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5,850 changes: 5,416 additions & 434 deletions markdown/NonlinearProblem/bruss.md
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514 changes: 282 additions & 232 deletions markdown/NonlinearProblem/nonlinear_battery_problem.md
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2,506 changes: 360 additions & 2,146 deletions markdown/NonlinearProblem/nonlinear_solver_23_tests.md
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483 changes: 255 additions & 228 deletions markdown/NonlinearProblem/quadratic_nonlinear.md
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513 changes: 265 additions & 248 deletions script/NonlinearProblem/bruss.jl
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38 changes: 21 additions & 17 deletions script/NonlinearProblem/nonlinear_battery_problem.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -2,30 +2,34 @@
using NonlinearSolve, LinearSolve, StaticArrays, Sundials, SpeedMapping,
BenchmarkTools, LinearAlgebra, DiffEqDevTools, PolyesterForwardDiff, CairoMakie
import MINPACK, NLsolve
RUS = RadiusUpdateSchemes;
import LineSearches

const RUS = RadiusUpdateSchemes;

DEFAULT_FORWARD_AD = AutoForwardDiff(; chunksize = 12)

HagerZhang() = LineSearchesJL(; method = LineSearches.HagerZhang())
MoreThuente() = LineSearchesJL(; method = LineSearches.MoreThuente())

# XXX: Add PETSc
solvers_all = [
(; pkg = :nonlinearsolve, name = "Default PolyAlgorithm", solver = Dict(:alg => FastShortcutNonlinearPolyalg(; autodiff = DEFAULT_FORWARD_AD))),
(; pkg = :nonlinearsolve, name = "Newton Raphson", solver = Dict(:alg => NewtonRaphson(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD))),
(; pkg = :nonlinearsolve, name = "Newton Raphson (HagerZhang LineSearch)", solver = Dict(:alg => NewtonRaphson(; linsolve = nothing, linesearch = HagerZhang()))),
(; pkg = :nonlinearsolve, name = "Newton Raphson (MoreThuente LineSearch)", solver = Dict(:alg => NewtonRaphson(; linsolve = nothing, linesearch = MoreThuente()))),
(; pkg = :nonlinearsolve, name = "Newton Raphson (BackTracking LineSearch)", solver = Dict(:alg => NewtonRaphson(; linsolve = nothing, linesearch = BackTracking()))),
(; pkg = :nonlinearsolve, name = "Default PolyAlgorithm", solver = Dict(:alg => FastShortcutNonlinearPolyalg())),
(; pkg = :nonlinearsolve, name = "Newton Raphson", solver = Dict(:alg => NewtonRaphson())),
(; pkg = :nonlinearsolve, name = "Newton Raphson (HagerZhang LineSearch)", solver = Dict(:alg => NewtonRaphson(; linesearch = HagerZhang()))),
(; pkg = :nonlinearsolve, name = "Newton Raphson (MoreThuente LineSearch)", solver = Dict(:alg => NewtonRaphson(; linesearch = MoreThuente()))),
(; pkg = :nonlinearsolve, name = "Newton Raphson (BackTracking LineSearch)", solver = Dict(:alg => NewtonRaphson(; linesearch = BackTracking()))),
(; pkg = :nonlinearsolve, name = "Newton Krylov with GMRES", solver = Dict(:alg => NewtonRaphson(; linsolve = KrylovJL_GMRES()))),
(; pkg = :nonlinearsolve, name = "DFSane", solver = Dict(:alg => DFSane())),
(; pkg = :nonlinearsolve, name = "Trust Region", solver = Dict(:alg => TrustRegion())),
(; pkg = :nonlinearsolve, name = "Trust Region (NLsolve Update)", solver = Dict(:alg => TrustRegion(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD, radius_update_scheme = RUS.NLsolve))),
(; pkg = :nonlinearsolve, name = "Trust Region (Nocedal Wright)", solver = Dict(:alg => TrustRegion(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD, radius_update_scheme = RUS.NocedalWright))),
(; pkg = :nonlinearsolve, name = "Trust Region (Hei)", solver = Dict(:alg => TrustRegion(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD, radius_update_scheme = RUS.Hei))),
(; pkg = :nonlinearsolve, name = "Trust Region (Yuan)", solver = Dict(:alg => TrustRegion(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD, radius_update_scheme = RUS.Yuan))),
(; pkg = :nonlinearsolve, name = "Trust Region (Bastin)", solver = Dict(:alg => TrustRegion(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD, radius_update_scheme = RUS.Bastin))),
(; pkg = :nonlinearsolve, name = "Trust Region (Fan)", solver = Dict(:alg => TrustRegion(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD, radius_update_scheme = RUS.Fan))),
(; pkg = :nonlinearsolve, name = "Levenberg-Marquardt", solver = Dict(:alg => LevenbergMarquardt(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD))),
(; pkg = :nonlinearsolve, name = "Levenberg-Marquardt with Cholesky", solver = Dict(:alg => LevenbergMarquardt(; autodiff = DEFAULT_FORWARD_AD, linsolve = CholeskyFactorization()))),
(; pkg = :nonlinearsolve, name = "Levenberg-Marquardt (No Geodesic Accln.)", solver = Dict(:alg => LevenbergMarquardt(; linsolve = nothing, disable_geodesic = Val(true), autodiff = DEFAULT_FORWARD_AD))),
(; pkg = :nonlinearsolve, name = "Levenberg-Marquardt (No Geodesic Accln.) with Cholesky", solver = Dict(:alg => LevenbergMarquardt(; disable_geodesic = Val(true), autodiff = DEFAULT_FORWARD_AD, linsolve = CholeskyFactorization()))),
(; pkg = :nonlinearsolve, name = "Trust Region (NLsolve Update)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.NLsolve))),
(; pkg = :nonlinearsolve, name = "Trust Region (Nocedal Wright)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.NocedalWright))),
(; pkg = :nonlinearsolve, name = "Trust Region (Hei)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Hei))),
(; pkg = :nonlinearsolve, name = "Trust Region (Yuan)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Yuan))),
(; pkg = :nonlinearsolve, name = "Trust Region (Bastin)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Bastin))),
(; pkg = :nonlinearsolve, name = "Trust Region (Fan)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Fan))),
(; pkg = :nonlinearsolve, name = "Levenberg-Marquardt", solver = Dict(:alg => LevenbergMarquardt())),
(; pkg = :nonlinearsolve, name = "Levenberg-Marquardt with Cholesky", solver = Dict(:alg => LevenbergMarquardt(; linsolve = CholeskyFactorization()))),
(; pkg = :nonlinearsolve, name = "Levenberg-Marquardt (No Geodesic Accln.)", solver = Dict(:alg => LevenbergMarquardt(; disable_geodesic = Val(true)))),
(; pkg = :nonlinearsolve, name = "Levenberg-Marquardt (No Geodesic Accln.) with Cholesky", solver = Dict(:alg => LevenbergMarquardt(; disable_geodesic = Val(true), linsolve = CholeskyFactorization()))),
(; pkg = :wrapper, name = "Modified Powell [MINPACK]", solver = Dict(:alg => CMINPACK(; method = :hybr))),
(; pkg = :wrapper, name = "Levenberg-Marquardt [MINPACK]", solver = Dict(:alg => CMINPACK(; method = :lm))),
(; pkg = :wrapper, name = "Newton Raphson [NLsolve.jl]", solver = Dict(:alg => NLsolveJL(; method = :newton, autodiff = :forward))),
Expand Down
63 changes: 24 additions & 39 deletions script/NonlinearProblem/nonlinear_solver_23_tests.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -2,29 +2,31 @@
using NonlinearSolve, LinearSolve, StaticArrays, Sundials, Setfield,
BenchmarkTools, LinearAlgebra, DiffEqDevTools, NonlinearProblemLibrary, CairoMakie
import PolyesterForwardDiff, MINPACK, NLsolve
RUS = RadiusUpdateSchemes;

const RUS = RadiusUpdateSchemes;


# XXX: Add PETSc
solvers_all = [
(; pkg = :nonlinearsolve, type = :general, name = "Default PolyAlg.", solver = Dict(:alg => FastShortcutNonlinearPolyalg(; u0_len = 10))),
(; pkg = :nonlinearsolve, type = :NR, name = "Newton Raphson", solver = Dict(:alg => NewtonRaphson(; linsolve = nothing))),
(; pkg = :nonlinearsolve, type = :NR, name = "NR (HagerZhang)", solver = Dict(:alg => NewtonRaphson(; linesearch = HagerZhang(), linsolve = nothing))),
(; pkg = :nonlinearsolve, type = :NR, name = "NR (MoreThuente)", solver = Dict(:alg => NewtonRaphson(; linesearch = MoreThuente(), linsolve = nothing))),
(; pkg = :nonlinearsolve, type = :NR, name = "NR (BackTracking)", solver = Dict(:alg => NewtonRaphson(; linesearch = BackTracking(), linsolve = nothing))),
(; pkg = :nonlinearsolve, type = :TR, name = "Trust Region", solver = Dict(:alg => TrustRegion(; linsolve = nothing))),
(; pkg = :nonlinearsolve, type = :TR, name = "TR (NLsolve Update)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.NLsolve, linsolve = nothing))),
(; pkg = :nonlinearsolve, type = :TR, name = "TR (Nocedal Wright)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.NocedalWright, linsolve = nothing))),
(; pkg = :nonlinearsolve, type = :TR, name = "TR (Hei)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Hei, linsolve = nothing))),
(; pkg = :nonlinearsolve, type = :TR, name = "TR (Yuan)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Yuan, linsolve = nothing))),
(; pkg = :nonlinearsolve, type = :TR, name = "TR (Bastin)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Bastin, linsolve = nothing))),
(; pkg = :nonlinearsolve, type = :TR, name = "TR (Fan)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Fan, linsolve = nothing))),
(; pkg = :nonlinearsolve, type = :NR, name = "Newton Raphson", solver = Dict(:alg => NewtonRaphson())),
(; pkg = :nonlinearsolve, type = :NR, name = "NR (HagerZhang)", solver = Dict(:alg => NewtonRaphson(; linesearch = HagerZhang()))),
(; pkg = :nonlinearsolve, type = :NR, name = "NR (MoreThuente)", solver = Dict(:alg => NewtonRaphson(; linesearch = MoreThuente()))),
(; pkg = :nonlinearsolve, type = :NR, name = "NR (BackTracking)", solver = Dict(:alg => NewtonRaphson(; linesearch = BackTracking()))),
(; pkg = :nonlinearsolve, type = :TR, name = "Trust Region", solver = Dict(:alg => TrustRegion())),
(; pkg = :nonlinearsolve, type = :TR, name = "TR (NLsolve Update)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.NLsolve))),
(; pkg = :nonlinearsolve, type = :TR, name = "TR (Nocedal Wright)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.NocedalWright))),
(; pkg = :nonlinearsolve, type = :TR, name = "TR (Hei)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Hei))),
(; pkg = :nonlinearsolve, type = :TR, name = "TR (Yuan)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Yuan))),
(; pkg = :nonlinearsolve, type = :TR, name = "TR (Bastin)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Bastin))),
(; pkg = :nonlinearsolve, type = :TR, name = "TR (Fan)", solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Fan))),
(; pkg = :nonlinearsolve, type = :LM, name = "Levenberg-Marquardt", solver = Dict(:alg => LevenbergMarquardt(; linsolve = QRFactorization()))),
(; pkg = :nonlinearsolve, type = :LM, name = "LM with Cholesky", solver = Dict(:alg => LevenbergMarquardt(; linsolve = CholeskyFactorization()))),
(; pkg = :nonlinearsolve, type = :LM, name = "LM (α_geodesic=0.5)", solver = Dict(:alg => LevenbergMarquardt(; linsolve = QRFactorization(), α_geodesic=0.5))),
(; pkg = :nonlinearsolve, type = :LM, name = "LM (α_geodesic=0.5) Chol.", solver = Dict(:alg => LevenbergMarquardt(; linsolve = CholeskyFactorization(), α_geodesic=0.5))),
(; pkg = :nonlinearsolve, type = :LM, name = "LM (no Accln.)", solver = Dict(:alg => LevenbergMarquardt(; linsolve = QRFactorization(), disable_geodesic = Val(true)))),
(; pkg = :nonlinearsolve, type = :LM, name = "LM (no Accln.) Chol.", solver = Dict(:alg => LevenbergMarquardt(; linsolve = CholeskyFactorization(), disable_geodesic = Val(true)))),
(; pkg = :nonlinearsolve, type = :general, name = "Pseudo Transient", solver = Dict(:alg => PseudoTransient(; linsolve = nothing, alpha_initial=10.0))),
(; pkg = :nonlinearsolve, type = :general, name = "Pseudo Transient", solver = Dict(:alg => PseudoTransient(; alpha_initial=10.0))),
(; pkg = :wrapper, type = :general, name = "Powell [MINPACK]", solver = Dict(:alg => CMINPACK(; method=:hybr))),
(; pkg = :wrapper, type = :general, name = "LM [MINPACK]", solver = Dict(:alg => CMINPACK(; method=:lm))),
(; pkg = :wrapper, type = :general, name = "NR [NLsolve.jl]", solver = Dict(:alg => NLsolveJL(; method=:newton))),
Expand All @@ -41,34 +43,13 @@ abstols = 1.0 ./ 10.0 .^ (4:12)
reltols = 1.0 ./ 10.0 .^ (4:12);


function set_ad_chunksize(solvers, u0)
ck = NonlinearSolve.pickchunksize(u0)
for i in 1:length(solvers)
@set! solvers[i].solver[:alg] = __set_ad_chunksize(solvers[i].solver[:alg], ck)
end
return solvers
end

function __set_ad_chunksize(solver::GeneralizedFirstOrderAlgorithm{CJ, N}, ck) where {CJ, N}
ad = AutoForwardDiff(; chunksize = ck)
return GeneralizedFirstOrderAlgorithm{CJ, N}(; solver.descent, solver.linesearch,
solver.trustregion, jacobian_ad = ad, solver.max_shrink_times, solver.forward_ad,
solver.reverse_ad)
end
function __set_ad_chunksize(solver::NonlinearSolvePolyAlgorithm{pType}, ck) where {pType}
algs = [__set_ad_chunksize(alg, ck) for alg in solver.algs]
return NonlinearSolvePolyAlgorithm(algs, Val(pType); solver.start_index)
end
__set_ad_chunksize(solver, ck) = solver

# Benchmarks a specific problem, checks which solvers can solve it and their performance
function benchmark_problem!(prob_name; solver_tracker=solver_tracker)
# Finds the problem and the true solution.
prob = nlprob_23_testcases[prob_name]

# Finds the solvers that can solve the problem
solvers_concrete = set_ad_chunksize(solvers_all, prob.prob.u0);
successful_solvers = filter(solver -> check_solver(prob, solver), solvers_concrete);
successful_solvers = filter(Base.Fix1(check_solver, prob), solvers_all);
push!(solver_tracker, prob_name => successful_solvers);

# Handles the non-general cases.
Expand All @@ -77,13 +58,16 @@ function benchmark_problem!(prob_name; solver_tracker=solver_tracker)
solvers_LM = filter(s -> s.type==:LM, successful_solvers)
wp_NR = WorkPrecisionSet(prob.prob, abstols, reltols, getfield.(solvers_NR, :solver);
names=getfield.(solvers_NR, :name), numruns=100, error_estimate=:l∞,
maxiters=1000, termination_condition = AbsNormTerminationMode())
maxiters=1000,
termination_condition = NonlinearSolve.AbsNormTerminationMode(Base.Fix1(maximum, abs)))
wp_TR = WorkPrecisionSet(prob.prob, abstols, reltols, getfield.(solvers_TR, :solver);
names=getfield.(solvers_TR, :name), numruns=100, error_estimate=:l∞,
maxiters=1000, termination_condition = AbsNormTerminationMode())
maxiters=1000,
termination_condition = NonlinearSolve.AbsNormTerminationMode(Base.Fix1(maximum, abs)))
wp_LM = WorkPrecisionSet(prob.prob, abstols, reltols, getfield.(solvers_LM, :solver);
names=getfield.(solvers_LM, :name), numruns=100, error_estimate=:l∞,
maxiters=1000, termination_condition = AbsNormTerminationMode())
maxiters=1000,
termination_condition = NonlinearSolve.AbsNormTerminationMode(Base.Fix1(maximum, abs)))

# Handles the general case
solvers_general = filter(s -> s.type==:general, successful_solvers)
Expand All @@ -108,7 +92,8 @@ end
function check_solver(prob, solver)
try
sol = solve(prob.prob, solver.solver[:alg]; abstol=1e-8, reltol=1e-8,
maxiters=1000000, termination_condition=AbsNormTerminationMode())
maxiters=1000000,
termination_condition=NonlinearSolve.AbsNormTerminationMode(Base.Fix1(maximum, abs)))
if norm(sol.resid, Inf) < 1e-6
Base.printstyled("[Info] Solver $(solver.name) returned retcode $(sol.retcode) \
with an residual norm = $(norm(sol.resid, Inf)).\n"; color=:green)
Expand Down
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