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Merge pull request #628 from SciML/sparse_linsolve
Create sparse linear solver PDE benchmark
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| Original file line number | Diff line number | Diff line change |
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| --- | ||
| title: Finite Difference Sparse PDE Jacobian Factorization Benchmarks | ||
| author: Jürgen Fuhrmann | ||
| --- | ||
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| ```julia | ||
| using BenchmarkTools, Random, VectorizationBase | ||
| using LinearAlgebra, SparseArrays, LinearSolve, Sparspak | ||
| import Pardiso | ||
| using Plots | ||
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| BenchmarkTools.DEFAULT_PARAMETERS.seconds = 0.5 | ||
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| # Why do I need to set this ? | ||
| BenchmarkTools.DEFAULT_PARAMETERS.samples = 10 | ||
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| # Sparse matrix generation on a n-dimensional rectangular grid. After | ||
| # https://discourse.julialang.org/t/seven-lines-of-julia-examples-sought/50416/135 | ||
| # by A. Braunstein. | ||
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| A ⊕ B = kron(I(size(B, 1)), A) + kron(B, I(size(A, 1))) | ||
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| function lattice(n; Tv = Float64) | ||
| d = fill(2 * one(Tv), n) | ||
| d[1] = one(Tv) | ||
| d[end] = one(Tv) | ||
| spdiagm(1 => -ones(Tv, n - 1), 0 => d, -1 => -ones(Tv, n - 1)) | ||
| end | ||
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| lattice(L...; Tv = Float64) = lattice(L[1]; Tv) ⊕ lattice(L[2:end]...; Tv) | ||
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| # | ||
| # Create a matrix similar to that of a finite difference discretization in a `dim`-dimensional | ||
| # unit cube of ``-Δu + δu`` with approximately N unknowns. It is strictly diagonally dominant. | ||
| # | ||
| function fdmatrix(N; dim = 2, Tv = Float64, δ = 1.0e-2) | ||
| n = N^(1 / dim) |> ceil |> Int | ||
| lattice([n for i in 1:dim]...; Tv) + Tv(δ) * I | ||
| end | ||
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| algs = [ | ||
| UMFPACKFactorization(), | ||
| KLUFactorization(), | ||
| SparspakFactorization(), | ||
| ] | ||
| cols = [:red, :blue, :green, :magenta, :turqoise] # one color per alg | ||
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| __parameterless_type(T) = Base.typename(T).wrapper | ||
| parameterless_type(x) = __parameterless_type(typeof(x)) | ||
| parameterless_type(::Type{T}) where {T} = __parameterless_type(T) | ||
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| # | ||
| # kmax=12 gives ≈ 40_000 unknowns max, can be watched in real time | ||
| # kmax=15 gives ≈ 328_000 unknows, you can go make a coffee. | ||
| # Main culprit is KLU factorization in 3D. | ||
| # | ||
| function run_and_plot(dim; kmax = 12) | ||
| ns = [10 * 2^k for k in 0:kmax] | ||
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| res = [Float64[] for i in 1:length(algs)] | ||
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| for i in 1:length(ns) | ||
| rng = MersenneTwister(123) | ||
| A = fdmatrix(ns[i]; dim) | ||
| n = size(A, 1) | ||
| @info "dim=$(dim): $n × $n" | ||
| b = rand(rng, n) | ||
| u0 = rand(rng, n) | ||
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| for j in 1:length(algs) | ||
| bt = @belapsed solve(prob, $(algs[j])).u setup=(prob = LinearProblem(copy($A), | ||
| copy($b); | ||
| u0 = copy($u0), | ||
| alias_A = true, | ||
| alias_b = true)) | ||
| push!(res[j], bt) | ||
| end | ||
| end | ||
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| p = plot(; | ||
| ylabel = "Time/s", | ||
| xlabel = "N", | ||
| yscale = :log10, | ||
| xscale = :log10, | ||
| title = "Time for NxN sparse LU Factorization $(dim)D", | ||
| label = string(Symbol(parameterless_type(algs[1]))), | ||
| legend = :outertopright) | ||
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| for i in 1:length(algs) | ||
| plot!(p, ns, res[i]; | ||
| linecolor = cols[i], | ||
| label = "$(string(Symbol(parameterless_type(algs[i]))))") | ||
| end | ||
| p | ||
| end | ||
| ``` | ||
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| ```julia | ||
| run_and_plot(1) | ||
| ``` | ||
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| ```julia | ||
| run_and_plot(2) | ||
| ``` | ||
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| ```julia | ||
| run_and_plot(3) | ||
| ``` |