Add support for f.jac in SimpleNewtonRaphson

Author: utkarsh530

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)

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)