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.
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
