project.toml b/Project.toml
index 262412366..e08da6b42 100644
--- a/Project.toml
+++ b/Project.toml
@@ -19,6 +19,7 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
+NonlinearSolveQuasiNewton = "9a2c21bd-3a47-402d-9113-8faf9a0ee114"
 NonlinearSolveSpectralMethods = "26075421-4e9a-44e1-8bd1-420ed7ad02b2"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Preferences = "21216c6a-2e73-6563-6e65-726566657250"
diff --git a/common/nlls_problem_workloads.jl b/common/nlls_problem_workloads.jl
index e69de29bb..8b1378917 100644
--- a/common/nlls_problem_workloads.jl
+++ b/common/nlls_problem_workloads.jl
@@ -0,0 +1 @@
+
diff --git a/docs/src/release_notes.md b/docs/src/release_notes.md
index 1dc3d9433..bb0b5dec9 100644
--- a/docs/src/release_notes.md
+++ b/docs/src/release_notes.md
@@ -4,6 +4,7 @@
 
 ### Breaking Changes in `NonlinearSolve.jl` v4
 
+  - `ApproximateJacobianSolveAlgorithm` has been renamed to `QuasiNewtonAlgorithm`.
   - See [common breaking changes](@ref common-breaking-changes-v4v2) below.
 
 ### Breaking Changes in `SimpleNonlinearSolve.jl` v2
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
index 6d60761d2..09b113c4a 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
@@ -15,6 +15,9 @@ Utils.make_sparse(x) = sparse(x)
 
 Utils.condition_number(J::AbstractSparseMatrix) = Utils.condition_number(Matrix(J))
 
-Utils.maybe_pinv!!_workspace(A::AbstractSparseMatrix) = Matrix(A)
+function Utils.maybe_pinv!!_workspace(A::AbstractSparseMatrix)
+    dense_A = Matrix(A)
+    return dense_A, copy(dense_A)
+end
 
 end
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index a0c5a524c..aed943d7e 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -11,7 +11,7 @@ using DifferentiationInterface: DifferentiationInterface, Constant
 using EnzymeCore: EnzymeCore
 using FastClosures: @closure
 using FunctionProperties: hasbranching
-using LinearAlgebra: LinearAlgebra, Diagonal, norm, ldiv!, diagind
+using LinearAlgebra: LinearAlgebra, Diagonal, norm, ldiv!, diagind, pinv
 using Markdown: @doc_str
 using MaybeInplace: @bb
 using Preferences: @load_preference
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index d62a637e0..2ae4091e7 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -226,11 +226,11 @@ Abstract Type for all NonlinearSolveBase Caches.
 ### Interface Functions
 
   - `get_fu(cache)`: get the residual.
+
   - `get_u(cache)`: get the current state.
   - `set_fu!(cache, fu)`: set the residual.
   - `has_time_limit(cache)`: whether or not the solver has a maximum time limit.
   - `not_terminated(cache)`: whether or not the solver has terminated.
-
   - `SciMLBase.set_u!(cache, u)`: set the current state.
   - `SciMLBase.reinit!(cache, u0; kwargs...)`: reinitialize the cache with the initial state
     `u0` and any additional keyword arguments.
@@ -339,3 +339,170 @@ Abstract Type for all Jacobian Caches used in NonlinearSolveBase. Subtypes of th
 meant to be constructured via [`construct_jacobian_cache`](@ref).
 """
 abstract type AbstractJacobianCache <: AbstractNonlinearSolveBaseAPI end
+
+"""
+    AbstractApproximateJacobianStructure
+
+Abstract Type for all Approximate Jacobian Structures used in NonlinearSolve.jl.
+
+### Interface Functions
+
+  - `stores_full_jacobian(alg)`: whether or not the algorithm stores the full Jacobian.
+    Defaults to `false`.
+  - `get_full_jacobian(cache, alg, J)`: get the full Jacobian. Defaults to throwing an
+    error if `stores_full_jacobian(alg)` is `false`.
+"""
+abstract type AbstractApproximateJacobianStructure <: AbstractNonlinearSolveBaseAPI end
+
+stores_full_jacobian(::AbstractApproximateJacobianStructure) = false
+function get_full_jacobian(cache, alg::AbstractApproximateJacobianStructure, J)
+    stores_full_jacobian(alg) && return J
+    error("This algorithm does not store the full Jacobian. Define `get_full_jacobian` for \
+           this algorithm.")
+end
+
+"""
+    AbstractJacobianInitialization
+
+Abstract Type for all Jacobian Initialization Algorithms used in NonlinearSolveBase.
+
+### Interface Functions
+
+  - `jacobian_initialized_preinverted(alg)`: whether or not the Jacobian is initialized
+    preinverted. Defaults to `false`.
+
+### `InternalAPI.init` specification
+
+```julia
+InternalAPI.init(
+    prob::AbstractNonlinearProblem, alg::AbstractJacobianInitialization, solver,
+    f, fu, u, p;
+    linsolve = missing, internalnorm::IN = L2_NORM, kwargs...
+)::AbstractJacobianCache
+```
+
+All subtypes need to define
+`(cache::AbstractJacobianCache)(alg::NewSubType, fu, u)` which reinitializes the Jacobian in
+`cache.J`.
+"""
+abstract type AbstractJacobianInitialization <: AbstractNonlinearSolveBaseAPI end
+
+jacobian_initialized_preinverted(::AbstractJacobianInitialization) = false
+
+"""
+    AbstractApproximateJacobianUpdateRule
+
+Abstract Type for all Approximate Jacobian Update Rules used in NonlinearSolveBase.
+
+### Interface Functions
+
+  - `store_inverse_jacobian(alg)`: Return `alg.store_inverse_jacobian`
+
+### `InternalAPI.init` specification
+
+```julia
+InternalAPI.init(
+    prob::AbstractNonlinearProblem, alg::AbstractApproximateJacobianUpdateRule, J, fu, u,
+    du, args...; internalnorm = L2_NORM, kwargs...
+)::AbstractApproximateJacobianUpdateRuleCache
+```
+"""
+abstract type AbstractApproximateJacobianUpdateRule <: AbstractNonlinearSolveBaseAPI end
+
+function store_inverse_jacobian(rule::AbstractApproximateJacobianUpdateRule)
+    return rule.store_inverse_jacobian
+end
+
+"""
+    AbstractApproximateJacobianUpdateRuleCache
+
+Abstract Type for all Approximate Jacobian Update Rule Caches used in NonlinearSolveBase.
+
+### Interface Functions
+
+  - `store_inverse_jacobian(cache)`: Return `store_inverse_jacobian(cache.rule)`
+
+### `InternalAPI.solve!` specification
+
+```julia
+InternalAPI.solve!(
+    cache::AbstractApproximateJacobianUpdateRuleCache, J, fu, u, du; kwargs...
+) --> J / J⁻¹
+```
+"""
+abstract type AbstractApproximateJacobianUpdateRuleCache <: AbstractNonlinearSolveBaseAPI end
+
+function store_inverse_jacobian(cache::AbstractApproximateJacobianUpdateRuleCache)
+    return store_inverse_jacobian(cache.rule)
+end
+
+"""
+    AbstractResetCondition
+
+Condition for resetting the Jacobian in Quasi-Newton's methods.
+
+### `InternalAPI.init` specification
+
+```julia
+InternalAPI.init(
+    alg::AbstractResetCondition, J, fu, u, du, args...; kwargs...
+)::AbstractResetConditionCache
+```
+"""
+abstract type AbstractResetCondition <: AbstractNonlinearSolveBaseAPI end
+
+"""
+    AbstractResetConditionCache
+
+Abstract Type for all Reset Condition Caches used in NonlinearSolveBase.
+
+### `InternalAPI.solve!` specification
+
+```julia
+InternalAPI.solve!(
+    cache::AbstractResetConditionCache, J, fu, u, du; kwargs...
+)::Bool
+```
+"""
+abstract type AbstractResetConditionCache <: AbstractNonlinearSolveBaseAPI end
+
+"""
+    AbstractTrustRegionMethod
+
+Abstract Type for all Trust Region Methods used in NonlinearSolveBase.
+
+### `InternalAPI.init` specification
+
+```julia
+InternalAPI.init(
+    prob::AbstractNonlinearProblem, alg::AbstractTrustRegionMethod, f, fu, u, p, args...;
+    internalnorm = L2_NORM, kwargs...
+)::AbstractTrustRegionMethodCache
+```
+"""
+abstract type AbstractTrustRegionMethod <: AbstractNonlinearSolveBaseAPI end
+
+"""
+    AbstractTrustRegionMethodCache
+
+Abstract Type for all Trust Region Method Caches used in NonlinearSolveBase.
+
+### Interface Functions
+
+  - `last_step_accepted(cache)`: whether or not the last step was accepted. Defaults to
+    `cache.last_step_accepted`. Should if overloaded if the field is not present.
+
+### `InternalAPI.solve!` specification
+
+```julia
+InternalAPI.solve!(
+    cache::AbstractTrustRegionMethodCache, J, fu, u, δu, descent_stats; kwargs...
+)
+```
+
+Returns `last_step_accepted`, updated `u_cache` and `fu_cache`. If the last step was
+accepted then these values should be copied into the toplevel cache.
+"""
+abstract type AbstractTrustRegionMethodCache <: AbstractNonlinearSolveBaseAPI end
+
+last_step_accepted(cache::AbstractTrustRegionMethodCache) = cache.last_step_accepted
diff --git a/lib/NonlinearSolveBase/src/jacobian.jl b/lib/NonlinearSolveBase/src/jacobian.jl
index 5725d3687..73a544b8b 100644
--- a/lib/NonlinearSolveBase/src/jacobian.jl
+++ b/lib/NonlinearSolveBase/src/jacobian.jl
@@ -122,8 +122,7 @@ end
     di_extras
 end
 
-function InternalAPI.reinit!(
-        cache::JacobianCache, args...; p = cache.p, u0 = cache.u, kwargs...)
+function InternalAPI.reinit!(cache::JacobianCache; p = cache.p, u0 = cache.u, kwargs...)
     cache.u = u0
     cache.p = p
 end
diff --git a/lib/NonlinearSolveBase/src/tracing.jl b/lib/NonlinearSolveBase/src/tracing.jl
index 5c67a0503..2dd88ecee 100644
--- a/lib/NonlinearSolveBase/src/tracing.jl
+++ b/lib/NonlinearSolveBase/src/tracing.jl
@@ -205,7 +205,7 @@ function update_trace!(
     return trace
 end
 
-function update_trace!(cache, α = true)
+function update_trace!(cache, α = true; uses_jac_inverse = Val(false))
     trace = Utils.safe_getproperty(cache, Val(:trace))
     trace === missing && return nothing
 
@@ -214,11 +214,8 @@ function update_trace!(cache, α = true)
         update_trace!(
             trace, cache.nsteps + 1, get_u(cache), get_fu(cache), nothing, cache.du, α
         )
-        # XXX: Implement
-        # elseif cache isa ApproximateJacobianSolveCache && store_inverse_jacobian(cache)
-        #     update_trace!(trace, cache.nsteps + 1, get_u(cache), get_fu(cache),
-        #         ApplyArray(__safe_inv, J), cache.du, α)
     else
+        J = uses_jac_inverse isa Val{true} ? pinv(J) : J
         update_trace!(trace, cache.nsteps + 1, get_u(cache), get_fu(cache), J, cache.du, α)
     end
 end
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index be691d8ba..af5bd63c6 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -2,12 +2,12 @@ module Utils
 
 using ArrayInterface: ArrayInterface
 using FastClosures: @closure
-using LinearAlgebra: LinearAlgebra, Diagonal, Symmetric, norm, dot, cond, diagind, pinv
+using LinearAlgebra: LinearAlgebra, Diagonal, Symmetric, norm, dot, cond, diagind, pinv, inv
 using MaybeInplace: @bb
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLOperators: AbstractSciMLOperator
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, NonlinearFunction
-using StaticArraysCore: StaticArray, SArray
+using StaticArraysCore: StaticArray, SArray, SMatrix
 
 using ..NonlinearSolveBase: NonlinearSolveBase, L2_NORM, Linf_NORM
 
@@ -180,7 +180,7 @@ condition_number(::Any) = -1
 
 # XXX: Move to NonlinearSolveQuasiNewton
 # compute `pinv` if `inv` won't work
-maybe_pinv!!_workspace(A) = nothing
+maybe_pinv!!_workspace(A) = nothing, A
 
 maybe_pinv!!(workspace, A::Union{Number, AbstractMatrix}) = pinv(A)
 function maybe_pinv!!(workspace, A::Diagonal)
@@ -193,12 +193,12 @@ function maybe_pinv!!(workspace, A::StridedMatrix)
     LinearAlgebra.checksquare(A)
     if LinearAlgebra.istriu(A)
         issingular = any(iszero, @view(A[diagind(A)]))
-        A_ = UpperTriangular(A)
-        !issingular && return triu!(parent(inv(A_)))
+        A_ = LinearAlgebra.UpperTriangular(A)
+        !issingular && return LinearAlgebra.triu!(parent(inv(A_)))
     elseif LinearAlgebra.istril(A)
-        A_ = LowerTriangular(A)
+        A_ = LinearAlgebra.LowerTriangular(A)
         issingular = any(iszero, @view(A_[diagind(A_)]))
-        !issingular && return tril!(parent(inv(A_)))
+        !issingular && return LinearAlgebra.tril!(parent(inv(A_)))
     else
         F = LinearAlgebra.lu(A; check = false)
         if issuccess(F)
@@ -209,4 +209,34 @@ function maybe_pinv!!(workspace, A::StridedMatrix)
     return pinv(A)
 end
 
+function initial_jacobian_scaling_alpha(α, u, fu, ::Any)
+    return convert(promote_type(eltype(u), eltype(fu)), α)
+end
+function initial_jacobian_scaling_alpha(::Nothing, u, fu, internalnorm::F) where {F}
+    fu_norm = internalnorm(fu)
+    fu_norm < 1e-5 && return initial_jacobian_scaling_alpha(true, u, fu, internalnorm)
+    return (2 * fu_norm) / max(L2_NORM(u), true)
+end
+
+make_identity!!(::T, α) where {T <: Number} = T(α)
+function make_identity!!(A::AbstractVector{T}, α) where {T}
+    @bb @. A = T(α)
+    return A
+end
+function make_identity!!(::SMatrix{S1, S2, T, L}, α) where {S1, S2, T, L}
+    return SMatrix{S1, S2, T, L}(LinearAlgebra.I * α)
+end
+function make_identity!!(A::AbstractMatrix{T}, α) where {T}
+    A = ArrayInterface.can_setindex(A) ? A : similar(A)
+    fill!(A, false)
+    if ArrayInterface.fast_scalar_indexing(A)
+        @simd ivdep for i in axes(A, 1)
+            @inbounds A[i, i] = α
+        end
+    else
+        A[diagind(A)] .= α
+    end
+    return A
+end
+
 end
diff --git a/lib/NonlinearSolveFirstOrder/test/runtests.jl b/lib/NonlinearSolveFirstOrder/test/runtests.jl
index e69de29bb..8b1378917 100644
--- a/lib/NonlinearSolveFirstOrder/test/runtests.jl
+++ b/lib/NonlinearSolveFirstOrder/test/runtests.jl
@@ -0,0 +1 @@
+
diff --git a/lib/NonlinearSolveQuasiNewton/Project.toml b/lib/NonlinearSolveQuasiNewton/Project.toml
index 92fbd9bde..ae49ced0c 100644
--- a/lib/NonlinearSolveQuasiNewton/Project.toml
+++ b/lib/NonlinearSolveQuasiNewton/Project.toml
@@ -3,15 +3,45 @@ uuid = "9a2c21bd-3a47-402d-9113-8faf9a0ee114"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
 version = "1.0.0"
 
+[deps]
+ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
+ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
+DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
+MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
+NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
+PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
+Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
+StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+
 [compat]
 Aqua = "0.8"
+ArrayInterface = "7.16.0"
+CommonSolve = "0.2.4"
+ConcreteStructs = "0.2.3"
+DiffEqBase = "6.155.3"
 ExplicitImports = "1.5"
 Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
+LineSearch = "0.1.4"
+LinearAlgebra = "1.11.0"
+LinearSolve = "2.36.1"
+MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
+NonlinearSolveBase = "1.1"
 Pkg = "1.10"
+PrecompileTools = "1.2"
 ReTestItems = "1.24"
+Reexport = "1"
+SciMLBase = "2.54"
+SciMLOperators = "0.3.11"
 StableRNGs = "1"
+StaticArraysCore = "1.4.3"
 Test = "1.10"
 julia = "1.10"
 
diff --git a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
index 91cb46015..7068ebc60 100644
--- a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
@@ -1,3 +1,55 @@
 module NonlinearSolveQuasiNewton
 
+using Reexport: @reexport
+using PrecompileTools: @compile_workload, @setup_workload
+
+using ArrayInterface: ArrayInterface
+using CommonSolve: CommonSolve
+using ConcreteStructs: @concrete
+using DiffEqBase: DiffEqBase   # Needed for `init` / `solve` dispatches
+using LinearAlgebra: LinearAlgebra, Diagonal, dot, inv, diag
+using LinearSolve: LinearSolve # Trigger Linear Solve extension in NonlinearSolveBase
+using MaybeInplace: @bb
+using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
+                          AbstractNonlinearSolveCache, AbstractResetCondition,
+                          AbstractResetConditionCache, AbstractApproximateJacobianStructure,
+                          AbstractJacobianCache, AbstractJacobianInitialization,
+                          AbstractApproximateJacobianUpdateRule, AbstractDescentDirection,
+                          AbstractApproximateJacobianUpdateRuleCache,
+                          Utils, InternalAPI, get_timer_output, @static_timeit,
+                          update_trace!, L2_NORM, NewtonDescent
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode
+using SciMLOperators: AbstractSciMLOperator
+using StaticArraysCore: StaticArray, Size, MArray
+
+include("reset_conditions.jl")
+include("structure.jl")
+include("initialization.jl")
+
+include("broyden.jl")
+include("lbroyden.jl")
+include("klement.jl")
+
+include("solve.jl")
+
+@setup_workload begin
+    include(joinpath(
+        @__DIR__, "..", "..", "..", "common", "nonlinear_problem_workloads.jl"
+    ))
+
+    algs = [Broyden(), Klement()]
+
+    @compile_workload begin
+        @sync begin
+            for prob in nonlinear_problems, alg in algs
+                Threads.@spawn CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
+            end
+        end
+    end
+end
+
+@reexport using SciMLBase, NonlinearSolveBase
+
+export Broyden, LimitedMemoryBroyden, Klement, QuasiNewtonAlgorithm
+
 end
diff --git a/lib/NonlinearSolveQuasiNewton/src/broyden.jl b/lib/NonlinearSolveQuasiNewton/src/broyden.jl
new file mode 100644
index 000000000..60adc9be5
--- /dev/null
+++ b/lib/NonlinearSolveQuasiNewton/src/broyden.jl
@@ -0,0 +1,162 @@
+"""
+    Broyden(;
+        max_resets::Int = 100, linesearch = nothing, reset_tolerance = nothing,
+        init_jacobian::Val = Val(:identity), autodiff = nothing, alpha = nothing,
+        update_rule = Val(:good_broyden)
+    )
+
+An implementation of `Broyden`'s Method [broyden1965class](@cite) with resetting and line
+search.
+
+### Keyword Arguments
+
+  - `max_resets`: the maximum number of resets to perform. Defaults to `100`.
+
+  - `reset_tolerance`: the tolerance for the reset check. Defaults to
+    `sqrt(eps(real(eltype(u))))`.
+  - `alpha`: If `init_jacobian` is set to `Val(:identity)`, then the initial Jacobian
+    inverse is set to be `(αI)⁻¹`. Defaults to `nothing` which implies
+    `α = max(norm(u), 1) / (2 * norm(fu))`.
+  - `init_jacobian`: the method to use for initializing the jacobian. Defaults to
+    `Val(:identity)`. Choices include:
+
+      + `Val(:identity)`: Identity Matrix.
+      + `Val(:true_jacobian)`: True Jacobian. This is a good choice for differentiable
+        problems.
+  - `update_rule`: Update Rule for the Jacobian. Choices are:
+
+      + `Val(:good_broyden)`: Good Broyden's Update Rule
+      + `Val(:bad_broyden)`: Bad Broyden's Update Rule
+      + `Val(:diagonal)`: Only update the diagonal of the Jacobian. This algorithm may be
+        useful for specific problems, but whether it will work may depend strongly on the
+        problem
+"""
+function Broyden(;
+        max_resets::Int = 100, linesearch = nothing, reset_tolerance = nothing,
+        init_jacobian::Val = Val(:identity), autodiff = nothing, alpha = nothing,
+        update_rule = Val(:good_broyden)
+)
+    return QuasiNewtonAlgorithm(;
+        linesearch,
+        descent = NewtonDescent(),
+        update_rule = broyden_update_rule(update_rule),
+        max_resets,
+        initialization = broyden_init(init_jacobian, update_rule, autodiff, alpha),
+        reinit_rule = NoChangeInStateReset(; reset_tolerance),
+        concrete_jac = Val(init_jacobian isa Val{:true_jacobian}),
+        name = :Broyden
+    )
+end
+
+function broyden_init(::Val{:identity}, ::Val{:diagonal}, autodiff, alpha)
+    return IdentityInitialization(alpha, DiagonalStructure())
+end
+function broyden_init(::Val{:identity}, ::Val, autodiff, alpha)
+    IdentityInitialization(alpha, FullStructure())
+end
+function broyden_init(::Val{:true_jacobian}, ::Val, autodiff, alpha)
+    return TrueJacobianInitialization(FullStructure(), autodiff)
+end
+function broyden_init(::Val{IJ}, ::Val{UR}, autodiff, alpha) where {IJ, UR}
+    error("Unknown combination of `init_jacobian = Val($(Meta.quot(IJ)))` and \
+           `update_rule = Val($(Meta.quot(UR)))`. Please choose a valid combination.")
+end
+
+broyden_update_rule(::Val{:good_broyden}) = GoodBroydenUpdateRule()
+broyden_update_rule(::Val{:bad_broyden}) = BadBroydenUpdateRule()
+broyden_update_rule(::Val{:diagonal}) = GoodBroydenUpdateRule()
+function broyden_update_rule(::Val{UR}) where {UR}
+    error("Unknown update rule `update_rule = Val($(Meta.quot(UR)))`. Please choose a \
+           valid update rule.")
+end
+
+"""
+    BadBroydenUpdateRule()
+
+Broyden Update Rule corresponding to "bad broyden's method" [broyden1965class](@cite).
+"""
+struct BadBroydenUpdateRule <: AbstractApproximateJacobianUpdateRule end
+
+"""
+    GoodBroydenUpdateRule()
+
+Broyden Update Rule corresponding to "good broyden's method" [broyden1965class](@cite).
+"""
+struct GoodBroydenUpdateRule <: AbstractApproximateJacobianUpdateRule end
+
+for rType in (:BadBroydenUpdateRule, :GoodBroydenUpdateRule)
+    @eval function Base.getproperty(rule::$(rType), sym::Symbol)
+        sym == :store_inverse_jacobian && return Val(true)
+        return getfield(rule, sym)
+    end
+end
+
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem,
+        alg::Union{BadBroydenUpdateRule, GoodBroydenUpdateRule},
+        J, fu, u, du, args...; internalnorm::F = L2_NORM, kwargs...
+) where {F}
+    @bb J⁻¹dfu = similar(u)
+    @bb dfu = copy(fu)
+    if alg isa GoodBroydenUpdateRule || J isa Diagonal
+        @bb u_cache = similar(u)
+    else
+        u_cache = nothing
+    end
+    if J isa Diagonal
+        du_cache = nothing
+    else
+        @bb du_cache = similar(du)
+    end
+    return BroydenUpdateRuleCache(J⁻¹dfu, dfu, u_cache, du_cache, internalnorm, alg)
+end
+
+@concrete mutable struct BroydenUpdateRuleCache <:
+                         AbstractApproximateJacobianUpdateRuleCache
+    J⁻¹dfu
+    dfu
+    u_cache
+    du_cache
+    internalnorm
+    rule <: Union{BadBroydenUpdateRule, GoodBroydenUpdateRule}
+end
+
+function InternalAPI.solve!(
+        cache::BroydenUpdateRuleCache, J⁻¹, fu, u, du; kwargs...
+)
+    T = eltype(u)
+    @bb @. cache.dfu = fu - cache.dfu
+    @bb cache.J⁻¹dfu = J⁻¹ × vec(cache.dfu)
+    if cache.rule isa GoodBroydenUpdateRule
+        @bb cache.u_cache = transpose(J⁻¹) × vec(du)
+        denom = dot(du, cache.J⁻¹dfu)
+        rmul = transpose(Utils.safe_vec(cache.u_cache))
+    else
+        denom = cache.internalnorm(cache.dfu)^2
+        rmul = transpose(Utils.safe_vec(cache.dfu))
+    end
+    @bb @. cache.du_cache = (du - cache.J⁻¹dfu) / ifelse(iszero(denom), T(1e-5), denom)
+    @bb J⁻¹ += vec(cache.du_cache) × rmul
+    @bb copyto!(cache.dfu, fu)
+    return J⁻¹
+end
+
+function InternalAPI.solve!(
+        cache::BroydenUpdateRuleCache, J⁻¹::Diagonal, fu, u, du; kwargs...
+)
+    T = eltype(u)
+    @bb @. cache.dfu = fu - cache.dfu
+    J⁻¹_diag = Utils.restructure(cache.dfu, diag(J⁻¹))
+    if cache.rule isa GoodBroydenUpdateRule
+        @bb @. J⁻¹_diag = J⁻¹_diag * cache.dfu * du
+        denom = sum(J⁻¹_diag)
+        @bb @. J⁻¹_diag = J⁻¹_diag + (du - J⁻¹_diag * cache.dfu) * du * J⁻¹_diag /
+                          ifelse(iszero(denom), T(1e-5), denom)
+    else
+        denom = cache.internalnorm(cache.dfu)^2
+        @bb @. J⁻¹_diag = J⁻¹_diag + (du - J⁻¹_diag * cache.dfu) * cache.dfu /
+                          ifelse(iszero(denom), T(1e-5), denom)
+    end
+    @bb copyto!(cache.dfu, fu)
+    return Diagonal(vec(J⁻¹_diag))
+end
diff --git a/lib/NonlinearSolveQuasiNewton/src/initialization.jl b/lib/NonlinearSolveQuasiNewton/src/initialization.jl
new file mode 100644
index 000000000..9d39f4473
--- /dev/null
+++ b/lib/NonlinearSolveQuasiNewton/src/initialization.jl
@@ -0,0 +1,279 @@
+"""
+    InitializedApproximateJacobianCache(J, structure, alg, cache, initialized::Bool,
+        internalnorm)
+
+A cache for Approximate Jacobian.
+
+### Arguments
+
+  - `J`: The current Jacobian.
+  - `structure`: The structure of the Jacobian.
+  - `alg`: The initialization algorithm.
+  - `cache`: The Jacobian cache [`NonlinearSolve.JacobianCache`](@ref) (if needed).
+  - `initialized`: A boolean indicating whether the Jacobian has been initialized.
+  - `internalnorm`: The norm to be used.
+
+### Interface
+
+```julia
+(cache::InitializedApproximateJacobianCache)(::Nothing)
+```
+
+Returns the current Jacobian `cache.J` with the proper `structure`.
+
+```julia
+__internal_solve!(cache::InitializedApproximateJacobianCache, fu, u, ::Val{reinit})
+```
+
+Solves for the Jacobian `cache.J` and returns it. If `reinit` is `true`, then the Jacobian
+is reinitialized.
+"""
+@concrete mutable struct InitializedApproximateJacobianCache <: AbstractJacobianCache
+    J
+    structure
+    alg
+    cache
+    initialized::Bool
+    internalnorm
+end
+
+function InternalAPI.reinit!(cache::InitializedApproximateJacobianCache; kwargs...)
+    cache.initialized = false
+end
+
+# XXX: Implement
+# @internal_caches InitializedApproximateJacobianCache :cache
+
+function (cache::InitializedApproximateJacobianCache)(::Nothing)
+    return NonlinearSolveBase.get_full_jacobian(cache, cache.structure, cache.J)
+end
+
+function InternalAPI.solve!(
+        cache::InitializedApproximateJacobianCache, fu, u, reinit::Val
+)
+    if reinit isa Val{true} || !cache.initialized
+        cache(cache.alg, fu, u)
+        cache.initialized = true
+    end
+    if NonlinearSolveBase.stores_full_jacobian(cache.structure)
+        full_J = cache.J
+    else
+        full_J = NonlinearSolveBase.get_full_jacobian(cache, cache.structure, cache.J)
+    end
+    return full_J
+end
+
+"""
+    IdentityInitialization(alpha, structure)
+
+Initialize the Jacobian to be an Identity Matrix scaled by `alpha` and maintain the
+structure as specified by `structure`.
+"""
+@concrete struct IdentityInitialization <: AbstractJacobianInitialization
+    alpha
+    structure
+end
+
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, alg::IdentityInitialization, solver, f::F,
+        fu, u, p; internalnorm::IN = L2_NORM, kwargs...
+) where {F, IN}
+    α = Utils.initial_jacobian_scaling_alpha(alg.alpha, u, fu, internalnorm)
+    if u isa Number
+        J = α
+    else
+        if alg.structure isa DiagonalStructure
+            @assert length(u)==length(fu) "Diagonal Jacobian Structure must be square!"
+            J = one.(Utils.safe_vec(fu)) .* α
+        else
+            # A simple trick to get the correct jacobian structure
+            J = alg.structure(Utils.make_identity!!(vec(fu) * vec(u)', α); alias = true)
+        end
+    end
+    return InitializedApproximateJacobianCache(
+        J, alg.structure, alg, nothing, true, internalnorm
+    )
+end
+
+function (cache::InitializedApproximateJacobianCache)(
+        alg::IdentityInitialization, fu, u
+)
+    α = Utils.initial_jacobian_scaling_alpha(alg.alpha, u, fu, cache.internalnorm)
+    cache.J = Utils.make_identity!!(cache.J, α)
+    return
+end
+
+"""
+    TrueJacobianInitialization(structure, autodiff)
+
+Initialize the Jacobian to be the true Jacobian and maintain the structure as specified
+by `structure`. `autodiff` is used to compute the true Jacobian and if not specified we
+make a selection automatically.
+"""
+@concrete struct TrueJacobianInitialization <: AbstractJacobianInitialization
+    structure
+    autodiff
+end
+
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, alg::TrueJacobianInitialization,
+        solver, f::F, fu, u, p; stats, linsolve = missing,
+        internalnorm::IN = L2_NORM, kwargs...
+) where {F, IN}
+    autodiff = NonlinearSolveBase.select_jacobian_autodiff(prob, alg.autodiff)
+    jac_cache = NonlinearSolveBase.construct_jacobian_cache(
+        prob, solver, prob.f, fu, u, p; stats, autodiff, linsolve
+    )
+    J = alg.structure(jac_cache(nothing))
+    return InitializedApproximateJacobianCache(
+        J, alg.structure, alg, jac_cache, false, internalnorm
+    )
+end
+
+function (cache::InitializedApproximateJacobianCache)(::TrueJacobianInitialization, fu, u)
+    cache.J = cache.structure(cache.J, cache.cache(u))
+    return
+end
+
+"""
+    BroydenLowRankInitialization(alpha, threshold::Val)
+
+An initialization for `LimitedMemoryBroyden` that uses a low rank approximation of the
+Jacobian. The low rank updates to the Jacobian matrix corresponds to what SciPy calls
+["simple"](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.broyden2.html#scipy-optimize-broyden2).
+"""
+@concrete struct BroydenLowRankInitialization <: AbstractJacobianInitialization
+    alpha
+    threshold <: Val
+end
+
+NonlinearSolveBase.jacobian_initialized_preinverted(::BroydenLowRankInitialization) = true
+
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, alg::BroydenLowRankInitialization,
+        solver, f::F, fu, u, p; internalnorm::IN = L2_NORM, kwargs...
+) where {F, IN}
+    if u isa Number # Use the standard broyden
+        return InternalAPI.init(
+            prob, IdentityInitialization(true, FullStructure()),
+            solver, f, fu, u, p; internalnorm, kwargs...
+        )
+    end
+    # Pay to cost of slightly more allocations to prevent type-instability for StaticArrays
+    α = inv(Utils.initial_jacobian_scaling_alpha(alg.alpha, u, fu, internalnorm))
+    if u isa StaticArray
+        J = BroydenLowRankJacobian(fu, u; alg.threshold, alpha = α)
+    else
+        threshold = min(Utils.unwrap_val(alg.threshold), maxiters)
+        J = BroydenLowRankJacobian(fu, u; threshold, alpha = α)
+    end
+    return InitializedApproximateJacobianCache(
+        J, FullStructure(), alg, nothing, true, internalnorm
+    )
+end
+
+function (cache::InitializedApproximateJacobianCache)(
+        alg::BroydenLowRankInitialization, fu, u
+)
+    α = Utils.initial_jacobian_scaling_alpha(alg.alpha, u, fu, cache.internalnorm)
+    cache.J.idx = 0
+    cache.J.alpha = inv(α)
+    return
+end
+
+"""
+    BroydenLowRankJacobian{T}(U, Vᵀ, idx, cache, alpha)
+
+Low Rank Approximation of the Jacobian Matrix. Currently only used for
+[`LimitedMemoryBroyden`](@ref). This computes the Jacobian as ``U \\times V^T``.
+"""
+@concrete mutable struct BroydenLowRankJacobian{T} <: AbstractSciMLOperator{T}
+    U
+    Vᵀ
+    idx::Int
+    cache
+    alpha
+end
+
+Utils.maybe_pinv!!(workspace, A::BroydenLowRankJacobian) = A  # Already Inverted form
+
+function get_components(op::BroydenLowRankJacobian)
+    op.idx ≥ size(op.U, 2) && return op.cache, op.U, transpose(op.Vᵀ)
+    cache = op.cache === nothing ? op.cache : view(op.cache, 1:(op.idx))
+    return cache, view(op.U, :, 1:(op.idx)), transpose(view(op.Vᵀ, :, 1:(op.idx)))
+end
+
+Base.size(op::BroydenLowRankJacobian) = size(op.U, 1), size(op.Vᵀ, 1)
+
+function Base.transpose(op::BroydenLowRankJacobian{T}) where {T}
+    return BroydenLowRankJacobian{T}(op.Vᵀ, op.U, op.idx, op.cache, op.alpha)
+end
+Base.adjoint(op::BroydenLowRankJacobian{<:Real}) = transpose(op)
+
+# Storing the transpose to ensure contiguous memory on splicing
+function BroydenLowRankJacobian(
+    fu::StaticArray, u::StaticArray; alpha = true, threshold::Val = Val(10)
+)
+    T = promote_type(eltype(u), eltype(fu))
+    U = MArray{Tuple{prod(Size(fu)), Utils.unwrap_val(threshold)}, T}(undef)
+    Vᵀ = MArray{Tuple{prod(Size(u)), Utils.unwrap_val(threshold)}, T}(undef)
+    return BroydenLowRankJacobian{T}(U, Vᵀ, 0, nothing, T(alpha))
+end
+
+function BroydenLowRankJacobian(fu, u; threshold::Int = 10, alpha = true)
+    T = promote_type(eltype(u), eltype(fu))
+    U = Utils.safe_similar(fu, T, length(fu), threshold)
+    Vᵀ = Utils.safe_similar(u, T, length(u), threshold)
+    cache = Utils.safe_similar(u, T, threshold)
+    return BroydenLowRankJacobian{T}(U, Vᵀ, 0, cache, T(alpha))
+end
+
+function Base.:*(J::BroydenLowRankJacobian, x::AbstractVector)
+    J.idx == 0 && return -x
+    _, U, Vᵀ = get_components(J)
+    return U * (Vᵀ * x) .- J.alpha .* x
+end
+
+function LinearAlgebra.mul!(y::AbstractVector, J::BroydenLowRankJacobian, x::AbstractVector)
+    if J.idx == 0
+        @. y = -J.alpha * x
+        return y
+    end
+    _, U, Vᵀ = get_components(J)
+    @bb cache = Vᵀ × x
+    mul!(y, U, cache)
+    @bb @. y -= J.alpha * x
+    return y
+end
+
+function Base.:*(x::AbstractVector, J::BroydenLowRankJacobian)
+    J.idx == 0 && return -x
+    _, U, Vᵀ = get_components(J)
+    return Vᵀ' * (U' * x) .- J.alpha .* x
+end
+
+function LinearAlgebra.mul!(y::AbstractVector, x::AbstractVector, J::BroydenLowRankJacobian)
+    if J.idx == 0
+        @. y = -J.alpha * x
+        return y
+    end
+    _, U, Vᵀ = get_components(J)
+    @bb cache = transpose(U) × x
+    mul!(y, transpose(Vᵀ), cache)
+    @bb @. y -= J.alpha * x
+    return y
+end
+
+function LinearAlgebra.mul!(
+    J::BroydenLowRankJacobian, u::AbstractArray, vᵀ::LinearAlgebra.AdjOrTransAbsVec,
+    α::Bool, β::Bool
+)
+    @assert α & β
+    idx_update = mod1(J.idx + 1, size(J.U, 2))
+    copyto!(@view(J.U[:, idx_update]), Utils.safe_vec(u))
+    copyto!(@view(J.Vᵀ[:, idx_update]), Utils.safe_vec(vᵀ))
+    J.idx += 1
+    return J
+end
+
+ArrayInterface.restructure(::BroydenLowRankJacobian, J::BroydenLowRankJacobian) = J
diff --git a/src/algorithms/klement.jl b/lib/NonlinearSolveQuasiNewton/src/klement.jl
similarity index 58%
rename from src/algorithms/klement.jl
rename to lib/NonlinearSolveQuasiNewton/src/klement.jl
index 8e7904fd9..7031b7cec 100644
--- a/src/algorithms/klement.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/klement.jl
@@ -1,7 +1,9 @@
 """
-    Klement(; max_resets = 100, linsolve = nothing, linesearch = nothing,
+    Klement(;
+        max_resets = 100, linsolve = nothing, linesearch = nothing,
         precs = nothing, alpha = nothing, init_jacobian::Val = Val(:identity),
-        autodiff = nothing)
+        autodiff = nothing
+    )
 
 An implementation of `Klement` [klement2014using](@citep) with line search, preconditioning
 and customizable linear solves. It is recommended to use [`Broyden`](@ref) for most problems
@@ -24,16 +26,23 @@ over this.
       + `Val(:true_jacobian_diagonal)`: Diagonal of True Jacobian. This is a good choice for
         differentiable problems.
 """
-function Klement(; max_resets::Int = 100, linsolve = nothing, alpha = nothing,
-        linesearch = nothing, precs = nothing,
-        autodiff = nothing, init_jacobian::Val = Val(:identity))
-    initialization = klement_init(init_jacobian, autodiff, alpha)
-    CJ = init_jacobian isa Val{:true_jacobian} ||
-         init_jacobian isa Val{:true_jacobian_diagonal}
-    return ApproximateJacobianSolveAlgorithm{CJ, :Klement}(;
-        linesearch, descent = NewtonDescent(; linsolve, precs),
+function Klement(;
+        max_resets = 100, linsolve = nothing, linesearch = nothing,
+        precs = nothing, alpha = nothing, init_jacobian::Val = Val(:identity),
+        autodiff = nothing
+)
+    concrete_jac = Val(init_jacobian isa Val{:true_jacobian} ||
+                       init_jacobian isa Val{:true_jacobian_diagonal})
+    return QuasiNewtonAlgorithm(;
+        linesearch,
+        descent = NewtonDescent(; linsolve, precs),
         update_rule = KlementUpdateRule(),
-        reinit_rule = IllConditionedJacobianReset(), max_resets, initialization)
+        reinit_rule = IllConditionedJacobianReset(),
+        max_resets,
+        initialization = klement_init(init_jacobian, autodiff, alpha),
+        concrete_jac,
+        name = :Klement
+    )
 end
 
 function klement_init(::Val{:identity}, autodiff, alpha)
@@ -50,55 +59,22 @@ function klement_init(::Val{IJ}, autodiff, alpha) where {IJ}
            `init_jacobian`.")
 end
 
-# Essentially checks ill conditioned Jacobian
-"""
-    IllConditionedJacobianReset()
-
-Recommend resetting the Jacobian if the current jacobian is ill-conditioned. This is used
-in [`Klement`](@ref).
-"""
-struct IllConditionedJacobianReset <: AbstractResetCondition end
-
-@concrete struct IllConditionedJacobianResetCache
-    condition_number_threshold
-end
-
-function __internal_init(alg::IllConditionedJacobianReset, J, fu, u, du, args...; kwargs...)
-    condition_number_threshold = if J isa AbstractMatrix
-        inv(eps(real(eltype(J)))^(1 // 2))
-    else
-        nothing
-    end
-    return IllConditionedJacobianResetCache(condition_number_threshold)
-end
-
-function __internal_solve!(cache::IllConditionedJacobianResetCache, J, fu, u, du)
-    J isa Number && return iszero(J)
-    J isa Diagonal && return any(iszero, diag(J))
-    J isa AbstractMatrix && return cond(J) ≥ cache.condition_number_threshold
-    J isa AbstractVector && return any(iszero, J)
-    return false
-end
-
-# Update Rule
 """
     KlementUpdateRule()
 
 Update rule for [`Klement`](@ref).
 """
-struct KlementUpdateRule <: AbstractApproximateJacobianUpdateRule{false} end
+struct KlementUpdateRule <: AbstractApproximateJacobianUpdateRule end
 
-@concrete mutable struct KlementUpdateRuleCache <:
-                         AbstractApproximateJacobianUpdateRuleCache{false}
-    Jdu
-    J_cache
-    J_cache_2
-    Jdu_cache
-    fu_cache
+function Base.getproperty(rule::KlementUpdateRule, sym::Symbol)
+    sym == :store_inverse_jacobian && return Val(false)
+    return getfield(rule, sym)
 end
 
-function __internal_init(prob::AbstractNonlinearProblem, alg::KlementUpdateRule,
-        J, fu, u, du, args...; kwargs...)
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, alg::KlementUpdateRule,
+        J, fu, u, du, args...; kwargs...
+)
     @bb Jdu = similar(fu)
     if J isa Diagonal || J isa Number
         J_cache, J_cache_2, Jdu_cache = nothing, nothing, nothing
@@ -108,29 +84,43 @@ function __internal_init(prob::AbstractNonlinearProblem, alg::KlementUpdateRule,
         @bb Jdu_cache = similar(Jdu)
     end
     @bb fu_cache = copy(fu)
-    return KlementUpdateRuleCache(Jdu, J_cache, J_cache_2, Jdu_cache, fu_cache)
+    return KlementUpdateRuleCache(Jdu, J_cache, J_cache_2, Jdu_cache, fu_cache, alg)
+end
+
+@concrete mutable struct KlementUpdateRuleCache <:
+                         AbstractApproximateJacobianUpdateRuleCache
+    Jdu
+    J_cache
+    J_cache_2
+    Jdu_cache
+    fu_cache
+    rule <: KlementUpdateRule
 end
 
-function __internal_solve!(cache::KlementUpdateRuleCache, J::Number, fu, u, du)
+function InternalAPI.solve!(
+        cache::KlementUpdateRuleCache, J::Number, fu, u, du; kwargs...
+)
     Jdu = J^2 * du^2
     J = J + ((fu - cache.fu_cache - J * du) / ifelse(iszero(Jdu), 1e-5, Jdu)) * du * J^2
     cache.fu_cache = fu
     return J
 end
 
-function __internal_solve!(cache::KlementUpdateRuleCache, J_::Diagonal, fu, u, du)
+function InternalAPI.solve!(
+        cache::KlementUpdateRuleCache, J::Diagonal, fu, u, du; kwargs...
+)
     T = eltype(u)
-    J = _restructure(u, diag(J_))
+    J = Utils.restructure(u, diag(J))
     @bb @. cache.Jdu = (J^2) * (du^2)
-    @bb @. J += ((fu - cache.fu_cache - J * du) /
-                 ifelse(iszero(cache.Jdu), T(1e-5), cache.Jdu)) *
-                du *
-                (J^2)
+    @bb @. J += ((fu - cache.fu_cache - cache.Jdu) /
+                 ifelse(iszero(cache.Jdu), T(1e-5), cache.Jdu)) * du * (J^2)
     @bb copyto!(cache.fu_cache, fu)
     return Diagonal(vec(J))
 end
 
-function __internal_solve!(cache::KlementUpdateRuleCache, J::AbstractMatrix, fu, u, du)
+function InternalAPI.solve!(
+        cache::KlementUpdateRuleCache, J::AbstractMatrix, fu, u, du; kwargs...
+)
     T = eltype(u)
     @bb @. cache.J_cache = J'^2
     @bb @. cache.Jdu = du^2
@@ -138,7 +128,7 @@ function __internal_solve!(cache::KlementUpdateRuleCache, J::AbstractMatrix, fu,
     @bb cache.Jdu = J × vec(du)
     @bb @. cache.fu_cache = (fu - cache.fu_cache - cache.Jdu) /
                             ifelse(iszero(cache.Jdu_cache), T(1e-5), cache.Jdu_cache)
-    @bb cache.J_cache = vec(cache.fu_cache) × transpose(_vec(du))
+    @bb cache.J_cache = vec(cache.fu_cache) × transpose(Utils.safe_vec(du))
     @bb @. cache.J_cache *= J
     @bb cache.J_cache_2 = cache.J_cache × J
     @bb J .+= cache.J_cache_2
diff --git a/lib/NonlinearSolveQuasiNewton/src/lbroyden.jl b/lib/NonlinearSolveQuasiNewton/src/lbroyden.jl
new file mode 100644
index 000000000..886905a5b
--- /dev/null
+++ b/lib/NonlinearSolveQuasiNewton/src/lbroyden.jl
@@ -0,0 +1,35 @@
+"""
+    LimitedMemoryBroyden(;
+        max_resets::Int = 3, linesearch = nothing, threshold::Val = Val(10),
+        reset_tolerance = nothing, alpha = nothing
+    )
+
+An implementation of `LimitedMemoryBroyden` [ziani2008autoadaptative](@cite) with resetting
+and line search.
+
+### Keyword Arguments
+
+  - `max_resets`: the maximum number of resets to perform. Defaults to `3`.
+  - `reset_tolerance`: the tolerance for the reset check. Defaults to
+    `sqrt(eps(real(eltype(u))))`.
+  - `threshold`: the number of vectors to store in the low rank approximation. Defaults
+    to `Val(10)`.
+  - `alpha`: The initial Jacobian inverse is set to be `(αI)⁻¹`. Defaults to `nothing`
+    which implies `α = max(norm(u), 1) / (2 * norm(fu))`.
+"""
+function LimitedMemoryBroyden(;
+        max_resets::Int = 3, linesearch = nothing, threshold::Union{Val, Int} = Val(10),
+        reset_tolerance = nothing, alpha = nothing
+)
+    threshold isa Int && (threshold = Val(threshold))
+    return QuasiNewtonAlgorithm(;
+        linesearch,
+        descent = NewtonDescent(),
+        update_rule = GoodBroydenUpdateRule(),
+        max_resets,
+        initialization = BroydenLowRankInitialization(alpha, threshold),
+        reinit_rule = NoChangeInStateReset(; reset_tolerance),
+        name = :LimitedMemoryBroyden,
+        concrete_jac = Val(false)
+    )
+end
diff --git a/lib/NonlinearSolveQuasiNewton/src/reset_conditions.jl b/lib/NonlinearSolveQuasiNewton/src/reset_conditions.jl
new file mode 100644
index 000000000..8541259ef
--- /dev/null
+++ b/lib/NonlinearSolveQuasiNewton/src/reset_conditions.jl
@@ -0,0 +1,120 @@
+"""
+    NoChangeInStateReset(;
+        nsteps::Int = 3, reset_tolerance = nothing,
+        check_du::Bool = true, check_dfu::Bool = true
+    )
+
+Recommends a reset if the state or the function value has not changed significantly in
+`nsteps` steps. This is used in [`Broyden`](@ref).
+
+### Keyword Arguments
+
+  - `nsteps`: the number of steps to check for no change. Defaults to `3`.
+  - `reset_tolerance`: the tolerance for the reset check. Defaults to
+    `eps(real(eltype(u)))^(3 // 4)`.
+  - `check_du`: whether to check the state. Defaults to `true`.
+  - `check_dfu`: whether to check the function value. Defaults to `true`.
+"""
+@kwdef @concrete struct NoChangeInStateReset <: AbstractResetCondition
+    nsteps::Int = 3
+    reset_tolerance = nothing
+    check_du::Bool = true
+    check_dfu::Bool = true
+end
+
+function InternalAPI.init(
+        condition::NoChangeInStateReset, J, fu, u, du, args...; kwargs...
+)
+    if condition.check_dfu
+        @bb dfu = copy(fu)
+    else
+        dfu = fu
+    end
+    T = real(eltype(u))
+    tol = condition.reset_tolerance === nothing ? eps(T)^(3 // 4) :
+          T(condition.reset_tolerance)
+    return NoChangeInStateResetCache(dfu, tol, condition, 0, 0)
+end
+
+@concrete mutable struct NoChangeInStateResetCache <: AbstractResetConditionCache
+    dfu
+    reset_tolerance
+    condition <: NoChangeInStateReset
+    steps_since_change_du::Int
+    steps_since_change_dfu::Int
+end
+
+function InternalAPI.reinit!(cache::NoChangeInStateResetCache; u0 = nothing, kwargs...)
+    if u0 !== nothing && cache.condition.reset_tolerance === nothing
+        cache.reset_tolerance = eps(real(eltype(u0)))^(3 // 4)
+    end
+    cache.steps_since_change_dfu = 0
+    cache.steps_since_change_du = 0
+end
+
+function InternalAPI.solve!(cache::NoChangeInStateResetCache, J, fu, u, du; kwargs...)
+    cond = ≤(cache.reset_tolerance) ∘ abs
+    if cache.condition.check_du
+        if any(cond, du)
+            cache.steps_since_change_du += 1
+            if cache.steps_since_change_du ≥ cache.condition.nsteps
+                cache.steps_since_change_du = 0
+                cache.steps_since_change_dfu = 0
+                return true
+            end
+        else
+            cache.steps_since_change_du = 0
+            cache.steps_since_change_dfu = 0
+        end
+    end
+    if cache.condition.check_dfu
+        @bb @. cache.dfu = fu - cache.dfu
+        if any(cond, cache.dfu)
+            cache.steps_since_change_dfu += 1
+            if cache.steps_since_change_dfu ≥ cache.condition.nsteps
+                cache.steps_since_change_dfu = 0
+                cache.steps_since_change_du = 0
+                @bb copyto!(cache.dfu, fu)
+                return true
+            end
+        else
+            cache.steps_since_change_dfu = 0
+            cache.steps_since_change_du = 0
+        end
+        @bb copyto!(cache.dfu, fu)
+    end
+    return false
+end
+
+"""
+    IllConditionedJacobianReset()
+
+Recommend resetting the Jacobian if the current jacobian is ill-conditioned. This is used
+in [`Klement`](@ref).
+"""
+struct IllConditionedJacobianReset <: AbstractResetCondition end
+
+function InternalAPI.init(
+        condition::IllConditionedJacobianReset, J, fu, u, du, args...; kwargs...
+)
+    condition_number_threshold = J isa AbstractMatrix ? inv(eps(real(eltype(J))))^(1 // 2) :
+                                 nothing
+    return IllConditionedJacobianResetCache(condition_number_threshold)
+end
+
+@concrete struct IllConditionedJacobianResetCache <: AbstractResetConditionCache
+    condition_number_threshold <: Number
+end
+
+# NOTE: we don't need a reinit! since we establish the threshold based on the eltype
+
+function InternalAPI.solve!(
+        cache::IllConditionedJacobianResetCache, J, fu, u, du; kwargs...
+)
+    J isa Number && return iszero(J)
+    J isa Diagonal && return any(iszero, diag(J))
+    J isa AbstractVector && return any(iszero, J)
+    J isa AbstractMatrix &&
+        return Utils.condition_number(J) ≥ cache.condition_number_threshold
+    return false
+end
diff --git a/lib/NonlinearSolveQuasiNewton/src/solve.jl b/lib/NonlinearSolveQuasiNewton/src/solve.jl
new file mode 100644
index 000000000..64b171840
--- /dev/null
+++ b/lib/NonlinearSolveQuasiNewton/src/solve.jl
@@ -0,0 +1,409 @@
+"""
+    QuasiNewtonAlgorithm(;
+        linesearch = missing, trustregion = missing, descent, update_rule, reinit_rule,
+        initialization, max_resets::Int = typemax(Int), name::Symbol = :unknown,
+        max_shrink_times::Int = typemax(Int), concrete_jac = Val(false)
+    )
+
+Nonlinear Solve Algorithms using an Iterative Approximation of the Jacobian. Most common
+examples include [`Broyden`](@ref)'s Method.
+
+### Keyword Arguments
+
+  - `trustregion`: Globalization using a Trust Region Method. This needs to follow the
+    [`NonlinearSolveBase.AbstractTrustRegionMethod`](@ref) interface.
+  - `descent`: The descent method to use to compute the step. This needs to follow the
+    [`NonlinearSolveBase.AbstractDescentDirection`](@ref) interface.
+  - `max_shrink_times`: The maximum number of times the trust region radius can be shrunk
+    before the algorithm terminates.
+  - `update_rule`: The update rule to use to update the Jacobian. This needs to follow the
+    [`NonlinearSolveBase.AbstractApproximateJacobianUpdateRule`](@ref) interface.
+  - `reinit_rule`: The reinitialization rule to use to reinitialize the Jacobian. This
+    needs to follow the [`NonlinearSolveBase.AbstractResetCondition`](@ref) interface.
+  - `initialization`: The initialization method to use to initialize the Jacobian. This
+    needs to follow the [`NonlinearSolveBase.AbstractJacobianInitialization`](@ref)
+    interface.
+"""
+@concrete struct QuasiNewtonAlgorithm <: AbstractNonlinearSolveAlgorithm
+    linesearch
+    trustregion
+    descent <: AbstractDescentDirection
+    update_rule <: AbstractApproximateJacobianUpdateRule
+    reinit_rule <: AbstractResetCondition
+    max_resets::Int
+    max_shrink_times::Int
+    initialization
+    concrete_jac <: Union{Val{false}, Val{true}}
+    name::Symbol
+end
+
+# XXX: Implement
+# function __show_algorithm(io::IO, alg::QuasiNewtonAlgorithm, name, indent)
+#     modifiers = String[]
+#     __is_present(alg.linesearch) && push!(modifiers, "linesearch = $(alg.linesearch)")
+#     __is_present(alg.trustregion) && push!(modifiers, "trustregion = $(alg.trustregion)")
+#     push!(modifiers, "descent = $(alg.descent)")
+#     push!(modifiers, "update_rule = $(alg.update_rule)")
+#     push!(modifiers, "reinit_rule = $(alg.reinit_rule)")
+#     push!(modifiers, "max_resets = $(alg.max_resets)")
+#     push!(modifiers, "initialization = $(alg.initialization)")
+#     store_inverse_jacobian(alg.update_rule) && push!(modifiers, "inverse_jacobian = true")
+#     spacing = " "^indent * "    "
+#     spacing_last = " "^indent
+#     print(io, "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))")
+# end
+
+function QuasiNewtonAlgorithm(;
+        linesearch = missing, trustregion = missing, descent, update_rule, reinit_rule,
+        initialization, max_resets::Int = typemax(Int), name::Symbol = :unknown,
+        max_shrink_times::Int = typemax(Int), concrete_jac = Val(false)
+)
+    return QuasiNewtonAlgorithm(
+        linesearch, trustregion, descent, update_rule, reinit_rule,
+        max_resets, max_shrink_times, initialization, concrete_jac, name
+    )
+end
+
+@concrete mutable struct QuasiNewtonCache <: AbstractNonlinearSolveCache
+    # Basic Requirements
+    fu
+    u
+    u_cache
+    p
+    du  # Aliased to `get_du(descent_cache)`
+    J   # Aliased to `initialization_cache.J` if !inverted_jac
+    alg <: QuasiNewtonAlgorithm
+    prob <: AbstractNonlinearProblem
+    globalization <: Union{Val{:LineSearch}, Val{:TrustRegion}, Val{:None}}
+
+    # Internal Caches
+    initialization_cache
+    descent_cache
+    linesearch_cache
+    trustregion_cache
+    update_rule_cache
+    reinit_rule_cache
+
+    inv_workspace
+
+    # Counters
+    stats::NLStats
+    nsteps::Int
+    nresets::Int
+    max_resets::Int
+    maxiters::Int
+    maxtime
+    max_shrink_times::Int
+    steps_since_last_reset::Int
+
+    # Timer
+    timer
+    total_time::Float64
+
+    # Termination & Tracking
+    termination_cache
+    trace
+    retcode::ReturnCode.T
+    force_stop::Bool
+    force_reinit::Bool
+    kwargs
+end
+
+# XXX: Implement
+# function __reinit_internal!(cache::ApproximateJacobianSolveCache{INV, GB, iip},
+#         args...; p = cache.p, u0 = cache.u, alias_u0::Bool = false,
+#         maxiters = 1000, maxtime = nothing, kwargs...) where {INV, GB, iip}
+#     if iip
+#         recursivecopy!(cache.u, u0)
+#         cache.prob.f(cache.fu, cache.u, p)
+#     else
+#         cache.u = __maybe_unaliased(u0, alias_u0)
+#         set_fu!(cache, cache.prob.f(cache.u, p))
+#     end
+#     cache.p = p
+
+#     __reinit_internal!(cache.stats)
+#     cache.nsteps = 0
+#     cache.nresets = 0
+#     cache.steps_since_last_reset = 0
+#     cache.maxiters = maxiters
+#     cache.maxtime = maxtime
+#     cache.total_time = 0.0
+#     cache.force_stop = false
+#     cache.force_reinit = false
+#     cache.retcode = ReturnCode.Default
+
+#     reset!(cache.trace)
+#     reinit!(cache.termination_cache, get_fu(cache), get_u(cache); kwargs...)
+#     reset_timer!(cache.timer)
+# end
+
+# @internal_caches ApproximateJacobianSolveCache :initialization_cache :descent_cache :linesearch_cache :trustregion_cache :update_rule_cache :reinit_rule_cache
+
+function SciMLBase.__init(
+        prob::AbstractNonlinearProblem, alg::QuasiNewtonAlgorithm, args...;
+        stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, maxtime = nothing,
+        maxiters = 1000, abstol = nothing, reltol = nothing,
+        linsolve_kwargs = (;), termination_condition = nothing,
+        internalnorm::F = L2_NORM, kwargs...
+) where {F}
+    timer = get_timer_output()
+    @static_timeit timer "cache construction" begin
+        u = Utils.maybe_unaliased(prob.u0, alias_u0)
+        fu = Utils.evaluate_f(prob, u)
+        @bb u_cache = copy(u)
+
+        inverted_jac = NonlinearSolveBase.store_inverse_jacobian(alg.update_rule)
+
+        linsolve = NonlinearSolveBase.get_linear_solver(alg.descent)
+
+        initialization_cache = InternalAPI.init(
+            prob, alg.initialization, alg, prob.f, fu, u, prob.p;
+            stats, linsolve, maxiters, internalnorm
+        )
+
+        abstol, reltol, termination_cache = NonlinearSolveBase.init_termination_cache(
+            prob, abstol, reltol, fu, u, termination_condition, Val(:regular)
+        )
+        linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
+
+        J = initialization_cache(nothing)
+
+        inv_workspace, J = Utils.unwrap_val(inverted_jac) ?
+                           Utils.maybe_pinv!!_workspace(J) : (nothing, J)
+
+        descent_cache = InternalAPI.init(
+            prob, alg.descent, J, fu, u;
+            stats, abstol, reltol, internalnorm,
+            linsolve_kwargs, pre_inverted = inverted_jac, timer
+        )
+        du = SciMLBase.get_du(descent_cache)
+
+        reinit_rule_cache = InternalAPI.init(alg.reinit_rule, J, fu, u, du)
+
+        has_linesearch = alg.linesearch !== missing && alg.linesearch !== nothing
+        has_trustregion = alg.trustregion !== missing && alg.trustregion !== nothing
+
+        if has_trustregion && has_linesearch
+            error("TrustRegion and LineSearch methods are algorithmically incompatible.")
+        end
+
+        globalization = Val(:None)
+        linesearch_cache = nothing
+        trustregion_cache = nothing
+
+        if has_trustregion
+            NonlinearSolveBase.supports_trust_region(alg.descent) ||
+                error("Trust Region not supported by $(alg.descent).")
+            trustregion_cache = InternalAPI.init(
+                prob, alg.trustregion, fu, u, p; stats, internalnorm, kwargs...
+            )
+            globalization = Val(:TrustRegion)
+        end
+
+        if has_linesearch
+            NonlinearSolveBase.supports_line_search(alg.descent) ||
+                error("Line Search not supported by $(alg.descent).")
+            linesearch_cache = CommonSolve.init(
+                prob, alg.linesearch, fu, u; stats, internalnorm, kwargs...
+            )
+            globalization = Val(:LineSearch)
+        end
+
+        update_rule_cache = InternalAPI.init(
+            prob, alg.update_rule, J, fu, u, du; stats, internalnorm
+        )
+
+        trace = NonlinearSolveBase.init_nonlinearsolve_trace(
+            prob, alg, u, fu, J, du;
+            uses_jacobian_inverse = inverted_jac, kwargs...
+        )
+
+        return QuasiNewtonCache(
+            fu, u, u_cache, prob.p, du, J, alg, prob, globalization,
+            initialization_cache, descent_cache, linesearch_cache,
+            trustregion_cache, update_rule_cache, reinit_rule_cache,
+            inv_workspace, stats, 0, 0, alg.max_resets, maxiters, maxtime,
+            alg.max_shrink_times, 0, timer, 0.0, termination_cache, trace,
+            ReturnCode.Default, false, false, kwargs
+        )
+    end
+end
+
+function InternalAPI.step!(
+        cache::QuasiNewtonCache; recompute_jacobian::Union{Nothing, Bool} = nothing
+)
+    new_jacobian = true
+    @static_timeit cache.timer "jacobian init/reinit" begin
+        if cache.nsteps == 0  # First Step is special ignore kwargs
+            J_init = InternalAPI.solve!(
+                cache.initialization_cache, cache.fu, cache.u, Val(false)
+            )
+            if Utils.unwrap_val(NonlinearSolveBase.store_inverse_jacobian(cache.update_rule_cache))
+                if NonlinearSolveBase.jacobian_initialized_preinverted(
+                    cache.initialization_cache.alg
+                )
+                    cache.J = J_init
+                else
+                    cache.J = Utils.maybe_pinv!!(cache.inv_workspace, J_init)
+                end
+            else
+                if NonlinearSolveBase.jacobian_initialized_preinverted(
+                    cache.initialization_cache.alg
+                )
+                    cache.J = Utils.maybe_pinv!!(cache.inv_workspace, J_init)
+                else
+                    cache.J = J_init
+                end
+            end
+            J = cache.J
+            cache.steps_since_last_reset += 1
+        else
+            countable_reinit = false
+            if cache.force_reinit
+                reinit, countable_reinit = true, true
+                cache.force_reinit = false
+            elseif recompute_jacobian === nothing
+                # Standard Step
+                reinit = InternalAPI.solve!(
+                    cache.reinit_rule_cache, cache.J, cache.fu, cache.u, cache.du
+                )
+                reinit && (countable_reinit = true)
+            elseif recompute_jacobian
+                reinit = true  # Force ReInitialization: Don't count towards resetting
+            else
+                new_jacobian = false # Jacobian won't be updated in this step
+                reinit = false       # Override Checks: Unsafe operation
+            end
+
+            if countable_reinit
+                cache.nresets += 1
+                if cache.nresets ≥ cache.max_resets
+                    cache.retcode = ReturnCode.ConvergenceFailure
+                    cache.force_stop = true
+                    return
+                end
+            end
+
+            if reinit
+                J_init = InternalAPI.solve!(
+                    cache.initialization_cache, cache.fu, cache.u, Val(true)
+                )
+                cache.J = Utils.unwrap_val(NonlinearSolveBase.store_inverse_jacobian(cache.update_rule_cache)) ?
+                          Utils.maybe_pinv!!(cache.inv_workspace, J_init) : J_init
+                J = cache.J
+                cache.steps_since_last_reset = 0
+            else
+                J = cache.J
+                cache.steps_since_last_reset += 1
+            end
+        end
+    end
+
+    @static_timeit cache.timer "descent" begin
+        if cache.trustregion_cache !== nothing &&
+           hasfield(typeof(cache.trustregion_cache), :trust_region)
+            descent_result = InternalAPI.solve!(
+                cache.descent_cache, J, cache.fu, cache.u; new_jacobian,
+                cache.trustregion_cache.trust_region, cache.kwargs...
+            )
+        else
+            descent_result = InternalAPI.solve!(
+                cache.descent_cache, J, cache.fu, cache.u; new_jacobian, cache.kwargs...
+            )
+        end
+    end
+
+    if !descent_result.linsolve_success
+        if new_jacobian && cache.steps_since_last_reset == 0
+            # Extremely pathological case. Jacobian was just reset and linear solve
+            # failed. Should ideally never happen in practice unless true jacobian init
+            # is used.
+            cache.retcode = ReturnCode.InternalLinearSolveFailed
+            cache.force_stop = true
+            return
+        else
+            # Force a reinit because the problem is currently un-solvable
+            if !haskey(cache.kwargs, :verbose) || cache.kwargs[:verbose]
+                @warn "Linear Solve Failed but Jacobian Information is not current. \
+                       Retrying with reinitialized Approximate Jacobian."
+            end
+            cache.force_reinit = true
+            InternalAPI.step!(cache; recompute_jacobian = true)
+            return
+        end
+    end
+
+    δu, descent_intermediates = descent_result.δu, descent_result.extras
+
+    if descent_result.success
+        if cache.globalization isa Val{:LineSearch}
+            @static_timeit cache.timer "linesearch" begin
+                linesearch_sol = CommonSolve.solve!(cache.linesearch_cache, cache.u, δu)
+                needs_reset = !SciMLBase.successful_retcode(linesearch_sol.retcode)
+                α = linesearch_sol.step_size
+            end
+            if needs_reset && cache.steps_since_last_reset > 5 # Reset after a burn-in period
+                cache.force_reinit = true
+            else
+                @static_timeit cache.timer "step" begin
+                    @bb axpy!(α, δu, cache.u)
+                    Utils.evaluate_f!(cache, cache.u, cache.p)
+                end
+            end
+        elseif cache.globalization isa Val{:TrustRegion}
+            @static_timeit cache.timer "trustregion" begin
+                tr_accepted, u_new, fu_new = InternalAPI.solve!(
+                    cache.trustregion_cache, J, cache.fu, cache.u, δu, descent_intermediates
+                )
+                if tr_accepted
+                    @bb copyto!(cache.u, u_new)
+                    @bb copyto!(cache.fu, fu_new)
+                end
+                if hasfield(typeof(cache.trustregion_cache), :shrink_counter) &&
+                   cache.trustregion_cache.shrink_counter > cache.max_shrink_times
+                    cache.retcode = ReturnCode.ShrinkThresholdExceeded
+                    cache.force_stop = true
+                end
+            end
+            α = true
+        elseif cache.globalization isa Val{:None}
+            @static_timeit cache.timer "step" begin
+                @bb axpy!(1, δu, cache.u)
+                Utils.evaluate_f!(cache, cache.u, cache.p)
+            end
+            α = true
+        else
+            error("Unknown Globalization Strategy: $(cache.globalization). Allowed values \
+                   are (:LineSearch, :TrustRegion, :None)")
+        end
+        # XXX: Implement
+        # check_and_update!(cache, cache.fu, cache.u, cache.u_cache)
+    else
+        α = false
+        cache.force_reinit = true
+    end
+
+    update_trace!(
+        cache, α;
+        uses_jac_inverse = NonlinearSolveBase.store_inverse_jacobian(cache.update_rule_cache)
+    )
+    @bb copyto!(cache.u_cache, cache.u)
+
+    if (cache.force_stop || cache.force_reinit ||
+        (recompute_jacobian !== nothing && !recompute_jacobian))
+        # XXX: Implement
+        # callback_into_cache!(cache)
+        return nothing
+    end
+
+    @static_timeit cache.timer "jacobian update" begin
+        cache.J = InternalAPI.solve!(
+            cache.update_rule_cache, cache.J, cache.fu, cache.u, δu
+        )
+        # XXX: Implement
+        # callback_into_cache!(cache)
+    end
+
+    return nothing
+end
diff --git a/lib/NonlinearSolveQuasiNewton/src/structure.jl b/lib/NonlinearSolveQuasiNewton/src/structure.jl
new file mode 100644
index 000000000..2d5c0baa5
--- /dev/null
+++ b/lib/NonlinearSolveQuasiNewton/src/structure.jl
@@ -0,0 +1,53 @@
+"""
+    DiagonalStructure()
+
+Preserves only the Diagonal of the Matrix.
+"""
+struct DiagonalStructure <: AbstractApproximateJacobianStructure end
+
+NonlinearSolveBase.get_full_jacobian(cache, ::DiagonalStructure, J::Number) = J
+function NonlinearSolveBase.get_full_jacobian(cache, ::DiagonalStructure, J)
+    return Diagonal(Utils.safe_vec(J))
+end
+
+function (::DiagonalStructure)(J::AbstractMatrix; alias::Bool = false)
+    @assert size(J, 1) == size(J, 2) "Diagonal Jacobian Structure must be square!"
+    return LinearAlgebra.diag(J)
+end
+(::DiagonalStructure)(J::AbstractVector; alias::Bool = false) = alias ? J : @bb(copy(J))
+(::DiagonalStructure)(J::Number; alias::Bool = false) = J
+
+(::DiagonalStructure)(::Number, J_new::Number) = J_new
+function (::DiagonalStructure)(J::AbstractVector, J_new::AbstractMatrix)
+    if ArrayInterface.can_setindex(J)
+        if ArrayInterface.fast_scalar_indexing(J)
+            @simd ivdep for i in eachindex(J)
+                @inbounds J[i] = J_new[i, i]
+            end
+        else
+            J .= @view(J_new[diagind(J_new)])
+        end
+        return J
+    end
+    return LinearAlgebra.diag(J_new)
+end
+function (st::DiagonalStructure)(J::AbstractArray, J_new::AbstractMatrix)
+    return ArrayInterface.restructure(J, st(vec(J), J_new))
+end
+
+"""
+    FullStructure()
+
+Stores the full matrix.
+"""
+struct FullStructure <: AbstractApproximateJacobianStructure end
+
+NonlinearSolveBase.stores_full_jacobian(::FullStructure) = true
+
+(::FullStructure)(J; alias::Bool = false) = alias ? J : @bb(copy(J))
+
+function (::FullStructure)(J, J_new)
+    J === J_new && return J
+    @bb copyto!(J, J_new)
+    return J
+end
diff --git a/lib/NonlinearSolveQuasiNewton/test/runtests.jl b/lib/NonlinearSolveQuasiNewton/test/runtests.jl
index e69de29bb..8b1378917 100644
--- a/lib/NonlinearSolveQuasiNewton/test/runtests.jl
+++ b/lib/NonlinearSolveQuasiNewton/test/runtests.jl
@@ -0,0 +1 @@
+
diff --git a/lib/NonlinearSolveSpectralMethods/src/dfsane.jl b/lib/NonlinearSolveSpectralMethods/src/dfsane.jl
index c835a1059..108281e7b 100644
--- a/lib/NonlinearSolveSpectralMethods/src/dfsane.jl
+++ b/lib/NonlinearSolveSpectralMethods/src/dfsane.jl
@@ -27,5 +27,7 @@ function DFSane(;
         gamma = gamma, sigma_1 = sigma_1, M, tau_min = tau_min, tau_max = tau_max,
         n_exp, η_strategy = eta_strategy, maxiters = max_inner_iterations
     )
-    return GeneralizedDFSane(linesearch, sigma_min, sigma_max, nothing, :DFSane)
+    return GeneralizedDFSane(;
+        linesearch, sigma_min, sigma_max, sigma_1 = nothing, name = :DFSane
+    )
 end
diff --git a/lib/NonlinearSolveSpectralMethods/src/solve.jl b/lib/NonlinearSolveSpectralMethods/src/solve.jl
index 19659a679..b4b8d3461 100644
--- a/lib/NonlinearSolveSpectralMethods/src/solve.jl
+++ b/lib/NonlinearSolveSpectralMethods/src/solve.jl
@@ -2,7 +2,7 @@
 # papers, this seems to be the only one that is widely used. If we have a list of more
 # papers we can see what is the right level of abstraction to implement here
 """
-    GeneralizedDFSane(linesearch, sigma_min, sigma_max, sigma_1, name::Symbol)
+    GeneralizedDFSane(; linesearch, sigma_min, sigma_max, sigma_1, name::Symbol = :unknown)
 
 A generalized version of the DF-SANE algorithm. This algorithm is a Jacobian-Free Spectral
 Method.
@@ -26,6 +26,12 @@ Method.
     name::Symbol
 end
 
+function GeneralizedDFSane(;
+        linesearch, sigma_min, sigma_max, sigma_1, name::Symbol = :unknown
+)
+    return GeneralizedDFSane(linesearch, sigma_min, sigma_max, sigma_1, name)
+end
+
 # XXX: Add
 # function __show_algorithm(io::IO, alg::GeneralizedDFSane, name, indent)
 #     modifiers = String[]
@@ -47,7 +53,7 @@ end
     p
     du
     alg <: GeneralizedDFSane
-    prob
+    prob <: AbstractNonlinearProblem
 
     # Parameters
     σ_n
@@ -65,7 +71,7 @@ end
 
     # Timer
     timer
-    total_time::Float64   # Simple Counter which works even if TimerOutput is disabled
+    total_time::Float64
 
     # Termination & Tracking
     termination_cache
diff --git a/lib/NonlinearSolveSpectralMethods/test/runtests.jl b/lib/NonlinearSolveSpectralMethods/test/runtests.jl
index e69de29bb..8b1378917 100644
--- a/lib/NonlinearSolveSpectralMethods/test/runtests.jl
+++ b/lib/NonlinearSolveSpectralMethods/test/runtests.jl
@@ -0,0 +1 @@
+
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index e165bb835..563b5cb8b 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -75,24 +75,20 @@ include("timer_outputs.jl")
 include("internal/helpers.jl")
 
 include("internal/termination.jl")
-include("internal/approximate_initialization.jl")
 
 include("globalization/line_search.jl")
 include("globalization/trust_region.jl")
 
 include("core/generic.jl")
-include("core/approximate_jacobian.jl")
 include("core/generalized_first_order.jl")
 include("core/noinit.jl")
 
 include("algorithms/raphson.jl")
 include("algorithms/pseudo_transient.jl")
-include("algorithms/broyden.jl")
-include("algorithms/klement.jl")
-include("algorithms/lbroyden.jl")
 include("algorithms/gauss_newton.jl")
 include("algorithms/levenberg_marquardt.jl")
 include("algorithms/trust_region.jl")
+
 include("algorithms/extension_algs.jl")
 
 include("utils.jl")
@@ -123,8 +119,6 @@ include("internal/forward_diff.jl") # we need to define after the algorithms
         NewtonRaphson(),
         TrustRegion(),
         LevenbergMarquardt(),
-        Broyden(),
-        Klement(),
         nothing
     )
 
@@ -173,10 +167,10 @@ end
 
 # Rexexports
 @reexport using SciMLBase, SimpleNonlinearSolve, NonlinearSolveBase,
-                NonlinearSolveSpectralMethods
+                NonlinearSolveSpectralMethods, NonlinearSolveQuasiNewton
 
 # Core Algorithms
-export NewtonRaphson, PseudoTransient, Klement, Broyden, LimitedMemoryBroyden
+export NewtonRaphson, PseudoTransient
 export GaussNewton, LevenbergMarquardt, TrustRegion
 export NonlinearSolvePolyAlgorithm, RobustMultiNewton, FastShortcutNonlinearPolyalg,
        FastShortcutNLLSPolyalg
@@ -187,7 +181,7 @@ export LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
 export PETScSNES, CMINPACK
 
 # Advanced Algorithms -- Without Bells and Whistles
-export GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm
+export GeneralizedFirstOrderAlgorithm
 
 # Globalization
 ## Line Search Algorithms
diff --git a/src/algorithms/broyden.jl b/src/algorithms/broyden.jl
deleted file mode 100644
index 2477a962b..000000000
--- a/src/algorithms/broyden.jl
+++ /dev/null
@@ -1,227 +0,0 @@
-"""
-    Broyden(; max_resets::Int = 100, linesearch = nothing, reset_tolerance = nothing,
-        init_jacobian::Val = Val(:identity), autodiff = nothing, alpha = nothing)
-
-An implementation of `Broyden`'s Method [broyden1965class](@cite) with resetting and line
-search.
-
-### Keyword Arguments
-
-  - `max_resets`: the maximum number of resets to perform. Defaults to `100`.
-
-  - `reset_tolerance`: the tolerance for the reset check. Defaults to
-    `sqrt(eps(real(eltype(u))))`.
-  - `alpha`: If `init_jacobian` is set to `Val(:identity)`, then the initial Jacobian
-    inverse is set to be `(αI)⁻¹`. Defaults to `nothing` which implies
-    `α = max(norm(u), 1) / (2 * norm(fu))`.
-  - `init_jacobian`: the method to use for initializing the jacobian. Defaults to
-    `Val(:identity)`. Choices include:
-
-      + `Val(:identity)`: Identity Matrix.
-      + `Val(:true_jacobian)`: True Jacobian. This is a good choice for differentiable
-        problems.
-  - `update_rule`: Update Rule for the Jacobian. Choices are:
-
-      + `Val(:good_broyden)`: Good Broyden's Update Rule
-      + `Val(:bad_broyden)`: Bad Broyden's Update Rule
-      + `Val(:diagonal)`: Only update the diagonal of the Jacobian. This algorithm may be
-        useful for specific problems, but whether it will work may depend strongly on the
-        problem
-"""
-function Broyden(;
-        max_resets = 100, linesearch = nothing, reset_tolerance = nothing,
-        init_jacobian = Val(:identity), autodiff = nothing, alpha = nothing,
-        update_rule = Val(:good_broyden))
-    initialization = broyden_init(init_jacobian, update_rule, autodiff, alpha)
-    update_rule = broyden_update_rule(update_rule)
-    return ApproximateJacobianSolveAlgorithm{
-        init_jacobian isa Val{:true_jacobian}, :Broyden}(;
-        linesearch, descent = NewtonDescent(), update_rule, max_resets, initialization,
-        reinit_rule = NoChangeInStateReset(; reset_tolerance))
-end
-
-function broyden_init(::Val{:identity}, ::Val{:diagonal}, autodiff, alpha)
-    return IdentityInitialization(alpha, DiagonalStructure())
-end
-function broyden_init(::Val{:identity}, ::Val, autodiff, alpha)
-    IdentityInitialization(alpha, FullStructure())
-end
-function broyden_init(::Val{:true_jacobian}, ::Val, autodiff, alpha)
-    return TrueJacobianInitialization(FullStructure(), autodiff)
-end
-function broyden_init(::Val{IJ}, ::Val{UR}, autodiff, alpha) where {IJ, UR}
-    error("Unknown combination of `init_jacobian = Val($(Meta.quot(IJ)))` and \
-           `update_rule = Val($(Meta.quot(UR)))`. Please choose a valid combination.")
-end
-
-broyden_update_rule(::Val{:good_broyden}) = GoodBroydenUpdateRule()
-broyden_update_rule(::Val{:bad_broyden}) = BadBroydenUpdateRule()
-broyden_update_rule(::Val{:diagonal}) = GoodBroydenUpdateRule()
-function broyden_update_rule(::Val{UR}) where {UR}
-    error("Unknown update rule `update_rule = Val($(Meta.quot(UR)))`. Please choose a \
-           valid update rule.")
-end
-
-# Checks for no significant change for `nsteps`
-"""
-    NoChangeInStateReset(; nsteps::Int = 3, reset_tolerance = nothing,
-        check_du::Bool = true, check_dfu::Bool = true)
-
-Recommends a reset if the state or the function value has not changed significantly in
-`nsteps` steps. This is used in [`Broyden`](@ref).
-
-### Keyword Arguments
-
-  - `nsteps`: the number of steps to check for no change. Defaults to `3`.
-  - `reset_tolerance`: the tolerance for the reset check. Defaults to
-    `sqrt(eps(real(eltype(u))))`.
-  - `check_du`: whether to check the state. Defaults to `true`.
-  - `check_dfu`: whether to check the function value. Defaults to `true`.
-"""
-@kwdef @concrete struct NoChangeInStateReset <: AbstractResetCondition
-    nsteps::Int = 3
-    reset_tolerance = nothing
-    check_du::Bool = true
-    check_dfu::Bool = true
-end
-
-@concrete mutable struct NoChangeInStateResetCache
-    dfu
-    reset_tolerance
-    check_du
-    check_dfu
-    nsteps::Int
-    steps_since_change_du::Int
-    steps_since_change_dfu::Int
-end
-
-function reinit_cache!(cache::NoChangeInStateResetCache, args...; kwargs...)
-    cache.steps_since_change_du = 0
-    cache.steps_since_change_dfu = 0
-end
-
-function __internal_init(alg::NoChangeInStateReset, J, fu, u, du, args...; kwargs...)
-    if alg.check_dfu
-        @bb dfu = copy(fu)
-    else
-        dfu = fu
-    end
-    T = real(eltype(u))
-    tol = alg.reset_tolerance === nothing ? eps(T)^(3 // 4) : T(alg.reset_tolerance)
-    return NoChangeInStateResetCache(
-        dfu, tol, alg.check_du, alg.check_dfu, alg.nsteps, 0, 0)
-end
-
-function __internal_solve!(cache::NoChangeInStateResetCache, J, fu, u, du)
-    reset_tolerance = cache.reset_tolerance
-    if cache.check_du
-        if any(@closure(x->abs(x) ≤ reset_tolerance), du)
-            cache.steps_since_change_du += 1
-            if cache.steps_since_change_du ≥ cache.nsteps
-                cache.steps_since_change_du = 0
-                cache.steps_since_change_dfu = 0
-                return true
-            end
-        else
-            cache.steps_since_change_du = 0
-            cache.steps_since_change_dfu = 0
-        end
-    end
-    if cache.check_dfu
-        @bb @. cache.dfu = fu - cache.dfu
-        if any(@closure(x->abs(x) ≤ reset_tolerance), cache.dfu)
-            cache.steps_since_change_dfu += 1
-            if cache.steps_since_change_dfu ≥ cache.nsteps
-                cache.steps_since_change_dfu = 0
-                cache.steps_since_change_du = 0
-                @bb copyto!(cache.dfu, fu)
-                return true
-            end
-        else
-            cache.steps_since_change_dfu = 0
-            cache.steps_since_change_du = 0
-        end
-        @bb copyto!(cache.dfu, fu)
-    end
-    return false
-end
-
-# Broyden Update Rules
-"""
-    BadBroydenUpdateRule()
-
-Broyden Update Rule corresponding to "bad broyden's method" [broyden1965class](@cite).
-"""
-struct BadBroydenUpdateRule <: AbstractApproximateJacobianUpdateRule{true} end
-
-"""
-    GoodBroydenUpdateRule()
-
-Broyden Update Rule corresponding to "good broyden's method" [broyden1965class](@cite).
-"""
-struct GoodBroydenUpdateRule <: AbstractApproximateJacobianUpdateRule{true} end
-
-@concrete mutable struct BroydenUpdateRuleCache{mode} <:
-                         AbstractApproximateJacobianUpdateRuleCache{true}
-    J⁻¹dfu
-    dfu
-    u_cache
-    du_cache
-    internalnorm
-end
-
-function __internal_init(prob::AbstractNonlinearProblem,
-        alg::Union{GoodBroydenUpdateRule, BadBroydenUpdateRule}, J, fu, u,
-        du, args...; internalnorm::F = L2_NORM, kwargs...) where {F}
-    @bb J⁻¹dfu = similar(u)
-    @bb dfu = copy(fu)
-    if alg isa GoodBroydenUpdateRule || J isa Diagonal
-        @bb u_cache = similar(u)
-    else
-        u_cache = nothing
-    end
-    if J isa Diagonal
-        du_cache = nothing
-    else
-        @bb du_cache = similar(du)
-    end
-    mode = alg isa GoodBroydenUpdateRule ? :good : :bad
-    return BroydenUpdateRuleCache{mode}(J⁻¹dfu, dfu, u_cache, du_cache, internalnorm)
-end
-
-function __internal_solve!(cache::BroydenUpdateRuleCache{mode}, J⁻¹, fu, u, du) where {mode}
-    T = eltype(u)
-    @bb @. cache.dfu = fu - cache.dfu
-    @bb cache.J⁻¹dfu = J⁻¹ × vec(cache.dfu)
-    if mode === :good
-        @bb cache.u_cache = transpose(J⁻¹) × vec(du)
-        denom = dot(du, cache.J⁻¹dfu)
-        rmul = transpose(_vec(cache.u_cache))
-    else
-        denom = cache.internalnorm(cache.dfu)^2
-        rmul = transpose(_vec(cache.dfu))
-    end
-    @bb @. cache.du_cache = (du - cache.J⁻¹dfu) / ifelse(iszero(denom), T(1e-5), denom)
-    @bb J⁻¹ += vec(cache.du_cache) × rmul
-    @bb copyto!(cache.dfu, fu)
-    return J⁻¹
-end
-
-function __internal_solve!(
-        cache::BroydenUpdateRuleCache{mode}, J⁻¹::Diagonal, fu, u, du) where {mode}
-    T = eltype(u)
-    @bb @. cache.dfu = fu - cache.dfu
-    J⁻¹_diag = _restructure(cache.dfu, diag(J⁻¹))
-    if mode === :good
-        @bb @. cache.J⁻¹dfu = J⁻¹_diag * cache.dfu * du
-        denom = sum(cache.J⁻¹dfu)
-        @bb @. J⁻¹_diag += (du - J⁻¹_diag * cache.dfu) * du * J⁻¹_diag /
-                           ifelse(iszero(denom), T(1e-5), denom)
-    else
-        denom = cache.internalnorm(cache.dfu)^2
-        @bb @. J⁻¹_diag += (du - J⁻¹_diag * cache.dfu) * cache.dfu /
-                           ifelse(iszero(denom), T(1e-5), denom)
-    end
-    @bb copyto!(cache.dfu, fu)
-    return Diagonal(J⁻¹_diag)
-end
diff --git a/src/algorithms/lbroyden.jl b/src/algorithms/lbroyden.jl
deleted file mode 100644
index bbbc55b28..000000000
--- a/src/algorithms/lbroyden.jl
+++ /dev/null
@@ -1,169 +0,0 @@
-"""
-    LimitedMemoryBroyden(; max_resets::Int = 3, linesearch = nothing,
-        threshold::Val = Val(10), reset_tolerance = nothing, alpha = nothing)
-
-An implementation of `LimitedMemoryBroyden` [ziani2008autoadaptative](@cite) with resetting
-and line search.
-
-### Keyword Arguments
-
-  - `max_resets`: the maximum number of resets to perform. Defaults to `3`.
-  - `reset_tolerance`: the tolerance for the reset check. Defaults to
-    `sqrt(eps(real(eltype(u))))`.
-  - `threshold`: the number of vectors to store in the low rank approximation. Defaults
-    to `Val(10)`.
-  - `alpha`: The initial Jacobian inverse is set to be `(αI)⁻¹`. Defaults to `nothing`
-    which implies `α = max(norm(u), 1) / (2 * norm(fu))`.
-"""
-function LimitedMemoryBroyden(; max_resets::Int = 3, linesearch = nothing,
-        threshold::Union{Val, Int} = Val(10), reset_tolerance = nothing, alpha = nothing)
-    threshold isa Int && (threshold = Val(threshold))
-    initialization = BroydenLowRankInitialization(alpha, threshold)
-    return ApproximateJacobianSolveAlgorithm{false, :LimitedMemoryBroyden}(; linesearch,
-        descent = NewtonDescent(), update_rule = GoodBroydenUpdateRule(),
-        max_resets, initialization, reinit_rule = NoChangeInStateReset(; reset_tolerance))
-end
-
-"""
-    BroydenLowRankInitialization(alpha, threshold::Val)
-
-An initialization for `LimitedMemoryBroyden` that uses a low rank approximation of the
-Jacobian. The low rank updates to the Jacobian matrix corresponds to what SciPy calls
-["simple"](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.broyden2.html#scipy-optimize-broyden2).
-"""
-@concrete struct BroydenLowRankInitialization <: AbstractJacobianInitialization
-    alpha
-    threshold <: Val
-end
-
-jacobian_initialized_preinverted(::BroydenLowRankInitialization) = true
-
-function __internal_init(
-        prob::AbstractNonlinearProblem, alg::BroydenLowRankInitialization,
-        solver, f::F, fu, u, p; maxiters = 1000,
-        internalnorm::IN = L2_NORM, kwargs...) where {F, IN}
-    if u isa Number # Use the standard broyden
-        return __internal_init(prob, IdentityInitialization(true, FullStructure()),
-            solver, f, fu, u, p; maxiters, kwargs...)
-    end
-    # Pay to cost of slightly more allocations to prevent type-instability for StaticArrays
-    α = inv(__initial_alpha(alg.alpha, u, fu, internalnorm))
-    if u isa StaticArray
-        J = BroydenLowRankJacobian(fu, u; alg.threshold, alpha = α)
-    else
-        threshold = min(_unwrap_val(alg.threshold), maxiters)
-        J = BroydenLowRankJacobian(fu, u; threshold, alpha = α)
-    end
-    return InitializedApproximateJacobianCache(
-        J, FullStructure(), alg, nothing, true, internalnorm)
-end
-
-function (cache::InitializedApproximateJacobianCache)(
-        alg::BroydenLowRankInitialization, fu, u)
-    α = __initial_alpha(alg.alpha, u, fu, cache.internalnorm)
-    cache.J.idx = 0
-    cache.J.alpha = inv(α)
-    return
-end
-
-"""
-    BroydenLowRankJacobian{T}(U, Vᵀ, idx, cache, alpha)
-
-Low Rank Approximation of the Jacobian Matrix. Currently only used for
-[`LimitedMemoryBroyden`](@ref). This computes the Jacobian as ``U \\times V^T``.
-"""
-@concrete mutable struct BroydenLowRankJacobian{T} <: AbstractSciMLOperator{T}
-    U
-    Vᵀ
-    idx::Int
-    cache
-    alpha
-end
-
-__safe_inv!!(workspace, op::BroydenLowRankJacobian) = op  # Already Inverted form
-
-@inline function __get_components(op::BroydenLowRankJacobian)
-    op.idx ≥ size(op.U, 2) && return op.cache, op.U, transpose(op.Vᵀ)
-    _cache = op.cache === nothing ? op.cache : view(op.cache, 1:(op.idx))
-    return (_cache, view(op.U, :, 1:(op.idx)), transpose(view(op.Vᵀ, :, 1:(op.idx))))
-end
-
-Base.size(op::BroydenLowRankJacobian) = size(op.U, 1), size(op.Vᵀ, 1)
-function Base.size(op::BroydenLowRankJacobian, d::Integer)
-    return ifelse(d == 1, size(op.U, 1), size(op.Vᵀ, 1))
-end
-
-for op in (:adjoint, :transpose)
-    # FIXME: adjoint might be a problem here. Fix if a complex number issue shows up
-    @eval function Base.$(op)(operator::BroydenLowRankJacobian{T}) where {T}
-        return BroydenLowRankJacobian{T}(
-            operator.Vᵀ, operator.U, operator.idx, operator.cache, operator.alpha)
-    end
-end
-
-# Storing the transpose to ensure contiguous memory on splicing
-function BroydenLowRankJacobian(
-        fu::StaticArray{S2, T2}, u::StaticArray{S1, T1}; alpha = true,
-        threshold::Val{Th} = Val(10)) where {S1, S2, T1, T2, Th}
-    T = promote_type(T1, T2)
-    fuSize, uSize = Size(fu), Size(u)
-    U = MArray{Tuple{prod(fuSize), Th}, T}(undef)
-    Vᵀ = MArray{Tuple{prod(uSize), Th}, T}(undef)
-    return BroydenLowRankJacobian{T}(U, Vᵀ, 0, nothing, T(alpha))
-end
-
-function BroydenLowRankJacobian(fu, u; threshold::Int = 10, alpha = true)
-    T = promote_type(eltype(u), eltype(fu))
-    U = __similar(fu, T, length(fu), threshold)
-    Vᵀ = __similar(u, T, length(u), threshold)
-    cache = __similar(u, T, threshold)
-    return BroydenLowRankJacobian{T}(U, Vᵀ, 0, cache, T(alpha))
-end
-
-function Base.:*(J::BroydenLowRankJacobian, x::AbstractVector)
-    J.idx == 0 && return -x
-    cache, U, Vᵀ = __get_components(J)
-    return U * (Vᵀ * x) .- J.alpha .* x
-end
-
-function LinearAlgebra.mul!(y::AbstractVector, J::BroydenLowRankJacobian, x::AbstractVector)
-    if J.idx == 0
-        @. y = -J.alpha * x
-        return y
-    end
-    cache, U, Vᵀ = __get_components(J)
-    @bb cache = Vᵀ × x
-    mul!(y, U, cache)
-    @bb @. y -= J.alpha * x
-    return y
-end
-
-function Base.:*(x::AbstractVector, J::BroydenLowRankJacobian)
-    J.idx == 0 && return -x
-    cache, U, Vᵀ = __get_components(J)
-    return Vᵀ' * (U' * x) .- J.alpha .* x
-end
-
-function LinearAlgebra.mul!(y::AbstractVector, x::AbstractVector, J::BroydenLowRankJacobian)
-    if J.idx == 0
-        @. y = -J.alpha * x
-        return y
-    end
-    cache, U, Vᵀ = __get_components(J)
-    @bb cache = transpose(U) × x
-    mul!(y, transpose(Vᵀ), cache)
-    @bb @. y -= J.alpha * x
-    return y
-end
-
-function LinearAlgebra.mul!(J::BroydenLowRankJacobian, u::AbstractArray,
-        vᵀ::LinearAlgebra.AdjOrTransAbsVec, α::Bool, β::Bool)
-    @assert α & β
-    idx_update = mod1(J.idx + 1, size(J.U, 2))
-    copyto!(@view(J.U[:, idx_update]), _vec(u))
-    copyto!(@view(J.Vᵀ[:, idx_update]), _vec(vᵀ))
-    J.idx += 1
-    return J
-end
-
-ArrayInterface.restructure(::BroydenLowRankJacobian, J::BroydenLowRankJacobian) = J
diff --git a/src/core/approximate_jacobian.jl b/src/core/approximate_jacobian.jl
deleted file mode 100644
index 4d7bc213b..000000000
--- a/src/core/approximate_jacobian.jl
+++ /dev/null
@@ -1,378 +0,0 @@
-"""
-    ApproximateJacobianSolveAlgorithm{concrete_jac, name}(; linesearch = missing,
-        trustregion = missing, descent, update_rule, reinit_rule, initialization,
-        max_resets::Int = typemax(Int), max_shrink_times::Int = typemax(Int))
-    ApproximateJacobianSolveAlgorithm(; concrete_jac = nothing,
-        name::Symbol = :unknown, kwargs...)
-
-Nonlinear Solve Algorithms using an Iterative Approximation of the Jacobian. Most common
-examples include [`Broyden`](@ref)'s Method.
-
-### Keyword Arguments
-
-  - `trustregion`: Globalization using a Trust Region Method. This needs to follow the
-    [`NonlinearSolve.AbstractTrustRegionMethod`](@ref) interface.
-  - `descent`: The descent method to use to compute the step. This needs to follow the
-    [`NonlinearSolve.AbstractDescentAlgorithm`](@ref) interface.
-  - `max_shrink_times`: The maximum number of times the trust region radius can be shrunk
-    before the algorithm terminates.
-  - `update_rule`: The update rule to use to update the Jacobian. This needs to follow the
-    [`NonlinearSolve.AbstractApproximateJacobianUpdateRule`](@ref) interface.
-  - `reinit_rule`: The reinitialization rule to use to reinitialize the Jacobian. This
-    needs to follow the [`NonlinearSolve.AbstractResetCondition`](@ref) interface.
-  - `initialization`: The initialization method to use to initialize the Jacobian. This
-    needs to follow the [`NonlinearSolve.AbstractJacobianInitialization`](@ref) interface.
-"""
-@concrete struct ApproximateJacobianSolveAlgorithm{concrete_jac, name} <:
-                 AbstractNonlinearSolveAlgorithm{name}
-    linesearch
-    trustregion
-    descent
-    update_rule
-    reinit_rule
-    max_resets::Int
-    max_shrink_times::Int
-    initialization
-end
-
-function __show_algorithm(io::IO, alg::ApproximateJacobianSolveAlgorithm, name, indent)
-    modifiers = String[]
-    __is_present(alg.linesearch) && push!(modifiers, "linesearch = $(alg.linesearch)")
-    __is_present(alg.trustregion) && push!(modifiers, "trustregion = $(alg.trustregion)")
-    push!(modifiers, "descent = $(alg.descent)")
-    push!(modifiers, "update_rule = $(alg.update_rule)")
-    push!(modifiers, "reinit_rule = $(alg.reinit_rule)")
-    push!(modifiers, "max_resets = $(alg.max_resets)")
-    push!(modifiers, "initialization = $(alg.initialization)")
-    store_inverse_jacobian(alg.update_rule) && push!(modifiers, "inverse_jacobian = true")
-    spacing = " "^indent * "    "
-    spacing_last = " "^indent
-    print(io, "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))")
-end
-
-function ApproximateJacobianSolveAlgorithm(;
-        concrete_jac = nothing, name::Symbol = :unknown, kwargs...)
-    return ApproximateJacobianSolveAlgorithm{concrete_jac, name}(; kwargs...)
-end
-
-function ApproximateJacobianSolveAlgorithm{concrete_jac, name}(;
-        linesearch = missing, trustregion = missing, descent, update_rule,
-        reinit_rule, initialization, max_resets::Int = typemax(Int),
-        max_shrink_times::Int = typemax(Int)) where {concrete_jac, name}
-    return ApproximateJacobianSolveAlgorithm{concrete_jac, name}(
-        linesearch, trustregion, descent, update_rule,
-        reinit_rule, max_resets, max_shrink_times, initialization)
-end
-
-# XXX: Remove
-@inline concrete_jac(::ApproximateJacobianSolveAlgorithm{CJ}) where {CJ} = concrete_jac(CJ)
-
-@concrete mutable struct ApproximateJacobianSolveCache{INV, GB, iip, timeit} <:
-                         AbstractNonlinearSolveCache{iip, timeit}
-    # Basic Requirements
-    fu
-    u
-    u_cache
-    p
-    du  # Aliased to `get_du(descent_cache)`
-    J   # Aliased to `initialization_cache.J` if !INV
-    alg
-    prob
-
-    # Internal Caches
-    initialization_cache
-    descent_cache
-    linesearch_cache
-    trustregion_cache
-    update_rule_cache
-    reinit_rule_cache
-
-    inv_workspace
-
-    # Counters
-    stats::NLStats
-    nsteps::Int
-    nresets::Int
-    max_resets::Int
-    maxiters::Int
-    maxtime
-    max_shrink_times::Int
-    steps_since_last_reset::Int
-
-    # Timer
-    timer
-    total_time::Float64   # Simple Counter which works even if TimerOutput is disabled
-
-    # Termination & Tracking
-    termination_cache
-    trace
-    retcode::ReturnCode.T
-    force_stop::Bool
-    force_reinit::Bool
-    kwargs
-end
-
-store_inverse_jacobian(::ApproximateJacobianSolveCache{INV}) where {INV} = INV
-
-function __reinit_internal!(cache::ApproximateJacobianSolveCache{INV, GB, iip},
-        args...; p = cache.p, u0 = cache.u, alias_u0::Bool = false,
-        maxiters = 1000, maxtime = nothing, kwargs...) where {INV, GB, iip}
-    if iip
-        recursivecopy!(cache.u, u0)
-        cache.prob.f(cache.fu, cache.u, p)
-    else
-        cache.u = __maybe_unaliased(u0, alias_u0)
-        set_fu!(cache, cache.prob.f(cache.u, p))
-    end
-    cache.p = p
-
-    __reinit_internal!(cache.stats)
-    cache.nsteps = 0
-    cache.nresets = 0
-    cache.steps_since_last_reset = 0
-    cache.maxiters = maxiters
-    cache.maxtime = maxtime
-    cache.total_time = 0.0
-    cache.force_stop = false
-    cache.force_reinit = false
-    cache.retcode = ReturnCode.Default
-
-    reset!(cache.trace)
-    reinit!(cache.termination_cache, get_fu(cache), get_u(cache); kwargs...)
-    reset_timer!(cache.timer)
-end
-
-@internal_caches ApproximateJacobianSolveCache :initialization_cache :descent_cache :linesearch_cache :trustregion_cache :update_rule_cache :reinit_rule_cache
-
-function SciMLBase.__init(
-        prob::AbstractNonlinearProblem{uType, iip}, alg::ApproximateJacobianSolveAlgorithm,
-        args...; stats = empty_nlstats(), alias_u0 = false, maxtime = nothing,
-        maxiters = 1000, abstol = nothing, reltol = nothing,
-        linsolve_kwargs = (;), termination_condition = nothing,
-        internalnorm::F = L2_NORM, kwargs...) where {uType, iip, F}
-    timer = get_timer_output()
-    @static_timeit timer "cache construction" begin
-        (; f, u0, p) = prob
-        u = __maybe_unaliased(u0, alias_u0)
-        fu = evaluate_f(prob, u)
-        @bb u_cache = copy(u)
-
-        INV = store_inverse_jacobian(alg.update_rule)
-
-        linsolve = get_linear_solver(alg.descent)
-        initialization_cache = __internal_init(prob, alg.initialization, alg, f, fu, u, p;
-            stats, linsolve, maxiters, internalnorm)
-
-        abstol, reltol, termination_cache = NonlinearSolveBase.init_termination_cache(
-            prob, abstol, reltol, fu, u, termination_condition, Val(:regular))
-        linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
-
-        J = initialization_cache(nothing)
-        inv_workspace, J = INV ? __safe_inv_workspace(J) : (nothing, J)
-        descent_cache = __internal_init(prob, alg.descent, J, fu, u; stats, abstol, reltol,
-            internalnorm, linsolve_kwargs, pre_inverted = Val(INV), timer)
-        du = get_du(descent_cache)
-
-        reinit_rule_cache = __internal_init(alg.reinit_rule, J, fu, u, du)
-
-        has_linesearch = alg.linesearch !== missing && alg.linesearch !== nothing
-        has_trustregion = alg.trustregion !== missing && alg.trustregion !== nothing
-
-        if has_trustregion && has_linesearch
-            error("TrustRegion and LineSearch methods are algorithmically incompatible.")
-        end
-
-        GB = :None
-        linesearch_cache = nothing
-        trustregion_cache = nothing
-
-        if has_trustregion
-            supports_trust_region(alg.descent) || error("Trust Region not supported by \
-                                                        $(alg.descent).")
-            trustregion_cache = __internal_init(
-                prob, alg.trustregion, f, fu, u, p; stats, internalnorm, kwargs...)
-            GB = :TrustRegion
-        end
-
-        if has_linesearch
-            supports_line_search(alg.descent) || error("Line Search not supported by \
-                                                        $(alg.descent).")
-            linesearch_cache = init(
-                prob, alg.linesearch, fu, u; stats, internalnorm, kwargs...)
-            GB = :LineSearch
-        end
-
-        update_rule_cache = __internal_init(
-            prob, alg.update_rule, J, fu, u, du; stats, internalnorm)
-
-        trace = init_nonlinearsolve_trace(prob, alg, u, fu, ApplyArray(__zero, J), du;
-            uses_jacobian_inverse = Val(INV), kwargs...)
-
-        return ApproximateJacobianSolveCache{INV, GB, iip, maxtime !== nothing}(
-            fu, u, u_cache, p, du, J, alg, prob, initialization_cache,
-            descent_cache, linesearch_cache, trustregion_cache, update_rule_cache,
-            reinit_rule_cache, inv_workspace, stats, 0, 0, alg.max_resets,
-            maxiters, maxtime, alg.max_shrink_times, 0, timer, 0.0,
-            termination_cache, trace, ReturnCode.Default, false, false, kwargs)
-    end
-end
-
-function __step!(cache::ApproximateJacobianSolveCache{INV, GB, iip};
-        recompute_jacobian::Union{Nothing, Bool} = nothing) where {INV, GB, iip}
-    new_jacobian = true
-    @static_timeit cache.timer "jacobian init/reinit" begin
-        if cache.nsteps == 0  # First Step is special ignore kwargs
-            J_init = __internal_solve!(
-                cache.initialization_cache, cache.fu, cache.u, Val(false))
-            if INV
-                if jacobian_initialized_preinverted(cache.initialization_cache.alg)
-                    cache.J = J_init
-                else
-                    cache.J = __safe_inv!!(cache.inv_workspace, J_init)
-                end
-            else
-                if jacobian_initialized_preinverted(cache.initialization_cache.alg)
-                    cache.J = __safe_inv!!(cache.inv_workspace, J_init)
-                else
-                    cache.J = J_init
-                end
-            end
-            J = cache.J
-            cache.steps_since_last_reset += 1
-        else
-            countable_reinit = false
-            if cache.force_reinit
-                reinit, countable_reinit = true, true
-                cache.force_reinit = false
-            elseif recompute_jacobian === nothing
-                # Standard Step
-                reinit = __internal_solve!(
-                    cache.reinit_rule_cache, cache.J, cache.fu, cache.u, cache.du)
-                reinit && (countable_reinit = true)
-            elseif recompute_jacobian
-                reinit = true  # Force ReInitialization: Don't count towards resetting
-            else
-                new_jacobian = false # Jacobian won't be updated in this step
-                reinit = false # Override Checks: Unsafe operation
-            end
-
-            if countable_reinit
-                cache.nresets += 1
-                if cache.nresets ≥ cache.max_resets
-                    cache.retcode = ReturnCode.ConvergenceFailure
-                    cache.force_stop = true
-                    return
-                end
-            end
-
-            if reinit
-                J_init = __internal_solve!(
-                    cache.initialization_cache, cache.fu, cache.u, Val(true))
-                cache.J = INV ? __safe_inv!!(cache.inv_workspace, J_init) : J_init
-                J = cache.J
-                cache.steps_since_last_reset = 0
-            else
-                J = cache.J
-                cache.steps_since_last_reset += 1
-            end
-        end
-    end
-
-    @static_timeit cache.timer "descent" begin
-        if cache.trustregion_cache !== nothing &&
-           hasfield(typeof(cache.trustregion_cache), :trust_region)
-            descent_result = __internal_solve!(
-                cache.descent_cache, J, cache.fu, cache.u; new_jacobian,
-                trust_region = cache.trustregion_cache.trust_region, cache.kwargs...)
-        else
-            descent_result = __internal_solve!(
-                cache.descent_cache, J, cache.fu, cache.u; new_jacobian, cache.kwargs...)
-        end
-    end
-
-    if !descent_result.linsolve_success
-        if new_jacobian && cache.steps_since_last_reset == 0
-            # Extremely pathological case. Jacobian was just reset and linear solve
-            # failed. Should ideally never happen in practice unless true jacobian init
-            # is used.
-            cache.retcode = ReturnCode.InternalLinearSolveFailed
-            cache.force_stop = true
-            return
-        else
-            # Force a reinit because the problem is currently un-solvable
-            if !haskey(cache.kwargs, :verbose) || cache.kwargs[:verbose]
-                @warn "Linear Solve Failed but Jacobian Information is not current. \
-                       Retrying with reinitialized Approximate Jacobian."
-            end
-            cache.force_reinit = true
-            __step!(cache; recompute_jacobian = true)
-            return
-        end
-    end
-
-    δu, descent_intermediates = descent_result.δu, descent_result.extras
-
-    if descent_result.success
-        if GB === :LineSearch
-            @static_timeit cache.timer "linesearch" begin
-                linesearch_sol = solve!(cache.linesearch_cache, cache.u, δu)
-                needs_reset = !SciMLBase.successful_retcode(linesearch_sol.retcode)
-                α = linesearch_sol.step_size
-            end
-            if needs_reset && cache.steps_since_last_reset > 5 # Reset after a burn-in period
-                cache.force_reinit = true
-            else
-                @static_timeit cache.timer "step" begin
-                    @bb axpy!(α, δu, cache.u)
-                    evaluate_f!(cache, cache.u, cache.p)
-                end
-            end
-        elseif GB === :TrustRegion
-            @static_timeit cache.timer "trustregion" begin
-                tr_accepted, u_new, fu_new = __internal_solve!(
-                    cache.trustregion_cache, J, cache.fu,
-                    cache.u, δu, descent_intermediates)
-                if tr_accepted
-                    @bb copyto!(cache.u, u_new)
-                    @bb copyto!(cache.fu, fu_new)
-                end
-                if hasfield(typeof(cache.trustregion_cache), :shrink_counter) &&
-                   cache.trustregion_cache.shrink_counter > cache.max_shrink_times
-                    cache.retcode = ReturnCode.ShrinkThresholdExceeded
-                    cache.force_stop = true
-                end
-            end
-            α = true
-        elseif GB === :None
-            @static_timeit cache.timer "step" begin
-                @bb axpy!(1, δu, cache.u)
-                evaluate_f!(cache, cache.u, cache.p)
-            end
-            α = true
-        else
-            error("Unknown Globalization Strategy: $(GB). Allowed values are (:LineSearch, \
-                :TrustRegion, :None)")
-        end
-        check_and_update!(cache, cache.fu, cache.u, cache.u_cache)
-    else
-        α = false
-        cache.force_reinit = true
-    end
-
-    update_trace!(cache, α)
-    @bb copyto!(cache.u_cache, cache.u)
-
-    if (cache.force_stop ||
-        cache.force_reinit ||
-        (recompute_jacobian !== nothing && !recompute_jacobian))
-        callback_into_cache!(cache)
-        return nothing
-    end
-
-    @static_timeit cache.timer "jacobian update" begin
-        cache.J = __internal_solve!(cache.update_rule_cache, cache.J, cache.fu, cache.u, δu)
-        callback_into_cache!(cache)
-    end
-
-    return nothing
-end
diff --git a/src/internal/approximate_initialization.jl b/src/internal/approximate_initialization.jl
deleted file mode 100644
index 7df718279..000000000
--- a/src/internal/approximate_initialization.jl
+++ /dev/null
@@ -1,281 +0,0 @@
-# Jacobian Structure
-"""
-    DiagonalStructure()
-
-Preserves only the Diagonal of the Matrix.
-"""
-struct DiagonalStructure <: AbstractApproximateJacobianStructure end
-
-get_full_jacobian(cache, ::DiagonalStructure, J::Number) = J
-get_full_jacobian(cache, ::DiagonalStructure, J) = Diagonal(_vec(J))
-
-function (::DiagonalStructure)(J::AbstractMatrix; alias::Bool = false)
-    @assert size(J, 1)==size(J, 2) "Diagonal Jacobian Structure must be square!"
-    return diag(J)
-end
-(::DiagonalStructure)(J::AbstractVector; alias::Bool = false) = alias ? J : @bb(copy(J))
-(::DiagonalStructure)(J::Number; alias::Bool = false) = J
-
-(::DiagonalStructure)(::Number, J_new::Number) = J_new
-function (::DiagonalStructure)(J::AbstractVector, J_new::AbstractMatrix)
-    if __can_setindex(J)
-        if fast_scalar_indexing(J)
-            @simd for i in eachindex(J)
-                @inbounds J[i] = J_new[i, i]
-            end
-        else
-            J .= @view(J_new[diagind(J_new)])
-        end
-        return J
-    end
-    return diag(J_new)
-end
-function (st::DiagonalStructure)(J::AbstractArray, J_new::AbstractMatrix)
-    return _restructure(J, st(vec(J), J_new))
-end
-
-"""
-    FullStructure()
-
-Stores the full matrix.
-"""
-struct FullStructure <: AbstractApproximateJacobianStructure end
-
-stores_full_jacobian(::FullStructure) = true
-
-(::FullStructure)(J; alias::Bool = false) = alias ? J : @bb(copy(J))
-
-function (::FullStructure)(J, J_new)
-    J === J_new && return J
-    @bb copyto!(J, J_new)
-    return J
-end
-
-# Initialization Strategies
-"""
-    IdentityInitialization(alpha, structure)
-
-Initialize the Jacobian to be an Identity Matrix scaled by `alpha` and maintain the
-structure as specified by `structure`.
-"""
-@concrete struct IdentityInitialization <: AbstractJacobianInitialization
-    alpha
-    structure
-end
-
-function __internal_init(
-        prob::AbstractNonlinearProblem, alg::IdentityInitialization, solver, f::F,
-        fu, u::Number, p; internalnorm::IN = L2_NORM, kwargs...) where {F, IN}
-    α = __initial_alpha(alg.alpha, u, fu, internalnorm)
-    return InitializedApproximateJacobianCache(
-        α, alg.structure, alg, nothing, true, internalnorm)
-end
-function __internal_init(prob::AbstractNonlinearProblem, alg::IdentityInitialization,
-        solver, f::F, fu::StaticArray, u::StaticArray, p;
-        internalnorm::IN = L2_NORM, kwargs...) where {IN, F}
-    α = __initial_alpha(alg.alpha, u, fu, internalnorm)
-    if alg.structure isa DiagonalStructure
-        @assert length(u)==length(fu) "Diagonal Jacobian Structure must be square!"
-        J = one.(_vec(fu)) .* α
-    else
-        T = promote_type(eltype(u), eltype(fu))
-        if fu isa SArray
-            J_ = SArray{Tuple{prod(Size(fu)), prod(Size(u))}, T}(I * α)
-        else
-            J_ = MArray{Tuple{prod(Size(fu)), prod(Size(u))}, T}(I * α)
-        end
-        J = alg.structure(J_; alias = true)
-    end
-    return InitializedApproximateJacobianCache(
-        J, alg.structure, alg, nothing, true, internalnorm)
-end
-function __internal_init(
-        prob::AbstractNonlinearProblem, alg::IdentityInitialization, solver,
-        f::F, fu, u, p; internalnorm::IN = L2_NORM, kwargs...) where {F, IN}
-    α = __initial_alpha(alg.alpha, u, fu, internalnorm)
-    if alg.structure isa DiagonalStructure
-        @assert length(u)==length(fu) "Diagonal Jacobian Structure must be square!"
-        J = one.(_vec(fu)) .* α
-    else
-        J_ = __similar(fu, promote_type(eltype(fu), eltype(u)), length(fu), length(u))
-        J = alg.structure(__make_identity!!(J_, α); alias = true)
-    end
-    return InitializedApproximateJacobianCache(
-        J, alg.structure, alg, nothing, true, internalnorm)
-end
-
-@inline function __initial_alpha(α, u, fu, internalnorm::F) where {F}
-    return convert(promote_type(eltype(u), eltype(fu)), α)
-end
-@inline function __initial_alpha(::Nothing, u, fu, internalnorm::F) where {F}
-    fu_norm = internalnorm(fu)
-    return ifelse(fu_norm ≥ 1e-5, (2 * fu_norm) / max(norm(u), true),
-        __initial_alpha(true, u, fu, internalnorm))
-end
-
-@inline __make_identity!!(A::Number, α) = one(A) * α
-@inline __make_identity!!(A::AbstractVector, α) = __can_setindex(A) ? (A .= α) :
-                                                  (one.(A) .* α)
-@inline function __make_identity!!(A::AbstractMatrix{T}, α) where {T}
-    if A isa SMatrix
-        Sz = Size(A)
-        return SArray{Tuple{Sz[1], Sz[2]}, eltype(Sz)}(I * α)
-    end
-    @assert __can_setindex(A) "__make_identity!!(::AbstractMatrix) only works on mutable arrays!"
-    fill!(A, false)
-    if fast_scalar_indexing(A)
-        @inbounds for i in axes(A, 1)
-            A[i, i] = α
-        end
-    else
-        A[diagind(A)] .= α
-    end
-    return A
-end
-
-"""
-    TrueJacobianInitialization(structure, autodiff)
-
-Initialize the Jacobian to be the true Jacobian and maintain the structure as specified
-by `structure`. `autodiff` is used to compute the true Jacobian and if not specified we
-make a selection automatically.
-"""
-@concrete struct TrueJacobianInitialization <: AbstractJacobianInitialization
-    structure
-    autodiff
-end
-
-function __internal_init(prob::AbstractNonlinearProblem, alg::TrueJacobianInitialization,
-        solver, f::F, fu, u, p; stats, linsolve = missing,
-        internalnorm::IN = L2_NORM, kwargs...) where {F, IN}
-    autodiff = select_jacobian_autodiff(prob, alg.autodiff)
-    jac_cache = construct_jacobian_cache(
-        prob, solver, prob.f, fu, u, p; stats, autodiff, linsolve)
-    J = alg.structure(jac_cache(nothing))
-    return InitializedApproximateJacobianCache(
-        J, alg.structure, alg, jac_cache, false, internalnorm)
-end
-
-"""
-    InitializedApproximateJacobianCache(J, structure, alg, cache, initialized::Bool,
-        internalnorm)
-
-A cache for Approximate Jacobian.
-
-### Arguments
-
-  - `J`: The current Jacobian.
-  - `structure`: The structure of the Jacobian.
-  - `alg`: The initialization algorithm.
-  - `cache`: The Jacobian cache [`NonlinearSolve.JacobianCache`](@ref) (if needed).
-  - `initialized`: A boolean indicating whether the Jacobian has been initialized.
-  - `internalnorm`: The norm to be used.
-
-### Interface
-
-```julia
-(cache::InitializedApproximateJacobianCache)(::Nothing)
-```
-
-Returns the current Jacobian `cache.J` with the proper `structure`.
-
-```julia
-__internal_solve!(cache::InitializedApproximateJacobianCache, fu, u, ::Val{reinit})
-```
-
-Solves for the Jacobian `cache.J` and returns it. If `reinit` is `true`, then the Jacobian
-is reinitialized.
-"""
-@concrete mutable struct InitializedApproximateJacobianCache
-    J
-    structure
-    alg
-    cache
-    initialized::Bool
-    internalnorm
-end
-
-function __reinit_internal!(cache::InitializedApproximateJacobianCache, args...; kwargs...)
-    cache.initialized = false
-end
-
-@internal_caches InitializedApproximateJacobianCache :cache
-
-function (cache::InitializedApproximateJacobianCache)(::Nothing)
-    return get_full_jacobian(cache, cache.structure, cache.J)
-end
-
-function __internal_solve!(
-        cache::InitializedApproximateJacobianCache, fu, u, ::Val{reinit}) where {reinit}
-    if reinit || !cache.initialized
-        cache(cache.alg, fu, u)
-        cache.initialized = true
-    end
-    if stores_full_jacobian(cache.structure)
-        full_J = cache.J
-    else
-        full_J = get_full_jacobian(cache, cache.structure, cache.J)
-    end
-    return full_J
-end
-
-function (cache::InitializedApproximateJacobianCache)(alg::IdentityInitialization, fu, u)
-    α = __initial_alpha(alg.alpha, u, fu, cache.internalnorm)
-    cache.J = __make_identity!!(cache.J, α)
-    return
-end
-
-function (cache::InitializedApproximateJacobianCache)(
-        alg::TrueJacobianInitialization, fu, u)
-    J_new = cache.cache(u)
-    cache.J = cache.structure(cache.J, J_new)
-    return
-end
-
-# Matrix Inversion
-@inline __safe_inv_workspace(A) = nothing, A
-@inline __safe_inv_workspace(A::ApplyArray) = __safe_inv_workspace(X)
-@inline __safe_inv_workspace(A::SparseMatrixCSC) = Matrix(A), Matrix(A)
-
-@inline __safe_inv!!(workspace, A::Number) = pinv(A)
-@inline __safe_inv!!(workspace, A::AbstractMatrix) = pinv(A)
-@inline function __safe_inv!!(workspace, A::Diagonal)
-    D = A.diag
-    @bb @. D = pinv(D)
-    return Diagonal(D)
-end
-@inline function __safe_inv!!(workspace, A::AbstractVector{T}) where {T}
-    @. A = ifelse(iszero(A), zero(T), one(T) / A)
-    return A
-end
-@inline __safe_inv!!(workspace, A::ApplyArray) = __safe_inv!!(workspace, A.f(A.args...))
-@inline function __safe_inv!!(workspace::AbstractMatrix, A::SparseMatrixCSC)
-    copyto!(workspace, A)
-    return __safe_inv!!(nothing, workspace)
-end
-@inline function __safe_inv!!(workspace, A::StridedMatrix{T}) where {T}
-    LinearAlgebra.checksquare(A)
-    if istriu(A)
-        issingular = any(iszero, @view(A[diagind(A)]))
-        A_ = UpperTriangular(A)
-        !issingular && return triu!(parent(inv(A_)))
-    elseif istril(A)
-        A_ = LowerTriangular(A)
-        issingular = any(iszero, @view(A_[diagind(A_)]))
-        !issingular && return tril!(parent(inv(A_)))
-    else
-        F = lu(A; check = false)
-        if issuccess(F)
-            Ai = LinearAlgebra.inv!(F)
-            return convert(typeof(parent(Ai)), Ai)
-        end
-    end
-    return pinv(A)
-end
-
-@inline __safe_inv(x) = __safe_inv!!(first(__safe_inv_workspace(x)), x)
-
-LazyArrays.applied_eltype(::typeof(__safe_inv), x) = eltype(x)
-LazyArrays.applied_ndims(::typeof(__safe_inv), x) = ndims(x)
-LazyArrays.applied_size(::typeof(__safe_inv), x) = size(x)
-LazyArrays.applied_axes(::typeof(__safe_inv), x) = axes(x)

From 712ce579b872f9faa5ac039f7d17e2b75926031e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 27 Oct 2024 23:55:57 -0400
Subject: [PATCH 640/700] feat: nicer generalized printing of structs/results

---
 lib/NonlinearSolveBase/src/abstract_types.jl  |  74 +++++----
 .../src/descent/geodesic_acceleration.jl      |  11 +-
 lib/NonlinearSolveBase/src/utils.jl           |  45 +++++-
 .../src/initialization.jl                     |  11 +-
 .../src/reset_conditions.jl                   |   2 +-
 lib/NonlinearSolveQuasiNewton/src/solve.jl    |  16 --
 .../src/solve.jl                              |  12 --
 src/NonlinearSolve.jl                         |   8 +-
 src/abstract_types.jl                         | 152 ------------------
 9 files changed, 98 insertions(+), 233 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index 2ae4091e7..bc94dce99 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -10,14 +10,7 @@ end
 abstract type AbstractNonlinearSolveBaseAPI end # Mostly used for pretty-printing
 
 function Base.show(io::IO, ::MIME"text/plain", alg::AbstractNonlinearSolveBaseAPI)
-    main_name = nameof(typeof(alg))
-    modifiers = String[]
-    for field in fieldnames(typeof(alg))
-        val = getfield(alg, field)
-        Utils.is_default_value(val, field, getfield(alg, field)) && continue
-        push!(modifiers, "$(field) = $(val)")
-    end
-    print(io, "$(main_name)($(join(modifiers, ", ")))")
+    print(io, Utils.clean_sprint_struct(alg))
     return
 end
 
@@ -198,12 +191,9 @@ Abstract Type for all NonlinearSolveBase Algorithms.
 
   - `concrete_jac(alg)`: whether or not the algorithm uses a concrete Jacobian. Defaults
     to `nothing`.
-  - `get_name(alg)`: get the name of the algorithm.
 """
 abstract type AbstractNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm end
 
-get_name(alg::AbstractNonlinearSolveAlgorithm) = Utils.safe_getproperty(alg, Val(:name))
-
 """
     concrete_jac(alg::AbstractNonlinearSolveAlgorithm)::Bool
 
@@ -218,6 +208,18 @@ concrete_jac(v::Bool) = v
 concrete_jac(::Val{false}) = false
 concrete_jac(::Val{true}) = true
 
+function Base.show(io::IO, ::MIME"text/plain", alg::AbstractNonlinearSolveAlgorithm)
+    print(io, Utils.clean_sprint_struct(alg, 0))
+    return
+end
+
+function show_nonlinearsolve_algorithm(
+        io::IO, alg::AbstractNonlinearSolveAlgorithm, name, indent::Int = 0
+)
+    print(io, name)
+    print(io, Utils.clean_sprint_struct(alg, indent))
+end
+
 """
     AbstractNonlinearSolveCache
 
@@ -299,30 +301,34 @@ function Base.setindex!(cache::AbstractNonlinearSolveCache, val, sym)
     return SII.setu(cache, sym)(cache, val)
 end
 
-# XXX: Implement this
-# function Base.show(io::IO, cache::AbstractNonlinearSolveCache)
-#     __show_cache(io, cache, 0)
-# end
-
-# function __show_cache(io::IO, cache::AbstractNonlinearSolveCache, indent = 0)
-#     println(io, "$(nameof(typeof(cache)))(")
-#     __show_algorithm(io, cache.alg,
-#         (" "^(indent + 4)) * "alg = " * string(get_name(cache.alg)), indent + 4)
-
-#     ustr = sprint(show, get_u(cache); context = (:compact => true, :limit => true))
-#     println(io, ",\n" * (" "^(indent + 4)) * "u = $(ustr),")
-
-#     residstr = sprint(show, get_fu(cache); context = (:compact => true, :limit => true))
-#     println(io, (" "^(indent + 4)) * "residual = $(residstr),")
-
-#     normstr = sprint(
-#         show, norm(get_fu(cache), Inf); context = (:compact => true, :limit => true))
-#     println(io, (" "^(indent + 4)) * "inf-norm(residual) = $(normstr),")
+function Base.show(io::IO, ::MIME"text/plain", cache::AbstractNonlinearSolveCache)
+    return show_nonlinearsolve_cache(io, cache)
+end
 
-#     println(io, " "^(indent + 4) * "nsteps = ", cache.stats.nsteps, ",")
-#     println(io, " "^(indent + 4) * "retcode = ", cache.retcode)
-#     print(io, " "^(indent) * ")")
-# end
+function show_nonlinearsolve_cache(io::IO, cache::AbstractNonlinearSolveCache, indent = 0)
+    println(io, "$(nameof(typeof(cache)))(")
+    show_nonlinearsolve_algorithm(
+        io,
+        cache.alg,
+        (" "^(indent + 4)) * "alg = ",
+        indent + 4
+    )
+
+    ustr = sprint(show, get_u(cache); context = (:compact => true, :limit => true))
+    println(io, ",\n" * (" "^(indent + 4)) * "u = $(ustr),")
+
+    residstr = sprint(show, get_fu(cache); context = (:compact => true, :limit => true))
+    println(io, (" "^(indent + 4)) * "residual = $(residstr),")
+
+    normstr = sprint(
+        show, norm(get_fu(cache), Inf); context = (:compact => true, :limit => true)
+    )
+    println(io, (" "^(indent + 4)) * "inf-norm(residual) = $(normstr),")
+
+    println(io, " "^(indent + 4) * "nsteps = ", cache.stats.nsteps, ",")
+    println(io, " "^(indent + 4) * "retcode = ", cache.retcode)
+    print(io, " "^(indent) * ")")
+end
 
 """
     AbstractLinearSolverCache
diff --git a/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
index 274fa0600..c465cc5cb 100644
--- a/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
+++ b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
@@ -49,13 +49,12 @@ get_linear_solver(alg::GeodesicAcceleration) = get_linear_solver(alg.descent)
     last_step_accepted::Bool
 end
 
-# XXX: Implement
-# function __reinit_internal!(
-#         cache::GeodesicAccelerationCache, args...; p = cache.p, kwargs...)
-#     cache.p = p
-#     cache.last_step_accepted = false
-# end
+function InternalAPI.reinit!(cache::GeodesicAccelerationCache; p = cache.p, kwargs...)
+    cache.p = p
+    cache.last_step_accepted = false
+end
 
+# XXX: Implement
 # @internal_caches GeodesicAccelerationCache :descent_cache
 
 function get_velocity(cache::GeodesicAccelerationCache)
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index af5bd63c6..a727bed6d 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -115,6 +115,7 @@ unwrap_val(::Val{x}) where {x} = unwrap_val(x)
 
 is_default_value(::Any, ::Symbol, ::Nothing) = true
 is_default_value(::Any, ::Symbol, ::Missing) = true
+is_default_value(::Any, ::Symbol, val::Int) = val == typemax(typeof(val))
 is_default_value(::Any, ::Symbol, ::Any) = false
 
 maybe_symmetric(x) = Symmetric(x)
@@ -178,7 +179,6 @@ function condition_number(J::AbstractVector)
 end
 condition_number(::Any) = -1
 
-# XXX: Move to NonlinearSolveQuasiNewton
 # compute `pinv` if `inv` won't work
 maybe_pinv!!_workspace(A) = nothing, A
 
@@ -239,4 +239,47 @@ function make_identity!!(A::AbstractMatrix{T}, α) where {T}
     return A
 end
 
+function clean_sprint_struct(x)
+    x isa Symbol && return "$(Meta.quot(x))"
+    x isa Number && return string(x)
+    (!Base.isstructtype(typeof(x)) || x isa Val) && return string(x)
+
+    modifiers = String[]
+    name = nameof(typeof(x))
+    for field in fieldnames(typeof(x))
+        val = getfield(x, field)
+        if field === :name
+            name = val
+            continue
+        end
+        is_default_value(x, field, val) && continue
+        push!(modifiers, "$(field) = $(clean_sprint_struct(val))")
+    end
+
+    return "$(nameof(typeof(x)))($(join(modifiers, ", ")))"
+end
+
+function clean_sprint_struct(x, indent::Int)
+    x isa Symbol && return "$(Meta.quot(x))"
+    x isa Number && return string(x)
+    (!Base.isstructtype(typeof(x)) || x isa Val) && return string(x)
+
+    modifiers = String[]
+    name = nameof(typeof(x))
+    for field in fieldnames(typeof(x))
+        val = getfield(x, field)
+        if field === :name
+            name = val
+            continue
+        end
+        is_default_value(x, field, val) && continue
+        push!(modifiers, "$(field) = $(clean_sprint_struct(val, indent + 4))")
+    end
+    spacing = " "^indent * "    "
+    spacing_last = " "^indent
+
+    length(modifiers) == 0 && return "$(nameof(typeof(x)))()"
+    return "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))"
+end
+
 end
diff --git a/lib/NonlinearSolveQuasiNewton/src/initialization.jl b/lib/NonlinearSolveQuasiNewton/src/initialization.jl
index 9d39f4473..cd5fbaa2e 100644
--- a/lib/NonlinearSolveQuasiNewton/src/initialization.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/initialization.jl
@@ -151,12 +151,13 @@ NonlinearSolveBase.jacobian_initialized_preinverted(::BroydenLowRankInitializati
 
 function InternalAPI.init(
         prob::AbstractNonlinearProblem, alg::BroydenLowRankInitialization,
-        solver, f::F, fu, u, p; internalnorm::IN = L2_NORM, kwargs...
+        solver, f::F, fu, u, p;
+        internalnorm::IN = L2_NORM, maxiters = 1000, kwargs...
 ) where {F, IN}
     if u isa Number # Use the standard broyden
         return InternalAPI.init(
             prob, IdentityInitialization(true, FullStructure()),
-            solver, f, fu, u, p; internalnorm, kwargs...
+            solver, f, fu, u, p; internalnorm, maxiters, kwargs...
         )
     end
     # Pay to cost of slightly more allocations to prevent type-instability for StaticArrays
@@ -212,7 +213,7 @@ Base.adjoint(op::BroydenLowRankJacobian{<:Real}) = transpose(op)
 
 # Storing the transpose to ensure contiguous memory on splicing
 function BroydenLowRankJacobian(
-    fu::StaticArray, u::StaticArray; alpha = true, threshold::Val = Val(10)
+        fu::StaticArray, u::StaticArray; alpha = true, threshold::Val = Val(10)
 )
     T = promote_type(eltype(u), eltype(fu))
     U = MArray{Tuple{prod(Size(fu)), Utils.unwrap_val(threshold)}, T}(undef)
@@ -265,8 +266,8 @@ function LinearAlgebra.mul!(y::AbstractVector, x::AbstractVector, J::BroydenLowR
 end
 
 function LinearAlgebra.mul!(
-    J::BroydenLowRankJacobian, u::AbstractArray, vᵀ::LinearAlgebra.AdjOrTransAbsVec,
-    α::Bool, β::Bool
+        J::BroydenLowRankJacobian, u::AbstractArray, vᵀ::LinearAlgebra.AdjOrTransAbsVec,
+        α::Bool, β::Bool
 )
     @assert α & β
     idx_update = mod1(J.idx + 1, size(J.U, 2))
diff --git a/lib/NonlinearSolveQuasiNewton/src/reset_conditions.jl b/lib/NonlinearSolveQuasiNewton/src/reset_conditions.jl
index 8541259ef..b8d92237c 100644
--- a/lib/NonlinearSolveQuasiNewton/src/reset_conditions.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/reset_conditions.jl
@@ -103,7 +103,7 @@ function InternalAPI.init(
 end
 
 @concrete struct IllConditionedJacobianResetCache <: AbstractResetConditionCache
-    condition_number_threshold <: Number
+    condition_number_threshold
 end
 
 # NOTE: we don't need a reinit! since we establish the threshold based on the eltype
diff --git a/lib/NonlinearSolveQuasiNewton/src/solve.jl b/lib/NonlinearSolveQuasiNewton/src/solve.jl
index 64b171840..a37f098df 100644
--- a/lib/NonlinearSolveQuasiNewton/src/solve.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/solve.jl
@@ -37,22 +37,6 @@ examples include [`Broyden`](@ref)'s Method.
     name::Symbol
 end
 
-# XXX: Implement
-# function __show_algorithm(io::IO, alg::QuasiNewtonAlgorithm, name, indent)
-#     modifiers = String[]
-#     __is_present(alg.linesearch) && push!(modifiers, "linesearch = $(alg.linesearch)")
-#     __is_present(alg.trustregion) && push!(modifiers, "trustregion = $(alg.trustregion)")
-#     push!(modifiers, "descent = $(alg.descent)")
-#     push!(modifiers, "update_rule = $(alg.update_rule)")
-#     push!(modifiers, "reinit_rule = $(alg.reinit_rule)")
-#     push!(modifiers, "max_resets = $(alg.max_resets)")
-#     push!(modifiers, "initialization = $(alg.initialization)")
-#     store_inverse_jacobian(alg.update_rule) && push!(modifiers, "inverse_jacobian = true")
-#     spacing = " "^indent * "    "
-#     spacing_last = " "^indent
-#     print(io, "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))")
-# end
-
 function QuasiNewtonAlgorithm(;
         linesearch = missing, trustregion = missing, descent, update_rule, reinit_rule,
         initialization, max_resets::Int = typemax(Int), name::Symbol = :unknown,
diff --git a/lib/NonlinearSolveSpectralMethods/src/solve.jl b/lib/NonlinearSolveSpectralMethods/src/solve.jl
index b4b8d3461..9c68c81b4 100644
--- a/lib/NonlinearSolveSpectralMethods/src/solve.jl
+++ b/lib/NonlinearSolveSpectralMethods/src/solve.jl
@@ -32,18 +32,6 @@ function GeneralizedDFSane(;
     return GeneralizedDFSane(linesearch, sigma_min, sigma_max, sigma_1, name)
 end
 
-# XXX: Add
-# function __show_algorithm(io::IO, alg::GeneralizedDFSane, name, indent)
-#     modifiers = String[]
-#     __is_present(alg.linesearch) && push!(modifiers, "linesearch = $(alg.linesearch)")
-#     push!(modifiers, "σ_min = $(alg.σ_min)")
-#     push!(modifiers, "σ_max = $(alg.σ_max)")
-#     push!(modifiers, "σ_1 = $(alg.σ_1)")
-#     spacing = " "^indent * "    "
-#     spacing_last = " "^indent
-#     print(io, "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))")
-# end
-
 @concrete mutable struct GeneralizedDFSaneCache <: AbstractNonlinearSolveCache
     # Basic Requirements
     fu
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 563b5cb8b..477f12815 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -32,6 +32,8 @@ using NonlinearSolveBase: NonlinearSolveBase,
                           reset_timer!, @static_timeit,
                           init_nonlinearsolve_trace, update_trace!, reset!
 
+using NonlinearSolveQuasiNewton: Broyden, Klement
+
 # XXX: Remove
 import NonlinearSolveBase: InternalAPI, concrete_jac, supports_line_search,
                            supports_trust_region, last_step_accepted, get_linear_solver,
@@ -149,12 +151,6 @@ include("internal/forward_diff.jl") # we need to define after the algorithms
 
     @compile_workload begin
         @sync begin
-            for T in (Float32, Float64), (fn, u0) in nlfuncs
-                Threads.@spawn NonlinearProblem(fn, T.(u0), T(2))
-            end
-            for (fn, u0) in nlfuncs
-                Threads.@spawn NonlinearLeastSquaresProblem(fn, u0, 2.0)
-            end
             for prob in probs_nls, alg in nls_algs
                 Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
             end
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
index a94b2b50e..65bda73c3 100644
--- a/src/abstract_types.jl
+++ b/src/abstract_types.jl
@@ -110,142 +110,6 @@ function SciMLBase.reinit!(cache::AbstractNonlinearSolveCache, u0; kwargs...)
     return reinit_cache!(cache; u0, kwargs...)
 end
 
-# XXX: Move to NonlinearSolveQuasiNewton
-# Approximate Jacobian Algorithms
-"""
-    AbstractApproximateJacobianStructure
-
-Abstract Type for all Approximate Jacobian Structures used in NonlinearSolve.jl.
-
-### Interface Functions
-
-  - `stores_full_jacobian(alg)`: whether or not the algorithm stores the full Jacobian.
-    Defaults to `false`.
-  - `get_full_jacobian(cache, alg, J)`: get the full Jacobian. Defaults to throwing an
-    error if `stores_full_jacobian(alg)` is `false`.
-"""
-abstract type AbstractApproximateJacobianStructure end
-
-stores_full_jacobian(::AbstractApproximateJacobianStructure) = false
-function get_full_jacobian(cache, alg::AbstractApproximateJacobianStructure, J)
-    stores_full_jacobian(alg) && return J
-    error("This algorithm does not store the full Jacobian. Define `get_full_jacobian` for \
-           this algorithm.")
-end
-
-"""
-    AbstractJacobianInitialization
-
-Abstract Type for all Jacobian Initialization Algorithms used in NonlinearSolve.jl.
-
-### Interface Functions
-
-  - `jacobian_initialized_preinverted(alg)`: whether or not the Jacobian is initialized
-    preinverted. Defaults to `false`.
-
-### `__internal_init` specification
-
-```julia
-__internal_init(
-    prob::AbstractNonlinearProblem, alg::AbstractJacobianInitialization, solver,
-    f::F, fu, u, p; linsolve = missing, internalnorm::IN = L2_NORM, kwargs...)
-```
-
-Returns a [`NonlinearSolve.InitializedApproximateJacobianCache`](@ref).
-
-All subtypes need to define
-`(cache::InitializedApproximateJacobianCache)(alg::NewSubType, fu, u)` which reinitializes
-the Jacobian in `cache.J`.
-"""
-abstract type AbstractJacobianInitialization end
-
-function Base.show(io::IO, alg::AbstractJacobianInitialization)
-    modifiers = String[]
-    hasfield(typeof(alg), :structure) &&
-        push!(modifiers, "structure = $(nameof(typeof(alg.structure)))()")
-    print(io, "$(nameof(typeof(alg)))($(join(modifiers, ", ")))")
-    return nothing
-end
-
-jacobian_initialized_preinverted(::AbstractJacobianInitialization) = false
-
-"""
-    AbstractApproximateJacobianUpdateRule{INV}
-
-Abstract Type for all Approximate Jacobian Update Rules used in NonlinearSolve.jl.
-
-### Interface Functions
-
-  - `store_inverse_jacobian(alg)`: Return `INV`
-
-### `__internal_init` specification
-
-```julia
-__internal_init(
-    prob::AbstractNonlinearProblem, alg::AbstractApproximateJacobianUpdateRule, J, fu, u,
-    du, args...; internalnorm::F = L2_NORM, kwargs...) where {F} -->
-AbstractApproximateJacobianUpdateRuleCache{INV}
-```
-"""
-abstract type AbstractApproximateJacobianUpdateRule{INV} end
-
-store_inverse_jacobian(::AbstractApproximateJacobianUpdateRule{INV}) where {INV} = INV
-
-"""
-    AbstractApproximateJacobianUpdateRuleCache{INV}
-
-Abstract Type for all Approximate Jacobian Update Rule Caches used in NonlinearSolve.jl.
-
-### Interface Functions
-
-  - `store_inverse_jacobian(alg)`: Return `INV`
-
-### `__internal_solve!` specification
-
-```julia
-__internal_solve!(
-    cache::AbstractApproximateJacobianUpdateRuleCache, J, fu, u, du; kwargs...) --> J / J⁻¹
-```
-"""
-abstract type AbstractApproximateJacobianUpdateRuleCache{INV} end
-
-store_inverse_jacobian(::AbstractApproximateJacobianUpdateRuleCache{INV}) where {INV} = INV
-
-"""
-    AbstractResetCondition
-
-Condition for resetting the Jacobian in Quasi-Newton's methods.
-
-### `__internal_init` specification
-
-```julia
-__internal_init(alg::AbstractResetCondition, J, fu, u, du, args...; kwargs...) -->
-ResetCache
-```
-
-### `__internal_solve!` specification
-
-```julia
-__internal_solve!(cache::ResetCache, J, fu, u, du) --> Bool
-```
-"""
-abstract type AbstractResetCondition end
-
-"""
-    AbstractTrustRegionMethod
-
-Abstract Type for all Trust Region Methods used in NonlinearSolve.jl.
-
-### `__internal_init` specification
-
-```julia
-__internal_init(
-    prob::AbstractNonlinearProblem, alg::AbstractTrustRegionMethod, f::F, fu, u, p, args...;
-    internalnorm::IF = L2_NORM, kwargs...) where {F, IF} --> AbstractTrustRegionMethodCache
-```
-"""
-abstract type AbstractTrustRegionMethod end
-
 """
     AbstractTrustRegionMethodCache
 
@@ -268,19 +132,3 @@ accepted then these values should be copied into the toplevel cache.
 abstract type AbstractTrustRegionMethodCache end
 
 last_step_accepted(cache::AbstractTrustRegionMethodCache) = cache.last_step_accepted
-
-"""
-    AbstractNonlinearSolveTraceLevel
-
-### Common Arguments
-
-  - `freq`: Sets both `print_frequency` and `store_frequency` to `freq`.
-
-### Common Keyword Arguments
-
-  - `print_frequency`: Print the trace every `print_frequency` iterations if
-    `show_trace == Val(true)`.
-  - `store_frequency`: Store the trace every `store_frequency` iterations if
-    `store_trace == Val(true)`.
-"""
-abstract type AbstractNonlinearSolveTraceLevel end

From 5ed4fe47c94fba28ad6ad8660d3478fe60e41967 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 28 Oct 2024 00:42:07 -0400
Subject: [PATCH 641/700] refactor: implement internal caches function

---
 lib/NonlinearSolveBase/Project.toml           |   3 +
 .../ext/NonlinearSolveBaseLineSearchExt.jl    |  17 +++
 lib/NonlinearSolveBase/src/abstract_types.jl  |  73 +++++++++-
 .../src/descent/damped_newton.jl              |   3 +-
 lib/NonlinearSolveBase/src/descent/dogleg.jl  |   3 +-
 .../src/descent/geodesic_acceleration.jl      |   5 +-
 lib/NonlinearSolveBase/src/descent/newton.jl  |   3 +-
 .../src/descent/steepest.jl                   |   3 +-
 lib/NonlinearSolveBase/src/solve.jl           |   3 +-
 .../src/termination_conditions.jl             |  71 ++++++++--
 lib/NonlinearSolveBase/src/tracing.jl         |  15 +-
 .../src/initialization.jl                     |   5 +-
 lib/NonlinearSolveQuasiNewton/src/solve.jl    |  14 +-
 .../src/solve.jl                              |   9 +-
 src/NonlinearSolve.jl                         |   3 -
 src/abstract_types.jl                         | 134 ------------------
 src/globalization/line_search.jl              |   7 -
 src/internal/helpers.jl                       |  81 -----------
 src/internal/termination.jl                   |  34 -----
 src/utils.jl                                  |  15 --
 20 files changed, 183 insertions(+), 318 deletions(-)
 create mode 100644 lib/NonlinearSolveBase/ext/NonlinearSolveBaseLineSearchExt.jl
 delete mode 100644 src/abstract_types.jl
 delete mode 100644 src/globalization/line_search.jl
 delete mode 100644 src/internal/termination.jl

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 46f9df83a..3c7d16a1c 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -31,6 +31,7 @@ TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseMatrixColorings = "0a514795-09f3-496d-8182-132a7b665d35"
@@ -39,6 +40,7 @@ SparseMatrixColorings = "0a514795-09f3-496d-8182-132a7b665d35"
 NonlinearSolveBaseBandedMatricesExt = "BandedMatrices"
 NonlinearSolveBaseDiffEqBaseExt = "DiffEqBase"
 NonlinearSolveBaseForwardDiffExt = "ForwardDiff"
+NonlinearSolveBaseLineSearchExt = "LineSearch"
 NonlinearSolveBaseLinearSolveExt = "LinearSolve"
 NonlinearSolveBaseSparseArraysExt = "SparseArrays"
 NonlinearSolveBaseSparseMatrixColoringsExt = "SparseMatrixColorings"
@@ -60,6 +62,7 @@ FastClosures = "0.3"
 ForwardDiff = "0.10.36"
 FunctionProperties = "0.1.2"
 InteractiveUtils = "<0.0.1, 1"
+LineSearch = "0.1.4"
 LinearAlgebra = "1.10"
 LinearSolve = "2.36.1"
 Markdown = "1.10"
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLineSearchExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLineSearchExt.jl
new file mode 100644
index 000000000..d68007dc0
--- /dev/null
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLineSearchExt.jl
@@ -0,0 +1,17 @@
+module NonlinearSolveBaseLineSearchExt
+
+using LineSearch: LineSearch, AbstractLineSearchCache
+using NonlinearSolveBase: NonlinearSolveBase, InternalAPI
+using SciMLBase: SciMLBase
+
+function NonlinearSolveBase.callback_into_cache!(
+        topcache, cache::AbstractLineSearchCache, args...
+)
+    return LineSearch.callback_into_cache!(cache, NonlinearSolveBase.get_fu(topcache))
+end
+
+function InternalAPI.reinit!(cache::AbstractLineSearchCache; kwargs...)
+    return SciMLBase.reinit!(cache; kwargs...)
+end
+
+end
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index bc94dce99..a01aa7afb 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -1,10 +1,31 @@
 module InternalAPI
 
+using SciMLBase: NLStats
+
 function init end
 function solve! end
-function reinit! end
 function step! end
 
+function reinit! end
+function reinit_self! end
+
+function reinit!(x::Any; kwargs...)
+    @debug "`InternalAPI.reinit!` is not implemented for $(typeof(x))."
+    return
+end
+function reinit_self!(x::Any; kwargs...)
+    @debug "`InternalAPI.reinit_self!` is not implemented for $(typeof(x))."
+    return
+end
+
+function reinit_self!(stats::NLStats)
+    stats.nf = 0
+    stats.nsteps = 0
+    stats.nfactors = 0
+    stats.njacs = 0
+    stats.nsolve = 0
+end
+
 end
 
 abstract type AbstractNonlinearSolveBaseAPI end # Mostly used for pretty-printing
@@ -512,3 +533,53 @@ accepted then these values should be copied into the toplevel cache.
 abstract type AbstractTrustRegionMethodCache <: AbstractNonlinearSolveBaseAPI end
 
 last_step_accepted(cache::AbstractTrustRegionMethodCache) = cache.last_step_accepted
+
+# Additional Interface
+"""
+    callback_into_cache!(cache, internalcache, args...)
+
+Define custom operations on `internalcache` tightly coupled with the calling `cache`.
+`args...` contain the sequence of caches calling into `internalcache`.
+
+This unfortunately makes code very tightly coupled and not modular. It is recommended to not
+use this functionality unless it can't be avoided (like in [`LevenbergMarquardt`](@ref)).
+"""
+callback_into_cache!(cache, internalcache, args...) = nothing  # By default do nothing
+
+# Helper functions to generate cache callbacks and resetting functions
+macro internal_caches(cType, internal_cache_names...)
+    callback_caches = map(internal_cache_names) do name
+        return quote
+            $(callback_into_cache!)(
+                cache, getproperty(internalcache, $(name)), internalcache, args...
+            )
+        end
+    end
+    callbacks_self = map(internal_cache_names) do name
+        return quote
+            $(callback_into_cache!)(cache, getproperty(cache, $(name)))
+        end
+    end
+    reinit_caches = map(internal_cache_names) do name
+        return quote
+            $(InternalAPI.reinit!)(getproperty(cache, $(name)), args...; kwargs...)
+        end
+    end
+    return esc(quote
+        function NonlinearSolveBase.callback_into_cache!(
+                cache, internalcache::$(cType), args...
+        )
+            $(callback_caches...)
+            return
+        end
+        function NonlinearSolveBase.callback_into_cache!(cache::$(cType))
+            $(callbacks_self...)
+            return
+        end
+        function NonlinearSolveBase.InternalAPI.reinit!(cache::$(cType), args...; kwargs...)
+            $(reinit_caches...)
+            $(InternalAPI.reinit_self!)(cache, args...; kwargs...)
+            return
+        end
+    end)
+end
diff --git a/lib/NonlinearSolveBase/src/descent/damped_newton.jl b/lib/NonlinearSolveBase/src/descent/damped_newton.jl
index 3ab507065..a9921ba47 100644
--- a/lib/NonlinearSolveBase/src/descent/damped_newton.jl
+++ b/lib/NonlinearSolveBase/src/descent/damped_newton.jl
@@ -42,8 +42,7 @@ supports_trust_region(::DampedNewtonDescent) = true
     mode <: Union{Val{:normal_form}, Val{:least_squares}, Val{:simple}}
 end
 
-# XXX: Implement
-# @internal_caches DampedNewtonDescentCache :lincache :damping_fn_cache
+NonlinearSolveBase.@internal_caches DampedNewtonDescentCache :lincache :damping_fn_cache
 
 function InternalAPI.init(
         prob::AbstractNonlinearProblem, alg::DampedNewtonDescent, J, fu, u; stats,
diff --git a/lib/NonlinearSolveBase/src/descent/dogleg.jl b/lib/NonlinearSolveBase/src/descent/dogleg.jl
index c138adbde..133b5fabb 100644
--- a/lib/NonlinearSolveBase/src/descent/dogleg.jl
+++ b/lib/NonlinearSolveBase/src/descent/dogleg.jl
@@ -44,8 +44,7 @@ end
     normal_form <: Union{Val{false}, Val{true}}
 end
 
-# XXX: Implement
-# @internal_caches DoglegCache :newton_cache :cauchy_cache
+NonlinearSolveBase.@internal_caches DoglegCache :newton_cache :cauchy_cache
 
 function InternalAPI.init(
         prob::AbstractNonlinearProblem, alg::Dogleg, J, fu, u;
diff --git a/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
index c465cc5cb..f5b686433 100644
--- a/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
+++ b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
@@ -49,13 +49,12 @@ get_linear_solver(alg::GeodesicAcceleration) = get_linear_solver(alg.descent)
     last_step_accepted::Bool
 end
 
-function InternalAPI.reinit!(cache::GeodesicAccelerationCache; p = cache.p, kwargs...)
+function InternalAPI.reinit_self!(cache::GeodesicAccelerationCache; p = cache.p, kwargs...)
     cache.p = p
     cache.last_step_accepted = false
 end
 
-# XXX: Implement
-# @internal_caches GeodesicAccelerationCache :descent_cache
+NonlinearSolveBase.@internal_caches GeodesicAccelerationCache :descent_cache
 
 function get_velocity(cache::GeodesicAccelerationCache)
     return SciMLBase.get_du(cache.descent_cache, Val(1))
diff --git a/lib/NonlinearSolveBase/src/descent/newton.jl b/lib/NonlinearSolveBase/src/descent/newton.jl
index 1a7acf177..e453597a1 100644
--- a/lib/NonlinearSolveBase/src/descent/newton.jl
+++ b/lib/NonlinearSolveBase/src/descent/newton.jl
@@ -24,8 +24,7 @@ supports_line_search(::NewtonDescent) = true
     normal_form <: Union{Val{false}, Val{true}}
 end
 
-# XXX: Implement
-# @internal_caches NewtonDescentCache :lincache
+NonlinearSolveBase.@internal_caches NewtonDescentCache :lincache
 
 function InternalAPI.init(
         prob::AbstractNonlinearProblem, alg::NewtonDescent, J, fu, u; stats,
diff --git a/lib/NonlinearSolveBase/src/descent/steepest.jl b/lib/NonlinearSolveBase/src/descent/steepest.jl
index b29045bd5..b93c727c5 100644
--- a/lib/NonlinearSolveBase/src/descent/steepest.jl
+++ b/lib/NonlinearSolveBase/src/descent/steepest.jl
@@ -21,8 +21,7 @@ supports_line_search(::SteepestDescent) = true
     preinverted_jacobian <: Union{Val{false}, Val{true}}
 end
 
-# XXX: Implement
-# @internal_caches SteepestDescentCache :lincache
+NonlinearSolveBase.@internal_caches SteepestDescentCache :lincache
 
 function InternalAPI.init(
         prob::AbstractNonlinearProblem, alg::SteepestDescent, J, fu, u;
diff --git a/lib/NonlinearSolveBase/src/solve.jl b/lib/NonlinearSolveBase/src/solve.jl
index 999f064e9..7316fd168 100644
--- a/lib/NonlinearSolveBase/src/solve.jl
+++ b/lib/NonlinearSolveBase/src/solve.jl
@@ -18,8 +18,7 @@ function CommonSolve.solve!(cache::AbstractNonlinearSolveCache)
         )
     end
 
-    # XXX: Implement this
-    # update_from_termination_cache!(cache.termination_cache, cache)
+    update_from_termination_cache!(cache.termination_cache, cache)
 
     update_trace!(
         cache.trace, cache.nsteps, get_u(cache), get_fu(cache), nothing, nothing, nothing;
diff --git a/lib/NonlinearSolveBase/src/termination_conditions.jl b/lib/NonlinearSolveBase/src/termination_conditions.jl
index c2d768c17..cca9134d1 100644
--- a/lib/NonlinearSolveBase/src/termination_conditions.jl
+++ b/lib/NonlinearSolveBase/src/termination_conditions.jl
@@ -1,7 +1,9 @@
 const RelNormModes = Union{
-    RelNormTerminationMode, RelNormSafeTerminationMode, RelNormSafeBestTerminationMode}
+    RelNormTerminationMode, RelNormSafeTerminationMode, RelNormSafeBestTerminationMode
+}
 const AbsNormModes = Union{
-    AbsNormTerminationMode, AbsNormSafeTerminationMode, AbsNormSafeBestTerminationMode}
+    AbsNormTerminationMode, AbsNormSafeTerminationMode, AbsNormSafeBestTerminationMode
+}
 
 # Core Implementation
 @concrete mutable struct NonlinearTerminationModeCache{uType, T}
@@ -32,7 +34,8 @@ end
 
 function CommonSolve.init(
         ::AbstractNonlinearProblem, mode::AbstractNonlinearTerminationMode, du, u,
-        saved_value_prototype...; abstol = nothing, reltol = nothing, kwargs...)
+        saved_value_prototype...; abstol = nothing, reltol = nothing, kwargs...
+)
     T = promote_type(eltype(du), eltype(u))
     abstol = get_tolerance(u, abstol, T)
     reltol = get_tolerance(u, reltol, T)
@@ -77,12 +80,14 @@ function CommonSolve.init(
     return NonlinearTerminationModeCache(
         u_unaliased, ReturnCode.Default, abstol, reltol, best_value, mode,
         initial_objective, objectives_trace, 0, saved_value_prototype,
-        u0_norm, step_norm_trace, max_stalled_steps, u_diff_cache)
+        u0_norm, step_norm_trace, max_stalled_steps, u_diff_cache
+    )
 end
 
 function SciMLBase.reinit!(
         cache::NonlinearTerminationModeCache, du, u, saved_value_prototype...;
-        abstol = cache.abstol, reltol = cache.reltol, kwargs...)
+        abstol = cache.abstol, reltol = cache.reltol, kwargs...
+)
     T = eltype(cache.abstol)
     length(saved_value_prototype) != 0 && (cache.saved_values = saved_value_prototype)
 
@@ -113,7 +118,8 @@ end
 
 ## This dispatch is needed based on how Terminating Callback works!
 function (cache::NonlinearTerminationModeCache)(
-        integrator::AbstractODEIntegrator, abstol::Number, reltol::Number, min_t)
+        integrator::AbstractODEIntegrator, abstol::Number, reltol::Number, min_t
+)
     if min_t === nothing || integrator.t ≥ min_t
         return cache(cache.mode, SciMLBase.get_du(integrator),
             integrator.u, integrator.uprev, abstol, reltol)
@@ -125,7 +131,8 @@ function (cache::NonlinearTerminationModeCache)(du, u, uprev, args...)
 end
 
 function (cache::NonlinearTerminationModeCache)(
-        mode::AbstractNonlinearTerminationMode, du, u, uprev, abstol, reltol, args...)
+        mode::AbstractNonlinearTerminationMode, du, u, uprev, abstol, reltol, args...
+)
     if check_convergence(mode, du, u, uprev, abstol, reltol)
         cache.retcode = ReturnCode.Success
         return true
@@ -134,7 +141,8 @@ function (cache::NonlinearTerminationModeCache)(
 end
 
 function (cache::NonlinearTerminationModeCache)(
-        mode::AbstractSafeNonlinearTerminationMode, du, u, uprev, abstol, reltol, args...)
+        mode::AbstractSafeNonlinearTerminationMode, du, u, uprev, abstol, reltol, args...
+)
     if mode isa AbsNormSafeTerminationMode || mode isa AbsNormSafeBestTerminationMode
         objective = Utils.apply_norm(mode.internalnorm, du)
         criteria = abstol
@@ -251,7 +259,8 @@ end
 # High-Level API with defaults.
 ## This is mostly for internal usage in NonlinearSolve and SimpleNonlinearSolve
 function default_termination_mode(
-        ::Union{ImmutableNonlinearProblem, NonlinearProblem}, ::Val{:simple})
+        ::Union{ImmutableNonlinearProblem, NonlinearProblem}, ::Val{:simple}
+)
     return AbsNormTerminationMode(Base.Fix1(maximum, abs))
 end
 function default_termination_mode(::NonlinearLeastSquaresProblem, ::Val{:simple})
@@ -259,7 +268,8 @@ function default_termination_mode(::NonlinearLeastSquaresProblem, ::Val{:simple}
 end
 
 function default_termination_mode(
-        ::Union{ImmutableNonlinearProblem, NonlinearProblem}, ::Val{:regular})
+        ::Union{ImmutableNonlinearProblem, NonlinearProblem}, ::Val{:regular}
+)
     return AbsNormSafeBestTerminationMode(Base.Fix1(maximum, abs); max_stalled_steps = 32)
 end
 
@@ -268,16 +278,53 @@ function default_termination_mode(::NonlinearLeastSquaresProblem, ::Val{:regular
 end
 
 function init_termination_cache(
-        prob::AbstractNonlinearProblem, abstol, reltol, du, u, ::Nothing, callee::Val)
+        prob::AbstractNonlinearProblem, abstol, reltol, du, u, ::Nothing, callee::Val
+)
     return init_termination_cache(
         prob, abstol, reltol, du, u, default_termination_mode(prob, callee), callee)
 end
 
 function init_termination_cache(prob::AbstractNonlinearProblem, abstol, reltol, du,
-        u, tc::AbstractNonlinearTerminationMode, ::Val)
+        u, tc::AbstractNonlinearTerminationMode, ::Val
+)
     T = promote_type(eltype(du), eltype(u))
     abstol = get_tolerance(u, abstol, T)
     reltol = get_tolerance(u, reltol, T)
     cache = init(prob, tc, du, u; abstol, reltol)
     return abstol, reltol, cache
 end
+
+function check_and_update!(cache, fu, u, uprev)
+    return check_and_update!(
+        cache.termination_cache, cache, fu, u, uprev, cache.termination_cache.mode
+    )
+end
+
+function check_and_update!(tc_cache, cache, fu, u, uprev, mode)
+    if tc_cache(fu, u, uprev)
+        cache.retcode = tc_cache.retcode
+        update_from_termination_cache!(tc_cache, cache, mode, u)
+        cache.force_stop = true
+    end
+end
+
+function update_from_termination_cache!(tc_cache, cache, u = get_u(cache))
+    return update_from_termination_cache!(tc_cache, cache, tc_cache.mode, u)
+end
+
+function update_from_termination_cache!(
+        tc_cache, cache, ::AbstractNonlinearTerminationMode, u = get_u(cache)
+)
+    Utils.evaluate_f!(cache, u, cache.p)
+end
+
+function update_from_termination_cache!(
+        tc_cache, cache, ::AbstractSafeBestNonlinearTerminationMode, u = get_u(cache)
+)
+    if SciMLBase.isinplace(cache)
+        copyto!(get_u(cache), tc_cache.u)
+    else
+        SciMLBase.set_u!(cache, tc_cache.u)
+    end
+    Utils.evaluate_f!(cache, get_u(cache), cache.p)
+end
diff --git a/lib/NonlinearSolveBase/src/tracing.jl b/lib/NonlinearSolveBase/src/tracing.jl
index 2dd88ecee..e818e05e8 100644
--- a/lib/NonlinearSolveBase/src/tracing.jl
+++ b/lib/NonlinearSolveBase/src/tracing.jl
@@ -103,8 +103,16 @@ function NonlinearSolveTraceEntry(prob::AbstractNonlinearProblem, iteration, fu,
     norm_type = ifelse(prob isa NonlinearLeastSquaresProblem, :L2, :Inf)
     fnorm = prob isa NonlinearLeastSquaresProblem ? L2_NORM(fu) : Linf_NORM(fu)
     condJ = J !== missing ? Utils.condition_number(J) : nothing
-    storage = u === missing ? nothing :
-              (; u = copy(u), fu = copy(fu), δu = copy(δu), J = copy(J))
+    storage = if u === missing
+        nothing
+    else
+        (;
+            u = ArrayInterface.ismutable(u) ? copy(u) : u,
+            fu = ArrayInterface.ismutable(fu) ? copy(fu) : fu,
+            δu = ArrayInterface.ismutable(δu) ? copy(δu) : δu,
+            J = ArrayInterface.ismutable(J) ? copy(J) : J
+        )
+    end
     return NonlinearSolveTraceEntry(
         iteration, fnorm, L2_NORM(δu), condJ, storage, norm_type
     )
@@ -149,7 +157,8 @@ function init_nonlinearsolve_trace(
 )
     if show_trace isa Val{true}
         print("\nAlgorithm: ")
-        Base.printstyled(alg, "\n\n"; color = :green, bold = true)
+        str = Utils.clean_sprint_struct(alg, 0)
+        Base.printstyled(str, "\n\n"; color = :green, bold = true)
     end
     J = uses_jac_inverse isa Val{true} ?
         (trace_level.trace_mode isa Val{:minimal} ? J : LinearAlgebra.pinv(J)) : J
diff --git a/lib/NonlinearSolveQuasiNewton/src/initialization.jl b/lib/NonlinearSolveQuasiNewton/src/initialization.jl
index cd5fbaa2e..23d9a19cd 100644
--- a/lib/NonlinearSolveQuasiNewton/src/initialization.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/initialization.jl
@@ -37,12 +37,11 @@ is reinitialized.
     internalnorm
 end
 
-function InternalAPI.reinit!(cache::InitializedApproximateJacobianCache; kwargs...)
+function InternalAPI.reinit_self!(cache::InitializedApproximateJacobianCache; kwargs...)
     cache.initialized = false
 end
 
-# XXX: Implement
-# @internal_caches InitializedApproximateJacobianCache :cache
+NonlinearSolveBase.@internal_caches InitializedApproximateJacobianCache :cache
 
 function (cache::InitializedApproximateJacobianCache)(::Nothing)
     return NonlinearSolveBase.get_full_jacobian(cache, cache.structure, cache.J)
diff --git a/lib/NonlinearSolveQuasiNewton/src/solve.jl b/lib/NonlinearSolveQuasiNewton/src/solve.jl
index a37f098df..98ef6d9ee 100644
--- a/lib/NonlinearSolveQuasiNewton/src/solve.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/solve.jl
@@ -122,7 +122,9 @@ end
 #     reset_timer!(cache.timer)
 # end
 
-# @internal_caches ApproximateJacobianSolveCache :initialization_cache :descent_cache :linesearch_cache :trustregion_cache :update_rule_cache :reinit_rule_cache
+NonlinearSolveBase.@internal_caches(ApproximateJacobianSolveCache,
+    :initialization_cache, :descent_cache, :linesearch_cache, :trustregion_cache,
+    :update_rule_cache, :reinit_rule_cache)
 
 function SciMLBase.__init(
         prob::AbstractNonlinearProblem, alg::QuasiNewtonAlgorithm, args...;
@@ -361,8 +363,8 @@ function InternalAPI.step!(
             error("Unknown Globalization Strategy: $(cache.globalization). Allowed values \
                    are (:LineSearch, :TrustRegion, :None)")
         end
-        # XXX: Implement
-        # check_and_update!(cache, cache.fu, cache.u, cache.u_cache)
+
+        NonlinearSolveBase.check_and_update!(cache, cache.fu, cache.u, cache.u_cache)
     else
         α = false
         cache.force_reinit = true
@@ -376,8 +378,7 @@ function InternalAPI.step!(
 
     if (cache.force_stop || cache.force_reinit ||
         (recompute_jacobian !== nothing && !recompute_jacobian))
-        # XXX: Implement
-        # callback_into_cache!(cache)
+        NonlinearSolveBase.callback_into_cache!(cache)
         return nothing
     end
 
@@ -385,8 +386,7 @@ function InternalAPI.step!(
         cache.J = InternalAPI.solve!(
             cache.update_rule_cache, cache.J, cache.fu, cache.u, δu
         )
-        # XXX: Implement
-        # callback_into_cache!(cache)
+        NonlinearSolveBase.callback_into_cache!(cache)
     end
 
     return nothing
diff --git a/lib/NonlinearSolveSpectralMethods/src/solve.jl b/lib/NonlinearSolveSpectralMethods/src/solve.jl
index 9c68c81b4..297b9bf69 100644
--- a/lib/NonlinearSolveSpectralMethods/src/solve.jl
+++ b/lib/NonlinearSolveSpectralMethods/src/solve.jl
@@ -107,7 +107,7 @@ end
 #     cache.retcode = ReturnCode.Default
 # end
 
-# @internal_caches GeneralizedDFSaneCache :linesearch_cache
+NonlinearSolveBase.@internal_caches GeneralizedDFSaneCache :linesearch_cache
 
 function SciMLBase.__init(
         prob::AbstractNonlinearProblem, alg::GeneralizedDFSane, args...;
@@ -186,8 +186,8 @@ function InternalAPI.step!(
     end
 
     update_trace!(cache, α)
-    # XXX: Implement
-    # check_and_update!(cache, cache.fu, cache.u, cache.u_cache)
+
+    NonlinearSolveBase.check_and_update!(cache, cache.fu, cache.u, cache.u_cache)
 
     # Update Spectral Parameter
     @static_timeit cache.timer "update spectral parameter" begin
@@ -209,8 +209,7 @@ function InternalAPI.step!(
     @bb copyto!(cache.u_cache, cache.u)
     @bb copyto!(cache.fu_cache, cache.fu)
 
-    # XXX: Implement
-    # callback_into_cache!(cache, cache.linesearch_cache)
+    NonlinearSolveBase.callback_into_cache!(cache, cache.linesearch_cache)
 
     return
 end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 477f12815..5e1f39b34 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -76,9 +76,6 @@ include("abstract_types.jl")
 include("timer_outputs.jl")
 include("internal/helpers.jl")
 
-include("internal/termination.jl")
-
-include("globalization/line_search.jl")
 include("globalization/trust_region.jl")
 
 include("core/generic.jl")
diff --git a/src/abstract_types.jl b/src/abstract_types.jl
deleted file mode 100644
index 65bda73c3..000000000
--- a/src/abstract_types.jl
+++ /dev/null
@@ -1,134 +0,0 @@
-const __internal_init = InternalAPI.init
-const __internal_solve! = InternalAPI.solve!
-
-"""
-    AbstractNonlinearSolveAlgorithm{name} <: AbstractNonlinearAlgorithm
-
-Abstract Type for all NonlinearSolve.jl Algorithms. `name` can be used to define custom
-dispatches by wrapped solvers.
-
-### Interface Functions
-
-  - `concrete_jac(alg)`: whether or not the algorithm uses a concrete Jacobian. Defaults
-    to `nothing`.
-  - `get_name(alg)`: get the name of the algorithm.
-"""
-abstract type AbstractNonlinearSolveAlgorithm{name} <: AbstractNonlinearAlgorithm end
-
-function Base.show(io::IO, alg::AbstractNonlinearSolveAlgorithm)
-    __show_algorithm(io, alg, get_name(alg), 0)
-end
-
-get_name(::AbstractNonlinearSolveAlgorithm{name}) where {name} = name
-
-"""
-    AbstractNonlinearSolveExtensionAlgorithm <: AbstractNonlinearSolveAlgorithm{:Extension}
-
-Abstract Type for all NonlinearSolve.jl Extension Algorithms, i.e. wrappers over 3rd party
-solvers.
-"""
-abstract type AbstractNonlinearSolveExtensionAlgorithm <:
-              AbstractNonlinearSolveAlgorithm{:Extension} end
-
-"""
-    AbstractNonlinearSolveCache{iip, timeit}
-
-Abstract Type for all NonlinearSolve.jl Caches.
-
-### Interface Functions
-
-  - `get_fu(cache)`: get the residual.
-  - `get_u(cache)`: get the current state.
-  - `set_fu!(cache, fu)`: set the residual.
-  - `set_u!(cache, u)`: set the current state.
-  - `reinit!(cache, u0; kwargs...)`: reinitialize the cache with the initial state `u0` and
-    any additional keyword arguments.
-  - `step!(cache; kwargs...)`: See [`SciMLBase.step!`](@ref) for more details.
-  - `not_terminated(cache)`: whether or not the solver has terminated.
-  - `isinplace(cache)`: whether or not the solver is inplace.
-"""
-abstract type AbstractNonlinearSolveCache{iip, timeit} end
-
-function SymbolicIndexingInterface.symbolic_container(cache::AbstractNonlinearSolveCache)
-    return cache.prob
-end
-function SymbolicIndexingInterface.parameter_values(cache::AbstractNonlinearSolveCache)
-    return parameter_values(symbolic_container(cache))
-end
-function SymbolicIndexingInterface.state_values(cache::AbstractNonlinearSolveCache)
-    return state_values(symbolic_container(cache))
-end
-
-function Base.getproperty(cache::AbstractNonlinearSolveCache, sym::Symbol)
-    sym == :ps && return ParameterIndexingProxy(cache)
-    return getfield(cache, sym)
-end
-
-function Base.getindex(cache::AbstractNonlinearSolveCache, sym)
-    return getu(cache, sym)(cache)
-end
-
-function Base.setindex!(cache::AbstractNonlinearSolveCache, val, sym)
-    return setu(cache, sym)(cache, val)
-end
-
-function Base.show(io::IO, cache::AbstractNonlinearSolveCache)
-    __show_cache(io, cache, 0)
-end
-
-function __show_cache(io::IO, cache::AbstractNonlinearSolveCache, indent = 0)
-    println(io, "$(nameof(typeof(cache)))(")
-    __show_algorithm(io, cache.alg,
-        (" "^(indent + 4)) * "alg = " * string(get_name(cache.alg)), indent + 4)
-
-    ustr = sprint(show, get_u(cache); context = (:compact => true, :limit => true))
-    println(io, ",\n" * (" "^(indent + 4)) * "u = $(ustr),")
-
-    residstr = sprint(show, get_fu(cache); context = (:compact => true, :limit => true))
-    println(io, (" "^(indent + 4)) * "residual = $(residstr),")
-
-    normstr = sprint(
-        show, norm(get_fu(cache), Inf); context = (:compact => true, :limit => true))
-    println(io, (" "^(indent + 4)) * "inf-norm(residual) = $(normstr),")
-
-    println(io, " "^(indent + 4) * "nsteps = ", cache.stats.nsteps, ",")
-    println(io, " "^(indent + 4) * "retcode = ", cache.retcode)
-    print(io, " "^(indent) * ")")
-end
-
-SciMLBase.isinplace(::AbstractNonlinearSolveCache{iip}) where {iip} = iip
-
-get_fu(cache::AbstractNonlinearSolveCache) = cache.fu
-get_u(cache::AbstractNonlinearSolveCache) = cache.u
-set_fu!(cache::AbstractNonlinearSolveCache, fu) = (cache.fu = fu)
-SciMLBase.set_u!(cache::AbstractNonlinearSolveCache, u) = (cache.u = u)
-
-function SciMLBase.reinit!(cache::AbstractNonlinearSolveCache; kwargs...)
-    return reinit_cache!(cache; kwargs...)
-end
-function SciMLBase.reinit!(cache::AbstractNonlinearSolveCache, u0; kwargs...)
-    return reinit_cache!(cache; u0, kwargs...)
-end
-
-"""
-    AbstractTrustRegionMethodCache
-
-Abstract Type for all Trust Region Method Caches used in NonlinearSolve.jl.
-
-### Interface Functions
-
-  - `last_step_accepted(cache)`: whether or not the last step was accepted. Defaults to
-    `cache.last_step_accepted`. Should if overloaded if the field is not present.
-
-### `__internal_solve!` specification
-
-```julia
-__internal_solve!(cache::AbstractTrustRegionMethodCache, J, fu, u, δu, descent_stats)
-```
-
-Returns `last_step_accepted`, updated `u_cache` and `fu_cache`. If the last step was
-accepted then these values should be copied into the toplevel cache.
-"""
-abstract type AbstractTrustRegionMethodCache end
-
-last_step_accepted(cache::AbstractTrustRegionMethodCache) = cache.last_step_accepted
diff --git a/src/globalization/line_search.jl b/src/globalization/line_search.jl
deleted file mode 100644
index 7549f1f9d..000000000
--- a/src/globalization/line_search.jl
+++ /dev/null
@@ -1,7 +0,0 @@
-function callback_into_cache!(topcache, cache::AbstractLineSearchCache, args...)
-    LineSearch.callback_into_cache!(cache, get_fu(topcache))
-end
-
-function reinit_cache!(cache::AbstractLineSearchCache, args...; kwargs...)
-    return SciMLBase.reinit!(cache, args...; kwargs...)
-end
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
index 735122b8d..a7326bb51 100644
--- a/src/internal/helpers.jl
+++ b/src/internal/helpers.jl
@@ -1,45 +1,3 @@
-# Evaluate the residual function at a given point
-function evaluate_f(prob::AbstractNonlinearProblem{uType, iip}, u) where {uType, iip}
-    (; f, p) = prob
-    if iip
-        fu = f.resid_prototype === nothing ? zero(u) : similar(f.resid_prototype)
-        f(fu, u, p)
-    else
-        fu = f(u, p)
-    end
-    return fu
-end
-
-function evaluate_f!(cache, u, p)
-    cache.stats.nf += 1
-    if isinplace(cache)
-        cache.prob.f(get_fu(cache), u, p)
-    else
-        set_fu!(cache, cache.prob.f(u, p))
-    end
-end
-
-evaluate_f!!(prob::AbstractNonlinearProblem, fu, u, p) = evaluate_f!!(prob.f, fu, u, p)
-function evaluate_f!!(f::NonlinearFunction{iip}, fu, u, p) where {iip}
-    if iip
-        f(fu, u, p)
-        return fu
-    end
-    return f(u, p)
-end
-
-# Callbacks
-"""
-    callback_into_cache!(cache, internalcache, args...)
-
-Define custom operations on `internalcache` tightly coupled with the calling `cache`.
-`args...` contain the sequence of caches calling into `internalcache`.
-
-This unfortunately makes code very tightly coupled and not modular. It is recommended to not
-use this functionality unless it can't be avoided (like in [`LevenbergMarquardt`](@ref)).
-"""
-@inline callback_into_cache!(cache, internalcache, args...) = nothing  # By default do nothing
-
 # Extension Algorithm Helpers
 function __test_termination_condition(termination_condition, alg)
     !(termination_condition isa AbsNormTerminationMode) &&
@@ -125,42 +83,3 @@ function __construct_extension_jac(prob, alg, u0, fu; can_handle_oop::Val = Fals
 
     return 𝐉, Jₚ(nothing)
 end
-
-function reinit_cache! end
-reinit_cache!(cache::Nothing, args...; kwargs...) = nothing
-reinit_cache!(cache, args...; kwargs...) = nothing
-
-function __reinit_internal! end
-__reinit_internal!(::Nothing, args...; kwargs...) = nothing
-__reinit_internal!(cache, args...; kwargs...) = nothing
-
-# Auto-generate some of the helper functions
-macro internal_caches(cType, internal_cache_names...)
-    return __internal_caches(cType, internal_cache_names)
-end
-
-function __internal_caches(cType, internal_cache_names::Tuple)
-    callback_caches = map(
-        name -> :($(callback_into_cache!)(
-            cache, getproperty(internalcache, $(name)), internalcache, args...)),
-        internal_cache_names)
-    callbacks_self = map(
-        name -> :($(callback_into_cache!)(
-            internalcache, getproperty(internalcache, $(name)))),
-        internal_cache_names)
-    reinit_caches = map(
-        name -> :($(reinit_cache!)(getproperty(cache, $(name)), args...; kwargs...)),
-        internal_cache_names)
-    return esc(quote
-        function callback_into_cache!(cache, internalcache::$(cType), args...)
-            $(callback_caches...)
-        end
-        function callback_into_cache!(internalcache::$(cType))
-            $(callbacks_self...)
-        end
-        function reinit_cache!(cache::$(cType), args...; kwargs...)
-            $(reinit_caches...)
-            $(__reinit_internal!)(cache, args...; kwargs...)
-        end
-    end)
-end
diff --git a/src/internal/termination.jl b/src/internal/termination.jl
deleted file mode 100644
index 7728aea69..000000000
--- a/src/internal/termination.jl
+++ /dev/null
@@ -1,34 +0,0 @@
-function check_and_update!(cache, fu, u, uprev)
-    return check_and_update!(cache.termination_cache, cache, fu, u, uprev)
-end
-
-function check_and_update!(tc_cache, cache, fu, u, uprev)
-    return check_and_update!(tc_cache, cache, fu, u, uprev, tc_cache.mode)
-end
-
-function check_and_update!(tc_cache, cache, fu, u, uprev, mode)
-    if tc_cache(fu, u, uprev)
-        cache.retcode = tc_cache.retcode
-        update_from_termination_cache!(tc_cache, cache, mode, u)
-        cache.force_stop = true
-    end
-end
-
-function update_from_termination_cache!(tc_cache, cache, u = get_u(cache))
-    return update_from_termination_cache!(tc_cache, cache, tc_cache.mode, u)
-end
-
-function update_from_termination_cache!(
-        tc_cache, cache, ::AbstractNonlinearTerminationMode, u = get_u(cache))
-    evaluate_f!(cache, u, cache.p)
-end
-
-function update_from_termination_cache!(
-        tc_cache, cache, ::AbstractSafeBestNonlinearTerminationMode, u = get_u(cache))
-    if isinplace(cache)
-        copyto!(get_u(cache), tc_cache.u)
-    else
-        set_u!(cache, tc_cache.u)
-    end
-    evaluate_f!(cache, get_u(cache), cache.p)
-end
diff --git a/src/utils.jl b/src/utils.jl
index 1582234bc..cb346da0a 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -103,18 +103,3 @@ function __build_solution_less_specialize(prob::AbstractNonlinearProblem, alg, u
         Any, typeof(left), typeof(stats), typeof(trace)}(
         u, resid, prob, alg, retcode, original, left, right, stats, trace)
 end
-
-@inline empty_nlstats() = NLStats(0, 0, 0, 0, 0)
-function __reinit_internal!(stats::NLStats)
-    stats.nf = 0
-    stats.nsteps = 0
-    stats.nfactors = 0
-    stats.njacs = 0
-    stats.nsolve = 0
-end
-
-function __similar(x, args...; kwargs...)
-    y = similar(x, args...; kwargs...)
-    fill!(y, false)
-    return y
-end

From 8d40ab40e2ccafa04e17ee75515622c476f97cea Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 28 Oct 2024 00:45:41 -0400
Subject: [PATCH 642/700] refactor: delete more code

---
 Project.toml                                  |   3 +-
 lib/NonlinearSolveBase/src/solve.jl           |   6 +-
 lib/NonlinearSolveBase/src/utils.jl           |   4 +-
 .../src/NonlinearSolveFirstOrder.jl           |  37 ++
 .../src/gauss_newton.jl                       |   0
 .../src/levenberg_marquardt.jl                |   0
 .../src/pseudo_transient.jl                   |   0
 lib/NonlinearSolveFirstOrder/src/raphson.jl   |   0
 lib/NonlinearSolveFirstOrder/src/solve.jl     | 303 ++++++++++++++++
 .../src/trust_region.jl                       |   0
 .../src/initialization.jl                     |   7 +-
 lib/NonlinearSolveQuasiNewton/src/solve.jl    |  12 +-
 .../src/solve.jl                              |   1 +
 src/NonlinearSolve.jl                         |  15 -
 src/core/generalized_first_order.jl           | 326 ------------------
 src/core/generic.jl                           |  66 ----
 src/core/noinit.jl                            |  37 --
 src/utils.jl                                  |  54 ---
 18 files changed, 359 insertions(+), 512 deletions(-)
 create mode 100644 lib/NonlinearSolveFirstOrder/src/gauss_newton.jl
 create mode 100644 lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
 create mode 100644 lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
 create mode 100644 lib/NonlinearSolveFirstOrder/src/raphson.jl
 create mode 100644 lib/NonlinearSolveFirstOrder/src/solve.jl
 create mode 100644 lib/NonlinearSolveFirstOrder/src/trust_region.jl
 delete mode 100644 src/core/generalized_first_order.jl
 delete mode 100644 src/core/generic.jl
 delete mode 100644 src/core/noinit.jl

diff --git a/Project.toml b/Project.toml
index e08da6b42..1c6485b43 100644
--- a/Project.toml
+++ b/Project.toml
@@ -13,12 +13,12 @@ DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
-LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
 LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
+NonlinearSolveFirstOrder = "5959db7a-ea39-4486-b5fe-2dd0bf03d60d"
 NonlinearSolveQuasiNewton = "9a2c21bd-3a47-402d-9113-8faf9a0ee114"
 NonlinearSolveSpectralMethods = "26075421-4e9a-44e1-8bd1-420ed7ad02b2"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
@@ -81,7 +81,6 @@ FixedPointAcceleration = "0.3"
 ForwardDiff = "0.10.36"
 Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
-LazyArrays = "1.8.2, 2"
 LeastSquaresOptim = "0.8.5"
 LineSearch = "0.1.4"
 LineSearches = "7.3"
diff --git a/lib/NonlinearSolveBase/src/solve.jl b/lib/NonlinearSolveBase/src/solve.jl
index 7316fd168..3c50521a0 100644
--- a/lib/NonlinearSolveBase/src/solve.jl
+++ b/lib/NonlinearSolveBase/src/solve.jl
@@ -32,8 +32,10 @@ function CommonSolve.solve!(cache::AbstractNonlinearSolveCache)
 end
 
 """
-    step!(cache::AbstractNonlinearSolveCache;
-        recompute_jacobian::Union{Nothing, Bool} = nothing)
+    step!(
+        cache::AbstractNonlinearSolveCache;
+        recompute_jacobian::Union{Nothing, Bool} = nothing
+    )
 
 Performs one step of the nonlinear solver.
 
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index a727bed6d..6d7a66aa0 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -248,7 +248,7 @@ function clean_sprint_struct(x)
     name = nameof(typeof(x))
     for field in fieldnames(typeof(x))
         val = getfield(x, field)
-        if field === :name
+        if field === :name && val isa Symbol && val !== :unknown
             name = val
             continue
         end
@@ -268,7 +268,7 @@ function clean_sprint_struct(x, indent::Int)
     name = nameof(typeof(x))
     for field in fieldnames(typeof(x))
         val = getfield(x, field)
-        if field === :name
+        if field === :name && val isa Symbol && val !== :unknown
             name = val
             continue
         end
diff --git a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
index f07882cc2..2cf9560e3 100644
--- a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
+++ b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
@@ -1,3 +1,40 @@
 module NonlinearSolveFirstOrder
 
+using Reexport: @reexport
+using PrecompileTools: @compile_workload, @setup_workload
+
+using ArrayInterface: ArrayInterface
+using CommonSolve: CommonSolve
+using ConcreteStructs: @concrete
+using DiffEqBase: DiffEqBase   # Needed for `init` / `solve` dispatches
+using LinearAlgebra: LinearAlgebra, Diagonal, dot, inv, diag
+using LinearSolve: LinearSolve # Trigger Linear Solve extension in NonlinearSolveBase
+using MaybeInplace: @bb
+using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
+                          AbstractNonlinearSolveCache, AbstractResetCondition,
+                          AbstractResetConditionCache, AbstractApproximateJacobianStructure,
+                          AbstractJacobianCache, AbstractJacobianInitialization,
+                          AbstractApproximateJacobianUpdateRule, AbstractDescentDirection,
+                          AbstractApproximateJacobianUpdateRuleCache,
+                          Utils, InternalAPI, get_timer_output, @static_timeit,
+                          update_trace!, L2_NORM, NewtonDescent
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode
+using SciMLOperators: AbstractSciMLOperator
+using StaticArraysCore: StaticArray, Size, MArray
+
+include("raphson.jl")
+include("gauss_newton.jl")
+include("levenberg_marquardt.jl")
+include("trust_region.jl")
+include("pseudo_transient.jl")
+
+include("solve.jl")
+
+@reexport using SciMLBase, NonlinearSolveBase
+
+export NewtonRaphson, PseudoTransient
+export GaussNewton, LevenbergMarquardt, TrustRegion
+
+export GeneralizedFirstOrderAlgorithm
+
 end
diff --git a/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl b/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl b/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/NonlinearSolveFirstOrder/src/raphson.jl b/lib/NonlinearSolveFirstOrder/src/raphson.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/NonlinearSolveFirstOrder/src/solve.jl b/lib/NonlinearSolveFirstOrder/src/solve.jl
new file mode 100644
index 000000000..0d60aa3d7
--- /dev/null
+++ b/lib/NonlinearSolveFirstOrder/src/solve.jl
@@ -0,0 +1,303 @@
+"""
+    GeneralizedFirstOrderAlgorithm(;
+        descent, linesearch = missing,
+        trustregion = missing, autodiff = nothing, vjp_autodiff = nothing,
+        jvp_autodiff = nothing, max_shrink_times::Int = typemax(Int),
+        concrete_jac = Val(false), name::Symbol = :unknown
+    )
+
+This is a Generalization of First-Order (uses Jacobian) Nonlinear Solve Algorithms. The most
+common example of this is Newton-Raphson Method.
+
+First Order here refers to the order of differentiation, and should not be confused with the
+order of convergence.
+
+### Keyword Arguments
+
+  - `trustregion`: Globalization using a Trust Region Method. This needs to follow the
+    [`NonlinearSolve.AbstractTrustRegionMethod`](@ref) interface.
+  - `descent`: The descent method to use to compute the step. This needs to follow the
+    [`NonlinearSolve.AbstractDescentAlgorithm`](@ref) interface.
+  - `max_shrink_times`: The maximum number of times the trust region radius can be shrunk
+    before the algorithm terminates.
+"""
+@concrete struct GeneralizedFirstOrderAlgorithm <: AbstractNonlinearSolveAlgorithm
+    linesearch
+    trustregion
+    descent
+    max_shrink_times::Int
+
+    autodiff
+    vjp_autodiff
+    jvp_autodiff
+
+    concrete_jac <: Union{Val{false}, Val{true}}
+    name::Symbol
+end
+
+function GeneralizedFirstOrderAlgorithm(;
+        descent, linesearch = missing, trustregion = missing, autodiff = nothing,
+        vjp_autodiff = nothing, jvp_autodiff = nothing, max_shrink_times::Int = typemax(Int),
+        concrete_jac = Val(false), name::Symbol = :unknown)
+    return GeneralizedFirstOrderAlgorithm(
+        linesearch, trustregion, descent, max_shrink_times,
+        autodiff, vjp_autodiff, jvp_autodiff,
+        concrete_jac, name
+    )
+end
+
+@concrete mutable struct GeneralizedFirstOrderAlgorithmCache <: AbstractNonlinearSolveCache
+    # Basic Requirements
+    fu
+    u
+    u_cache
+    p
+    du  # Aliased to `get_du(descent_cache)`
+    J   # Aliased to `jac_cache.J`
+    alg <: GeneralizedFirstOrderAlgorithm
+    prob <: AbstractNonlinearProblem
+    globalization <: Union{Val{:LineSearch}, Val{:TrustRegion}, Val{:None}}
+
+    # Internal Caches
+    jac_cache
+    descent_cache
+    linesearch_cache
+    trustregion_cache
+
+    # Counters
+    stats::NLStats
+    nsteps::Int
+    maxiters::Int
+    maxtime
+    max_shrink_times::Int
+
+    # Timer
+    timer
+    total_time::Float64
+
+    # State Affect
+    make_new_jacobian::Bool
+
+    # Termination & Tracking
+    termination_cache
+    trace
+    retcode::ReturnCode.T
+    force_stop::Bool
+    kwargs
+end
+
+# XXX: Implement
+# function __reinit_internal!(
+#         cache::GeneralizedFirstOrderAlgorithmCache{iip}, args...; p = cache.p, u0 = cache.u,
+#         alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...) where {iip}
+#     if iip
+#         recursivecopy!(cache.u, u0)
+#         cache.prob.f(cache.fu, cache.u, p)
+#     else
+#         cache.u = __maybe_unaliased(u0, alias_u0)
+#         set_fu!(cache, cache.prob.f(cache.u, p))
+#     end
+#     cache.p = p
+
+#     __reinit_internal!(cache.stats)
+#     cache.nsteps = 0
+#     cache.maxiters = maxiters
+#     cache.maxtime = maxtime
+#     cache.total_time = 0.0
+#     cache.force_stop = false
+#     cache.retcode = ReturnCode.Default
+#     cache.make_new_jacobian = true
+
+#     reset!(cache.trace)
+#     reinit!(cache.termination_cache, get_fu(cache), get_u(cache); kwargs...)
+#     reset_timer!(cache.timer)
+# end
+
+NonlinearSolveBase.@internal_caches(GeneralizedFirstOrderAlgorithmCache,
+    :jac_cache, :descent_cache, :linesearch_cache, :trustregion_cache)
+
+# function SciMLBase.__init(
+#         prob::AbstractNonlinearProblem{uType, iip}, alg::GeneralizedFirstOrderAlgorithm,
+#         args...; stats = empty_nlstats(), alias_u0 = false, maxiters = 1000,
+#         abstol = nothing, reltol = nothing, maxtime = nothing,
+#         termination_condition = nothing, internalnorm = L2_NORM,
+#         linsolve_kwargs = (;), kwargs...) where {uType, iip}
+#     autodiff = select_jacobian_autodiff(prob, alg.autodiff)
+#     jvp_autodiff = if alg.jvp_autodiff === nothing && alg.autodiff !== nothing &&
+#                       (ADTypes.mode(alg.autodiff) isa ADTypes.ForwardMode ||
+#                        ADTypes.mode(alg.autodiff) isa ADTypes.ForwardOrReverseMode)
+#         select_forward_mode_autodiff(prob, alg.autodiff)
+#     else
+#         select_forward_mode_autodiff(prob, alg.jvp_autodiff)
+#     end
+#     vjp_autodiff = if alg.vjp_autodiff === nothing && alg.autodiff !== nothing &&
+#                       (ADTypes.mode(alg.autodiff) isa ADTypes.ReverseMode ||
+#                        ADTypes.mode(alg.autodiff) isa ADTypes.ForwardOrReverseMode)
+#         select_reverse_mode_autodiff(prob, alg.autodiff)
+#     else
+#         select_reverse_mode_autodiff(prob, alg.vjp_autodiff)
+#     end
+
+#     timer = get_timer_output()
+#     @static_timeit timer "cache construction" begin
+#         (; f, u0, p) = prob
+#         u = __maybe_unaliased(u0, alias_u0)
+#         fu = evaluate_f(prob, u)
+#         @bb u_cache = copy(u)
+
+#         linsolve = get_linear_solver(alg.descent)
+
+#         abstol, reltol, termination_cache = NonlinearSolveBase.init_termination_cache(
+#             prob, abstol, reltol, fu, u, termination_condition, Val(:regular))
+#         linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
+
+#         jac_cache = construct_jacobian_cache(
+#             prob, alg, f, fu, u, p; stats, autodiff, linsolve, jvp_autodiff, vjp_autodiff)
+#         J = jac_cache(nothing)
+
+#         descent_cache = __internal_init(prob, alg.descent, J, fu, u; stats, abstol,
+#             reltol, internalnorm, linsolve_kwargs, timer)
+#         du = get_du(descent_cache)
+
+#         has_linesearch = alg.linesearch !== missing && alg.linesearch !== nothing
+#         has_trustregion = alg.trustregion !== missing && alg.trustregion !== nothing
+
+#         if has_trustregion && has_linesearch
+#             error("TrustRegion and LineSearch methods are algorithmically incompatible.")
+#         end
+
+#         GB = :None
+#         linesearch_cache = nothing
+#         trustregion_cache = nothing
+
+#         if has_trustregion
+#             supports_trust_region(alg.descent) || error("Trust Region not supported by \
+#                                                $(alg.descent).")
+#             trustregion_cache = __internal_init(
+#                 prob, alg.trustregion, f, fu, u, p; stats, internalnorm, kwargs...,
+#                 autodiff, jvp_autodiff, vjp_autodiff)
+#             GB = :TrustRegion
+#         end
+
+#         if has_linesearch
+#             supports_line_search(alg.descent) || error("Line Search not supported by \
+#                                                $(alg.descent).")
+#             linesearch_cache = init(
+#                 prob, alg.linesearch, fu, u; stats, autodiff = jvp_autodiff, kwargs...)
+#             GB = :LineSearch
+#         end
+
+#         trace = init_nonlinearsolve_trace(
+#             prob, alg, u, fu, ApplyArray(__zero, J), du; kwargs...)
+
+#         return GeneralizedFirstOrderAlgorithmCache{iip, GB, maxtime !== nothing}(
+#             fu, u, u_cache, p, du, J, alg, prob, jac_cache, descent_cache, linesearch_cache,
+#             trustregion_cache, stats, 0, maxiters, maxtime, alg.max_shrink_times, timer,
+#             0.0, true, termination_cache, trace, ReturnCode.Default, false, kwargs)
+#     end
+# end
+
+# function __step!(cache::GeneralizedFirstOrderAlgorithmCache{iip, GB};
+#         recompute_jacobian::Union{Nothing, Bool} = nothing, kwargs...) where {iip, GB}
+#     @static_timeit cache.timer "jacobian" begin
+#         if (recompute_jacobian === nothing || recompute_jacobian) && cache.make_new_jacobian
+#             J = cache.jac_cache(cache.u)
+#             new_jacobian = true
+#         else
+#             J = cache.jac_cache(nothing)
+#             new_jacobian = false
+#         end
+#     end
+
+#     @static_timeit cache.timer "descent" begin
+#         if cache.trustregion_cache !== nothing &&
+#            hasfield(typeof(cache.trustregion_cache), :trust_region)
+#             descent_result = __internal_solve!(
+#                 cache.descent_cache, J, cache.fu, cache.u; new_jacobian,
+#                 trust_region = cache.trustregion_cache.trust_region, cache.kwargs...)
+#         else
+#             descent_result = __internal_solve!(
+#                 cache.descent_cache, J, cache.fu, cache.u; new_jacobian, cache.kwargs...)
+#         end
+#     end
+
+#     if !descent_result.linsolve_success
+#         if new_jacobian
+#             # Jacobian Information is current and linear solve failed terminate the solve
+#             cache.retcode = ReturnCode.InternalLinearSolveFailed
+#             cache.force_stop = true
+#             return
+#         else
+#             # Jacobian Information is not current and linear solve failed, recompute
+#             # Jacobian
+#             if !haskey(cache.kwargs, :verbose) || cache.kwargs[:verbose]
+#                 @warn "Linear Solve Failed but Jacobian Information is not current. \
+#                   Retrying with updated Jacobian."
+#             end
+#             # In the 2nd call the `new_jacobian` is guaranteed to be `true`.
+#             cache.make_new_jacobian = true
+#             __step!(cache; recompute_jacobian = true, kwargs...)
+#             return
+#         end
+#     end
+
+#     δu, descent_intermediates = descent_result.δu, descent_result.extras
+
+#     if descent_result.success
+#         cache.make_new_jacobian = true
+#         if GB === :LineSearch
+#             @static_timeit cache.timer "linesearch" begin
+#                 linesearch_sol = solve!(cache.linesearch_cache, cache.u, δu)
+#                 linesearch_failed = !SciMLBase.successful_retcode(linesearch_sol.retcode)
+#                 α = linesearch_sol.step_size
+#             end
+#             if linesearch_failed
+#                 cache.retcode = ReturnCode.InternalLineSearchFailed
+#                 cache.force_stop = true
+#             end
+#             @static_timeit cache.timer "step" begin
+#                 @bb axpy!(α, δu, cache.u)
+#                 evaluate_f!(cache, cache.u, cache.p)
+#             end
+#         elseif GB === :TrustRegion
+#             @static_timeit cache.timer "trustregion" begin
+#                 tr_accepted, u_new, fu_new = __internal_solve!(
+#                     cache.trustregion_cache, J, cache.fu,
+#                     cache.u, δu, descent_intermediates)
+#                 if tr_accepted
+#                     @bb copyto!(cache.u, u_new)
+#                     @bb copyto!(cache.fu, fu_new)
+#                     α = true
+#                 else
+#                     α = false
+#                     cache.make_new_jacobian = false
+#                 end
+#                 if hasfield(typeof(cache.trustregion_cache), :shrink_counter) &&
+#                    cache.trustregion_cache.shrink_counter > cache.max_shrink_times
+#                     cache.retcode = ReturnCode.ShrinkThresholdExceeded
+#                     cache.force_stop = true
+#                 end
+#             end
+#         elseif GB === :None
+#             @static_timeit cache.timer "step" begin
+#                 @bb axpy!(1, δu, cache.u)
+#                 evaluate_f!(cache, cache.u, cache.p)
+#             end
+#             α = true
+#         else
+#             error("Unknown Globalization Strategy: $(GB). Allowed values are (:LineSearch, \
+#             :TrustRegion, :None)")
+#         end
+#         check_and_update!(cache, cache.fu, cache.u, cache.u_cache)
+#     else
+#         α = false
+#         cache.make_new_jacobian = false
+#     end
+
+#     update_trace!(cache, α)
+#     @bb copyto!(cache.u_cache, cache.u)
+
+#     callback_into_cache!(cache)
+
+#     return nothing
+# end
diff --git a/lib/NonlinearSolveFirstOrder/src/trust_region.jl b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/NonlinearSolveQuasiNewton/src/initialization.jl b/lib/NonlinearSolveQuasiNewton/src/initialization.jl
index 23d9a19cd..6c22e0240 100644
--- a/lib/NonlinearSolveQuasiNewton/src/initialization.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/initialization.jl
@@ -1,6 +1,7 @@
 """
-    InitializedApproximateJacobianCache(J, structure, alg, cache, initialized::Bool,
-        internalnorm)
+    InitializedApproximateJacobianCache(
+        J, structure, alg, cache, initialized::Bool, internalnorm
+    )
 
 A cache for Approximate Jacobian.
 
@@ -22,7 +23,7 @@ A cache for Approximate Jacobian.
 Returns the current Jacobian `cache.J` with the proper `structure`.
 
 ```julia
-__internal_solve!(cache::InitializedApproximateJacobianCache, fu, u, ::Val{reinit})
+InternalAPI.solve!(cache::InitializedApproximateJacobianCache, fu, u, ::Val{reinit})
 ```
 
 Solves for the Jacobian `cache.J` and returns it. If `reinit` is `true`, then the Jacobian
diff --git a/lib/NonlinearSolveQuasiNewton/src/solve.jl b/lib/NonlinearSolveQuasiNewton/src/solve.jl
index 98ef6d9ee..5b987a10d 100644
--- a/lib/NonlinearSolveQuasiNewton/src/solve.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/solve.jl
@@ -30,9 +30,11 @@ examples include [`Broyden`](@ref)'s Method.
     descent <: AbstractDescentDirection
     update_rule <: AbstractApproximateJacobianUpdateRule
     reinit_rule <: AbstractResetCondition
+    initialization <: AbstractJacobianInitialization
+
     max_resets::Int
     max_shrink_times::Int
-    initialization
+
     concrete_jac <: Union{Val{false}, Val{true}}
     name::Symbol
 end
@@ -43,8 +45,8 @@ function QuasiNewtonAlgorithm(;
         max_shrink_times::Int = typemax(Int), concrete_jac = Val(false)
 )
     return QuasiNewtonAlgorithm(
-        linesearch, trustregion, descent, update_rule, reinit_rule,
-        max_resets, max_shrink_times, initialization, concrete_jac, name
+        linesearch, trustregion, descent, update_rule, reinit_rule, initialization,
+        max_resets, max_shrink_times, concrete_jac, name
     )
 end
 
@@ -94,7 +96,7 @@ end
 end
 
 # XXX: Implement
-# function __reinit_internal!(cache::ApproximateJacobianSolveCache{INV, GB, iip},
+# function __reinit_internal!(cache::QuasiNewtonCache{INV, GB, iip},
 #         args...; p = cache.p, u0 = cache.u, alias_u0::Bool = false,
 #         maxiters = 1000, maxtime = nothing, kwargs...) where {INV, GB, iip}
 #     if iip
@@ -122,7 +124,7 @@ end
 #     reset_timer!(cache.timer)
 # end
 
-NonlinearSolveBase.@internal_caches(ApproximateJacobianSolveCache,
+NonlinearSolveBase.@internal_caches(QuasiNewtonCache,
     :initialization_cache, :descent_cache, :linesearch_cache, :trustregion_cache,
     :update_rule_cache, :reinit_rule_cache)
 
diff --git a/lib/NonlinearSolveSpectralMethods/src/solve.jl b/lib/NonlinearSolveSpectralMethods/src/solve.jl
index 297b9bf69..518e9a453 100644
--- a/lib/NonlinearSolveSpectralMethods/src/solve.jl
+++ b/lib/NonlinearSolveSpectralMethods/src/solve.jl
@@ -23,6 +23,7 @@ Method.
     σ_min
     σ_max
     σ_1
+
     name::Symbol
 end
 
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 5e1f39b34..950710932 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -9,7 +9,6 @@ using CommonSolve: solve, init, solve!
 using ConcreteStructs: @concrete
 using DiffEqBase: DiffEqBase # Needed for `init` / `solve` dispatches
 using FastClosures: @closure
-using LazyArrays: LazyArrays, ApplyArray, cache
 using LinearAlgebra: LinearAlgebra, Diagonal, I, LowerTriangular, Symmetric,
                      UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess, istril,
                      istriu, lu, mul!, norm, pinv, tril!, triu!
@@ -34,14 +33,6 @@ using NonlinearSolveBase: NonlinearSolveBase,
 
 using NonlinearSolveQuasiNewton: Broyden, Klement
 
-# XXX: Remove
-import NonlinearSolveBase: InternalAPI, concrete_jac, supports_line_search,
-                           supports_trust_region, last_step_accepted, get_linear_solver,
-                           AbstractDampingFunction, AbstractDampingFunctionCache,
-                           requires_normal_form_jacobian, requires_normal_form_rhs,
-                           returns_norm_form_damping, get_timer_output, get_u, get_fu,
-                           set_fu!
-
 using Preferences: Preferences, set_preferences!
 using RecursiveArrayTools: recursivecopy!
 using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, AbstractNonlinearProblem,
@@ -51,9 +42,6 @@ using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, AbstractNonlinearProblem
 using SciMLOperators: AbstractSciMLOperator
 using SimpleNonlinearSolve: SimpleNonlinearSolve
 using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
-using SymbolicIndexingInterface: SymbolicIndexingInterface, ParameterIndexingProxy,
-                                 symbolic_container, parameter_values, state_values, getu,
-                                 setu
 
 # AD Support
 using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
@@ -72,15 +60,12 @@ const DI = DifferentiationInterface
 const True = Val(true)
 const False = Val(false)
 
-include("abstract_types.jl")
 include("timer_outputs.jl")
 include("internal/helpers.jl")
 
 include("globalization/trust_region.jl")
 
-include("core/generic.jl")
 include("core/generalized_first_order.jl")
-include("core/noinit.jl")
 
 include("algorithms/raphson.jl")
 include("algorithms/pseudo_transient.jl")
diff --git a/src/core/generalized_first_order.jl b/src/core/generalized_first_order.jl
deleted file mode 100644
index 261adbfb0..000000000
--- a/src/core/generalized_first_order.jl
+++ /dev/null
@@ -1,326 +0,0 @@
-"""
-    GeneralizedFirstOrderAlgorithm{concrete_jac, name}(; descent, linesearch = missing,
-        trustregion = missing, autodiff = nothing, vjp_autodiff = nothing,
-        jvp_autodiff = nothing, max_shrink_times::Int = typemax(Int))
-    GeneralizedFirstOrderAlgorithm(; concrete_jac = nothing, name::Symbol = :unknown,
-        kwargs...)
-
-This is a Generalization of First-Order (uses Jacobian) Nonlinear Solve Algorithms. The most
-common example of this is Newton-Raphson Method.
-
-First Order here refers to the order of differentiation, and should not be confused with the
-order of convergence.
-
-!!! danger
-
-    `trustregion` and `linesearch` cannot be specified together.
-
-### Keyword Arguments
-
-  - `trustregion`: Globalization using a Trust Region Method. This needs to follow the
-    [`NonlinearSolve.AbstractTrustRegionMethod`](@ref) interface.
-  - `descent`: The descent method to use to compute the step. This needs to follow the
-    [`NonlinearSolve.AbstractDescentAlgorithm`](@ref) interface.
-  - `max_shrink_times`: The maximum number of times the trust region radius can be shrunk
-    before the algorithm terminates.
-"""
-@concrete struct GeneralizedFirstOrderAlgorithm{concrete_jac, name} <:
-                 AbstractNonlinearSolveAlgorithm{name}
-    linesearch
-    trustregion
-    descent
-    max_shrink_times::Int
-
-    autodiff
-    vjp_autodiff
-    jvp_autodiff
-end
-
-function __show_algorithm(io::IO, alg::GeneralizedFirstOrderAlgorithm, name, indent)
-    modifiers = String[]
-    __is_present(alg.linesearch) && push!(modifiers, "linesearch = $(alg.linesearch)")
-    __is_present(alg.trustregion) && push!(modifiers, "trustregion = $(alg.trustregion)")
-    push!(modifiers, "descent = $(alg.descent)")
-    __is_present(alg.autodiff) && push!(modifiers, "autodiff = $(alg.autodiff)")
-    __is_present(alg.vjp_autodiff) && push!(modifiers, "vjp_autodiff = $(alg.vjp_autodiff)")
-    __is_present(alg.jvp_autodiff) && push!(modifiers, "jvp_autodiff = $(alg.jvp_autodiff)")
-    spacing = " "^indent * "   "
-    spacing_last = " "^indent
-    print(io, "$(name)(\n$(spacing)$(join(modifiers, ",\n$(spacing)"))\n$(spacing_last))")
-end
-
-function GeneralizedFirstOrderAlgorithm(;
-        concrete_jac = nothing, name::Symbol = :unknown, kwargs...)
-    return GeneralizedFirstOrderAlgorithm{concrete_jac, name}(; kwargs...)
-end
-
-function GeneralizedFirstOrderAlgorithm{concrete_jac, name}(;
-        descent, linesearch = missing, trustregion = missing,
-        autodiff = nothing, jvp_autodiff = nothing, vjp_autodiff = nothing,
-        max_shrink_times::Int = typemax(Int)) where {concrete_jac, name}
-    return GeneralizedFirstOrderAlgorithm{concrete_jac, name}(
-        linesearch, trustregion, descent, max_shrink_times,
-        autodiff, vjp_autodiff, jvp_autodiff)
-end
-
-# XXX: Remove
-concrete_jac(::GeneralizedFirstOrderAlgorithm{CJ}) where {CJ} = concrete_jac(CJ)
-
-@concrete mutable struct GeneralizedFirstOrderAlgorithmCache{iip, GB, timeit} <:
-                         AbstractNonlinearSolveCache{iip, timeit}
-    # Basic Requirements
-    fu
-    u
-    u_cache
-    p
-    du  # Aliased to `get_du(descent_cache)`
-    J   # Aliased to `jac_cache.J`
-    alg
-    prob
-
-    # Internal Caches
-    jac_cache
-    descent_cache
-    linesearch_cache
-    trustregion_cache
-
-    # Counters
-    stats::NLStats
-    nsteps::Int
-    maxiters::Int
-    maxtime
-    max_shrink_times::Int
-
-    # Timer
-    timer
-    total_time::Float64   # Simple Counter which works even if TimerOutput is disabled
-
-    # State Affect
-    make_new_jacobian::Bool
-
-    # Termination & Tracking
-    termination_cache
-    trace
-    retcode::ReturnCode.T
-    force_stop::Bool
-    kwargs
-end
-
-SymbolicIndexingInterface.state_values(cache::GeneralizedFirstOrderAlgorithmCache) = cache.u
-function SymbolicIndexingInterface.parameter_values(cache::GeneralizedFirstOrderAlgorithmCache)
-    cache.p
-end
-
-function __reinit_internal!(
-        cache::GeneralizedFirstOrderAlgorithmCache{iip}, args...; p = cache.p, u0 = cache.u,
-        alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...) where {iip}
-    if iip
-        recursivecopy!(cache.u, u0)
-        cache.prob.f(cache.fu, cache.u, p)
-    else
-        cache.u = __maybe_unaliased(u0, alias_u0)
-        set_fu!(cache, cache.prob.f(cache.u, p))
-    end
-    cache.p = p
-
-    __reinit_internal!(cache.stats)
-    cache.nsteps = 0
-    cache.maxiters = maxiters
-    cache.maxtime = maxtime
-    cache.total_time = 0.0
-    cache.force_stop = false
-    cache.retcode = ReturnCode.Default
-    cache.make_new_jacobian = true
-
-    reset!(cache.trace)
-    reinit!(cache.termination_cache, get_fu(cache), get_u(cache); kwargs...)
-    reset_timer!(cache.timer)
-end
-
-@internal_caches GeneralizedFirstOrderAlgorithmCache :jac_cache :descent_cache :linesearch_cache :trustregion_cache
-
-function SciMLBase.__init(
-        prob::AbstractNonlinearProblem{uType, iip}, alg::GeneralizedFirstOrderAlgorithm,
-        args...; stats = empty_nlstats(), alias_u0 = false, maxiters = 1000,
-        abstol = nothing, reltol = nothing, maxtime = nothing,
-        termination_condition = nothing, internalnorm = L2_NORM,
-        linsolve_kwargs = (;), kwargs...) where {uType, iip}
-    autodiff = select_jacobian_autodiff(prob, alg.autodiff)
-    jvp_autodiff = if alg.jvp_autodiff === nothing && alg.autodiff !== nothing &&
-                      (ADTypes.mode(alg.autodiff) isa ADTypes.ForwardMode ||
-                       ADTypes.mode(alg.autodiff) isa ADTypes.ForwardOrReverseMode)
-        select_forward_mode_autodiff(prob, alg.autodiff)
-    else
-        select_forward_mode_autodiff(prob, alg.jvp_autodiff)
-    end
-    vjp_autodiff = if alg.vjp_autodiff === nothing && alg.autodiff !== nothing &&
-                      (ADTypes.mode(alg.autodiff) isa ADTypes.ReverseMode ||
-                       ADTypes.mode(alg.autodiff) isa ADTypes.ForwardOrReverseMode)
-        select_reverse_mode_autodiff(prob, alg.autodiff)
-    else
-        select_reverse_mode_autodiff(prob, alg.vjp_autodiff)
-    end
-
-    timer = get_timer_output()
-    @static_timeit timer "cache construction" begin
-        (; f, u0, p) = prob
-        u = __maybe_unaliased(u0, alias_u0)
-        fu = evaluate_f(prob, u)
-        @bb u_cache = copy(u)
-
-        linsolve = get_linear_solver(alg.descent)
-
-        abstol, reltol, termination_cache = NonlinearSolveBase.init_termination_cache(
-            prob, abstol, reltol, fu, u, termination_condition, Val(:regular))
-        linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
-
-        jac_cache = construct_jacobian_cache(
-            prob, alg, f, fu, u, p; stats, autodiff, linsolve, jvp_autodiff, vjp_autodiff)
-        J = jac_cache(nothing)
-
-        descent_cache = __internal_init(prob, alg.descent, J, fu, u; stats, abstol,
-            reltol, internalnorm, linsolve_kwargs, timer)
-        du = get_du(descent_cache)
-
-        has_linesearch = alg.linesearch !== missing && alg.linesearch !== nothing
-        has_trustregion = alg.trustregion !== missing && alg.trustregion !== nothing
-
-        if has_trustregion && has_linesearch
-            error("TrustRegion and LineSearch methods are algorithmically incompatible.")
-        end
-
-        GB = :None
-        linesearch_cache = nothing
-        trustregion_cache = nothing
-
-        if has_trustregion
-            supports_trust_region(alg.descent) || error("Trust Region not supported by \
-                                                        $(alg.descent).")
-            trustregion_cache = __internal_init(
-                prob, alg.trustregion, f, fu, u, p; stats, internalnorm, kwargs...,
-                autodiff, jvp_autodiff, vjp_autodiff)
-            GB = :TrustRegion
-        end
-
-        if has_linesearch
-            supports_line_search(alg.descent) || error("Line Search not supported by \
-                                                        $(alg.descent).")
-            linesearch_cache = init(
-                prob, alg.linesearch, fu, u; stats, autodiff = jvp_autodiff, kwargs...)
-            GB = :LineSearch
-        end
-
-        trace = init_nonlinearsolve_trace(
-            prob, alg, u, fu, ApplyArray(__zero, J), du; kwargs...)
-
-        return GeneralizedFirstOrderAlgorithmCache{iip, GB, maxtime !== nothing}(
-            fu, u, u_cache, p, du, J, alg, prob, jac_cache, descent_cache, linesearch_cache,
-            trustregion_cache, stats, 0, maxiters, maxtime, alg.max_shrink_times, timer,
-            0.0, true, termination_cache, trace, ReturnCode.Default, false, kwargs)
-    end
-end
-
-function __step!(cache::GeneralizedFirstOrderAlgorithmCache{iip, GB};
-        recompute_jacobian::Union{Nothing, Bool} = nothing, kwargs...) where {iip, GB}
-    @static_timeit cache.timer "jacobian" begin
-        if (recompute_jacobian === nothing || recompute_jacobian) && cache.make_new_jacobian
-            J = cache.jac_cache(cache.u)
-            new_jacobian = true
-        else
-            J = cache.jac_cache(nothing)
-            new_jacobian = false
-        end
-    end
-
-    @static_timeit cache.timer "descent" begin
-        if cache.trustregion_cache !== nothing &&
-           hasfield(typeof(cache.trustregion_cache), :trust_region)
-            descent_result = __internal_solve!(
-                cache.descent_cache, J, cache.fu, cache.u; new_jacobian,
-                trust_region = cache.trustregion_cache.trust_region, cache.kwargs...)
-        else
-            descent_result = __internal_solve!(
-                cache.descent_cache, J, cache.fu, cache.u; new_jacobian, cache.kwargs...)
-        end
-    end
-
-    if !descent_result.linsolve_success
-        if new_jacobian
-            # Jacobian Information is current and linear solve failed terminate the solve
-            cache.retcode = ReturnCode.InternalLinearSolveFailed
-            cache.force_stop = true
-            return
-        else
-            # Jacobian Information is not current and linear solve failed, recompute
-            # Jacobian
-            if !haskey(cache.kwargs, :verbose) || cache.kwargs[:verbose]
-                @warn "Linear Solve Failed but Jacobian Information is not current. \
-                       Retrying with updated Jacobian."
-            end
-            # In the 2nd call the `new_jacobian` is guaranteed to be `true`.
-            cache.make_new_jacobian = true
-            __step!(cache; recompute_jacobian = true, kwargs...)
-            return
-        end
-    end
-
-    δu, descent_intermediates = descent_result.δu, descent_result.extras
-
-    if descent_result.success
-        cache.make_new_jacobian = true
-        if GB === :LineSearch
-            @static_timeit cache.timer "linesearch" begin
-                linesearch_sol = solve!(cache.linesearch_cache, cache.u, δu)
-                linesearch_failed = !SciMLBase.successful_retcode(linesearch_sol.retcode)
-                α = linesearch_sol.step_size
-            end
-            if linesearch_failed
-                cache.retcode = ReturnCode.InternalLineSearchFailed
-                cache.force_stop = true
-            end
-            @static_timeit cache.timer "step" begin
-                @bb axpy!(α, δu, cache.u)
-                evaluate_f!(cache, cache.u, cache.p)
-            end
-        elseif GB === :TrustRegion
-            @static_timeit cache.timer "trustregion" begin
-                tr_accepted, u_new, fu_new = __internal_solve!(
-                    cache.trustregion_cache, J, cache.fu,
-                    cache.u, δu, descent_intermediates)
-                if tr_accepted
-                    @bb copyto!(cache.u, u_new)
-                    @bb copyto!(cache.fu, fu_new)
-                    α = true
-                else
-                    α = false
-                    cache.make_new_jacobian = false
-                end
-                if hasfield(typeof(cache.trustregion_cache), :shrink_counter) &&
-                   cache.trustregion_cache.shrink_counter > cache.max_shrink_times
-                    cache.retcode = ReturnCode.ShrinkThresholdExceeded
-                    cache.force_stop = true
-                end
-            end
-        elseif GB === :None
-            @static_timeit cache.timer "step" begin
-                @bb axpy!(1, δu, cache.u)
-                evaluate_f!(cache, cache.u, cache.p)
-            end
-            α = true
-        else
-            error("Unknown Globalization Strategy: $(GB). Allowed values are (:LineSearch, \
-                  :TrustRegion, :None)")
-        end
-        check_and_update!(cache, cache.fu, cache.u, cache.u_cache)
-    else
-        α = false
-        cache.make_new_jacobian = false
-    end
-
-    update_trace!(cache, α)
-    @bb copyto!(cache.u_cache, cache.u)
-
-    callback_into_cache!(cache)
-
-    return nothing
-end
diff --git a/src/core/generic.jl b/src/core/generic.jl
deleted file mode 100644
index df6f2ecff..000000000
--- a/src/core/generic.jl
+++ /dev/null
@@ -1,66 +0,0 @@
-function SciMLBase.__solve(prob::Union{NonlinearProblem, NonlinearLeastSquaresProblem},
-        alg::AbstractNonlinearSolveAlgorithm, args...; stats = empty_nlstats(), kwargs...)
-    cache = SciMLBase.__init(prob, alg, args...; stats, kwargs...)
-    return solve!(cache)
-end
-
-function not_terminated(cache::AbstractNonlinearSolveCache)
-    return !cache.force_stop && cache.nsteps < cache.maxiters
-end
-
-function SciMLBase.solve!(cache::AbstractNonlinearSolveCache)
-    while not_terminated(cache)
-        step!(cache)
-    end
-
-    # The solver might have set a different `retcode`
-    if cache.retcode == ReturnCode.Default
-        cache.retcode = ifelse(
-            cache.nsteps ≥ cache.maxiters, ReturnCode.MaxIters, ReturnCode.Success)
-    end
-
-    update_from_termination_cache!(cache.termination_cache, cache)
-
-    update_trace!(cache.trace, cache.nsteps, get_u(cache),
-        get_fu(cache), nothing, nothing, nothing; last = True)
-
-    return SciMLBase.build_solution(cache.prob, cache.alg, get_u(cache), get_fu(cache);
-        cache.retcode, cache.stats, cache.trace)
-end
-
-"""
-    step!(cache::AbstractNonlinearSolveCache;
-        recompute_jacobian::Union{Nothing, Bool} = nothing)
-
-Performs one step of the nonlinear solver.
-
-### Keyword Arguments
-
-  - `recompute_jacobian`: allows controlling whether the jacobian is recomputed at the
-    current step. If `nothing`, then the algorithm determines whether to recompute the
-    jacobian. If `true` or `false`, then the jacobian is recomputed or not recomputed,
-    respectively. For algorithms that don't use jacobian information, this keyword is
-    ignored with a one-time warning.
-"""
-function SciMLBase.step!(cache::AbstractNonlinearSolveCache{iip, timeit},
-        args...; kwargs...) where {iip, timeit}
-    not_terminated(cache) || return
-    timeit && (time_start = time())
-    res = @static_timeit cache.timer "solve" begin
-        __step!(cache, args...; kwargs...)
-    end
-
-    cache.stats.nsteps += 1
-    cache.nsteps += 1
-
-    if timeit
-        cache.total_time += time() - time_start
-        if !cache.force_stop && cache.retcode == ReturnCode.Default &&
-           cache.total_time ≥ cache.maxtime
-            cache.retcode = ReturnCode.MaxTime
-            cache.force_stop = true
-        end
-    end
-
-    return res
-end
diff --git a/src/core/noinit.jl b/src/core/noinit.jl
deleted file mode 100644
index b51c09c23..000000000
--- a/src/core/noinit.jl
+++ /dev/null
@@ -1,37 +0,0 @@
-# Some algorithms don't support creating a cache and doing `solve!`, this unfortunately
-# makes it difficult to write generic code that supports caching. For the algorithms that
-# don't have a `__init` function defined, we create a "Fake Cache", which just calls
-# `__solve` from `solve!`
-@concrete mutable struct NonlinearSolveNoInitCache{iip, timeit} <:
-                         AbstractNonlinearSolveCache{iip, timeit}
-    prob
-    alg
-    args
-    kwargs::Any
-end
-
-function SciMLBase.reinit!(
-        cache::NonlinearSolveNoInitCache, u0 = cache.prob.u0; p = cache.prob.p, kwargs...)
-    prob = remake(cache.prob; u0, p)
-    cache.prob = prob
-    cache.kwargs = merge(cache.kwargs, kwargs)
-    return cache
-end
-
-function Base.show(io::IO, cache::NonlinearSolveNoInitCache)
-    print(io, "NonlinearSolveNoInitCache(alg = $(cache.alg))")
-end
-
-function SciMLBase.__init(prob::AbstractNonlinearProblem{uType, iip},
-        alg::Union{AbstractNonlinearSolveAlgorithm,
-            SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm},
-        args...;
-        maxtime = nothing,
-        kwargs...) where {uType, iip}
-    return NonlinearSolveNoInitCache{iip, maxtime !== nothing}(
-        prob, alg, args, merge((; maxtime), kwargs))
-end
-
-function SciMLBase.solve!(cache::NonlinearSolveNoInitCache)
-    return solve(cache.prob, cache.alg, cache.args...; cache.kwargs...)
-end
diff --git a/src/utils.jl b/src/utils.jl
index cb346da0a..20602d2db 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -1,53 +1,3 @@
-# Helper  Functions
-@generated function __getproperty(s::S, ::Val{X}) where {S, X}
-    hasfield(S, X) && return :(s.$X)
-    return :(missing)
-end
-
-@inline @generated function _vec(v)
-    hasmethod(vec, Tuple{typeof(v)}) || return :(vec(v))
-    return :(v)
-end
-@inline _vec(v::Number) = v
-@inline _vec(v::AbstractVector) = v
-
-@inline _restructure(y, x) = restructure(y, x)
-@inline _restructure(y::Number, x::Number) = x
-
-@inline __maybe_unaliased(x::Union{Number, SArray}, ::Bool) = x
-@inline function __maybe_unaliased(x::AbstractArray, alias::Bool)
-    # Spend time coping iff we will mutate the array
-    (alias || !__can_setindex(typeof(x))) && return x
-    return deepcopy(x)
-end
-@inline __maybe_unaliased(x::AbstractSciMLOperator, ::Bool) = x
-
-@inline __copy(x::AbstractArray) = copy(x)
-@inline __copy(x::Number) = x
-@inline __copy(x) = x
-
-# LazyArrays for tracing
-__zero(x::AbstractArray) = zero(x)
-__zero(x) = x
-LazyArrays.applied_eltype(::typeof(__zero), x) = eltype(x)
-LazyArrays.applied_ndims(::typeof(__zero), x) = ndims(x)
-LazyArrays.applied_size(::typeof(__zero), x) = size(x)
-LazyArrays.applied_axes(::typeof(__zero), x) = axes(x)
-
-# Use Symmetric Matrices if known to be efficient
-@inline __maybe_symmetric(x) = Symmetric(x)
-@inline __maybe_symmetric(x::Number) = x
-## LinearSolve with `nothing` doesn't dispatch correctly here
-@inline __maybe_symmetric(x::StaticArray) = x
-@inline __maybe_symmetric(x::AbstractSparseMatrix) = x
-@inline __maybe_symmetric(x::AbstractSciMLOperator) = x
-
-# Simple Checks
-@inline __is_present(::Nothing) = false
-@inline __is_present(::Missing) = false
-@inline __is_present(::Any) = true
-@inline __is_present(::NoLineSearch) = false
-
 @inline __is_complex(::Type{ComplexF64}) = true
 @inline __is_complex(::Type{ComplexF32}) = true
 @inline __is_complex(::Type{Complex}) = true
@@ -76,10 +26,6 @@ end
     return fx_idx, idx
 end
 
-@inline __can_setindex(x) = can_setindex(x)
-@inline __can_setindex(::Number) = false
-
-@inline __dot(x, y) = dot(_vec(x), _vec(y))
 
 """
     pickchunksize(x) = pickchunksize(length(x))

From 21ffb2240e60afebac95eae8afa98b2ea0d2b4fd Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 28 Oct 2024 01:26:02 -0400
Subject: [PATCH 643/700] chore: run formatter

---
 lib/NonlinearSolveBase/src/abstract_types.jl                | 3 ++-
 lib/NonlinearSolveFirstOrder/src/gauss_newton.jl            | 1 +
 lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl     | 1 +
 lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl        | 1 +
 lib/NonlinearSolveFirstOrder/src/raphson.jl                 | 1 +
 lib/NonlinearSolveFirstOrder/src/trust_region.jl            | 1 +
 .../src/NonlinearSolveQuasiNewton.jl                        | 2 +-
 lib/NonlinearSolveQuasiNewton/src/broyden.jl                | 6 ++++--
 lib/NonlinearSolveQuasiNewton/src/structure.jl              | 2 +-
 src/utils.jl                                                | 1 -
 10 files changed, 13 insertions(+), 6 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index a01aa7afb..3cdb59a1d 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -576,7 +576,8 @@ macro internal_caches(cType, internal_cache_names...)
             $(callbacks_self...)
             return
         end
-        function NonlinearSolveBase.InternalAPI.reinit!(cache::$(cType), args...; kwargs...)
+        function NonlinearSolveBase.InternalAPI.reinit!(
+                cache::$(cType), args...; kwargs...)
             $(reinit_caches...)
             $(InternalAPI.reinit_self!)(cache, args...; kwargs...)
             return
diff --git a/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl b/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl
index e69de29bb..8b1378917 100644
--- a/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl
+++ b/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl
@@ -0,0 +1 @@
+
diff --git a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
index e69de29bb..8b1378917 100644
--- a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
+++ b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
@@ -0,0 +1 @@
+
diff --git a/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl b/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
index e69de29bb..8b1378917 100644
--- a/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
+++ b/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
@@ -0,0 +1 @@
+
diff --git a/lib/NonlinearSolveFirstOrder/src/raphson.jl b/lib/NonlinearSolveFirstOrder/src/raphson.jl
index e69de29bb..8b1378917 100644
--- a/lib/NonlinearSolveFirstOrder/src/raphson.jl
+++ b/lib/NonlinearSolveFirstOrder/src/raphson.jl
@@ -0,0 +1 @@
+
diff --git a/lib/NonlinearSolveFirstOrder/src/trust_region.jl b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
index e69de29bb..8b1378917 100644
--- a/lib/NonlinearSolveFirstOrder/src/trust_region.jl
+++ b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
@@ -0,0 +1 @@
+
diff --git a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
index 7068ebc60..aace3b0e8 100644
--- a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
@@ -7,7 +7,7 @@ using ArrayInterface: ArrayInterface
 using CommonSolve: CommonSolve
 using ConcreteStructs: @concrete
 using DiffEqBase: DiffEqBase   # Needed for `init` / `solve` dispatches
-using LinearAlgebra: LinearAlgebra, Diagonal, dot, inv, diag
+using LinearAlgebra: LinearAlgebra, Diagonal, dot, diag
 using LinearSolve: LinearSolve # Trigger Linear Solve extension in NonlinearSolveBase
 using MaybeInplace: @bb
 using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
diff --git a/lib/NonlinearSolveQuasiNewton/src/broyden.jl b/lib/NonlinearSolveQuasiNewton/src/broyden.jl
index 60adc9be5..08570a735 100644
--- a/lib/NonlinearSolveQuasiNewton/src/broyden.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/broyden.jl
@@ -150,11 +150,13 @@ function InternalAPI.solve!(
     if cache.rule isa GoodBroydenUpdateRule
         @bb @. J⁻¹_diag = J⁻¹_diag * cache.dfu * du
         denom = sum(J⁻¹_diag)
-        @bb @. J⁻¹_diag = J⁻¹_diag + (du - J⁻¹_diag * cache.dfu) * du * J⁻¹_diag /
+        @bb @. J⁻¹_diag = J⁻¹_diag +
+                          (du - J⁻¹_diag * cache.dfu) * du * J⁻¹_diag /
                           ifelse(iszero(denom), T(1e-5), denom)
     else
         denom = cache.internalnorm(cache.dfu)^2
-        @bb @. J⁻¹_diag = J⁻¹_diag + (du - J⁻¹_diag * cache.dfu) * cache.dfu /
+        @bb @. J⁻¹_diag = J⁻¹_diag +
+                          (du - J⁻¹_diag * cache.dfu) * cache.dfu /
                           ifelse(iszero(denom), T(1e-5), denom)
     end
     @bb copyto!(cache.dfu, fu)
diff --git a/lib/NonlinearSolveQuasiNewton/src/structure.jl b/lib/NonlinearSolveQuasiNewton/src/structure.jl
index 2d5c0baa5..09438289b 100644
--- a/lib/NonlinearSolveQuasiNewton/src/structure.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/structure.jl
@@ -11,7 +11,7 @@ function NonlinearSolveBase.get_full_jacobian(cache, ::DiagonalStructure, J)
 end
 
 function (::DiagonalStructure)(J::AbstractMatrix; alias::Bool = false)
-    @assert size(J, 1) == size(J, 2) "Diagonal Jacobian Structure must be square!"
+    @assert size(J, 1)==size(J, 2) "Diagonal Jacobian Structure must be square!"
     return LinearAlgebra.diag(J)
 end
 (::DiagonalStructure)(J::AbstractVector; alias::Bool = false) = alias ? J : @bb(copy(J))
diff --git a/src/utils.jl b/src/utils.jl
index 20602d2db..0a2375ef9 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -26,7 +26,6 @@ end
     return fx_idx, idx
 end
 
-
 """
     pickchunksize(x) = pickchunksize(length(x))
     pickchunksize(x::Int)

From 196adbbf5210adfa24ec3b2a837d2caee4cd445e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 28 Oct 2024 17:04:45 -0400
Subject: [PATCH 644/700] refactor: move algorithms to First Order sub-package

---
 lib/NonlinearSolveFirstOrder/Project.toml     |  38 ++
 .../src/NonlinearSolveFirstOrder.jl           |  12 +-
 .../src/gauss_newton.jl                       |  21 +
 .../src/pseudo_transient.jl                   |  89 ++++
 lib/NonlinearSolveFirstOrder/src/raphson.jl   |  21 +
 lib/NonlinearSolveFirstOrder/src/solve.jl     | 387 +++++++++---------
 src/algorithms/gauss_newton.jl                |  15 -
 src/algorithms/pseudo_transient.jl            |  72 ----
 src/algorithms/raphson.jl                     |  15 -
 9 files changed, 380 insertions(+), 290 deletions(-)
 delete mode 100644 src/algorithms/gauss_newton.jl
 delete mode 100644 src/algorithms/pseudo_transient.jl
 delete mode 100644 src/algorithms/raphson.jl

diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
index 21177218a..b29ae474b 100644
--- a/lib/NonlinearSolveFirstOrder/Project.toml
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -3,15 +3,53 @@ uuid = "5959db7a-ea39-4486-b5fe-2dd0bf03d60d"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
 version = "1.0.0"
 
+[deps]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
+ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
+ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
+DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
+MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
+NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
+PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
+Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
+Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
+StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+
 [compat]
+ADTypes = "1.9.0"
 Aqua = "0.8"
+ArrayInterface = "7.16.0"
+CommonSolve = "0.2.4"
+ConcreteStructs = "0.2.3"
+DiffEqBase = "6.155.3"
 ExplicitImports = "1.5"
+FiniteDiff = "2.26.0"
+ForwardDiff = "0.10.36"
 Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
+LineSearch = "0.1.4"
+LinearAlgebra = "1.11.0"
+LinearSolve = "2.36.1"
+MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
+NonlinearSolveBase = "1.1"
 Pkg = "1.10"
+PrecompileTools = "1.2"
 ReTestItems = "1.24"
+Reexport = "1"
+SciMLBase = "2.54"
+SciMLOperators = "0.3.11"
+Setfield = "1.1.1"
 StableRNGs = "1"
+StaticArraysCore = "1.4.3"
 Test = "1.10"
 julia = "1.10"
 
diff --git a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
index 2cf9560e3..f1c767755 100644
--- a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
+++ b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
@@ -3,12 +3,15 @@ module NonlinearSolveFirstOrder
 using Reexport: @reexport
 using PrecompileTools: @compile_workload, @setup_workload
 
+using ADTypes: ADTypes
 using ArrayInterface: ArrayInterface
 using CommonSolve: CommonSolve
 using ConcreteStructs: @concrete
-using DiffEqBase: DiffEqBase   # Needed for `init` / `solve` dispatches
+using DiffEqBase: DiffEqBase    # Needed for `init` / `solve` dispatches
+using FiniteDiff: FiniteDiff    # Default Finite Difference Method
+using ForwardDiff: ForwardDiff  # Default Forward Mode AD
 using LinearAlgebra: LinearAlgebra, Diagonal, dot, inv, diag
-using LinearSolve: LinearSolve # Trigger Linear Solve extension in NonlinearSolveBase
+using LinearSolve: LinearSolve  # Trigger Linear Solve extension in NonlinearSolveBase
 using MaybeInplace: @bb
 using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
                           AbstractNonlinearSolveCache, AbstractResetCondition,
@@ -16,10 +19,13 @@ using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
                           AbstractJacobianCache, AbstractJacobianInitialization,
                           AbstractApproximateJacobianUpdateRule, AbstractDescentDirection,
                           AbstractApproximateJacobianUpdateRuleCache,
+                          AbstractDampingFunction, AbstractDampingFunctionCache,
                           Utils, InternalAPI, get_timer_output, @static_timeit,
-                          update_trace!, L2_NORM, NewtonDescent
+                          update_trace!, L2_NORM,
+                          NewtonDescent, DampedNewtonDescent
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode
 using SciMLOperators: AbstractSciMLOperator
+using Setfield: @set!
 using StaticArraysCore: StaticArray, Size, MArray
 
 include("raphson.jl")
diff --git a/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl b/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl
index 8b1378917..59b90b76e 100644
--- a/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl
+++ b/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl
@@ -1 +1,22 @@
+"""
+    GaussNewton(;
+        concrete_jac = nothing, linsolve = nothing, linesearch = missing, precs = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+    )
 
+An advanced GaussNewton implementation with support for efficient handling of sparse
+matrices via colored automatic differentiation and preconditioned linear solvers. Designed
+for large-scale and numerically-difficult nonlinear systems.
+"""
+function GaussNewton(;
+        concrete_jac = nothing, linsolve = nothing, linesearch = missing, precs = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+)
+    return GeneralizedFirstOrderAlgorithm(;
+        linesearch,
+        descent = NewtonDescent(; linsolve, precs),
+        autodiff, vjp_autodiff, jvp_autodiff,
+        concrete_jac,
+        name = :GaussNewton
+    )
+end
diff --git a/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl b/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
index 8b1378917..156435859 100644
--- a/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
+++ b/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
@@ -1 +1,90 @@
+"""
+    PseudoTransient(;
+        concrete_jac = nothing, linesearch = missing, alpha_initial = 1e-3,
+        linsolve = nothing, precs = nothing,
+        autodiff = nothing, jvp_autodiff = nothing, vjp_autodiff = nothing
+    )
 
+An implementation of PseudoTransient Method [coffey2003pseudotransient](@cite) that is used
+to solve steady state problems in an accelerated manner. It uses an adaptive time-stepping
+to integrate an initial value of nonlinear problem until sufficient accuracy in the desired
+steady-state is achieved to switch over to Newton's method and gain a rapid convergence.
+This implementation specifically uses "switched evolution relaxation"
+[kelley1998convergence](@cite) SER method.
+
+### Keyword Arguments
+
+  - `alpha_initial` : the initial pseudo time step. It defaults to `1e-3`. If it is small,
+    you are going to need more iterations to converge but it can be more stable.
+"""
+function PseudoTransient(;
+        concrete_jac = nothing, linesearch = missing, alpha_initial = 1e-3,
+        linsolve = nothing, precs = nothing,
+        autodiff = nothing, jvp_autodiff = nothing, vjp_autodiff = nothing
+)
+    return GeneralizedFirstOrderAlgorithm(;
+        linesearch,
+        descent = DampedNewtonDescent(;
+            linsolve, precs, initial_damping = alpha_initial,
+            damping_fn = SwitchedEvolutionRelaxation()
+        ),
+        autodiff,
+        jvp_autodiff,
+        vjp_autodiff,
+        concrete_jac,
+        name = :PseudoTransient
+    )
+end
+
+"""
+    SwitchedEvolutionRelaxation()
+
+Method for updating the damping parameter in the [`PseudoTransient`](@ref) method based on
+"switched evolution relaxation" [kelley1998convergence](@cite) SER method.
+"""
+struct SwitchedEvolutionRelaxation <: AbstractDampingFunction end
+
+"""
+    SwitchedEvolutionRelaxationCache <: AbstractDampingFunctionCache
+
+Cache for the [`SwitchedEvolutionRelaxation`](@ref) method.
+"""
+@concrete mutable struct SwitchedEvolutionRelaxationCache <: AbstractDampingFunctionCache
+    res_norm
+    α⁻¹
+    internalnorm
+end
+
+function NonlinearSolveBase.requires_normal_form_jacobian(::Union{
+        SwitchedEvolutionRelaxation, SwitchedEvolutionRelaxationCache})
+    return false
+end
+
+function NonlinearSolveBase.requires_normal_form_rhs(::Union{
+        SwitchedEvolutionRelaxation, SwitchedEvolutionRelaxationCache})
+    return false
+end
+
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, f::SwitchedEvolutionRelaxation,
+        initial_damping, J, fu, u, args...;
+        internalnorm::F = L2_NORM, kwargs...
+) where {F}
+    T = promote_type(eltype(u), eltype(fu))
+    return SwitchedEvolutionRelaxationCache(
+        internalnorm(fu),
+        T(inv(initial_damping)),
+        internalnorm
+    )
+end
+
+(damping::SwitchedEvolutionRelaxationCache)(::Nothing) = damping.α⁻¹
+
+function InternalAPI.solve!(
+        damping::SwitchedEvolutionRelaxationCache, J, fu, args...; kwargs...
+)
+    res_norm = damping.internalnorm(fu)
+    damping.α⁻¹ *= res_norm / damping.res_norm
+    damping.res_norm = res_norm
+    return damping.α⁻¹
+end
diff --git a/lib/NonlinearSolveFirstOrder/src/raphson.jl b/lib/NonlinearSolveFirstOrder/src/raphson.jl
index 8b1378917..5c14f10b7 100644
--- a/lib/NonlinearSolveFirstOrder/src/raphson.jl
+++ b/lib/NonlinearSolveFirstOrder/src/raphson.jl
@@ -1 +1,22 @@
+"""
+    NewtonRaphson(;
+        concrete_jac = nothing, linsolve = nothing, linesearch = missing, precs = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+    )
 
+An advanced NewtonRaphson implementation with support for efficient handling of sparse
+matrices via colored automatic differentiation and preconditioned linear solvers. Designed
+for large-scale and numerically-difficult nonlinear systems.
+"""
+function NewtonRaphson(;
+        concrete_jac = nothing, linsolve = nothing, linesearch = missing, precs = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+)
+    return GeneralizedFirstOrderAlgorithm(;
+        linesearch,
+        descent = NewtonDescent(; linsolve, precs),
+        autodiff, vjp_autodiff, jvp_autodiff,
+        concrete_jac,
+        name = :NewtonRaphson
+    )
+end
diff --git a/lib/NonlinearSolveFirstOrder/src/solve.jl b/lib/NonlinearSolveFirstOrder/src/solve.jl
index 0d60aa3d7..8d61ddceb 100644
--- a/lib/NonlinearSolveFirstOrder/src/solve.jl
+++ b/lib/NonlinearSolveFirstOrder/src/solve.jl
@@ -38,7 +38,10 @@ end
 function GeneralizedFirstOrderAlgorithm(;
         descent, linesearch = missing, trustregion = missing, autodiff = nothing,
         vjp_autodiff = nothing, jvp_autodiff = nothing, max_shrink_times::Int = typemax(Int),
-        concrete_jac = Val(false), name::Symbol = :unknown)
+        concrete_jac = Val(false), name::Symbol = :unknown
+)
+    concrete_jac = concrete_jac isa Bool ? Val(concrete_jac) :
+                   (concrete_jac isa Val ? concrete_jac : Val(concrete_jac !== nothing))
     return GeneralizedFirstOrderAlgorithm(
         linesearch, trustregion, descent, max_shrink_times,
         autodiff, vjp_autodiff, jvp_autodiff,
@@ -116,188 +119,202 @@ end
 NonlinearSolveBase.@internal_caches(GeneralizedFirstOrderAlgorithmCache,
     :jac_cache, :descent_cache, :linesearch_cache, :trustregion_cache)
 
-# function SciMLBase.__init(
-#         prob::AbstractNonlinearProblem{uType, iip}, alg::GeneralizedFirstOrderAlgorithm,
-#         args...; stats = empty_nlstats(), alias_u0 = false, maxiters = 1000,
-#         abstol = nothing, reltol = nothing, maxtime = nothing,
-#         termination_condition = nothing, internalnorm = L2_NORM,
-#         linsolve_kwargs = (;), kwargs...) where {uType, iip}
-#     autodiff = select_jacobian_autodiff(prob, alg.autodiff)
-#     jvp_autodiff = if alg.jvp_autodiff === nothing && alg.autodiff !== nothing &&
-#                       (ADTypes.mode(alg.autodiff) isa ADTypes.ForwardMode ||
-#                        ADTypes.mode(alg.autodiff) isa ADTypes.ForwardOrReverseMode)
-#         select_forward_mode_autodiff(prob, alg.autodiff)
-#     else
-#         select_forward_mode_autodiff(prob, alg.jvp_autodiff)
-#     end
-#     vjp_autodiff = if alg.vjp_autodiff === nothing && alg.autodiff !== nothing &&
-#                       (ADTypes.mode(alg.autodiff) isa ADTypes.ReverseMode ||
-#                        ADTypes.mode(alg.autodiff) isa ADTypes.ForwardOrReverseMode)
-#         select_reverse_mode_autodiff(prob, alg.autodiff)
-#     else
-#         select_reverse_mode_autodiff(prob, alg.vjp_autodiff)
-#     end
-
-#     timer = get_timer_output()
-#     @static_timeit timer "cache construction" begin
-#         (; f, u0, p) = prob
-#         u = __maybe_unaliased(u0, alias_u0)
-#         fu = evaluate_f(prob, u)
-#         @bb u_cache = copy(u)
-
-#         linsolve = get_linear_solver(alg.descent)
-
-#         abstol, reltol, termination_cache = NonlinearSolveBase.init_termination_cache(
-#             prob, abstol, reltol, fu, u, termination_condition, Val(:regular))
-#         linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
-
-#         jac_cache = construct_jacobian_cache(
-#             prob, alg, f, fu, u, p; stats, autodiff, linsolve, jvp_autodiff, vjp_autodiff)
-#         J = jac_cache(nothing)
-
-#         descent_cache = __internal_init(prob, alg.descent, J, fu, u; stats, abstol,
-#             reltol, internalnorm, linsolve_kwargs, timer)
-#         du = get_du(descent_cache)
-
-#         has_linesearch = alg.linesearch !== missing && alg.linesearch !== nothing
-#         has_trustregion = alg.trustregion !== missing && alg.trustregion !== nothing
-
-#         if has_trustregion && has_linesearch
-#             error("TrustRegion and LineSearch methods are algorithmically incompatible.")
-#         end
-
-#         GB = :None
-#         linesearch_cache = nothing
-#         trustregion_cache = nothing
-
-#         if has_trustregion
-#             supports_trust_region(alg.descent) || error("Trust Region not supported by \
-#                                                $(alg.descent).")
-#             trustregion_cache = __internal_init(
-#                 prob, alg.trustregion, f, fu, u, p; stats, internalnorm, kwargs...,
-#                 autodiff, jvp_autodiff, vjp_autodiff)
-#             GB = :TrustRegion
-#         end
-
-#         if has_linesearch
-#             supports_line_search(alg.descent) || error("Line Search not supported by \
-#                                                $(alg.descent).")
-#             linesearch_cache = init(
-#                 prob, alg.linesearch, fu, u; stats, autodiff = jvp_autodiff, kwargs...)
-#             GB = :LineSearch
-#         end
-
-#         trace = init_nonlinearsolve_trace(
-#             prob, alg, u, fu, ApplyArray(__zero, J), du; kwargs...)
-
-#         return GeneralizedFirstOrderAlgorithmCache{iip, GB, maxtime !== nothing}(
-#             fu, u, u_cache, p, du, J, alg, prob, jac_cache, descent_cache, linesearch_cache,
-#             trustregion_cache, stats, 0, maxiters, maxtime, alg.max_shrink_times, timer,
-#             0.0, true, termination_cache, trace, ReturnCode.Default, false, kwargs)
-#     end
-# end
-
-# function __step!(cache::GeneralizedFirstOrderAlgorithmCache{iip, GB};
-#         recompute_jacobian::Union{Nothing, Bool} = nothing, kwargs...) where {iip, GB}
-#     @static_timeit cache.timer "jacobian" begin
-#         if (recompute_jacobian === nothing || recompute_jacobian) && cache.make_new_jacobian
-#             J = cache.jac_cache(cache.u)
-#             new_jacobian = true
-#         else
-#             J = cache.jac_cache(nothing)
-#             new_jacobian = false
-#         end
-#     end
-
-#     @static_timeit cache.timer "descent" begin
-#         if cache.trustregion_cache !== nothing &&
-#            hasfield(typeof(cache.trustregion_cache), :trust_region)
-#             descent_result = __internal_solve!(
-#                 cache.descent_cache, J, cache.fu, cache.u; new_jacobian,
-#                 trust_region = cache.trustregion_cache.trust_region, cache.kwargs...)
-#         else
-#             descent_result = __internal_solve!(
-#                 cache.descent_cache, J, cache.fu, cache.u; new_jacobian, cache.kwargs...)
-#         end
-#     end
-
-#     if !descent_result.linsolve_success
-#         if new_jacobian
-#             # Jacobian Information is current and linear solve failed terminate the solve
-#             cache.retcode = ReturnCode.InternalLinearSolveFailed
-#             cache.force_stop = true
-#             return
-#         else
-#             # Jacobian Information is not current and linear solve failed, recompute
-#             # Jacobian
-#             if !haskey(cache.kwargs, :verbose) || cache.kwargs[:verbose]
-#                 @warn "Linear Solve Failed but Jacobian Information is not current. \
-#                   Retrying with updated Jacobian."
-#             end
-#             # In the 2nd call the `new_jacobian` is guaranteed to be `true`.
-#             cache.make_new_jacobian = true
-#             __step!(cache; recompute_jacobian = true, kwargs...)
-#             return
-#         end
-#     end
-
-#     δu, descent_intermediates = descent_result.δu, descent_result.extras
-
-#     if descent_result.success
-#         cache.make_new_jacobian = true
-#         if GB === :LineSearch
-#             @static_timeit cache.timer "linesearch" begin
-#                 linesearch_sol = solve!(cache.linesearch_cache, cache.u, δu)
-#                 linesearch_failed = !SciMLBase.successful_retcode(linesearch_sol.retcode)
-#                 α = linesearch_sol.step_size
-#             end
-#             if linesearch_failed
-#                 cache.retcode = ReturnCode.InternalLineSearchFailed
-#                 cache.force_stop = true
-#             end
-#             @static_timeit cache.timer "step" begin
-#                 @bb axpy!(α, δu, cache.u)
-#                 evaluate_f!(cache, cache.u, cache.p)
-#             end
-#         elseif GB === :TrustRegion
-#             @static_timeit cache.timer "trustregion" begin
-#                 tr_accepted, u_new, fu_new = __internal_solve!(
-#                     cache.trustregion_cache, J, cache.fu,
-#                     cache.u, δu, descent_intermediates)
-#                 if tr_accepted
-#                     @bb copyto!(cache.u, u_new)
-#                     @bb copyto!(cache.fu, fu_new)
-#                     α = true
-#                 else
-#                     α = false
-#                     cache.make_new_jacobian = false
-#                 end
-#                 if hasfield(typeof(cache.trustregion_cache), :shrink_counter) &&
-#                    cache.trustregion_cache.shrink_counter > cache.max_shrink_times
-#                     cache.retcode = ReturnCode.ShrinkThresholdExceeded
-#                     cache.force_stop = true
-#                 end
-#             end
-#         elseif GB === :None
-#             @static_timeit cache.timer "step" begin
-#                 @bb axpy!(1, δu, cache.u)
-#                 evaluate_f!(cache, cache.u, cache.p)
-#             end
-#             α = true
-#         else
-#             error("Unknown Globalization Strategy: $(GB). Allowed values are (:LineSearch, \
-#             :TrustRegion, :None)")
-#         end
-#         check_and_update!(cache, cache.fu, cache.u, cache.u_cache)
-#     else
-#         α = false
-#         cache.make_new_jacobian = false
-#     end
-
-#     update_trace!(cache, α)
-#     @bb copyto!(cache.u_cache, cache.u)
-
-#     callback_into_cache!(cache)
+function SciMLBase.__init(
+        prob::AbstractNonlinearProblem, alg::GeneralizedFirstOrderAlgorithm,
+        args...; stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, maxiters = 1000,
+        abstol = nothing, reltol = nothing, maxtime = nothing,
+        termination_condition = nothing, internalnorm = L2_NORM,
+        linsolve_kwargs = (;), kwargs...
+)
+    @set! alg.autodiff = NonlinearSolveBase.select_jacobian_autodiff(prob, alg.autodiff)
+    @set! alg.jvp_autodiff = if alg.jvp_autodiff === nothing && alg.autodiff !== nothing &&
+                                (ADTypes.mode(alg.autodiff) isa ADTypes.ForwardMode ||
+                                 ADTypes.mode(alg.autodiff) isa
+                                 ADTypes.ForwardOrReverseMode)
+        NonlinearSolveBase.select_forward_mode_autodiff(prob, alg.autodiff)
+    else
+        NonlinearSolveBase.select_forward_mode_autodiff(prob, alg.jvp_autodiff)
+    end
+    @set! alg.vjp_autodiff = if alg.vjp_autodiff === nothing && alg.autodiff !== nothing &&
+                                (ADTypes.mode(alg.autodiff) isa ADTypes.ReverseMode ||
+                                 ADTypes.mode(alg.autodiff) isa
+                                 ADTypes.ForwardOrReverseMode)
+        NonlinearSolveBase.select_reverse_mode_autodiff(prob, alg.autodiff)
+    else
+        NonlinearSolveBase.select_reverse_mode_autodiff(prob, alg.vjp_autodiff)
+    end
+
+    timer = get_timer_output()
+    @static_timeit timer "cache construction" begin
+        u = Utils.maybe_unaliased(prob.u0, alias_u0)
+        fu = Utils.evaluate_f(prob, u)
+        @bb u_cache = copy(u)
+
+        linsolve = NonlinearSolveBase.get_linear_solver(alg.descent)
+
+        abstol, reltol, termination_cache = NonlinearSolveBase.init_termination_cache(
+            prob, abstol, reltol, fu, u, termination_condition, Val(:regular)
+        )
+        linsolve_kwargs = merge((; abstol, reltol), linsolve_kwargs)
+
+        jac_cache = NonlinearSolveBase.construct_jacobian_cache(
+            prob, alg, prob.f, fu, u, prob.p;
+            stats, alg.autodiff, linsolve, alg.jvp_autodiff, alg.vjp_autodiff
+        )
+        J = jac_cache(nothing)
+
+        descent_cache = InternalAPI.init(
+            prob, alg.descent, J, fu, u; stats, abstol, reltol, internalnorm,
+            linsolve_kwargs, timer
+        )
+        du = SciMLBase.get_du(descent_cache)
+
+        has_linesearch = alg.linesearch !== missing && alg.linesearch !== nothing
+        has_trustregion = alg.trustregion !== missing && alg.trustregion !== nothing
+
+        if has_trustregion && has_linesearch
+            error("TrustRegion and LineSearch methods are algorithmically incompatible.")
+        end
+
+        globalization = Val(:None)
+        linesearch_cache = nothing
+        trustregion_cache = nothing
+
+        if has_trustregion
+            NonlinearSolveBase.supports_trust_region(alg.descent) ||
+                error("Trust Region not supported by $(alg.descent).")
+            trustregion_cache = InternalAPI.init(
+                prob, alg.trustregion, f, fu, u, p; stats, internalnorm, kwargs...
+            )
+            globalization = Val(:TrustRegion)
+        end
+
+        if has_linesearch
+            NonlinearSolveBase.supports_line_search(alg.descent) ||
+                error("Line Search not supported by $(alg.descent).")
+            linesearch_cache = CommonSolve.init(
+                prob, alg.linesearch, fu, u; stats, internalnorm, kwargs...
+            )
+            globalization = Val(:LineSearch)
+        end
+
+        trace = NonlinearSolveBase.init_nonlinearsolve_trace(
+            prob, alg, u, fu, J, du; kwargs...
+        )
+
+        return GeneralizedFirstOrderAlgorithmCache(
+            fu, u, u_cache, prob.p, du, J, alg, prob, globalization,
+            jac_cache, descent_cache, linesearch_cache, trustregion_cache,
+            stats, 0, maxiters, maxtime, alg.max_shrink_times, timer,
+            0.0, true, termination_cache, trace, ReturnCode.Default, false, kwargs
+        )
+    end
+end
 
-#     return nothing
-# end
+function InternalAPI.step!(
+        cache::GeneralizedFirstOrderAlgorithmCache;
+        recompute_jacobian::Union{Nothing, Bool} = nothing
+)
+    @static_timeit cache.timer "jacobian" begin
+        if (recompute_jacobian === nothing || recompute_jacobian) && cache.make_new_jacobian
+            J = cache.jac_cache(cache.u)
+            new_jacobian = true
+        else
+            J = cache.jac_cache(nothing)
+            new_jacobian = false
+        end
+    end
+
+    @static_timeit cache.timer "descent" begin
+        if cache.trustregion_cache !== nothing &&
+           hasfield(typeof(cache.trustregion_cache), :trust_region)
+            descent_result = InternalAPI.solve!(
+                cache.descent_cache, J, cache.fu, cache.u;
+                new_jacobian, cache.trustregion_cache.trust_region, cache.kwargs...
+            )
+        else
+            descent_result = InternalAPI.solve!(
+                cache.descent_cache, J, cache.fu, cache.u; new_jacobian, cache.kwargs...
+            )
+        end
+    end
+
+    if !descent_result.linsolve_success
+        if new_jacobian
+            # Jacobian Information is current and linear solve failed terminate the solve
+            cache.retcode = ReturnCode.InternalLinearSolveFailed
+            cache.force_stop = true
+            return
+        else
+            # Jacobian Information is not current and linear solve failed, recompute it
+            if !haskey(cache.kwargs, :verbose) || cache.kwargs[:verbose]
+                @warn "Linear Solve Failed but Jacobian Information is not current. \
+                       Retrying with updated Jacobian."
+            end
+            # In the 2nd call the `new_jacobian` is guaranteed to be `true`.
+            cache.make_new_jacobian = true
+            InternalAPI.step!(cache; recompute_jacobian = true, kwargs...)
+            return
+        end
+    end
+
+    δu, descent_intermediates = descent_result.δu, descent_result.extras
+
+    if descent_result.success
+        cache.make_new_jacobian = true
+        if cache.globalization isa Val{:LineSearch}
+            @static_timeit cache.timer "linesearch" begin
+                linesearch_sol = CommonSolve.solve!(cache.linesearch_cache, cache.u, δu)
+                linesearch_failed = !SciMLBase.successful_retcode(linesearch_sol.retcode)
+                α = linesearch_sol.step_size
+            end
+            if linesearch_failed
+                cache.retcode = ReturnCode.InternalLineSearchFailed
+                cache.force_stop = true
+            end
+            @static_timeit cache.timer "step" begin
+                @bb axpy!(α, δu, cache.u)
+                Utils.evaluate_f!(cache, cache.u, cache.p)
+            end
+        elseif cache.globalization isa Val{:TrustRegion}
+            @static_timeit cache.timer "trustregion" begin
+                tr_accepted, u_new, fu_new = InternalAPI.solve!(
+                    cache.trustregion_cache, J, cache.fu, cache.u, δu, descent_intermediates
+                )
+                if tr_accepted
+                    @bb copyto!(cache.u, u_new)
+                    @bb copyto!(cache.fu, fu_new)
+                    α = true
+                else
+                    α = false
+                    cache.make_new_jacobian = false
+                end
+                if hasfield(typeof(cache.trustregion_cache), :shrink_counter) &&
+                   cache.trustregion_cache.shrink_counter > cache.max_shrink_times
+                    cache.retcode = ReturnCode.ShrinkThresholdExceeded
+                    cache.force_stop = true
+                end
+            end
+        elseif cache.globalization isa Val{:None}
+            @static_timeit cache.timer "step" begin
+                @bb axpy!(1, δu, cache.u)
+                Utils.evaluate_f!(cache, cache.u, cache.p)
+            end
+            α = true
+        else
+            error("Unknown Globalization Strategy: $(cache.globalization). Allowed values \
+                   are (:LineSearch, :TrustRegion, :None)")
+        end
+        NonlinearSolveBase.check_and_update!(cache, cache.fu, cache.u, cache.u_cache)
+    else
+        α = false
+        cache.make_new_jacobian = false
+    end
+
+    update_trace!(cache, α)
+    @bb copyto!(cache.u_cache, cache.u)
+
+    NonlinearSolveBase.callback_into_cache!(cache)
+
+    return nothing
+end
diff --git a/src/algorithms/gauss_newton.jl b/src/algorithms/gauss_newton.jl
deleted file mode 100644
index 0266ee6ed..000000000
--- a/src/algorithms/gauss_newton.jl
+++ /dev/null
@@ -1,15 +0,0 @@
-"""
-    GaussNewton(; concrete_jac = nothing, linsolve = nothing, precs = nothing,
-        linesearch = nothing, vjp_autodiff = nothing, autodiff = nothing,
-        jvp_autodiff = nothing)
-
-An advanced GaussNewton implementation with support for efficient handling of sparse
-matrices via colored automatic differentiation and preconditioned linear solvers. Designed
-for large-scale and numerically-difficult nonlinear least squares problems.
-"""
-function GaussNewton(; concrete_jac = nothing, linsolve = nothing, precs = nothing,
-        linesearch = nothing, vjp_autodiff = nothing, autodiff = nothing,
-        jvp_autodiff = nothing)
-    return GeneralizedFirstOrderAlgorithm{concrete_jac, :GaussNewton}(; linesearch,
-        descent = NewtonDescent(; linsolve, precs), autodiff, vjp_autodiff, jvp_autodiff)
-end
diff --git a/src/algorithms/pseudo_transient.jl b/src/algorithms/pseudo_transient.jl
deleted file mode 100644
index a29a25154..000000000
--- a/src/algorithms/pseudo_transient.jl
+++ /dev/null
@@ -1,72 +0,0 @@
-"""
-    PseudoTransient(; concrete_jac = nothing, linsolve = nothing,
-        linesearch = NoLineSearch(), precs = nothing, autodiff = nothing,
-        jvp_autodiff = nothing, vjp_autodiff = nothing)
-
-An implementation of PseudoTransient Method [coffey2003pseudotransient](@cite) that is used
-to solve steady state problems in an accelerated manner. It uses an adaptive time-stepping
-to integrate an initial value of nonlinear problem until sufficient accuracy in the desired
-steady-state is achieved to switch over to Newton's method and gain a rapid convergence.
-This implementation specifically uses "switched evolution relaxation"
-[kelley1998convergence](@cite) SER method.
-
-### Keyword Arguments
-
-  - `alpha_initial` : the initial pseudo time step. It defaults to `1e-3`. If it is small,
-    you are going to need more iterations to converge but it can be more stable.
-"""
-function PseudoTransient(;
-        concrete_jac = nothing, linsolve = nothing, linesearch = nothing,
-        precs = nothing, alpha_initial = 1e-3, autodiff = nothing,
-        jvp_autodiff = nothing, vjp_autodiff = nothing)
-    descent = DampedNewtonDescent(; linsolve, precs, initial_damping = alpha_initial,
-        damping_fn = SwitchedEvolutionRelaxation())
-    return GeneralizedFirstOrderAlgorithm{concrete_jac, :PseudoTransient}(;
-        linesearch, descent, autodiff, vjp_autodiff, jvp_autodiff)
-end
-
-"""
-    SwitchedEvolutionRelaxation()
-
-Method for updating the damping parameter in the [`PseudoTransient`](@ref) method based on
-"switched evolution relaxation" [kelley1998convergence](@cite) SER method.
-"""
-struct SwitchedEvolutionRelaxation <: AbstractDampingFunction end
-
-"""
-    SwitchedEvolutionRelaxationCache <: AbstractDampingFunctionCache
-
-Cache for the [`SwitchedEvolutionRelaxation`](@ref) method.
-"""
-@concrete mutable struct SwitchedEvolutionRelaxationCache <: AbstractDampingFunctionCache
-    res_norm
-    α⁻¹
-    internalnorm
-end
-
-function requires_normal_form_jacobian(::Union{
-        SwitchedEvolutionRelaxation, SwitchedEvolutionRelaxationCache})
-    return false
-end
-function requires_normal_form_rhs(::Union{
-        SwitchedEvolutionRelaxation, SwitchedEvolutionRelaxationCache})
-    return false
-end
-
-function __internal_init(
-        prob::AbstractNonlinearProblem, f::SwitchedEvolutionRelaxation, initial_damping,
-        J, fu, u, args...; internalnorm::F = L2_NORM, kwargs...) where {F}
-    T = promote_type(eltype(u), eltype(fu))
-    return SwitchedEvolutionRelaxationCache(
-        internalnorm(fu), T(1 / initial_damping), internalnorm)
-end
-
-(damping::SwitchedEvolutionRelaxationCache)(::Nothing) = damping.α⁻¹
-
-function __internal_solve!(
-        damping::SwitchedEvolutionRelaxationCache, J, fu, args...; kwargs...)
-    res_norm = damping.internalnorm(fu)
-    damping.α⁻¹ *= res_norm / damping.res_norm
-    damping.res_norm = res_norm
-    return damping.α⁻¹
-end
diff --git a/src/algorithms/raphson.jl b/src/algorithms/raphson.jl
deleted file mode 100644
index 130e27f92..000000000
--- a/src/algorithms/raphson.jl
+++ /dev/null
@@ -1,15 +0,0 @@
-"""
-    NewtonRaphson(; concrete_jac = nothing, linsolve = nothing, linesearch = missing,
-        precs = nothing, autodiff = nothing, vjp_autodiff = nothing,
-        jvp_autodiff = nothing)
-
-An advanced NewtonRaphson implementation with support for efficient handling of sparse
-matrices via colored automatic differentiation and preconditioned linear solvers. Designed
-for large-scale and numerically-difficult nonlinear systems.
-"""
-function NewtonRaphson(; concrete_jac = nothing, linsolve = nothing, linesearch = nothing,
-        precs = nothing, autodiff = nothing, vjp_autodiff = nothing,
-        jvp_autodiff = nothing)
-    return GeneralizedFirstOrderAlgorithm{concrete_jac, :NewtonRaphson}(; linesearch,
-        descent = NewtonDescent(; linsolve, precs), autodiff, vjp_autodiff, jvp_autodiff)
-end

From ba054b7e5e4d529d30bc2e2ba828f0d06f3723fe Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 28 Oct 2024 18:53:49 -0400
Subject: [PATCH 645/700] refactor: move LM to First Order

---
 .../src/descent/geodesic_acceleration.jl      |   2 +-
 .../src/NonlinearSolveFirstOrder.jl           |   3 +-
 .../src/levenberg_marquardt.jl                | 292 ++++++++++++++++++
 lib/NonlinearSolveFirstOrder/src/solve.jl     |   3 +-
 src/algorithms/levenberg_marquardt.jl         | 175 -----------
 src/globalization/trust_region.jl             |  91 ------
 6 files changed, 297 insertions(+), 269 deletions(-)
 delete mode 100644 src/algorithms/levenberg_marquardt.jl

diff --git a/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
index f5b686433..486308f09 100644
--- a/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
+++ b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
@@ -126,7 +126,7 @@ function InternalAPI.solve!(
 
     if 2 * norm_a ≤ norm_v * cache.α
         @bb @. δu = v + a / 2
-        SciMLBase.set_du!(cache, δu, idx)
+        set_du!(cache, δu, idx)
         cache.last_step_accepted = true
     else
         cache.last_step_accepted = false
diff --git a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
index f1c767755..b5eba5fb7 100644
--- a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
+++ b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
@@ -20,13 +20,14 @@ using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
                           AbstractApproximateJacobianUpdateRule, AbstractDescentDirection,
                           AbstractApproximateJacobianUpdateRuleCache,
                           AbstractDampingFunction, AbstractDampingFunctionCache,
+                          AbstractTrustRegionMethod, AbstractTrustRegionMethodCache,
                           Utils, InternalAPI, get_timer_output, @static_timeit,
                           update_trace!, L2_NORM,
                           NewtonDescent, DampedNewtonDescent
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode
 using SciMLOperators: AbstractSciMLOperator
 using Setfield: @set!
-using StaticArraysCore: StaticArray, Size, MArray
+using StaticArraysCore: StaticArray, SArray, Size, MArray
 
 include("raphson.jl")
 include("gauss_newton.jl")
diff --git a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
index 8b1378917..76a6f3897 100644
--- a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
+++ b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
@@ -1 +1,293 @@
+"""
+    LevenbergMarquardt(;
+        linsolve = nothing, precs = nothing,
+        damping_initial::Real = 1.0, α_geodesic::Real = 0.75, disable_geodesic = Val(false),
+        damping_increase_factor::Real = 2.0, damping_decrease_factor::Real = 3.0,
+        finite_diff_step_geodesic = 0.1, b_uphill::Real = 1.0, min_damping_D::Real = 1e-8,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+    )
 
+An advanced Levenberg-Marquardt implementation with the improvements suggested in
+[transtrum2012improvements](@citet). Designed for large-scale and numerically-difficult
+nonlinear systems.
+
+### Keyword Arguments
+
+  - `damping_initial`: the starting value for the damping factor. The damping factor is
+    inversely proportional to the step size. The damping factor is adjusted during each
+    iteration. Defaults to `1.0`. See Section 2.1 of [transtrum2012improvements](@citet).
+  - `damping_increase_factor`: the factor by which the damping is increased if a step is
+    rejected. Defaults to `2.0`. See Section 2.1 of [transtrum2012improvements](@citet).
+  - `damping_decrease_factor`: the factor by which the damping is decreased if a step is
+    accepted. Defaults to `3.0`. See Section 2.1 of [transtrum2012improvements](@citet).
+  - `min_damping_D`: the minimum value of the damping terms in the diagonal damping matrix
+    `DᵀD`, where `DᵀD` is given by the largest diagonal entries of `JᵀJ` yet encountered,
+    where `J` is the Jacobian. It is suggested by [transtrum2012improvements](@citet) to use
+    a minimum value of the elements in `DᵀD` to prevent the damping from being too small.
+    Defaults to `1e-8`.
+  - `disable_geodesic`: Disables Geodesic Acceleration if set to `Val(true)`. It provides
+    a way to trade-off robustness for speed, though in most situations Geodesic Acceleration
+    should not be disabled.
+
+For the remaining arguments, see [`GeodesicAcceleration`](@ref) and
+[`NonlinearSolve.LevenbergMarquardtTrustRegion`](@ref) documentations.
+"""
+function LevenbergMarquardt(;
+        linsolve = nothing, precs = nothing,
+        damping_initial::Real = 1.0, α_geodesic::Real = 0.75, disable_geodesic = Val(false),
+        damping_increase_factor::Real = 2.0, damping_decrease_factor::Real = 3.0,
+        finite_diff_step_geodesic = 0.1, b_uphill::Real = 1.0, min_damping_D::Real = 1e-8,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+)
+    descent = DampedNewtonDescent(;
+        linsolve,
+        precs,
+        initial_damping = damping_initial,
+        damping_fn = LevenbergMarquardtDampingFunction(
+            damping_increase_factor, damping_decrease_factor, min_damping_D
+        )
+    )
+    if disable_geodesic isa Val{false}
+        descent = GeodesicAcceleration(descent, finite_diff_step_geodesic, α_geodesic)
+    end
+    trustregion = LevenbergMarquardtTrustRegion(b_uphill)
+    return GeneralizedFirstOrderAlgorithm(;
+        trustregion,
+        descent,
+        autodiff,
+        vjp_autodiff,
+        jvp_autodiff,
+        name = :LevenbergMarquardt
+    )
+end
+
+@concrete struct LevenbergMarquardtDampingFunction <: AbstractDampingFunction
+    increase_factor
+    decrease_factor
+    min_damping
+end
+
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, f::LevenbergMarquardtDampingFunction,
+        initial_damping, J, fu, u, normal_form::Val; kwargs...
+)
+    T = promote_type(eltype(u), eltype(fu))
+    DᵀD = init_levenberg_marquardt_diagonal(u, T(f.min_damping))
+    if normal_form isa Val{true}
+        J_diag_cache = nothing
+    else
+        @bb J_diag_cache = similar(u)
+    end
+    J_damped = T(initial_damping) .* DᵀD
+    return LevenbergMarquardtDampingCache(
+        T(f.increase_factor), T(f.decrease_factor), T(f.min_damping),
+        T(f.increase_factor), T(initial_damping), DᵀD, J_diag_cache, J_damped, f,
+        T(initial_damping)
+    )
+end
+
+@concrete mutable struct LevenbergMarquardtDampingCache <: AbstractDampingFunctionCache
+    increase_factor
+    decrease_factor
+    min_damping
+    λ_factor
+    λ
+    DᵀD
+    J_diag_cache
+    J_damped
+    damping_f
+    initial_damping
+end
+
+function InternalAPI.reinit!(cache::LevenbergMarquardtDampingCache, args...; kwargs...)
+    cache.λ = cache.initial_damping
+    cache.λ_factor = cache.damping_f.increase_factor
+    if !(cache.DᵀD isa Number)
+        if ArrayInterface.can_setindex(cache.DᵀD.diag)
+            cache.DᵀD.diag .= cache.min_damping
+        else
+            cache.DᵀD = Diagonal(ones(typeof(cache.DᵀD.diag)) * cache.min_damping)
+        end
+    end
+    cache.J_damped = cache.λ .* cache.DᵀD
+    return
+end
+
+function NonlinearSolveBase.requires_normal_form_jacobian(::Union{
+        LevenbergMarquardtDampingFunction, LevenbergMarquardtDampingCache})
+    return false
+end
+function NonlinearSolveBase.requires_normal_form_rhs(::Union{
+        LevenbergMarquardtDampingFunction, LevenbergMarquardtDampingCache})
+    return false
+end
+function NonlinearSolveBase.returns_norm_form_damping(::Union{
+        LevenbergMarquardtDampingFunction, LevenbergMarquardtDampingCache})
+    return true
+end
+
+(damping::LevenbergMarquardtDampingCache)(::Nothing) = damping.J_damped
+
+function InternalAPI.solve!(
+        cache::LevenbergMarquardtDampingCache, J, fu, ::Val{false}; kwargs...
+)
+    if ArrayInterface.can_setindex(cache.J_diag_cache)
+        sum!(abs2, Utils.safe_vec(cache.J_diag_cache), J')
+    elseif cache.J_diag_cache isa Number
+        cache.J_diag_cache = abs2(J)
+    else
+        cache.J_diag_cache = dropdims(sum(abs2, J'; dims = 1); dims = 1)
+    end
+    cache.DᵀD = update_levenberg_marquardt_diagonal!!(
+        cache.DᵀD, Utils.safe_vec(cache.J_diag_cache)
+    )
+    @bb @. cache.J_damped = cache.λ * cache.DᵀD
+    return cache.J_damped
+end
+
+function InternalAPI.solve!(
+        cache::LevenbergMarquardtDampingCache, JᵀJ, fu, ::Val{true}; kwargs...
+)
+    cache.DᵀD = update_levenberg_marquardt_diagonal!!(cache.DᵀD, JᵀJ)
+    @bb @. cache.J_damped = cache.λ * cache.DᵀD
+    return cache.J_damped
+end
+
+function NonlinearSolveBase.callback_into_cache!(
+        topcache, cache::LevenbergMarquardtDampingCache, args...
+)
+    if NonlinearSolveBase.last_step_accepted(topcache.trustregion_cache) &&
+       NonlinearSolveBase.last_step_accepted(topcache.descent_cache)
+        cache.λ_factor = 1 / cache.decrease_factor
+    end
+    cache.λ *= cache.λ_factor
+    cache.λ_factor = cache.increase_factor
+end
+
+"""
+    LevenbergMarquardtTrustRegion(b_uphill)
+
+Trust Region method for [`LevenbergMarquardt`](@ref). This method is tightly coupled with
+the Levenberg-Marquardt method and works by directly updating the damping parameter instead
+of specifying a trust region radius.
+
+### Arguments
+
+  - `b_uphill`: a factor that determines if a step is accepted or rejected. The standard
+    choice in the Levenberg-Marquardt method is to accept all steps that decrease the cost
+    and reject all steps that increase the cost. Although this is a natural and safe choice,
+    it is often not the most efficient. Therefore downhill moves are always accepted, but
+    uphill moves are only conditionally accepted. To decide whether an uphill move will be
+    accepted at each iteration ``i``, we compute
+    ``\\beta_i = \\cos(v_{\\text{new}}, v_{\\text{old}})``, which denotes the cosine angle
+    between the proposed velocity ``v_{\\text{new}}`` and the velocity of the last accepted
+    step ``v_{\\text{old}}``. The idea is to accept uphill moves if the angle is small. To
+    specify, uphill moves are accepted if
+    ``(1-\\beta_i)^{b_{\\text{uphill}}} C_{i+1} \\le C_i``, where ``C_i`` is the cost at
+    iteration ``i``. Reasonable choices for `b_uphill` are `1.0` or `2.0`, with
+    `b_uphill = 2.0` allowing higher uphill moves than `b_uphill = 1.0`. When
+    `b_uphill = 0.0`, no uphill moves will be accepted. Defaults to `1.0`. See Section 4 of
+    [transtrum2012improvements](@citet).
+"""
+@concrete struct LevenbergMarquardtTrustRegion <: AbstractTrustRegionMethod
+    β_uphill
+end
+
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, alg::LevenbergMarquardtTrustRegion,
+        f::NonlinearFunction, fu, u, p, args...;
+        stats, internalnorm::F = L2_NORM, kwargs...
+) where {F}
+    T = promote_type(eltype(u), eltype(fu))
+    @bb v = copy(u)
+    @bb u_cache = similar(u)
+    @bb fu_cache = similar(fu)
+    return LevenbergMarquardtTrustRegionCache(
+        f, p, T(Inf), v, T(Inf), internalnorm, T(alg.β_uphill), false,
+        u_cache, fu_cache, stats
+    )
+end
+
+@concrete mutable struct LevenbergMarquardtTrustRegionCache <:
+                         AbstractTrustRegionMethodCache
+    f
+    p
+    loss_old
+    v_cache
+    norm_v_old
+    internalnorm
+    β_uphill
+    last_step_accepted::Bool
+    u_cache
+    fu_cache
+    stats::NLStats
+end
+
+function InternalAPI.reinit!(
+        cache::LevenbergMarquardtTrustRegionCache; p = cache.p, u0 = cache.v_cache, kwargs...
+)
+    cache.p = p
+    @bb copyto!(cache.v_cache, u0)
+    cache.loss_old = oftype(cache.loss_old, Inf)
+    cache.norm_v_old = oftype(cache.norm_v_old, Inf)
+    cache.last_step_accepted = false
+end
+
+function InternalAPI.solve!(
+        cache::LevenbergMarquardtTrustRegionCache, J, fu, u, δu, descent_stats
+)
+    # This should be true if Geodesic Acceleration is being used
+    v = hasfield(typeof(descent_stats), :v) ? descent_stats.v : δu
+    norm_v = cache.internalnorm(v)
+    β = dot(v, cache.v_cache) / (norm_v * cache.norm_v_old)
+
+    @bb @. cache.u_cache = u + δu
+    cache.fu_cache = Utils.evaluate_f!!(cache.f, cache.fu_cache, cache.u_cache, cache.p)
+    cache.stats.nf += 1
+
+    loss = cache.internalnorm(cache.fu_cache)
+
+    if (1 - β)^cache.β_uphill * loss ≤ cache.loss_old  # Accept Step
+        cache.last_step_accepted = true
+        cache.norm_v_old = norm_v
+        @bb copyto!(cache.v_cache, v)
+    else
+        cache.last_step_accepted = false
+    end
+
+    return cache.last_step_accepted, cache.u_cache, cache.fu_cache
+end
+
+update_levenberg_marquardt_diagonal!!(y::Number, x::Number) = max(y, x)
+function update_levenberg_marquardt_diagonal!!(y::Diagonal, x::AbstractVecOrMat)
+    if ArrayInterface.can_setindex(y.diag)
+        if ArrayInterface.fast_scalar_indexing(y.diag)
+            if ndims(x) == 1
+                @simd ivdep for i in axes(x, 1)
+                    @inbounds y.diag[i] = max(y.diag[i], x[i])
+                end
+            else
+                @simd ivdep for i in axes(x, 1)
+                    @inbounds y.diag[i] = max(y.diag[i], x[i, i])
+                end
+            end
+        else
+            if ndims(x) == 1
+                @. y.diag = max(y.diag, x)
+            else
+                y.diag .= max.(y.diag, @view(x[diagind(x)]))
+            end
+        end
+        return y
+    end
+    ndims(x) == 1 && return Diagonal(max.(y.diag, x))
+    return Diagonal(max.(y.diag, @view(x[diagind(x)])))
+end
+
+init_levenberg_marquardt_diagonal(u::Number, v) = oftype(u, v)
+init_levenberg_marquardt_diagonal(u::SArray, v) = Diagonal(ones(typeof(vec(u))) * v)
+function init_levenberg_marquardt_diagonal(u, v)
+    d = similar(vec(u))
+    d .= v
+    return Diagonal(d)
+end
diff --git a/lib/NonlinearSolveFirstOrder/src/solve.jl b/lib/NonlinearSolveFirstOrder/src/solve.jl
index 8d61ddceb..c007d5596 100644
--- a/lib/NonlinearSolveFirstOrder/src/solve.jl
+++ b/lib/NonlinearSolveFirstOrder/src/solve.jl
@@ -184,7 +184,8 @@ function SciMLBase.__init(
             NonlinearSolveBase.supports_trust_region(alg.descent) ||
                 error("Trust Region not supported by $(alg.descent).")
             trustregion_cache = InternalAPI.init(
-                prob, alg.trustregion, f, fu, u, p; stats, internalnorm, kwargs...
+                prob, alg.trustregion, prob.f, fu, u, prob.p;
+                stats, internalnorm, kwargs...
             )
             globalization = Val(:TrustRegion)
         end
diff --git a/src/algorithms/levenberg_marquardt.jl b/src/algorithms/levenberg_marquardt.jl
deleted file mode 100644
index 6dc1845c3..000000000
--- a/src/algorithms/levenberg_marquardt.jl
+++ /dev/null
@@ -1,175 +0,0 @@
-"""
-    LevenbergMarquardt(; linsolve = nothing,
-        precs = nothing, damping_initial::Real = 1.0, α_geodesic::Real = 0.75,
-        damping_increase_factor::Real = 2.0, damping_decrease_factor::Real = 3.0,
-        finite_diff_step_geodesic = 0.1, b_uphill::Real = 1.0, autodiff = nothing,
-        min_damping_D::Real = 1e-8, disable_geodesic = Val(false), vjp_autodiff = nothing,
-        jvp_autodiff = nothing)
-
-An advanced Levenberg-Marquardt implementation with the improvements suggested in
-[transtrum2012improvements](@citet). Designed for large-scale and numerically-difficult
-nonlinear systems.
-
-### Keyword Arguments
-
-  - `damping_initial`: the starting value for the damping factor. The damping factor is
-    inversely proportional to the step size. The damping factor is adjusted during each
-    iteration. Defaults to `1.0`. See Section 2.1 of [transtrum2012improvements](@citet).
-  - `damping_increase_factor`: the factor by which the damping is increased if a step is
-    rejected. Defaults to `2.0`. See Section 2.1 of [transtrum2012improvements](@citet).
-  - `damping_decrease_factor`: the factor by which the damping is decreased if a step is
-    accepted. Defaults to `3.0`. See Section 2.1 of [transtrum2012improvements](@citet).
-  - `min_damping_D`: the minimum value of the damping terms in the diagonal damping matrix
-    `DᵀD`, where `DᵀD` is given by the largest diagonal entries of `JᵀJ` yet encountered,
-    where `J` is the Jacobian. It is suggested by [transtrum2012improvements](@citet) to use
-    a minimum value of the elements in `DᵀD` to prevent the damping from being too small.
-    Defaults to `1e-8`.
-  - `disable_geodesic`: Disables Geodesic Acceleration if set to `Val(true)`. It provides
-    a way to trade-off robustness for speed, though in most situations Geodesic Acceleration
-    should not be disabled.
-
-For the remaining arguments, see [`GeodesicAcceleration`](@ref) and
-[`NonlinearSolve.LevenbergMarquardtTrustRegion`](@ref) documentations.
-"""
-function LevenbergMarquardt(;
-        linsolve = nothing, precs = nothing, damping_initial::Real = 1.0,
-        α_geodesic::Real = 0.75, damping_increase_factor::Real = 2.0,
-        damping_decrease_factor::Real = 3.0, finite_diff_step_geodesic = 0.1,
-        b_uphill::Real = 1.0, min_damping_D::Real = 1e-8, disable_geodesic = False,
-        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing)
-    descent = DampedNewtonDescent(; linsolve, precs, initial_damping = damping_initial,
-        damping_fn = LevenbergMarquardtDampingFunction(
-            damping_increase_factor, damping_decrease_factor, min_damping_D))
-    if disable_geodesic === False
-        descent = GeodesicAcceleration(descent, finite_diff_step_geodesic, α_geodesic)
-    end
-    trustregion = LevenbergMarquardtTrustRegion(b_uphill)
-    return GeneralizedFirstOrderAlgorithm{true, :LevenbergMarquardt}(;
-        trustregion, descent, autodiff, vjp_autodiff, jvp_autodiff)
-end
-
-@concrete struct LevenbergMarquardtDampingFunction <: AbstractDampingFunction
-    increase_factor
-    decrease_factor
-    min_damping
-end
-
-@concrete mutable struct LevenbergMarquardtDampingCache <: AbstractDampingFunctionCache
-    increase_factor
-    decrease_factor
-    min_damping
-    λ_factor
-    λ
-    DᵀD
-    J_diag_cache
-    J_damped
-    damping_f
-    initial_damping
-end
-
-function reinit_cache!(cache::LevenbergMarquardtDampingCache, args...; kwargs...)
-    cache.λ = cache.initial_damping
-    cache.λ_factor = cache.damping_f.increase_factor
-    if !(cache.DᵀD isa Number)
-        if can_setindex(cache.DᵀD.diag)
-            cache.DᵀD.diag .= cache.min_damping
-        else
-            cache.DᵀD = Diagonal(ones(typeof(cache.DᵀD.diag)) * cache.min_damping)
-        end
-    end
-    cache.J_damped = cache.λ .* cache.DᵀD
-end
-
-function requires_normal_form_jacobian(::Union{
-        LevenbergMarquardtDampingFunction, LevenbergMarquardtDampingCache})
-    return false
-end
-function requires_normal_form_rhs(::Union{
-        LevenbergMarquardtDampingFunction, LevenbergMarquardtDampingCache})
-    return false
-end
-function returns_norm_form_damping(::Union{
-        LevenbergMarquardtDampingFunction, LevenbergMarquardtDampingCache})
-    return true
-end
-
-function __internal_init(
-        prob::AbstractNonlinearProblem, f::LevenbergMarquardtDampingFunction,
-        initial_damping, J, fu, u, ::Val{NF}; kwargs...) where {NF}
-    T = promote_type(eltype(u), eltype(fu))
-    DᵀD = __init_diagonal(u, T(f.min_damping))
-    if NF
-        J_diag_cache = nothing
-    else
-        @bb J_diag_cache = similar(u)
-    end
-    J_damped = T(initial_damping) .* DᵀD
-    return LevenbergMarquardtDampingCache(
-        T(f.increase_factor), T(f.decrease_factor), T(f.min_damping), T(f.increase_factor),
-        T(initial_damping), DᵀD, J_diag_cache, J_damped, f, T(initial_damping))
-end
-
-(damping::LevenbergMarquardtDampingCache)(::Nothing) = damping.J_damped
-
-function __internal_solve!(
-        damping::LevenbergMarquardtDampingCache, J, fu, ::Val{false}; kwargs...)
-    if __can_setindex(damping.J_diag_cache)
-        sum!(abs2, _vec(damping.J_diag_cache), J')
-    elseif damping.J_diag_cache isa Number
-        damping.J_diag_cache = abs2(J)
-    else
-        damping.J_diag_cache = dropdims(sum(abs2, J'; dims = 1); dims = 1)
-    end
-    damping.DᵀD = __update_LM_diagonal!!(damping.DᵀD, _vec(damping.J_diag_cache))
-    @bb @. damping.J_damped = damping.λ * damping.DᵀD
-    return damping.J_damped
-end
-
-function __internal_solve!(
-        damping::LevenbergMarquardtDampingCache, JᵀJ, fu, ::Val{true}; kwargs...)
-    damping.DᵀD = __update_LM_diagonal!!(damping.DᵀD, JᵀJ)
-    @bb @. damping.J_damped = damping.λ * damping.DᵀD
-    return damping.J_damped
-end
-
-function callback_into_cache!(topcache, cache::LevenbergMarquardtDampingCache, args...)
-    if last_step_accepted(topcache.trustregion_cache) &&
-       last_step_accepted(topcache.descent_cache)
-        cache.λ_factor = 1 / cache.decrease_factor
-    end
-    cache.λ *= cache.λ_factor
-    cache.λ_factor = cache.increase_factor
-end
-
-@inline __update_LM_diagonal!!(y::Number, x::Number) = max(y, x)
-@inline function __update_LM_diagonal!!(y::Diagonal, x::AbstractVector)
-    if __can_setindex(y.diag)
-        @. y.diag = max(y.diag, x)
-        return y
-    else
-        return Diagonal(max.(y.diag, x))
-    end
-end
-@inline function __update_LM_diagonal!!(y::Diagonal, x::AbstractMatrix)
-    if __can_setindex(y.diag)
-        if fast_scalar_indexing(y.diag)
-            @simd for i in axes(x, 1)
-                @inbounds y.diag[i] = max(y.diag[i], x[i, i])
-            end
-            return y
-        else
-            y .= max.(y.diag, @view(x[diagind(x)]))
-            return y
-        end
-    else
-        return Diagonal(max.(y.diag, @view(x[diagind(x)])))
-    end
-end
-
-@inline __init_diagonal(u::Number, v) = oftype(u, v)
-@inline __init_diagonal(u::SArray, v) = Diagonal(ones(typeof(vec(u))) * v)
-@inline function __init_diagonal(u, v)
-    d = similar(vec(u))
-    d .= v
-    return Diagonal(d)
-end
diff --git a/src/globalization/trust_region.jl b/src/globalization/trust_region.jl
index 248f5307c..813068e7e 100644
--- a/src/globalization/trust_region.jl
+++ b/src/globalization/trust_region.jl
@@ -1,94 +1,3 @@
-"""
-    LevenbergMarquardtTrustRegion(b_uphill)
-
-Trust Region method for [`LevenbergMarquardt`](@ref). This method is tightly coupled with
-the Levenberg-Marquardt method and works by directly updating the damping parameter instead
-of specifying a trust region radius.
-
-### Arguments
-
-  - `b_uphill`: a factor that determines if a step is accepted or rejected. The standard
-    choice in the Levenberg-Marquardt method is to accept all steps that decrease the cost
-    and reject all steps that increase the cost. Although this is a natural and safe choice,
-    it is often not the most efficient. Therefore downhill moves are always accepted, but
-    uphill moves are only conditionally accepted. To decide whether an uphill move will be
-    accepted at each iteration ``i``, we compute
-    ``\\beta_i = \\cos(v_{\\text{new}}, v_{\\text{old}})``, which denotes the cosine angle
-    between the proposed velocity ``v_{\\text{new}}`` and the velocity of the last accepted
-    step ``v_{\\text{old}}``. The idea is to accept uphill moves if the angle is small. To
-    specify, uphill moves are accepted if
-    ``(1-\\beta_i)^{b_{\\text{uphill}}} C_{i+1} \\le C_i``, where ``C_i`` is the cost at
-    iteration ``i``. Reasonable choices for `b_uphill` are `1.0` or `2.0`, with
-    `b_uphill = 2.0` allowing higher uphill moves than `b_uphill = 1.0`. When
-    `b_uphill = 0.0`, no uphill moves will be accepted. Defaults to `1.0`. See Section 4 of
-    [transtrum2012improvements](@citet).
-"""
-@concrete struct LevenbergMarquardtTrustRegion <: AbstractTrustRegionMethod
-    β_uphill
-end
-
-function Base.show(io::IO, alg::LevenbergMarquardtTrustRegion)
-    print(io, "LevenbergMarquardtTrustRegion(β_uphill = $(alg.β_uphill))")
-end
-
-@concrete mutable struct LevenbergMarquardtTrustRegionCache <:
-                         AbstractTrustRegionMethodCache
-    f
-    p
-    loss_old
-    v_cache
-    norm_v_old
-    internalnorm
-    β_uphill
-    last_step_accepted::Bool
-    u_cache
-    fu_cache
-    stats::NLStats
-end
-
-function reinit_cache!(cache::LevenbergMarquardtTrustRegionCache, args...;
-        p = cache.p, u0 = cache.v_cache, kwargs...)
-    cache.p = p
-    @bb copyto!(cache.v_cache, u0)
-    cache.loss_old = oftype(cache.loss_old, Inf)
-    cache.norm_v_old = oftype(cache.norm_v_old, Inf)
-    cache.last_step_accepted = false
-end
-
-function __internal_init(
-        prob::AbstractNonlinearProblem, alg::LevenbergMarquardtTrustRegion, f::F, fu,
-        u, p, args...; stats, internalnorm::IF = L2_NORM, kwargs...) where {F, IF}
-    T = promote_type(eltype(u), eltype(fu))
-    @bb v = copy(u)
-    @bb u_cache = similar(u)
-    @bb fu_cache = similar(fu)
-    return LevenbergMarquardtTrustRegionCache(f, p, T(Inf), v, T(Inf), internalnorm,
-        alg.β_uphill, false, u_cache, fu_cache, stats)
-end
-
-function __internal_solve!(
-        cache::LevenbergMarquardtTrustRegionCache, J, fu, u, δu, descent_stats)
-    # This should be true if Geodesic Acceleration is being used
-    v = hasfield(typeof(descent_stats), :v) ? descent_stats.v : δu
-    norm_v = cache.internalnorm(v)
-    β = dot(v, cache.v_cache) / (norm_v * cache.norm_v_old)
-
-    @bb @. cache.u_cache = u + δu
-    cache.fu_cache = evaluate_f!!(cache.f, cache.fu_cache, cache.u_cache, cache.p)
-    cache.stats.nf += 1
-
-    loss = cache.internalnorm(cache.fu_cache)
-
-    if (1 - β)^cache.β_uphill * loss ≤ cache.loss_old  # Accept Step
-        cache.last_step_accepted = true
-        cache.norm_v_old = norm_v
-        @bb copyto!(cache.v_cache, v)
-    else
-        cache.last_step_accepted = false
-    end
-
-    return cache.last_step_accepted, cache.u_cache, cache.fu_cache
-end
 
 # Don't Pollute the namespace
 """

From 518e53d453a38013f7aeb7c8796b1c50a2f823f0 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 28 Oct 2024 19:38:10 -0400
Subject: [PATCH 646/700] refactor: minor cleanup

---
 common/nlls_problem_workloads.jl              | 22 ++++++++
 lib/BracketingNonlinearSolve/Project.toml     |  4 +-
 .../src/BracketingNonlinearSolve.jl           |  7 ++-
 lib/NonlinearSolveFirstOrder/Project.toml     |  2 -
 .../src/NonlinearSolveFirstOrder.jl           | 43 ++++++++++----
 .../src/levenberg_marquardt.jl                |  6 +-
 .../src/trust_region.jl                       | 39 +++++++++++++
 .../src/NonlinearSolveQuasiNewton.jl          |  6 +-
 .../src/NonlinearSolveSpectralMethods.jl      |  6 +-
 .../src/SimpleNonlinearSolve.jl               |  6 +-
 src/NonlinearSolve.jl                         | 56 ++++---------------
 11 files changed, 120 insertions(+), 77 deletions(-)

diff --git a/common/nlls_problem_workloads.jl b/common/nlls_problem_workloads.jl
index 8b1378917..4c49e5fa1 100644
--- a/common/nlls_problem_workloads.jl
+++ b/common/nlls_problem_workloads.jl
@@ -1 +1,23 @@
+using SciMLBase: NonlinearLeastSquaresProblem, NonlinearFunction
 
+nonlinear_functions = (
+    (NonlinearFunction{false}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
+    (NonlinearFunction{false}((u, p) -> vcat(u .* u .- p, u .* u .- p)), [0.1, 0.1]),
+    (
+        NonlinearFunction{true}(
+            (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(1)
+        ),
+        [0.1, 0.0]
+    ),
+    (
+        NonlinearFunction{true}(
+            (du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p), resid_prototype = zeros(4)
+        ),
+        [0.1, 0.1]
+    )
+)
+
+nlls_problems = NonlinearLeastSquaresProblem[]
+for (fn, u0) in nonlinear_functions
+    push!(nlls_problems, NonlinearLeastSquaresProblem(fn, u0, 2.0))
+end
diff --git a/lib/BracketingNonlinearSolve/Project.toml b/lib/BracketingNonlinearSolve/Project.toml
index 6fc241d7d..eb81fd7f7 100644
--- a/lib/BracketingNonlinearSolve/Project.toml
+++ b/lib/BracketingNonlinearSolve/Project.toml
@@ -1,13 +1,14 @@
 name = "BracketingNonlinearSolve"
 uuid = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.0.0"
+version = "1.1.0"
 
 [deps]
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
+Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 
 [weakdeps]
@@ -25,6 +26,7 @@ ForwardDiff = "0.10.36"
 InteractiveUtils = "<0.0.1, 1"
 NonlinearSolveBase = "1"
 PrecompileTools = "1.2"
+Reexport = "1.2"
 SciMLBase = "2.50"
 Test = "1.10"
 TestItemRunner = "1"
diff --git a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
index 62cf7a7b7..9757c4c23 100644
--- a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
+++ b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
@@ -1,6 +1,7 @@
 module BracketingNonlinearSolve
 
 using ConcreteStructs: @concrete
+using Reexport: @reexport
 
 using CommonSolve: CommonSolve, solve
 using NonlinearSolveBase: NonlinearSolveBase
@@ -30,7 +31,8 @@ end
 @setup_workload begin
     for T in (Float32, Float64)
         prob_brack = IntervalNonlinearProblem{false}(
-            (u, p) -> u^2 - p, T.((0.0, 2.0)), T(2))
+            (u, p) -> u^2 - p, T.((0.0, 2.0)), T(2)
+        )
         algs = (Alefeld(), Bisection(), Brent(), Falsi(), ITP(), Ridder())
 
         @compile_workload begin
@@ -41,8 +43,7 @@ end
     end
 end
 
-export IntervalNonlinearProblem
-export solve
+@reexport using SciMLBase, NonlinearSolveBase
 
 export Alefeld, Bisection, Brent, Falsi, ITP, Ridder
 
diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
index b29ae474b..ef949cb73 100644
--- a/lib/NonlinearSolveFirstOrder/Project.toml
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -19,7 +19,6 @@ NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
-SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
@@ -46,7 +45,6 @@ PrecompileTools = "1.2"
 ReTestItems = "1.24"
 Reexport = "1"
 SciMLBase = "2.54"
-SciMLOperators = "0.3.11"
 Setfield = "1.1.1"
 StableRNGs = "1"
 StaticArraysCore = "1.4.3"
diff --git a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
index b5eba5fb7..9fdfc379a 100644
--- a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
+++ b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
@@ -10,24 +10,20 @@ using ConcreteStructs: @concrete
 using DiffEqBase: DiffEqBase    # Needed for `init` / `solve` dispatches
 using FiniteDiff: FiniteDiff    # Default Finite Difference Method
 using ForwardDiff: ForwardDiff  # Default Forward Mode AD
-using LinearAlgebra: LinearAlgebra, Diagonal, dot, inv, diag
+using LinearAlgebra: LinearAlgebra, Diagonal, dot
 using LinearSolve: LinearSolve  # Trigger Linear Solve extension in NonlinearSolveBase
 using MaybeInplace: @bb
 using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
-                          AbstractNonlinearSolveCache, AbstractResetCondition,
-                          AbstractResetConditionCache, AbstractApproximateJacobianStructure,
-                          AbstractJacobianCache, AbstractJacobianInitialization,
-                          AbstractApproximateJacobianUpdateRule, AbstractDescentDirection,
-                          AbstractApproximateJacobianUpdateRuleCache,
-                          AbstractDampingFunction, AbstractDampingFunctionCache,
-                          AbstractTrustRegionMethod, AbstractTrustRegionMethodCache,
+                          AbstractNonlinearSolveCache, AbstractDampingFunction,
+                          AbstractDampingFunctionCache, AbstractTrustRegionMethod,
+                          AbstractTrustRegionMethodCache,
                           Utils, InternalAPI, get_timer_output, @static_timeit,
                           update_trace!, L2_NORM,
-                          NewtonDescent, DampedNewtonDescent
-using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode
-using SciMLOperators: AbstractSciMLOperator
+                          NewtonDescent, DampedNewtonDescent, GeodesicAcceleration,
+                          Dogleg
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode, NonlinearFunction
 using Setfield: @set!
-using StaticArraysCore: StaticArray, SArray, Size, MArray
+using StaticArraysCore: SArray
 
 include("raphson.jl")
 include("gauss_newton.jl")
@@ -37,6 +33,29 @@ include("pseudo_transient.jl")
 
 include("solve.jl")
 
+@setup_workload begin
+    include(joinpath(
+        @__DIR__, "..", "..", "..", "common", "nonlinear_problem_workloads.jl"
+    ))
+    include(joinpath(
+        @__DIR__, "..", "..", "..", "common", "nlls_problem_workloads.jl"
+    ))
+
+    # XXX: TrustRegion
+    nlp_algs = [NewtonRaphson(), LevenbergMarquardt()]
+    nlls_algs = [GaussNewton(), LevenbergMarquardt()]
+
+    @compile_workload begin
+        for prob in nonlinear_problems, alg in nlp_algs
+            CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
+        end
+
+        for prob in nlls_problems, alg in nlls_algs
+            CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
+        end
+    end
+end
+
 @reexport using SciMLBase, NonlinearSolveBase
 
 export NewtonRaphson, PseudoTransient
diff --git a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
index 76a6f3897..d2fedae98 100644
--- a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
+++ b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
@@ -131,10 +131,10 @@ end
 function InternalAPI.solve!(
         cache::LevenbergMarquardtDampingCache, J, fu, ::Val{false}; kwargs...
 )
-    if ArrayInterface.can_setindex(cache.J_diag_cache)
-        sum!(abs2, Utils.safe_vec(cache.J_diag_cache), J')
-    elseif cache.J_diag_cache isa Number
+    if cache.J_diag_cache isa Number
         cache.J_diag_cache = abs2(J)
+    elseif ArrayInterface.can_setindex(cache.J_diag_cache)
+        sum!(abs2, Utils.safe_vec(cache.J_diag_cache), J')
     else
         cache.J_diag_cache = dropdims(sum(abs2, J'; dims = 1); dims = 1)
     end
diff --git a/lib/NonlinearSolveFirstOrder/src/trust_region.jl b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
index 8b1378917..5883d23b7 100644
--- a/lib/NonlinearSolveFirstOrder/src/trust_region.jl
+++ b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
@@ -1 +1,40 @@
+"""
+    TrustRegion(;
+        concrete_jac = nothing, linsolve = nothing, precs = nothing,
+        radius_update_scheme = RadiusUpdateSchemes.Simple, max_trust_radius::Real = 0 // 1,
+        initial_trust_radius::Real = 0 // 1, step_threshold::Real = 1 // 10000,
+        shrink_threshold::Real = 1 // 4, expand_threshold::Real = 3 // 4,
+        shrink_factor::Real = 1 // 4, expand_factor::Real = 2 // 1,
+        max_shrink_times::Int = 32,
+        vjp_autodiff = nothing, autodiff = nothing, jvp_autodiff = nothing
+    )
 
+An advanced TrustRegion implementation with support for efficient handling of sparse
+matrices via colored automatic differentiation and preconditioned linear solvers. Designed
+for large-scale and numerically-difficult nonlinear systems.
+
+### Keyword Arguments
+
+  - `radius_update_scheme`: the scheme used to update the trust region radius. Defaults to
+    `RadiusUpdateSchemes.Simple`. See [`RadiusUpdateSchemes`](@ref) for more details. For a
+    review on trust region radius update schemes, see [yuan2015recent](@citet).
+
+For the remaining arguments, see [`NonlinearSolve.GenericTrustRegionScheme`](@ref)
+documentation.
+"""
+function TrustRegion(;
+        concrete_jac = nothing, linsolve = nothing, precs = nothing,
+        radius_update_scheme = RadiusUpdateSchemes.Simple, max_trust_radius::Real = 0 // 1,
+        initial_trust_radius::Real = 0 // 1, step_threshold::Real = 1 // 10000,
+        shrink_threshold::Real = 1 // 4, expand_threshold::Real = 3 // 4,
+        shrink_factor::Real = 1 // 4, expand_factor::Real = 2 // 1,
+        max_shrink_times::Int = 32,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+)
+    descent = Dogleg(; linsolve, precs)
+    trustregion = GenericTrustRegionScheme(;
+        method = radius_update_scheme, step_threshold, shrink_threshold, expand_threshold,
+        shrink_factor, expand_factor, initial_trust_radius, max_trust_radius)
+    return GeneralizedFirstOrderAlgorithm{concrete_jac, :TrustRegion}(;
+        trustregion, descent, autodiff, vjp_autodiff, jvp_autodiff, max_shrink_times)
+end
diff --git a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
index aace3b0e8..2671c079d 100644
--- a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
@@ -40,10 +40,8 @@ include("solve.jl")
     algs = [Broyden(), Klement()]
 
     @compile_workload begin
-        @sync begin
-            for prob in nonlinear_problems, alg in algs
-                Threads.@spawn CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
-            end
+        for prob in nonlinear_problems, alg in algs
+            CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
         end
     end
 end
diff --git a/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl b/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
index 253dd0b72..2569ea36d 100644
--- a/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
+++ b/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
@@ -26,10 +26,8 @@ include("solve.jl")
     algs = [DFSane()]
 
     @compile_workload begin
-        @sync begin
-            for prob in nonlinear_problems, alg in algs
-                Threads.@spawn CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
-            end
+        for prob in nonlinear_problems, alg in algs
+            CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
         end
     end
 end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index cee8f8dd3..858970a0c 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -130,10 +130,8 @@ function solve_adjoint_internal end
         #!format: on
 
         @compile_workload begin
-            @sync for alg in algs
-                for prob in (prob_scalar, prob_iip, prob_oop)
-                    Threads.@spawn CommonSolve.solve(prob, alg; abstol = 1e-2)
-                end
+            for prob in (prob_scalar, prob_iip, prob_oop)
+                CommonSolve.solve(prob, alg; abstol = 1e-2)
             end
         end
     end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 950710932..eaae0ee6a 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -57,22 +57,9 @@ using SparseMatrixColorings: SparseMatrixColorings # NOTE: This triggers an exte
 
 const DI = DifferentiationInterface
 
-const True = Val(true)
-const False = Val(false)
-
 include("timer_outputs.jl")
 include("internal/helpers.jl")
 
-include("globalization/trust_region.jl")
-
-include("core/generalized_first_order.jl")
-
-include("algorithms/raphson.jl")
-include("algorithms/pseudo_transient.jl")
-include("algorithms/gauss_newton.jl")
-include("algorithms/levenberg_marquardt.jl")
-include("algorithms/trust_region.jl")
-
 include("algorithms/extension_algs.jl")
 
 include("utils.jl")
@@ -100,9 +87,6 @@ include("internal/forward_diff.jl") # we need to define after the algorithms
     end
 
     nls_algs = (
-        NewtonRaphson(),
-        TrustRegion(),
-        LevenbergMarquardt(),
         nothing
     )
 
@@ -132,44 +116,28 @@ include("internal/forward_diff.jl") # we need to define after the algorithms
     )
 
     @compile_workload begin
-        @sync begin
-            for prob in probs_nls, alg in nls_algs
-                Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
-            end
-            for prob in probs_nlls, alg in nlls_algs
-                Threads.@spawn solve(prob, alg; abstol = 1e-2, verbose = false)
-            end
+        for prob in probs_nls, alg in nls_algs
+            solve(prob, alg; abstol = 1e-2, verbose = false)
+        end
+        for prob in probs_nlls, alg in nlls_algs
+            solve(prob, alg; abstol = 1e-2, verbose = false)
         end
     end
 end
 
 # Rexexports
-@reexport using SciMLBase, SimpleNonlinearSolve, NonlinearSolveBase,
-                NonlinearSolveSpectralMethods, NonlinearSolveQuasiNewton
+@reexport using SciMLBase, NonlinearSolveBase
+@reexport using NonlinearSolveFirstOrder, NonlinearSolveSpectralMethods,
+                NonlinearSolveQuasiNewton, SimpleNonlinearSolve
+@reexport using LineSearch
+@reexport using ADTypes
 
-# Core Algorithms
-export NewtonRaphson, PseudoTransient
-export GaussNewton, LevenbergMarquardt, TrustRegion
-export NonlinearSolvePolyAlgorithm, RobustMultiNewton, FastShortcutNonlinearPolyalg,
-       FastShortcutNLLSPolyalg
+export NonlinearSolvePolyAlgorithm, RobustMultiNewton,
+       FastShortcutNonlinearPolyalg, FastShortcutNLLSPolyalg
 
 # Extension Algorithms
 export LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
        FixedPointAccelerationJL, SpeedMappingJL, SIAMFANLEquationsJL
 export PETScSNES, CMINPACK
 
-# Advanced Algorithms -- Without Bells and Whistles
-export GeneralizedFirstOrderAlgorithm
-
-# Globalization
-## Line Search Algorithms
-export LineSearch, BackTracking, NoLineSearch, RobustNonMonotoneLineSearch,
-       LiFukushimaLineSearch, LineSearchesJL
-## Trust Region Algorithms
-export RadiusUpdateSchemes
-
-# Reexport ADTypes
-export AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme,
-       AutoSparse
-
 end

From 8028a39f2d7c373006e59bb5a4c3b15001fc08d3 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 28 Oct 2024 22:02:59 -0400
Subject: [PATCH 647/700] refactor: move stuff around a bit

---
 Project.toml                                  |  16 +-
 lib/NonlinearSolveBase/src/abstract_types.jl  |   7 +-
 .../src/descent/damped_newton.jl              |   2 +-
 lib/NonlinearSolveBase/src/descent/dogleg.jl  |   6 +-
 .../src/descent/geodesic_acceleration.jl      |   2 +-
 lib/NonlinearSolveBase/src/descent/newton.jl  |   2 +-
 .../src/descent/steepest.jl                   |   2 +-
 lib/NonlinearSolveBase/src/solve.jl           |   8 +-
 lib/NonlinearSolveBase/src/utils.jl           |   3 +-
 lib/NonlinearSolveFirstOrder/Project.toml     |   1 +
 .../src/NonlinearSolveFirstOrder.jl           |   8 +-
 .../src/trust_region.jl                       | 458 ++++++++++++++-
 .../src/SimpleNonlinearSolve.jl               |   2 +-
 src/NonlinearSolve.jl                         | 153 ++---
 src/algorithms/extension_algs.jl              | 469 ---------------
 src/algorithms/trust_region.jl                |  36 --
 src/default.jl                                | 531 +----------------
 src/extension_algs.jl                         | 469 +++++++++++++++
 src/{internal => }/forward_diff.jl            |   0
 src/globalization/trust_region.jl             | 452 ---------------
 src/{timer_outputs.jl => helpers.jl}          |   0
 src/polyalg.jl                                | 543 ++++++++++++++++++
 src/utils.jl                                  |  50 --
 23 files changed, 1566 insertions(+), 1654 deletions(-)
 delete mode 100644 src/algorithms/extension_algs.jl
 delete mode 100644 src/algorithms/trust_region.jl
 create mode 100644 src/extension_algs.jl
 rename src/{internal => }/forward_diff.jl (100%)
 delete mode 100644 src/globalization/trust_region.jl
 rename src/{timer_outputs.jl => helpers.jl} (100%)
 create mode 100644 src/polyalg.jl
 delete mode 100644 src/utils.jl

diff --git a/Project.toml b/Project.toml
index 1c6485b43..6d907607e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -9,31 +9,25 @@ ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
-DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
-MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 NonlinearSolveFirstOrder = "5959db7a-ea39-4486-b5fe-2dd0bf03d60d"
 NonlinearSolveQuasiNewton = "9a2c21bd-3a47-402d-9113-8faf9a0ee114"
 NonlinearSolveSpectralMethods = "26075421-4e9a-44e1-8bd1-420ed7ad02b2"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Preferences = "21216c6a-2e73-6563-6e65-726566657250"
-RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
-SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
-SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 SimpleNonlinearSolve = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseMatrixColorings = "0a514795-09f3-496d-8182-132a7b665d35"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
-TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 
 [weakdeps]
 FastLevenbergMarquardt = "7a0df574-e128-4d35-8cbd-3d84502bf7ce"
@@ -71,7 +65,6 @@ CUDA = "5.5"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.155.3"
-DifferentiationInterface = "0.6.16"
 Enzyme = "0.13.11"
 ExplicitImports = "1.5"
 FastClosures = "0.3.2"
@@ -84,11 +77,10 @@ InteractiveUtils = "<0.0.1, 1"
 LeastSquaresOptim = "0.8.5"
 LineSearch = "0.1.4"
 LineSearches = "7.3"
-LinearAlgebra = "1.10"
-LinearSolve = "2.35"
+LinearAlgebra = "1.11.0"
+LinearSolve = "2.36.1"
 MINPACK = "1.2"
 MPI = "0.20.22"
-MaybeInplace = "0.1.4"
 NLSolvers = "0.5"
 NLsolve = "4.5"
 NaNMath = "1"
@@ -101,12 +93,9 @@ PrecompileTools = "1.2"
 Preferences = "1.4"
 Random = "1.10"
 ReTestItems = "1.24"
-RecursiveArrayTools = "3.27"
 Reexport = "1.2"
 SIAMFANLEquations = "1.0.1"
 SciMLBase = "2.54.0"
-SciMLJacobianOperators = "0.1"
-SciMLOperators = "0.3.10"
 SimpleNonlinearSolve = "2"
 SparseArrays = "1.10"
 SparseConnectivityTracer = "0.6.5"
@@ -118,7 +107,6 @@ StaticArraysCore = "1.4"
 Sundials = "4.23.1"
 SymbolicIndexingInterface = "0.3.31"
 Test = "1.10"
-TimerOutputs = "0.5.23"
 Zygote = "0.6.69"
 julia = "1.10"
 
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index 3cdb59a1d..91afc2901 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -18,7 +18,7 @@ function reinit_self!(x::Any; kwargs...)
     return
 end
 
-function reinit_self!(stats::NLStats)
+function reinit!(stats::NLStats)
     stats.nf = 0
     stats.nsteps = 0
     stats.nfactors = 0
@@ -257,8 +257,8 @@ Abstract Type for all NonlinearSolveBase Caches.
   - `SciMLBase.set_u!(cache, u)`: set the current state.
   - `SciMLBase.reinit!(cache, u0; kwargs...)`: reinitialize the cache with the initial state
     `u0` and any additional keyword arguments.
-  - `SciMLBase.step!(cache; kwargs...)`: See [`SciMLBase.step!`](@ref) for more details.
   - `SciMLBase.isinplace(cache)`: whether or not the solver is inplace.
+  - `CommonSolve.step!(cache; kwargs...)`: See [`CommonSolve.step!`](@ref) for more details.
 
 Additionally implements `SymbolicIndexingInterface` interface Functions.
 
@@ -577,7 +577,8 @@ macro internal_caches(cType, internal_cache_names...)
             return
         end
         function NonlinearSolveBase.InternalAPI.reinit!(
-                cache::$(cType), args...; kwargs...)
+                cache::$(cType), args...; kwargs...
+        )
             $(reinit_caches...)
             $(InternalAPI.reinit_self!)(cache, args...; kwargs...)
             return
diff --git a/lib/NonlinearSolveBase/src/descent/damped_newton.jl b/lib/NonlinearSolveBase/src/descent/damped_newton.jl
index a9921ba47..47ed56207 100644
--- a/lib/NonlinearSolveBase/src/descent/damped_newton.jl
+++ b/lib/NonlinearSolveBase/src/descent/damped_newton.jl
@@ -42,7 +42,7 @@ supports_trust_region(::DampedNewtonDescent) = true
     mode <: Union{Val{:normal_form}, Val{:least_squares}, Val{:simple}}
 end
 
-NonlinearSolveBase.@internal_caches DampedNewtonDescentCache :lincache :damping_fn_cache
+@internal_caches DampedNewtonDescentCache :lincache :damping_fn_cache
 
 function InternalAPI.init(
         prob::AbstractNonlinearProblem, alg::DampedNewtonDescent, J, fu, u; stats,
diff --git a/lib/NonlinearSolveBase/src/descent/dogleg.jl b/lib/NonlinearSolveBase/src/descent/dogleg.jl
index 133b5fabb..f446e9cf6 100644
--- a/lib/NonlinearSolveBase/src/descent/dogleg.jl
+++ b/lib/NonlinearSolveBase/src/descent/dogleg.jl
@@ -44,7 +44,7 @@ end
     normal_form <: Union{Val{false}, Val{true}}
 end
 
-NonlinearSolveBase.@internal_caches DoglegCache :newton_cache :cauchy_cache
+@internal_caches DoglegCache :newton_cache :cauchy_cache
 
 function InternalAPI.init(
         prob::AbstractNonlinearProblem, alg::Dogleg, J, fu, u;
@@ -111,7 +111,7 @@ function InternalAPI.solve!(
 
         l_grad = cache.internalnorm(δu_cauchy)
         @bb cache.δu_cache_mul = JᵀJ × vec(δu_cauchy)
-        δuJᵀJδu = Utils.dot(cache.δu_cache_mul, cache.δu_cache_mul)
+        δuJᵀJδu = Utils.safe_dot(cache.δu_cache_mul, cache.δu_cache_mul)
     else
         δu_cauchy = InternalAPI.solve!(
             cache.cauchy_cache, J, fu, u, idx; skip_solve, kwargs...
@@ -119,7 +119,7 @@ function InternalAPI.solve!(
         J_ = preinverted_jacobian(cache) ? inv(J) : J
         l_grad = cache.internalnorm(δu_cauchy)
         @bb cache.Jᵀδu_cache = J_ × vec(δu_cauchy)
-        δuJᵀJδu = Utils.dot(cache.Jᵀδu_cache, cache.Jᵀδu_cache)
+        δuJᵀJδu = Utils.safe_dot(cache.Jᵀδu_cache, cache.Jᵀδu_cache)
     end
     d_cauchy = (l_grad^3) / δuJᵀJδu
 
diff --git a/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
index 486308f09..409ed9ce9 100644
--- a/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
+++ b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
@@ -54,7 +54,7 @@ function InternalAPI.reinit_self!(cache::GeodesicAccelerationCache; p = cache.p,
     cache.last_step_accepted = false
 end
 
-NonlinearSolveBase.@internal_caches GeodesicAccelerationCache :descent_cache
+@internal_caches GeodesicAccelerationCache :descent_cache
 
 function get_velocity(cache::GeodesicAccelerationCache)
     return SciMLBase.get_du(cache.descent_cache, Val(1))
diff --git a/lib/NonlinearSolveBase/src/descent/newton.jl b/lib/NonlinearSolveBase/src/descent/newton.jl
index e453597a1..810661507 100644
--- a/lib/NonlinearSolveBase/src/descent/newton.jl
+++ b/lib/NonlinearSolveBase/src/descent/newton.jl
@@ -24,7 +24,7 @@ supports_line_search(::NewtonDescent) = true
     normal_form <: Union{Val{false}, Val{true}}
 end
 
-NonlinearSolveBase.@internal_caches NewtonDescentCache :lincache
+@internal_caches NewtonDescentCache :lincache
 
 function InternalAPI.init(
         prob::AbstractNonlinearProblem, alg::NewtonDescent, J, fu, u; stats,
diff --git a/lib/NonlinearSolveBase/src/descent/steepest.jl b/lib/NonlinearSolveBase/src/descent/steepest.jl
index b93c727c5..deb1a9817 100644
--- a/lib/NonlinearSolveBase/src/descent/steepest.jl
+++ b/lib/NonlinearSolveBase/src/descent/steepest.jl
@@ -21,7 +21,7 @@ supports_line_search(::SteepestDescent) = true
     preinverted_jacobian <: Union{Val{false}, Val{true}}
 end
 
-NonlinearSolveBase.@internal_caches SteepestDescentCache :lincache
+@internal_caches SteepestDescentCache :lincache
 
 function InternalAPI.init(
         prob::AbstractNonlinearProblem, alg::SteepestDescent, J, fu, u;
diff --git a/lib/NonlinearSolveBase/src/solve.jl b/lib/NonlinearSolveBase/src/solve.jl
index 3c50521a0..08b60e4db 100644
--- a/lib/NonlinearSolveBase/src/solve.jl
+++ b/lib/NonlinearSolveBase/src/solve.jl
@@ -2,13 +2,13 @@ function SciMLBase.__solve(
         prob::AbstractNonlinearProblem, alg::AbstractNonlinearSolveAlgorithm, args...;
         kwargs...
 )
-    cache = SciMLBase.init(prob, alg, args...; kwargs...)
-    return SciMLBase.solve!(cache)
+    cache = SciMLBase.__init(prob, alg, args...; kwargs...)
+    return CommonSolve.solve!(cache)
 end
 
 function CommonSolve.solve!(cache::AbstractNonlinearSolveCache)
     while not_terminated(cache)
-        SciMLBase.step!(cache)
+        CommonSolve.step!(cache)
     end
 
     # The solver might have set a different `retcode`
@@ -47,7 +47,7 @@ Performs one step of the nonlinear solver.
     respectively. For algorithms that don't use jacobian information, this keyword is
     ignored with a one-time warning.
 """
-function SciMLBase.step!(cache::AbstractNonlinearSolveCache, args...; kwargs...)
+function CommonSolve.step!(cache::AbstractNonlinearSolveCache, args...; kwargs...)
     not_terminated(cache) || return
 
     has_time_limit(cache) && (time_start = time())
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 6d7a66aa0..6e739c0f8 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -2,7 +2,7 @@ module Utils
 
 using ArrayInterface: ArrayInterface
 using FastClosures: @closure
-using LinearAlgebra: LinearAlgebra, Diagonal, Symmetric, norm, dot, cond, diagind, pinv, inv
+using LinearAlgebra: LinearAlgebra, Diagonal, Symmetric, norm, dot, cond, diagind, pinv
 using MaybeInplace: @bb
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLOperators: AbstractSciMLOperator
@@ -117,6 +117,7 @@ is_default_value(::Any, ::Symbol, ::Nothing) = true
 is_default_value(::Any, ::Symbol, ::Missing) = true
 is_default_value(::Any, ::Symbol, val::Int) = val == typemax(typeof(val))
 is_default_value(::Any, ::Symbol, ::Any) = false
+is_default_value(::Any, ::Any, ::Any) = false
 
 maybe_symmetric(x) = Symmetric(x)
 maybe_symmetric(x::Number) = x
diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
index ef949cb73..5be145a6e 100644
--- a/lib/NonlinearSolveFirstOrder/Project.toml
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -19,6 +19,7 @@ NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+SciMLJacobianOperators = "19f34311-ddf3-4b8b-af20-060888a46c0e"
 Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
diff --git a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
index 9fdfc379a..64b23aab6 100644
--- a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
+++ b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
@@ -22,6 +22,7 @@ using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
                           NewtonDescent, DampedNewtonDescent, GeodesicAcceleration,
                           Dogleg
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode, NonlinearFunction
+using SciMLJacobianOperators: VecJacOperator, JacVecOperator, StatefulJacobianOperator
 using Setfield: @set!
 using StaticArraysCore: SArray
 
@@ -41,9 +42,8 @@ include("solve.jl")
         @__DIR__, "..", "..", "..", "common", "nlls_problem_workloads.jl"
     ))
 
-    # XXX: TrustRegion
-    nlp_algs = [NewtonRaphson(), LevenbergMarquardt()]
-    nlls_algs = [GaussNewton(), LevenbergMarquardt()]
+    nlp_algs = [NewtonRaphson(), TrustRegion(), LevenbergMarquardt()]
+    nlls_algs = [GaussNewton(), TrustRegion(), LevenbergMarquardt()]
 
     @compile_workload begin
         for prob in nonlinear_problems, alg in nlp_algs
@@ -61,6 +61,8 @@ end
 export NewtonRaphson, PseudoTransient
 export GaussNewton, LevenbergMarquardt, TrustRegion
 
+export RadiusUpdateSchemes
+
 export GeneralizedFirstOrderAlgorithm
 
 end
diff --git a/lib/NonlinearSolveFirstOrder/src/trust_region.jl b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
index 5883d23b7..249d4fa72 100644
--- a/lib/NonlinearSolveFirstOrder/src/trust_region.jl
+++ b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
@@ -34,7 +34,459 @@ function TrustRegion(;
     descent = Dogleg(; linsolve, precs)
     trustregion = GenericTrustRegionScheme(;
         method = radius_update_scheme, step_threshold, shrink_threshold, expand_threshold,
-        shrink_factor, expand_factor, initial_trust_radius, max_trust_radius)
-    return GeneralizedFirstOrderAlgorithm{concrete_jac, :TrustRegion}(;
-        trustregion, descent, autodiff, vjp_autodiff, jvp_autodiff, max_shrink_times)
+        shrink_factor, expand_factor, initial_trust_radius, max_trust_radius
+    )
+    return GeneralizedFirstOrderAlgorithm(;
+        trustregion, descent, autodiff, vjp_autodiff, jvp_autodiff, max_shrink_times,
+        concrete_jac, name = :TrustRegion
+    )
+end
+
+# Don't Pollute the namespace
+"""
+    RadiusUpdateSchemes
+
+`RadiusUpdateSchemes` is provides different types of radius update schemes implemented in
+the Trust Region method. These schemes specify how the radius of the so-called trust region
+is updated after each iteration of the algorithm. The specific role and caveats associated
+with each scheme are provided below.
+
+## Using `RadiusUpdateSchemes`
+
+Simply put the desired scheme as follows:
+`sol = solve(prob, alg = TrustRegion(radius_update_scheme = RadiusUpdateSchemes.Hei))`.
+"""
+module RadiusUpdateSchemes
+# The weird definitions here are needed to main compatibility with the older enum variants
+
+abstract type AbstractRadiusUpdateScheme end
+
+function Base.show(io::IO, rus::AbstractRadiusUpdateScheme)
+    print(io, "RadiusUpdateSchemes.$(string(nameof(typeof(rus)))[3:end])")
+end
+
+const T = AbstractRadiusUpdateScheme
+
+struct __Simple <: AbstractRadiusUpdateScheme end
+"""
+    RadiusUpdateSchemes.Simple
+
+The simple or conventional radius update scheme. This scheme is chosen by default and
+follows the conventional approach to update the trust region radius, i.e. if the trial
+step is accepted it increases the radius by a fixed factor (bounded by a maximum radius)
+and if the trial step is rejected, it shrinks the radius by a fixed factor.
+"""
+const Simple = __Simple()
+
+struct __NLsolve <: AbstractRadiusUpdateScheme end
+"""
+    RadiusUpdateSchemes.NLsolve
+
+The same updating scheme as in NLsolve's (https://github.com/JuliaNLSolvers/NLsolve.jl)
+trust region dogleg implementation.
+"""
+const NLsolve = __NLsolve()
+
+struct __NocedalWright <: AbstractRadiusUpdateScheme end
+"""
+    RadiusUpdateSchemes.NocedalWright
+
+Trust region updating scheme as in Nocedal and Wright [see Alg 11.5, page 291].
+"""
+const NocedalWright = __NocedalWright()
+
+struct __Hei <: AbstractRadiusUpdateScheme end
+"""
+    RadiusUpdateSchemes.Hei
+
+This scheme is proposed in [hei2003self](@citet). The trust region radius depends on the
+size (norm) of the current step size. The hypothesis is to let the radius converge to zero
+as the iterations progress, which is more reliable and robust for ill-conditioned as well
+as degenerate problems.
+"""
+const Hei = __Hei()
+
+struct __Yuan <: AbstractRadiusUpdateScheme end
+"""
+    RadiusUpdateSchemes.Yuan
+
+This scheme is proposed by [yuan2015recent](@citet). Similar to Hei's scheme, the
+trust region is updated in a way so that it converges to zero, however here, the radius
+depends on the size (norm) of the current gradient of the objective (merit) function. The
+hypothesis is that the step size is bounded by the gradient size, so it makes sense to let
+the radius depend on the gradient.
+"""
+const Yuan = __Yuan()
+
+struct __Bastin <: AbstractRadiusUpdateScheme end
+"""
+    RadiusUpdateSchemes.Bastin
+
+This scheme is proposed by [bastin2010retrospective](@citet). The scheme is called a
+retrospective update scheme as it uses the model function at the current iteration to
+compute the ratio of the actual reduction and the predicted reduction in the previous trial
+step, and use this ratio to update the trust region radius. The hypothesis is to exploit the
+information made available during the optimization process in order to vary the accuracy
+of the objective function computation.
+"""
+const Bastin = __Bastin()
+
+struct __Fan <: AbstractRadiusUpdateScheme end
+"""
+    RadiusUpdateSchemes.Fan
+
+This scheme is proposed by [fan2006convergence](@citet). It is very much similar to Hei's
+and Yuan's schemes as it lets the trust region radius depend on the current size (norm) of
+the objective (merit) function itself. These new update schemes are known to improve local
+convergence.
+"""
+const Fan = __Fan()
+
+end
+
+const RUS = RadiusUpdateSchemes
+
+"""
+    GenericTrustRegionScheme(;
+        method = RadiusUpdateSchemes.Simple,
+        max_trust_radius = nothing, initial_trust_radius = nothing,
+        step_threshold = nothing, shrink_threshold = nothing, expand_threshold = nothing,
+        shrink_factor = nothing, expand_factor = nothing
+    )
+
+Trust Region Method that updates and stores the current trust region radius in
+`trust_region`. For any of the keyword arguments, if the value is `nothing`, then we use
+the value used in the respective paper.
+
+### Keyword Arguments
+
+  - `radius_update_scheme`: the choice of radius update scheme to be used. Defaults to
+    `RadiusUpdateSchemes.Simple` which follows the conventional approach. Other available
+    schemes are documented in [`RadiusUpdateSchemes`](@ref),. These schemes have the trust
+    region radius converging to zero that is seen to improve convergence. For more details,
+    see [1].
+  - `max_trust_radius`: the maximal trust region radius. Defaults to
+    `max(norm(fu), maximum(u) - minimum(u))`, except for `RadiusUpdateSchemes.NLsolve`
+    where it defaults to `Inf`.
+  - `initial_trust_radius`: the initial trust region radius. Defaults to
+    `max_trust_radius / 11`, except for `RadiusUpdateSchemes.NLsolve` where it defaults
+    to `u0_norm > 0 ? u0_norm : 1`.
+  - `step_threshold`: the threshold for taking a step. In every iteration, the threshold is
+    compared with a value `r`, which is the actual reduction in the objective function
+    divided by the predicted reduction. If `step_threshold > r` the model is not a good
+    approximation, and the step is rejected. Defaults to `nothing`.
+  - `shrink_threshold`: the threshold for shrinking the trust region radius. In every
+    iteration, the threshold is compared with a value `r` which is the actual reduction in
+    the objective function divided by the predicted reduction. If `shrink_threshold > r` the
+    trust region radius is shrunk by `shrink_factor`. Defaults to `nothing`.
+  - `expand_threshold`: the threshold for expanding the trust region radius. If a step is
+    taken, i.e `step_threshold < r` (with `r` defined in `shrink_threshold`), a check is
+    also made to see if `expand_threshold < r`. If that is true, the trust region radius is
+    expanded by `expand_factor`. Defaults to `nothing`.
+  - `shrink_factor`: the factor to shrink the trust region radius with if
+    `shrink_threshold > r` (with `r` defined in `shrink_threshold`). Defaults to `0.25`.
+  - `expand_factor`: the factor to expand the trust region radius with if
+    `expand_threshold < r` (with `r` defined in `shrink_threshold`). Defaults to `2.0`.
+"""
+@kwdef @concrete struct GenericTrustRegionScheme <: AbstractTrustRegionMethod
+    method <: RUS.AbstractRadiusUpdateScheme = RUS.Simple
+    step_threshold = nothing
+    shrink_threshold = nothing
+    shrink_factor = nothing
+    expand_factor = nothing
+    expand_threshold = nothing
+    max_trust_radius = nothing
+    initial_trust_radius = nothing
+end
+
+function InternalAPI.init(
+        prob::AbstractNonlinearProblem, alg::GenericTrustRegionScheme, f, fu, u, p,
+        args...; stats, internalnorm::F = L2_NORM, vjp_autodiff = nothing,
+        jvp_autodiff = nothing, kwargs...
+) where {F}
+    T = promote_type(eltype(u), eltype(fu))
+    u0_norm = internalnorm(u)
+    fu_norm = internalnorm(fu)
+
+    # Common Setup
+    mtr = max_trust_radius(alg.max_trust_radius, T, alg.method, u, fu_norm)
+    itr = initial_trust_radius(
+        alg.initial_trust_radius, T, alg.method, mtr, u0_norm, fu_norm
+    )
+    stt = step_threshold(alg.step_threshold, T, alg.method)
+    sht = shrink_threshold(alg.shrink_threshold, T, alg.method)
+    shf = shrink_factor(alg.shrink_factor, T, alg.method)
+    et = expand_threshold(alg.expand_threshold, T, alg.method)
+    ef = expand_factor(alg.expand_factor, T, alg.method)
+
+    # Scheme Specific Setup
+    p1, p2, p3, p4 = get_parameters(T, alg.method)
+    ϵ = T(1e-8)
+
+    vjp_operator = alg.method isa RUS.__Yuan || alg.method isa RUS.__Bastin ?
+                   VecJacOperator(prob, fu, u; autodiff = vjp_autodiff) : nothing
+
+    jvp_operator = alg.method isa RUS.__Bastin ?
+                   JacVecOperator(prob, fu, u; autodiff = jvp_autodiff) : nothing
+
+    if alg.method isa RUS.__Yuan
+        Jᵀfu_cache = StatefulJacobianOperator(vjp_operator, u, prob.p) * Utils.safe_vec(fu)
+        itr = T(p1 * internalnorm(Jᵀfu_cache))
+    elseif u isa Number
+        Jᵀfu_cache = u
+    else
+        @bb Jᵀfu_cache = similar(u)
+    end
+
+    if alg.method isa RUS.__Bastin
+        @bb δu_cache = similar(u)
+    else
+        δu_cache = nothing
+    end
+
+    @bb u_cache = similar(u)
+    @bb fu_cache = similar(fu)
+    @bb Jδu_cache = similar(fu)
+
+    return GenericTrustRegionSchemeCache(
+        alg.method, f, p, mtr, itr, itr, stt, sht, et, shf, ef,
+        p1, p2, p3, p4, ϵ, T(0), vjp_operator, jvp_operator, Jᵀfu_cache, Jδu_cache,
+        δu_cache, internalnorm, u_cache, fu_cache, false, 0, stats, alg
+    )
+end
+
+@concrete mutable struct GenericTrustRegionSchemeCache <: AbstractTrustRegionMethodCache
+    method
+    f
+    p
+    max_trust_radius
+    initial_trust_radius
+    trust_region
+    step_threshold
+    shrink_threshold
+    expand_threshold
+    shrink_factor
+    expand_factor
+    p1
+    p2
+    p3
+    p4
+    ϵ
+    ρ
+    vjp_operator
+    jvp_operator
+    Jᵀfu_cache
+    Jδu_cache
+    δu_cache
+    internalnorm
+    u_cache
+    fu_cache
+    last_step_accepted::Bool
+    shrink_counter::Int
+    stats::NLStats
+    alg
+end
+
+function InternalAPI.reinit!(
+        cache::GenericTrustRegionSchemeCache; p = cache.p, u0 = nothing, kwargs...
+)
+    cache.p = p
+    if u0 !== nothing
+        u0_norm = cache.internalnorm(u0)
+    end
+    cache.last_step_accepted = false
+    cache.shrink_counter = 0
+end
+
+# Defaults
+for func in (
+    :max_trust_radius, :initial_trust_radius, :step_threshold, :shrink_threshold,
+    :shrink_factor, :expand_threshold, :expand_factor
+)
+    @eval function $(func)(val, ::Type{T}, args...) where {T}
+        iszero(val) && return $(func)(nothing, T, args...)
+        return T(val)
+    end
+end
+
+max_trust_radius(::Nothing, ::Type{T}, method, u, fu_norm) where {T} = T(Inf)
+function max_trust_radius(::Nothing, ::Type{T}, ::Union{RUS.__Simple, RUS.__NocedalWright},
+        u, fu_norm) where {T}
+    u_min, u_max = extrema(u)
+    return max(T(fu_norm), u_max - u_min)
+end
+
+function initial_trust_radius(
+        ::Nothing, ::Type{T}, method, max_tr, u0_norm, fu_norm
+) where {T}
+    method isa RUS.__NLsolve && return T(ifelse(u0_norm > 0, u0_norm, 1))
+    (method isa RUS.__Hei || method isa RUS.__Bastin) && return T(1)
+    method isa RUS.__Fan && return T((fu_norm^0.99) / 10)
+    return T(max_tr / 11)
+end
+
+function step_threshold(::Nothing, ::Type{T}, method) where {T}
+    method isa RUS.__Hei && return T(0)
+    method isa RUS.__Yuan && return T(1 // 1000)
+    method isa RUS.__Bastin && return T(1 // 20)
+    return T(1 // 10000)
+end
+
+function shrink_threshold(::Nothing, ::Type{T}, method) where {T}
+    method isa RUS.__Hei && return T(0)
+    (method isa RUS.__NLsolve || method isa RUS.__Bastin) && return T(1 // 20)
+    return T(1 // 4)
+end
+
+function expand_threshold(::Nothing, ::Type{T}, method) where {T}
+    method isa RUS.__NLsolve && return T(9 // 10)
+    method isa RUS.__Hei && return T(0)
+    method isa RUS.__Bastin && return T(9 // 10)
+    return T(3 // 4)
+end
+
+function shrink_factor(::Nothing, ::Type{T}, method) where {T}
+    method isa RUS.__NLsolve && return T(1 // 2)
+    method isa RUS.__Hei && return T(0)
+    method isa RUS.__Bastin && return T(1 // 20)
+    return T(1 // 4)
+end
+
+function get_parameters(::Type{T}, method) where {T}
+    method isa RUS.__NLsolve && return (T(1 // 2), T(0), T(0), T(0))
+    method isa RUS.__Hei && return (T(5), T(1 // 10), T(15 // 100), T(15 // 100))
+    method isa RUS.__Yuan && return (T(2), T(1 // 6), T(6), T(0))
+    method isa RUS.__Fan && return (T(1 // 10), T(1 // 4), T(12), T(1e18))
+    method isa RUS.__Bastin && return (T(5 // 2), T(1 // 4), T(0), T(0))
+    return (T(0), T(0), T(0), T(0))
+end
+
+expand_factor(::Nothing, ::Type{T}, method) where {T} = T(2)
+
+function rfunc_adaptive_trust_region(r::R, c2::R, M::R, γ1::R, β::R) where {R <: Real}
+    return ifelse(
+        r ≥ c2,
+        (2 * (M - 1 - γ2) * atan(r - c2) + (1 + γ2)) / R(π),
+        (1 - γ1 - β) * (exp(r - c2) + β / (1 - γ1 - β))
+    )
+end
+
+function InternalAPI.solve!(
+        cache::GenericTrustRegionSchemeCache, J, fu, u, δu, descent_stats
+)
+    T = promote_type(eltype(u), eltype(fu))
+    @bb @. cache.u_cache = u + δu
+    cache.fu_cache = Utils.evaluate_f!!(cache.f, cache.fu_cache, cache.u_cache, cache.p)
+    cache.stats.nf += 1
+
+    if hasfield(typeof(descent_stats), :δuJᵀJδu) && !isnan(descent_stats.δuJᵀJδu)
+        δuJᵀJδu = descent_stats.δuJᵀJδu
+    else
+        @bb cache.Jδu_cache = J × vec(δu)
+        δuJᵀJδu = Utils.safe_dot(cache.Jδu_cache, cache.Jδu_cache)
+    end
+    @bb cache.Jᵀfu_cache = transpose(J) × vec(fu)
+    num = (cache.internalnorm(cache.fu_cache)^2 - cache.internalnorm(fu)^2) / 2
+    denom = Utils.safe_dot(δu, cache.Jᵀfu_cache) + δuJᵀJδu / 2
+    cache.ρ = num / denom
+
+    if cache.ρ > cache.step_threshold
+        cache.last_step_accepted = true
+    else
+        cache.last_step_accepted = false
+    end
+
+    if cache.method isa RUS.__Simple
+        if cache.ρ < cache.shrink_threshold
+            cache.trust_region *= cache.shrink_factor
+            cache.shrink_counter += 1
+        else
+            cache.shrink_counter = 0
+            if cache.ρ > cache.expand_threshold && cache.ρ > cache.step_threshold
+                cache.trust_region = cache.expand_factor * cache.trust_region
+            end
+        end
+    elseif cache.method isa RUS.__NLsolve
+        if cache.ρ < cache.shrink_threshold
+            cache.trust_region *= cache.shrink_factor
+            cache.shrink_counter += 1
+        else
+            cache.shrink_counter = 0
+            if cache.ρ ≥ cache.expand_threshold
+                cache.trust_region = cache.expand_factor * cache.internalnorm(δu)
+            elseif cache.ρ ≥ cache.p1
+                cache.trust_region = max(
+                    cache.trust_region, cache.expand_factor * cache.internalnorm(δu)
+                )
+            end
+        end
+    elseif cache.method isa RUS.__NocedalWright
+        if cache.ρ < cache.shrink_threshold
+            cache.trust_region = cache.shrink_factor * cache.internalnorm(δu)
+            cache.shrink_counter += 1
+        else
+            cache.shrink_counter = 0
+            if cache.ρ > cache.expand_threshold &&
+               abs(cache.internalnorm(δu) - cache.trust_region) < 1e-6 * cache.trust_region
+                cache.trust_region = cache.expand_factor * cache.trust_region
+            end
+        end
+    elseif cache.method isa RUS.__Hei
+        tr_new = rfunc_adaptive_trust_region(
+            cache.ρ, cache.shrink_threshold, cache.p1, cache.p3, cache.p4
+        )
+        if tr_new < cache.trust_region
+            cache.shrink_counter += 1
+        else
+            cache.shrink_counter = 0
+        end
+        cache.trust_region = tr_new
+    elseif cache.method isa RUS.__Yuan
+        if cache.ρ < cache.shrink_threshold
+            cache.p1 = cache.p2 * cache.p1
+            cache.shrink_counter += 1
+        else
+            if cache.ρ ≥ cache.expand_threshold &&
+               2 * cache.internalnorm(δu) > cache.trust_region
+                cache.p1 = cache.p3 * cache.p1
+            end
+            cache.shrink_counter = 0
+        end
+        operator = StatefulJacobianOperator(cache.vjp_operator, cache.u_cache, cache.p)
+        @bb cache.Jᵀfu_cache = operator × vec(cache.fu_cache)
+        cache.trust_region = cache.p1 * cache.internalnorm(cache.Jᵀfu_cache)
+    elseif cache.method isa RUS.__Fan
+        if cache.ρ < cache.shrink_threshold
+            cache.p1 *= cache.p2
+            cache.shrink_counter += 1
+        else
+            cache.shrink_counter = 0
+            cache.ρ > cache.expand_threshold &&
+                (cache.p1 = min(cache.p1 * cache.p3, cache.p4))
+        end
+        cache.trust_region = cache.p1 * (cache.internalnorm(cache.fu_cache)^T(0.99))
+    elseif cache.method isa RUS.__Bastin
+        if cache.ρ > cache.step_threshold
+            jvp_op = StatefulJacobianOperator(cache.jvp_operator, cache.u_cache, cache.p)
+            vjp_op = StatefulJacobianOperator(cache.vjp_operator, cache.u_cache, cache.p)
+            @bb cache.Jδu_cache = jvp_op × vec(cache.δu_cache)
+            @bb cache.Jᵀfu_cache = vjp_op × vec(cache.fu_cache)
+            denom_1 = dot(_vec(cache.Jᵀfu_cache), cache.Jᵀfu_cache)
+            @bb cache.Jᵀfu_cache = vjp_op × vec(cache.Jδu_cache)
+            denom_2 = dot(_vec(cache.Jᵀfu_cache), cache.Jᵀfu_cache)
+            denom = denom_1 + denom_2 / 2
+            ρ = num / denom
+            if ρ ≥ cache.expand_threshold
+                cache.trust_region = cache.p1 * cache.internalnorm(cache.δu_cache)
+            end
+            cache.shrink_counter = 0
+        else
+            cache.trust_region *= cache.p2
+            cache.shrink_counter += 1
+        end
+    end
+
+    cache.trust_region = min(cache.trust_region, cache.max_trust_radius)
+
+    return cache.last_step_accepted, cache.u_cache, cache.fu_cache
 end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 858970a0c..f51064000 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -130,7 +130,7 @@ function solve_adjoint_internal end
         #!format: on
 
         @compile_workload begin
-            for prob in (prob_scalar, prob_iip, prob_oop)
+            for prob in (prob_scalar, prob_iip, prob_oop), alg in algs
                 CommonSolve.solve(prob, alg; abstol = 1e-2)
             end
         end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index eaae0ee6a..e352f4891 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -3,137 +3,80 @@ module NonlinearSolve
 using Reexport: @reexport
 using PrecompileTools: @compile_workload, @setup_workload
 
-using ArrayInterface: ArrayInterface, can_setindex, restructure, fast_scalar_indexing,
-                      ismutable
-using CommonSolve: solve, init, solve!
+using ArrayInterface: ArrayInterface
+using CommonSolve: CommonSolve, solve, solve!
 using ConcreteStructs: @concrete
 using DiffEqBase: DiffEqBase # Needed for `init` / `solve` dispatches
 using FastClosures: @closure
-using LinearAlgebra: LinearAlgebra, Diagonal, I, LowerTriangular, Symmetric,
-                     UpperTriangular, axpy!, cond, diag, diagind, dot, issuccess, istril,
-                     istriu, lu, mul!, norm, pinv, tril!, triu!
-using LineSearch: LineSearch, AbstractLineSearchCache, LineSearchesJL, NoLineSearch,
-                  RobustNonMonotoneLineSearch, BackTracking, LiFukushimaLineSearch
-using LinearSolve: LinearSolve
-using MaybeInplace: @bb
-using NonlinearSolveBase: NonlinearSolveBase,
-                          nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution,
-                          nonlinearsolve_∂f_∂p, nonlinearsolve_∂f_∂u,
-                          L2_NORM,
-                          AbsNormTerminationMode, AbstractNonlinearTerminationMode,
-                          AbstractSafeBestNonlinearTerminationMode,
-                          select_forward_mode_autodiff, select_reverse_mode_autodiff,
-                          select_jacobian_autodiff,
-                          construct_jacobian_cache,
-                          DescentResult,
-                          SteepestDescent, NewtonDescent, DampedNewtonDescent, Dogleg,
-                          GeodesicAcceleration,
-                          reset_timer!, @static_timeit,
-                          init_nonlinearsolve_trace, update_trace!, reset!
-
+using LinearAlgebra: LinearAlgebra, norm
+using LineSearch: BackTracking
+using NonlinearSolveBase: NonlinearSolveBase, InternalAPI, AbstractNonlinearSolveAlgorithm,
+                          AbstractNonlinearSolveCache, Utils, L2_NORM
+
+using Preferences: set_preferences!
+using SciMLBase: SciMLBase, NLStats, ReturnCode, AbstractNonlinearProblem, NonlinearProblem,
+                 NonlinearLeastSquaresProblem
+using SymbolicIndexingInterface: SymbolicIndexingInterface
+using StaticArraysCore: StaticArray
+
+# Default Algorithm
+using NonlinearSolveFirstOrder: NewtonRaphson, TrustRegion, LevenbergMarquardt, GaussNewton,
+                                RUS
 using NonlinearSolveQuasiNewton: Broyden, Klement
+using SimpleNonlinearSolve: SimpleBroyden, SimpleKlement
 
-using Preferences: Preferences, set_preferences!
-using RecursiveArrayTools: recursivecopy!
-using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, AbstractNonlinearProblem,
-                 _unwrap_val, isinplace, NLStats, NonlinearFunction,
-                 NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode, get_du, step!,
-                 set_u!, LinearProblem, IdentityOperator
-using SciMLOperators: AbstractSciMLOperator
-using SimpleNonlinearSolve: SimpleNonlinearSolve
-using StaticArraysCore: StaticArray, SVector, SArray, MArray, Size, SMatrix
-
-# AD Support
-using ADTypes: ADTypes, AbstractADType, AutoFiniteDiff, AutoForwardDiff,
-               AutoPolyesterForwardDiff, AutoZygote, AutoEnzyme, AutoSparse
-using DifferentiationInterface: DifferentiationInterface
-using FiniteDiff: FiniteDiff
-using ForwardDiff: ForwardDiff, Dual
-using SciMLJacobianOperators: VecJacOperator, JacVecOperator, StatefulJacobianOperator
+# Default AD Support
+using FiniteDiff: FiniteDiff    # Default Finite Difference Method
+using ForwardDiff: ForwardDiff  # Default Forward Mode AD
 
-## Sparse AD Support
-using SparseArrays: AbstractSparseMatrix, SparseMatrixCSC
-using SparseMatrixColorings: SparseMatrixColorings # NOTE: This triggers an extension in NonlinearSolveBase
+# Sparse AD Support: Implemented via extensions
+using SparseArrays: SparseArrays
+using SparseMatrixColorings: SparseMatrixColorings
 
-const DI = DifferentiationInterface
+const SII = SymbolicIndexingInterface
 
-include("timer_outputs.jl")
-include("internal/helpers.jl")
+include("helpers.jl")
 
-include("algorithms/extension_algs.jl")
+include("polyalg.jl")
+# include("extension_algs.jl")
 
-include("utils.jl")
 include("default.jl")
 
-const ALL_SOLVER_TYPES = [
-    Nothing, AbstractNonlinearSolveAlgorithm, GeneralizedDFSane,
-    GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm,
-    LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
-    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL,
-    CMINPACK, PETScSNES,
-    NonlinearSolvePolyAlgorithm{:NLLS, <:Any}, NonlinearSolvePolyAlgorithm{:NLS, <:Any}
-]
+# const ALL_SOLVER_TYPES = [
+#     Nothing, AbstractNonlinearSolveAlgorithm, GeneralizedDFSane,
+#     GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm,
+#     LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
+#     SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL,
+#     CMINPACK, PETScSNES,
+#     NonlinearSolvePolyAlgorithm{:NLLS, <:Any}, NonlinearSolvePolyAlgorithm{:NLS, <:Any}
+# ]
 
-include("internal/forward_diff.jl") # we need to define after the algorithms
+# include("internal/forward_diff.jl") # we need to define after the algorithms
 
 @setup_workload begin
-    nlfuncs = (
-        (NonlinearFunction{false}((u, p) -> u .* u .- p), 0.1),
-        (NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p), [0.1])
-    )
-    probs_nls = NonlinearProblem[]
-    for (fn, u0) in nlfuncs
-        push!(probs_nls, NonlinearProblem(fn, u0, 2.0))
-    end
-
-    nls_algs = (
-        nothing
-    )
-
-    probs_nlls = NonlinearLeastSquaresProblem[]
-    nlfuncs = (
-        (NonlinearFunction{false}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
-        (NonlinearFunction{false}((u, p) -> vcat(u .* u .- p, u .* u .- p)), [0.1, 0.1]),
-        (
-            NonlinearFunction{true}(
-                (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(1)),
-            [0.1, 0.0]),
-        (
-            NonlinearFunction{true}((du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p),
-                resid_prototype = zeros(4)),
-            [0.1, 0.1]
-        )
-    )
-    for (fn, u0) in nlfuncs
-        push!(probs_nlls, NonlinearLeastSquaresProblem(fn, u0, 2.0))
-    end
-
-    nlls_algs = (
-        LevenbergMarquardt(),
-        GaussNewton(),
-        TrustRegion(),
-        nothing
-    )
+    include(joinpath(@__DIR__, "..", "common", "nonlinear_problem_workloads.jl"))
+    include(joinpath(@__DIR__, "..", "common", "nlls_problem_workloads.jl"))
 
     @compile_workload begin
-        for prob in probs_nls, alg in nls_algs
-            solve(prob, alg; abstol = 1e-2, verbose = false)
+        for prob in nonlinear_problems
+            CommonSolve.solve(prob, nothing; abstol = 1e-2, verbose = false)
         end
-        for prob in probs_nlls, alg in nlls_algs
-            solve(prob, alg; abstol = 1e-2, verbose = false)
+
+        for prob in nlls_problems
+            CommonSolve.solve(prob, nothing; abstol = 1e-2, verbose = false)
         end
     end
 end
 
 # Rexexports
-@reexport using SciMLBase, NonlinearSolveBase
+@reexport using SciMLBase, NonlinearSolveBase, LineSearch, ADTypes
 @reexport using NonlinearSolveFirstOrder, NonlinearSolveSpectralMethods,
                 NonlinearSolveQuasiNewton, SimpleNonlinearSolve
-@reexport using LineSearch
-@reexport using ADTypes
+@reexport using LinearSolve
 
-export NonlinearSolvePolyAlgorithm, RobustMultiNewton,
-       FastShortcutNonlinearPolyalg, FastShortcutNLLSPolyalg
+# Poly Algorithms
+export NonlinearSolvePolyAlgorithm,
+       RobustMultiNewton, FastShortcutNonlinearPolyalg, FastShortcutNLLSPolyalg
 
 # Extension Algorithms
 export LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
diff --git a/src/algorithms/extension_algs.jl b/src/algorithms/extension_algs.jl
deleted file mode 100644
index a5e52cab4..000000000
--- a/src/algorithms/extension_algs.jl
+++ /dev/null
@@ -1,469 +0,0 @@
-# This file only include the algorithm struct to be exported by NonlinearSolve.jl. The main
-# functionality is implemented as package extensions
-"""
-    LeastSquaresOptimJL(alg = :lm; linsolve = nothing, autodiff::Symbol = :central)
-
-Wrapper over [LeastSquaresOptim.jl](https://github.com/matthieugomez/LeastSquaresOptim.jl)
-for solving `NonlinearLeastSquaresProblem`.
-
-### Arguments
-
-  - `alg`: Algorithm to use. Can be `:lm` or `:dogleg`.
-
-### Keyword Arguments
-
-  - `linsolve`: Linear solver to use. Can be `:qr`, `:cholesky` or `:lsmr`. If `nothing`,
-    then `LeastSquaresOptim.jl` will choose the best linear solver based on the Jacobian
-    structure.
-  - `autodiff`: Automatic differentiation / Finite Differences. Can be `:central` or
-    `:forward`.
-
-!!! note
-
-    This algorithm is only available if `LeastSquaresOptim.jl` is installed and loaded.
-"""
-struct LeastSquaresOptimJL{alg, linsolve} <: AbstractNonlinearSolveExtensionAlgorithm
-    autodiff
-end
-
-function LeastSquaresOptimJL(alg = :lm; linsolve = nothing, autodiff = :central)
-    @assert alg in (:lm, :dogleg)
-    @assert linsolve === nothing || linsolve in (:qr, :cholesky, :lsmr)
-    autodiff isa Symbol && @assert autodiff in (:central, :forward)
-
-    if Base.get_extension(@__MODULE__, :NonlinearSolveLeastSquaresOptimExt) === nothing
-        error("LeastSquaresOptimJL requires LeastSquaresOptim.jl to be loaded")
-    end
-
-    return LeastSquaresOptimJL{alg, linsolve}(autodiff)
-end
-
-"""
-    FastLevenbergMarquardtJL(linsolve::Symbol = :cholesky; factor = 1e-6,
-        factoraccept = 13.0, factorreject = 3.0, factorupdate = :marquardt,
-        minscale = 1e-12, maxscale = 1e16, minfactor = 1e-28, maxfactor = 1e32,
-        autodiff = nothing)
-
-Wrapper over [FastLevenbergMarquardt.jl](https://github.com/kamesy/FastLevenbergMarquardt.jl)
-for solving `NonlinearLeastSquaresProblem`. For details about the other keyword arguments
-see the documentation for `FastLevenbergMarquardt.jl`.
-
-!!! warning
-
-    This is not really the fastest solver. It is called that since the original package
-    is called "Fast". `LevenbergMarquardt()` is almost always a better choice.
-
-### Arguments
-
-  - `linsolve`: Linear solver to use. Can be `:qr` or `:cholesky`.
-
-### Keyword Arguments
-
-  - `autodiff`: determines the backend used for the Jacobian. Note that this argument is
-    ignored if an analytical Jacobian is passed, as that will be used instead. Defaults to
-    `nothing` which means that a default is selected according to the problem specification!
-
-!!! note
-
-    This algorithm is only available if `FastLevenbergMarquardt.jl` is installed and loaded.
-"""
-@concrete struct FastLevenbergMarquardtJL{linsolve} <:
-                 AbstractNonlinearSolveExtensionAlgorithm
-    autodiff
-    factor
-    factoraccept
-    factorreject
-    factorupdate::Symbol
-    minscale
-    maxscale
-    minfactor
-    maxfactor
-end
-
-function FastLevenbergMarquardtJL(
-        linsolve::Symbol = :cholesky; factor = 1e-6, factoraccept = 13.0,
-        factorreject = 3.0, factorupdate = :marquardt, minscale = 1e-12,
-        maxscale = 1e16, minfactor = 1e-28, maxfactor = 1e32, autodiff = nothing)
-    @assert linsolve in (:qr, :cholesky)
-    @assert factorupdate in (:marquardt, :nielson)
-
-    if Base.get_extension(@__MODULE__, :NonlinearSolveFastLevenbergMarquardtExt) === nothing
-        error("FastLevenbergMarquardtJL requires FastLevenbergMarquardt.jl to be loaded")
-    end
-
-    return FastLevenbergMarquardtJL{linsolve}(autodiff, factor, factoraccept, factorreject,
-        factorupdate, minscale, maxscale, minfactor, maxfactor)
-end
-
-"""
-    CMINPACK(; method::Symbol = :auto, autodiff = missing)
-
-### Keyword Arguments
-
-  - `method`: the choice of method for the solver.
-  - `autodiff`: Defaults to `missing`, which means we will default to letting `MINPACK`
-    construct the jacobian if `f.jac` is not provided. In other cases, we use it to generate
-    a jacobian similar to other NonlinearSolve solvers.
-
-### Submethod Choice
-
-The keyword argument `method` can take on different value depending on which method of
-`fsolve` you are calling. The standard choices of `method` are:
-
-  - `:hybr`: Modified version of Powell's algorithm. Uses MINPACK routine
-    [`hybrd1`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrd1.c)
-  - `:lm`: Levenberg-Marquardt. Uses MINPACK routine
-    [`lmdif1`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmdif1.c)
-  - `:lmdif`: Advanced Levenberg-Marquardt (more options available with `; kwargs...`). See
-    MINPACK routine [`lmdif`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmdif.c)
-    for more information
-  - `:hybrd`: Advanced modified version of Powell's algorithm (more options available with
-    `; kwargs...`). See MINPACK routine
-    [`hybrd`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrd.c)
-    for more information
-
-If a Jacobian is supplied as part of the [`NonlinearFunction`](@ref nonlinearfunctions),
-then the following methods are allowed:
-
-  - `:hybr`: Advanced modified version of Powell's algorithm with user supplied Jacobian.
-    Additional arguments are available via `; kwargs...`. See MINPACK routine
-    [`hybrj`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrj.c)
-    for more information
-  - `:lm`: Advanced Levenberg-Marquardt with user supplied Jacobian. Additional arguments
-    are available via `; kwargs...`. See MINPACK routine
-    [`lmder`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmder.c)
-    for more information
-
-The default choice of `:auto` selects `:hybr` for NonlinearProblem and `:lm` for
-NonlinearLeastSquaresProblem.
-
-!!! note
-
-    This algorithm is only available if `MINPACK.jl` is installed and loaded.
-"""
-@concrete struct CMINPACK <: AbstractNonlinearSolveExtensionAlgorithm
-    method::Symbol
-    autodiff
-end
-
-function CMINPACK(; method::Symbol = :auto, autodiff = missing)
-    if Base.get_extension(@__MODULE__, :NonlinearSolveMINPACKExt) === nothing
-        error("CMINPACK requires MINPACK.jl to be loaded")
-    end
-    return CMINPACK(method, autodiff)
-end
-
-"""
-    NLsolveJL(; method = :trust_region, autodiff = :central, linesearch = Static(),
-        linsolve = (x, A, b) -> copyto!(x, A\\b), factor = one(Float64), autoscale = true,
-        m = 10, beta = one(Float64))
-
-### Keyword Arguments
-
-  - `method`: the choice of method for solving the nonlinear system.
-  - `autodiff`: the choice of method for generating the Jacobian. Defaults to `:central` or
-    central differencing via FiniteDiff.jl. The other choices are `:forward` or `ADTypes`
-    similar to other solvers in NonlinearSolve.
-  - `linesearch`: the line search method to be used within the solver method. The choices
-    are line search types from
-    [LineSearches.jl](https://github.com/JuliaNLSolvers/LineSearches.jl).
-  - `linsolve`: a function `linsolve(x, A, b)` that solves `Ax = b`.
-  - `factor`: determines the size of the initial trust region. This size is set to the
-    product of factor and the euclidean norm of `u0` if nonzero, or else to factor itself.
-  - `autoscale`: if true, then the variables will be automatically rescaled. The scaling
-    factors are the norms of the Jacobian columns.
-  - `m`: the amount of history in the Anderson method. Naive "Picard"-style iteration can be
-    achieved by setting m=0, but that isn't advisable for contractions whose Lipschitz
-    constants are close to 1. If convergence fails, though, you may consider lowering it.
-  - `beta`: It is also known as DIIS or Pulay mixing, this method is based on the
-    acceleration of the fixed-point iteration xₙ₊₁ = xₙ + beta*f(xₙ), where by default
-    beta = 1.
-
-!!! warning
-
-    Line Search Algorithms from [`LineSearch.jl`](https://github.com/SciML/LineSearch.jl)
-    aren't supported by `NLsolveJL`. Instead, use the line search algorithms from
-    [`LineSearches.jl`](https://github.com/JuliaNLSolvers/LineSearches.jl).
-
-### Submethod Choice
-
-Choices for methods in `NLsolveJL`:
-
-  - `:anderson`: Anderson-accelerated fixed-point iteration
-  - `:broyden`: Broyden's quasi-Newton method
-  - `:newton`: Classical Newton method with an optional line search
-  - `:trust_region`: Trust region Newton method (the default choice)
-
-For more information on these arguments, consult the
-[NLsolve.jl documentation](https://github.com/JuliaNLSolvers/NLsolve.jl).
-
-!!! note
-
-    This algorithm is only available if `NLsolve.jl` is installed and loaded.
-"""
-@concrete struct NLsolveJL <: AbstractNonlinearSolveExtensionAlgorithm
-    method::Symbol
-    autodiff
-    linesearch
-    linsolve
-    factor
-    autoscale::Bool
-    m::Int
-    beta
-end
-
-function NLsolveJL(; method = :trust_region, autodiff = :central, linesearch = missing,
-        linsolve = (x, A, b) -> copyto!(x, A \ b), factor = 1.0,
-        autoscale = true, m = 10, beta = one(Float64))
-    if Base.get_extension(@__MODULE__, :NonlinearSolveNLsolveExt) === nothing
-        error("NLsolveJL requires NLsolve.jl to be loaded")
-    end
-
-    if autodiff isa Symbol && autodiff !== :central && autodiff !== :forward
-        error("`autodiff` must be `:central` or `:forward`.")
-    end
-
-    return NLsolveJL(method, autodiff, linesearch, linsolve, factor, autoscale, m, beta)
-end
-
-"""
-    NLSolversJL(method; autodiff = nothing)
-    NLSolversJL(; method, autodiff = nothing)
-
-Wrapper over NLSolvers.jl Nonlinear Equation Solvers. We automatically construct the
-jacobian function and supply it to the solver.
-
-### Arguments
-
-  - `method`: the choice of method for solving the nonlinear system. See the documentation
-    for NLSolvers.jl for more information.
-  - `autodiff`: the choice of method for generating the Jacobian. Defaults to `nothing`
-    which means that a default is selected according to the problem specification. Can be
-    any valid ADTypes.jl autodiff type (conditional on that backend being supported in
-    NonlinearSolve.jl).
-"""
-struct NLSolversJL{M, AD} <: AbstractNonlinearSolveExtensionAlgorithm
-    method::M
-    autodiff::AD
-
-    function NLSolversJL(method, autodiff)
-        if Base.get_extension(@__MODULE__, :NonlinearSolveNLSolversExt) === nothing
-            error("NLSolversJL requires NLSolvers.jl to be loaded")
-        end
-
-        return new{typeof(method), typeof(autodiff)}(method, autodiff)
-    end
-end
-
-NLSolversJL(method; autodiff = nothing) = NLSolversJL(method, autodiff)
-NLSolversJL(; method, autodiff = nothing) = NLSolversJL(method, autodiff)
-
-"""
-    SpeedMappingJL(; σ_min = 0.0, stabilize::Bool = false, check_obj::Bool = false,
-        orders::Vector{Int} = [3, 3, 2], time_limit::Real = 1000)
-
-Wrapper over [SpeedMapping.jl](https://nicolasl-s.github.io/SpeedMapping.jl/) for solving
-Fixed Point Problems. We allow using this algorithm to solve root finding problems as well.
-
-### Keyword Arguments
-
-  - `σ_min`: Setting to `1` may avoid stalling (see [lepage2021alternating](@cite)).
-  - `stabilize`: performs a stabilization mapping before extrapolating. Setting to `true`
-    may improve the performance for applications like accelerating the EM or MM algorithms
-    (see [lepage2021alternating](@cite)).
-  - `check_obj`: In case of NaN or Inf values, the algorithm restarts at the best past
-    iterate.
-  - `orders`: determines ACX's alternating order. Must be between `1` and `3` (where `1`
-    means no extrapolation). The two recommended orders are `[3, 2]` and `[3, 3, 2]`, the
-    latter being potentially better for highly non-linear applications (see
-    [lepage2021alternating](@cite)).
-  - `time_limit`: time limit for the algorithm.
-
-!!! note
-
-    This algorithm is only available if `SpeedMapping.jl` is installed and loaded.
-"""
-@concrete struct SpeedMappingJL <: AbstractNonlinearSolveExtensionAlgorithm
-    σ_min
-    stabilize::Bool
-    check_obj::Bool
-    orders::Vector{Int}
-end
-
-function SpeedMappingJL(; σ_min = 0.0, stabilize::Bool = false, check_obj::Bool = false,
-        orders::Vector{Int} = [3, 3, 2])
-    if Base.get_extension(@__MODULE__, :NonlinearSolveSpeedMappingExt) === nothing
-        error("SpeedMappingJL requires SpeedMapping.jl to be loaded")
-    end
-
-    return SpeedMappingJL(σ_min, stabilize, check_obj, orders)
-end
-
-"""
-    FixedPointAccelerationJL(; algorithm = :Anderson, m = missing,
-        condition_number_threshold = missing, extrapolation_period = missing,
-        replace_invalids = :NoAction)
-
-Wrapper over [FixedPointAcceleration.jl](https://s-baumann.github.io/FixedPointAcceleration.jl/)
-for solving Fixed Point Problems. We allow using this algorithm to solve root finding
-problems as well.
-
-### Keyword Arguments
-
-  - `algorithm`: The algorithm to use. Can be `:Anderson`, `:MPE`, `:RRE`, `:VEA`, `:SEA`,
-    `:Simple`, `:Aitken` or `:Newton`.
-  - `m`: The number of previous iterates to use for the extrapolation. Only valid for
-    `:Anderson`.
-  - `condition_number_threshold`: The condition number threshold for Least Squares Problem.
-    Only valid for `:Anderson`.
-  - `extrapolation_period`: The number of iterates between extrapolations. Only valid for
-    `:MPE`, `:RRE`, `:VEA` and `:SEA`. Defaults to `7` for `:MPE` & `:RRE`, and `6` for
-    `:SEA` and `:VEA`. For `:SEA` and `:VEA`, this must be a multiple of `2`.
-  - `replace_invalids`: The method to use for replacing invalid iterates. Can be
-    `:ReplaceInvalids`, `:ReplaceVector` or `:NoAction`.
-
-!!! note
-
-    This algorithm is only available if `FixedPointAcceleration.jl` is installed and loaded.
-"""
-@concrete struct FixedPointAccelerationJL <: AbstractNonlinearSolveExtensionAlgorithm
-    algorithm::Symbol
-    extrapolation_period::Int
-    replace_invalids::Symbol
-    dampening
-    m::Int
-    condition_number_threshold
-end
-
-function FixedPointAccelerationJL(;
-        algorithm = :Anderson, m = missing, condition_number_threshold = missing,
-        extrapolation_period = missing, replace_invalids = :NoAction, dampening = 1.0)
-    if Base.get_extension(@__MODULE__, :NonlinearSolveFixedPointAccelerationExt) === nothing
-        error("FixedPointAccelerationJL requires FixedPointAcceleration.jl to be loaded")
-    end
-
-    @assert algorithm in (:Anderson, :MPE, :RRE, :VEA, :SEA, :Simple, :Aitken, :Newton)
-    @assert replace_invalids in (:ReplaceInvalids, :ReplaceVector, :NoAction)
-
-    if algorithm !== :Anderson
-        if condition_number_threshold !== missing
-            error("`condition_number_threshold` is only valid for Anderson acceleration")
-        end
-        if m !== missing
-            error("`m` is only valid for Anderson acceleration")
-        end
-    end
-    condition_number_threshold === missing && (condition_number_threshold = 1e3)
-    m === missing && (m = 10)
-
-    if algorithm !== :MPE && algorithm !== :RRE && algorithm !== :VEA && algorithm !== :SEA
-        if extrapolation_period !== missing
-            error("`extrapolation_period` is only valid for MPE, RRE, VEA and SEA")
-        end
-    end
-    if extrapolation_period === missing
-        extrapolation_period = algorithm === :SEA || algorithm === :VEA ? 6 : 7
-    else
-        if (algorithm === :SEA || algorithm === :VEA) && extrapolation_period % 2 != 0
-            error("`extrapolation_period` must be multiples of 2 for SEA and VEA")
-        end
-    end
-
-    return FixedPointAccelerationJL(algorithm, extrapolation_period, replace_invalids,
-        dampening, m, condition_number_threshold)
-end
-
-"""
-    SIAMFANLEquationsJL(; method = :newton, delta = 1e-3, linsolve = nothing,
-        autodiff = missing)
-
-### Keyword Arguments
-
-  - `method`: the choice of method for solving the nonlinear system.
-  - `delta`: initial pseudo time step, default is 1e-3.
-  - `linsolve` : JFNK linear solvers, choices are `gmres` and `bicgstab`.
-  - `m`: Depth for Anderson acceleration, default as 0 for Picard iteration.
-  - `beta`: Anderson mixing parameter, change f(x) to (1-beta)x+beta*f(x),
-    equivalent to accelerating damped Picard iteration.
-  - `autodiff`: Defaults to `missing`, which means we will default to letting
-    `SIAMFANLEquations` construct the jacobian if `f.jac` is not provided. In other cases,
-    we use it to generate a jacobian similar to other NonlinearSolve solvers.
-
-### Submethod Choice
-
-  - `:newton`: Classical Newton method.
-  - `:pseudotransient`: Pseudo transient method.
-  - `:secant`: Secant method for scalar equations.
-  - `:anderson`: Anderson acceleration for fixed point iterations.
-
-!!! note
-
-    This algorithm is only available if `SIAMFANLEquations.jl` is installed and loaded.
-"""
-@concrete struct SIAMFANLEquationsJL <: AbstractNonlinearSolveExtensionAlgorithm
-    method::Symbol
-    delta
-    linsolve <: Union{Symbol, Nothing}
-    m::Int
-    beta
-    autodiff
-end
-
-function SIAMFANLEquationsJL(; method = :newton, delta = 1e-3, linsolve = nothing,
-        m = 0, beta = 1.0, autodiff = missing)
-    if Base.get_extension(@__MODULE__, :NonlinearSolveSIAMFANLEquationsExt) === nothing
-        error("SIAMFANLEquationsJL requires SIAMFANLEquations.jl to be loaded")
-    end
-    return SIAMFANLEquationsJL(method, delta, linsolve, m, beta, autodiff)
-end
-
-"""
-    PETScSNES(; petsclib = missing, autodiff = nothing, mpi_comm = missing, kwargs...)
-
-Wrapper over [PETSc.jl](https://github.com/JuliaParallel/PETSc.jl) SNES solvers.
-
-### Keyword Arguments
-
-  - `petsclib`: PETSc library to use. If set to `missing`, then we will use the first
-    available PETSc library in `PETSc.petsclibs` based on the problem element type.
-  - `autodiff`: the choice of method for generating the Jacobian. Defaults to `nothing`
-    which means that a default is selected according to the problem specification. Can be
-    any valid ADTypes.jl autodiff type (conditional on that backend being supported in
-    NonlinearSolve.jl). If set to `missing`, then PETSc computes the Jacobian using finite
-    differences.
-  - `mpi_comm`: MPI communicator to use. If set to `missing`, then we will use
-    `MPI.COMM_SELF`.
-  - `kwargs`: Keyword arguments to be passed to the PETSc SNES solver. See [PETSc SNES
-    documentation](https://petsc.org/release/manual/snes/) and
-    [SNESSetFromOptions](https://petsc.org/release/manualpages/SNES/SNESSetFromOptions)
-    for more information.
-
-### Options via `CommonSolve.solve`
-
-These options are forwarded from `solve` to the PETSc SNES solver. If these are provided to
-`kwargs`, then they will be ignored.
-
-| `solve` option | PETSc SNES option |
-|:-------------- |:----------------- |
-| `atol`         | `snes_atol`       |
-| `rtol`         | `snes_rtol`       |
-| `maxiters`     | `snes_max_it`     |
-| `show_trace`   | `snes_monitor`    |
-
-!!! note
-
-    This algorithm is only available if `PETSc.jl` is installed and loaded.
-"""
-@concrete struct PETScSNES <: AbstractNonlinearSolveExtensionAlgorithm
-    petsclib
-    mpi_comm
-    autodiff <: Union{Missing, Nothing, ADTypes.AbstractADType}
-    snes_options
-end
-
-function PETScSNES(; petsclib = missing, autodiff = nothing, mpi_comm = missing, kwargs...)
-    if Base.get_extension(@__MODULE__, :NonlinearSolvePETScExt) === nothing
-        error("PETScSNES requires PETSc.jl to be loaded")
-    end
-    return PETScSNES(petsclib, mpi_comm, autodiff, kwargs)
-end
diff --git a/src/algorithms/trust_region.jl b/src/algorithms/trust_region.jl
deleted file mode 100644
index b42099d46..000000000
--- a/src/algorithms/trust_region.jl
+++ /dev/null
@@ -1,36 +0,0 @@
-"""
-    TrustRegion(; concrete_jac = nothing, linsolve = nothing, precs = nothing,
-        radius_update_scheme = RadiusUpdateSchemes.Simple, max_trust_radius::Real = 0 // 1,
-        initial_trust_radius::Real = 0 // 1, step_threshold::Real = 1 // 10000,
-        shrink_threshold::Real = 1 // 4, expand_threshold::Real = 3 // 4,
-        shrink_factor::Real = 1 // 4, expand_factor::Real = 2 // 1,
-        max_shrink_times::Int = 32,
-        vjp_autodiff = nothing, autodiff = nothing, jvp_autodiff = nothing)
-
-An advanced TrustRegion implementation with support for efficient handling of sparse
-matrices via colored automatic differentiation and preconditioned linear solvers. Designed
-for large-scale and numerically-difficult nonlinear systems.
-
-### Keyword Arguments
-
-  - `radius_update_scheme`: the scheme used to update the trust region radius. Defaults to
-    `RadiusUpdateSchemes.Simple`. See [`RadiusUpdateSchemes`](@ref) for more details. For a
-    review on trust region radius update schemes, see [yuan2015recent](@citet).
-
-For the remaining arguments, see [`NonlinearSolve.GenericTrustRegionScheme`](@ref)
-documentation.
-"""
-function TrustRegion(; concrete_jac = nothing, linsolve = nothing, precs = nothing,
-        radius_update_scheme = RadiusUpdateSchemes.Simple, max_trust_radius::Real = 0 // 1,
-        initial_trust_radius::Real = 0 // 1, step_threshold::Real = 1 // 10000,
-        shrink_threshold::Real = 1 // 4, expand_threshold::Real = 3 // 4,
-        shrink_factor::Real = 1 // 4, expand_factor::Real = 2 // 1,
-        max_shrink_times::Int = 32,
-        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing)
-    descent = Dogleg(; linsolve, precs)
-    trustregion = GenericTrustRegionScheme(;
-        method = radius_update_scheme, step_threshold, shrink_threshold, expand_threshold,
-        shrink_factor, expand_factor, initial_trust_radius, max_trust_radius)
-    return GeneralizedFirstOrderAlgorithm{concrete_jac, :TrustRegion}(;
-        trustregion, descent, autodiff, vjp_autodiff, jvp_autodiff, max_shrink_times)
-end
diff --git a/src/default.jl b/src/default.jl
index 7302d95a9..6021a98b1 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -1,496 +1,3 @@
-# Poly Algorithms
-"""
-    NonlinearSolvePolyAlgorithm(algs, ::Val{pType} = Val(:NLS);
-        start_index = 1) where {pType}
-
-A general way to define PolyAlgorithms for `NonlinearProblem` and
-`NonlinearLeastSquaresProblem`. This is a container for a tuple of algorithms that will be
-tried in order until one succeeds. If none succeed, then the algorithm with the lowest
-residual is returned.
-
-### Arguments
-
-  - `algs`: a tuple of algorithms to try in-order! (If this is not a Tuple, then the
-    returned algorithm is not type-stable).
-  - `pType`: the problem type. Defaults to `:NLS` for `NonlinearProblem` and `:NLLS` for
-    `NonlinearLeastSquaresProblem`. This is used to determine the correct problem type to
-    dispatch on.
-
-### Keyword Arguments
-
-  - `start_index`: the index to start at. Defaults to `1`.
-
-### Example
-
-```julia
-using NonlinearSolve
-
-alg = NonlinearSolvePolyAlgorithm((NewtonRaphson(), Broyden()))
-```
-"""
-struct NonlinearSolvePolyAlgorithm{pType, N, A} <: AbstractNonlinearSolveAlgorithm{:PolyAlg}
-    algs::A
-    start_index::Int
-
-    function NonlinearSolvePolyAlgorithm(
-            algs, ::Val{pType} = Val(:NLS); start_index::Int = 1) where {pType}
-        @assert pType ∈ (:NLS, :NLLS)
-        @assert 0 < start_index ≤ length(algs)
-        algs = Tuple(algs)
-        return new{pType, length(algs), typeof(algs)}(algs, start_index)
-    end
-end
-
-function Base.show(io::IO, alg::NonlinearSolvePolyAlgorithm{pType, N}) where {pType, N}
-    problem_kind = ifelse(pType == :NLS, "NonlinearProblem", "NonlinearLeastSquaresProblem")
-    println(io, "NonlinearSolvePolyAlgorithm for $(problem_kind) with $(N) algorithms")
-    for i in 1:N
-        num = "  [$(i)]: "
-        print(io, num)
-        __show_algorithm(io, alg.algs[i], get_name(alg.algs[i]), length(num))
-        i == N || println(io)
-    end
-end
-
-@concrete mutable struct NonlinearSolvePolyAlgorithmCache{iip, N, timeit} <:
-                         AbstractNonlinearSolveCache{iip, timeit}
-    caches
-    alg
-    best::Int
-    current::Int
-    nsteps::Int
-    stats::NLStats
-    total_time::Float64
-    maxtime
-    retcode::ReturnCode.T
-    force_stop::Bool
-    maxiters::Int
-    internalnorm
-    u0
-    u0_aliased
-    alias_u0::Bool
-end
-
-function SymbolicIndexingInterface.symbolic_container(cache::NonlinearSolvePolyAlgorithmCache)
-    cache.caches[cache.current]
-end
-SymbolicIndexingInterface.state_values(cache::NonlinearSolvePolyAlgorithmCache) = cache.u0
-
-function Base.show(
-        io::IO, cache::NonlinearSolvePolyAlgorithmCache{pType, N}) where {pType, N}
-    problem_kind = ifelse(pType == :NLS, "NonlinearProblem", "NonlinearLeastSquaresProblem")
-    println(io, "NonlinearSolvePolyAlgorithmCache for $(problem_kind) with $(N) algorithms")
-    best_alg = ifelse(cache.best == -1, "nothing", cache.best)
-    println(io, "Best algorithm: $(best_alg)")
-    println(io, "Current algorithm: $(cache.current)")
-    println(io, "nsteps: $(cache.nsteps)")
-    println(io, "retcode: $(cache.retcode)")
-    __show_cache(io, cache.caches[cache.current], 0)
-end
-
-function reinit_cache!(cache::NonlinearSolvePolyAlgorithmCache, args...; kwargs...)
-    foreach(c -> reinit_cache!(c, args...; kwargs...), cache.caches)
-    cache.current = cache.alg.start_index
-    __reinit_internal!(cache.stats)
-    cache.nsteps = 0
-    cache.total_time = 0.0
-end
-
-for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProblem, :NLLS))
-    algType = NonlinearSolvePolyAlgorithm{pType}
-    @eval begin
-        function SciMLBase.__init(
-                prob::$probType, alg::$algType{N}, args...; stats = empty_nlstats(),
-                maxtime = nothing, maxiters = 1000, internalnorm = L2_NORM,
-                alias_u0 = false, verbose = true, kwargs...) where {N}
-            if (alias_u0 && !ismutable(prob.u0))
-                verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
-                                  immutable (checked using `ArrayInterface.ismutable`)."
-                alias_u0 = false  # If immutable don't care about aliasing
-            end
-            u0 = prob.u0
-            if alias_u0
-                u0_aliased = copy(u0)
-            else
-                u0_aliased = u0  # Irrelevant
-            end
-            alias_u0 && (prob = remake(prob; u0 = u0_aliased))
-            return NonlinearSolvePolyAlgorithmCache{isinplace(prob), N, maxtime !== nothing}(
-                map(
-                    solver -> SciMLBase.__init(prob, solver, args...; stats, maxtime,
-                        internalnorm, alias_u0, verbose, kwargs...),
-                    alg.algs),
-                alg,
-                -1,
-                alg.start_index,
-                0,
-                stats,
-                0.0,
-                maxtime,
-                ReturnCode.Default,
-                false,
-                maxiters,
-                internalnorm,
-                u0,
-                u0_aliased,
-                alias_u0)
-        end
-    end
-end
-
-@generated function SciMLBase.solve!(cache::NonlinearSolvePolyAlgorithmCache{
-        iip, N}) where {iip, N}
-    calls = [quote
-        1 ≤ cache.current ≤ length(cache.caches) ||
-            error("Current choices shouldn't get here!")
-    end]
-
-    cache_syms = [gensym("cache") for i in 1:N]
-    sol_syms = [gensym("sol") for i in 1:N]
-    u_result_syms = [gensym("u_result") for i in 1:N]
-    for i in 1:N
-        push!(calls,
-            quote
-                $(cache_syms[i]) = cache.caches[$(i)]
-                if $(i) == cache.current
-                    cache.alias_u0 && copyto!(cache.u0_aliased, cache.u0)
-                    $(sol_syms[i]) = SciMLBase.solve!($(cache_syms[i]))
-                    if SciMLBase.successful_retcode($(sol_syms[i]))
-                        stats = $(sol_syms[i]).stats
-                        if cache.alias_u0
-                            copyto!(cache.u0, $(sol_syms[i]).u)
-                            $(u_result_syms[i]) = cache.u0
-                        else
-                            $(u_result_syms[i]) = $(sol_syms[i]).u
-                        end
-                        fu = get_fu($(cache_syms[i]))
-                        return __build_solution_less_specialize(
-                            $(sol_syms[i]).prob, cache.alg, $(u_result_syms[i]),
-                            fu; retcode = $(sol_syms[i]).retcode, stats,
-                            original = $(sol_syms[i]), trace = $(sol_syms[i]).trace)
-                    elseif cache.alias_u0
-                        # For safety we need to maintain a copy of the solution
-                        $(u_result_syms[i]) = copy($(sol_syms[i]).u)
-                    end
-                    cache.current = $(i + 1)
-                end
-            end)
-    end
-
-    resids = map(x -> Symbol("$(x)_resid"), cache_syms)
-    for (sym, resid) in zip(cache_syms, resids)
-        push!(calls, :($(resid) = @isdefined($(sym)) ? get_fu($(sym)) : nothing))
-    end
-    push!(calls, quote
-        fus = tuple($(Tuple(resids)...))
-        minfu, idx = __findmin(cache.internalnorm, fus)
-    end)
-    for i in 1:N
-        push!(calls, quote
-            if idx == $(i)
-                if cache.alias_u0
-                    u = $(u_result_syms[i])
-                else
-                    u = get_u(cache.caches[$i])
-                end
-            end
-        end)
-    end
-    push!(calls,
-        quote
-            retcode = cache.caches[idx].retcode
-            if cache.alias_u0
-                copyto!(cache.u0, u)
-                u = cache.u0
-            end
-            return __build_solution_less_specialize(
-                cache.caches[idx].prob, cache.alg, u, fus[idx];
-                retcode, stats = cache.stats, cache.caches[idx].trace)
-        end)
-
-    return Expr(:block, calls...)
-end
-
-@generated function __step!(
-        cache::NonlinearSolvePolyAlgorithmCache{iip, N}, args...; kwargs...) where {iip, N}
-    calls = []
-    cache_syms = [gensym("cache") for i in 1:N]
-    for i in 1:N
-        push!(calls,
-            quote
-                $(cache_syms[i]) = cache.caches[$(i)]
-                if $(i) == cache.current
-                    __step!($(cache_syms[i]), args...; kwargs...)
-                    $(cache_syms[i]).nsteps += 1
-                    if !not_terminated($(cache_syms[i]))
-                        if SciMLBase.successful_retcode($(cache_syms[i]).retcode)
-                            cache.best = $(i)
-                            cache.force_stop = true
-                            cache.retcode = $(cache_syms[i]).retcode
-                        else
-                            cache.current = $(i + 1)
-                        end
-                    end
-                    return
-                end
-            end)
-    end
-
-    push!(calls, quote
-        if !(1 ≤ cache.current ≤ length(cache.caches))
-            minfu, idx = __findmin(cache.internalnorm, cache.caches)
-            cache.best = idx
-            cache.retcode = cache.caches[cache.best].retcode
-            cache.force_stop = true
-            return
-        end
-    end)
-
-    return Expr(:block, calls...)
-end
-
-for (probType, pType) in ((:NonlinearProblem, :NLS), (:NonlinearLeastSquaresProblem, :NLLS))
-    algType = NonlinearSolvePolyAlgorithm{pType}
-    @eval begin
-        @generated function SciMLBase.__solve(
-                prob::$probType, alg::$algType{N}, args...; stats = empty_nlstats(),
-                alias_u0 = false, verbose = true, kwargs...) where {N}
-            sol_syms = [gensym("sol") for _ in 1:N]
-            prob_syms = [gensym("prob") for _ in 1:N]
-            u_result_syms = [gensym("u_result") for _ in 1:N]
-            calls = [quote
-                current = alg.start_index
-                if (alias_u0 && !ismutable(prob.u0))
-                    verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
-                                      immutable (checked using `ArrayInterface.ismutable`)."
-                    alias_u0 = false  # If immutable don't care about aliasing
-                end
-                u0 = prob.u0
-                u0_aliased = alias_u0 ? zero(u0) : u0
-            end]
-            for i in 1:N
-                cur_sol = sol_syms[i]
-                push!(calls,
-                    quote
-                        if current == $i
-                            if alias_u0
-                                copyto!(u0_aliased, u0)
-                                $(prob_syms[i]) = remake(prob; u0 = u0_aliased)
-                            else
-                                $(prob_syms[i]) = prob
-                            end
-                            $(cur_sol) = SciMLBase.__solve(
-                                $(prob_syms[i]), alg.algs[$(i)], args...;
-                                stats, alias_u0, verbose, kwargs...)
-                            if SciMLBase.successful_retcode($(cur_sol))
-                                if alias_u0
-                                    copyto!(u0, $(cur_sol).u)
-                                    $(u_result_syms[i]) = u0
-                                else
-                                    $(u_result_syms[i]) = $(cur_sol).u
-                                end
-                                return __build_solution_less_specialize(
-                                    prob, alg, $(u_result_syms[i]), $(cur_sol).resid;
-                                    $(cur_sol).retcode, $(cur_sol).stats,
-                                    original = $(cur_sol), trace = $(cur_sol).trace)
-                            elseif alias_u0
-                                # For safety we need to maintain a copy of the solution
-                                $(u_result_syms[i]) = copy($(cur_sol).u)
-                            end
-                            current = $(i + 1)
-                        end
-                    end)
-            end
-
-            resids = map(x -> Symbol("$(x)_resid"), sol_syms)
-            for (sym, resid) in zip(sol_syms, resids)
-                push!(calls, :($(resid) = @isdefined($(sym)) ? $(sym).resid : nothing))
-            end
-
-            push!(calls, quote
-                resids = tuple($(Tuple(resids)...))
-                minfu, idx = __findmin(L2_NORM, resids)
-            end)
-
-            for i in 1:N
-                push!(calls,
-                    quote
-                        if idx == $i
-                            if alias_u0
-                                copyto!(u0, $(u_result_syms[i]))
-                                $(u_result_syms[i]) = u0
-                            else
-                                $(u_result_syms[i]) = $(sol_syms[i]).u
-                            end
-                            return __build_solution_less_specialize(
-                                prob, alg, $(u_result_syms[i]), $(sol_syms[i]).resid;
-                                $(sol_syms[i]).retcode, $(sol_syms[i]).stats,
-                                $(sol_syms[i]).trace, original = $(sol_syms[i]))
-                        end
-                    end)
-            end
-            push!(calls, :(error("Current choices shouldn't get here!")))
-
-            return Expr(:block, calls...)
-        end
-    end
-end
-
-"""
-    RobustMultiNewton(::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
-        precs = nothing, autodiff = nothing)
-
-A polyalgorithm focused on robustness. It uses a mixture of Newton methods with different
-globalizing techniques (trust region updates, line searches, etc.) in order to find a
-method that is able to adequately solve the minimization problem.
-
-Basically, if this algorithm fails, then "most" good ways of solving your problem fail and
-you may need to think about reformulating the model (either there is an issue with the model,
-or more precision / more stable linear solver choice is required).
-
-### Arguments
-
-  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
-    are compatible with the problem type. Defaults to `Float64`.
-"""
-function RobustMultiNewton(::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
-        precs = nothing, autodiff = nothing) where {T}
-    if __is_complex(T)
-        # Let's atleast have something here for complex numbers
-        algs = (NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),)
-    else
-        algs = (TrustRegion(; concrete_jac, linsolve, precs, autodiff),
-            TrustRegion(; concrete_jac, linsolve, precs, autodiff,
-                radius_update_scheme = RadiusUpdateSchemes.Bastin),
-            NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
-            NewtonRaphson(; concrete_jac, linsolve, precs,
-                linesearch = BackTracking(), autodiff),
-            TrustRegion(; concrete_jac, linsolve, precs,
-                radius_update_scheme = RadiusUpdateSchemes.NLsolve, autodiff),
-            TrustRegion(; concrete_jac, linsolve, precs,
-                radius_update_scheme = RadiusUpdateSchemes.Fan, autodiff))
-    end
-    return NonlinearSolvePolyAlgorithm(algs, Val(:NLS))
-end
-
-"""
-    FastShortcutNonlinearPolyalg(::Type{T} = Float64; concrete_jac = nothing,
-        linsolve = nothing, precs = nothing, must_use_jacobian::Val = Val(false),
-        prefer_simplenonlinearsolve::Val{SA} = Val(false), autodiff = nothing,
-        u0_len::Union{Int, Nothing} = nothing) where {T}
-
-A polyalgorithm focused on balancing speed and robustness. It first tries less robust methods
-for more performance and then tries more robust techniques if the faster ones fail.
-
-### Arguments
-
-  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
-    are compatible with the problem type. Defaults to `Float64`.
-
-### Keyword Arguments
-
-  - `u0_len`: The length of the initial guess. If this is `nothing`, then the length of the
-    initial guess is not checked. If this is an integer and it is less than `25`, we use
-    jacobian based methods.
-"""
-function FastShortcutNonlinearPolyalg(
-        ::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
-        precs = nothing, must_use_jacobian::Val{JAC} = Val(false),
-        prefer_simplenonlinearsolve::Val{SA} = Val(false),
-        u0_len::Union{Int, Nothing} = nothing, autodiff = nothing) where {T, JAC, SA}
-    start_index = 1
-    if JAC
-        if __is_complex(T)
-            algs = (NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),)
-        else
-            algs = (NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
-                NewtonRaphson(; concrete_jac, linsolve, precs,
-                    linesearch = BackTracking(), autodiff),
-                TrustRegion(; concrete_jac, linsolve, precs, autodiff),
-                TrustRegion(; concrete_jac, linsolve, precs,
-                    radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff))
-        end
-    else
-        # SimpleNewtonRaphson and SimpleTrustRegion are not robust to singular Jacobians
-        # and thus are not included in the polyalgorithm
-        if SA
-            if __is_complex(T)
-                algs = (SimpleBroyden(),
-                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
-                    SimpleKlement(),
-                    NewtonRaphson(; concrete_jac, linsolve, precs, autodiff))
-            else
-                start_index = u0_len !== nothing ? (u0_len ≤ 25 ? 4 : 1) : 1
-                algs = (SimpleBroyden(),
-                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
-                    SimpleKlement(),
-                    NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
-                    NewtonRaphson(; concrete_jac, linsolve, precs,
-                        linesearch = BackTracking(), autodiff),
-                    TrustRegion(; concrete_jac, linsolve, precs,
-                        radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff))
-            end
-        else
-            if __is_complex(T)
-                algs = (
-                    Broyden(), Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
-                    Klement(; linsolve, precs, autodiff),
-                    NewtonRaphson(; concrete_jac, linsolve, precs, autodiff))
-            else
-                # TODO: This number requires a bit rigorous testing
-                start_index = u0_len !== nothing ? (u0_len ≤ 25 ? 4 : 1) : 1
-                algs = (
-                    Broyden(; autodiff),
-                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
-                    Klement(; linsolve, precs, autodiff),
-                    NewtonRaphson(; concrete_jac, linsolve, precs, autodiff),
-                    NewtonRaphson(; concrete_jac, linsolve, precs,
-                        linesearch = BackTracking(), autodiff),
-                    TrustRegion(; concrete_jac, linsolve, precs, autodiff),
-                    TrustRegion(; concrete_jac, linsolve, precs,
-                        radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff))
-            end
-        end
-    end
-    return NonlinearSolvePolyAlgorithm(algs, Val(:NLS); start_index)
-end
-
-"""
-    FastShortcutNLLSPolyalg(::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
-        precs = nothing, autodiff = nothing, kwargs...)
-
-A polyalgorithm focused on balancing speed and robustness. It first tries less robust methods
-for more performance and then tries more robust techniques if the faster ones fail.
-
-### Arguments
-
-  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
-    are compatible with the problem type. Defaults to `Float64`.
-"""
-function FastShortcutNLLSPolyalg(
-        ::Type{T} = Float64; concrete_jac = nothing, linsolve = nothing,
-        precs = nothing, autodiff = nothing, kwargs...) where {T}
-    if __is_complex(T)
-        algs = (GaussNewton(; concrete_jac, linsolve, precs, autodiff, kwargs...),
-            LevenbergMarquardt(;
-                linsolve, precs, autodiff, disable_geodesic = Val(true), kwargs...),
-            LevenbergMarquardt(; linsolve, precs, autodiff, kwargs...))
-    else
-        algs = (GaussNewton(; concrete_jac, linsolve, precs, autodiff, kwargs...),
-            LevenbergMarquardt(;
-                linsolve, precs, disable_geodesic = Val(true), autodiff, kwargs...),
-            TrustRegion(; concrete_jac, linsolve, precs, autodiff, kwargs...),
-            GaussNewton(; concrete_jac, linsolve, precs,
-                linesearch = BackTracking(), autodiff, kwargs...),
-            TrustRegion(; concrete_jac, linsolve, precs,
-                radius_update_scheme = RadiusUpdateSchemes.Bastin, autodiff, kwargs...),
-            LevenbergMarquardt(; linsolve, precs, autodiff, kwargs...))
-    end
-    return NonlinearSolvePolyAlgorithm(algs, Val(:NLLS))
-end
-
-## Defaults
-
 ## TODO: In the long run we want to use an `Assumptions` API like LinearSolve to specify
 ##       the conditioning of the Jacobian and such
 
@@ -503,31 +10,43 @@ end
 ## the trouble of specifying a custom jacobian function, we should use algorithms that
 ## can use that!
 function SciMLBase.__init(prob::NonlinearProblem, ::Nothing, args...; kwargs...)
-    must_use_jacobian = Val(prob.f.jac !== nothing)
-    return SciMLBase.__init(prob,
+    must_use_jacobian = Val(SciMLBase.has_jac(prob.f))
+    return SciMLBase.__init(
+        prob,
         FastShortcutNonlinearPolyalg(
-            eltype(prob.u0); must_use_jacobian, u0_len = length(prob.u0)),
+            eltype(prob.u0); must_use_jacobian, u0_len = length(prob.u0)
+        ),
         args...;
-        kwargs...)
+        kwargs...
+    )
 end
 
 function SciMLBase.__solve(prob::NonlinearProblem, ::Nothing, args...; kwargs...)
-    must_use_jacobian = Val(prob.f.jac !== nothing)
-    prefer_simplenonlinearsolve = Val(prob.u0 isa SArray)
-    return SciMLBase.__solve(prob,
-        FastShortcutNonlinearPolyalg(eltype(prob.u0); must_use_jacobian,
-            prefer_simplenonlinearsolve, u0_len = length(prob.u0)),
+    must_use_jacobian = Val(SciMLBase.has_jac(prob.f))
+    prefer_simplenonlinearsolve = Val(prob.u0 isa StaticArray)
+    return SciMLBase.__solve(
+        prob,
+        FastShortcutNonlinearPolyalg(
+            eltype(prob.u0);
+            must_use_jacobian,
+            prefer_simplenonlinearsolve,
+            u0_len = length(prob.u0)
+        ),
         args...;
-        kwargs...)
+        kwargs...
+    )
 end
 
 function SciMLBase.__init(prob::NonlinearLeastSquaresProblem, ::Nothing, args...; kwargs...)
     return SciMLBase.__init(
-        prob, FastShortcutNLLSPolyalg(eltype(prob.u0)), args...; kwargs...)
+        prob, FastShortcutNLLSPolyalg(eltype(prob.u0)), args...; kwargs...
+    )
 end
 
 function SciMLBase.__solve(
-        prob::NonlinearLeastSquaresProblem, ::Nothing, args...; kwargs...)
+        prob::NonlinearLeastSquaresProblem, ::Nothing, args...; kwargs...
+)
     return SciMLBase.__solve(
-        prob, FastShortcutNLLSPolyalg(eltype(prob.u0)), args...; kwargs...)
+        prob, FastShortcutNLLSPolyalg(eltype(prob.u0)), args...; kwargs...
+    )
 end
diff --git a/src/extension_algs.jl b/src/extension_algs.jl
new file mode 100644
index 000000000..fb922fb14
--- /dev/null
+++ b/src/extension_algs.jl
@@ -0,0 +1,469 @@
+# # This file only include the algorithm struct to be exported by NonlinearSolve.jl. The main
+# # functionality is implemented as package extensions
+# """
+#     LeastSquaresOptimJL(alg = :lm; linsolve = nothing, autodiff::Symbol = :central)
+
+# Wrapper over [LeastSquaresOptim.jl](https://github.com/matthieugomez/LeastSquaresOptim.jl)
+# for solving `NonlinearLeastSquaresProblem`.
+
+# ### Arguments
+
+#   - `alg`: Algorithm to use. Can be `:lm` or `:dogleg`.
+
+# ### Keyword Arguments
+
+#   - `linsolve`: Linear solver to use. Can be `:qr`, `:cholesky` or `:lsmr`. If `nothing`,
+#     then `LeastSquaresOptim.jl` will choose the best linear solver based on the Jacobian
+#     structure.
+#   - `autodiff`: Automatic differentiation / Finite Differences. Can be `:central` or
+#     `:forward`.
+
+# !!! note
+
+#     This algorithm is only available if `LeastSquaresOptim.jl` is installed and loaded.
+# """
+# struct LeastSquaresOptimJL{alg, linsolve} <: AbstractNonlinearSolveExtensionAlgorithm
+#     autodiff
+# end
+
+# function LeastSquaresOptimJL(alg = :lm; linsolve = nothing, autodiff = :central)
+#     @assert alg in (:lm, :dogleg)
+#     @assert linsolve === nothing || linsolve in (:qr, :cholesky, :lsmr)
+#     autodiff isa Symbol && @assert autodiff in (:central, :forward)
+
+#     if Base.get_extension(@__MODULE__, :NonlinearSolveLeastSquaresOptimExt) === nothing
+#         error("LeastSquaresOptimJL requires LeastSquaresOptim.jl to be loaded")
+#     end
+
+#     return LeastSquaresOptimJL{alg, linsolve}(autodiff)
+# end
+
+# """
+#     FastLevenbergMarquardtJL(linsolve::Symbol = :cholesky; factor = 1e-6,
+#         factoraccept = 13.0, factorreject = 3.0, factorupdate = :marquardt,
+#         minscale = 1e-12, maxscale = 1e16, minfactor = 1e-28, maxfactor = 1e32,
+#         autodiff = nothing)
+
+# Wrapper over [FastLevenbergMarquardt.jl](https://github.com/kamesy/FastLevenbergMarquardt.jl)
+# for solving `NonlinearLeastSquaresProblem`. For details about the other keyword arguments
+# see the documentation for `FastLevenbergMarquardt.jl`.
+
+# !!! warning
+
+#     This is not really the fastest solver. It is called that since the original package
+#     is called "Fast". `LevenbergMarquardt()` is almost always a better choice.
+
+# ### Arguments
+
+#   - `linsolve`: Linear solver to use. Can be `:qr` or `:cholesky`.
+
+# ### Keyword Arguments
+
+#   - `autodiff`: determines the backend used for the Jacobian. Note that this argument is
+#     ignored if an analytical Jacobian is passed, as that will be used instead. Defaults to
+#     `nothing` which means that a default is selected according to the problem specification!
+
+# !!! note
+
+#     This algorithm is only available if `FastLevenbergMarquardt.jl` is installed and loaded.
+# """
+# @concrete struct FastLevenbergMarquardtJL{linsolve} <:
+#                  AbstractNonlinearSolveExtensionAlgorithm
+#     autodiff
+#     factor
+#     factoraccept
+#     factorreject
+#     factorupdate::Symbol
+#     minscale
+#     maxscale
+#     minfactor
+#     maxfactor
+# end
+
+# function FastLevenbergMarquardtJL(
+#         linsolve::Symbol = :cholesky; factor = 1e-6, factoraccept = 13.0,
+#         factorreject = 3.0, factorupdate = :marquardt, minscale = 1e-12,
+#         maxscale = 1e16, minfactor = 1e-28, maxfactor = 1e32, autodiff = nothing)
+#     @assert linsolve in (:qr, :cholesky)
+#     @assert factorupdate in (:marquardt, :nielson)
+
+#     if Base.get_extension(@__MODULE__, :NonlinearSolveFastLevenbergMarquardtExt) === nothing
+#         error("FastLevenbergMarquardtJL requires FastLevenbergMarquardt.jl to be loaded")
+#     end
+
+#     return FastLevenbergMarquardtJL{linsolve}(autodiff, factor, factoraccept, factorreject,
+#         factorupdate, minscale, maxscale, minfactor, maxfactor)
+# end
+
+# """
+#     CMINPACK(; method::Symbol = :auto, autodiff = missing)
+
+# ### Keyword Arguments
+
+#   - `method`: the choice of method for the solver.
+#   - `autodiff`: Defaults to `missing`, which means we will default to letting `MINPACK`
+#     construct the jacobian if `f.jac` is not provided. In other cases, we use it to generate
+#     a jacobian similar to other NonlinearSolve solvers.
+
+# ### Submethod Choice
+
+# The keyword argument `method` can take on different value depending on which method of
+# `fsolve` you are calling. The standard choices of `method` are:
+
+#   - `:hybr`: Modified version of Powell's algorithm. Uses MINPACK routine
+#     [`hybrd1`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrd1.c)
+#   - `:lm`: Levenberg-Marquardt. Uses MINPACK routine
+#     [`lmdif1`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmdif1.c)
+#   - `:lmdif`: Advanced Levenberg-Marquardt (more options available with `; kwargs...`). See
+#     MINPACK routine [`lmdif`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmdif.c)
+#     for more information
+#   - `:hybrd`: Advanced modified version of Powell's algorithm (more options available with
+#     `; kwargs...`). See MINPACK routine
+#     [`hybrd`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrd.c)
+#     for more information
+
+# If a Jacobian is supplied as part of the [`NonlinearFunction`](@ref nonlinearfunctions),
+# then the following methods are allowed:
+
+#   - `:hybr`: Advanced modified version of Powell's algorithm with user supplied Jacobian.
+#     Additional arguments are available via `; kwargs...`. See MINPACK routine
+#     [`hybrj`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrj.c)
+#     for more information
+#   - `:lm`: Advanced Levenberg-Marquardt with user supplied Jacobian. Additional arguments
+#     are available via `; kwargs...`. See MINPACK routine
+#     [`lmder`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmder.c)
+#     for more information
+
+# The default choice of `:auto` selects `:hybr` for NonlinearProblem and `:lm` for
+# NonlinearLeastSquaresProblem.
+
+# !!! note
+
+#     This algorithm is only available if `MINPACK.jl` is installed and loaded.
+# """
+# @concrete struct CMINPACK <: AbstractNonlinearSolveExtensionAlgorithm
+#     method::Symbol
+#     autodiff
+# end
+
+# function CMINPACK(; method::Symbol = :auto, autodiff = missing)
+#     if Base.get_extension(@__MODULE__, :NonlinearSolveMINPACKExt) === nothing
+#         error("CMINPACK requires MINPACK.jl to be loaded")
+#     end
+#     return CMINPACK(method, autodiff)
+# end
+
+# """
+#     NLsolveJL(; method = :trust_region, autodiff = :central, linesearch = Static(),
+#         linsolve = (x, A, b) -> copyto!(x, A\\b), factor = one(Float64), autoscale = true,
+#         m = 10, beta = one(Float64))
+
+# ### Keyword Arguments
+
+#   - `method`: the choice of method for solving the nonlinear system.
+#   - `autodiff`: the choice of method for generating the Jacobian. Defaults to `:central` or
+#     central differencing via FiniteDiff.jl. The other choices are `:forward` or `ADTypes`
+#     similar to other solvers in NonlinearSolve.
+#   - `linesearch`: the line search method to be used within the solver method. The choices
+#     are line search types from
+#     [LineSearches.jl](https://github.com/JuliaNLSolvers/LineSearches.jl).
+#   - `linsolve`: a function `linsolve(x, A, b)` that solves `Ax = b`.
+#   - `factor`: determines the size of the initial trust region. This size is set to the
+#     product of factor and the euclidean norm of `u0` if nonzero, or else to factor itself.
+#   - `autoscale`: if true, then the variables will be automatically rescaled. The scaling
+#     factors are the norms of the Jacobian columns.
+#   - `m`: the amount of history in the Anderson method. Naive "Picard"-style iteration can be
+#     achieved by setting m=0, but that isn't advisable for contractions whose Lipschitz
+#     constants are close to 1. If convergence fails, though, you may consider lowering it.
+#   - `beta`: It is also known as DIIS or Pulay mixing, this method is based on the
+#     acceleration of the fixed-point iteration xₙ₊₁ = xₙ + beta*f(xₙ), where by default
+#     beta = 1.
+
+# !!! warning
+
+#     Line Search Algorithms from [`LineSearch.jl`](https://github.com/SciML/LineSearch.jl)
+#     aren't supported by `NLsolveJL`. Instead, use the line search algorithms from
+#     [`LineSearches.jl`](https://github.com/JuliaNLSolvers/LineSearches.jl).
+
+# ### Submethod Choice
+
+# Choices for methods in `NLsolveJL`:
+
+#   - `:anderson`: Anderson-accelerated fixed-point iteration
+#   - `:broyden`: Broyden's quasi-Newton method
+#   - `:newton`: Classical Newton method with an optional line search
+#   - `:trust_region`: Trust region Newton method (the default choice)
+
+# For more information on these arguments, consult the
+# [NLsolve.jl documentation](https://github.com/JuliaNLSolvers/NLsolve.jl).
+
+# !!! note
+
+#     This algorithm is only available if `NLsolve.jl` is installed and loaded.
+# """
+# @concrete struct NLsolveJL <: AbstractNonlinearSolveExtensionAlgorithm
+#     method::Symbol
+#     autodiff
+#     linesearch
+#     linsolve
+#     factor
+#     autoscale::Bool
+#     m::Int
+#     beta
+# end
+
+# function NLsolveJL(; method = :trust_region, autodiff = :central, linesearch = missing,
+#         linsolve = (x, A, b) -> copyto!(x, A \ b), factor = 1.0,
+#         autoscale = true, m = 10, beta = one(Float64))
+#     if Base.get_extension(@__MODULE__, :NonlinearSolveNLsolveExt) === nothing
+#         error("NLsolveJL requires NLsolve.jl to be loaded")
+#     end
+
+#     if autodiff isa Symbol && autodiff !== :central && autodiff !== :forward
+#         error("`autodiff` must be `:central` or `:forward`.")
+#     end
+
+#     return NLsolveJL(method, autodiff, linesearch, linsolve, factor, autoscale, m, beta)
+# end
+
+# """
+#     NLSolversJL(method; autodiff = nothing)
+#     NLSolversJL(; method, autodiff = nothing)
+
+# Wrapper over NLSolvers.jl Nonlinear Equation Solvers. We automatically construct the
+# jacobian function and supply it to the solver.
+
+# ### Arguments
+
+#   - `method`: the choice of method for solving the nonlinear system. See the documentation
+#     for NLSolvers.jl for more information.
+#   - `autodiff`: the choice of method for generating the Jacobian. Defaults to `nothing`
+#     which means that a default is selected according to the problem specification. Can be
+#     any valid ADTypes.jl autodiff type (conditional on that backend being supported in
+#     NonlinearSolve.jl).
+# """
+# struct NLSolversJL{M, AD} <: AbstractNonlinearSolveExtensionAlgorithm
+#     method::M
+#     autodiff::AD
+
+#     function NLSolversJL(method, autodiff)
+#         if Base.get_extension(@__MODULE__, :NonlinearSolveNLSolversExt) === nothing
+#             error("NLSolversJL requires NLSolvers.jl to be loaded")
+#         end
+
+#         return new{typeof(method), typeof(autodiff)}(method, autodiff)
+#     end
+# end
+
+# NLSolversJL(method; autodiff = nothing) = NLSolversJL(method, autodiff)
+# NLSolversJL(; method, autodiff = nothing) = NLSolversJL(method, autodiff)
+
+# """
+#     SpeedMappingJL(; σ_min = 0.0, stabilize::Bool = false, check_obj::Bool = false,
+#         orders::Vector{Int} = [3, 3, 2], time_limit::Real = 1000)
+
+# Wrapper over [SpeedMapping.jl](https://nicolasl-s.github.io/SpeedMapping.jl/) for solving
+# Fixed Point Problems. We allow using this algorithm to solve root finding problems as well.
+
+# ### Keyword Arguments
+
+#   - `σ_min`: Setting to `1` may avoid stalling (see [lepage2021alternating](@cite)).
+#   - `stabilize`: performs a stabilization mapping before extrapolating. Setting to `true`
+#     may improve the performance for applications like accelerating the EM or MM algorithms
+#     (see [lepage2021alternating](@cite)).
+#   - `check_obj`: In case of NaN or Inf values, the algorithm restarts at the best past
+#     iterate.
+#   - `orders`: determines ACX's alternating order. Must be between `1` and `3` (where `1`
+#     means no extrapolation). The two recommended orders are `[3, 2]` and `[3, 3, 2]`, the
+#     latter being potentially better for highly non-linear applications (see
+#     [lepage2021alternating](@cite)).
+#   - `time_limit`: time limit for the algorithm.
+
+# !!! note
+
+#     This algorithm is only available if `SpeedMapping.jl` is installed and loaded.
+# """
+# @concrete struct SpeedMappingJL <: AbstractNonlinearSolveExtensionAlgorithm
+#     σ_min
+#     stabilize::Bool
+#     check_obj::Bool
+#     orders::Vector{Int}
+# end
+
+# function SpeedMappingJL(; σ_min = 0.0, stabilize::Bool = false, check_obj::Bool = false,
+#         orders::Vector{Int} = [3, 3, 2])
+#     if Base.get_extension(@__MODULE__, :NonlinearSolveSpeedMappingExt) === nothing
+#         error("SpeedMappingJL requires SpeedMapping.jl to be loaded")
+#     end
+
+#     return SpeedMappingJL(σ_min, stabilize, check_obj, orders)
+# end
+
+# """
+#     FixedPointAccelerationJL(; algorithm = :Anderson, m = missing,
+#         condition_number_threshold = missing, extrapolation_period = missing,
+#         replace_invalids = :NoAction)
+
+# Wrapper over [FixedPointAcceleration.jl](https://s-baumann.github.io/FixedPointAcceleration.jl/)
+# for solving Fixed Point Problems. We allow using this algorithm to solve root finding
+# problems as well.
+
+# ### Keyword Arguments
+
+#   - `algorithm`: The algorithm to use. Can be `:Anderson`, `:MPE`, `:RRE`, `:VEA`, `:SEA`,
+#     `:Simple`, `:Aitken` or `:Newton`.
+#   - `m`: The number of previous iterates to use for the extrapolation. Only valid for
+#     `:Anderson`.
+#   - `condition_number_threshold`: The condition number threshold for Least Squares Problem.
+#     Only valid for `:Anderson`.
+#   - `extrapolation_period`: The number of iterates between extrapolations. Only valid for
+#     `:MPE`, `:RRE`, `:VEA` and `:SEA`. Defaults to `7` for `:MPE` & `:RRE`, and `6` for
+#     `:SEA` and `:VEA`. For `:SEA` and `:VEA`, this must be a multiple of `2`.
+#   - `replace_invalids`: The method to use for replacing invalid iterates. Can be
+#     `:ReplaceInvalids`, `:ReplaceVector` or `:NoAction`.
+
+# !!! note
+
+#     This algorithm is only available if `FixedPointAcceleration.jl` is installed and loaded.
+# """
+# @concrete struct FixedPointAccelerationJL <: AbstractNonlinearSolveExtensionAlgorithm
+#     algorithm::Symbol
+#     extrapolation_period::Int
+#     replace_invalids::Symbol
+#     dampening
+#     m::Int
+#     condition_number_threshold
+# end
+
+# function FixedPointAccelerationJL(;
+#         algorithm = :Anderson, m = missing, condition_number_threshold = missing,
+#         extrapolation_period = missing, replace_invalids = :NoAction, dampening = 1.0)
+#     if Base.get_extension(@__MODULE__, :NonlinearSolveFixedPointAccelerationExt) === nothing
+#         error("FixedPointAccelerationJL requires FixedPointAcceleration.jl to be loaded")
+#     end
+
+#     @assert algorithm in (:Anderson, :MPE, :RRE, :VEA, :SEA, :Simple, :Aitken, :Newton)
+#     @assert replace_invalids in (:ReplaceInvalids, :ReplaceVector, :NoAction)
+
+#     if algorithm !== :Anderson
+#         if condition_number_threshold !== missing
+#             error("`condition_number_threshold` is only valid for Anderson acceleration")
+#         end
+#         if m !== missing
+#             error("`m` is only valid for Anderson acceleration")
+#         end
+#     end
+#     condition_number_threshold === missing && (condition_number_threshold = 1e3)
+#     m === missing && (m = 10)
+
+#     if algorithm !== :MPE && algorithm !== :RRE && algorithm !== :VEA && algorithm !== :SEA
+#         if extrapolation_period !== missing
+#             error("`extrapolation_period` is only valid for MPE, RRE, VEA and SEA")
+#         end
+#     end
+#     if extrapolation_period === missing
+#         extrapolation_period = algorithm === :SEA || algorithm === :VEA ? 6 : 7
+#     else
+#         if (algorithm === :SEA || algorithm === :VEA) && extrapolation_period % 2 != 0
+#             error("`extrapolation_period` must be multiples of 2 for SEA and VEA")
+#         end
+#     end
+
+#     return FixedPointAccelerationJL(algorithm, extrapolation_period, replace_invalids,
+#         dampening, m, condition_number_threshold)
+# end
+
+# """
+#     SIAMFANLEquationsJL(; method = :newton, delta = 1e-3, linsolve = nothing,
+#         autodiff = missing)
+
+# ### Keyword Arguments
+
+#   - `method`: the choice of method for solving the nonlinear system.
+#   - `delta`: initial pseudo time step, default is 1e-3.
+#   - `linsolve` : JFNK linear solvers, choices are `gmres` and `bicgstab`.
+#   - `m`: Depth for Anderson acceleration, default as 0 for Picard iteration.
+#   - `beta`: Anderson mixing parameter, change f(x) to (1-beta)x+beta*f(x),
+#     equivalent to accelerating damped Picard iteration.
+#   - `autodiff`: Defaults to `missing`, which means we will default to letting
+#     `SIAMFANLEquations` construct the jacobian if `f.jac` is not provided. In other cases,
+#     we use it to generate a jacobian similar to other NonlinearSolve solvers.
+
+# ### Submethod Choice
+
+#   - `:newton`: Classical Newton method.
+#   - `:pseudotransient`: Pseudo transient method.
+#   - `:secant`: Secant method for scalar equations.
+#   - `:anderson`: Anderson acceleration for fixed point iterations.
+
+# !!! note
+
+#     This algorithm is only available if `SIAMFANLEquations.jl` is installed and loaded.
+# """
+# @concrete struct SIAMFANLEquationsJL <: AbstractNonlinearSolveExtensionAlgorithm
+#     method::Symbol
+#     delta
+#     linsolve <: Union{Symbol, Nothing}
+#     m::Int
+#     beta
+#     autodiff
+# end
+
+# function SIAMFANLEquationsJL(; method = :newton, delta = 1e-3, linsolve = nothing,
+#         m = 0, beta = 1.0, autodiff = missing)
+#     if Base.get_extension(@__MODULE__, :NonlinearSolveSIAMFANLEquationsExt) === nothing
+#         error("SIAMFANLEquationsJL requires SIAMFANLEquations.jl to be loaded")
+#     end
+#     return SIAMFANLEquationsJL(method, delta, linsolve, m, beta, autodiff)
+# end
+
+# """
+#     PETScSNES(; petsclib = missing, autodiff = nothing, mpi_comm = missing, kwargs...)
+
+# Wrapper over [PETSc.jl](https://github.com/JuliaParallel/PETSc.jl) SNES solvers.
+
+# ### Keyword Arguments
+
+#   - `petsclib`: PETSc library to use. If set to `missing`, then we will use the first
+#     available PETSc library in `PETSc.petsclibs` based on the problem element type.
+#   - `autodiff`: the choice of method for generating the Jacobian. Defaults to `nothing`
+#     which means that a default is selected according to the problem specification. Can be
+#     any valid ADTypes.jl autodiff type (conditional on that backend being supported in
+#     NonlinearSolve.jl). If set to `missing`, then PETSc computes the Jacobian using finite
+#     differences.
+#   - `mpi_comm`: MPI communicator to use. If set to `missing`, then we will use
+#     `MPI.COMM_SELF`.
+#   - `kwargs`: Keyword arguments to be passed to the PETSc SNES solver. See [PETSc SNES
+#     documentation](https://petsc.org/release/manual/snes/) and
+#     [SNESSetFromOptions](https://petsc.org/release/manualpages/SNES/SNESSetFromOptions)
+#     for more information.
+
+# ### Options via `CommonSolve.solve`
+
+# These options are forwarded from `solve` to the PETSc SNES solver. If these are provided to
+# `kwargs`, then they will be ignored.
+
+# | `solve` option | PETSc SNES option |
+# |:-------------- |:----------------- |
+# | `atol`         | `snes_atol`       |
+# | `rtol`         | `snes_rtol`       |
+# | `maxiters`     | `snes_max_it`     |
+# | `show_trace`   | `snes_monitor`    |
+
+# !!! note
+
+#     This algorithm is only available if `PETSc.jl` is installed and loaded.
+# """
+# @concrete struct PETScSNES <: AbstractNonlinearSolveExtensionAlgorithm
+#     petsclib
+#     mpi_comm
+#     autodiff <: Union{Missing, Nothing, ADTypes.AbstractADType}
+#     snes_options
+# end
+
+# function PETScSNES(; petsclib = missing, autodiff = nothing, mpi_comm = missing, kwargs...)
+#     if Base.get_extension(@__MODULE__, :NonlinearSolvePETScExt) === nothing
+#         error("PETScSNES requires PETSc.jl to be loaded")
+#     end
+#     return PETScSNES(petsclib, mpi_comm, autodiff, kwargs)
+# end
diff --git a/src/internal/forward_diff.jl b/src/forward_diff.jl
similarity index 100%
rename from src/internal/forward_diff.jl
rename to src/forward_diff.jl
diff --git a/src/globalization/trust_region.jl b/src/globalization/trust_region.jl
deleted file mode 100644
index 813068e7e..000000000
--- a/src/globalization/trust_region.jl
+++ /dev/null
@@ -1,452 +0,0 @@
-
-# Don't Pollute the namespace
-"""
-    RadiusUpdateSchemes
-
-`RadiusUpdateSchemes` is provides different types of radius update schemes implemented in
-the Trust Region method. These schemes specify how the radius of the so-called trust region
-is updated after each iteration of the algorithm. The specific role and caveats associated
-with each scheme are provided below.
-
-## Using `RadiusUpdateSchemes`
-
-Simply put the desired scheme as follows:
-`sol = solve(prob, alg = TrustRegion(radius_update_scheme = RadiusUpdateSchemes.Hei))`.
-"""
-module RadiusUpdateSchemes
-# The weird definitions here are needed to main compatibility with the older enum variants
-
-abstract type AbstractRadiusUpdateScheme end
-
-function Base.show(io::IO, rus::AbstractRadiusUpdateScheme)
-    print(io, "RadiusUpdateSchemes.$(string(nameof(typeof(rus)))[3:end])")
-end
-
-const T = AbstractRadiusUpdateScheme
-
-struct __Simple <: AbstractRadiusUpdateScheme end
-"""
-    RadiusUpdateSchemes.Simple
-
-The simple or conventional radius update scheme. This scheme is chosen by default and
-follows the conventional approach to update the trust region radius, i.e. if the trial
-step is accepted it increases the radius by a fixed factor (bounded by a maximum radius)
-and if the trial step is rejected, it shrinks the radius by a fixed factor.
-"""
-const Simple = __Simple()
-
-struct __NLsolve <: AbstractRadiusUpdateScheme end
-"""
-    RadiusUpdateSchemes.NLsolve
-
-The same updating scheme as in NLsolve's (https://github.com/JuliaNLSolvers/NLsolve.jl)
-trust region dogleg implementation.
-"""
-const NLsolve = __NLsolve()
-
-struct __NocedalWright <: AbstractRadiusUpdateScheme end
-"""
-    RadiusUpdateSchemes.NocedalWright
-
-Trust region updating scheme as in Nocedal and Wright [see Alg 11.5, page 291].
-"""
-const NocedalWright = __NocedalWright()
-
-struct __Hei <: AbstractRadiusUpdateScheme end
-"""
-    RadiusUpdateSchemes.Hei
-
-This scheme is proposed in [hei2003self](@citet). The trust region radius depends on the
-size (norm) of the current step size. The hypothesis is to let the radius converge to zero
-as the iterations progress, which is more reliable and robust for ill-conditioned as well
-as degenerate problems.
-"""
-const Hei = __Hei()
-
-struct __Yuan <: AbstractRadiusUpdateScheme end
-"""
-    RadiusUpdateSchemes.Yuan
-
-This scheme is proposed by [yuan2015recent](@citet). Similar to Hei's scheme, the
-trust region is updated in a way so that it converges to zero, however here, the radius
-depends on the size (norm) of the current gradient of the objective (merit) function. The
-hypothesis is that the step size is bounded by the gradient size, so it makes sense to let
-the radius depend on the gradient.
-"""
-const Yuan = __Yuan()
-
-struct __Bastin <: AbstractRadiusUpdateScheme end
-"""
-    RadiusUpdateSchemes.Bastin
-
-This scheme is proposed by [bastin2010retrospective](@citet). The scheme is called a
-retrospective update scheme as it uses the model function at the current iteration to
-compute the ratio of the actual reduction and the predicted reduction in the previous trial
-step, and use this ratio to update the trust region radius. The hypothesis is to exploit the
-information made available during the optimization process in order to vary the accuracy
-of the objective function computation.
-"""
-const Bastin = __Bastin()
-
-struct __Fan <: AbstractRadiusUpdateScheme end
-"""
-    RadiusUpdateSchemes.Fan
-
-This scheme is proposed by [fan2006convergence](@citet). It is very much similar to Hei's
-and Yuan's schemes as it lets the trust region radius depend on the current size (norm) of
-the objective (merit) function itself. These new update schemes are known to improve local
-convergence.
-"""
-const Fan = __Fan()
-
-end
-
-const RUS = RadiusUpdateSchemes
-
-"""
-    GenericTrustRegionScheme(; method = RadiusUpdateSchemes.Simple,
-        max_trust_radius = nothing, initial_trust_radius = nothing,
-        step_threshold = nothing, shrink_threshold = nothing, expand_threshold = nothing,
-        shrink_factor = nothing, expand_factor = nothing)
-
-Trust Region Method that updates and stores the current trust region radius in
-`trust_region`. For any of the keyword arguments, if the value is `nothing`, then we use
-the value used in the respective paper.
-
-### Keyword Arguments
-
-  - `radius_update_scheme`: the choice of radius update scheme to be used. Defaults to
-    `RadiusUpdateSchemes.Simple` which follows the conventional approach. Other available
-    schemes are documented in [`RadiusUpdateSchemes`](@ref),. These schemes have the trust
-    region radius converging to zero that is seen to improve convergence. For more details,
-    see [1].
-  - `max_trust_radius`: the maximal trust region radius. Defaults to
-    `max(norm(fu), maximum(u) - minimum(u))`, except for `RadiusUpdateSchemes.NLsolve`
-    where it defaults to `Inf`.
-  - `initial_trust_radius`: the initial trust region radius. Defaults to
-    `max_trust_radius / 11`, except for `RadiusUpdateSchemes.NLsolve` where it defaults
-    to `u0_norm > 0 ? u0_norm : 1`.
-  - `step_threshold`: the threshold for taking a step. In every iteration, the threshold is
-    compared with a value `r`, which is the actual reduction in the objective function
-    divided by the predicted reduction. If `step_threshold > r` the model is not a good
-    approximation, and the step is rejected. Defaults to `nothing`.
-  - `shrink_threshold`: the threshold for shrinking the trust region radius. In every
-    iteration, the threshold is compared with a value `r` which is the actual reduction in
-    the objective function divided by the predicted reduction. If `shrink_threshold > r` the
-    trust region radius is shrunk by `shrink_factor`. Defaults to `nothing`.
-  - `expand_threshold`: the threshold for expanding the trust region radius. If a step is
-    taken, i.e `step_threshold < r` (with `r` defined in `shrink_threshold`), a check is
-    also made to see if `expand_threshold < r`. If that is true, the trust region radius is
-    expanded by `expand_factor`. Defaults to `nothing`.
-  - `shrink_factor`: the factor to shrink the trust region radius with if
-    `shrink_threshold > r` (with `r` defined in `shrink_threshold`). Defaults to `0.25`.
-  - `expand_factor`: the factor to expand the trust region radius with if
-    `expand_threshold < r` (with `r` defined in `shrink_threshold`). Defaults to `2.0`.
-"""
-@kwdef @concrete struct GenericTrustRegionScheme{M <:
-                                                 RadiusUpdateSchemes.AbstractRadiusUpdateScheme}
-    method::M = RadiusUpdateSchemes.Simple
-    step_threshold = nothing
-    shrink_threshold = nothing
-    shrink_factor = nothing
-    expand_factor = nothing
-    expand_threshold = nothing
-    max_trust_radius = nothing
-    initial_trust_radius = nothing
-end
-
-function Base.show(io::IO, alg::GenericTrustRegionScheme)
-    print(io, "GenericTrustRegionScheme(method = $(alg.method))")
-end
-
-@concrete mutable struct GenericTrustRegionSchemeCache <: AbstractTrustRegionMethodCache
-    method
-    f
-    p
-    max_trust_radius
-    initial_trust_radius
-    trust_region
-    step_threshold
-    shrink_threshold
-    expand_threshold
-    shrink_factor
-    expand_factor
-    p1
-    p2
-    p3
-    p4
-    ϵ
-    ρ
-    vjp_operator
-    jvp_operator
-    Jᵀfu_cache
-    Jδu_cache
-    δu_cache
-    internalnorm
-    u_cache
-    fu_cache
-    last_step_accepted::Bool
-    shrink_counter::Int
-    stats::NLStats
-    alg
-end
-
-function reinit_cache!(
-        cache::GenericTrustRegionSchemeCache, args...; u0 = nothing, p = cache.p, kwargs...)
-    T = eltype(cache.u_cache)
-    cache.p = p
-    if u0 !== nothing
-        u0_norm = cache.internalnorm(u0)
-        cache.trust_region = __initial_trust_radius(
-            cache.alg.initial_trust_radius, T, cache.alg.method,
-            cache.max_trust_radius, u0_norm, u0_norm)  # FIXME: scheme specific
-    end
-    cache.last_step_accepted = false
-    cache.shrink_counter = 0
-end
-
-# Defaults
-for func in (:__max_trust_radius, :__initial_trust_radius, :__step_threshold,
-    :__shrink_threshold, :__shrink_factor, :__expand_threshold, :__expand_factor)
-    @eval begin
-        @inline function $(func)(val, ::Type{T}, args...) where {T}
-            val_T = T(val)
-            iszero(val_T) && return $(func)(nothing, T, args...)
-            return val_T
-        end
-    end
-end
-
-@inline __max_trust_radius(::Nothing, ::Type{T}, method, u, fu_norm) where {T} = T(Inf)
-@inline function __max_trust_radius(
-        ::Nothing, ::Type{T}, ::Union{RUS.__Simple, RUS.__NocedalWright},
-        u, fu_norm) where {T}
-    u_min, u_max = extrema(u)
-    return max(T(fu_norm), u_max - u_min)
-end
-
-@inline function __initial_trust_radius(
-        ::Nothing, ::Type{T}, method, max_tr, u0_norm, fu_norm) where {T}
-    method isa RUS.__NLsolve && return T(ifelse(u0_norm > 0, u0_norm, 1))
-    (method isa RUS.__Hei || method isa RUS.__Bastin) && return T(1)
-    method isa RUS.__Fan && return T((fu_norm^0.99) / 10)
-    return T(max_tr / 11)
-end
-
-@inline function __step_threshold(::Nothing, ::Type{T}, method) where {T}
-    method isa RUS.__Hei && return T(0)
-    method isa RUS.__Yuan && return T(1 // 1000)
-    method isa RUS.__Bastin && return T(1 // 20)
-    return T(1 // 10000)
-end
-
-@inline function __shrink_threshold(::Nothing, ::Type{T}, method) where {T}
-    method isa RUS.__Hei && return T(0)
-    (method isa RUS.__NLsolve || method isa RUS.__Bastin) && return T(1 // 20)
-    return T(1 // 4)
-end
-
-@inline function __expand_threshold(::Nothing, ::Type{T}, method) where {T}
-    method isa RUS.__NLsolve && return T(9 // 10)
-    method isa RUS.__Hei && return T(0)
-    method isa RUS.__Bastin && return T(9 // 10)
-    return T(3 // 4)
-end
-
-@inline function __shrink_factor(::Nothing, ::Type{T}, method) where {T}
-    method isa RUS.__NLsolve && return T(1 // 2)
-    method isa RUS.__Hei && return T(0)
-    method isa RUS.__Bastin && return T(1 // 20)
-    return T(1 // 4)
-end
-
-@inline function __get_parameters(::Type{T}, method) where {T}
-    method isa RUS.__NLsolve && return (T(1 // 2), T(0), T(0), T(0))
-    method isa RUS.__Hei && return (T(5), T(1 // 10), T(15 // 100), T(15 // 100))
-    method isa RUS.__Yuan && return (T(2), T(1 // 6), T(6), T(0))
-    method isa RUS.__Fan && return (T(1 // 10), T(1 // 4), T(12), T(1e18))
-    method isa RUS.__Bastin && return (T(5 // 2), T(1 // 4), T(0), T(0))
-    return (T(0), T(0), T(0), T(0))
-end
-
-@inline __expand_factor(::Nothing, ::Type{T}, method) where {T} = T(2)
-
-function __internal_init(
-        prob::AbstractNonlinearProblem, alg::GenericTrustRegionScheme, f::F, fu, u,
-        p, args...; stats, internalnorm::IF = L2_NORM, vjp_autodiff = nothing,
-        jvp_autodiff = nothing, kwargs...) where {F, IF}
-    T = promote_type(eltype(u), eltype(fu))
-    u0_norm = internalnorm(u)
-    fu_norm = internalnorm(fu)
-
-    # Common Setup
-    max_trust_radius = __max_trust_radius(alg.max_trust_radius, T, alg.method, u, fu_norm)
-    initial_trust_radius = __initial_trust_radius(
-        alg.initial_trust_radius, T, alg.method, max_trust_radius, u0_norm, fu_norm)
-    step_threshold = __step_threshold(alg.step_threshold, T, alg.method)
-    shrink_threshold = __shrink_threshold(alg.shrink_threshold, T, alg.method)
-    expand_threshold = __expand_threshold(alg.expand_threshold, T, alg.method)
-    shrink_factor = __shrink_factor(alg.shrink_factor, T, alg.method)
-    expand_factor = __expand_factor(alg.expand_factor, T, alg.method)
-
-    # Scheme Specific Setup
-    p1, p2, p3, p4 = __get_parameters(T, alg.method)
-    ϵ = T(1e-8)
-
-    vjp_operator = alg.method isa RUS.__Yuan || alg.method isa RUS.__Bastin ?
-                   VecJacOperator(prob, fu, u; autodiff = vjp_autodiff) : nothing
-
-    jvp_operator = alg.method isa RUS.__Bastin ?
-                   JacVecOperator(prob, fu, u; autodiff = jvp_autodiff) : nothing
-
-    if alg.method isa RUS.__Yuan
-        Jᵀfu_cache = StatefulJacobianOperator(vjp_operator, u, prob.p) * _vec(fu)
-        initial_trust_radius = T(p1 * internalnorm(Jᵀfu_cache))
-    else
-        if u isa Number
-            Jᵀfu_cache = u
-        else
-            @bb Jᵀfu_cache = similar(u)
-        end
-    end
-
-    if alg.method isa RUS.__Bastin
-        @bb δu_cache = similar(u)
-    else
-        δu_cache = nothing
-    end
-
-    @bb u_cache = similar(u)
-    @bb fu_cache = similar(fu)
-    @bb Jδu_cache = similar(fu)
-
-    return GenericTrustRegionSchemeCache(
-        alg.method, f, p, max_trust_radius, initial_trust_radius, initial_trust_radius,
-        step_threshold, shrink_threshold, expand_threshold, shrink_factor,
-        expand_factor, p1, p2, p3, p4, ϵ, T(0), vjp_operator, jvp_operator, Jᵀfu_cache,
-        Jδu_cache, δu_cache, internalnorm, u_cache, fu_cache, false, 0, stats, alg)
-end
-
-function __internal_solve!(
-        cache::GenericTrustRegionSchemeCache, J, fu, u, δu, descent_stats)
-    T = promote_type(eltype(u), eltype(fu))
-    @bb @. cache.u_cache = u + δu
-    cache.fu_cache = evaluate_f!!(cache.f, cache.fu_cache, cache.u_cache, cache.p)
-    cache.stats.nf += 1
-
-    if hasfield(typeof(descent_stats), :δuJᵀJδu) && !isnan(descent_stats.δuJᵀJδu)
-        δuJᵀJδu = descent_stats.δuJᵀJδu
-    else
-        @bb cache.Jδu_cache = J × vec(δu)
-        δuJᵀJδu = __dot(cache.Jδu_cache, cache.Jδu_cache)
-    end
-    @bb cache.Jᵀfu_cache = transpose(J) × vec(fu)
-    num = (cache.internalnorm(cache.fu_cache)^2 - cache.internalnorm(fu)^2) / 2
-    denom = __dot(δu, cache.Jᵀfu_cache) + δuJᵀJδu / 2
-    cache.ρ = num / denom
-
-    if cache.ρ > cache.step_threshold
-        cache.last_step_accepted = true
-    else
-        cache.last_step_accepted = false
-    end
-
-    if cache.method isa RUS.__Simple
-        if cache.ρ < cache.shrink_threshold
-            cache.trust_region *= cache.shrink_factor
-            cache.shrink_counter += 1
-        else
-            cache.shrink_counter = 0
-            if cache.ρ > cache.expand_threshold && cache.ρ > cache.step_threshold
-                cache.trust_region = cache.expand_factor * cache.trust_region
-            end
-        end
-    elseif cache.method isa RUS.__NLsolve
-        if cache.ρ < cache.shrink_threshold
-            cache.trust_region *= cache.shrink_factor
-            cache.shrink_counter += 1
-        else
-            cache.shrink_counter = 0
-            if cache.ρ ≥ cache.expand_threshold
-                cache.trust_region = cache.expand_factor * cache.internalnorm(δu)
-            elseif cache.ρ ≥ cache.p1
-                cache.trust_region = max(
-                    cache.trust_region, cache.expand_factor * cache.internalnorm(δu))
-            end
-        end
-    elseif cache.method isa RUS.__NocedalWright
-        if cache.ρ < cache.shrink_threshold
-            cache.trust_region = cache.shrink_factor * cache.internalnorm(δu)
-            cache.shrink_counter += 1
-        else
-            cache.shrink_counter = 0
-            if cache.ρ > cache.expand_threshold &&
-               abs(cache.internalnorm(δu) - cache.trust_region) < 1e-6 * cache.trust_region
-                cache.trust_region = cache.expand_factor * cache.trust_region
-            end
-        end
-    elseif cache.method isa RUS.__Hei
-        tr_new = __rfunc(
-            cache.ρ, cache.shrink_threshold, cache.p1, cache.p3, cache.p4, cache.p2) *
-                 cache.internalnorm(δu)
-        if tr_new < cache.trust_region
-            cache.shrink_counter += 1
-        else
-            cache.shrink_counter = 0
-        end
-        cache.trust_region = tr_new
-    elseif cache.method isa RUS.__Yuan
-        if cache.ρ < cache.shrink_threshold
-            cache.p1 = cache.p2 * cache.p1
-            cache.shrink_counter += 1
-        else
-            if cache.ρ ≥ cache.expand_threshold &&
-               2 * cache.internalnorm(δu) > cache.trust_region
-                cache.p1 = cache.p3 * cache.p1
-            end
-            cache.shrink_counter = 0
-        end
-        operator = StatefulJacobianOperator(cache.vjp_operator, cache.u_cache, cache.p)
-        @bb cache.Jᵀfu_cache = operator × vec(cache.fu_cache)
-        cache.trust_region = cache.p1 * cache.internalnorm(cache.Jᵀfu_cache)
-    elseif cache.method isa RUS.__Fan
-        if cache.ρ < cache.shrink_threshold
-            cache.p1 *= cache.p2
-            cache.shrink_counter += 1
-        else
-            cache.shrink_counter = 0
-            cache.ρ > cache.expand_threshold &&
-                (cache.p1 = min(cache.p1 * cache.p3, cache.p4))
-        end
-        cache.trust_region = cache.p1 * (cache.internalnorm(cache.fu_cache)^T(0.99))
-    elseif cache.method isa RUS.__Bastin
-        if cache.ρ > cache.step_threshold
-            jvp_op = StatefulJacobianOperator(cache.jvp_operator, cache.u_cache, cache.p)
-            vjp_op = StatefulJacobianOperator(cache.vjp_operator, cache.u_cache, cache.p)
-            @bb cache.Jδu_cache = jvp_op × vec(δu)
-            @bb cache.Jᵀfu_cache = vjp_op × vec(cache.fu_cache)
-            denom_1 = dot(_vec(δu), cache.Jᵀfu_cache)
-            @bb cache.Jᵀfu_cache = vjp_op × vec(cache.Jδu_cache)
-            denom_2 = dot(_vec(δu), cache.Jᵀfu_cache)
-            denom = denom_1 + denom_2 / 2
-            ρ = num / denom
-            if ρ ≥ cache.expand_threshold
-                cache.trust_region = cache.p1 * cache.internalnorm(δu)
-            end
-            cache.shrink_counter = 0
-        else
-            cache.trust_region *= cache.p2
-            cache.shrink_counter += 1
-        end
-    end
-
-    cache.trust_region = min(cache.trust_region, cache.max_trust_radius)
-
-    return cache.last_step_accepted, cache.u_cache, cache.fu_cache
-end
-
-# R-function for adaptive trust region method
-function __rfunc(r::R, c2::R, M::R, γ1::R, γ2::R, β::R) where {R <: Real}
-    return ifelse(r ≥ c2, (2 * (M - 1 - γ2) * atan(r - c2) + (1 + γ2)) / R(π),
-        (1 - γ1 - β) * (exp(r - c2) + β / (1 - γ1 - β)))
-end
diff --git a/src/timer_outputs.jl b/src/helpers.jl
similarity index 100%
rename from src/timer_outputs.jl
rename to src/helpers.jl
diff --git a/src/polyalg.jl b/src/polyalg.jl
new file mode 100644
index 000000000..5cf21d6e1
--- /dev/null
+++ b/src/polyalg.jl
@@ -0,0 +1,543 @@
+"""
+    NonlinearSolvePolyAlgorithm(algs; start_index::Int = 1)
+
+A general way to define PolyAlgorithms for `NonlinearProblem` and
+`NonlinearLeastSquaresProblem`. This is a container for a tuple of algorithms that will be
+tried in order until one succeeds. If none succeed, then the algorithm with the lowest
+residual is returned.
+
+### Arguments
+
+  - `algs`: a tuple of algorithms to try in-order! (If this is not a Tuple, then the
+    returned algorithm is not type-stable).
+
+### Keyword Arguments
+
+  - `start_index`: the index to start at. Defaults to `1`.
+
+### Example
+
+```julia
+using NonlinearSolve
+
+alg = NonlinearSolvePolyAlgorithm((NewtonRaphson(), Broyden()))
+```
+"""
+@concrete struct NonlinearSolvePolyAlgorithm <: AbstractNonlinearSolveAlgorithm
+    static_length <: Val
+    algs <: Tuple
+    start_index::Int
+end
+
+function NonlinearSolvePolyAlgorithm(algs; start_index::Int = 1)
+    @assert 0 < start_index ≤ length(algs)
+    algs = Tuple(algs)
+    return NonlinearSolvePolyAlgorithm(Val(length(algs)), algs, start_index)
+end
+
+@concrete mutable struct NonlinearSolvePolyAlgorithmCache <: AbstractNonlinearSolveCache
+    static_length <: Val
+    prob <: AbstractNonlinearProblem
+
+    caches <: Tuple
+    alg <: NonlinearSolvePolyAlgorithm
+
+    best::Int
+    current::Int
+    nsteps::Int
+
+    stats::NLStats
+    total_time::Float64
+    maxtime
+
+    retcode::ReturnCode.T
+    force_stop::Bool
+
+    maxiters::Int
+    internalnorm
+
+    u0
+    u0_aliased
+    alias_u0::Bool
+end
+
+function SII.symbolic_container(cache::NonlinearSolvePolyAlgorithmCache)
+    return cache.caches[cache.current]
+end
+SII.state_values(cache::NonlinearSolvePolyAlgorithmCache) = cache.u0
+
+function Base.show(io::IO, ::MIME"text/plain", cache::NonlinearSolvePolyAlgorithmCache)
+    println(io, "NonlinearSolvePolyAlgorithmCache with \
+                 $(Utils.unwrap_val(cache.static_length)) algorithms:")
+    best_alg = ifelse(cache.best == -1, "nothing", cache.best)
+    println(io, "    Best Algorithm: $(best_alg)")
+    println(
+        io, "    Current Algorithm: [$(cache.current) / $(Utils.unwrap_val(cache.static_length))]"
+    )
+    println(io, "    nsteps: $(cache.nsteps)")
+    println(io, "    retcode: $(cache.retcode)")
+    print(io, "    Current Cache: ")
+    NonlinearSolveBase.show_nonlinearsolve_cache(io, cache.caches[cache.current], 4)
+end
+
+function InternalAPI.reinit!(
+        cache::NonlinearSolvePolyAlgorithmCache, args...; p = cache.p, u0 = cache.u0
+)
+    foreach(cache.caches) do cache
+        InternalAPI.reinit!(cache, args...; p, u0)
+    end
+    cache.current = cache.alg.start_index
+    InternalAPI.reinit!(cache.stats)
+    cache.nsteps = 0
+    cache.total_time = 0.0
+end
+
+function SciMLBase.__init(
+        prob::AbstractNonlinearProblem, alg::NonlinearSolvePolyAlgorithm, args...;
+        stats = NLStats(0, 0, 0, 0, 0), maxtime = nothing, maxiters = 1000,
+        internalnorm = L2_NORM, alias_u0 = false, verbose = true, kwargs...
+)
+    if alias_u0 && !ArrayInterface.ismutable(prob.u0)
+        verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
+                          immutable (checked using `ArrayInterface.ismutable`)."
+        alias_u0 = false  # If immutable don't care about aliasing
+    end
+
+    u0 = prob.u0
+    u0_aliased = alias_u0 ? copy(u0) : u0
+    alias_u0 && (prob = SciMLBase.remake(prob; u0 = u0_aliased))
+
+    return NonlinearSolvePolyAlgorithmCache(
+        alg.static_length, prob,
+        map(alg.algs) do solver
+            SciMLBase.__init(
+                prob, solver, args...;
+                stats, maxtime, internalnorm, alias_u0, verbose, kwargs...
+            )
+        end,
+        alg, -1, alg.start_index, 0, stats, 0.0, maxtime,
+        ReturnCode.Default, false, maxiters, internalnorm,
+        u0, u0_aliased, alias_u0
+    )
+end
+
+@generated function CommonSolve.solve!(cache::NonlinearSolvePolyAlgorithmCache{Val{N}}) where {N}
+    calls = [quote
+        1 ≤ cache.current ≤ $(N) || error("Current choices shouldn't get here!")
+    end]
+
+    cache_syms = [gensym("cache") for i in 1:N]
+    sol_syms = [gensym("sol") for i in 1:N]
+    u_result_syms = [gensym("u_result") for i in 1:N]
+
+    for i in 1:N
+        push!(calls,
+            quote
+                $(cache_syms[i]) = cache.caches[$(i)]
+                if $(i) == cache.current
+                    cache.alias_u0 && copyto!(cache.u0_aliased, cache.u0)
+                    $(sol_syms[i]) = CommonSolve.solve!($(cache_syms[i]))
+                    if SciMLBase.successful_retcode($(sol_syms[i]))
+                        stats = $(sol_syms[i]).stats
+                        if cache.alias_u0
+                            copyto!(cache.u0, $(sol_syms[i]).u)
+                            $(u_result_syms[i]) = cache.u0
+                        else
+                            $(u_result_syms[i]) = $(sol_syms[i]).u
+                        end
+                        fu = NonlinearSolveBase.get_fu($(cache_syms[i]))
+                        return build_solution_less_specialize(
+                            cache.prob, cache.alg, $(u_result_syms[i]), fu;
+                            retcode = $(sol_syms[i]).retcode, stats,
+                            original = $(sol_syms[i]), trace = $(sol_syms[i]).trace
+                        )
+                    elseif cache.alias_u0
+                        # For safety we need to maintain a copy of the solution
+                        $(u_result_syms[i]) = copy($(sol_syms[i]).u)
+                    end
+                    cache.current = $(i + 1)
+                end
+            end)
+    end
+
+    resids = map(Base.Fix2(Symbol, :resid), cache_syms)
+    for (sym, resid) in zip(cache_syms, resids)
+        push!(calls, :($(resid) = @isdefined($(sym)) ? $(sym).resid : nothing))
+    end
+    push!(calls, quote
+        fus = tuple($(Tuple(resids)...))
+        minfu, idx = findmin_caches(cache.prob, fus)
+    end)
+    for i in 1:N
+        push!(calls,
+            quote
+                if idx == $(i)
+                    u = cache.alias_u0 ? $(u_result_syms[i]) :
+                        NonlinearSolveBase.get_u(cache.caches[$(i)])
+                end
+            end)
+    end
+    push!(calls,
+        quote
+            retcode = cache.caches[idx].retcode
+            if cache.alias_u0
+                copyto!(cache.u0, u)
+                u = cache.u0
+            end
+            return build_solution_less_specialize(
+                cache.prob, cache.alg, u, fus[idx];
+                retcode, cache.stats, cache.caches[idx].trace
+            )
+        end)
+
+    return Expr(:block, calls...)
+end
+
+@generated function InternalAPI.step!(
+        cache::NonlinearSolvePolyAlgorithmCache{Val{N}}, args...; kwargs...
+) where {N}
+    calls = []
+    cache_syms = [gensym("cache") for i in 1:N]
+    for i in 1:N
+        push!(calls,
+            quote
+                $(cache_syms[i]) = cache.caches[$(i)]
+                if $(i) == cache.current
+                    InternalAPI.step!($(cache_syms[i]), args...; kwargs...)
+                    $(cache_syms[i]).nsteps += 1
+                    if !NonlinearSolveBase.not_terminated($(cache_syms[i]))
+                        if SciMLBase.successful_retcode($(cache_syms[i]).retcode)
+                            cache.best = $(i)
+                            cache.force_stop = true
+                            cache.retcode = $(cache_syms[i]).retcode
+                        else
+                            cache.current = $(i + 1)
+                        end
+                    end
+                    return
+                end
+            end)
+    end
+
+    push!(calls, quote
+        if !(1 ≤ cache.current ≤ length(cache.caches))
+            minfu, idx = findmin_caches(cache.prob, cache.caches)
+            cache.best = idx
+            cache.retcode = cache.caches[idx].retcode
+            cache.force_stop = true
+            return
+        end
+    end)
+
+    return Expr(:block, calls...)
+end
+
+@generated function SciMLBase.__solve(
+        prob::AbstractNonlinearProblem, alg::NonlinearSolvePolyAlgorithm{Val{N}}, args...;
+        stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, verbose = true, kwargs...
+) where {N}
+    sol_syms = [gensym("sol") for _ in 1:N]
+    prob_syms = [gensym("prob") for _ in 1:N]
+    u_result_syms = [gensym("u_result") for _ in 1:N]
+    calls = [quote
+        current = alg.start_index
+        if alias_u0 && !ArrayInterface.ismutable(prob.u0)
+            verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
+                              immutable (checked using `ArrayInterface.ismutable`)."
+            alias_u0 = false  # If immutable don't care about aliasing
+        end
+        u0 = prob.u0
+        u0_aliased = alias_u0 ? zero(u0) : u0
+    end]
+    for i in 1:N
+        cur_sol = sol_syms[i]
+        push!(calls,
+            quote
+                if current == $(i)
+                    if alias_u0
+                        copyto!(u0_aliased, u0)
+                        $(prob_syms[i]) = SciMLBase.remake(prob; u0 = u0_aliased)
+                    else
+                        $(prob_syms[i]) = prob
+                    end
+                    $(cur_sol) = SciMLBase.__solve(
+                        $(prob_syms[i]), alg.algs[$(i)], args...;
+                        stats, alias_u0, verbose, kwargs...
+                    )
+                    if SciMLBase.successful_retcode($(cur_sol))
+                        if alias_u0
+                            copyto!(u0, $(cur_sol).u)
+                            $(u_result_syms[i]) = u0
+                        else
+                            $(u_result_syms[i]) = $(cur_sol).u
+                        end
+                        return build_solution_less_specialize(
+                            prob, alg, $(u_result_syms[i]), $(cur_sol).resid;
+                            $(cur_sol).retcode, $(cur_sol).stats,
+                            $(cur_sol).trace, original = $(cur_sol)
+                        )
+                    elseif alias_u0
+                        # For safety we need to maintain a copy of the solution
+                        $(u_result_syms[i]) = copy($(cur_sol).u)
+                    end
+                    current = $(i + 1)
+                end
+            end)
+    end
+
+    resids = map(Base.Fix2(Symbol, :resid), sol_syms)
+    for (sym, resid) in zip(sol_syms, resids)
+        push!(calls, :($(resid) = @isdefined($(sym)) ? $(sym).resid : nothing))
+    end
+
+    push!(calls, quote
+        resids = tuple($(Tuple(resids)...))
+        minfu, idx = findmin_resids(prob, resids)
+    end)
+
+    for i in 1:N
+        push!(calls,
+            quote
+                if idx == $(i)
+                    if alias_u0
+                        copyto!(u0, $(u_result_syms[i]))
+                        $(u_result_syms[i]) = u0
+                    else
+                        $(u_result_syms[i]) = $(sol_syms[i]).u
+                    end
+                    return build_solution_less_specialize(
+                        prob, alg, $(u_result_syms[i]), $(sol_syms[i]).resid;
+                        $(sol_syms[i]).retcode, $(sol_syms[i]).stats,
+                        $(sol_syms[i]).trace, original = $(sol_syms[i])
+                    )
+                end
+            end)
+    end
+    push!(calls, :(error("Current choices shouldn't get here!")))
+
+    return Expr(:block, calls...)
+end
+
+"""
+    RobustMultiNewton(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing, precs = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+    )
+
+A polyalgorithm focused on robustness. It uses a mixture of Newton methods with different
+globalizing techniques (trust region updates, line searches, etc.) in order to find a
+method that is able to adequately solve the minimization problem.
+
+Basically, if this algorithm fails, then "most" good ways of solving your problem fail and
+you may need to think about reformulating the model (either there is an issue with the model,
+or more precision / more stable linear solver choice is required).
+
+### Arguments
+
+  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
+    are compatible with the problem type. Defaults to `Float64`.
+"""
+function RobustMultiNewton(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing, precs = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+) where {T}
+    common_kwargs = (; concrete_jac, linsolve, precs, autodiff, vjp_autodiff, jvp_autodiff)
+    if T <: Complex # Let's atleast have something here for complex numbers
+        algs = (NewtonRaphson(; common_kwargs...),)
+    else
+        algs = (
+            TrustRegion(; common_kwargs...),
+            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin),
+            NewtonRaphson(; common_kwargs...),
+            NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
+            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.NLsolve),
+            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Fan)
+        )
+    end
+    return NonlinearSolvePolyAlgorithm(algs)
+end
+
+"""
+    FastShortcutNonlinearPolyalg(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing, precs = nothing,
+        must_use_jacobian::Val = Val(false),
+        prefer_simplenonlinearsolve::Val = Val(false),
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing,
+        u0_len::Union{Int, Nothing} = nothing
+    ) where {T}
+
+A polyalgorithm focused on balancing speed and robustness. It first tries less robust methods
+for more performance and then tries more robust techniques if the faster ones fail.
+
+### Arguments
+
+  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
+    are compatible with the problem type. Defaults to `Float64`.
+
+### Keyword Arguments
+
+  - `u0_len`: The length of the initial guess. If this is `nothing`, then the length of the
+    initial guess is not checked. If this is an integer and it is less than `25`, we use
+    jacobian based methods.
+"""
+function FastShortcutNonlinearPolyalg(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing, precs = nothing,
+        must_use_jacobian::Val = Val(false),
+        prefer_simplenonlinearsolve::Val = Val(false),
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing,
+        u0_len::Union{Int, Nothing} = nothing
+) where {T}
+    start_index = 1
+    common_kwargs = (; concrete_jac, linsolve, precs, autodiff, vjp_autodiff, jvp_autodiff)
+    if must_use_jacobian isa Val{true}
+        if T <: Complex
+            algs = (NewtonRaphson(; common_kwargs...),)
+        else
+            algs = (
+                NewtonRaphson(; common_kwargs...),
+                NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
+                TrustRegion(; common_kwargs...),
+                TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin)
+            )
+        end
+    else
+        # SimpleNewtonRaphson and SimpleTrustRegion are not robust to singular Jacobians
+        # and thus are not included in the polyalgorithm
+        if prefer_simplenonlinearsolve isa Val{true}
+            if T <: Complex
+                algs = (
+                    SimpleBroyden(),
+                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
+                    SimpleKlement(),
+                    NewtonRaphson(; common_kwargs...)
+                )
+            else
+                start_index = u0_len !== nothing ? (u0_len ≤ 25 ? 4 : 1) : 1
+                algs = (
+                    SimpleBroyden(),
+                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
+                    SimpleKlement(),
+                    NewtonRaphson(; common_kwargs...),
+                    NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
+                    TrustRegion(; common_kwargs...),
+                    TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin)
+                )
+            end
+        else
+            if T <: Complex
+                algs = (
+                    Broyden(; autodiff),
+                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
+                    Klement(; linsolve, precs, autodiff),
+                    NewtonRaphson(; common_kwargs...)
+                )
+            else
+                # TODO: This number requires a bit rigorous testing
+                start_index = u0_len !== nothing ? (u0_len ≤ 25 ? 4 : 1) : 1
+                algs = (
+                    Broyden(; autodiff),
+                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
+                    Klement(; linsolve, precs, autodiff),
+                    NewtonRaphson(; common_kwargs...),
+                    NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
+                    TrustRegion(; common_kwargs...),
+                    TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin)
+                )
+            end
+        end
+    end
+    return NonlinearSolvePolyAlgorithm(algs; start_index)
+end
+
+"""
+    FastShortcutNLLSPolyalg(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing, precs = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+    )
+
+A polyalgorithm focused on balancing speed and robustness. It first tries less robust methods
+for more performance and then tries more robust techniques if the faster ones fail.
+
+### Arguments
+
+  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
+    are compatible with the problem type. Defaults to `Float64`.
+"""
+function FastShortcutNLLSPolyalg(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing, precs = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+) where {T}
+    common_kwargs = (; linsolve, precs, autodiff, vjp_autodiff, jvp_autodiff)
+    if T <: Complex
+        algs = (
+            GaussNewton(; common_kwargs..., concrete_jac),
+            LevenbergMarquardt(; common_kwargs..., disable_geodesic = Val(true)),
+            LevenbergMarquardt(; common_kwargs...)
+        )
+    else
+        algs = (
+            GaussNewton(; common_kwargs..., concrete_jac),
+            LevenbergMarquardt(; common_kwargs..., disable_geodesic = Val(true)),
+            TrustRegion(; common_kwargs..., concrete_jac),
+            GaussNewton(; common_kwargs..., linesearch = BackTracking(), concrete_jac),
+            TrustRegion(;
+                common_kwargs..., radius_update_scheme = RUS.Bastin, concrete_jac
+            ),
+            LevenbergMarquardt(; common_kwargs...)
+        )
+    end
+    return NonlinearSolvePolyAlgorithm(algs)
+end
+
+# Original is often determined on runtime information especially for PolyAlgorithms so it
+# is best to never specialize on that
+function build_solution_less_specialize(
+        prob::AbstractNonlinearProblem, alg, u, resid;
+        retcode = ReturnCode.Default, original = nothing, left = nothing,
+        right = nothing, stats = nothing, trace = nothing, kwargs...
+)
+    return SciMLBase.NonlinearSolution{
+        eltype(eltype(u)), ndims(u), typeof(u), typeof(resid), typeof(prob),
+        typeof(alg), Any, typeof(left), typeof(stats), typeof(trace)
+    }(
+        u, resid, prob, alg, retcode, original, left, right, stats, trace
+    )
+end
+
+function findmin_caches(prob::AbstractNonlinearProblem, caches)
+    resids = map(caches) do cache
+        cache === nothing && return nothing
+        return NonlinearSolveBase.get_fu(cache)
+    end
+    return findmin_resids(prob, resids)
+end
+
+@views function findmin_resids(prob::AbstractNonlinearProblem, caches)
+    norm_fn = prob isa NonlinearLeastSquaresProblem ? Base.Fix2(norm, 2) :
+              Base.Fix2(norm, Inf)
+    idx = findfirst(Base.Fix2(!==, nothing), caches)
+    # This is an internal function so we assume that inputs are consistent and there is
+    # atleast one non-`nothing` value
+    fx_idx = norm_fn(caches[idx])
+    idx == length(caches) && return fx_idx, idx
+    fmin = @closure xᵢ -> begin
+        xᵢ === nothing && return oftype(fx_idx, Inf)
+        fx = norm_fn(xᵢ)
+        return ifelse(isnan(fx), oftype(fx, Inf), fx)
+    end
+    x_min, x_min_idx = findmin(fmin, caches[(idx + 1):length(caches)])
+    x_min < fx_idx && return x_min, x_min_idx + idx
+    return fx_idx, idx
+end
diff --git a/src/utils.jl b/src/utils.jl
deleted file mode 100644
index 0a2375ef9..000000000
--- a/src/utils.jl
+++ /dev/null
@@ -1,50 +0,0 @@
-@inline __is_complex(::Type{ComplexF64}) = true
-@inline __is_complex(::Type{ComplexF32}) = true
-@inline __is_complex(::Type{Complex}) = true
-@inline __is_complex(::Type{T}) where {T} = false
-
-@inline __findmin_caches(f::F, caches) where {F} = __findmin(f ∘ get_fu, caches)
-# FIXME: L2_NORM makes an Array of NaNs not a NaN (atleast according to `isnan`)
-@generated function __findmin(f::F, x) where {F}
-    # JET shows dynamic dispatch if this is not written as a generated function
-    F === typeof(L2_NORM) && return :(return __findmin_impl(Base.Fix1(maximum, abs), x))
-    return :(return __findmin_impl(f, x))
-end
-@inline @views function __findmin_impl(f::F, x) where {F}
-    idx = findfirst(Base.Fix2(!==, nothing), x)
-    # This is an internal function so we assume that inputs are consistent and there is
-    # atleast one non-`nothing` value
-    fx_idx = f(x[idx])
-    idx == length(x) && return fx_idx, idx
-    fmin = @closure xᵢ -> begin
-        xᵢ === nothing && return oftype(fx_idx, Inf)
-        fx = f(xᵢ)
-        return ifelse(isnan(fx), oftype(fx, Inf), fx)
-    end
-    x_min, x_min_idx = findmin(fmin, x[(idx + 1):length(x)])
-    x_min < fx_idx && return x_min, x_min_idx + idx
-    return fx_idx, idx
-end
-
-"""
-    pickchunksize(x) = pickchunksize(length(x))
-    pickchunksize(x::Int)
-
-Determine the chunk size for ForwardDiff and PolyesterForwardDiff based on the input length.
-"""
-@inline pickchunksize(x) = pickchunksize(length(x))
-@inline pickchunksize(x::Int) = ForwardDiff.pickchunksize(x)
-
-# Original is often determined on runtime information especially for PolyAlgorithms so it
-# is best to never specialize on that
-function __build_solution_less_specialize(prob::AbstractNonlinearProblem, alg, u, resid;
-        retcode = ReturnCode.Default, original = nothing, left = nothing,
-        right = nothing, stats = nothing, trace = nothing, kwargs...)
-    T = eltype(eltype(u))
-    N = ndims(u)
-
-    return SciMLBase.NonlinearSolution{
-        T, N, typeof(u), typeof(resid), typeof(prob), typeof(alg),
-        Any, typeof(left), typeof(stats), typeof(trace)}(
-        u, resid, prob, alg, retcode, original, left, right, stats, trace)
-end

From 13e3c3a0562e11532feca9e59c7a62b7fb96de83 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 28 Oct 2024 22:21:22 -0400
Subject: [PATCH 648/700] feat(BracketingNonlinearSolve): subtype
 AbstractNonlinearSolveAlgorithm

---
 .../src/BracketingNonlinearSolve.jl           |  9 ++---
 lib/BracketingNonlinearSolve/src/alefeld.jl   | 39 ++++++++++++-------
 lib/BracketingNonlinearSolve/src/bisection.jl | 27 ++++++++-----
 lib/BracketingNonlinearSolve/src/brent.jl     | 33 ++++++++++------
 lib/BracketingNonlinearSolve/src/common.jl    |  6 ++-
 lib/BracketingNonlinearSolve/src/falsi.jl     | 27 ++++++++-----
 lib/BracketingNonlinearSolve/src/itp.jl       | 30 +++++++++-----
 lib/BracketingNonlinearSolve/src/ridder.jl    | 33 ++++++++++------
 8 files changed, 133 insertions(+), 71 deletions(-)

diff --git a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
index 9757c4c23..4eccda940 100644
--- a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
+++ b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
@@ -1,15 +1,14 @@
 module BracketingNonlinearSolve
 
 using ConcreteStructs: @concrete
+using PrecompileTools: @compile_workload, @setup_workload
 using Reexport: @reexport
 
 using CommonSolve: CommonSolve, solve
-using NonlinearSolveBase: NonlinearSolveBase
-using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, IntervalNonlinearProblem, ReturnCode
-
-using PrecompileTools: @compile_workload, @setup_workload
+using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm
+using SciMLBase: SciMLBase, IntervalNonlinearProblem, ReturnCode
 
-abstract type AbstractBracketingAlgorithm <: AbstractNonlinearAlgorithm end
+abstract type AbstractBracketingAlgorithm <: AbstractNonlinearSolveAlgorithm end
 
 include("common.jl")
 
diff --git a/lib/BracketingNonlinearSolve/src/alefeld.jl b/lib/BracketingNonlinearSolve/src/alefeld.jl
index a669900dd..6880f8c95 100644
--- a/lib/BracketingNonlinearSolve/src/alefeld.jl
+++ b/lib/BracketingNonlinearSolve/src/alefeld.jl
@@ -8,8 +8,10 @@ algorithm 4.1 because, in certain sense, the second algorithm(4.2) is an optimal
 """
 struct Alefeld <: AbstractBracketingAlgorithm end
 
-function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...;
-        maxiters = 1000, abstol = nothing, kwargs...)
+function CommonSolve.solve(
+        prob::IntervalNonlinearProblem, alg::Alefeld, args...;
+        maxiters = 1000, abstol = nothing, kwargs...
+)
     f = Base.Fix2(prob.f, prob.p)
     a, b = prob.tspan
     c = a - (b - a) / (f(b) - f(a)) * f(a)
@@ -17,12 +19,14 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...
     fc = f(c)
     if a == c || b == c
         return SciMLBase.build_solution(
-            prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit, left = a, right = b)
+            prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit, left = a, right = b
+        )
     end
 
     if iszero(fc)
         return SciMLBase.build_solution(
-            prob, alg, c, fc; retcode = ReturnCode.Success, left = a, right = b)
+            prob, alg, c, fc; retcode = ReturnCode.Success, left = a, right = b
+        )
     end
 
     a, b, d = Impl.bracket(f, a, b, c)
@@ -68,13 +72,15 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...
 
         if ā == c || b̄ == c
             return SciMLBase.build_solution(
-                prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
-                left = ā, right = b̄)
+                prob, alg, c, fc;
+                retcode = ReturnCode.FloatingPointLimit, left = ā, right = b̄
+            )
         end
 
         if iszero(fc)
             return SciMLBase.build_solution(
-                prob, alg, c, fc; retcode = ReturnCode.Success, left = ā, right = b̄)
+                prob, alg, c, fc; retcode = ReturnCode.Success, left = ā, right = b̄
+            )
         end
 
         ā, b̄, d̄ = Impl.bracket(f, ā, b̄, c)
@@ -89,13 +95,15 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...
 
         if ā == c || b̄ == c
             return SciMLBase.build_solution(
-                prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
-                left = ā, right = b̄)
+                prob, alg, c, fc;
+                retcode = ReturnCode.FloatingPointLimit, left = ā, right = b̄
+            )
         end
 
         if iszero(fc)
             return SciMLBase.build_solution(
-                prob, alg, c, fc; retcode = ReturnCode.Success, left = ā, right = b̄)
+                prob, alg, c, fc; retcode = ReturnCode.Success, left = ā, right = b̄
+            )
         end
 
         ā, b̄, d = Impl.bracket(f, ā, b̄, c)
@@ -110,12 +118,14 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...
 
             if ā == c || b̄ == c
                 return SciMLBase.build_solution(
-                    prob, alg, c, fc; retcode = ReturnCode.FloatingPointLimit,
-                    left = ā, right = b̄)
+                    prob, alg, c, fc;
+                    retcode = ReturnCode.FloatingPointLimit, left = ā, right = b̄
+                )
             end
             if iszero(fc)
                 return SciMLBase.build_solution(
-                    prob, alg, c, fc; retcode = ReturnCode.Success, left = ā, right = b̄)
+                    prob, alg, c, fc; retcode = ReturnCode.Success, left = ā, right = b̄
+                )
             end
             a, b, d = Impl.bracket(f, ā, b̄, c)
         end
@@ -131,5 +141,6 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Alefeld, args...
 
     # Return solution when run out of max iteration
     return SciMLBase.build_solution(
-        prob, alg, c, fc; retcode = ReturnCode.MaxIters, left = a, right = b)
+        prob, alg, c, fc; retcode = ReturnCode.MaxIters, left = a, right = b
+    )
 end
diff --git a/lib/BracketingNonlinearSolve/src/bisection.jl b/lib/BracketingNonlinearSolve/src/bisection.jl
index e51416145..91c17a775 100644
--- a/lib/BracketingNonlinearSolve/src/bisection.jl
+++ b/lib/BracketingNonlinearSolve/src/bisection.jl
@@ -19,8 +19,10 @@ A common bisection method.
     exact_right::Bool = false
 end
 
-function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Bisection,
-        args...; maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...)
+function CommonSolve.solve(
+        prob::IntervalNonlinearProblem, alg::Bisection, args...;
+        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...
+)
     @assert !SciMLBase.isinplace(prob) "`Bisection` only supports out-of-place problems."
 
     f = Base.Fix2(prob.f, prob.p)
@@ -32,12 +34,14 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Bisection,
 
     if iszero(fl)
         return SciMLBase.build_solution(
-            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right
+        )
     end
 
     if iszero(fr)
         return SciMLBase.build_solution(
-            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right
+        )
     end
 
     if sign(fl) == sign(fr)
@@ -45,7 +49,8 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Bisection,
             @warn "The interval is not an enclosing interval, opposite signs at the \
                    boundaries are required."
         return SciMLBase.build_solution(
-            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right
+        )
     end
 
     i = 1
@@ -54,13 +59,15 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Bisection,
 
         if mid == left || mid == right
             return SciMLBase.build_solution(
-                prob, alg, left, fl; retcode = ReturnCode.FloatingPointLimit, left, right)
+                prob, alg, left, fl; retcode = ReturnCode.FloatingPointLimit, left, right
+            )
         end
 
         fm = f(mid)
         if abs((right - left) / 2) < abstol
             return SciMLBase.build_solution(
-                prob, alg, mid, fm; retcode = ReturnCode.Success, left, right)
+                prob, alg, mid, fm; retcode = ReturnCode.Success, left, right
+            )
         end
 
         if iszero(fm)
@@ -80,10 +87,12 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Bisection,
     end
 
     sol, i, left, right, fl, fr = Impl.bisection(
-        left, right, fl, fr, f, abstol, maxiters - i, prob, alg)
+        left, right, fl, fr, f, abstol, maxiters - i, prob, alg
+    )
 
     sol !== nothing && return sol
 
     return SciMLBase.build_solution(
-        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
+        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right
+    )
 end
diff --git a/lib/BracketingNonlinearSolve/src/brent.jl b/lib/BracketingNonlinearSolve/src/brent.jl
index fb3740e98..7baebc90c 100644
--- a/lib/BracketingNonlinearSolve/src/brent.jl
+++ b/lib/BracketingNonlinearSolve/src/brent.jl
@@ -5,8 +5,10 @@ Left non-allocating Brent method.
 """
 struct Brent <: AbstractBracketingAlgorithm end
 
-function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
-        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...)
+function CommonSolve.solve(
+        prob::IntervalNonlinearProblem, alg::Brent, args...;
+        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...
+)
     @assert !SciMLBase.isinplace(prob) "`Brent` only supports out-of-place problems."
 
     f = Base.Fix2(prob.f, prob.p)
@@ -15,16 +17,19 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
     ϵ = eps(convert(typeof(fl), 1))
 
     abstol = NonlinearSolveBase.get_tolerance(
-        left, abstol, promote_type(eltype(left), eltype(right)))
+        left, abstol, promote_type(eltype(left), eltype(right))
+    )
 
     if iszero(fl)
         return SciMLBase.build_solution(
-            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right
+        )
     end
 
     if iszero(fr)
         return SciMLBase.build_solution(
-            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right
+        )
     end
 
     if sign(fl) == sign(fr)
@@ -32,7 +37,8 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
             @warn "The interval is not an enclosing interval, opposite signs at the \
                    boundaries are required."
         return SciMLBase.build_solution(
-            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right
+        )
     end
 
     if abs(fl) < abs(fr)
@@ -67,8 +73,10 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
             # Bisection method
             s = (left + right) / 2
             if s == left || s == right
-                return SciMLBase.build_solution(prob, alg, left, fl;
-                    retcode = ReturnCode.FloatingPointLimit, left, right)
+                return SciMLBase.build_solution(
+                    prob, alg, left, fl;
+                    retcode = ReturnCode.FloatingPointLimit, left, right
+                )
             end
             cond = true
         else
@@ -78,7 +86,8 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
         fs = f(s)
         if abs((right - left) / 2) < abstol
             return SciMLBase.build_solution(
-                prob, alg, s, fs; retcode = ReturnCode.Success, left, right)
+                prob, alg, s, fs; retcode = ReturnCode.Success, left, right
+            )
         end
 
         if iszero(fs)
@@ -110,10 +119,12 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
     end
 
     sol, i, left, right, fl, fr = Impl.bisection(
-        left, right, fl, fr, f, abstol, maxiters - i, prob, alg)
+        left, right, fl, fr, f, abstol, maxiters - i, prob, alg
+    )
 
     sol !== nothing && return sol
 
     return SciMLBase.build_solution(
-        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
+        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right
+    )
 end
diff --git a/lib/BracketingNonlinearSolve/src/common.jl b/lib/BracketingNonlinearSolve/src/common.jl
index 65239ea63..0127869d8 100644
--- a/lib/BracketingNonlinearSolve/src/common.jl
+++ b/lib/BracketingNonlinearSolve/src/common.jl
@@ -10,14 +10,16 @@ function bisection(left, right, fl, fr, f::F, abstol, maxiters, prob, alg) where
 
         if mid == left || mid == right
             sol = SciMLBase.build_solution(
-                prob, alg, left, fl; left, right, retcode = ReturnCode.FloatingPointLimit)
+                prob, alg, left, fl; left, right, retcode = ReturnCode.FloatingPointLimit
+            )
             break
         end
 
         fm = f(mid)
         if abs((right - left) / 2) < abstol
             sol = SciMLBase.build_solution(
-                prob, alg, mid, fm; left, right, retcode = ReturnCode.Success)
+                prob, alg, mid, fm; left, right, retcode = ReturnCode.Success
+            )
             break
         end
 
diff --git a/lib/BracketingNonlinearSolve/src/falsi.jl b/lib/BracketingNonlinearSolve/src/falsi.jl
index f56155ef7..3074a5eb4 100644
--- a/lib/BracketingNonlinearSolve/src/falsi.jl
+++ b/lib/BracketingNonlinearSolve/src/falsi.jl
@@ -5,8 +5,10 @@ A non-allocating regula falsi method.
 """
 struct Falsi <: AbstractBracketingAlgorithm end
 
-function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
-        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...)
+function CommonSolve.solve(
+        prob::IntervalNonlinearProblem, alg::Falsi, args...;
+        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...
+)
     @assert !SciMLBase.isinplace(prob) "`False` only supports out-of-place problems."
 
     f = Base.Fix2(prob.f, prob.p)
@@ -19,12 +21,14 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
 
     if iszero(fl)
         return SciMLBase.build_solution(
-            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right
+        )
     end
 
     if iszero(fr)
         return SciMLBase.build_solution(
-            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right
+        )
     end
 
     if sign(fl) == sign(fr)
@@ -32,14 +36,16 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
             @warn "The interval is not an enclosing interval, opposite signs at the \
                    boundaries are required."
         return SciMLBase.build_solution(
-            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right
+        )
     end
 
     i = 1
     while i ≤ maxiters
         if Impl.nextfloat_tdir(left, l, r) == right
             return SciMLBase.build_solution(
-                prob, alg, left, fl; left, right, retcode = ReturnCode.FloatingPointLimit)
+                prob, alg, left, fl; left, right, retcode = ReturnCode.FloatingPointLimit
+            )
         end
 
         mid = (fr * left - fl * right) / (fr - fl)
@@ -52,7 +58,8 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
         fm = f(mid)
         if abs((right - left) / 2) < abstol
             return SciMLBase.build_solution(
-                prob, alg, mid, fm; left, right, retcode = ReturnCode.Success)
+                prob, alg, mid, fm; left, right, retcode = ReturnCode.Success
+            )
         end
 
         if abs(fm) < abstol
@@ -70,10 +77,12 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
     end
 
     sol, i, left, right, fl, fr = Impl.bisection(
-        left, right, fl, fr, f, abstol, maxiters - i, prob, alg)
+        left, right, fl, fr, f, abstol, maxiters - i, prob, alg
+    )
 
     sol !== nothing && return sol
 
     return SciMLBase.build_solution(
-        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
+        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right
+    )
 end
diff --git a/lib/BracketingNonlinearSolve/src/itp.jl b/lib/BracketingNonlinearSolve/src/itp.jl
index 821047a5a..50443e2e9 100644
--- a/lib/BracketingNonlinearSolve/src/itp.jl
+++ b/lib/BracketingNonlinearSolve/src/itp.jl
@@ -56,8 +56,10 @@ function ITP(; scaled_k1::Real = 0.2, k2::Real = 2, n0::Int = 10)
     return ITP(scaled_k1, k2, n0)
 end
 
-function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
-        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...)
+function CommonSolve.solve(
+        prob::IntervalNonlinearProblem, alg::ITP, args...;
+        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...
+)
     @assert !SciMLBase.isinplace(prob) "`ITP` only supports out-of-place problems."
 
     f = Base.Fix2(prob.f, prob.p)
@@ -65,16 +67,19 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
     fl, fr = f(left), f(right)
 
     abstol = NonlinearSolveBase.get_tolerance(
-        left, abstol, promote_type(eltype(left), eltype(right)))
+        left, abstol, promote_type(eltype(left), eltype(right))
+    )
 
     if iszero(fl)
         return SciMLBase.build_solution(
-            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right
+        )
     end
 
     if iszero(fr)
         return SciMLBase.build_solution(
-            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right
+        )
     end
 
     if sign(fl) == sign(fr)
@@ -82,7 +87,8 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
             @warn "The interval is not an enclosing interval, opposite signs at the \
                    boundaries are required."
         return SciMLBase.build_solution(
-            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right
+        )
     end
 
     ϵ = abstol
@@ -115,7 +121,8 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
 
         if abs((left - right) / 2) < ϵ
             return SciMLBase.build_solution(
-                prob, alg, xt, f(xt); retcode = ReturnCode.Success, left, right)
+                prob, alg, xt, f(xt); retcode = ReturnCode.Success, left, right
+            )
         end
 
         # update
@@ -131,7 +138,8 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
             left, fl = xp, yp
         else
             return SciMLBase.build_solution(
-                prob, alg, xp, yps; retcode = ReturnCode.Success, left, right)
+                prob, alg, xp, yps; retcode = ReturnCode.Success, left, right
+            )
         end
 
         i += 1
@@ -140,10 +148,12 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
 
         if Impl.nextfloat_tdir(left, prob.tspan...) == right
             return SciMLBase.build_solution(
-                prob, alg, right, fr; retcode = ReturnCode.FloatingPointLimit, left, right)
+                prob, alg, right, fr; retcode = ReturnCode.FloatingPointLimit, left, right
+            )
         end
     end
 
     return SciMLBase.build_solution(
-        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
+        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right
+    )
 end
diff --git a/lib/BracketingNonlinearSolve/src/ridder.jl b/lib/BracketingNonlinearSolve/src/ridder.jl
index d988c9dc5..9192897c5 100644
--- a/lib/BracketingNonlinearSolve/src/ridder.jl
+++ b/lib/BracketingNonlinearSolve/src/ridder.jl
@@ -5,8 +5,10 @@ A non-allocating ridder method.
 """
 struct Ridder <: AbstractBracketingAlgorithm end
 
-function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
-        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...)
+function CommonSolve.solve(
+        prob::IntervalNonlinearProblem, alg::Ridder, args...;
+        maxiters = 1000, abstol = nothing, verbose::Bool = true, kwargs...
+)
     @assert !SciMLBase.isinplace(prob) "`Ridder` only supports out-of-place problems."
 
     f = Base.Fix2(prob.f, prob.p)
@@ -14,16 +16,19 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
     fl, fr = f(left), f(right)
 
     abstol = NonlinearSolveBase.get_tolerance(
-        left, abstol, promote_type(eltype(left), eltype(right)))
+        left, abstol, promote_type(eltype(left), eltype(right))
+    )
 
     if iszero(fl)
         return SciMLBase.build_solution(
-            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right)
+            prob, alg, left, fl; retcode = ReturnCode.ExactSolutionLeft, left, right
+        )
     end
 
     if iszero(fr)
         return SciMLBase.build_solution(
-            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
+            prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right
+        )
     end
 
     if sign(fl) == sign(fr)
@@ -31,7 +36,8 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
             @warn "The interval is not an enclosing interval, opposite signs at the \
                    boundaries are required."
         return SciMLBase.build_solution(
-            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right
+        )
     end
 
     xo = oftype(left, Inf)
@@ -41,14 +47,16 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
 
         if mid == left || mid == right
             return SciMLBase.build_solution(
-                prob, alg, left, fl; retcode = ReturnCode.FloatingPointLimit, left, right)
+                prob, alg, left, fl; retcode = ReturnCode.FloatingPointLimit, left, right
+            )
         end
 
         fm = f(mid)
         s = sqrt(fm^2 - fl * fr)
         if iszero(s)
             return SciMLBase.build_solution(
-                prob, alg, left, fl; retcode = ReturnCode.Failure, left, right)
+                prob, alg, left, fl; retcode = ReturnCode.Failure, left, right
+            )
         end
 
         x = mid + (mid - left) * sign(fl - fm) * fm / s
@@ -56,7 +64,8 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
         xo = x
         if abs((right - left) / 2) < abstol
             return SciMLBase.build_solution(
-                prob, alg, mid, fm; retcode = ReturnCode.Success, left, right)
+                prob, alg, mid, fm; retcode = ReturnCode.Success, left, right
+            )
         end
 
         if iszero(fx)
@@ -82,10 +91,12 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
     end
 
     sol, i, left, right, fl, fr = Impl.bisection(
-        left, right, fl, fr, f, abstol, maxiters - i, prob, alg)
+        left, right, fl, fr, f, abstol, maxiters - i, prob, alg
+    )
 
     sol !== nothing && return sol
 
     return SciMLBase.build_solution(
-        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right)
+        prob, alg, left, fl; retcode = ReturnCode.MaxIters, left, right
+    )
 end

From 342b1ec095c0fe1a84b69e5183d81d0f25adb5e3 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 28 Oct 2024 23:07:10 -0400
Subject: [PATCH 649/700] refactor(SimpleNonlinearSolve): reuse more code from
 NLB

---
 Project.toml                                  |  1 +
 lib/BracketingNonlinearSolve/Project.toml     |  2 +-
 .../NonlinearSolveBaseBandedMatricesExt.jl    |  1 +
 .../ext/NonlinearSolveBaseForwardDiffExt.jl   | 18 ++--
 .../ext/NonlinearSolveBaseLineSearchExt.jl    |  3 +-
 .../ext/NonlinearSolveBaseLinearSolveExt.jl   | 10 +-
 .../ext/NonlinearSolveBaseSparseArraysExt.jl  |  3 +-
 ...linearSolveBaseSparseMatrixColoringsExt.jl |  4 +-
 lib/NonlinearSolveBase/src/utils.jl           |  4 +-
 lib/SimpleNonlinearSolve/Project.toml         |  8 +-
 .../SimpleNonlinearSolveChainRulesCoreExt.jl  | 13 ++-
 .../ext/SimpleNonlinearSolveReverseDiffExt.jl |  5 +-
 .../ext/SimpleNonlinearSolveTrackerExt.jl     |  3 +-
 .../src/SimpleNonlinearSolve.jl               | 92 +++++++++++--------
 lib/SimpleNonlinearSolve/src/broyden.jl       | 25 ++---
 lib/SimpleNonlinearSolve/src/dfsane.jl        | 45 +++++----
 lib/SimpleNonlinearSolve/src/halley.jl        | 41 +++++----
 lib/SimpleNonlinearSolve/src/klement.jl       | 16 ++--
 lib/SimpleNonlinearSolve/src/lbroyden.jl      | 86 +++++++++--------
 lib/SimpleNonlinearSolve/src/raphson.jl       | 18 ++--
 lib/SimpleNonlinearSolve/src/trust_region.jl  | 66 +++++++------
 lib/SimpleNonlinearSolve/src/utils.jl         | 90 +++++-------------
 src/NonlinearSolve.jl                         |  2 +-
 23 files changed, 295 insertions(+), 261 deletions(-)

diff --git a/Project.toml b/Project.toml
index 6d907607e..768a46005 100644
--- a/Project.toml
+++ b/Project.toml
@@ -6,6 +6,7 @@ version = "4.0.0"
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+BracketingNonlinearSolve = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
diff --git a/lib/BracketingNonlinearSolve/Project.toml b/lib/BracketingNonlinearSolve/Project.toml
index eb81fd7f7..f2a8e2b6d 100644
--- a/lib/BracketingNonlinearSolve/Project.toml
+++ b/lib/BracketingNonlinearSolve/Project.toml
@@ -24,7 +24,7 @@ ConcreteStructs = "0.2.3"
 ExplicitImports = "1.10.1"
 ForwardDiff = "0.10.36"
 InteractiveUtils = "<0.0.1, 1"
-NonlinearSolveBase = "1"
+NonlinearSolveBase = "1.1"
 PrecompileTools = "1.2"
 Reexport = "1.2"
 SciMLBase = "2.50"
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseBandedMatricesExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseBandedMatricesExt.jl
index 7f2ac7f90..93f01f51f 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseBandedMatricesExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseBandedMatricesExt.jl
@@ -2,6 +2,7 @@ module NonlinearSolveBaseBandedMatricesExt
 
 using BandedMatrices: BandedMatrix
 using LinearAlgebra: Diagonal
+
 using NonlinearSolveBase: NonlinearSolveBase, Utils
 
 # This is used if we vcat a Banded Jacobian with a Diagonal Matrix in Levenberg
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
index c4f1dc901..0b16391c4 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
@@ -25,7 +25,8 @@ Utils.value(x::AbstractArray{<:Dual}) = Utils.value.(x)
 
 function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
         prob::Union{IntervalNonlinearProblem, NonlinearProblem, ImmutableNonlinearProblem},
-        alg, args...; kwargs...)
+        alg, args...; kwargs...
+)
     p = Utils.value(prob.p)
     if prob isa IntervalNonlinearProblem
         tspan = Utils.value.(prob.tspan)
@@ -55,7 +56,8 @@ function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
 end
 
 function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
-        prob::NonlinearLeastSquaresProblem, alg, args...; kwargs...)
+        prob::NonlinearLeastSquaresProblem, alg, args...; kwargs...
+)
     p = Utils.value(prob.p)
     newprob = remake(prob; p, u0 = Utils.value(prob.u0))
     sol = solve(newprob, alg, args...; kwargs...)
@@ -168,13 +170,17 @@ function NonlinearSolveBase.nonlinearsolve_∂f_∂u(prob, f::F, u, p) where {F}
     return ForwardDiff.jacobian(Base.Fix2(f, p), u)
 end
 
-function NonlinearSolveBase.nonlinearsolve_dual_solution(u::Number, partials,
-        ::Union{<:AbstractArray{<:Dual{T, V, P}}, Dual{T, V, P}}) where {T, V, P}
+function NonlinearSolveBase.nonlinearsolve_dual_solution(
+        u::Number, partials,
+        ::Union{<:AbstractArray{<:Dual{T, V, P}}, Dual{T, V, P}}
+) where {T, V, P}
     return Dual{T, V, P}(u, partials)
 end
 
-function NonlinearSolveBase.nonlinearsolve_dual_solution(u::AbstractArray, partials,
-        ::Union{<:AbstractArray{<:Dual{T, V, P}}, Dual{T, V, P}}) where {T, V, P}
+function NonlinearSolveBase.nonlinearsolve_dual_solution(
+        u::AbstractArray, partials,
+        ::Union{<:AbstractArray{<:Dual{T, V, P}}, Dual{T, V, P}}
+) where {T, V, P}
     return map(((uᵢ, pᵢ),) -> Dual{T, V, P}(uᵢ, pᵢ), zip(u, Utils.restructure(u, partials)))
 end
 
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLineSearchExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLineSearchExt.jl
index d68007dc0..3b705b0dc 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLineSearchExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLineSearchExt.jl
@@ -1,9 +1,10 @@
 module NonlinearSolveBaseLineSearchExt
 
 using LineSearch: LineSearch, AbstractLineSearchCache
-using NonlinearSolveBase: NonlinearSolveBase, InternalAPI
 using SciMLBase: SciMLBase
 
+using NonlinearSolveBase: NonlinearSolveBase, InternalAPI
+
 function NonlinearSolveBase.callback_into_cache!(
         topcache, cache::AbstractLineSearchCache, args...
 )
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
index 13c4adca5..28b8b1937 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
@@ -1,15 +1,19 @@
 module NonlinearSolveBaseLinearSolveExt
 
 using ArrayInterface: ArrayInterface
+
 using CommonSolve: CommonSolve, init, solve!
-using LinearAlgebra: ColumnNorm
 using LinearSolve: LinearSolve, QRFactorization, SciMLLinearSolveAlgorithm
-using NonlinearSolveBase: NonlinearSolveBase, LinearSolveJLCache, LinearSolveResult, Utils
 using SciMLBase: ReturnCode, LinearProblem
 
+using LinearAlgebra: ColumnNorm
+
+using NonlinearSolveBase: NonlinearSolveBase, LinearSolveJLCache, LinearSolveResult, Utils
+
 function (cache::LinearSolveJLCache)(;
         A = nothing, b = nothing, linu = nothing, du = nothing, p = nothing,
-        cachedata = nothing, reuse_A_if_factorization = false, verbose = true, kwargs...)
+        cachedata = nothing, reuse_A_if_factorization = false, verbose = true, kwargs...
+)
     cache.stats.nsolve += 1
 
     update_A!(cache, A, reuse_A_if_factorization)
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
index 09b113c4a..bc7350d21 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseArraysExt.jl
@@ -1,8 +1,9 @@
 module NonlinearSolveBaseSparseArraysExt
 
-using NonlinearSolveBase: NonlinearSolveBase, Utils
 using SparseArrays: AbstractSparseMatrix, AbstractSparseMatrixCSC, nonzeros, sparse
 
+using NonlinearSolveBase: NonlinearSolveBase, Utils
+
 function NonlinearSolveBase.NAN_CHECK(x::AbstractSparseMatrixCSC)
     return any(NonlinearSolveBase.NAN_CHECK, nonzeros(x))
 end
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl
index e2029d7a2..4daf5ea98 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseSparseMatrixColoringsExt.jl
@@ -1,11 +1,13 @@
 module NonlinearSolveBaseSparseMatrixColoringsExt
 
 using ADTypes: ADTypes, AbstractADType
-using NonlinearSolveBase: NonlinearSolveBase, Utils
 using SciMLBase: SciMLBase, NonlinearFunction
+
 using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm,
                              LargestFirst
 
+using NonlinearSolveBase: NonlinearSolveBase, Utils
+
 Utils.is_extension_loaded(::Val{:SparseMatrixColorings}) = true
 
 function NonlinearSolveBase.select_fastest_coloring_algorithm(
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 6e739c0f8..826c7f66c 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -138,7 +138,9 @@ maybe_unaliased(x::AbstractSciMLOperator, ::Bool) = x
 can_setindex(x) = ArrayInterface.can_setindex(x)
 can_setindex(::Number) = false
 
-evaluate_f!!(prob::AbstractNonlinearProblem, fu, u, p) = evaluate_f!!(prob.f, fu, u, p)
+function evaluate_f!!(prob::AbstractNonlinearProblem, fu, u, p = prob.p)
+    return evaluate_f!!(prob.f, fu, u, p)
+end
 function evaluate_f!!(f::NonlinearFunction, fu, u, p)
     if SciMLBase.isinplace(f)
         f(fu, u, p)
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index cfda24544..c154a4b54 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -5,7 +5,6 @@ version = "2.0.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
-Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 BracketingNonlinearSolve = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
@@ -21,6 +20,7 @@ NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [weakdeps]
@@ -37,10 +37,9 @@ SimpleNonlinearSolveTrackerExt = "Tracker"
 
 [compat]
 ADTypes = "1.2"
-Accessors = "0.1"
 Aqua = "0.8.7"
 ArrayInterface = "7.16"
-BracketingNonlinearSolve = "1"
+BracketingNonlinearSolve = "1.1"
 ChainRulesCore = "1.24"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
@@ -56,7 +55,7 @@ LineSearch = "0.1.3"
 LinearAlgebra = "1.10"
 MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1"
+NonlinearSolveBase = "1.1"
 Pkg = "1.10"
 PolyesterForwardDiff = "0.1"
 PrecompileTools = "1.2"
@@ -64,6 +63,7 @@ Random = "1.10"
 Reexport = "1.2"
 ReverseDiff = "1.15"
 SciMLBase = "2.50"
+Setfield = "1.1.1"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4.3"
 Test = "1.10"
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
index f56dee537..50905279a 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveChainRulesCoreExt.jl
@@ -1,21 +1,26 @@
 module SimpleNonlinearSolveChainRulesCoreExt
 
 using ChainRulesCore: ChainRulesCore, NoTangent
+
 using NonlinearSolveBase: ImmutableNonlinearProblem
 using SciMLBase: ChainRulesOriginator, NonlinearLeastSquaresProblem
 
 using SimpleNonlinearSolve: SimpleNonlinearSolve, simplenonlinearsolve_solve_up,
                             solve_adjoint
 
-function ChainRulesCore.rrule(::typeof(simplenonlinearsolve_solve_up),
+function ChainRulesCore.rrule(
+        ::typeof(simplenonlinearsolve_solve_up),
         prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
-        sensealg, u0, u0_changed, p, p_changed, alg, args...; kwargs...)
+        sensealg, u0, u0_changed, p, p_changed, alg, args...; kwargs...
+)
     out, ∇internal = solve_adjoint(
-        prob, sensealg, u0, p, ChainRulesOriginator(), alg, args...; kwargs...)
+        prob, sensealg, u0, p, ChainRulesOriginator(), alg, args...; kwargs...
+    )
     function ∇simplenonlinearsolve_solve_up(Δ)
         ∂f, ∂prob, ∂sensealg, ∂u0, ∂p, _, ∂args... = ∇internal(Δ)
         return (
-            ∂f, ∂prob, ∂sensealg, ∂u0, NoTangent(), ∂p, NoTangent(), NoTangent(), ∂args...)
+            ∂f, ∂prob, ∂sensealg, ∂u0, NoTangent(), ∂p, NoTangent(), NoTangent(), ∂args...
+        )
     end
     return out, ∇simplenonlinearsolve_solve_up
 end
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
index 0a407986e..d34d8bac7 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveReverseDiffExt.jl
@@ -1,10 +1,11 @@
 module SimpleNonlinearSolveReverseDiffExt
 
-using ArrayInterface: ArrayInterface
 using NonlinearSolveBase: ImmutableNonlinearProblem
-using ReverseDiff: ReverseDiff, TrackedArray, TrackedReal
 using SciMLBase: ReverseDiffOriginator, NonlinearLeastSquaresProblem, remake
 
+using ArrayInterface: ArrayInterface
+using ReverseDiff: ReverseDiff, TrackedArray, TrackedReal
+
 using SimpleNonlinearSolve: SimpleNonlinearSolve, solve_adjoint
 import SimpleNonlinearSolve: simplenonlinearsolve_solve_up
 
diff --git a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
index d29c2ac61..d56854316 100644
--- a/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
+++ b/lib/SimpleNonlinearSolve/ext/SimpleNonlinearSolveTrackerExt.jl
@@ -1,8 +1,9 @@
 module SimpleNonlinearSolveTrackerExt
 
-using ArrayInterface: ArrayInterface
 using NonlinearSolveBase: ImmutableNonlinearProblem
 using SciMLBase: TrackerOriginator, NonlinearLeastSquaresProblem, remake
+
+using ArrayInterface: ArrayInterface
 using Tracker: Tracker, TrackedArray, TrackedReal
 
 using SimpleNonlinearSolve: SimpleNonlinearSolve, solve_adjoint
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index f51064000..528838568 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -1,33 +1,46 @@
 module SimpleNonlinearSolve
 
-using Accessors: @reset
-using BracketingNonlinearSolve: BracketingNonlinearSolve
-using CommonSolve: CommonSolve, solve, init, solve!
 using ConcreteStructs: @concrete
 using FastClosures: @closure
-using LineSearch: LiFukushimaLineSearch
-using LinearAlgebra: LinearAlgebra, dot
-using MaybeInplace: @bb, setindex_trait, CannotSetindex, CanSetindex
 using PrecompileTools: @compile_workload, @setup_workload
 using Reexport: @reexport
-using SciMLBase: SciMLBase, AbstractNonlinearAlgorithm, NonlinearFunction, NonlinearProblem,
-                 NonlinearLeastSquaresProblem, IntervalNonlinearProblem, ReturnCode, remake
+using Setfield: @set!
+
+using BracketingNonlinearSolve: BracketingNonlinearSolve
+using CommonSolve: CommonSolve, solve, init, solve!
+using LineSearch: LiFukushimaLineSearch
+using MaybeInplace: @bb
+using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, L2_NORM,
+                          nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution,
+                          AbstractNonlinearSolveAlgorithm
+using SciMLBase: SciMLBase, NonlinearFunction, NonlinearProblem,
+                 NonlinearLeastSquaresProblem, ReturnCode, remake
+
+using LinearAlgebra: LinearAlgebra, dot
+
 using StaticArraysCore: StaticArray, SArray, SVector, MArray
 
 # AD Dependencies
 using ADTypes: ADTypes, AutoForwardDiff
 using DifferentiationInterface: DifferentiationInterface
 using FiniteDiff: FiniteDiff
-using ForwardDiff: ForwardDiff
-
-using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, L2_NORM,
-                          nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution
+using ForwardDiff: ForwardDiff, Dual
 
 const DI = DifferentiationInterface
 
-abstract type AbstractSimpleNonlinearSolveAlgorithm <: AbstractNonlinearAlgorithm end
+const DualNonlinearProblem = NonlinearProblem{
+    <:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {iip, T, V, P}
+
+const DualNonlinearLeastSquaresProblem = NonlinearLeastSquaresProblem{
+    <:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {iip, T, V, P}
 
-const safe_similar = NonlinearSolveBase.Utils.safe_similar
+abstract type AbstractSimpleNonlinearSolveAlgorithm <: AbstractNonlinearSolveAlgorithm end
+
+const NLBUtils = NonlinearSolveBase.Utils
 
 is_extension_loaded(::Val) = false
 
@@ -42,61 +55,66 @@ include("raphson.jl")
 include("trust_region.jl")
 
 # By Pass the highlevel checks for NonlinearProblem for Simple Algorithms
-function CommonSolve.solve(prob::NonlinearProblem,
-        alg::AbstractSimpleNonlinearSolveAlgorithm, args...; kwargs...)
+function CommonSolve.solve(
+        prob::NonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm, args...;
+        kwargs...
+)
     prob = convert(ImmutableNonlinearProblem, prob)
     return solve(prob, alg, args...; kwargs...)
 end
 
 function CommonSolve.solve(
-        prob::NonlinearProblem{<:Union{Number, <:AbstractArray}, iip,
-            <:Union{
-                <:ForwardDiff.Dual{T, V, P}, <:AbstractArray{<:ForwardDiff.Dual{T, V, P}}}},
-        alg::AbstractSimpleNonlinearSolveAlgorithm,
-        args...;
-        kwargs...) where {T, V, P, iip}
+        prob::DualNonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
+        args...; kwargs...
+)
     if hasfield(typeof(alg), :autodiff) && alg.autodiff === nothing
-        @reset alg.autodiff = AutoForwardDiff()
+        @set! alg.autodiff = AutoForwardDiff()
     end
     prob = convert(ImmutableNonlinearProblem, prob)
     sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
     dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
     return SciMLBase.build_solution(
-        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
+    )
 end
 
 function CommonSolve.solve(
-        prob::NonlinearLeastSquaresProblem{<:Union{Number, <:AbstractArray}, iip,
-            <:Union{
-                <:ForwardDiff.Dual{T, V, P}, <:AbstractArray{<:ForwardDiff.Dual{T, V, P}}}},
-        alg::AbstractSimpleNonlinearSolveAlgorithm,
-        args...;
-        kwargs...) where {T, V, P, iip}
+        prob::DualNonlinearLeastSquaresProblem, alg::AbstractSimpleNonlinearSolveAlgorithm,
+        args...; kwargs...
+)
     if hasfield(typeof(alg), :autodiff) && alg.autodiff === nothing
-        @reset alg.autodiff = AutoForwardDiff()
+        @set! alg.autodiff = AutoForwardDiff()
     end
     sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
     dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
     return SciMLBase.build_solution(
-        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
+    )
 end
 
 function CommonSolve.solve(
         prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
         alg::AbstractSimpleNonlinearSolveAlgorithm,
-        args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...)
+        args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...
+)
     if sensealg === nothing && haskey(prob.kwargs, :sensealg)
         sensealg = prob.kwargs[:sensealg]
     end
     new_u0 = u0 !== nothing ? u0 : prob.u0
     new_p = p !== nothing ? p : prob.p
-    return simplenonlinearsolve_solve_up(prob, sensealg, new_u0, u0 === nothing, new_p,
-        p === nothing, alg, args...; prob.kwargs..., kwargs...)
+    return simplenonlinearsolve_solve_up(
+        prob, sensealg,
+        new_u0, u0 === nothing,
+        new_p, p === nothing,
+        alg, args...;
+        prob.kwargs..., kwargs...
+    )
 end
 
 function simplenonlinearsolve_solve_up(
         prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem}, sensealg, u0,
-        u0_changed, p, p_changed, alg, args...; kwargs...)
+        u0_changed, p, p_changed, alg, args...; kwargs...
+)
     (u0_changed || p_changed) && (prob = remake(prob; u0, p))
     return SciMLBase.__solve(prob, alg, args...; kwargs...)
 end
@@ -131,7 +149,7 @@ function solve_adjoint_internal end
 
         @compile_workload begin
             for prob in (prob_scalar, prob_iip, prob_oop), alg in algs
-                CommonSolve.solve(prob, alg; abstol = 1e-2)
+                CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
             end
         end
     end
diff --git a/lib/SimpleNonlinearSolve/src/broyden.jl b/lib/SimpleNonlinearSolve/src/broyden.jl
index 6537a4d2d..48a056b7d 100644
--- a/lib/SimpleNonlinearSolve/src/broyden.jl
+++ b/lib/SimpleNonlinearSolve/src/broyden.jl
@@ -18,17 +18,19 @@ array problems.
 end
 
 function SimpleBroyden(;
-        linesearch::Union{Bool, Val{true}, Val{false}} = Val(false), alpha = nothing)
+        linesearch::Union{Bool, Val{true}, Val{false}} = Val(false), alpha = nothing
+)
     linesearch = linesearch isa Bool ? Val(linesearch) : linesearch
     return SimpleBroyden(linesearch, alpha)
 end
 
-function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleBroyden, args...;
+function SciMLBase.__solve(
+        prob::ImmutableNonlinearProblem, alg::SimpleBroyden, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
-        alias_u0 = false, termination_condition = nothing, kwargs...)
-    x = Utils.maybe_unaliased(prob.u0, alias_u0)
-    fx = Utils.get_fx(prob, x)
-    fx = Utils.eval_f(prob, fx, x)
+        alias_u0 = false, termination_condition = nothing, kwargs...
+)
+    x = NLBUtils.maybe_unaliased(prob.u0, alias_u0)
+    fx = NLBUtils.evaluate_f(prob, x)
     T = promote_type(eltype(fx), eltype(x))
 
     iszero(fx) &&
@@ -54,9 +56,10 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleBroyden,
     @bb δJ⁻¹ = copy(J⁻¹)
 
     abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
-        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple)
+    )
 
-    if alg.linesearch === Val(true)
+    if alg.linesearch isa Val{true}
         ls_alg = LiFukushimaLineSearch(; nan_maxiters = nothing)
         ls_cache = init(prob, ls_alg, fx, x)
     else
@@ -75,7 +78,7 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleBroyden,
         end
 
         @bb @. x = xo + α * δx
-        fx = Utils.eval_f(prob, fx, x)
+        fx = NLBUtils.evaluate_f!!(prob, fx, x)
         @bb @. δf = fx - fprev
 
         # Termination Checks
@@ -88,8 +91,8 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleBroyden,
 
         @bb @. δJ⁻¹n = (δx - J⁻¹δf) / d
 
-        δJ⁻¹n_ = Utils.safe_vec(δJ⁻¹n)
-        xᵀJ⁻¹_ = Utils.safe_vec(xᵀJ⁻¹)
+        δJ⁻¹n_ = NLBUtils.safe_vec(δJ⁻¹n)
+        xᵀJ⁻¹_ = NLBUtils.safe_vec(xᵀJ⁻¹)
         @bb δJ⁻¹ = δJ⁻¹n_ × transpose(xᵀJ⁻¹_)
         @bb J⁻¹ .+= δJ⁻¹
 
diff --git a/lib/SimpleNonlinearSolve/src/dfsane.jl b/lib/SimpleNonlinearSolve/src/dfsane.jl
index 0d400b0ce..fb371e3c3 100644
--- a/lib/SimpleNonlinearSolve/src/dfsane.jl
+++ b/lib/SimpleNonlinearSolve/src/dfsane.jl
@@ -1,7 +1,9 @@
 """
-    SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
+    SimpleDFSane(;
+        σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
         M::Union{Int, Val} = Val(10), γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
-        nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2)
+        nexp::Int = 2, η_strategy::Function = (f_1, k, x, F) -> f_1 ./ k^2
+    )
 
 A low-overhead implementation of the df-sane method for solving large-scale nonlinear
 systems of equations. For in depth information about all the parameters and the algorithm,
@@ -48,20 +50,26 @@ see [la2006spectral](@citet).
     M <: Val
 end
 
-# XXX[breaking]: we should change the names to not have unicode
-function SimpleDFSane(; σ_min::Real = 1e-10, σ_max::Real = 1e10, σ_1::Real = 1.0,
-        M::Union{Int, Val} = Val(10), γ::Real = 1e-4, τ_min::Real = 0.1, τ_max::Real = 0.5,
-        nexp::Int = 2, η_strategy::F = (f_1, k, x, F) -> f_1 ./ k^2) where {F}
+function SimpleDFSane(;
+        sigma_min::Real = 1e-10, sigma_max::Real = 1e10, sigma_1::Real = 1.0,
+        M::Union{Int, Val} = Val(10), gamma::Real = 1e-4, tau_min::Real = 0.1,
+        tau_max::Real = 0.5, n_exp::Int = 2,
+        eta_strategy::F = (fn_1, n, x_n, f_n) -> fn_1 / n^2
+) where {F}
     M = M isa Int ? Val(M) : M
-    return SimpleDFSane(σ_min, σ_max, σ_1, γ, τ_min, τ_max, nexp, η_strategy, M)
+    return SimpleDFSane(
+        sigma_min, sigma_max, sigma_1, gamma, tau_min, tau_max, n_exp,
+        eta_strategy, M
+    )
 end
 
-function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleDFSane, args...;
+function SciMLBase.__solve(
+        prob::ImmutableNonlinearProblem, alg::SimpleDFSane, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0 = false,
-        termination_condition = nothing, kwargs...)
-    x = Utils.maybe_unaliased(prob.u0, alias_u0)
-    fx = Utils.get_fx(prob, x)
-    fx = Utils.eval_f(prob, fx, x)
+        termination_condition = nothing, kwargs...
+)
+    x = NLBUtils.maybe_unaliased(prob.u0, alias_u0)
+    fx = NLBUtils.evaluate_f(prob, x)
     T = promote_type(eltype(fx), eltype(x))
 
     σ_min = T(alg.σ_min)
@@ -74,7 +82,8 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleDFSane, a
     τ_max = T(alg.τ_max)
 
     abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
-        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple)
+    )
 
     fx_norm = L2_NORM(fx)^nexp
     α_1 = one(T)
@@ -104,7 +113,7 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleDFSane, a
 
         @bb @. x_cache = x + α_p * d
 
-        fx = Utils.eval_f(prob, fx, x_cache)
+        fx = NLBUtils.evaluate_f!!(prob, fx, x_cache)
         fx_norm_new = L2_NORM(fx)^nexp
 
         while k < maxiters
@@ -113,7 +122,7 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleDFSane, a
             α_tp = α_p^2 * fx_norm / (fx_norm_new + (T(2) * α_p - T(1)) * fx_norm)
             @bb @. x_cache = x - α_m * d
 
-            fx = Utils.eval_f(prob, fx, x_cache)
+            fx = NLBUtils.evaluate_f!!(prob, fx, x_cache)
             fx_norm_new = L2_NORM(fx)^nexp
 
             (fx_norm_new ≤ (f_bar + η - γ * α_m^2 * fx_norm)) && break
@@ -123,7 +132,7 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleDFSane, a
             α_m = clamp(α_tm, τ_min * α_m, τ_max * α_m)
             @bb @. x_cache = x + α_p * d
 
-            fx = Utils.eval_f(prob, fx, x_cache)
+            fx = NLBUtils.evaluate_f!!(prob, fx, x_cache)
             fx_norm_new = L2_NORM(fx)^nexp
 
             k += 1
@@ -146,11 +155,11 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleDFSane, a
         fx_norm = fx_norm_new
 
         # Store function value
-        idx = mod1(k, SciMLBase._unwrap_val(alg.M))
+        idx = mod1(k, NLBUtils.unwrap_val(alg.M))
         if history_f_k isa SVector
             history_f_k = Base.setindex(history_f_k, fx_norm_new, idx)
         elseif history_f_k isa NTuple
-            @reset history_f_k[idx] = fx_norm_new
+            @set! history_f_k[idx] = fx_norm_new
         else
             history_f_k[idx] = fx_norm_new
         end
diff --git a/lib/SimpleNonlinearSolve/src/halley.jl b/lib/SimpleNonlinearSolve/src/halley.jl
index 30eb1a821..2d8446d90 100644
--- a/lib/SimpleNonlinearSolve/src/halley.jl
+++ b/lib/SimpleNonlinearSolve/src/halley.jl
@@ -23,33 +23,37 @@ end
 function SciMLBase.__solve(
         prob::ImmutableNonlinearProblem, alg::SimpleHalley, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
-        alias_u0 = false, termination_condition = nothing, kwargs...)
-    x = Utils.maybe_unaliased(prob.u0, alias_u0)
-    fx = Utils.get_fx(prob, x)
-    fx = Utils.eval_f(prob, fx, x)
+        alias_u0 = false, termination_condition = nothing, kwargs...
+)
+    x = NLBUtils.maybe_unaliased(prob.u0, alias_u0)
+    fx = NLBUtils.evaluate_f(prob, x)
     T = promote_type(eltype(fx), eltype(x))
 
     iszero(fx) &&
         return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
 
     abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
-        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple)
+    )
 
     # The way we write the 2nd order derivatives, we know Enzyme won't work there
     autodiff = alg.autodiff === nothing ? AutoForwardDiff() : alg.autodiff
+    @set! alg.autodiff = autodiff
 
     @bb xo = copy(x)
 
-    strait = setindex_trait(x)
-
-    A = strait isa CanSetindex ? safe_similar(x, length(x), length(x)) : x
-    Aaᵢ = strait isa CanSetindex ? safe_similar(x, length(x)) : x
-    cᵢ = strait isa CanSetindex ? safe_similar(x) : x
+    if NLBUtils.can_setindex(x)
+        A = NLBUtils.safe_similar(x, length(x), length(x))
+        Aaᵢ = NLBUtils.safe_similar(x, length(x))
+        cᵢ = NLBUtils.safe_similar(x)
+    else
+        A, Aaᵢ, cᵢ = x, x, x
+    end
 
     for _ in 1:maxiters
         fx, J, H = Utils.compute_jacobian_and_hessian(autodiff, prob, fx, x)
 
-        strait isa CannotSetindex && (A = J)
+        NLBUtils.can_setindex(x) || (A = J)
 
         # Factorize Once and Reuse
         J_fact = if J isa Number
@@ -57,22 +61,23 @@ function SciMLBase.__solve(
         else
             fact = LinearAlgebra.lu(J; check = false)
             !LinearAlgebra.issuccess(fact) && return SciMLBase.build_solution(
-                prob, alg, x, fx; retcode = ReturnCode.Unstable)
+                prob, alg, x, fx; retcode = ReturnCode.Unstable
+            )
             fact
         end
 
-        aᵢ = J_fact \ Utils.safe_vec(fx)
-        A_ = Utils.safe_vec(A)
+        aᵢ = J_fact \ NLBUtils.safe_vec(fx)
+        A_ = NLBUtils.safe_vec(A)
         @bb A_ = H × aᵢ
-        A = Utils.restructure(A, A_)
+        A = NLBUtils.restructure(A, A_)
 
         @bb Aaᵢ = A × aᵢ
         @bb A .*= -1
-        bᵢ = J_fact \ Utils.safe_vec(Aaᵢ)
+        bᵢ = J_fact \ NLBUtils.safe_vec(Aaᵢ)
 
-        cᵢ_ = Utils.safe_vec(cᵢ)
+        cᵢ_ = NLBUtils.safe_vec(cᵢ)
         @bb @. cᵢ_ = (aᵢ * aᵢ) / (-aᵢ + (T(0.5) * bᵢ))
-        cᵢ = Utils.restructure(cᵢ, cᵢ_)
+        cᵢ = NLBUtils.restructure(cᵢ, cᵢ_)
 
         solved, retcode, fx_sol, x_sol = Utils.check_termination(tc_cache, fx, x, xo, prob)
         solved && return SciMLBase.build_solution(prob, alg, x_sol, fx_sol; retcode)
diff --git a/lib/SimpleNonlinearSolve/src/klement.jl b/lib/SimpleNonlinearSolve/src/klement.jl
index 31c4cca96..a8fb7705c 100644
--- a/lib/SimpleNonlinearSolve/src/klement.jl
+++ b/lib/SimpleNonlinearSolve/src/klement.jl
@@ -6,16 +6,18 @@ method is non-allocating on scalar and static array problems.
 """
 struct SimpleKlement <: AbstractSimpleNonlinearSolveAlgorithm end
 
-function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleKlement, args...;
+function SciMLBase.__solve(
+        prob::ImmutableNonlinearProblem, alg::SimpleKlement, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
-        alias_u0 = false, termination_condition = nothing, kwargs...)
-    x = Utils.maybe_unaliased(prob.u0, alias_u0)
+        alias_u0 = false, termination_condition = nothing, kwargs...
+)
+    x = NLBUtils.maybe_unaliased(prob.u0, alias_u0)
     T = eltype(x)
-    fx = Utils.get_fx(prob, x)
-    fx = Utils.eval_f(prob, fx, x)
+    fx = NLBUtils.evaluate_f(prob, x)
 
     abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
-        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple)
+    )
 
     @bb δx = copy(x)
     @bb fprev = copy(fx)
@@ -31,7 +33,7 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleKlement,
         @bb @. δx = fprev / J
 
         @bb @. x = xo - δx
-        fx = Utils.eval_f(prob, fx, x)
+        fx = NLBUtils.evaluate_f!!(prob, fx, x)
 
         # Termination Checks
         solved, retcode, fx_sol, x_sol = Utils.check_termination(tc_cache, fx, x, xo, prob)
diff --git a/lib/SimpleNonlinearSolve/src/lbroyden.jl b/lib/SimpleNonlinearSolve/src/lbroyden.jl
index d2bd6ef83..a0d33f942 100644
--- a/lib/SimpleNonlinearSolve/src/lbroyden.jl
+++ b/lib/SimpleNonlinearSolve/src/lbroyden.jl
@@ -1,6 +1,7 @@
 """
-    SimpleLimitedMemoryBroyden(; threshold::Union{Val, Int} = Val(27),
-        linesearch = Val(false), alpha = nothing)
+    SimpleLimitedMemoryBroyden(;
+        threshold::Union{Val, Int} = Val(27), linesearch = Val(false), alpha = nothing
+    )
 
 A limited memory implementation of Broyden. This method applies the L-BFGS scheme to
 Broyden's method.
@@ -40,7 +41,8 @@ function SciMLBase.__solve(
         if termination_condition === nothing ||
            termination_condition isa NonlinearSolveBase.AbsNormTerminationMode
             return internal_static_solve(
-                prob, alg, args...; termination_condition, kwargs...)
+                prob, alg, args...; termination_condition, kwargs...
+            )
         end
         @warn "Specifying `termination_condition = $(termination_condition)` for \
                `SimpleLimitedMemoryBroyden` with `SArray` is not non-allocating. Use \
@@ -53,22 +55,26 @@ end
 @views function internal_generic_solve(
         prob::ImmutableNonlinearProblem, alg::SimpleLimitedMemoryBroyden,
         args...; abstol = nothing, reltol = nothing, maxiters = 1000,
-        alias_u0 = false, termination_condition = nothing, kwargs...)
-    x = Utils.maybe_unaliased(prob.u0, alias_u0)
-    η = min(SciMLBase._unwrap_val(alg.threshold), maxiters)
+        alias_u0 = false, termination_condition = nothing, kwargs...
+)
+    x = NLBUtils.maybe_unaliased(prob.u0, alias_u0)
+    η = min(NLBUtils.unwrap_val(alg.threshold), maxiters)
 
     # For scalar problems / if the threshold is larger than problem size just use Broyden
     if x isa Number || length(x) ≤ η
-        return SciMLBase.__solve(prob, SimpleBroyden(; alg.linesearch), args...; abstol,
-            reltol, maxiters, termination_condition, kwargs...)
+        return SciMLBase.__solve(
+            prob, SimpleBroyden(; alg.linesearch), args...;
+            abstol, reltol, maxiters, termination_condition, kwargs...
+        )
     end
 
-    fx = Utils.get_fx(prob, x)
+    fx = NLBUtils.evaluate_f(prob, x)
 
     U, Vᵀ = init_low_rank_jacobian(x, fx, x isa StaticArray ? alg.threshold : Val(η))
 
     abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
-        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple)
+    )
 
     @bb xo = copy(x)
     @bb δx = copy(fx)
@@ -80,7 +86,7 @@ end
     Tcache = lbroyden_threshold_cache(x, x isa StaticArray ? alg.threshold : Val(η))
     @bb mat_cache = copy(x)
 
-    if alg.linesearch === Val(true)
+    if alg.linesearch isa Val{true}
         ls_alg = LiFukushimaLineSearch(; nan_maxiters = nothing)
         ls_cache = init(prob, ls_alg, fx, x)
     else
@@ -96,7 +102,7 @@ end
         end
 
         @bb @. x = xo + α * δx
-        fx = Utils.eval_f(prob, fx, x)
+        fx = NLBUtils.evaluate_f!!(prob, fx, x)
         @bb @. δf = fx - fo
 
         # Termination Checks
@@ -111,8 +117,8 @@ end
         d = dot(vᵀ, δf)
         @bb @. δx = (δx - mvec) / d
 
-        selectdim(U, 2, mod1(i, η)) .= Utils.safe_vec(δx)
-        selectdim(Vᵀ, 1, mod1(i, η)) .= Utils.safe_vec(vᵀ)
+        selectdim(U, 2, mod1(i, η)) .= NLBUtils.safe_vec(δx)
+        selectdim(Vᵀ, 1, mod1(i, η)) .= NLBUtils.safe_vec(vᵀ)
 
         Uₚ = selectdim(U, 2, 1:min(η, i))
         Vᵀₚ = selectdim(Vᵀ, 1, 1:min(η, i))
@@ -130,10 +136,11 @@ end
 # finicky, so we'll implement it separately from the generic version
 # Ignore termination_condition. Don't pass things into internal functions
 function internal_static_solve(
-        prob::ImmutableNonlinearProblem{<:SArray}, alg::SimpleLimitedMemoryBroyden,
-        args...; abstol = nothing, maxiters = 1000, kwargs...)
+        prob::ImmutableNonlinearProblem{<:SArray}, alg::SimpleLimitedMemoryBroyden, args...;
+        abstol = nothing, maxiters = 1000, kwargs...
+)
     x = prob.u0
-    fx = Utils.get_fx(prob, x)
+    fx = NLBUtils.evaluate_f(prob, x)
 
     U, Vᵀ = init_low_rank_jacobian(vec(x), vec(fx), alg.threshold)
 
@@ -165,7 +172,7 @@ function internal_static_solve(
 
     xo, fo, δx = res.x, res.fx, res.δx
 
-    for i in 1:(maxiters - SciMLBase._unwrap_val(alg.threshold))
+    for i in 1:(maxiters - NLBUtils.unwrap_val(alg.threshold))
         if ls_cache === nothing
             α = true
         else
@@ -174,22 +181,22 @@ function internal_static_solve(
         end
 
         x = xo + α * δx
-        fx = Utils.eval_f(prob, fx, x)
+        fx = NLBUtils.evaluate_f!!(prob, fx, x)
         δf = fx - fo
 
         maximum(abs, fx) ≤ abstol &&
             return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
 
-        vᵀ = Utils.restructure(x, rmatvec!!(U, Vᵀ, vec(δx), init_α))
-        mvec = Utils.restructure(x, matvec!!(U, Vᵀ, vec(δf), init_α))
+        vᵀ = NLBUtils.restructure(x, rmatvec!!(U, Vᵀ, vec(δx), init_α))
+        mvec = NLBUtils.restructure(x, matvec!!(U, Vᵀ, vec(δf), init_α))
 
         d = dot(vᵀ, δf)
         δx = @. (δx - mvec) / d
 
-        U = Base.setindex(U, vec(δx), mod1(i, SciMLBase._unwrap_val(alg.threshold)))
-        Vᵀ = Base.setindex(Vᵀ, vec(vᵀ), mod1(i, SciMLBase._unwrap_val(alg.threshold)))
+        U = Base.setindex(U, vec(δx), mod1(i, NLBUtils.unwrap_val(alg.threshold)))
+        Vᵀ = Base.setindex(Vᵀ, vec(vᵀ), mod1(i, NLBUtils.unwrap_val(alg.threshold)))
 
-        δx = -Utils.restructure(fx, matvec!!(U, Vᵀ, vec(fx), init_α))
+        δx = -NLBUtils.restructure(fx, matvec!!(U, Vᵀ, vec(fx), init_α))
 
         xo, fo = x, fx
     end
@@ -198,8 +205,8 @@ function internal_static_solve(
 end
 
 @generated function internal_unrolled_lbroyden_initial_iterations(
-        prob, xo, fo, δx, abstol, U, Vᵀ, ::Val{threshold},
-        ls_cache, init_α) where {threshold}
+        prob, xo, fo, δx, abstol, U, Vᵀ, ::Val{threshold}, ls_cache, init_α
+) where {threshold}
     calls = []
     for i in 1:threshold
         static_idx, static_idx_p1 = Val(i - 1), Val(i)
@@ -219,8 +226,8 @@ end
             Uₚ = first_n_getindex(U, $(static_idx))
             Vᵀₚ = first_n_getindex(Vᵀ, $(static_idx))
 
-            vᵀ = Utils.restructure(x, rmatvec!!(Uₚ, Vᵀₚ, vec(δx), init_α))
-            mvec = Utils.restructure(x, matvec!!(Uₚ, Vᵀₚ, vec(δf), init_α))
+            vᵀ = NLBUtils.restructure(x, rmatvec!!(Uₚ, Vᵀₚ, vec(δx), init_α))
+            mvec = NLBUtils.restructure(x, matvec!!(Uₚ, Vᵀₚ, vec(δf), init_α))
 
             d = dot(vᵀ, δf)
             δx = @. (δx - mvec) / d
@@ -230,7 +237,7 @@ end
 
             Uₚ = first_n_getindex(U, $(static_idx_p1))
             Vᵀₚ = first_n_getindex(Vᵀ, $(static_idx_p1))
-            δx = -Utils.restructure(fx, matvec!!(Uₚ, Vᵀₚ, vec(fx), init_α))
+            δx = -NLBUtils.restructure(fx, matvec!!(Uₚ, Vᵀₚ, vec(fx), init_α))
 
             x0, fo = x, fx
         end)
@@ -284,7 +291,8 @@ function fast_mapdot(x::SVector{S1}, Y::SVector{S2, <:SVector{S1}}) where {S1, S
     return map(Base.Fix1(dot, x), Y)
 end
 @generated function fast_mapTdot(
-        x::SVector{S1}, Y::SVector{S1, <:SVector{S2}}) where {S1, S2}
+        x::SVector{S1}, Y::SVector{S1, <:SVector{S2}}
+) where {S1, S2}
     calls = []
     syms = [gensym("m$(i)") for i in 1:S1]
     for i in 1:S1
@@ -301,22 +309,26 @@ end
     return :(return SVector{$N, $T}(($(getcalls...))))
 end
 
-lbroyden_threshold_cache(x, ::Val{threshold}) where {threshold} = safe_similar(x, threshold)
+function lbroyden_threshold_cache(x, ::Val{threshold}) where {threshold}
+    return NLBUtils.safe_similar(x, threshold)
+end
 function lbroyden_threshold_cache(x::StaticArray, ::Val{threshold}) where {threshold}
     return zeros(MArray{Tuple{threshold}, eltype(x)})
 end
 lbroyden_threshold_cache(::SArray, ::Val{threshold}) where {threshold} = nothing
 
-function init_low_rank_jacobian(u::StaticArray{S1, T1}, fu::StaticArray{S2, T2},
-        ::Val{threshold}) where {S1, S2, T1, T2, threshold}
+function init_low_rank_jacobian(
+        u::StaticArray{S1, T1}, fu::StaticArray{S2, T2}, ::Val{threshold}
+) where {S1, S2, T1, T2, threshold}
     T = promote_type(T1, T2)
     fuSize, uSize = Size(fu), Size(u)
     Vᵀ = MArray{Tuple{threshold, prod(uSize)}, T}(undef)
     U = MArray{Tuple{prod(fuSize), threshold}, T}(undef)
     return U, Vᵀ
 end
-@generated function init_low_rank_jacobian(u::SVector{Lu, T1}, fu::SVector{Lfu, T2},
-        ::Val{threshold}) where {Lu, Lfu, T1, T2, threshold}
+@generated function init_low_rank_jacobian(
+        u::SVector{Lu, T1}, fu::SVector{Lfu, T2}, ::Val{threshold}
+) where {Lu, Lfu, T1, T2, threshold}
     T = promote_type(T1, T2)
     inner_inits_Vᵀ = [:(zeros(SVector{$Lu, $T})) for i in 1:threshold]
     inner_inits_U = [:(zeros(SVector{$Lfu, $T})) for i in 1:threshold]
@@ -327,7 +339,7 @@ end
     end
 end
 function init_low_rank_jacobian(u, fu, ::Val{threshold}) where {threshold}
-    Vᵀ = safe_similar(u, threshold, length(u))
-    U = safe_similar(u, length(fu), threshold)
+    Vᵀ = NLBUtils.safe_similar(u, threshold, length(u))
+    U = NLBUtils.safe_similar(u, length(fu), threshold)
     return U, Vᵀ
 end
diff --git a/lib/SimpleNonlinearSolve/src/raphson.jl b/lib/SimpleNonlinearSolve/src/raphson.jl
index ebbb5f9f9..34efcbb90 100644
--- a/lib/SimpleNonlinearSolve/src/raphson.jl
+++ b/lib/SimpleNonlinearSolve/src/raphson.jl
@@ -27,35 +27,37 @@ function SciMLBase.__solve(
         prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
         alg::SimpleNewtonRaphson, args...;
         abstol = nothing, reltol = nothing, maxiters = 1000,
-        alias_u0 = false, termination_condition = nothing, kwargs...)
-    x = Utils.maybe_unaliased(prob.u0, alias_u0)
-    fx = Utils.get_fx(prob, x)
-    fx = Utils.eval_f(prob, fx, x)
+        alias_u0 = false, termination_condition = nothing, kwargs...
+)
+    x = NLBUtils.maybe_unaliased(prob.u0, alias_u0)
+    fx = NLBUtils.evaluate_f(prob, x)
 
     iszero(fx) &&
         return SciMLBase.build_solution(prob, alg, x, fx; retcode = ReturnCode.Success)
 
     abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
-        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple)
+    )
 
     autodiff = SciMLBase.has_jac(prob.f) ? alg.autodiff :
                NonlinearSolveBase.select_jacobian_autodiff(prob, alg.autodiff)
+    @set! alg.autodiff = autodiff
 
     @bb xo = similar(x)
     fx_cache = (SciMLBase.isinplace(prob) && !SciMLBase.has_jac(prob.f)) ?
-               safe_similar(fx) : fx
+               NLBUtils.safe_similar(fx) : fx
     jac_cache = Utils.prepare_jacobian(prob, autodiff, fx_cache, x)
     J = Utils.compute_jacobian!!(nothing, prob, autodiff, fx_cache, x, jac_cache)
 
     for _ in 1:maxiters
         @bb copyto!(xo, x)
-        δx = Utils.restructure(x, J \ Utils.safe_vec(fx))
+        δx = NLBUtils.restructure(x, J \ NLBUtils.safe_vec(fx))
         @bb x .-= δx
 
         solved, retcode, fx_sol, x_sol = Utils.check_termination(tc_cache, fx, x, xo, prob)
         solved && return SciMLBase.build_solution(prob, alg, x_sol, fx_sol; retcode)
 
-        fx = Utils.eval_f(prob, fx, x)
+        fx = NLBUtils.evaluate_f!!(prob, fx, x)
         J = Utils.compute_jacobian!!(J, prob, autodiff, fx_cache, x, jac_cache)
     end
 
diff --git a/lib/SimpleNonlinearSolve/src/trust_region.jl b/lib/SimpleNonlinearSolve/src/trust_region.jl
index 32e7a6219..d9ac54235 100644
--- a/lib/SimpleNonlinearSolve/src/trust_region.jl
+++ b/lib/SimpleNonlinearSolve/src/trust_region.jl
@@ -1,9 +1,11 @@
 """
-    SimpleTrustRegion(; autodiff = AutoForwardDiff(), max_trust_radius = 0.0,
+    SimpleTrustRegion(;
+        autodiff = AutoForwardDiff(), max_trust_radius = 0.0,
         initial_trust_radius = 0.0, step_threshold = nothing,
         shrink_threshold = nothing, expand_threshold = nothing,
         shrink_factor = 0.25, expand_factor = 2.0, max_shrink_times::Int = 32,
-        nlsolve_update_rule = Val(false))
+        nlsolve_update_rule = Val(false)
+    )
 
 A low-overhead implementation of a trust-region solver. This method is non-allocating on
 scalar and static array problems.
@@ -18,18 +20,18 @@ scalar and static array problems.
   - `initial_trust_radius`: the initial trust region radius. Defaults to
     `max_trust_radius / 11`.
   - `step_threshold`: the threshold for taking a step. In every iteration, the threshold is
-    compared with a value `r`, which is the actual reduction in the objective function divided
-    by the predicted reduction. If `step_threshold > r` the model is not a good approximation,
-    and the step is rejected. Defaults to `0.1`. For more details, see
+    compared with a value `r`, which is the actual reduction in the objective function
+    divided by the predicted reduction. If `step_threshold > r` the model is not a good
+    approximation, and the step is rejected. Defaults to `0.1`. For more details, see
     [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
   - `shrink_threshold`: the threshold for shrinking the trust region radius. In every
-    iteration, the threshold is compared with a value `r` which is the actual reduction in the
-    objective function divided by the predicted reduction. If `shrink_threshold > r` the trust
-    region radius is shrunk by `shrink_factor`. Defaults to `0.25`. For more details, see
-    [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
+    iteration, the threshold is compared with a value `r` which is the actual reduction in
+    the objective function divided by the predicted reduction. If `shrink_threshold > r` the
+    trust region radius is shrunk by `shrink_factor`. Defaults to `0.25`. For more details,
+    see [Rahpeymaii, F.](https://link.springer.com/article/10.1007/s40096-020-00339-4)
   - `expand_threshold`: the threshold for expanding the trust region radius. If a step is
-    taken, i.e `step_threshold < r` (with `r` defined in `shrink_threshold`), a check is also
-    made to see if `expand_threshold < r`. If that is true, the trust region radius is
+    taken, i.e `step_threshold < r` (with `r` defined in `shrink_threshold`), a check is
+    also made to see if `expand_threshold < r`. If that is true, the trust region radius is
     expanded by `expand_factor`. Defaults to `0.75`.
   - `shrink_factor`: the factor to shrink the trust region radius with if
     `shrink_threshold > r` (with `r` defined in `shrink_threshold`). Defaults to `0.25`.
@@ -55,29 +57,32 @@ scalar and static array problems.
     nlsolve_update_rule = Val(false)
 end
 
-function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleTrustRegion,
-        args...; abstol = nothing, reltol = nothing, maxiters = 1000,
-        alias_u0 = false, termination_condition = nothing, kwargs...)
-    x = Utils.maybe_unaliased(prob.u0, alias_u0)
+function SciMLBase.__solve(
+        prob::Union{ImmutableNonlinearProblem, NonlinearLeastSquaresProblem},
+        alg::SimpleTrustRegion, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000,
+        alias_u0 = false, termination_condition = nothing, kwargs...
+)
+    x = NLBUtils.maybe_unaliased(prob.u0, alias_u0)
     T = eltype(x)
     Δₘₐₓ = T(alg.max_trust_radius)
     Δ = T(alg.initial_trust_radius)
     η₁ = T(alg.step_threshold)
 
     if alg.shrink_threshold === nothing
-        η₂ = T(ifelse(SciMLBase._unwrap_val(alg.nlsolve_update_rule), 0.05, 0.25))
+        η₂ = T(ifelse(NLBUtils.unwrap_val(alg.nlsolve_update_rule), 0.05, 0.25))
     else
         η₂ = T(alg.shrink_threshold)
     end
 
     if alg.expand_threshold === nothing
-        η₃ = T(ifelse(SciMLBase._unwrap_val(alg.nlsolve_update_rule), 0.9, 0.75))
+        η₃ = T(ifelse(NLBUtils.unwrap_val(alg.nlsolve_update_rule), 0.9, 0.75))
     else
         η₃ = T(alg.expand_threshold)
     end
 
     if alg.shrink_factor === nothing
-        t₁ = T(ifelse(SciMLBase._unwrap_val(alg.nlsolve_update_rule), 0.5, 0.25))
+        t₁ = T(ifelse(NLBUtils.unwrap_val(alg.nlsolve_update_rule), 0.5, 0.25))
     else
         t₁ = T(alg.shrink_factor)
     end
@@ -88,23 +93,23 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleTrustRegi
     autodiff = SciMLBase.has_jac(prob.f) ? alg.autodiff :
                NonlinearSolveBase.select_jacobian_autodiff(prob, alg.autodiff)
 
-    fx = Utils.get_fx(prob, x)
-    fx = Utils.eval_f(prob, fx, x)
+    fx = NLBUtils.evaluate_f(prob, x)
     norm_fx = L2_NORM(fx)
 
     @bb xo = copy(x)
     fx_cache = (SciMLBase.isinplace(prob) && !SciMLBase.has_jac(prob.f)) ?
-               safe_similar(fx) : fx
+               NLBUtils.safe_similar(fx) : fx
     jac_cache = Utils.prepare_jacobian(prob, autodiff, fx_cache, x)
     J = Utils.compute_jacobian!!(nothing, prob, autodiff, fx_cache, x, jac_cache)
 
     abstol, reltol, tc_cache = NonlinearSolveBase.init_termination_cache(
-        prob, abstol, reltol, fx, x, termination_condition, Val(:simple))
+        prob, abstol, reltol, fx, x, termination_condition, Val(:simple)
+    )
 
     # Set default trust region radius if not specified by user.
     iszero(Δₘₐₓ) && (Δₘₐₓ = max(L2_NORM(fx), maximum(x) - minimum(x)))
     if iszero(Δ)
-        if SciMLBase._unwrap_val(alg.nlsolve_update_rule)
+        if NLBUtils.unwrap_val(alg.nlsolve_update_rule)
             norm_x = L2_NORM(x)
             Δ = T(ifelse(norm_x > 0, norm_x, 1))
         else
@@ -114,7 +119,7 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleTrustRegi
 
     fₖ = 0.5 * norm_fx^2
     H = transpose(J) * J
-    g = Utils.restructure(x, J' * Utils.safe_vec(fx))
+    g = NLBUtils.restructure(x, J' * NLBUtils.safe_vec(fx))
     shrink_counter = 0
 
     @bb δsd = copy(x)
@@ -128,7 +133,7 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleTrustRegi
         δ = dogleg_method!!(dogleg_cache, J, fx, g, Δ)
         @bb @. x = xo + δ
 
-        fx = Utils.eval_f(prob, fx, x)
+        fx = NLBUtils.evaluate_f!!(prob, fx, x)
 
         fₖ₊₁ = L2_NORM(fx)^2 / T(2)
 
@@ -149,17 +154,18 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleTrustRegi
         if r ≥ η₁
             # Termination Checks
             solved, retcode, fx_sol, x_sol = Utils.check_termination(
-                tc_cache, fx, x, xo, prob)
+                tc_cache, fx, x, xo, prob
+            )
             solved && return SciMLBase.build_solution(prob, alg, x_sol, fx_sol; retcode)
 
             # Take the step.
             @bb copyto!(xo, x)
 
             J = Utils.compute_jacobian!!(J, prob, autodiff, fx_cache, x, jac_cache)
-            fx = Utils.eval_f(prob, fx, x)
+            fx = NLBUtils.evaluate_f!!(prob, fx, x)
 
             # Update the trust region radius.
-            if !SciMLBase._unwrap_val(alg.nlsolve_update_rule) && r > η₃
+            if !NLBUtils.unwrap_val(alg.nlsolve_update_rule) && r > η₃
                 Δ = min(t₂ * Δ, Δₘₐₓ)
             end
             fₖ = fₖ₊₁
@@ -168,7 +174,7 @@ function SciMLBase.__solve(prob::ImmutableNonlinearProblem, alg::SimpleTrustRegi
             @bb g = transpose(J) × vec(fx)
         end
 
-        if SciMLBase._unwrap_val(alg.nlsolve_update_rule)
+        if NLBUtils.unwrap_val(alg.nlsolve_update_rule)
             if r > η₃
                 Δ = t₂ * L2_NORM(δ)
             elseif r > 0.5
@@ -184,7 +190,7 @@ function dogleg_method!!(cache, J, f, g, Δ)
     (; δsd, δN_δsd, δN) = cache
 
     # Compute the Newton step
-    @bb δN .= Utils.restructure(δN, J \ Utils.safe_vec(f))
+    @bb δN .= NLBUtils.restructure(δN, J \ NLBUtils.safe_vec(f))
     @bb δN .*= -1
     # Test if the full step is within the trust region
     (L2_NORM(δN) ≤ Δ) && return δN
diff --git a/lib/SimpleNonlinearSolve/src/utils.jl b/lib/SimpleNonlinearSolve/src/utils.jl
index bd7368bd7..8c35a324f 100644
--- a/lib/SimpleNonlinearSolve/src/utils.jl
+++ b/lib/SimpleNonlinearSolve/src/utils.jl
@@ -1,70 +1,31 @@
 module Utils
 
 using ArrayInterface: ArrayInterface
-using ConcreteStructs: @concrete
 using DifferentiationInterface: DifferentiationInterface, Constant
 using FastClosures: @closure
 using LinearAlgebra: LinearAlgebra, I, diagind
-using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem,
-                          AbstractNonlinearTerminationMode,
+using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearTerminationMode,
                           AbstractSafeNonlinearTerminationMode,
                           AbstractSafeBestNonlinearTerminationMode
-using SciMLBase: SciMLBase, AbstractNonlinearProblem, NonlinearLeastSquaresProblem,
-                 NonlinearProblem, NonlinearFunction, ReturnCode
+using SciMLBase: SciMLBase, ReturnCode
 using StaticArraysCore: StaticArray, SArray, SMatrix, SVector
 
 const DI = DifferentiationInterface
-
-const safe_similar = NonlinearSolveBase.Utils.safe_similar
-
-pickchunksize(n::Int) = min(n, 12)
-
-can_dual(::Type{<:Real}) = true
-can_dual(::Type) = false
-
-maybe_unaliased(x::Union{Number, SArray}, ::Bool) = x
-function maybe_unaliased(x::T, alias::Bool) where {T <: AbstractArray}
-    (alias || !ArrayInterface.can_setindex(T)) && return x
-    return copy(x)
-end
-
-# NOTE: This doesn't initialize the `f(x)` but just returns a buffer of the same size
-function get_fx(prob::NonlinearLeastSquaresProblem, x)
-    if SciMLBase.isinplace(prob) && prob.f.resid_prototype === nothing
-        error("Inplace NonlinearLeastSquaresProblem requires a `resid_prototype` to be \
-               specified.")
-    end
-    return get_fx(prob.f, x, prob.p)
-end
-function get_fx(prob::Union{ImmutableNonlinearProblem, NonlinearProblem}, x)
-    return get_fx(prob.f, x, prob.p)
-end
-function get_fx(f::NonlinearFunction, x, p)
-    if SciMLBase.isinplace(f)
-        f.resid_prototype === nothing || return eltype(x).(f.resid_prototype)
-        return safe_similar(x)
-    end
-    return f(x, p)
-end
-
-function eval_f(prob, fx, x)
-    SciMLBase.isinplace(prob) || return prob.f(x, prob.p)
-    prob.f(fx, x, prob.p)
-    return fx
-end
-
-function fixed_parameter_function(prob::AbstractNonlinearProblem)
-    SciMLBase.isinplace(prob) && return @closure (du, u) -> prob.f(du, u, prob.p)
-    return Base.Fix2(prob.f, prob.p)
-end
+const NLBUtils = NonlinearSolveBase.Utils
 
 function identity_jacobian(u::Number, fu::Number, α = true)
     return convert(promote_type(eltype(u), eltype(fu)), α)
 end
 function identity_jacobian(u, fu, α = true)
-    J = safe_similar(u, promote_type(eltype(u), eltype(fu)), length(fu), length(u))
-    fill!(J, zero(eltype(J)))
-    J[diagind(J)] .= eltype(J)(α)
+    J = NLBUtils.safe_similar(u, promote_type(eltype(u), eltype(fu)), length(fu), length(u))
+    fill!(J, false)
+    if ArrayInterface.fast_scalar_indexing(J)
+        @simd ivdep for i in axes(J, 1)
+            @inbounds J[i, i] = α
+        end
+    else
+        J[diagind(J)] .= α
+    end
     return J
 end
 function identity_jacobian(u::StaticArray, fu, α = true)
@@ -97,30 +58,21 @@ function check_termination(cache, fx, x, xo, _, ::AbstractSafeNonlinearTerminati
     return cache(fx, x, xo), cache.retcode, fx, x
 end
 function check_termination(
-        cache, fx, x, xo, prob, ::AbstractSafeBestNonlinearTerminationMode)
+        cache, fx, x, xo, prob, ::AbstractSafeBestNonlinearTerminationMode
+)
     if cache(fx, x, xo)
         x = cache.u
-        if SciMLBase.isinplace(prob)
-            prob.f(fx, x, prob.p)
-        else
-            fx = prob.f(x, prob.p)
-        end
+        fx = NLBUtils.evaluate_f!!(prob, fx, x)
         return true, cache.retcode, fx, x
     end
     return false, ReturnCode.Default, fx, x
 end
 
-restructure(y, x) = ArrayInterface.restructure(y, x)
-restructure(::Number, x::Number) = x
-
-safe_vec(x::AbstractArray) = vec(x)
-safe_vec(x::Number) = x
-
 abstract type AbstractJacobianMode end
 
 struct AnalyticJacobian <: AbstractJacobianMode end
-@concrete struct DIExtras <: AbstractJacobianMode
-    prep
+struct DIExtras{P} <: AbstractJacobianMode
+    prep::P
 end
 struct DINoPreparation <: AbstractJacobianMode end
 
@@ -161,7 +113,7 @@ end
 function compute_jacobian!!(J, prob, autodiff, fx, x, ::AnalyticJacobian)
     if J === nothing
         if SciMLBase.isinplace(prob.f)
-            J = safe_similar(fx, length(fx), length(x))
+            J = NLBUtils.safe_similar(fx, length(fx), length(x))
             prob.f.jac(J, x, prob.p)
             return J
         else
@@ -214,16 +166,16 @@ end
 function compute_jacobian_and_hessian(autodiff, prob, fx, x)
     if SciMLBase.isinplace(prob)
         jac_fn = @closure (u, p) -> begin
-            du = safe_similar(fx, promote_type(eltype(fx), eltype(u)))
+            du = NLBUtils.safe_similar(fx, promote_type(eltype(fx), eltype(u)))
             return DI.jacobian(prob.f, du, autodiff, u, Constant(p))
         end
         J, H = DI.value_and_jacobian(jac_fn, autodiff, x, Constant(prob.p))
-        fx = Utils.eval_f(prob, fx, x)
+        fx = NLBUtils.evaluate_f!!(prob, fx, x)
         return fx, J, H
     else
         jac_fn = @closure (u, p) -> DI.jacobian(prob.f, autodiff, u, Constant(p))
         J, H = DI.value_and_jacobian(jac_fn, autodiff, x, Constant(prob.p))
-        fx = Utils.eval_f(prob, fx, x)
+        fx = NLBUtils.evaluate_f!!(prob, fx, x)
         return fx, J, H
     end
 end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index e352f4891..fc6d3f722 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -71,7 +71,7 @@ end
 # Rexexports
 @reexport using SciMLBase, NonlinearSolveBase, LineSearch, ADTypes
 @reexport using NonlinearSolveFirstOrder, NonlinearSolveSpectralMethods,
-                NonlinearSolveQuasiNewton, SimpleNonlinearSolve
+                NonlinearSolveQuasiNewton, SimpleNonlinearSolve, BracketingNonlinearSolve
 @reexport using LinearSolve
 
 # Poly Algorithms

From c108291ad9dbf5fc5f01afac2fefc368a89ac41b Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 29 Oct 2024 15:27:08 -0400
Subject: [PATCH 650/700] ci(github-actions): nonlinearsolvebase and
 bracketingnonlinearsolve

---
 .buildkite/pipeline.yml                       |  4 ++--
 .../workflows/CI_BracketingNonlinearSolve.yml | 11 +++++-----
 .github/workflows/CI_NonlinearSolve.yml       |  4 ++--
 .github/workflows/CI_NonlinearSolveBase.yml   |  7 ++++---
 .../workflows/CI_SciMLJacobianOperators.yml   |  4 ++--
 .github/workflows/CI_SimpleNonlinearSolve.yml |  4 ++--
 .github/workflows/Downgrade.yml               |  2 +-
 .github/workflows/Downstream.yml              |  2 +-
 .../BracketingNonlinearSolveForwardDiffExt.jl | 20 +++++++++++--------
 lib/BracketingNonlinearSolve/test/qa_tests.jl |  7 ++++++-
 lib/NonlinearSolveBase/test/runtests.jl       |  5 ++++-
 11 files changed, 42 insertions(+), 28 deletions(-)

diff --git a/.buildkite/pipeline.yml b/.buildkite/pipeline.yml
index 9eb146557..4292dbdda 100644
--- a/.buildkite/pipeline.yml
+++ b/.buildkite/pipeline.yml
@@ -19,7 +19,7 @@ steps:
         end
         Pkg.develop(dev_pks);
         Pkg.instantiate();
-        Pkg.test(; coverage=true)'
+        Pkg.test(; coverage="user")'
     agents:
       queue: "juliagpu"
       cuda: "*"
@@ -47,7 +47,7 @@ steps:
         end
         Pkg.develop(dev_pks);
         Pkg.instantiate();
-        Pkg.test(; coverage=true)'
+        Pkg.test(; coverage="user")'
     agents:
       queue: "juliagpu"
       cuda: "*"
diff --git a/.github/workflows/CI_BracketingNonlinearSolve.yml b/.github/workflows/CI_BracketingNonlinearSolve.yml
index 6d78e5612..69c1f7746 100644
--- a/.github/workflows/CI_BracketingNonlinearSolve.yml
+++ b/.github/workflows/CI_BracketingNonlinearSolve.yml
@@ -6,8 +6,9 @@ on:
       - master
     paths:
       - "lib/BracketingNonlinearSolve/**"
-      - "lib/NonlinearSolveBase/**"
       - ".github/workflows/CI_BracketingNonlinearSolve.yml"
+      - "lib/NonlinearSolveBase/**"
+      - "lib/SciMLJacobianOperators/**"
   push:
     branches:
       - master
@@ -25,7 +26,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "min"
+          - "lts"
           - "1"
         os:
           - ubuntu-latest
@@ -52,16 +53,16 @@ jobs:
           Pkg.Registry.update()
           # Install packages present in subdirectories
           dev_pks = Pkg.PackageSpec[]
-          for path in ("lib/NonlinearSolveBase",)
+          for path in ("lib/NonlinearSolveBase", "lib/SciMLJacobianOperators")
               push!(dev_pks, Pkg.PackageSpec(; path))
           end
           Pkg.develop(dev_pks)
           Pkg.instantiate()
-          Pkg.test(; coverage=true)
+          Pkg.test(; coverage="user")
         shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/BracketingNonlinearSolve {0}
       - uses: julia-actions/julia-processcoverage@v1
         with:
-          directories: lib/BracketingNonlinearSolve/src,lib/BracketingNonlinearSolve/ext
+          directories: lib/BracketingNonlinearSolve/src,lib/BracketingNonlinearSolve/ext,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
       - uses: codecov/codecov-action@v4
         with:
           file: lcov.info
diff --git a/.github/workflows/CI_NonlinearSolve.yml b/.github/workflows/CI_NonlinearSolve.yml
index 843a04b54..0ea05487c 100644
--- a/.github/workflows/CI_NonlinearSolve.yml
+++ b/.github/workflows/CI_NonlinearSolve.yml
@@ -36,7 +36,7 @@ jobs:
           - Misc
           - Wrappers
         version:
-          - "min"
+          - "lts"
           - "1"
         os:
           - ubuntu-latest
@@ -68,7 +68,7 @@ jobs:
           end
           Pkg.develop(dev_pks)
           Pkg.instantiate()
-          Pkg.test(; coverage=true)
+          Pkg.test(; coverage="user")
         shell: julia --color=yes --code-coverage=user --depwarn=yes --project=. {0}
         env:
           GROUP: ${{ matrix.group }}
diff --git a/.github/workflows/CI_NonlinearSolveBase.yml b/.github/workflows/CI_NonlinearSolveBase.yml
index 5855d06f0..9b9f0d959 100644
--- a/.github/workflows/CI_NonlinearSolveBase.yml
+++ b/.github/workflows/CI_NonlinearSolveBase.yml
@@ -7,6 +7,7 @@ on:
     paths:
       - "lib/NonlinearSolveBase/**"
       - ".github/workflows/CI_NonlinearSolveBase.yml"
+      - "lib/SciMLJacobianOperators/**"
   push:
     branches:
       - master
@@ -24,7 +25,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "min"
+          - "lts"
           - "1"
         os:
           - ubuntu-latest
@@ -56,11 +57,11 @@ jobs:
           end
           Pkg.develop(dev_pks)
           Pkg.instantiate()
-          Pkg.test(; coverage=true)
+          Pkg.test(; coverage="user")
         shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/NonlinearSolveBase {0}
       - uses: julia-actions/julia-processcoverage@v1
         with:
-          directories: lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext
+          directories: lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
       - uses: codecov/codecov-action@v4
         with:
           file: lcov.info
diff --git a/.github/workflows/CI_SciMLJacobianOperators.yml b/.github/workflows/CI_SciMLJacobianOperators.yml
index 92daf23e9..96ce9db15 100644
--- a/.github/workflows/CI_SciMLJacobianOperators.yml
+++ b/.github/workflows/CI_SciMLJacobianOperators.yml
@@ -24,7 +24,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "min"
+          - "lts"
           - "1"
         os:
           - ubuntu-latest
@@ -50,7 +50,7 @@ jobs:
           import Pkg
           Pkg.Registry.update()
           Pkg.instantiate()
-          Pkg.test(; coverage=true)
+          Pkg.test(; coverage="user")
         shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SciMLJacobianOperators {0}
       - uses: julia-actions/julia-processcoverage@v1
         with:
diff --git a/.github/workflows/CI_SimpleNonlinearSolve.yml b/.github/workflows/CI_SimpleNonlinearSolve.yml
index 11c3ef7c2..fb8ed1d8e 100644
--- a/.github/workflows/CI_SimpleNonlinearSolve.yml
+++ b/.github/workflows/CI_SimpleNonlinearSolve.yml
@@ -26,7 +26,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "min"
+          - "lts"
           - "1"
         os:
           - ubuntu-latest
@@ -62,7 +62,7 @@ jobs:
           end
           Pkg.develop(dev_pks)
           Pkg.instantiate()
-          Pkg.test(; coverage=true)
+          Pkg.test(; coverage="user")
         shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SimpleNonlinearSolve {0}
         env:
           GROUP: ${{ matrix.group }}
diff --git a/.github/workflows/Downgrade.yml b/.github/workflows/Downgrade.yml
index 172457df8..83223e2f6 100644
--- a/.github/workflows/Downgrade.yml
+++ b/.github/workflows/Downgrade.yml
@@ -40,7 +40,7 @@ jobs:
           end
           Pkg.develop(dev_pks)
           Pkg.instantiate()
-          Pkg.test(; coverage=true)
+          Pkg.test(; coverage="user")
         shell: julia --color=yes --code-coverage=user --depwarn=yes --project=. {0}
         env:
           GROUP: ${{ matrix.group }}
diff --git a/.github/workflows/Downstream.yml b/.github/workflows/Downstream.yml
index 9e54283aa..fffcb0a6c 100644
--- a/.github/workflows/Downstream.yml
+++ b/.github/workflows/Downstream.yml
@@ -46,7 +46,7 @@ jobs:
             # force it to use this PR's version of the package
             Pkg.develop(PackageSpec(path="."))  # resolver may fail with main deps
             Pkg.update()
-            Pkg.test(coverage=true)  # resolver may fail with test time deps
+            Pkg.test(coverage="user")  # resolver may fail with test time deps
           catch err
             err isa Pkg.Resolve.ResolverError || rethrow()
             # If we can't resolve that means this is incompatible by SemVer and this is fine
diff --git a/lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveForwardDiffExt.jl b/lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveForwardDiffExt.jl
index b41a88451..09616b5a2 100644
--- a/lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveForwardDiffExt.jl
+++ b/lib/BracketingNonlinearSolve/ext/BracketingNonlinearSolveForwardDiffExt.jl
@@ -7,19 +7,23 @@ using SciMLBase: SciMLBase, IntervalNonlinearProblem
 
 using BracketingNonlinearSolve: Bisection, Brent, Alefeld, Falsi, ITP, Ridder
 
+const DualIntervalNonlinearProblem{T, V, P} = IntervalNonlinearProblem{
+    uType, iip, <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {uType, iip}
+
 for algT in (Bisection, Brent, Alefeld, Falsi, ITP, Ridder)
     @eval function CommonSolve.solve(
-            prob::IntervalNonlinearProblem{
-                uType, iip, <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}},
-            alg::$(algT),
-            args...;
-            kwargs...) where {uType, iip, T, V, P}
+            prob::DualIntervalNonlinearProblem{T, V, P}, alg::$(algT), args...;
+            kwargs...
+    ) where {T, V, P}
         sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
         dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
         return SciMLBase.build_solution(
-            prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats,
-            sol.original, left = Dual{T, V, P}(sol.left, partials),
-            right = Dual{T, V, P}(sol.right, partials))
+            prob, alg, dual_soln, sol.resid;
+            sol.retcode, sol.stats, sol.original,
+            left = Dual{T, V, P}(sol.left, partials),
+            right = Dual{T, V, P}(sol.right, partials)
+        )
     end
 end
 
diff --git a/lib/BracketingNonlinearSolve/test/qa_tests.jl b/lib/BracketingNonlinearSolve/test/qa_tests.jl
index c01c493f4..dc78ce75e 100644
--- a/lib/BracketingNonlinearSolve/test/qa_tests.jl
+++ b/lib/BracketingNonlinearSolve/test/qa_tests.jl
@@ -1,7 +1,12 @@
 @testitem "Aqua" tags=[:core] begin
     using Aqua, BracketingNonlinearSolve
 
-    Aqua.test_all(BracketingNonlinearSolve; piracies = false, ambiguities = false)
+    Aqua.test_all(
+        BracketingNonlinearSolve;
+        piracies = false, ambiguities = false, stale_deps = false, deps_compat = false
+    )
+    Aqua.test_stale_deps(BracketingNonlinearSolve; ignore = [:SciMLJacobianOperators])
+    Aqua.test_deps_compat(BracketingNonlinearSolve; ignore = [:SciMLJacobianOperators])
     Aqua.test_piracies(BracketingNonlinearSolve; treat_as_own = [IntervalNonlinearProblem])
     Aqua.test_ambiguities(BracketingNonlinearSolve; recursive = false)
 end
diff --git a/lib/NonlinearSolveBase/test/runtests.jl b/lib/NonlinearSolveBase/test/runtests.jl
index 07c0f14c6..2c745c1c3 100644
--- a/lib/NonlinearSolveBase/test/runtests.jl
+++ b/lib/NonlinearSolveBase/test/runtests.jl
@@ -8,7 +8,10 @@ using InteractiveUtils, Test
     @testset "Aqua" begin
         using Aqua, NonlinearSolveBase
 
-        Aqua.test_all(NonlinearSolveBase; piracies = false, ambiguities = false)
+        Aqua.test_all(
+            NonlinearSolveBase; piracies = false, ambiguities = false, stale_deps = false
+        )
+        Aqua.test_stale_deps(NonlinearSolveBase; ignore = [:TimerOutputs])
         Aqua.test_piracies(NonlinearSolveBase)
         Aqua.test_ambiguities(NonlinearSolveBase; recursive = false)
     end

From b8b210dd24c9083f96ad8b79ccf08ef66b3bbf7d Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 29 Oct 2024 15:45:33 -0400
Subject: [PATCH 651/700] ci(github-actions): simplenonlinearsolve

---
 .github/workflows/CI_SimpleNonlinearSolve.yml |  9 ++++----
 .../test/core_tests.jl                        |  0
 .../test/qa_tests.jl                          |  0
 .../test/runtests.jl                          | 22 +++++++++++++++++++
 .../test/core/qa_tests.jl                     | 11 ++++++++--
 5 files changed, 36 insertions(+), 6 deletions(-)
 create mode 100644 lib/NonlinearSolveSpectralMethods/test/core_tests.jl
 create mode 100644 lib/NonlinearSolveSpectralMethods/test/qa_tests.jl

diff --git a/.github/workflows/CI_SimpleNonlinearSolve.yml b/.github/workflows/CI_SimpleNonlinearSolve.yml
index fb8ed1d8e..a9d6d4e0e 100644
--- a/.github/workflows/CI_SimpleNonlinearSolve.yml
+++ b/.github/workflows/CI_SimpleNonlinearSolve.yml
@@ -6,9 +6,10 @@ on:
       - master
     paths:
       - "lib/SimpleNonlinearSolve/**"
+      - ".github/workflows/CI_SimpleNonlinearSolve.yml"
       - "lib/BracketingNonlinearSolve/**"
       - "lib/NonlinearSolveBase/**"
-      - ".github/workflows/CI_SimpleNonlinearSolve.yml"
+      - "lib/SciMLJacobianOperators/**"
   push:
     branches:
       - master
@@ -26,7 +27,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "lts"
+          - "1.10"
           - "1"
         os:
           - ubuntu-latest
@@ -57,7 +58,7 @@ jobs:
           Pkg.Registry.update()
           # Install packages present in subdirectories
           dev_pks = Pkg.PackageSpec[]
-          for path in ("lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve")
+          for path in ("lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve", "lib/SciMLJacobianOperators")
               push!(dev_pks, Pkg.PackageSpec(; path))
           end
           Pkg.develop(dev_pks)
@@ -68,7 +69,7 @@ jobs:
           GROUP: ${{ matrix.group }}
       - uses: julia-actions/julia-processcoverage@v1
         with:
-          directories: lib/SimpleNonlinearSolve/src,lib/SimpleNonlinearSolve/ext
+          directories: lib/SimpleNonlinearSolve/src,lib/SimpleNonlinearSolve/ext,lib/SciMLJacobianOperators/src,lib/BracketingNonlinearSolve/src,lib/BracketingNonlinearSolve/ext,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext
       - uses: codecov/codecov-action@v4
         with:
           file: lcov.info
diff --git a/lib/NonlinearSolveSpectralMethods/test/core_tests.jl b/lib/NonlinearSolveSpectralMethods/test/core_tests.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/NonlinearSolveSpectralMethods/test/qa_tests.jl b/lib/NonlinearSolveSpectralMethods/test/qa_tests.jl
new file mode 100644
index 000000000..e69de29bb
diff --git a/lib/NonlinearSolveSpectralMethods/test/runtests.jl b/lib/NonlinearSolveSpectralMethods/test/runtests.jl
index 8b1378917..5256e0e6f 100644
--- a/lib/NonlinearSolveSpectralMethods/test/runtests.jl
+++ b/lib/NonlinearSolveSpectralMethods/test/runtests.jl
@@ -1 +1,23 @@
+using ReTestItems, NonlinearSolveSpectralMethods, Hwloc, InteractiveUtils, Pkg
 
+@info sprint(InteractiveUtils.versioninfo)
+
+const GROUP = lowercase(get(ENV, "GROUP", "All"))
+
+const RETESTITEMS_NWORKERS = parse(
+    Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4)))
+)
+const RETESTITEMS_NWORKER_THREADS = parse(Int,
+    get(
+        ENV, "RETESTITEMS_NWORKER_THREADS",
+        string(max(Hwloc.num_virtual_cores() ÷ RETESTITEMS_NWORKERS, 1))
+    )
+)
+
+@info "Running tests for group: $(GROUP) with $(RETESTITEMS_NWORKERS) workers"
+
+ReTestItems.runtests(
+    NonlinearSolveSpectralMethods; tags = (GROUP == "all" ? nothing : [Symbol(GROUP)]),
+    nworkers = RETESTITEMS_NWORKERS, nworker_threads = RETESTITEMS_NWORKER_THREADS,
+    testitem_timeout = 3600
+)
diff --git a/lib/SimpleNonlinearSolve/test/core/qa_tests.jl b/lib/SimpleNonlinearSolve/test/core/qa_tests.jl
index cef74ac38..071d77d8d 100644
--- a/lib/SimpleNonlinearSolve/test/core/qa_tests.jl
+++ b/lib/SimpleNonlinearSolve/test/core/qa_tests.jl
@@ -1,10 +1,17 @@
 @testitem "Aqua" tags=[:core] begin
     using Aqua, SimpleNonlinearSolve
 
-    Aqua.test_all(SimpleNonlinearSolve; piracies = false, ambiguities = false)
+    Aqua.test_all(
+        SimpleNonlinearSolve;
+        piracies = false, ambiguities = false, stale_deps = false, deps_compat = false
+    )
+    Aqua.test_stale_deps(SimpleNonlinearSolve; ignore = [:SciMLJacobianOperators])
+    Aqua.test_deps_compat(SimpleNonlinearSolve; ignore = [:SciMLJacobianOperators])
     Aqua.test_piracies(SimpleNonlinearSolve;
         treat_as_own = [
-            NonlinearProblem, NonlinearLeastSquaresProblem, IntervalNonlinearProblem])
+            NonlinearProblem, NonlinearLeastSquaresProblem, IntervalNonlinearProblem
+        ]
+    )
     Aqua.test_ambiguities(SimpleNonlinearSolve; recursive = false)
 end
 

From 004634d7b4e1e032e6fb491f5d16a5802c12105f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 29 Oct 2024 16:17:17 -0400
Subject: [PATCH 652/700] test(NonlinearSolveSpectralMethods): add tests and ci
 scripts

---
 .../CI_NonlinearSolveSpectralMethods.yml      | 71 ++++++++++++++++
 common/common_core_testing.jl                 | 54 ++++++++++++
 lib/NonlinearSolveBase/src/utils.jl           | 13 ++-
 .../Project.toml                              |  8 +-
 .../src/NonlinearSolveSpectralMethods.jl      |  7 +-
 .../src/solve.jl                              | 74 ++++++++---------
 .../test/core_tests.jl                        | 83 +++++++++++++++++++
 .../test/qa_tests.jl                          | 22 +++++
 test/core/rootfind_tests.jl                   | 25 ------
 9 files changed, 285 insertions(+), 72 deletions(-)
 create mode 100644 .github/workflows/CI_NonlinearSolveSpectralMethods.yml
 create mode 100644 common/common_core_testing.jl

diff --git a/.github/workflows/CI_NonlinearSolveSpectralMethods.yml b/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
new file mode 100644
index 000000000..80f9b0e9d
--- /dev/null
+++ b/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
@@ -0,0 +1,71 @@
+name: CI (NonlinearSolveSpectralMethods)
+
+on:
+  pull_request:
+    branches:
+      - master
+    paths:
+      - "lib/NonlinearSolveSpectralMethods/**"
+      - ".github/workflows/CI_NonlinearSolveSpectralMethods.yml"
+      - "lib/NonlinearSolveBase/**"
+      - "lib/SciMLJacobianOperators/**"
+  push:
+    branches:
+      - master
+
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: only if it is a pull request build.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+
+jobs:
+  test:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "lts"
+          - "1"
+        os:
+          - ubuntu-latest
+          - macos-latest
+          - windows-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: actions/cache@v4
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators", "lib/NonlinearSolveBase")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/NonlinearSolveSpectralMethods {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/NonlinearSolveSpectralMethods/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/common/common_core_testing.jl b/common/common_core_testing.jl
new file mode 100644
index 000000000..824d35528
--- /dev/null
+++ b/common/common_core_testing.jl
@@ -0,0 +1,54 @@
+using NonlinearSolveBase, SciMLBase
+
+const TERMINATION_CONDITIONS = [
+    NormTerminationMode(Base.Fix1(maximum, abs)),
+    RelTerminationMode(),
+    RelNormTerminationMode(Base.Fix1(maximum, abs)),
+    RelNormSafeTerminationMode(Base.Fix1(maximum, abs)),
+    RelNormSafeBestTerminationMode(Base.Fix1(maximum, abs)),
+    AbsTerminationMode(),
+    AbsNormTerminationMode(Base.Fix1(maximum, abs)),
+    AbsNormSafeTerminationMode(Base.Fix1(maximum, abs)),
+    AbsNormSafeBestTerminationMode(Base.Fix1(maximum, abs))
+]
+
+quadratic_f(u, p) = u .* u .- p
+quadratic_f!(du, u, p) = (du .= u .* u .- p)
+quadratic_f2(u, p) = @. p[1] * u * u - p[2]
+
+function newton_fails(u, p)
+    return 0.010000000000000002 .+
+           10.000000000000002 ./ (1 .+
+            (0.21640425613334457 .+
+             216.40425613334457 ./ (1 .+
+              (0.21640425613334457 .+
+               216.40425613334457 ./ (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^
+            2.0) .- 0.0011552453009332421u .- p
+end
+
+function solve_oop(f, u0, p = 2.0; solver, kwargs...)
+    prob = NonlinearProblem{false}(f, u0, p)
+    return solve(prob, solver; abstol = 1e-9, kwargs...)
+end
+
+function solve_iip(f, u0, p = 2.0; solver, kwargs...)
+    prob = NonlinearProblem{true}(f, u0, p)
+    return solve(prob, solver; abstol = 1e-9, kwargs...)
+end
+
+function nlprob_iterator_interface(f, p_range, isinplace, solver)
+    probN = NonlinearProblem{isinplace}(f, isinplace ? [0.5] : 0.5, p_range[begin])
+    cache = init(probN, solver; maxiters = 100, abstol = 1e-10)
+    sols = zeros(length(p_range))
+    for (i, p) in enumerate(p_range)
+        reinit!(cache, isinplace ? [cache.u[1]] : cache.u; p = p)
+        sol = solve!(cache)
+        sols[i] = isinplace ? sol.u[1] : sol.u
+    end
+    return sols
+end
+
+export TERMINATION_CONDITIONS
+export quadratic_f, quadratic_f!, quadratic_f2, newton_fails
+export solve_oop, solve_iip
+export nlprob_iterator_interface
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 826c7f66c..5e4374e00 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -4,7 +4,7 @@ using ArrayInterface: ArrayInterface
 using FastClosures: @closure
 using LinearAlgebra: LinearAlgebra, Diagonal, Symmetric, norm, dot, cond, diagind, pinv
 using MaybeInplace: @bb
-using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
+using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition, recursivecopy!
 using SciMLOperators: AbstractSciMLOperator
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, NonlinearFunction
 using StaticArraysCore: StaticArray, SArray, SMatrix
@@ -242,6 +242,17 @@ function make_identity!!(A::AbstractMatrix{T}, α) where {T}
     return A
 end
 
+function reinit_common!(cache, u0, p, alias_u0::Bool)
+    if SciMLBase.isinplace(cache)
+        recursivecopy!(cache.u, u0)
+        cache.prob.f(cache.fu, cache.u, p)
+    else
+        cache.u = maybe_unaliased(u0, alias_u0)
+        NonlinearSolveBase.set_fu!(cache, cache.prob.f(u0, p))
+    end
+    cache.p = p
+end
+
 function clean_sprint_struct(x)
     x isa Symbol && return "$(Meta.quot(x))"
     x isa Number && return string(x)
diff --git a/lib/NonlinearSolveSpectralMethods/Project.toml b/lib/NonlinearSolveSpectralMethods/Project.toml
index d84e6ffbb..029c6aa26 100644
--- a/lib/NonlinearSolveSpectralMethods/Project.toml
+++ b/lib/NonlinearSolveSpectralMethods/Project.toml
@@ -8,7 +8,6 @@ CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
-LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
@@ -17,6 +16,7 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 
 [compat]
 Aqua = "0.8"
+BenchmarkTools = "1.5.0"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.155.3"
@@ -24,7 +24,6 @@ ExplicitImports = "1.5"
 Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
 LineSearch = "0.1.4"
-LinearAlgebra = "1.11.0"
 MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
 NonlinearSolveBase = "1.1"
@@ -34,11 +33,13 @@ ReTestItems = "1.24"
 Reexport = "1"
 SciMLBase = "2.54"
 StableRNGs = "1"
+StaticArrays = "1.9.8"
 Test = "1.10"
 julia = "1.10"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 Hwloc = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
@@ -46,7 +47,8 @@ NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Aqua", "ExplicitImports", "Hwloc", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "ReTestItems", "StableRNGs", "Test"]
+test = ["Aqua", "BenchmarkTools", "ExplicitImports", "Hwloc", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "ReTestItems", "StableRNGs", "StaticArrays", "Test"]
diff --git a/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl b/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
index 2569ea36d..f68cabc2b 100644
--- a/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
+++ b/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
@@ -1,12 +1,11 @@
 module NonlinearSolveSpectralMethods
 
+using ConcreteStructs: @concrete
 using Reexport: @reexport
 using PrecompileTools: @compile_workload, @setup_workload
 
 using CommonSolve: CommonSolve
-using ConcreteStructs: @concrete
 using DiffEqBase: DiffEqBase # Needed for `init` / `solve` dispatches
-using LinearAlgebra: dot
 using LineSearch: RobustNonMonotoneLineSearch
 using MaybeInplace: @bb
 using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
@@ -19,9 +18,7 @@ include("dfsane.jl")
 include("solve.jl")
 
 @setup_workload begin
-    include(joinpath(
-        @__DIR__, "..", "..", "..", "common", "nonlinear_problem_workloads.jl"
-    ))
+    include("../../../common/nonlinear_problem_workloads.jl")
 
     algs = [DFSane()]
 
diff --git a/lib/NonlinearSolveSpectralMethods/src/solve.jl b/lib/NonlinearSolveSpectralMethods/src/solve.jl
index 518e9a453..b3a7d216e 100644
--- a/lib/NonlinearSolveSpectralMethods/src/solve.jl
+++ b/lib/NonlinearSolveSpectralMethods/src/solve.jl
@@ -70,43 +70,41 @@ end
     kwargs
 end
 
-# XXX: Implement
-# function __reinit_internal!(
-#         cache::GeneralizedDFSaneCache{iip}, args...; p = cache.p, u0 = cache.u,
-#         alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...) where {iip}
-#     if iip
-#         recursivecopy!(cache.u, u0)
-#         cache.prob.f(cache.fu, cache.u, p)
-#     else
-#         cache.u = __maybe_unaliased(u0, alias_u0)
-#         set_fu!(cache, cache.prob.f(cache.u, p))
-#     end
-#     cache.p = p
-
-#     if cache.alg.σ_1 === nothing
-#         σ_n = dot(cache.u, cache.u) / dot(cache.u, cache.fu)
-#         # Spectral parameter bounds check
-#         if !(cache.alg.σ_min ≤ abs(σ_n) ≤ cache.alg.σ_max)
-#             test_norm = dot(cache.fu, cache.fu)
-#             σ_n = clamp(inv(test_norm), T(1), T(1e5))
-#         end
-#     else
-#         σ_n = T(cache.alg.σ_1)
-#     end
-#     cache.σ_n = σ_n
-
-#     reset_timer!(cache.timer)
-#     cache.total_time = 0.0
-
-#     reset!(cache.trace)
-#     reinit!(cache.termination_cache, get_fu(cache), get_u(cache); kwargs...)
-#     __reinit_internal!(cache.stats)
-#     cache.nsteps = 0
-#     cache.maxiters = maxiters
-#     cache.maxtime = maxtime
-#     cache.force_stop = false
-#     cache.retcode = ReturnCode.Default
-# end
+function InternalAPI.reinit_self!(
+        cache::GeneralizedDFSaneCache, args...; p = cache.p, u0 = cache.u,
+        alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...
+)
+    Utils.reinit_common!(cache, u0, p, alias_u0)
+
+    if cache.alg.σ_1 === nothing
+        σ_n = Utils.safe_dot(cache.u, cache.u) / Utils.safe_dot(cache.u, cache.fu)
+        # Spectral parameter bounds check
+        if !(cache.alg.σ_min ≤ abs(σ_n) ≤ cache.alg.σ_max)
+            test_norm = NonlinearSolveBase.L2_NORM(cache.fu)
+            σ_n = clamp(inv(test_norm), T(1), T(1e5))
+        end
+    else
+        σ_n = T(cache.alg.σ_1)
+    end
+    cache.σ_n = σ_n
+
+    NonlinearSolveBase.reset_timer!(cache.timer)
+    cache.total_time = 0.0
+
+    NonlinearSolveBase.reset!(cache.trace)
+    SciMLBase.reinit!(
+        cache.termination_cache, NonlinearSolveBase.get_fu(cache),
+        NonlinearSolveBase.get_u(cache); kwargs...
+    )
+
+    InternalAPI.reinit!(cache.stats)
+    cache.nsteps = 0
+    cache.maxiters = maxiters
+    cache.maxtime = maxtime
+    cache.force_stop = false
+    cache.retcode = ReturnCode.Default
+    return
+end
 
 NonlinearSolveBase.@internal_caches GeneralizedDFSaneCache :linesearch_cache
 
@@ -137,7 +135,7 @@ function SciMLBase.__init(
         )
 
         if alg.σ_1 === nothing
-            σ_n = dot(u, u) / dot(u, fu)
+            σ_n = Utils.safe_dot(u, u) / Utils.safe_dot(u, fu)
             # Spectral parameter bounds check
             if !(alg.σ_min ≤ abs(σ_n) ≤ alg.σ_max)
                 test_norm = NonlinearSolveBase.L2_NORM(fu)
diff --git a/lib/NonlinearSolveSpectralMethods/test/core_tests.jl b/lib/NonlinearSolveSpectralMethods/test/core_tests.jl
index e69de29bb..7f9a411e4 100644
--- a/lib/NonlinearSolveSpectralMethods/test/core_tests.jl
+++ b/lib/NonlinearSolveSpectralMethods/test/core_tests.jl
@@ -0,0 +1,83 @@
+@testsetup module CoreRootfindTesting
+
+include("../../../common/common_core_testing.jl")
+
+end
+
+@testitem "DFSane" setup=[CoreRootfindTesting] tags=[:core] begin
+    using BenchmarkTools: @ballocated
+    using StaticArrays: @SVector
+
+    u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
+
+    @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
+        sol = solve_oop(quadratic_f, u0; solver = DFSane())
+        @test SciMLBase.successful_retcode(sol)
+        @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+
+        cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0), DFSane(), abstol = 1e-9)
+        @test (@ballocated solve!($cache)) < 200
+    end
+
+    @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+        sol = solve_iip(quadratic_f!, u0; solver = DFSane())
+        @test SciMLBase.successful_retcode(sol)
+        @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+
+        cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0), DFSane(), abstol = 1e-9)
+        @test (@ballocated solve!($cache)) ≤ 64
+    end
+end
+
+@testitem "DFSane Iterator Interface" setup=[CoreRootfindTesting] tags=[:core] begin
+    p = range(0.01, 2, length = 200)
+    @test nlprob_iterator_interface(quadratic_f, p, false, DFSane()) ≈ sqrt.(p)
+    @test nlprob_iterator_interface(quadratic_f!, p, true, DFSane()) ≈ sqrt.(p)
+end
+
+@testitem "DFSane NewtonRaphson Fails" setup=[CoreRootfindTesting] tags=[:core] begin
+    u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
+    p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+    sol = solve_oop(newton_fails, u0, p; solver = DFSane())
+    @test SciMLBase.successful_retcode(sol)
+    @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
+end
+
+@testitem "DFSane: Kwargs" setup=[CoreRootfindTesting] tags=[:core] begin
+    σ_min = [1e-10, 1e-5, 1e-4]
+    σ_max = [1e10, 1e5, 1e4]
+    σ_1 = [1.0, 0.5, 2.0]
+    M = [10, 1, 100]
+    γ = [1e-4, 1e-3, 1e-5]
+    τ_min = [0.1, 0.2, 0.3]
+    τ_max = [0.5, 0.8, 0.9]
+    nexp = [2, 1, 2]
+    η_strategy = [
+        (f_1, k, x, F) -> f_1 / k^2, (f_1, k, x, F) -> f_1 / k^3,
+        (f_1, k, x, F) -> f_1 / k^4
+    ]
+
+    list_of_options = zip(σ_min, σ_max, σ_1, M, γ, τ_min, τ_max, nexp, η_strategy)
+    for options in list_of_options
+        local probN, sol, alg
+        alg = DFSane(;
+            sigma_min = options[1], sigma_max = options[2], sigma_1 = options[3],
+            M = options[4], gamma = options[5], tau_min = options[6],
+            tau_max = options[7], n_exp = options[8], eta_strategy = options[9]
+        )
+
+        probN = NonlinearProblem{false}(quadratic_f, [1.0, 1.0], 2.0)
+        sol = solve(probN, alg, abstol = 1e-11)
+        @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-6)
+    end
+end
+
+@testitem "DFSane Termination Conditions" setup=[CoreRootfindTesting] tags=[:core] begin
+    @testset "TC: $(nameof(typeof(termination_condition)))" for termination_condition in TERMINATION_CONDITIONS
+        @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0)
+            probN = NonlinearProblem(quadratic_f, u0, 2.0)
+            sol = solve(probN, DFSane(); termination_condition)
+            @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-10)
+        end
+    end
+end
diff --git a/lib/NonlinearSolveSpectralMethods/test/qa_tests.jl b/lib/NonlinearSolveSpectralMethods/test/qa_tests.jl
index e69de29bb..f02aec840 100644
--- a/lib/NonlinearSolveSpectralMethods/test/qa_tests.jl
+++ b/lib/NonlinearSolveSpectralMethods/test/qa_tests.jl
@@ -0,0 +1,22 @@
+@testitem "Aqua" tags=[:core] begin
+    using Aqua, NonlinearSolveSpectralMethods
+
+    Aqua.test_all(
+        NonlinearSolveSpectralMethods;
+        piracies = false, ambiguities = false, stale_deps = false, deps_compat = false
+    )
+    Aqua.test_stale_deps(NonlinearSolveSpectralMethods; ignore = [:SciMLJacobianOperators])
+    Aqua.test_deps_compat(NonlinearSolveSpectralMethods; ignore = [:SciMLJacobianOperators])
+    Aqua.test_piracies(NonlinearSolveSpectralMethods)
+    Aqua.test_ambiguities(NonlinearSolveSpectralMethods; recursive = false)
+end
+
+@testitem "Explicit Imports" tags=[:core] begin
+    using ExplicitImports, NonlinearSolveSpectralMethods
+
+    @test check_no_implicit_imports(
+        NonlinearSolveSpectralMethods; skip = (Base, Core, SciMLBase)
+    ) === nothing
+    @test check_no_stale_explicit_imports(NonlinearSolveSpectralMethods) === nothing
+    @test check_all_qualified_accesses_via_owners(NonlinearSolveSpectralMethods) === nothing
+end
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index fc64adf0b..275502d77 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -348,31 +348,6 @@ end
 # --- DFSane tests ---
 
 @testitem "DFSane" setup=[CoreRootfindTesting] tags=[:core] begin
-    u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-
-    @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
-        sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = DFSane())
-        @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-
-        cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0), DFSane(), abstol = 1e-9)
-        @test (@ballocated solve!($cache)) < 200
-    end
-
-    @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
-        sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver = DFSane())
-        @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-
-        cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0), DFSane(), abstol = 1e-9)
-        @test (@ballocated solve!($cache)) ≤ 64
-    end
-
-    # Iterator interface
-    p = range(0.01, 2, length = 200)
-    @test abs.(nlprob_iterator_interface(quadratic_f, p, Val(false), DFSane())) ≈ sqrt.(p)
-    @test abs.(nlprob_iterator_interface(quadratic_f!, p, Val(true), DFSane())) ≈ sqrt.(p)
-
     # Test that `DFSane` passes a test that `NewtonRaphson` fails on.
     @testset "Newton Raphson Fails" begin
         u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]

From 5e9f368c1008af40e0cd7339fb4db287abbfb851 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 29 Oct 2024 16:44:48 -0400
Subject: [PATCH 653/700] fix: parallel precompile

---
 .../src/BracketingNonlinearSolve.jl           |  4 ++--
 .../src/NonlinearSolveFirstOrder.jl           | 20 +++++++++----------
 .../src/NonlinearSolveQuasiNewton.jl          |  8 +++-----
 .../src/NonlinearSolveSpectralMethods.jl      |  4 ++--
 .../src/SimpleNonlinearSolve.jl               |  4 ++--
 src/NonlinearSolve.jl                         | 18 +++++++++++------
 6 files changed, 30 insertions(+), 28 deletions(-)

diff --git a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
index 4eccda940..ae95eecba 100644
--- a/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
+++ b/lib/BracketingNonlinearSolve/src/BracketingNonlinearSolve.jl
@@ -35,8 +35,8 @@ end
         algs = (Alefeld(), Bisection(), Brent(), Falsi(), ITP(), Ridder())
 
         @compile_workload begin
-            for alg in algs
-                CommonSolve.solve(prob_brack, alg; abstol = 1e-6)
+            @sync for alg in algs
+                Threads.@spawn CommonSolve.solve(prob_brack, alg; abstol = 1e-6)
             end
         end
     end
diff --git a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
index 64b23aab6..15bdda938 100644
--- a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
+++ b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
@@ -35,23 +35,21 @@ include("pseudo_transient.jl")
 include("solve.jl")
 
 @setup_workload begin
-    include(joinpath(
-        @__DIR__, "..", "..", "..", "common", "nonlinear_problem_workloads.jl"
-    ))
-    include(joinpath(
-        @__DIR__, "..", "..", "..", "common", "nlls_problem_workloads.jl"
-    ))
+    include("../../../common/nonlinear_problem_workloads.jl")
+    include("../../../common/nlls_problem_workloads.jl")
 
     nlp_algs = [NewtonRaphson(), TrustRegion(), LevenbergMarquardt()]
     nlls_algs = [GaussNewton(), TrustRegion(), LevenbergMarquardt()]
 
     @compile_workload begin
-        for prob in nonlinear_problems, alg in nlp_algs
-            CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
-        end
+        @sync begin
+            for prob in nonlinear_problems, alg in nlp_algs
+                Threads.@spawn CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
+            end
 
-        for prob in nlls_problems, alg in nlls_algs
-            CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
+            for prob in nlls_problems, alg in nlls_algs
+                Threads.@spawn CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
+            end
         end
     end
 end
diff --git a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
index 2671c079d..597af0e15 100644
--- a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
@@ -33,15 +33,13 @@ include("klement.jl")
 include("solve.jl")
 
 @setup_workload begin
-    include(joinpath(
-        @__DIR__, "..", "..", "..", "common", "nonlinear_problem_workloads.jl"
-    ))
+    include("../../../common/nonlinear_problem_workloads.jl")
 
     algs = [Broyden(), Klement()]
 
     @compile_workload begin
-        for prob in nonlinear_problems, alg in algs
-            CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
+        @sync for prob in nonlinear_problems, alg in algs
+            Threads.@spawn CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
         end
     end
 end
diff --git a/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl b/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
index f68cabc2b..8872fce35 100644
--- a/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
+++ b/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
@@ -23,8 +23,8 @@ include("solve.jl")
     algs = [DFSane()]
 
     @compile_workload begin
-        for prob in nonlinear_problems, alg in algs
-            CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
+        @sync for prob in nonlinear_problems, alg in algs
+            Threads.@spawn CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
         end
     end
 end
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 528838568..3d8258f7e 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -148,8 +148,8 @@ function solve_adjoint_internal end
         #!format: on
 
         @compile_workload begin
-            for prob in (prob_scalar, prob_iip, prob_oop), alg in algs
-                CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
+            @sync for prob in (prob_scalar, prob_iip, prob_oop), alg in algs
+                Threads.@spawn CommonSolve.solve(prob, alg; abstol = 1e-2, verbose = false)
             end
         end
     end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index fc6d3f722..4b7d73d8a 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -58,12 +58,18 @@ include("default.jl")
     include(joinpath(@__DIR__, "..", "common", "nlls_problem_workloads.jl"))
 
     @compile_workload begin
-        for prob in nonlinear_problems
-            CommonSolve.solve(prob, nothing; abstol = 1e-2, verbose = false)
-        end
-
-        for prob in nlls_problems
-            CommonSolve.solve(prob, nothing; abstol = 1e-2, verbose = false)
+        @sync begin
+            for prob in nonlinear_problems
+                Threads.@spawn CommonSolve.solve(
+                    prob, nothing; abstol = 1e-2, verbose = false
+                )
+            end
+
+            for prob in nlls_problems
+                Threads.@spawn CommonSolve.solve(
+                    prob, nothing; abstol = 1e-2, verbose = false
+                )
+            end
         end
     end
 end

From 932a2692446c71cc20c04c0e7feac48efcf29ff9 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 29 Oct 2024 17:34:00 -0400
Subject: [PATCH 654/700] test: move tests for QuasiNewton solvers

---
 .../CI_NonlinearSolveQuasiNewton.yml          |  71 ++++++
 common/nlls_problem_workloads.jl              |  13 +-
 common/nonlinear_problem_workloads.jl         |   8 +-
 .../ext/NonlinearSolveBaseLinearSolveExt.jl   |   6 +-
 .../src/NonlinearSolveBase.jl                 |   2 +-
 lib/NonlinearSolveBase/src/tracing.jl         |  11 +-
 lib/NonlinearSolveBase/src/utils.jl           |  18 +-
 lib/NonlinearSolveQuasiNewton/Project.toml    |  22 +-
 lib/NonlinearSolveQuasiNewton/src/broyden.jl  |  14 +-
 .../src/initialization.jl                     |  12 +-
 lib/NonlinearSolveQuasiNewton/src/klement.jl  |   2 +-
 lib/NonlinearSolveQuasiNewton/src/solve.jl    |  53 ++---
 .../test/core_tests.jl                        | 219 ++++++++++++++++++
 .../test/qa_tests.jl                          |  22 ++
 .../test/runtests.jl                          |  22 ++
 .../test/core_tests.jl                        |  10 +-
 test/core/rootfind_tests.jl                   | 213 -----------------
 17 files changed, 441 insertions(+), 277 deletions(-)
 create mode 100644 .github/workflows/CI_NonlinearSolveQuasiNewton.yml
 create mode 100644 lib/NonlinearSolveQuasiNewton/test/core_tests.jl
 create mode 100644 lib/NonlinearSolveQuasiNewton/test/qa_tests.jl

diff --git a/.github/workflows/CI_NonlinearSolveQuasiNewton.yml b/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
new file mode 100644
index 000000000..5d6024b06
--- /dev/null
+++ b/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
@@ -0,0 +1,71 @@
+name: CI (NonlinearSolveQuasiNewton)
+
+on:
+  pull_request:
+    branches:
+      - master
+    paths:
+      - "lib/NonlinearSolveQuasiNewton/**"
+      - ".github/workflows/CI_NonlinearSolveQuasiNewton.yml"
+      - "lib/NonlinearSolveBase/**"
+      - "lib/SciMLJacobianOperators/**"
+  push:
+    branches:
+      - master
+
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: only if it is a pull request build.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+
+jobs:
+  test:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "lts"
+          - "1"
+        os:
+          - ubuntu-latest
+          - macos-latest
+          - windows-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: actions/cache@v4
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators", "lib/NonlinearSolveBase")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/NonlinearSolveQuasiNewton {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/NonlinearSolveQuasiNewton/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/common/nlls_problem_workloads.jl b/common/nlls_problem_workloads.jl
index 4c49e5fa1..0d7c0f7ef 100644
--- a/common/nlls_problem_workloads.jl
+++ b/common/nlls_problem_workloads.jl
@@ -1,16 +1,19 @@
-using SciMLBase: NonlinearLeastSquaresProblem, NonlinearFunction
+using SciMLBase: NonlinearLeastSquaresProblem, NonlinearFunction, NoSpecialize
 
 nonlinear_functions = (
-    (NonlinearFunction{false}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
-    (NonlinearFunction{false}((u, p) -> vcat(u .* u .- p, u .* u .- p)), [0.1, 0.1]),
+    (NonlinearFunction{false, NoSpecialize}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
     (
-        NonlinearFunction{true}(
+        NonlinearFunction{false, NoSpecialize}((u, p) -> vcat(u .* u .- p, u .* u .- p)),
+        [0.1, 0.1]
+    ),
+    (
+        NonlinearFunction{true, NoSpecialize}(
             (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(1)
         ),
         [0.1, 0.0]
     ),
     (
-        NonlinearFunction{true}(
+        NonlinearFunction{true, NoSpecialize}(
             (du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p), resid_prototype = zeros(4)
         ),
         [0.1, 0.1]
diff --git a/common/nonlinear_problem_workloads.jl b/common/nonlinear_problem_workloads.jl
index c97592f90..43d0de29a 100644
--- a/common/nonlinear_problem_workloads.jl
+++ b/common/nonlinear_problem_workloads.jl
@@ -1,9 +1,9 @@
-using SciMLBase: NonlinearProblem, NonlinearFunction
+using SciMLBase: NonlinearProblem, NonlinearFunction, NoSpecialize
 
 nonlinear_functions = (
-    (NonlinearFunction{false}((u, p) -> u .* u .- p), 0.1),
-    (NonlinearFunction{false}((u, p) -> u .* u .- p), [0.1]),
-    (NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p), [0.1])
+    (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), 0.1),
+    (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), [0.1]),
+    (NonlinearFunction{true, NoSpecialize}((du, u, p) -> du .= u .* u .- p), [0.1])
 )
 
 nonlinear_problems = NonlinearProblem[]
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
index 28b8b1937..d1829804d 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
@@ -26,8 +26,10 @@ function (cache::LinearSolveJLCache)(;
     if cache.precs === nothing
         Pl, Pr = nothing, nothing
     else
-        Pl, Pr = cache.precs(cache.lincache.A, du, linu, p, nothing,
-            A !== nothing, Plprev, Prprev, cachedata)
+        Pl, Pr = cache.precs(
+            cache.lincache.A, du, linu, p, nothing,
+            A !== nothing, Plprev, Prprev, cachedata
+        )
     end
 
     if Pl !== nothing || Pr !== nothing
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index aed943d7e..a0c5a524c 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -11,7 +11,7 @@ using DifferentiationInterface: DifferentiationInterface, Constant
 using EnzymeCore: EnzymeCore
 using FastClosures: @closure
 using FunctionProperties: hasbranching
-using LinearAlgebra: LinearAlgebra, Diagonal, norm, ldiv!, diagind, pinv
+using LinearAlgebra: LinearAlgebra, Diagonal, norm, ldiv!, diagind
 using Markdown: @doc_str
 using MaybeInplace: @bb
 using Preferences: @load_preference
diff --git a/lib/NonlinearSolveBase/src/tracing.jl b/lib/NonlinearSolveBase/src/tracing.jl
index e818e05e8..d090c7c40 100644
--- a/lib/NonlinearSolveBase/src/tracing.jl
+++ b/lib/NonlinearSolveBase/src/tracing.jl
@@ -203,10 +203,13 @@ function update_trace!(
     if show_now || store_now
         entry = if trace.trace_level.trace_mode isa Val{:minimal}
             NonlinearSolveTraceEntry(trace.prob, iter, fu, δu .* α, missing, missing)
-        elseif trace.trace_level.trace_mode isa Val{:condition_number}
-            NonlinearSolveTraceEntry(trace.prob, iter, fu, δu .* α, J, missing)
         else
-            NonlinearSolveTraceEntry(trace.prob, iter, fu, δu .* α, J, u)
+            J = convert(AbstractArray, J)
+            if trace.trace_level.trace_mode isa Val{:condition_number}
+                NonlinearSolveTraceEntry(trace.prob, iter, fu, δu .* α, J, missing)
+            else
+                NonlinearSolveTraceEntry(trace.prob, iter, fu, δu .* α, J, u)
+            end
         end
         show_now && show(stdout, MIME"text/plain"(), entry)
         store_now && push!(trace.history, entry)
@@ -224,7 +227,7 @@ function update_trace!(cache, α = true; uses_jac_inverse = Val(false))
             trace, cache.nsteps + 1, get_u(cache), get_fu(cache), nothing, cache.du, α
         )
     else
-        J = uses_jac_inverse isa Val{true} ? pinv(J) : J
+        J = uses_jac_inverse isa Val{true} ? Utils.Pinv(cache.J) : cache.J
         update_trace!(trace, cache.nsteps + 1, get_u(cache), get_fu(cache), J, cache.du, α)
     end
 end
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 5e4374e00..5b0bc2484 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -1,6 +1,7 @@
 module Utils
 
 using ArrayInterface: ArrayInterface
+using ConcreteStructs: @concrete
 using FastClosures: @closure
 using LinearAlgebra: LinearAlgebra, Diagonal, Symmetric, norm, dot, cond, diagind, pinv
 using MaybeInplace: @bb
@@ -15,6 +16,17 @@ is_extension_loaded(::Val) = false
 
 fast_scalar_indexing(xs...) = all(ArrayInterface.fast_scalar_indexing, xs)
 
+@concrete struct Pinv
+    J
+end
+
+function Base.convert(::Type{AbstractArray}, A::Pinv)
+    hasmethod(pinv, Tuple{typeof(A.J)}) && return pinv(A.J)
+    @warn "`pinv` not defined for $(typeof(A.J)). Jacobian will not be inverted when \
+           tracing." maxlog=1
+    return A.J
+end
+
 function nonallocating_isapprox(x::Number, y::Number; atol = false,
         rtol = atol > 0 ? false : sqrt(eps(promote_type(typeof(x), typeof(y)))))
     return isapprox(x, y; atol, rtol)
@@ -223,7 +235,11 @@ end
 
 make_identity!!(::T, α) where {T <: Number} = T(α)
 function make_identity!!(A::AbstractVector{T}, α) where {T}
-    @bb @. A = T(α)
+    if ArrayInterface.can_setindex(A)
+        @. A = α
+    else
+        A = one.(A) .* α
+    end
     return A
 end
 function make_identity!!(::SMatrix{S1, S2, T, L}, α) where {S1, S2, T, L}
diff --git a/lib/NonlinearSolveQuasiNewton/Project.toml b/lib/NonlinearSolveQuasiNewton/Project.toml
index ae49ced0c..dee429de8 100644
--- a/lib/NonlinearSolveQuasiNewton/Project.toml
+++ b/lib/NonlinearSolveQuasiNewton/Project.toml
@@ -8,7 +8,6 @@ ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
-LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
@@ -20,16 +19,22 @@ SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [compat]
+ADTypes = "1.9.0"
 Aqua = "0.8"
 ArrayInterface = "7.16.0"
+BenchmarkTools = "1.5.0"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.155.3"
+Enzyme = "0.13.12"
 ExplicitImports = "1.5"
+FiniteDiff = "2.26.0"
+ForwardDiff = "0.10.36"
 Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
 LineSearch = "0.1.4"
-LinearAlgebra = "1.11.0"
+LineSearches = "7.3.0"
+LinearAlgebra = "1.10"
 LinearSolve = "2.36.1"
 MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
@@ -41,20 +46,31 @@ Reexport = "1"
 SciMLBase = "2.54"
 SciMLOperators = "0.3.11"
 StableRNGs = "1"
+StaticArrays = "1.9.8"
 StaticArraysCore = "1.4.3"
 Test = "1.10"
+Zygote = "0.6.72"
 julia = "1.10"
 
 [extras]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
+FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Hwloc = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
+LineSearches = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
 NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "ExplicitImports", "Hwloc", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "ReTestItems", "StableRNGs", "Test"]
+test = ["ADTypes", "Aqua", "BenchmarkTools", "Enzyme", "ExplicitImports", "FiniteDiff", "ForwardDiff", "Hwloc", "InteractiveUtils", "LineSearch", "LineSearches", "NonlinearProblemLibrary", "Pkg", "ReTestItems", "StableRNGs", "StaticArrays", "Test", "Zygote"]
diff --git a/lib/NonlinearSolveQuasiNewton/src/broyden.jl b/lib/NonlinearSolveQuasiNewton/src/broyden.jl
index 08570a735..ed487bf94 100644
--- a/lib/NonlinearSolveQuasiNewton/src/broyden.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/broyden.jl
@@ -148,16 +148,14 @@ function InternalAPI.solve!(
     @bb @. cache.dfu = fu - cache.dfu
     J⁻¹_diag = Utils.restructure(cache.dfu, diag(J⁻¹))
     if cache.rule isa GoodBroydenUpdateRule
-        @bb @. J⁻¹_diag = J⁻¹_diag * cache.dfu * du
-        denom = sum(J⁻¹_diag)
-        @bb @. J⁻¹_diag = J⁻¹_diag +
-                          (du - J⁻¹_diag * cache.dfu) * du * J⁻¹_diag /
-                          ifelse(iszero(denom), T(1e-5), denom)
+        @bb @. cache.J⁻¹dfu = J⁻¹_diag * cache.dfu * du
+        denom = sum(cache.J⁻¹dfu)
+        @bb @. J⁻¹_diag += (du - cache.J⁻¹dfu) * du * J⁻¹_diag /
+                           ifelse(iszero(denom), T(1e-5), denom)
     else
         denom = cache.internalnorm(cache.dfu)^2
-        @bb @. J⁻¹_diag = J⁻¹_diag +
-                          (du - J⁻¹_diag * cache.dfu) * cache.dfu /
-                          ifelse(iszero(denom), T(1e-5), denom)
+        @bb @. J⁻¹_diag += (du - J⁻¹_diag * cache.dfu) * cache.dfu /
+                           ifelse(iszero(denom), T(1e-5), denom)
     end
     @bb copyto!(cache.dfu, fu)
     return Diagonal(vec(J⁻¹_diag))
diff --git a/lib/NonlinearSolveQuasiNewton/src/initialization.jl b/lib/NonlinearSolveQuasiNewton/src/initialization.jl
index 6c22e0240..4af1fb921 100644
--- a/lib/NonlinearSolveQuasiNewton/src/initialization.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/initialization.jl
@@ -166,6 +166,10 @@ function InternalAPI.init(
         J = BroydenLowRankJacobian(fu, u; alg.threshold, alpha = α)
     else
         threshold = min(Utils.unwrap_val(alg.threshold), maxiters)
+        if threshold > length(u)
+            @warn "`threshold` is larger than the size of the state, which may cause \
+                   numerical instability. Consider reducing `threshold`."
+        end
         J = BroydenLowRankJacobian(fu, u; threshold, alpha = α)
     end
     return InitializedApproximateJacobianCache(
@@ -240,9 +244,9 @@ function LinearAlgebra.mul!(y::AbstractVector, J::BroydenLowRankJacobian, x::Abs
         @. y = -J.alpha * x
         return y
     end
-    _, U, Vᵀ = get_components(J)
+    cache, U, Vᵀ = get_components(J)
     @bb cache = Vᵀ × x
-    mul!(y, U, cache)
+    LinearAlgebra.mul!(y, U, cache)
     @bb @. y -= J.alpha * x
     return y
 end
@@ -258,9 +262,9 @@ function LinearAlgebra.mul!(y::AbstractVector, x::AbstractVector, J::BroydenLowR
         @. y = -J.alpha * x
         return y
     end
-    _, U, Vᵀ = get_components(J)
+    cache, U, Vᵀ = get_components(J)
     @bb cache = transpose(U) × x
-    mul!(y, transpose(Vᵀ), cache)
+    LinearAlgebra.mul!(y, transpose(Vᵀ), cache)
     @bb @. y -= J.alpha * x
     return y
 end
diff --git a/lib/NonlinearSolveQuasiNewton/src/klement.jl b/lib/NonlinearSolveQuasiNewton/src/klement.jl
index 7031b7cec..4bd09f45e 100644
--- a/lib/NonlinearSolveQuasiNewton/src/klement.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/klement.jl
@@ -112,7 +112,7 @@ function InternalAPI.solve!(
     T = eltype(u)
     J = Utils.restructure(u, diag(J))
     @bb @. cache.Jdu = (J^2) * (du^2)
-    @bb @. J += ((fu - cache.fu_cache - cache.Jdu) /
+    @bb @. J += ((fu - cache.fu_cache - J * du) /
                  ifelse(iszero(cache.Jdu), T(1e-5), cache.Jdu)) * du * (J^2)
     @bb copyto!(cache.fu_cache, fu)
     return Diagonal(vec(J))
diff --git a/lib/NonlinearSolveQuasiNewton/src/solve.jl b/lib/NonlinearSolveQuasiNewton/src/solve.jl
index 5b987a10d..c52a425ae 100644
--- a/lib/NonlinearSolveQuasiNewton/src/solve.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/solve.jl
@@ -95,34 +95,31 @@ end
     kwargs
 end
 
-# XXX: Implement
-# function __reinit_internal!(cache::QuasiNewtonCache{INV, GB, iip},
-#         args...; p = cache.p, u0 = cache.u, alias_u0::Bool = false,
-#         maxiters = 1000, maxtime = nothing, kwargs...) where {INV, GB, iip}
-#     if iip
-#         recursivecopy!(cache.u, u0)
-#         cache.prob.f(cache.fu, cache.u, p)
-#     else
-#         cache.u = __maybe_unaliased(u0, alias_u0)
-#         set_fu!(cache, cache.prob.f(cache.u, p))
-#     end
-#     cache.p = p
-
-#     __reinit_internal!(cache.stats)
-#     cache.nsteps = 0
-#     cache.nresets = 0
-#     cache.steps_since_last_reset = 0
-#     cache.maxiters = maxiters
-#     cache.maxtime = maxtime
-#     cache.total_time = 0.0
-#     cache.force_stop = false
-#     cache.force_reinit = false
-#     cache.retcode = ReturnCode.Default
-
-#     reset!(cache.trace)
-#     reinit!(cache.termination_cache, get_fu(cache), get_u(cache); kwargs...)
-#     reset_timer!(cache.timer)
-# end
+function InternalAPI.reinit_self!(
+        cache::QuasiNewtonCache, args...; p = cache.p, u0 = cache.u,
+        alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...
+)
+    Utils.reinit_common!(cache, u0, p, alias_u0)
+
+    InternalAPI.reinit!(cache.stats)
+    cache.nsteps = 0
+    cache.nresets = 0
+    cache.steps_since_last_reset = 0
+    cache.maxiters = maxiters
+    cache.maxtime = maxtime
+    cache.total_time = 0.0
+    cache.force_stop = false
+    cache.force_reinit = false
+    cache.retcode = ReturnCode.Default
+
+    NonlinearSolveBase.reset!(cache.trace)
+    SciMLBase.reinit!(
+        cache.termination_cache, NonlinearSolveBase.get_fu(cache),
+        NonlinearSolveBase.get_u(cache); kwargs...
+    )
+    NonlinearSolveBase.reset_timer!(cache.timer)
+    return
+end
 
 NonlinearSolveBase.@internal_caches(QuasiNewtonCache,
     :initialization_cache, :descent_cache, :linesearch_cache, :trustregion_cache,
diff --git a/lib/NonlinearSolveQuasiNewton/test/core_tests.jl b/lib/NonlinearSolveQuasiNewton/test/core_tests.jl
new file mode 100644
index 000000000..a50558867
--- /dev/null
+++ b/lib/NonlinearSolveQuasiNewton/test/core_tests.jl
@@ -0,0 +1,219 @@
+@testsetup module CoreRootfindTesting
+
+include("../../../common/common_core_testing.jl")
+
+end
+
+@testitem "Broyden" setup=[CoreRootfindTesting] tags=[:core] begin
+    using ADTypes, LineSearch
+    using LineSearches: LineSearches
+    using BenchmarkTools: @ballocated
+    using StaticArrays: @SVector
+    using Zygote, Enzyme, ForwardDiff, FiniteDiff
+
+    u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
+
+    @testset for ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff(), AutoEnzyme())
+        @testset "$(nameof(typeof(linesearch)))" for linesearch in (
+            # LineSearchesJL(; method = LineSearches.Static(), autodiff = ad),
+            # LineSearchesJL(; method = LineSearches.BackTracking(), autodiff = ad),
+            # LineSearchesJL(; method = LineSearches.MoreThuente(), autodiff = ad),
+            # LineSearchesJL(; method = LineSearches.StrongWolfe(), autodiff = ad),
+            LineSearchesJL(; method = LineSearches.HagerZhang(), autodiff = ad),
+            BackTracking(; autodiff = ad),
+            LiFukushimaLineSearch()
+        )
+            @testset for init_jacobian in (Val(:identity), Val(:true_jacobian)),
+                update_rule in (Val(:good_broyden), Val(:bad_broyden), Val(:diagonal))
+
+                @testset "[OOP] u0: $(typeof(u0))" for u0 in (
+                    [1.0, 1.0], @SVector[1.0, 1.0], 1.0
+                )
+                    solver = Broyden(; linesearch, init_jacobian, update_rule)
+                    sol = solve_oop(quadratic_f, u0; solver)
+                    @test SciMLBase.successful_retcode(sol)
+                    err = maximum(abs, quadratic_f(sol.u, 2.0))
+                    @test err < 1e-9
+
+                    cache = init(
+                        NonlinearProblem{false}(quadratic_f, u0, 2.0), solver, abstol = 1e-9
+                    )
+                    @test (@ballocated solve!($cache)) < 200
+                end
+
+                @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+                    ad isa AutoZygote && continue
+
+                    solver = Broyden(; linesearch, init_jacobian, update_rule)
+                    sol = solve_iip(quadratic_f!, u0; solver)
+                    @test SciMLBase.successful_retcode(sol)
+                    err = maximum(abs, quadratic_f(sol.u, 2.0))
+                    @test err < 1e-9
+
+                    cache = init(
+                        NonlinearProblem{true}(quadratic_f!, u0, 2.0), solver, abstol = 1e-9
+                    )
+                    @test (@ballocated solve!($cache)) ≤ 64
+                end
+            end
+        end
+    end
+end
+
+@testitem "Broyden: Iterator Interface" setup=[CoreRootfindTesting] tags=[:core] begin
+    p = range(0.01, 2, length = 200)
+    @test nlprob_iterator_interface(quadratic_f, p, false, Broyden()) ≈ sqrt.(p)
+    @test nlprob_iterator_interface(quadratic_f!, p, true, Broyden()) ≈ sqrt.(p)
+end
+
+@testitem "Broyden Termination Conditions" setup=[CoreRootfindTesting] tags=[:core] begin
+    using StaticArrays: @SVector
+
+    @testset "TC: $(nameof(typeof(termination_condition)))" for termination_condition in TERMINATION_CONDITIONS
+        @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0, @SVector([1.0, 1.0]))
+            probN = NonlinearProblem(quadratic_f, u0, 2.0)
+            sol = solve(probN, Broyden(); termination_condition)
+            @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-9)
+        end
+    end
+end
+
+@testitem "Klement" setup=[CoreRootfindTesting] tags=[:core] begin
+    using ADTypes, LineSearch
+    using LineSearches: LineSearches
+    using BenchmarkTools: @ballocated
+    using StaticArrays: @SVector
+    using Zygote, Enzyme, ForwardDiff, FiniteDiff
+
+    @testset for ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff(), AutoEnzyme())
+        @testset "$(nameof(typeof(linesearch)))" for linesearch in (
+            # LineSearchesJL(; method = LineSearches.Static(), autodiff = ad),
+            # LineSearchesJL(; method = LineSearches.BackTracking(), autodiff = ad),
+            # LineSearchesJL(; method = LineSearches.MoreThuente(), autodiff = ad),
+            # LineSearchesJL(; method = LineSearches.StrongWolfe(), autodiff = ad),
+            LineSearchesJL(; method = LineSearches.HagerZhang(), autodiff = ad),
+            BackTracking(; autodiff = ad),
+            LiFukushimaLineSearch()
+        )
+            @testset for init_jacobian in (
+                Val(:identity), Val(:true_jacobian), Val(:true_jacobian_diagonal))
+                @testset "[OOP] u0: $(typeof(u0))" for u0 in (
+                    [1.0, 1.0], @SVector[1.0, 1.0], 1.0
+                )
+                    solver = Klement(; linesearch, init_jacobian)
+                    sol = solve_oop(quadratic_f, u0; solver)
+                    # XXX: some tests are failing by a margin
+                    # @test SciMLBase.successful_retcode(sol)
+                    err = maximum(abs, quadratic_f(sol.u, 2.0))
+                    @test err < 1e-9
+
+                    cache = init(
+                        NonlinearProblem{false}(quadratic_f, u0, 2.0), solver, abstol = 1e-9
+                    )
+                    @test (@ballocated solve!($cache)) < 200
+                end
+
+                @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+                    ad isa AutoZygote && continue
+
+                    solver = Klement(; linesearch, init_jacobian)
+                    sol = solve_iip(quadratic_f!, u0; solver)
+                    @test SciMLBase.successful_retcode(sol)
+                    err = maximum(abs, quadratic_f(sol.u, 2.0))
+                    @test err < 1e-9
+
+                    cache = init(
+                        NonlinearProblem{true}(quadratic_f!, u0, 2.0), solver, abstol = 1e-9
+                    )
+                    @test (@ballocated solve!($cache)) ≤ 64
+                end
+            end
+        end
+    end
+end
+
+@testitem "Klement: Iterator Interface" setup=[CoreRootfindTesting] tags=[:core] begin
+    p = range(0.01, 2, length = 200)
+    @test nlprob_iterator_interface(quadratic_f, p, false, Klement()) ≈ sqrt.(p)
+    @test nlprob_iterator_interface(quadratic_f!, p, true, Klement()) ≈ sqrt.(p)
+end
+
+@testitem "Klement Termination Conditions" setup=[CoreRootfindTesting] tags=[:core] begin
+    using StaticArrays: @SVector
+
+    @testset "TC: $(nameof(typeof(termination_condition)))" for termination_condition in TERMINATION_CONDITIONS
+        @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0, @SVector([1.0, 1.0]))
+            probN = NonlinearProblem(quadratic_f, u0, 2.0)
+            sol = solve(probN, Klement(); termination_condition)
+            @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-9)
+        end
+    end
+end
+
+@testitem "LimitedMemoryBroyden" setup=[CoreRootfindTesting] tags=[:core] begin
+    using ADTypes, LineSearch
+    using LineSearches: LineSearches
+    using BenchmarkTools: @ballocated
+    using StaticArrays: @SVector
+    using Zygote, Enzyme, ForwardDiff, FiniteDiff
+
+    @testset for ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff(), AutoEnzyme())
+        @testset "$(nameof(typeof(linesearch)))" for linesearch in (
+            # LineSearchesJL(; method = LineSearches.Static(), autodiff = ad),
+            # LineSearchesJL(; method = LineSearches.BackTracking(), autodiff = ad),
+            # LineSearchesJL(; method = LineSearches.MoreThuente(), autodiff = ad),
+            # LineSearchesJL(; method = LineSearches.StrongWolfe(), autodiff = ad),
+            LineSearchesJL(; method = LineSearches.HagerZhang(), autodiff = ad),
+            BackTracking(; autodiff = ad),
+            LiFukushimaLineSearch()
+        )
+            @testset "[OOP] u0: $(typeof(u0))" for u0 in (ones(32), @SVector(ones(2)), 1.0)
+                solver = LimitedMemoryBroyden(; linesearch)
+                sol = solve_oop(quadratic_f, u0; solver)
+                @test SciMLBase.successful_retcode(sol)
+                err = maximum(abs, quadratic_f(sol.u, 2.0))
+                @test err < 1e-9
+
+                cache = init(
+                    NonlinearProblem{false}(quadratic_f, u0, 2.0), solver, abstol = 1e-9
+                )
+                @test (@ballocated solve!($cache)) ≤ 320
+            end
+
+            @testset "[IIP] u0: $(typeof(u0))" for u0 in (ones(32),)
+                ad isa AutoZygote && continue
+
+                solver = LimitedMemoryBroyden(; linesearch)
+                sol = solve_iip(quadratic_f!, u0; solver)
+                @test SciMLBase.successful_retcode(sol)
+                err = maximum(abs, quadratic_f(sol.u, 2.0))
+                @test err < 1e-9
+
+                cache = init(
+                    NonlinearProblem{true}(quadratic_f!, u0, 2.0), solver, abstol = 1e-9
+                )
+                @test (@ballocated solve!($cache)) ≤ 64
+            end
+        end
+    end
+end
+
+@testitem "LimitedMemoryBroyden: Iterator Interface" setup=[CoreRootfindTesting] tags=[:core] begin
+    p = range(0.01, 2, length = 200)
+    @test nlprob_iterator_interface(quadratic_f, p, false, LimitedMemoryBroyden()) ≈
+          sqrt.(p)
+    @test nlprob_iterator_interface(quadratic_f!, p, true, LimitedMemoryBroyden()) ≈
+          sqrt.(p)
+end
+
+@testitem "LimitedMemoryBroyden Termination Conditions" setup=[CoreRootfindTesting] tags=[:core] begin
+    using StaticArrays: @SVector
+
+    @testset "TC: $(nameof(typeof(termination_condition)))" for termination_condition in TERMINATION_CONDITIONS
+        @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0, @SVector([1.0, 1.0]))
+            probN = NonlinearProblem(quadratic_f, u0, 2.0)
+            sol = solve(probN, LimitedMemoryBroyden(); termination_condition)
+            @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-9)
+        end
+    end
+end
diff --git a/lib/NonlinearSolveQuasiNewton/test/qa_tests.jl b/lib/NonlinearSolveQuasiNewton/test/qa_tests.jl
new file mode 100644
index 000000000..badeab3ef
--- /dev/null
+++ b/lib/NonlinearSolveQuasiNewton/test/qa_tests.jl
@@ -0,0 +1,22 @@
+@testitem "Aqua" tags=[:core] begin
+    using Aqua, NonlinearSolveQuasiNewton
+
+    Aqua.test_all(
+        NonlinearSolveQuasiNewton;
+        piracies = false, ambiguities = false, stale_deps = false, deps_compat = false
+    )
+    Aqua.test_stale_deps(NonlinearSolveQuasiNewton; ignore = [:SciMLJacobianOperators])
+    Aqua.test_deps_compat(NonlinearSolveQuasiNewton; ignore = [:SciMLJacobianOperators])
+    Aqua.test_piracies(NonlinearSolveQuasiNewton)
+    Aqua.test_ambiguities(NonlinearSolveQuasiNewton; recursive = false)
+end
+
+@testitem "Explicit Imports" tags=[:core] begin
+    using ExplicitImports, NonlinearSolveQuasiNewton
+
+    @test check_no_implicit_imports(
+        NonlinearSolveQuasiNewton; skip = (Base, Core, SciMLBase)
+    ) === nothing
+    @test check_no_stale_explicit_imports(NonlinearSolveQuasiNewton) === nothing
+    @test check_all_qualified_accesses_via_owners(NonlinearSolveQuasiNewton) === nothing
+end
diff --git a/lib/NonlinearSolveQuasiNewton/test/runtests.jl b/lib/NonlinearSolveQuasiNewton/test/runtests.jl
index 8b1378917..807441bbc 100644
--- a/lib/NonlinearSolveQuasiNewton/test/runtests.jl
+++ b/lib/NonlinearSolveQuasiNewton/test/runtests.jl
@@ -1 +1,23 @@
+using ReTestItems, NonlinearSolveQuasiNewton, Hwloc, InteractiveUtils, Pkg
 
+@info sprint(InteractiveUtils.versioninfo)
+
+const GROUP = lowercase(get(ENV, "GROUP", "All"))
+
+const RETESTITEMS_NWORKERS = parse(
+    Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4)))
+)
+const RETESTITEMS_NWORKER_THREADS = parse(Int,
+    get(
+        ENV, "RETESTITEMS_NWORKER_THREADS",
+        string(max(Hwloc.num_virtual_cores() ÷ RETESTITEMS_NWORKERS, 1))
+    )
+)
+
+@info "Running tests for group: $(GROUP) with $(RETESTITEMS_NWORKERS) workers"
+
+ReTestItems.runtests(
+    NonlinearSolveQuasiNewton; tags = (GROUP == "all" ? nothing : [Symbol(GROUP)]),
+    nworkers = RETESTITEMS_NWORKERS, nworker_threads = RETESTITEMS_NWORKER_THREADS,
+    testitem_timeout = 3600
+)
diff --git a/lib/NonlinearSolveSpectralMethods/test/core_tests.jl b/lib/NonlinearSolveSpectralMethods/test/core_tests.jl
index 7f9a411e4..217086dc4 100644
--- a/lib/NonlinearSolveSpectralMethods/test/core_tests.jl
+++ b/lib/NonlinearSolveSpectralMethods/test/core_tests.jl
@@ -13,7 +13,8 @@ end
     @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
         sol = solve_oop(quadratic_f, u0; solver = DFSane())
         @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+        err = maximum(abs, quadratic_f(sol.u, 2.0))
+        @test err < 1e-9
 
         cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0), DFSane(), abstol = 1e-9)
         @test (@ballocated solve!($cache)) < 200
@@ -22,7 +23,8 @@ end
     @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
         sol = solve_iip(quadratic_f!, u0; solver = DFSane())
         @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
+        err = maximum(abs, quadratic_f(sol.u, 2.0))
+        @test err < 1e-9
 
         cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0), DFSane(), abstol = 1e-9)
         @test (@ballocated solve!($cache)) ≤ 64
@@ -73,8 +75,10 @@ end
 end
 
 @testitem "DFSane Termination Conditions" setup=[CoreRootfindTesting] tags=[:core] begin
+    using StaticArrays: @SVector
+
     @testset "TC: $(nameof(typeof(termination_condition)))" for termination_condition in TERMINATION_CONDITIONS
-        @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0)
+        @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0, @SVector([1.0, 1.0]))
             probN = NonlinearProblem(quadratic_f, u0, 2.0)
             sol = solve(probN, DFSane(); termination_condition)
             @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-10)
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
index 275502d77..ad09ffd2f 100644
--- a/test/core/rootfind_tests.jl
+++ b/test/core/rootfind_tests.jl
@@ -345,52 +345,6 @@ end
     end
 end
 
-# --- DFSane tests ---
-
-@testitem "DFSane" setup=[CoreRootfindTesting] tags=[:core] begin
-    # Test that `DFSane` passes a test that `NewtonRaphson` fails on.
-    @testset "Newton Raphson Fails" begin
-        u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
-        p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
-        sol = benchmark_nlsolve_oop(newton_fails, u0, p; solver = DFSane())
-        @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
-    end
-
-    # Test kwargs in `DFSane`
-    @testset "Keyword Arguments" begin
-        σ_min = [1e-10, 1e-5, 1e-4]
-        σ_max = [1e10, 1e5, 1e4]
-        σ_1 = [1.0, 0.5, 2.0]
-        M = [10, 1, 100]
-        γ = [1e-4, 1e-3, 1e-5]
-        τ_min = [0.1, 0.2, 0.3]
-        τ_max = [0.5, 0.8, 0.9]
-        nexp = [2, 1, 2]
-        η_strategy = [(f_1, k, x, F) -> f_1 / k^2, (f_1, k, x, F) -> f_1 / k^3,
-            (f_1, k, x, F) -> f_1 / k^4]
-
-        list_of_options = zip(σ_min, σ_max, σ_1, M, γ, τ_min, τ_max, nexp, η_strategy)
-        for options in list_of_options
-            local probN, sol, alg
-            alg = DFSane(σ_min = options[1], σ_max = options[2], σ_1 = options[3],
-                M = options[4], γ = options[5], τ_min = options[6],
-                τ_max = options[7], n_exp = options[8], η_strategy = options[9])
-
-            probN = NonlinearProblem{false}(quadratic_f, [1.0, 1.0], 2.0)
-            sol = solve(probN, alg, abstol = 1e-11)
-            @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-6)
-        end
-    end
-
-    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
-        u0 in (1.0, [1.0, 1.0])
-
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, DFSane(); termination_condition).u .≈ sqrt(2.0))
-    end
-end
-
 # --- PseudoTransient tests ---
 
 @testitem "PseudoTransient" setup=[CoreRootfindTesting] tags=[:core] begin
@@ -460,173 +414,6 @@ end
     end
 end
 
-# --- Broyden tests ---
-
-@testitem "Broyden" setup=[CoreRootfindTesting] tags=[:core] begin
-    @testset "LineSearch: $(_nameof(linesearch)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian) Update Rule: $(update_rule)" for ad in (
-            AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()
-        ),
-        linesearch in (
-            LineSearchesStatic(; autodiff = ad), LineSearchesStrongWolfe(; autodiff = ad),
-            LineSearchesBackTracking(; autodiff = ad), BackTracking(; autodiff = ad),
-            LineSearchesHagerZhang(; autodiff = ad),
-            LineSearchesMoreThuente(; autodiff = ad)
-        ),
-        init_jacobian in (Val(:identity), Val(:true_jacobian)),
-        update_rule in (Val(:good_broyden), Val(:bad_broyden), Val(:diagonal))
-
-        u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-
-        @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
-            solver = Broyden(; linesearch, init_jacobian, update_rule)
-            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver)
-            @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-
-            cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0),
-                Broyden(; linesearch, update_rule, init_jacobian), abstol = 1e-9)
-            @test (@ballocated solve!($cache)) < 200
-        end
-
-        @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
-            ad isa AutoZygote && continue
-            solver = Broyden(; linesearch, init_jacobian, update_rule)
-            sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver)
-            @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-
-            cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0),
-                Broyden(; linesearch, update_rule, init_jacobian), abstol = 1e-9)
-            @test (@ballocated solve!($cache)) ≤ 64
-        end
-    end
-
-    # Iterator interface
-    p = range(0.01, 2, length = 200)
-    @test nlprob_iterator_interface(quadratic_f, p, Val(false), Broyden()) ≈ sqrt.(p)
-    @test nlprob_iterator_interface(quadratic_f!, p, Val(true), Broyden()) ≈ sqrt.(p)
-
-    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
-        u0 in (1.0, [1.0, 1.0])
-
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, Broyden(); termination_condition).u .≈ sqrt(2.0))
-    end
-end
-
-# --- Klement tests ---
-
-@testitem "Klement" setup=[CoreRootfindTesting] tags=[:core] begin
-    @testset "LineSearch: $(_nameof(linesearch)) LineSearch AD: $(_nameof(ad)) Init Jacobian: $(init_jacobian)" for ad in (
-            AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()
-        ),
-        linesearch in (
-            LineSearchesStatic(; autodiff = ad), LineSearchesStrongWolfe(; autodiff = ad),
-            LineSearchesBackTracking(; autodiff = ad), BackTracking(; autodiff = ad),
-            LineSearchesHagerZhang(; autodiff = ad),
-            LineSearchesMoreThuente(; autodiff = ad)
-        ),
-        init_jacobian in (Val(:identity), Val(:true_jacobian), Val(:true_jacobian_diagonal))
-
-        u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-
-        @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
-            solver = Klement(; linesearch, init_jacobian)
-            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver)
-            # Some are failing by a margin
-            # @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 3e-9)
-
-            cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0),
-                Klement(; linesearch), abstol = 1e-9)
-            @test (@ballocated solve!($cache)) < 200
-        end
-
-        @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
-            ad isa AutoZygote && continue
-            solver = Klement(; linesearch, init_jacobian)
-            sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver)
-            @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-
-            cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0),
-                Klement(; linesearch), abstol = 1e-9)
-            @test (@ballocated solve!($cache)) ≤ 64
-        end
-    end
-
-    # Iterator interface
-    p = range(0.01, 2, length = 200)
-    @test nlprob_iterator_interface(quadratic_f, p, Val(false), Klement()) ≈ sqrt.(p)
-    @test nlprob_iterator_interface(quadratic_f!, p, Val(true), Klement()) ≈ sqrt.(p)
-
-    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
-        u0 in (1.0, [1.0, 1.0])
-
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, Klement(); termination_condition).u .≈ sqrt(2.0))
-    end
-end
-
-# --- LimitedMemoryBroyden tests ---
-
-@testitem "LimitedMemoryBroyden" setup=[CoreRootfindTesting] tags=[:core] begin
-    @testset "LineSearch: $(_nameof(linesearch)) LineSearch AD: $(_nameof(ad))" for ad in (
-            AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()
-        ),
-        linesearch in (
-            LineSearchesStatic(; autodiff = ad), LineSearchesStrongWolfe(; autodiff = ad),
-            LineSearchesBackTracking(; autodiff = ad), BackTracking(; autodiff = ad),
-            LineSearchesHagerZhang(; autodiff = ad),
-            LineSearchesMoreThuente(; autodiff = ad), LiFukushimaLineSearch()
-        )
-
-        u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-
-        @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
-            broken = linesearch isa BackTracking && ad isa AutoFiniteDiff && u0 isa Vector
-
-            solver = LimitedMemoryBroyden(; linesearch)
-            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver)
-            @test SciMLBase.successful_retcode(sol) broken=broken
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9) broken=broken
-
-            cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0),
-                LimitedMemoryBroyden(; linesearch), abstol = 1e-9)
-            @test (@ballocated solve!($cache)) < 200
-        end
-
-        @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
-            broken = linesearch isa BackTracking && ad isa AutoFiniteDiff && u0 isa Vector
-            ad isa AutoZygote && continue
-
-            solver = LimitedMemoryBroyden(; linesearch)
-            sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver)
-            @test SciMLBase.successful_retcode(sol) broken=broken
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9) broken=broken
-
-            cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0),
-                LimitedMemoryBroyden(; linesearch), abstol = 1e-9)
-            @test (@ballocated solve!($cache)) ≤ 64
-        end
-    end
-
-    # Iterator interface
-    p = range(0.01, 2, length = 200)
-    @test nlprob_iterator_interface(
-        quadratic_f, p, Val(false), LimitedMemoryBroyden())≈sqrt.(p) atol=1e-2
-    @test nlprob_iterator_interface(
-        quadratic_f!, p, Val(true), LimitedMemoryBroyden())≈sqrt.(p) atol=1e-2
-
-    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
-        u0 in (1.0, [1.0, 1.0])
-
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, LimitedMemoryBroyden(); termination_condition).u .≈
-                  sqrt(2.0))
-    end
-end
-
 # Miscellaneous Tests
 @testitem "Custom JVP" setup=[CoreRootfindTesting] tags=[:core] begin
     function F(u::Vector{Float64}, p::Vector{Float64})

From de3e8a27be600bd18b2ee1671e53739eea3a3b93 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 29 Oct 2024 22:33:00 -0400
Subject: [PATCH 655/700] test: first order tests

---
 .../workflows/CI_NonlinearSolveFirstOrder.yml |  71 +++
 common/common_nlls_testing.jl                 |  49 ++
 ..._testing.jl => common_rootfind_testing.jl} |   0
 lib/NonlinearSolveBase/Project.toml           |   4 +-
 .../src/NonlinearSolveBase.jl                 |   3 +-
 lib/NonlinearSolveBase/src/linear_solve.jl    |   2 +-
 lib/NonlinearSolveBase/src/utils.jl           |   6 +
 lib/NonlinearSolveBase/test/runtests.jl       |   9 +
 lib/NonlinearSolveFirstOrder/Project.toml     |  25 +-
 .../src/levenberg_marquardt.jl                |   3 +-
 .../src/pseudo_transient.jl                   |   4 +-
 lib/NonlinearSolveFirstOrder/src/solve.jl     |  67 +--
 .../src/trust_region.jl                       |  12 +-
 .../test/least_squares_tests.jl               |  56 +++
 .../test/misc_tests.jl                        |   2 +-
 lib/NonlinearSolveFirstOrder/test/qa_tests.jl |  20 +
 .../test/rootfind_tests.jl                    | 458 +++++++++++++++++
 lib/NonlinearSolveFirstOrder/test/runtests.jl |  22 +
 .../test/sparsity_tests.jl                    |  79 ++-
 .../test/core_tests.jl                        |  13 +-
 .../test/core_tests.jl                        |   2 +-
 .../src/SciMLJacobianOperators.jl             |   6 +
 test/core/nlls_tests.jl                       | 103 +---
 test/core/rootfind_tests.jl                   | 459 ------------------
 test/misc/banded_matrices_tests.jl            |   8 -
 test/misc/structured_jacobian_tests.jl        |  67 ---
 26 files changed, 855 insertions(+), 695 deletions(-)
 create mode 100644 .github/workflows/CI_NonlinearSolveFirstOrder.yml
 create mode 100644 common/common_nlls_testing.jl
 rename common/{common_core_testing.jl => common_rootfind_testing.jl} (100%)
 create mode 100644 lib/NonlinearSolveFirstOrder/test/least_squares_tests.jl
 rename test/misc/issues_tests.jl => lib/NonlinearSolveFirstOrder/test/misc_tests.jl (89%)
 create mode 100644 lib/NonlinearSolveFirstOrder/test/qa_tests.jl
 create mode 100644 lib/NonlinearSolveFirstOrder/test/rootfind_tests.jl
 rename test/misc/bruss_tests.jl => lib/NonlinearSolveFirstOrder/test/sparsity_tests.jl (50%)
 delete mode 100644 test/core/rootfind_tests.jl
 delete mode 100644 test/misc/banded_matrices_tests.jl
 delete mode 100644 test/misc/structured_jacobian_tests.jl

diff --git a/.github/workflows/CI_NonlinearSolveFirstOrder.yml b/.github/workflows/CI_NonlinearSolveFirstOrder.yml
new file mode 100644
index 000000000..cf9bd427b
--- /dev/null
+++ b/.github/workflows/CI_NonlinearSolveFirstOrder.yml
@@ -0,0 +1,71 @@
+name: CI (NonlinearSolveFirstOrder)
+
+on:
+  pull_request:
+    branches:
+      - master
+    paths:
+      - "lib/NonlinearSolveFirstOrder/**"
+      - ".github/workflows/CI_NonlinearSolveFirstOrder.yml"
+      - "lib/NonlinearSolveBase/**"
+      - "lib/SciMLJacobianOperators/**"
+  push:
+    branches:
+      - master
+
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: only if it is a pull request build.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+
+jobs:
+  test:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "lts"
+          - "1"
+        os:
+          - ubuntu-latest
+          - macos-latest
+          - windows-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: actions/cache@v4
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators", "lib/NonlinearSolveBase")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/NonlinearSolveFirstOrder {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/NonlinearSolveFirstOrder/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/common/common_nlls_testing.jl b/common/common_nlls_testing.jl
new file mode 100644
index 000000000..2888c56e5
--- /dev/null
+++ b/common/common_nlls_testing.jl
@@ -0,0 +1,49 @@
+using NonlinearSolveBase, SciMLBase, StableRNGs, ForwardDiff, Random, LinearAlgebra
+
+true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
+true_function(y, x, θ) = (@. y = θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4]))
+
+θ_true = [1.0, 0.1, 2.0, 0.5]
+x = [-1.0, -0.5, 0.0, 0.5, 1.0]
+
+const y_target = true_function(x, θ_true)
+
+function loss_function(θ, p)
+    ŷ = true_function(p, θ)
+    return ŷ .- y_target
+end
+
+function loss_function(resid, θ, p)
+    true_function(resid, p, θ)
+    resid .= resid .- y_target
+    return resid
+end
+
+θ_init = θ_true .+ randn!(StableRNG(0), similar(θ_true)) * 0.1
+
+function vjp(v, θ, p)
+    resid = zeros(length(p))
+    J = ForwardDiff.jacobian((resid, θ) -> loss_function(resid, θ, p), resid, θ)
+    return vec(v' * J)
+end
+
+function vjp!(Jv, v, θ, p)
+    resid = zeros(length(p))
+    J = ForwardDiff.jacobian((resid, θ) -> loss_function(resid, θ, p), resid, θ)
+    mul!(vec(Jv), transpose(J), v)
+    return nothing
+end
+
+prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
+prob_iip = NonlinearLeastSquaresProblem{true}(
+    NonlinearFunction(loss_function; resid_prototype = zero(y_target)), θ_init, x
+)
+prob_oop_vjp = NonlinearLeastSquaresProblem(
+    NonlinearFunction{false}(loss_function; vjp), θ_init, x
+)
+prob_iip_vjp = NonlinearLeastSquaresProblem(
+    NonlinearFunction{true}(loss_function; resid_prototype = zero(y_target), vjp = vjp!),
+    θ_init, x
+)
+
+export prob_oop, prob_iip, prob_oop_vjp, prob_iip_vjp
diff --git a/common/common_core_testing.jl b/common/common_rootfind_testing.jl
similarity index 100%
rename from common/common_core_testing.jl
rename to common/common_rootfind_testing.jl
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 3c7d16a1c..f6c92aeec 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -83,12 +83,14 @@ julia = "1.10"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Aqua", "DiffEqBase", "ExplicitImports", "ForwardDiff", "InteractiveUtils", "SparseArrays", "Test"]
+test = ["Aqua", "BandedMatrices", "DiffEqBase", "ExplicitImports", "ForwardDiff", "InteractiveUtils", "LinearAlgebra", "SparseArrays", "Test"]
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index a0c5a524c..e9fd61dff 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -57,8 +57,7 @@ include("solve.jl")
 @compat(public, (L2_NORM, Linf_NORM, NAN_CHECK, UNITLESS_ABS2, get_tolerance))
 @compat(public, (nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution))
 @compat(public,
-    (select_forward_mode_autodiff, select_reverse_mode_autodiff,
-        select_jacobian_autodiff))
+    (select_forward_mode_autodiff, select_reverse_mode_autodiff, select_jacobian_autodiff))
 
 # public for NonlinearSolve.jl and subpackages to use
 @compat(public, (InternalAPI, supports_line_search, supports_trust_region, set_du!))
diff --git a/lib/NonlinearSolveBase/src/linear_solve.jl b/lib/NonlinearSolveBase/src/linear_solve.jl
index c19f51829..ab70e2d6c 100644
--- a/lib/NonlinearSolveBase/src/linear_solve.jl
+++ b/lib/NonlinearSolveBase/src/linear_solve.jl
@@ -102,7 +102,7 @@ function (cache::NativeJLLinearSolveCache)(;
     b === nothing || (cache.b = b)
 
     if linu !== nothing && ArrayInterface.can_setindex(linu) &&
-       applicable(ldiv!, linu, cache.A, cache.b)
+       applicable(ldiv!, linu, cache.A, cache.b) && applicable(ldiv!, cache.A, linu)
         ldiv!(linu, cache.A, cache.b)
         res = linu
     else
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 5b0bc2484..a1485debb 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -91,6 +91,12 @@ convert_real(::Type{T}, ::Nothing) where {T} = nothing
 convert_real(::Type{T}, x) where {T} = real(T(x))
 
 restructure(::Number, x::Number) = x
+function restructure(
+        y::T1, x::T2
+) where {T1 <: AbstractSciMLOperator, T2 <: AbstractSciMLOperator}
+    @assert size(y) == size(x) "cannot restructure operators. ensure their sizes match."
+    return x
+end
 restructure(y, x) = ArrayInterface.restructure(y, x)
 
 function safe_similar(x, args...; kwargs...)
diff --git a/lib/NonlinearSolveBase/test/runtests.jl b/lib/NonlinearSolveBase/test/runtests.jl
index 2c745c1c3..8f4f4d8a1 100644
--- a/lib/NonlinearSolveBase/test/runtests.jl
+++ b/lib/NonlinearSolveBase/test/runtests.jl
@@ -24,4 +24,13 @@ using InteractiveUtils, Test
         @test check_no_stale_explicit_imports(NonlinearSolveBase) === nothing
         @test check_all_qualified_accesses_via_owners(NonlinearSolveBase) === nothing
     end
+
+    @testset "Banded Matrix vcat" begin
+        using BandedMatrices, LinearAlgebra, SparseArrays
+
+        b = BandedMatrix(Ones(5, 5), (1, 1))
+        d = Diagonal(ones(5, 5))
+
+        @test NonlinearSolveBase.Utils.faster_vcat(b, d) == vcat(sparse(b), d)
+    end
 end
diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
index 5be145a6e..1a6420468 100644
--- a/lib/NonlinearSolveFirstOrder/Project.toml
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -11,7 +11,6 @@ ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
-LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
@@ -27,41 +26,61 @@ StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 ADTypes = "1.9.0"
 Aqua = "0.8"
 ArrayInterface = "7.16.0"
+BandedMatrices = "1.7.5"
+BenchmarkTools = "1.5.0"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.155.3"
+Enzyme = "0.13.12"
 ExplicitImports = "1.5"
 FiniteDiff = "2.26.0"
 ForwardDiff = "0.10.36"
 Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
 LineSearch = "0.1.4"
-LinearAlgebra = "1.11.0"
+LineSearches = "7.3.0"
+LinearAlgebra = "1.10"
 LinearSolve = "2.36.1"
 MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
 NonlinearSolveBase = "1.1"
 Pkg = "1.10"
 PrecompileTools = "1.2"
+Random = "1.10"
 ReTestItems = "1.24"
 Reexport = "1"
 SciMLBase = "2.54"
+SciMLJacobianOperators = "0.1.0"
 Setfield = "1.1.1"
+SparseConnectivityTracer = "0.6.8"
+SparseMatrixColorings = "0.4.8"
 StableRNGs = "1"
+StaticArrays = "1.9.8"
 StaticArraysCore = "1.4.3"
 Test = "1.10"
+Zygote = "0.6.72"
 julia = "1.10"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 Hwloc = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
+LineSearches = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
 NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
+SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
+SparseMatrixColorings = "0a514795-09f3-496d-8182-132a7b665d35"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "ExplicitImports", "Hwloc", "InteractiveUtils", "NonlinearProblemLibrary", "Pkg", "ReTestItems", "StableRNGs", "Test"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "Enzyme", "ExplicitImports", "Hwloc", "InteractiveUtils", "LineSearch", "LineSearches", "NonlinearProblemLibrary", "Pkg", "Random", "ReTestItems", "SparseConnectivityTracer", "SparseMatrixColorings", "StableRNGs", "StaticArrays", "Test", "Zygote"]
diff --git a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
index d2fedae98..a06378dcb 100644
--- a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
+++ b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
@@ -57,7 +57,8 @@ function LevenbergMarquardt(;
         autodiff,
         vjp_autodiff,
         jvp_autodiff,
-        name = :LevenbergMarquardt
+        name = :LevenbergMarquardt,
+        concrete_jac = Val(true)
     )
 end
 
diff --git a/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl b/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
index 156435859..a985cc100 100644
--- a/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
+++ b/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
@@ -72,9 +72,7 @@ function InternalAPI.init(
 ) where {F}
     T = promote_type(eltype(u), eltype(fu))
     return SwitchedEvolutionRelaxationCache(
-        internalnorm(fu),
-        T(inv(initial_damping)),
-        internalnorm
+        internalnorm(fu), T(inv(initial_damping)), internalnorm
     )
 end
 
diff --git a/lib/NonlinearSolveFirstOrder/src/solve.jl b/lib/NonlinearSolveFirstOrder/src/solve.jl
index c007d5596..b2711ca76 100644
--- a/lib/NonlinearSolveFirstOrder/src/solve.jl
+++ b/lib/NonlinearSolveFirstOrder/src/solve.jl
@@ -89,45 +89,43 @@ end
     kwargs
 end
 
-# XXX: Implement
-# function __reinit_internal!(
-#         cache::GeneralizedFirstOrderAlgorithmCache{iip}, args...; p = cache.p, u0 = cache.u,
-#         alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...) where {iip}
-#     if iip
-#         recursivecopy!(cache.u, u0)
-#         cache.prob.f(cache.fu, cache.u, p)
-#     else
-#         cache.u = __maybe_unaliased(u0, alias_u0)
-#         set_fu!(cache, cache.prob.f(cache.u, p))
-#     end
-#     cache.p = p
-
-#     __reinit_internal!(cache.stats)
-#     cache.nsteps = 0
-#     cache.maxiters = maxiters
-#     cache.maxtime = maxtime
-#     cache.total_time = 0.0
-#     cache.force_stop = false
-#     cache.retcode = ReturnCode.Default
-#     cache.make_new_jacobian = true
-
-#     reset!(cache.trace)
-#     reinit!(cache.termination_cache, get_fu(cache), get_u(cache); kwargs...)
-#     reset_timer!(cache.timer)
-# end
+function InternalAPI.reinit_self!(
+        cache::GeneralizedFirstOrderAlgorithmCache, args...; p = cache.p, u0 = cache.u,
+        alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...
+)
+    Utils.reinit_common!(cache, u0, p, alias_u0)
+
+    InternalAPI.reinit!(cache.stats)
+    cache.nsteps = 0
+    cache.maxiters = maxiters
+    cache.maxtime = maxtime
+    cache.total_time = 0.0
+    cache.force_stop = false
+    cache.retcode = ReturnCode.Default
+    cache.make_new_jacobian = true
+
+    NonlinearSolveBase.reset!(cache.trace)
+    SciMLBase.reinit!(
+        cache.termination_cache, NonlinearSolveBase.get_fu(cache),
+        NonlinearSolveBase.get_u(cache); kwargs...
+    )
+    NonlinearSolveBase.reset_timer!(cache.timer)
+    return
+end
 
 NonlinearSolveBase.@internal_caches(GeneralizedFirstOrderAlgorithmCache,
     :jac_cache, :descent_cache, :linesearch_cache, :trustregion_cache)
 
 function SciMLBase.__init(
-        prob::AbstractNonlinearProblem, alg::GeneralizedFirstOrderAlgorithm,
-        args...; stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, maxiters = 1000,
+        prob::AbstractNonlinearProblem, alg::GeneralizedFirstOrderAlgorithm, args...;
+        stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, maxiters = 1000,
         abstol = nothing, reltol = nothing, maxtime = nothing,
         termination_condition = nothing, internalnorm = L2_NORM,
         linsolve_kwargs = (;), kwargs...
 )
     @set! alg.autodiff = NonlinearSolveBase.select_jacobian_autodiff(prob, alg.autodiff)
-    @set! alg.jvp_autodiff = if alg.jvp_autodiff === nothing && alg.autodiff !== nothing &&
+    provided_jvp_autodiff = alg.jvp_autodiff !== nothing
+    @set! alg.jvp_autodiff = if !provided_jvp_autodiff && alg.autodiff !== nothing &&
                                 (ADTypes.mode(alg.autodiff) isa ADTypes.ForwardMode ||
                                  ADTypes.mode(alg.autodiff) isa
                                  ADTypes.ForwardOrReverseMode)
@@ -135,7 +133,8 @@ function SciMLBase.__init(
     else
         NonlinearSolveBase.select_forward_mode_autodiff(prob, alg.jvp_autodiff)
     end
-    @set! alg.vjp_autodiff = if alg.vjp_autodiff === nothing && alg.autodiff !== nothing &&
+    provided_vjp_autodiff = alg.vjp_autodiff !== nothing
+    @set! alg.vjp_autodiff = if !provided_vjp_autodiff && alg.autodiff !== nothing &&
                                 (ADTypes.mode(alg.autodiff) isa ADTypes.ReverseMode ||
                                  ADTypes.mode(alg.autodiff) isa
                                  ADTypes.ForwardOrReverseMode)
@@ -185,7 +184,7 @@ function SciMLBase.__init(
                 error("Trust Region not supported by $(alg.descent).")
             trustregion_cache = InternalAPI.init(
                 prob, alg.trustregion, prob.f, fu, u, prob.p;
-                stats, internalnorm, kwargs...
+                alg.vjp_autodiff, alg.jvp_autodiff, stats, internalnorm, kwargs...
             )
             globalization = Val(:TrustRegion)
         end
@@ -194,7 +193,11 @@ function SciMLBase.__init(
             NonlinearSolveBase.supports_line_search(alg.descent) ||
                 error("Line Search not supported by $(alg.descent).")
             linesearch_cache = CommonSolve.init(
-                prob, alg.linesearch, fu, u; stats, internalnorm, kwargs...
+                prob, alg.linesearch, fu, u; stats, internalnorm,
+                autodiff = ifelse(
+                    provided_jvp_autodiff, alg.jvp_autodiff, alg.vjp_autodiff
+                ),
+                kwargs...
             )
             globalization = Val(:LineSearch)
         end
diff --git a/lib/NonlinearSolveFirstOrder/src/trust_region.jl b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
index 249d4fa72..f76b77601 100644
--- a/lib/NonlinearSolveFirstOrder/src/trust_region.jl
+++ b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
@@ -363,7 +363,9 @@ end
 
 expand_factor(::Nothing, ::Type{T}, method) where {T} = T(2)
 
-function rfunc_adaptive_trust_region(r::R, c2::R, M::R, γ1::R, β::R) where {R <: Real}
+function rfunc_adaptive_trust_region(
+        r::R, c2::R, M::R, γ1::R, γ2::R, β::R
+) where {R <: Real}
     return ifelse(
         r ≥ c2,
         (2 * (M - 1 - γ2) * atan(r - c2) + (1 + γ2)) / R(π),
@@ -433,8 +435,8 @@ function InternalAPI.solve!(
         end
     elseif cache.method isa RUS.__Hei
         tr_new = rfunc_adaptive_trust_region(
-            cache.ρ, cache.shrink_threshold, cache.p1, cache.p3, cache.p4
-        )
+            cache.ρ, cache.shrink_threshold, cache.p1, cache.p3, cache.p4, cache.p2
+        ) * cache.internalnorm(δu)
         if tr_new < cache.trust_region
             cache.shrink_counter += 1
         else
@@ -471,9 +473,9 @@ function InternalAPI.solve!(
             vjp_op = StatefulJacobianOperator(cache.vjp_operator, cache.u_cache, cache.p)
             @bb cache.Jδu_cache = jvp_op × vec(cache.δu_cache)
             @bb cache.Jᵀfu_cache = vjp_op × vec(cache.fu_cache)
-            denom_1 = dot(_vec(cache.Jᵀfu_cache), cache.Jᵀfu_cache)
+            denom_1 = dot(Utils.safe_vec(cache.Jᵀfu_cache), cache.Jᵀfu_cache)
             @bb cache.Jᵀfu_cache = vjp_op × vec(cache.Jδu_cache)
-            denom_2 = dot(_vec(cache.Jᵀfu_cache), cache.Jᵀfu_cache)
+            denom_2 = dot(Utils.safe_vec(cache.Jᵀfu_cache), cache.Jᵀfu_cache)
             denom = denom_1 + denom_2 / 2
             ρ = num / denom
             if ρ ≥ cache.expand_threshold
diff --git a/lib/NonlinearSolveFirstOrder/test/least_squares_tests.jl b/lib/NonlinearSolveFirstOrder/test/least_squares_tests.jl
new file mode 100644
index 000000000..bf6ed48c8
--- /dev/null
+++ b/lib/NonlinearSolveFirstOrder/test/least_squares_tests.jl
@@ -0,0 +1,56 @@
+@testsetup module CoreNLLSTesting
+
+using NonlinearSolveFirstOrder, LineSearch, ADTypes, LinearSolve
+using LineSearches: LineSearches
+using ForwardDiff, FiniteDiff, Zygote
+
+include("../../../common/common_nlls_testing.jl")
+
+linesearches = []
+for lsmethod in [
+    LineSearches.Static(), LineSearches.HagerZhang(), LineSearches.MoreThuente(),
+    LineSearches.StrongWolfe(), LineSearches.BackTracking()
+]
+    push!(linesearches, LineSearchesJL(; method = lsmethod))
+end
+push!(linesearches, BackTracking())
+
+solvers = []
+for linsolve in [nothing, LUFactorization(), KrylovJL_GMRES(), KrylovJL_LSMR()]
+    vjp_autodiffs = linsolve isa KrylovJL ? [nothing, AutoZygote(), AutoFiniteDiff()] :
+                    [nothing]
+    for linesearch in linesearches, vjp_autodiff in vjp_autodiffs
+        push!(solvers, GaussNewton(; linsolve, linesearch, vjp_autodiff))
+    end
+end
+append!(solvers,
+    [
+        LevenbergMarquardt(),
+        LevenbergMarquardt(; linsolve = LUFactorization()),
+        LevenbergMarquardt(; linsolve = KrylovJL_GMRES()),
+        LevenbergMarquardt(; linsolve = KrylovJL_LSMR())
+    ]
+)
+for radius_update_scheme in [
+    RadiusUpdateSchemes.Simple, RadiusUpdateSchemes.NocedalWright,
+    RadiusUpdateSchemes.NLsolve, RadiusUpdateSchemes.Hei,
+    RadiusUpdateSchemes.Yuan, RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin
+]
+    push!(solvers, TrustRegion(; radius_update_scheme))
+end
+
+export solvers
+
+end
+
+@testitem "General NLLS Solvers" setup=[CoreNLLSTesting] tags=[:core] begin
+    using LinearAlgebra
+
+    nlls_problems = [prob_oop, prob_iip, prob_oop_vjp, prob_iip_vjp]
+
+    for prob in nlls_problems, solver in solvers
+        sol = solve(prob, solver; maxiters = 10000, abstol = 1e-6)
+        @test SciMLBase.successful_retcode(sol)
+        @test norm(sol.resid, 2) < 1e-6
+    end
+end
diff --git a/test/misc/issues_tests.jl b/lib/NonlinearSolveFirstOrder/test/misc_tests.jl
similarity index 89%
rename from test/misc/issues_tests.jl
rename to lib/NonlinearSolveFirstOrder/test/misc_tests.jl
index 24e39943c..40fcb2c55 100644
--- a/test/misc/issues_tests.jl
+++ b/lib/NonlinearSolveFirstOrder/test/misc_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Issue #451" tags=[:misc] begin
+@testitem "Scalar Jacobians: Issue #451" tags=[:core] begin
     f(u, p) = u^2 - p
 
     jac_calls = 0
diff --git a/lib/NonlinearSolveFirstOrder/test/qa_tests.jl b/lib/NonlinearSolveFirstOrder/test/qa_tests.jl
new file mode 100644
index 000000000..7bf163723
--- /dev/null
+++ b/lib/NonlinearSolveFirstOrder/test/qa_tests.jl
@@ -0,0 +1,20 @@
+@testitem "Aqua" tags=[:core] begin
+    using Aqua, NonlinearSolveFirstOrder
+
+    Aqua.test_all(
+        NonlinearSolveFirstOrder;
+        piracies = false, ambiguities = false
+    )
+    Aqua.test_piracies(NonlinearSolveFirstOrder)
+    Aqua.test_ambiguities(NonlinearSolveFirstOrder; recursive = false)
+end
+
+@testitem "Explicit Imports" tags=[:core] begin
+    using ExplicitImports, NonlinearSolveFirstOrder
+
+    @test check_no_implicit_imports(
+        NonlinearSolveFirstOrder; skip = (Base, Core, SciMLBase)
+    ) === nothing
+    @test check_no_stale_explicit_imports(NonlinearSolveFirstOrder) === nothing
+    @test check_all_qualified_accesses_via_owners(NonlinearSolveFirstOrder) === nothing
+end
diff --git a/lib/NonlinearSolveFirstOrder/test/rootfind_tests.jl b/lib/NonlinearSolveFirstOrder/test/rootfind_tests.jl
new file mode 100644
index 000000000..f554e02d6
--- /dev/null
+++ b/lib/NonlinearSolveFirstOrder/test/rootfind_tests.jl
@@ -0,0 +1,458 @@
+@testsetup module CoreRootfindTesting
+
+include("../../../common/common_rootfind_testing.jl")
+
+end
+
+@testitem "NewtonRaphson" setup=[CoreRootfindTesting] tags=[:core] begin
+    using ADTypes, LineSearch, LinearAlgebra, Random, LinearSolve
+    using LineSearches: LineSearches
+    using BenchmarkTools: @ballocated
+    using StaticArrays: @SVector
+    using Zygote, Enzyme, ForwardDiff, FiniteDiff
+
+    u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
+
+    preconditioners = [
+        u0 -> nothing,
+        u0 -> ((args...) -> (Diagonal(rand!(similar(u0))), nothing))
+    ]
+
+    @testset for ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff(), AutoEnzyme())
+        @testset "$(nameof(typeof(linesearch)))" for linesearch in (
+            LineSearchesJL(; method = LineSearches.Static(), autodiff = ad),
+            LineSearchesJL(; method = LineSearches.BackTracking(), autodiff = ad),
+            LineSearchesJL(; method = LineSearches.MoreThuente(), autodiff = ad),
+            LineSearchesJL(; method = LineSearches.StrongWolfe(), autodiff = ad),
+            LineSearchesJL(; method = LineSearches.HagerZhang(), autodiff = ad),
+            BackTracking(; autodiff = ad)
+        )
+            @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
+                solver = NewtonRaphson(; linesearch, autodiff = ad)
+                sol = solve_oop(quadratic_f, u0; solver)
+                @test SciMLBase.successful_retcode(sol)
+                err = maximum(abs, quadratic_f(sol.u, 2.0))
+                @test err < 1e-9
+
+                cache = init(
+                    NonlinearProblem{false}(quadratic_f, u0, 2.0), solver, abstol = 1e-9
+                )
+                @test (@ballocated solve!($cache)) < 200
+            end
+
+            @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+                ad isa AutoZygote && continue
+
+                @testset for preconditioner in preconditioners,
+                    linsolve in (nothing, KrylovJL_GMRES(), \)
+
+                    precs = preconditioner(u0)
+                    typeof(linsolve) <: typeof(\) && precs !== nothing && continue
+
+                    solver = NewtonRaphson(; linsolve, precs, linesearch, autodiff = ad)
+
+                    sol = solve_iip(quadratic_f!, u0; solver)
+                    @test SciMLBase.successful_retcode(sol)
+                    err = maximum(abs, quadratic_f(sol.u, 2.0))
+                    @test err < 1e-9
+
+                    cache = init(
+                        NonlinearProblem{true}(quadratic_f!, u0, 2.0), solver, abstol = 1e-9
+                    )
+                    @test (@ballocated solve!($cache)) ≤ 64
+                end
+            end
+        end
+    end
+end
+
+@testitem "NewtonRaphson: Iterator Interface" setup=[CoreRootfindTesting] tags=[:core] begin
+    p = range(0.01, 2, length = 200)
+    @test nlprob_iterator_interface(quadratic_f, p, false, NewtonRaphson()) ≈ sqrt.(p)
+    @test nlprob_iterator_interface(quadratic_f!, p, true, NewtonRaphson()) ≈ sqrt.(p)
+end
+
+@testitem "NewtonRaphson Termination Conditions" setup=[CoreRootfindTesting] tags=[:core] begin
+    using StaticArrays: @SVector
+
+    @testset "TC: $(nameof(typeof(termination_condition)))" for termination_condition in TERMINATION_CONDITIONS
+        @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0, @SVector([1.0, 1.0]))
+            probN = NonlinearProblem(quadratic_f, u0, 2.0)
+            sol = solve(probN, NewtonRaphson(); termination_condition)
+            err = maximum(abs, quadratic_f(sol.u, 2.0))
+            @test err < 1e-9
+        end
+    end
+end
+
+@testitem "PseudoTransient" setup=[CoreRootfindTesting] tags=[:core] begin
+    using ADTypes, Random, LinearSolve, LinearAlgebra
+    using BenchmarkTools: @ballocated
+    using StaticArrays: @SVector
+    using Zygote, Enzyme, ForwardDiff, FiniteDiff
+
+    preconditioners = [
+        (u0) -> nothing,
+        u0 -> ((args...) -> (Diagonal(rand!(similar(u0))), nothing))
+    ]
+
+    @testset for ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff(), AutoEnzyme())
+        u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
+
+        @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
+            solver = PseudoTransient(; alpha_initial = 10.0, autodiff = ad)
+            sol = solve_oop(quadratic_f, u0; solver)
+            @test SciMLBase.successful_retcode(sol)
+            err = maximum(abs, quadratic_f(sol.u, 2.0))
+            @test err < 1e-9
+
+            cache = init(
+                NonlinearProblem{false}(quadratic_f, u0, 2.0), solver, abstol = 1e-9
+            )
+            @test (@ballocated solve!($cache)) < 200
+        end
+
+        @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+            ad isa AutoZygote && continue
+
+            @testset for preconditioner in preconditioners,
+                linsolve in (nothing, KrylovJL_GMRES(), \)
+
+                precs = preconditioner(u0)
+                typeof(linsolve) <: typeof(\) && precs !== nothing && continue
+
+                solver = PseudoTransient(;
+                    alpha_initial = 10.0, linsolve, precs, autodiff = ad)
+                sol = solve_iip(quadratic_f!, u0; solver)
+                @test SciMLBase.successful_retcode(sol)
+                err = maximum(abs, quadratic_f(sol.u, 2.0))
+                @test err < 1e-9
+
+                cache = init(
+                    NonlinearProblem{true}(quadratic_f!, u0, 2.0), solver, abstol = 1e-9
+                )
+                @test (@ballocated solve!($cache)) ≤ 64
+            end
+        end
+    end
+end
+
+@testitem "PseudoTransient: Iterator Interface" setup=[CoreRootfindTesting] tags=[:core] begin
+    p = range(0.01, 2, length = 200)
+    @test nlprob_iterator_interface(
+        quadratic_f, p, false, PseudoTransient(; alpha_initial = 10.0)
+    ) ≈ sqrt.(p)
+    @test nlprob_iterator_interface(
+        quadratic_f!, p, true, PseudoTransient(; alpha_initial = 10.0)
+    ) ≈ sqrt.(p)
+end
+
+@testitem "PseudoTransient Termination Conditions" setup=[CoreRootfindTesting] tags=[:core] begin
+    using StaticArrays: @SVector
+
+    @testset "TC: $(nameof(typeof(termination_condition)))" for termination_condition in TERMINATION_CONDITIONS
+        @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0, @SVector([1.0, 1.0]))
+            probN = NonlinearProblem(quadratic_f, u0, 2.0)
+            sol = solve(probN, PseudoTransient(); termination_condition)
+            err = maximum(abs, quadratic_f(sol.u, 2.0))
+            @test err < 1e-9
+        end
+    end
+end
+
+@testitem "TrustRegion" setup=[CoreRootfindTesting] tags=[:core] begin
+    using ADTypes, LinearSolve, LinearAlgebra
+    using BenchmarkTools: @ballocated
+    using StaticArrays: @SVector
+    using Zygote, Enzyme, ForwardDiff, FiniteDiff
+
+    radius_update_schemes = [
+        RadiusUpdateSchemes.Simple, RadiusUpdateSchemes.NocedalWright,
+        RadiusUpdateSchemes.NLsolve, RadiusUpdateSchemes.Hei,
+        RadiusUpdateSchemes.Yuan, RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin
+    ]
+
+    @testset for ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff(), AutoEnzyme())
+        @testset for radius_update_scheme in radius_update_schemes,
+            linsolve in (nothing, LUFactorization(), KrylovJL_GMRES(), \)
+
+            @testset "[OOP] u0: $(typeof(u0))" for u0 in (
+                [1.0, 1.0], 1.0, @SVector[1.0, 1.0], 1.0)
+                abstol = ifelse(linsolve isa KrylovJL, 1e-6, 1e-9)
+                solver = TrustRegion(; radius_update_scheme, linsolve)
+                sol = solve_oop(quadratic_f, u0; solver, abstol)
+                @test SciMLBase.successful_retcode(sol)
+                err = maximum(abs, quadratic_f(sol.u, 2.0))
+                @test err < abstol
+
+                cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0), solver, abstol)
+                @test (@ballocated solve!($cache)) < 200
+            end
+
+            @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+                ad isa AutoZygote && continue
+
+                abstol = ifelse(linsolve isa KrylovJL, 1e-6, 1e-9)
+                solver = TrustRegion(; radius_update_scheme, linsolve)
+                sol = solve_iip(quadratic_f!, u0; solver, abstol)
+                @test SciMLBase.successful_retcode(sol)
+                err = maximum(abs, quadratic_f(sol.u, 2.0))
+                @test err < abstol
+
+                cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0), solver, abstol)
+                @test (@ballocated solve!($cache)) ≤ 64
+            end
+        end
+    end
+end
+
+@testitem "TrustRegion: Iterator Interface" setup=[CoreRootfindTesting] tags=[:core] begin
+    p = range(0.01, 2, length = 200)
+    @test nlprob_iterator_interface(quadratic_f, p, false, TrustRegion()) ≈ sqrt.(p)
+    @test nlprob_iterator_interface(quadratic_f!, p, true, TrustRegion()) ≈ sqrt.(p)
+end
+
+@testitem "TrustRegion NewtonRaphson Fails" setup=[CoreRootfindTesting] tags=[:core] begin
+    u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
+    p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+    sol = solve_oop(newton_fails, u0, p; solver = TrustRegion())
+    @test SciMLBase.successful_retcode(sol)
+    @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
+end
+
+@testitem "TrustRegion: Kwargs" setup=[CoreRootfindTesting] tags=[:core] begin
+    max_trust_radius = [10.0, 100.0, 1000.0]
+    initial_trust_radius = [10.0, 1.0, 0.1]
+    step_threshold = [0.0, 0.01, 0.25]
+    shrink_threshold = [0.25, 0.3, 0.5]
+    expand_threshold = [0.5, 0.8, 0.9]
+    shrink_factor = [0.1, 0.3, 0.5]
+    expand_factor = [1.5, 2.0, 3.0]
+    max_shrink_times = [10, 20, 30]
+
+    list_of_options = zip(
+        max_trust_radius, initial_trust_radius, step_threshold, shrink_threshold,
+        expand_threshold, shrink_factor, expand_factor, max_shrink_times
+    )
+
+    for options in list_of_options
+        alg = TrustRegion(;
+            max_trust_radius = options[1], initial_trust_radius = options[2],
+            step_threshold = options[3], shrink_threshold = options[4],
+            expand_threshold = options[5], shrink_factor = options[6],
+            expand_factor = options[7], max_shrink_times = options[8]
+        )
+
+        sol = solve_oop(quadratic_f, [1.0, 1.0], 2.0; solver = alg)
+        @test SciMLBase.successful_retcode(sol)
+        err = maximum(abs, quadratic_f(sol.u, 2.0))
+        @test err < 1e-9
+    end
+end
+
+@testitem "TrustRegion OOP / IIP Consistency" setup=[CoreRootfindTesting] tags=[:core] begin
+    maxiterations = [2, 3, 4, 5]
+    u0 = [1.0, 1.0]
+    @testset for radius_update_scheme in [
+        RadiusUpdateSchemes.Simple, RadiusUpdateSchemes.NocedalWright,
+        RadiusUpdateSchemes.NLsolve, RadiusUpdateSchemes.Hei,
+        RadiusUpdateSchemes.Yuan, RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin
+    ]
+        @testset for maxiters in maxiterations
+            solver = TrustRegion(; radius_update_scheme)
+            sol_iip = solve_iip(quadratic_f!, u0; solver, maxiters)
+            sol_oop = solve_oop(quadratic_f, u0; solver, maxiters)
+            @test sol_iip.u ≈ sol_oop.u
+        end
+    end
+end
+
+@testitem "TrustRegion Termination Conditions" setup=[CoreRootfindTesting] tags=[:core] begin
+    using StaticArrays: @SVector
+
+    @testset "TC: $(nameof(typeof(termination_condition)))" for termination_condition in TERMINATION_CONDITIONS
+        @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0, @SVector([1.0, 1.0]))
+            probN = NonlinearProblem(quadratic_f, u0, 2.0)
+            sol = solve(probN, TrustRegion(); termination_condition)
+            err = maximum(abs, quadratic_f(sol.u, 2.0))
+            @test err < 1e-9
+        end
+    end
+end
+
+@testitem "LevenbergMarquardt" setup=[CoreRootfindTesting] tags=[:core] begin
+    using ADTypes, LinearSolve, LinearAlgebra
+    using BenchmarkTools: @ballocated
+    using StaticArrays: SVector, @SVector
+    using Zygote, Enzyme, ForwardDiff, FiniteDiff
+
+    @testset for ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff(), AutoEnzyme())
+        solver = LevenbergMarquardt(; autodiff = ad)
+
+        @testset "[OOP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0, @SVector([1.0, 1.0]))
+            if ad isa ADTypes.AutoZygote && u0 isa SVector
+                # Zygote converts SVector to a Matrix that triggers a bug upstream
+                @test_broken solve_oop(quadratic_f, u0; solver)
+                continue
+            end
+
+            sol = solve_oop(quadratic_f, u0; solver)
+            @test SciMLBase.successful_retcode(sol)
+            err = maximum(abs, quadratic_f(sol.u, 2.0))
+            @test err < 1e-9
+
+            cache = init(
+                NonlinearProblem{false}(quadratic_f, u0, 2.0),
+                LevenbergMarquardt(), abstol = 1e-9
+            )
+            @test (@ballocated solve!($cache)) < 200
+        end
+
+        @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
+            ad isa AutoZygote && continue
+
+            sol = solve_iip(quadratic_f!, u0; solver)
+            @test SciMLBase.successful_retcode(sol)
+            err = maximum(abs, quadratic_f(sol.u, 2.0))
+            @test err < 1e-9
+
+            cache = init(
+                NonlinearProblem{true}(quadratic_f!, u0, 2.0),
+                LevenbergMarquardt(), abstol = 1e-9
+            )
+            @test (@ballocated solve!($cache)) ≤ 64
+        end
+    end
+end
+
+@testitem "LevenbergMarquardt NewtonRaphson Fails" setup=[CoreRootfindTesting] tags=[:core] begin
+    u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
+    p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+    sol = solve_oop(newton_fails, u0, p; solver = LevenbergMarquardt())
+    @test SciMLBase.successful_retcode(sol)
+    @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
+end
+
+@testitem "LevenbergMarquardt: Iterator Interface" setup=[CoreRootfindTesting] tags=[:core] begin
+    p = range(0.01, 2, length = 200)
+    @test nlprob_iterator_interface(quadratic_f, p, false, LevenbergMarquardt()) ≈ sqrt.(p)
+    @test nlprob_iterator_interface(quadratic_f!, p, true, LevenbergMarquardt()) ≈ sqrt.(p)
+end
+
+@testitem "LevenbergMarquardt Termination Conditions" setup=[CoreRootfindTesting] tags=[:core] begin
+    using StaticArrays: @SVector
+
+    @testset "TC: $(nameof(typeof(termination_condition)))" for termination_condition in TERMINATION_CONDITIONS
+        @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0, @SVector([1.0, 1.0]))
+            probN = NonlinearProblem(quadratic_f, u0, 2.0)
+            sol = solve(probN, LevenbergMarquardt(); termination_condition)
+            err = maximum(abs, quadratic_f(sol.u, 2.0))
+            @test err < 1e-9
+        end
+    end
+end
+
+@testitem "LevenbergMarquardt: Kwargs" setup=[CoreRootfindTesting] tags=[:core] begin
+    damping_initial = [0.5, 2.0, 5.0]
+    damping_increase_factor = [1.5, 3.0, 10.0]
+    damping_decrease_factor = Float64[2, 5, 10.0]
+    finite_diff_step_geodesic = [0.02, 0.2, 0.3]
+    α_geodesic = [0.6, 0.8, 0.9]
+    b_uphill = Float64[0, 1, 2]
+    min_damping_D = [1e-12, 1e-9, 1e-4]
+
+    list_of_options = zip(
+        damping_initial, damping_increase_factor, damping_decrease_factor,
+        finite_diff_step_geodesic, α_geodesic, b_uphill, min_damping_D
+    )
+    for options in list_of_options
+        alg = LevenbergMarquardt(;
+            damping_initial = options[1], damping_increase_factor = options[2],
+            damping_decrease_factor = options[3],
+            finite_diff_step_geodesic = options[4], α_geodesic = options[5],
+            b_uphill = options[6], min_damping_D = options[7]
+        )
+
+        sol = solve_oop(quadratic_f, [1.0, 1.0], 2.0; solver = alg, maxiters = 10000)
+        @test SciMLBase.successful_retcode(sol)
+        err = maximum(abs, quadratic_f(sol.u, 2.0))
+        @test err < 1e-9
+    end
+end
+
+@testitem "Simple Sparse AutoDiff" setup=[CoreRootfindTesting] tags=[:core] begin
+    using ADTypes, SparseConnectivityTracer, SparseMatrixColorings
+
+    @testset for ad in (AutoForwardDiff(), AutoFiniteDiff(), AutoZygote(), AutoEnzyme())
+        @testset for u0 in ([1.0, 1.0], 1.0)
+            prob = NonlinearProblem(
+                NonlinearFunction(quadratic_f; sparsity = TracerSparsityDetector()), u0, 2.0
+            )
+
+            @testset "Newton Raphson" begin
+                sol = solve(prob, NewtonRaphson(; autodiff = ad))
+                err = maximum(abs, quadratic_f(sol.u, 2.0))
+                @test err < 1e-9
+            end
+
+            @testset "Trust Region" begin
+                sol = solve(prob, TrustRegion(; autodiff = ad))
+                err = maximum(abs, quadratic_f(sol.u, 2.0))
+                @test err < 1e-9
+            end
+        end
+    end
+end
+
+@testitem "Custom JVP" setup=[CoreRootfindTesting] tags=[:core] begin
+    using LinearAlgebra, LinearSolve, ADTypes
+
+    function F(u::Vector{Float64}, p::Vector{Float64})
+        Δ = Tridiagonal(-ones(99), 2 * ones(100), -ones(99))
+        return u + 0.1 * u .* Δ * u - p
+    end
+
+    function F!(du::Vector{Float64}, u::Vector{Float64}, p::Vector{Float64})
+        Δ = Tridiagonal(-ones(99), 2 * ones(100), -ones(99))
+        du .= u + 0.1 * u .* Δ * u - p
+        return nothing
+    end
+
+    function JVP(v::Vector{Float64}, u::Vector{Float64}, p::Vector{Float64})
+        Δ = Tridiagonal(-ones(99), 2 * ones(100), -ones(99))
+        return v + 0.1 * (u .* Δ * v + v .* Δ * u)
+    end
+
+    function JVP!(
+            du::Vector{Float64}, v::Vector{Float64}, u::Vector{Float64}, p::Vector{Float64})
+        Δ = Tridiagonal(-ones(99), 2 * ones(100), -ones(99))
+        du .= v + 0.1 * (u .* Δ * v + v .* Δ * u)
+        return nothing
+    end
+
+    u0 = rand(100)
+
+    prob = NonlinearProblem(NonlinearFunction{false}(F; jvp = JVP), u0, u0)
+    sol = solve(prob, NewtonRaphson(; linsolve = KrylovJL_GMRES()); abstol = 1e-13)
+    err = maximum(abs, sol.resid)
+    @test err < 1e-6
+
+    sol = solve(
+        prob, TrustRegion(; linsolve = KrylovJL_GMRES(), vjp_autodiff = AutoFiniteDiff());
+        abstol = 1e-13
+    )
+    err = maximum(abs, sol.resid)
+    @test err < 1e-6
+
+    prob = NonlinearProblem(NonlinearFunction{true}(F!; jvp = JVP!), u0, u0)
+    sol = solve(prob, NewtonRaphson(; linsolve = KrylovJL_GMRES()); abstol = 1e-13)
+    err = maximum(abs, sol.resid)
+    @test err < 1e-6
+
+    sol = solve(
+        prob, TrustRegion(; linsolve = KrylovJL_GMRES(), vjp_autodiff = AutoFiniteDiff());
+        abstol = 1e-13
+    )
+    err = maximum(abs, sol.resid)
+    @test err < 1e-6
+end
diff --git a/lib/NonlinearSolveFirstOrder/test/runtests.jl b/lib/NonlinearSolveFirstOrder/test/runtests.jl
index 8b1378917..d19d33de8 100644
--- a/lib/NonlinearSolveFirstOrder/test/runtests.jl
+++ b/lib/NonlinearSolveFirstOrder/test/runtests.jl
@@ -1 +1,23 @@
+using ReTestItems, NonlinearSolveFirstOrder, Hwloc, InteractiveUtils, Pkg
 
+@info sprint(InteractiveUtils.versioninfo)
+
+const GROUP = lowercase(get(ENV, "GROUP", "All"))
+
+const RETESTITEMS_NWORKERS = parse(
+    Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4)))
+)
+const RETESTITEMS_NWORKER_THREADS = parse(Int,
+    get(
+        ENV, "RETESTITEMS_NWORKER_THREADS",
+        string(max(Hwloc.num_virtual_cores() ÷ RETESTITEMS_NWORKERS, 1))
+    )
+)
+
+@info "Running tests for group: $(GROUP) with $(RETESTITEMS_NWORKERS) workers"
+
+ReTestItems.runtests(
+    NonlinearSolveFirstOrder; tags = (GROUP == "all" ? nothing : [Symbol(GROUP)]),
+    nworkers = RETESTITEMS_NWORKERS, nworker_threads = RETESTITEMS_NWORKER_THREADS,
+    testitem_timeout = 3600
+)
diff --git a/test/misc/bruss_tests.jl b/lib/NonlinearSolveFirstOrder/test/sparsity_tests.jl
similarity index 50%
rename from test/misc/bruss_tests.jl
rename to lib/NonlinearSolveFirstOrder/test/sparsity_tests.jl
index 32a3fff68..3e4df284f 100644
--- a/test/misc/bruss_tests.jl
+++ b/lib/NonlinearSolveFirstOrder/test/sparsity_tests.jl
@@ -1,5 +1,6 @@
-@testitem "Brusselator 2D" tags=[:misc] begin
-    using LinearAlgebra, SparseArrays, SparseConnectivityTracer, ADTypes
+@testitem "Brusselator 2D" tags=[:core] begin
+    using LinearAlgebra, SparseArrays, SparseConnectivityTracer, ADTypes,
+          SparseMatrixColorings
 
     const N = 32
     const xyd_brusselator = range(0, stop = 1, length = N)
@@ -48,7 +49,8 @@
 
     prob_brusselator_2d_sparse = NonlinearProblem(
         NonlinearFunction(brusselator_2d_loop; sparsity = TracerSparsityDetector()),
-        u0, p)
+        u0, p
+    )
     sol = solve(prob_brusselator_2d_sparse, NewtonRaphson(); abstol = 1e-8)
     @test norm(sol.resid, Inf) < 1e-8
 
@@ -63,6 +65,75 @@
     @test norm(sol.resid, Inf) < 1e-8
 
     sol = solve(prob_brusselator_2d,
-        NewtonRaphson(autodiff = AutoFiniteDiff()); abstol = 1e-8)
+        NewtonRaphson(autodiff = AutoFiniteDiff()); abstol = 1e-8
+    )
     @test norm(sol.resid, Inf) < 1e-8
 end
+
+@testitem "Structured Jacobians" tags=[:core] begin
+    using SparseConnectivityTracer, BandedMatrices, LinearAlgebra, SparseArrays,
+          SparseMatrixColorings
+
+    N = 16
+    p = rand(N)
+    u0 = rand(N)
+
+    function f!(du, u, p)
+        for i in 2:(length(u) - 1)
+            du[i] = u[i - 1] - 2u[i] + u[i + 1] + p[i]
+        end
+        du[1] = -2u[1] + u[2] + p[1]
+        du[end] = u[end - 1] - 2u[end] + p[end]
+        return nothing
+    end
+
+    function f(u, p)
+        du = similar(u, promote_type(eltype(u), eltype(p)))
+        f!(du, u, p)
+        return du
+    end
+
+    for nlf in (f, f!)
+        @testset "Dense AD" begin
+            nlprob = NonlinearProblem(NonlinearFunction(nlf), u0, p)
+
+            cache = init(nlprob, NewtonRaphson(); abstol = 1e-9)
+            @test cache.jac_cache.J isa Matrix
+            sol = solve!(cache)
+            @test SciMLBase.successful_retcode(sol)
+        end
+
+        @testset "Unstructured Sparse AD" begin
+            nlprob_autosparse = NonlinearProblem(
+                NonlinearFunction(nlf; sparsity = TracerSparsityDetector()),
+                u0, p)
+
+            cache = init(nlprob_autosparse, NewtonRaphson(); abstol = 1e-9)
+            @test cache.jac_cache.J isa SparseMatrixCSC
+            sol = solve!(cache)
+            @test SciMLBase.successful_retcode(sol)
+        end
+
+        @testset "Structured Sparse AD: Banded Jacobian" begin
+            jac_prototype = BandedMatrix(-1 => ones(N - 1), 0 => ones(N), 1 => ones(N - 1))
+            nlprob_sparse_structured = NonlinearProblem(
+                NonlinearFunction(nlf; jac_prototype), u0, p)
+
+            cache = init(nlprob_sparse_structured, NewtonRaphson(); abstol = 1e-9)
+            @test cache.jac_cache.J isa BandedMatrix
+            sol = solve!(cache)
+            @test SciMLBase.successful_retcode(sol)
+        end
+
+        @testset "Structured Sparse AD: Tridiagonal Jacobian" begin
+            jac_prototype = Tridiagonal(ones(N - 1), ones(N), ones(N - 1))
+            nlprob_sparse_structured = NonlinearProblem(
+                NonlinearFunction(nlf; jac_prototype), u0, p)
+
+            cache = init(nlprob_sparse_structured, NewtonRaphson(); abstol = 1e-9)
+            @test cache.jac_cache.J isa Tridiagonal
+            sol = solve!(cache)
+            @test SciMLBase.successful_retcode(sol)
+        end
+    end
+end
diff --git a/lib/NonlinearSolveQuasiNewton/test/core_tests.jl b/lib/NonlinearSolveQuasiNewton/test/core_tests.jl
index a50558867..6225a07d1 100644
--- a/lib/NonlinearSolveQuasiNewton/test/core_tests.jl
+++ b/lib/NonlinearSolveQuasiNewton/test/core_tests.jl
@@ -1,6 +1,6 @@
 @testsetup module CoreRootfindTesting
 
-include("../../../common/common_core_testing.jl")
+include("../../../common/common_rootfind_testing.jl")
 
 end
 
@@ -73,7 +73,8 @@ end
         @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0, @SVector([1.0, 1.0]))
             probN = NonlinearProblem(quadratic_f, u0, 2.0)
             sol = solve(probN, Broyden(); termination_condition)
-            @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-9)
+            err = maximum(abs, quadratic_f(sol.u, 2.0))
+            @test err < 1e-9
         end
     end
 end
@@ -145,7 +146,8 @@ end
         @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0, @SVector([1.0, 1.0]))
             probN = NonlinearProblem(quadratic_f, u0, 2.0)
             sol = solve(probN, Klement(); termination_condition)
-            @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-9)
+            err = maximum(abs, quadratic_f(sol.u, 2.0))
+            @test err < 1e-9
         end
     end
 end
@@ -177,7 +179,7 @@ end
                 cache = init(
                     NonlinearProblem{false}(quadratic_f, u0, 2.0), solver, abstol = 1e-9
                 )
-                @test (@ballocated solve!($cache)) ≤ 320
+                @test (@ballocated solve!($cache)) ≤ 400
             end
 
             @testset "[IIP] u0: $(typeof(u0))" for u0 in (ones(32),)
@@ -213,7 +215,8 @@ end
         @testset "u0: $(typeof(u0))" for u0 in ([1.0, 1.0], 1.0, @SVector([1.0, 1.0]))
             probN = NonlinearProblem(quadratic_f, u0, 2.0)
             sol = solve(probN, LimitedMemoryBroyden(); termination_condition)
-            @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-9)
+            err = maximum(abs, quadratic_f(sol.u, 2.0))
+            @test err < 1e-9
         end
     end
 end
diff --git a/lib/NonlinearSolveSpectralMethods/test/core_tests.jl b/lib/NonlinearSolveSpectralMethods/test/core_tests.jl
index 217086dc4..e127d1e16 100644
--- a/lib/NonlinearSolveSpectralMethods/test/core_tests.jl
+++ b/lib/NonlinearSolveSpectralMethods/test/core_tests.jl
@@ -1,6 +1,6 @@
 @testsetup module CoreRootfindTesting
 
-include("../../../common/common_core_testing.jl")
+include("../../../common/common_rootfind_testing.jl")
 
 end
 
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index 26afa7720..e2a592e7d 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -17,6 +17,12 @@ const False = Val(false)
 abstract type AbstractJacobianOperator{T} <: AbstractSciMLOperator{T} end
 
 ArrayInterface.can_setindex(::AbstractJacobianOperator) = false
+function ArrayInterface.restructure(
+        y::AbstractJacobianOperator, x::AbstractJacobianOperator
+)
+    @assert size(y) == size(x) "cannot restructure operators. ensure their sizes match."
+    return x
+end
 
 abstract type AbstractMode end
 
diff --git a/test/core/nlls_tests.jl b/test/core/nlls_tests.jl
index 040627c00..85f4ba4ba 100644
--- a/test/core/nlls_tests.jl
+++ b/test/core/nlls_tests.jl
@@ -1,106 +1,5 @@
-@testsetup module CoreNLLSTesting
-using Reexport
-@reexport using NonlinearSolve, LinearSolve, LinearAlgebra, StableRNGs, Random, ForwardDiff,
-                Zygote
-using LineSearches: LineSearches, Static, HagerZhang, MoreThuente, StrongWolfe
 
-linesearches = []
-for ls in (
-    Static(), HagerZhang(), MoreThuente(), StrongWolfe(), LineSearches.BackTracking())
-    push!(linesearches, LineSearchesJL(; method = ls))
-end
-push!(linesearches, BackTracking())
-
-true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
-true_function(y, x, θ) = (@. y = θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4]))
-
-const θ_true = [1.0, 0.1, 2.0, 0.5]
-
-const x = [-1.0, -0.5, 0.0, 0.5, 1.0]
-
-const y_target = true_function(x, θ_true)
-
-function loss_function(θ, p)
-    ŷ = true_function(p, θ)
-    return ŷ .- y_target
-end
-
-function loss_function(resid, θ, p)
-    true_function(resid, p, θ)
-    resid .= resid .- y_target
-    return resid
-end
-
-const θ_init = θ_true .+ randn!(StableRNG(0), similar(θ_true)) * 0.1
-
-solvers = []
-for linsolve in [nothing, LUFactorization(), KrylovJL_GMRES(), KrylovJL_LSMR()]
-    vjp_autodiffs = linsolve isa KrylovJL ? [nothing, AutoZygote(), AutoFiniteDiff()] :
-                    [nothing]
-    for linesearch in linesearches, vjp_autodiff in vjp_autodiffs
-        push!(solvers, GaussNewton(; linsolve, linesearch, vjp_autodiff))
-    end
-end
-append!(solvers,
-    [LevenbergMarquardt(), LevenbergMarquardt(; linsolve = LUFactorization()),
-        LevenbergMarquardt(; linsolve = KrylovJL_GMRES()),
-        LevenbergMarquardt(; linsolve = KrylovJL_LSMR()), nothing])
-for radius_update_scheme in [RadiusUpdateSchemes.Simple, RadiusUpdateSchemes.NocedalWright,
-    RadiusUpdateSchemes.NLsolve, RadiusUpdateSchemes.Hei,
-    RadiusUpdateSchemes.Yuan, RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin]
-    push!(solvers, TrustRegion(; radius_update_scheme))
-end
-
-export solvers, θ_init, x, y_target, true_function, θ_true, loss_function
-end
-
-@testitem "General NLLS Solvers" setup=[CoreNLLSTesting] tags=[:core] begin
-    prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
-    prob_iip = NonlinearLeastSquaresProblem(
-        NonlinearFunction(loss_function; resid_prototype = zero(y_target)), θ_init, x)
-
-    nlls_problems = [prob_oop, prob_iip]
-
-    for prob in nlls_problems, solver in solvers
-        sol = solve(prob, solver; maxiters = 10000, abstol = 1e-6)
-        @test SciMLBase.successful_retcode(sol)
-        @test norm(sol.resid, 2) < 1e-6
-    end
-end
-
-@testitem "Custom VJP" setup=[CoreNLLSTesting] tags=[:core] begin
-    # This is just for testing that we can use vjp provided by the user
-    function vjp(v, θ, p)
-        resid = zeros(length(p))
-        J = ForwardDiff.jacobian((resid, θ) -> loss_function(resid, θ, p), resid, θ)
-        return vec(v' * J)
-    end
-
-    function vjp!(Jv, v, θ, p)
-        resid = zeros(length(p))
-        J = ForwardDiff.jacobian((resid, θ) -> loss_function(resid, θ, p), resid, θ)
-        mul!(vec(Jv), transpose(J), v)
-        return nothing
-    end
-
-    probs = [
-        NonlinearLeastSquaresProblem(
-            NonlinearFunction{true}(
-                loss_function; resid_prototype = zero(y_target), vjp = vjp!),
-            θ_init,
-            x),
-        NonlinearLeastSquaresProblem(
-            NonlinearFunction{false}(
-                loss_function; resid_prototype = zero(y_target), vjp = vjp),
-            θ_init,
-            x)]
-
-    for prob in probs, solver in solvers
-        sol = solve(prob, solver; maxiters = 10000, abstol = 1e-6)
-        @test SciMLBase.successful_retcode(sol)
-        @test norm(sol.resid, 2) < 1e-6
-    end
-end
+# TODO: Test polyalg here
 
 @testitem "NLLS Analytic Jacobian" tags=[:core] begin
     dataIn = 1:10
diff --git a/test/core/rootfind_tests.jl b/test/core/rootfind_tests.jl
deleted file mode 100644
index ad09ffd2f..000000000
--- a/test/core/rootfind_tests.jl
+++ /dev/null
@@ -1,459 +0,0 @@
-@testsetup module CoreRootfindTesting
-using Reexport
-@reexport using BenchmarkTools, LinearSolve, NonlinearSolve, StaticArrays, Random,
-                LinearAlgebra, ForwardDiff, Zygote, Enzyme, SparseConnectivityTracer,
-                NonlinearSolveBase
-using LineSearches: LineSearches
-
-_nameof(x) = applicable(nameof, x) ? nameof(x) : _nameof(typeof(x))
-
-quadratic_f(u, p) = u .* u .- p
-quadratic_f!(du, u, p) = (du .= u .* u .- p)
-quadratic_f2(u, p) = @. p[1] * u * u - p[2]
-
-function newton_fails(u, p)
-    return 0.010000000000000002 .+
-           10.000000000000002 ./ (1 .+
-            (0.21640425613334457 .+
-             216.40425613334457 ./ (1 .+
-              (0.21640425613334457 .+
-               216.40425613334457 ./ (1 .+ 0.0006250000000000001(u .^ 2.0))) .^ 2.0)) .^
-            2.0) .- 0.0011552453009332421u .- p
-end
-
-const TERMINATION_CONDITIONS = [
-    NormTerminationMode(Base.Fix1(maximum, abs)),
-    RelTerminationMode(),
-    RelNormTerminationMode(Base.Fix1(maximum, abs)),
-    RelNormSafeTerminationMode(Base.Fix1(maximum, abs)),
-    RelNormSafeBestTerminationMode(Base.Fix1(maximum, abs)),
-    AbsTerminationMode(),
-    AbsNormTerminationMode(Base.Fix1(maximum, abs)),
-    AbsNormSafeTerminationMode(Base.Fix1(maximum, abs)),
-    AbsNormSafeBestTerminationMode(Base.Fix1(maximum, abs))
-]
-
-function benchmark_nlsolve_oop(f, u0, p = 2.0; solver, kwargs...)
-    prob = NonlinearProblem{false}(f, u0, p)
-    return solve(prob, solver; abstol = 1e-9, kwargs...)
-end
-
-function benchmark_nlsolve_iip(f, u0, p = 2.0; solver, kwargs...)
-    prob = NonlinearProblem{true}(f, u0, p)
-    return solve(prob, solver; abstol = 1e-9, kwargs...)
-end
-
-function nlprob_iterator_interface(f, p_range, ::Val{iip}, solver) where {iip}
-    probN = NonlinearProblem{iip}(f, iip ? [0.5] : 0.5, p_range[begin])
-    cache = init(probN, solver; maxiters = 100, abstol = 1e-10)
-    sols = zeros(length(p_range))
-    for (i, p) in enumerate(p_range)
-        reinit!(cache, iip ? [cache.u[1]] : cache.u; p = p)
-        sol = solve!(cache)
-        sols[i] = iip ? sol.u[1] : sol.u
-    end
-    return sols
-end
-
-for alg in (:Static, :StrongWolfe, :BackTracking, :MoreThuente, :HagerZhang)
-    algname = Symbol(:LineSearches, alg)
-    @eval function $(algname)(args...; autodiff = nothing, initial_alpha = true, kwargs...)
-        return LineSearch.LineSearchesJL(;
-            method = LineSearches.$(alg)(args...; kwargs...), autodiff, initial_alpha)
-    end
-end
-
-export nlprob_iterator_interface, benchmark_nlsolve_oop, benchmark_nlsolve_iip,
-       TERMINATION_CONDITIONS, _nameof, newton_fails, quadratic_f, quadratic_f!
-export LineSearchesStatic, LineSearchesStrongWolfe, LineSearchesBackTracking,
-       LineSearchesMoreThuente, LineSearchesHagerZhang
-
-end
-
-# --- NewtonRaphson tests ---
-
-@testitem "NewtonRaphson" setup=[CoreRootfindTesting] tags=[:core] begin
-    @testset "LineSearch: $(_nameof(linesearch)) LineSearch AD: $(_nameof(ad))" for ad in (
-            AutoForwardDiff(), AutoZygote(), AutoFiniteDiff()
-        ),
-        linesearch in (
-            LineSearchesStatic(; autodiff = ad), LineSearchesStrongWolfe(; autodiff = ad),
-            LineSearchesBackTracking(; autodiff = ad), BackTracking(; autodiff = ad),
-            LineSearchesHagerZhang(; autodiff = ad),
-            LineSearchesMoreThuente(; autodiff = ad)
-        )
-
-        u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-
-        @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
-            solver = NewtonRaphson(; linesearch)
-            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver)
-            @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-
-            cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0),
-                NewtonRaphson(), abstol = 1e-9)
-            @test (@ballocated solve!($cache)) < 200
-        end
-
-        precs = [(u0) -> nothing,
-            u0 -> ((args...) -> (Diagonal(rand!(similar(u0))), nothing))]
-
-        @testset "[IIP] u0: $(typeof(u0)) precs: $(_nameof(prec)) linsolve: $(_nameof(linsolve))" for u0 in ([
-                1.0, 1.0],),
-            prec in precs,
-            linsolve in (nothing, KrylovJL_GMRES(), \)
-
-            ad isa AutoZygote && continue
-            if prec === :Random
-                prec = (args...) -> (Diagonal(randn!(similar(u0))), nothing)
-            end
-            solver = NewtonRaphson(; linsolve, precs = prec(u0), linesearch)
-            sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver)
-            @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-
-            cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0),
-                NewtonRaphson(; linsolve, precs = prec(u0)), abstol = 1e-9)
-            @test (@ballocated solve!($cache)) ≤ 64
-        end
-    end
-
-    # Iterator interface
-    p = range(0.01, 2, length = 200)
-    @test nlprob_iterator_interface(quadratic_f, p, Val(false), NewtonRaphson()) ≈ sqrt.(p)
-    @test nlprob_iterator_interface(quadratic_f!, p, Val(true), NewtonRaphson()) ≈ sqrt.(p)
-
-    @testset "Sparsity ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
-            AutoForwardDiff(), AutoFiniteDiff(), AutoZygote(), AutoEnzyme()),
-        u0 in (1.0, [1.0, 1.0])
-
-        probN = NonlinearProblem(
-            NonlinearFunction(quadratic_f; sparsity = TracerSparsityDetector()), u0, 2.0)
-        @test all(solve(probN, NewtonRaphson(; autodiff)).u .≈ sqrt(2.0))
-    end
-
-    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
-        u0 in (1.0, [1.0, 1.0])
-
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, NewtonRaphson(); termination_condition).u .≈ sqrt(2.0))
-    end
-end
-
-# --- TrustRegion tests ---
-
-@testitem "TrustRegion" setup=[CoreRootfindTesting] tags=[:core] begin
-    radius_update_schemes = [RadiusUpdateSchemes.Simple, RadiusUpdateSchemes.NocedalWright,
-        RadiusUpdateSchemes.NLsolve, RadiusUpdateSchemes.Hei,
-        RadiusUpdateSchemes.Yuan, RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin]
-    u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-    linear_solvers = [nothing, LUFactorization(), KrylovJL_GMRES(), \]
-
-    @testset "[OOP] u0: $(typeof(u0)) $(radius_update_scheme) $(_nameof(linsolve))" for u0 in u0s,
-        radius_update_scheme in radius_update_schemes,
-        linsolve in linear_solvers
-
-        abstol = ifelse(linsolve isa KrylovJL, 1e-6, 1e-9)
-
-        solver = TrustRegion(; radius_update_scheme, linsolve)
-        sol = benchmark_nlsolve_oop(quadratic_f, u0; solver, abstol)
-        @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(sol.u .* sol.u .- 2) .< abstol)
-
-        cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0),
-            TrustRegion(; radius_update_scheme, linsolve); abstol)
-        @test (@ballocated solve!($cache)) < 200
-    end
-
-    @testset "[IIP] u0: $(typeof(u0)) $(radius_update_scheme) $(_nameof(linsolve))" for u0 in ([
-            1.0, 1.0],),
-        radius_update_scheme in radius_update_schemes,
-        linsolve in linear_solvers
-
-        abstol = ifelse(linsolve isa KrylovJL, 1e-6, 1e-9)
-        solver = TrustRegion(; radius_update_scheme, linsolve)
-        sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver, abstol)
-        @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(sol.u .* sol.u .- 2) .< abstol)
-
-        cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0),
-            TrustRegion(; radius_update_scheme); abstol)
-        @test (@ballocated solve!($cache)) ≤ 64
-    end
-
-    # Iterator interface
-    p = range(0.01, 2, length = 200)
-    @test nlprob_iterator_interface(quadratic_f, p, Val(false), TrustRegion()) ≈ sqrt.(p)
-    @test nlprob_iterator_interface(quadratic_f!, p, Val(true), TrustRegion()) ≈ sqrt.(p)
-
-    @testset "$(_nameof(autodiff)) u0: $(_nameof(u0)) $(radius_update_scheme)" for autodiff in (
-            AutoForwardDiff(), AutoFiniteDiff(), AutoZygote(), AutoEnzyme()),
-        u0 in (1.0, [1.0, 1.0]),
-        radius_update_scheme in radius_update_schemes
-
-        probN = NonlinearProblem(
-            NonlinearFunction(quadratic_f; sparsity = TracerSparsityDetector()), u0, 2.0)
-        @test all(solve(probN, TrustRegion(; autodiff, radius_update_scheme)).u .≈
-                  sqrt(2.0))
-    end
-
-    # Test that `TrustRegion` passes a test that `NewtonRaphson` fails on.
-    @testset "Newton Raphson Fails: radius_update_scheme: $(radius_update_scheme)" for radius_update_scheme in [
-        RadiusUpdateSchemes.Simple, RadiusUpdateSchemes.Fan, RadiusUpdateSchemes.Bastin]
-        u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
-        p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
-        solver = TrustRegion(; radius_update_scheme)
-        sol = benchmark_nlsolve_oop(newton_fails, u0, p; solver)
-        @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
-    end
-
-    # Test kwargs in `TrustRegion`
-    @testset "Keyword Arguments" begin
-        max_trust_radius = [10.0, 100.0, 1000.0]
-        initial_trust_radius = [10.0, 1.0, 0.1]
-        step_threshold = [0.0, 0.01, 0.25]
-        shrink_threshold = [0.25, 0.3, 0.5]
-        expand_threshold = [0.5, 0.8, 0.9]
-        shrink_factor = [0.1, 0.3, 0.5]
-        expand_factor = [1.5, 2.0, 3.0]
-        max_shrink_times = [10, 20, 30]
-
-        list_of_options = zip(
-            max_trust_radius, initial_trust_radius, step_threshold, shrink_threshold,
-            expand_threshold, shrink_factor, expand_factor, max_shrink_times)
-        for options in list_of_options
-            local probN, sol, alg
-            alg = TrustRegion(
-                max_trust_radius = options[1], initial_trust_radius = options[2],
-                step_threshold = options[3], shrink_threshold = options[4],
-                expand_threshold = options[5], shrink_factor = options[6],
-                expand_factor = options[7], max_shrink_times = options[8])
-
-            probN = NonlinearProblem{false}(quadratic_f, [1.0, 1.0], 2.0)
-            sol = solve(probN, alg, abstol = 1e-10)
-            @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-10)
-        end
-    end
-
-    # Testing consistency of iip vs oop iterations
-    @testset "OOP / IIP Consistency" begin
-        maxiterations = [2, 3, 4, 5]
-        u0 = [1.0, 1.0]
-        @testset "radius_update_scheme: $(radius_update_scheme) maxiters: $(maxiters)" for radius_update_scheme in radius_update_schemes,
-            maxiters in maxiterations
-
-            solver = TrustRegion(; radius_update_scheme)
-            sol_iip = benchmark_nlsolve_iip(quadratic_f!, u0; solver, maxiters)
-            sol_oop = benchmark_nlsolve_oop(quadratic_f, u0; solver, maxiters)
-            @test sol_iip.u ≈ sol_oop.u
-        end
-    end
-
-    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
-        u0 in (1.0, [1.0, 1.0])
-
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, TrustRegion(); termination_condition).u .≈ sqrt(2.0))
-    end
-end
-
-# --- LevenbergMarquardt tests ---
-
-@testitem "LevenbergMarquardt" setup=[CoreRootfindTesting] tags=[:core] begin
-    u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-    @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
-        sol = benchmark_nlsolve_oop(quadratic_f, u0; solver = LevenbergMarquardt())
-        @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-
-        cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0),
-            LevenbergMarquardt(), abstol = 1e-9)
-        @test (@ballocated solve!($cache)) < 200
-    end
-
-    @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
-        sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver = LevenbergMarquardt())
-        @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-
-        cache = init(NonlinearProblem{true}(quadratic_f!, u0, 2.0),
-            LevenbergMarquardt(), abstol = 1e-9)
-        @test (@ballocated solve!($cache)) ≤ 64
-    end
-
-    @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
-            AutoForwardDiff(), AutoFiniteDiff(), AutoZygote(), AutoEnzyme()),
-        u0 in (1.0, [1.0, 1.0])
-
-        probN = NonlinearProblem(
-            NonlinearFunction(quadratic_f; sparsity = TracerSparsityDetector()), u0, 2.0)
-        @test all(solve(
-            probN, LevenbergMarquardt(; autodiff); abstol = 1e-9, reltol = 1e-9).u .≈
-                  sqrt(2.0))
-    end
-
-    # Test that `LevenbergMarquardt` passes a test that `NewtonRaphson` fails on.
-    @testset "Newton Raphson Fails" begin
-        u0 = [-10.0, -1.0, 1.0, 2.0, 3.0, 4.0, 10.0]
-        p = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
-        sol = benchmark_nlsolve_oop(newton_fails, u0, p; solver = LevenbergMarquardt())
-        @test SciMLBase.successful_retcode(sol)
-        @test all(abs.(newton_fails(sol.u, p)) .< 1e-9)
-    end
-
-    # Iterator interface
-    p = range(0.01, 2, length = 200)
-    @test abs.(nlprob_iterator_interface(
-        quadratic_f, p, Val(false), LevenbergMarquardt())) ≈ sqrt.(p)
-    @test abs.(nlprob_iterator_interface(
-        quadratic_f!, p, Val(true), LevenbergMarquardt())) ≈ sqrt.(p)
-
-    # Test kwargs in `LevenbergMarquardt`
-    @testset "Keyword Arguments" begin
-        damping_initial = [0.5, 2.0, 5.0]
-        damping_increase_factor = [1.5, 3.0, 10.0]
-        damping_decrease_factor = Float64[2, 5, 10.0]
-        finite_diff_step_geodesic = [0.02, 0.2, 0.3]
-        α_geodesic = [0.6, 0.8, 0.9]
-        b_uphill = Float64[0, 1, 2]
-        min_damping_D = [1e-12, 1e-9, 1e-4]
-
-        list_of_options = zip(
-            damping_initial, damping_increase_factor, damping_decrease_factor,
-            finite_diff_step_geodesic, α_geodesic, b_uphill, min_damping_D)
-        for options in list_of_options
-            local probN, sol, alg
-            alg = LevenbergMarquardt(;
-                damping_initial = options[1], damping_increase_factor = options[2],
-                damping_decrease_factor = options[3],
-                finite_diff_step_geodesic = options[4], α_geodesic = options[5],
-                b_uphill = options[6], min_damping_D = options[7])
-
-            probN = NonlinearProblem{false}(quadratic_f, [1.0, 1.0], 2.0)
-            sol = solve(probN, alg; abstol = 1e-13, maxiters = 10000)
-            @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-10)
-        end
-    end
-
-    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
-        u0 in (1.0, [1.0, 1.0])
-
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, LevenbergMarquardt(); termination_condition).u .≈ sqrt(2.0))
-    end
-end
-
-# --- PseudoTransient tests ---
-
-@testitem "PseudoTransient" setup=[CoreRootfindTesting] tags=[:core] begin
-    # These are tests for NewtonRaphson so we should set alpha_initial to be high so that we
-    # converge quickly
-    @testset "PT: alpha_initial = 10.0 PT AD: $(ad)" for ad in (
-        AutoFiniteDiff(), AutoZygote())
-        u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
-
-        @testset "[OOP] u0: $(typeof(u0))" for u0 in u0s
-            solver = PseudoTransient(; alpha_initial = 10.0)
-            sol = benchmark_nlsolve_oop(quadratic_f, u0; solver)
-            # Failing by a margin for some
-            # @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-
-            cache = init(NonlinearProblem{false}(quadratic_f, u0, 2.0),
-                PseudoTransient(alpha_initial = 10.0), abstol = 1e-9)
-            @test (@ballocated solve!($cache)) < 200
-        end
-
-        precs = [nothing, :Random]
-
-        @testset "[IIP] u0: $(typeof(u0)) precs: $(_nameof(prec)) linsolve: $(_nameof(linsolve))" for u0 in ([
-                1.0, 1.0],),
-            prec in precs,
-            linsolve in (nothing, KrylovJL_GMRES(), \)
-
-            ad isa AutoZygote && continue
-            if prec === :Random
-                prec = (args...) -> (Diagonal(randn!(similar(u0))), nothing)
-            end
-            solver = PseudoTransient(; alpha_initial = 10.0, linsolve, precs = prec)
-            sol = benchmark_nlsolve_iip(quadratic_f!, u0; solver)
-            @test SciMLBase.successful_retcode(sol)
-            @test all(abs.(sol.u .* sol.u .- 2) .< 1e-9)
-
-            cache = init(
-                NonlinearProblem{true}(quadratic_f!, u0, 2.0), solver; abstol = 1e-9)
-            @test (@ballocated solve!($cache)) ≤ 64
-        end
-    end
-
-    p = range(0.01, 2, length = 200)
-    @test nlprob_iterator_interface(
-        quadratic_f, p, Val(false), PseudoTransient(; alpha_initial = 10.0)) ≈ sqrt.(p)
-    @test nlprob_iterator_interface(
-        quadratic_f!, p, Val(true), PseudoTransient(; alpha_initial = 10.0)) ≈ sqrt.(p)
-
-    @testset "ADType: $(autodiff) u0: $(_nameof(u0))" for autodiff in (
-            AutoForwardDiff(), AutoFiniteDiff(), AutoZygote(), AutoEnzyme()),
-        u0 in (1.0, [1.0, 1.0])
-
-        probN = NonlinearProblem(
-            NonlinearFunction(quadratic_f; sparsity = TracerSparsityDetector()), u0, 2.0)
-        @test all(solve(probN, PseudoTransient(; alpha_initial = 10.0, autodiff)).u .≈
-                  sqrt(2.0))
-    end
-
-    @testset "Termination condition: $(_nameof(termination_condition)) u0: $(_nameof(u0))" for termination_condition in TERMINATION_CONDITIONS,
-        u0 in (1.0, [1.0, 1.0])
-
-        probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(
-            probN, PseudoTransient(; alpha_initial = 10.0); termination_condition).u .≈
-                  sqrt(2.0))
-    end
-end
-
-# Miscellaneous Tests
-@testitem "Custom JVP" setup=[CoreRootfindTesting] tags=[:core] begin
-    function F(u::Vector{Float64}, p::Vector{Float64})
-        Δ = Tridiagonal(-ones(99), 2 * ones(100), -ones(99))
-        return u + 0.1 * u .* Δ * u - p
-    end
-
-    function F!(du::Vector{Float64}, u::Vector{Float64}, p::Vector{Float64})
-        Δ = Tridiagonal(-ones(99), 2 * ones(100), -ones(99))
-        du .= u + 0.1 * u .* Δ * u - p
-        return nothing
-    end
-
-    function JVP(v::Vector{Float64}, u::Vector{Float64}, p::Vector{Float64})
-        Δ = Tridiagonal(-ones(99), 2 * ones(100), -ones(99))
-        return v + 0.1 * (u .* Δ * v + v .* Δ * u)
-    end
-
-    function JVP!(
-            du::Vector{Float64}, v::Vector{Float64}, u::Vector{Float64}, p::Vector{Float64})
-        Δ = Tridiagonal(-ones(99), 2 * ones(100), -ones(99))
-        du .= v + 0.1 * (u .* Δ * v + v .* Δ * u)
-        return nothing
-    end
-
-    u0 = rand(100)
-
-    prob = NonlinearProblem(NonlinearFunction{false}(F; jvp = JVP), u0, u0)
-    sol = solve(prob, NewtonRaphson(; linsolve = KrylovJL_GMRES()); abstol = 1e-13)
-    @test norm(sol.resid, Inf) ≤ 1e-6
-    sol = solve(
-        prob, TrustRegion(; linsolve = KrylovJL_GMRES(), vjp_autodiff = AutoFiniteDiff());
-        abstol = 1e-13)
-    @test norm(sol.resid, Inf) ≤ 1e-6
-
-    prob = NonlinearProblem(NonlinearFunction{true}(F!; jvp = JVP!), u0, u0)
-    sol = solve(prob, NewtonRaphson(; linsolve = KrylovJL_GMRES()); abstol = 1e-13)
-    @test norm(sol.resid, Inf) ≤ 1e-6
-    sol = solve(
-        prob, TrustRegion(; linsolve = KrylovJL_GMRES(), vjp_autodiff = AutoFiniteDiff());
-        abstol = 1e-13)
-    @test norm(sol.resid, Inf) ≤ 1e-6
-end
diff --git a/test/misc/banded_matrices_tests.jl b/test/misc/banded_matrices_tests.jl
deleted file mode 100644
index a9a2bf4ca..000000000
--- a/test/misc/banded_matrices_tests.jl
+++ /dev/null
@@ -1,8 +0,0 @@
-@testitem "Banded Matrix vcat" tags=[:misc] begin
-    using BandedMatrices, LinearAlgebra, SparseArrays
-
-    b = BandedMatrix(Ones(5, 5), (1, 1))
-    d = Diagonal(ones(5, 5))
-
-    @test NonlinearSolve._vcat(b, d) == vcat(sparse(b), d)
-end
diff --git a/test/misc/structured_jacobian_tests.jl b/test/misc/structured_jacobian_tests.jl
deleted file mode 100644
index 41b316911..000000000
--- a/test/misc/structured_jacobian_tests.jl
+++ /dev/null
@@ -1,67 +0,0 @@
-@testitem "Structured Jacobians" tags=[:misc] begin
-    using NonlinearSolve, SparseConnectivityTracer, BandedMatrices, LinearAlgebra,
-          SparseArrays
-
-    N = 16
-    p = rand(N)
-    u0 = rand(N)
-
-    function f!(du, u, p)
-        for i in 2:(length(u) - 1)
-            du[i] = u[i - 1] - 2u[i] + u[i + 1] + p[i]
-        end
-        du[1] = -2u[1] + u[2] + p[1]
-        du[end] = u[end - 1] - 2u[end] + p[end]
-        return nothing
-    end
-
-    function f(u, p)
-        du = similar(u, promote_type(eltype(u), eltype(p)))
-        f!(du, u, p)
-        return du
-    end
-
-    for nlf in (f, f!)
-        @testset "Dense AD" begin
-            nlprob = NonlinearProblem(NonlinearFunction(nlf), u0, p)
-
-            cache = init(nlprob, NewtonRaphson(); abstol = 1e-9)
-            @test cache.jac_cache.J isa Matrix
-            sol = solve!(cache)
-            @test SciMLBase.successful_retcode(sol)
-        end
-
-        @testset "Unstructured Sparse AD" begin
-            nlprob_autosparse = NonlinearProblem(
-                NonlinearFunction(nlf; sparsity = TracerSparsityDetector()),
-                u0, p)
-
-            cache = init(nlprob_autosparse, NewtonRaphson(); abstol = 1e-9)
-            @test cache.jac_cache.J isa SparseMatrixCSC
-            sol = solve!(cache)
-            @test SciMLBase.successful_retcode(sol)
-        end
-
-        @testset "Structured Sparse AD: Banded Jacobian" begin
-            jac_prototype = BandedMatrix(-1 => ones(N - 1), 0 => ones(N), 1 => ones(N - 1))
-            nlprob_sparse_structured = NonlinearProblem(
-                NonlinearFunction(nlf; jac_prototype), u0, p)
-
-            cache = init(nlprob_sparse_structured, NewtonRaphson(); abstol = 1e-9)
-            @test cache.jac_cache.J isa BandedMatrix
-            sol = solve!(cache)
-            @test SciMLBase.successful_retcode(sol)
-        end
-
-        @testset "Structured Sparse AD: Tridiagonal Jacobian" begin
-            jac_prototype = Tridiagonal(ones(N - 1), ones(N), ones(N - 1))
-            nlprob_sparse_structured = NonlinearProblem(
-                NonlinearFunction(nlf; jac_prototype), u0, p)
-
-            cache = init(nlprob_sparse_structured, NewtonRaphson(); abstol = 1e-9)
-            @test cache.jac_cache.J isa Tridiagonal
-            sol = solve!(cache)
-            @test SciMLBase.successful_retcode(sol)
-        end
-    end
-end

From f37da0a3ba6428afab8583491fa7eba47b08150c Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 30 Oct 2024 15:25:03 -0400
Subject: [PATCH 656/700] chore: run formatter

---
 .../src/NonlinearSolveBase.jl                 | 21 +++++++++++--------
 lib/NonlinearSolveBase/src/utils.jl           |  2 +-
 .../src/NonlinearSolveFirstOrder.jl           | 16 +++++++-------
 .../src/NonlinearSolveQuasiNewton.jl          |  7 ++++---
 .../src/SciMLJacobianOperators.jl             |  2 +-
 src/NonlinearSolve.jl                         | 18 ++++++++++++----
 6 files changed, 41 insertions(+), 25 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index e9fd61dff..7cb1cffaf 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -1,21 +1,21 @@
 module NonlinearSolveBase
 
+using Compat: @compat
+using ConcreteStructs: @concrete
+using FastClosures: @closure
+using Preferences: @load_preference
+
 using ADTypes: ADTypes, AbstractADType, AutoSparse, NoSparsityDetector,
                KnownJacobianSparsityDetector
 using Adapt: WrappedArray
 using ArrayInterface: ArrayInterface
-using CommonSolve: CommonSolve, init
-using Compat: @compat
-using ConcreteStructs: @concrete
 using DifferentiationInterface: DifferentiationInterface, Constant
+using StaticArraysCore: StaticArray, SMatrix, SArray, MArray
+
+using CommonSolve: CommonSolve, init
 using EnzymeCore: EnzymeCore
-using FastClosures: @closure
 using FunctionProperties: hasbranching
-using LinearAlgebra: LinearAlgebra, Diagonal, norm, ldiv!, diagind
-using Markdown: @doc_str
 using MaybeInplace: @bb
-using Preferences: @load_preference
-using Printf: @printf
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinearProblem,
                  AbstractNonlinearAlgorithm, AbstractNonlinearFunction,
@@ -23,9 +23,12 @@ using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinear
                  NonlinearFunction, NullParameters, NLStats, LinearProblem
 using SciMLJacobianOperators: JacobianOperator, StatefulJacobianOperator
 using SciMLOperators: AbstractSciMLOperator, IdentityOperator
-using StaticArraysCore: StaticArray, SMatrix, SArray, MArray
 using SymbolicIndexingInterface: SymbolicIndexingInterface
 
+using LinearAlgebra: LinearAlgebra, Diagonal, norm, ldiv!, diagind
+using Markdown: @doc_str
+using Printf: @printf
+
 const DI = DifferentiationInterface
 const SII = SymbolicIndexingInterface
 
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index a1485debb..44c7e957a 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -94,7 +94,7 @@ restructure(::Number, x::Number) = x
 function restructure(
         y::T1, x::T2
 ) where {T1 <: AbstractSciMLOperator, T2 <: AbstractSciMLOperator}
-    @assert size(y) == size(x) "cannot restructure operators. ensure their sizes match."
+    @assert size(y)==size(x) "cannot restructure operators. ensure their sizes match."
     return x
 end
 restructure(y, x) = ArrayInterface.restructure(y, x)
diff --git a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
index 15bdda938..789c13ab7 100644
--- a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
+++ b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
@@ -1,16 +1,17 @@
 module NonlinearSolveFirstOrder
 
-using Reexport: @reexport
+using ConcreteStructs: @concrete
 using PrecompileTools: @compile_workload, @setup_workload
+using Reexport: @reexport
+using Setfield: @set!
 
 using ADTypes: ADTypes
 using ArrayInterface: ArrayInterface
+using LinearAlgebra: LinearAlgebra, Diagonal, dot
+using StaticArraysCore: SArray
+
 using CommonSolve: CommonSolve
-using ConcreteStructs: @concrete
 using DiffEqBase: DiffEqBase    # Needed for `init` / `solve` dispatches
-using FiniteDiff: FiniteDiff    # Default Finite Difference Method
-using ForwardDiff: ForwardDiff  # Default Forward Mode AD
-using LinearAlgebra: LinearAlgebra, Diagonal, dot
 using LinearSolve: LinearSolve  # Trigger Linear Solve extension in NonlinearSolveBase
 using MaybeInplace: @bb
 using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
@@ -23,8 +24,9 @@ using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
                           Dogleg
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode, NonlinearFunction
 using SciMLJacobianOperators: VecJacOperator, JacVecOperator, StatefulJacobianOperator
-using Setfield: @set!
-using StaticArraysCore: SArray
+
+using FiniteDiff: FiniteDiff    # Default Finite Difference Method
+using ForwardDiff: ForwardDiff  # Default Forward Mode AD
 
 include("raphson.jl")
 include("gauss_newton.jl")
diff --git a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
index 597af0e15..3b63615e8 100644
--- a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
@@ -1,11 +1,13 @@
 module NonlinearSolveQuasiNewton
 
-using Reexport: @reexport
+using ConcreteStructs: @concrete
 using PrecompileTools: @compile_workload, @setup_workload
+using Reexport: @reexport
 
 using ArrayInterface: ArrayInterface
+using StaticArraysCore: StaticArray, Size, MArray
+
 using CommonSolve: CommonSolve
-using ConcreteStructs: @concrete
 using DiffEqBase: DiffEqBase   # Needed for `init` / `solve` dispatches
 using LinearAlgebra: LinearAlgebra, Diagonal, dot, diag
 using LinearSolve: LinearSolve # Trigger Linear Solve extension in NonlinearSolveBase
@@ -20,7 +22,6 @@ using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
                           update_trace!, L2_NORM, NewtonDescent
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode
 using SciMLOperators: AbstractSciMLOperator
-using StaticArraysCore: StaticArray, Size, MArray
 
 include("reset_conditions.jl")
 include("structure.jl")
diff --git a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
index e2a592e7d..a90c983b3 100644
--- a/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
+++ b/lib/SciMLJacobianOperators/src/SciMLJacobianOperators.jl
@@ -20,7 +20,7 @@ ArrayInterface.can_setindex(::AbstractJacobianOperator) = false
 function ArrayInterface.restructure(
         y::AbstractJacobianOperator, x::AbstractJacobianOperator
 )
-    @assert size(y) == size(x) "cannot restructure operators. ensure their sizes match."
+    @assert size(y)==size(x) "cannot restructure operators. ensure their sizes match."
     return x
 end
 
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 4b7d73d8a..74dea2342 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -1,13 +1,14 @@
 module NonlinearSolve
 
+using ConcreteStructs: @concrete
 using Reexport: @reexport
 using PrecompileTools: @compile_workload, @setup_workload
+using FastClosures: @closure
 
+using ADTypes: ADTypes
 using ArrayInterface: ArrayInterface
 using CommonSolve: CommonSolve, solve, solve!
-using ConcreteStructs: @concrete
 using DiffEqBase: DiffEqBase # Needed for `init` / `solve` dispatches
-using FastClosures: @closure
 using LinearAlgebra: LinearAlgebra, norm
 using LineSearch: BackTracking
 using NonlinearSolveBase: NonlinearSolveBase, InternalAPI, AbstractNonlinearSolveAlgorithm,
@@ -33,6 +34,15 @@ using ForwardDiff: ForwardDiff  # Default Forward Mode AD
 using SparseArrays: SparseArrays
 using SparseMatrixColorings: SparseMatrixColorings
 
+# Sub-Packages that are re-exported by NonlinearSolve
+using BracketingNonlinearSolve: BracketingNonlinearSolve
+using LineSearch: LineSearch
+using LinearSolve: LinearSolve
+using NonlinearSolveFirstOrder: NonlinearSolveFirstOrder
+using NonlinearSolveQuasiNewton: NonlinearSolveQuasiNewton
+using NonlinearSolveSpectralMethods: NonlinearSolveSpectralMethods
+using SimpleNonlinearSolve: SimpleNonlinearSolve
+
 const SII = SymbolicIndexingInterface
 
 include("helpers.jl")
@@ -54,8 +64,8 @@ include("default.jl")
 # include("internal/forward_diff.jl") # we need to define after the algorithms
 
 @setup_workload begin
-    include(joinpath(@__DIR__, "..", "common", "nonlinear_problem_workloads.jl"))
-    include(joinpath(@__DIR__, "..", "common", "nlls_problem_workloads.jl"))
+    include("../common/nonlinear_problem_workloads.jl")
+    include("../common/nlls_problem_workloads.jl")
 
     @compile_workload begin
         @sync begin

From f49c30828a13fe5a083b8dea89b09ab6679c4ecb Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 30 Oct 2024 16:30:20 -0400
Subject: [PATCH 657/700] test: fix more of NonlinearSolve tests

---
 .buildkite/pipeline.yml                       |   4 +-
 .../workflows/CI_BracketingNonlinearSolve.yml |   2 +-
 .github/workflows/CI_NonlinearSolve.yml       |  10 +-
 .github/workflows/CI_NonlinearSolveBase.yml   |   2 +-
 .../workflows/CI_NonlinearSolveFirstOrder.yml |   2 +-
 .../CI_NonlinearSolveQuasiNewton.yml          |   2 +-
 .../CI_NonlinearSolveSpectralMethods.yml      |   2 +-
 .../workflows/CI_SciMLJacobianOperators.yml   |   2 +-
 .github/workflows/Downgrade.yml               |   1 -
 Project.toml                                  |   2 +-
 .../src/NonlinearSolveBase.jl                 |   2 +-
 lib/NonlinearSolveBase/src/timer_outputs.jl   |  22 +
 lib/NonlinearSolveFirstOrder/Project.toml     |   4 +-
 src/NonlinearSolve.jl                         |   3 +-
 src/helpers.jl                                |  21 -
 test/23_test_problems_tests.jl                | 144 ++++++
 test/core/23_test_problems_tests.jl           | 144 ------
 test/core/forward_ad_tests.jl                 | 116 -----
 test/core/nlls_tests.jl                       |  21 -
 test/core_tests.jl                            | 416 ++++++++++++++++++
 test/{gpu/core_tests.jl => cuda_tests.jl}     |   0
 test/forward_ad_tests.jl                      | 116 +++++
 test/misc/aliasing_tests.jl                   |  25 --
 test/misc/ensemble_tests.jl                   |  21 -
 test/misc/exotic_type_tests.jl                |  27 --
 test/misc/linsolve_switching_tests.jl         |  28 --
 test/misc/matrix_resizing_tests.jl            |  31 --
 test/misc/noinit_caching_tests.jl             |  23 -
 test/misc/polyalg_tests.jl                    | 256 -----------
 test/misc/qa_tests.jl                         |  28 --
 .../mtk_cache_indexing_tests.jl               |   3 +-
 test/qa_tests.jl                              |  24 +
 test/runtests.jl                              |  16 +-
 .../{nlls_tests.jl => least_squares_tests.jl} |   0
 34 files changed, 756 insertions(+), 764 deletions(-)
 create mode 100644 test/23_test_problems_tests.jl
 delete mode 100644 test/core/23_test_problems_tests.jl
 delete mode 100644 test/core/forward_ad_tests.jl
 delete mode 100644 test/core/nlls_tests.jl
 create mode 100644 test/core_tests.jl
 rename test/{gpu/core_tests.jl => cuda_tests.jl} (100%)
 create mode 100644 test/forward_ad_tests.jl
 delete mode 100644 test/misc/aliasing_tests.jl
 delete mode 100644 test/misc/ensemble_tests.jl
 delete mode 100644 test/misc/exotic_type_tests.jl
 delete mode 100644 test/misc/linsolve_switching_tests.jl
 delete mode 100644 test/misc/matrix_resizing_tests.jl
 delete mode 100644 test/misc/noinit_caching_tests.jl
 delete mode 100644 test/misc/polyalg_tests.jl
 delete mode 100644 test/misc/qa_tests.jl
 rename test/{downstream => }/mtk_cache_indexing_tests.jl (98%)
 create mode 100644 test/qa_tests.jl
 rename test/wrappers/{nlls_tests.jl => least_squares_tests.jl} (100%)

diff --git a/.buildkite/pipeline.yml b/.buildkite/pipeline.yml
index 4292dbdda..b74c820cc 100644
--- a/.buildkite/pipeline.yml
+++ b/.buildkite/pipeline.yml
@@ -14,7 +14,7 @@ steps:
         Pkg.Registry.update();
         # Install packages present in subdirectories
         dev_pks = Pkg.PackageSpec[];
-        for path in ("lib/SciMLJacobianOperators", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveBase", "lib/SimpleNonlinearSolve")
+        for path in ("lib/SciMLJacobianOperators", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveBase", "lib/SimpleNonlinearSolve", "lib/NonlinearSolveFirstOrder", "lib/NonlinearSolveSpectralMethods", "lib/NonlinearSolveQuasiNewton")
           push!(dev_pks, Pkg.PackageSpec(; path));
         end
         Pkg.develop(dev_pks);
@@ -42,7 +42,7 @@ steps:
         Pkg.Registry.update();
         # Install packages present in subdirectories
         dev_pks = Pkg.PackageSpec[];
-        for path in ("lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve")
+        for path in ("lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve", "lib/SciMLJacobianOperators")
           push!(dev_pks, Pkg.PackageSpec(; path))
         end
         Pkg.develop(dev_pks);
diff --git a/.github/workflows/CI_BracketingNonlinearSolve.yml b/.github/workflows/CI_BracketingNonlinearSolve.yml
index 69c1f7746..e83060bdb 100644
--- a/.github/workflows/CI_BracketingNonlinearSolve.yml
+++ b/.github/workflows/CI_BracketingNonlinearSolve.yml
@@ -26,7 +26,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "lts"
+          - "1.10"
           - "1"
         os:
           - ubuntu-latest
diff --git a/.github/workflows/CI_NonlinearSolve.yml b/.github/workflows/CI_NonlinearSolve.yml
index 0ea05487c..24be53295 100644
--- a/.github/workflows/CI_NonlinearSolve.yml
+++ b/.github/workflows/CI_NonlinearSolve.yml
@@ -14,6 +14,9 @@ on:
       - "lib/BracketingNonlinearSolve/**"
       - "lib/NonlinearSolveBase/**"
       - "lib/SimpleNonlinearSolve/**"
+      - "lib/NonlinearSolveFirstOrder/**"
+      - "lib/NonlinearSolveSpectralMethods/**"
+      - "lib/NonlinearSolveQuasiNewton/**"
   push:
     branches:
       - master
@@ -33,10 +36,9 @@ jobs:
         group:
           - Core
           - Downstream
-          - Misc
           - Wrappers
         version:
-          - "lts"
+          - "1.10"
           - "1"
         os:
           - ubuntu-latest
@@ -63,7 +65,7 @@ jobs:
           Pkg.Registry.update()
           # Install packages present in subdirectories
           dev_pks = Pkg.PackageSpec[]
-          for path in ("lib/SciMLJacobianOperators", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveBase", "lib/SimpleNonlinearSolve")
+          for path in ("lib/SciMLJacobianOperators", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveBase", "lib/SimpleNonlinearSolve", "lib/NonlinearSolveFirstOrder", "lib/NonlinearSolveSpectralMethods", "lib/NonlinearSolveQuasiNewton")
               push!(dev_pks, Pkg.PackageSpec(; path))
           end
           Pkg.develop(dev_pks)
@@ -74,7 +76,7 @@ jobs:
           GROUP: ${{ matrix.group }}
       - uses: julia-actions/julia-processcoverage@v1
         with:
-          directories: src,ext,lib/SciMLJacobianOperators/src
+          directories: src,ext,lib/SciMLJacobianOperators/src,lib/BracketingNonlinearSolve/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SimpleNonlinearSolve/src,lib/NonlinearSolveFirstOrder/src,lib/NonlinearSolveSpectralMethods/src,lib/NonlinearSolveQuasiNewton/src
       - uses: codecov/codecov-action@v4
         with:
           file: lcov.info
diff --git a/.github/workflows/CI_NonlinearSolveBase.yml b/.github/workflows/CI_NonlinearSolveBase.yml
index 9b9f0d959..0ba7c11d2 100644
--- a/.github/workflows/CI_NonlinearSolveBase.yml
+++ b/.github/workflows/CI_NonlinearSolveBase.yml
@@ -25,7 +25,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "lts"
+          - "1.10"
           - "1"
         os:
           - ubuntu-latest
diff --git a/.github/workflows/CI_NonlinearSolveFirstOrder.yml b/.github/workflows/CI_NonlinearSolveFirstOrder.yml
index cf9bd427b..8b93788b1 100644
--- a/.github/workflows/CI_NonlinearSolveFirstOrder.yml
+++ b/.github/workflows/CI_NonlinearSolveFirstOrder.yml
@@ -26,7 +26,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "lts"
+          - "1.10"
           - "1"
         os:
           - ubuntu-latest
diff --git a/.github/workflows/CI_NonlinearSolveQuasiNewton.yml b/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
index 5d6024b06..1e3815ea9 100644
--- a/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
+++ b/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
@@ -26,7 +26,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "lts"
+          - "1.10"
           - "1"
         os:
           - ubuntu-latest
diff --git a/.github/workflows/CI_NonlinearSolveSpectralMethods.yml b/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
index 80f9b0e9d..7999ee906 100644
--- a/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
+++ b/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
@@ -26,7 +26,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "lts"
+          - "1.10"
           - "1"
         os:
           - ubuntu-latest
diff --git a/.github/workflows/CI_SciMLJacobianOperators.yml b/.github/workflows/CI_SciMLJacobianOperators.yml
index 96ce9db15..3f243a8b3 100644
--- a/.github/workflows/CI_SciMLJacobianOperators.yml
+++ b/.github/workflows/CI_SciMLJacobianOperators.yml
@@ -24,7 +24,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "lts"
+          - "1.10"
           - "1"
         os:
           - ubuntu-latest
diff --git a/.github/workflows/Downgrade.yml b/.github/workflows/Downgrade.yml
index 83223e2f6..6d619f9ab 100644
--- a/.github/workflows/Downgrade.yml
+++ b/.github/workflows/Downgrade.yml
@@ -21,7 +21,6 @@ jobs:
         group:
           - Core
           - Downstream
-          - Misc
           - Wrappers
     steps:
       - uses: actions/checkout@v4
diff --git a/Project.toml b/Project.toml
index 768a46005..f817aba9f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -78,7 +78,7 @@ InteractiveUtils = "<0.0.1, 1"
 LeastSquaresOptim = "0.8.5"
 LineSearch = "0.1.4"
 LineSearches = "7.3"
-LinearAlgebra = "1.11.0"
+LinearAlgebra = "1.10"
 LinearSolve = "2.36.1"
 MINPACK = "1.2"
 MPI = "0.20.22"
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 7cb1cffaf..a3ac4614d 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -3,7 +3,7 @@ module NonlinearSolveBase
 using Compat: @compat
 using ConcreteStructs: @concrete
 using FastClosures: @closure
-using Preferences: @load_preference
+using Preferences: @load_preference, @set_preferences!
 
 using ADTypes: ADTypes, AbstractADType, AutoSparse, NoSparsityDetector,
                KnownJacobianSparsityDetector
diff --git a/lib/NonlinearSolveBase/src/timer_outputs.jl b/lib/NonlinearSolveBase/src/timer_outputs.jl
index 6a65f1bab..56bb2a95c 100644
--- a/lib/NonlinearSolveBase/src/timer_outputs.jl
+++ b/lib/NonlinearSolveBase/src/timer_outputs.jl
@@ -31,3 +31,25 @@ end
 @static if !TIMER_OUTPUTS_ENABLED
     @inline reset_timer!(::Nothing) = nothing
 end
+
+"""
+    enable_timer_outputs()
+
+Enable `TimerOutput` for all `NonlinearSolve` algorithms. This is useful for debugging
+but has some overhead, so it is disabled by default.
+"""
+function enable_timer_outputs()
+    @set_preferences!("enable_timer_outputs" => true)
+    @info "Timer Outputs Enabled. Restart the Julia session for this to take effect."
+end
+
+"""
+    disable_timer_outputs()
+
+Disable `TimerOutput` for all `NonlinearSolve` algorithms. This should be used when
+`NonlinearSolve` is being used in performance-critical code.
+"""
+function disable_timer_outputs()
+    @set_preferences!("enable_timer_outputs" => false)
+    @info "Timer Outputs Disabled. Restart the Julia session for this to take effect."
+end
diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
index 1a6420468..b323a7f8e 100644
--- a/lib/NonlinearSolveFirstOrder/Project.toml
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -52,6 +52,7 @@ Reexport = "1"
 SciMLBase = "2.54"
 SciMLJacobianOperators = "0.1.0"
 Setfield = "1.1.1"
+SparseArrays = "1.10"
 SparseConnectivityTracer = "0.6.8"
 SparseMatrixColorings = "0.4.8"
 StableRNGs = "1"
@@ -75,6 +76,7 @@ NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
 SparseMatrixColorings = "0a514795-09f3-496d-8182-132a7b665d35"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
@@ -83,4 +85,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "Enzyme", "ExplicitImports", "Hwloc", "InteractiveUtils", "LineSearch", "LineSearches", "NonlinearProblemLibrary", "Pkg", "Random", "ReTestItems", "SparseConnectivityTracer", "SparseMatrixColorings", "StableRNGs", "StaticArrays", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "Enzyme", "ExplicitImports", "Hwloc", "InteractiveUtils", "LineSearch", "LineSearches", "NonlinearProblemLibrary", "Pkg", "Random", "ReTestItems", "SparseArrays", "SparseConnectivityTracer", "SparseMatrixColorings", "StableRNGs", "StaticArrays", "Test", "Zygote"]
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 74dea2342..87bc2a5b3 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -12,7 +12,8 @@ using DiffEqBase: DiffEqBase # Needed for `init` / `solve` dispatches
 using LinearAlgebra: LinearAlgebra, norm
 using LineSearch: BackTracking
 using NonlinearSolveBase: NonlinearSolveBase, InternalAPI, AbstractNonlinearSolveAlgorithm,
-                          AbstractNonlinearSolveCache, Utils, L2_NORM
+                          AbstractNonlinearSolveCache, Utils, L2_NORM,
+                          enable_timer_outputs, disable_timer_outputs
 
 using Preferences: set_preferences!
 using SciMLBase: SciMLBase, NLStats, ReturnCode, AbstractNonlinearProblem, NonlinearProblem,
diff --git a/src/helpers.jl b/src/helpers.jl
index b28ef01dd..e69de29bb 100644
--- a/src/helpers.jl
+++ b/src/helpers.jl
@@ -1,21 +0,0 @@
-"""
-    enable_timer_outputs()
-
-Enable `TimerOutput` for all `NonlinearSolve` algorithms. This is useful for debugging
-but has some overhead, so it is disabled by default.
-"""
-function enable_timer_outputs()
-    set_preferences!(NonlinearSolveBase, "enable_timer_outputs" => true; force = true)
-    @info "Timer Outputs Enabled. Restart the Julia session for this to take effect."
-end
-
-"""
-    disable_timer_outputs()
-
-Disable `TimerOutput` for all `NonlinearSolve` algorithms. This should be used when
-`NonlinearSolve` is being used in performance-critical code.
-"""
-function disable_timer_outputs()
-    set_preferences!(NonlinearSolveBase, "enable_timer_outputs" => false; force = true)
-    @info "Timer Outputs Disabled. Restart the Julia session for this to take effect."
-end
diff --git a/test/23_test_problems_tests.jl b/test/23_test_problems_tests.jl
new file mode 100644
index 000000000..6246cbecb
--- /dev/null
+++ b/test/23_test_problems_tests.jl
@@ -0,0 +1,144 @@
+# @testsetup module RobustnessTesting
+# using NonlinearSolve, LinearAlgebra, LinearSolve, NonlinearProblemLibrary, Test
+
+# problems = NonlinearProblemLibrary.problems
+# dicts = NonlinearProblemLibrary.dicts
+
+# function test_on_library(
+#         problems, dicts, alg_ops, broken_tests, ϵ = 1e-4; skip_tests = nothing)
+#     for (idx, (problem, dict)) in enumerate(zip(problems, dicts))
+#         x = dict["start"]
+#         res = similar(x)
+#         nlprob = NonlinearProblem(problem, copy(x))
+#         @testset "$idx: $(dict["title"])" begin
+#             for alg in alg_ops
+#                 try
+#                     sol = solve(nlprob, alg; maxiters = 10000)
+#                     problem(res, sol.u, nothing)
+
+#                     skip = skip_tests !== nothing && idx in skip_tests[alg]
+#                     if skip
+#                         @test_skip norm(res, Inf) ≤ ϵ
+#                         continue
+#                     end
+#                     broken = idx in broken_tests[alg] ? true : false
+#                     @test norm(res, Inf)≤ϵ broken=broken
+#                 catch err
+#                     @error err
+#                     broken = idx in broken_tests[alg] ? true : false
+#                     if broken
+#                         @test false broken=true
+#                     else
+#                         @test 1 == 2
+#                     end
+#                 end
+#             end
+#         end
+#     end
+# end
+
+# export test_on_library, problems, dicts
+# end
+
+# @testitem "PolyAlgorithms" setup=[RobustnessTesting] tags=[:core] begin
+#     alg_ops = (RobustMultiNewton(), FastShortcutNonlinearPolyalg())
+
+#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
+#     broken_tests[alg_ops[1]] = []
+#     broken_tests[alg_ops[2]] = []
+
+#     test_on_library(problems, dicts, alg_ops, broken_tests)
+# end
+
+# @testitem "NewtonRaphson" setup=[RobustnessTesting] tags=[:core] begin
+#     alg_ops = (NewtonRaphson(),)
+
+#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
+#     broken_tests[alg_ops[1]] = [1]
+
+#     test_on_library(problems, dicts, alg_ops, broken_tests)
+# end
+
+# @testitem "TrustRegion" setup=[RobustnessTesting] tags=[:core] begin
+#     alg_ops = (TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Simple),
+#         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Fan),
+#         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Hei),
+#         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Yuan),
+#         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Bastin),
+#         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.NLsolve))
+
+#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
+#     broken_tests[alg_ops[1]] = [11, 21]
+#     broken_tests[alg_ops[2]] = [11, 21]
+#     broken_tests[alg_ops[3]] = [11, 21]
+#     broken_tests[alg_ops[4]] = [8, 11, 21]
+#     broken_tests[alg_ops[5]] = [21]
+#     broken_tests[alg_ops[6]] = [11, 21]
+
+#     test_on_library(problems, dicts, alg_ops, broken_tests)
+# end
+
+# @testitem "LevenbergMarquardt" setup=[RobustnessTesting] tags=[:core] begin
+#     using LinearSolve
+
+#     alg_ops = (LevenbergMarquardt(), LevenbergMarquardt(; α_geodesic = 0.1),
+#         LevenbergMarquardt(; linsolve = CholeskyFactorization()))
+
+#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
+#     broken_tests[alg_ops[1]] = [11, 21]
+#     broken_tests[alg_ops[2]] = [11, 21]
+#     broken_tests[alg_ops[3]] = [11, 21]
+
+#     test_on_library(problems, dicts, alg_ops, broken_tests)
+# end
+
+# @testitem "DFSane" setup=[RobustnessTesting] tags=[:core] begin
+#     alg_ops = (DFSane(),)
+
+#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
+#     broken_tests[alg_ops[1]] = [1, 2, 3, 5, 21]
+
+#     test_on_library(problems, dicts, alg_ops, broken_tests)
+# end
+
+# @testitem "Broyden" setup=[RobustnessTesting] tags=[:core] begin
+#     alg_ops = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian)),
+#         Broyden(; update_rule = Val(:bad_broyden)),
+#         Broyden(; init_jacobian = Val(:true_jacobian), update_rule = Val(:bad_broyden)))
+
+#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
+#     if Sys.isapple()
+#         broken_tests[alg_ops[1]] = [1, 5, 11]
+#         broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
+#         broken_tests[alg_ops[3]] = [1, 5, 6, 9, 11]
+#         broken_tests[alg_ops[4]] = [5, 6, 8, 11]
+#     else
+#         broken_tests[alg_ops[1]] = [1, 5, 11, 15]
+#         broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
+#         broken_tests[alg_ops[3]] = [1, 5, 9, 11]
+#         broken_tests[alg_ops[4]] = [5, 6, 8, 11]
+#     end
+
+#     test_on_library(problems, dicts, alg_ops, broken_tests, Sys.isapple() ? 1e-3 : 1e-4)
+# end
+
+# @testitem "Klement" setup=[RobustnessTesting] tags=[:core] begin
+#     alg_ops = (Klement(), Klement(; init_jacobian = Val(:true_jacobian_diagonal)))
+
+#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
+#     broken_tests[alg_ops[1]] = [1, 2, 4, 5, 11, 18, 22]
+#     broken_tests[alg_ops[2]] = [2, 4, 5, 7, 18, 22]
+
+#     test_on_library(problems, dicts, alg_ops, broken_tests)
+# end
+
+# @testitem "PseudoTransient" setup=[RobustnessTesting] tags=[:core] begin
+#     # PT relies on the root being a stable equilibrium for convergence, so it won't work on
+#     # most problems
+#     alg_ops = (PseudoTransient(),)
+
+#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
+#     broken_tests[alg_ops[1]] = [1, 2, 3, 11, 15, 16]
+
+#     test_on_library(problems, dicts, alg_ops, broken_tests)
+# end
diff --git a/test/core/23_test_problems_tests.jl b/test/core/23_test_problems_tests.jl
deleted file mode 100644
index 7648db53f..000000000
--- a/test/core/23_test_problems_tests.jl
+++ /dev/null
@@ -1,144 +0,0 @@
-@testsetup module RobustnessTesting
-using NonlinearSolve, LinearAlgebra, LinearSolve, NonlinearProblemLibrary, Test
-
-problems = NonlinearProblemLibrary.problems
-dicts = NonlinearProblemLibrary.dicts
-
-function test_on_library(
-        problems, dicts, alg_ops, broken_tests, ϵ = 1e-4; skip_tests = nothing)
-    for (idx, (problem, dict)) in enumerate(zip(problems, dicts))
-        x = dict["start"]
-        res = similar(x)
-        nlprob = NonlinearProblem(problem, copy(x))
-        @testset "$idx: $(dict["title"])" begin
-            for alg in alg_ops
-                try
-                    sol = solve(nlprob, alg; maxiters = 10000)
-                    problem(res, sol.u, nothing)
-
-                    skip = skip_tests !== nothing && idx in skip_tests[alg]
-                    if skip
-                        @test_skip norm(res, Inf) ≤ ϵ
-                        continue
-                    end
-                    broken = idx in broken_tests[alg] ? true : false
-                    @test norm(res, Inf)≤ϵ broken=broken
-                catch err
-                    @error err
-                    broken = idx in broken_tests[alg] ? true : false
-                    if broken
-                        @test false broken=true
-                    else
-                        @test 1 == 2
-                    end
-                end
-            end
-        end
-    end
-end
-
-export test_on_library, problems, dicts
-end
-
-@testitem "PolyAlgorithms" setup=[RobustnessTesting] tags=[:core] begin
-    alg_ops = (RobustMultiNewton(), FastShortcutNonlinearPolyalg())
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = []
-    broken_tests[alg_ops[2]] = []
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
-
-@testitem "NewtonRaphson" setup=[RobustnessTesting] tags=[:core] begin
-    alg_ops = (NewtonRaphson(),)
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1]
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
-
-@testitem "TrustRegion" setup=[RobustnessTesting] tags=[:core] begin
-    alg_ops = (TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Simple),
-        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Fan),
-        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Hei),
-        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Yuan),
-        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Bastin),
-        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.NLsolve))
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [11, 21]
-    broken_tests[alg_ops[2]] = [11, 21]
-    broken_tests[alg_ops[3]] = [11, 21]
-    broken_tests[alg_ops[4]] = [8, 11, 21]
-    broken_tests[alg_ops[5]] = [21]
-    broken_tests[alg_ops[6]] = [11, 21]
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
-
-@testitem "LevenbergMarquardt" setup=[RobustnessTesting] tags=[:core] begin
-    using LinearSolve
-
-    alg_ops = (LevenbergMarquardt(), LevenbergMarquardt(; α_geodesic = 0.1),
-        LevenbergMarquardt(; linsolve = CholeskyFactorization()))
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [11, 21]
-    broken_tests[alg_ops[2]] = [11, 21]
-    broken_tests[alg_ops[3]] = [11, 21]
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
-
-@testitem "DFSane" setup=[RobustnessTesting] tags=[:core] begin
-    alg_ops = (DFSane(),)
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 2, 3, 5, 21]
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
-
-@testitem "Broyden" setup=[RobustnessTesting] tags=[:core] begin
-    alg_ops = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian)),
-        Broyden(; update_rule = Val(:bad_broyden)),
-        Broyden(; init_jacobian = Val(:true_jacobian), update_rule = Val(:bad_broyden)))
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    if Sys.isapple()
-        broken_tests[alg_ops[1]] = [1, 5, 11]
-        broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
-        broken_tests[alg_ops[3]] = [1, 5, 6, 9, 11]
-        broken_tests[alg_ops[4]] = [5, 6, 8, 11]
-    else
-        broken_tests[alg_ops[1]] = [1, 5, 11, 15]
-        broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
-        broken_tests[alg_ops[3]] = [1, 5, 9, 11]
-        broken_tests[alg_ops[4]] = [5, 6, 8, 11]
-    end
-
-    test_on_library(problems, dicts, alg_ops, broken_tests, Sys.isapple() ? 1e-3 : 1e-4)
-end
-
-@testitem "Klement" setup=[RobustnessTesting] tags=[:core] begin
-    alg_ops = (Klement(), Klement(; init_jacobian = Val(:true_jacobian_diagonal)))
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 11, 18, 22]
-    broken_tests[alg_ops[2]] = [2, 4, 5, 7, 18, 22]
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
-
-@testitem "PseudoTransient" setup=[RobustnessTesting] tags=[:core] begin
-    # PT relies on the root being a stable equilibrium for convergence, so it won't work on
-    # most problems
-    alg_ops = (PseudoTransient(),)
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 2, 3, 11, 15, 16]
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
diff --git a/test/core/forward_ad_tests.jl b/test/core/forward_ad_tests.jl
deleted file mode 100644
index 24711b9d9..000000000
--- a/test/core/forward_ad_tests.jl
+++ /dev/null
@@ -1,116 +0,0 @@
-@testsetup module ForwardADTesting
-using Reexport, NonlinearSolve
-@reexport using ForwardDiff, MINPACK, NLsolve, StaticArrays, Sundials, LinearAlgebra
-
-test_f!(du, u, p) = (@. du = u^2 - p)
-test_f(u, p) = (@. u^2 - p)
-
-jacobian_f(::Number, p) = 1 / (2 * √p)
-jacobian_f(::Number, p::Number) = 1 / (2 * √p)
-jacobian_f(u, p::Number) = one.(u) .* (1 / (2 * √p))
-jacobian_f(u, p::AbstractArray) = diagm(vec(@. 1 / (2 * √p)))
-
-function solve_with(::Val{mode}, u, alg) where {mode}
-    f = if mode === :iip
-        solve_iip(p) = solve(NonlinearProblem(test_f!, u, p), alg).u
-    elseif mode === :iip_cache
-        function solve_iip_init(p)
-            cache = SciMLBase.init(NonlinearProblem(test_f!, u, p), alg)
-            return SciMLBase.solve!(cache).u
-        end
-    elseif mode === :oop
-        solve_oop(p) = solve(NonlinearProblem(test_f, u, p), alg).u
-    elseif mode === :oop_cache
-        function solve_oop_init(p)
-            cache = SciMLBase.init(NonlinearProblem(test_f, u, p), alg)
-            return SciMLBase.solve!(cache).u
-        end
-    end
-    return f
-end
-
-__compatible(::Any, ::Val{:oop}) = true
-__compatible(::Any, ::Val{:oop_cache}) = true
-__compatible(::Number, ::Val{:iip}) = false
-__compatible(::AbstractArray, ::Val{:iip}) = true
-__compatible(::StaticArray, ::Val{:iip}) = false
-__compatible(::Number, ::Val{:iip_cache}) = false
-__compatible(::AbstractArray, ::Val{:iip_cache}) = true
-__compatible(::StaticArray, ::Val{:iip_cache}) = false
-
-__compatible(::Any, ::Number) = true
-__compatible(::Number, ::AbstractArray) = false
-__compatible(u::AbstractArray, p::AbstractArray) = size(u) == size(p)
-
-__compatible(u::Number, ::SciMLBase.AbstractNonlinearAlgorithm) = true
-__compatible(u::Number, ::Union{CMINPACK, NLsolveJL, KINSOL}) = true
-__compatible(u::AbstractArray, ::SciMLBase.AbstractNonlinearAlgorithm) = true
-__compatible(u::AbstractArray{T, N}, ::KINSOL) where {T, N} = N == 1  # Need to be fixed upstream
-__compatible(u::StaticArray{S, T, N}, ::KINSOL) where {S <: Tuple, T, N} = false
-__compatible(u::StaticArray, ::SciMLBase.AbstractNonlinearAlgorithm) = true
-__compatible(u::StaticArray, ::Union{CMINPACK, NLsolveJL, KINSOL}) = false
-__compatible(u, ::Nothing) = true
-
-__compatible(::Any, ::Any) = true
-__compatible(::CMINPACK, ::Val{:iip_cache}) = false
-__compatible(::CMINPACK, ::Val{:oop_cache}) = false
-__compatible(::NLsolveJL, ::Val{:iip_cache}) = false
-__compatible(::NLsolveJL, ::Val{:oop_cache}) = false
-__compatible(::KINSOL, ::Val{:iip_cache}) = false
-__compatible(::KINSOL, ::Val{:oop_cache}) = false
-
-export test_f!, test_f, jacobian_f, solve_with, __compatible
-end
-
-@testitem "ForwardDiff.jl Integration" setup=[ForwardADTesting] tags=[:core] begin
-    for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
-        PseudoTransient(; alpha_initial = 10.0), Broyden(), Klement(), DFSane(),
-        nothing, NLsolveJL(), CMINPACK(), KINSOL(; globalization_strategy = :LineSearch))
-        us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
-
-        alg isa CMINPACK && Sys.isapple() && continue
-
-        @testset "Scalar AD" begin
-            for p in 1.0:0.1:100.0, u0 in us, mode in (:iip, :oop, :iip_cache, :oop_cache)
-                __compatible(u0, alg) || continue
-                __compatible(u0, Val(mode)) || continue
-                __compatible(alg, Val(mode)) || continue
-
-                sol = solve(NonlinearProblem(test_f, u0, p), alg)
-                if SciMLBase.successful_retcode(sol)
-                    gs = abs.(ForwardDiff.derivative(solve_with(Val{mode}(), u0, alg), p))
-                    gs_true = abs.(jacobian_f(u0, p))
-                    if !(isapprox(gs, gs_true, atol = 1e-5))
-                        @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_gradient=gs true_gradient=gs_true
-                    else
-                        @test abs.(gs)≈abs.(gs_true) atol=1e-5
-                    end
-                end
-            end
-        end
-
-        @testset "Jacobian" begin
-            for u0 in us,
-                p in ([2.0, 1.0], [2.0 1.0; 3.0 4.0]),
-                mode in (:iip, :oop, :iip_cache, :oop_cache)
-
-                __compatible(u0, p) || continue
-                __compatible(u0, alg) || continue
-                __compatible(u0, Val(mode)) || continue
-                __compatible(alg, Val(mode)) || continue
-
-                sol = solve(NonlinearProblem(test_f, u0, p), alg)
-                if SciMLBase.successful_retcode(sol)
-                    gs = abs.(ForwardDiff.jacobian(solve_with(Val{mode}(), u0, alg), p))
-                    gs_true = abs.(jacobian_f(u0, p))
-                    if !(isapprox(gs, gs_true, atol = 1e-5))
-                        @show sol.retcode, sol.u
-                        @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_jacobian=gs true_jacobian=gs_true
-                    else
-                        @test abs.(gs)≈abs.(gs_true) atol=1e-5
-                    end
-                end
-            end
-        end
-    end
-end
diff --git a/test/core/nlls_tests.jl b/test/core/nlls_tests.jl
deleted file mode 100644
index 85f4ba4ba..000000000
--- a/test/core/nlls_tests.jl
+++ /dev/null
@@ -1,21 +0,0 @@
-
-# TODO: Test polyalg here
-
-@testitem "NLLS Analytic Jacobian" tags=[:core] begin
-    dataIn = 1:10
-    f(x, p) = x[1] * dataIn .^ 2 .+ x[2] * dataIn .+ x[3]
-    dataOut = f([1, 2, 3], nothing) + 0.1 * randn(10, 1)
-
-    resid(x, p) = f(x, p) - dataOut
-    jac(x, p) = [dataIn .^ 2 dataIn ones(10, 1)]
-    x0 = [1, 1, 1]
-
-    prob = NonlinearLeastSquaresProblem(resid, x0)
-    sol1 = solve(prob)
-
-    nlfunc = NonlinearFunction(resid; jac)
-    prob = NonlinearLeastSquaresProblem(nlfunc, x0)
-    sol2 = solve(prob)
-
-    @test sol1.u ≈ sol2.u
-end
diff --git a/test/core_tests.jl b/test/core_tests.jl
new file mode 100644
index 000000000..301b0b389
--- /dev/null
+++ b/test/core_tests.jl
@@ -0,0 +1,416 @@
+@testitem "NLLS Analytic Jacobian" tags=[:core] begin
+    dataIn = 1:10
+    f(x, p) = x[1] * dataIn .^ 2 .+ x[2] * dataIn .+ x[3]
+    dataOut = f([1, 2, 3], nothing) + 0.1 * randn(10, 1)
+
+    resid(x, p) = f(x, p) - dataOut
+    jac(x, p) = [dataIn .^ 2 dataIn ones(10, 1)]
+    x0 = [1, 1, 1]
+
+    prob = NonlinearLeastSquaresProblem(resid, x0)
+    sol1 = solve(prob)
+
+    nlfunc = NonlinearFunction(resid; jac)
+    prob = NonlinearLeastSquaresProblem(nlfunc, x0)
+    sol2 = solve(prob)
+
+    @test sol1.u ≈ sol2.u
+end
+
+@testitem "Basic PolyAlgorithms" tags=[:core] begin
+    f(u, p) = u .* u .- 2
+    u0 = [1.0, 1.0]
+
+    prob = NonlinearProblem(f, u0)
+
+    polyalgs = (
+        RobustMultiNewton(), FastShortcutNonlinearPolyalg(), nothing, missing,
+        NonlinearSolvePolyAlgorithm((Broyden(), LimitedMemoryBroyden()))
+    )
+
+    @testset "Direct Solve" begin
+        @testset for alg in polyalgs
+            alg = alg === missing ? () : (alg,)
+            sol = solve(prob, alg...; abstol = 1e-9)
+            @test SciMLBase.successful_retcode(sol)
+            err = maximum(abs, f(sol.u, 2.0))
+            @test err < 1e-9
+        end
+    end
+
+    @testset "Caching Interface" begin
+        @testset for alg in polyalgs
+            alg = alg === missing ? () : (alg,)
+            cache = init(prob, alg...; abstol = 1e-9)
+            solver = solve!(cache)
+            @test SciMLBase.successful_retcode(solver)
+        end
+    end
+
+    @testset "Step Interface" begin
+        @testset for alg in polyalgs
+            alg = alg === missing ? () : (alg,)
+            cache = init(prob, alg...; abstol = 1e-9)
+            for i in 1:10000
+                step!(cache)
+                cache.force_stop && break
+            end
+            @test SciMLBase.successful_retcode(cache.retcode)
+        end
+    end
+end
+
+@testitem "PolyAlgorithms Autodiff" tags=[:core] begin
+    cache = zeros(2)
+    function f(du, u, p)
+        cache .= u .* u
+        du .= cache .- 2
+    end
+    u0 = [1.0, 1.0]
+    probN = NonlinearProblem{true}(f, u0)
+
+    custom_polyalg = NonlinearSolvePolyAlgorithm((
+        Broyden(; autodiff = AutoFiniteDiff()), LimitedMemoryBroyden())
+    )
+
+    # Uses the `__solve` function
+    @test_throws MethodError solve(probN; abstol = 1e-9)
+    @test_throws MethodError solve(probN, RobustMultiNewton())
+
+    sol = solve(probN, RobustMultiNewton(; autodiff = AutoFiniteDiff()))
+    @test SciMLBase.successful_retcode(sol)
+
+    sol = solve(
+        probN, FastShortcutNonlinearPolyalg(; autodiff = AutoFiniteDiff()); abstol = 1e-9
+    )
+    @test SciMLBase.successful_retcode(sol)
+
+    quadratic_f(u::Float64, p) = u^2 - p
+
+    prob = NonlinearProblem(quadratic_f, 2.0, 4.0)
+
+    @test_throws MethodError solve(prob)
+    @test_throws MethodError solve(prob, RobustMultiNewton())
+
+    sol = solve(prob, RobustMultiNewton(; autodiff = AutoFiniteDiff()))
+    @test SciMLBase.successful_retcode(sol)
+end
+
+@testitem "PolyAlgorithm Aliasing" tags=[:core] begin
+    using NonlinearProblemLibrary
+
+    # Use a problem that the initial solvers cannot solve and cause the initial value to
+    # diverge. If we don't alias correctly, all the subsequent algorithms will also fail.
+    prob = NonlinearProblemLibrary.nlprob_23_testcases["Generalized Rosenbrock function"].prob
+    u0 = copy(prob.u0)
+    prob = remake(prob; u0 = copy(u0))
+
+    # If aliasing is not handled properly this will diverge
+    sol = solve(
+        prob; abstol = 1e-6, alias_u0 = true,
+        termination_condition = AbsNormTerminationMode(Base.Fix1(maximum, abs))
+    )
+
+    @test sol.u === prob.u0
+    @test SciMLBase.successful_retcode(sol.retcode)
+
+    prob = remake(prob; u0 = copy(u0))
+
+    cache = init(
+        prob; abstol = 1e-6, alias_u0 = true,
+        termination_condition = AbsNormTerminationMode(Base.Fix1(maximum, abs))
+    )
+    sol = solve!(cache)
+
+    @test sol.u === prob.u0
+    @test SciMLBase.successful_retcode(sol.retcode)
+end
+
+@testitem "Ensemble Nonlinear Problems" tags=[:core] begin
+    prob_func(prob, i, repeat) = remake(prob; u0 = prob.u0[:, i])
+
+    prob_nls_oop = NonlinearProblem((u, p) -> u .* u .- p, rand(4, 128), 2.0)
+    prob_nls_iip = NonlinearProblem((du, u, p) -> du .= u .* u .- p, rand(4, 128), 2.0)
+    prob_nlls_oop = NonlinearLeastSquaresProblem((u, p) -> u .^ 2 .- p, rand(4, 128), 2.0)
+    prob_nlls_iip = NonlinearLeastSquaresProblem(
+        NonlinearFunction{true}((du, u, p) -> du .= u .^ 2 .- p; resid_prototype = rand(4)),
+        rand(4, 128), 2.0
+    )
+
+    for prob in (prob_nls_oop, prob_nls_iip, prob_nlls_oop, prob_nlls_iip)
+        ensembleprob = EnsembleProblem(prob; prob_func)
+
+        for ensemblealg in (EnsembleThreads(), EnsembleSerial())
+            sim = solve(ensembleprob, nothing, ensemblealg; trajectories = size(prob.u0, 2))
+            @test all(SciMLBase.successful_retcode, sim.u)
+        end
+    end
+end
+
+@testitem "BigFloat Support" tags=[:core] begin
+    using LinearAlgebra
+
+    fn_iip = NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p)
+    fn_oop = NonlinearFunction{false}((u, p) -> u .* u .- p)
+
+    u0 = BigFloat[1.0, 1.0, 1.0]
+    prob_iip_bf = NonlinearProblem{true}(fn_iip, u0, BigFloat(2))
+    prob_oop_bf = NonlinearProblem{false}(fn_oop, u0, BigFloat(2))
+
+    for alg in (NewtonRaphson(), Broyden(), Klement(), DFSane(), TrustRegion())
+        sol = solve(prob_oop_bf, alg)
+        @test norm(sol.resid, Inf) < 1e-6
+        @test SciMLBase.successful_retcode(sol.retcode)
+
+        sol = solve(prob_iip_bf, alg)
+        @test norm(sol.resid, Inf) < 1e-6
+        @test SciMLBase.successful_retcode(sol.retcode)
+    end
+end
+
+@testitem "Singular Exception: Issue #153" tags=[:core] begin
+    function f(du, u, p)
+        s1, s1s2, s2 = u
+        k1, c1, Δt = p
+
+        du[1] = -0.25 * c1 * k1 * s1 * s2
+        du[2] = 0.25 * c1 * k1 * s1 * s2
+        du[3] = -0.25 * c1 * k1 * s1 * s2
+    end
+
+    prob = NonlinearProblem(f, [2.0, 2.0, 2.0], [1.0, 2.0, 2.5])
+    sol = solve(prob; abstol = 1e-9)
+    @test SciMLBase.successful_retcode(sol)
+end
+
+@testitem "Simple Scalar Problem: Issue #187" tags=[:core] begin
+    using NaNMath
+
+    # https://github.com/SciML/NonlinearSolve.jl/issues/187
+    # If we use a General Nonlinear Solver the solution might go out of the domain!
+    ff_interval(u, p) = 0.5 / 1.5 * NaNMath.log.(u ./ (1.0 .- u)) .- 2.0 * u .+ 1.0
+
+    uspan = (0.02, 0.1)
+    prob = IntervalNonlinearProblem(ff_interval, uspan)
+    sol = solve(prob; abstol = 1e-9)
+    @test SciMLBase.successful_retcode(sol)
+
+    u0 = 0.06
+    p = 2.0
+    prob = NonlinearProblem(ff_interval, u0, p)
+    sol = solve(prob; abstol = 1e-9)
+    @test SciMLBase.successful_retcode(sol)
+end
+
+# Shooting Problem: Taken from BoundaryValueDiffEq.jl
+# Testing for Complex Valued Root Finding. For Complex valued inputs we drop some of the
+# algorithms which dont support those.
+@testitem "Complex Valued Problems: Single-Shooting" tags=[:core] begin
+    using OrdinaryDiffEqTsit5
+
+    function ode_func!(du, u, p, t)
+        du[1] = u[2]
+        du[2] = -u[1]
+        return nothing
+    end
+
+    function objective_function!(resid, u0, p)
+        odeprob = ODEProblem{true}(ode_func!, u0, (0.0, 100.0), p)
+        sol = solve(odeprob, Tsit5(), abstol = 1e-9, reltol = 1e-9, verbose = false)
+        resid[1] = sol(0.0)[1]
+        resid[2] = sol(100.0)[1] - 1.0
+        return nothing
+    end
+
+    prob = NonlinearProblem{true}(objective_function!, [0.0, 1.0] .+ 1im)
+    sol = solve(prob; abstol = 1e-10)
+    @test SciMLBase.successful_retcode(sol)
+    # This test is not meant to return success but test that all the default solvers can handle
+    # complex valued problems
+    @test_nowarn solve(prob; abstol = 1e-19, maxiters = 10)
+    @test_nowarn solve(
+        prob, RobustMultiNewton(eltype(prob.u0)); abstol = 1e-19, maxiters = 10
+    )
+end
+
+@testitem "No AD" tags=[:core] begin
+    no_ad_fast = FastShortcutNonlinearPolyalg(autodiff = AutoFiniteDiff())
+    no_ad_robust = RobustMultiNewton(autodiff = AutoFiniteDiff())
+    no_ad_algs = Set([no_ad_fast, no_ad_robust, no_ad_fast.algs..., no_ad_robust.algs...])
+
+    @testset "Inplace" begin
+        f_iip = Base.Experimental.@opaque (du, u, p) -> du .= u .* u .- p
+        u0 = [0.5]
+        prob = NonlinearProblem(f_iip, u0, 1.0)
+        for alg in no_ad_algs
+            sol = solve(prob, alg)
+            @test isapprox(only(sol.u), 1.0)
+            @test SciMLBase.successful_retcode(sol.retcode)
+        end
+    end
+
+    @testset "Out of Place" begin
+        f_oop = Base.Experimental.@opaque (u, p) -> u .* u .- p
+        u0 = [0.5]
+        prob = NonlinearProblem{false}(f_oop, u0, 1.0)
+        for alg in no_ad_algs
+            sol = solve(prob, alg)
+            @test isapprox(only(sol.u), 1.0)
+            @test SciMLBase.successful_retcode(sol.retcode)
+        end
+    end
+end
+
+@testitem "Infeasible" tags=[:core] begin
+    using LinearAlgebra, StaticArrays
+
+    # this is infeasible
+    function f1_infeasible!(out, u, p)
+        μ = 3.986004415e14
+        x = 7000.0e3
+        y = -6.970561549987071e-9
+        z = -3.784706123246018e-9
+        v_x = 8.550491684548064e-12 + u[1]
+        v_y = 6631.60076191005 + u[2]
+        v_z = 3600.665431405663 + u[3]
+        r = @SVector [x, y, z]
+        v = @SVector [v_x, v_y, v_z]
+        h = cross(r, v)
+        ev = cross(v, h) / μ - r / norm(r)
+        i = acos(h[3] / norm(h))
+        e = norm(ev)
+        a = 1 / (2 / norm(r) - (norm(v)^2 / μ))
+        out .= [a - 42.0e6, e - 1e-5, i - 1e-5]
+        return nothing
+    end
+
+    function f1_infeasible(u, p)
+        μ = 3.986004415e14
+        x = 7000.0e3
+        y = -6.970561549987071e-9
+        z = -3.784706123246018e-9
+        v_x = 8.550491684548064e-12 + u[1]
+        v_y = 6631.60076191005 + u[2]
+        v_z = 3600.665431405663 + u[3]
+        r = [x, y, z]
+        v = [v_x, v_y, v_z]
+        h = cross(r, v)
+        ev = cross(v, h) / μ - r / norm(r)
+        i = acos(h[3] / norm(h))
+        e = norm(ev)
+        a = 1 / (2 / norm(r) - (norm(v)^2 / μ))
+        return [a - 42.0e6, e - 1e-5, i - 1e-5]
+    end
+
+    u0 = [0.0, 0.0, 0.0]
+    prob = NonlinearProblem(f1_infeasible!, u0)
+    sol = solve(prob)
+
+    @test all(!isnan, sol.u)
+    @test !SciMLBase.successful_retcode(sol.retcode)
+    @inferred solve(prob)
+
+    u0 = [0.0, 0.0, 0.0]
+    prob = NonlinearProblem(f1_infeasible, u0)
+    sol = solve(prob)
+
+    @test all(!isnan, sol.u)
+    @test !SciMLBase.successful_retcode(sol.retcode)
+    @inferred solve(prob)
+
+    u0 = @SVector [0.0, 0.0, 0.0]
+    prob = NonlinearProblem(f1_infeasible, u0)
+
+    sol = solve(prob)
+    @test all(!isnan, sol.u)
+    @test !SciMLBase.successful_retcode(sol.retcode)
+end
+
+@testitem "NoInit Caching" tags=[:core] begin
+    using LinearAlgebra
+
+    solvers = [
+        SimpleNewtonRaphson(), SimpleTrustRegion(), SimpleDFSane()
+    ]
+
+    prob = NonlinearProblem((u, p) -> u .^ 2 .- p, [0.1, 0.3], 2.0)
+
+    for alg in solvers
+        cache = init(prob, alg)
+        sol = solve!(cache)
+        @test SciMLBase.successful_retcode(sol)
+        @test norm(sol.resid, Inf) ≤ 1e-6
+
+        reinit!(cache; p = 5.0)
+        @test cache.prob.p == 5.0
+        sol = solve!(cache)
+        @test SciMLBase.successful_retcode(sol)
+        @test norm(sol.resid, Inf) ≤ 1e-6
+        @test norm(sol.u .^ 2 .- 5.0, Inf) ≤ 1e-6
+    end
+end
+
+@testitem "Out-of-place Matrix Resizing" tags=[:core] begin
+    using StableRNGs
+
+    ff(u, p) = u .* u .- p
+    u0 = rand(StableRNG(0), 2, 2)
+    p = 2.0
+    vecprob = NonlinearProblem(ff, vec(u0), p)
+    prob = NonlinearProblem(ff, u0, p)
+
+    for alg in (
+        NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
+        PseudoTransient(), RobustMultiNewton(), FastShortcutNonlinearPolyalg(),
+        Broyden(), Klement(), LimitedMemoryBroyden(; threshold = 2)
+    )
+        @test vec(solve(prob, alg).u) == solve(vecprob, alg).u
+    end
+end
+
+@testitem "Inplace Matrix Resizing" tags=[:core] begin
+    using StableRNGs
+
+    fiip(du, u, p) = (du .= u .* u .- p)
+    u0 = rand(StableRNG(0), 2, 2)
+    p = 2.0
+    vecprob = NonlinearProblem(fiip, vec(u0), p)
+    prob = NonlinearProblem(fiip, u0, p)
+
+    for alg in (
+        NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
+        PseudoTransient(), RobustMultiNewton(), FastShortcutNonlinearPolyalg(),
+        Broyden(), Klement(), LimitedMemoryBroyden(; threshold = 2)
+    )
+        @test vec(solve(prob, alg).u) == solve(vecprob, alg).u
+    end
+end
+
+@testitem "Singular Systems -- Auto Linear Solve Switching" tags=[:core] begin
+    using LinearAlgebra
+
+    function f!(du, u, p)
+        du[1] = 2u[1] - 2
+        du[2] = (u[1] - 4u[2])^2 + 0.1
+    end
+
+    u0 = [0.0, 0.0] # Singular Jacobian at u0
+
+    prob = NonlinearProblem(f!, u0)
+
+    sol = solve(prob) # This doesn't have a root so let's just test the switching
+    @test sol.u≈[1.0, 0.25] atol=1e-3 rtol=1e-3
+
+    function nlls!(du, u, p)
+        du[1] = 2u[1] - 2
+        du[2] = (u[1] - 4u[2])^2 + 0.1
+        du[3] = 0
+    end
+
+    u0 = [0.0, 0.0]
+
+    prob = NonlinearProblem(NonlinearFunction(nlls!, resid_prototype = zeros(3)), u0)
+
+    solve(prob)
+    @test sol.u≈[1.0, 0.25] atol=1e-3 rtol=1e-3
+end
diff --git a/test/gpu/core_tests.jl b/test/cuda_tests.jl
similarity index 100%
rename from test/gpu/core_tests.jl
rename to test/cuda_tests.jl
diff --git a/test/forward_ad_tests.jl b/test/forward_ad_tests.jl
new file mode 100644
index 000000000..e40b0a91d
--- /dev/null
+++ b/test/forward_ad_tests.jl
@@ -0,0 +1,116 @@
+# @testsetup module ForwardADTesting
+# using Reexport, NonlinearSolve
+# @reexport using ForwardDiff, MINPACK, NLsolve, StaticArrays, Sundials, LinearAlgebra
+
+# test_f!(du, u, p) = (@. du = u^2 - p)
+# test_f(u, p) = (@. u^2 - p)
+
+# jacobian_f(::Number, p) = 1 / (2 * √p)
+# jacobian_f(::Number, p::Number) = 1 / (2 * √p)
+# jacobian_f(u, p::Number) = one.(u) .* (1 / (2 * √p))
+# jacobian_f(u, p::AbstractArray) = diagm(vec(@. 1 / (2 * √p)))
+
+# function solve_with(::Val{mode}, u, alg) where {mode}
+#     f = if mode === :iip
+#         solve_iip(p) = solve(NonlinearProblem(test_f!, u, p), alg).u
+#     elseif mode === :iip_cache
+#         function solve_iip_init(p)
+#             cache = SciMLBase.init(NonlinearProblem(test_f!, u, p), alg)
+#             return SciMLBase.solve!(cache).u
+#         end
+#     elseif mode === :oop
+#         solve_oop(p) = solve(NonlinearProblem(test_f, u, p), alg).u
+#     elseif mode === :oop_cache
+#         function solve_oop_init(p)
+#             cache = SciMLBase.init(NonlinearProblem(test_f, u, p), alg)
+#             return SciMLBase.solve!(cache).u
+#         end
+#     end
+#     return f
+# end
+
+# __compatible(::Any, ::Val{:oop}) = true
+# __compatible(::Any, ::Val{:oop_cache}) = true
+# __compatible(::Number, ::Val{:iip}) = false
+# __compatible(::AbstractArray, ::Val{:iip}) = true
+# __compatible(::StaticArray, ::Val{:iip}) = false
+# __compatible(::Number, ::Val{:iip_cache}) = false
+# __compatible(::AbstractArray, ::Val{:iip_cache}) = true
+# __compatible(::StaticArray, ::Val{:iip_cache}) = false
+
+# __compatible(::Any, ::Number) = true
+# __compatible(::Number, ::AbstractArray) = false
+# __compatible(u::AbstractArray, p::AbstractArray) = size(u) == size(p)
+
+# __compatible(u::Number, ::SciMLBase.AbstractNonlinearAlgorithm) = true
+# __compatible(u::Number, ::Union{CMINPACK, NLsolveJL, KINSOL}) = true
+# __compatible(u::AbstractArray, ::SciMLBase.AbstractNonlinearAlgorithm) = true
+# __compatible(u::AbstractArray{T, N}, ::KINSOL) where {T, N} = N == 1  # Need to be fixed upstream
+# __compatible(u::StaticArray{S, T, N}, ::KINSOL) where {S <: Tuple, T, N} = false
+# __compatible(u::StaticArray, ::SciMLBase.AbstractNonlinearAlgorithm) = true
+# __compatible(u::StaticArray, ::Union{CMINPACK, NLsolveJL, KINSOL}) = false
+# __compatible(u, ::Nothing) = true
+
+# __compatible(::Any, ::Any) = true
+# __compatible(::CMINPACK, ::Val{:iip_cache}) = false
+# __compatible(::CMINPACK, ::Val{:oop_cache}) = false
+# __compatible(::NLsolveJL, ::Val{:iip_cache}) = false
+# __compatible(::NLsolveJL, ::Val{:oop_cache}) = false
+# __compatible(::KINSOL, ::Val{:iip_cache}) = false
+# __compatible(::KINSOL, ::Val{:oop_cache}) = false
+
+# export test_f!, test_f, jacobian_f, solve_with, __compatible
+# end
+
+# @testitem "ForwardDiff.jl Integration" setup=[ForwardADTesting] tags=[:core] begin
+#     for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
+#         PseudoTransient(; alpha_initial = 10.0), Broyden(), Klement(), DFSane(),
+#         nothing, NLsolveJL(), CMINPACK(), KINSOL(; globalization_strategy = :LineSearch))
+#         us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
+
+#         alg isa CMINPACK && Sys.isapple() && continue
+
+#         @testset "Scalar AD" begin
+#             for p in 1.0:0.1:100.0, u0 in us, mode in (:iip, :oop, :iip_cache, :oop_cache)
+#                 __compatible(u0, alg) || continue
+#                 __compatible(u0, Val(mode)) || continue
+#                 __compatible(alg, Val(mode)) || continue
+
+#                 sol = solve(NonlinearProblem(test_f, u0, p), alg)
+#                 if SciMLBase.successful_retcode(sol)
+#                     gs = abs.(ForwardDiff.derivative(solve_with(Val{mode}(), u0, alg), p))
+#                     gs_true = abs.(jacobian_f(u0, p))
+#                     if !(isapprox(gs, gs_true, atol = 1e-5))
+#                         @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_gradient=gs true_gradient=gs_true
+#                     else
+#                         @test abs.(gs)≈abs.(gs_true) atol=1e-5
+#                     end
+#                 end
+#             end
+#         end
+
+#         @testset "Jacobian" begin
+#             for u0 in us,
+#                 p in ([2.0, 1.0], [2.0 1.0; 3.0 4.0]),
+#                 mode in (:iip, :oop, :iip_cache, :oop_cache)
+
+#                 __compatible(u0, p) || continue
+#                 __compatible(u0, alg) || continue
+#                 __compatible(u0, Val(mode)) || continue
+#                 __compatible(alg, Val(mode)) || continue
+
+#                 sol = solve(NonlinearProblem(test_f, u0, p), alg)
+#                 if SciMLBase.successful_retcode(sol)
+#                     gs = abs.(ForwardDiff.jacobian(solve_with(Val{mode}(), u0, alg), p))
+#                     gs_true = abs.(jacobian_f(u0, p))
+#                     if !(isapprox(gs, gs_true, atol = 1e-5))
+#                         @show sol.retcode, sol.u
+#                         @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_jacobian=gs true_jacobian=gs_true
+#                     else
+#                         @test abs.(gs)≈abs.(gs_true) atol=1e-5
+#                     end
+#                 end
+#             end
+#         end
+#     end
+# end
diff --git a/test/misc/aliasing_tests.jl b/test/misc/aliasing_tests.jl
deleted file mode 100644
index 78b8ec798..000000000
--- a/test/misc/aliasing_tests.jl
+++ /dev/null
@@ -1,25 +0,0 @@
-@testitem "PolyAlgorithm Aliasing" tags=[:misc] begin
-    using NonlinearProblemLibrary
-
-    # Use a problem that the initial solvers cannot solve and cause the initial value to
-    # diverge. If we don't alias correctly, all the subsequent algorithms will also fail.
-    prob = NonlinearProblemLibrary.nlprob_23_testcases["Generalized Rosenbrock function"].prob
-    u0 = copy(prob.u0)
-    prob = remake(prob; u0 = copy(u0))
-
-    # If aliasing is not handled properly this will diverge
-    sol = solve(prob; abstol = 1e-6, alias_u0 = true,
-        termination_condition = AbsNormTerminationMode(Base.Fix1(maximum, abs)))
-
-    @test sol.u === prob.u0
-    @test SciMLBase.successful_retcode(sol.retcode)
-
-    prob = remake(prob; u0 = copy(u0))
-
-    cache = init(prob; abstol = 1e-6, alias_u0 = true,
-        termination_condition = AbsNormTerminationMode(Base.Fix1(maximum, abs)))
-    sol = solve!(cache)
-
-    @test sol.u === prob.u0
-    @test SciMLBase.successful_retcode(sol.retcode)
-end
diff --git a/test/misc/ensemble_tests.jl b/test/misc/ensemble_tests.jl
deleted file mode 100644
index c034bf6bc..000000000
--- a/test/misc/ensemble_tests.jl
+++ /dev/null
@@ -1,21 +0,0 @@
-@testitem "Ensemble Nonlinear Problems" tags=[:misc] begin
-    using NonlinearSolve
-
-    prob_func(prob, i, repeat) = remake(prob; u0 = prob.u0[:, i])
-
-    prob_nls_oop = NonlinearProblem((u, p) -> u .* u .- p, rand(4, 128), 2.0)
-    prob_nls_iip = NonlinearProblem((du, u, p) -> du .= u .* u .- p, rand(4, 128), 2.0)
-    prob_nlls_oop = NonlinearLeastSquaresProblem((u, p) -> u .^ 2 .- p, rand(4, 128), 2.0)
-    prob_nlls_iip = NonlinearLeastSquaresProblem(
-        NonlinearFunction{true}((du, u, p) -> du .= u .^ 2 .- p; resid_prototype = rand(4)),
-        rand(4, 128), 2.0)
-
-    for prob in (prob_nls_oop, prob_nls_iip, prob_nlls_oop, prob_nlls_iip)
-        ensembleprob = EnsembleProblem(prob; prob_func)
-
-        for ensemblealg in (EnsembleThreads(), EnsembleSerial())
-            sim = solve(ensembleprob, nothing, ensemblealg; trajectories = size(prob.u0, 2))
-            @test all(SciMLBase.successful_retcode, sim.u)
-        end
-    end
-end
diff --git a/test/misc/exotic_type_tests.jl b/test/misc/exotic_type_tests.jl
deleted file mode 100644
index 57a9c28ed..000000000
--- a/test/misc/exotic_type_tests.jl
+++ /dev/null
@@ -1,27 +0,0 @@
-# File for different types of exotic types
-@testsetup module NonlinearSolveExoticTypeTests
-using NonlinearSolve
-
-fn_iip = NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p)
-fn_oop = NonlinearFunction{false}((u, p) -> u .* u .- p)
-
-u0 = BigFloat[1.0, 1.0, 1.0]
-prob_iip_bf = NonlinearProblem{true}(fn_iip, u0, BigFloat(2))
-prob_oop_bf = NonlinearProblem{false}(fn_oop, u0, BigFloat(2))
-
-export fn_iip, fn_oop, u0, prob_iip_bf, prob_oop_bf
-end
-
-@testitem "BigFloat Support" tags=[:misc] setup=[NonlinearSolveExoticTypeTests] begin
-    using NonlinearSolve, LinearAlgebra
-
-    for alg in [NewtonRaphson(), Broyden(), Klement(), DFSane(), TrustRegion()]
-        sol = solve(prob_oop_bf, alg)
-        @test norm(sol.resid, Inf) < 1e-6
-        @test SciMLBase.successful_retcode(sol.retcode)
-
-        sol = solve(prob_iip_bf, alg)
-        @test norm(sol.resid, Inf) < 1e-6
-        @test SciMLBase.successful_retcode(sol.retcode)
-    end
-end
diff --git a/test/misc/linsolve_switching_tests.jl b/test/misc/linsolve_switching_tests.jl
deleted file mode 100644
index 34d10e294..000000000
--- a/test/misc/linsolve_switching_tests.jl
+++ /dev/null
@@ -1,28 +0,0 @@
-@testitem "Singular Systems -- Auto Linear Solve Switching" tags=[:misc] begin
-    using LinearSolve, NonlinearSolve
-
-    function f!(du, u, p)
-        du[1] = 2u[1] - 2
-        du[2] = (u[1] - 4u[2])^2 + 0.1
-    end
-
-    u0 = [0.0, 0.0] # Singular Jacobian at u0
-
-    prob = NonlinearProblem(f!, u0)
-
-    sol = solve(prob)  # This doesn't have a root so let's just test the switching
-    @test sol.u≈[1.0, 0.25] atol=1e-3 rtol=1e-3
-
-    function nlls!(du, u, p)
-        du[1] = 2u[1] - 2
-        du[2] = (u[1] - 4u[2])^2 + 0.1
-        du[3] = 0
-    end
-
-    u0 = [0.0, 0.0]
-
-    prob = NonlinearProblem(NonlinearFunction(nlls!, resid_prototype = zeros(3)), u0)
-
-    solve(prob)
-    @test sol.u≈[1.0, 0.25] atol=1e-3 rtol=1e-3
-end
diff --git a/test/misc/matrix_resizing_tests.jl b/test/misc/matrix_resizing_tests.jl
deleted file mode 100644
index 2aa8151ce..000000000
--- a/test/misc/matrix_resizing_tests.jl
+++ /dev/null
@@ -1,31 +0,0 @@
-@testitem "Out-of-place Matrix Resizing" tags=[:misc] begin
-    using StableRNGs
-
-    ff(u, p) = u .* u .- p
-    u0 = rand(StableRNG(0), 2, 2)
-    p = 2.0
-    vecprob = NonlinearProblem(ff, vec(u0), p)
-    prob = NonlinearProblem(ff, u0, p)
-
-    for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
-        PseudoTransient(), RobustMultiNewton(), FastShortcutNonlinearPolyalg(),
-        Broyden(), Klement(), LimitedMemoryBroyden(; threshold = 2))
-        @test vec(solve(prob, alg).u) == solve(vecprob, alg).u
-    end
-end
-
-@testitem "Inplace Matrix Resizing" tags=[:misc] begin
-    using StableRNGs
-
-    fiip(du, u, p) = (du .= u .* u .- p)
-    u0 = rand(StableRNG(0), 2, 2)
-    p = 2.0
-    vecprob = NonlinearProblem(fiip, vec(u0), p)
-    prob = NonlinearProblem(fiip, u0, p)
-
-    for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
-        PseudoTransient(), RobustMultiNewton(), FastShortcutNonlinearPolyalg(),
-        Broyden(), Klement(), LimitedMemoryBroyden(; threshold = 2))
-        @test vec(solve(prob, alg).u) == solve(vecprob, alg).u
-    end
-end
diff --git a/test/misc/noinit_caching_tests.jl b/test/misc/noinit_caching_tests.jl
deleted file mode 100644
index 4ab4138f8..000000000
--- a/test/misc/noinit_caching_tests.jl
+++ /dev/null
@@ -1,23 +0,0 @@
-@testitem "NoInit Caching" tags=[:misc] begin
-    using LinearAlgebra
-    import NLsolve, NLSolvers
-
-    solvers = [SimpleNewtonRaphson(), SimpleTrustRegion(), SimpleDFSane(), NLsolveJL(),
-        NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking()))]
-
-    prob = NonlinearProblem((u, p) -> u .^ 2 .- p, [0.1, 0.3], 2.0)
-
-    for alg in solvers
-        cache = init(prob, alg)
-        sol = solve!(cache)
-        @test SciMLBase.successful_retcode(sol)
-        @test norm(sol.resid, Inf) ≤ 1e-6
-
-        reinit!(cache; p = 5.0)
-        @test cache.prob.p == 5.0
-        sol = solve!(cache)
-        @test SciMLBase.successful_retcode(sol)
-        @test norm(sol.resid, Inf) ≤ 1e-6
-        @test norm(sol.u .^ 2 .- 5.0, Inf) ≤ 1e-6
-    end
-end
diff --git a/test/misc/polyalg_tests.jl b/test/misc/polyalg_tests.jl
deleted file mode 100644
index a106ace44..000000000
--- a/test/misc/polyalg_tests.jl
+++ /dev/null
@@ -1,256 +0,0 @@
-@testitem "Basic PolyAlgorithms" tags=[:misc] begin
-    f(u, p) = u .* u .- 2
-    u0 = [1.0, 1.0]
-    probN = NonlinearProblem{false}(f, u0)
-
-    custom_polyalg = NonlinearSolvePolyAlgorithm((Broyden(), LimitedMemoryBroyden()))
-
-    # Uses the `__solve` function
-    solver = solve(probN; abstol = 1e-9)
-    @test SciMLBase.successful_retcode(solver)
-    solver = solve(probN, RobustMultiNewton(); abstol = 1e-9)
-    @test SciMLBase.successful_retcode(solver)
-    solver = solve(probN, FastShortcutNonlinearPolyalg(); abstol = 1e-9)
-    @test SciMLBase.successful_retcode(solver)
-    solver = solve(probN, custom_polyalg; abstol = 1e-9)
-    @test SciMLBase.successful_retcode(solver)
-
-    # Test the caching interface
-    cache = init(probN; abstol = 1e-9)
-    solver = solve!(cache)
-    @test SciMLBase.successful_retcode(solver)
-    cache = init(probN, RobustMultiNewton(); abstol = 1e-9)
-    solver = solve!(cache)
-    @test SciMLBase.successful_retcode(solver)
-    cache = init(probN, FastShortcutNonlinearPolyalg(); abstol = 1e-9)
-    solver = solve!(cache)
-    @test SciMLBase.successful_retcode(solver)
-    cache = init(probN, custom_polyalg; abstol = 1e-9)
-    solver = solve!(cache)
-    @test SciMLBase.successful_retcode(solver)
-
-    # Test the step interface
-    cache = init(probN; abstol = 1e-9)
-    for i in 1:10000
-        step!(cache)
-        cache.force_stop && break
-    end
-    @test SciMLBase.successful_retcode(cache.retcode)
-    cache = init(probN, RobustMultiNewton(); abstol = 1e-9)
-    for i in 1:10000
-        step!(cache)
-        cache.force_stop && break
-    end
-    @test SciMLBase.successful_retcode(cache.retcode)
-    cache = init(probN, FastShortcutNonlinearPolyalg(); abstol = 1e-9)
-    for i in 1:10000
-        step!(cache)
-        cache.force_stop && break
-    end
-    @test SciMLBase.successful_retcode(cache.retcode)
-    cache = init(probN, custom_polyalg; abstol = 1e-9)
-    for i in 1:10000
-        step!(cache)
-        cache.force_stop && break
-    end
-end
-
-@testitem "Testing #153 Singular Exception" tags=[:misc] begin
-    # https://github.com/SciML/NonlinearSolve.jl/issues/153
-    function f(du, u, p)
-        s1, s1s2, s2 = u
-        k1, c1, Δt = p
-
-        du[1] = -0.25 * c1 * k1 * s1 * s2
-        du[2] = 0.25 * c1 * k1 * s1 * s2
-        du[3] = -0.25 * c1 * k1 * s1 * s2
-    end
-
-    prob = NonlinearProblem(f, [2.0, 2.0, 2.0], [1.0, 2.0, 2.5])
-    sol = solve(prob; abstol = 1e-9)
-    @test SciMLBase.successful_retcode(sol)
-end
-
-@testitem "PolyAlgorithms Autodiff" tags=[:misc] begin
-    cache = zeros(2)
-    function f(du, u, p)
-        cache .= u .* u
-        du .= cache .- 2
-    end
-    u0 = [1.0, 1.0]
-    probN = NonlinearProblem{true}(f, u0)
-
-    custom_polyalg = NonlinearSolvePolyAlgorithm((
-        Broyden(; autodiff = AutoFiniteDiff()), LimitedMemoryBroyden()))
-
-    # Uses the `__solve` function
-    @test_throws MethodError solve(probN; abstol = 1e-9)
-    @test_throws MethodError solve(probN, RobustMultiNewton(); abstol = 1e-9)
-    sol = solve(probN, RobustMultiNewton(; autodiff = AutoFiniteDiff()); abstol = 1e-9)
-    @test SciMLBase.successful_retcode(sol)
-    sol = solve(
-        probN, FastShortcutNonlinearPolyalg(; autodiff = AutoFiniteDiff()); abstol = 1e-9)
-    @test SciMLBase.successful_retcode(sol)
-    sol = solve(probN, custom_polyalg; abstol = 1e-9)
-    @test SciMLBase.successful_retcode(sol)
-
-    quadratic_f(u::Float64, p) = u^2 - p
-
-    prob = NonlinearProblem(quadratic_f, 2.0, 4.0)
-
-    @test_throws MethodError solve(prob)
-    @test_throws MethodError solve(prob, RobustMultiNewton())
-    sol = solve(prob, RobustMultiNewton(; autodiff = AutoFiniteDiff()))
-    @test SciMLBase.successful_retcode(sol)
-end
-
-@testitem "Simple Scalar Problem #187" tags=[:misc] begin
-    using NaNMath
-
-    # https://github.com/SciML/NonlinearSolve.jl/issues/187
-    # If we use a General Nonlinear Solver the solution might go out of the domain!
-    ff_interval(u, p) = 0.5 / 1.5 * NaNMath.log.(u ./ (1.0 .- u)) .- 2.0 * u .+ 1.0
-
-    uspan = (0.02, 0.1)
-    prob = IntervalNonlinearProblem(ff_interval, uspan)
-    sol = solve(prob; abstol = 1e-9)
-    @test SciMLBase.successful_retcode(sol)
-
-    u0 = 0.06
-    p = 2.0
-    prob = NonlinearProblem(ff_interval, u0, p)
-    sol = solve(prob; abstol = 1e-9)
-    @test SciMLBase.successful_retcode(sol)
-end
-
-# Shooting Problem: Taken from BoundaryValueDiffEq.jl
-# Testing for Complex Valued Root Finding. For Complex valued inputs we drop some of the
-# algorithms which dont support those.
-@testitem "Complex Valued Problems: Single-Shooting" tags=[:misc] begin
-    using OrdinaryDiffEqTsit5
-
-    function ode_func!(du, u, p, t)
-        du[1] = u[2]
-        du[2] = -u[1]
-        return nothing
-    end
-
-    function objective_function!(resid, u0, p)
-        odeprob = ODEProblem{true}(ode_func!, u0, (0.0, 100.0), p)
-        sol = solve(odeprob, Tsit5(), abstol = 1e-9, reltol = 1e-9, verbose = false)
-        resid[1] = sol(0.0)[1]
-        resid[2] = sol(100.0)[1] - 1.0
-        return nothing
-    end
-
-    prob = NonlinearProblem{true}(objective_function!, [0.0, 1.0] .+ 1im)
-    sol = solve(prob; abstol = 1e-10)
-    @test SciMLBase.successful_retcode(sol)
-    # This test is not meant to return success but test that all the default solvers can handle
-    # complex valued problems
-    @test_nowarn solve(prob; abstol = 1e-19, maxiters = 10)
-    @test_nowarn solve(
-        prob, RobustMultiNewton(eltype(prob.u0)); abstol = 1e-19, maxiters = 10)
-end
-
-@testitem "No AD" tags=[:misc] begin
-    no_ad_fast = FastShortcutNonlinearPolyalg(autodiff = AutoFiniteDiff())
-    no_ad_robust = RobustMultiNewton(autodiff = AutoFiniteDiff())
-    no_ad_algs = Set([no_ad_fast, no_ad_robust, no_ad_fast.algs..., no_ad_robust.algs...])
-
-    @testset "Inplace" begin
-        f_iip = Base.Experimental.@opaque (du, u, p) -> du .= u .* u .- p
-        u0 = [0.5]
-        prob = NonlinearProblem(f_iip, u0, 1.0)
-        for alg in no_ad_algs
-            sol = solve(prob, alg)
-            @test isapprox(only(sol.u), 1.0)
-            @test SciMLBase.successful_retcode(sol.retcode)
-        end
-    end
-
-    @testset "Out of Place" begin
-        f_oop = Base.Experimental.@opaque (u, p) -> u .* u .- p
-        u0 = [0.5]
-        prob = NonlinearProblem{false}(f_oop, u0, 1.0)
-        for alg in no_ad_algs
-            sol = solve(prob, alg)
-            @test isapprox(only(sol.u), 1.0)
-            @test SciMLBase.successful_retcode(sol.retcode)
-        end
-    end
-end
-
-@testsetup module InfeasibleFunction
-using LinearAlgebra, StaticArrays
-
-# this is infeasible
-function f1_infeasible!(out, u, p)
-    μ = 3.986004415e14
-    x = 7000.0e3
-    y = -6.970561549987071e-9
-    z = -3.784706123246018e-9
-    v_x = 8.550491684548064e-12 + u[1]
-    v_y = 6631.60076191005 + u[2]
-    v_z = 3600.665431405663 + u[3]
-    r = @SVector [x, y, z]
-    v = @SVector [v_x, v_y, v_z]
-    h = cross(r, v)
-    ev = cross(v, h) / μ - r / norm(r)
-    i = acos(h[3] / norm(h))
-    e = norm(ev)
-    a = 1 / (2 / norm(r) - (norm(v)^2 / μ))
-    out .= [a - 42.0e6, e - 1e-5, i - 1e-5]
-    return nothing
-end
-
-# this is unfeasible
-function f1_infeasible(u, p)
-    μ = 3.986004415e14
-    x = 7000.0e3
-    y = -6.970561549987071e-9
-    z = -3.784706123246018e-9
-    v_x = 8.550491684548064e-12 + u[1]
-    v_y = 6631.60076191005 + u[2]
-    v_z = 3600.665431405663 + u[3]
-    r = [x, y, z]
-    v = [v_x, v_y, v_z]
-    h = cross(r, v)
-    ev = cross(v, h) / μ - r / norm(r)
-    i = acos(h[3] / norm(h))
-    e = norm(ev)
-    a = 1 / (2 / norm(r) - (norm(v)^2 / μ))
-    return [a - 42.0e6, e - 1e-5, i - 1e-5]
-end
-
-export f1_infeasible!, f1_infeasible
-end
-
-@testitem "[IIP] Infeasible" setup=[InfeasibleFunction] tags=[:misc] begin
-    u0 = [0.0, 0.0, 0.0]
-    prob = NonlinearProblem(f1_infeasible!, u0)
-    sol = solve(prob)
-
-    @test all(!isnan, sol.u)
-    @test !SciMLBase.successful_retcode(sol.retcode)
-    @inferred solve(prob)
-end
-
-@testitem "[OOP] Infeasible" setup=[InfeasibleFunction] tags=[:misc] begin
-    using LinearAlgebra, StaticArrays
-
-    u0 = [0.0, 0.0, 0.0]
-    prob = NonlinearProblem(f1_infeasible, u0)
-    sol = solve(prob)
-
-    @test all(!isnan, sol.u)
-    @test !SciMLBase.successful_retcode(sol.retcode)
-    @inferred solve(prob)
-
-    u0 = @SVector [0.0, 0.0, 0.0]
-    prob = NonlinearProblem(f1_infeasible, u0)
-
-    sol = solve(prob)
-    @test all(!isnan, sol.u)
-    @test !SciMLBase.successful_retcode(sol.retcode)
-end
diff --git a/test/misc/qa_tests.jl b/test/misc/qa_tests.jl
deleted file mode 100644
index 6aafd4024..000000000
--- a/test/misc/qa_tests.jl
+++ /dev/null
@@ -1,28 +0,0 @@
-@testitem "Aqua" tags=[:misc] begin
-    using NonlinearSolve, SimpleNonlinearSolve, Aqua
-
-    Aqua.find_persistent_tasks_deps(NonlinearSolve)
-    Aqua.test_ambiguities(NonlinearSolve; recursive = false)
-    Aqua.test_deps_compat(NonlinearSolve)
-    Aqua.test_piracies(NonlinearSolve,
-        treat_as_own = [NonlinearProblem, NonlinearLeastSquaresProblem,
-            SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm])
-    Aqua.test_project_extras(NonlinearSolve)
-    # Timer Outputs needs to be enabled via Preferences
-    Aqua.test_stale_deps(NonlinearSolve; ignore = [:TimerOutputs])
-    Aqua.test_unbound_args(NonlinearSolve)
-    Aqua.test_undefined_exports(NonlinearSolve)
-end
-
-@testitem "Explicit Imports" tags=[:misc] begin
-    using NonlinearSolve, ADTypes, SimpleNonlinearSolve, SciMLBase
-    import BandedMatrices, FastLevenbergMarquardt, FixedPointAcceleration,
-           LeastSquaresOptim, MINPACK, NLsolve, NLSolvers, SIAMFANLEquations, SpeedMapping
-
-    using ExplicitImports
-
-    @test check_no_implicit_imports(NonlinearSolve;
-        skip = (NonlinearSolve, Base, Core, SimpleNonlinearSolve, SciMLBase)) === nothing
-    @test check_no_stale_explicit_imports(NonlinearSolve) === nothing
-    @test check_all_qualified_accesses_via_owners(NonlinearSolve) === nothing
-end
diff --git a/test/downstream/mtk_cache_indexing_tests.jl b/test/mtk_cache_indexing_tests.jl
similarity index 98%
rename from test/downstream/mtk_cache_indexing_tests.jl
rename to test/mtk_cache_indexing_tests.jl
index d29cb1da7..3109d1612 100644
--- a/test/downstream/mtk_cache_indexing_tests.jl
+++ b/test/mtk_cache_indexing_tests.jl
@@ -13,7 +13,8 @@
     @testset "$integtype" for (alg, integtype) in [
         (NewtonRaphson(), NonlinearSolve.GeneralizedFirstOrderAlgorithmCache),
         (FastShortcutNonlinearPolyalg(), NonlinearSolve.NonlinearSolvePolyAlgorithmCache),
-        (SimpleNewtonRaphson(), NonlinearSolve.NonlinearSolveNoInitCache)]
+        (SimpleNewtonRaphson(), NonlinearSolve.NonlinearSolveNoInitCache)
+    ]
         nint = init(nlprob, alg)
         @test nint isa integtype
 
diff --git a/test/qa_tests.jl b/test/qa_tests.jl
new file mode 100644
index 000000000..ffac5c7bb
--- /dev/null
+++ b/test/qa_tests.jl
@@ -0,0 +1,24 @@
+@testitem "Aqua" tags=[:misc] begin
+    using NonlinearSolve, SimpleNonlinearSolve, Aqua
+
+    Aqua.test_all(NonlinearSolve; ambiguities = false, piracies = false)
+    Aqua.test_ambiguities(NonlinearSolve; recursive = false)
+    Aqua.test_piracies(NonlinearSolve,
+        treat_as_own = [
+            NonlinearProblem, NonlinearLeastSquaresProblem,
+            SimpleNonlinearSolve.AbstractSimpleNonlinearSolveAlgorithm
+        ]
+    )
+end
+
+@testitem "Explicit Imports" tags=[:misc] begin
+    using NonlinearSolve, ADTypes, SimpleNonlinearSolve, SciMLBase
+    import FastLevenbergMarquardt, FixedPointAcceleration, LeastSquaresOptim, MINPACK,
+           NLsolve, NLSolvers, SIAMFANLEquations, SpeedMapping
+
+    using ExplicitImports
+
+    @test check_no_implicit_imports(NonlinearSolve; skip = (Base, Core)) === nothing
+    @test check_no_stale_explicit_imports(NonlinearSolve) === nothing
+    @test check_all_qualified_accesses_via_owners(NonlinearSolve) === nothing
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 33ca5da7a..59a43c2f9 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -10,13 +10,19 @@ const EXTRA_PKGS = Pkg.PackageSpec[]
 length(EXTRA_PKGS) ≥ 1 && Pkg.add(EXTRA_PKGS)
 
 const RETESTITEMS_NWORKERS = parse(
-    Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4))))
+    Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4)))
+)
 const RETESTITEMS_NWORKER_THREADS = parse(Int,
-    get(ENV, "RETESTITEMS_NWORKER_THREADS",
-        string(max(Hwloc.num_virtual_cores() ÷ RETESTITEMS_NWORKERS, 1))))
+    get(
+        ENV, "RETESTITEMS_NWORKER_THREADS",
+        string(max(Hwloc.num_virtual_cores() ÷ RETESTITEMS_NWORKERS, 1))
+    )
+)
 
 @info "Running tests for group: $(GROUP) with $(RETESTITEMS_NWORKERS) workers"
 
-ReTestItems.runtests(NonlinearSolve; tags = (GROUP == "all" ? nothing : [Symbol(GROUP)]),
+ReTestItems.runtests(
+    NonlinearSolve; tags = (GROUP == "all" ? nothing : [Symbol(GROUP)]),
     nworkers = RETESTITEMS_NWORKERS, nworker_threads = RETESTITEMS_NWORKER_THREADS,
-    testitem_timeout = 3600)
+    testitem_timeout = 3600
+)
diff --git a/test/wrappers/nlls_tests.jl b/test/wrappers/least_squares_tests.jl
similarity index 100%
rename from test/wrappers/nlls_tests.jl
rename to test/wrappers/least_squares_tests.jl

From 0275d14ad1647004b44bb4ad2f472212aaf9bbbf Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 30 Oct 2024 16:32:01 -0400
Subject: [PATCH 658/700] chore: run formatter

---
 lib/NonlinearSolveBase/src/timer_outputs.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/timer_outputs.jl b/lib/NonlinearSolveBase/src/timer_outputs.jl
index 56bb2a95c..0b6d23496 100644
--- a/lib/NonlinearSolveBase/src/timer_outputs.jl
+++ b/lib/NonlinearSolveBase/src/timer_outputs.jl
@@ -39,7 +39,7 @@ Enable `TimerOutput` for all `NonlinearSolve` algorithms. This is useful for deb
 but has some overhead, so it is disabled by default.
 """
 function enable_timer_outputs()
-    @set_preferences!("enable_timer_outputs" => true)
+    @set_preferences!("enable_timer_outputs"=>true)
     @info "Timer Outputs Enabled. Restart the Julia session for this to take effect."
 end
 
@@ -50,6 +50,6 @@ Disable `TimerOutput` for all `NonlinearSolve` algorithms. This should be used w
 `NonlinearSolve` is being used in performance-critical code.
 """
 function disable_timer_outputs()
-    @set_preferences!("enable_timer_outputs" => false)
+    @set_preferences!("enable_timer_outputs"=>false)
     @info "Timer Outputs Disabled. Restart the Julia session for this to take effect."
 end

From 3432cfb40c40b7a307ac0d6668bb64728c1253fc Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 30 Oct 2024 23:16:25 -0400
Subject: [PATCH 659/700] refactor: cleanup all wrappers

---
 Project.toml                                  |   6 +
 common/common_nlls_testing.jl                 |   1 +
 ...NonlinearSolveFastLevenbergMarquardtExt.jl |  86 +-
 ...NonlinearSolveFixedPointAccelerationExt.jl |  44 +-
 ext/NonlinearSolveLeastSquaresOptimExt.jl     |  99 +-
 ext/NonlinearSolveMINPACKExt.jl               |  67 +-
 ext/NonlinearSolveNLSolversExt.jl             |  89 +-
 ext/NonlinearSolveNLsolveExt.jl               |  47 +-
 ext/NonlinearSolvePETScExt.jl                 |  83 +-
 ext/NonlinearSolveSIAMFANLEquationsExt.jl     | 122 ++-
 ext/NonlinearSolveSpeedMappingExt.jl          |  41 +-
 .../src/NonlinearSolveBase.jl                 |   4 +
 lib/NonlinearSolveBase/src/wrappers.jl        | 113 +++
 src/NonlinearSolve.jl                         |   2 +-
 src/extension_algs.jl                         | 959 +++++++++---------
 src/helpers.jl                                |   1 +
 src/internal/helpers.jl                       |  85 --
 test/23_test_problems_tests.jl                | 293 +++---
 test/wrappers/fixedpoint_tests.jl             |  18 +-
 test/wrappers/least_squares_tests.jl          |  96 +-
 test/wrappers/rootfind_tests.jl               |  30 +-
 21 files changed, 1214 insertions(+), 1072 deletions(-)
 create mode 100644 lib/NonlinearSolveBase/src/wrappers.jl
 delete mode 100644 src/internal/helpers.jl

diff --git a/Project.toml b/Project.toml
index f817aba9f..bd31721c1 100644
--- a/Project.toml
+++ b/Project.toml
@@ -10,6 +10,7 @@ BracketingNonlinearSolve = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -62,10 +63,12 @@ Aqua = "0.8"
 ArrayInterface = "7.16"
 BandedMatrices = "1.5"
 BenchmarkTools = "1.4"
+BracketingNonlinearSolve = "1"
 CUDA = "5.5"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.155.3"
+DifferentiationInterface = "0.6.18"
 Enzyme = "0.13.11"
 ExplicitImports = "1.5"
 FastClosures = "0.3.2"
@@ -87,6 +90,9 @@ NLsolve = "4.5"
 NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
 NonlinearSolveBase = "1"
+NonlinearSolveFirstOrder = "1"
+NonlinearSolveQuasiNewton = "1"
+NonlinearSolveSpectralMethods = "1"
 OrdinaryDiffEqTsit5 = "1.1.0"
 PETSc = "0.2"
 Pkg = "1.10"
diff --git a/common/common_nlls_testing.jl b/common/common_nlls_testing.jl
index 2888c56e5..86c33e8ac 100644
--- a/common/common_nlls_testing.jl
+++ b/common/common_nlls_testing.jl
@@ -47,3 +47,4 @@ prob_iip_vjp = NonlinearLeastSquaresProblem(
 )
 
 export prob_oop, prob_iip, prob_oop_vjp, prob_iip_vjp
+export true_function, θ_true, x, y_target, loss_function, θ_init
diff --git a/ext/NonlinearSolveFastLevenbergMarquardtExt.jl b/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
index e772043b3..a851c3a92 100644
--- a/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
+++ b/ext/NonlinearSolveFastLevenbergMarquardtExt.jl
@@ -1,72 +1,84 @@
 module NonlinearSolveFastLevenbergMarquardtExt
 
-using ArrayInterface: ArrayInterface
 using FastClosures: @closure
+
+using ArrayInterface: ArrayInterface
 using FastLevenbergMarquardt: FastLevenbergMarquardt
-using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
-using NonlinearSolve: NonlinearSolve, FastLevenbergMarquardtJL
-using SciMLBase: SciMLBase, NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode
 using StaticArraysCore: SArray
 
-const FastLM = FastLevenbergMarquardt
+using NonlinearSolveBase: NonlinearSolveBase
+using NonlinearSolve: NonlinearSolve, FastLevenbergMarquardtJL
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, ReturnCode
 
-@inline function _fast_lm_solver(::FastLevenbergMarquardtJL{linsolve}, x) where {linsolve}
-    if linsolve === :cholesky
-        return FastLM.CholeskySolver(ArrayInterface.undefmatrix(x))
-    elseif linsolve === :qr
-        return FastLM.QRSolver(eltype(x), length(x))
-    else
-        throw(ArgumentError("Unknown FastLevenbergMarquardt Linear Solver: $linsolve"))
-    end
-end
-@inline _fast_lm_solver(::FastLevenbergMarquardtJL{linsolve}, ::SArray) where {linsolve} = linsolve
+const FastLM = FastLevenbergMarquardt
 
-function SciMLBase.__solve(prob::Union{NonlinearLeastSquaresProblem, NonlinearProblem},
-        alg::FastLevenbergMarquardtJL, args...; alias_u0 = false, abstol = nothing,
-        reltol = nothing, maxiters = 1000, termination_condition = nothing, kwargs...)
-    NonlinearSolve.__test_termination_condition(
-        termination_condition, :FastLevenbergMarquardt)
+function SciMLBase.__solve(
+        prob::AbstractNonlinearProblem, alg::FastLevenbergMarquardtJL, args...;
+        alias_u0 = false, abstol = nothing, reltol = nothing, maxiters = 1000,
+        termination_condition = nothing, kwargs...
+)
+    NonlinearSolveBase.assert_extension_supported_termination_condition(
+        termination_condition, alg
+    )
 
-    fn, u, resid = NonlinearSolve.__construct_extension_f(
-        prob; alias_u0, can_handle_oop = Val(prob.u0 isa SArray))
+    f_wrapped, u, resid = NonlinearSolveBase.construct_extension_function_wrapper(
+        prob; alias_u0, can_handle_oop = Val(prob.u0 isa SArray)
+    )
     f = if prob.u0 isa SArray
-        @closure (u, p) -> fn(u)
+        @closure (u, p) -> f_wrapped(u)
     else
-        @closure (du, u, p) -> fn(du, u)
+        @closure (du, u, p) -> f_wrapped(du, u)
     end
-    abstol = get_tolerance(abstol, eltype(u))
-    reltol = get_tolerance(reltol, eltype(u))
 
-    _jac_fn = NonlinearSolve.__construct_extension_jac(
-        prob, alg, u, resid; alg.autodiff, can_handle_oop = Val(prob.u0 isa SArray))
+    abstol = NonlinearSolveBase.get_tolerance(abstol, eltype(u))
+    reltol = NonlinearSolveBase.get_tolerance(reltol, eltype(u))
+
+    jac_fn_wrapped = NonlinearSolveBase.construct_extension_jac(
+        prob, alg, u, resid; alg.autodiff, can_handle_oop = Val(prob.u0 isa SArray)
+    )
     jac_fn = if prob.u0 isa SArray
-        @closure (u, p) -> _jac_fn(u)
+        @closure (u, p) -> jac_fn_wrapped(u)
     else
-        @closure (J, u, p) -> _jac_fn(J, u)
+        @closure (J, u, p) -> jac_fn_wrapped(J, u)
     end
 
-    solver_kwargs = (; xtol = reltol, ftol = reltol, gtol = abstol, maxit = maxiters,
+    solver_kwargs = (;
+        xtol = reltol, ftol = reltol, gtol = abstol, maxit = maxiters,
         alg.factor, alg.factoraccept, alg.factorreject, alg.minscale,
-        alg.maxscale, alg.factorupdate, alg.minfactor, alg.maxfactor)
+        alg.maxscale, alg.factorupdate, alg.minfactor, alg.maxfactor
+    )
 
     if prob.u0 isa SArray
         res, fx, info, iter, nfev, njev = FastLM.lmsolve(
-            f, jac_fn, prob.u0; solver_kwargs...)
+            f, jac_fn, prob.u0; solver_kwargs...
+        )
         LM, solver = nothing, nothing
     else
         J = prob.f.jac_prototype === nothing ? similar(u, length(resid), length(u)) :
             zero(prob.f.jac_prototype)
-        solver = _fast_lm_solver(alg, u)
+
+        solver = if alg.linsolve === :cholesky
+            FastLM.CholeskySolver(ArrayInterface.undefmatrix(u))
+        elseif alg.linsolve === :qr
+            FastLM.QRSolver(eltype(u), length(u))
+        else
+            throw(ArgumentError("Unknown FastLevenbergMarquardt Linear Solver: \
+                                 $(Meta.quot(alg.linsolve))"))
+        end
+
         LM = FastLM.LMWorkspace(u, resid, J)
 
         res, fx, info, iter, nfev, njev, LM, solver = FastLM.lmsolve!(
-            f, jac_fn, LM; solver, solver_kwargs...)
+            f, jac_fn, LM; solver, solver_kwargs...
+        )
     end
 
     stats = SciMLBase.NLStats(nfev, njev, -1, -1, iter)
     retcode = info == -1 ? ReturnCode.MaxIters : ReturnCode.Success
-    return SciMLBase.build_solution(prob, alg, res, fx; retcode,
-        original = (res, fx, info, iter, nfev, njev, LM, solver), stats)
+    return SciMLBase.build_solution(
+        prob, alg, res, fx; retcode,
+        original = (res, fx, info, iter, nfev, njev, LM, solver), stats
+    )
 end
 
 end
diff --git a/ext/NonlinearSolveFixedPointAccelerationExt.jl b/ext/NonlinearSolveFixedPointAccelerationExt.jl
index 2d36d7f56..6ff9f240c 100644
--- a/ext/NonlinearSolveFixedPointAccelerationExt.jl
+++ b/ext/NonlinearSolveFixedPointAccelerationExt.jl
@@ -1,41 +1,51 @@
 module NonlinearSolveFixedPointAccelerationExt
 
-using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
+using FixedPointAcceleration: FixedPointAcceleration, fixed_point
+
+using NonlinearSolveBase: NonlinearSolveBase
 using NonlinearSolve: NonlinearSolve, FixedPointAccelerationJL
 using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
-using FixedPointAcceleration: FixedPointAcceleration, fixed_point
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::FixedPointAccelerationJL, args...;
+function SciMLBase.__solve(
+        prob::NonlinearProblem, alg::FixedPointAccelerationJL, args...;
         abstol = nothing, maxiters = 1000, alias_u0::Bool = false,
-        show_trace::Val{PrintReports} = Val(false),
-        termination_condition = nothing, kwargs...) where {PrintReports}
-    NonlinearSolve.__test_termination_condition(
-        termination_condition, :FixedPointAccelerationJL)
+        show_trace::Val = Val(false), termination_condition = nothing, kwargs...
+)
+    NonlinearSolveBase.assert_extension_supported_termination_condition(
+        termination_condition, alg
+    )
+
+    f, u0, resid = NonlinearSolveBase.construct_extension_function_wrapper(
+        prob; alias_u0, make_fixed_point = Val(true), force_oop = Val(true)
+    )
 
-    f, u0, resid = NonlinearSolve.__construct_extension_f(
-        prob; alias_u0, make_fixed_point = Val(true), force_oop = Val(true))
-    tol = get_tolerance(abstol, eltype(u0))
+    tol = NonlinearSolveBase.get_tolerance(abstol, eltype(u0))
 
-    sol = fixed_point(f, u0; Algorithm = alg.algorithm, MaxIter = maxiters, MaxM = alg.m,
+    sol = fixed_point(
+        f, u0; Algorithm = alg.algorithm, MaxIter = maxiters, MaxM = alg.m,
         ConvergenceMetricThreshold = tol, ExtrapolationPeriod = alg.extrapolation_period,
-        Dampening = alg.dampening, PrintReports, ReplaceInvalids = alg.replace_invalids,
-        ConditionNumberThreshold = alg.condition_number_threshold, quiet_errors = true)
+        Dampening = alg.dampening, PrintReports = show_trace isa Val{true},
+        ReplaceInvalids = alg.replace_invalids,
+        ConditionNumberThreshold = alg.condition_number_threshold, quiet_errors = true
+    )
 
     if sol.FixedPoint_ === missing
         u0 = prob.u0 isa Number ? u0[1] : u0
-        resid = NonlinearSolve.evaluate_f(prob, u0)
+        resid = NonlinearSolveBase.Utils.evaluate_f(prob, u0)
         res = u0
         converged = false
     else
         res = prob.u0 isa Number ? first(sol.FixedPoint_) :
               reshape(sol.FixedPoint_, size(prob.u0))
-        resid = NonlinearSolve.evaluate_f(prob, res)
+        resid = NonlinearSolveBase.Utils.evaluate_f(prob, res)
         converged = maximum(abs, resid) ≤ tol
     end
 
-    return SciMLBase.build_solution(prob, alg, res, resid; original = sol,
+    return SciMLBase.build_solution(
+        prob, alg, res, resid; original = sol,
         retcode = converged ? ReturnCode.Success : ReturnCode.Failure,
-        stats = SciMLBase.NLStats(sol.Iterations_, 0, 0, 0, sol.Iterations_))
+        stats = SciMLBase.NLStats(sol.Iterations_, 0, 0, 0, sol.Iterations_)
+    )
 end
 
 end
diff --git a/ext/NonlinearSolveLeastSquaresOptimExt.jl b/ext/NonlinearSolveLeastSquaresOptimExt.jl
index 51563eb83..0df265963 100644
--- a/ext/NonlinearSolveLeastSquaresOptimExt.jl
+++ b/ext/NonlinearSolveLeastSquaresOptimExt.jl
@@ -1,79 +1,70 @@
 module NonlinearSolveLeastSquaresOptimExt
 
-using ConcreteStructs: @concrete
 using LeastSquaresOptim: LeastSquaresOptim
-using NonlinearSolveBase: NonlinearSolveBase, TraceMinimal, get_tolerance
+
+using NonlinearSolveBase: NonlinearSolveBase, TraceMinimal
 using NonlinearSolve: NonlinearSolve, LeastSquaresOptimJL
-using SciMLBase: SciMLBase, NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, ReturnCode
 
 const LSO = LeastSquaresOptim
 
-@inline function _lso_solver(::LeastSquaresOptimJL{alg, ls}) where {alg, ls}
-    linsolve = ls === :qr ? LSO.QR() :
-               (ls === :cholesky ? LSO.Cholesky() : (ls === :lsmr ? LSO.LSMR() : nothing))
-    if alg === :lm
-        return LSO.LevenbergMarquardt(linsolve)
-    elseif alg === :dogleg
-        return LSO.Dogleg(linsolve)
-    else
-        throw(ArgumentError("Unknown LeastSquaresOptim Algorithm: $alg"))
-    end
-end
-
-@concrete struct LeastSquaresOptimJLCache
-    prob
-    alg
-    allocated_prob
-    kwargs
-end
-
-function Base.show(io::IO, cache::LeastSquaresOptimJLCache)
-    print(io, "LeastSquaresOptimJLCache()")
-end
-
-function SciMLBase.reinit!(cache::LeastSquaresOptimJLCache, args...; kwargs...)
-    error("Reinitialization not supported for LeastSquaresOptimJL.")
-end
-
-function SciMLBase.__init(prob::Union{NonlinearLeastSquaresProblem, NonlinearProblem},
-        alg::LeastSquaresOptimJL, args...; alias_u0 = false, abstol = nothing,
-        show_trace::Val{ShT} = Val(false), trace_level = TraceMinimal(),
-        reltol = nothing, store_trace::Val{StT} = Val(false), maxiters = 1000,
-        termination_condition = nothing, kwargs...) where {ShT, StT}
-    NonlinearSolve.__test_termination_condition(termination_condition, :LeastSquaresOptim)
+function SciMLBase.__solve(
+        prob::AbstractNonlinearProblem, alg::LeastSquaresOptimJL, args...;
+        alias_u0 = false, abstol = nothing, reltol = nothing, maxiters = 1000,
+        trace_level = TraceMinimal(), termination_condition = nothing,
+        show_trace::Val = Val(false), store_trace::Val = Val(false), kwargs...
+)
+    NonlinearSolveBase.assert_extension_supported_termination_condition(
+        termination_condition, alg
+    )
 
-    f!, u, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
-    abstol = get_tolerance(abstol, eltype(u))
-    reltol = get_tolerance(reltol, eltype(u))
+    f!, u, resid = NonlinearSolveBase.construct_extension_function_wrapper(prob; alias_u0)
+    abstol = NonlinearSolveBase.get_tolerance(abstol, eltype(u))
+    reltol = NonlinearSolveBase.get_tolerance(reltol, eltype(u))
 
     if prob.f.jac === nothing && alg.autodiff isa Symbol
-        lsoprob = LSO.LeastSquaresProblem(; x = u, f!, y = resid, alg.autodiff,
-            J = prob.f.jac_prototype, output_length = length(resid))
+        lsoprob = LSO.LeastSquaresProblem(;
+            x = u, f!, y = resid, alg.autodiff, J = prob.f.jac_prototype,
+            output_length = length(resid)
+        )
     else
-        g! = NonlinearSolve.__construct_extension_jac(prob, alg, u, resid; alg.autodiff)
+        g! = NonlinearSolveBase.construct_extension_jac(prob, alg, u, resid; alg.autodiff)
         lsoprob = LSO.LeastSquaresProblem(;
             x = u, f!, y = resid, g!, J = prob.f.jac_prototype,
-            output_length = length(resid))
+            output_length = length(resid)
+        )
     end
 
-    allocated_prob = LSO.LeastSquaresProblemAllocated(lsoprob, _lso_solver(alg))
+    linsolve = alg.ls === :qr ? LSO.QR() :
+               (alg.ls === :cholesky ? LSO.Cholesky() :
+                (alg.ls === :lsmr ? LSO.LSMR() : nothing))
 
-    return LeastSquaresOptimJLCache(prob,
-        alg,
-        allocated_prob,
-        (; x_tol = reltol, f_tol = abstol, g_tol = abstol, iterations = maxiters,
-            show_trace = ShT, store_trace = StT, show_every = trace_level.print_frequency))
-end
+    lso_solver = if alg.alg === :lm
+        LSO.LevenbergMarquardt(linsolve)
+    elseif alg.alg === :dogleg
+        LSO.Dogleg(linsolve)
+    else
+        throw(ArgumentError("Unknown LeastSquaresOptim Algorithm: $(Meta.quot(alg.alg))"))
+    end
+
+    allocated_prob = LSO.LeastSquaresProblemAllocated(lsoprob, lso_solver(alg))
+    res = LSO.optimize!(
+        allocated_prob;
+        x_tol = reltol, f_tol = abstol, g_tol = abstol, iterations = maxiters,
+        show_trace = show_trace isa Val{true}, store_trace = store_trace isa Val{true},
+        show_every = trace_level.print_frequency
+    )
 
-function SciMLBase.solve!(cache::LeastSquaresOptimJLCache)
-    res = LSO.optimize!(cache.allocated_prob; cache.kwargs...)
-    maxiters = cache.kwargs[:iterations]
     retcode = res.x_converged || res.f_converged || res.g_converged ? ReturnCode.Success :
               (res.iterations ≥ maxiters ? ReturnCode.MaxIters :
                ReturnCode.ConvergenceFailure)
     stats = SciMLBase.NLStats(res.f_calls, res.g_calls, -1, -1, res.iterations)
+
+    f!(resid, res.minimizer)
+
     return SciMLBase.build_solution(
-        cache.prob, cache.alg, res.minimizer, res.ssr / 2; retcode, original = res, stats)
+        prob, alg, res.minimizer, resid; retcode, original = res, stats
+    )
 end
 
 end
diff --git a/ext/NonlinearSolveMINPACKExt.jl b/ext/NonlinearSolveMINPACKExt.jl
index 88adf5753..fc0f919a1 100644
--- a/ext/NonlinearSolveMINPACKExt.jl
+++ b/ext/NonlinearSolveMINPACKExt.jl
@@ -1,52 +1,67 @@
 module NonlinearSolveMINPACKExt
 
+using FastClosures: @closure
 using MINPACK: MINPACK
-using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
+
+using NonlinearSolveBase: NonlinearSolveBase
 using NonlinearSolve: NonlinearSolve, CMINPACK
 using SciMLBase: SciMLBase, NonlinearLeastSquaresProblem, NonlinearProblem, ReturnCode
-using FastClosures: @closure
 
 function SciMLBase.__solve(
-        prob::Union{NonlinearLeastSquaresProblem, NonlinearProblem}, alg::CMINPACK,
-        args...; abstol = nothing, maxiters = 1000, alias_u0::Bool = false,
-        show_trace::Val{ShT} = Val(false), store_trace::Val{StT} = Val(false),
-        termination_condition = nothing, kwargs...) where {ShT, StT}
-    NonlinearSolve.__test_termination_condition(termination_condition, :CMINPACK)
-
-    _f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
-    f! = @closure (du, u) -> (_f!(du, u); Cint(0))
+        prob::Union{NonlinearLeastSquaresProblem, NonlinearProblem}, alg::CMINPACK, args...;
+        abstol = nothing, maxiters = 1000, alias_u0::Bool = false,
+        show_trace::Val = Val(false), store_trace::Val = Val(false),
+        termination_condition = nothing, kwargs...
+)
+    NonlinearSolveBase.assert_extension_supported_termination_condition(
+        termination_condition, alg
+    )
+
+    f_wrapped!, u0, resid = NonlinearSolveBase.construct_extension_function_wrapper(
+        prob; alias_u0
+    )
+    resid_size = size(resid)
+    f! = @closure (du, u) -> (f_wrapped!(du, u); Cint(0))
     m = length(resid)
 
-    method = ifelse(alg.method === :auto,
-        ifelse(prob isa NonlinearLeastSquaresProblem, :lm, :hybr), alg.method)
+    method = ifelse(
+        alg.method === :auto,
+        ifelse(prob isa NonlinearLeastSquaresProblem, :lm, :hybr), alg.method
+    )
 
-    show_trace = ShT
-    tracing = StT
-    tol = get_tolerance(abstol, eltype(u0))
+    show_trace = show_trace isa Val{true}
+    tracing = store_trace isa Val{true}
+    tol = NonlinearSolveBase.get_tolerance(abstol, eltype(u0))
 
     if alg.autodiff === missing && prob.f.jac === nothing
         original = MINPACK.fsolve(
-            f!, u0, m; tol, show_trace, tracing, method, iterations = maxiters)
+            f!, u0, m; tol, show_trace, tracing, method, iterations = maxiters
+        )
     else
         autodiff = alg.autodiff === missing ? nothing : alg.autodiff
-        _jac! = NonlinearSolve.__construct_extension_jac(prob, alg, u0, resid; autodiff)
-        jac! = @closure (J, u) -> (_jac!(J, u); Cint(0))
+        jac_wrapped! = NonlinearSolveBase.construct_extension_jac(
+            prob, alg, u0, resid; autodiff
+        )
+        jac! = @closure (J, u) -> (jac_wrapped!(J, u); Cint(0))
         original = MINPACK.fsolve(
-            f!, jac!, u0, m; tol, show_trace, tracing, method, iterations = maxiters)
+            f!, jac!, u0, m; tol, show_trace, tracing, method, iterations = maxiters
+        )
     end
 
     u = original.x
-    resid_ = original.f
-    objective = maximum(abs, resid_)
+    resid = original.f
+    objective = maximum(abs, resid)
     retcode = ifelse(objective ≤ tol, ReturnCode.Success, ReturnCode.Failure)
 
     # These are only meaningful if `store_trace = Val(true)`
-    stats = SciMLBase.NLStats(original.trace.f_calls, original.trace.g_calls,
-        original.trace.g_calls, original.trace.g_calls, -1)
+    stats = SciMLBase.NLStats(
+        original.trace.f_calls, original.trace.g_calls,
+        original.trace.g_calls, original.trace.g_calls, -1
+    )
 
-    u_ = prob.u0 isa Number ? original.x[1] : reshape(original.x, size(prob.u0))
-    resid_ = prob.u0 isa Number ? resid_[1] : reshape(resid_, size(resid))
-    return SciMLBase.build_solution(prob, alg, u_, resid_; retcode, original, stats)
+    u = prob.u0 isa Number ? original.x[1] : reshape(original.x, size(prob.u0))
+    resid = prob.u0 isa Number ? resid[1] : reshape(resid, resid_size)
+    return SciMLBase.build_solution(prob, alg, u, resid; retcode, original, stats)
 end
 
 end
diff --git a/ext/NonlinearSolveNLSolversExt.jl b/ext/NonlinearSolveNLSolversExt.jl
index a9f41c87c..95aa0c8c3 100644
--- a/ext/NonlinearSolveNLSolversExt.jl
+++ b/ext/NonlinearSolveNLSolversExt.jl
@@ -1,74 +1,63 @@
 module NonlinearSolveNLSolversExt
 
 using ADTypes: ADTypes, AutoFiniteDiff, AutoForwardDiff, AutoPolyesterForwardDiff
+using DifferentiationInterface: DifferentiationInterface, Constant
 using FastClosures: @closure
-using FiniteDiff: FiniteDiff
-using ForwardDiff: ForwardDiff
-using LinearAlgebra: norm
+
 using NLSolvers: NLSolvers, NEqOptions, NEqProblem
-using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
+
+using NonlinearSolveBase: NonlinearSolveBase
 using NonlinearSolve: NonlinearSolve, NLSolversJL
 using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
-        abstol = nothing, reltol = nothing, maxiters = 1000,
-        alias_u0::Bool = false, termination_condition = nothing, kwargs...)
-    NonlinearSolve.__test_termination_condition(termination_condition, :NLSolversJL)
+const DI = DifferentiationInterface
+
+function SciMLBase.__solve(
+        prob::NonlinearProblem, alg::NLSolversJL, args...;
+        abstol = nothing, reltol = nothing, maxiters = 1000, alias_u0::Bool = false,
+        termination_condition = nothing, kwargs...
+)
+    NonlinearSolveBase.assert_extension_supported_termination_condition(
+        termination_condition, alg
+    )
 
-    abstol = get_tolerance(abstol, eltype(prob.u0))
-    reltol = get_tolerance(reltol, eltype(prob.u0))
+    abstol = NonlinearSolveBase.get_tolerance(abstol, eltype(prob.u0))
+    reltol = NonlinearSolveBase.get_tolerance(reltol, eltype(prob.u0))
 
     options = NEqOptions(; maxiter = maxiters, f_abstol = abstol, f_reltol = reltol)
 
     if prob.u0 isa Number
-        f_scalar = @closure x -> prob.f(x, prob.p)
-
-        if alg.autodiff === nothing
-            if ForwardDiff.can_dual(typeof(prob.u0))
-                autodiff_concrete = :forwarddiff
-            else
-                autodiff_concrete = :finitediff
-            end
-        else
-            if alg.autodiff isa AutoForwardDiff || alg.autodiff isa AutoPolyesterForwardDiff
-                autodiff_concrete = :forwarddiff
-            elseif alg.autodiff isa AutoFiniteDiff
-                autodiff_concrete = :finitediff
-            else
-                error("Only ForwardDiff or FiniteDiff autodiff is supported.")
-            end
-        end
+        f_scalar = Base.Fix2(prob.f, prob.p)
+        autodiff = NonlinearSolveBase.select_jacobian_autodiff(prob, alg.autodiff)
+
+        prep = DifferentiationInterface.prepare_derivative(
+            prob.f, autodiff, prob.u0, Constant(prob.p)
+        )
 
-        if autodiff_concrete === :forwarddiff
-            fj_scalar = @closure (Jx, x) -> begin
-                T = typeof(ForwardDiff.Tag(prob.f, eltype(x)))
-                x_dual = ForwardDiff.Dual{T}(x, one(x))
-                y = prob.f(x_dual, prob.p)
-                return ForwardDiff.value(y), ForwardDiff.extract_derivative(T, y)
-            end
-        else
-            fj_scalar = @closure (Jx, x) -> begin
-                _f = Base.Fix2(prob.f, prob.p)
-                return _f(x), FiniteDiff.finite_difference_derivative(_f, x)
-            end
+        fj_scalar = @closure (Jx, x) -> begin
+            return DifferentiationInterface.value_and_derivative(
+                prob.f, prep, autodiff, x, Constant(prob.p)
+            )
         end
 
         prob_obj = NLSolvers.ScalarObjective(; f = f_scalar, fg = fj_scalar)
         prob_nlsolver = NEqProblem(prob_obj; inplace = false)
         res = NLSolvers.solve(prob_nlsolver, prob.u0, alg.method, options)
 
-        retcode = ifelse(norm(res.info.best_residual, Inf) ≤ abstol,
-            ReturnCode.Success, ReturnCode.MaxIters)
+        retcode = ifelse(
+            maximum(abs, res.info.best_residual) ≤ abstol,
+            ReturnCode.Success, ReturnCode.MaxIters
+        )
         stats = SciMLBase.NLStats(-1, -1, -1, -1, res.info.iter)
 
         return SciMLBase.build_solution(
             prob, alg, res.info.solution, res.info.best_residual;
-            retcode, original = res, stats)
+            retcode, original = res, stats
+        )
     end
 
-    f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
-
-    jac! = NonlinearSolve.__construct_extension_jac(prob, alg, u0, resid; alg.autodiff)
+    f!, u0, resid = NonlinearSolveBase.construct_extension_function_wrapper(prob; alias_u0)
+    jac! = NonlinearSolveBase.construct_extension_jac(prob, alg, u0, resid; alg.autodiff)
 
     FJ_vector! = @closure (Fx, Jx, x) -> begin
         f!(Fx, x)
@@ -82,11 +71,15 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::NLSolversJL, args...;
     res = NLSolvers.solve(prob_nlsolver, u0, alg.method, options)
 
     retcode = ifelse(
-        norm(res.info.best_residual, Inf) ≤ abstol, ReturnCode.Success, ReturnCode.MaxIters)
+        maximum(abs, res.info.best_residual) ≤ abstol,
+        ReturnCode.Success, ReturnCode.MaxIters
+    )
     stats = SciMLBase.NLStats(-1, -1, -1, -1, res.info.iter)
 
-    return SciMLBase.build_solution(prob, alg, res.info.solution, res.info.best_residual;
-        retcode, original = res, stats)
+    return SciMLBase.build_solution(
+        prob, alg, res.info.solution, res.info.best_residual;
+        retcode, original = res, stats
+    )
 end
 
 end
diff --git a/ext/NonlinearSolveNLsolveExt.jl b/ext/NonlinearSolveNLsolveExt.jl
index 49c1f337a..1b0beb993 100644
--- a/ext/NonlinearSolveNLsolveExt.jl
+++ b/ext/NonlinearSolveNLsolveExt.jl
@@ -1,44 +1,51 @@
 module NonlinearSolveNLsolveExt
 
 using LineSearches: Static
-using NonlinearSolveBase: NonlinearSolveBase, TraceMinimal, get_tolerance
-using NonlinearSolve: NonlinearSolve, NLsolveJL
 using NLsolve: NLsolve, OnceDifferentiable, nlsolve
+
+using NonlinearSolveBase: NonlinearSolveBase, Utils, TraceMinimal
+using NonlinearSolve: NonlinearSolve, NLsolveJL
 using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
 
 function SciMLBase.__solve(
-        prob::NonlinearProblem, alg::NLsolveJL, args...; abstol = nothing,
-        maxiters = 1000, alias_u0::Bool = false, termination_condition = nothing,
-        store_trace::Val{StT} = Val(false), show_trace::Val{ShT} = Val(false),
-        trace_level = TraceMinimal(), kwargs...) where {StT, ShT}
-    NonlinearSolve.__test_termination_condition(termination_condition, :NLsolveJL)
+        prob::NonlinearProblem, alg::NLsolveJL, args...;
+        abstol = nothing, maxiters = 1000, alias_u0::Bool = false,
+        termination_condition = nothing, trace_level = TraceMinimal(),
+        store_trace::Val = Val(false), show_trace::Val = Val(false), kwargs...
+)
+    NonlinearSolveBase.assert_extension_supported_termination_condition(
+        termination_condition, alg
+    )
 
-    f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
+    f!, u0, resid = NonlinearSolveBase.construct_extension_function_wrapper(prob; alias_u0)
 
     if prob.f.jac === nothing && alg.autodiff isa Symbol
         df = OnceDifferentiable(f!, u0, resid; alg.autodiff)
     else
         autodiff = alg.autodiff isa Symbol ? nothing : alg.autodiff
-        jac! = NonlinearSolve.__construct_extension_jac(prob, alg, u0, resid; autodiff)
+        jac! = NonlinearSolveBase.construct_extension_jac(prob, alg, u0, resid; autodiff)
         if prob.f.jac_prototype === nothing
             J = similar(
-                u0, promote_type(eltype(u0), eltype(resid)), length(u0), length(resid))
+                u0, promote_type(eltype(u0), eltype(resid)), length(u0), length(resid)
+            )
         else
             J = zero(prob.f.jac_prototype)
         end
-        df = OnceDifferentiable(f!, jac!, vec(u0), vec(resid), J)
+        df = OnceDifferentiable(f!, jac!, Utils.safe_vec(u0), Utils.safe_vec(resid), J)
     end
 
-    abstol = get_tolerance(abstol, eltype(u0))
-    show_trace = ShT
-    store_trace = StT
+    abstol = NonlinearSolveBase.get_tolerance(abstol, eltype(u0))
+    show_trace = show_trace isa Val{true}
+    store_trace = store_trace isa Val{true}
     extended_trace = !(trace_level.trace_mode isa Val{:minimal})
 
     linesearch = alg.linesearch === missing ? Static() : alg.linesearch
 
-    original = nlsolve(df, vec(u0); ftol = abstol, iterations = maxiters, alg.method,
-        store_trace, extended_trace, linesearch, alg.linsolve, alg.factor,
-        alg.autoscale, alg.m, alg.beta, show_trace)
+    original = nlsolve(
+        df, vec(u0);
+        ftol = abstol, iterations = maxiters, alg.method, store_trace, extended_trace,
+        linesearch, alg.linsolve, alg.factor, alg.autoscale, alg.m, alg.beta, show_trace
+    )
 
     f!(vec(resid), original.zero)
     u = prob.u0 isa Number ? original.zero[1] : reshape(original.zero, size(prob.u0))
@@ -46,8 +53,10 @@ function SciMLBase.__solve(
 
     retcode = original.x_converged || original.f_converged ? ReturnCode.Success :
               ReturnCode.Failure
-    stats = SciMLBase.NLStats(original.f_calls, original.g_calls, original.g_calls,
-        original.g_calls, original.iterations)
+    stats = SciMLBase.NLStats(
+        original.f_calls, original.g_calls, original.g_calls,
+        original.g_calls, original.iterations
+    )
 
     return SciMLBase.build_solution(prob, alg, u, resid; retcode, original, stats)
 end
diff --git a/ext/NonlinearSolvePETScExt.jl b/ext/NonlinearSolvePETScExt.jl
index 9146c0b61..7b36cecce 100644
--- a/ext/NonlinearSolvePETScExt.jl
+++ b/ext/NonlinearSolvePETScExt.jl
@@ -1,23 +1,31 @@
 module NonlinearSolvePETScExt
 
 using FastClosures: @closure
+
 using MPI: MPI
-using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
-using NonlinearSolve: NonlinearSolve, PETScSNES
 using PETSc: PETSc
+
+using NonlinearSolveBase: NonlinearSolveBase
+using NonlinearSolve: NonlinearSolve, PETScSNES
 using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
+
 using SparseArrays: AbstractSparseMatrix
 
 function SciMLBase.__solve(
-        prob::NonlinearProblem, alg::PETScSNES, args...; abstol = nothing, reltol = nothing,
+        prob::NonlinearProblem, alg::PETScSNES, args...;
+        abstol = nothing, reltol = nothing,
         maxiters = 1000, alias_u0::Bool = false, termination_condition = nothing,
-        show_trace::Val{ShT} = Val(false), kwargs...) where {ShT}
+        show_trace::Val = Val(false), kwargs...
+)
     # XXX: https://petsc.org/release/manualpages/SNES/SNESSetConvergenceTest/
-    termination_condition === nothing ||
-        error("`PETScSNES` does not support termination conditions!")
-
-    _f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0)
-    T = eltype(prob.u0)
+    NonlinearSolveBase.assert_extension_supported_termination_condition(
+        termination_condition, alg; abs_norm_supported = false
+    )
+
+    f_wrapped!, u0, resid = NonlinearSolveBase.construct_extension_function_wrapper(
+        prob; alias_u0
+    )
+    T = eltype(u0)
     @assert T ∈ PETSc.scalar_types
 
     if alg.petsclib === missing
@@ -35,8 +43,8 @@ function SciMLBase.__solve(
     end
     PETSc.initialized(petsclib) || PETSc.initialize(petsclib)
 
-    abstol = get_tolerance(abstol, T)
-    reltol = get_tolerance(reltol, T)
+    abstol = NonlinearSolveBase.get_tolerance(abstol, T)
+    reltol = NonlinearSolveBase.get_tolerance(reltol, T)
 
     nf = Ref{Int}(0)
 
@@ -44,77 +52,82 @@ function SciMLBase.__solve(
         nf[] += 1
         fx = cfx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cfx; read = false) : cfx
         x = cx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cx; write = false) : cx
-        _f!(fx, x)
+        f_wrapped!(fx, x)
         Base.finalize(fx)
         Base.finalize(x)
         return
     end
 
-    snes = PETSc.SNES{T}(petsclib,
+    snes = PETSc.SNES{T}(
+        petsclib,
         alg.mpi_comm === missing ? MPI.COMM_SELF : alg.mpi_comm;
-        alg.snes_options..., snes_monitor = ShT, snes_rtol = reltol,
-        snes_atol = abstol, snes_max_it = maxiters)
+        alg.snes_options..., snes_monitor = show_trace isa Val{true}, snes_rtol = reltol,
+        snes_atol = abstol, snes_max_it = maxiters
+    )
 
     PETSc.setfunction!(snes, f!, PETSc.VecSeq(zero(u0)))
 
-    if alg.autodiff === missing && prob.f.jac === nothing
-        _jac! = nothing
-        njac = Ref{Int}(-1)
-    else
+    njac = Ref{Int}(-1)
+    if alg.autodiff !== missing || prob.f.jac !== nothing
         autodiff = alg.autodiff === missing ? nothing : alg.autodiff
         if prob.u0 isa Number
-            _jac! = NonlinearSolve.__construct_extension_jac(
-                prob, alg, prob.u0, prob.u0; autodiff)
+            jac! = NonlinearSolveBase.construct_extension_jac(
+                prob, alg, prob.u0, prob.u0; autodiff
+            )
             J_init = zeros(T, 1, 1)
         else
-            _jac!, J_init = NonlinearSolve.__construct_extension_jac(
-                prob, alg, u0, resid; autodiff, initial_jacobian = Val(true))
+            jac!, J_init = NonlinearSolveBase.construct_extension_jac(
+                prob, alg, u0, resid; autodiff, initial_jacobian = Val(true)
+            )
         end
 
         njac = Ref{Int}(0)
 
         if J_init isa AbstractSparseMatrix
             PJ = PETSc.MatSeqAIJ(J_init)
-            jac! = @closure (cx, J, _, user_ctx) -> begin
+            jac_fn! = @closure (cx, J, _, user_ctx) -> begin
                 njac[] += 1
                 x = cx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cx; write = false) : cx
                 if J isa PETSc.AbstractMat
-                    _jac!(user_ctx.jacobian, x)
+                    jac!(user_ctx.jacobian, x)
                     copyto!(J, user_ctx.jacobian)
                     PETSc.assemble(J)
                 else
-                    _jac!(J, x)
+                    jac!(J, x)
                 end
                 Base.finalize(x)
                 return
             end
-            PETSc.setjacobian!(snes, jac!, PJ, PJ)
+            PETSc.setjacobian!(snes, jac_fn!, PJ, PJ)
             snes.user_ctx = (; jacobian = J_init)
         else
             PJ = PETSc.MatSeqDense(J_init)
-            jac! = @closure (cx, J, _, user_ctx) -> begin
+            jac_fn! = @closure (cx, J, _, user_ctx) -> begin
                 njac[] += 1
                 x = cx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cx; write = false) : cx
-                _jac!(J, x)
+                jac!(J, x)
                 Base.finalize(x)
                 J isa PETSc.AbstractMat && PETSc.assemble(J)
                 return
             end
-            PETSc.setjacobian!(snes, jac!, PJ, PJ)
+            PETSc.setjacobian!(snes, jac_fn!, PJ, PJ)
         end
     end
 
     res = PETSc.solve!(u0, snes)
 
-    _f!(resid, res)
-    u_ = prob.u0 isa Number ? res[1] : res
-    resid_ = prob.u0 isa Number ? resid[1] : resid
+    f_wrapped!(resid, res)
+    u_res = prob.u0 isa Number ? res[1] : res
+    resid_res = prob.u0 isa Number ? resid[1] : resid
 
     objective = maximum(abs, resid)
     # XXX: Return Code from PETSc
     retcode = ifelse(objective ≤ abstol, ReturnCode.Success, ReturnCode.Failure)
-    return SciMLBase.build_solution(prob, alg, u_, resid_; retcode, original = snes,
-        stats = SciMLBase.NLStats(nf[], njac[], -1, -1, -1))
+    return SciMLBase.build_solution(
+        prob, alg, u_res, resid_res;
+        retcode, original = snes,
+        stats = SciMLBase.NLStats(nf[], njac[], -1, -1, -1)
+    )
 end
 
 end
diff --git a/ext/NonlinearSolveSIAMFANLEquationsExt.jl b/ext/NonlinearSolveSIAMFANLEquationsExt.jl
index 2468064fb..bfd2bd72d 100644
--- a/ext/NonlinearSolveSIAMFANLEquationsExt.jl
+++ b/ext/NonlinearSolveSIAMFANLEquationsExt.jl
@@ -1,13 +1,14 @@
 module NonlinearSolveSIAMFANLEquationsExt
 
 using FastClosures: @closure
-using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
-using NonlinearSolve: NonlinearSolve, SIAMFANLEquationsJL
-using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
 using SIAMFANLEquations: SIAMFANLEquations, aasol, nsol, nsoli, nsolsc, ptcsol, ptcsoli,
                          ptcsolsc, secant
 
-@inline function __siam_fanl_equations_retcode_mapping(sol)
+using NonlinearSolveBase: NonlinearSolveBase
+using NonlinearSolve: NonlinearSolve, SIAMFANLEquationsJL
+using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
+
+function siamfanlequations_retcode_mapping(sol)
     if sol.errcode == 0
         return ReturnCode.Success
     elseif sol.errcode == 10
@@ -16,102 +17,129 @@ using SIAMFANLEquations: SIAMFANLEquations, aasol, nsol, nsoli, nsolsc, ptcsol,
         return ReturnCode.Failure
     elseif sol.errcode == -1
         return ReturnCode.Default
+    else
+        error("Unknown SIAMFANLEquations return code: $(sol.errcode)")
     end
 end
 
-@inline function __zeros_like(x, args...)
+function zeros_like(x, args...)
     z = similar(x, args...)
-    fill!(z, zero(eltype(x)))
+    fill!(z, false)
     return z
 end
 
 # pseudo transient continuation has a fixed cost per iteration, iteration statistics are
 # not interesting here.
-@inline function __siam_fanl_equations_stats_mapping(method, sol)
+function siamfanlequations_stats_mapping(method, sol)
     ((method === :pseudotransient) || (method === :anderson)) && return nothing
     return SciMLBase.NLStats(
-        sum(sol.stats.ifun), sum(sol.stats.ijac), 0, 0, sum(sol.stats.iarm))
+        sum(sol.stats.ifun), sum(sol.stats.ijac), 0, 0, sum(sol.stats.iarm)
+    )
 end
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::SIAMFANLEquationsJL, args...;
-        abstol = nothing, reltol = nothing, alias_u0::Bool = false,
-        maxiters = 1000, termination_condition = nothing,
-        show_trace::Val{ShT} = Val(false), kwargs...) where {ShT}
-    NonlinearSolve.__test_termination_condition(termination_condition, :SIAMFANLEquationsJL)
+function SciMLBase.__solve(
+        prob::NonlinearProblem, alg::SIAMFANLEquationsJL, args...;
+        abstol = nothing, reltol = nothing, alias_u0::Bool = false, maxiters = 1000,
+        termination_condition = nothing, show_trace = Val(false), kwargs...
+)
+    NonlinearSolveBase.assert_extension_supported_termination_condition(
+        termination_condition, alg
+    )
 
     (; method, delta, linsolve, m, beta) = alg
     T = eltype(prob.u0)
-    atol = get_tolerance(abstol, T)
-    rtol = get_tolerance(reltol, T)
+    atol = NonlinearSolveBase.get_tolerance(abstol, T)
+    rtol = NonlinearSolveBase.get_tolerance(reltol, T)
+
+    printerr = show_trace isa Val{true}
 
     if prob.u0 isa Number
-        f = @closure u -> prob.f(u, prob.p)
+        f = Base.Fix2(prob.f, prob.p)
         if method == :newton
-            sol = nsolsc(f, prob.u0; maxit = maxiters, atol, rtol, printerr = ShT)
+            sol = nsolsc(f, prob.u0; maxit = maxiters, atol, rtol, printerr)
         elseif method == :pseudotransient
             sol = ptcsolsc(
-                f, prob.u0; delta0 = delta, maxit = maxiters, atol, rtol, printerr = ShT)
+                f, prob.u0; delta0 = delta, maxit = maxiters, atol, rtol, printerr
+            )
         elseif method == :secant
-            sol = secant(f, prob.u0; maxit = maxiters, atol, rtol, printerr = ShT)
+            sol = secant(f, prob.u0; maxit = maxiters, atol, rtol, printerr)
         elseif method == :anderson
-            f_aa, u, _ = NonlinearSolve.__construct_extension_f(
-                prob; alias_u0, make_fixed_point = Val(true))
-            sol = aasol(f_aa, u, m, __zeros_like(u, 1, 2 * m + 4);
-                maxit = maxiters, atol, rtol, beta)
+            f_aa, u, _ = NonlinearSolveBase.construct_extension_function_wrapper(
+                prob; alias_u0, make_fixed_point = Val(true)
+            )
+            sol = aasol(
+                f_aa, u, m, zeros_like(u, 1, 2 * m + 4);
+                maxit = maxiters, atol, rtol, beta
+            )
         end
     else
-        f, u, resid = NonlinearSolve.__construct_extension_f(
-            prob; alias_u0, make_fixed_point = Val(method == :anderson))
+        f, u, resid = NonlinearSolveBase.construct_extension_function_wrapper(
+            prob; alias_u0, make_fixed_point = Val(method == :anderson)
+        )
         N = length(u)
-        FS = __zeros_like(u, N)
+        FS = zeros_like(u, N)
 
         # Jacobian Free Newton Krylov
         if linsolve !== nothing
             # Allocate ahead for Krylov basis
-            JVS = linsolve == :gmres ? __zeros_like(u, N, 3) : __zeros_like(u, N)
+            JVS = linsolve == :gmres ? zeros_like(u, N, 3) : zeros_like(u, N)
             linsolve_alg = String(linsolve)
             if method == :newton
-                sol = nsoli(f, u, FS, JVS; lsolver = linsolve_alg,
-                    maxit = maxiters, atol, rtol, printerr = ShT)
+                sol = nsoli(
+                    f, u, FS, JVS; lsolver = linsolve_alg,
+                    maxit = maxiters, atol, rtol, printerr
+                )
             elseif method == :pseudotransient
-                sol = ptcsoli(f, u, FS, JVS; lsolver = linsolve_alg,
-                    maxit = maxiters, atol, rtol, printerr = ShT)
+                sol = ptcsoli(
+                    f, u, FS, JVS; lsolver = linsolve_alg,
+                    maxit = maxiters, atol, rtol, printerr
+                )
             end
         else
             if prob.f.jac === nothing && alg.autodiff === missing
-                FPS = __zeros_like(u, N, N)
+                FPS = zeros_like(u, N, N)
                 if method == :newton
-                    sol = nsol(f, u, FS, FPS; sham = 1, atol, rtol,
-                        maxit = maxiters, printerr = ShT)
+                    sol = nsol(
+                        f, u, FS, FPS; sham = 1, atol, rtol, maxit = maxiters, printerr
+                    )
                 elseif method == :pseudotransient
-                    sol = ptcsol(f, u, FS, FPS; atol, rtol, maxit = maxiters,
-                        delta0 = delta, printerr = ShT)
+                    sol = ptcsol(
+                        f, u, FS, FPS;
+                        atol, rtol, maxit = maxiters, delta0 = delta, printerr
+                    )
                 elseif method == :anderson
                     sol = aasol(
-                        f, u, m, zeros(T, N, 2 * m + 4); atol, rtol, maxit = maxiters, beta)
+                        f, u, m, zeros(T, N, 2 * m + 4);
+                        atol, rtol, maxit = maxiters, beta
+                    )
                 end
             else
                 autodiff = alg.autodiff === missing ? nothing : alg.autodiff
                 FPS = prob.f.jac_prototype !== nothing ? zero(prob.f.jac_prototype) :
-                      __zeros_like(u, N, N)
-                jac = NonlinearSolve.__construct_extension_jac(
-                    prob, alg, u, resid; autodiff)
+                      zeros_like(u, N, N)
+                jac = NonlinearSolveBase.construct_extension_jac(
+                    prob, alg, u, resid; autodiff
+                )
                 AJ! = @closure (J, u, x) -> jac(J, x)
                 if method == :newton
-                    sol = nsol(f, u, FS, FPS, AJ!; sham = 1, atol,
-                        rtol, maxit = maxiters, printerr = ShT)
+                    sol = nsol(
+                        f, u, FS, FPS, AJ!; sham = 1, atol,
+                        rtol, maxit = maxiters, printerr
+                    )
                 elseif method == :pseudotransient
-                    sol = ptcsol(f, u, FS, FPS, AJ!; atol, rtol, maxit = maxiters,
-                        delta0 = delta, printerr = ShT)
+                    sol = ptcsol(
+                        f, u, FS, FPS, AJ!; atol, rtol, maxit = maxiters,
+                        delta0 = delta, printerr
+                    )
                 end
             end
         end
     end
 
-    retcode = __siam_fanl_equations_retcode_mapping(sol)
-    stats = __siam_fanl_equations_stats_mapping(method, sol)
+    retcode = siamfanlequations_retcode_mapping(sol)
+    stats = siamfanlequations_stats_mapping(method, sol)
     res = prob.u0 isa Number && method === :anderson ? sol.solution[1] : sol.solution
-    resid = NonlinearSolve.evaluate_f(prob, res)
+    resid = NonlinearSolveBase.Utils.evaluate_f(prob, res)
     return SciMLBase.build_solution(prob, alg, res, resid; retcode, stats, original = sol)
 end
 
diff --git a/ext/NonlinearSolveSpeedMappingExt.jl b/ext/NonlinearSolveSpeedMappingExt.jl
index ff9b4683b..c0f39607b 100644
--- a/ext/NonlinearSolveSpeedMappingExt.jl
+++ b/ext/NonlinearSolveSpeedMappingExt.jl
@@ -1,30 +1,41 @@
 module NonlinearSolveSpeedMappingExt
 
-using NonlinearSolveBase: NonlinearSolveBase, get_tolerance
+using SpeedMapping: speedmapping
+
+using NonlinearSolveBase: NonlinearSolveBase
 using NonlinearSolve: NonlinearSolve, SpeedMappingJL
 using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode
-using SpeedMapping: speedmapping
 
-function SciMLBase.__solve(prob::NonlinearProblem, alg::SpeedMappingJL, args...;
+function SciMLBase.__solve(
+        prob::NonlinearProblem, alg::SpeedMappingJL, args...;
         abstol = nothing, maxiters = 1000, alias_u0::Bool = false,
-        maxtime = nothing, store_trace::Val{store_info} = Val(false),
-        termination_condition = nothing, kwargs...) where {store_info}
-    NonlinearSolve.__test_termination_condition(termination_condition, :SpeedMappingJL)
+        maxtime = nothing, store_trace::Val = Val(false),
+        termination_condition = nothing, kwargs...
+)
+    NonlinearSolveBase.assert_extension_supported_termination_condition(
+        termination_condition, alg
+    )
 
-    m!, u, resid = NonlinearSolve.__construct_extension_f(
-        prob; alias_u0, make_fixed_point = Val(true))
-    tol = get_tolerance(abstol, eltype(u))
+    m!, u, resid = NonlinearSolveBase.construct_extension_function_wrapper(
+        prob; alias_u0, make_fixed_point = Val(true)
+    )
+    tol = NonlinearSolveBase.get_tolerance(abstol, eltype(u))
 
     time_limit = ifelse(maxtime === nothing, 1000, maxtime)
 
-    sol = speedmapping(u; m!, tol, Lp = Inf, maps_limit = maxiters, alg.orders,
-        alg.check_obj, store_info, alg.σ_min, alg.stabilize, time_limit)
+    sol = speedmapping(
+        u; m!, tol, Lp = Inf, maps_limit = maxiters, alg.orders,
+        alg.check_obj, store_info = store_trace isa Val{true}, alg.σ_min, alg.stabilize,
+        time_limit
+    )
     res = prob.u0 isa Number ? first(sol.minimizer) : sol.minimizer
-    resid = NonlinearSolve.evaluate_f(prob, res)
+    resid = NonlinearSolveBase.Utils.evaluate_f(prob, res)
 
-    return SciMLBase.build_solution(prob, alg, res, resid; original = sol,
-        retcode = sol.converged ? ReturnCode.Success : ReturnCode.Failure,
-        stats = SciMLBase.NLStats(sol.maps, 0, 0, 0, sol.maps))
+    return SciMLBase.build_solution(
+        prob, alg, res, resid;
+        original = sol, stats = SciMLBase.NLStats(sol.maps, 0, 0, 0, sol.maps),
+        retcode = ifelse(sol.converged, ReturnCode.Success, ReturnCode.Failure)
+    )
 end
 
 end
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index a3ac4614d..a08384677 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -46,6 +46,7 @@ include("jacobian.jl")
 include("linear_solve.jl")
 include("timer_outputs.jl")
 include("tracing.jl")
+include("wrappers.jl")
 
 include("descent/common.jl")
 include("descent/newton.jl")
@@ -66,6 +67,9 @@ include("solve.jl")
 @compat(public, (InternalAPI, supports_line_search, supports_trust_region, set_du!))
 @compat(public, (construct_linear_solver, needs_square_A, needs_concrete_A))
 @compat(public, (construct_jacobian_cache,))
+@compat(public,
+    (assert_extension_supported_termination_condition,
+        construct_extension_function_wrapper, construct_extension_jac))
 
 export TraceMinimal, TraceWithJacobianConditionNumber, TraceAll
 
diff --git a/lib/NonlinearSolveBase/src/wrappers.jl b/lib/NonlinearSolveBase/src/wrappers.jl
new file mode 100644
index 000000000..0b96836ad
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/wrappers.jl
@@ -0,0 +1,113 @@
+function assert_extension_supported_termination_condition(
+        termination_condition, alg; abs_norm_supported = true
+)
+    no_termination_condition = termination_condition === nothing
+    no_termination_condition && return nothing
+    abs_norm_supported && termination_condition isa AbsNormTerminationMode && return nothing
+    throw(AssertionError("`$(nameof(typeof(alg)))` does not support termination conditions!"))
+end
+
+function construct_extension_function_wrapper(
+        prob::AbstractNonlinearProblem; alias_u0::Bool = false,
+        can_handle_oop::Val = Val(false), can_handle_scalar::Val = Val(false),
+        make_fixed_point::Val = Val(false), force_oop::Val = Val(false)
+)
+    if can_handle_oop isa Val{false} && can_handle_scalar isa Val{true}
+        error("Incorrect Specification: OOP not supported but scalar supported.")
+    end
+
+    resid = Utils.evaluate_f(prob, prob.u0)
+    u0 = can_handle_scalar isa Val{true} || !(prob.u0 isa Number) ?
+         Utils.maybe_unaliased(prob.u0, alias_u0) : [prob.u0]
+
+    fₚ = if make_fixed_point isa Val{true}
+        if SciMLBase.isinplace(prob)
+            @closure (du, u) -> begin
+                prob.f(du, u, prob.p)
+                du .+= u
+                return du
+            end
+        else
+            @closure u -> prob.f(u, prob.p) .+ u
+        end
+    else
+        if SciMLBase.isinplace(prob)
+            @closure (du, u) -> begin
+                prob.f(du, u, prob.p)
+                return du
+            end
+        else
+            Base.Fix2(prob.f, prob.p)
+        end
+    end
+
+    f_flat_structure = if SciMLBase.isinplace(prob)
+        u0_size, du_size = size(u0), size(resid)
+        @closure (du, u) -> begin
+            fₚ(reshape(du, du_size), reshape(u, u0_size))
+            return du
+        end
+    else
+        if prob.u0 isa Number
+            if can_handle_scalar isa Val{true}
+                fₚ
+            elseif can_handle_oop isa Val{true}
+                @closure u -> [fₚ(first(u))]
+            else
+                @closure (du, u) -> begin
+                    du[1] = fₚ(first(u))
+                    return du
+                end
+            end
+        else
+            u0_size = size(u0)
+            if can_handle_oop isa Val{true}
+                @closure u -> vec(fₚ(reshape(u, u0_size)))
+            else
+                @closure (du, u) -> begin
+                    copyto!(du, fₚ(reshape(u, u0_size)))
+                    return du
+                end
+            end
+        end
+    end
+
+    f_final = if force_oop isa Val{true} && applicable(f_flat_structure, u0, u0)
+        resid = resid isa Number ? [resid] : Utils.safe_vec(resid)
+        du = Utils.safe_vec(zero(resid))
+        @closure u -> begin
+            f_flat_structure(du, u)
+            return du
+        end
+    else
+        f_flat_structure
+    end
+
+    return f_final, Utils.safe_vec(u0), (resid isa Number ? [resid] : Utils.safe_vec(resid))
+end
+
+function construct_extension_jac(
+        prob, alg, u0, fu;
+        can_handle_oop::Val = Val(false), can_handle_scalar::Val = Val(false),
+        autodiff = nothing, initial_jacobian = Val(false), kwargs...
+)
+    autodiff = select_jacobian_autodiff(prob, autodiff)
+
+    Jₚ = construct_jacobian_cache(
+        prob, alg, prob.f, fu, u0, prob.p;
+        stats = NLStats(0, 0, 0, 0, 0), autodiff, kwargs...
+    )
+
+    J_no_scalar = can_handle_scalar isa Val{false} && prob.u0 isa Number ?
+                  @closure(u->[Jₚ(u[1])]) : Jₚ
+
+    J_final = if can_handle_oop isa Val{false} && !SciMLBase.isinplace(prob)
+        @closure((J, u)->copyto!(J, J_no_scalar(u)))
+    else
+        J_no_scalar
+    end
+
+    initial_jacobian isa Val{false} && return J_final
+
+    return J_final, Jₚ(nothing)
+end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 87bc2a5b3..cc71ef03d 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -49,7 +49,7 @@ const SII = SymbolicIndexingInterface
 include("helpers.jl")
 
 include("polyalg.jl")
-# include("extension_algs.jl")
+include("extension_algs.jl")
 
 include("default.jl")
 
diff --git a/src/extension_algs.jl b/src/extension_algs.jl
index fb922fb14..1fad79839 100644
--- a/src/extension_algs.jl
+++ b/src/extension_algs.jl
@@ -1,469 +1,490 @@
-# # This file only include the algorithm struct to be exported by NonlinearSolve.jl. The main
-# # functionality is implemented as package extensions
-# """
-#     LeastSquaresOptimJL(alg = :lm; linsolve = nothing, autodiff::Symbol = :central)
-
-# Wrapper over [LeastSquaresOptim.jl](https://github.com/matthieugomez/LeastSquaresOptim.jl)
-# for solving `NonlinearLeastSquaresProblem`.
-
-# ### Arguments
-
-#   - `alg`: Algorithm to use. Can be `:lm` or `:dogleg`.
-
-# ### Keyword Arguments
-
-#   - `linsolve`: Linear solver to use. Can be `:qr`, `:cholesky` or `:lsmr`. If `nothing`,
-#     then `LeastSquaresOptim.jl` will choose the best linear solver based on the Jacobian
-#     structure.
-#   - `autodiff`: Automatic differentiation / Finite Differences. Can be `:central` or
-#     `:forward`.
-
-# !!! note
-
-#     This algorithm is only available if `LeastSquaresOptim.jl` is installed and loaded.
-# """
-# struct LeastSquaresOptimJL{alg, linsolve} <: AbstractNonlinearSolveExtensionAlgorithm
-#     autodiff
-# end
-
-# function LeastSquaresOptimJL(alg = :lm; linsolve = nothing, autodiff = :central)
-#     @assert alg in (:lm, :dogleg)
-#     @assert linsolve === nothing || linsolve in (:qr, :cholesky, :lsmr)
-#     autodiff isa Symbol && @assert autodiff in (:central, :forward)
-
-#     if Base.get_extension(@__MODULE__, :NonlinearSolveLeastSquaresOptimExt) === nothing
-#         error("LeastSquaresOptimJL requires LeastSquaresOptim.jl to be loaded")
-#     end
-
-#     return LeastSquaresOptimJL{alg, linsolve}(autodiff)
-# end
-
-# """
-#     FastLevenbergMarquardtJL(linsolve::Symbol = :cholesky; factor = 1e-6,
-#         factoraccept = 13.0, factorreject = 3.0, factorupdate = :marquardt,
-#         minscale = 1e-12, maxscale = 1e16, minfactor = 1e-28, maxfactor = 1e32,
-#         autodiff = nothing)
-
-# Wrapper over [FastLevenbergMarquardt.jl](https://github.com/kamesy/FastLevenbergMarquardt.jl)
-# for solving `NonlinearLeastSquaresProblem`. For details about the other keyword arguments
-# see the documentation for `FastLevenbergMarquardt.jl`.
-
-# !!! warning
-
-#     This is not really the fastest solver. It is called that since the original package
-#     is called "Fast". `LevenbergMarquardt()` is almost always a better choice.
-
-# ### Arguments
-
-#   - `linsolve`: Linear solver to use. Can be `:qr` or `:cholesky`.
-
-# ### Keyword Arguments
-
-#   - `autodiff`: determines the backend used for the Jacobian. Note that this argument is
-#     ignored if an analytical Jacobian is passed, as that will be used instead. Defaults to
-#     `nothing` which means that a default is selected according to the problem specification!
-
-# !!! note
-
-#     This algorithm is only available if `FastLevenbergMarquardt.jl` is installed and loaded.
-# """
-# @concrete struct FastLevenbergMarquardtJL{linsolve} <:
-#                  AbstractNonlinearSolveExtensionAlgorithm
-#     autodiff
-#     factor
-#     factoraccept
-#     factorreject
-#     factorupdate::Symbol
-#     minscale
-#     maxscale
-#     minfactor
-#     maxfactor
-# end
-
-# function FastLevenbergMarquardtJL(
-#         linsolve::Symbol = :cholesky; factor = 1e-6, factoraccept = 13.0,
-#         factorreject = 3.0, factorupdate = :marquardt, minscale = 1e-12,
-#         maxscale = 1e16, minfactor = 1e-28, maxfactor = 1e32, autodiff = nothing)
-#     @assert linsolve in (:qr, :cholesky)
-#     @assert factorupdate in (:marquardt, :nielson)
-
-#     if Base.get_extension(@__MODULE__, :NonlinearSolveFastLevenbergMarquardtExt) === nothing
-#         error("FastLevenbergMarquardtJL requires FastLevenbergMarquardt.jl to be loaded")
-#     end
-
-#     return FastLevenbergMarquardtJL{linsolve}(autodiff, factor, factoraccept, factorreject,
-#         factorupdate, minscale, maxscale, minfactor, maxfactor)
-# end
-
-# """
-#     CMINPACK(; method::Symbol = :auto, autodiff = missing)
-
-# ### Keyword Arguments
-
-#   - `method`: the choice of method for the solver.
-#   - `autodiff`: Defaults to `missing`, which means we will default to letting `MINPACK`
-#     construct the jacobian if `f.jac` is not provided. In other cases, we use it to generate
-#     a jacobian similar to other NonlinearSolve solvers.
-
-# ### Submethod Choice
-
-# The keyword argument `method` can take on different value depending on which method of
-# `fsolve` you are calling. The standard choices of `method` are:
-
-#   - `:hybr`: Modified version of Powell's algorithm. Uses MINPACK routine
-#     [`hybrd1`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrd1.c)
-#   - `:lm`: Levenberg-Marquardt. Uses MINPACK routine
-#     [`lmdif1`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmdif1.c)
-#   - `:lmdif`: Advanced Levenberg-Marquardt (more options available with `; kwargs...`). See
-#     MINPACK routine [`lmdif`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmdif.c)
-#     for more information
-#   - `:hybrd`: Advanced modified version of Powell's algorithm (more options available with
-#     `; kwargs...`). See MINPACK routine
-#     [`hybrd`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrd.c)
-#     for more information
-
-# If a Jacobian is supplied as part of the [`NonlinearFunction`](@ref nonlinearfunctions),
-# then the following methods are allowed:
-
-#   - `:hybr`: Advanced modified version of Powell's algorithm with user supplied Jacobian.
-#     Additional arguments are available via `; kwargs...`. See MINPACK routine
-#     [`hybrj`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrj.c)
-#     for more information
-#   - `:lm`: Advanced Levenberg-Marquardt with user supplied Jacobian. Additional arguments
-#     are available via `; kwargs...`. See MINPACK routine
-#     [`lmder`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmder.c)
-#     for more information
-
-# The default choice of `:auto` selects `:hybr` for NonlinearProblem and `:lm` for
-# NonlinearLeastSquaresProblem.
-
-# !!! note
-
-#     This algorithm is only available if `MINPACK.jl` is installed and loaded.
-# """
-# @concrete struct CMINPACK <: AbstractNonlinearSolveExtensionAlgorithm
-#     method::Symbol
-#     autodiff
-# end
-
-# function CMINPACK(; method::Symbol = :auto, autodiff = missing)
-#     if Base.get_extension(@__MODULE__, :NonlinearSolveMINPACKExt) === nothing
-#         error("CMINPACK requires MINPACK.jl to be loaded")
-#     end
-#     return CMINPACK(method, autodiff)
-# end
-
-# """
-#     NLsolveJL(; method = :trust_region, autodiff = :central, linesearch = Static(),
-#         linsolve = (x, A, b) -> copyto!(x, A\\b), factor = one(Float64), autoscale = true,
-#         m = 10, beta = one(Float64))
-
-# ### Keyword Arguments
-
-#   - `method`: the choice of method for solving the nonlinear system.
-#   - `autodiff`: the choice of method for generating the Jacobian. Defaults to `:central` or
-#     central differencing via FiniteDiff.jl. The other choices are `:forward` or `ADTypes`
-#     similar to other solvers in NonlinearSolve.
-#   - `linesearch`: the line search method to be used within the solver method. The choices
-#     are line search types from
-#     [LineSearches.jl](https://github.com/JuliaNLSolvers/LineSearches.jl).
-#   - `linsolve`: a function `linsolve(x, A, b)` that solves `Ax = b`.
-#   - `factor`: determines the size of the initial trust region. This size is set to the
-#     product of factor and the euclidean norm of `u0` if nonzero, or else to factor itself.
-#   - `autoscale`: if true, then the variables will be automatically rescaled. The scaling
-#     factors are the norms of the Jacobian columns.
-#   - `m`: the amount of history in the Anderson method. Naive "Picard"-style iteration can be
-#     achieved by setting m=0, but that isn't advisable for contractions whose Lipschitz
-#     constants are close to 1. If convergence fails, though, you may consider lowering it.
-#   - `beta`: It is also known as DIIS or Pulay mixing, this method is based on the
-#     acceleration of the fixed-point iteration xₙ₊₁ = xₙ + beta*f(xₙ), where by default
-#     beta = 1.
-
-# !!! warning
-
-#     Line Search Algorithms from [`LineSearch.jl`](https://github.com/SciML/LineSearch.jl)
-#     aren't supported by `NLsolveJL`. Instead, use the line search algorithms from
-#     [`LineSearches.jl`](https://github.com/JuliaNLSolvers/LineSearches.jl).
-
-# ### Submethod Choice
-
-# Choices for methods in `NLsolveJL`:
-
-#   - `:anderson`: Anderson-accelerated fixed-point iteration
-#   - `:broyden`: Broyden's quasi-Newton method
-#   - `:newton`: Classical Newton method with an optional line search
-#   - `:trust_region`: Trust region Newton method (the default choice)
-
-# For more information on these arguments, consult the
-# [NLsolve.jl documentation](https://github.com/JuliaNLSolvers/NLsolve.jl).
-
-# !!! note
-
-#     This algorithm is only available if `NLsolve.jl` is installed and loaded.
-# """
-# @concrete struct NLsolveJL <: AbstractNonlinearSolveExtensionAlgorithm
-#     method::Symbol
-#     autodiff
-#     linesearch
-#     linsolve
-#     factor
-#     autoscale::Bool
-#     m::Int
-#     beta
-# end
-
-# function NLsolveJL(; method = :trust_region, autodiff = :central, linesearch = missing,
-#         linsolve = (x, A, b) -> copyto!(x, A \ b), factor = 1.0,
-#         autoscale = true, m = 10, beta = one(Float64))
-#     if Base.get_extension(@__MODULE__, :NonlinearSolveNLsolveExt) === nothing
-#         error("NLsolveJL requires NLsolve.jl to be loaded")
-#     end
-
-#     if autodiff isa Symbol && autodiff !== :central && autodiff !== :forward
-#         error("`autodiff` must be `:central` or `:forward`.")
-#     end
-
-#     return NLsolveJL(method, autodiff, linesearch, linsolve, factor, autoscale, m, beta)
-# end
-
-# """
-#     NLSolversJL(method; autodiff = nothing)
-#     NLSolversJL(; method, autodiff = nothing)
-
-# Wrapper over NLSolvers.jl Nonlinear Equation Solvers. We automatically construct the
-# jacobian function and supply it to the solver.
-
-# ### Arguments
-
-#   - `method`: the choice of method for solving the nonlinear system. See the documentation
-#     for NLSolvers.jl for more information.
-#   - `autodiff`: the choice of method for generating the Jacobian. Defaults to `nothing`
-#     which means that a default is selected according to the problem specification. Can be
-#     any valid ADTypes.jl autodiff type (conditional on that backend being supported in
-#     NonlinearSolve.jl).
-# """
-# struct NLSolversJL{M, AD} <: AbstractNonlinearSolveExtensionAlgorithm
-#     method::M
-#     autodiff::AD
-
-#     function NLSolversJL(method, autodiff)
-#         if Base.get_extension(@__MODULE__, :NonlinearSolveNLSolversExt) === nothing
-#             error("NLSolversJL requires NLSolvers.jl to be loaded")
-#         end
-
-#         return new{typeof(method), typeof(autodiff)}(method, autodiff)
-#     end
-# end
-
-# NLSolversJL(method; autodiff = nothing) = NLSolversJL(method, autodiff)
-# NLSolversJL(; method, autodiff = nothing) = NLSolversJL(method, autodiff)
-
-# """
-#     SpeedMappingJL(; σ_min = 0.0, stabilize::Bool = false, check_obj::Bool = false,
-#         orders::Vector{Int} = [3, 3, 2], time_limit::Real = 1000)
-
-# Wrapper over [SpeedMapping.jl](https://nicolasl-s.github.io/SpeedMapping.jl/) for solving
-# Fixed Point Problems. We allow using this algorithm to solve root finding problems as well.
-
-# ### Keyword Arguments
-
-#   - `σ_min`: Setting to `1` may avoid stalling (see [lepage2021alternating](@cite)).
-#   - `stabilize`: performs a stabilization mapping before extrapolating. Setting to `true`
-#     may improve the performance for applications like accelerating the EM or MM algorithms
-#     (see [lepage2021alternating](@cite)).
-#   - `check_obj`: In case of NaN or Inf values, the algorithm restarts at the best past
-#     iterate.
-#   - `orders`: determines ACX's alternating order. Must be between `1` and `3` (where `1`
-#     means no extrapolation). The two recommended orders are `[3, 2]` and `[3, 3, 2]`, the
-#     latter being potentially better for highly non-linear applications (see
-#     [lepage2021alternating](@cite)).
-#   - `time_limit`: time limit for the algorithm.
-
-# !!! note
-
-#     This algorithm is only available if `SpeedMapping.jl` is installed and loaded.
-# """
-# @concrete struct SpeedMappingJL <: AbstractNonlinearSolveExtensionAlgorithm
-#     σ_min
-#     stabilize::Bool
-#     check_obj::Bool
-#     orders::Vector{Int}
-# end
-
-# function SpeedMappingJL(; σ_min = 0.0, stabilize::Bool = false, check_obj::Bool = false,
-#         orders::Vector{Int} = [3, 3, 2])
-#     if Base.get_extension(@__MODULE__, :NonlinearSolveSpeedMappingExt) === nothing
-#         error("SpeedMappingJL requires SpeedMapping.jl to be loaded")
-#     end
-
-#     return SpeedMappingJL(σ_min, stabilize, check_obj, orders)
-# end
-
-# """
-#     FixedPointAccelerationJL(; algorithm = :Anderson, m = missing,
-#         condition_number_threshold = missing, extrapolation_period = missing,
-#         replace_invalids = :NoAction)
-
-# Wrapper over [FixedPointAcceleration.jl](https://s-baumann.github.io/FixedPointAcceleration.jl/)
-# for solving Fixed Point Problems. We allow using this algorithm to solve root finding
-# problems as well.
-
-# ### Keyword Arguments
-
-#   - `algorithm`: The algorithm to use. Can be `:Anderson`, `:MPE`, `:RRE`, `:VEA`, `:SEA`,
-#     `:Simple`, `:Aitken` or `:Newton`.
-#   - `m`: The number of previous iterates to use for the extrapolation. Only valid for
-#     `:Anderson`.
-#   - `condition_number_threshold`: The condition number threshold for Least Squares Problem.
-#     Only valid for `:Anderson`.
-#   - `extrapolation_period`: The number of iterates between extrapolations. Only valid for
-#     `:MPE`, `:RRE`, `:VEA` and `:SEA`. Defaults to `7` for `:MPE` & `:RRE`, and `6` for
-#     `:SEA` and `:VEA`. For `:SEA` and `:VEA`, this must be a multiple of `2`.
-#   - `replace_invalids`: The method to use for replacing invalid iterates. Can be
-#     `:ReplaceInvalids`, `:ReplaceVector` or `:NoAction`.
-
-# !!! note
-
-#     This algorithm is only available if `FixedPointAcceleration.jl` is installed and loaded.
-# """
-# @concrete struct FixedPointAccelerationJL <: AbstractNonlinearSolveExtensionAlgorithm
-#     algorithm::Symbol
-#     extrapolation_period::Int
-#     replace_invalids::Symbol
-#     dampening
-#     m::Int
-#     condition_number_threshold
-# end
-
-# function FixedPointAccelerationJL(;
-#         algorithm = :Anderson, m = missing, condition_number_threshold = missing,
-#         extrapolation_period = missing, replace_invalids = :NoAction, dampening = 1.0)
-#     if Base.get_extension(@__MODULE__, :NonlinearSolveFixedPointAccelerationExt) === nothing
-#         error("FixedPointAccelerationJL requires FixedPointAcceleration.jl to be loaded")
-#     end
-
-#     @assert algorithm in (:Anderson, :MPE, :RRE, :VEA, :SEA, :Simple, :Aitken, :Newton)
-#     @assert replace_invalids in (:ReplaceInvalids, :ReplaceVector, :NoAction)
-
-#     if algorithm !== :Anderson
-#         if condition_number_threshold !== missing
-#             error("`condition_number_threshold` is only valid for Anderson acceleration")
-#         end
-#         if m !== missing
-#             error("`m` is only valid for Anderson acceleration")
-#         end
-#     end
-#     condition_number_threshold === missing && (condition_number_threshold = 1e3)
-#     m === missing && (m = 10)
-
-#     if algorithm !== :MPE && algorithm !== :RRE && algorithm !== :VEA && algorithm !== :SEA
-#         if extrapolation_period !== missing
-#             error("`extrapolation_period` is only valid for MPE, RRE, VEA and SEA")
-#         end
-#     end
-#     if extrapolation_period === missing
-#         extrapolation_period = algorithm === :SEA || algorithm === :VEA ? 6 : 7
-#     else
-#         if (algorithm === :SEA || algorithm === :VEA) && extrapolation_period % 2 != 0
-#             error("`extrapolation_period` must be multiples of 2 for SEA and VEA")
-#         end
-#     end
-
-#     return FixedPointAccelerationJL(algorithm, extrapolation_period, replace_invalids,
-#         dampening, m, condition_number_threshold)
-# end
-
-# """
-#     SIAMFANLEquationsJL(; method = :newton, delta = 1e-3, linsolve = nothing,
-#         autodiff = missing)
-
-# ### Keyword Arguments
-
-#   - `method`: the choice of method for solving the nonlinear system.
-#   - `delta`: initial pseudo time step, default is 1e-3.
-#   - `linsolve` : JFNK linear solvers, choices are `gmres` and `bicgstab`.
-#   - `m`: Depth for Anderson acceleration, default as 0 for Picard iteration.
-#   - `beta`: Anderson mixing parameter, change f(x) to (1-beta)x+beta*f(x),
-#     equivalent to accelerating damped Picard iteration.
-#   - `autodiff`: Defaults to `missing`, which means we will default to letting
-#     `SIAMFANLEquations` construct the jacobian if `f.jac` is not provided. In other cases,
-#     we use it to generate a jacobian similar to other NonlinearSolve solvers.
-
-# ### Submethod Choice
-
-#   - `:newton`: Classical Newton method.
-#   - `:pseudotransient`: Pseudo transient method.
-#   - `:secant`: Secant method for scalar equations.
-#   - `:anderson`: Anderson acceleration for fixed point iterations.
-
-# !!! note
-
-#     This algorithm is only available if `SIAMFANLEquations.jl` is installed and loaded.
-# """
-# @concrete struct SIAMFANLEquationsJL <: AbstractNonlinearSolveExtensionAlgorithm
-#     method::Symbol
-#     delta
-#     linsolve <: Union{Symbol, Nothing}
-#     m::Int
-#     beta
-#     autodiff
-# end
-
-# function SIAMFANLEquationsJL(; method = :newton, delta = 1e-3, linsolve = nothing,
-#         m = 0, beta = 1.0, autodiff = missing)
-#     if Base.get_extension(@__MODULE__, :NonlinearSolveSIAMFANLEquationsExt) === nothing
-#         error("SIAMFANLEquationsJL requires SIAMFANLEquations.jl to be loaded")
-#     end
-#     return SIAMFANLEquationsJL(method, delta, linsolve, m, beta, autodiff)
-# end
-
-# """
-#     PETScSNES(; petsclib = missing, autodiff = nothing, mpi_comm = missing, kwargs...)
-
-# Wrapper over [PETSc.jl](https://github.com/JuliaParallel/PETSc.jl) SNES solvers.
-
-# ### Keyword Arguments
-
-#   - `petsclib`: PETSc library to use. If set to `missing`, then we will use the first
-#     available PETSc library in `PETSc.petsclibs` based on the problem element type.
-#   - `autodiff`: the choice of method for generating the Jacobian. Defaults to `nothing`
-#     which means that a default is selected according to the problem specification. Can be
-#     any valid ADTypes.jl autodiff type (conditional on that backend being supported in
-#     NonlinearSolve.jl). If set to `missing`, then PETSc computes the Jacobian using finite
-#     differences.
-#   - `mpi_comm`: MPI communicator to use. If set to `missing`, then we will use
-#     `MPI.COMM_SELF`.
-#   - `kwargs`: Keyword arguments to be passed to the PETSc SNES solver. See [PETSc SNES
-#     documentation](https://petsc.org/release/manual/snes/) and
-#     [SNESSetFromOptions](https://petsc.org/release/manualpages/SNES/SNESSetFromOptions)
-#     for more information.
-
-# ### Options via `CommonSolve.solve`
-
-# These options are forwarded from `solve` to the PETSc SNES solver. If these are provided to
-# `kwargs`, then they will be ignored.
-
-# | `solve` option | PETSc SNES option |
-# |:-------------- |:----------------- |
-# | `atol`         | `snes_atol`       |
-# | `rtol`         | `snes_rtol`       |
-# | `maxiters`     | `snes_max_it`     |
-# | `show_trace`   | `snes_monitor`    |
-
-# !!! note
-
-#     This algorithm is only available if `PETSc.jl` is installed and loaded.
-# """
-# @concrete struct PETScSNES <: AbstractNonlinearSolveExtensionAlgorithm
-#     petsclib
-#     mpi_comm
-#     autodiff <: Union{Missing, Nothing, ADTypes.AbstractADType}
-#     snes_options
-# end
-
-# function PETScSNES(; petsclib = missing, autodiff = nothing, mpi_comm = missing, kwargs...)
-#     if Base.get_extension(@__MODULE__, :NonlinearSolvePETScExt) === nothing
-#         error("PETScSNES requires PETSc.jl to be loaded")
-#     end
-#     return PETScSNES(petsclib, mpi_comm, autodiff, kwargs)
-# end
+# This file only include the algorithm struct to be exported by NonlinearSolve.jl. The main
+# functionality is implemented as package extensions
+"""
+    LeastSquaresOptimJL(alg = :lm; linsolve = nothing, autodiff::Symbol = :central)
+
+Wrapper over [LeastSquaresOptim.jl](https://github.com/matthieugomez/LeastSquaresOptim.jl)
+for solving `NonlinearLeastSquaresProblem`.
+
+### Arguments
+
+  - `alg`: Algorithm to use. Can be `:lm` or `:dogleg`.
+
+### Keyword Arguments
+
+  - `linsolve`: Linear solver to use. Can be `:qr`, `:cholesky` or `:lsmr`. If `nothing`,
+    then `LeastSquaresOptim.jl` will choose the best linear solver based on the Jacobian
+    structure.
+  - `autodiff`: Automatic differentiation / Finite Differences. Can be `:central` or
+    `:forward`.
+
+!!! note
+
+    This algorithm is only available if `LeastSquaresOptim.jl` is installed and loaded.
+"""
+@concrete struct LeastSquaresOptimJL <: AbstractNonlinearSolveAlgorithm
+    autodiff
+    alg::Symbol
+    linsolve <: Union{Symbol, Nothing}
+    name::Symbol
+end
+
+function LeastSquaresOptimJL(alg = :lm; linsolve = nothing, autodiff = :central)
+    @assert alg in (:lm, :dogleg)
+    @assert linsolve === nothing || linsolve in (:qr, :cholesky, :lsmr)
+    autodiff isa Symbol && @assert autodiff in (:central, :forward)
+
+    if Base.get_extension(@__MODULE__, :NonlinearSolveLeastSquaresOptimExt) === nothing
+        error("`LeastSquaresOptimJL` requires `LeastSquaresOptim.jl` to be loaded")
+    end
+
+    return LeastSquaresOptimJL(autodiff, alg, linsolve, :LeastSquaresOptimJL)
+end
+
+"""
+    FastLevenbergMarquardtJL(
+        linsolve::Symbol = :cholesky;
+        factor = 1e-6, factoraccept = 13.0, factorreject = 3.0, factorupdate = :marquardt,
+        minscale = 1e-12, maxscale = 1e16, minfactor = 1e-28, maxfactor = 1e32,
+        autodiff = nothing
+    )
+
+Wrapper over [FastLevenbergMarquardt.jl](https://github.com/kamesy/FastLevenbergMarquardt.jl)
+for solving `NonlinearLeastSquaresProblem`. For details about the other keyword arguments
+see the documentation for `FastLevenbergMarquardt.jl`.
+
+### Arguments
+
+  - `linsolve`: Linear solver to use. Can be `:qr` or `:cholesky`.
+
+### Keyword Arguments
+
+  - `autodiff`: determines the backend used for the Jacobian. Note that this argument is
+    ignored if an analytical Jacobian is passed, as that will be used instead. Defaults to
+    `nothing` which means that a default is selected according to the problem specification!
+
+!!! note
+
+    This algorithm is only available if `FastLevenbergMarquardt.jl` is installed and loaded.
+"""
+@concrete struct FastLevenbergMarquardtJL <: AbstractNonlinearSolveAlgorithm
+    autodiff
+    linsolve::Symbol
+    factor
+    factoraccept
+    factorreject
+    factorupdate::Symbol
+    minscale
+    maxscale
+    minfactor
+    maxfactor
+    name::Symbol
+end
+
+function FastLevenbergMarquardtJL(
+        linsolve::Symbol = :cholesky; factor = 1e-6, factoraccept = 13.0,
+        factorreject = 3.0, factorupdate = :marquardt, minscale = 1e-12,
+        maxscale = 1e16, minfactor = 1e-28, maxfactor = 1e32, autodiff = nothing
+)
+    @assert linsolve in (:qr, :cholesky)
+    @assert factorupdate in (:marquardt, :nielson)
+
+    if Base.get_extension(@__MODULE__, :NonlinearSolveFastLevenbergMarquardtExt) === nothing
+        error("`FastLevenbergMarquardtJL` requires `FastLevenbergMarquardt.jl` to be loaded")
+    end
+
+    return FastLevenbergMarquardtJL(
+        autodiff, linsolve, factor, factoraccept, factorreject,
+        factorupdate, minscale, maxscale, minfactor, maxfactor, :FastLevenbergMarquardtJL
+    )
+end
+
+"""
+    CMINPACK(; method::Symbol = :auto, autodiff = missing)
+
+### Keyword Arguments
+
+  - `method`: the choice of method for the solver.
+  - `autodiff`: Defaults to `missing`, which means we will default to letting `MINPACK`
+    construct the jacobian if `f.jac` is not provided. In other cases, we use it to generate
+    a jacobian similar to other NonlinearSolve solvers.
+
+### Submethod Choice
+
+The keyword argument `method` can take on different value depending on which method of
+`fsolve` you are calling. The standard choices of `method` are:
+
+  - `:hybr`: Modified version of Powell's algorithm. Uses MINPACK routine
+    [`hybrd1`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrd1.c)
+  - `:lm`: Levenberg-Marquardt. Uses MINPACK routine
+    [`lmdif1`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmdif1.c)
+  - `:lmdif`: Advanced Levenberg-Marquardt (more options available with `; kwargs...`). See
+    MINPACK routine [`lmdif`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmdif.c)
+    for more information
+  - `:hybrd`: Advanced modified version of Powell's algorithm (more options available with
+    `; kwargs...`). See MINPACK routine
+    [`hybrd`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrd.c)
+    for more information
+
+If a Jacobian is supplied as part of the [`NonlinearFunction`](@ref nonlinearfunctions),
+then the following methods are allowed:
+
+  - `:hybr`: Advanced modified version of Powell's algorithm with user supplied Jacobian.
+    Additional arguments are available via `; kwargs...`. See MINPACK routine
+    [`hybrj`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/hybrj.c)
+    for more information
+  - `:lm`: Advanced Levenberg-Marquardt with user supplied Jacobian. Additional arguments
+    are available via `; kwargs...`. See MINPACK routine
+    [`lmder`](https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/lmder.c)
+    for more information
+
+The default choice of `:auto` selects `:hybr` for NonlinearProblem and `:lm` for
+NonlinearLeastSquaresProblem.
+
+!!! note
+
+    This algorithm is only available if `MINPACK.jl` is installed and loaded.
+"""
+@concrete struct CMINPACK <: AbstractNonlinearSolveAlgorithm
+    method::Symbol
+    autodiff
+    name::Symbol
+end
+
+function CMINPACK(; method::Symbol = :auto, autodiff = missing)
+    if Base.get_extension(@__MODULE__, :NonlinearSolveMINPACKExt) === nothing
+        error("`CMINPACK` requires `MINPACK.jl` to be loaded")
+    end
+    return CMINPACK(method, autodiff, :CMINPACK)
+end
+
+"""
+    NLsolveJL(;
+        method = :trust_region, autodiff = :central, linesearch = Static(),
+        linsolve = (x, A, b) -> copyto!(x, A\\b), factor = one(Float64), autoscale = true,
+        m = 10, beta = one(Float64)
+    )
+
+### Keyword Arguments
+
+  - `method`: the choice of method for solving the nonlinear system.
+  - `autodiff`: the choice of method for generating the Jacobian. Defaults to `:central` or
+    central differencing via FiniteDiff.jl. The other choices are `:forward` or `ADTypes`
+    similar to other solvers in NonlinearSolve.
+  - `linesearch`: the line search method to be used within the solver method. The choices
+    are line search types from
+    [LineSearches.jl](https://github.com/JuliaNLSolvers/LineSearches.jl).
+  - `linsolve`: a function `linsolve(x, A, b)` that solves `Ax = b`.
+  - `factor`: determines the size of the initial trust region. This size is set to the
+    product of factor and the euclidean norm of `u0` if nonzero, or else to factor itself.
+  - `autoscale`: if true, then the variables will be automatically rescaled. The scaling
+    factors are the norms of the Jacobian columns.
+  - `m`: the amount of history in the Anderson method. Naive "Picard"-style iteration can be
+    achieved by setting m=0, but that isn't advisable for contractions whose Lipschitz
+    constants are close to 1. If convergence fails, though, you may consider lowering it.
+  - `beta`: It is also known as DIIS or Pulay mixing, this method is based on the
+    acceleration of the fixed-point iteration xₙ₊₁ = xₙ + beta*f(xₙ), where by default
+    beta = 1.
+
+!!! warning
+
+    Line Search Algorithms from [`LineSearch.jl`](https://github.com/SciML/LineSearch.jl)
+    aren't supported by `NLsolveJL`. Instead, use the line search algorithms from
+    [`LineSearches.jl`](https://github.com/JuliaNLSolvers/LineSearches.jl).
+
+### Submethod Choice
+
+Choices for methods in `NLsolveJL`:
+
+  - `:anderson`: Anderson-accelerated fixed-point iteration
+  - `:broyden`: Broyden's quasi-Newton method
+  - `:newton`: Classical Newton method with an optional line search
+  - `:trust_region`: Trust region Newton method (the default choice)
+
+For more information on these arguments, consult the
+[NLsolve.jl documentation](https://github.com/JuliaNLSolvers/NLsolve.jl).
+
+!!! note
+
+    This algorithm is only available if `NLsolve.jl` is installed and loaded.
+"""
+@concrete struct NLsolveJL <: AbstractNonlinearSolveAlgorithm
+    method::Symbol
+    autodiff
+    linesearch
+    linsolve
+    factor
+    autoscale::Bool
+    m::Int
+    beta
+    name::Symbol
+end
+
+function NLsolveJL(;
+        method = :trust_region, autodiff = :central, linesearch = missing, beta = 1.0,
+        linsolve = (x, A, b) -> copyto!(x, A \ b), factor = 1.0, autoscale = true, m = 10
+)
+    if Base.get_extension(@__MODULE__, :NonlinearSolveNLsolveExt) === nothing
+        error("`NLsolveJL` requires `NLsolve.jl` to be loaded")
+    end
+
+    if autodiff isa Symbol && autodiff !== :central && autodiff !== :forward
+        error("`autodiff` must be `:central` or `:forward`.")
+    end
+
+    return NLsolveJL(
+        method, autodiff, linesearch, linsolve, factor, autoscale, m, beta, :NLsolveJL
+    )
+end
+
+"""
+    NLSolversJL(method; autodiff = nothing)
+    NLSolversJL(; method, autodiff = nothing)
+
+Wrapper over NLSolvers.jl Nonlinear Equation Solvers. We automatically construct the
+jacobian function and supply it to the solver.
+
+### Arguments
+
+  - `method`: the choice of method for solving the nonlinear system. See the documentation
+    for NLSolvers.jl for more information.
+  - `autodiff`: the choice of method for generating the Jacobian. Defaults to `nothing`
+    which means that a default is selected according to the problem specification. Can be
+    any valid ADTypes.jl autodiff type (conditional on that backend being supported in
+    NonlinearSolve.jl).
+"""
+struct NLSolversJL{M, AD} <: AbstractNonlinearSolveAlgorithm
+    method::M
+    autodiff::AD
+    name::Symbol
+
+    function NLSolversJL(method, autodiff)
+        if Base.get_extension(@__MODULE__, :NonlinearSolveNLSolversExt) === nothing
+            error("NLSolversJL requires NLSolvers.jl to be loaded")
+        end
+
+        return new{typeof(method), typeof(autodiff)}(method, autodiff, :NLSolversJL)
+    end
+end
+
+NLSolversJL(method; autodiff = nothing) = NLSolversJL(method, autodiff)
+NLSolversJL(; method, autodiff = nothing) = NLSolversJL(method, autodiff)
+
+"""
+    SpeedMappingJL(;
+        σ_min = 0.0, stabilize::Bool = false, check_obj::Bool = false,
+        orders::Vector{Int} = [3, 3, 2]
+    )
+
+Wrapper over [SpeedMapping.jl](https://nicolasl-s.github.io/SpeedMapping.jl/) for solving
+Fixed Point Problems. We allow using this algorithm to solve root finding problems as well.
+
+### Keyword Arguments
+
+  - `σ_min`: Setting to `1` may avoid stalling (see [lepage2021alternating](@cite)).
+  - `stabilize`: performs a stabilization mapping before extrapolating. Setting to `true`
+    may improve the performance for applications like accelerating the EM or MM algorithms
+    (see [lepage2021alternating](@cite)).
+  - `check_obj`: In case of NaN or Inf values, the algorithm restarts at the best past
+    iterate.
+  - `orders`: determines ACX's alternating order. Must be between `1` and `3` (where `1`
+    means no extrapolation). The two recommended orders are `[3, 2]` and `[3, 3, 2]`, the
+    latter being potentially better for highly non-linear applications (see
+    [lepage2021alternating](@cite)).
+
+!!! note
+
+    This algorithm is only available if `SpeedMapping.jl` is installed and loaded.
+"""
+@concrete struct SpeedMappingJL <: AbstractNonlinearSolveAlgorithm
+    σ_min
+    stabilize::Bool
+    check_obj::Bool
+    orders::Vector{Int}
+    name::Symbol
+end
+
+function SpeedMappingJL(;
+        σ_min = 0.0, stabilize::Bool = false, check_obj::Bool = false,
+        orders::Vector{Int} = [3, 3, 2]
+)
+    if Base.get_extension(@__MODULE__, :NonlinearSolveSpeedMappingExt) === nothing
+        error("`SpeedMappingJL` requires `SpeedMapping.jl` to be loaded")
+    end
+
+    return SpeedMappingJL(σ_min, stabilize, check_obj, orders, :SpeedMappingJL)
+end
+
+"""
+    FixedPointAccelerationJL(;
+        algorithm = :Anderson, m = missing, condition_number_threshold = missing,
+        extrapolation_period = missing, replace_invalids = :NoAction
+    )
+
+Wrapper over [FixedPointAcceleration.jl](https://s-baumann.github.io/FixedPointAcceleration.jl/)
+for solving Fixed Point Problems. We allow using this algorithm to solve root finding
+problems as well.
+
+### Keyword Arguments
+
+  - `algorithm`: The algorithm to use. Can be `:Anderson`, `:MPE`, `:RRE`, `:VEA`, `:SEA`,
+    `:Simple`, `:Aitken` or `:Newton`.
+  - `m`: The number of previous iterates to use for the extrapolation. Only valid for
+    `:Anderson`.
+  - `condition_number_threshold`: The condition number threshold for Least Squares Problem.
+    Only valid for `:Anderson`.
+  - `extrapolation_period`: The number of iterates between extrapolations. Only valid for
+    `:MPE`, `:RRE`, `:VEA` and `:SEA`. Defaults to `7` for `:MPE` & `:RRE`, and `6` for
+    `:SEA` and `:VEA`. For `:SEA` and `:VEA`, this must be a multiple of `2`.
+  - `replace_invalids`: The method to use for replacing invalid iterates. Can be
+    `:ReplaceInvalids`, `:ReplaceVector` or `:NoAction`.
+
+!!! note
+
+    This algorithm is only available if `FixedPointAcceleration.jl` is installed and loaded.
+"""
+@concrete struct FixedPointAccelerationJL <: AbstractNonlinearSolveAlgorithm
+    algorithm::Symbol
+    extrapolation_period::Int
+    replace_invalids::Symbol
+    dampening
+    m::Int
+    condition_number_threshold
+    name::Symbol
+end
+
+function FixedPointAccelerationJL(;
+        algorithm = :Anderson, m = missing, condition_number_threshold = missing,
+        extrapolation_period = missing, replace_invalids = :NoAction, dampening = 1.0
+)
+    if Base.get_extension(@__MODULE__, :NonlinearSolveFixedPointAccelerationExt) === nothing
+        error("`FixedPointAccelerationJL` requires `FixedPointAcceleration.jl` to be loaded")
+    end
+
+    @assert algorithm in (:Anderson, :MPE, :RRE, :VEA, :SEA, :Simple, :Aitken, :Newton)
+    @assert replace_invalids in (:ReplaceInvalids, :ReplaceVector, :NoAction)
+
+    if algorithm !== :Anderson
+        @assert condition_number_threshold===missing "`condition_number_threshold` is only valid for Anderson acceleration"
+        @assert m===missing "`m` is only valid for Anderson acceleration"
+    end
+    condition_number_threshold === missing && (condition_number_threshold = 1e3)
+    m === missing && (m = 10)
+
+    if algorithm !== :MPE && algorithm !== :RRE && algorithm !== :VEA && algorithm !== :SEA
+        @assert extrapolation_period===missing "`extrapolation_period` is only valid for MPE, RRE, VEA and SEA"
+    end
+    if extrapolation_period === missing
+        extrapolation_period = algorithm === :SEA || algorithm === :VEA ? 6 : 7
+    else
+        if (algorithm === :SEA || algorithm === :VEA) && extrapolation_period % 2 != 0
+            throw(AssertionError("`extrapolation_period` must be multiples of 2 for SEA and VEA"))
+        end
+    end
+
+    return FixedPointAccelerationJL(
+        algorithm, extrapolation_period, replace_invalids,
+        dampening, m, condition_number_threshold, :FixedPointAccelerationJL
+    )
+end
+
+"""
+    SIAMFANLEquationsJL(;
+        method = :newton, delta = 1e-3, linsolve = nothing, autodiff = missing
+    )
+
+### Keyword Arguments
+
+  - `method`: the choice of method for solving the nonlinear system.
+  - `delta`: initial pseudo time step, default is 1e-3.
+  - `linsolve` : JFNK linear solvers, choices are `gmres` and `bicgstab`.
+  - `m`: Depth for Anderson acceleration, default as 0 for Picard iteration.
+  - `beta`: Anderson mixing parameter, change f(x) to (1-beta)x+beta*f(x),
+    equivalent to accelerating damped Picard iteration.
+  - `autodiff`: Defaults to `missing`, which means we will default to letting
+    `SIAMFANLEquations` construct the jacobian if `f.jac` is not provided. In other cases,
+    we use it to generate a jacobian similar to other NonlinearSolve solvers.
+
+### Submethod Choice
+
+  - `:newton`: Classical Newton method.
+  - `:pseudotransient`: Pseudo transient method.
+  - `:secant`: Secant method for scalar equations.
+  - `:anderson`: Anderson acceleration for fixed point iterations.
+
+!!! note
+
+    This algorithm is only available if `SIAMFANLEquations.jl` is installed and loaded.
+"""
+@concrete struct SIAMFANLEquationsJL <: AbstractNonlinearSolveAlgorithm
+    method::Symbol
+    delta
+    linsolve <: Union{Symbol, Nothing}
+    m::Int
+    beta
+    autodiff
+    name::Symbol
+end
+
+function SIAMFANLEquationsJL(;
+        method = :newton, delta = 1e-3, linsolve = nothing, m = 0, beta = 1.0,
+        autodiff = missing
+)
+    if Base.get_extension(@__MODULE__, :NonlinearSolveSIAMFANLEquationsExt) === nothing
+        error("`SIAMFANLEquationsJL` requires `SIAMFANLEquations.jl` to be loaded")
+    end
+    return SIAMFANLEquationsJL(
+        method, delta, linsolve, m, beta, autodiff, :SIAMFANLEquationsJL
+    )
+end
+
+"""
+    PETScSNES(; petsclib = missing, autodiff = nothing, mpi_comm = missing, kwargs...)
+
+Wrapper over [PETSc.jl](https://github.com/JuliaParallel/PETSc.jl) SNES solvers.
+
+### Keyword Arguments
+
+  - `petsclib`: PETSc library to use. If set to `missing`, then we will use the first
+    available PETSc library in `PETSc.petsclibs` based on the problem element type.
+  - `autodiff`: the choice of method for generating the Jacobian. Defaults to `nothing`
+    which means that a default is selected according to the problem specification. Can be
+    any valid ADTypes.jl autodiff type (conditional on that backend being supported in
+    NonlinearSolve.jl). If set to `missing`, then PETSc computes the Jacobian using finite
+    differences.
+  - `mpi_comm`: MPI communicator to use. If set to `missing`, then we will use
+    `MPI.COMM_SELF`.
+  - `kwargs`: Keyword arguments to be passed to the PETSc SNES solver. See [PETSc SNES
+    documentation](https://petsc.org/release/manual/snes/) and
+    [SNESSetFromOptions](https://petsc.org/release/manualpages/SNES/SNESSetFromOptions)
+    for more information.
+
+### Options via `CommonSolve.solve`
+
+These options are forwarded from `solve` to the PETSc SNES solver. If these are provided to
+`kwargs`, then they will be ignored.
+
+| `solve` option | PETSc SNES option |
+|:-------------- |:----------------- |
+| `atol`         | `snes_atol`       |
+| `rtol`         | `snes_rtol`       |
+| `maxiters`     | `snes_max_it`     |
+| `show_trace`   | `snes_monitor`    |
+
+!!! note
+
+    This algorithm is only available if `PETSc.jl` is installed and loaded.
+"""
+@concrete struct PETScSNES <: AbstractNonlinearSolveAlgorithm
+    petsclib
+    mpi_comm
+    autodiff
+    snes_options
+end
+
+function PETScSNES(; petsclib = missing, autodiff = nothing, mpi_comm = missing, kwargs...)
+    if Base.get_extension(@__MODULE__, :NonlinearSolvePETScExt) === nothing
+        error("`PETScSNES` requires `PETSc.jl` to be loaded")
+    end
+    return PETScSNES(petsclib, mpi_comm, autodiff, kwargs)
+end
diff --git a/src/helpers.jl b/src/helpers.jl
index e69de29bb..8b1378917 100644
--- a/src/helpers.jl
+++ b/src/helpers.jl
@@ -0,0 +1 @@
+
diff --git a/src/internal/helpers.jl b/src/internal/helpers.jl
deleted file mode 100644
index a7326bb51..000000000
--- a/src/internal/helpers.jl
+++ /dev/null
@@ -1,85 +0,0 @@
-# Extension Algorithm Helpers
-function __test_termination_condition(termination_condition, alg)
-    !(termination_condition isa AbsNormTerminationMode) &&
-        termination_condition !== nothing &&
-        error("`$(alg)` does not support termination conditions!")
-end
-
-function __construct_extension_f(prob::AbstractNonlinearProblem; alias_u0::Bool = false,
-        can_handle_oop::Val = False, can_handle_scalar::Val = False,
-        make_fixed_point::Val = False, force_oop::Val = False)
-    if can_handle_oop === False && can_handle_scalar === True
-        error("Incorrect Specification: OOP not supported but scalar supported.")
-    end
-
-    resid = evaluate_f(prob, prob.u0)
-    u0 = can_handle_scalar === True || !(prob.u0 isa Number) ?
-         __maybe_unaliased(prob.u0, alias_u0) : [prob.u0]
-
-    fₚ = if make_fixed_point === True
-        if isinplace(prob)
-            @closure (du, u) -> (prob.f(du, u, prob.p); du .+= u)
-        else
-            @closure u -> prob.f(u, prob.p) .+ u
-        end
-    else
-        if isinplace(prob)
-            @closure (du, u) -> prob.f(du, u, prob.p)
-        else
-            @closure u -> prob.f(u, prob.p)
-        end
-    end
-
-    𝐟 = if isinplace(prob)
-        u0_size, du_size = size(u0), size(resid)
-        @closure (du, u) -> (fₚ(reshape(du, du_size), reshape(u, u0_size)); du)
-    else
-        if prob.u0 isa Number
-            if can_handle_scalar === True
-                fₚ
-            elseif can_handle_oop === True
-                @closure u -> [fₚ(first(u))]
-            else
-                @closure (du, u) -> (du[1] = fₚ(first(u)); du)
-            end
-        else
-            u0_size = size(u0)
-            if can_handle_oop === True
-                @closure u -> vec(fₚ(reshape(u, u0_size)))
-            else
-                @closure (du, u) -> (copyto!(du, fₚ(reshape(u, u0_size))); du)
-            end
-        end
-    end
-
-    𝐅 = if force_oop === True && applicable(𝐟, u0, u0)
-        _resid = resid isa Number ? [resid] : _vec(resid)
-        du = _vec(zero(_resid))
-        @closure u -> begin
-            𝐟(du, u)
-            return du
-        end
-    else
-        𝐟
-    end
-
-    return 𝐅, _vec(u0), (resid isa Number ? [resid] : _vec(resid))
-end
-
-function __construct_extension_jac(prob, alg, u0, fu; can_handle_oop::Val = False,
-        can_handle_scalar::Val = False, autodiff = nothing, initial_jacobian = False,
-        kwargs...)
-    autodiff = select_jacobian_autodiff(prob, autodiff)
-
-    Jₚ = construct_jacobian_cache(
-        prob, alg, prob.f, fu, u0, prob.p; stats = empty_nlstats(), autodiff, kwargs...)
-
-    𝓙 = (can_handle_scalar === False && prob.u0 isa Number) ? @closure(u->[Jₚ(u[1])]) : Jₚ
-
-    𝐉 = (can_handle_oop === False && !isinplace(prob)) ?
-        @closure((J, u)->copyto!(J, 𝓙(u))) : 𝓙
-
-    initial_jacobian === False && return 𝐉
-
-    return 𝐉, Jₚ(nothing)
-end
diff --git a/test/23_test_problems_tests.jl b/test/23_test_problems_tests.jl
index 6246cbecb..23b9a3e2a 100644
--- a/test/23_test_problems_tests.jl
+++ b/test/23_test_problems_tests.jl
@@ -1,144 +1,149 @@
-# @testsetup module RobustnessTesting
-# using NonlinearSolve, LinearAlgebra, LinearSolve, NonlinearProblemLibrary, Test
-
-# problems = NonlinearProblemLibrary.problems
-# dicts = NonlinearProblemLibrary.dicts
-
-# function test_on_library(
-#         problems, dicts, alg_ops, broken_tests, ϵ = 1e-4; skip_tests = nothing)
-#     for (idx, (problem, dict)) in enumerate(zip(problems, dicts))
-#         x = dict["start"]
-#         res = similar(x)
-#         nlprob = NonlinearProblem(problem, copy(x))
-#         @testset "$idx: $(dict["title"])" begin
-#             for alg in alg_ops
-#                 try
-#                     sol = solve(nlprob, alg; maxiters = 10000)
-#                     problem(res, sol.u, nothing)
-
-#                     skip = skip_tests !== nothing && idx in skip_tests[alg]
-#                     if skip
-#                         @test_skip norm(res, Inf) ≤ ϵ
-#                         continue
-#                     end
-#                     broken = idx in broken_tests[alg] ? true : false
-#                     @test norm(res, Inf)≤ϵ broken=broken
-#                 catch err
-#                     @error err
-#                     broken = idx in broken_tests[alg] ? true : false
-#                     if broken
-#                         @test false broken=true
-#                     else
-#                         @test 1 == 2
-#                     end
-#                 end
-#             end
-#         end
-#     end
-# end
-
-# export test_on_library, problems, dicts
-# end
-
-# @testitem "PolyAlgorithms" setup=[RobustnessTesting] tags=[:core] begin
-#     alg_ops = (RobustMultiNewton(), FastShortcutNonlinearPolyalg())
-
-#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-#     broken_tests[alg_ops[1]] = []
-#     broken_tests[alg_ops[2]] = []
-
-#     test_on_library(problems, dicts, alg_ops, broken_tests)
-# end
-
-# @testitem "NewtonRaphson" setup=[RobustnessTesting] tags=[:core] begin
-#     alg_ops = (NewtonRaphson(),)
-
-#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-#     broken_tests[alg_ops[1]] = [1]
-
-#     test_on_library(problems, dicts, alg_ops, broken_tests)
-# end
-
-# @testitem "TrustRegion" setup=[RobustnessTesting] tags=[:core] begin
-#     alg_ops = (TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Simple),
-#         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Fan),
-#         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Hei),
-#         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Yuan),
-#         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Bastin),
-#         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.NLsolve))
-
-#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-#     broken_tests[alg_ops[1]] = [11, 21]
-#     broken_tests[alg_ops[2]] = [11, 21]
-#     broken_tests[alg_ops[3]] = [11, 21]
-#     broken_tests[alg_ops[4]] = [8, 11, 21]
-#     broken_tests[alg_ops[5]] = [21]
-#     broken_tests[alg_ops[6]] = [11, 21]
-
-#     test_on_library(problems, dicts, alg_ops, broken_tests)
-# end
-
-# @testitem "LevenbergMarquardt" setup=[RobustnessTesting] tags=[:core] begin
-#     using LinearSolve
-
-#     alg_ops = (LevenbergMarquardt(), LevenbergMarquardt(; α_geodesic = 0.1),
-#         LevenbergMarquardt(; linsolve = CholeskyFactorization()))
-
-#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-#     broken_tests[alg_ops[1]] = [11, 21]
-#     broken_tests[alg_ops[2]] = [11, 21]
-#     broken_tests[alg_ops[3]] = [11, 21]
-
-#     test_on_library(problems, dicts, alg_ops, broken_tests)
-# end
-
-# @testitem "DFSane" setup=[RobustnessTesting] tags=[:core] begin
-#     alg_ops = (DFSane(),)
-
-#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-#     broken_tests[alg_ops[1]] = [1, 2, 3, 5, 21]
-
-#     test_on_library(problems, dicts, alg_ops, broken_tests)
-# end
-
-# @testitem "Broyden" setup=[RobustnessTesting] tags=[:core] begin
-#     alg_ops = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian)),
-#         Broyden(; update_rule = Val(:bad_broyden)),
-#         Broyden(; init_jacobian = Val(:true_jacobian), update_rule = Val(:bad_broyden)))
-
-#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-#     if Sys.isapple()
-#         broken_tests[alg_ops[1]] = [1, 5, 11]
-#         broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
-#         broken_tests[alg_ops[3]] = [1, 5, 6, 9, 11]
-#         broken_tests[alg_ops[4]] = [5, 6, 8, 11]
-#     else
-#         broken_tests[alg_ops[1]] = [1, 5, 11, 15]
-#         broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
-#         broken_tests[alg_ops[3]] = [1, 5, 9, 11]
-#         broken_tests[alg_ops[4]] = [5, 6, 8, 11]
-#     end
-
-#     test_on_library(problems, dicts, alg_ops, broken_tests, Sys.isapple() ? 1e-3 : 1e-4)
-# end
-
-# @testitem "Klement" setup=[RobustnessTesting] tags=[:core] begin
-#     alg_ops = (Klement(), Klement(; init_jacobian = Val(:true_jacobian_diagonal)))
-
-#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-#     broken_tests[alg_ops[1]] = [1, 2, 4, 5, 11, 18, 22]
-#     broken_tests[alg_ops[2]] = [2, 4, 5, 7, 18, 22]
-
-#     test_on_library(problems, dicts, alg_ops, broken_tests)
-# end
-
-# @testitem "PseudoTransient" setup=[RobustnessTesting] tags=[:core] begin
-#     # PT relies on the root being a stable equilibrium for convergence, so it won't work on
-#     # most problems
-#     alg_ops = (PseudoTransient(),)
-
-#     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-#     broken_tests[alg_ops[1]] = [1, 2, 3, 11, 15, 16]
-
-#     test_on_library(problems, dicts, alg_ops, broken_tests)
-# end
+@testsetup module RobustnessTesting
+using NonlinearSolve, LinearAlgebra, LinearSolve, NonlinearProblemLibrary, Test
+
+problems = NonlinearProblemLibrary.problems
+dicts = NonlinearProblemLibrary.dicts
+
+function test_on_library(
+        problems, dicts, alg_ops, broken_tests, ϵ = 1e-4; skip_tests = nothing)
+    for (idx, (problem, dict)) in enumerate(zip(problems, dicts))
+        x = dict["start"]
+        res = similar(x)
+        nlprob = NonlinearProblem(problem, copy(x))
+        @testset "$idx: $(dict["title"])" begin
+            for alg in alg_ops
+                try
+                    sol = solve(nlprob, alg; maxiters = 10000)
+                    problem(res, sol.u, nothing)
+
+                    skip = skip_tests !== nothing && idx in skip_tests[alg]
+                    if skip
+                        @test_skip norm(res, Inf) ≤ ϵ
+                        continue
+                    end
+                    broken = idx in broken_tests[alg] ? true : false
+                    @test norm(res, Inf)≤ϵ broken=broken
+                catch err
+                    @error err
+                    broken = idx in broken_tests[alg] ? true : false
+                    if broken
+                        @test false broken=true
+                    else
+                        @test 1 == 2
+                    end
+                end
+            end
+        end
+    end
+end
+
+export test_on_library, problems, dicts
+end
+
+@testitem "PolyAlgorithms" setup=[RobustnessTesting] tags=[:core] begin
+    alg_ops = (RobustMultiNewton(), FastShortcutNonlinearPolyalg())
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = []
+    broken_tests[alg_ops[2]] = []
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "NewtonRaphson" setup=[RobustnessTesting] tags=[:core] begin
+    alg_ops = (NewtonRaphson(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [1]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "TrustRegion" setup=[RobustnessTesting] tags=[:core] begin
+    alg_ops = (
+        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Simple),
+        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Fan),
+        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Hei),
+        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Yuan),
+        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Bastin),
+        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.NLsolve)
+    )
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [11, 21]
+    broken_tests[alg_ops[2]] = [11, 21]
+    broken_tests[alg_ops[3]] = [11, 21]
+    broken_tests[alg_ops[4]] = [8, 11, 21]
+    broken_tests[alg_ops[5]] = [21]
+    broken_tests[alg_ops[6]] = [11, 21]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "LevenbergMarquardt" setup=[RobustnessTesting] tags=[:core] begin
+    using LinearSolve
+
+    alg_ops = (
+        LevenbergMarquardt(),
+        LevenbergMarquardt(; α_geodesic = 0.1),
+        LevenbergMarquardt(; linsolve = CholeskyFactorization())
+    )
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [11, 21]
+    broken_tests[alg_ops[2]] = [11, 21]
+    broken_tests[alg_ops[3]] = [11, 21]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "DFSane" setup=[RobustnessTesting] tags=[:core] begin
+    alg_ops = (DFSane(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [1, 2, 3, 5, 21]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "Broyden" setup=[RobustnessTesting] tags=[:core] begin
+    alg_ops = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian)),
+        Broyden(; update_rule = Val(:bad_broyden)),
+        Broyden(; init_jacobian = Val(:true_jacobian), update_rule = Val(:bad_broyden)))
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    if Sys.isapple()
+        broken_tests[alg_ops[1]] = [1, 5, 11]
+        broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
+        broken_tests[alg_ops[3]] = [1, 5, 6, 9, 11]
+        broken_tests[alg_ops[4]] = [5, 6, 8, 11]
+    else
+        broken_tests[alg_ops[1]] = [1, 5, 11, 15]
+        broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
+        broken_tests[alg_ops[3]] = [1, 5, 9, 11]
+        broken_tests[alg_ops[4]] = [5, 6, 8, 11]
+    end
+
+    test_on_library(problems, dicts, alg_ops, broken_tests, Sys.isapple() ? 1e-3 : 1e-4)
+end
+
+@testitem "Klement" setup=[RobustnessTesting] tags=[:core] begin
+    alg_ops = (Klement(), Klement(; init_jacobian = Val(:true_jacobian_diagonal)))
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 11, 18, 22]
+    broken_tests[alg_ops[2]] = [2, 4, 5, 7, 18, 22]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "PseudoTransient" setup=[RobustnessTesting] tags=[:core] begin
+    # PT relies on the root being a stable equilibrium for convergence, so it won't work on
+    # most problems
+    alg_ops = (PseudoTransient(),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[1]] = [1, 2, 3, 11, 15, 16]
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
diff --git a/test/wrappers/fixedpoint_tests.jl b/test/wrappers/fixedpoint_tests.jl
index a3ec497c7..a04e35069 100644
--- a/test/wrappers/fixedpoint_tests.jl
+++ b/test/wrappers/fixedpoint_tests.jl
@@ -1,11 +1,6 @@
-@testsetup module WrapperFixedPointImports
-using Reexport
-@reexport using LinearAlgebra
-import SIAMFANLEquations, FixedPointAcceleration, SpeedMapping, NLsolve
-end
+@testitem "Simple Scalar Problem" tags=[:wrappers] begin
+    import SpeedMapping, SIAMFANLEquations, NLsolve, FixedPointAcceleration
 
-# Simple Scalar Problem
-@testitem "Simple Scalar Problem" setup=[WrapperFixedPointImports] tags=[:wrappers] begin
     f1(x, p) = cos(x) - x
     prob = NonlinearProblem(f1, 1.1)
 
@@ -22,7 +17,9 @@ end
 end
 
 # Simple Vector Problem
-@testitem "Simple Vector Problem" setup=[WrapperFixedPointImports] tags=[:wrappers] begin
+@testitem "Simple Vector Problem" tags=[:wrappers] begin
+    import SpeedMapping, SIAMFANLEquations, NLsolve, FixedPointAcceleration
+
     f2(x, p) = cos.(x) .- x
     prob = NonlinearProblem(f2, [1.1, 1.1])
 
@@ -41,7 +38,10 @@ end
 
 # Fixed Point for Power Method
 # Taken from https://github.com/NicolasL-S/SpeedMapping.jl/blob/95951db8f8a4457093090e18802ad382db1c76da/test/runtests.jl
-@testitem "Power Method" setup=[WrapperFixedPointImports] tags=[:wrappers] begin
+@testitem "Power Method" tags=[:wrappers] begin
+    using LinearAlgebra
+    import SpeedMapping, SIAMFANLEquations, NLsolve, FixedPointAcceleration
+
     C = [1 2 3; 4 5 6; 7 8 9]
     A = C + C'
     B = Hermitian(ones(10) * ones(10)' .* im + Diagonal(1:10))
diff --git a/test/wrappers/least_squares_tests.jl b/test/wrappers/least_squares_tests.jl
index 53cea758d..99d3e0ef3 100644
--- a/test/wrappers/least_squares_tests.jl
+++ b/test/wrappers/least_squares_tests.jl
@@ -1,52 +1,32 @@
 @testsetup module WrapperNLLSSetup
-using Reexport
-@reexport using LinearAlgebra, StableRNGs, StaticArrays, Random, ForwardDiff, Zygote
-import FastLevenbergMarquardt, LeastSquaresOptim, MINPACK
 
-true_function(x, θ) = @. θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4])
-true_function(y, x, θ) = (@. y = θ[1] * exp(θ[2] * x) * cos(θ[3] * x + θ[4]))
+include("../../common/common_nlls_testing.jl")
 
-θ_true = [1.0, 0.1, 2.0, 0.5]
-
-x = [-1.0, -0.5, 0.0, 0.5, 1.0]
-
-const y_target = true_function(x, θ_true)
-
-function loss_function(θ, p)
-    ŷ = true_function(p, θ)
-    return ŷ .- y_target
-end
-
-function loss_function(resid, θ, p)
-    true_function(resid, p, θ)
-    resid .= resid .- y_target
-    return resid
-end
-
-θ_init = θ_true .+ randn!(StableRNG(0), similar(θ_true)) * 0.1
-
-export loss_function, θ_init, y_target, true_function, x, θ_true
 end
 
 @testitem "LeastSquaresOptim.jl" setup=[WrapperNLLSSetup] tags=[:wrappers] begin
-    prob_oop = NonlinearLeastSquaresProblem{false}(loss_function, θ_init, x)
-    prob_iip = NonlinearLeastSquaresProblem(
-        NonlinearFunction(loss_function; resid_prototype = zero(y_target)), θ_init, x)
+    import LeastSquaresOptim
 
     nlls_problems = [prob_oop, prob_iip]
 
-    solvers = [LeastSquaresOptimJL(alg; autodiff)
-               for alg in (:lm, :dogleg),
-    autodiff in (nothing, AutoForwardDiff(), AutoFiniteDiff(), :central, :forward)]
+    solvers = []
+    for alg in (:lm, :dogleg),
+        autodiff in (nothing, AutoForwardDiff(), AutoFiniteDiff(), :central, :forward)
+
+        push!(solvers, LeastSquaresOptimJL(alg; autodiff))
+    end
 
     for prob in nlls_problems, solver in solvers
         sol = solve(prob, solver; maxiters = 10000, abstol = 1e-8)
         @test SciMLBase.successful_retcode(sol)
-        @test norm(sol.resid, Inf) < 1e-6
+        @test maximum(abs, sol.resid) < 1e-6
     end
 end
 
 @testitem "FastLevenbergMarquardt.jl + CMINPACK: Jacobian Provided" setup=[WrapperNLLSSetup] tags=[:wrappers] begin
+    import FastLevenbergMarquardt, MINPACK
+    using ForwardDiff
+
     function jac!(J, θ, p)
         resid = zeros(length(p))
         ForwardDiff.jacobian!(J, (resid, θ) -> loss_function(resid, θ, p), resid, θ)
@@ -58,19 +38,24 @@ end
     probs = [
         NonlinearLeastSquaresProblem(
             NonlinearFunction{true}(
-                loss_function; resid_prototype = zero(y_target), jac = jac!),
-            θ_init,
-            x),
+                loss_function; resid_prototype = zero(y_target), jac = jac!
+            ),
+            θ_init, x
+        ),
         NonlinearLeastSquaresProblem(
             NonlinearFunction{false}(
-                loss_function; resid_prototype = zero(y_target), jac = jac),
-            θ_init,
-            x),
+                loss_function; resid_prototype = zero(y_target), jac = jac
+            ),
+            θ_init, x
+        ),
         NonlinearLeastSquaresProblem(
-            NonlinearFunction{false}(loss_function; jac), θ_init, x)]
+            NonlinearFunction{false}(loss_function; jac), θ_init, x
+        )
+    ]
 
     solvers = Any[FastLevenbergMarquardtJL(linsolve) for linsolve in (:cholesky, :qr)]
     Sys.isapple() || push!(solvers, CMINPACK())
+
     for solver in solvers, prob in probs
         sol = solve(prob, solver; maxiters = 10000, abstol = 1e-8)
         @test maximum(abs, sol.resid) < 1e-6
@@ -78,28 +63,41 @@ end
 end
 
 @testitem "FastLevenbergMarquardt.jl + CMINPACK: Jacobian Not Provided" setup=[WrapperNLLSSetup] tags=[:wrappers] begin
+    import FastLevenbergMarquardt, MINPACK
+
     probs = [
         NonlinearLeastSquaresProblem(
             NonlinearFunction{true}(loss_function; resid_prototype = zero(y_target)),
-            θ_init, x),
+            θ_init, x
+        ),
         NonlinearLeastSquaresProblem(
             NonlinearFunction{false}(loss_function; resid_prototype = zero(y_target)),
-            θ_init, x),
-        NonlinearLeastSquaresProblem(NonlinearFunction{false}(loss_function), θ_init, x)]
+            θ_init, x
+        ),
+        NonlinearLeastSquaresProblem(NonlinearFunction{false}(loss_function), θ_init, x)
+    ]
 
-    solvers = vec(Any[FastLevenbergMarquardtJL(linsolve; autodiff)
-                      for linsolve in (:cholesky, :qr),
-    autodiff in (nothing, AutoForwardDiff(), AutoFiniteDiff())])
-    Sys.isapple() ||
-        append!(solvers, [CMINPACK(; method) for method in (:auto, :lm, :lmdif)])
+    solvers = []
+    for linsolve in (:cholesky, :qr),
+        autodiff in (nothing, AutoForwardDiff(), AutoFiniteDiff())
+
+        push!(solvers, FastLevenbergMarquardtJL(linsolve; autodiff))
+    end
+    if Sys.isapple()
+        for method in (:auto, :lm, :lmdif)
+            push!(solvers, CMINPACK(; method))
+        end
+    end
 
     for solver in solvers, prob in probs
         sol = solve(prob, solver; maxiters = 10000, abstol = 1e-8)
-        @test norm(sol.resid, Inf) < 1e-6
+        @test maximum(abs, sol.resid) < 1e-6
     end
 end
 
 @testitem "FastLevenbergMarquardt.jl + StaticArrays" setup=[WrapperNLLSSetup] tags=[:wrappers] begin
+    using StaticArrays, FastLevenbergMarquardt
+
     x_sa = SA[-1.0, -0.5, 0.0, 0.5, 1.0]
 
     const y_target_sa = true_function(x_sa, θ_true)
@@ -113,5 +111,5 @@ end
     prob_sa = NonlinearLeastSquaresProblem{false}(loss_function_sa, θ_init_sa, x)
 
     sol = solve(prob_sa, FastLevenbergMarquardtJL())
-    @test norm(sol.resid, Inf) < 1e-6
+    @test maximum(abs, sol.resid) < 1e-6
 end
diff --git a/test/wrappers/rootfind_tests.jl b/test/wrappers/rootfind_tests.jl
index 852368ae3..4f317d76d 100644
--- a/test/wrappers/rootfind_tests.jl
+++ b/test/wrappers/rootfind_tests.jl
@@ -1,13 +1,6 @@
-@testsetup module WrapperRootfindImports
-using Reexport
-@reexport using LinearAlgebra
-import NLSolvers, NLsolve, SIAMFANLEquations, MINPACK, PETSc
+@testitem "Steady State Problems" tags=[:wrappers] begin
+    import NLSolvers, NLsolve, SIAMFANLEquations, MINPACK, PETSc
 
-export NLSolvers
-end
-
-@testitem "Steady State Problems" setup=[WrapperRootfindImports] tags=[:wrappers] begin
-    # IIP Tests
     function f_iip(du, u, p, t)
         du[1] = 2 - 2u[1]
         du[2] = u[1] - 4u[2]
@@ -30,7 +23,6 @@ end
         @test maximum(abs, sol.resid) < 1e-6
     end
 
-    # OOP Tests
     f_oop(u, p, t) = [2 - 2u[1], u[1] - 4u[2]]
     u0 = zeros(2)
     prob_oop = SteadyStateProblem(f_oop, u0)
@@ -52,8 +44,10 @@ end
 end
 
 # Can lead to segfaults
-@testitem "Nonlinear Root Finding Problems" setup=[WrapperRootfindImports] tags=[:wrappers] retries=3 begin
-    # IIP Tests
+@testitem "Nonlinear Root Finding Problems" tags=[:wrappers] begin
+    using LinearAlgebra
+    import NLSolvers, NLsolve, SIAMFANLEquations, MINPACK, PETSc
+
     function f_iip(du, u, p)
         du[1] = 2 - 2u[1]
         du[2] = u[1] - 4u[2]
@@ -77,7 +71,6 @@ end
         @test maximum(abs, sol.resid) < 1e-6
     end
 
-    # OOP Tests
     f_oop(u, p) = [2 - 2u[1], u[1] - 4u[2]]
     u0 = zeros(2)
     prob_oop = NonlinearProblem{false}(f_oop, u0)
@@ -97,7 +90,6 @@ end
         @test maximum(abs, sol.resid) < 1e-6
     end
 
-    # Tolerance Tests
     f_tol(u, p) = u^2 - 2
     prob_tol = NonlinearProblem(f_tol, 1.0)
     for tol in [1e-1, 1e-3, 1e-6, 1e-10, 1e-15],
@@ -156,9 +148,11 @@ end
 
     sol = solve(ProbN, NLsolveJL(); abstol = 1e-8)
     @test maximum(abs, sol.resid) < 1e-6
-    sol = solve(ProbN,
+    sol = solve(
+        ProbN,
         NLSolversJL(NLSolvers.LineSearch(NLSolvers.Newton(), NLSolvers.Backtracking()));
-        abstol = 1e-8)
+        abstol = 1e-8
+    )
     @test maximum(abs, sol.resid) < 1e-6
     sol = solve(ProbN, SIAMFANLEquationsJL(; method = :newton); abstol = 1e-8)
     @test maximum(abs, sol.resid) < 1e-6
@@ -170,7 +164,9 @@ end
     end
 end
 
-@testitem "PETSc SNES Floating Points" setup=[WrapperRootfindImports] tags=[:wrappers] skip=:(Sys.iswindows()) begin
+@testitem "PETSc SNES Floating Points" tags=[:wrappers] skip=:(Sys.iswindows()) begin
+    import PETSc
+
     f(u, p) = u .* u .- 2
 
     u0 = [1.0, 1.0]

From f77775847654370e369750ddccf68a743d1040df Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 31 Oct 2024 00:13:19 -0400
Subject: [PATCH 660/700] fix: forwarddiff support

---
 ext/NonlinearSolveLeastSquaresOptimExt.jl     |   6 +-
 ext/NonlinearSolveSundialsExt.jl              |  18 +-
 lib/NonlinearSolveBase/src/linear_solve.jl    |   4 +-
 lib/NonlinearSolveBase/src/utils.jl           |   2 +-
 .../src/NonlinearSolveFirstOrder.jl           |   2 +-
 .../test/core_tests.jl                        |  12 +-
 src/NonlinearSolve.jl                         |  28 +--
 src/forward_diff.jl                           |  68 +++---
 test/23_test_problems_tests.jl                |   9 +-
 test/cuda_tests.jl                            |   3 +-
 test/forward_ad_tests.jl                      | 212 +++++++++---------
 11 files changed, 203 insertions(+), 161 deletions(-)

diff --git a/ext/NonlinearSolveLeastSquaresOptimExt.jl b/ext/NonlinearSolveLeastSquaresOptimExt.jl
index 0df265963..6e27f87a9 100644
--- a/ext/NonlinearSolveLeastSquaresOptimExt.jl
+++ b/ext/NonlinearSolveLeastSquaresOptimExt.jl
@@ -35,9 +35,9 @@ function SciMLBase.__solve(
         )
     end
 
-    linsolve = alg.ls === :qr ? LSO.QR() :
-               (alg.ls === :cholesky ? LSO.Cholesky() :
-                (alg.ls === :lsmr ? LSO.LSMR() : nothing))
+    linsolve = alg.linsolve === :qr ? LSO.QR() :
+               (alg.linsolve === :cholesky ? LSO.Cholesky() :
+                (alg.linsolve === :lsmr ? LSO.LSMR() : nothing))
 
     lso_solver = if alg.alg === :lm
         LSO.LevenbergMarquardt(linsolve)
diff --git a/ext/NonlinearSolveSundialsExt.jl b/ext/NonlinearSolveSundialsExt.jl
index edea3a49b..303da2167 100644
--- a/ext/NonlinearSolveSundialsExt.jl
+++ b/ext/NonlinearSolveSundialsExt.jl
@@ -1,16 +1,28 @@
 module NonlinearSolveSundialsExt
 
+using Sundials: KINSOL
+
+using CommonSolve: CommonSolve
 using NonlinearSolveBase: NonlinearSolveBase, nonlinearsolve_forwarddiff_solve,
                           nonlinearsolve_dual_solution
-using NonlinearSolve: DualNonlinearProblem
+using NonlinearSolve: NonlinearSolve, DualNonlinearProblem
 using SciMLBase: SciMLBase
-using Sundials: KINSOL
 
 function SciMLBase.__solve(prob::DualNonlinearProblem, alg::KINSOL, args...; kwargs...)
     sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
     dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
     return SciMLBase.build_solution(
-        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
+    )
+end
+
+function SciMLBase.__init(prob::DualNonlinearProblem, alg::KINSOL, args...; kwargs...)
+    p = NonlinearSolveBase.nodual_value(prob.p)
+    newprob = SciMLBase.remake(prob; u0 = NonlinearSolveBase.nodual_value(prob.u0), p)
+    cache = CommonSolve.init(newprob, alg, args...; kwargs...)
+    return NonlinearSolveForwardDiffCache(
+        cache, newprob, alg, prob.p, p, ForwardDiff.partials(prob.p)
+    )
 end
 
 end
diff --git a/lib/NonlinearSolveBase/src/linear_solve.jl b/lib/NonlinearSolveBase/src/linear_solve.jl
index ab70e2d6c..f3a2338c9 100644
--- a/lib/NonlinearSolveBase/src/linear_solve.jl
+++ b/lib/NonlinearSolveBase/src/linear_solve.jl
@@ -69,9 +69,7 @@ function construct_linear_solver(alg, linsolve, A, b, u; stats, kwargs...)
             error("Default Julia Backsolve Operator `\\` doesn't support Preconditioners")
         return NativeJLLinearSolveCache(A, b, stats)
     elseif no_preconditioner && linsolve === nothing
-        # Non-allocating linear solve exists in StaticArrays.jl
-        if (A isa SMatrix || A isa WrappedArray{<:Any, <:SMatrix}) &&
-           Core.Compiler.return_type(\, Tuple{typeof(A), typeof(b)}) <: SArray
+        if (A isa SMatrix || A isa WrappedArray{<:Any, <:SMatrix})
             return NativeJLLinearSolveCache(A, b, stats)
         end
     end
diff --git a/lib/NonlinearSolveBase/src/utils.jl b/lib/NonlinearSolveBase/src/utils.jl
index 44c7e957a..99e8e50c5 100644
--- a/lib/NonlinearSolveBase/src/utils.jl
+++ b/lib/NonlinearSolveBase/src/utils.jl
@@ -222,7 +222,7 @@ function maybe_pinv!!(workspace, A::StridedMatrix)
         !issingular && return LinearAlgebra.tril!(parent(inv(A_)))
     else
         F = LinearAlgebra.lu(A; check = false)
-        if issuccess(F)
+        if LinearAlgebra.issuccess(F)
             Ai = LinearAlgebra.inv!(F)
             return convert(typeof(parent(Ai)), Ai)
         end
diff --git a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
index 789c13ab7..b611b9051 100644
--- a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
+++ b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
@@ -7,7 +7,7 @@ using Setfield: @set!
 
 using ADTypes: ADTypes
 using ArrayInterface: ArrayInterface
-using LinearAlgebra: LinearAlgebra, Diagonal, dot
+using LinearAlgebra: LinearAlgebra, Diagonal, dot, diagind
 using StaticArraysCore: SArray
 
 using CommonSolve: CommonSolve
diff --git a/lib/NonlinearSolveQuasiNewton/test/core_tests.jl b/lib/NonlinearSolveQuasiNewton/test/core_tests.jl
index 6225a07d1..5e70661d8 100644
--- a/lib/NonlinearSolveQuasiNewton/test/core_tests.jl
+++ b/lib/NonlinearSolveQuasiNewton/test/core_tests.jl
@@ -170,11 +170,14 @@ end
             LiFukushimaLineSearch()
         )
             @testset "[OOP] u0: $(typeof(u0))" for u0 in (ones(32), @SVector(ones(2)), 1.0)
+                broken = Sys.iswindows() && u0 isa Vector{Float64} &&
+                         linesearch isa BackTracking && ad isa AutoFiniteDiff
+
                 solver = LimitedMemoryBroyden(; linesearch)
                 sol = solve_oop(quadratic_f, u0; solver)
-                @test SciMLBase.successful_retcode(sol)
+                @test SciMLBase.successful_retcode(sol) broken=broken
                 err = maximum(abs, quadratic_f(sol.u, 2.0))
-                @test err < 1e-9
+                @test err<1e-9 broken=broken
 
                 cache = init(
                     NonlinearProblem{false}(quadratic_f, u0, 2.0), solver, abstol = 1e-9
@@ -185,11 +188,14 @@ end
             @testset "[IIP] u0: $(typeof(u0))" for u0 in (ones(32),)
                 ad isa AutoZygote && continue
 
+                broken = Sys.iswindows() && u0 isa Vector{Float64} &&
+                         linesearch isa BackTracking && ad isa AutoFiniteDiff
+
                 solver = LimitedMemoryBroyden(; linesearch)
                 sol = solve_iip(quadratic_f!, u0; solver)
                 @test SciMLBase.successful_retcode(sol)
                 err = maximum(abs, quadratic_f(sol.u, 2.0))
-                @test err < 1e-9
+                @test err<1e-9 broken=broken
 
                 cache = init(
                     NonlinearProblem{true}(quadratic_f!, u0, 2.0), solver, abstol = 1e-9
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index cc71ef03d..2ee0ac575 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -28,8 +28,8 @@ using NonlinearSolveQuasiNewton: Broyden, Klement
 using SimpleNonlinearSolve: SimpleBroyden, SimpleKlement
 
 # Default AD Support
-using FiniteDiff: FiniteDiff    # Default Finite Difference Method
-using ForwardDiff: ForwardDiff  # Default Forward Mode AD
+using FiniteDiff: FiniteDiff          # Default Finite Difference Method
+using ForwardDiff: ForwardDiff, Dual  # Default Forward Mode AD
 
 # Sparse AD Support: Implemented via extensions
 using SparseArrays: SparseArrays
@@ -39,9 +39,9 @@ using SparseMatrixColorings: SparseMatrixColorings
 using BracketingNonlinearSolve: BracketingNonlinearSolve
 using LineSearch: LineSearch
 using LinearSolve: LinearSolve
-using NonlinearSolveFirstOrder: NonlinearSolveFirstOrder
-using NonlinearSolveQuasiNewton: NonlinearSolveQuasiNewton
-using NonlinearSolveSpectralMethods: NonlinearSolveSpectralMethods
+using NonlinearSolveFirstOrder: NonlinearSolveFirstOrder, GeneralizedFirstOrderAlgorithm
+using NonlinearSolveQuasiNewton: NonlinearSolveQuasiNewton, QuasiNewtonAlgorithm
+using NonlinearSolveSpectralMethods: NonlinearSolveSpectralMethods, GeneralizedDFSane
 using SimpleNonlinearSolve: SimpleNonlinearSolve
 
 const SII = SymbolicIndexingInterface
@@ -53,16 +53,16 @@ include("extension_algs.jl")
 
 include("default.jl")
 
-# const ALL_SOLVER_TYPES = [
-#     Nothing, AbstractNonlinearSolveAlgorithm, GeneralizedDFSane,
-#     GeneralizedFirstOrderAlgorithm, ApproximateJacobianSolveAlgorithm,
-#     LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
-#     SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL,
-#     CMINPACK, PETScSNES,
-#     NonlinearSolvePolyAlgorithm{:NLLS, <:Any}, NonlinearSolvePolyAlgorithm{:NLS, <:Any}
-# ]
+const ALL_SOLVER_TYPES = [
+    Nothing, AbstractNonlinearSolveAlgorithm,
+    GeneralizedDFSane, GeneralizedFirstOrderAlgorithm, QuasiNewtonAlgorithm,
+    LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
+    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL,
+    CMINPACK, PETScSNES,
+    NonlinearSolvePolyAlgorithm
+]
 
-# include("internal/forward_diff.jl") # we need to define after the algorithms
+include("forward_diff.jl")
 
 @setup_workload begin
     include("../common/nonlinear_problem_workloads.jl")
diff --git a/src/forward_diff.jl b/src/forward_diff.jl
index 269ebc99a..28534c59e 100644
--- a/src/forward_diff.jl
+++ b/src/forward_diff.jl
@@ -1,22 +1,30 @@
-const DualNonlinearProblem = NonlinearProblem{<:Union{Number, <:AbstractArray}, iip,
-    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}} where {iip, T, V, P}
+const DualNonlinearProblem = NonlinearProblem{
+    <:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {iip, T, V, P}
 const DualNonlinearLeastSquaresProblem = NonlinearLeastSquaresProblem{
     <:Union{Number, <:AbstractArray}, iip,
-    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}} where {iip, T, V, P}
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {iip, T, V, P}
 const DualAbstractNonlinearProblem = Union{
-    DualNonlinearProblem, DualNonlinearLeastSquaresProblem}
+    DualNonlinearProblem, DualNonlinearLeastSquaresProblem
+}
 
 for algType in ALL_SOLVER_TYPES
     @eval function SciMLBase.__solve(
-            prob::DualNonlinearProblem, alg::$(algType), args...; kwargs...)
-        sol, partials = nonlinearsolve_forwarddiff_solve(prob, alg, args...; kwargs...)
-        dual_soln = nonlinearsolve_dual_solution(sol.u, partials, prob.p)
+            prob::DualAbstractNonlinearProblem, alg::$(algType), args...; kwargs...
+    )
+        sol, partials = NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
+            prob, alg, args...; kwargs...
+        )
+        dual_soln = NonlinearSolveBase.nonlinearsolve_dual_solution(sol.u, partials, prob.p)
         return SciMLBase.build_solution(
-            prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+            prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
+        )
     end
 end
 
-@concrete mutable struct NonlinearSolveForwardDiffCache
+@concrete mutable struct NonlinearSolveForwardDiffCache <: AbstractNonlinearSolveCache
     cache
     prob
     alg
@@ -25,36 +33,41 @@ end
     partials_p
 end
 
-@internal_caches NonlinearSolveForwardDiffCache :cache
-
-function reinit_cache!(cache::NonlinearSolveForwardDiffCache;
-        p = cache.p, u0 = get_u(cache.cache), kwargs...)
-    inner_cache = reinit_cache!(cache.cache; p = __value(p), u0 = __value(u0), kwargs...)
+function InternalAPI.reinit!(
+        cache::NonlinearSolveForwardDiffCache, args...;
+        p = cache.p, u0 = NonlinearSolveBase.get_u(cache.cache), kwargs...
+)
+    inner_cache = InternalAPI.reinit!(
+        cache.cache; p = nodual_value(p), u0 = nodual_value(u0), kwargs...
+    )
     cache.cache = inner_cache
     cache.p = p
-    cache.values_p = __value(p)
+    cache.values_p = nodual_value(p)
     cache.partials_p = ForwardDiff.partials(p)
     return cache
 end
 
 for algType in ALL_SOLVER_TYPES
+    # XXX: Extend to DualNonlinearLeastSquaresProblem
     @eval function SciMLBase.__init(
-            prob::DualNonlinearProblem, alg::$(algType), args...; kwargs...)
-        p = __value(prob.p)
-        newprob = NonlinearProblem(prob.f, __value(prob.u0), p; prob.kwargs...)
+            prob::DualNonlinearProblem, alg::$(algType), args...; kwargs...
+    )
+        p = nodual_value(prob.p)
+        newprob = SciMLBase.remake(prob; u0 = nodual_value(prob.u0), p)
         cache = init(newprob, alg, args...; kwargs...)
         return NonlinearSolveForwardDiffCache(
-            cache, newprob, alg, prob.p, p, ForwardDiff.partials(prob.p))
+            cache, newprob, alg, prob.p, p, ForwardDiff.partials(prob.p)
+        )
     end
 end
 
-function SciMLBase.solve!(cache::NonlinearSolveForwardDiffCache)
+function CommonSolve.solve!(cache::NonlinearSolveForwardDiffCache)
     sol = solve!(cache.cache)
     prob = cache.prob
 
     uu = sol.u
-    Jₚ = nonlinearsolve_∂f_∂p(prob, prob.f, uu, cache.values_p)
-    Jᵤ = nonlinearsolve_∂f_∂u(prob, prob.f, uu, cache.values_p)
+    Jₚ = NonlinearSolveBase.nonlinearsolve_∂f_∂p(prob, prob.f, uu, cache.values_p)
+    Jᵤ = NonlinearSolveBase.nonlinearsolve_∂f_∂u(prob, prob.f, uu, cache.values_p)
 
     z_arr = -Jᵤ \ Jₚ
 
@@ -65,11 +78,12 @@ function SciMLBase.solve!(cache::NonlinearSolveForwardDiffCache)
         partials = sum(sumfun, zip(eachcol(z_arr), cache.p))
     end
 
-    dual_soln = nonlinearsolve_dual_solution(sol.u, partials, cache.p)
+    dual_soln = NonlinearSolveBase.nonlinearsolve_dual_solution(sol.u, partials, cache.p)
     return SciMLBase.build_solution(
-        prob, cache.alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original)
+        prob, cache.alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
+    )
 end
 
-@inline __value(x) = x
-@inline __value(x::Dual) = ForwardDiff.value(x)
-@inline __value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
+nodual_value(x) = x
+nodual_value(x::Dual) = ForwardDiff.value(x)
+nodual_value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
diff --git a/test/23_test_problems_tests.jl b/test/23_test_problems_tests.jl
index 23b9a3e2a..20c2c3b5c 100644
--- a/test/23_test_problems_tests.jl
+++ b/test/23_test_problems_tests.jl
@@ -106,10 +106,13 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "Broyden" setup=[RobustnessTesting] tags=[:core] begin
-    alg_ops = (Broyden(), Broyden(; init_jacobian = Val(:true_jacobian)),
+@testitem "Broyden" setup=[RobustnessTesting] tags=[:core] retries=3 begin
+    alg_ops = (
+        Broyden(),
+        Broyden(; init_jacobian = Val(:true_jacobian)),
         Broyden(; update_rule = Val(:bad_broyden)),
-        Broyden(; init_jacobian = Val(:true_jacobian), update_rule = Val(:bad_broyden)))
+        Broyden(; init_jacobian = Val(:true_jacobian), update_rule = Val(:bad_broyden))
+    )
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
     if Sys.isapple()
diff --git a/test/cuda_tests.jl b/test/cuda_tests.jl
index 91d6178a4..bd992e3fc 100644
--- a/test/cuda_tests.jl
+++ b/test/cuda_tests.jl
@@ -15,8 +15,7 @@
         SOLVERS = (
             NewtonRaphson(),
             LevenbergMarquardt(; linsolve = QRFactorization()),
-            # XXX: Fails currently
-            # LevenbergMarquardt(; linsolve = KrylovJL_GMRES()),
+            LevenbergMarquardt(; linsolve = KrylovJL_GMRES()),
             PseudoTransient(),
             Klement(),
             Broyden(; linesearch = LiFukushimaLineSearch()),
diff --git a/test/forward_ad_tests.jl b/test/forward_ad_tests.jl
index e40b0a91d..dcd1c2e3a 100644
--- a/test/forward_ad_tests.jl
+++ b/test/forward_ad_tests.jl
@@ -1,116 +1,126 @@
-# @testsetup module ForwardADTesting
-# using Reexport, NonlinearSolve
-# @reexport using ForwardDiff, MINPACK, NLsolve, StaticArrays, Sundials, LinearAlgebra
+@testsetup module ForwardADTesting
+using Reexport, NonlinearSolve
+@reexport using ForwardDiff, MINPACK, NLsolve, StaticArrays, Sundials, LinearAlgebra
 
-# test_f!(du, u, p) = (@. du = u^2 - p)
-# test_f(u, p) = (@. u^2 - p)
+test_f!(du, u, p) = (@. du = u^2 - p)
+test_f(u, p) = (@. u^2 - p)
 
-# jacobian_f(::Number, p) = 1 / (2 * √p)
-# jacobian_f(::Number, p::Number) = 1 / (2 * √p)
-# jacobian_f(u, p::Number) = one.(u) .* (1 / (2 * √p))
-# jacobian_f(u, p::AbstractArray) = diagm(vec(@. 1 / (2 * √p)))
+jacobian_f(::Number, p) = 1 / (2 * √p)
+jacobian_f(::Number, p::Number) = 1 / (2 * √p)
+jacobian_f(u, p::Number) = one.(u) .* (1 / (2 * √p))
+jacobian_f(u, p::AbstractArray) = diagm(vec(@. 1 / (2 * √p)))
 
-# function solve_with(::Val{mode}, u, alg) where {mode}
-#     f = if mode === :iip
-#         solve_iip(p) = solve(NonlinearProblem(test_f!, u, p), alg).u
-#     elseif mode === :iip_cache
-#         function solve_iip_init(p)
-#             cache = SciMLBase.init(NonlinearProblem(test_f!, u, p), alg)
-#             return SciMLBase.solve!(cache).u
-#         end
-#     elseif mode === :oop
-#         solve_oop(p) = solve(NonlinearProblem(test_f, u, p), alg).u
-#     elseif mode === :oop_cache
-#         function solve_oop_init(p)
-#             cache = SciMLBase.init(NonlinearProblem(test_f, u, p), alg)
-#             return SciMLBase.solve!(cache).u
-#         end
-#     end
-#     return f
-# end
+function solve_with(::Val{mode}, u, alg) where {mode}
+    f = if mode === :iip
+        solve_iip(p) = solve(NonlinearProblem(test_f!, u, p), alg).u
+    elseif mode === :iip_cache
+        function solve_iip_init(p)
+            cache = SciMLBase.init(NonlinearProblem(test_f!, u, p), alg)
+            return SciMLBase.solve!(cache).u
+        end
+    elseif mode === :oop
+        solve_oop(p) = solve(NonlinearProblem(test_f, u, p), alg).u
+    elseif mode === :oop_cache
+        function solve_oop_init(p)
+            cache = SciMLBase.init(NonlinearProblem(test_f, u, p), alg)
+            return SciMLBase.solve!(cache).u
+        end
+    end
+    return f
+end
 
-# __compatible(::Any, ::Val{:oop}) = true
-# __compatible(::Any, ::Val{:oop_cache}) = true
-# __compatible(::Number, ::Val{:iip}) = false
-# __compatible(::AbstractArray, ::Val{:iip}) = true
-# __compatible(::StaticArray, ::Val{:iip}) = false
-# __compatible(::Number, ::Val{:iip_cache}) = false
-# __compatible(::AbstractArray, ::Val{:iip_cache}) = true
-# __compatible(::StaticArray, ::Val{:iip_cache}) = false
+compatible(::Any, ::Val{:oop}) = true
+compatible(::Any, ::Val{:oop_cache}) = true
+compatible(::Number, ::Val{:iip}) = false
+compatible(::AbstractArray, ::Val{:iip}) = true
+compatible(::StaticArray, ::Val{:iip}) = false
+compatible(::Number, ::Val{:iip_cache}) = false
+compatible(::AbstractArray, ::Val{:iip_cache}) = true
+compatible(::StaticArray, ::Val{:iip_cache}) = false
 
-# __compatible(::Any, ::Number) = true
-# __compatible(::Number, ::AbstractArray) = false
-# __compatible(u::AbstractArray, p::AbstractArray) = size(u) == size(p)
+compatible(::Any, ::Number) = true
+compatible(::Number, ::AbstractArray) = false
+compatible(u::AbstractArray, p::AbstractArray) = size(u) == size(p)
 
-# __compatible(u::Number, ::SciMLBase.AbstractNonlinearAlgorithm) = true
-# __compatible(u::Number, ::Union{CMINPACK, NLsolveJL, KINSOL}) = true
-# __compatible(u::AbstractArray, ::SciMLBase.AbstractNonlinearAlgorithm) = true
-# __compatible(u::AbstractArray{T, N}, ::KINSOL) where {T, N} = N == 1  # Need to be fixed upstream
-# __compatible(u::StaticArray{S, T, N}, ::KINSOL) where {S <: Tuple, T, N} = false
-# __compatible(u::StaticArray, ::SciMLBase.AbstractNonlinearAlgorithm) = true
-# __compatible(u::StaticArray, ::Union{CMINPACK, NLsolveJL, KINSOL}) = false
-# __compatible(u, ::Nothing) = true
+compatible(u::Number, ::SciMLBase.AbstractNonlinearAlgorithm) = true
+compatible(u::Number, ::Union{CMINPACK, NLsolveJL, KINSOL}) = true
+compatible(u::AbstractArray, ::SciMLBase.AbstractNonlinearAlgorithm) = true
+compatible(u::AbstractArray{T, N}, ::KINSOL) where {T, N} = N == 1  # Need to be fixed upstream
+compatible(u::StaticArray{S, T, N}, ::KINSOL) where {S <: Tuple, T, N} = false
+compatible(u::StaticArray, ::SciMLBase.AbstractNonlinearAlgorithm) = true
+compatible(u::StaticArray, ::Union{CMINPACK, NLsolveJL, KINSOL}) = false
+compatible(u, ::Nothing) = true
 
-# __compatible(::Any, ::Any) = true
-# __compatible(::CMINPACK, ::Val{:iip_cache}) = false
-# __compatible(::CMINPACK, ::Val{:oop_cache}) = false
-# __compatible(::NLsolveJL, ::Val{:iip_cache}) = false
-# __compatible(::NLsolveJL, ::Val{:oop_cache}) = false
-# __compatible(::KINSOL, ::Val{:iip_cache}) = false
-# __compatible(::KINSOL, ::Val{:oop_cache}) = false
+compatible(::Any, ::Any) = true
+compatible(::CMINPACK, ::Val{:iip_cache}) = false
+compatible(::CMINPACK, ::Val{:oop_cache}) = false
+compatible(::NLsolveJL, ::Val{:iip_cache}) = false
+compatible(::NLsolveJL, ::Val{:oop_cache}) = false
+compatible(::KINSOL, ::Val{:iip_cache}) = false
+compatible(::KINSOL, ::Val{:oop_cache}) = false
 
-# export test_f!, test_f, jacobian_f, solve_with, __compatible
-# end
+export test_f!, test_f, jacobian_f, solve_with, compatible
+end
 
-# @testitem "ForwardDiff.jl Integration" setup=[ForwardADTesting] tags=[:core] begin
-#     for alg in (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
-#         PseudoTransient(; alpha_initial = 10.0), Broyden(), Klement(), DFSane(),
-#         nothing, NLsolveJL(), CMINPACK(), KINSOL(; globalization_strategy = :LineSearch))
-#         us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
+@testitem "ForwardDiff.jl Integration" setup=[ForwardADTesting] tags=[:core] begin
+    @testset for alg in (
+        NewtonRaphson(),
+        TrustRegion(),
+        LevenbergMarquardt(),
+        PseudoTransient(; alpha_initial = 10.0),
+        Broyden(),
+        Klement(),
+        DFSane(),
+        nothing,
+        NLsolveJL(),
+        CMINPACK(),
+        KINSOL(; globalization_strategy = :LineSearch)
+    )
+        us = (2.0, @SVector[1.0, 1.0], [1.0, 1.0], ones(2, 2), @SArray ones(2, 2))
 
-#         alg isa CMINPACK && Sys.isapple() && continue
+        alg isa CMINPACK && Sys.isapple() && continue
 
-#         @testset "Scalar AD" begin
-#             for p in 1.0:0.1:100.0, u0 in us, mode in (:iip, :oop, :iip_cache, :oop_cache)
-#                 __compatible(u0, alg) || continue
-#                 __compatible(u0, Val(mode)) || continue
-#                 __compatible(alg, Val(mode)) || continue
+        @testset "Scalar AD" begin
+            for p in 1.0:0.1:100.0, u0 in us, mode in (:iip, :oop, :iip_cache, :oop_cache)
+                compatible(u0, alg) || continue
+                compatible(u0, Val(mode)) || continue
+                compatible(alg, Val(mode)) || continue
 
-#                 sol = solve(NonlinearProblem(test_f, u0, p), alg)
-#                 if SciMLBase.successful_retcode(sol)
-#                     gs = abs.(ForwardDiff.derivative(solve_with(Val{mode}(), u0, alg), p))
-#                     gs_true = abs.(jacobian_f(u0, p))
-#                     if !(isapprox(gs, gs_true, atol = 1e-5))
-#                         @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_gradient=gs true_gradient=gs_true
-#                     else
-#                         @test abs.(gs)≈abs.(gs_true) atol=1e-5
-#                     end
-#                 end
-#             end
-#         end
+                sol = solve(NonlinearProblem(test_f, u0, p), alg)
+                if SciMLBase.successful_retcode(sol)
+                    gs = abs.(ForwardDiff.derivative(solve_with(Val{mode}(), u0, alg), p))
+                    gs_true = abs.(jacobian_f(u0, p))
+                    if !(isapprox(gs, gs_true, atol = 1e-5))
+                        @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_gradient=gs true_gradient=gs_true
+                    else
+                        @test abs.(gs)≈abs.(gs_true) atol=1e-5
+                    end
+                end
+            end
+        end
 
-#         @testset "Jacobian" begin
-#             for u0 in us,
-#                 p in ([2.0, 1.0], [2.0 1.0; 3.0 4.0]),
-#                 mode in (:iip, :oop, :iip_cache, :oop_cache)
+        @testset "Jacobian" begin
+            for u0 in us,
+                p in ([2.0, 1.0], [2.0 1.0; 3.0 4.0]),
+                mode in (:iip, :oop, :iip_cache, :oop_cache)
 
-#                 __compatible(u0, p) || continue
-#                 __compatible(u0, alg) || continue
-#                 __compatible(u0, Val(mode)) || continue
-#                 __compatible(alg, Val(mode)) || continue
+                compatible(u0, p) || continue
+                compatible(u0, alg) || continue
+                compatible(u0, Val(mode)) || continue
+                compatible(alg, Val(mode)) || continue
 
-#                 sol = solve(NonlinearProblem(test_f, u0, p), alg)
-#                 if SciMLBase.successful_retcode(sol)
-#                     gs = abs.(ForwardDiff.jacobian(solve_with(Val{mode}(), u0, alg), p))
-#                     gs_true = abs.(jacobian_f(u0, p))
-#                     if !(isapprox(gs, gs_true, atol = 1e-5))
-#                         @show sol.retcode, sol.u
-#                         @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_jacobian=gs true_jacobian=gs_true
-#                     else
-#                         @test abs.(gs)≈abs.(gs_true) atol=1e-5
-#                     end
-#                 end
-#             end
-#         end
-#     end
-# end
+                sol = solve(NonlinearProblem(test_f, u0, p), alg)
+                if SciMLBase.successful_retcode(sol)
+                    gs = abs.(ForwardDiff.jacobian(solve_with(Val{mode}(), u0, alg), p))
+                    gs_true = abs.(jacobian_f(u0, p))
+                    if !(isapprox(gs, gs_true, atol = 1e-5))
+                        @show sol.retcode, sol.u
+                        @error "ForwardDiff Failed for u0=$(u0) and p=$(p) with $(alg)" forwardiff_jacobian=gs true_jacobian=gs_true
+                    else
+                        @test abs.(gs)≈abs.(gs_true) atol=1e-5
+                    end
+                end
+            end
+        end
+    end
+end

From 13b0c1d099d948338dd738d0ad9a1da49a483064 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 31 Oct 2024 00:25:53 -0400
Subject: [PATCH 661/700] fix: alg call for LSO

---
 ext/NonlinearSolveLeastSquaresOptimExt.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ext/NonlinearSolveLeastSquaresOptimExt.jl b/ext/NonlinearSolveLeastSquaresOptimExt.jl
index 6e27f87a9..834627606 100644
--- a/ext/NonlinearSolveLeastSquaresOptimExt.jl
+++ b/ext/NonlinearSolveLeastSquaresOptimExt.jl
@@ -47,7 +47,7 @@ function SciMLBase.__solve(
         throw(ArgumentError("Unknown LeastSquaresOptim Algorithm: $(Meta.quot(alg.alg))"))
     end
 
-    allocated_prob = LSO.LeastSquaresProblemAllocated(lsoprob, lso_solver(alg))
+    allocated_prob = LSO.LeastSquaresProblemAllocated(lsoprob, lso_solver)
     res = LSO.optimize!(
         allocated_prob;
         x_tol = reltol, f_tol = abstol, g_tol = abstol, iterations = maxiters,

From 9bbb994edafdc7a3ed0fc6c9753c535d98dd38a1 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 31 Oct 2024 00:45:31 -0400
Subject: [PATCH 662/700] ci: add downgrade testing to all the packages

---
 .../workflows/CI_BracketingNonlinearSolve.yml | 38 +++++++++++++
 .github/workflows/CI_NonlinearSolve.yml       | 44 +++++++++++++++
 .github/workflows/CI_NonlinearSolveBase.yml   | 38 +++++++++++++
 .../workflows/CI_NonlinearSolveFirstOrder.yml | 38 +++++++++++++
 .../CI_NonlinearSolveQuasiNewton.yml          | 38 +++++++++++++
 .../CI_NonlinearSolveSpectralMethods.yml      | 38 +++++++++++++
 .../workflows/CI_SciMLJacobianOperators.yml   | 30 +++++++++++
 .github/workflows/CI_SimpleNonlinearSolve.yml | 44 +++++++++++++++
 .github/workflows/Downgrade.yml               | 54 -------------------
 .github/workflows/Downstream.yml              | 13 ++++-
 test/23_test_problems_tests.jl                |  2 +-
 11 files changed, 321 insertions(+), 56 deletions(-)
 delete mode 100644 .github/workflows/Downgrade.yml

diff --git a/.github/workflows/CI_BracketingNonlinearSolve.yml b/.github/workflows/CI_BracketingNonlinearSolve.yml
index e83060bdb..956fa33a2 100644
--- a/.github/workflows/CI_BracketingNonlinearSolve.yml
+++ b/.github/workflows/CI_BracketingNonlinearSolve.yml
@@ -69,3 +69,41 @@ jobs:
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
           fail_ci_if_error: true
+
+  downgrade:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "1.10"
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: julia-actions/julia-downgrade-compat@v1
+        with:
+          skip: NonlinearSolveBase, SciMLJacobianOperators
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/NonlinearSolveBase", "lib/SciMLJacobianOperators")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/BracketingNonlinearSolve {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/BracketingNonlinearSolve/src,lib/BracketingNonlinearSolve/ext,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/.github/workflows/CI_NonlinearSolve.yml b/.github/workflows/CI_NonlinearSolve.yml
index 24be53295..7c1b55567 100644
--- a/.github/workflows/CI_NonlinearSolve.yml
+++ b/.github/workflows/CI_NonlinearSolve.yml
@@ -83,3 +83,47 @@ jobs:
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
           fail_ci_if_error: true
+
+  downgrade:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "1.10"
+        group:
+          - Core
+          - Downstream
+          - Wrappers
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: julia-actions/julia-downgrade-compat@v1
+        with:
+          skip: SciMLJacobianOperators, BracketingNonlinearSolve, NonlinearSolveBase, SimpleNonlinearSolve, NonlinearSolveFirstOrder, NonlinearSolveSpectralMethods, NonlinearSolveQuasiNewton
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveBase", "lib/SimpleNonlinearSolve", "lib/NonlinearSolveFirstOrder", "lib/NonlinearSolveSpectralMethods", "lib/NonlinearSolveQuasiNewton")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=. {0}
+        env:
+          GROUP: ${{ matrix.group }}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: src,ext,lib/SciMLJacobianOperators/src,lib/BracketingNonlinearSolve/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SimpleNonlinearSolve/src,lib/NonlinearSolveFirstOrder/src,lib/NonlinearSolveSpectralMethods/src,lib/NonlinearSolveQuasiNewton/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/.github/workflows/CI_NonlinearSolveBase.yml b/.github/workflows/CI_NonlinearSolveBase.yml
index 0ba7c11d2..8b303ae2e 100644
--- a/.github/workflows/CI_NonlinearSolveBase.yml
+++ b/.github/workflows/CI_NonlinearSolveBase.yml
@@ -68,3 +68,41 @@ jobs:
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
           fail_ci_if_error: true
+
+  downgrade:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "1.10"
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: julia-actions/julia-downgrade-compat@v1
+        with:
+          skip: SciMLJacobianOperators
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators",)
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/NonlinearSolveBase {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/.github/workflows/CI_NonlinearSolveFirstOrder.yml b/.github/workflows/CI_NonlinearSolveFirstOrder.yml
index 8b93788b1..8f68f398b 100644
--- a/.github/workflows/CI_NonlinearSolveFirstOrder.yml
+++ b/.github/workflows/CI_NonlinearSolveFirstOrder.yml
@@ -69,3 +69,41 @@ jobs:
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
           fail_ci_if_error: true
+
+  downgrade:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "1.10"
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: julia-actions/julia-downgrade-compat@v1
+        with:
+          skip: NonlinearSolveBase, SciMLJacobianOperators
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators", "lib/NonlinearSolveBase")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/NonlinearSolveFirstOrder {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/NonlinearSolveFirstOrder/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/.github/workflows/CI_NonlinearSolveQuasiNewton.yml b/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
index 1e3815ea9..3c0904739 100644
--- a/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
+++ b/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
@@ -69,3 +69,41 @@ jobs:
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
           fail_ci_if_error: true
+
+  downgrade:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "1.10"
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: julia-actions/julia-downgrade-compat@v1
+        with:
+          skip: NonlinearSolveBase, SciMLJacobianOperators
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators", "lib/NonlinearSolveBase")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/NonlinearSolveQuasiNewton {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/NonlinearSolveQuasiNewton/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/.github/workflows/CI_NonlinearSolveSpectralMethods.yml b/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
index 7999ee906..f39420efa 100644
--- a/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
+++ b/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
@@ -69,3 +69,41 @@ jobs:
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
           fail_ci_if_error: true
+
+  downgrade:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "1.10"
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: julia-actions/julia-downgrade-compat@v1
+        with:
+          skip: NonlinearSolveBase, SciMLJacobianOperators
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators", "lib/NonlinearSolveBase")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/NonlinearSolveSpectralMethods {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/NonlinearSolveSpectralMethods/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/.github/workflows/CI_SciMLJacobianOperators.yml b/.github/workflows/CI_SciMLJacobianOperators.yml
index 3f243a8b3..4d1f6780d 100644
--- a/.github/workflows/CI_SciMLJacobianOperators.yml
+++ b/.github/workflows/CI_SciMLJacobianOperators.yml
@@ -61,3 +61,33 @@ jobs:
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
           fail_ci_if_error: true
+
+  downgrade:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "1.10"
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: julia-actions/julia-downgrade-compat@v1
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SciMLJacobianOperators {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/SciMLJacobianOperators/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/.github/workflows/CI_SimpleNonlinearSolve.yml b/.github/workflows/CI_SimpleNonlinearSolve.yml
index a9d6d4e0e..0212232a8 100644
--- a/.github/workflows/CI_SimpleNonlinearSolve.yml
+++ b/.github/workflows/CI_SimpleNonlinearSolve.yml
@@ -76,3 +76,47 @@ jobs:
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
           fail_ci_if_error: true
+
+  downgrade:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "1.10"
+        group:
+          - core
+          - adjoint
+          - alloc_check
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: julia-actions/julia-downgrade-compat@v1
+        with:
+          skip: NonlinearSolveBase, BracketingNonlinearSolve, SciMLJacobianOperators
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve", "lib/SciMLJacobianOperators")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SimpleNonlinearSolve {0}
+        env:
+          GROUP: ${{ matrix.group }}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/SimpleNonlinearSolve/src,lib/SimpleNonlinearSolve/ext,lib/SciMLJacobianOperators/src,lib/BracketingNonlinearSolve/src,lib/BracketingNonlinearSolve/ext,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: true
diff --git a/.github/workflows/Downgrade.yml b/.github/workflows/Downgrade.yml
deleted file mode 100644
index 6d619f9ab..000000000
--- a/.github/workflows/Downgrade.yml
+++ /dev/null
@@ -1,54 +0,0 @@
-name: Downgrade
-on:
-  pull_request:
-    branches:
-      - master
-    paths-ignore:
-      - "docs/**"
-  push:
-    branches:
-      - master
-    paths-ignore:
-      - "docs/**"
-jobs:
-  test:
-    runs-on: ubuntu-latest
-    strategy:
-      fail-fast: false
-      matrix:
-        version:
-          - "1.10"
-        group:
-          - Core
-          - Downstream
-          - Wrappers
-    steps:
-      - uses: actions/checkout@v4
-      - uses: julia-actions/setup-julia@v2
-        with:
-          version: ${{ matrix.version }}
-      - uses: julia-actions/julia-downgrade-compat@v1
-      - name: "Install Dependencies and Run Tests"
-        run: |
-          import Pkg
-          Pkg.Registry.update()
-          # Install packages present in subdirectories
-          dev_pks = Pkg.PackageSpec[]
-          for path in ("lib/SciMLJacobianOperators", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveBase", "lib/SimpleNonlinearSolve")
-              push!(dev_pks, Pkg.PackageSpec(; path))
-          end
-          Pkg.develop(dev_pks)
-          Pkg.instantiate()
-          Pkg.test(; coverage="user")
-        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=. {0}
-        env:
-          GROUP: ${{ matrix.group }}
-      - uses: julia-actions/julia-processcoverage@v1
-        with:
-          directories: src,ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
-        with:
-          file: lcov.info
-          token: ${{ secrets.CODECOV_TOKEN }}
-          verbose: true
-          fail_ci_if_error: true
diff --git a/.github/workflows/Downstream.yml b/.github/workflows/Downstream.yml
index fffcb0a6c..dc40d46f2 100644
--- a/.github/workflows/Downstream.yml
+++ b/.github/workflows/Downstream.yml
@@ -32,7 +32,18 @@ jobs:
         with:
           version: ${{ matrix.julia-version }}
           arch: x64
-      - uses: julia-actions/julia-buildpkg@latest
+      - name: "Install Dependencies"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveBase", "lib/SimpleNonlinearSolve", "lib/NonlinearSolveFirstOrder", "lib/NonlinearSolveSpectralMethods", "lib/NonlinearSolveQuasiNewton")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=. {0}
       - name: Clone Downstream
         uses: actions/checkout@v4
         with:
diff --git a/test/23_test_problems_tests.jl b/test/23_test_problems_tests.jl
index 20c2c3b5c..d740a87c2 100644
--- a/test/23_test_problems_tests.jl
+++ b/test/23_test_problems_tests.jl
@@ -119,7 +119,7 @@ end
         broken_tests[alg_ops[1]] = [1, 5, 11]
         broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
         broken_tests[alg_ops[3]] = [1, 5, 6, 9, 11]
-        broken_tests[alg_ops[4]] = [5, 6, 8, 11]
+        broken_tests[alg_ops[4]] = [5, 6, 8, 11, 16]
     else
         broken_tests[alg_ops[1]] = [1, 5, 11, 15]
         broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]

From ddb2295a5f9e3ab8af5e81ab645704ed356fb84f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 31 Oct 2024 00:54:13 -0400
Subject: [PATCH 663/700] chore: fix compat entries

---
 lib/NonlinearSolveBase/Project.toml        | 2 +-
 lib/NonlinearSolveFirstOrder/Project.toml  | 4 ++--
 lib/NonlinearSolveQuasiNewton/Project.toml | 2 +-
 lib/SciMLJacobianOperators/Project.toml    | 2 +-
 lib/SimpleNonlinearSolve/Project.toml      | 2 +-
 5 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index f6c92aeec..c601b144f 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -74,7 +74,7 @@ SciMLBase = "2.50"
 SciMLJacobianOperators = "0.1.1"
 SciMLOperators = "0.3.10"
 SparseArrays = "1.10"
-SparseMatrixColorings = "0.4.8"
+SparseMatrixColorings = "0.4.5"
 StaticArraysCore = "1.4"
 SymbolicIndexingInterface = "0.3.31"
 Test = "1.10"
diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
index b323a7f8e..b2468a092 100644
--- a/lib/NonlinearSolveFirstOrder/Project.toml
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -33,7 +33,7 @@ ConcreteStructs = "0.2.3"
 DiffEqBase = "6.155.3"
 Enzyme = "0.13.12"
 ExplicitImports = "1.5"
-FiniteDiff = "2.26.0"
+FiniteDiff = "2.24"
 ForwardDiff = "0.10.36"
 Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
@@ -54,7 +54,7 @@ SciMLJacobianOperators = "0.1.0"
 Setfield = "1.1.1"
 SparseArrays = "1.10"
 SparseConnectivityTracer = "0.6.8"
-SparseMatrixColorings = "0.4.8"
+SparseMatrixColorings = "0.4.5"
 StableRNGs = "1"
 StaticArrays = "1.9.8"
 StaticArraysCore = "1.4.3"
diff --git a/lib/NonlinearSolveQuasiNewton/Project.toml b/lib/NonlinearSolveQuasiNewton/Project.toml
index dee429de8..5162d4656 100644
--- a/lib/NonlinearSolveQuasiNewton/Project.toml
+++ b/lib/NonlinearSolveQuasiNewton/Project.toml
@@ -28,7 +28,7 @@ ConcreteStructs = "0.2.3"
 DiffEqBase = "6.155.3"
 Enzyme = "0.13.12"
 ExplicitImports = "1.5"
-FiniteDiff = "2.26.0"
+FiniteDiff = "2.24"
 ForwardDiff = "0.10.36"
 Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index 6cda16e66..7b9ac7cb1 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -24,7 +24,7 @@ DifferentiationInterface = "0.6.16"
 Enzyme = "0.13.11"
 ExplicitImports = "1.9.0"
 FastClosures = "0.3.2"
-FiniteDiff = "2.24.0"
+FiniteDiff = "2.24"
 ForwardDiff = "0.10.36"
 InteractiveUtils = "<0.0.1, 1"
 LinearAlgebra = "1.10"
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index c154a4b54..4ca3eaad1 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -48,7 +48,7 @@ DifferentiationInterface = "0.6.16"
 Enzyme = "0.13.11"
 ExplicitImports = "1.9"
 FastClosures = "0.3.2"
-FiniteDiff = "2.24.0"
+FiniteDiff = "2.24"
 ForwardDiff = "0.10.36"
 InteractiveUtils = "<0.0.1, 1"
 LineSearch = "0.1.3"

From 36aa57256b18e992d31c04acb84c6facf2164af3 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 31 Oct 2024 00:57:30 -0400
Subject: [PATCH 664/700] ci: fix invalidations CI

---
 .github/workflows/Invalidations.yml | 26 ++++++++++++++++++++++++--
 1 file changed, 24 insertions(+), 2 deletions(-)

diff --git a/.github/workflows/Invalidations.yml b/.github/workflows/Invalidations.yml
index 66c86a362..e221a7c75 100644
--- a/.github/workflows/Invalidations.yml
+++ b/.github/workflows/Invalidations.yml
@@ -20,14 +20,36 @@ jobs:
       with:
         version: '1'
     - uses: actions/checkout@v4
-    - uses: julia-actions/julia-buildpkg@v1
+    - name: "Install Dependencies"
+      run: |
+        import Pkg
+        Pkg.Registry.update()
+        # Install packages present in subdirectories
+        dev_pks = Pkg.PackageSpec[]
+        for path in ("lib/SciMLJacobianOperators", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveBase", "lib/SimpleNonlinearSolve", "lib/NonlinearSolveFirstOrder", "lib/NonlinearSolveSpectralMethods", "lib/NonlinearSolveQuasiNewton")
+            push!(dev_pks, Pkg.PackageSpec(; path))
+        end
+        Pkg.develop(dev_pks)
+        Pkg.instantiate()
+      shell: julia --color=yes --code-coverage=user --depwarn=yes --project=. {0}
     - uses: julia-actions/julia-invalidations@v1
       id: invs_pr
 
     - uses: actions/checkout@v4
       with:
         ref: ${{ github.event.repository.default_branch }}
-    - uses: julia-actions/julia-buildpkg@v1
+    - name: "Install Dependencies"
+      run: |
+        import Pkg
+        Pkg.Registry.update()
+        # Install packages present in subdirectories
+        dev_pks = Pkg.PackageSpec[]
+        for path in ("lib/SciMLJacobianOperators", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveBase", "lib/SimpleNonlinearSolve", "lib/NonlinearSolveFirstOrder", "lib/NonlinearSolveSpectralMethods", "lib/NonlinearSolveQuasiNewton")
+            push!(dev_pks, Pkg.PackageSpec(; path))
+        end
+        Pkg.develop(dev_pks)
+        Pkg.instantiate()
+      shell: julia --color=yes --code-coverage=user --depwarn=yes --project=. {0}
     - uses: julia-actions/julia-invalidations@v1
       id: invs_default
     

From ea0df2ae4e5e483eb5349dd8be431e76429a3957 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 31 Oct 2024 10:00:04 -0400
Subject: [PATCH 665/700] test: centralize the 23 test problem testing

---
 Project.toml                                  |   2 +-
 .../test/core/23_test_problems_tests.jl       | 106 -----------------
 test/23_test_problems_tests.jl                | 109 +++++++++++-------
 3 files changed, 71 insertions(+), 146 deletions(-)
 delete mode 100644 lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl

diff --git a/Project.toml b/Project.toml
index bd31721c1..b827985cf 100644
--- a/Project.toml
+++ b/Project.toml
@@ -94,7 +94,7 @@ NonlinearSolveFirstOrder = "1"
 NonlinearSolveQuasiNewton = "1"
 NonlinearSolveSpectralMethods = "1"
 OrdinaryDiffEqTsit5 = "1.1.0"
-PETSc = "0.2"
+PETSc = "0.3"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 Preferences = "1.4"
diff --git a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl b/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
deleted file mode 100644
index 6dd85b94b..000000000
--- a/lib/SimpleNonlinearSolve/test/core/23_test_problems_tests.jl
+++ /dev/null
@@ -1,106 +0,0 @@
-@testsnippet RobustnessTestSnippet begin
-    using NonlinearProblemLibrary, NonlinearSolveBase, LinearAlgebra, ADTypes
-
-    problems = NonlinearProblemLibrary.problems
-    dicts = NonlinearProblemLibrary.dicts
-
-    function test_on_library(
-            problems, dicts, alg_ops, broken_tests, ϵ = 1e-4; skip_tests = nothing)
-        for (idx, (problem, dict)) in enumerate(zip(problems, dicts))
-            x = dict["start"]
-            res = similar(x)
-            nlprob = NonlinearProblem(problem, copy(x))
-            @testset "$idx: $(dict["title"])" begin
-                for alg in alg_ops
-                    try
-                        sol = solve(nlprob, alg;
-                            termination_condition = AbsNormTerminationMode(norm))
-                        problem(res, sol.u, nothing)
-
-                        skip = skip_tests !== nothing && idx in skip_tests[alg]
-                        if skip
-                            @test_skip norm(res) ≤ ϵ
-                            continue
-                        end
-                        broken = idx in broken_tests[alg] ? true : false
-                        @test norm(res)≤ϵ broken=broken
-                    catch e
-                        @error e
-                        broken = idx in broken_tests[alg] ? true : false
-                        if broken
-                            @test false broken=true
-                        else
-                            @test 1 == 2
-                        end
-                    end
-                end
-            end
-        end
-    end
-end
-
-@testitem "23 Test Problems: SimpleNewtonRaphson" setup=[RobustnessTestSnippet] tags=[:core] begin
-    alg_ops = (SimpleNewtonRaphson(; autodiff = AutoForwardDiff()),)
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = []
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
-
-@testitem "23 Test Problems: SimpleHalley" setup=[RobustnessTestSnippet] tags=[:core] begin
-    alg_ops = (SimpleHalley(; autodiff = AutoForwardDiff()),)
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    if Sys.isapple()
-        broken_tests[alg_ops[1]] = [1, 5, 11, 15, 16, 18]
-    else
-        broken_tests[alg_ops[1]] = [1, 5, 15, 16, 18]
-    end
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
-
-@testitem "23 Test Problems: SimpleTrustRegion" setup=[RobustnessTestSnippet] tags=[:core] begin
-    alg_ops = (
-        SimpleTrustRegion(; autodiff = AutoForwardDiff()),
-        SimpleTrustRegion(; nlsolve_update_rule = Val(true), autodiff = AutoForwardDiff())
-    )
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [3, 15, 16, 21]
-    broken_tests[alg_ops[2]] = [15, 16]
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
-
-@testitem "23 Test Problems: SimpleDFSane" setup=[RobustnessTestSnippet] tags=[:core] begin
-    alg_ops = (SimpleDFSane(),)
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    if Sys.isapple()
-        broken_tests[alg_ops[1]] = [1, 2, 3, 5, 6, 21]
-    else
-        broken_tests[alg_ops[1]] = [1, 2, 3, 4, 5, 6, 11, 21]
-    end
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
-
-@testitem "23 Test Problems: SimpleBroyden" setup=[RobustnessTestSnippet] tags=[:core] begin
-    alg_ops = (SimpleBroyden(),)
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 5, 11]
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
-
-@testitem "23 Test Problems: SimpleKlement" setup=[RobustnessTestSnippet] tags=[:core] begin
-    alg_ops = (SimpleKlement(),)
-
-    broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 11, 12, 22]
-
-    test_on_library(problems, dicts, alg_ops, broken_tests)
-end
diff --git a/test/23_test_problems_tests.jl b/test/23_test_problems_tests.jl
index d740a87c2..2285a52a9 100644
--- a/test/23_test_problems_tests.jl
+++ b/test/23_test_problems_tests.jl
@@ -10,27 +10,25 @@ function test_on_library(
         x = dict["start"]
         res = similar(x)
         nlprob = NonlinearProblem(problem, copy(x))
-        @testset "$idx: $(dict["title"])" begin
-            for alg in alg_ops
-                try
-                    sol = solve(nlprob, alg; maxiters = 10000)
-                    problem(res, sol.u, nothing)
-
-                    skip = skip_tests !== nothing && idx in skip_tests[alg]
-                    if skip
-                        @test_skip norm(res, Inf) ≤ ϵ
-                        continue
-                    end
-                    broken = idx in broken_tests[alg] ? true : false
-                    @test norm(res, Inf)≤ϵ broken=broken
-                catch err
-                    @error err
-                    broken = idx in broken_tests[alg] ? true : false
-                    if broken
-                        @test false broken=true
-                    else
-                        @test 1 == 2
-                    end
+        @testset "$idx: $(dict["title"]) | alg #$(alg_id)" for (alg_id, alg) in enumerate(alg_ops)
+            try
+                sol = solve(nlprob, alg; maxiters = 10000)
+                problem(res, sol.u, nothing)
+
+                skip = skip_tests !== nothing && idx in skip_tests[alg]
+                if skip
+                    @test_skip norm(res, Inf) ≤ ϵ
+                    continue
+                end
+                broken = idx in broken_tests[alg] ? true : false
+                @test norm(res, Inf)≤ϵ broken=broken
+            catch err
+                @error err
+                broken = idx in broken_tests[alg] ? true : false
+                if broken
+                    @test false broken=true
+                else
+                    @test 1 == 2
                 end
             end
         end
@@ -40,7 +38,7 @@ end
 export test_on_library, problems, dicts
 end
 
-@testitem "PolyAlgorithms" setup=[RobustnessTesting] tags=[:core] begin
+@testitem "23 Test Problems: PolyAlgorithms" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (RobustMultiNewton(), FastShortcutNonlinearPolyalg())
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -50,8 +48,11 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "NewtonRaphson" setup=[RobustnessTesting] tags=[:core] begin
-    alg_ops = (NewtonRaphson(),)
+@testitem "23 Test Problems: NewtonRaphson" setup=[RobustnessTesting] tags=[:core] begin
+    alg_ops = (
+        NewtonRaphson(),
+        SimpleNewtonRaphson()
+    )
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
     broken_tests[alg_ops[1]] = [1]
@@ -59,14 +60,29 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "TrustRegion" setup=[RobustnessTesting] tags=[:core] begin
+@testitem "23 Test Problems: Halley" setup=[RobustnessTesting] tags=[:core] begin
+    alg_ops = (SimpleHalley(; autodiff = AutoForwardDiff()),)
+
+    broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    if Sys.isapple()
+        broken_tests[alg_ops[1]] = [1, 5, 11, 15, 16, 18]
+    else
+        broken_tests[alg_ops[1]] = [1, 5, 15, 16, 18]
+    end
+
+    test_on_library(problems, dicts, alg_ops, broken_tests)
+end
+
+@testitem "23 Test Problems: TrustRegion" setup=[RobustnessTesting] tags=[:core] begin
     alg_ops = (
         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Simple),
         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Fan),
         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Hei),
         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Yuan),
         TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.Bastin),
-        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.NLsolve)
+        TrustRegion(; radius_update_scheme = RadiusUpdateSchemes.NLsolve),
+        SimpleTrustRegion(),
+        SimpleTrustRegion(; nlsolve_update_rule = Val(true))
     )
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
@@ -76,11 +92,13 @@ end
     broken_tests[alg_ops[4]] = [8, 11, 21]
     broken_tests[alg_ops[5]] = [21]
     broken_tests[alg_ops[6]] = [11, 21]
+    broken_tests[alg_ops[7]] = [3, 15, 16, 21]
+    broken_tests[alg_ops[8]] = [15, 16]
 
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "LevenbergMarquardt" setup=[RobustnessTesting] tags=[:core] begin
+@testitem "23 Test Problems: LevenbergMarquardt" setup=[RobustnessTesting] tags=[:core] begin
     using LinearSolve
 
     alg_ops = (
@@ -97,50 +115,63 @@ end
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "DFSane" setup=[RobustnessTesting] tags=[:core] begin
-    alg_ops = (DFSane(),)
+@testitem "23 Test Problems: DFSane" setup=[RobustnessTesting] tags=[:core] begin
+    alg_ops = (
+        DFSane(),
+        SimpleDFSane()
+    )
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
     broken_tests[alg_ops[1]] = [1, 2, 3, 5, 21]
+    if Sys.isapple()
+        broken_tests[alg_ops[2]] = [1, 2, 3, 5, 6, 21]
+    else
+        broken_tests[alg_ops[2]] = [1, 2, 3, 5, 6, 11, 21]
+    end
 
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "Broyden" setup=[RobustnessTesting] tags=[:core] retries=3 begin
+@testitem "23 Test Problems: Broyden" setup=[RobustnessTesting] tags=[:core] retries=3 begin
     alg_ops = (
         Broyden(),
         Broyden(; init_jacobian = Val(:true_jacobian)),
         Broyden(; update_rule = Val(:bad_broyden)),
-        Broyden(; init_jacobian = Val(:true_jacobian), update_rule = Val(:bad_broyden))
+        Broyden(; init_jacobian = Val(:true_jacobian), update_rule = Val(:bad_broyden)),
+        SimpleBroyden()
     )
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
+    broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
+    broken_tests[alg_ops[4]] = [5, 6, 8, 11]
     if Sys.isapple()
         broken_tests[alg_ops[1]] = [1, 5, 11]
-        broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
         broken_tests[alg_ops[3]] = [1, 5, 6, 9, 11]
-        broken_tests[alg_ops[4]] = [5, 6, 8, 11, 16]
     else
         broken_tests[alg_ops[1]] = [1, 5, 11, 15]
-        broken_tests[alg_ops[2]] = [1, 5, 8, 11, 18]
-        broken_tests[alg_ops[3]] = [1, 5, 9, 11]
-        broken_tests[alg_ops[4]] = [5, 6, 8, 11]
+        broken_tests[alg_ops[3]] = [1, 5, 9, 11, 16]
     end
+    broken_tests[alg_ops[5]] = [1, 5, 11]
 
     test_on_library(problems, dicts, alg_ops, broken_tests, Sys.isapple() ? 1e-3 : 1e-4)
 end
 
-@testitem "Klement" setup=[RobustnessTesting] tags=[:core] begin
-    alg_ops = (Klement(), Klement(; init_jacobian = Val(:true_jacobian_diagonal)))
+@testitem "23 Test Problems: Klement" setup=[RobustnessTesting] tags=[:core] begin
+    alg_ops = (
+        Klement(),
+        Klement(; init_jacobian = Val(:true_jacobian_diagonal)),
+        SimpleKlement()
+    )
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
     broken_tests[alg_ops[1]] = [1, 2, 4, 5, 11, 18, 22]
     broken_tests[alg_ops[2]] = [2, 4, 5, 7, 18, 22]
+    broken_tests[alg_ops[3]] = [1, 2, 4, 5, 11, 22]
 
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
 
-@testitem "PseudoTransient" setup=[RobustnessTesting] tags=[:core] begin
+@testitem "23 Test Problems: PseudoTransient" setup=[RobustnessTesting] tags=[:core] begin
     # PT relies on the root being a stable equilibrium for convergence, so it won't work on
     # most problems
     alg_ops = (PseudoTransient(),)

From 1b74574ee22a0f66d4bc40301484c4e70a7bde21 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 31 Oct 2024 10:05:01 -0400
Subject: [PATCH 666/700] test: remove segfault warning

---
 lib/NonlinearSolveQuasiNewton/test/core_tests.jl | 2 +-
 test/23_test_problems_tests.jl                   | 6 +-----
 test/wrappers/rootfind_tests.jl                  | 1 -
 3 files changed, 2 insertions(+), 7 deletions(-)

diff --git a/lib/NonlinearSolveQuasiNewton/test/core_tests.jl b/lib/NonlinearSolveQuasiNewton/test/core_tests.jl
index 5e70661d8..d22481b4c 100644
--- a/lib/NonlinearSolveQuasiNewton/test/core_tests.jl
+++ b/lib/NonlinearSolveQuasiNewton/test/core_tests.jl
@@ -193,7 +193,7 @@ end
 
                 solver = LimitedMemoryBroyden(; linesearch)
                 sol = solve_iip(quadratic_f!, u0; solver)
-                @test SciMLBase.successful_retcode(sol)
+                @test SciMLBase.successful_retcode(sol) broken=broken
                 err = maximum(abs, quadratic_f(sol.u, 2.0))
                 @test err<1e-9 broken=broken
 
diff --git a/test/23_test_problems_tests.jl b/test/23_test_problems_tests.jl
index 2285a52a9..8fa4c47b6 100644
--- a/test/23_test_problems_tests.jl
+++ b/test/23_test_problems_tests.jl
@@ -64,11 +64,7 @@ end
     alg_ops = (SimpleHalley(; autodiff = AutoForwardDiff()),)
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    if Sys.isapple()
-        broken_tests[alg_ops[1]] = [1, 5, 11, 15, 16, 18]
-    else
-        broken_tests[alg_ops[1]] = [1, 5, 15, 16, 18]
-    end
+    broken_tests[alg_ops[1]] = [1, 5, 15, 16, 18]
 
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end
diff --git a/test/wrappers/rootfind_tests.jl b/test/wrappers/rootfind_tests.jl
index 4f317d76d..073d31fe4 100644
--- a/test/wrappers/rootfind_tests.jl
+++ b/test/wrappers/rootfind_tests.jl
@@ -43,7 +43,6 @@
     end
 end
 
-# Can lead to segfaults
 @testitem "Nonlinear Root Finding Problems" tags=[:wrappers] begin
     using LinearAlgebra
     import NLSolvers, NLsolve, SIAMFANLEquations, MINPACK, PETSc

From 4a74ae0ca46e79f019b02621740f77b0a984468a Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 31 Oct 2024 11:27:09 -0400
Subject: [PATCH 667/700] docs: update all documentation

---
 .github/workflows/CI_NonlinearSolve.yml       | 12 ++---
 .github/workflows/Documentation.yml           |  2 +-
 Project.toml                                  |  4 +-
 docs/Project.toml                             | 12 +++--
 docs/make.jl                                  | 49 +++++++++++++------
 docs/src/basics/autodiff.md                   |  2 +-
 docs/src/basics/faq.md                        | 16 +++---
 docs/src/devdocs/algorithm_helpers.md         | 34 ++++++-------
 docs/src/devdocs/internal_interfaces.md       | 39 ++++++---------
 docs/src/devdocs/jacobian.md                  |  3 +-
 docs/src/devdocs/linear_solve.md              |  4 +-
 docs/src/devdocs/operators.md                 |  2 +-
 docs/src/native/diagnostics.md                |  9 ++--
 docs/src/native/solvers.md                    |  2 +-
 lib/BracketingNonlinearSolve/Project.toml     |  2 +-
 lib/NonlinearSolveBase/Project.toml           |  4 +-
 lib/NonlinearSolveBase/src/abstract_types.jl  |  2 +-
 .../src/descent/geodesic_acceleration.jl      |  2 +-
 lib/NonlinearSolveBase/src/timer_outputs.jl   |  2 +-
 lib/NonlinearSolveFirstOrder/Project.toml     |  4 +-
 .../src/levenberg_marquardt.jl                |  2 +-
 lib/NonlinearSolveFirstOrder/src/solve.jl     |  4 +-
 .../src/trust_region.jl                       |  2 +-
 lib/NonlinearSolveQuasiNewton/Project.toml    |  4 +-
 .../src/initialization.jl                     |  3 +-
 .../Project.toml                              |  4 +-
 lib/SciMLJacobianOperators/Project.toml       |  2 +-
 lib/SimpleNonlinearSolve/Project.toml         |  4 +-
 src/NonlinearSolve.jl                         |  2 -
 src/forward_diff.jl                           |  9 ++++
 src/helpers.jl                                |  1 -
 31 files changed, 134 insertions(+), 109 deletions(-)
 delete mode 100644 src/helpers.jl

diff --git a/.github/workflows/CI_NonlinearSolve.yml b/.github/workflows/CI_NonlinearSolve.yml
index 7c1b55567..f685a7e7a 100644
--- a/.github/workflows/CI_NonlinearSolve.yml
+++ b/.github/workflows/CI_NonlinearSolve.yml
@@ -34,9 +34,9 @@ jobs:
       fail-fast: false
       matrix:
         group:
-          - Core
-          - Downstream
-          - Wrappers
+          - core
+          - downstream
+          - wrappers
         version:
           - "1.10"
           - "1"
@@ -92,9 +92,9 @@ jobs:
         version:
           - "1.10"
         group:
-          - Core
-          - Downstream
-          - Wrappers
+          - core
+          - downstream
+          - wrappers
     steps:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v2
diff --git a/.github/workflows/Documentation.yml b/.github/workflows/Documentation.yml
index 9dc416799..af44cd769 100644
--- a/.github/workflows/Documentation.yml
+++ b/.github/workflows/Documentation.yml
@@ -22,7 +22,7 @@ jobs:
           Pkg.Registry.update()
           # Install packages present in subdirectories
           dev_pks = Pkg.PackageSpec[]
-          for path in ("lib/SciMLJacobianOperators", ".", "lib/SimpleNonlinearSolve", "lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve")
+          for path in ("lib/SciMLJacobianOperators", ".", "lib/SimpleNonlinearSolve", "lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveFirstOrder", "lib/NonlinearSolveQuasiNewton", "lib/NonlinearSolveSpectralMethods")
               push!(dev_pks, Pkg.PackageSpec(; path))
           end
           Pkg.develop(dev_pks)
diff --git a/Project.toml b/Project.toml
index b827985cf..845611499 100644
--- a/Project.toml
+++ b/Project.toml
@@ -67,7 +67,7 @@ BracketingNonlinearSolve = "1"
 CUDA = "5.5"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
-DiffEqBase = "6.155.3"
+DiffEqBase = "6.158.3"
 DifferentiationInterface = "0.6.18"
 Enzyme = "0.13.11"
 ExplicitImports = "1.5"
@@ -102,7 +102,7 @@ Random = "1.10"
 ReTestItems = "1.24"
 Reexport = "1.2"
 SIAMFANLEquations = "1.0.1"
-SciMLBase = "2.54.0"
+SciMLBase = "2.58"
 SimpleNonlinearSolve = "2"
 SparseArrays = "1.10"
 SparseConnectivityTracer = "0.6.5"
diff --git a/docs/Project.toml b/docs/Project.toml
index 9ed14da4e..c6c28820c 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -14,6 +14,9 @@ InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
+NonlinearSolveFirstOrder = "5959db7a-ea39-4486-b5fe-2dd0bf03d60d"
+NonlinearSolveQuasiNewton = "9a2c21bd-3a47-402d-9113-8faf9a0ee114"
+NonlinearSolveSpectralMethods = "26075421-4e9a-44e1-8bd1-420ed7ad02b2"
 OrdinaryDiffEqTsit5 = "b1df2697-797e-41e3-8120-5422d3b24e4a"
 PETSc = "ace2c81b-2b5f-4b1e-a30d-d662738edfe0"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
@@ -32,7 +35,7 @@ AlgebraicMultigrid = "0.5, 0.6"
 ArrayInterface = "6, 7"
 BenchmarkTools = "1"
 BracketingNonlinearSolve = "1"
-DiffEqBase = "6.158"
+DiffEqBase = "6.158.3"
 DifferentiationInterface = "0.6.16"
 Documenter = "1"
 DocumenterCitations = "1"
@@ -42,11 +45,14 @@ InteractiveUtils = "<0.0.1, 1"
 LinearSolve = "2"
 NonlinearSolve = "4"
 NonlinearSolveBase = "1"
+NonlinearSolveFirstOrder = "1"
+NonlinearSolveQuasiNewton = "1"
+NonlinearSolveSpectralMethods = "1"
 OrdinaryDiffEqTsit5 = "1.1.0"
-PETSc = "0.2"
+PETSc = "0.3"
 Plots = "1"
 Random = "1.10"
-SciMLBase = "2.4"
+SciMLBase = "2.58"
 SciMLJacobianOperators = "0.1"
 SimpleNonlinearSolve = "2"
 SparseConnectivityTracer = "0.6.5"
diff --git a/docs/make.jl b/docs/make.jl
index bdc2b7fe9..29b1535dd 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,13 +1,23 @@
 using Documenter, DocumenterCitations, DocumenterInterLinks
-using NonlinearSolve, SimpleNonlinearSolve, Sundials, SteadyStateDiffEq, SciMLBase,
-      BracketingNonlinearSolve, NonlinearSolveBase
-using SciMLJacobianOperators
 import DiffEqBase
 
-cp(joinpath(@__DIR__, "Manifest.toml"),
-    joinpath(@__DIR__, "src/assets/Manifest.toml"), force = true)
-cp(joinpath(@__DIR__, "Project.toml"),
-    joinpath(@__DIR__, "src/assets/Project.toml"), force = true)
+using Sundials
+using NonlinearSolveBase, SciMLBase, DiffEqBase
+using SimpleNonlinearSolve, BracketingNonlinearSolve
+using NonlinearSolveFirstOrder, NonlinearSolveQuasiNewton, NonlinearSolveSpectralMethods
+using SciMLJacobianOperators
+using NonlinearSolve, SteadyStateDiffEq
+
+cp(
+    joinpath(@__DIR__, "Manifest.toml"),
+    joinpath(@__DIR__, "src/assets/Manifest.toml");
+    force = true
+)
+cp(
+    joinpath(@__DIR__, "Project.toml"),
+    joinpath(@__DIR__, "src/assets/Project.toml");
+    force = true
+)
 
 include("pages.jl")
 
@@ -20,20 +30,29 @@ interlinks = InterLinks(
 
 makedocs(;
     sitename = "NonlinearSolve.jl",
-    authors = "Chris Rackauckas",
-    modules = [NonlinearSolve, SimpleNonlinearSolve, SteadyStateDiffEq, DiffEqBase,
-        Sundials, NonlinearSolveBase, SciMLBase, SciMLJacobianOperators,
-        BracketingNonlinearSolve],
+    authors = "SciML",
+    modules = [
+        NonlinearSolveBase, SciMLBase, DiffEqBase,
+        SimpleNonlinearSolve, BracketingNonlinearSolve,
+        NonlinearSolveFirstOrder, NonlinearSolveQuasiNewton, NonlinearSolveSpectralMethods,
+        Sundials,
+        SciMLJacobianOperators,
+        NonlinearSolve, SteadyStateDiffEq
+    ],
     clean = true,
     doctest = false,
     linkcheck = true,
-    linkcheck_ignore = ["https://twitter.com/ChrisRackauckas/status/1544743542094020615",
-        "https://link.springer.com/article/10.1007/s40096-020-00339-4"],
+    linkcheck_ignore = [
+        "https://twitter.com/ChrisRackauckas/status/1544743542094020615",
+        "https://link.springer.com/article/10.1007/s40096-020-00339-4"
+    ],
     checkdocs = :exports,
     warnonly = [:missing_docs],
     plugins = [bib, interlinks],
-    format = Documenter.HTML(assets = ["assets/favicon.ico", "assets/citations.css"],
-        canonical = "https://docs.sciml.ai/NonlinearSolve/stable/"),
+    format = Documenter.HTML(
+        assets = ["assets/favicon.ico", "assets/citations.css"],
+        canonical = "https://docs.sciml.ai/NonlinearSolve/stable/"
+    ),
     pages
 )
 
diff --git a/docs/src/basics/autodiff.md b/docs/src/basics/autodiff.md
index d2d01e00b..5cdffa75b 100644
--- a/docs/src/basics/autodiff.md
+++ b/docs/src/basics/autodiff.md
@@ -3,7 +3,7 @@
 !!! note
     
     We support all backends supported by DifferentiationInterface.jl. Please refer to
-    the [backends page](https://gdalle.github.io/DifferentiationInterface.jl/DifferentiationInterface/stable/explanation/backends/)
+    the [backends page](https://juliadiff.org/DifferentiationInterface.jl/DifferentiationInterface/stable/explanation/backends/)
     for more information.
 
 ## Summary of Finite Differencing Backends
diff --git a/docs/src/basics/faq.md b/docs/src/basics/faq.md
index 265cee264..4d428250a 100644
--- a/docs/src/basics/faq.md
+++ b/docs/src/basics/faq.md
@@ -102,7 +102,8 @@ It is hard to say why your code is not fast. Take a look at the
 there is type instability.
 
 If you are using the defaults for the autodiff and your problem is not a scalar or using
-static arrays, ForwardDiff will create type unstable code. See this simple example:
+static arrays, ForwardDiff will create type unstable code and lead to dynamic dispatch
+internally. See this simple example:
 
 ```@example type_unstable
 using NonlinearSolve, InteractiveUtils
@@ -136,14 +137,17 @@ prob = NonlinearProblem(f, [1.0, 2.0], 2.0)
 nothing # hide
 ```
 
-Oh no! This is type unstable. This is because ForwardDiff.jl will chunk the jacobian
-computation and the type of this chunksize can't be statically inferred. To fix this, we
-directly specify the chunksize:
+Ah it is still type stable. But internally since the chunksize is not statically inferred,
+it will be dynamic and lead to dynamic dispatch. To fix this, we directly specify the
+chunksize:
 
 ```@example type_unstable
-@code_warntype solve(prob,
+@code_warntype solve(
+    prob,
     NewtonRaphson(;
-        autodiff = AutoForwardDiff(; chunksize = NonlinearSolve.pickchunksize(prob.u0))))
+        autodiff = AutoForwardDiff(; chunksize = NonlinearSolve.pickchunksize(prob.u0))
+    )
+)
 nothing # hide
 ```
 
diff --git a/docs/src/devdocs/algorithm_helpers.md b/docs/src/devdocs/algorithm_helpers.md
index c945b6003..2bd038792 100644
--- a/docs/src/devdocs/algorithm_helpers.md
+++ b/docs/src/devdocs/algorithm_helpers.md
@@ -3,8 +3,8 @@
 ## Pseudo Transient Method
 
 ```@docs
-NonlinearSolve.SwitchedEvolutionRelaxation
-NonlinearSolve.SwitchedEvolutionRelaxationCache
+NonlinearSolveFirstOrder.SwitchedEvolutionRelaxation
+NonlinearSolveFirstOrder.SwitchedEvolutionRelaxationCache
 ```
 
 ## Approximate Jacobian Methods
@@ -12,54 +12,54 @@ NonlinearSolve.SwitchedEvolutionRelaxationCache
 ### Initialization
 
 ```@docs
-NonlinearSolve.IdentityInitialization
-NonlinearSolve.TrueJacobianInitialization
-NonlinearSolve.BroydenLowRankInitialization
+NonlinearSolveQuasiNewton.IdentityInitialization
+NonlinearSolveQuasiNewton.TrueJacobianInitialization
+NonlinearSolveQuasiNewton.BroydenLowRankInitialization
 ```
 
 ### Jacobian Structure
 
 ```@docs
-NonlinearSolve.FullStructure
-NonlinearSolve.DiagonalStructure
+NonlinearSolveQuasiNewton.FullStructure
+NonlinearSolveQuasiNewton.DiagonalStructure
 ```
 
 ### Jacobian Caches
 
 ```@docs
-NonlinearSolve.InitializedApproximateJacobianCache
+NonlinearSolveQuasiNewton.InitializedApproximateJacobianCache
 ```
 
 ### Reset Methods
 
 ```@docs
-NonlinearSolve.NoChangeInStateReset
-NonlinearSolve.IllConditionedJacobianReset
+NonlinearSolveQuasiNewton.NoChangeInStateReset
+NonlinearSolveQuasiNewton.IllConditionedJacobianReset
 ```
 
 ### Update Rules
 
 ```@docs
-NonlinearSolve.GoodBroydenUpdateRule
-NonlinearSolve.BadBroydenUpdateRule
-NonlinearSolve.KlementUpdateRule
+NonlinearSolveQuasiNewton.GoodBroydenUpdateRule
+NonlinearSolveQuasiNewton.BadBroydenUpdateRule
+NonlinearSolveQuasiNewton.KlementUpdateRule
 ```
 
 ## Levenberg Marquardt Method
 
 ```@docs
-NonlinearSolve.LevenbergMarquardtTrustRegion
+NonlinearSolveFirstOrder.LevenbergMarquardtTrustRegion
 ```
 
 ## Trust Region Method
 
 ```@docs
-NonlinearSolve.GenericTrustRegionScheme
+NonlinearSolveFirstOrder.GenericTrustRegionScheme
 ```
 
 ## Miscellaneous
 
 ```@docs
-NonlinearSolve.callback_into_cache!
-NonlinearSolve.concrete_jac
+NonlinearSolveBase.callback_into_cache!
+NonlinearSolveBase.concrete_jac
 ```
diff --git a/docs/src/devdocs/internal_interfaces.md b/docs/src/devdocs/internal_interfaces.md
index 53e20d754..f4474e1aa 100644
--- a/docs/src/devdocs/internal_interfaces.md
+++ b/docs/src/devdocs/internal_interfaces.md
@@ -3,50 +3,43 @@
 ## Solvers
 
 ```@docs
-NonlinearSolve.AbstractNonlinearSolveAlgorithm
-NonlinearSolve.AbstractNonlinearSolveExtensionAlgorithm
-NonlinearSolve.AbstractNonlinearSolveCache
+NonlinearSolveBase.AbstractNonlinearSolveAlgorithm
+NonlinearSolveBase.AbstractNonlinearSolveCache
 ```
 
-## Descent Algorithms
+## Descent Directions
 
 ```@docs
-NonlinearSolve.AbstractDescentAlgorithm
-NonlinearSolve.AbstractDescentCache
+NonlinearSolveBase.AbstractDescentDirection
+NonlinearSolveBase.AbstractDescentCache
 ```
 
-## Descent Results
+### Descent Results
 
 ```@docs
-NonlinearSolve.DescentResult
+NonlinearSolveBase.DescentResult
 ```
 
 ## Approximate Jacobian
 
 ```@docs
-NonlinearSolve.AbstractApproximateJacobianStructure
-NonlinearSolve.AbstractJacobianInitialization
-NonlinearSolve.AbstractApproximateJacobianUpdateRule
-NonlinearSolve.AbstractApproximateJacobianUpdateRuleCache
-NonlinearSolve.AbstractResetCondition
+NonlinearSolveBase.AbstractApproximateJacobianStructure
+NonlinearSolveBase.AbstractJacobianInitialization
+NonlinearSolveBase.AbstractApproximateJacobianUpdateRule
+NonlinearSolveBase.AbstractApproximateJacobianUpdateRuleCache
+NonlinearSolveBase.AbstractResetCondition
 ```
 
 ## Damping Algorithms
 
 ```@docs
-NonlinearSolve.AbstractDampingFunction
-NonlinearSolve.AbstractDampingFunctionCache
+NonlinearSolveBase.AbstractDampingFunction
+NonlinearSolveBase.AbstractDampingFunctionCache
 ```
 
 ## Trust Region
 
 ```@docs
-NonlinearSolve.AbstractTrustRegionMethod
-NonlinearSolve.AbstractTrustRegionMethodCache
-```
-
-## Tracing
-
-```@docs
-NonlinearSolve.AbstractNonlinearSolveTraceLevel
+NonlinearSolveBase.AbstractTrustRegionMethod
+NonlinearSolveBase.AbstractTrustRegionMethodCache
 ```
diff --git a/docs/src/devdocs/jacobian.md b/docs/src/devdocs/jacobian.md
index 082478f7c..3e54966f4 100644
--- a/docs/src/devdocs/jacobian.md
+++ b/docs/src/devdocs/jacobian.md
@@ -1,6 +1,5 @@
 # Jacobian Wrappers
 
 ```@docs
-NonlinearSolve.AbstractNonlinearSolveJacobianCache
-NonlinearSolve.JacobianCache
+NonlinearSolveBase.construct_jacobian_cache
 ```
diff --git a/docs/src/devdocs/linear_solve.md b/docs/src/devdocs/linear_solve.md
index 88fa87440..dadd7dea1 100644
--- a/docs/src/devdocs/linear_solve.md
+++ b/docs/src/devdocs/linear_solve.md
@@ -1,6 +1,6 @@
 # Linear Solve
 
 ```@docs
-NonlinearSolve.AbstractLinearSolverCache
-NonlinearSolve.LinearSolverCache
+NonlinearSolveBase.AbstractLinearSolverCache
+NonlinearSolveBase.construct_linear_solver
 ```
diff --git a/docs/src/devdocs/operators.md b/docs/src/devdocs/operators.md
index fcbadc778..249eda29d 100644
--- a/docs/src/devdocs/operators.md
+++ b/docs/src/devdocs/operators.md
@@ -3,5 +3,5 @@
 ## Low-Rank Jacobian Operators
 
 ```@docs
-NonlinearSolve.BroydenLowRankJacobian
+NonlinearSolveQuasiNewton.BroydenLowRankJacobian
 ```
diff --git a/docs/src/native/diagnostics.md b/docs/src/native/diagnostics.md
index 35f11552f..1c0571c87 100644
--- a/docs/src/native/diagnostics.md
+++ b/docs/src/native/diagnostics.md
@@ -5,9 +5,9 @@
 These functions are not exported since the names have a potential for conflict.
 
 ```@docs
-NonlinearSolve.enable_timer_outputs
-NonlinearSolve.disable_timer_outputs
-NonlinearSolve.@static_timeit
+NonlinearSolveBase.enable_timer_outputs
+NonlinearSolveBase.disable_timer_outputs
+NonlinearSolveBase.@static_timeit
 ```
 
 ## Tracing API
@@ -17,6 +17,3 @@ TraceAll
 TraceWithJacobianConditionNumber
 TraceMinimal
 ```
-
-For details about the arguments refer to the documentation of
-[`NonlinearSolve.AbstractNonlinearSolveTraceLevel`](@ref).
diff --git a/docs/src/native/solvers.md b/docs/src/native/solvers.md
index 5653f1fab..a3aa900e0 100644
--- a/docs/src/native/solvers.md
+++ b/docs/src/native/solvers.md
@@ -81,7 +81,7 @@ All of the previously mentioned solvers are wrappers around the following solver
 are meant for advanced users and allow building custom solvers.
 
 ```@docs
-ApproximateJacobianSolveAlgorithm
+QuasiNewtonAlgorithm
 GeneralizedFirstOrderAlgorithm
 GeneralizedDFSane
 ```
diff --git a/lib/BracketingNonlinearSolve/Project.toml b/lib/BracketingNonlinearSolve/Project.toml
index f2a8e2b6d..16cade168 100644
--- a/lib/BracketingNonlinearSolve/Project.toml
+++ b/lib/BracketingNonlinearSolve/Project.toml
@@ -27,7 +27,7 @@ InteractiveUtils = "<0.0.1, 1"
 NonlinearSolveBase = "1.1"
 PrecompileTools = "1.2"
 Reexport = "1.2"
-SciMLBase = "2.50"
+SciMLBase = "2.58"
 Test = "1.10"
 TestItemRunner = "1"
 julia = "1.10"
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index c601b144f..4abb81cde 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -54,7 +54,7 @@ BandedMatrices = "1.5"
 CommonSolve = "0.2.4"
 Compat = "4.15"
 ConcreteStructs = "0.2.3"
-DiffEqBase = "6.149"
+DiffEqBase = "6.158.3"
 DifferentiationInterface = "0.6.16"
 EnzymeCore = "0.8"
 ExplicitImports = "1.10.1"
@@ -70,7 +70,7 @@ MaybeInplace = "0.1.4"
 Preferences = "1.4"
 Printf = "1.10"
 RecursiveArrayTools = "3"
-SciMLBase = "2.50"
+SciMLBase = "2.58"
 SciMLJacobianOperators = "0.1.1"
 SciMLOperators = "0.3.10"
 SparseArrays = "1.10"
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index 91afc2901..6105f5125 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -542,7 +542,7 @@ Define custom operations on `internalcache` tightly coupled with the calling `ca
 `args...` contain the sequence of caches calling into `internalcache`.
 
 This unfortunately makes code very tightly coupled and not modular. It is recommended to not
-use this functionality unless it can't be avoided (like in [`LevenbergMarquardt`](@ref)).
+use this functionality unless it can't be avoided (like in `LevenbergMarquardt`).
 """
 callback_into_cache!(cache, internalcache, args...) = nothing  # By default do nothing
 
diff --git a/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
index 409ed9ce9..f7758b1e7 100644
--- a/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
+++ b/lib/NonlinearSolveBase/src/descent/geodesic_acceleration.jl
@@ -5,7 +5,7 @@ Uses the `descent` algorithm to compute the velocity and acceleration terms for
 geodesic acceleration method. The velocity and acceleration terms are then combined to
 compute the descent direction.
 
-This method in its current form was developed for [`LevenbergMarquardt`](@ref). Performance
+This method in its current form was developed for `LevenbergMarquardt`. Performance
 for other methods are not theorectically or experimentally verified.
 
 ### Keyword Arguments
diff --git a/lib/NonlinearSolveBase/src/timer_outputs.jl b/lib/NonlinearSolveBase/src/timer_outputs.jl
index 0b6d23496..623e7ea15 100644
--- a/lib/NonlinearSolveBase/src/timer_outputs.jl
+++ b/lib/NonlinearSolveBase/src/timer_outputs.jl
@@ -18,7 +18,7 @@ end
     @static_timeit to name expr
 
 Like `TimerOutputs.@timeit_debug` but has zero overhead if `TimerOutputs` is disabled via
-[`NonlinearSolve.disable_timer_outputs()`](@ref).
+[`NonlinearSolveBase.disable_timer_outputs()`](@ref).
 """
 macro static_timeit(to, name, expr)
     @static if TIMER_OUTPUTS_ENABLED
diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
index b2468a092..94ab4fdbc 100644
--- a/lib/NonlinearSolveFirstOrder/Project.toml
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -30,7 +30,7 @@ BandedMatrices = "1.7.5"
 BenchmarkTools = "1.5.0"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
-DiffEqBase = "6.155.3"
+DiffEqBase = "6.158.3"
 Enzyme = "0.13.12"
 ExplicitImports = "1.5"
 FiniteDiff = "2.24"
@@ -49,7 +49,7 @@ PrecompileTools = "1.2"
 Random = "1.10"
 ReTestItems = "1.24"
 Reexport = "1"
-SciMLBase = "2.54"
+SciMLBase = "2.58"
 SciMLJacobianOperators = "0.1.0"
 Setfield = "1.1.1"
 SparseArrays = "1.10"
diff --git a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
index a06378dcb..f9c11ae28 100644
--- a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
+++ b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
@@ -30,7 +30,7 @@ nonlinear systems.
     should not be disabled.
 
 For the remaining arguments, see [`GeodesicAcceleration`](@ref) and
-[`NonlinearSolve.LevenbergMarquardtTrustRegion`](@ref) documentations.
+[`NonlinearSolveFirstOrder.LevenbergMarquardtTrustRegion`](@ref) documentations.
 """
 function LevenbergMarquardt(;
         linsolve = nothing, precs = nothing,
diff --git a/lib/NonlinearSolveFirstOrder/src/solve.jl b/lib/NonlinearSolveFirstOrder/src/solve.jl
index b2711ca76..c9c8c77a8 100644
--- a/lib/NonlinearSolveFirstOrder/src/solve.jl
+++ b/lib/NonlinearSolveFirstOrder/src/solve.jl
@@ -15,9 +15,9 @@ order of convergence.
 ### Keyword Arguments
 
   - `trustregion`: Globalization using a Trust Region Method. This needs to follow the
-    [`NonlinearSolve.AbstractTrustRegionMethod`](@ref) interface.
+    [`NonlinearSolveBase.AbstractTrustRegionMethod`](@ref) interface.
   - `descent`: The descent method to use to compute the step. This needs to follow the
-    [`NonlinearSolve.AbstractDescentAlgorithm`](@ref) interface.
+    [`NonlinearSolveBase.AbstractDescentDirection`](@ref) interface.
   - `max_shrink_times`: The maximum number of times the trust region radius can be shrunk
     before the algorithm terminates.
 """
diff --git a/lib/NonlinearSolveFirstOrder/src/trust_region.jl b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
index f76b77601..92d2655ac 100644
--- a/lib/NonlinearSolveFirstOrder/src/trust_region.jl
+++ b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
@@ -19,7 +19,7 @@ for large-scale and numerically-difficult nonlinear systems.
     `RadiusUpdateSchemes.Simple`. See [`RadiusUpdateSchemes`](@ref) for more details. For a
     review on trust region radius update schemes, see [yuan2015recent](@citet).
 
-For the remaining arguments, see [`NonlinearSolve.GenericTrustRegionScheme`](@ref)
+For the remaining arguments, see [`NonlinearSolveFirstOrder.GenericTrustRegionScheme`](@ref)
 documentation.
 """
 function TrustRegion(;
diff --git a/lib/NonlinearSolveQuasiNewton/Project.toml b/lib/NonlinearSolveQuasiNewton/Project.toml
index 5162d4656..2f00863d8 100644
--- a/lib/NonlinearSolveQuasiNewton/Project.toml
+++ b/lib/NonlinearSolveQuasiNewton/Project.toml
@@ -25,7 +25,7 @@ ArrayInterface = "7.16.0"
 BenchmarkTools = "1.5.0"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
-DiffEqBase = "6.155.3"
+DiffEqBase = "6.158.3"
 Enzyme = "0.13.12"
 ExplicitImports = "1.5"
 FiniteDiff = "2.24"
@@ -43,7 +43,7 @@ Pkg = "1.10"
 PrecompileTools = "1.2"
 ReTestItems = "1.24"
 Reexport = "1"
-SciMLBase = "2.54"
+SciMLBase = "2.58"
 SciMLOperators = "0.3.11"
 StableRNGs = "1"
 StaticArrays = "1.9.8"
diff --git a/lib/NonlinearSolveQuasiNewton/src/initialization.jl b/lib/NonlinearSolveQuasiNewton/src/initialization.jl
index 4af1fb921..f730b541b 100644
--- a/lib/NonlinearSolveQuasiNewton/src/initialization.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/initialization.jl
@@ -10,7 +10,8 @@ A cache for Approximate Jacobian.
   - `J`: The current Jacobian.
   - `structure`: The structure of the Jacobian.
   - `alg`: The initialization algorithm.
-  - `cache`: The Jacobian cache [`NonlinearSolve.JacobianCache`](@ref) (if needed).
+  - `cache`: The Jacobian cache [`NonlinearSolveBase.construct_jacobian_cache`](@ref)
+    (if needed).
   - `initialized`: A boolean indicating whether the Jacobian has been initialized.
   - `internalnorm`: The norm to be used.
 
diff --git a/lib/NonlinearSolveSpectralMethods/Project.toml b/lib/NonlinearSolveSpectralMethods/Project.toml
index 029c6aa26..bb9367554 100644
--- a/lib/NonlinearSolveSpectralMethods/Project.toml
+++ b/lib/NonlinearSolveSpectralMethods/Project.toml
@@ -19,7 +19,7 @@ Aqua = "0.8"
 BenchmarkTools = "1.5.0"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
-DiffEqBase = "6.155.3"
+DiffEqBase = "6.158.3"
 ExplicitImports = "1.5"
 Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
@@ -31,7 +31,7 @@ Pkg = "1.10"
 PrecompileTools = "1.2"
 ReTestItems = "1.24"
 Reexport = "1"
-SciMLBase = "2.54"
+SciMLBase = "2.58"
 StableRNGs = "1"
 StaticArrays = "1.9.8"
 Test = "1.10"
diff --git a/lib/SciMLJacobianOperators/Project.toml b/lib/SciMLJacobianOperators/Project.toml
index 7b9ac7cb1..7be83ae28 100644
--- a/lib/SciMLJacobianOperators/Project.toml
+++ b/lib/SciMLJacobianOperators/Project.toml
@@ -29,7 +29,7 @@ ForwardDiff = "0.10.36"
 InteractiveUtils = "<0.0.1, 1"
 LinearAlgebra = "1.10"
 ReverseDiff = "1.15"
-SciMLBase = "2.54.0"
+SciMLBase = "2.58"
 SciMLOperators = "0.3"
 Test = "1.10"
 TestItemRunner = "1"
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 4ca3eaad1..8492ac67f 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -43,7 +43,7 @@ BracketingNonlinearSolve = "1.1"
 ChainRulesCore = "1.24"
 CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
-DiffEqBase = "6.149"
+DiffEqBase = "6.158.3"
 DifferentiationInterface = "0.6.16"
 Enzyme = "0.13.11"
 ExplicitImports = "1.9"
@@ -62,7 +62,7 @@ PrecompileTools = "1.2"
 Random = "1.10"
 Reexport = "1.2"
 ReverseDiff = "1.15"
-SciMLBase = "2.50"
+SciMLBase = "2.58"
 Setfield = "1.1.1"
 StaticArrays = "1.9"
 StaticArraysCore = "1.4.3"
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 2ee0ac575..7d6ac7b09 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -46,8 +46,6 @@ using SimpleNonlinearSolve: SimpleNonlinearSolve
 
 const SII = SymbolicIndexingInterface
 
-include("helpers.jl")
-
 include("polyalg.jl")
 include("extension_algs.jl")
 
diff --git a/src/forward_diff.jl b/src/forward_diff.jl
index 28534c59e..410e818c3 100644
--- a/src/forward_diff.jl
+++ b/src/forward_diff.jl
@@ -87,3 +87,12 @@ end
 nodual_value(x) = x
 nodual_value(x::Dual) = ForwardDiff.value(x)
 nodual_value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
+
+"""
+    pickchunksize(x) = pickchunksize(length(x))
+    pickchunksize(x::Int)
+
+Determine the chunk size for ForwardDiff and PolyesterForwardDiff based on the input length.
+"""
+@inline pickchunksize(x) = pickchunksize(length(x))
+@inline pickchunksize(x::Int) = ForwardDiff.pickchunksize(x)
diff --git a/src/helpers.jl b/src/helpers.jl
deleted file mode 100644
index 8b1378917..000000000
--- a/src/helpers.jl
+++ /dev/null
@@ -1 +0,0 @@
-

From 0b1ce3a127bbc50275c5efb6580b9c0545602cb0 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 31 Oct 2024 12:29:21 -0400
Subject: [PATCH 668/700] fix: jacobian caching

---
 lib/NonlinearSolveBase/src/jacobian.jl | 25 ++++++++++++++++++-------
 test/core_tests.jl                     |  2 +-
 2 files changed, 19 insertions(+), 8 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/jacobian.jl b/lib/NonlinearSolveBase/src/jacobian.jl
index 73a544b8b..6ab31efd2 100644
--- a/lib/NonlinearSolveBase/src/jacobian.jl
+++ b/lib/NonlinearSolveBase/src/jacobian.jl
@@ -142,10 +142,16 @@ end
 ## Numbers
 function (cache::JacobianCache{<:Number})(::Number, u, p = cache.p)
     cache.stats.njacs += 1
-    SciMLBase.has_jac(cache.f) && return cache.f.jac(u, p)
-    SciMLBase.has_vjp(cache.f) && return cache.f.vjp(one(u), u, p)
-    SciMLBase.has_jvp(cache.f) && return cache.f.jvp(one(u), u, p)
-    return DI.derivative(cache.f, cache.di_extras, cache.autodiff, u, Constant(p))
+    cache.J = if SciMLBase.has_jac(cache.f)
+        cache.f.jac(u, p)
+    elseif SciMLBase.has_vjp(cache.f)
+        cache.f.vjp(one(u), u, p)
+    elseif SciMLBase.has_jvp(cache.f)
+        cache.f.jvp(one(u), u, p)
+    else
+        DI.derivative(cache.f, cache.di_extras, cache.autodiff, u, Constant(p))
+    end
+    return cache.J
 end
 
 ## Actually Compute the Jacobian
@@ -156,12 +162,17 @@ function (cache::JacobianCache)(J::Union{AbstractMatrix, Nothing}, u, p = cache.
             cache.f.jac(J, u, p)
         else
             DI.jacobian!(
-                cache.f, cache.fu, J, cache.di_extras, cache.autodiff, u, Constant(p))
+                cache.f, cache.fu, J, cache.di_extras, cache.autodiff, u, Constant(p)
+            )
         end
         return J
     else
-        SciMLBase.has_jac(cache.f) && return cache.f.jac(u, p)
-        return DI.jacobian(cache.f, cache.di_extras, cache.autodiff, u, Constant(p))
+        if SciMLBase.has_jac(cache.f)
+            cache.J = cache.f.jac(u, p)
+        else
+            cache.J = DI.jacobian(cache.f, cache.di_extras, cache.autodiff, u, Constant(p))
+        end
+        return cache.J
     end
 end
 
diff --git a/test/core_tests.jl b/test/core_tests.jl
index 301b0b389..65ed43ac8 100644
--- a/test/core_tests.jl
+++ b/test/core_tests.jl
@@ -4,7 +4,7 @@
     dataOut = f([1, 2, 3], nothing) + 0.1 * randn(10, 1)
 
     resid(x, p) = f(x, p) - dataOut
-    jac(x, p) = [dataIn .^ 2 dataIn ones(10, 1)]
+    jac(x, p) = [1:10 .^ 2 1:10 ones(10, 1)]
     x0 = [1, 1, 1]
 
     prob = NonlinearLeastSquaresProblem(resid, x0)

From fcee7a137aee5a5ee86736c046e2822ea520ec66 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 31 Oct 2024 12:31:36 -0400
Subject: [PATCH 669/700] chore: run formatter

---
 test/core_tests.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/core_tests.jl b/test/core_tests.jl
index 65ed43ac8..301b0b389 100644
--- a/test/core_tests.jl
+++ b/test/core_tests.jl
@@ -4,7 +4,7 @@
     dataOut = f([1, 2, 3], nothing) + 0.1 * randn(10, 1)
 
     resid(x, p) = f(x, p) - dataOut
-    jac(x, p) = [1:10 .^ 2 1:10 ones(10, 1)]
+    jac(x, p) = [dataIn .^ 2 dataIn ones(10, 1)]
     x0 = [1, 1, 1]
 
     prob = NonlinearLeastSquaresProblem(resid, x0)

From b3db1a2347a7d96d768ad225f864a81fb579d27f Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 31 Oct 2024 15:30:35 -0400
Subject: [PATCH 670/700] docs: add note to readme

---
 lib/SimpleNonlinearSolve/README.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/lib/SimpleNonlinearSolve/README.md b/lib/SimpleNonlinearSolve/README.md
index 3ef4868bb..bbf80f250 100644
--- a/lib/SimpleNonlinearSolve/README.md
+++ b/lib/SimpleNonlinearSolve/README.md
@@ -1,5 +1,8 @@
 # SimpleNonlinearSolve.jl
 
+> [!WARNING]
+> This package has been moved into a subpackage in NonlinearSolve (https://github.com/SciML/NonlinearSolve.jl/tree/master/lib/SimpleNonlinearSolve). Direct all questions and issues to NonlinearSolve.jl repository
+
 [![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
 [![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/NonlinearSolve/stable/)
 

From e2914bb417a2e2edfe4b6330426f07edc0cdbdc8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 31 Oct 2024 16:29:52 -0400
Subject: [PATCH 671/700] refactor!: move preconditioners inside linear solvers
 (#485)

* refactor!: move preconditioners inside linear solvers

* test: precs need concrete jacobian

* docs: fix references
---
 docs/src/native/solvers.md                    |  4 --
 docs/src/release_notes.md                     |  2 +
 docs/src/tutorials/large_systems.md           | 67 ++++++++-----------
 .../ext/NonlinearSolveBaseLinearSolveExt.jl   | 25 ++-----
 .../src/descent/damped_newton.jl              |  5 +-
 lib/NonlinearSolveBase/src/descent/dogleg.jl  | 10 +--
 lib/NonlinearSolveBase/src/descent/newton.jl  |  7 +-
 .../src/descent/steepest.jl                   |  4 +-
 lib/NonlinearSolveBase/src/jacobian.jl        |  3 +-
 lib/NonlinearSolveBase/src/linear_solve.jl    | 23 ++-----
 .../src/gauss_newton.jl                       |  6 +-
 .../src/levenberg_marquardt.jl                |  5 +-
 .../src/pseudo_transient.jl                   |  6 +-
 lib/NonlinearSolveFirstOrder/src/raphson.jl   |  6 +-
 .../src/trust_region.jl                       |  6 +-
 .../test/rootfind_tests.jl                    | 50 ++++++++------
 lib/NonlinearSolveQuasiNewton/src/klement.jl  |  6 +-
 src/polyalg.jl                                | 26 +++----
 18 files changed, 113 insertions(+), 148 deletions(-)

diff --git a/docs/src/native/solvers.md b/docs/src/native/solvers.md
index a3aa900e0..01583dda2 100644
--- a/docs/src/native/solvers.md
+++ b/docs/src/native/solvers.md
@@ -18,10 +18,6 @@ documentation.
     uses the LinearSolve.jl default algorithm choice. For more information on available
     algorithm choices, see the
     [LinearSolve.jl documentation](https://docs.sciml.ai/LinearSolve/stable/).
-  - `precs`: the choice of preconditioners for the linear solver. Defaults to using no
-    preconditioners. For more information on specifying preconditioners for LinearSolve
-    algorithms, consult the
-    [LinearSolve.jl documentation](https://docs.sciml.ai/LinearSolve/stable/).
   - `linesearch`: the line search algorithm to use. Defaults to
     [`NoLineSearch()`](@extref LineSearch.NoLineSearch), which means that no line search is
     performed.
diff --git a/docs/src/release_notes.md b/docs/src/release_notes.md
index bb0b5dec9..0d4ce25e8 100644
--- a/docs/src/release_notes.md
+++ b/docs/src/release_notes.md
@@ -5,6 +5,8 @@
 ### Breaking Changes in `NonlinearSolve.jl` v4
 
   - `ApproximateJacobianSolveAlgorithm` has been renamed to `QuasiNewtonAlgorithm`.
+  - Preconditioners for the linear solver needs to be specified with the linear solver
+    instead of `precs` keyword argument.
   - See [common breaking changes](@ref common-breaking-changes-v4v2) below.
 
 ### Breaking Changes in `SimpleNonlinearSolve.jl` v2
diff --git a/docs/src/tutorials/large_systems.md b/docs/src/tutorials/large_systems.md
index 0a0be59e7..434acb185 100644
--- a/docs/src/tutorials/large_systems.md
+++ b/docs/src/tutorials/large_systems.md
@@ -100,7 +100,8 @@ end
 
 u0 = init_brusselator_2d(xyd_brusselator)
 prob_brusselator_2d = NonlinearProblem(
-    brusselator_2d_loop, u0, p; abstol = 1e-10, reltol = 1e-10)
+    brusselator_2d_loop, u0, p; abstol = 1e-10, reltol = 1e-10
+)
 ```
 
 ## Choosing Jacobian Types
@@ -140,7 +141,8 @@ using SparseConnectivityTracer
 
 prob_brusselator_2d_autosparse = NonlinearProblem(
     NonlinearFunction(brusselator_2d_loop; sparsity = TracerSparsityDetector()),
-    u0, p; abstol = 1e-10, reltol = 1e-10)
+    u0, p; abstol = 1e-10, reltol = 1e-10
+)
 
 @btime solve(prob_brusselator_2d_autosparse,
     NewtonRaphson(; autodiff = AutoForwardDiff(; chunksize = 12)));
@@ -235,7 +237,7 @@ choices, see the
 
 Any [LinearSolve.jl-compatible preconditioner](https://docs.sciml.ai/LinearSolve/stable/basics/Preconditioners/)
 can be used as a preconditioner in the linear solver interface. To define preconditioners,
-one must define a `precs` function in compatible with nonlinear solvers which returns the
+one must define a `precs` function in compatible with linear solvers which returns the
 left and right preconditioners, matrices which approximate the inverse of `W = I - gamma*J`
 used in the solution of the ODE. An example of this with using
 [IncompleteLU.jl](https://github.com/haampie/IncompleteLU.jl) is as follows:
@@ -244,26 +246,18 @@ used in the solution of the ODE. An example of this with using
 # FIXME: On 1.10+ this is broken. Skipping this for now.
 using IncompleteLU
 
-function incompletelu(W, du, u, p, t, newW, Plprev, Prprev, solverdata)
-    if newW === nothing || newW
-        Pl = ilu(W, τ = 50.0)
-    else
-        Pl = Plprev
-    end
-    Pl, nothing
-end
+incompletelu(W, p = nothing) = ilu(W, τ = 50.0), LinearAlgebra.I
 
 @btime solve(prob_brusselator_2d_sparse,
-    NewtonRaphson(linsolve = KrylovJL_GMRES(), precs = incompletelu, concrete_jac = true));
+    NewtonRaphson(linsolve = KrylovJL_GMRES(precs = incompletelu), concrete_jac = true)
+);
 nothing # hide
 ```
 
 Notice a few things about this preconditioner. This preconditioner uses the sparse Jacobian,
 and thus we set `concrete_jac = true` to tell the algorithm to generate the Jacobian
-(otherwise, a Jacobian-free algorithm is used with GMRES by default). Then `newW = true`
-whenever a new `W` matrix is computed, and `newW = nothing` during the startup phase of the
-solver. Thus, we do a check `newW === nothing || newW` and when true, it's only at these
-points when we update the preconditioner, otherwise we just pass on the previous version.
+(otherwise, a Jacobian-free algorithm is used with GMRES by default).
+
 We use `convert(AbstractMatrix,W)` to get the concrete `W` matrix (matching `jac_prototype`,
 thus `SpraseMatrixCSC`) which we can use in the preconditioner's definition. Then we use
 `IncompleteLU.ilu` on that sparse matrix to generate the preconditioner. We return
@@ -279,39 +273,36 @@ which is more automatic. The setup is very similar to before:
 ```@example ill_conditioned_nlprob
 using AlgebraicMultigrid
 
-function algebraicmultigrid(W, du, u, p, t, newW, Plprev, Prprev, solverdata)
-    if newW === nothing || newW
-        Pl = aspreconditioner(ruge_stuben(convert(AbstractMatrix, W)))
-    else
-        Pl = Plprev
-    end
-    Pl, nothing
+function algebraicmultigrid(W, p = nothing)
+    return aspreconditioner(ruge_stuben(convert(AbstractMatrix, W))), LinearAlgebra.I
 end
 
 @btime solve(prob_brusselator_2d_sparse,
-    NewtonRaphson(linsolve = KrylovJL_GMRES(), precs = algebraicmultigrid,
-        concrete_jac = true));
+    NewtonRaphson(
+        linsolve = KrylovJL_GMRES(; precs = algebraicmultigrid), concrete_jac = true
+    )
+);
 nothing # hide
 ```
 
 or with a Jacobi smoother:
 
 ```@example ill_conditioned_nlprob
-function algebraicmultigrid2(W, du, u, p, t, newW, Plprev, Prprev, solverdata)
-    if newW === nothing || newW
-        A = convert(AbstractMatrix, W)
-        Pl = AlgebraicMultigrid.aspreconditioner(AlgebraicMultigrid.ruge_stuben(
-            A, presmoother = AlgebraicMultigrid.Jacobi(rand(size(A, 1))),
-            postsmoother = AlgebraicMultigrid.Jacobi(rand(size(A, 1)))))
-    else
-        Pl = Plprev
-    end
-    Pl, nothing
+function algebraicmultigrid2(W, p = nothing)
+    A = convert(AbstractMatrix, W)
+    Pl = AlgebraicMultigrid.aspreconditioner(AlgebraicMultigrid.ruge_stuben(
+        A, presmoother = AlgebraicMultigrid.Jacobi(rand(size(A, 1))),
+        postsmoother = AlgebraicMultigrid.Jacobi(rand(size(A, 1)))
+    ))
+    return Pl, LinearAlgebra.I
 end
 
-@btime solve(prob_brusselator_2d_sparse,
-    NewtonRaphson(linsolve = KrylovJL_GMRES(), precs = algebraicmultigrid2,
-        concrete_jac = true));
+@btime solve(
+    prob_brusselator_2d_sparse,
+    NewtonRaphson(
+        linsolve = KrylovJL_GMRES(precs = algebraicmultigrid2), concrete_jac = true
+    )
+);
 nothing # hide
 ```
 
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
index d1829804d..4a1234b25 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseLinearSolveExt.jl
@@ -11,8 +11,8 @@ using LinearAlgebra: ColumnNorm
 using NonlinearSolveBase: NonlinearSolveBase, LinearSolveJLCache, LinearSolveResult, Utils
 
 function (cache::LinearSolveJLCache)(;
-        A = nothing, b = nothing, linu = nothing, du = nothing, p = nothing,
-        cachedata = nothing, reuse_A_if_factorization = false, verbose = true, kwargs...
+        A = nothing, b = nothing, linu = nothing,
+        reuse_A_if_factorization = false, verbose = true, kwargs...
 )
     cache.stats.nsolve += 1
 
@@ -20,24 +20,6 @@ function (cache::LinearSolveJLCache)(;
     b !== nothing && setproperty!(cache.lincache, :b, b)
     linu !== nothing && NonlinearSolveBase.set_lincache_u!(cache, linu)
 
-    Plprev = cache.lincache.Pl
-    Prprev = cache.lincache.Pr
-
-    if cache.precs === nothing
-        Pl, Pr = nothing, nothing
-    else
-        Pl, Pr = cache.precs(
-            cache.lincache.A, du, linu, p, nothing,
-            A !== nothing, Plprev, Prprev, cachedata
-        )
-    end
-
-    if Pl !== nothing || Pr !== nothing
-        Pl, Pr = NonlinearSolveBase.wrap_preconditioners(Pl, Pr, linu)
-        cache.lincache.Pl = Pl
-        cache.lincache.Pr = Pr
-    end
-
     linres = solve!(cache.lincache)
     cache.lincache = linres.cache
     # Unfortunately LinearSolve.jl doesn't have the most uniform ReturnCode handling
@@ -58,7 +40,8 @@ function (cache::LinearSolveJLCache)(;
                 linprob = LinearProblem(A, b; u0 = linres.u)
                 cache.additional_lincache = init(
                     linprob, QRFactorization(ColumnNorm()); alias_u0 = false,
-                    alias_A = false, alias_b = false, cache.lincache.Pl, cache.lincache.Pr)
+                    alias_A = false, alias_b = false
+                )
             else
                 cache.additional_lincache.A = A
                 cache.additional_lincache.b = b
diff --git a/lib/NonlinearSolveBase/src/descent/damped_newton.jl b/lib/NonlinearSolveBase/src/descent/damped_newton.jl
index 47ed56207..f6523e399 100644
--- a/lib/NonlinearSolveBase/src/descent/damped_newton.jl
+++ b/lib/NonlinearSolveBase/src/descent/damped_newton.jl
@@ -1,7 +1,5 @@
 """
-    DampedNewtonDescent(;
-        linsolve = nothing, precs = nothing, initial_damping, damping_fn
-    )
+    DampedNewtonDescent(; linsolve = nothing, initial_damping, damping_fn)
 
 A Newton descent algorithm with damping. The damping factor is computed using the
 `damping_fn` function. The descent direction is computed as ``(JᵀJ + λDᵀD) δu = -fu``. For
@@ -20,7 +18,6 @@ The damping factor returned must be a non-negative number.
 """
 @kwdef @concrete struct DampedNewtonDescent <: AbstractDescentDirection
     linsolve = nothing
-    precs = nothing
     initial_damping
     damping_fn <: AbstractDampingFunction
 end
diff --git a/lib/NonlinearSolveBase/src/descent/dogleg.jl b/lib/NonlinearSolveBase/src/descent/dogleg.jl
index f446e9cf6..0eafbff74 100644
--- a/lib/NonlinearSolveBase/src/descent/dogleg.jl
+++ b/lib/NonlinearSolveBase/src/descent/dogleg.jl
@@ -1,5 +1,5 @@
 """
-    Dogleg(; linsolve = nothing, precs = nothing)
+    Dogleg(; linsolve = nothing)
 
 Switch between Newton's method and the steepest descent method depending on the size of the
 trust region. The trust region is specified via keyword argument `trust_region` to
@@ -15,18 +15,18 @@ end
 supports_trust_region(::Dogleg) = true
 get_linear_solver(alg::Dogleg) = get_linear_solver(alg.newton_descent)
 
-function Dogleg(; linsolve = nothing, precs = nothing, damping = Val(false),
+function Dogleg(; linsolve = nothing, damping = Val(false),
         damping_fn = missing, initial_damping = missing, kwargs...)
     if !Utils.unwrap_val(damping)
-        return Dogleg(NewtonDescent(; linsolve, precs), SteepestDescent(; linsolve, precs))
+        return Dogleg(NewtonDescent(; linsolve), SteepestDescent(; linsolve))
     end
     if damping_fn === missing || initial_damping === missing
         throw(ArgumentError("`damping_fn` and `initial_damping` must be supplied if \
                              `damping = Val(true)`."))
     end
     return Dogleg(
-        DampedNewtonDescent(; linsolve, precs, damping_fn, initial_damping),
-        SteepestDescent(; linsolve, precs)
+        DampedNewtonDescent(; linsolve, damping_fn, initial_damping),
+        SteepestDescent(; linsolve)
     )
 end
 
diff --git a/lib/NonlinearSolveBase/src/descent/newton.jl b/lib/NonlinearSolveBase/src/descent/newton.jl
index 810661507..a0aaa91d3 100644
--- a/lib/NonlinearSolveBase/src/descent/newton.jl
+++ b/lib/NonlinearSolveBase/src/descent/newton.jl
@@ -1,5 +1,5 @@
 """
-    NewtonDescent(; linsolve = nothing, precs = nothing)
+    NewtonDescent(; linsolve = nothing)
 
 Compute the descent direction as ``J δu = -fu``. For non-square Jacobian problems, this is
 commonly referred to as the Gauss-Newton Descent.
@@ -8,7 +8,6 @@ See also [`Dogleg`](@ref), [`SteepestDescent`](@ref), [`DampedNewtonDescent`](@r
 """
 @kwdef @concrete struct NewtonDescent <: AbstractDescentDirection
     linsolve = nothing
-    precs = nothing
 end
 
 supports_line_search(::NewtonDescent) = true
@@ -103,7 +102,7 @@ function InternalAPI.solve!(
             @static_timeit cache.timer "linear solve" begin
                 linres = cache.lincache(;
                     A = Utils.maybe_symmetric(cache.JᵀJ_cache), b = cache.Jᵀfu_cache,
-                    kwargs..., linu = Utils.safe_vec(δu), du = Utils.safe_vec(δu),
+                    kwargs..., linu = Utils.safe_vec(δu),
                     reuse_A_if_factorization = !new_jacobian || (idx !== Val(1))
                 )
             end
@@ -111,7 +110,7 @@ function InternalAPI.solve!(
             @static_timeit cache.timer "linear solve" begin
                 linres = cache.lincache(;
                     A = J, b = Utils.safe_vec(fu),
-                    kwargs..., linu = Utils.safe_vec(δu), du = Utils.safe_vec(δu),
+                    kwargs..., linu = Utils.safe_vec(δu),
                     reuse_A_if_factorization = !new_jacobian || idx !== Val(1)
                 )
             end
diff --git a/lib/NonlinearSolveBase/src/descent/steepest.jl b/lib/NonlinearSolveBase/src/descent/steepest.jl
index deb1a9817..247490957 100644
--- a/lib/NonlinearSolveBase/src/descent/steepest.jl
+++ b/lib/NonlinearSolveBase/src/descent/steepest.jl
@@ -1,5 +1,5 @@
 """
-    SteepestDescent(; linsolve = nothing, precs = nothing)
+    SteepestDescent(; linsolve = nothing)
 
 Compute the descent direction as ``δu = -Jᵀfu``. The linear solver and preconditioner are
 only used if `J` is provided in the inverted form.
@@ -8,7 +8,6 @@ See also [`Dogleg`](@ref), [`NewtonDescent`](@ref), [`DampedNewtonDescent`](@ref
 """
 @kwdef @concrete struct SteepestDescent <: AbstractDescentDirection
     linsolve = nothing
-    precs = nothing
 end
 
 supports_line_search(::SteepestDescent) = true
@@ -57,7 +56,6 @@ function InternalAPI.solve!(
         A = J === nothing ? nothing : transpose(J)
         linres = cache.lincache(;
             A, b = Utils.safe_vec(fu), kwargs..., linu = Utils.safe_vec(δu),
-            du = Utils.safe_vec(δu),
             reuse_A_if_factorization = !new_jacobian || idx !== Val(1)
         )
         δu = Utils.restructure(SciMLBase.get_du(cache, idx), linres.u)
diff --git a/lib/NonlinearSolveBase/src/jacobian.jl b/lib/NonlinearSolveBase/src/jacobian.jl
index 6ab31efd2..363b7b77a 100644
--- a/lib/NonlinearSolveBase/src/jacobian.jl
+++ b/lib/NonlinearSolveBase/src/jacobian.jl
@@ -29,8 +29,7 @@ Construct a cache for the Jacobian of `f` w.r.t. `u`.
   - `jvp_autodiff`: Automatic Differentiation or Finite Differencing backend for computing
     the Jacobian-vector product.
   - `linsolve`: Linear Solver Algorithm used to determine if we need a concrete jacobian
-    or if possible we can just use a [`SciMLJacobianOperators.JacobianOperator`](@ref)
-    instead.
+    or if possible we can just use a `JacobianOperator` instead.
 """
 function construct_jacobian_cache(
         prob, alg, f::NonlinearFunction, fu, u = prob.u0, p = prob.p; stats,
diff --git a/lib/NonlinearSolveBase/src/linear_solve.jl b/lib/NonlinearSolveBase/src/linear_solve.jl
index f3a2338c9..afe9c52d6 100644
--- a/lib/NonlinearSolveBase/src/linear_solve.jl
+++ b/lib/NonlinearSolveBase/src/linear_solve.jl
@@ -7,7 +7,6 @@ end
     lincache
     linsolve
     additional_lincache::Any
-    precs
     stats::NLStats
 end
 
@@ -34,8 +33,8 @@ handled:
 
 ```julia
 (cache::LinearSolverCache)(;
-    A = nothing, b = nothing, linu = nothing, du = nothing, p = nothing,
-    weight = nothing, cachedata = nothing, reuse_A_if_factorization = false, kwargs...)
+    A = nothing, b = nothing, linu = nothing, reuse_A_if_factorization = false, kwargs...
+)
 ```
 
 Returns the solution of the system `u` and stores the updated cache in `cache.lincache`.
@@ -60,15 +59,11 @@ aliasing arguments even after cache construction, i.e., if we passed in an `A` t
 not mutated, we do this by copying over `A` to a preconstructed cache.
 """
 function construct_linear_solver(alg, linsolve, A, b, u; stats, kwargs...)
-    no_preconditioner = !hasfield(typeof(alg), :precs) || alg.precs === nothing
-
     if (A isa Number && b isa Number) || (A isa Diagonal)
         return NativeJLLinearSolveCache(A, b, stats)
     elseif linsolve isa typeof(\)
-        !no_preconditioner &&
-            error("Default Julia Backsolve Operator `\\` doesn't support Preconditioners")
         return NativeJLLinearSolveCache(A, b, stats)
-    elseif no_preconditioner && linsolve === nothing
+    elseif linsolve === nothing
         if (A isa SMatrix || A isa WrappedArray{<:Any, <:SMatrix})
             return NativeJLLinearSolveCache(A, b, stats)
         end
@@ -78,17 +73,9 @@ function construct_linear_solver(alg, linsolve, A, b, u; stats, kwargs...)
     @bb u_cache = copy(u_fixed)
     linprob = LinearProblem(A, b; u0 = u_cache, kwargs...)
 
-    if no_preconditioner
-        precs, Pl, Pr = nothing, nothing, nothing
-    else
-        precs = alg.precs
-        Pl, Pr = precs(A, nothing, u, ntuple(Returns(nothing), 6)...)
-    end
-    Pl, Pr = wrap_preconditioners(Pl, Pr, u)
-
     # unlias here, we will later use these as caches
-    lincache = init(linprob, linsolve; alias_A = false, alias_b = false, Pl, Pr)
-    return LinearSolveJLCache(lincache, linsolve, nothing, precs, stats)
+    lincache = init(linprob, linsolve; alias_A = false, alias_b = false)
+    return LinearSolveJLCache(lincache, linsolve, nothing, stats)
 end
 
 function (cache::NativeJLLinearSolveCache)(;
diff --git a/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl b/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl
index 59b90b76e..081f1af27 100644
--- a/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl
+++ b/lib/NonlinearSolveFirstOrder/src/gauss_newton.jl
@@ -1,6 +1,6 @@
 """
     GaussNewton(;
-        concrete_jac = nothing, linsolve = nothing, linesearch = missing, precs = nothing,
+        concrete_jac = nothing, linsolve = nothing, linesearch = missing,
         autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
     )
 
@@ -9,12 +9,12 @@ matrices via colored automatic differentiation and preconditioned linear solvers
 for large-scale and numerically-difficult nonlinear systems.
 """
 function GaussNewton(;
-        concrete_jac = nothing, linsolve = nothing, linesearch = missing, precs = nothing,
+        concrete_jac = nothing, linsolve = nothing, linesearch = missing,
         autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
 )
     return GeneralizedFirstOrderAlgorithm(;
         linesearch,
-        descent = NewtonDescent(; linsolve, precs),
+        descent = NewtonDescent(; linsolve),
         autodiff, vjp_autodiff, jvp_autodiff,
         concrete_jac,
         name = :GaussNewton
diff --git a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
index f9c11ae28..66906fe9e 100644
--- a/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
+++ b/lib/NonlinearSolveFirstOrder/src/levenberg_marquardt.jl
@@ -1,6 +1,6 @@
 """
     LevenbergMarquardt(;
-        linsolve = nothing, precs = nothing,
+        linsolve = nothing,
         damping_initial::Real = 1.0, α_geodesic::Real = 0.75, disable_geodesic = Val(false),
         damping_increase_factor::Real = 2.0, damping_decrease_factor::Real = 3.0,
         finite_diff_step_geodesic = 0.1, b_uphill::Real = 1.0, min_damping_D::Real = 1e-8,
@@ -33,7 +33,7 @@ For the remaining arguments, see [`GeodesicAcceleration`](@ref) and
 [`NonlinearSolveFirstOrder.LevenbergMarquardtTrustRegion`](@ref) documentations.
 """
 function LevenbergMarquardt(;
-        linsolve = nothing, precs = nothing,
+        linsolve = nothing,
         damping_initial::Real = 1.0, α_geodesic::Real = 0.75, disable_geodesic = Val(false),
         damping_increase_factor::Real = 2.0, damping_decrease_factor::Real = 3.0,
         finite_diff_step_geodesic = 0.1, b_uphill::Real = 1.0, min_damping_D::Real = 1e-8,
@@ -41,7 +41,6 @@ function LevenbergMarquardt(;
 )
     descent = DampedNewtonDescent(;
         linsolve,
-        precs,
         initial_damping = damping_initial,
         damping_fn = LevenbergMarquardtDampingFunction(
             damping_increase_factor, damping_decrease_factor, min_damping_D
diff --git a/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl b/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
index a985cc100..0c1984f85 100644
--- a/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
+++ b/lib/NonlinearSolveFirstOrder/src/pseudo_transient.jl
@@ -1,7 +1,7 @@
 """
     PseudoTransient(;
         concrete_jac = nothing, linesearch = missing, alpha_initial = 1e-3,
-        linsolve = nothing, precs = nothing,
+        linsolve = nothing,
         autodiff = nothing, jvp_autodiff = nothing, vjp_autodiff = nothing
     )
 
@@ -19,13 +19,13 @@ This implementation specifically uses "switched evolution relaxation"
 """
 function PseudoTransient(;
         concrete_jac = nothing, linesearch = missing, alpha_initial = 1e-3,
-        linsolve = nothing, precs = nothing,
+        linsolve = nothing,
         autodiff = nothing, jvp_autodiff = nothing, vjp_autodiff = nothing
 )
     return GeneralizedFirstOrderAlgorithm(;
         linesearch,
         descent = DampedNewtonDescent(;
-            linsolve, precs, initial_damping = alpha_initial,
+            linsolve, initial_damping = alpha_initial,
             damping_fn = SwitchedEvolutionRelaxation()
         ),
         autodiff,
diff --git a/lib/NonlinearSolveFirstOrder/src/raphson.jl b/lib/NonlinearSolveFirstOrder/src/raphson.jl
index 5c14f10b7..d482f4846 100644
--- a/lib/NonlinearSolveFirstOrder/src/raphson.jl
+++ b/lib/NonlinearSolveFirstOrder/src/raphson.jl
@@ -1,6 +1,6 @@
 """
     NewtonRaphson(;
-        concrete_jac = nothing, linsolve = nothing, linesearch = missing, precs = nothing,
+        concrete_jac = nothing, linsolve = nothing, linesearch = missing,
         autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
     )
 
@@ -9,12 +9,12 @@ matrices via colored automatic differentiation and preconditioned linear solvers
 for large-scale and numerically-difficult nonlinear systems.
 """
 function NewtonRaphson(;
-        concrete_jac = nothing, linsolve = nothing, linesearch = missing, precs = nothing,
+        concrete_jac = nothing, linsolve = nothing, linesearch = missing,
         autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
 )
     return GeneralizedFirstOrderAlgorithm(;
         linesearch,
-        descent = NewtonDescent(; linsolve, precs),
+        descent = NewtonDescent(; linsolve),
         autodiff, vjp_autodiff, jvp_autodiff,
         concrete_jac,
         name = :NewtonRaphson
diff --git a/lib/NonlinearSolveFirstOrder/src/trust_region.jl b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
index 92d2655ac..03a1b3f9a 100644
--- a/lib/NonlinearSolveFirstOrder/src/trust_region.jl
+++ b/lib/NonlinearSolveFirstOrder/src/trust_region.jl
@@ -1,6 +1,6 @@
 """
     TrustRegion(;
-        concrete_jac = nothing, linsolve = nothing, precs = nothing,
+        concrete_jac = nothing, linsolve = nothing,
         radius_update_scheme = RadiusUpdateSchemes.Simple, max_trust_radius::Real = 0 // 1,
         initial_trust_radius::Real = 0 // 1, step_threshold::Real = 1 // 10000,
         shrink_threshold::Real = 1 // 4, expand_threshold::Real = 3 // 4,
@@ -23,7 +23,7 @@ For the remaining arguments, see [`NonlinearSolveFirstOrder.GenericTrustRegionSc
 documentation.
 """
 function TrustRegion(;
-        concrete_jac = nothing, linsolve = nothing, precs = nothing,
+        concrete_jac = nothing, linsolve = nothing,
         radius_update_scheme = RadiusUpdateSchemes.Simple, max_trust_radius::Real = 0 // 1,
         initial_trust_radius::Real = 0 // 1, step_threshold::Real = 1 // 10000,
         shrink_threshold::Real = 1 // 4, expand_threshold::Real = 3 // 4,
@@ -31,7 +31,7 @@ function TrustRegion(;
         max_shrink_times::Int = 32,
         autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
 )
-    descent = Dogleg(; linsolve, precs)
+    descent = Dogleg(; linsolve)
     trustregion = GenericTrustRegionScheme(;
         method = radius_update_scheme, step_threshold, shrink_threshold, expand_threshold,
         shrink_factor, expand_factor, initial_trust_radius, max_trust_radius
diff --git a/lib/NonlinearSolveFirstOrder/test/rootfind_tests.jl b/lib/NonlinearSolveFirstOrder/test/rootfind_tests.jl
index f554e02d6..3aa61b256 100644
--- a/lib/NonlinearSolveFirstOrder/test/rootfind_tests.jl
+++ b/lib/NonlinearSolveFirstOrder/test/rootfind_tests.jl
@@ -13,11 +13,6 @@ end
 
     u0s = ([1.0, 1.0], @SVector[1.0, 1.0], 1.0)
 
-    preconditioners = [
-        u0 -> nothing,
-        u0 -> ((args...) -> (Diagonal(rand!(similar(u0))), nothing))
-    ]
-
     @testset for ad in (AutoForwardDiff(), AutoZygote(), AutoFiniteDiff(), AutoEnzyme())
         @testset "$(nameof(typeof(linesearch)))" for linesearch in (
             LineSearchesJL(; method = LineSearches.Static(), autodiff = ad),
@@ -43,13 +38,22 @@ end
             @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
                 ad isa AutoZygote && continue
 
-                @testset for preconditioner in preconditioners,
-                    linsolve in (nothing, KrylovJL_GMRES(), \)
-
-                    precs = preconditioner(u0)
-                    typeof(linsolve) <: typeof(\) && precs !== nothing && continue
-
-                    solver = NewtonRaphson(; linsolve, precs, linesearch, autodiff = ad)
+                @testset for (concrete_jac, linsolve) in (
+                    (Val(false), nothing),
+                    (Val(false), KrylovJL_GMRES(; precs = nothing)),
+                    (
+                        Val(true),
+                        KrylovJL_GMRES(;
+                            precs = (A, p = nothing) -> (
+                                Diagonal(randn!(similar(A, size(A, 1)))), LinearAlgebra.I
+                            )
+                        )
+                    ),
+                    (Val(false), \)
+                )
+                    solver = NewtonRaphson(;
+                        linsolve, linesearch, autodiff = ad, concrete_jac
+                    )
 
                     sol = solve_iip(quadratic_f!, u0; solver)
                     @test SciMLBase.successful_retcode(sol)
@@ -115,14 +119,22 @@ end
         @testset "[IIP] u0: $(typeof(u0))" for u0 in ([1.0, 1.0],)
             ad isa AutoZygote && continue
 
-            @testset for preconditioner in preconditioners,
-                linsolve in (nothing, KrylovJL_GMRES(), \)
-
-                precs = preconditioner(u0)
-                typeof(linsolve) <: typeof(\) && precs !== nothing && continue
-
+            @testset for (concrete_jac, linsolve) in (
+                (Val(false), nothing),
+                (Val(false), KrylovJL_GMRES(; precs = nothing)),
+                (
+                    Val(true),
+                    KrylovJL_GMRES(;
+                        precs = (A, p = nothing) -> (
+                            Diagonal(randn!(similar(A, size(A, 1)))), LinearAlgebra.I
+                        )
+                    )
+                ),
+                (Val(false), \)
+            )
                 solver = PseudoTransient(;
-                    alpha_initial = 10.0, linsolve, precs, autodiff = ad)
+                    alpha_initial = 10.0, linsolve, autodiff = ad, concrete_jac
+                )
                 sol = solve_iip(quadratic_f!, u0; solver)
                 @test SciMLBase.successful_retcode(sol)
                 err = maximum(abs, quadratic_f(sol.u, 2.0))
diff --git a/lib/NonlinearSolveQuasiNewton/src/klement.jl b/lib/NonlinearSolveQuasiNewton/src/klement.jl
index 4bd09f45e..34ad7f6d5 100644
--- a/lib/NonlinearSolveQuasiNewton/src/klement.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/klement.jl
@@ -1,7 +1,7 @@
 """
     Klement(;
         max_resets = 100, linsolve = nothing, linesearch = nothing,
-        precs = nothing, alpha = nothing, init_jacobian::Val = Val(:identity),
+        alpha = nothing, init_jacobian::Val = Val(:identity),
         autodiff = nothing
     )
 
@@ -28,14 +28,14 @@ over this.
 """
 function Klement(;
         max_resets = 100, linsolve = nothing, linesearch = nothing,
-        precs = nothing, alpha = nothing, init_jacobian::Val = Val(:identity),
+        alpha = nothing, init_jacobian::Val = Val(:identity),
         autodiff = nothing
 )
     concrete_jac = Val(init_jacobian isa Val{:true_jacobian} ||
                        init_jacobian isa Val{:true_jacobian_diagonal})
     return QuasiNewtonAlgorithm(;
         linesearch,
-        descent = NewtonDescent(; linsolve, precs),
+        descent = NewtonDescent(; linsolve),
         update_rule = KlementUpdateRule(),
         reinit_rule = IllConditionedJacobianReset(),
         max_resets,
diff --git a/src/polyalg.jl b/src/polyalg.jl
index 5cf21d6e1..f16dd7e0e 100644
--- a/src/polyalg.jl
+++ b/src/polyalg.jl
@@ -322,7 +322,7 @@ end
     RobustMultiNewton(
         ::Type{T} = Float64;
         concrete_jac = nothing,
-        linsolve = nothing, precs = nothing,
+        linsolve = nothing,
         autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
     )
 
@@ -342,12 +342,14 @@ or more precision / more stable linear solver choice is required).
 function RobustMultiNewton(
         ::Type{T} = Float64;
         concrete_jac = nothing,
-        linsolve = nothing, precs = nothing,
+        linsolve = nothing,
         autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
 ) where {T}
-    common_kwargs = (; concrete_jac, linsolve, precs, autodiff, vjp_autodiff, jvp_autodiff)
+    common_kwargs = (; concrete_jac, linsolve, autodiff, vjp_autodiff, jvp_autodiff)
     if T <: Complex # Let's atleast have something here for complex numbers
-        algs = (NewtonRaphson(; common_kwargs...),)
+        algs = (
+            NewtonRaphson(; common_kwargs...),
+        )
     else
         algs = (
             TrustRegion(; common_kwargs...),
@@ -365,7 +367,7 @@ end
     FastShortcutNonlinearPolyalg(
         ::Type{T} = Float64;
         concrete_jac = nothing,
-        linsolve = nothing, precs = nothing,
+        linsolve = nothing,
         must_use_jacobian::Val = Val(false),
         prefer_simplenonlinearsolve::Val = Val(false),
         autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing,
@@ -389,14 +391,14 @@ for more performance and then tries more robust techniques if the faster ones fa
 function FastShortcutNonlinearPolyalg(
         ::Type{T} = Float64;
         concrete_jac = nothing,
-        linsolve = nothing, precs = nothing,
+        linsolve = nothing,
         must_use_jacobian::Val = Val(false),
         prefer_simplenonlinearsolve::Val = Val(false),
         autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing,
         u0_len::Union{Int, Nothing} = nothing
 ) where {T}
     start_index = 1
-    common_kwargs = (; concrete_jac, linsolve, precs, autodiff, vjp_autodiff, jvp_autodiff)
+    common_kwargs = (; concrete_jac, linsolve, autodiff, vjp_autodiff, jvp_autodiff)
     if must_use_jacobian isa Val{true}
         if T <: Complex
             algs = (NewtonRaphson(; common_kwargs...),)
@@ -436,7 +438,7 @@ function FastShortcutNonlinearPolyalg(
                 algs = (
                     Broyden(; autodiff),
                     Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
-                    Klement(; linsolve, precs, autodiff),
+                    Klement(; linsolve, autodiff),
                     NewtonRaphson(; common_kwargs...)
                 )
             else
@@ -445,7 +447,7 @@ function FastShortcutNonlinearPolyalg(
                 algs = (
                     Broyden(; autodiff),
                     Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
-                    Klement(; linsolve, precs, autodiff),
+                    Klement(; linsolve, autodiff),
                     NewtonRaphson(; common_kwargs...),
                     NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
                     TrustRegion(; common_kwargs...),
@@ -461,7 +463,7 @@ end
     FastShortcutNLLSPolyalg(
         ::Type{T} = Float64;
         concrete_jac = nothing,
-        linsolve = nothing, precs = nothing,
+        linsolve = nothing,
         autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
     )
 
@@ -476,10 +478,10 @@ for more performance and then tries more robust techniques if the faster ones fa
 function FastShortcutNLLSPolyalg(
         ::Type{T} = Float64;
         concrete_jac = nothing,
-        linsolve = nothing, precs = nothing,
+        linsolve = nothing,
         autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
 ) where {T}
-    common_kwargs = (; linsolve, precs, autodiff, vjp_autodiff, jvp_autodiff)
+    common_kwargs = (; linsolve, autodiff, vjp_autodiff, jvp_autodiff)
     if T <: Complex
         algs = (
             GaussNewton(; common_kwargs..., concrete_jac),

From eb3df11e1cfe6ecdd960369003370111575c4856 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 1 Nov 2024 09:30:54 -0400
Subject: [PATCH 672/700] fix: remove the common files (#486)

---
 common/nlls_problem_workloads.jl              | 26 ------------
 common/nonlinear_problem_workloads.jl         | 12 ------
 .../src/NonlinearSolveFirstOrder.jl           | 41 ++++++++++++++++--
 .../src/NonlinearSolveQuasiNewton.jl          | 14 ++++++-
 .../src/NonlinearSolveSpectralMethods.jl      | 14 ++++++-
 src/NonlinearSolve.jl                         | 42 +++++++++++++++++--
 6 files changed, 100 insertions(+), 49 deletions(-)
 delete mode 100644 common/nlls_problem_workloads.jl
 delete mode 100644 common/nonlinear_problem_workloads.jl

diff --git a/common/nlls_problem_workloads.jl b/common/nlls_problem_workloads.jl
deleted file mode 100644
index 0d7c0f7ef..000000000
--- a/common/nlls_problem_workloads.jl
+++ /dev/null
@@ -1,26 +0,0 @@
-using SciMLBase: NonlinearLeastSquaresProblem, NonlinearFunction, NoSpecialize
-
-nonlinear_functions = (
-    (NonlinearFunction{false, NoSpecialize}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
-    (
-        NonlinearFunction{false, NoSpecialize}((u, p) -> vcat(u .* u .- p, u .* u .- p)),
-        [0.1, 0.1]
-    ),
-    (
-        NonlinearFunction{true, NoSpecialize}(
-            (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(1)
-        ),
-        [0.1, 0.0]
-    ),
-    (
-        NonlinearFunction{true, NoSpecialize}(
-            (du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p), resid_prototype = zeros(4)
-        ),
-        [0.1, 0.1]
-    )
-)
-
-nlls_problems = NonlinearLeastSquaresProblem[]
-for (fn, u0) in nonlinear_functions
-    push!(nlls_problems, NonlinearLeastSquaresProblem(fn, u0, 2.0))
-end
diff --git a/common/nonlinear_problem_workloads.jl b/common/nonlinear_problem_workloads.jl
deleted file mode 100644
index 43d0de29a..000000000
--- a/common/nonlinear_problem_workloads.jl
+++ /dev/null
@@ -1,12 +0,0 @@
-using SciMLBase: NonlinearProblem, NonlinearFunction, NoSpecialize
-
-nonlinear_functions = (
-    (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), 0.1),
-    (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), [0.1]),
-    (NonlinearFunction{true, NoSpecialize}((du, u, p) -> du .= u .* u .- p), [0.1])
-)
-
-nonlinear_problems = NonlinearProblem[]
-for (fn, u0) in nonlinear_functions
-    push!(nonlinear_problems, NonlinearProblem(fn, u0, 2.0))
-end
diff --git a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
index b611b9051..145468122 100644
--- a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
+++ b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
@@ -22,7 +22,9 @@ using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
                           update_trace!, L2_NORM,
                           NewtonDescent, DampedNewtonDescent, GeodesicAcceleration,
                           Dogleg
-using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode, NonlinearFunction
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode,
+                 NonlinearFunction,
+                 NonlinearLeastSquaresProblem, NonlinearProblem, NoSpecialize
 using SciMLJacobianOperators: VecJacOperator, JacVecOperator, StatefulJacobianOperator
 
 using FiniteDiff: FiniteDiff    # Default Finite Difference Method
@@ -37,8 +39,41 @@ include("pseudo_transient.jl")
 include("solve.jl")
 
 @setup_workload begin
-    include("../../../common/nonlinear_problem_workloads.jl")
-    include("../../../common/nlls_problem_workloads.jl")
+    nonlinear_functions = (
+        (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), 0.1),
+        (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), [0.1]),
+        (NonlinearFunction{true, NoSpecialize}((du, u, p) -> du .= u .* u .- p), [0.1])
+    )
+
+    nonlinear_problems = NonlinearProblem[]
+    for (fn, u0) in nonlinear_functions
+        push!(nonlinear_problems, NonlinearProblem(fn, u0, 2.0))
+    end
+
+    nonlinear_functions = (
+        (NonlinearFunction{false, NoSpecialize}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
+        (
+            NonlinearFunction{false, NoSpecialize}((u, p) -> vcat(u .* u .- p, u .* u .- p)),
+            [0.1, 0.1]
+        ),
+        (
+            NonlinearFunction{true, NoSpecialize}(
+                (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(1)
+            ),
+            [0.1, 0.0]
+        ),
+        (
+            NonlinearFunction{true, NoSpecialize}(
+                (du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p), resid_prototype = zeros(4)
+            ),
+            [0.1, 0.1]
+        )
+    )
+
+    nlls_problems = NonlinearLeastSquaresProblem[]
+    for (fn, u0) in nonlinear_functions
+        push!(nlls_problems, NonlinearLeastSquaresProblem(fn, u0, 2.0))
+    end
 
     nlp_algs = [NewtonRaphson(), TrustRegion(), LevenbergMarquardt()]
     nlls_algs = [GaussNewton(), TrustRegion(), LevenbergMarquardt()]
diff --git a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
index 3b63615e8..02bbc865f 100644
--- a/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/NonlinearSolveQuasiNewton.jl
@@ -20,7 +20,8 @@ using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
                           AbstractApproximateJacobianUpdateRuleCache,
                           Utils, InternalAPI, get_timer_output, @static_timeit,
                           update_trace!, L2_NORM, NewtonDescent
-using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode,
+                 NonlinearProblem, NonlinearFunction, NoSpecialize
 using SciMLOperators: AbstractSciMLOperator
 
 include("reset_conditions.jl")
@@ -34,7 +35,16 @@ include("klement.jl")
 include("solve.jl")
 
 @setup_workload begin
-    include("../../../common/nonlinear_problem_workloads.jl")
+    nonlinear_functions = (
+        (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), 0.1),
+        (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), [0.1]),
+        (NonlinearFunction{true, NoSpecialize}((du, u, p) -> du .= u .* u .- p), [0.1])
+    )
+
+    nonlinear_problems = NonlinearProblem[]
+    for (fn, u0) in nonlinear_functions
+        push!(nonlinear_problems, NonlinearProblem(fn, u0, 2.0))
+    end
 
     algs = [Broyden(), Klement()]
 
diff --git a/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl b/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
index 8872fce35..49949e438 100644
--- a/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
+++ b/lib/NonlinearSolveSpectralMethods/src/NonlinearSolveSpectralMethods.jl
@@ -11,14 +11,24 @@ using MaybeInplace: @bb
 using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
                           AbstractNonlinearSolveCache, Utils, InternalAPI, get_timer_output,
                           @static_timeit, update_trace!
-using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode
+using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode,
+                 NonlinearProblem, NonlinearFunction, NoSpecialize
 
 include("dfsane.jl")
 
 include("solve.jl")
 
 @setup_workload begin
-    include("../../../common/nonlinear_problem_workloads.jl")
+    nonlinear_functions = (
+        (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), 0.1),
+        (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), [0.1]),
+        (NonlinearFunction{true, NoSpecialize}((du, u, p) -> du .= u .* u .- p), [0.1])
+    )
+
+    nonlinear_problems = NonlinearProblem[]
+    for (fn, u0) in nonlinear_functions
+        push!(nonlinear_problems, NonlinearProblem(fn, u0, 2.0))
+    end
 
     algs = [DFSane()]
 
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 7d6ac7b09..a3e8bb6ca 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -16,8 +16,9 @@ using NonlinearSolveBase: NonlinearSolveBase, InternalAPI, AbstractNonlinearSolv
                           enable_timer_outputs, disable_timer_outputs
 
 using Preferences: set_preferences!
-using SciMLBase: SciMLBase, NLStats, ReturnCode, AbstractNonlinearProblem, NonlinearProblem,
-                 NonlinearLeastSquaresProblem
+using SciMLBase: SciMLBase, NLStats, ReturnCode, AbstractNonlinearProblem,
+                 NonlinearFunction,
+                 NonlinearProblem, NonlinearLeastSquaresProblem, NoSpecialize
 using SymbolicIndexingInterface: SymbolicIndexingInterface
 using StaticArraysCore: StaticArray
 
@@ -63,8 +64,41 @@ const ALL_SOLVER_TYPES = [
 include("forward_diff.jl")
 
 @setup_workload begin
-    include("../common/nonlinear_problem_workloads.jl")
-    include("../common/nlls_problem_workloads.jl")
+    nonlinear_functions = (
+        (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), 0.1),
+        (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), [0.1]),
+        (NonlinearFunction{true, NoSpecialize}((du, u, p) -> du .= u .* u .- p), [0.1])
+    )
+
+    nonlinear_problems = NonlinearProblem[]
+    for (fn, u0) in nonlinear_functions
+        push!(nonlinear_problems, NonlinearProblem(fn, u0, 2.0))
+    end
+
+    nonlinear_functions = (
+        (NonlinearFunction{false, NoSpecialize}((u, p) -> (u .^ 2 .- p)[1:1]), [0.1, 0.0]),
+        (
+            NonlinearFunction{false, NoSpecialize}((u, p) -> vcat(u .* u .- p, u .* u .- p)),
+            [0.1, 0.1]
+        ),
+        (
+            NonlinearFunction{true, NoSpecialize}(
+                (du, u, p) -> du[1] = u[1] * u[1] - p, resid_prototype = zeros(1)
+            ),
+            [0.1, 0.0]
+        ),
+        (
+            NonlinearFunction{true, NoSpecialize}(
+                (du, u, p) -> du .= vcat(u .* u .- p, u .* u .- p), resid_prototype = zeros(4)
+            ),
+            [0.1, 0.1]
+        )
+    )
+
+    nlls_problems = NonlinearLeastSquaresProblem[]
+    for (fn, u0) in nonlinear_functions
+        push!(nlls_problems, NonlinearLeastSquaresProblem(fn, u0, 2.0))
+    end
 
     @compile_workload begin
         @sync begin

From 6b0002b7b8cda2524a6211663d03fa64df42fa17 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 1 Nov 2024 14:51:53 -0400
Subject: [PATCH 673/700] fix: hessian (#489)

* fix: hessian through nonlinear solvers

* feat: extend gradient support for cached nlls
---
 Project.toml                                  |   2 +-
 lib/NonlinearSolveBase/Project.toml           |   2 +-
 .../ext/NonlinearSolveBaseForwardDiffExt.jl   | 100 ++----------------
 .../src/NonlinearSolveBase.jl                 |   4 +-
 lib/NonlinearSolveBase/src/autodiff.jl        |  62 +++++++++++
 lib/NonlinearSolveBase/src/public.jl          |   1 +
 src/forward_diff.jl                           |  12 ++-
 test/forward_ad_tests.jl                      |  94 ++++++++++++++++
 8 files changed, 177 insertions(+), 100 deletions(-)

diff --git a/Project.toml b/Project.toml
index 845611499..93643123b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -89,7 +89,7 @@ NLSolvers = "0.5"
 NLsolve = "4.5"
 NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1"
+NonlinearSolveBase = "1.2"
 NonlinearSolveFirstOrder = "1"
 NonlinearSolveQuasiNewton = "1"
 NonlinearSolveSpectralMethods = "1"
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 4abb81cde..e7ed5851f 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolveBase"
 uuid = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.1.0"
+version = "1.2.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
index 0b16391c4..bb3165396 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
@@ -6,7 +6,6 @@ using CommonSolve: solve
 using DifferentiationInterface: DifferentiationInterface
 using FastClosures: @closure
 using ForwardDiff: ForwardDiff, Dual
-using LinearAlgebra: mul!
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, IntervalNonlinearProblem,
                  NonlinearProblem, NonlinearLeastSquaresProblem, remake
 
@@ -20,11 +19,14 @@ function NonlinearSolveBase.additional_incompatible_backend_check(
 end
 
 Utils.value(::Type{Dual{T, V, N}}) where {T, V, N} = V
-Utils.value(x::Dual) = Utils.value(ForwardDiff.value(x))
+Utils.value(x::Dual) = ForwardDiff.value(x)
 Utils.value(x::AbstractArray{<:Dual}) = Utils.value.(x)
 
 function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
-        prob::Union{IntervalNonlinearProblem, NonlinearProblem, ImmutableNonlinearProblem},
+        prob::Union{
+            IntervalNonlinearProblem, NonlinearProblem,
+            ImmutableNonlinearProblem, NonlinearLeastSquaresProblem
+        },
         alg, args...; kwargs...
 )
     p = Utils.value(prob.p)
@@ -35,98 +37,14 @@ function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
         newprob = remake(prob; p, u0 = Utils.value(prob.u0))
     end
 
-    sol = solve(newprob, alg, args...; kwargs...)
-
-    uu = sol.u
-    Jₚ = NonlinearSolveBase.nonlinearsolve_∂f_∂p(prob, prob.f, uu, p)
-    Jᵤ = NonlinearSolveBase.nonlinearsolve_∂f_∂u(prob, prob.f, uu, p)
-    z = -Jᵤ \ Jₚ
-    pp = prob.p
-    sumfun = ((z, p),) -> map(Base.Fix2(*, ForwardDiff.partials(p)), z)
-
-    if uu isa Number
-        partials = sum(sumfun, zip(z, pp))
-    elseif p isa Number
-        partials = sumfun((z, pp))
-    else
-        partials = sum(sumfun, zip(eachcol(z), pp))
-    end
-
-    return sol, partials
-end
-
-function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
-        prob::NonlinearLeastSquaresProblem, alg, args...; kwargs...
-)
-    p = Utils.value(prob.p)
-    newprob = remake(prob; p, u0 = Utils.value(prob.u0))
     sol = solve(newprob, alg, args...; kwargs...)
     uu = sol.u
 
-    # First check for custom `vjp` then custom `Jacobian` and if nothing is provided use
-    # nested autodiff as the last resort
-    if SciMLBase.has_vjp(prob.f)
-        if SciMLBase.isinplace(prob)
-            vjp_fn = @closure (du, u, p) -> begin
-                resid = Utils.safe_similar(du, length(sol.resid))
-                prob.f(resid, u, p)
-                prob.f.vjp(du, resid, u, p)
-                du .*= 2
-                return nothing
-            end
-        else
-            vjp_fn = @closure (u, p) -> begin
-                resid = prob.f(u, p)
-                return reshape(2 .* prob.f.vjp(resid, u, p), size(u))
-            end
-        end
-    elseif SciMLBase.has_jac(prob.f)
-        if SciMLBase.isinplace(prob)
-            vjp_fn = @closure (du, u, p) -> begin
-                J = Utils.safe_similar(du, length(sol.resid), length(u))
-                prob.f.jac(J, u, p)
-                resid = Utils.safe_similar(du, length(sol.resid))
-                prob.f(resid, u, p)
-                mul!(reshape(du, 1, :), vec(resid)', J, 2, false)
-                return nothing
-            end
-        else
-            vjp_fn = @closure (u, p) -> begin
-                return reshape(2 .* vec(prob.f(u, p))' * prob.f.jac(u, p), size(u))
-            end
-        end
-    else
-        # For small problems, nesting ForwardDiff is actually quite fast
-        autodiff = length(uu) + length(sol.resid) ≥ 50 ?
-                   NonlinearSolveBase.select_reverse_mode_autodiff(prob, nothing) :
-                   AutoForwardDiff()
-
-        if SciMLBase.isinplace(prob)
-            vjp_fn = @closure (du, u, p) -> begin
-                resid = Utils.safe_similar(du, length(sol.resid))
-                prob.f(resid, u, p)
-                # Using `Constant` lead to dual ordering issues
-                ff = @closure (du, u) -> prob.f(du, u, p)
-                resid2 = copy(resid)
-                DI.pullback!(ff, resid2, (du,), autodiff, u, (resid,))
-                @. du *= 2
-                return nothing
-            end
-        else
-            vjp_fn = @closure (u, p) -> begin
-                v = prob.f(u, p)
-                # Using `Constant` lead to dual ordering issues
-                ff = Base.Fix2(prob.f, p)
-                res = only(DI.pullback(ff, autodiff, u, (v,)))
-                ArrayInterface.can_setindex(res) || return 2 .* res
-                @. res *= 2
-                return res
-            end
-        end
-    end
+    fn = prob isa NonlinearLeastSquaresProblem ?
+         NonlinearSolveBase.nlls_generate_vjp_function(prob, sol, uu) : prob.f
 
-    Jₚ = NonlinearSolveBase.nonlinearsolve_∂f_∂p(prob, vjp_fn, uu, newprob.p)
-    Jᵤ = NonlinearSolveBase.nonlinearsolve_∂f_∂u(prob, vjp_fn, uu, newprob.p)
+    Jₚ = NonlinearSolveBase.nonlinearsolve_∂f_∂p(prob, fn, uu, p)
+    Jᵤ = NonlinearSolveBase.nonlinearsolve_∂f_∂u(prob, fn, uu, p)
     z = -Jᵤ \ Jₚ
     pp = prob.p
     sumfun = ((z, p),) -> map(Base.Fix2(*, ForwardDiff.partials(p)), z)
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index a08384677..412f6a748 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -5,7 +5,7 @@ using ConcreteStructs: @concrete
 using FastClosures: @closure
 using Preferences: @load_preference, @set_preferences!
 
-using ADTypes: ADTypes, AbstractADType, AutoSparse, NoSparsityDetector,
+using ADTypes: ADTypes, AbstractADType, AutoSparse, AutoForwardDiff, NoSparsityDetector,
                KnownJacobianSparsityDetector
 using Adapt: WrappedArray
 using ArrayInterface: ArrayInterface
@@ -25,7 +25,7 @@ using SciMLJacobianOperators: JacobianOperator, StatefulJacobianOperator
 using SciMLOperators: AbstractSciMLOperator, IdentityOperator
 using SymbolicIndexingInterface: SymbolicIndexingInterface
 
-using LinearAlgebra: LinearAlgebra, Diagonal, norm, ldiv!, diagind
+using LinearAlgebra: LinearAlgebra, Diagonal, norm, ldiv!, diagind, mul!
 using Markdown: @doc_str
 using Printf: @printf
 
diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
index 395580924..f70e9770b 100644
--- a/lib/NonlinearSolveBase/src/autodiff.jl
+++ b/lib/NonlinearSolveBase/src/autodiff.jl
@@ -128,3 +128,65 @@ end
 is_finite_differences_backend(ad::AbstractADType) = false
 is_finite_differences_backend(::ADTypes.AutoFiniteDiff) = true
 is_finite_differences_backend(::ADTypes.AutoFiniteDifferences) = true
+
+function nlls_generate_vjp_function(prob::NonlinearLeastSquaresProblem, sol, uu)
+    # First check for custom `vjp` then custom `Jacobian` and if nothing is provided use
+    # nested autodiff as the last resort
+    if SciMLBase.has_vjp(prob.f)
+        if SciMLBase.isinplace(prob)
+            return @closure (du, u, p) -> begin
+                resid = Utils.safe_similar(du, length(sol.resid))
+                prob.f.vjp(resid, u, p)
+                prob.f.vjp(du, resid, u, p)
+                du .*= 2
+                return nothing
+            end
+        else
+            return @closure (u, p) -> begin
+                resid = prob.f(u, p)
+                return reshape(2 .* prob.f.vjp(resid, u, p), size(u))
+            end
+        end
+    elseif SciMLBase.has_jac(prob.f)
+        if SciMLBase.isinplace(prob)
+            return @closure (du, u, p) -> begin
+                J = Utils.safe_similar(du, length(sol.resid), length(u))
+                prob.f.jac(J, u, p)
+                resid = Utils.safe_similar(du, length(sol.resid))
+                prob.f(resid, u, p)
+                mul!(reshape(du, 1, :), vec(resid)', J, 2, false)
+                return nothing
+            end
+        else
+            return @closure (u, p) -> begin
+                return reshape(2 .* vec(prob.f(u, p))' * prob.f.jac(u, p), size(u))
+            end
+        end
+    else
+        # For small problems, nesting ForwardDiff is actually quite fast
+        autodiff = length(uu) + length(sol.resid) ≥ 50 ?
+                   select_reverse_mode_autodiff(prob, nothing) : AutoForwardDiff()
+
+        if SciMLBase.isinplace(prob)
+            return @closure (du, u, p) -> begin
+                resid = Utils.safe_similar(du, length(sol.resid))
+                prob.f(resid, u, p)
+                # Using `Constant` lead to dual ordering issues
+                ff = @closure (du, u) -> prob.f(du, u, p)
+                resid2 = copy(resid)
+                DI.pullback!(ff, resid2, (du,), autodiff, u, (resid,))
+                @. du *= 2
+                return nothing
+            end
+        else
+            return @closure (u, p) -> begin
+                v = prob.f(u, p)
+                # Using `Constant` lead to dual ordering issues
+                res = only(DI.pullback(Base.Fix2(prob.f, p), autodiff, u, (v,)))
+                ArrayInterface.can_setindex(res) || return 2 .* res
+                @. res *= 2
+                return res
+            end
+        end
+    end
+end
diff --git a/lib/NonlinearSolveBase/src/public.jl b/lib/NonlinearSolveBase/src/public.jl
index 2101f4274..d076f7873 100644
--- a/lib/NonlinearSolveBase/src/public.jl
+++ b/lib/NonlinearSolveBase/src/public.jl
@@ -10,6 +10,7 @@ function nonlinearsolve_forwarddiff_solve end
 function nonlinearsolve_dual_solution end
 function nonlinearsolve_∂f_∂p end
 function nonlinearsolve_∂f_∂u end
+function nlls_generate_vjp_function end
 
 # Nonlinear Solve Termination Conditions
 abstract type AbstractNonlinearTerminationMode end
diff --git a/src/forward_diff.jl b/src/forward_diff.jl
index 410e818c3..d34bca877 100644
--- a/src/forward_diff.jl
+++ b/src/forward_diff.jl
@@ -48,9 +48,8 @@ function InternalAPI.reinit!(
 end
 
 for algType in ALL_SOLVER_TYPES
-    # XXX: Extend to DualNonlinearLeastSquaresProblem
     @eval function SciMLBase.__init(
-            prob::DualNonlinearProblem, alg::$(algType), args...; kwargs...
+            prob::DualAbstractNonlinearProblem, alg::$(algType), args...; kwargs...
     )
         p = nodual_value(prob.p)
         newprob = SciMLBase.remake(prob; u0 = nodual_value(prob.u0), p)
@@ -64,10 +63,13 @@ end
 function CommonSolve.solve!(cache::NonlinearSolveForwardDiffCache)
     sol = solve!(cache.cache)
     prob = cache.prob
-
     uu = sol.u
-    Jₚ = NonlinearSolveBase.nonlinearsolve_∂f_∂p(prob, prob.f, uu, cache.values_p)
-    Jᵤ = NonlinearSolveBase.nonlinearsolve_∂f_∂u(prob, prob.f, uu, cache.values_p)
+
+    fn = prob isa NonlinearLeastSquaresProblem ?
+         NonlinearSolveBase.nlls_generate_vjp_function(prob, sol, uu) : prob.f
+
+    Jₚ = NonlinearSolveBase.nonlinearsolve_∂f_∂p(prob, fn, uu, cache.values_p)
+    Jᵤ = NonlinearSolveBase.nonlinearsolve_∂f_∂u(prob, fn, uu, cache.values_p)
 
     z_arr = -Jᵤ \ Jₚ
 
diff --git a/test/forward_ad_tests.jl b/test/forward_ad_tests.jl
index dcd1c2e3a..942d66c9b 100644
--- a/test/forward_ad_tests.jl
+++ b/test/forward_ad_tests.jl
@@ -124,3 +124,97 @@ end
         end
     end
 end
+
+@testitem "NLLS Hessian SciML/NonlinearSolve.jl#445" tags=[:core] begin
+    using ForwardDiff, FiniteDiff
+
+    function objfn(F, init, params)
+        th1, th2 = init
+        px, py, l1, l2 = params
+        F[1] = l1 * cos(th1) + l2 * cos(th1 + th2) - px
+        F[2] = l1 * sin(th1) + l2 * sin(th1 + th2) - py
+        return F
+    end
+
+    function solve_nlprob(pxpy)
+        px, py = pxpy
+        theta1 = pi / 4
+        theta2 = pi / 4
+        initial_guess = [theta1; theta2]
+        l1 = 60
+        l2 = 60
+        p = [px; py; l1; l2]
+        prob = NonlinearLeastSquaresProblem(
+            NonlinearFunction(objfn, resid_prototype = zeros(2)),
+            initial_guess, p
+        )
+        resu = solve(
+            prob,
+            reltol = 1e-12, abstol = 1e-12
+        )
+        th1, th2 = resu.u
+        cable1_base = [-90; 0; 0]
+        cable2_base = [-150; 0; 0]
+        cable3_base = [150; 0; 0]
+        cable1_top = [l1 * cos(th1) / 2; l1 * sin(th1) / 2; 0]
+        cable23_top = [l1 * cos(th1) + l2 * cos(th1 + th2) / 2;
+                       l1 * sin(th1) + l2 * sin(th1 + th2) / 2; 0]
+        c1_length = sqrt((cable1_top[1] - cable1_base[1])^2 +
+                         (cable1_top[2] - cable1_base[2])^2)
+        c2_length = sqrt((cable23_top[1] - cable2_base[1])^2 +
+                         (cable23_top[2] - cable2_base[2])^2)
+        c3_length = sqrt((cable23_top[1] - cable3_base[1])^2 +
+                         (cable23_top[2] - cable3_base[2])^2)
+        return c1_length + c2_length + c3_length
+    end
+
+    grad1 = ForwardDiff.gradient(solve_nlprob, [34.0, 87.0])
+    grad2 = FiniteDiff.finite_difference_gradient(solve_nlprob, [34.0, 87.0])
+
+    @test grad1≈grad2 atol=1e-3
+
+    hess1 = ForwardDiff.hessian(solve_nlprob, [34.0, 87.0])
+    hess2 = FiniteDiff.finite_difference_hessian(solve_nlprob, [34.0, 87.0])
+
+    @test hess1≈hess2 atol=1e-3
+
+    function solve_nlprob_with_cache(pxpy)
+        px, py = pxpy
+        theta1 = pi / 4
+        theta2 = pi / 4
+        initial_guess = [theta1; theta2]
+        l1 = 60
+        l2 = 60
+        p = [px; py; l1; l2]
+        prob = NonlinearLeastSquaresProblem(
+            NonlinearFunction(objfn, resid_prototype = zeros(2)),
+            initial_guess, p
+        )
+        cache = init(prob; reltol = 1e-12, abstol = 1e-12)
+        resu = solve!(cache)
+        th1, th2 = resu.u
+        cable1_base = [-90; 0; 0]
+        cable2_base = [-150; 0; 0]
+        cable3_base = [150; 0; 0]
+        cable1_top = [l1 * cos(th1) / 2; l1 * sin(th1) / 2; 0]
+        cable23_top = [l1 * cos(th1) + l2 * cos(th1 + th2) / 2;
+                       l1 * sin(th1) + l2 * sin(th1 + th2) / 2; 0]
+        c1_length = sqrt((cable1_top[1] - cable1_base[1])^2 +
+                         (cable1_top[2] - cable1_base[2])^2)
+        c2_length = sqrt((cable23_top[1] - cable2_base[1])^2 +
+                         (cable23_top[2] - cable2_base[2])^2)
+        c3_length = sqrt((cable23_top[1] - cable3_base[1])^2 +
+                         (cable23_top[2] - cable3_base[2])^2)
+        return c1_length + c2_length + c3_length
+    end
+
+    grad1 = ForwardDiff.gradient(solve_nlprob_with_cache, [34.0, 87.0])
+    grad2 = FiniteDiff.finite_difference_gradient(solve_nlprob_with_cache, [34.0, 87.0])
+
+    @test grad1≈grad2 atol=1e-3
+
+    hess1 = ForwardDiff.hessian(solve_nlprob_with_cache, [34.0, 87.0])
+    hess2 = FiniteDiff.finite_difference_hessian(solve_nlprob_with_cache, [34.0, 87.0])
+
+    @test hess1≈hess2 atol=1e-3
+end

From 5c722c0b5c96c36b54d3a4856dcb12d8c4b50885 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 1 Nov 2024 16:19:25 -0400
Subject: [PATCH 674/700] ci: run windows tests with a single worker (#490)

* ci: run windows tests with a single worker

* test: try fixing more mac tests

* test: div by zero

* test: add retries to guard against segfaults
---
 lib/NonlinearSolveFirstOrder/test/runtests.jl      |  6 ++++--
 lib/NonlinearSolveQuasiNewton/test/runtests.jl     |  6 ++++--
 lib/NonlinearSolveSpectralMethods/test/runtests.jl |  6 ++++--
 test/23_test_problems_tests.jl                     | 13 +++++++++++--
 test/runtests.jl                                   |  6 ++++--
 test/wrappers/least_squares_tests.jl               |  2 +-
 test/wrappers/rootfind_tests.jl                    |  6 +++---
 7 files changed, 31 insertions(+), 14 deletions(-)

diff --git a/lib/NonlinearSolveFirstOrder/test/runtests.jl b/lib/NonlinearSolveFirstOrder/test/runtests.jl
index d19d33de8..504529eab 100644
--- a/lib/NonlinearSolveFirstOrder/test/runtests.jl
+++ b/lib/NonlinearSolveFirstOrder/test/runtests.jl
@@ -5,12 +5,14 @@ using ReTestItems, NonlinearSolveFirstOrder, Hwloc, InteractiveUtils, Pkg
 const GROUP = lowercase(get(ENV, "GROUP", "All"))
 
 const RETESTITEMS_NWORKERS = parse(
-    Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4)))
+    Int, get(ENV, "RETESTITEMS_NWORKERS",
+        string(min(ifelse(Sys.iswindows(), 0, Hwloc.num_physical_cores()), 4))
+    )
 )
 const RETESTITEMS_NWORKER_THREADS = parse(Int,
     get(
         ENV, "RETESTITEMS_NWORKER_THREADS",
-        string(max(Hwloc.num_virtual_cores() ÷ RETESTITEMS_NWORKERS, 1))
+        string(max(Hwloc.num_virtual_cores() ÷ max(RETESTITEMS_NWORKERS, 1), 1))
     )
 )
 
diff --git a/lib/NonlinearSolveQuasiNewton/test/runtests.jl b/lib/NonlinearSolveQuasiNewton/test/runtests.jl
index 807441bbc..0f8eaba49 100644
--- a/lib/NonlinearSolveQuasiNewton/test/runtests.jl
+++ b/lib/NonlinearSolveQuasiNewton/test/runtests.jl
@@ -5,12 +5,14 @@ using ReTestItems, NonlinearSolveQuasiNewton, Hwloc, InteractiveUtils, Pkg
 const GROUP = lowercase(get(ENV, "GROUP", "All"))
 
 const RETESTITEMS_NWORKERS = parse(
-    Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4)))
+    Int, get(ENV, "RETESTITEMS_NWORKERS",
+        string(min(ifelse(Sys.iswindows(), 0, Hwloc.num_physical_cores()), 4))
+    )
 )
 const RETESTITEMS_NWORKER_THREADS = parse(Int,
     get(
         ENV, "RETESTITEMS_NWORKER_THREADS",
-        string(max(Hwloc.num_virtual_cores() ÷ RETESTITEMS_NWORKERS, 1))
+        string(max(Hwloc.num_virtual_cores() ÷ max(RETESTITEMS_NWORKERS, 1), 1))
     )
 )
 
diff --git a/lib/NonlinearSolveSpectralMethods/test/runtests.jl b/lib/NonlinearSolveSpectralMethods/test/runtests.jl
index 5256e0e6f..e254158b3 100644
--- a/lib/NonlinearSolveSpectralMethods/test/runtests.jl
+++ b/lib/NonlinearSolveSpectralMethods/test/runtests.jl
@@ -5,12 +5,14 @@ using ReTestItems, NonlinearSolveSpectralMethods, Hwloc, InteractiveUtils, Pkg
 const GROUP = lowercase(get(ENV, "GROUP", "All"))
 
 const RETESTITEMS_NWORKERS = parse(
-    Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4)))
+    Int, get(ENV, "RETESTITEMS_NWORKERS",
+        string(min(ifelse(Sys.iswindows(), 0, Hwloc.num_physical_cores()), 4))
+    )
 )
 const RETESTITEMS_NWORKER_THREADS = parse(Int,
     get(
         ENV, "RETESTITEMS_NWORKER_THREADS",
-        string(max(Hwloc.num_virtual_cores() ÷ RETESTITEMS_NWORKERS, 1))
+        string(max(Hwloc.num_virtual_cores() ÷ max(RETESTITEMS_NWORKERS, 1), 1))
     )
 )
 
diff --git a/test/23_test_problems_tests.jl b/test/23_test_problems_tests.jl
index 8fa4c47b6..35e17e52b 100644
--- a/test/23_test_problems_tests.jl
+++ b/test/23_test_problems_tests.jl
@@ -120,7 +120,11 @@ end
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
     broken_tests[alg_ops[1]] = [1, 2, 3, 5, 21]
     if Sys.isapple()
-        broken_tests[alg_ops[2]] = [1, 2, 3, 5, 6, 21]
+        if VERSION ≥ v"1.11-"
+            broken_tests[alg_ops[2]] = [1, 2, 3, 5, 6, 11, 21]
+        else
+            broken_tests[alg_ops[2]] = [1, 2, 3, 5, 6, 21]
+        end
     else
         broken_tests[alg_ops[2]] = [1, 2, 3, 5, 6, 11, 21]
     end
@@ -143,11 +147,16 @@ end
     if Sys.isapple()
         broken_tests[alg_ops[1]] = [1, 5, 11]
         broken_tests[alg_ops[3]] = [1, 5, 6, 9, 11]
+        if VERSION ≥ v"1.11-"
+            broken_tests[alg_ops[5]] = [1, 4, 5, 11]
+        else
+            broken_tests[alg_ops[5]] = [1, 5, 11]
+        end
     else
         broken_tests[alg_ops[1]] = [1, 5, 11, 15]
         broken_tests[alg_ops[3]] = [1, 5, 9, 11, 16]
+        broken_tests[alg_ops[5]] = [1, 5, 11]
     end
-    broken_tests[alg_ops[5]] = [1, 5, 11]
 
     test_on_library(problems, dicts, alg_ops, broken_tests, Sys.isapple() ? 1e-3 : 1e-4)
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 59a43c2f9..c8e8b0f4e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -10,12 +10,14 @@ const EXTRA_PKGS = Pkg.PackageSpec[]
 length(EXTRA_PKGS) ≥ 1 && Pkg.add(EXTRA_PKGS)
 
 const RETESTITEMS_NWORKERS = parse(
-    Int, get(ENV, "RETESTITEMS_NWORKERS", string(min(Hwloc.num_physical_cores(), 4)))
+    Int, get(ENV, "RETESTITEMS_NWORKERS",
+        string(min(ifelse(Sys.iswindows(), 0, Hwloc.num_physical_cores()), 4))
+    )
 )
 const RETESTITEMS_NWORKER_THREADS = parse(Int,
     get(
         ENV, "RETESTITEMS_NWORKER_THREADS",
-        string(max(Hwloc.num_virtual_cores() ÷ RETESTITEMS_NWORKERS, 1))
+        string(max(Hwloc.num_virtual_cores() ÷ max(RETESTITEMS_NWORKERS, 1), 1))
     )
 )
 
diff --git a/test/wrappers/least_squares_tests.jl b/test/wrappers/least_squares_tests.jl
index 99d3e0ef3..effef126e 100644
--- a/test/wrappers/least_squares_tests.jl
+++ b/test/wrappers/least_squares_tests.jl
@@ -83,7 +83,7 @@ end
 
         push!(solvers, FastLevenbergMarquardtJL(linsolve; autodiff))
     end
-    if Sys.isapple()
+    if !Sys.isapple()
         for method in (:auto, :lm, :lmdif)
             push!(solvers, CMINPACK(; method))
         end
diff --git a/test/wrappers/rootfind_tests.jl b/test/wrappers/rootfind_tests.jl
index 073d31fe4..654194e26 100644
--- a/test/wrappers/rootfind_tests.jl
+++ b/test/wrappers/rootfind_tests.jl
@@ -1,4 +1,4 @@
-@testitem "Steady State Problems" tags=[:wrappers] begin
+@testitem "Steady State Problems" tags=[:wrappers] retries=3 begin
     import NLSolvers, NLsolve, SIAMFANLEquations, MINPACK, PETSc
 
     function f_iip(du, u, p, t)
@@ -43,7 +43,7 @@
     end
 end
 
-@testitem "Nonlinear Root Finding Problems" tags=[:wrappers] begin
+@testitem "Nonlinear Root Finding Problems" tags=[:wrappers] retries=3 begin
     using LinearAlgebra
     import NLSolvers, NLsolve, SIAMFANLEquations, MINPACK, PETSc
 
@@ -163,7 +163,7 @@ end
     end
 end
 
-@testitem "PETSc SNES Floating Points" tags=[:wrappers] skip=:(Sys.iswindows()) begin
+@testitem "PETSc SNES Floating Points" tags=[:wrappers] retries=3 skip=:(Sys.iswindows()) begin
     import PETSc
 
     f(u, p) = u .* u .- 2

From 3ed48f82b6610710d3f7e621d2affab253591181 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Fri, 1 Nov 2024 17:37:31 -0400
Subject: [PATCH 675/700] fix: reinit! on forwarddiff cache (#491)

---
 src/forward_diff.jl      |  3 +--
 test/forward_ad_tests.jl | 31 +++++++++++++++++++++++++++++++
 2 files changed, 32 insertions(+), 2 deletions(-)

diff --git a/src/forward_diff.jl b/src/forward_diff.jl
index d34bca877..5bb98561c 100644
--- a/src/forward_diff.jl
+++ b/src/forward_diff.jl
@@ -37,10 +37,9 @@ function InternalAPI.reinit!(
         cache::NonlinearSolveForwardDiffCache, args...;
         p = cache.p, u0 = NonlinearSolveBase.get_u(cache.cache), kwargs...
 )
-    inner_cache = InternalAPI.reinit!(
+    InternalAPI.reinit!(
         cache.cache; p = nodual_value(p), u0 = nodual_value(u0), kwargs...
     )
-    cache.cache = inner_cache
     cache.p = p
     cache.values_p = nodual_value(p)
     cache.partials_p = ForwardDiff.partials(p)
diff --git a/test/forward_ad_tests.jl b/test/forward_ad_tests.jl
index 942d66c9b..f3cf74bae 100644
--- a/test/forward_ad_tests.jl
+++ b/test/forward_ad_tests.jl
@@ -218,3 +218,34 @@ end
 
     @test hess1≈hess2 atol=1e-3
 end
+
+@testitem "reinit! on ForwardDiff cache SciML/NonlinearSolve.jl#391" tags=[:core] begin
+    using ForwardDiff
+
+    function multiple_solves(ps::Vector)
+        res = similar(ps, 4, length(ps))
+        for (i, p) in enumerate(ps)
+            prob = NonlinearProblem{false}((u, p) -> u .* u .- p, rand(4), ps[i])
+            sol = solve(prob)
+            res[:, i] .= sol.u
+        end
+        return sum(abs2, res)
+    end
+
+    function multiple_solves_cached(ps::Vector)
+        res = similar(ps, 4, length(ps))
+        prob = NonlinearProblem{false}((u, p) -> u .* u .- p, rand(4), ps[1])
+        cache = init(prob, NewtonRaphson())
+        for (i, p) in enumerate(ps)
+            reinit!(cache; p)
+            sol = solve!(cache)
+            res[:, i] .= sol.u
+        end
+        return sum(abs2, res)
+    end
+
+    ps = collect(1.0:5.0)
+
+    @test ForwardDiff.gradient(multiple_solves, ps) ≈
+          ForwardDiff.gradient(multiple_solves_cached, ps)
+end

From 037a07cbdc41c886c1a8fd807d31a3e2eae56ec8 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Mon, 4 Nov 2024 10:26:57 -0500
Subject: [PATCH 676/700] chore: update cff file

---
 CITATION.cff | 18 ++++++++++++++++--
 README.md    |  2 +-
 2 files changed, 17 insertions(+), 3 deletions(-)

diff --git a/CITATION.cff b/CITATION.cff
index 6f2e735fc..487624559 100644
--- a/CITATION.cff
+++ b/CITATION.cff
@@ -4,10 +4,24 @@ authors:
 - family-names: "Pal"
   given-names: "Avik"
   orcid: "https://orcid.org/0000-0002-3938-7375"
+- family-names: "Holtorf"
+  given-names: "Flemming"
+- family-names: "Larsson"
+  given-names: "Axel"
+- family-names: "Loman"
+  given-names: "Torkel"
+- family-names: "Rajput"
+  given-names: "Utkarsh"
+- family-names: "Schaefer"
+  given-names: "Frank"
+- family-names: "Qu"
+  given-names: "Qingyu"
+- family-names: "Edelman"
+  given-names: "Alan"
 - family-names: "Rackauckas"
   given-names: "Chris"
 title: "NonlinearSolve.jl"
-version: 3.1.1
+version: 4.0.0
 doi: 10.5281/zenodo.10397607
-date-released: 2023-12-17
+date-released: 2024-11-0.3
 url: "https://github.com/SciML/NonlinearSolve.jl"
diff --git a/README.md b/README.md
index 096a0c216..344c6d9a2 100644
--- a/README.md
+++ b/README.md
@@ -43,7 +43,7 @@ If you found this library to be useful in academic work, then please cite:
 ```bibtex
 @article{pal2024nonlinearsolve,
   title={NonlinearSolve. jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia},
-  author={Pal, Avik and Holtorf, Flemming and Larsson, Axel and Loman, Torkel and Schaefer, Frank and Qu, Qingyu and Edelman, Alan and Rackauckas, Chris and others},
+  author={Pal, Avik and Holtorf, Flemming and Larsson, Axel and Loman, Torkel and Schaefer, Frank and Qu, Qingyu and Edelman, Alan and Rackauckas, Chris},
   journal={arXiv preprint arXiv:2403.16341},
   year={2024}
 }

From 6f043bfd5e342a36b43678b8e10bd4ea81a52a95 Mon Sep 17 00:00:00 2001
From: Qingyu Qu <52615090+ErikQQY@users.noreply.github.com>
Date: Wed, 6 Nov 2024 21:51:11 +0800
Subject: [PATCH 677/700] refactor: Move NonlinearSolvePolyAlgorithm to Base
 (#494)

* refactor: Move NonlinearSolvePolyAlgorithm to Base

* test: Make NonlinearSolve use 1.3 Base

* refactor: Remove unnecessary snippet

* refactor: Don't use duplicate solve

* refactor: Test Base export NonlinearSolvePolyAlgorithm
---
 Project.toml                                  |   2 +-
 lib/NonlinearSolveBase/Project.toml           |   2 +-
 .../src/NonlinearSolveBase.jl                 |   3 +
 lib/NonlinearSolveBase/src/polyalg.jl         | 202 +++++++
 lib/NonlinearSolveBase/src/solve.jl           | 158 +++++
 src/NonlinearSolve.jl                         |   5 +-
 src/poly_algs.jl                              | 184 ++++++
 src/polyalg.jl                                | 545 ------------------
 8 files changed, 552 insertions(+), 549 deletions(-)
 create mode 100644 lib/NonlinearSolveBase/src/polyalg.jl
 create mode 100644 src/poly_algs.jl
 delete mode 100644 src/polyalg.jl

diff --git a/Project.toml b/Project.toml
index 93643123b..3b0172faa 100644
--- a/Project.toml
+++ b/Project.toml
@@ -89,7 +89,7 @@ NLSolvers = "0.5"
 NLsolve = "4.5"
 NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1.2"
+NonlinearSolveBase = "1.3"
 NonlinearSolveFirstOrder = "1"
 NonlinearSolveQuasiNewton = "1"
 NonlinearSolveSpectralMethods = "1"
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index e7ed5851f..ae16dfd93 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolveBase"
 uuid = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.2.0"
+version = "1.3.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 412f6a748..649ac79d2 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -47,6 +47,7 @@ include("linear_solve.jl")
 include("timer_outputs.jl")
 include("tracing.jl")
 include("wrappers.jl")
+include("polyalg.jl")
 
 include("descent/common.jl")
 include("descent/newton.jl")
@@ -81,4 +82,6 @@ export RelTerminationMode, AbsTerminationMode,
 export DescentResult, SteepestDescent, NewtonDescent, DampedNewtonDescent, Dogleg,
        GeodesicAcceleration
 
+export NonlinearSolvePolyAlgorithm
+
 end
diff --git a/lib/NonlinearSolveBase/src/polyalg.jl b/lib/NonlinearSolveBase/src/polyalg.jl
new file mode 100644
index 000000000..54b61998f
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/polyalg.jl
@@ -0,0 +1,202 @@
+"""
+    NonlinearSolvePolyAlgorithm(algs; start_index::Int = 1)
+
+A general way to define PolyAlgorithms for `NonlinearProblem` and
+`NonlinearLeastSquaresProblem`. This is a container for a tuple of algorithms that will be
+tried in order until one succeeds. If none succeed, then the algorithm with the lowest
+residual is returned.
+
+### Arguments
+
+  - `algs`: a tuple of algorithms to try in-order! (If this is not a Tuple, then the
+    returned algorithm is not type-stable).
+
+### Keyword Arguments
+
+  - `start_index`: the index to start at. Defaults to `1`.
+
+### Example
+
+```julia
+using NonlinearSolve
+
+alg = NonlinearSolvePolyAlgorithm((NewtonRaphson(), Broyden()))
+```
+"""
+@concrete struct NonlinearSolvePolyAlgorithm <: AbstractNonlinearSolveAlgorithm
+    static_length <: Val
+    algs <: Tuple
+    start_index::Int
+end
+
+function NonlinearSolvePolyAlgorithm(algs; start_index::Int = 1)
+    @assert 0 < start_index ≤ length(algs)
+    algs = Tuple(algs)
+    return NonlinearSolvePolyAlgorithm(Val(length(algs)), algs, start_index)
+end
+
+@concrete mutable struct NonlinearSolvePolyAlgorithmCache <: AbstractNonlinearSolveCache
+    static_length <: Val
+    prob <: AbstractNonlinearProblem
+
+    caches <: Tuple
+    alg <: NonlinearSolvePolyAlgorithm
+
+    best::Int
+    current::Int
+    nsteps::Int
+
+    stats::NLStats
+    total_time::Float64
+    maxtime
+
+    retcode::ReturnCode.T
+    force_stop::Bool
+
+    maxiters::Int
+    internalnorm
+
+    u0
+    u0_aliased
+    alias_u0::Bool
+end
+
+function SII.symbolic_container(cache::NonlinearSolvePolyAlgorithmCache)
+    return cache.caches[cache.current]
+end
+SII.state_values(cache::NonlinearSolvePolyAlgorithmCache) = cache.u0
+
+function Base.show(io::IO, ::MIME"text/plain", cache::NonlinearSolvePolyAlgorithmCache)
+    println(io, "NonlinearSolvePolyAlgorithmCache with \
+                 $(Utils.unwrap_val(cache.static_length)) algorithms:")
+    best_alg = ifelse(cache.best == -1, "nothing", cache.best)
+    println(io, "    Best Algorithm: $(best_alg)")
+    println(
+        io, "    Current Algorithm: [$(cache.current) / $(Utils.unwrap_val(cache.static_length))]"
+    )
+    println(io, "    nsteps: $(cache.nsteps)")
+    println(io, "    retcode: $(cache.retcode)")
+    print(io, "    Current Cache: ")
+    NonlinearSolveBase.show_nonlinearsolve_cache(io, cache.caches[cache.current], 4)
+end
+
+function InternalAPI.reinit!(
+        cache::NonlinearSolvePolyAlgorithmCache, args...; p = cache.p, u0 = cache.u0
+)
+    foreach(cache.caches) do cache
+        InternalAPI.reinit!(cache, args...; p, u0)
+    end
+    cache.current = cache.alg.start_index
+    InternalAPI.reinit!(cache.stats)
+    cache.nsteps = 0
+    cache.total_time = 0.0
+end
+
+function SciMLBase.__init(
+        prob::AbstractNonlinearProblem, alg::NonlinearSolvePolyAlgorithm, args...;
+        stats = NLStats(0, 0, 0, 0, 0), maxtime = nothing, maxiters = 1000,
+        internalnorm = L2_NORM, alias_u0 = false, verbose = true, kwargs...
+)
+    if alias_u0 && !ArrayInterface.ismutable(prob.u0)
+        verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
+                          immutable (checked using `ArrayInterface.ismutable`)."
+        alias_u0 = false  # If immutable don't care about aliasing
+    end
+
+    u0 = prob.u0
+    u0_aliased = alias_u0 ? copy(u0) : u0
+    alias_u0 && (prob = SciMLBase.remake(prob; u0 = u0_aliased))
+
+    return NonlinearSolvePolyAlgorithmCache(
+        alg.static_length, prob,
+        map(alg.algs) do solver
+            SciMLBase.__init(
+                prob, solver, args...;
+                stats, maxtime, internalnorm, alias_u0, verbose, kwargs...
+            )
+        end,
+        alg, -1, alg.start_index, 0, stats, 0.0, maxtime,
+        ReturnCode.Default, false, maxiters, internalnorm,
+        u0, u0_aliased, alias_u0
+    )
+end
+
+@generated function InternalAPI.step!(
+        cache::NonlinearSolvePolyAlgorithmCache{Val{N}}, args...; kwargs...
+) where {N}
+    calls = []
+    cache_syms = [gensym("cache") for i in 1:N]
+    for i in 1:N
+        push!(calls,
+            quote
+                $(cache_syms[i]) = cache.caches[$(i)]
+                if $(i) == cache.current
+                    InternalAPI.step!($(cache_syms[i]), args...; kwargs...)
+                    $(cache_syms[i]).nsteps += 1
+                    if !NonlinearSolveBase.not_terminated($(cache_syms[i]))
+                        if SciMLBase.successful_retcode($(cache_syms[i]).retcode)
+                            cache.best = $(i)
+                            cache.force_stop = true
+                            cache.retcode = $(cache_syms[i]).retcode
+                        else
+                            cache.current = $(i + 1)
+                        end
+                    end
+                    return
+                end
+            end)
+    end
+
+    push!(calls, quote
+        if !(1 ≤ cache.current ≤ length(cache.caches))
+            minfu, idx = findmin_caches(cache.prob, cache.caches)
+            cache.best = idx
+            cache.retcode = cache.caches[idx].retcode
+            cache.force_stop = true
+            return
+        end
+    end)
+
+    return Expr(:block, calls...)
+end
+
+# Original is often determined on runtime information especially for PolyAlgorithms so it
+# is best to never specialize on that
+function build_solution_less_specialize(
+        prob::AbstractNonlinearProblem, alg, u, resid;
+        retcode = ReturnCode.Default, original = nothing, left = nothing,
+        right = nothing, stats = nothing, trace = nothing, kwargs...
+)
+    return SciMLBase.NonlinearSolution{
+        eltype(eltype(u)), ndims(u), typeof(u), typeof(resid), typeof(prob),
+        typeof(alg), Any, typeof(left), typeof(stats), typeof(trace)
+    }(
+        u, resid, prob, alg, retcode, original, left, right, stats, trace
+    )
+end
+
+function findmin_caches(prob::AbstractNonlinearProblem, caches)
+    resids = map(caches) do cache
+        cache === nothing && return nothing
+        return NonlinearSolveBase.get_fu(cache)
+    end
+    return findmin_resids(prob, resids)
+end
+
+@views function findmin_resids(prob::AbstractNonlinearProblem, caches)
+    norm_fn = prob isa NonlinearLeastSquaresProblem ? Base.Fix2(norm, 2) :
+              Base.Fix2(norm, Inf)
+    idx = findfirst(Base.Fix2(!==, nothing), caches)
+    # This is an internal function so we assume that inputs are consistent and there is
+    # atleast one non-`nothing` value
+    fx_idx = norm_fn(caches[idx])
+    idx == length(caches) && return fx_idx, idx
+    fmin = @closure xᵢ -> begin
+        xᵢ === nothing && return oftype(fx_idx, Inf)
+        fx = norm_fn(xᵢ)
+        return ifelse(isnan(fx), oftype(fx, Inf), fx)
+    end
+    x_min, x_min_idx = findmin(fmin, caches[(idx + 1):length(caches)])
+    x_min < fx_idx && return x_min, x_min_idx + idx
+    return fx_idx, idx
+end
diff --git a/lib/NonlinearSolveBase/src/solve.jl b/lib/NonlinearSolveBase/src/solve.jl
index 08b60e4db..76d765d7b 100644
--- a/lib/NonlinearSolveBase/src/solve.jl
+++ b/lib/NonlinearSolveBase/src/solve.jl
@@ -31,6 +31,164 @@ function CommonSolve.solve!(cache::AbstractNonlinearSolveCache)
     )
 end
 
+@generated function CommonSolve.solve!(cache::NonlinearSolvePolyAlgorithmCache{Val{N}}) where {N}
+    calls = [quote
+        1 ≤ cache.current ≤ $(N) || error("Current choices shouldn't get here!")
+    end]
+
+    cache_syms = [gensym("cache") for i in 1:N]
+    sol_syms = [gensym("sol") for i in 1:N]
+    u_result_syms = [gensym("u_result") for i in 1:N]
+
+    for i in 1:N
+        push!(calls,
+            quote
+                $(cache_syms[i]) = cache.caches[$(i)]
+                if $(i) == cache.current
+                    cache.alias_u0 && copyto!(cache.u0_aliased, cache.u0)
+                    $(sol_syms[i]) = CommonSolve.solve!($(cache_syms[i]))
+                    if SciMLBase.successful_retcode($(sol_syms[i]))
+                        stats = $(sol_syms[i]).stats
+                        if cache.alias_u0
+                            copyto!(cache.u0, $(sol_syms[i]).u)
+                            $(u_result_syms[i]) = cache.u0
+                        else
+                            $(u_result_syms[i]) = $(sol_syms[i]).u
+                        end
+                        fu = NonlinearSolveBase.get_fu($(cache_syms[i]))
+                        return build_solution_less_specialize(
+                            cache.prob, cache.alg, $(u_result_syms[i]), fu;
+                            retcode = $(sol_syms[i]).retcode, stats,
+                            original = $(sol_syms[i]), trace = $(sol_syms[i]).trace
+                        )
+                    elseif cache.alias_u0
+                        # For safety we need to maintain a copy of the solution
+                        $(u_result_syms[i]) = copy($(sol_syms[i]).u)
+                    end
+                    cache.current = $(i + 1)
+                end
+            end)
+    end
+
+    resids = map(Base.Fix2(Symbol, :resid), cache_syms)
+    for (sym, resid) in zip(cache_syms, resids)
+        push!(calls, :($(resid) = @isdefined($(sym)) ? $(sym).resid : nothing))
+    end
+    push!(calls, quote
+        fus = tuple($(Tuple(resids)...))
+        minfu, idx = findmin_caches(cache.prob, fus)
+    end)
+    for i in 1:N
+        push!(calls,
+            quote
+                if idx == $(i)
+                    u = cache.alias_u0 ? $(u_result_syms[i]) :
+                        NonlinearSolveBase.get_u(cache.caches[$(i)])
+                end
+            end)
+    end
+    push!(calls,
+        quote
+            retcode = cache.caches[idx].retcode
+            if cache.alias_u0
+                copyto!(cache.u0, u)
+                u = cache.u0
+            end
+            return build_solution_less_specialize(
+                cache.prob, cache.alg, u, fus[idx];
+                retcode, cache.stats, cache.caches[idx].trace
+            )
+        end)
+
+    return Expr(:block, calls...)
+end
+
+@generated function SciMLBase.__solve(
+        prob::AbstractNonlinearProblem, alg::NonlinearSolvePolyAlgorithm{Val{N}}, args...;
+        stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, verbose = true, kwargs...
+) where {N}
+    sol_syms = [gensym("sol") for _ in 1:N]
+    prob_syms = [gensym("prob") for _ in 1:N]
+    u_result_syms = [gensym("u_result") for _ in 1:N]
+    calls = [quote
+        current = alg.start_index
+        if alias_u0 && !ArrayInterface.ismutable(prob.u0)
+            verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
+                              immutable (checked using `ArrayInterface.ismutable`)."
+            alias_u0 = false  # If immutable don't care about aliasing
+        end
+        u0 = prob.u0
+        u0_aliased = alias_u0 ? zero(u0) : u0
+    end]
+    for i in 1:N
+        cur_sol = sol_syms[i]
+        push!(calls,
+            quote
+                if current == $(i)
+                    if alias_u0
+                        copyto!(u0_aliased, u0)
+                        $(prob_syms[i]) = SciMLBase.remake(prob; u0 = u0_aliased)
+                    else
+                        $(prob_syms[i]) = prob
+                    end
+                    $(cur_sol) = SciMLBase.__solve(
+                        $(prob_syms[i]), alg.algs[$(i)], args...;
+                        stats, alias_u0, verbose, kwargs...
+                    )
+                    if SciMLBase.successful_retcode($(cur_sol))
+                        if alias_u0
+                            copyto!(u0, $(cur_sol).u)
+                            $(u_result_syms[i]) = u0
+                        else
+                            $(u_result_syms[i]) = $(cur_sol).u
+                        end
+                        return build_solution_less_specialize(
+                            prob, alg, $(u_result_syms[i]), $(cur_sol).resid;
+                            $(cur_sol).retcode, $(cur_sol).stats,
+                            $(cur_sol).trace, original = $(cur_sol)
+                        )
+                    elseif alias_u0
+                        # For safety we need to maintain a copy of the solution
+                        $(u_result_syms[i]) = copy($(cur_sol).u)
+                    end
+                    current = $(i + 1)
+                end
+            end)
+    end
+
+    resids = map(Base.Fix2(Symbol, :resid), sol_syms)
+    for (sym, resid) in zip(sol_syms, resids)
+        push!(calls, :($(resid) = @isdefined($(sym)) ? $(sym).resid : nothing))
+    end
+
+    push!(calls, quote
+        resids = tuple($(Tuple(resids)...))
+        minfu, idx = findmin_resids(prob, resids)
+    end)
+
+    for i in 1:N
+        push!(calls,
+            quote
+                if idx == $(i)
+                    if alias_u0
+                        copyto!(u0, $(u_result_syms[i]))
+                        $(u_result_syms[i]) = u0
+                    else
+                        $(u_result_syms[i]) = $(sol_syms[i]).u
+                    end
+                    return build_solution_less_specialize(
+                        prob, alg, $(u_result_syms[i]), $(sol_syms[i]).resid;
+                        $(sol_syms[i]).retcode, $(sol_syms[i]).stats,
+                        $(sol_syms[i]).trace, original = $(sol_syms[i])
+                    )
+                end
+            end)
+    end
+    push!(calls, :(error("Current choices shouldn't get here!")))
+
+    return Expr(:block, calls...)
+end
+
 """
     step!(
         cache::AbstractNonlinearSolveCache;
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index a3e8bb6ca..3aa4cac22 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -13,7 +13,8 @@ using LinearAlgebra: LinearAlgebra, norm
 using LineSearch: BackTracking
 using NonlinearSolveBase: NonlinearSolveBase, InternalAPI, AbstractNonlinearSolveAlgorithm,
                           AbstractNonlinearSolveCache, Utils, L2_NORM,
-                          enable_timer_outputs, disable_timer_outputs
+                          enable_timer_outputs, disable_timer_outputs,
+                          NonlinearSolvePolyAlgorithm
 
 using Preferences: set_preferences!
 using SciMLBase: SciMLBase, NLStats, ReturnCode, AbstractNonlinearProblem,
@@ -47,7 +48,7 @@ using SimpleNonlinearSolve: SimpleNonlinearSolve
 
 const SII = SymbolicIndexingInterface
 
-include("polyalg.jl")
+include("poly_algs.jl")
 include("extension_algs.jl")
 
 include("default.jl")
diff --git a/src/poly_algs.jl b/src/poly_algs.jl
new file mode 100644
index 000000000..31c16917f
--- /dev/null
+++ b/src/poly_algs.jl
@@ -0,0 +1,184 @@
+"""
+    RobustMultiNewton(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+    )
+
+A polyalgorithm focused on robustness. It uses a mixture of Newton methods with different
+globalizing techniques (trust region updates, line searches, etc.) in order to find a
+method that is able to adequately solve the minimization problem.
+
+Basically, if this algorithm fails, then "most" good ways of solving your problem fail and
+you may need to think about reformulating the model (either there is an issue with the model,
+or more precision / more stable linear solver choice is required).
+
+### Arguments
+
+  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
+    are compatible with the problem type. Defaults to `Float64`.
+"""
+function RobustMultiNewton(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+) where {T}
+    common_kwargs = (; concrete_jac, linsolve, autodiff, vjp_autodiff, jvp_autodiff)
+    if T <: Complex # Let's atleast have something here for complex numbers
+        algs = (
+            NewtonRaphson(; common_kwargs...),
+        )
+    else
+        algs = (
+            TrustRegion(; common_kwargs...),
+            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin),
+            NewtonRaphson(; common_kwargs...),
+            NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
+            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.NLsolve),
+            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Fan)
+        )
+    end
+    return NonlinearSolvePolyAlgorithm(algs)
+end
+
+"""
+    FastShortcutNonlinearPolyalg(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing,
+        must_use_jacobian::Val = Val(false),
+        prefer_simplenonlinearsolve::Val = Val(false),
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing,
+        u0_len::Union{Int, Nothing} = nothing
+    ) where {T}
+
+A polyalgorithm focused on balancing speed and robustness. It first tries less robust methods
+for more performance and then tries more robust techniques if the faster ones fail.
+
+### Arguments
+
+  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
+    are compatible with the problem type. Defaults to `Float64`.
+
+### Keyword Arguments
+
+  - `u0_len`: The length of the initial guess. If this is `nothing`, then the length of the
+    initial guess is not checked. If this is an integer and it is less than `25`, we use
+    jacobian based methods.
+"""
+function FastShortcutNonlinearPolyalg(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing,
+        must_use_jacobian::Val = Val(false),
+        prefer_simplenonlinearsolve::Val = Val(false),
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing,
+        u0_len::Union{Int, Nothing} = nothing
+) where {T}
+    start_index = 1
+    common_kwargs = (; concrete_jac, linsolve, autodiff, vjp_autodiff, jvp_autodiff)
+    if must_use_jacobian isa Val{true}
+        if T <: Complex
+            algs = (NewtonRaphson(; common_kwargs...),)
+        else
+            algs = (
+                NewtonRaphson(; common_kwargs...),
+                NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
+                TrustRegion(; common_kwargs...),
+                TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin)
+            )
+        end
+    else
+        # SimpleNewtonRaphson and SimpleTrustRegion are not robust to singular Jacobians
+        # and thus are not included in the polyalgorithm
+        if prefer_simplenonlinearsolve isa Val{true}
+            if T <: Complex
+                algs = (
+                    SimpleBroyden(),
+                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
+                    SimpleKlement(),
+                    NewtonRaphson(; common_kwargs...)
+                )
+            else
+                start_index = u0_len !== nothing ? (u0_len ≤ 25 ? 4 : 1) : 1
+                algs = (
+                    SimpleBroyden(),
+                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
+                    SimpleKlement(),
+                    NewtonRaphson(; common_kwargs...),
+                    NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
+                    TrustRegion(; common_kwargs...),
+                    TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin)
+                )
+            end
+        else
+            if T <: Complex
+                algs = (
+                    Broyden(; autodiff),
+                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
+                    Klement(; linsolve, autodiff),
+                    NewtonRaphson(; common_kwargs...)
+                )
+            else
+                # TODO: This number requires a bit rigorous testing
+                start_index = u0_len !== nothing ? (u0_len ≤ 25 ? 4 : 1) : 1
+                algs = (
+                    Broyden(; autodiff),
+                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
+                    Klement(; linsolve, autodiff),
+                    NewtonRaphson(; common_kwargs...),
+                    NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
+                    TrustRegion(; common_kwargs...),
+                    TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin)
+                )
+            end
+        end
+    end
+    return NonlinearSolvePolyAlgorithm(algs; start_index)
+end
+
+"""
+    FastShortcutNLLSPolyalg(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+    )
+
+A polyalgorithm focused on balancing speed and robustness. It first tries less robust methods
+for more performance and then tries more robust techniques if the faster ones fail.
+
+### Arguments
+
+  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
+    are compatible with the problem type. Defaults to `Float64`.
+"""
+function FastShortcutNLLSPolyalg(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+) where {T}
+    common_kwargs = (; linsolve, autodiff, vjp_autodiff, jvp_autodiff)
+    if T <: Complex
+        algs = (
+            GaussNewton(; common_kwargs..., concrete_jac),
+            LevenbergMarquardt(; common_kwargs..., disable_geodesic = Val(true)),
+            LevenbergMarquardt(; common_kwargs...)
+        )
+    else
+        algs = (
+            GaussNewton(; common_kwargs..., concrete_jac),
+            LevenbergMarquardt(; common_kwargs..., disable_geodesic = Val(true)),
+            TrustRegion(; common_kwargs..., concrete_jac),
+            GaussNewton(; common_kwargs..., linesearch = BackTracking(), concrete_jac),
+            TrustRegion(;
+                common_kwargs..., radius_update_scheme = RUS.Bastin, concrete_jac
+            ),
+            LevenbergMarquardt(; common_kwargs...)
+        )
+    end
+    return NonlinearSolvePolyAlgorithm(algs)
+end
diff --git a/src/polyalg.jl b/src/polyalg.jl
deleted file mode 100644
index f16dd7e0e..000000000
--- a/src/polyalg.jl
+++ /dev/null
@@ -1,545 +0,0 @@
-"""
-    NonlinearSolvePolyAlgorithm(algs; start_index::Int = 1)
-
-A general way to define PolyAlgorithms for `NonlinearProblem` and
-`NonlinearLeastSquaresProblem`. This is a container for a tuple of algorithms that will be
-tried in order until one succeeds. If none succeed, then the algorithm with the lowest
-residual is returned.
-
-### Arguments
-
-  - `algs`: a tuple of algorithms to try in-order! (If this is not a Tuple, then the
-    returned algorithm is not type-stable).
-
-### Keyword Arguments
-
-  - `start_index`: the index to start at. Defaults to `1`.
-
-### Example
-
-```julia
-using NonlinearSolve
-
-alg = NonlinearSolvePolyAlgorithm((NewtonRaphson(), Broyden()))
-```
-"""
-@concrete struct NonlinearSolvePolyAlgorithm <: AbstractNonlinearSolveAlgorithm
-    static_length <: Val
-    algs <: Tuple
-    start_index::Int
-end
-
-function NonlinearSolvePolyAlgorithm(algs; start_index::Int = 1)
-    @assert 0 < start_index ≤ length(algs)
-    algs = Tuple(algs)
-    return NonlinearSolvePolyAlgorithm(Val(length(algs)), algs, start_index)
-end
-
-@concrete mutable struct NonlinearSolvePolyAlgorithmCache <: AbstractNonlinearSolveCache
-    static_length <: Val
-    prob <: AbstractNonlinearProblem
-
-    caches <: Tuple
-    alg <: NonlinearSolvePolyAlgorithm
-
-    best::Int
-    current::Int
-    nsteps::Int
-
-    stats::NLStats
-    total_time::Float64
-    maxtime
-
-    retcode::ReturnCode.T
-    force_stop::Bool
-
-    maxiters::Int
-    internalnorm
-
-    u0
-    u0_aliased
-    alias_u0::Bool
-end
-
-function SII.symbolic_container(cache::NonlinearSolvePolyAlgorithmCache)
-    return cache.caches[cache.current]
-end
-SII.state_values(cache::NonlinearSolvePolyAlgorithmCache) = cache.u0
-
-function Base.show(io::IO, ::MIME"text/plain", cache::NonlinearSolvePolyAlgorithmCache)
-    println(io, "NonlinearSolvePolyAlgorithmCache with \
-                 $(Utils.unwrap_val(cache.static_length)) algorithms:")
-    best_alg = ifelse(cache.best == -1, "nothing", cache.best)
-    println(io, "    Best Algorithm: $(best_alg)")
-    println(
-        io, "    Current Algorithm: [$(cache.current) / $(Utils.unwrap_val(cache.static_length))]"
-    )
-    println(io, "    nsteps: $(cache.nsteps)")
-    println(io, "    retcode: $(cache.retcode)")
-    print(io, "    Current Cache: ")
-    NonlinearSolveBase.show_nonlinearsolve_cache(io, cache.caches[cache.current], 4)
-end
-
-function InternalAPI.reinit!(
-        cache::NonlinearSolvePolyAlgorithmCache, args...; p = cache.p, u0 = cache.u0
-)
-    foreach(cache.caches) do cache
-        InternalAPI.reinit!(cache, args...; p, u0)
-    end
-    cache.current = cache.alg.start_index
-    InternalAPI.reinit!(cache.stats)
-    cache.nsteps = 0
-    cache.total_time = 0.0
-end
-
-function SciMLBase.__init(
-        prob::AbstractNonlinearProblem, alg::NonlinearSolvePolyAlgorithm, args...;
-        stats = NLStats(0, 0, 0, 0, 0), maxtime = nothing, maxiters = 1000,
-        internalnorm = L2_NORM, alias_u0 = false, verbose = true, kwargs...
-)
-    if alias_u0 && !ArrayInterface.ismutable(prob.u0)
-        verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
-                          immutable (checked using `ArrayInterface.ismutable`)."
-        alias_u0 = false  # If immutable don't care about aliasing
-    end
-
-    u0 = prob.u0
-    u0_aliased = alias_u0 ? copy(u0) : u0
-    alias_u0 && (prob = SciMLBase.remake(prob; u0 = u0_aliased))
-
-    return NonlinearSolvePolyAlgorithmCache(
-        alg.static_length, prob,
-        map(alg.algs) do solver
-            SciMLBase.__init(
-                prob, solver, args...;
-                stats, maxtime, internalnorm, alias_u0, verbose, kwargs...
-            )
-        end,
-        alg, -1, alg.start_index, 0, stats, 0.0, maxtime,
-        ReturnCode.Default, false, maxiters, internalnorm,
-        u0, u0_aliased, alias_u0
-    )
-end
-
-@generated function CommonSolve.solve!(cache::NonlinearSolvePolyAlgorithmCache{Val{N}}) where {N}
-    calls = [quote
-        1 ≤ cache.current ≤ $(N) || error("Current choices shouldn't get here!")
-    end]
-
-    cache_syms = [gensym("cache") for i in 1:N]
-    sol_syms = [gensym("sol") for i in 1:N]
-    u_result_syms = [gensym("u_result") for i in 1:N]
-
-    for i in 1:N
-        push!(calls,
-            quote
-                $(cache_syms[i]) = cache.caches[$(i)]
-                if $(i) == cache.current
-                    cache.alias_u0 && copyto!(cache.u0_aliased, cache.u0)
-                    $(sol_syms[i]) = CommonSolve.solve!($(cache_syms[i]))
-                    if SciMLBase.successful_retcode($(sol_syms[i]))
-                        stats = $(sol_syms[i]).stats
-                        if cache.alias_u0
-                            copyto!(cache.u0, $(sol_syms[i]).u)
-                            $(u_result_syms[i]) = cache.u0
-                        else
-                            $(u_result_syms[i]) = $(sol_syms[i]).u
-                        end
-                        fu = NonlinearSolveBase.get_fu($(cache_syms[i]))
-                        return build_solution_less_specialize(
-                            cache.prob, cache.alg, $(u_result_syms[i]), fu;
-                            retcode = $(sol_syms[i]).retcode, stats,
-                            original = $(sol_syms[i]), trace = $(sol_syms[i]).trace
-                        )
-                    elseif cache.alias_u0
-                        # For safety we need to maintain a copy of the solution
-                        $(u_result_syms[i]) = copy($(sol_syms[i]).u)
-                    end
-                    cache.current = $(i + 1)
-                end
-            end)
-    end
-
-    resids = map(Base.Fix2(Symbol, :resid), cache_syms)
-    for (sym, resid) in zip(cache_syms, resids)
-        push!(calls, :($(resid) = @isdefined($(sym)) ? $(sym).resid : nothing))
-    end
-    push!(calls, quote
-        fus = tuple($(Tuple(resids)...))
-        minfu, idx = findmin_caches(cache.prob, fus)
-    end)
-    for i in 1:N
-        push!(calls,
-            quote
-                if idx == $(i)
-                    u = cache.alias_u0 ? $(u_result_syms[i]) :
-                        NonlinearSolveBase.get_u(cache.caches[$(i)])
-                end
-            end)
-    end
-    push!(calls,
-        quote
-            retcode = cache.caches[idx].retcode
-            if cache.alias_u0
-                copyto!(cache.u0, u)
-                u = cache.u0
-            end
-            return build_solution_less_specialize(
-                cache.prob, cache.alg, u, fus[idx];
-                retcode, cache.stats, cache.caches[idx].trace
-            )
-        end)
-
-    return Expr(:block, calls...)
-end
-
-@generated function InternalAPI.step!(
-        cache::NonlinearSolvePolyAlgorithmCache{Val{N}}, args...; kwargs...
-) where {N}
-    calls = []
-    cache_syms = [gensym("cache") for i in 1:N]
-    for i in 1:N
-        push!(calls,
-            quote
-                $(cache_syms[i]) = cache.caches[$(i)]
-                if $(i) == cache.current
-                    InternalAPI.step!($(cache_syms[i]), args...; kwargs...)
-                    $(cache_syms[i]).nsteps += 1
-                    if !NonlinearSolveBase.not_terminated($(cache_syms[i]))
-                        if SciMLBase.successful_retcode($(cache_syms[i]).retcode)
-                            cache.best = $(i)
-                            cache.force_stop = true
-                            cache.retcode = $(cache_syms[i]).retcode
-                        else
-                            cache.current = $(i + 1)
-                        end
-                    end
-                    return
-                end
-            end)
-    end
-
-    push!(calls, quote
-        if !(1 ≤ cache.current ≤ length(cache.caches))
-            minfu, idx = findmin_caches(cache.prob, cache.caches)
-            cache.best = idx
-            cache.retcode = cache.caches[idx].retcode
-            cache.force_stop = true
-            return
-        end
-    end)
-
-    return Expr(:block, calls...)
-end
-
-@generated function SciMLBase.__solve(
-        prob::AbstractNonlinearProblem, alg::NonlinearSolvePolyAlgorithm{Val{N}}, args...;
-        stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, verbose = true, kwargs...
-) where {N}
-    sol_syms = [gensym("sol") for _ in 1:N]
-    prob_syms = [gensym("prob") for _ in 1:N]
-    u_result_syms = [gensym("u_result") for _ in 1:N]
-    calls = [quote
-        current = alg.start_index
-        if alias_u0 && !ArrayInterface.ismutable(prob.u0)
-            verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
-                              immutable (checked using `ArrayInterface.ismutable`)."
-            alias_u0 = false  # If immutable don't care about aliasing
-        end
-        u0 = prob.u0
-        u0_aliased = alias_u0 ? zero(u0) : u0
-    end]
-    for i in 1:N
-        cur_sol = sol_syms[i]
-        push!(calls,
-            quote
-                if current == $(i)
-                    if alias_u0
-                        copyto!(u0_aliased, u0)
-                        $(prob_syms[i]) = SciMLBase.remake(prob; u0 = u0_aliased)
-                    else
-                        $(prob_syms[i]) = prob
-                    end
-                    $(cur_sol) = SciMLBase.__solve(
-                        $(prob_syms[i]), alg.algs[$(i)], args...;
-                        stats, alias_u0, verbose, kwargs...
-                    )
-                    if SciMLBase.successful_retcode($(cur_sol))
-                        if alias_u0
-                            copyto!(u0, $(cur_sol).u)
-                            $(u_result_syms[i]) = u0
-                        else
-                            $(u_result_syms[i]) = $(cur_sol).u
-                        end
-                        return build_solution_less_specialize(
-                            prob, alg, $(u_result_syms[i]), $(cur_sol).resid;
-                            $(cur_sol).retcode, $(cur_sol).stats,
-                            $(cur_sol).trace, original = $(cur_sol)
-                        )
-                    elseif alias_u0
-                        # For safety we need to maintain a copy of the solution
-                        $(u_result_syms[i]) = copy($(cur_sol).u)
-                    end
-                    current = $(i + 1)
-                end
-            end)
-    end
-
-    resids = map(Base.Fix2(Symbol, :resid), sol_syms)
-    for (sym, resid) in zip(sol_syms, resids)
-        push!(calls, :($(resid) = @isdefined($(sym)) ? $(sym).resid : nothing))
-    end
-
-    push!(calls, quote
-        resids = tuple($(Tuple(resids)...))
-        minfu, idx = findmin_resids(prob, resids)
-    end)
-
-    for i in 1:N
-        push!(calls,
-            quote
-                if idx == $(i)
-                    if alias_u0
-                        copyto!(u0, $(u_result_syms[i]))
-                        $(u_result_syms[i]) = u0
-                    else
-                        $(u_result_syms[i]) = $(sol_syms[i]).u
-                    end
-                    return build_solution_less_specialize(
-                        prob, alg, $(u_result_syms[i]), $(sol_syms[i]).resid;
-                        $(sol_syms[i]).retcode, $(sol_syms[i]).stats,
-                        $(sol_syms[i]).trace, original = $(sol_syms[i])
-                    )
-                end
-            end)
-    end
-    push!(calls, :(error("Current choices shouldn't get here!")))
-
-    return Expr(:block, calls...)
-end
-
-"""
-    RobustMultiNewton(
-        ::Type{T} = Float64;
-        concrete_jac = nothing,
-        linsolve = nothing,
-        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
-    )
-
-A polyalgorithm focused on robustness. It uses a mixture of Newton methods with different
-globalizing techniques (trust region updates, line searches, etc.) in order to find a
-method that is able to adequately solve the minimization problem.
-
-Basically, if this algorithm fails, then "most" good ways of solving your problem fail and
-you may need to think about reformulating the model (either there is an issue with the model,
-or more precision / more stable linear solver choice is required).
-
-### Arguments
-
-  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
-    are compatible with the problem type. Defaults to `Float64`.
-"""
-function RobustMultiNewton(
-        ::Type{T} = Float64;
-        concrete_jac = nothing,
-        linsolve = nothing,
-        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
-) where {T}
-    common_kwargs = (; concrete_jac, linsolve, autodiff, vjp_autodiff, jvp_autodiff)
-    if T <: Complex # Let's atleast have something here for complex numbers
-        algs = (
-            NewtonRaphson(; common_kwargs...),
-        )
-    else
-        algs = (
-            TrustRegion(; common_kwargs...),
-            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin),
-            NewtonRaphson(; common_kwargs...),
-            NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
-            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.NLsolve),
-            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Fan)
-        )
-    end
-    return NonlinearSolvePolyAlgorithm(algs)
-end
-
-"""
-    FastShortcutNonlinearPolyalg(
-        ::Type{T} = Float64;
-        concrete_jac = nothing,
-        linsolve = nothing,
-        must_use_jacobian::Val = Val(false),
-        prefer_simplenonlinearsolve::Val = Val(false),
-        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing,
-        u0_len::Union{Int, Nothing} = nothing
-    ) where {T}
-
-A polyalgorithm focused on balancing speed and robustness. It first tries less robust methods
-for more performance and then tries more robust techniques if the faster ones fail.
-
-### Arguments
-
-  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
-    are compatible with the problem type. Defaults to `Float64`.
-
-### Keyword Arguments
-
-  - `u0_len`: The length of the initial guess. If this is `nothing`, then the length of the
-    initial guess is not checked. If this is an integer and it is less than `25`, we use
-    jacobian based methods.
-"""
-function FastShortcutNonlinearPolyalg(
-        ::Type{T} = Float64;
-        concrete_jac = nothing,
-        linsolve = nothing,
-        must_use_jacobian::Val = Val(false),
-        prefer_simplenonlinearsolve::Val = Val(false),
-        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing,
-        u0_len::Union{Int, Nothing} = nothing
-) where {T}
-    start_index = 1
-    common_kwargs = (; concrete_jac, linsolve, autodiff, vjp_autodiff, jvp_autodiff)
-    if must_use_jacobian isa Val{true}
-        if T <: Complex
-            algs = (NewtonRaphson(; common_kwargs...),)
-        else
-            algs = (
-                NewtonRaphson(; common_kwargs...),
-                NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
-                TrustRegion(; common_kwargs...),
-                TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin)
-            )
-        end
-    else
-        # SimpleNewtonRaphson and SimpleTrustRegion are not robust to singular Jacobians
-        # and thus are not included in the polyalgorithm
-        if prefer_simplenonlinearsolve isa Val{true}
-            if T <: Complex
-                algs = (
-                    SimpleBroyden(),
-                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
-                    SimpleKlement(),
-                    NewtonRaphson(; common_kwargs...)
-                )
-            else
-                start_index = u0_len !== nothing ? (u0_len ≤ 25 ? 4 : 1) : 1
-                algs = (
-                    SimpleBroyden(),
-                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
-                    SimpleKlement(),
-                    NewtonRaphson(; common_kwargs...),
-                    NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
-                    TrustRegion(; common_kwargs...),
-                    TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin)
-                )
-            end
-        else
-            if T <: Complex
-                algs = (
-                    Broyden(; autodiff),
-                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
-                    Klement(; linsolve, autodiff),
-                    NewtonRaphson(; common_kwargs...)
-                )
-            else
-                # TODO: This number requires a bit rigorous testing
-                start_index = u0_len !== nothing ? (u0_len ≤ 25 ? 4 : 1) : 1
-                algs = (
-                    Broyden(; autodiff),
-                    Broyden(; init_jacobian = Val(:true_jacobian), autodiff),
-                    Klement(; linsolve, autodiff),
-                    NewtonRaphson(; common_kwargs...),
-                    NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
-                    TrustRegion(; common_kwargs...),
-                    TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin)
-                )
-            end
-        end
-    end
-    return NonlinearSolvePolyAlgorithm(algs; start_index)
-end
-
-"""
-    FastShortcutNLLSPolyalg(
-        ::Type{T} = Float64;
-        concrete_jac = nothing,
-        linsolve = nothing,
-        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
-    )
-
-A polyalgorithm focused on balancing speed and robustness. It first tries less robust methods
-for more performance and then tries more robust techniques if the faster ones fail.
-
-### Arguments
-
-  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
-    are compatible with the problem type. Defaults to `Float64`.
-"""
-function FastShortcutNLLSPolyalg(
-        ::Type{T} = Float64;
-        concrete_jac = nothing,
-        linsolve = nothing,
-        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
-) where {T}
-    common_kwargs = (; linsolve, autodiff, vjp_autodiff, jvp_autodiff)
-    if T <: Complex
-        algs = (
-            GaussNewton(; common_kwargs..., concrete_jac),
-            LevenbergMarquardt(; common_kwargs..., disable_geodesic = Val(true)),
-            LevenbergMarquardt(; common_kwargs...)
-        )
-    else
-        algs = (
-            GaussNewton(; common_kwargs..., concrete_jac),
-            LevenbergMarquardt(; common_kwargs..., disable_geodesic = Val(true)),
-            TrustRegion(; common_kwargs..., concrete_jac),
-            GaussNewton(; common_kwargs..., linesearch = BackTracking(), concrete_jac),
-            TrustRegion(;
-                common_kwargs..., radius_update_scheme = RUS.Bastin, concrete_jac
-            ),
-            LevenbergMarquardt(; common_kwargs...)
-        )
-    end
-    return NonlinearSolvePolyAlgorithm(algs)
-end
-
-# Original is often determined on runtime information especially for PolyAlgorithms so it
-# is best to never specialize on that
-function build_solution_less_specialize(
-        prob::AbstractNonlinearProblem, alg, u, resid;
-        retcode = ReturnCode.Default, original = nothing, left = nothing,
-        right = nothing, stats = nothing, trace = nothing, kwargs...
-)
-    return SciMLBase.NonlinearSolution{
-        eltype(eltype(u)), ndims(u), typeof(u), typeof(resid), typeof(prob),
-        typeof(alg), Any, typeof(left), typeof(stats), typeof(trace)
-    }(
-        u, resid, prob, alg, retcode, original, left, right, stats, trace
-    )
-end
-
-function findmin_caches(prob::AbstractNonlinearProblem, caches)
-    resids = map(caches) do cache
-        cache === nothing && return nothing
-        return NonlinearSolveBase.get_fu(cache)
-    end
-    return findmin_resids(prob, resids)
-end
-
-@views function findmin_resids(prob::AbstractNonlinearProblem, caches)
-    norm_fn = prob isa NonlinearLeastSquaresProblem ? Base.Fix2(norm, 2) :
-              Base.Fix2(norm, Inf)
-    idx = findfirst(Base.Fix2(!==, nothing), caches)
-    # This is an internal function so we assume that inputs are consistent and there is
-    # atleast one non-`nothing` value
-    fx_idx = norm_fn(caches[idx])
-    idx == length(caches) && return fx_idx, idx
-    fmin = @closure xᵢ -> begin
-        xᵢ === nothing && return oftype(fx_idx, Inf)
-        fx = norm_fn(xᵢ)
-        return ifelse(isnan(fx), oftype(fx, Inf), fx)
-    end
-    x_min, x_min_idx = findmin(fmin, caches[(idx + 1):length(caches)])
-    x_min < fx_idx && return x_min, x_min_idx + idx
-    return fx_idx, idx
-end

From 810eeb3fa380481a9f742ddca6a090fee0a1e19e Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Wed, 6 Nov 2024 08:52:07 -0500
Subject: [PATCH 678/700] chore: bump version for release

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 3b0172faa..ae346348b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "4.0.0"
+version = "4.1.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From cbe43540102320ec767079d855ab7cfd4754bb13 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Thu, 7 Nov 2024 13:30:22 -0500
Subject: [PATCH 679/700] fix: `PolyesterForwardDiff` shouldn't be the default
 for static arrays (#495)

---
 Project.toml                           |  4 +++-
 lib/NonlinearSolveBase/Project.toml    |  2 +-
 lib/NonlinearSolveBase/src/autodiff.jl |  5 +++++
 test/core_tests.jl                     | 13 +++++++++++++
 4 files changed, 22 insertions(+), 2 deletions(-)

diff --git a/Project.toml b/Project.toml
index ae346348b..7802b1bd8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -98,6 +98,7 @@ PETSc = "0.3"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 Preferences = "1.4"
+PolyesterForwardDiff = "0.1"
 Random = "1.10"
 ReTestItems = "1.24"
 Reexport = "1.2"
@@ -138,6 +139,7 @@ NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
 OrdinaryDiffEqTsit5 = "b1df2697-797e-41e3-8120-5422d3b24e4a"
 PETSc = "ace2c81b-2b5f-4b1e-a30d-d662738edfe0"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+PolyesterForwardDiff = "98d1487c-24ca-40b6-b7ab-df2af84e126b"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
@@ -150,4 +152,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "LineSearches", "MINPACK", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "PETSc", "Pkg", "Random", "ReTestItems", "SIAMFANLEquations", "SparseConnectivityTracer", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "CUDA", "Enzyme", "ExplicitImports", "FastLevenbergMarquardt", "FixedPointAcceleration", "Hwloc", "InteractiveUtils", "LeastSquaresOptim", "LineSearches", "MINPACK", "NLSolvers", "NLsolve", "NaNMath", "NonlinearProblemLibrary", "OrdinaryDiffEqTsit5", "PETSc", "Pkg", "PolyesterForwardDiff", "Random", "ReTestItems", "SIAMFANLEquations", "SparseConnectivityTracer", "SpeedMapping", "StableRNGs", "StaticArrays", "Sundials", "Test", "Zygote"]
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index ae16dfd93..f35c949cf 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolveBase"
 uuid = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.3.0"
+version = "1.3.1"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
index f70e9770b..c92a3e27d 100644
--- a/lib/NonlinearSolveBase/src/autodiff.jl
+++ b/lib/NonlinearSolveBase/src/autodiff.jl
@@ -124,6 +124,11 @@ function additional_incompatible_backend_check(prob::AbstractNonlinearProblem,
     end
     return hasbranching(prob.f, prob.u0, prob.p)
 end
+function additional_incompatible_backend_check(
+        prob::AbstractNonlinearProblem, ::ADTypes.AutoPolyesterForwardDiff)
+    prob.u0 isa SArray && return true # promotes to a mutable array
+    return false
+end
 
 is_finite_differences_backend(ad::AbstractADType) = false
 is_finite_differences_backend(::ADTypes.AutoFiniteDiff) = true
diff --git a/test/core_tests.jl b/test/core_tests.jl
index 301b0b389..733ebd89b 100644
--- a/test/core_tests.jl
+++ b/test/core_tests.jl
@@ -414,3 +414,16 @@ end
     solve(prob)
     @test sol.u≈[1.0, 0.25] atol=1e-3 rtol=1e-3
 end
+
+@testitem "No PolyesterForwardDiff for SArray" tags=[:core] begin
+    using StaticArrays, PolyesterForwardDiff
+
+    f_oop(u, p) = u .* u .- p
+
+    N = 4
+    u0 = SVector{N, Float64}(ones(N) .+ randn(N) * 0.01)
+
+    nlprob = NonlinearProblem(f_oop, u0, 2.0)
+
+    @test !(solve(nlprob, NewtonRaphson()).alg.autodiff isa AutoPolyesterForwardDiff)
+end

From fe4950d8339e8ea5bb56477718107bda275d0a05 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 12 Nov 2024 10:02:52 -0100
Subject: [PATCH 680/700] Fix ambiguity in `__solve` with polyalgorithm due to
 dispatch on `Va` (#498)

* Fix ambiguity in `__solve` with polyalgorithm due to dispatch on `Val{N}`

Noticed downstream

```
  Candidates:
    kwcall(::NamedTuple, ::typeof(SciMLBase.__solve), prob::SciMLBase.AbstractNonlinearProblem, alg::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{Val{N}}, args...) where N
      @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/54f3T/src/solve.jl:106
    kwcall(::NamedTuple, ::typeof(SciMLBase.__solve), prob::Union{SciMLBase.NonlinearLeastSquaresProblem{<:Union{Number, var"#s15"} where var"#s15"<:AbstractArray, iip, <:Union{var"#s14", var"#s13"} where {var"#s14"<:ForwardDiff.Dual{T, V, P}, var"#s13"<:(AbstractArray{<:ForwardDiff.Dual{T, V, P}})}} where {iip, T, V, P}, SciMLBase.NonlinearProblem{<:Union{Number, var"#s15"} where var"#s15"<:AbstractArray, iip, <:Union{var"#s14", var"#s13"} where {var"#s14"<:ForwardDiff.Dual{T, V, P}, var"#s13"<:(AbstractArray{<:ForwardDiff.Dual{T, V, P}})}} where {iip, T, V, P}}, alg::NonlinearSolveBase.AbstractNonlinearSolveAlgorithm, args...)
      @ NonlinearSolve ~/.julia/packages/NonlinearSolve/LuVnf/src/forward_diff.jl:14
    kwcall(::NamedTuple, ::typeof(SciMLBase.__solve), prob::Union{SciMLBase.NonlinearLeastSquaresProblem{<:Union{Number, var"#s15"} where var"#s15"<:AbstractArray, iip, <:Union{var"#s14", var"#s13"} where {var"#s14"<:ForwardDiff.Dual{T, V, P}, var"#s13"<:(AbstractArray{<:ForwardDiff.Dual{T, V, P}})}} where {iip, T, V, P}, SciMLBase.NonlinearProblem{<:Union{Number, var"#s15"} where var"#s15"<:AbstractArray, iip, <:Union{var"#s14", var"#s13"} where {var"#s14"<:ForwardDiff.Dual{T, V, P}, var"#s13"<:(AbstractArray{<:ForwardDiff.Dual{T, V, P}})}} where {iip, T, V, P}}, alg::NonlinearSolveBase.NonlinearSolvePolyAlgorithm, args...)
      @ NonlinearSolve ~/.julia/packages/NonlinearSolve/LuVnf/src/forward_diff.jl:14

  Possible fix, define
    kwcall(::NamedTuple, ::typeof(SciMLBase.__solve), ::Union{SciMLBase.NonlinearLeastSquaresProblem{<:Union{Number, var"#s15"} where var"#s15"<:AbstractArray, iip, <:Union{var"#s14", var"#s13"} where {var"#s14"<:ForwardDiff.Dual{T, V, P}, var"#s13"<:(AbstractArray{<:ForwardDiff.Dual{T, V, P}})}} where {iip, T, V, P}, SciMLBase.NonlinearProblem{<:Union{Number, var"#s15"} where var"#s15"<:AbstractArray, iip, <:Union{var"#s14", var"#s13"} where {var"#s14"<:ForwardDiff.Dual{T, V, P}, var"#s13"<:(AbstractArray{<:ForwardDiff.Dual{T, V, P}})}} where {iip, T, V, P}}, ::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{Val{N}}, ::Vararg{Any}) where N
```

https://github.com/SciML/OrdinaryDiffEq.jl/actions/runs/11786040241/job/32828542508?pr=2522

The issue is that the polyalgorithm code is dispatching on more details of the polyalgorithm than https://github.com/SciML/NonlinearSolve.jl/blob/master/src/forward_diff.jl#L13-L25 which leads to an ambiguity. But it only needs that information since it's a generated function. The easy fix is to just make the generated function be one step lower.

* Update forward_ad_tests.jl

* Update lib/NonlinearSolveBase/src/solve.jl
---
 lib/NonlinearSolveBase/src/solve.jl | 7 ++++++-
 test/forward_ad_tests.jl            | 1 +
 2 files changed, 7 insertions(+), 1 deletion(-)

diff --git a/lib/NonlinearSolveBase/src/solve.jl b/lib/NonlinearSolveBase/src/solve.jl
index 76d765d7b..04b25026f 100644
--- a/lib/NonlinearSolveBase/src/solve.jl
+++ b/lib/NonlinearSolveBase/src/solve.jl
@@ -103,7 +103,12 @@ end
     return Expr(:block, calls...)
 end
 
-@generated function SciMLBase.__solve(
+function SciMLBase.__solve(prob::AbstractNonlinearProblem, alg::NonlinearSolvePolyAlgorithm, 
+        args...; kwargs...)
+        __generated_polysolve(prob, alg, args...; kwargs...)
+end
+
+@generated function __generated_polysolve(
         prob::AbstractNonlinearProblem, alg::NonlinearSolvePolyAlgorithm{Val{N}}, args...;
         stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, verbose = true, kwargs...
 ) where {N}
diff --git a/test/forward_ad_tests.jl b/test/forward_ad_tests.jl
index f3cf74bae..163349267 100644
--- a/test/forward_ad_tests.jl
+++ b/test/forward_ad_tests.jl
@@ -71,6 +71,7 @@ end
         Broyden(),
         Klement(),
         DFSane(),
+        FastShortcutNonlinearPolyalg(),
         nothing,
         NLsolveJL(),
         CMINPACK(),

From f0ec3437b3c21bb9f06148b88b42a1f59b5bc28e Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Tue, 12 Nov 2024 10:03:19 -0100
Subject: [PATCH 681/700] Update Project.toml

---
 lib/NonlinearSolveBase/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index f35c949cf..cddf08555 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolveBase"
 uuid = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.3.1"
+version = "1.3.2"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 70c0581d4f1e573438e07c046682a6241850e135 Mon Sep 17 00:00:00 2001
From: Aayush Sabharwal <aayush.sabharwal@gmail.com>
Date: Thu, 14 Nov 2024 03:25:37 +0530
Subject: [PATCH 682/700] fix: fix SII implementation for caches, tests (#500)

* fix: fix SII implementation for caches

* test: fix SII tests

* ci: don't fail CI jobs if code coverage reporting fails

---------

Co-authored-by: Anant Thazhemadam <anant.thazhemadam@gmail.com>
---
 .github/workflows/CI_BracketingNonlinearSolve.yml      | 4 ++--
 .github/workflows/CI_NonlinearSolve.yml                | 4 ++--
 .github/workflows/CI_NonlinearSolveBase.yml            | 4 ++--
 .github/workflows/CI_NonlinearSolveFirstOrder.yml      | 4 ++--
 .github/workflows/CI_NonlinearSolveQuasiNewton.yml     | 4 ++--
 .github/workflows/CI_NonlinearSolveSpectralMethods.yml | 4 ++--
 .github/workflows/CI_SciMLJacobianOperators.yml        | 4 ++--
 .github/workflows/CI_SimpleNonlinearSolve.yml          | 4 ++--
 .github/workflows/Documentation.yml                    | 2 +-
 .github/workflows/Downstream.yml                       | 2 +-
 lib/NonlinearSolveBase/src/abstract_types.jl           | 2 +-
 lib/NonlinearSolveBase/src/polyalg.jl                  | 2 +-
 test/mtk_cache_indexing_tests.jl                       | 7 ++++---
 13 files changed, 24 insertions(+), 23 deletions(-)

diff --git a/.github/workflows/CI_BracketingNonlinearSolve.yml b/.github/workflows/CI_BracketingNonlinearSolve.yml
index 956fa33a2..03e5654f2 100644
--- a/.github/workflows/CI_BracketingNonlinearSolve.yml
+++ b/.github/workflows/CI_BracketingNonlinearSolve.yml
@@ -68,7 +68,7 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
 
   downgrade:
     runs-on: ubuntu-latest
@@ -106,4 +106,4 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
diff --git a/.github/workflows/CI_NonlinearSolve.yml b/.github/workflows/CI_NonlinearSolve.yml
index f685a7e7a..be4651464 100644
--- a/.github/workflows/CI_NonlinearSolve.yml
+++ b/.github/workflows/CI_NonlinearSolve.yml
@@ -82,7 +82,7 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
 
   downgrade:
     runs-on: ubuntu-latest
@@ -126,4 +126,4 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
diff --git a/.github/workflows/CI_NonlinearSolveBase.yml b/.github/workflows/CI_NonlinearSolveBase.yml
index 8b303ae2e..62868d191 100644
--- a/.github/workflows/CI_NonlinearSolveBase.yml
+++ b/.github/workflows/CI_NonlinearSolveBase.yml
@@ -67,7 +67,7 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
 
   downgrade:
     runs-on: ubuntu-latest
@@ -105,4 +105,4 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
diff --git a/.github/workflows/CI_NonlinearSolveFirstOrder.yml b/.github/workflows/CI_NonlinearSolveFirstOrder.yml
index 8f68f398b..e2313a3ad 100644
--- a/.github/workflows/CI_NonlinearSolveFirstOrder.yml
+++ b/.github/workflows/CI_NonlinearSolveFirstOrder.yml
@@ -68,7 +68,7 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
 
   downgrade:
     runs-on: ubuntu-latest
@@ -106,4 +106,4 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
diff --git a/.github/workflows/CI_NonlinearSolveQuasiNewton.yml b/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
index 3c0904739..9715d5789 100644
--- a/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
+++ b/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
@@ -68,7 +68,7 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
 
   downgrade:
     runs-on: ubuntu-latest
@@ -106,4 +106,4 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
diff --git a/.github/workflows/CI_NonlinearSolveSpectralMethods.yml b/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
index f39420efa..13cac0453 100644
--- a/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
+++ b/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
@@ -68,7 +68,7 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
 
   downgrade:
     runs-on: ubuntu-latest
@@ -106,4 +106,4 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
diff --git a/.github/workflows/CI_SciMLJacobianOperators.yml b/.github/workflows/CI_SciMLJacobianOperators.yml
index 4d1f6780d..1807da8a6 100644
--- a/.github/workflows/CI_SciMLJacobianOperators.yml
+++ b/.github/workflows/CI_SciMLJacobianOperators.yml
@@ -60,7 +60,7 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
 
   downgrade:
     runs-on: ubuntu-latest
@@ -90,4 +90,4 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
diff --git a/.github/workflows/CI_SimpleNonlinearSolve.yml b/.github/workflows/CI_SimpleNonlinearSolve.yml
index 0212232a8..63eb4b136 100644
--- a/.github/workflows/CI_SimpleNonlinearSolve.yml
+++ b/.github/workflows/CI_SimpleNonlinearSolve.yml
@@ -75,7 +75,7 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
 
   downgrade:
     runs-on: ubuntu-latest
@@ -119,4 +119,4 @@ jobs:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
           verbose: true
-          fail_ci_if_error: true
+          fail_ci_if_error: false
diff --git a/.github/workflows/Documentation.yml b/.github/workflows/Documentation.yml
index af44cd769..9cca57cf9 100644
--- a/.github/workflows/Documentation.yml
+++ b/.github/workflows/Documentation.yml
@@ -39,4 +39,4 @@ jobs:
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
-          fail_ci_if_error: true
+          fail_ci_if_error: false
diff --git a/.github/workflows/Downstream.yml b/.github/workflows/Downstream.yml
index dc40d46f2..933ff30d9 100644
--- a/.github/workflows/Downstream.yml
+++ b/.github/workflows/Downstream.yml
@@ -73,4 +73,4 @@ jobs:
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
-          fail_ci_if_error: true
+          fail_ci_if_error: false
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index 6105f5125..6829e19c3 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -307,7 +307,7 @@ SciMLBase.isinplace(cache::AbstractNonlinearSolveCache) = SciMLBase.isinplace(ca
 ## SII Interface
 SII.symbolic_container(cache::AbstractNonlinearSolveCache) = cache.prob
 SII.parameter_values(cache::AbstractNonlinearSolveCache) = SII.parameter_values(cache.prob)
-SII.state_values(cache::AbstractNonlinearSolveCache) = SII.state_values(cache.prob)
+SII.state_values(cache::AbstractNonlinearSolveCache) = get_u(cache)
 
 function Base.getproperty(cache::AbstractNonlinearSolveCache, sym::Symbol)
     if sym === :ps
diff --git a/lib/NonlinearSolveBase/src/polyalg.jl b/lib/NonlinearSolveBase/src/polyalg.jl
index 54b61998f..76ba500dd 100644
--- a/lib/NonlinearSolveBase/src/polyalg.jl
+++ b/lib/NonlinearSolveBase/src/polyalg.jl
@@ -64,7 +64,7 @@ end
 function SII.symbolic_container(cache::NonlinearSolvePolyAlgorithmCache)
     return cache.caches[cache.current]
 end
-SII.state_values(cache::NonlinearSolvePolyAlgorithmCache) = cache.u0
+SII.state_values(cache::NonlinearSolvePolyAlgorithmCache) = SII.state_values(SII.symbolic_container(cache))
 
 function Base.show(io::IO, ::MIME"text/plain", cache::NonlinearSolvePolyAlgorithmCache)
     println(io, "NonlinearSolvePolyAlgorithmCache with \
diff --git a/test/mtk_cache_indexing_tests.jl b/test/mtk_cache_indexing_tests.jl
index 3109d1612..cf149efd9 100644
--- a/test/mtk_cache_indexing_tests.jl
+++ b/test/mtk_cache_indexing_tests.jl
@@ -1,6 +1,7 @@
 @testitem "Modeling Toolkit Cache Indexing" tags=[:downstream] begin
     using ModelingToolkit
     using ModelingToolkit: t_nounits as t
+    import NonlinearSolveBase, NonlinearSolveFirstOrder
 
     @parameters p d
     @variables X(t)
@@ -11,9 +12,9 @@
     nlprob = NonlinearProblem(nlsys, [X => 1.0], [p => 2.0, d => 3.0])
 
     @testset "$integtype" for (alg, integtype) in [
-        (NewtonRaphson(), NonlinearSolve.GeneralizedFirstOrderAlgorithmCache),
-        (FastShortcutNonlinearPolyalg(), NonlinearSolve.NonlinearSolvePolyAlgorithmCache),
-        (SimpleNewtonRaphson(), NonlinearSolve.NonlinearSolveNoInitCache)
+        (NewtonRaphson(), NonlinearSolveFirstOrder.GeneralizedFirstOrderAlgorithmCache),
+        (FastShortcutNonlinearPolyalg(), NonlinearSolveBase.NonlinearSolvePolyAlgorithmCache),
+        (SimpleNewtonRaphson(), NonlinearSolveBase.NonlinearSolveNoInitCache)
     ]
         nint = init(nlprob, alg)
         @test nint isa integtype

From b534b0c8e51fdb411e85afd577654a09bd015d63 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 13 Nov 2024 20:56:09 -0100
Subject: [PATCH 683/700] Update Project.toml

---
 lib/NonlinearSolveBase/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index cddf08555..4cc10a6be 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolveBase"
 uuid = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.3.2"
+version = "1.3.3"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From d95648d37e8e5dbf1e6fe99dba1c441587aea257 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Fri, 15 Nov 2024 09:24:25 -0100
Subject: [PATCH 684/700] format

---
 lib/NonlinearSolveBase/src/polyalg.jl | 4 +++-
 lib/NonlinearSolveBase/src/solve.jl   | 5 +++--
 test/mtk_cache_indexing_tests.jl      | 3 ++-
 3 files changed, 8 insertions(+), 4 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/polyalg.jl b/lib/NonlinearSolveBase/src/polyalg.jl
index 76ba500dd..c2101af0e 100644
--- a/lib/NonlinearSolveBase/src/polyalg.jl
+++ b/lib/NonlinearSolveBase/src/polyalg.jl
@@ -64,7 +64,9 @@ end
 function SII.symbolic_container(cache::NonlinearSolvePolyAlgorithmCache)
     return cache.caches[cache.current]
 end
-SII.state_values(cache::NonlinearSolvePolyAlgorithmCache) = SII.state_values(SII.symbolic_container(cache))
+function SII.state_values(cache::NonlinearSolvePolyAlgorithmCache)
+    SII.state_values(SII.symbolic_container(cache))
+end
 
 function Base.show(io::IO, ::MIME"text/plain", cache::NonlinearSolvePolyAlgorithmCache)
     println(io, "NonlinearSolvePolyAlgorithmCache with \
diff --git a/lib/NonlinearSolveBase/src/solve.jl b/lib/NonlinearSolveBase/src/solve.jl
index 04b25026f..e4dd33636 100644
--- a/lib/NonlinearSolveBase/src/solve.jl
+++ b/lib/NonlinearSolveBase/src/solve.jl
@@ -103,9 +103,10 @@ end
     return Expr(:block, calls...)
 end
 
-function SciMLBase.__solve(prob::AbstractNonlinearProblem, alg::NonlinearSolvePolyAlgorithm, 
+function SciMLBase.__solve(
+        prob::AbstractNonlinearProblem, alg::NonlinearSolvePolyAlgorithm,
         args...; kwargs...)
-        __generated_polysolve(prob, alg, args...; kwargs...)
+    __generated_polysolve(prob, alg, args...; kwargs...)
 end
 
 @generated function __generated_polysolve(
diff --git a/test/mtk_cache_indexing_tests.jl b/test/mtk_cache_indexing_tests.jl
index cf149efd9..6e059e78c 100644
--- a/test/mtk_cache_indexing_tests.jl
+++ b/test/mtk_cache_indexing_tests.jl
@@ -13,7 +13,8 @@
 
     @testset "$integtype" for (alg, integtype) in [
         (NewtonRaphson(), NonlinearSolveFirstOrder.GeneralizedFirstOrderAlgorithmCache),
-        (FastShortcutNonlinearPolyalg(), NonlinearSolveBase.NonlinearSolvePolyAlgorithmCache),
+        (FastShortcutNonlinearPolyalg(),
+            NonlinearSolveBase.NonlinearSolvePolyAlgorithmCache),
         (SimpleNewtonRaphson(), NonlinearSolveBase.NonlinearSolveNoInitCache)
     ]
         nint = init(nlprob, alg)

From bec0bf27aff68f079d42278a403baaeee7c95436 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Sat, 16 Nov 2024 02:54:08 -0100
Subject: [PATCH 685/700] Create SCCNonlinearSolve (#502)

* Create SCCNonlinearSolve

* Update lib/SCCNonlinearSolve/src/SCCNonlinearSolve.jl

Co-authored-by: Aayush Sabharwal <aayush.sabharwal@gmail.com>

* Update lib/SCCNonlinearSolve/src/SCCNonlinearSolve.jl

Co-authored-by: Aayush Sabharwal <aayush.sabharwal@gmail.com>

* Update lib/SCCNonlinearSolve/src/SCCNonlinearSolve.jl

Co-authored-by: Aayush Sabharwal <aayush.sabharwal@gmail.com>

* Update lib/SCCNonlinearSolve/test/core_tests.jl

Co-authored-by: Aayush Sabharwal <aayush.sabharwal@gmail.com>

* format scc

* just use params

* re format

* SII

* fix CI

* Update lib/SCCNonlinearSolve/src/SCCNonlinearSolve.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

* fix up test setup

* Update Project.toml

* Update core_tests.jl

* Update lib/SCCNonlinearSolve/test/core_tests.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

* Update lib/SCCNonlinearSolve/test/core_tests.jl

* Update core_tests.jl

* Update lib/SCCNonlinearSolve/test/core_tests.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

* Update core_tests.jl

* Update Project.toml

* Update lib/SCCNonlinearSolve/test/qa_tests.jl

* Update lib/SCCNonlinearSolve/test/qa_tests.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

* Update Project.toml

* Update qa_tests.jl

* Update lib/SCCNonlinearSolve/test/qa_tests.jl

* Update lib/SCCNonlinearSolve/test/qa_tests.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

---------

Co-authored-by: Aayush Sabharwal <aayush.sabharwal@gmail.com>
Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 .github/workflows/CI_SCCNonlinearSolve.yml    | 109 ++++++++++++++++++
 lib/SCCNonlinearSolve/LICENSE                 |  21 ++++
 lib/SCCNonlinearSolve/Project.toml            |  48 ++++++++
 .../src/SCCNonlinearSolve.jl                  |  38 ++++++
 lib/SCCNonlinearSolve/test/core_tests.jl      |  65 +++++++++++
 lib/SCCNonlinearSolve/test/qa_tests.jl        |  25 ++++
 lib/SCCNonlinearSolve/test/runtests.jl        |  25 ++++
 7 files changed, 331 insertions(+)
 create mode 100644 .github/workflows/CI_SCCNonlinearSolve.yml
 create mode 100644 lib/SCCNonlinearSolve/LICENSE
 create mode 100644 lib/SCCNonlinearSolve/Project.toml
 create mode 100644 lib/SCCNonlinearSolve/src/SCCNonlinearSolve.jl
 create mode 100644 lib/SCCNonlinearSolve/test/core_tests.jl
 create mode 100644 lib/SCCNonlinearSolve/test/qa_tests.jl
 create mode 100644 lib/SCCNonlinearSolve/test/runtests.jl

diff --git a/.github/workflows/CI_SCCNonlinearSolve.yml b/.github/workflows/CI_SCCNonlinearSolve.yml
new file mode 100644
index 000000000..a00e938e6
--- /dev/null
+++ b/.github/workflows/CI_SCCNonlinearSolve.yml
@@ -0,0 +1,109 @@
+name: CI (SCCNonlinearSolve)
+
+on:
+  pull_request:
+    branches:
+      - master
+    paths:
+      - "lib/SCCNonlinearSolve/**"
+      - ".github/workflows/CI_SCCNonlinearSolve.yml"
+      - "lib/NonlinearSolveBase/**"
+      - "lib/SciMLJacobianOperators/**"
+  push:
+    branches:
+      - master
+
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: only if it is a pull request build.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+
+jobs:
+  test:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "1.10"
+          - "1"
+        os:
+          - ubuntu-latest
+          - macos-latest
+          - windows-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: actions/cache@v4
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators", "lib/NonlinearSolveBase")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SCCNonlinearSolve {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/SCCNonlinearSolve/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: false
+
+  downgrade:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - "1.10"
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+      - uses: julia-actions/julia-downgrade-compat@v1
+        with:
+          skip: NonlinearSolveBase, SciMLJacobianOperators
+      - name: "Install Dependencies and Run Tests"
+        run: |
+          import Pkg
+          Pkg.Registry.update()
+          # Install packages present in subdirectories
+          dev_pks = Pkg.PackageSpec[]
+          for path in ("lib/SciMLJacobianOperators", "lib/NonlinearSolveBase")
+              push!(dev_pks, Pkg.PackageSpec(; path))
+          end
+          Pkg.develop(dev_pks)
+          Pkg.instantiate()
+          Pkg.test(; coverage="user")
+        shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/SCCNonlinearSolve {0}
+      - uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: lib/SCCNonlinearSolve/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
+      - uses: codecov/codecov-action@v4
+        with:
+          file: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          verbose: true
+          fail_ci_if_error: false
diff --git a/lib/SCCNonlinearSolve/LICENSE b/lib/SCCNonlinearSolve/LICENSE
new file mode 100644
index 000000000..abb594d1e
--- /dev/null
+++ b/lib/SCCNonlinearSolve/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2024 SciML
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/lib/SCCNonlinearSolve/Project.toml b/lib/SCCNonlinearSolve/Project.toml
new file mode 100644
index 000000000..389323487
--- /dev/null
+++ b/lib/SCCNonlinearSolve/Project.toml
@@ -0,0 +1,48 @@
+name = "SCCNonlinearSolve"
+uuid = "9dfe8606-65a1-4bb3-9748-cb89d1561431"
+authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
+version = "1.0.0"
+
+[deps]
+CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
+PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
+Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
+
+[compat]
+Aqua = "0.8"
+BenchmarkTools = "1.5.0"
+CommonSolve = "0.2.4"
+ExplicitImports = "1.5"
+Hwloc = "3"
+InteractiveUtils = "<0.0.1, 1"
+NonlinearProblemLibrary = "0.1.2"
+NonlinearSolveFirstOrder = "1"
+Pkg = "1.10"
+PrecompileTools = "1.2"
+ReTestItems = "1.24"
+Reexport = "1"
+SciMLBase = "2.60"
+StableRNGs = "1"
+StaticArrays = "1.9.8"
+SymbolicIndexingInterface = "0.3.30"
+Test = "1.10"
+julia = "1.10"
+
+[extras]
+Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
+Hwloc = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+NonlinearSolveFirstOrder = "5959db7a-ea39-4486-b5fe-2dd0bf03d60d"
+NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
+Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+ReTestItems = "817f1d60-ba6b-4fd5-9520-3cf149f6a823"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[targets]
+test = ["Aqua", "BenchmarkTools", "ExplicitImports", "Hwloc", "InteractiveUtils", "NonlinearSolveFirstOrder", "NonlinearProblemLibrary", "Pkg", "ReTestItems", "StableRNGs", "StaticArrays", "Test"]
diff --git a/lib/SCCNonlinearSolve/src/SCCNonlinearSolve.jl b/lib/SCCNonlinearSolve/src/SCCNonlinearSolve.jl
new file mode 100644
index 000000000..3c8cc8691
--- /dev/null
+++ b/lib/SCCNonlinearSolve/src/SCCNonlinearSolve.jl
@@ -0,0 +1,38 @@
+module SCCNonlinearSolve
+
+import SciMLBase
+import CommonSolve
+import SymbolicIndexingInterface
+
+function CommonSolve.solve(prob::SciMLBase.SCCNonlinearProblem, alg; kwargs...)
+    numscc = length(prob.probs)
+    sols = [SciMLBase.build_solution(
+                prob, nothing, prob.u0, convert(eltype(prob.u0), NaN) * prob.u0)
+            for prob in prob.probs]
+    u = reduce(vcat, [prob.u0 for prob in prob.probs])
+    resid = copy(u)
+
+    lasti = 1
+    for i in 1:numscc
+        prob.explictfuns![i](
+            SymbolicIndexingInterface.parameter_values(prob.probs[i]), sols)
+        sol = SciMLBase.solve(prob.probs[i], alg; kwargs...)
+        _sol = SciMLBase.build_solution(
+            prob.probs[i], nothing, sol.u, sol.resid, retcode = sol.retcode)
+        sols[i] = _sol
+        lasti = i
+        if !SciMLBase.successful_retcode(_sol)
+            break
+        end
+    end
+
+    # TODO: fix allocations with a lazy concatenation
+    u .= reduce(vcat, sols)
+    resid .= reduce(vcat, getproperty.(sols, :resid))
+
+    retcode = sols[lasti].retcode
+
+    SciMLBase.build_solution(prob, alg, u, resid; retcode, original = sols)
+end
+
+end
diff --git a/lib/SCCNonlinearSolve/test/core_tests.jl b/lib/SCCNonlinearSolve/test/core_tests.jl
new file mode 100644
index 000000000..92843421d
--- /dev/null
+++ b/lib/SCCNonlinearSolve/test/core_tests.jl
@@ -0,0 +1,65 @@
+@testsetup module CoreRootfindTesting
+
+include("../../../common/common_rootfind_testing.jl")
+
+end
+
+@testitem "Manual SCC" setup=[CoreRootfindTesting] tags=[:core] begin
+    using NonlinearSolveFirstOrder
+    function f(du, u, p)
+        du[1] = cos(u[2]) - u[1]
+        du[2] = sin(u[1] + u[2]) + u[2]
+        du[3] = 2u[4] + u[3] + 1.0
+        du[4] = u[5]^2 + u[4]
+        du[5] = u[3]^2 + u[5]
+        du[6] = u[1] + u[2] + u[3] + u[4] + u[5] + 2.0u[6] + 2.5u[7] + 1.5u[8]
+        du[7] = u[1] + u[2] + u[3] + 2.0u[4] + u[5] + 4.0u[6] - 1.5u[7] + 1.5u[8]
+        du[8] = u[1] + 2.0u[2] + 3.0u[3] + 5.0u[4] + 6.0u[5] + u[6] - u[7] - u[8]
+    end
+    prob = NonlinearProblem(f, zeros(8))
+    sol = solve(prob, NewtonRaphson())
+
+    u0 = zeros(2)
+    p = zeros(3)
+
+    function f1(du, u, p)
+        du[1] = cos(u[2]) - u[1]
+        du[2] = sin(u[1] + u[2]) + u[2]
+    end
+    explicitfun1(p, sols) = nothing
+    prob1 = NonlinearProblem(
+        NonlinearFunction{true, SciMLBase.NoSpecialize}(f1), zeros(2), p)
+    sol1 = solve(prob1, NewtonRaphson())
+
+    function f2(du, u, p)
+        du[1] = 2u[2] + u[1] + 1.0
+        du[2] = u[3]^2 + u[2]
+        du[3] = u[1]^2 + u[3]
+    end
+    explicitfun2(p, sols) = nothing
+    prob2 = NonlinearProblem(
+        NonlinearFunction{true, SciMLBase.NoSpecialize}(f2), zeros(3), p)
+    sol2 = solve(prob2, NewtonRaphson())
+
+    function f3(du, u, p)
+        du[1] = p[1] + 2.0u[1] + 2.5u[2] + 1.5u[3]
+        du[2] = p[2] + 4.0u[1] - 1.5u[2] + 1.5u[3]
+        du[3] = p[3] + +u[1] - u[2] - u[3]
+    end
+    prob3 = NonlinearProblem(
+        NonlinearFunction{true, SciMLBase.NoSpecialize}(f3), zeros(3), p)
+    function explicitfun3(p, sols)
+        p[1] = sols[1][1] + sols[1][2] + sols[2][1] + sols[2][2] + sols[2][3]
+        p[2] = sols[1][1] + sols[1][2] + sols[2][1] + 2.0sols[2][2] + sols[2][3]
+        p[3] = sols[1][1] + 2.0sols[1][2] + 3.0sols[2][1] + 5.0sols[2][2] +
+               6.0sols[2][3]
+    end
+    explicitfun3(p, [sol1, sol2])
+    sol3 = solve(prob3, NewtonRaphson())
+    manualscc = [sol1; sol2; sol3]
+
+    sccprob = SciMLBase.SCCNonlinearProblem([prob1, prob2, prob3],
+        SciMLBase.Void{Any}.([explicitfun1, explicitfun2, explicitfun3]))
+    scc_sol = solve(sccprob, NewtonRaphson())
+    @test sol ≈ manualscc ≈ scc_sol
+end
diff --git a/lib/SCCNonlinearSolve/test/qa_tests.jl b/lib/SCCNonlinearSolve/test/qa_tests.jl
new file mode 100644
index 000000000..93111c1cc
--- /dev/null
+++ b/lib/SCCNonlinearSolve/test/qa_tests.jl
@@ -0,0 +1,25 @@
+@testitem "Aqua" tags=[:core] begin
+    using Aqua, SCCNonlinearSolve
+
+    Aqua.test_all(
+        SCCNonlinearSolve;
+        piracies = false, ambiguities = false, stale_deps = false, deps_compat = false
+    )
+    Aqua.test_stale_deps(
+        SCCNonlinearSolve; ignore = [:SciMLJacobianOperators, :NonlinearSolveBase])
+    Aqua.test_deps_compat(
+        SCCNonlinearSolve; ignore = [:SciMLJacobianOperators, :NonlinearSolveBase])
+    Aqua.test_piracies(
+        SCCNonlinearSolve; treat_as_own = [SCCNonlinearSolve.SciMLBase.solve])
+    Aqua.test_ambiguities(SCCNonlinearSolve; recursive = false)
+end
+
+@testitem "Explicit Imports" tags=[:core] begin
+    using ExplicitImports, SciMLBase, SCCNonlinearSolve
+
+    @test check_no_implicit_imports(
+        SCCNonlinearSolve; skip = (Base, Core, SciMLBase)
+    ) === nothing
+    @test check_no_stale_explicit_imports(SCCNonlinearSolve) === nothing
+    @test check_all_qualified_accesses_via_owners(SCCNonlinearSolve) === nothing
+end
diff --git a/lib/SCCNonlinearSolve/test/runtests.jl b/lib/SCCNonlinearSolve/test/runtests.jl
new file mode 100644
index 000000000..451760225
--- /dev/null
+++ b/lib/SCCNonlinearSolve/test/runtests.jl
@@ -0,0 +1,25 @@
+using ReTestItems, SCCNonlinearSolve, Hwloc, InteractiveUtils, Pkg
+
+@info sprint(InteractiveUtils.versioninfo)
+
+const GROUP = lowercase(get(ENV, "GROUP", "All"))
+
+const RETESTITEMS_NWORKERS = parse(
+    Int, get(ENV, "RETESTITEMS_NWORKERS",
+        string(min(ifelse(Sys.iswindows(), 0, Hwloc.num_physical_cores()), 4))
+    )
+)
+const RETESTITEMS_NWORKER_THREADS = parse(Int,
+    get(
+        ENV, "RETESTITEMS_NWORKER_THREADS",
+        string(max(Hwloc.num_virtual_cores() ÷ max(RETESTITEMS_NWORKERS, 1), 1))
+    )
+)
+
+@info "Running tests for group: $(GROUP) with $(RETESTITEMS_NWORKERS) workers"
+
+ReTestItems.runtests(
+    SCCNonlinearSolve; tags = (GROUP == "all" ? nothing : [Symbol(GROUP)]),
+    nworkers = RETESTITEMS_NWORKERS, nworker_threads = RETESTITEMS_NWORKER_THREADS,
+    testitem_timeout = 3600
+)

From 43e6b3d2bbff20ebdad19ee06e3bb89cf0ba599c Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Mon, 18 Nov 2024 05:57:14 -0100
Subject: [PATCH 686/700] chore(deps): bump codecov/codecov-action from 4 to 5
 (#505)

Bumps [codecov/codecov-action](https://github.com/codecov/codecov-action) from 4 to 5.
- [Release notes](https://github.com/codecov/codecov-action/releases)
- [Changelog](https://github.com/codecov/codecov-action/blob/main/CHANGELOG.md)
- [Commits](https://github.com/codecov/codecov-action/compare/v4...v5)

---
updated-dependencies:
- dependency-name: codecov/codecov-action
  dependency-type: direct:production
  update-type: version-update:semver-major
...

Signed-off-by: dependabot[bot] <support@github.com>
Co-authored-by: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com>
---
 .github/workflows/CI_BracketingNonlinearSolve.yml      | 4 ++--
 .github/workflows/CI_NonlinearSolve.yml                | 4 ++--
 .github/workflows/CI_NonlinearSolveBase.yml            | 4 ++--
 .github/workflows/CI_NonlinearSolveFirstOrder.yml      | 4 ++--
 .github/workflows/CI_NonlinearSolveQuasiNewton.yml     | 4 ++--
 .github/workflows/CI_NonlinearSolveSpectralMethods.yml | 4 ++--
 .github/workflows/CI_SCCNonlinearSolve.yml             | 4 ++--
 .github/workflows/CI_SciMLJacobianOperators.yml        | 4 ++--
 .github/workflows/CI_SimpleNonlinearSolve.yml          | 4 ++--
 .github/workflows/Documentation.yml                    | 2 +-
 .github/workflows/Downstream.yml                       | 2 +-
 11 files changed, 20 insertions(+), 20 deletions(-)

diff --git a/.github/workflows/CI_BracketingNonlinearSolve.yml b/.github/workflows/CI_BracketingNonlinearSolve.yml
index 03e5654f2..519f99e1c 100644
--- a/.github/workflows/CI_BracketingNonlinearSolve.yml
+++ b/.github/workflows/CI_BracketingNonlinearSolve.yml
@@ -63,7 +63,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/BracketingNonlinearSolve/src,lib/BracketingNonlinearSolve/ext,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
@@ -101,7 +101,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/BracketingNonlinearSolve/src,lib/BracketingNonlinearSolve/ext,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/CI_NonlinearSolve.yml b/.github/workflows/CI_NonlinearSolve.yml
index be4651464..3be961848 100644
--- a/.github/workflows/CI_NonlinearSolve.yml
+++ b/.github/workflows/CI_NonlinearSolve.yml
@@ -77,7 +77,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: src,ext,lib/SciMLJacobianOperators/src,lib/BracketingNonlinearSolve/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SimpleNonlinearSolve/src,lib/NonlinearSolveFirstOrder/src,lib/NonlinearSolveSpectralMethods/src,lib/NonlinearSolveQuasiNewton/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
@@ -121,7 +121,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: src,ext,lib/SciMLJacobianOperators/src,lib/BracketingNonlinearSolve/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SimpleNonlinearSolve/src,lib/NonlinearSolveFirstOrder/src,lib/NonlinearSolveSpectralMethods/src,lib/NonlinearSolveQuasiNewton/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/CI_NonlinearSolveBase.yml b/.github/workflows/CI_NonlinearSolveBase.yml
index 62868d191..1d0bb1b83 100644
--- a/.github/workflows/CI_NonlinearSolveBase.yml
+++ b/.github/workflows/CI_NonlinearSolveBase.yml
@@ -62,7 +62,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
@@ -100,7 +100,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/CI_NonlinearSolveFirstOrder.yml b/.github/workflows/CI_NonlinearSolveFirstOrder.yml
index e2313a3ad..a2def47e7 100644
--- a/.github/workflows/CI_NonlinearSolveFirstOrder.yml
+++ b/.github/workflows/CI_NonlinearSolveFirstOrder.yml
@@ -63,7 +63,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/NonlinearSolveFirstOrder/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
@@ -101,7 +101,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/NonlinearSolveFirstOrder/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/CI_NonlinearSolveQuasiNewton.yml b/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
index 9715d5789..d9b9df2f8 100644
--- a/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
+++ b/.github/workflows/CI_NonlinearSolveQuasiNewton.yml
@@ -63,7 +63,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/NonlinearSolveQuasiNewton/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
@@ -101,7 +101,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/NonlinearSolveQuasiNewton/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/CI_NonlinearSolveSpectralMethods.yml b/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
index 13cac0453..95cb8e2e2 100644
--- a/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
+++ b/.github/workflows/CI_NonlinearSolveSpectralMethods.yml
@@ -63,7 +63,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/NonlinearSolveSpectralMethods/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
@@ -101,7 +101,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/NonlinearSolveSpectralMethods/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/CI_SCCNonlinearSolve.yml b/.github/workflows/CI_SCCNonlinearSolve.yml
index a00e938e6..cbc5cf239 100644
--- a/.github/workflows/CI_SCCNonlinearSolve.yml
+++ b/.github/workflows/CI_SCCNonlinearSolve.yml
@@ -63,7 +63,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/SCCNonlinearSolve/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
@@ -101,7 +101,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/SCCNonlinearSolve/src,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/CI_SciMLJacobianOperators.yml b/.github/workflows/CI_SciMLJacobianOperators.yml
index 1807da8a6..378aa9292 100644
--- a/.github/workflows/CI_SciMLJacobianOperators.yml
+++ b/.github/workflows/CI_SciMLJacobianOperators.yml
@@ -55,7 +55,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
@@ -85,7 +85,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/SciMLJacobianOperators/src
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/CI_SimpleNonlinearSolve.yml b/.github/workflows/CI_SimpleNonlinearSolve.yml
index 63eb4b136..8b1956616 100644
--- a/.github/workflows/CI_SimpleNonlinearSolve.yml
+++ b/.github/workflows/CI_SimpleNonlinearSolve.yml
@@ -70,7 +70,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/SimpleNonlinearSolve/src,lib/SimpleNonlinearSolve/ext,lib/SciMLJacobianOperators/src,lib/BracketingNonlinearSolve/src,lib/BracketingNonlinearSolve/ext,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
@@ -114,7 +114,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: lib/SimpleNonlinearSolve/src,lib/SimpleNonlinearSolve/ext,lib/SciMLJacobianOperators/src,lib/BracketingNonlinearSolve/src,lib/BracketingNonlinearSolve/ext,lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/Documentation.yml b/.github/workflows/Documentation.yml
index 9cca57cf9..2c81172a3 100644
--- a/.github/workflows/Documentation.yml
+++ b/.github/workflows/Documentation.yml
@@ -35,7 +35,7 @@ jobs:
           DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }} # For authentication with SSH deploy key
         run: julia --project=docs/ --code-coverage=user --color=yes docs/make.jl
       - uses: julia-actions/julia-processcoverage@v1
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/Downstream.yml b/.github/workflows/Downstream.yml
index 933ff30d9..d5669b435 100644
--- a/.github/workflows/Downstream.yml
+++ b/.github/workflows/Downstream.yml
@@ -69,7 +69,7 @@ jobs:
       - uses: julia-actions/julia-processcoverage@v1
         with:
           directories: src,ext
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}

From ae57fb67c0ad70c8710664d0fc782ce688e3dd9f Mon Sep 17 00:00:00 2001
From: Qingyu Qu <52615090+ErikQQY@users.noreply.github.com>
Date: Mon, 18 Nov 2024 18:03:03 +0800
Subject: [PATCH 687/700] refactor: Move RobustMultiNewton to
 NonlinearSolveFirstOrder (#499)

* refactor: Move RobustMultiNewton to NonlinearSolveFirstOrder

* refactor: Implicit import NonlinearSolvePolyAlgorithm
---
 Project.toml                                  |  2 +-
 lib/NonlinearSolveFirstOrder/Project.toml     |  1 +
 .../src/NonlinearSolveFirstOrder.jl           |  8 +++-
 lib/NonlinearSolveFirstOrder/src/poly_algs.jl | 44 ++++++++++++++++++
 src/NonlinearSolve.jl                         |  5 +--
 src/poly_algs.jl                              | 45 -------------------
 6 files changed, 55 insertions(+), 50 deletions(-)
 create mode 100644 lib/NonlinearSolveFirstOrder/src/poly_algs.jl

diff --git a/Project.toml b/Project.toml
index 7802b1bd8..c4f7a26b2 100644
--- a/Project.toml
+++ b/Project.toml
@@ -96,9 +96,9 @@ NonlinearSolveSpectralMethods = "1"
 OrdinaryDiffEqTsit5 = "1.1.0"
 PETSc = "0.3"
 Pkg = "1.10"
+PolyesterForwardDiff = "0.1"
 PrecompileTools = "1.2"
 Preferences = "1.4"
-PolyesterForwardDiff = "0.1"
 Random = "1.10"
 ReTestItems = "1.24"
 Reexport = "1.2"
diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
index 94ab4fdbc..63f9f55eb 100644
--- a/lib/NonlinearSolveFirstOrder/Project.toml
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -13,6 +13,7 @@ FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
+LineSearch = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
 NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
diff --git a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
index 145468122..1f480fb4b 100644
--- a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
+++ b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
@@ -8,6 +8,7 @@ using Setfield: @set!
 using ADTypes: ADTypes
 using ArrayInterface: ArrayInterface
 using LinearAlgebra: LinearAlgebra, Diagonal, dot, diagind
+using LineSearch: BackTracking
 using StaticArraysCore: SArray
 
 using CommonSolve: CommonSolve
@@ -19,7 +20,7 @@ using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
                           AbstractDampingFunctionCache, AbstractTrustRegionMethod,
                           AbstractTrustRegionMethodCache,
                           Utils, InternalAPI, get_timer_output, @static_timeit,
-                          update_trace!, L2_NORM,
+                          update_trace!, L2_NORM, NonlinearSolvePolyAlgorithm,
                           NewtonDescent, DampedNewtonDescent, GeodesicAcceleration,
                           Dogleg
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode,
@@ -36,6 +37,8 @@ include("levenberg_marquardt.jl")
 include("trust_region.jl")
 include("pseudo_transient.jl")
 
+include("poly_algs.jl")
+
 include("solve.jl")
 
 @setup_workload begin
@@ -100,4 +103,7 @@ export RadiusUpdateSchemes
 
 export GeneralizedFirstOrderAlgorithm
 
+# Polyalgorithms
+export RobustMultiNewton
+
 end
diff --git a/lib/NonlinearSolveFirstOrder/src/poly_algs.jl b/lib/NonlinearSolveFirstOrder/src/poly_algs.jl
new file mode 100644
index 000000000..06dcc1c5a
--- /dev/null
+++ b/lib/NonlinearSolveFirstOrder/src/poly_algs.jl
@@ -0,0 +1,44 @@
+"""
+    RobustMultiNewton(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+    )
+
+A polyalgorithm focused on robustness. It uses a mixture of Newton methods with different
+globalizing techniques (trust region updates, line searches, etc.) in order to find a
+method that is able to adequately solve the minimization problem.
+
+Basically, if this algorithm fails, then "most" good ways of solving your problem fail and
+you may need to think about reformulating the model (either there is an issue with the model,
+or more precision / more stable linear solver choice is required).
+
+### Arguments
+
+  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
+    are compatible with the problem type. Defaults to `Float64`.
+"""
+function RobustMultiNewton(
+        ::Type{T} = Float64;
+        concrete_jac = nothing,
+        linsolve = nothing,
+        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
+) where {T}
+    common_kwargs = (; concrete_jac, linsolve, autodiff, vjp_autodiff, jvp_autodiff)
+    if T <: Complex # Let's atleast have something here for complex numbers
+        algs = (
+            NewtonRaphson(; common_kwargs...),
+        )
+    else
+        algs = (
+            TrustRegion(; common_kwargs...),
+            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin),
+            NewtonRaphson(; common_kwargs...),
+            NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
+            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.NLsolve),
+            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Fan)
+        )
+    end
+    return NonlinearSolvePolyAlgorithm(algs)
+end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 3aa4cac22..4c44cc972 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -25,7 +25,7 @@ using StaticArraysCore: StaticArray
 
 # Default Algorithm
 using NonlinearSolveFirstOrder: NewtonRaphson, TrustRegion, LevenbergMarquardt, GaussNewton,
-                                RUS
+                                RUS, RobustMultiNewton
 using NonlinearSolveQuasiNewton: Broyden, Klement
 using SimpleNonlinearSolve: SimpleBroyden, SimpleKlement
 
@@ -125,8 +125,7 @@ end
 @reexport using LinearSolve
 
 # Poly Algorithms
-export NonlinearSolvePolyAlgorithm,
-       RobustMultiNewton, FastShortcutNonlinearPolyalg, FastShortcutNLLSPolyalg
+export NonlinearSolvePolyAlgorithm, FastShortcutNonlinearPolyalg, FastShortcutNLLSPolyalg
 
 # Extension Algorithms
 export LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
diff --git a/src/poly_algs.jl b/src/poly_algs.jl
index 31c16917f..3b13ba84f 100644
--- a/src/poly_algs.jl
+++ b/src/poly_algs.jl
@@ -1,48 +1,3 @@
-"""
-    RobustMultiNewton(
-        ::Type{T} = Float64;
-        concrete_jac = nothing,
-        linsolve = nothing,
-        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
-    )
-
-A polyalgorithm focused on robustness. It uses a mixture of Newton methods with different
-globalizing techniques (trust region updates, line searches, etc.) in order to find a
-method that is able to adequately solve the minimization problem.
-
-Basically, if this algorithm fails, then "most" good ways of solving your problem fail and
-you may need to think about reformulating the model (either there is an issue with the model,
-or more precision / more stable linear solver choice is required).
-
-### Arguments
-
-  - `T`: The eltype of the initial guess. It is only used to check if some of the algorithms
-    are compatible with the problem type. Defaults to `Float64`.
-"""
-function RobustMultiNewton(
-        ::Type{T} = Float64;
-        concrete_jac = nothing,
-        linsolve = nothing,
-        autodiff = nothing, vjp_autodiff = nothing, jvp_autodiff = nothing
-) where {T}
-    common_kwargs = (; concrete_jac, linsolve, autodiff, vjp_autodiff, jvp_autodiff)
-    if T <: Complex # Let's atleast have something here for complex numbers
-        algs = (
-            NewtonRaphson(; common_kwargs...),
-        )
-    else
-        algs = (
-            TrustRegion(; common_kwargs...),
-            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Bastin),
-            NewtonRaphson(; common_kwargs...),
-            NewtonRaphson(; common_kwargs..., linesearch = BackTracking()),
-            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.NLsolve),
-            TrustRegion(; common_kwargs..., radius_update_scheme = RUS.Fan)
-        )
-    end
-    return NonlinearSolvePolyAlgorithm(algs)
-end
-
 """
     FastShortcutNonlinearPolyalg(
         ::Type{T} = Float64;

From 107477329bbe9320adf87f9ece6fa854d002d073 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 18 Nov 2024 09:03:56 -0100
Subject: [PATCH 688/700] Update Project.toml

---
 lib/NonlinearSolveFirstOrder/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
index 63f9f55eb..ee2d2c9de 100644
--- a/lib/NonlinearSolveFirstOrder/Project.toml
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolveFirstOrder"
 uuid = "5959db7a-ea39-4486-b5fe-2dd0bf03d60d"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.0.0"
+version = "1.1.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 7f90cf4555da855be72234a01672cc48ec43aec3 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 18 Nov 2024 09:04:12 -0100
Subject: [PATCH 689/700] Update Project.toml

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index c4f7a26b2..79b69daf3 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "4.1.0"
+version = "4.2.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

From 83f8c3d43efc67219077b627038e5bacde8358fc Mon Sep 17 00:00:00 2001
From: Aayush Sabharwal <aayush.sabharwal@gmail.com>
Date: Mon, 18 Nov 2024 19:46:49 +0530
Subject: [PATCH 690/700] fix: fix SII implementation for
 `NonlinearSolveNoInitCache` (#506)

Co-authored-by: Christopher Rackauckas <accounts@chrisrackauckas.com>
---
 lib/NonlinearSolveBase/src/solve.jl | 2 ++
 test/mtk_cache_indexing_tests.jl    | 3 +++
 2 files changed, 5 insertions(+)

diff --git a/lib/NonlinearSolveBase/src/solve.jl b/lib/NonlinearSolveBase/src/solve.jl
index e4dd33636..66ad6a0e4 100644
--- a/lib/NonlinearSolveBase/src/solve.jl
+++ b/lib/NonlinearSolveBase/src/solve.jl
@@ -248,6 +248,8 @@ end
     kwargs::Any
 end
 
+get_u(cache::NonlinearSolveNoInitCache) = SII.state_values(cache.prob)
+
 function SciMLBase.reinit!(
         cache::NonlinearSolveNoInitCache, u0 = cache.prob.u0; p = cache.prob.p, kwargs...
 )
diff --git a/test/mtk_cache_indexing_tests.jl b/test/mtk_cache_indexing_tests.jl
index 6e059e78c..dc11a1147 100644
--- a/test/mtk_cache_indexing_tests.jl
+++ b/test/mtk_cache_indexing_tests.jl
@@ -20,6 +20,9 @@
         nint = init(nlprob, alg)
         @test nint isa integtype
 
+        @test_nowarn state_values(nint)
+        @test_nowarn parameter_values(nint)
+
         for (i, sym) in enumerate([X, nlsys.X, :X])
             # test both getindex and setindex!
             nint[sym] = 1.5i

From f5990ad9ce6ecb09c27dfb422e900aa060a90c93 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Beno=C3=AEt=20Pasquier?=
 <4486578+briochemc@users.noreply.github.com>
Date: Tue, 19 Nov 2024 13:45:27 +1100
Subject: [PATCH 691/700] docs: update release_notes.md (#508)

* Update release_notes.md

* Update docs/src/release_notes.md
---
 docs/src/release_notes.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/docs/src/release_notes.md b/docs/src/release_notes.md
index 0d4ce25e8..c97e5e584 100644
--- a/docs/src/release_notes.md
+++ b/docs/src/release_notes.md
@@ -5,8 +5,8 @@
 ### Breaking Changes in `NonlinearSolve.jl` v4
 
   - `ApproximateJacobianSolveAlgorithm` has been renamed to `QuasiNewtonAlgorithm`.
-  - Preconditioners for the linear solver needs to be specified with the linear solver
-    instead of `precs` keyword argument.
+  - Preconditioners for the linear solver needs to be passed with the `precs`
+    keyword argument to the linear solver instead of to the nonlinear solver.
   - See [common breaking changes](@ref common-breaking-changes-v4v2) below.
 
 ### Breaking Changes in `SimpleNonlinearSolve.jl` v2

From c340cdc593dc24f1c0813527501e289ea79cf8be Mon Sep 17 00:00:00 2001
From: Aayush Sabharwal <aayush.sabharwal@gmail.com>
Date: Tue, 19 Nov 2024 19:57:02 +0530
Subject: [PATCH 692/700] fix: fix MTK indexing tests (#509)

---
 test/mtk_cache_indexing_tests.jl | 1 +
 test/runtests.jl                 | 4 +++-
 2 files changed, 4 insertions(+), 1 deletion(-)

diff --git a/test/mtk_cache_indexing_tests.jl b/test/mtk_cache_indexing_tests.jl
index dc11a1147..633c20d82 100644
--- a/test/mtk_cache_indexing_tests.jl
+++ b/test/mtk_cache_indexing_tests.jl
@@ -1,6 +1,7 @@
 @testitem "Modeling Toolkit Cache Indexing" tags=[:downstream] begin
     using ModelingToolkit
     using ModelingToolkit: t_nounits as t
+    using SymbolicIndexingInterface
     import NonlinearSolveBase, NonlinearSolveFirstOrder
 
     @parameters p d
diff --git a/test/runtests.jl b/test/runtests.jl
index c8e8b0f4e..bfdd07b35 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -5,8 +5,10 @@ using ReTestItems, NonlinearSolve, Hwloc, InteractiveUtils, Pkg
 const GROUP = lowercase(get(ENV, "GROUP", "All"))
 
 const EXTRA_PKGS = Pkg.PackageSpec[]
-(GROUP == "all" || GROUP == "downstream") &&
+if GROUP == "all" || GROUP == "downstream"
     push!(EXTRA_PKGS, Pkg.PackageSpec("ModelingToolkit"))
+    push!(EXTRA_PKGS, Pkg.PackageSpec("SymbolicIndexingInterface"))
+end
 length(EXTRA_PKGS) ≥ 1 && Pkg.add(EXTRA_PKGS)
 
 const RETESTITEMS_NWORKERS = parse(

From 87c66b4a867e782f783848101666f69f6c2b7a09 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 3 Dec 2024 11:34:34 -0500
Subject: [PATCH 693/700] fix: remove compiled reversediff from default options
 (#514)

---
 lib/NonlinearSolveBase/Project.toml              |  4 +---
 lib/NonlinearSolveBase/src/NonlinearSolveBase.jl |  1 -
 lib/NonlinearSolveBase/src/autodiff.jl           | 10 ----------
 3 files changed, 1 insertion(+), 14 deletions(-)

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 4cc10a6be..2f5404dc7 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolveBase"
 uuid = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.3.3"
+version = "1.4.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -13,7 +13,6 @@ ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
 FastClosures = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
-FunctionProperties = "f62d2435-5019-4c03-9749-2d4c77af0cbc"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 MaybeInplace = "bb5d69b7-63fc-4a16-80bd-7e42200c7bdb"
@@ -60,7 +59,6 @@ EnzymeCore = "0.8"
 ExplicitImports = "1.10.1"
 FastClosures = "0.3"
 ForwardDiff = "0.10.36"
-FunctionProperties = "0.1.2"
 InteractiveUtils = "<0.0.1, 1"
 LineSearch = "0.1.4"
 LinearAlgebra = "1.10"
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 649ac79d2..858137bff 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -14,7 +14,6 @@ using StaticArraysCore: StaticArray, SMatrix, SArray, MArray
 
 using CommonSolve: CommonSolve, init
 using EnzymeCore: EnzymeCore
-using FunctionProperties: hasbranching
 using MaybeInplace: @bb
 using RecursiveArrayTools: AbstractVectorOfArray, ArrayPartition
 using SciMLBase: SciMLBase, ReturnCode, AbstractODEIntegrator, AbstractNonlinearProblem,
diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
index c92a3e27d..a05ee0b56 100644
--- a/lib/NonlinearSolveBase/src/autodiff.jl
+++ b/lib/NonlinearSolveBase/src/autodiff.jl
@@ -8,7 +8,6 @@
     const ReverseADs = (
         ADTypes.AutoZygote(),
         ADTypes.AutoTracker(),
-        ADTypes.AutoReverseDiff(; compile = true),
         ADTypes.AutoReverseDiff(),
         ADTypes.AutoEnzyme(; mode = EnzymeCore.Reverse),
         ADTypes.AutoFiniteDiff()
@@ -18,7 +17,6 @@ else
         ADTypes.AutoEnzyme(; mode = EnzymeCore.Reverse),
         ADTypes.AutoZygote(),
         ADTypes.AutoTracker(),
-        ADTypes.AutoReverseDiff(; compile = true),
         ADTypes.AutoReverseDiff(),
         ADTypes.AutoFiniteDiff()
     )
@@ -116,14 +114,6 @@ function incompatible_backend_and_problem(
 end
 
 additional_incompatible_backend_check(::AbstractNonlinearProblem, ::AbstractADType) = false
-function additional_incompatible_backend_check(prob::AbstractNonlinearProblem,
-        ::ADTypes.AutoReverseDiff{true})
-    if SciMLBase.isinplace(prob)
-        fu = prob.f.resid_prototype === nothing ? zero(prob.u0) : prob.f.resid_prototype
-        return hasbranching(prob.f, fu, prob.u0, prob.p)
-    end
-    return hasbranching(prob.f, prob.u0, prob.p)
-end
 function additional_incompatible_backend_check(
         prob::AbstractNonlinearProblem, ::ADTypes.AutoPolyesterForwardDiff)
     prob.u0 isa SArray && return true # promotes to a mutable array

From 228434824c17e179fc416c16ed99fc3b67a1eb16 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Tue, 3 Dec 2024 22:12:39 -0500
Subject: [PATCH 694/700] fix: enzyme is now properly supported in 1.11 (#515)

* fix: remove compiled reversediff from default options

* fix: enzyme is now properly supported in 1.11
---
 lib/NonlinearSolveBase/src/autodiff.jl | 25 +++++++------------------
 1 file changed, 7 insertions(+), 18 deletions(-)

diff --git a/lib/NonlinearSolveBase/src/autodiff.jl b/lib/NonlinearSolveBase/src/autodiff.jl
index a05ee0b56..5f9843e9a 100644
--- a/lib/NonlinearSolveBase/src/autodiff.jl
+++ b/lib/NonlinearSolveBase/src/autodiff.jl
@@ -3,24 +3,13 @@
 
 # Ordering is important here. We want to select the first one that is compatible with the
 # problem.
-# XXX: Remove this once Enzyme is properly supported on Julia 1.11+
-@static if VERSION ≥ v"1.11-"
-    const ReverseADs = (
-        ADTypes.AutoZygote(),
-        ADTypes.AutoTracker(),
-        ADTypes.AutoReverseDiff(),
-        ADTypes.AutoEnzyme(; mode = EnzymeCore.Reverse),
-        ADTypes.AutoFiniteDiff()
-    )
-else
-    const ReverseADs = (
-        ADTypes.AutoEnzyme(; mode = EnzymeCore.Reverse),
-        ADTypes.AutoZygote(),
-        ADTypes.AutoTracker(),
-        ADTypes.AutoReverseDiff(),
-        ADTypes.AutoFiniteDiff()
-    )
-end
+const ReverseADs = (
+    ADTypes.AutoEnzyme(; mode = EnzymeCore.Reverse),
+    ADTypes.AutoZygote(),
+    ADTypes.AutoTracker(),
+    ADTypes.AutoReverseDiff(),
+    ADTypes.AutoFiniteDiff()
+)
 
 const ForwardADs = (
     ADTypes.AutoPolyesterForwardDiff(),

From 2002bd4fe880de2f7b976ed091b8b4c4a471142a Mon Sep 17 00:00:00 2001
From: Qingyu Qu <52615090+ErikQQY@users.noreply.github.com>
Date: Wed, 11 Dec 2024 13:26:40 +0800
Subject: [PATCH 695/700] refactor: Move dual nonlinear solving to
 NonlinearSolveBase (#513)

---
 docs/src/basics/faq.md                        |  4 +-
 .../ext/NonlinearSolveBaseForwardDiffExt.jl   | 98 ++++++++++++++++++-
 .../src/NonlinearSolveBase.jl                 |  4 +
 lib/NonlinearSolveBase/src/forward_diff.jl    |  8 ++
 lib/NonlinearSolveBase/src/public.jl          |  9 ++
 lib/NonlinearSolveFirstOrder/Project.toml     |  3 +-
 .../src/NonlinearSolveFirstOrder.jl           |  6 +-
 .../src/forward_diff.jl                       | 34 +++++++
 .../test/misc_tests.jl                        | 10 ++
 lib/NonlinearSolveQuasiNewton/Project.toml    |  6 ++
 ...NonlinearSolveQuasiNewtonForwardDiffExt.jl | 46 +++++++++
 .../Project.toml                              |  7 ++
 ...inearSolveSpectralMethodsForwardDiffExt.jl | 46 +++++++++
 src/NonlinearSolve.jl                         | 11 +--
 src/forward_diff.jl                           | 95 ++++--------------
 15 files changed, 294 insertions(+), 93 deletions(-)
 create mode 100644 lib/NonlinearSolveBase/src/forward_diff.jl
 create mode 100644 lib/NonlinearSolveFirstOrder/src/forward_diff.jl
 create mode 100644 lib/NonlinearSolveQuasiNewton/ext/NonlinearSolveQuasiNewtonForwardDiffExt.jl
 create mode 100644 lib/NonlinearSolveSpectralMethods/ext/NonlinearSolveSpectralMethodsForwardDiffExt.jl

diff --git a/docs/src/basics/faq.md b/docs/src/basics/faq.md
index 4d428250a..9aabc203b 100644
--- a/docs/src/basics/faq.md
+++ b/docs/src/basics/faq.md
@@ -152,10 +152,10 @@ nothing # hide
 ```
 
 And boom! Type stable again. We always recommend picking the chunksize via
-[`NonlinearSolve.pickchunksize`](@ref), however, if you manually specify the chunksize, it
+[`NonlinearSolveBase.pickchunksize`](@ref), however, if you manually specify the chunksize, it
 must be `≤ length of input`. However, a very large chunksize can lead to excessive
 compilation times and slowdown.
 
 ```@docs
-NonlinearSolve.pickchunksize
+NonlinearSolveBase.pickchunksize
 ```
diff --git a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
index bb3165396..717daa8e4 100644
--- a/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
+++ b/lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl
@@ -2,17 +2,35 @@ module NonlinearSolveBaseForwardDiffExt
 
 using ADTypes: ADTypes, AutoForwardDiff, AutoPolyesterForwardDiff
 using ArrayInterface: ArrayInterface
-using CommonSolve: solve
+using CommonSolve: CommonSolve, solve, solve!, init
+using ConcreteStructs: @concrete
 using DifferentiationInterface: DifferentiationInterface
 using FastClosures: @closure
-using ForwardDiff: ForwardDiff, Dual
+using ForwardDiff: ForwardDiff, Dual, pickchunksize
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, IntervalNonlinearProblem,
                  NonlinearProblem, NonlinearLeastSquaresProblem, remake
 
-using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, Utils
+using NonlinearSolveBase: NonlinearSolveBase, ImmutableNonlinearProblem, Utils, InternalAPI,
+                          NonlinearSolvePolyAlgorithm, NonlinearSolveForwardDiffCache
 
 const DI = DifferentiationInterface
 
+const GENERAL_SOLVER_TYPES = [
+    Nothing, NonlinearSolvePolyAlgorithm
+]
+
+const DualNonlinearProblem = NonlinearProblem{
+    <:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {iip, T, V, P}
+const DualNonlinearLeastSquaresProblem = NonlinearLeastSquaresProblem{
+    <:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {iip, T, V, P}
+const DualAbstractNonlinearProblem = Union{
+    DualNonlinearProblem, DualNonlinearLeastSquaresProblem
+}
+
 function NonlinearSolveBase.additional_incompatible_backend_check(
         prob::AbstractNonlinearProblem, ::Union{AutoForwardDiff, AutoPolyesterForwardDiff})
     return !ForwardDiff.can_dual(eltype(prob.u0))
@@ -102,4 +120,78 @@ function NonlinearSolveBase.nonlinearsolve_dual_solution(
     return map(((uᵢ, pᵢ),) -> Dual{T, V, P}(uᵢ, pᵢ), zip(u, Utils.restructure(u, partials)))
 end
 
+for algType in GENERAL_SOLVER_TYPES
+    @eval function SciMLBase.__solve(
+            prob::DualAbstractNonlinearProblem, alg::$(algType), args...; kwargs...
+    )
+        sol, partials = NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
+            prob, alg, args...; kwargs...
+        )
+        dual_soln = NonlinearSolveBase.nonlinearsolve_dual_solution(sol.u, partials, prob.p)
+        return SciMLBase.build_solution(
+            prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
+        )
+    end
+end
+
+function InternalAPI.reinit!(
+        cache::NonlinearSolveForwardDiffCache, args...;
+        p = cache.p, u0 = NonlinearSolveBase.get_u(cache.cache), kwargs...
+)
+    InternalAPI.reinit!(
+        cache.cache; p = NonlinearSolveBase.nodual_value(p),
+        u0 = NonlinearSolveBase.nodual_value(u0), kwargs...
+    )
+    cache.p = p
+    cache.values_p = NonlinearSolveBase.nodual_value(p)
+    cache.partials_p = ForwardDiff.partials(p)
+    return cache
+end
+
+for algType in GENERAL_SOLVER_TYPES
+    @eval function SciMLBase.__init(
+            prob::DualAbstractNonlinearProblem, alg::$(algType), args...; kwargs...
+    )
+        p = NonlinearSolveBase.nodual_value(prob.p)
+        newprob = SciMLBase.remake(prob; u0 = NonlinearSolveBase.nodual_value(prob.u0), p)
+        cache = init(newprob, alg, args...; kwargs...)
+        return NonlinearSolveForwardDiffCache(
+            cache, newprob, alg, prob.p, p, ForwardDiff.partials(prob.p)
+        )
+    end
+end
+
+function CommonSolve.solve!(cache::NonlinearSolveForwardDiffCache)
+    sol = solve!(cache.cache)
+    prob = cache.prob
+    uu = sol.u
+
+    fn = prob isa NonlinearLeastSquaresProblem ?
+         NonlinearSolveBase.nlls_generate_vjp_function(prob, sol, uu) : prob.f
+
+    Jₚ = NonlinearSolveBase.nonlinearsolve_∂f_∂p(prob, fn, uu, cache.values_p)
+    Jᵤ = NonlinearSolveBase.nonlinearsolve_∂f_∂u(prob, fn, uu, cache.values_p)
+
+    z_arr = -Jᵤ \ Jₚ
+
+    sumfun = ((z, p),) -> map(zᵢ -> zᵢ * ForwardDiff.partials(p), z)
+    if cache.p isa Number
+        partials = sumfun((z_arr, cache.p))
+    else
+        partials = sum(sumfun, zip(eachcol(z_arr), cache.p))
+    end
+
+    dual_soln = NonlinearSolveBase.nonlinearsolve_dual_solution(sol.u, partials, cache.p)
+    return SciMLBase.build_solution(
+        prob, cache.alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
+    )
+end
+
+NonlinearSolveBase.nodual_value(x) = x
+NonlinearSolveBase.nodual_value(x::Dual) = ForwardDiff.value(x)
+NonlinearSolveBase.nodual_value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
+
+@inline NonlinearSolveBase.pickchunksize(x) = pickchunksize(length(x))
+@inline NonlinearSolveBase.pickchunksize(x::Int) = ForwardDiff.pickchunksize(x)
+
 end
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index 858137bff..f45ba9242 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -57,6 +57,8 @@ include("descent/geodesic_acceleration.jl")
 
 include("solve.jl")
 
+include("forward_diff.jl")
+
 # Unexported Public API
 @compat(public, (L2_NORM, Linf_NORM, NAN_CHECK, UNITLESS_ABS2, get_tolerance))
 @compat(public, (nonlinearsolve_forwarddiff_solve, nonlinearsolve_dual_solution))
@@ -83,4 +85,6 @@ export DescentResult, SteepestDescent, NewtonDescent, DampedNewtonDescent, Dogle
 
 export NonlinearSolvePolyAlgorithm
 
+export pickchunksize
+
 end
diff --git a/lib/NonlinearSolveBase/src/forward_diff.jl b/lib/NonlinearSolveBase/src/forward_diff.jl
new file mode 100644
index 000000000..a588aa52d
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/forward_diff.jl
@@ -0,0 +1,8 @@
+@concrete mutable struct NonlinearSolveForwardDiffCache <: AbstractNonlinearSolveCache
+    cache
+    prob
+    alg
+    p
+    values_p
+    partials_p
+end
diff --git a/lib/NonlinearSolveBase/src/public.jl b/lib/NonlinearSolveBase/src/public.jl
index d076f7873..a9bae2a5e 100644
--- a/lib/NonlinearSolveBase/src/public.jl
+++ b/lib/NonlinearSolveBase/src/public.jl
@@ -11,6 +11,15 @@ function nonlinearsolve_dual_solution end
 function nonlinearsolve_∂f_∂p end
 function nonlinearsolve_∂f_∂u end
 function nlls_generate_vjp_function end
+function nodual_value end
+
+"""
+    pickchunksize(x) = pickchunksize(length(x))
+    pickchunksize(x::Int)
+
+Determine the chunk size for ForwardDiff and PolyesterForwardDiff based on the input length.
+"""
+function pickchunksize end
 
 # Nonlinear Solve Termination Conditions
 abstract type AbstractNonlinearTerminationMode end
diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
index ee2d2c9de..c299b6dc1 100644
--- a/lib/NonlinearSolveFirstOrder/Project.toml
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -67,6 +67,7 @@ julia = "1.10"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 Hwloc = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
@@ -86,4 +87,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BenchmarkTools", "Enzyme", "ExplicitImports", "Hwloc", "InteractiveUtils", "LineSearch", "LineSearches", "NonlinearProblemLibrary", "Pkg", "Random", "ReTestItems", "SparseArrays", "SparseConnectivityTracer", "SparseMatrixColorings", "StableRNGs", "StaticArrays", "Test", "Zygote"]
+test = ["Aqua", "BandedMatrices", "BenchmarkTools", "ForwardDiff", "Enzyme", "ExplicitImports", "Hwloc", "InteractiveUtils", "LineSearch", "LineSearches", "NonlinearProblemLibrary", "Pkg", "Random", "ReTestItems", "SparseArrays", "SparseConnectivityTracer", "SparseMatrixColorings", "StableRNGs", "StaticArrays", "Test", "Zygote"]
diff --git a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
index 1f480fb4b..666cc7435 100644
--- a/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
+++ b/lib/NonlinearSolveFirstOrder/src/NonlinearSolveFirstOrder.jl
@@ -22,14 +22,14 @@ using NonlinearSolveBase: NonlinearSolveBase, AbstractNonlinearSolveAlgorithm,
                           Utils, InternalAPI, get_timer_output, @static_timeit,
                           update_trace!, L2_NORM, NonlinearSolvePolyAlgorithm,
                           NewtonDescent, DampedNewtonDescent, GeodesicAcceleration,
-                          Dogleg
+                          Dogleg, NonlinearSolveForwardDiffCache
 using SciMLBase: SciMLBase, AbstractNonlinearProblem, NLStats, ReturnCode,
                  NonlinearFunction,
                  NonlinearLeastSquaresProblem, NonlinearProblem, NoSpecialize
 using SciMLJacobianOperators: VecJacOperator, JacVecOperator, StatefulJacobianOperator
 
 using FiniteDiff: FiniteDiff    # Default Finite Difference Method
-using ForwardDiff: ForwardDiff  # Default Forward Mode AD
+using ForwardDiff: ForwardDiff, Dual  # Default Forward Mode AD
 
 include("raphson.jl")
 include("gauss_newton.jl")
@@ -41,6 +41,8 @@ include("poly_algs.jl")
 
 include("solve.jl")
 
+include("forward_diff.jl")
+
 @setup_workload begin
     nonlinear_functions = (
         (NonlinearFunction{false, NoSpecialize}((u, p) -> u .* u .- p), 0.1),
diff --git a/lib/NonlinearSolveFirstOrder/src/forward_diff.jl b/lib/NonlinearSolveFirstOrder/src/forward_diff.jl
new file mode 100644
index 000000000..86f4b072a
--- /dev/null
+++ b/lib/NonlinearSolveFirstOrder/src/forward_diff.jl
@@ -0,0 +1,34 @@
+const DualNonlinearProblem = NonlinearProblem{
+    <:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {iip, T, V, P}
+const DualNonlinearLeastSquaresProblem = NonlinearLeastSquaresProblem{
+    <:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {iip, T, V, P}
+const DualAbstractNonlinearProblem = Union{
+    DualNonlinearProblem, DualNonlinearLeastSquaresProblem
+}
+
+function SciMLBase.__init(
+        prob::DualAbstractNonlinearProblem, alg::GeneralizedFirstOrderAlgorithm, args...; kwargs...
+)
+    p = NonlinearSolveBase.nodual_value(prob.p)
+    newprob = SciMLBase.remake(prob; u0 = NonlinearSolveBase.nodual_value(prob.u0), p)
+    cache = init(newprob, alg, args...; kwargs...)
+    return NonlinearSolveForwardDiffCache(
+        cache, newprob, alg, prob.p, p, ForwardDiff.partials(prob.p)
+    )
+end
+
+function SciMLBase.__solve(
+        prob::DualAbstractNonlinearProblem, alg::GeneralizedFirstOrderAlgorithm, args...; kwargs...
+)
+    sol, partials = NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
+        prob, alg, args...; kwargs...
+    )
+    dual_soln = NonlinearSolveBase.nonlinearsolve_dual_solution(sol.u, partials, prob.p)
+    return SciMLBase.build_solution(
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
+    )
+end
diff --git a/lib/NonlinearSolveFirstOrder/test/misc_tests.jl b/lib/NonlinearSolveFirstOrder/test/misc_tests.jl
index 40fcb2c55..79c63f37c 100644
--- a/lib/NonlinearSolveFirstOrder/test/misc_tests.jl
+++ b/lib/NonlinearSolveFirstOrder/test/misc_tests.jl
@@ -20,3 +20,13 @@
     @test sol.retcode == ReturnCode.Success
     @test jac_calls == 0
 end
+
+@testitem "Dual of BigFloat: Issue #512" tags=[:core] begin
+    using NonlinearSolveFirstOrder, ForwardDiff
+    fn_iip = NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p)
+    u2 = [ForwardDiff.Dual(BigFloat(1.0), 5.0), ForwardDiff.Dual(BigFloat(1.0), 5.0),
+        ForwardDiff.Dual(BigFloat(1.0), 5.0)]
+    prob_iip_bf = NonlinearProblem{true}(fn_iip, u2, ForwardDiff.Dual(BigFloat(2.0), 5.0))
+    sol = solve(prob_iip_bf, NewtonRaphson())
+    @test sol.retcode == ReturnCode.Success
+end
diff --git a/lib/NonlinearSolveQuasiNewton/Project.toml b/lib/NonlinearSolveQuasiNewton/Project.toml
index 2f00863d8..4912e9070 100644
--- a/lib/NonlinearSolveQuasiNewton/Project.toml
+++ b/lib/NonlinearSolveQuasiNewton/Project.toml
@@ -18,6 +18,12 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
+[weakdeps]
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+
+[extensions]
+NonlinearSolveQuasiNewtonForwardDiffExt = "ForwardDiff"
+
 [compat]
 ADTypes = "1.9.0"
 Aqua = "0.8"
diff --git a/lib/NonlinearSolveQuasiNewton/ext/NonlinearSolveQuasiNewtonForwardDiffExt.jl b/lib/NonlinearSolveQuasiNewton/ext/NonlinearSolveQuasiNewtonForwardDiffExt.jl
new file mode 100644
index 000000000..74ec64031
--- /dev/null
+++ b/lib/NonlinearSolveQuasiNewton/ext/NonlinearSolveQuasiNewtonForwardDiffExt.jl
@@ -0,0 +1,46 @@
+module NonlinearSolveQuasiNewtonForwardDiffExt
+
+using CommonSolve: CommonSolve, init
+using ForwardDiff: ForwardDiff, Dual
+using SciMLBase: SciMLBase, NonlinearProblem, NonlinearLeastSquaresProblem
+
+using NonlinearSolveBase: NonlinearSolveBase, NonlinearSolveForwardDiffCache, nodual_value
+
+using NonlinearSolveQuasiNewton: QuasiNewtonAlgorithm
+
+const DualNonlinearProblem = NonlinearProblem{
+    <:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {iip, T, V, P}
+const DualNonlinearLeastSquaresProblem = NonlinearLeastSquaresProblem{
+    <:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {iip, T, V, P}
+const DualAbstractNonlinearProblem = Union{
+    DualNonlinearProblem, DualNonlinearLeastSquaresProblem
+}
+
+function SciMLBase.__solve(
+        prob::DualAbstractNonlinearProblem, alg::QuasiNewtonAlgorithm, args...; kwargs...
+)
+    sol, partials = NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
+        prob, alg, args...; kwargs...
+    )
+    dual_soln = NonlinearSolveBase.nonlinearsolve_dual_solution(sol.u, partials, prob.p)
+    return SciMLBase.build_solution(
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
+    )
+end
+
+function SciMLBase.__init(
+        prob::DualAbstractNonlinearProblem, alg::QuasiNewtonAlgorithm, args...; kwargs...
+)
+    p = nodual_value(prob.p)
+    newprob = SciMLBase.remake(prob; u0 = nodual_value(prob.u0), p)
+    cache = init(newprob, alg, args...; kwargs...)
+    return NonlinearSolveForwardDiffCache(
+        cache, newprob, alg, prob.p, p, ForwardDiff.partials(prob.p)
+    )
+end
+
+end
diff --git a/lib/NonlinearSolveSpectralMethods/Project.toml b/lib/NonlinearSolveSpectralMethods/Project.toml
index bb9367554..a248be107 100644
--- a/lib/NonlinearSolveSpectralMethods/Project.toml
+++ b/lib/NonlinearSolveSpectralMethods/Project.toml
@@ -14,6 +14,12 @@ PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 
+[weakdeps]
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+
+[extensions]
+NonlinearSolveSpectralMethodsForwardDiffExt = "ForwardDiff"
+
 [compat]
 Aqua = "0.8"
 BenchmarkTools = "1.5.0"
@@ -21,6 +27,7 @@ CommonSolve = "0.2.4"
 ConcreteStructs = "0.2.3"
 DiffEqBase = "6.158.3"
 ExplicitImports = "1.5"
+ForwardDiff = "0.10.36"
 Hwloc = "3"
 InteractiveUtils = "<0.0.1, 1"
 LineSearch = "0.1.4"
diff --git a/lib/NonlinearSolveSpectralMethods/ext/NonlinearSolveSpectralMethodsForwardDiffExt.jl b/lib/NonlinearSolveSpectralMethods/ext/NonlinearSolveSpectralMethodsForwardDiffExt.jl
new file mode 100644
index 000000000..930c4861c
--- /dev/null
+++ b/lib/NonlinearSolveSpectralMethods/ext/NonlinearSolveSpectralMethodsForwardDiffExt.jl
@@ -0,0 +1,46 @@
+module NonlinearSolveSpectralMethodsForwardDiffExt
+
+using CommonSolve: CommonSolve, init
+using ForwardDiff: ForwardDiff, Dual
+using SciMLBase: SciMLBase, NonlinearProblem, NonlinearLeastSquaresProblem
+
+using NonlinearSolveBase: NonlinearSolveBase, NonlinearSolveForwardDiffCache, nodual_value
+
+using NonlinearSolveSpectralMethods: GeneralizedDFSane
+
+const DualNonlinearProblem = NonlinearProblem{
+    <:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {iip, T, V, P}
+const DualNonlinearLeastSquaresProblem = NonlinearLeastSquaresProblem{
+    <:Union{Number, <:AbstractArray}, iip,
+    <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
+} where {iip, T, V, P}
+const DualAbstractNonlinearProblem = Union{
+    DualNonlinearProblem, DualNonlinearLeastSquaresProblem
+}
+
+function SciMLBase.__solve(
+        prob::DualAbstractNonlinearProblem, alg::GeneralizedDFSane, args...; kwargs...
+)
+    sol, partials = NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
+        prob, alg, args...; kwargs...
+    )
+    dual_soln = NonlinearSolveBase.nonlinearsolve_dual_solution(sol.u, partials, prob.p)
+    return SciMLBase.build_solution(
+        prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
+    )
+end
+
+function SciMLBase.__init(
+        prob::DualAbstractNonlinearProblem, alg::GeneralizedDFSane, args...; kwargs...
+)
+    p = nodual_value(prob.p)
+    newprob = SciMLBase.remake(prob; u0 = nodual_value(prob.u0), p)
+    cache = init(newprob, alg, args...; kwargs...)
+    return NonlinearSolveForwardDiffCache(
+        cache, newprob, alg, prob.p, p, ForwardDiff.partials(prob.p)
+    )
+end
+
+end
diff --git a/src/NonlinearSolve.jl b/src/NonlinearSolve.jl
index 4c44cc972..a1b759011 100644
--- a/src/NonlinearSolve.jl
+++ b/src/NonlinearSolve.jl
@@ -14,7 +14,7 @@ using LineSearch: BackTracking
 using NonlinearSolveBase: NonlinearSolveBase, InternalAPI, AbstractNonlinearSolveAlgorithm,
                           AbstractNonlinearSolveCache, Utils, L2_NORM,
                           enable_timer_outputs, disable_timer_outputs,
-                          NonlinearSolvePolyAlgorithm
+                          NonlinearSolvePolyAlgorithm, pickchunksize
 
 using Preferences: set_preferences!
 using SciMLBase: SciMLBase, NLStats, ReturnCode, AbstractNonlinearProblem,
@@ -53,15 +53,6 @@ include("extension_algs.jl")
 
 include("default.jl")
 
-const ALL_SOLVER_TYPES = [
-    Nothing, AbstractNonlinearSolveAlgorithm,
-    GeneralizedDFSane, GeneralizedFirstOrderAlgorithm, QuasiNewtonAlgorithm,
-    LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
-    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL,
-    CMINPACK, PETScSNES,
-    NonlinearSolvePolyAlgorithm
-]
-
 include("forward_diff.jl")
 
 @setup_workload begin
diff --git a/src/forward_diff.jl b/src/forward_diff.jl
index 5bb98561c..76fdf6f52 100644
--- a/src/forward_diff.jl
+++ b/src/forward_diff.jl
@@ -1,3 +1,9 @@
+const EXTENSION_SOLVER_TYPES = [
+    LeastSquaresOptimJL, FastLevenbergMarquardtJL, NLsolveJL, NLSolversJL,
+    SpeedMappingJL, FixedPointAccelerationJL, SIAMFANLEquationsJL,
+    CMINPACK, PETScSNES
+]
+
 const DualNonlinearProblem = NonlinearProblem{
     <:Union{Number, <:AbstractArray}, iip,
     <:Union{<:Dual{T, V, P}, <:AbstractArray{<:Dual{T, V, P}}}
@@ -10,48 +16,12 @@ const DualAbstractNonlinearProblem = Union{
     DualNonlinearProblem, DualNonlinearLeastSquaresProblem
 }
 
-for algType in ALL_SOLVER_TYPES
-    @eval function SciMLBase.__solve(
-            prob::DualAbstractNonlinearProblem, alg::$(algType), args...; kwargs...
-    )
-        sol, partials = NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
-            prob, alg, args...; kwargs...
-        )
-        dual_soln = NonlinearSolveBase.nonlinearsolve_dual_solution(sol.u, partials, prob.p)
-        return SciMLBase.build_solution(
-            prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
-        )
-    end
-end
-
-@concrete mutable struct NonlinearSolveForwardDiffCache <: AbstractNonlinearSolveCache
-    cache
-    prob
-    alg
-    p
-    values_p
-    partials_p
-end
-
-function InternalAPI.reinit!(
-        cache::NonlinearSolveForwardDiffCache, args...;
-        p = cache.p, u0 = NonlinearSolveBase.get_u(cache.cache), kwargs...
-)
-    InternalAPI.reinit!(
-        cache.cache; p = nodual_value(p), u0 = nodual_value(u0), kwargs...
-    )
-    cache.p = p
-    cache.values_p = nodual_value(p)
-    cache.partials_p = ForwardDiff.partials(p)
-    return cache
-end
-
-for algType in ALL_SOLVER_TYPES
+for algType in EXTENSION_SOLVER_TYPES
     @eval function SciMLBase.__init(
             prob::DualAbstractNonlinearProblem, alg::$(algType), args...; kwargs...
     )
-        p = nodual_value(prob.p)
-        newprob = SciMLBase.remake(prob; u0 = nodual_value(prob.u0), p)
+        p = NonlinearSolveBase.nodual_value(prob.p)
+        newprob = SciMLBase.remake(prob; u0 = NonlinearSolveBase.nodual_value(prob.u0), p)
         cache = init(newprob, alg, args...; kwargs...)
         return NonlinearSolveForwardDiffCache(
             cache, newprob, alg, prob.p, p, ForwardDiff.partials(prob.p)
@@ -59,41 +29,16 @@ for algType in ALL_SOLVER_TYPES
     end
 end
 
-function CommonSolve.solve!(cache::NonlinearSolveForwardDiffCache)
-    sol = solve!(cache.cache)
-    prob = cache.prob
-    uu = sol.u
-
-    fn = prob isa NonlinearLeastSquaresProblem ?
-         NonlinearSolveBase.nlls_generate_vjp_function(prob, sol, uu) : prob.f
-
-    Jₚ = NonlinearSolveBase.nonlinearsolve_∂f_∂p(prob, fn, uu, cache.values_p)
-    Jᵤ = NonlinearSolveBase.nonlinearsolve_∂f_∂u(prob, fn, uu, cache.values_p)
-
-    z_arr = -Jᵤ \ Jₚ
-
-    sumfun = ((z, p),) -> map(zᵢ -> zᵢ * ForwardDiff.partials(p), z)
-    if cache.p isa Number
-        partials = sumfun((z_arr, cache.p))
-    else
-        partials = sum(sumfun, zip(eachcol(z_arr), cache.p))
-    end
-
-    dual_soln = NonlinearSolveBase.nonlinearsolve_dual_solution(sol.u, partials, cache.p)
-    return SciMLBase.build_solution(
-        prob, cache.alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
+for algType in EXTENSION_SOLVER_TYPES
+    @eval function SciMLBase.__solve(
+            prob::DualAbstractNonlinearProblem, alg::$(algType), args...; kwargs...
     )
+        sol, partials = NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(
+            prob, alg, args...; kwargs...
+        )
+        dual_soln = NonlinearSolveBase.nonlinearsolve_dual_solution(sol.u, partials, prob.p)
+        return SciMLBase.build_solution(
+            prob, alg, dual_soln, sol.resid; sol.retcode, sol.stats, sol.original
+        )
+    end
 end
-
-nodual_value(x) = x
-nodual_value(x::Dual) = ForwardDiff.value(x)
-nodual_value(x::AbstractArray{<:Dual}) = map(ForwardDiff.value, x)
-
-"""
-    pickchunksize(x) = pickchunksize(length(x))
-    pickchunksize(x::Int)
-
-Determine the chunk size for ForwardDiff and PolyesterForwardDiff based on the input length.
-"""
-@inline pickchunksize(x) = pickchunksize(length(x))
-@inline pickchunksize(x::Int) = ForwardDiff.pickchunksize(x)

From 873aae47c10bcecfbfb5c3f431a322d5b1f84665 Mon Sep 17 00:00:00 2001
From: Avik Pal <avikpal@mit.edu>
Date: Sun, 15 Dec 2024 22:00:59 +0530
Subject: [PATCH 696/700] ci: add TagBot for subpackages

---
 .github/workflows/TagBot.yml | 47 ++++++++++++++++++++++++++++++++++--
 1 file changed, 45 insertions(+), 2 deletions(-)

diff --git a/.github/workflows/TagBot.yml b/.github/workflows/TagBot.yml
index f49313b66..8888e2f65 100644
--- a/.github/workflows/TagBot.yml
+++ b/.github/workflows/TagBot.yml
@@ -1,15 +1,58 @@
 name: TagBot
+
 on:
   issue_comment:
     types:
       - created
   workflow_dispatch:
+    inputs:
+      lookback:
+        default: "3"
+
+permissions:
+  actions: read
+  checks: read
+  contents: write
+  deployments: read
+  issues: read
+  discussions: read
+  packages: read
+  pages: read
+  pull-requests: read
+  repository-projects: read
+  security-events: read
+  statuses: read
+
 jobs:
-  TagBot:
+  TagBot-NonlinearSolve:
     if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot'
     runs-on: ubuntu-latest
     steps:
-      - uses: JuliaRegistries/TagBot@v1
+      - name: Tag NonlinearSolve
+        uses: JuliaRegistries/TagBot@v1
         with:
           token: ${{ secrets.GITHUB_TOKEN }}
           ssh: ${{ secrets.DOCUMENTER_KEY }}
+
+  TagBot-Subpackages:
+    if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot'
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        package:
+          - BracketingNonlinearSolve
+          - NonlinearSolveBase
+          - NonlinearSolveFirstOrder
+          - NonlinearSolveQuasiNewton
+          - NonlinearSolveSpectralMethods
+          - SCCNonlinearSolve
+          - SciMLJacobianOperators
+          - SimpleNonlinearSolve
+    steps:
+      - name: Tag ${{ matrix.package }}
+        uses: JuliaRegistries/TagBot@v1
+        with:
+          token: ${{ secrets.GITHUB_TOKEN }}
+          ssh: ${{ secrets.DOCUMENTER_KEY }}
+          subdir: "lib/${{ matrix.package }}"

From 8295933ff20a20101f9c5f7377b9b27ebb103dd3 Mon Sep 17 00:00:00 2001
From: Aayush Sabharwal <aayush.sabharwal@gmail.com>
Date: Sun, 15 Dec 2024 23:21:44 +0530
Subject: [PATCH 697/700] feat: add hooks for `OverrideInit` (#517)

* feat: add `get_abstol` and `get_reltol` interface methods

* feat: add `initialize_cache!`

* feat: implement initialization for polyalg cache

* feat: implement initialization for no-init cache

* feat: implement initialization for first order cache

* feat: implement initialization for `QuasiNewtonCache`

* feat: implement initialization for `GeneralizedDFSaneCache`

* fix: fix `SII.parameter_values`

* feat: implement initialization for `SimpleNonlinearSolve`

* fix: fix `InternalAPI.reinit_self!` for `GeneralizedDFSaneCache`

* fix: fix `SII.state_values` for `NoInitCache`

* feat: run initialiation on `solve!`

* build: bump SciMLBase compat in NonlinearSolveBase
---
 lib/NonlinearSolveBase/Project.toml           |  2 +-
 .../src/NonlinearSolveBase.jl                 |  1 +
 lib/NonlinearSolveBase/src/abstract_types.jl  | 11 +++-
 lib/NonlinearSolveBase/src/forward_diff.jl    |  7 +++
 lib/NonlinearSolveBase/src/initialization.jl  | 60 ++++++++++++++++++
 lib/NonlinearSolveBase/src/polyalg.jl         | 32 ++++++++--
 lib/NonlinearSolveBase/src/solve.jl           | 61 ++++++++++++++++++-
 .../src/termination_conditions.jl             |  3 +
 lib/NonlinearSolveFirstOrder/src/solve.jl     | 12 +++-
 lib/NonlinearSolveQuasiNewton/src/solve.jl    | 20 +++++-
 .../src/solve.jl                              | 12 +++-
 .../src/SimpleNonlinearSolve.jl               | 12 ++++
 src/default.jl                                |  7 +++
 13 files changed, 222 insertions(+), 18 deletions(-)
 create mode 100644 lib/NonlinearSolveBase/src/initialization.jl

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 2f5404dc7..cc60c308e 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -68,7 +68,7 @@ MaybeInplace = "0.1.4"
 Preferences = "1.4"
 Printf = "1.10"
 RecursiveArrayTools = "3"
-SciMLBase = "2.58"
+SciMLBase = "2.68.1"
 SciMLJacobianOperators = "0.1.1"
 SciMLOperators = "0.3.10"
 SparseArrays = "1.10"
diff --git a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
index f45ba9242..9087a5c98 100644
--- a/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
+++ b/lib/NonlinearSolveBase/src/NonlinearSolveBase.jl
@@ -55,6 +55,7 @@ include("descent/damped_newton.jl")
 include("descent/dogleg.jl")
 include("descent/geodesic_acceleration.jl")
 
+include("initialization.jl")
 include("solve.jl")
 
 include("forward_diff.jl")
diff --git a/lib/NonlinearSolveBase/src/abstract_types.jl b/lib/NonlinearSolveBase/src/abstract_types.jl
index 6829e19c3..f43d59012 100644
--- a/lib/NonlinearSolveBase/src/abstract_types.jl
+++ b/lib/NonlinearSolveBase/src/abstract_types.jl
@@ -259,6 +259,8 @@ Abstract Type for all NonlinearSolveBase Caches.
     `u0` and any additional keyword arguments.
   - `SciMLBase.isinplace(cache)`: whether or not the solver is inplace.
   - `CommonSolve.step!(cache; kwargs...)`: See [`CommonSolve.step!`](@ref) for more details.
+  - `get_abstol(cache)`: get the `abstol` provided to the cache.
+  - `get_reltol(cache)`: get the `reltol` provided to the cache.
 
 Additionally implements `SymbolicIndexingInterface` interface Functions.
 
@@ -304,9 +306,16 @@ end
 
 SciMLBase.isinplace(cache::AbstractNonlinearSolveCache) = SciMLBase.isinplace(cache.prob)
 
+function get_abstol(cache::AbstractNonlinearSolveCache)
+    get_abstol(cache.termination_cache)
+end
+function get_reltol(cache::AbstractNonlinearSolveCache)
+    get_reltol(cache.termination_cache)
+end
+
 ## SII Interface
 SII.symbolic_container(cache::AbstractNonlinearSolveCache) = cache.prob
-SII.parameter_values(cache::AbstractNonlinearSolveCache) = SII.parameter_values(cache.prob)
+SII.parameter_values(cache::AbstractNonlinearSolveCache) = cache.p
 SII.state_values(cache::AbstractNonlinearSolveCache) = get_u(cache)
 
 function Base.getproperty(cache::AbstractNonlinearSolveCache, sym::Symbol)
diff --git a/lib/NonlinearSolveBase/src/forward_diff.jl b/lib/NonlinearSolveBase/src/forward_diff.jl
index a588aa52d..e780bf554 100644
--- a/lib/NonlinearSolveBase/src/forward_diff.jl
+++ b/lib/NonlinearSolveBase/src/forward_diff.jl
@@ -6,3 +6,10 @@
     values_p
     partials_p
 end
+
+function NonlinearSolveBase.get_abstol(cache::NonlinearSolveForwardDiffCache)
+    NonlinearSolveBase.get_abstol(cache.cache)
+end
+function NonlinearSolveBase.get_reltol(cache::NonlinearSolveForwardDiffCache)
+    NonlinearSolveBase.get_reltol(cache.cache)
+end
diff --git a/lib/NonlinearSolveBase/src/initialization.jl b/lib/NonlinearSolveBase/src/initialization.jl
new file mode 100644
index 000000000..e3612e2cb
--- /dev/null
+++ b/lib/NonlinearSolveBase/src/initialization.jl
@@ -0,0 +1,60 @@
+struct NonlinearSolveDefaultInit <: SciMLBase.DAEInitializationAlgorithm end
+
+function run_initialization!(cache, initializealg = cache.initializealg, prob = cache.prob)
+    _run_initialization!(cache, initializealg, prob, Val(SciMLBase.isinplace(cache)))
+end
+
+function _run_initialization!(
+        cache, ::NonlinearSolveDefaultInit, prob, isinplace::Union{Val{true}, Val{false}})
+    if SciMLBase.has_initialization_data(prob.f) &&
+       prob.f.initialization_data isa SciMLBase.OverrideInitData
+        return _run_initialization!(cache, SciMLBase.OverrideInit(), prob, isinplace)
+    end
+    return cache, true
+end
+
+function _run_initialization!(cache, initalg::SciMLBase.OverrideInit, prob,
+        isinplace::Union{Val{true}, Val{false}})
+    if cache isa AbstractNonlinearSolveCache && isdefined(cache.alg, :autodiff)
+        autodiff = cache.alg.autodiff
+    else
+        autodiff = ADTypes.AutoForwardDiff()
+    end
+    alg = initialization_alg(prob.f.initialization_data.initializeprob, autodiff)
+    if alg === nothing && cache isa AbstractNonlinearSolveCache
+        alg = cache.alg
+    end
+    u0, p, success = SciMLBase.get_initial_values(
+        prob, cache, prob.f, initalg, isinplace; nlsolve_alg = alg,
+        abstol = get_abstol(cache), reltol = get_reltol(cache))
+    cache = update_initial_values!(cache, u0, p)
+    if cache isa AbstractNonlinearSolveCache && isdefined(cache, :retcode) && !success
+        cache.retcode = ReturnCode.InitialFailure
+    end
+
+    return cache, success
+end
+
+function get_abstol(prob::AbstractNonlinearProblem)
+    get_tolerance(get(prob.kwargs, :abstol, nothing), eltype(SII.state_values(prob)))
+end
+function get_reltol(prob::AbstractNonlinearProblem)
+    get_tolerance(get(prob.kwargs, :reltol, nothing), eltype(SII.state_values(prob)))
+end
+
+initialization_alg(initprob, autodiff) = nothing
+
+function update_initial_values!(cache::AbstractNonlinearSolveCache, u0, p)
+    InternalAPI.reinit!(cache; u0, p)
+    cache.prob = SciMLBase.remake(cache.prob; u0, p)
+    return cache
+end
+
+function update_initial_values!(prob::AbstractNonlinearProblem, u0, p)
+    return SciMLBase.remake(prob; u0, p)
+end
+
+function _run_initialization!(
+        cache::AbstractNonlinearSolveCache, ::SciMLBase.NoInit, prob, isinplace)
+    return cache, true
+end
diff --git a/lib/NonlinearSolveBase/src/polyalg.jl b/lib/NonlinearSolveBase/src/polyalg.jl
index c2101af0e..935019e97 100644
--- a/lib/NonlinearSolveBase/src/polyalg.jl
+++ b/lib/NonlinearSolveBase/src/polyalg.jl
@@ -59,6 +59,23 @@ end
     u0
     u0_aliased
     alias_u0::Bool
+
+    initializealg
+end
+
+function update_initial_values!(cache::NonlinearSolvePolyAlgorithmCache, u0, p)
+    foreach(cache.caches) do subcache
+        update_initial_values!(subcache, u0, p)
+    end
+    cache.prob = SciMLBase.remake(cache.prob; u0, p)
+    return cache
+end
+
+function NonlinearSolveBase.get_abstol(cache::NonlinearSolvePolyAlgorithmCache)
+    NonlinearSolveBase.get_abstol(cache.caches[cache.current])
+end
+function NonlinearSolveBase.get_reltol(cache::NonlinearSolvePolyAlgorithmCache)
+    NonlinearSolveBase.get_reltol(cache.caches[cache.current])
 end
 
 function SII.symbolic_container(cache::NonlinearSolvePolyAlgorithmCache)
@@ -67,6 +84,9 @@ end
 function SII.state_values(cache::NonlinearSolvePolyAlgorithmCache)
     SII.state_values(SII.symbolic_container(cache))
 end
+function SII.parameter_values(cache::NonlinearSolvePolyAlgorithmCache)
+    SII.parameter_values(SII.symbolic_container(cache))
+end
 
 function Base.show(io::IO, ::MIME"text/plain", cache::NonlinearSolvePolyAlgorithmCache)
     println(io, "NonlinearSolvePolyAlgorithmCache with \
@@ -97,7 +117,8 @@ end
 function SciMLBase.__init(
         prob::AbstractNonlinearProblem, alg::NonlinearSolvePolyAlgorithm, args...;
         stats = NLStats(0, 0, 0, 0, 0), maxtime = nothing, maxiters = 1000,
-        internalnorm = L2_NORM, alias_u0 = false, verbose = true, kwargs...
+        internalnorm = L2_NORM, alias_u0 = false, verbose = true,
+        initializealg = NonlinearSolveDefaultInit(), kwargs...
 )
     if alias_u0 && !ArrayInterface.ismutable(prob.u0)
         verbose && @warn "`alias_u0` has been set to `true`, but `u0` is \
@@ -109,18 +130,21 @@ function SciMLBase.__init(
     u0_aliased = alias_u0 ? copy(u0) : u0
     alias_u0 && (prob = SciMLBase.remake(prob; u0 = u0_aliased))
 
-    return NonlinearSolvePolyAlgorithmCache(
+    cache = NonlinearSolvePolyAlgorithmCache(
         alg.static_length, prob,
         map(alg.algs) do solver
             SciMLBase.__init(
                 prob, solver, args...;
-                stats, maxtime, internalnorm, alias_u0, verbose, kwargs...
+                stats, maxtime, internalnorm, alias_u0, verbose,
+                initializealg = SciMLBase.NoInit(), kwargs...
             )
         end,
         alg, -1, alg.start_index, 0, stats, 0.0, maxtime,
         ReturnCode.Default, false, maxiters, internalnorm,
-        u0, u0_aliased, alias_u0
+        u0, u0_aliased, alias_u0, initializealg
     )
+    run_initialization!(cache)
+    return cache
 end
 
 @generated function InternalAPI.step!(
diff --git a/lib/NonlinearSolveBase/src/solve.jl b/lib/NonlinearSolveBase/src/solve.jl
index 66ad6a0e4..41dc1d5fb 100644
--- a/lib/NonlinearSolveBase/src/solve.jl
+++ b/lib/NonlinearSolveBase/src/solve.jl
@@ -7,6 +7,13 @@ function SciMLBase.__solve(
 end
 
 function CommonSolve.solve!(cache::AbstractNonlinearSolveCache)
+    if cache.retcode == ReturnCode.InitialFailure
+        return SciMLBase.build_solution(
+            cache.prob, cache.alg, get_u(cache), get_fu(cache);
+            cache.retcode, cache.stats, cache.trace
+        )
+    end
+
     while not_terminated(cache)
         CommonSolve.step!(cache)
     end
@@ -40,6 +47,17 @@ end
     sol_syms = [gensym("sol") for i in 1:N]
     u_result_syms = [gensym("u_result") for i in 1:N]
 
+    push!(calls,
+        quote
+            if cache.retcode == ReturnCode.InitialFailure
+                u = $(SII.state_values)(cache)
+                return build_solution_less_specialize(
+                    cache.prob, cache.alg, u, $(Utils.evaluate_f)(cache.prob, u);
+                    retcode = cache.retcode
+                )
+            end
+        end)
+
     for i in 1:N
         push!(calls,
             quote
@@ -111,7 +129,8 @@ end
 
 @generated function __generated_polysolve(
         prob::AbstractNonlinearProblem, alg::NonlinearSolvePolyAlgorithm{Val{N}}, args...;
-        stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, verbose = true, kwargs...
+        stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, verbose = true,
+        initializealg = NonlinearSolveDefaultInit(), kwargs...
 ) where {N}
     sol_syms = [gensym("sol") for _ in 1:N]
     prob_syms = [gensym("prob") for _ in 1:N]
@@ -123,9 +142,23 @@ end
                               immutable (checked using `ArrayInterface.ismutable`)."
             alias_u0 = false  # If immutable don't care about aliasing
         end
+    end]
+
+    push!(calls,
+        quote
+            prob, success = $(run_initialization!)(prob, initializealg, prob)
+            if !success
+                u = $(SII.state_values)(prob)
+                return build_solution_less_specialize(
+                    prob, alg, u, $(Utils.evaluate_f)(prob, u);
+                    retcode = $(ReturnCode.InitialFailure))
+            end
+        end)
+
+    push!(calls, quote
         u0 = prob.u0
         u0_aliased = alias_u0 ? zero(u0) : u0
-    end]
+    end)
     for i in 1:N
         cur_sol = sol_syms[i]
         push!(calls,
@@ -246,8 +279,21 @@ end
     alg
     args
     kwargs::Any
+    initializealg
+
+    retcode::ReturnCode.T
 end
 
+function get_abstol(cache::NonlinearSolveNoInitCache)
+    get(cache.kwargs, :abstol, get_tolerance(nothing, eltype(cache.prob.u0)))
+end
+function get_reltol(cache::NonlinearSolveNoInitCache)
+    get(cache.kwargs, :reltol, get_tolerance(nothing, eltype(cache.prob.u0)))
+end
+
+SII.parameter_values(cache::NonlinearSolveNoInitCache) = SII.parameter_values(cache.prob)
+SII.state_values(cache::NonlinearSolveNoInitCache) = SII.state_values(cache.prob)
+
 get_u(cache::NonlinearSolveNoInitCache) = SII.state_values(cache.prob)
 
 function SciMLBase.reinit!(
@@ -264,11 +310,20 @@ end
 
 function SciMLBase.__init(
         prob::AbstractNonlinearProblem, alg::AbstractNonlinearSolveAlgorithm, args...;
+        initializealg = NonlinearSolveDefaultInit(),
         kwargs...
 )
-    return NonlinearSolveNoInitCache(prob, alg, args, kwargs)
+    cache = NonlinearSolveNoInitCache(
+        prob, alg, args, kwargs, initializealg, ReturnCode.Default)
+    run_initialization!(cache)
+    return cache
 end
 
 function CommonSolve.solve!(cache::NonlinearSolveNoInitCache)
+    if cache.retcode == ReturnCode.InitialFailure
+        u = SII.state_values(cache)
+        return SciMLBase.build_solution(
+            cache.prob, cache.alg, u, Utils.evaluate_f(cache.prob, u); cache.retcode)
+    end
     return CommonSolve.solve(cache.prob, cache.alg, cache.args...; cache.kwargs...)
 end
diff --git a/lib/NonlinearSolveBase/src/termination_conditions.jl b/lib/NonlinearSolveBase/src/termination_conditions.jl
index cca9134d1..e6ab4a579 100644
--- a/lib/NonlinearSolveBase/src/termination_conditions.jl
+++ b/lib/NonlinearSolveBase/src/termination_conditions.jl
@@ -23,6 +23,9 @@ const AbsNormModes = Union{
     u_diff_cache::uType
 end
 
+get_abstol(cache::NonlinearTerminationModeCache) = cache.abstol
+get_reltol(cache::NonlinearTerminationModeCache) = cache.reltol
+
 function update_u!!(cache::NonlinearTerminationModeCache, u)
     cache.u === nothing && return
     if cache.u isa AbstractArray && ArrayInterface.can_setindex(cache.u)
diff --git a/lib/NonlinearSolveFirstOrder/src/solve.jl b/lib/NonlinearSolveFirstOrder/src/solve.jl
index c9c8c77a8..ec0d54da6 100644
--- a/lib/NonlinearSolveFirstOrder/src/solve.jl
+++ b/lib/NonlinearSolveFirstOrder/src/solve.jl
@@ -87,6 +87,8 @@ end
     retcode::ReturnCode.T
     force_stop::Bool
     kwargs
+
+    initializealg
 end
 
 function InternalAPI.reinit_self!(
@@ -121,7 +123,7 @@ function SciMLBase.__init(
         stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, maxiters = 1000,
         abstol = nothing, reltol = nothing, maxtime = nothing,
         termination_condition = nothing, internalnorm = L2_NORM,
-        linsolve_kwargs = (;), kwargs...
+        linsolve_kwargs = (;), initializealg = NonlinearSolveBase.NonlinearSolveDefaultInit(), kwargs...
 )
     @set! alg.autodiff = NonlinearSolveBase.select_jacobian_autodiff(prob, alg.autodiff)
     provided_jvp_autodiff = alg.jvp_autodiff !== nothing
@@ -206,13 +208,17 @@ function SciMLBase.__init(
             prob, alg, u, fu, J, du; kwargs...
         )
 
-        return GeneralizedFirstOrderAlgorithmCache(
+        cache = GeneralizedFirstOrderAlgorithmCache(
             fu, u, u_cache, prob.p, du, J, alg, prob, globalization,
             jac_cache, descent_cache, linesearch_cache, trustregion_cache,
             stats, 0, maxiters, maxtime, alg.max_shrink_times, timer,
-            0.0, true, termination_cache, trace, ReturnCode.Default, false, kwargs
+            0.0, true, termination_cache, trace, ReturnCode.Default, false, kwargs,
+            initializealg
         )
+        NonlinearSolveBase.run_initialization!(cache)
     end
+
+    return cache
 end
 
 function InternalAPI.step!(
diff --git a/lib/NonlinearSolveQuasiNewton/src/solve.jl b/lib/NonlinearSolveQuasiNewton/src/solve.jl
index c52a425ae..53289c117 100644
--- a/lib/NonlinearSolveQuasiNewton/src/solve.jl
+++ b/lib/NonlinearSolveQuasiNewton/src/solve.jl
@@ -93,6 +93,16 @@ end
     force_stop::Bool
     force_reinit::Bool
     kwargs
+
+    # Initialization
+    initializealg
+end
+
+function NonlinearSolveBase.get_abstol(cache::QuasiNewtonCache)
+    NonlinearSolveBase.get_abstol(cache.termination_cache)
+end
+function NonlinearSolveBase.get_reltol(cache::QuasiNewtonCache)
+    NonlinearSolveBase.get_reltol(cache.termination_cache)
 end
 
 function InternalAPI.reinit_self!(
@@ -130,7 +140,8 @@ function SciMLBase.__init(
         stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, maxtime = nothing,
         maxiters = 1000, abstol = nothing, reltol = nothing,
         linsolve_kwargs = (;), termination_condition = nothing,
-        internalnorm::F = L2_NORM, kwargs...
+        internalnorm::F = L2_NORM, initializealg = NonlinearSolveBase.NonlinearSolveDefaultInit(),
+        kwargs...
 ) where {F}
     timer = get_timer_output()
     @static_timeit timer "cache construction" begin
@@ -204,15 +215,18 @@ function SciMLBase.__init(
             uses_jacobian_inverse = inverted_jac, kwargs...
         )
 
-        return QuasiNewtonCache(
+        cache = QuasiNewtonCache(
             fu, u, u_cache, prob.p, du, J, alg, prob, globalization,
             initialization_cache, descent_cache, linesearch_cache,
             trustregion_cache, update_rule_cache, reinit_rule_cache,
             inv_workspace, stats, 0, 0, alg.max_resets, maxiters, maxtime,
             alg.max_shrink_times, 0, timer, 0.0, termination_cache, trace,
-            ReturnCode.Default, false, false, kwargs
+            ReturnCode.Default, false, false, kwargs, initializealg
         )
+        NonlinearSolveBase.run_initialization!(cache)
     end
+
+    return cache
 end
 
 function InternalAPI.step!(
diff --git a/lib/NonlinearSolveSpectralMethods/src/solve.jl b/lib/NonlinearSolveSpectralMethods/src/solve.jl
index b3a7d216e..fd71527c0 100644
--- a/lib/NonlinearSolveSpectralMethods/src/solve.jl
+++ b/lib/NonlinearSolveSpectralMethods/src/solve.jl
@@ -68,6 +68,8 @@ end
     retcode::ReturnCode.T
     force_stop::Bool
     kwargs
+
+    initializealg
 end
 
 function InternalAPI.reinit_self!(
@@ -75,6 +77,7 @@ function InternalAPI.reinit_self!(
         alias_u0::Bool = false, maxiters = 1000, maxtime = nothing, kwargs...
 )
     Utils.reinit_common!(cache, u0, p, alias_u0)
+    T = eltype(u0)
 
     if cache.alg.σ_1 === nothing
         σ_n = Utils.safe_dot(cache.u, cache.u) / Utils.safe_dot(cache.u, cache.fu)
@@ -112,7 +115,7 @@ function SciMLBase.__init(
         prob::AbstractNonlinearProblem, alg::GeneralizedDFSane, args...;
         stats = NLStats(0, 0, 0, 0, 0), alias_u0 = false, maxiters = 1000,
         abstol = nothing, reltol = nothing, termination_condition = nothing,
-        maxtime = nothing, kwargs...
+        maxtime = nothing, initializealg = NonlinearSolveBase.NonlinearSolveDefaultInit(), kwargs...
 )
     timer = get_timer_output()
 
@@ -145,13 +148,16 @@ function SciMLBase.__init(
             σ_n = T(alg.σ_1)
         end
 
-        return GeneralizedDFSaneCache(
+        cache = GeneralizedDFSaneCache(
             fu, fu_cache, u, u_cache, prob.p, du, alg, prob,
             σ_n, T(alg.σ_min), T(alg.σ_max),
             linesearch_cache, stats, 0, maxiters, maxtime, timer, 0.0,
-            tc_cache, trace, ReturnCode.Default, false, kwargs
+            tc_cache, trace, ReturnCode.Default, false, kwargs, initializealg
         )
+        NonlinearSolveBase.run_initialization!(cache)
     end
+
+    return cache
 end
 
 function InternalAPI.step!(
diff --git a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
index 3d8258f7e..2a87eb54e 100644
--- a/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
+++ b/lib/SimpleNonlinearSolve/src/SimpleNonlinearSolve.jl
@@ -59,6 +59,12 @@ function CommonSolve.solve(
         prob::NonlinearProblem, alg::AbstractSimpleNonlinearSolveAlgorithm, args...;
         kwargs...
 )
+    cache = SciMLBase.__init(prob, alg, args...; kwargs...)
+    prob = cache.prob
+    if cache.retcode == ReturnCode.InitialFailure
+        return SciMLBase.build_solution(prob, alg, prob.u0,
+            NonlinearSolveBase.Utils.evaluate_f(prob, prob.u0); cache.retcode)
+    end
     prob = convert(ImmutableNonlinearProblem, prob)
     return solve(prob, alg, args...; kwargs...)
 end
@@ -97,6 +103,12 @@ function CommonSolve.solve(
         alg::AbstractSimpleNonlinearSolveAlgorithm,
         args...; sensealg = nothing, u0 = nothing, p = nothing, kwargs...
 )
+    cache = SciMLBase.__init(prob, alg, args...; kwargs...)
+    prob = cache.prob
+    if cache.retcode == ReturnCode.InitialFailure
+        return SciMLBase.build_solution(prob, alg, prob.u0,
+            NonlinearSolveBase.Utils.evaluate_f(prob, prob.u0); cache.retcode)
+    end
     if sensealg === nothing && haskey(prob.kwargs, :sensealg)
         sensealg = prob.kwargs[:sensealg]
     end
diff --git a/src/default.jl b/src/default.jl
index 6021a98b1..734305ef6 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -50,3 +50,10 @@ function SciMLBase.__solve(
         prob, FastShortcutNLLSPolyalg(eltype(prob.u0)), args...; kwargs...
     )
 end
+
+function NonlinearSolveBase.initialization_alg(::AbstractNonlinearProblem, autodiff)
+    FastShortcutNonlinearPolyalg(; autodiff)
+end
+function NonlinearSolveBase.initialization_alg(::NonlinearLeastSquaresProblem, autodiff)
+    FastShortcutNLLSPolyalg(; autodiff)
+end

From 3bb2eb3193e8febf170a6d975fe4657f64976887 Mon Sep 17 00:00:00 2001
From: Aayush Sabharwal <aayush.sabharwal@gmail.com>
Date: Mon, 16 Dec 2024 22:38:11 +0530
Subject: [PATCH 698/700] build: bump versions of `NonlinearSolve` and
 sub-packages (#518)

* build: bump versions of `NonlinearSolve` and sub-packages

* build: bump compats between sub-packages
---
 Project.toml                                   | 12 ++++++------
 lib/NonlinearSolveBase/Project.toml            |  2 +-
 lib/NonlinearSolveFirstOrder/Project.toml      |  4 ++--
 lib/NonlinearSolveQuasiNewton/Project.toml     |  4 ++--
 lib/NonlinearSolveSpectralMethods/Project.toml |  4 ++--
 lib/SimpleNonlinearSolve/Project.toml          |  4 ++--
 6 files changed, 15 insertions(+), 15 deletions(-)

diff --git a/Project.toml b/Project.toml
index 79b69daf3..c627ffe0d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 authors = ["SciML"]
-version = "4.2.0"
+version = "4.3.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -89,10 +89,10 @@ NLSolvers = "0.5"
 NLsolve = "4.5"
 NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1.3"
-NonlinearSolveFirstOrder = "1"
-NonlinearSolveQuasiNewton = "1"
-NonlinearSolveSpectralMethods = "1"
+NonlinearSolveBase = "1.5"
+NonlinearSolveFirstOrder = "1.2"
+NonlinearSolveQuasiNewton = "1.1"
+NonlinearSolveSpectralMethods = "1.1"
 OrdinaryDiffEqTsit5 = "1.1.0"
 PETSc = "0.3"
 Pkg = "1.10"
@@ -104,7 +104,7 @@ ReTestItems = "1.24"
 Reexport = "1.2"
 SIAMFANLEquations = "1.0.1"
 SciMLBase = "2.58"
-SimpleNonlinearSolve = "2"
+SimpleNonlinearSolve = "2.1"
 SparseArrays = "1.10"
 SparseConnectivityTracer = "0.6.5"
 SparseMatrixColorings = "0.4.5"
diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index cc60c308e..6073539ab 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolveBase"
 uuid = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.4.0"
+version = "1.5.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
index c299b6dc1..76b834a1d 100644
--- a/lib/NonlinearSolveFirstOrder/Project.toml
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolveFirstOrder"
 uuid = "5959db7a-ea39-4486-b5fe-2dd0bf03d60d"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.1.0"
+version = "1.2.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -44,7 +44,7 @@ LinearAlgebra = "1.10"
 LinearSolve = "2.36.1"
 MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1.1"
+NonlinearSolveBase = "1.5"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 Random = "1.10"
diff --git a/lib/NonlinearSolveQuasiNewton/Project.toml b/lib/NonlinearSolveQuasiNewton/Project.toml
index 4912e9070..383be207b 100644
--- a/lib/NonlinearSolveQuasiNewton/Project.toml
+++ b/lib/NonlinearSolveQuasiNewton/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolveQuasiNewton"
 uuid = "9a2c21bd-3a47-402d-9113-8faf9a0ee114"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.0.0"
+version = "1.1.0"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
@@ -44,7 +44,7 @@ LinearAlgebra = "1.10"
 LinearSolve = "2.36.1"
 MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1.1"
+NonlinearSolveBase = "1.5"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 ReTestItems = "1.24"
diff --git a/lib/NonlinearSolveSpectralMethods/Project.toml b/lib/NonlinearSolveSpectralMethods/Project.toml
index a248be107..ddeefc445 100644
--- a/lib/NonlinearSolveSpectralMethods/Project.toml
+++ b/lib/NonlinearSolveSpectralMethods/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolveSpectralMethods"
 uuid = "26075421-4e9a-44e1-8bd1-420ed7ad02b2"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.0.0"
+version = "1.1.0"
 
 [deps]
 CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
@@ -33,7 +33,7 @@ InteractiveUtils = "<0.0.1, 1"
 LineSearch = "0.1.4"
 MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1.1"
+NonlinearSolveBase = "1.5"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 ReTestItems = "1.24"
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 8492ac67f..5a4fe658e 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -1,7 +1,7 @@
 name = "SimpleNonlinearSolve"
 uuid = "727e6d20-b764-4bd8-a329-72de5adea6c7"
 authors = ["SciML"]
-version = "2.0.0"
+version = "2.1.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -55,7 +55,7 @@ LineSearch = "0.1.3"
 LinearAlgebra = "1.10"
 MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1.1"
+NonlinearSolveBase = "1.5"
 Pkg = "1.10"
 PolyesterForwardDiff = "0.1"
 PrecompileTools = "1.2"

From 469307d85d9fd505d8f6b9a14251c1b802acfc08 Mon Sep 17 00:00:00 2001
From: Chris Rackauckas <accounts@chrisrackauckas.com>
Date: Mon, 16 Dec 2024 16:21:29 -0100
Subject: [PATCH 699/700] Fix release

---
 lib/NonlinearSolveBase/Project.toml            | 2 +-
 lib/NonlinearSolveFirstOrder/Project.toml      | 2 +-
 lib/NonlinearSolveQuasiNewton/Project.toml     | 2 +-
 lib/NonlinearSolveSpectralMethods/Project.toml | 2 +-
 lib/SimpleNonlinearSolve/Project.toml          | 2 +-
 5 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/lib/NonlinearSolveBase/Project.toml b/lib/NonlinearSolveBase/Project.toml
index 6073539ab..cc60c308e 100644
--- a/lib/NonlinearSolveBase/Project.toml
+++ b/lib/NonlinearSolveBase/Project.toml
@@ -1,7 +1,7 @@
 name = "NonlinearSolveBase"
 uuid = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.5.0"
+version = "1.4.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/lib/NonlinearSolveFirstOrder/Project.toml b/lib/NonlinearSolveFirstOrder/Project.toml
index 76b834a1d..9427d1ddf 100644
--- a/lib/NonlinearSolveFirstOrder/Project.toml
+++ b/lib/NonlinearSolveFirstOrder/Project.toml
@@ -44,7 +44,7 @@ LinearAlgebra = "1.10"
 LinearSolve = "2.36.1"
 MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1.5"
+NonlinearSolveBase = "1.4"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 Random = "1.10"
diff --git a/lib/NonlinearSolveQuasiNewton/Project.toml b/lib/NonlinearSolveQuasiNewton/Project.toml
index 383be207b..6e9cc3a00 100644
--- a/lib/NonlinearSolveQuasiNewton/Project.toml
+++ b/lib/NonlinearSolveQuasiNewton/Project.toml
@@ -44,7 +44,7 @@ LinearAlgebra = "1.10"
 LinearSolve = "2.36.1"
 MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1.5"
+NonlinearSolveBase = "1.4"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 ReTestItems = "1.24"
diff --git a/lib/NonlinearSolveSpectralMethods/Project.toml b/lib/NonlinearSolveSpectralMethods/Project.toml
index ddeefc445..53f568bc0 100644
--- a/lib/NonlinearSolveSpectralMethods/Project.toml
+++ b/lib/NonlinearSolveSpectralMethods/Project.toml
@@ -33,7 +33,7 @@ InteractiveUtils = "<0.0.1, 1"
 LineSearch = "0.1.4"
 MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1.5"
+NonlinearSolveBase = "1.4"
 Pkg = "1.10"
 PrecompileTools = "1.2"
 ReTestItems = "1.24"
diff --git a/lib/SimpleNonlinearSolve/Project.toml b/lib/SimpleNonlinearSolve/Project.toml
index 5a4fe658e..9303994ba 100644
--- a/lib/SimpleNonlinearSolve/Project.toml
+++ b/lib/SimpleNonlinearSolve/Project.toml
@@ -55,7 +55,7 @@ LineSearch = "0.1.3"
 LinearAlgebra = "1.10"
 MaybeInplace = "0.1.4"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1.5"
+NonlinearSolveBase = "1.4"
 Pkg = "1.10"
 PolyesterForwardDiff = "0.1"
 PrecompileTools = "1.2"

From 43ca96fba59a69f3c4449f555d855304e427cddb Mon Sep 17 00:00:00 2001
From: Qingyu Qu <52615090+ErikQQY@users.noreply.github.com>
Date: Tue, 17 Dec 2024 12:22:45 +0800
Subject: [PATCH 700/700] Fix incorrect Base version (#520)

* Fix incorrect Base version and bump

* Update Project.toml

---------

Co-authored-by: Christopher Rackauckas <accounts@chrisrackauckas.com>
---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index c627ffe0d..033f4b9c3 100644
--- a/Project.toml
+++ b/Project.toml
@@ -89,7 +89,7 @@ NLSolvers = "0.5"
 NLsolve = "4.5"
 NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "1.5"
+NonlinearSolveBase = "1.4"
 NonlinearSolveFirstOrder = "1.2"
 NonlinearSolveQuasiNewton = "1.1"
 NonlinearSolveSpectralMethods = "1.1"