Add tests and doc

Author: tansongchen

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)

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
 

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(),