From c3752b10e864385dda79091e96db440336923402 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 01/16] itp method begin

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

diff --git a/src/SimpleNonlinearSolve.jl b/src/SimpleNonlinearSolve.jl
index 8749aa7..5074d44 100644
--- a/src/SimpleNonlinearSolve.jl
+++ b/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/src/itp.jl b/src/itp.jl
new file mode 100644
index 0000000..e69de29

From 356602f5b673a773b79617fc96defe14ff6d24cc 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 02/16] ipt alg

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

diff --git a/src/itp.jl b/src/itp.jl
index e69de29..49a5656 100644
--- a/src/itp.jl
+++ b/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 fa82128a9734f781bc7ed92e6b8dc487bfe88ec2 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 03/16] minor fix

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

diff --git a/src/SimpleNonlinearSolve.jl b/src/SimpleNonlinearSolve.jl
index 5074d44..8177dd2 100644
--- a/src/SimpleNonlinearSolve.jl
+++ b/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 2e7d41a2f4919e2f6b0d12e6493aabe8be73d6f7 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 04/16] defined cache

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

diff --git a/src/itp.jl b/src/itp.jl
index 49a5656..ff84848 100644
--- a/src/itp.jl
+++ b/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 98be6834b96ff7e4a61e8f638d03fc6095a338ff 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 05/16] complete alg

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

diff --git a/src/itp.jl b/src/itp.jl
index ff84848..2df125a 100644
--- a/src/itp.jl
+++ b/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 8308ee9be16b997c7fbbae1b478b977b87bd5b0d 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 06/16] hyperparams checks

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

diff --git a/src/itp.jl b/src/itp.jl
index 2df125a..853c3aa 100644
--- a/src/itp.jl
+++ b/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 b1c611476fff0bac8ce1b2143ae2b48353c8c40c 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 07/16] abstol fix

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

diff --git a/src/itp.jl b/src/itp.jl
index 853c3aa..8eed6d9 100644
--- a/src/itp.jl
+++ b/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 fb139fee61e36bad637d2ea6a4b9b38cb59b6e6d 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 08/16] right retcode

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

diff --git a/src/itp.jl b/src/itp.jl
index 8eed6d9..014e321 100644
--- a/src/itp.jl
+++ b/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 195dd58d1d7b9e18ec716e7d8a01ae7788bdc3e6 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 09/16] update SimpleNonlinearSolve.jl

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

diff --git a/src/SimpleNonlinearSolve.jl b/src/SimpleNonlinearSolve.jl
index 8177dd2..ca787c2 100644
--- a/src/SimpleNonlinearSolve.jl
+++ b/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/src/itp.jl b/src/itp.jl
index 014e321..085f80f 100644
--- a/src/itp.jl
+++ b/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 d7a70bcd5486e7385971ea6f14a6c55c79c08a55 Mon Sep 17 00:00:00 2001
From: Christopher Rackauckas <accounts@chrisrackauckas.com>
Date: Wed, 28 Jun 2023 09:00:35 -0400
Subject: [PATCH 10/16] Update src/itp.jl

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

diff --git a/src/itp.jl b/src/itp.jl
index 085f80f..bd5f888 100644
--- a/src/itp.jl
+++ b/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 195c5aa49129dbef6d43bfb84dbff3cf8c61edfd 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 11/16] final fixes

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

diff --git a/src/itp.jl b/src/itp.jl
index bd5f888..b233c4f 100644
--- a/src/itp.jl
+++ b/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 17942d3ef55b644a2390bfeea49b89685040a0f8 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 12/16] added itp tests

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

diff --git a/src/itp.jl b/src/itp.jl
index b233c4f..c0d69f5 100644
--- a/src/itp.jl
+++ b/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/test/basictests.jl b/test/basictests.jl
index aea1731..34ef709 100644
--- a/test/basictests.jl
+++ b/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 2018f4176c4b70e0c214254bae61c8089b77a835 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 13/16] hyper param change

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

diff --git a/src/itp.jl b/src/itp.jl
index c0d69f5..568bb71 100644
--- a/src/itp.jl
+++ b/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 071fd44ffcc8a5800bf0c57ee9f6fd57ec66cbbf 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 14/16] final hyper params, tol and some modifications

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

diff --git a/src/itp.jl b/src/itp.jl
index 568bb71..5a91df0 100644
--- a/src/itp.jl
+++ b/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 7cccd62e609b7e350ffd79731e8805e233d5ac72 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 15/16] error check tests

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

diff --git a/test/basictests.jl b/test/basictests.jl
index 34ef709..1515360 100644
--- a/test/basictests.jl
+++ b/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 6a1a40f7903c0451f108b931f8cebf4a79ae88dd 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 16/16] format

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

diff --git a/src/itp.jl b/src/itp.jl
index 5a91df0..9968cba 100644
--- a/src/itp.jl
+++ b/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