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benchmarks.jl
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benchmarks.jl
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#=
Created on Tuesday 2 July 2019
Last update: Saturday 27 July 2019
@author: Michiel Stock
michielfmstock@gmail.com
Benchmarking Kroncker.jl compated to native functions.
=#
using Kronecker, Plots, LinearAlgebra
using BenchmarkTools
sizes = [5, 10, 25, 50, 100, 250, 500, 1000, 5000]
tmax = 10
# inverse
times_kron = []
times_naive = []
for s in sizes
A = randn(s, s) / s^2
B = rand(s, s) / s^2
v = rand(s^2)
K = A ⊗ B
t = @belapsed inv($K)
push!(times_kron, t)
if s^2 < 5000
K = collect(K)
t = @belapsed inv($K)
push!(times_naive, t)
compute_naive = t < tmax
end
end
plot(sizes.^2, times_kron, label="matrix inverse", color=:blue, legend=:bottomright, lw=2)
plot!(sizes[1:length(times_naive)].^2, times_naive, color=:blue, ls=:dash, label="", lw=2 )
# determinant
times_kron = []
times_naive = []
@belapsed det(Kwarmup)
for s in sizes
A = randn(s, s)
B = rand(s, s)
v = rand(s^2)
K = A ⊗ B
t = @belapsed det($K)
push!(times_kron, t)
if s^2 < 5000
K = collect(K)
t = @belapsed det($K)
push!(times_naive, t)
compute_naive = t < tmax
end
end
plot!(sizes.^2, times_kron, label="determinant", color=:green, lw=2)
plot!(sizes[1:length(times_naive)].^2, times_naive, color=:green, ls=:dash, label="", lw=2)
# squaring
times_kron = []
times_naive = []
v = rand(100)
@belapsed Kwarmup * Kwarmup
for s in sizes
A = randn(s, s)
B = rand(s, s)
v = rand(s^2)
K = A ⊗ B
t = @belapsed $K * $K
push!(times_kron, t)
if s^2 < 5000
K = collect(K)
t = @belapsed $K * $K
push!(times_naive, t)
compute_naive = t < tmax
end
end
plot!(sizes.^2, times_kron, label="squaring", color=:red, lw=2)
plot!(sizes[1:length(times_naive)].^2, times_naive, color=:red, ls=:dash, label="", lw=2)
# vector multiplication
times_kron = []
times_naive = []
for s in sizes
A = randn(s, s)
B = rand(s, s)
v = rand(s^2)
K = A ⊗ B
t = @belapsed $K * $v
push!(times_kron, t)
if s^2 < 5000
K = collect(K)
t = @belapsed $K * $v
push!(times_naive, t)
compute_naive = t < tmax
end
end
plot!(sizes.^2, times_kron, label="matrix-vector mult.", color=:orange, lw=2)
plot!(sizes[1:length(times_naive)].^2, times_naive, color=:orange, ls=:dash, label="", lw=2)
yaxis!(:log10)
ylabel!("CPU time (s)")
xaxis!(:log10)
xlabel!("Kronecker product size")
title!("Performance Kronecker.jl (-) vs. native code (--)")
savefig("benchmark.svg")