Scalar Falsi

Project.toml

@@ -18,7 +18,7 @@ ForwardDiff = "0.10.3"
 RecursiveArrayTools = "2"
 Reexport = "0.2"
 Setfield = "0.7"
-StaticArrays = "1.0"
+StaticArrays = "0.12,1.0"
 UnPack = "1.0"
 julia = "1"
 

src/scalar.jl

@@ -53,7 +53,7 @@ function solve(prob::NonlinearProblem{<:Number, iip, <:AbstractArray{<:Dual{T,V,
 end
 
 # avoid ambiguities
-for Alg in [Bisection, Falsi]
+for Alg in [Bisection]
   @eval function 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 BracketingSolution(Dual{T,V,P}(sol.left, partials), Dual{T,V,P}(sol.right, partials), sol.retcode)
@@ -110,3 +110,61 @@ function solve(prob::NonlinearProblem, ::Bisection, args...; maxiters = 1000, kw
 
   return BracketingSolution(left, right, MAXITERS_EXCEED)
 end
+
+function solve(prob::NonlinearProblem, ::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 BracketingSolution(left, right, EXACT_SOLUTION_LEFT)
+  end
+
+  i = 1
+  if !iszero(fr)
+    while i < maxiters
+      if nextfloat_tdir(left, prob.u0...) == right
+        return BracketingSolution(left, right, FLOATING_POINT_LIMIT)
+      end
+      mid = (fr * left - fl * right) / (fr - fl)
+      for i in 1:10
+        mid = max(left, prevfloat_tdir(mid, 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 BracketingSolution(left, right, FLOATING_POINT_LIMIT)
+    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 BracketingSolution(left, right, MAXITERS_EXCEED)
+end

test/runtests.jl

@@ -56,6 +56,7 @@ end
 # Scalar
 f, u0 = (u, p) -> u * u - p, 1.0
 
+# NewtonRaphson
 g = function (p)
     probN = NonlinearProblem{false}(f, oftype(p, u0), p)
     sol = solve(probN, NewtonRaphson())
@@ -69,6 +70,19 @@ for p in 1.1:0.1:100.0
     @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]