Benchmarking backslash in Julia with Float64, ComplexF64, and Dual128 (via DualMatrixTools.jl)

Benchmark_backslash.jl

using LinearAlgebra, SparseArrays, SuiteSparse
using DualNumbers, DualMatrixTools
using BenchmarkTools

n = 1000 ;

y = rand(n) ;

A = sprand(n, n, 20/n) ;
i, j, v = findnz(A) ;

v2 = rand(length(v)) ;

complex_A = sparse(i, j, v .+ im .* v2 .* 1e-50) ;
dual_A = sparse(i, j, v .+ ε .* v2) ;

Af = factorize(A) ;
complex_Af = factorize(complex_A) ;
dual_Af = factorize(dual_A) ;

# factorization benchmark
@btime $A \ $y ;
@btime factorize($A) ;
@btime $Af \ $y ;

# complex version
@btime $complex_A \ $y ;
@btime factorize($complex_A) ;
@btime $complex_Af \ $y ;

# dual version
@btime $dual_A \ $y ;
@btime factorize($dual_A) ;
@btime $dual_Af \ $y ;