Quadratic Nonlinear Rootfinding Benchmark
This is a test of a simple small nonlinear rootfinding problem.
using NonlinearSolve, StaticArrays, DiffEqDevTools, Sundials, CairoMakie, LinearSolve,
LinearAlgebra, StableRNGs, BenchmarkTools, Setfield, RecursiveFactorization
import PolyesterForwardDiff, MINPACK, NLsolve, SpeedMapping
const RUS = RadiusUpdateSchemes;
BenchmarkTools.DEFAULT_PARAMETERS.seconds = 0.5;
f_oop(u, p) = u .* u .- p
f_iip(du, u, p) = @. du = u * u - p
function generate_prob(::Val{N}, ::Val{static}) where {N, static}
u0_ = ones(N) .+ randn(StableRNG(0), N) * 0.01
u0 = static ? SVector{N, Float64}(u0_) : u0_
prob = static ?
NonlinearProblem{false}(f_oop, u0, 2.0) :
NonlinearProblem{true}(f_iip, u0, 2.0)
return prob
endgenerate_prob (generic function with 1 method)List of Solvers to Benchmark:
solvers = [
(; pkg = :nonlinearsolve, full_pkgname = "NonlinearSolve.jl", name = "Default PolyAlgorithm", solver = Dict(:alg => nothing)),
(; pkg = :simplenonlinearsolve, full_pkgname = "SimpleNonlinearSolve.jl", name = "Simple Newton Raphson", solver = Dict(:alg => SimpleNewtonRaphson())),
(; pkg = :simplenonlinearsolve, full_pkgname = "SimpleNonlinearSolve.jl", name = "Simple DFSane", solver = Dict(:alg => SimpleDFSane())),
(; pkg = :simplenonlinearsolve, full_pkgname = "SimpleNonlinearSolve.jl", name = "Simple Trust Region", solver = Dict(:alg => SimpleTrustRegion(; nlsolve_update_rule = Val(true)))),
(; pkg = :simplenonlinearsolve, full_pkgname = "SimpleNonlinearSolve.jl", name = "Simple Broyden", solver = Dict(:alg => SimpleBroyden())),
(; pkg = :simplenonlinearsolve, full_pkgname = "SimpleNonlinearSolve.jl", name = "Simple Klement", solver = Dict(:alg => SimpleKlement())),
(; pkg = :nonlinearsolve, full_pkgname = "NonlinearSolve.jl", name = "Newton Raphson", solver = Dict(:alg => NewtonRaphson(; linsolve = \))),
(; pkg = :nonlinearsolve, full_pkgname = "NonlinearSolve.jl", name = "DFSane", solver = Dict(:alg => DFSane())),
(; pkg = :nonlinearsolve, full_pkgname = "NonlinearSolve.jl", name = "Trust Region", solver = Dict(:alg => TrustRegion(; linsolve = \, radius_update_scheme = RUS.NLsolve))),
(; pkg = :nonlinearsolve, full_pkgname = "NonlinearSolve.jl", name = "Broyden", solver = Dict(:alg => Broyden())),
(; pkg = :nonlinearsolve, full_pkgname = "NonlinearSolve.jl", name = "Klement", solver = Dict(:alg => Klement(; linsolve = \))),
(; pkg = :wrapper, full_pkgname = "NLsolve.jl", name = "Newton Raphson (NLsolve.jl)", solver = Dict(:alg => NLsolveJL(; method = :newton, autodiff = :forward))),
(; pkg = :wrapper, full_pkgname = "NLsolve.jl", name = "Trust Region (NLsolve.jl)", solver = Dict(:alg => NLsolveJL(; autodiff = :forward))),
(; pkg = :wrapper, full_pkgname = "Sundials", name = "Newton Raphson (Sundials)", solver = Dict(:alg => KINSOL())),
(; pkg = :wrapper, full_pkgname = "SpeedMapping.jl", name = "Speed Mapping (SpeedMapping.jl)", solver = Dict(:alg => SpeedMappingJL())),
];Configurations:
abstols = 1.0 ./ 10.0 .^ (3:2:12)
reltols = 1.0 ./ 10.0 .^ (3:2:12)5-element Vector{Float64}:
0.001
1.0e-5
1.0e-7
1.0e-9
1.0e-11Helper Functions:
function check_solver(prob, solver)
prob.u0 isa StaticArray && solver.pkg === :wrapper && return false
try
sol = solve(prob, solver.solver[:alg]; abstol = 1e-5, reltol = 1e-5,
maxiters = 10000)
err = norm(sol.resid)
if !SciMLBase.successful_retcode(sol.retcode)
Base.printstyled("[Warn] Solver $(solver.name) returned retcode $(sol.retcode) \
with an residual norm = $(norm(sol.resid)).\n"; color = :red)
return false
elseif err > 1e3
Base.printstyled("[Warn] Solver $(solver.name) had a very large residual (norm \
= $(norm(sol.resid))).\n"; color = :red)
return false
elseif isinf(err) || isnan(err)
Base.printstyled("[Warn] Solver $(solver.name) had a residual of $(err).\n";
color = :red)
return false
end
Base.printstyled("[Info] Solver $(solver.name) successfully solved the problem \
(norm = $(norm(sol.resid))).\n"; color = :green)
catch e
Base.printstyled("[Warn] Solver $(solver.name) threw an error: $e.\n"; color = :red)
return false
end
return true
end
function generate_wpset(prob, solvers)
successful_solvers = filter(solver -> check_solver(prob, solver), solvers)
return WorkPrecisionSet(prob, abstols, reltols, getfield.(successful_solvers, :solver);
numruns = 50, error_estimate = :l∞, names = getfield.(successful_solvers, :name),
maxiters = 10000), successful_solvers
endgenerate_wpset (generic function with 1 method)Plotting Functions:
# This is hardcoded for 4 input length
function plot_all_wpsets(wpset_list, solver_all, titles, suptitle)
@assert length(wpset_list) == length(titles) == 4
LINESTYLES = Dict(:nonlinearsolve => :solid, :simplenonlinearsolve => :dash,
:wrapper => :dot)
ASPECT_RATIO = 0.7
WIDTH = 1400
HEIGHT = round(Int, WIDTH * ASPECT_RATIO)
STROKEWIDTH = 2.5
colors = cgrad(:tableau_20, length(solver_all); categorical = true)
cycle = Cycle([:marker], covary = true)
plot_theme = Theme(Lines = (; cycle,), Scatter = (; cycle,))
fig = with_theme(plot_theme) do
fig = Figure(; size = (WIDTH, HEIGHT))
# `textbf` doesn't work
axs = Matrix{Any}(undef, 2, 2)
for i in 1:2, j in 1:2
ylabel = j == 1 ? L"$\mathrm{\mathbf{Time}}$ $\mathbf{(s)}$" : ""
xlabel = i == 2 ? L"Error: $\mathbf{||f(u^\ast)||_\infty}$" : ""
ax = Axis(fig[i, j]; ylabel = ylabel, title = titles[2 * (i - 1) + j],
titlegap = 10, titlesize = 22, xlabelsize = 22, ylabelsize = 22,
xticklabelsize = 20, yticklabelsize = 20,
xlabel = xlabel, xticksvisible = i == 2, yticksvisible = j == 1,
xticklabelsvisible = i == 2, yticklabelsvisible = j == 1,
xscale = log10, yscale = log10, xtickwidth = STROKEWIDTH,
ytickwidth = STROKEWIDTH, spinewidth = STROKEWIDTH)
axs[i, j] = ax
end
ls, scs = [], []
label_list = []
for (idx_solver, solver) in enumerate(reverse(solver_all))
first_success = true
for i in 1:2, j in 1:2
wpset, successful_solvers = wpset_list[2 * (i - 1) + j]
idx = findfirst(==(solver.name), [solver.name for solver in successful_solvers])
idx === nothing && continue
(; name, times, errors) = wpset.wps[idx]
errors = [err.l∞ for err in errors]
l = lines!(axs[i, j], errors, times; linestyle = LINESTYLES[solver.pkg],
label = name, linewidth = 3, color = colors[idx_solver])
sc = scatter!(axs[i, j], errors, times; label = name, markersize = 16,
strokewidth = 1, marker = Cycled(idx_solver),
color = colors[idx_solver])
if first_success
push!(ls, l)
push!(scs, sc)
push!(label_list, solver.name)
first_success = false
end
end
end
linkaxes!(axs...)
Legend(fig[3, :], collect(reverse([[l, sc] for (l, sc) in zip(ls, scs)])),
collect(reverse(label_list)),
"Successful Solvers"; framevisible=true, framewidth = STROKEWIDTH,
orientation = :horizontal,
titlesize = 16, nbanks = 3, labelsize = 16,
tellheight = true, tellwidth = false, patchsize = (40.0f0, 20.0f0))
fig[0, :] = Label(fig, "Quadratic Problem with $(suptitle): Work Precision Diagram", fontsize = 24, tellwidth = false, font = :bold)
fig
end
return fig
endplot_all_wpsets (generic function with 1 method)Static Array Versions
probs = [generate_prob(Val(N), Val(true)) for N in [2, 4, 8, 12]];
wpsets = [generate_wpset(prob, solvers) for prob in probs];
titles = ["N = 2", "N = 4", "N = 8", "N = 12"];
fig = plot_all_wpsets(wpsets, solvers, titles, "Static Arrays")[Info] Solver Default PolyAlgorithm successfully solved the problem (norm =
8.903708005997684e-6).
[Info] Solver Simple Newton Raphson successfully solved the problem (norm =
8.903708005997684e-6).
[Info] Solver Simple DFSane successfully solved the problem (norm = 2.21391
17217408527e-7).
[Info] Solver Simple Trust Region successfully solved the problem (norm = 8
.903708005997684e-6).
[Info] Solver Simple Broyden successfully solved the problem (norm = 7.7435
50661734637e-6).
[Info] Solver Simple Klement successfully solved the problem (norm = 8.7705
08340460738e-6).
[Info] Solver Newton Raphson successfully solved the problem (norm = 8.9037
08005997684e-6).
[Info] Solver DFSane successfully solved the problem (norm = 8.925226244970
55e-6).
[Info] Solver Trust Region successfully solved the problem (norm = 8.903708
005997684e-6).
[Info] Solver Broyden successfully solved the problem (norm = 7.74355066173
4637e-6).
[Info] Solver Klement successfully solved the problem (norm = 7.74279203948
5169e-6).
[Info] Solver Default PolyAlgorithm successfully solved the problem (norm =
1.3175515250018797e-5).
[Info] Solver Simple Newton Raphson successfully solved the problem (norm =
1.3175515250018797e-5).
[Info] Solver Simple DFSane successfully solved the problem (norm = 3.21318
9867783094e-7).
[Info] Solver Simple Trust Region successfully solved the problem (norm = 1
.3175515250018797e-5).
[Info] Solver Simple Broyden successfully solved the problem (norm = 1.0524
944462494045e-5).
[Info] Solver Simple Klement successfully solved the problem (norm = 1.2719
355158575668e-5).
[Info] Solver Newton Raphson successfully solved the problem (norm = 1.3175
515250018797e-5).
[Info] Solver DFSane successfully solved the problem (norm = 1.367124759680
58e-5).
[Info] Solver Trust Region successfully solved the problem (norm = 1.317551
5250018797e-5).
[Info] Solver Broyden successfully solved the problem (norm = 1.05249444628
89887e-5).
[Info] Solver Klement successfully solved the problem (norm = 1.04709031908
2685e-5).
[Info] Solver Default PolyAlgorithm successfully solved the problem (norm =
1.9046552208413456e-5).
[Info] Solver Simple Newton Raphson successfully solved the problem (norm =
1.9046552208413456e-5).
[Info] Solver Simple DFSane successfully solved the problem (norm = 4.64939
18801382363e-7).
[Info] Solver Simple Trust Region successfully solved the problem (norm = 1
.9046552208413456e-5).
[Info] Solver Simple Broyden successfully solved the problem (norm = 1.4246
490327013533e-5).
[Info] Solver Simple Klement successfully solved the problem (norm = 1.8259
373704793516e-5).
[Info] Solver Newton Raphson successfully solved the problem (norm = 1.9046
552208413456e-5).
[Info] Solver DFSane successfully solved the problem (norm = 1.973829931575
864e-5).
[Info] Solver Trust Region successfully solved the problem (norm = 1.904655
2208413456e-5).
[Info] Solver Broyden successfully solved the problem (norm = 1.42464903270
13533e-5).
[Info] Solver Klement successfully solved the problem (norm = 1.41180265390
8467e-5).
[Info] Solver Default PolyAlgorithm successfully solved the problem (norm =
2.2187014239665903e-5).
[Info] Solver Simple Newton Raphson successfully solved the problem (norm =
2.2187014239665903e-5).
[Info] Solver Simple DFSane successfully solved the problem (norm = 5.40467
1405346579e-7).
[Info] Solver Simple Trust Region successfully solved the problem (norm = 2
.2187014239665903e-5).
[Info] Solver Simple Broyden successfully solved the problem (norm = 1.9287
85498427112e-5).
[Info] Solver Simple Klement successfully solved the problem (norm = 2.1607
111134434963e-5).
[Info] Solver Newton Raphson successfully solved the problem (norm = 2.2187
014239665903e-5).
[Info] Solver DFSane successfully solved the problem (norm = 2.295755366158
96e-5).
[Info] Solver Trust Region successfully solved the problem (norm = 2.218701
4239665903e-5).
[Info] Solver Broyden successfully solved the problem (norm = 1.92878549841
49875e-5).
[Info] Solver Klement successfully solved the problem (norm = 1.92365300994
5377e-5).
save("static_arrays_quadratic.svg", fig)CairoMakie.Screen{SVG}Regular Julia Arrays
probs = [generate_prob(Val(N), Val(false)) for N in [4, 16, 128, 1024]]
wpsets = [(@show length(prob.u0); generate_wpset(prob, solvers)) for prob in probs]
titles = ["N = 4", "N = 16", "N = 128", "N = 1024"]
fig = plot_all_wpsets(wpsets, solvers, titles, "Regular Julia Arrays")length(prob.u0) = 4
[Info] Solver Default PolyAlgorithm successfully solved the problem (norm =
1.3175515250018797e-5).
[Info] Solver Simple Newton Raphson successfully solved the problem (norm =
1.3175515250018797e-5).
[Info] Solver Simple DFSane successfully solved the problem (norm = 3.21318
9867783094e-7).
[Info] Solver Simple Trust Region successfully solved the problem (norm = 1
.3175515250018797e-5).
[Info] Solver Simple Broyden successfully solved the problem (norm = 1.0524
944462889887e-5).
[Info] Solver Simple Klement successfully solved the problem (norm = 1.2719
355158575668e-5).
[Info] Solver Newton Raphson successfully solved the problem (norm = 1.3175
515250018797e-5).
[Info] Solver DFSane successfully solved the problem (norm = 1.367124759680
58e-5).
[Info] Solver Trust Region successfully solved the problem (norm = 1.317551
5250018797e-5).
[Info] Solver Broyden successfully solved the problem (norm = 1.05249444628
89887e-5).
[Info] Solver Klement successfully solved the problem (norm = 1.04709031908
2685e-5).
[Info] Solver Newton Raphson (NLsolve.jl) successfully solved the problem (
norm = 1.3175515250018797e-5).
[Info] Solver Trust Region (NLsolve.jl) successfully solved the problem (no
rm = 1.3175515250018797e-5).
[Info] Solver Newton Raphson (Sundials) successfully solved the problem (no
rm = 3.507854466145342e-9).
[Info] Solver Speed Mapping (SpeedMapping.jl) successfully solved the probl
em (norm = 1.9601492832512963e-5).
length(prob.u0) = 16
[Info] Solver Default PolyAlgorithm successfully solved the problem (norm =
2.5044494662558595e-5).
[Info] Solver Simple Newton Raphson successfully solved the problem (norm =
2.5044494662558595e-5).
[Info] Solver Simple DFSane successfully solved the problem (norm = 6.11269
711700824e-7).
[Info] Solver Simple Trust Region successfully solved the problem (norm = 2
.5044494662558595e-5).
[Info] Solver Simple Broyden successfully solved the problem (norm = 2.3141
389150698733e-5).
[Info] Solver Simple Klement successfully solved the problem (norm = 2.4583
675020896853e-5).
[Info] Solver Newton Raphson successfully solved the problem (norm = 2.5044
494662558595e-5).
[Info] Solver DFSane successfully solved the problem (norm = 2.578212922891
9075e-5).
[Info] Solver Trust Region successfully solved the problem (norm = 2.504449
4662558595e-5).
[Info] Solver Broyden successfully solved the problem (norm = 2.31413891506
98733e-5).
[Info] Solver Klement successfully solved the problem (norm = 2.31146141902
84395e-5).
[Info] Solver Newton Raphson (NLsolve.jl) successfully solved the problem (
norm = 2.5044494662558595e-5).
[Info] Solver Trust Region (NLsolve.jl) successfully solved the problem (no
rm = 2.5044494662558595e-5).
[Info] Solver Newton Raphson (Sundials) successfully solved the problem (no
rm = 6.033406020887388e-9).
[Info] Solver Speed Mapping (SpeedMapping.jl) successfully solved the probl
em (norm = 5.21219858681873e-5).
length(prob.u0) = 128
[Info] Solver Default PolyAlgorithm successfully solved the problem (norm =
6.545361092122703e-5).
[Info] Solver Simple Newton Raphson successfully solved the problem (norm =
6.283767496044401e-11).
[Info] Solver Simple DFSane successfully solved the problem (norm = 1.73578
10548996058e-6).
[Info] Solver Simple Trust Region successfully solved the problem (norm = 6
.283767496044401e-11).
[Info] Solver Simple Broyden successfully solved the problem (norm = 6.5453
61092122703e-5).
[Info] Solver Simple Klement successfully solved the problem (norm = 7.0177
89716845796e-5).
[Info] Solver Newton Raphson successfully solved the problem (norm = 6.2837
67496044401e-11).
[Info] Solver DFSane successfully solved the problem (norm = 7.685980582924
527e-5).
[Info] Solver Trust Region successfully solved the problem (norm = 6.283767
496044401e-11).
[Info] Solver Broyden successfully solved the problem (norm = 6.54536109212
2703e-5).
[Info] Solver Klement successfully solved the problem (norm = 6.53197265210
3389e-5).
[Info] Solver Newton Raphson (NLsolve.jl) successfully solved the problem (
norm = 6.283767496044401e-11).
[Info] Solver Trust Region (NLsolve.jl) successfully solved the problem (no
rm = 6.283767496044401e-11).
[Info] Solver Newton Raphson (Sundials) successfully solved the problem (no
rm = 2.0068313703523284e-8).
[Info] Solver Speed Mapping (SpeedMapping.jl) successfully solved the probl
em (norm = 5.551313074230362e-10).
length(prob.u0) = 1024
[Info] Solver Default PolyAlgorithm successfully solved the problem (norm =
0.00019052993535286191).
[Info] Solver Simple Newton Raphson successfully solved the problem (norm =
1.7311553941286643e-10).
[Info] Solver Simple DFSane successfully solved the problem (norm = 4.84115
0649443264e-6).
[Info] Solver Simple Trust Region successfully solved the problem (norm = 1
.7311553941286643e-10).
[Info] Solver Simple Broyden successfully solved the problem (norm = 0.0001
9052993535286191).
[Info] Solver Simple Klement successfully solved the problem (norm = 0.0001
967925659287559).
[Info] Solver Newton Raphson successfully solved the problem (norm = 1.7311
553941286643e-10).
[Info] Solver DFSane successfully solved the problem (norm = 0.000216303516
23678866).
[Info] Solver Trust Region successfully solved the problem (norm = 1.731155
3941286643e-10).
[Info] Solver Broyden successfully solved the problem (norm = 0.00019052993
535286191).
[Info] Solver Klement successfully solved the problem (norm = 0.00019007289
32153426).
[Info] Solver Newton Raphson (NLsolve.jl) successfully solved the problem (
norm = 1.7311553941286643e-10).
[Info] Solver Trust Region (NLsolve.jl) successfully solved the problem (no
rm = 1.7311553941286643e-10).
[Info] Solver Newton Raphson (Sundials) successfully solved the problem (no
rm = 5.408987237602836e-8).
[Info] Solver Speed Mapping (SpeedMapping.jl) successfully solved the probl
em (norm = 2.009517968000003e-9).
save("regular_arrays_quadratic.svg", fig)CairoMakie.Screen{SVG}Comparison against SimpleNonlinearSolve
function benchmark_combinations(solvers, probs)
return map(Iterators.product(solvers, probs)) do (solver, prob)
try
solver_concrete = solver.solver[:alg]
termination_condition = NonlinearSolveBase.AbsNormTerminationMode(
Base.Fix1(maximum, abs))
sol = solve(prob, solver_concrete; abstol = 1e-10, reltol = 1e-10,
maxiters = 1000, termination_condition)
@info "Solver $(solver.name) successfully solved the problem with norm = \
$(norm(sol.resid, Inf))."
if norm(sol.resid, Inf) ≤ 1e-10
tt = @belapsed solve($prob, $solver_concrete; abstol = 1e-10,
reltol = 1e-10, maxiters = 1000,
termination_condition = $termination_condition)
@info "Solver $(solver.name) took $(tt) seconds."
return tt
else
return NaN
end
catch e
@error "Solver $(solver.name) threw an error $(e)."
return NaN
end
end
end
probs_sa = [generate_prob(Val(N), Val(true)) for N in [2, 4, 8, 12]];
solve_timings_sa = benchmark_combinations(solvers, probs_sa)
probs_reg = [generate_prob(Val(N), Val(false)) for N in [4, 16, 128, 1024]];
solve_timings_reg = benchmark_combinations(solvers, probs_reg)
function create_structure_data(solve_timings)
df = []
for (i, solver_setup) in enumerate(solvers)
if solver_setup.pkg === :simplenonlinearsolve
alg_name = string(solver_setup.name[8:end])
timings = solve_timings[i, :]
list = []
for (j, other_solver) in enumerate(solvers)
if other_solver.pkg !== :simplenonlinearsolve &&
contains(other_solver.name, alg_name)
this_timings = solve_timings[j, :]
push!(list, other_solver.name => this_timings ./ timings)
end
end
push!(df, alg_name => list)
end
end
return df
end
df_sa = create_structure_data(solve_timings_sa)
df_reg = create_structure_data(solve_timings_reg)
fig = begin
ASPECT_RATIO = 0.7
WIDTH = 1200
HEIGHT = round(Int, WIDTH * ASPECT_RATIO)
STROKEWIDTH = 2.5
fig = Figure(; size = (WIDTH, HEIGHT))
axs = Matrix{Any}(undef, 1, 4)
xs = reduce(vcat, [fill(i, length(dfᵢ.second)) for (i, dfᵢ) in enumerate(df_sa)])
dodge = reduce(vcat, [collect(1:length(dfᵢ.second)) for (i, dfᵢ) in enumerate(df_sa)])
for i in 1:4
ys = reduce(vcat, [[xx.second[i] for xx in dfᵢ.second] for dfᵢ in df_sa])
ax = Axis(fig[1, i];
ylabel = "",
title = L"$N = %$(length(probs_sa[i].u0))$",
titlegap = 10, xticksvisible = false, yticksvisible = true,
xticklabelsvisible = false, yticklabelsvisible = true, titlesize = 22,
spinewidth = STROKEWIDTH, xlabelsize = 22, ylabelsize = 22,
xticklabelrotation = π / 4, xticklabelsize = 20, yticklabelsize = 20)
axs[1, i] = ax
barplot!(ax, xs, ys; color = dodge, colormap = :tableau_20, strokewidth = 2)
hlines!(ax, [1.0], color = :black, linestyle = :dash, linewidth = 2)
end
linkaxes!(axs...)
axs = Matrix{Any}(undef, 1, 4)
xs = reduce(vcat, [fill(i, length(dfᵢ.second)) for (i, dfᵢ) in enumerate(df_reg)])
dodge = reduce(vcat, [collect(1:length(dfᵢ.second)) for (i, dfᵢ) in enumerate(df_reg)])
for i in 1:4
ys = reduce(vcat, [[xx.second[i] for xx in dfᵢ.second] for dfᵢ in df_reg])
ax = Axis(fig[2, i];
ylabel = "",
title = L"$N = %$(length(probs_reg[i].u0))$",
titlegap = 10, xticksvisible = true, yticksvisible = true,
xticklabelsvisible = true, yticklabelsvisible = true, titlesize = 22,
spinewidth = STROKEWIDTH, xlabelsize = 22, ylabelsize = 22,
xticks = (1:length(df_sa), [d.first for d in df_sa]),
xticklabelrotation = π / 4, xticklabelsize = 20, yticklabelsize = 20)
axs[1, i] = ax
barplot!(ax, xs, ys; color = dodge, dodge = dodge, colormap = :tableau_20,
strokewidth = 3)
hlines!(ax, [1.0], color = :black, linestyle = :dash, linewidth = 3)
end
linkaxes!(axs...)
fig[0, :] = Label(fig, "Simple Algorithms on Quadratic Root-Finding Problem",
fontsize = 24, font = :bold)
fig[1, 0] = Label(fig, "Static Arrays",
fontsize = 24, rotation = π / 2, tellheight = false)
fig[2, 0] = Label(fig, "Regular Julia Arrays",
fontsize = 24, rotation = π / 2, tellheight = false)
fig[1:2, end + 1] = Label(fig, "Relative to SimpleNonlinearSolve.jl (Higher is Better)",
fontsize = 22, tellheight = false, rotation = π / 2)
labels = ["NonlinearSolve.jl", "NLsolve.jl", "Sundials"]
colors = cgrad(:tableau_20, length(labels); categorical = true)
elements = [PolyElement(; polycolor = colors[i], strokewidth = 3) for i in 1:3]
axislegend(axs[1, 4], elements, labels, "Package", patchsize = (20, 20),
labelsize = 16, titlesize = 20, framewidth = STROKEWIDTH, rowgap = 5)
fig
end
save("summary_plot_simplenonlinearsolve.svg", fig)CairoMakie.Screen{SVG}Appendix
These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.
To locally run this benchmark, do the following commands:
using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/NonlinearProblem","quadratic_nonlinear.jmd")Computer Information:
Julia Version 1.10.9
Commit 5595d20a287 (2025-03-10 12:51 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 128 × AMD EPYC 7502 32-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
Threads: 1 default, 0 interactive, 1 GC (on 128 virtual cores)
Environment:
JULIA_CPU_THREADS = 128
JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953
Package Information:
Status `/cache/build/exclusive-amdci3-0/julialang/scimlbenchmarks-dot-jl/benchmarks/NonlinearProblem/Project.toml`
[2169fc97] AlgebraicMultigrid v1.0.0
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[13f3f980] CairoMakie v0.13.4
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[f3b72e0c] DiffEqDevTools v2.48.0
[a0c0ee7d] DifferentiationInterface v0.6.52
⌃ [7da242da] Enzyme v0.13.37
[40713840] IncompleteLU v0.2.1
[b964fa9f] LaTeXStrings v1.4.0
[d3d80556] LineSearches v7.3.0
[7ed4a6bd] LinearSolve v3.8.0
[4854310b] MINPACK v1.3.0
[2774e3e8] NLsolve v4.5.1
[b7050fa9] NonlinearProblemLibrary v0.1.3
[8913a72c] NonlinearSolve v4.6.0
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[efcf1570] Setfield v1.1.2
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[0c5d862f] Symbolics v6.38.0
Info Packages marked with ⌃ have new versions available and may be upgradable.
Warning The project dependencies or compat requirements have changed since the manifest was last resolved. It is recommended to `Pkg.resolve()` or consider `Pkg.update()` if necessary.And the full manifest:
Status `/cache/build/exclusive-amdci3-0/julialang/scimlbenchmarks-dot-jl/benchmarks/NonlinearProblem/Manifest.toml`
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[7b1f6079] FileWatching
[9fa8497b] Future
[b77e0a4c] InteractiveUtils
[4af54fe1] LazyArtifacts
[b27032c2] LibCURL v0.6.4
[76f85450] LibGit2
[8f399da3] Libdl
[37e2e46d] LinearAlgebra
[56ddb016] Logging
[d6f4376e] Markdown
[a63ad114] Mmap
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.10.0
[de0858da] Printf
[9abbd945] Profile
[3fa0cd96] REPL
[9a3f8284] Random
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization
[1a1011a3] SharedArrays
[6462fe0b] Sockets
[2f01184e] SparseArrays v1.10.0
[10745b16] Statistics v1.10.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test
[cf7118a7] UUIDs
[4ec0a83e] Unicode
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[deac9b47] LibCURL_jll v8.4.0+0
[e37daf67] LibGit2_jll v1.6.4+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.2+1
[14a3606d] MozillaCACerts_jll v2023.1.10
[4536629a] OpenBLAS_jll v0.3.23+4
[05823500] OpenLibm_jll v0.8.1+4
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.2.1+1
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.52.0+1
[3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`
Warning The project dependencies or compat requirements have changed since the manifest was last resolved. It is recommended to `Pkg.resolve()` or consider `Pkg.update()` if necessary.