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Efficient Vectorization of For Loop

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I have three matrices and C and am trying to compute a fourth matrix Min the following way:
for p = 1:N
for q = 1:N
M(p,q) = 2 * sum(A(:,q) .* conj(B(:,p)) .* C(:,q));
All matrices are . I am trying to compute this for N = 750 or so and the computation is extremely slow. I cannot find any obvious way to vectorize the code. Any help would be very much appreciated.

Accepted Answer

Bruno Luong
Bruno Luong on 15 Apr 2024
Edited: Bruno Luong on 15 Apr 2024
Not tested but the sign reading tell me
M = 2*B' * (A.*C);
James Tursa
James Tursa on 15 Apr 2024
Edited: James Tursa on 15 Apr 2024
I would guess that having 2*B' at the front will force MATLAB to physically compute the conjugate transpose of B first. However, if you segregate the 2* operation as 2 * (B' * (A.*C)), the B' would not need to be physically formed to do the conjugate transpose matrix multiply since this will be handled by flags passed into the BLAS routine. Maybe a bit faster? E.g.,
A = rand(5000); B = rand(5000); C = rand(5000);
timeit(@()2*B' * (A.*C))
ans = 0.5515
timeit(@()2*(B' * (A.*C)))
ans = 0.4901

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