mtimesm, an efficient nD matrix multiplication routine.

A wrapper of `MTIMESX` and `PAGEMTIMES`. Created for people who have old matlab or have difficulties in compiling mex-file.

MTIMESX (`PAGEMTIMES`) is a very efficient matrix multiply routine for n-Dimensional (nD, n > 2) arrays.

However, you have to update your MATLAB (`PAGEMTIMES` was introduced in R2020b), or build a mex-file.

So, I created this function (m-file) for people who have only old matlab or have difficulties in compiling mex-file.

This function follows the same behaviour as MTIMESX (`PAGEMTIMES`).

Run the following codes for demonstration.

ctest = 2000;
nfs1 = 45;
nfs2 = 55;
nks1 = 5;
nks2 = 7;
A = rand(nks1, nks1, nfs1, nfs2);
B = rand(nks2, nks1, nfs1, nfs2);
tic;
for ii = 1:ctest
    C1 = zeros(nks1, nks2, nfs1, nfs2);
    for ff = 1:nfs1
        for gg = 1:nfs2
            C1(:,:, ff, gg) = conj(A(:,:, ff, gg)).'*B(:,:, ff, gg).';
        end
    end
end
t1 = toc
tic, for jj = 1:ctest, C2 = mtimesx(A, 'c', B, 't');end, t2 =toc
tic; for kk = 1:ctest, C3 = mtimesm(A, 'c', B, 't', true);end, t3 = toc
tic; for oo = 1:ctest, C4 = pagemtimes(A, 'c', B, 't');end, t4 = toc
max(abs(C1(:)-C2(:)))
max(abs(C1(:)-C3(:)))
max(abs(C1(:)-C4(:)))

% on my notebook (i7-8550u), t1 ~17 sec; t2 ~1.3 sec; t3 ~3.8 sec; t4 ~0.39 sec.

% `PAGEMTIMES` is the fast in this case.