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Solve sparse perturbations with PureKLUFactorization #105

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hersle merged 1 commit into from
Jul 6, 2026
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Solve sparse perturbations with PureKLUFactorization #105

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2 changes: 1 addition & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -58,7 +58,7 @@ ForwardDiffChainRules = "0.3.0"
GraphRecipes = "0.5.13"
Integrals = "4.5.0, 5.0.0"
LinearAlgebra = "1.10.0"
LinearSolve = "3.19.0"
LinearSolve = "3.83.0"
MatterPower = "0.5.0"
ModelingToolkit = "11.0.0"
ModelingToolkitBase = "1.0.0"
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20 changes: 10 additions & 10 deletions docs/src/benchmarks.md
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Expand Up @@ -106,7 +106,7 @@ The points on each curve correspond to a sequence of tolerances.
```@example bench
# TODO: test different nlsolve # hide
# TODO: add AdaptiveRadau/RadauIIA5 when they support sparse J: https://github.com/SciML/OrdinaryDiffEq.jl/issues/2892 # hide
linsolve = KLUFactorization()
linsolve = PureKLUFactorization()
ptalgs = [algtype(; linsolve) for algtype in [TRBDF2, KenCarp4, KenCarp47, KenCarp5, Kvaerno5, Rodas4P, Rodas5P, Rodas6P, QNDF, FBDF]]
ptprobgen = SymBoltz.setuppt(prob.pt, bgsol)
refalg = Rodas5P(; linsolve)
Expand Down Expand Up @@ -185,15 +185,15 @@ prob_jac = prob # CosmologyProblem(M, pars; jac = true, sparse = true)
prob_nojac = CosmologyProblem(M, pars; jac = false, sparse = true)

bgopts = (alg = Rodas5P(linsolve = RFLUFactorization(),),)
ptopts = (alg = Rodas5P(linsolve = KLUFactorization(),), save_everystep = false) # generate function for J symbolically
ptopts = (alg = Rodas5P(linsolve = PureKLUFactorization(),), save_everystep = false) # generate function for J symbolically
bench["symbolic"] = @benchmarkable $solve($prob_jac, $ks; bgopts = $bgopts, ptopts = $ptopts) samples=5 seconds=30

bgopts = (alg = Rodas5P(linsolve = RFLUFactorization(), autodiff = SymBoltz.AutoForwardDiff()),)
ptopts = (alg = Rodas5P(linsolve = KLUFactorization(), autodiff = SymBoltz.AutoForwardDiff()), save_everystep = false) # compute J with forward-mode AD
ptopts = (alg = Rodas5P(linsolve = PureKLUFactorization(), autodiff = SymBoltz.AutoForwardDiff()), save_everystep = false) # compute J with forward-mode AD
bench["forward diff"] = @benchmarkable $solve($prob_nojac, $ks; bgopts = $bgopts, ptopts = $ptopts) samples=5 seconds=30

bgopts = (alg = Rodas5P(linsolve = RFLUFactorization(), autodiff = SymBoltz.AutoForwardDiff()),) # fails with finite diff background J
ptopts = (alg = Rodas5P(linsolve = KLUFactorization(), autodiff = SymBoltz.AutoFiniteDiff()), save_everystep = false) # compute J with finite differences
ptopts = (alg = Rodas5P(linsolve = PureKLUFactorization(), autodiff = SymBoltz.AutoFiniteDiff()), save_everystep = false) # compute J with finite differences
bench["finite diff"] = @benchmarkable $solve($prob_nojac, $ks; bgopts = $bgopts, ptopts = $ptopts) samples=5 seconds=30

results = run(bench; verbose = true)
Expand Down Expand Up @@ -240,12 +240,12 @@ This plot compares the time to solve several perturbation $k$-modes with differe
ks = 10 .^ range(-2, 4, length=75)
ptopts1 = (alg = Rodas5P(linsolve = LUFactorization()), save_everystep = false)
ptopts2 = (alg = Rodas5P(linsolve = RFLUFactorization()), save_everystep = false)
ptopts3 = (alg = Rodas5P(linsolve = KLUFactorization()), save_everystep = false)
ptopts3 = (alg = Rodas5P(linsolve = PureKLUFactorization()), save_everystep = false)
ptopts4 = (alg = Rodas5P(linsolve = UMFPACKFactorization()), save_everystep = false)
ts1 = [minimum(@elapsed solve(prob, ks; ptopts = ptopts1, verbose = true) for i in 1:3) for prob in probs_dense]
ts2 = [minimum(@elapsed solve(prob, ks; ptopts = ptopts2, verbose = true) for i in 1:3) for prob in probs_dense]
ts3 = [minimum(@elapsed solve(prob, ks; ptopts = ptopts3, verbose = true) for i in 1:3) for prob in probs_sparse]
ts4 = [minimum(@elapsed solve(prob, ks; ptopts = ptopts4, verbose = true) for i in 1:3) for prob in probs_sparse]
ts1 = [minimum(@elapsed solve(prob, ks; ptopts = ptopts1) for i in 1:3) for prob in probs_dense]
ts2 = [minimum(@elapsed solve(prob, ks; ptopts = ptopts2) for i in 1:3) for prob in probs_dense]
ts3 = [minimum(@elapsed solve(prob, ks; ptopts = ptopts3) for i in 1:3) for prob in probs_sparse]
ts4 = [minimum(@elapsed solve(prob, ks; ptopts = ptopts4) for i in 1:3) for prob in probs_sparse]

p1 = plot(ylabel = "time / s", xticks = (lmaxs, ""), ylims = (0.0, ceil(max(maximum(ts1), maximum(ts2), maximum(ts3), maximum(ts4)))))
marker = :circle
Expand Down Expand Up @@ -273,7 +273,7 @@ plot!(p2, lmaxs, speedups4; marker, label = nothing)
plot(p1, p2; size = (800, 600), layout = grid(2, 1, heights=(3//4, 1//4)))
```

Except for models with a very small perturbation system, it is a good idea to generate the sparse Jacobian and use the sparse `KLUFactorization` linear solver.
Except for models with a very small perturbation system, it is a good idea to generate the sparse Jacobian and use the sparse `PureKLUFactorization` linear solver.

```@setup
# TODO: tune Krylov with verbose = 1, ILU, ..., atol, rtol # hide
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4 changes: 2 additions & 2 deletions src/solve.jl
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Expand Up @@ -312,7 +312,7 @@ issparse(prob::ODEProblem) = issparse(prob.f.jac_prototype)

function bgalg(prob::ODEProblem; stiff = true)
if issparse(prob)
linsolve = KLUFactorization()
linsolve = PureKLUFactorization()
else
linsolve = RFLUFactorization(throwerror = true)
end
Expand All @@ -326,7 +326,7 @@ bgalg(prob::CosmologyProblem; kwargs...) = bgalg(prob.bg; kwargs...)

function ptalg(prob::ODEProblem; accuracy = 2)
if issparse(prob)
linsolve = KLUFactorization()
linsolve = PureKLUFactorization()
else
linsolve = RFLUFactorization(throwerror = true)
end
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8 changes: 4 additions & 4 deletions test/runtests.jl
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Expand Up @@ -593,14 +593,14 @@ end

# with ΛCDM model
k = [1e0, 1e1, 1e2, 1e3]
sol = solve(prob_sparse, k; bgopts = (alg = SymBoltz.Rodas4P(linsolve = SymBoltz.LUFactorization()),), ptopts = (alg = SymBoltz.KenCarp4(linsolve = SymBoltz.KLUFactorization()),))
sol = solve(prob_sparse, k; bgopts = (alg = SymBoltz.Rodas4P(linsolve = SymBoltz.LUFactorization()),), ptopts = (alg = SymBoltz.KenCarp4(linsolve = SymBoltz.PureKLUFactorization()),))
@test issuccess(sol)

M2 = RMΛ()
pars2 = Dict(M2.m.Ω₀ => 0.3, M2.r.Ω₀ => 1e-5, M2.g.h => NaN, M2.r.T₀ => NaN)
prob2 = CosmologyProblem(M2, pars2; jac = true, sparse = true, bgopts = (sparse = true,)) # demand sparse background
bgopts = (alg = SymBoltz.Rodas4P(linsolve = SymBoltz.KLUFactorization()),)
ptopts = (alg = SymBoltz.KenCarp4(linsolve = SymBoltz.KLUFactorization()),)
bgopts = (alg = SymBoltz.Rodas4P(linsolve = SymBoltz.PureKLUFactorization()),)
ptopts = (alg = SymBoltz.KenCarp4(linsolve = SymBoltz.PureKLUFactorization()),)
sol = solve(prob2, k; bgopts, ptopts)
@test issuccess(sol)
end
Expand All @@ -612,7 +612,7 @@ end
@test issuccess(solve(prob_sparse, 1.0))
@test issuccess(solve(prob_dense, 1.0; bgopts = (alg = SymBoltz.Rodas5P(),), ptopts = (alg = SymBoltz.Rodas5P(),))) # should automatically find compatible linsolves
@test issuccess(solve(prob_sparse, 1.0; bgopts = (alg = SymBoltz.Rodas5P(),), ptopts = (alg = SymBoltz.Rodas5P(),)))
@test_throws "dense Jacobian must be solved with dense" solve(prob_dense; bgopts = (alg = SymBoltz.Rodas5P(linsolve = SymBoltz.KLUFactorization()),)) # has dense background
@test_throws "dense Jacobian must be solved with dense" solve(prob_dense; bgopts = (alg = SymBoltz.Rodas5P(linsolve = SymBoltz.PureKLUFactorization()),)) # has dense background
@test_throws "sparse Jacobian must be solved with sparse" solve(prob_sparse, 1.0; ptopts = (alg = SymBoltz.Rodas5P(linsolve = SymBoltz.RFLUFactorization()),)) # has sparse perturbations
@test issuccess(solve(prob_dense, 1.0; bgopts = (alg = SymBoltz.bgalg(prob_dense),), ptopts = (alg = SymBoltz.ptalg(prob_dense; accuracy = 0),)))
@test issuccess(solve(prob_dense, 1.0; bgopts = (alg = SymBoltz.bgalg(prob_dense),), ptopts = (alg = SymBoltz.ptalg(prob_dense; accuracy = 1),)))
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