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Efficient Vectorization of For Loop

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Shreyas Bharadwaj
Shreyas Bharadwaj 2024-4-15
评论： Shreyas Bharadwaj 2024-4-16
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.

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Bruno Luong
Bruno Luong 2024-4-15
编辑：Bruno Luong 2024-4-15
Not tested but the sign reading tell me
M = 2*B' * (A.*C);
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James Tursa
James Tursa 2024-4-15
编辑：James Tursa 2024-4-15
Ran in:
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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