Efficient Vectorization of For Loop

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Shreyas Bharadwaj
Shreyas Bharadwaj il 15 Apr 2024 alle 21:08
Commentato: Shreyas Bharadwaj il 16 Apr 2024 alle 14:44
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 il 15 Apr 2024 alle 21:57
Modificato: Bruno Luong il 15 Apr 2024 alle 22:12
Not tested but the sign reading tell me
M = 2*B' * (A.*C);
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James Tursa
James Tursa il 15 Apr 2024 alle 22:31
Modificato: James Tursa il 15 Apr 2024 alle 22:33
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
Shreyas Bharadwaj
Shreyas Bharadwaj il 16 Apr 2024 alle 14:44
Thank you!

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