I was testing this package from this repository, it is faster than A \ b
I do not know any other competitor for calculating Gaussian Elimination that can be measured with @time. If anyone knows, I would like to know and do benchmark test on all of them.
This is from Julia REPL and JupyterNotebook:
A couple of suggestions: do not test with @time in the global scope. Use BenchmarkTools to test performance.
For instance
julia> b = rand(3)
3-element Vector{Float64}:
8.30429e-01
1.46162e-01
8.75693e-02
julia> A = rand(3, 3)
3×3 Matrix{Float64}:
2.81443e-01 1.72279e-01 4.03091e-01
2.49288e-01 2.35197e-01 2.02405e-01
2.82910e-01 8.54934e-01 9.42708e-01
julia> using BenchmarkTools
julia> @btime $A \ $b
563.934 ns (3 allocations: 288 bytes)
3-element Vector{Float64}:
1.46582e+00
-2.88576e+00
2.27007e+00
julia>
Great suggestion, what is the different with this BenchmarkTools?
The result is the other way around now.
You should take a look at the BenchmarkTools documentation, where it is explained why you should not use global variables when benchmarking. Note the dollar signs in @PetrKryslUCSD’s code. Also, it is nicer to provide example code and outputs in code blocks rather than using screen images. That way other people can copy and paste your examples.
A couple more packages for you to look at: MKL and RecursiveFactorization.
LAPACK, OpenBLAS, MKL etc are all optimized for large matrices. For a tiny matrix like 3x3 they introduce a lot of overhead and a simple loop will often be faster.
But if you have lots of tiny 3x3 systems it will be faster still to use StaticArrays, which can unroll and inline everything.
I try BenchmarkTools on finding a solution of a linear system and compare the time for two different methods in Julia:
A = [1 2 3;
2 5 3;
1 0 8]
b = [5; 3; 17]
using BenchmarkTools
@btime $A \ $b
@btime inv(A)*b
