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Merge pull request #50 from SciML/staticarrays
specialize Newton on static arrays
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,181 @@ | ||
| using NonlinearSolve | ||
| using StaticArrays | ||
| using BenchmarkTools | ||
| using Test | ||
|
|
||
| function benchmark_immutable(f, u0) | ||
| probN = NonlinearProblem{false}(f, u0) | ||
| solver = init(probN, NewtonRaphson(), tol = 1e-9) | ||
| sol = solve!(solver) | ||
| end | ||
|
|
||
| function benchmark_mutable(f, u0) | ||
| probN = NonlinearProblem{false}(f, u0) | ||
| solver = init(probN, NewtonRaphson(), tol = 1e-9) | ||
| sol = (reinit!(solver, probN); solve!(solver)) | ||
| end | ||
|
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| function benchmark_scalar(f, u0) | ||
| probN = NonlinearProblem{false}(f, u0) | ||
| sol = (solve(probN, NewtonRaphson())) | ||
| end | ||
|
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||
| 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 | ||
|
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| sol = benchmark_immutable(ff, cu0) | ||
| @test sol.retcode === Symbol(NonlinearSolve.DEFAULT) | ||
| @test all(sol.u .* sol.u .- 2 .< 1e-9) | ||
| sol = benchmark_mutable(ff, cu0) | ||
| @test sol.retcode === Symbol(NonlinearSolve.DEFAULT) | ||
| @test all(sol.u .* sol.u .- 2 .< 1e-9) | ||
| sol = benchmark_scalar(sf, csu0) | ||
| @test sol.retcode === Symbol(NonlinearSolve.DEFAULT) | ||
| @test sol.u * sol.u - 2 < 1e-9 | ||
|
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||
| @test (@ballocated benchmark_immutable(ff, cu0)) == 0 | ||
| @test (@ballocated benchmark_mutable(ff, cu0)) < 200 | ||
| @test (@ballocated benchmark_scalar(sf, csu0)) == 0 | ||
|
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||
| # AD Tests | ||
| using ForwardDiff | ||
|
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| # Immutable | ||
| f, u0 = (u, p) -> u .* u .- p, @SVector[1.0, 1.0] | ||
|
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||
| g = function (p) | ||
| probN = NonlinearProblem{false}(f, csu0, p) | ||
| sol = solve(probN, NewtonRaphson(), tol = 1e-9) | ||
| return sol.u[end] | ||
| end | ||
|
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||
| for p in 1.0:0.1:100.0 | ||
| @test g(p) ≈ sqrt(p) | ||
| @test ForwardDiff.derivative(g, p) ≈ 1/(2*sqrt(p)) | ||
| end | ||
|
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||
| # Scalar | ||
| f, u0 = (u, p) -> u * u - p, 1.0 | ||
|
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| # NewtonRaphson | ||
| g = function (p) | ||
| probN = NonlinearProblem{false}(f, oftype(p, u0), p) | ||
| sol = solve(probN, NewtonRaphson()) | ||
| return sol.u | ||
| end | ||
|
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||
| @test ForwardDiff.derivative(g, 1.0) ≈ 0.5 | ||
|
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||
| for p in 1.1:0.1:100.0 | ||
| @test g(p) ≈ sqrt(p) | ||
| @test ForwardDiff.derivative(g, p) ≈ 1/(2*sqrt(p)) | ||
| end | ||
|
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||
| 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 | ||
|
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||
| for p in 1.1:0.1:100.0 | ||
| @test g(p) ≈ sqrt(p) | ||
| @test ForwardDiff.derivative(g, p) ≈ 1/(2*sqrt(p)) | ||
| end | ||
|
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||
| 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 | ||
|
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||
| @test g(p) ≈ [sqrt(p[2] / p[1])] | ||
| @test ForwardDiff.jacobian(g, p) ≈ ForwardDiff.jacobian(t, p) | ||
| end | ||
|
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||
| gnewton = function (p) | ||
| probN = NonlinearProblem{false}(f, 0.5, p) | ||
| sol = solve(probN, NewtonRaphson()) | ||
| return [sol.u] | ||
| end | ||
| @test gnewton(p) ≈ [sqrt(p[2] / p[1])] | ||
| @test ForwardDiff.jacobian(gnewton, p) ≈ ForwardDiff.jacobian(t, p) | ||
|
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| # Error Checks | ||
|
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| f, u0 = (u, p) -> u .* u .- 2.0, @SVector[1.0, 1.0] | ||
| probN = NonlinearProblem(f, u0) | ||
|
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| @test solve(probN, NewtonRaphson()).u[end] ≈ sqrt(2.0) | ||
| @test solve(probN, NewtonRaphson(); immutable = false).u[end] ≈ sqrt(2.0) | ||
| @test solve(probN, NewtonRaphson(;autodiff=false)).u[end] ≈ sqrt(2.0) | ||
| @test solve(probN, NewtonRaphson(;autodiff=false)).u[end] ≈ sqrt(2.0) | ||
|
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| 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 | ||
|
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| @test solve(probN, NewtonRaphson()).u ≈ sol | ||
| @test solve(probN, NewtonRaphson()).u ≈ sol | ||
| @test solve(probN, NewtonRaphson(;autodiff=false)).u ≈ sol | ||
| end | ||
|
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||
| # Bisection Tests | ||
| f, u0 = (u, p) -> u .* u .- 2.0, (1.0, 2.0) | ||
| probB = NonlinearProblem(f, u0) | ||
|
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| # Falsi | ||
| solver = init(probB, Falsi()) | ||
| sol = solve!(solver) | ||
| @test sol.left ≈ sqrt(2.0) | ||
|
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| # this should call the fast scalar overload | ||
| @test solve(probB, Bisection()).left ≈ sqrt(2.0) | ||
|
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| # these should call the iterator version | ||
| solver = init(probB, Bisection()) | ||
| @test solver isa NonlinearSolve.BracketingImmutableSolver | ||
| @test solve!(solver).left ≈ sqrt(2.0) | ||
|
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| # 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)) | ||
|
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| solver = init(probB, Bisection(;exact_left = true)) | ||
| sol = solve!(solver) | ||
| @test f(sol.left, nothing) < 0.0 | ||
| @test f(nextfloat(sol.left), nothing) >= 0.0 | ||
|
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| solver = init(probB, Bisection(;exact_right = true)) | ||
| sol = solve!(solver) | ||
| @test f(sol.right, nothing) > 0.0 | ||
| @test f(prevfloat(sol.right), nothing) <= 0.0 | ||
|
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| solver = init(probB, Bisection(;exact_left = true, exact_right = true); immutable = false) | ||
| sol = solve!(solver) | ||
| @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 |
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