Efficient Vectorization of For Loop

Hi,

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));
    end
end

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.

Thanks.

Answer 1

[Bruno Luong]

Not tested but the sign reading tell me

M = 2*B' * (A.*C);

[Voss]

Very good +1. But don't forget the factor of 2.

[Bruno Luong]

Fixed

[James Tursa]

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

[Shreyas Bharadwaj]

Thank you!