Multiplication times for complex matrices: julia vs Matla

@kw_martin wrote:

I’ve been looking at some different filter approaches for analyzing ECG signals using Matlab and have recently implemented them in julia in order to get a speed improvement. I have not been seeing the expected improvements and have tracked the issue down to the time for multiplying complex matrices. I have made some simple examples in both cases to evaluate the times. The julia example is rough as I am new to julia.

#!/usr/local/bin/julia

module TmMlt

ENV["CMPLXROOT"] = "/home/martin/Dropbox/Matlab/Complex/KM_ComplexFilterToolbox"
using MAT, LinearAlgebra, Printf, BenchmarkTools

tms = zeros(Float64,2,1)
f(a,b) = a*b
for n = [64 128 256 512 1024]
    a = ones(Complex, n, n);
    b = ones(Complex, n, n);
    tm1 = time();
    f(a,b);
    tm2 = time();
    @printf("n: %u, time: %f\n",n,tm2 - tm1)
end
end
n = 1024
a = ones(Complex, n, n);
b = ones(Complex, n, n);
@btime f(a,b)

which gave me:

julia> include("TmMlt.jl")
WARNING: replacing module TmMlt.
n: 64, time: 0.018154
n: 128, time: 0.238965
n: 256, time: 1.620080
n: 512, time: 13.005956
n: 1024, time: 126.109016
  127.565 s (2152726530 allocations: 64.16 GiB)

The matlab script I ran was:

function tmMltplys()
    for n=[64 128 256 512 1024 2048 4096]
        fprintf('For n=%d ',n);
        a = rand(n,n) + j*rand(n,n);
        b = rand(n,n) + j*rand(n,n);
        c = mlt(a,b);
    end


    function c = mlt(a, b)
    % multiply two matrices
        tic
        c = a*b;
        toc
    end
end

which gave:

>> tmMltplys
For n=64 Elapsed time is 0.000240 seconds.
For n=128 Elapsed time is 0.000493 seconds.
For n=256 Elapsed time is 0.001726 seconds.
For n=512 Elapsed time is 0.013201 seconds.
For n=1024 Elapsed time is 0.150515 seconds.
For n=2048 Elapsed time is 0.741310 seconds.
For n=4096 Elapsed time is 5.980977 seconds.
>> 

I couldn’t go over n=1024 in julia as it took too long. I must be doing something drastically wrong as the julia times for multiplying two comlex matrices are over 1000 times longer than matlab times. I also coded a julia multiply using for loops; these times were very similar (slightly faster) than just using the simple function shown above. If anyone can help identify what I am doing wrong, it would be much appreciated. Thanks.
-Ken

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