Speeding up a code involving nested for loops

2011 6 1
1 个回答
4 次查看（30 天）

1 个投票

[EDIT: Wed Jun 1 16:10:09 UTC 2011 - Reformat - MKF]
The following is a simplified version of a code that I need to run many times. The 'rand' function is replacing calculations that are of the same order of complexity. Any intelligent way of converting the nested loops (and the multiply-sum operation)into matrix (or faster) operations would be greatly appreciated.
M=1000;
N=1000;
PSI_conv = zeros (M,N);
PSI_ab = rand(M,N);
for s = 1 : M % M = 1000
for t = 1 : N % N = 1000
PHI_sph = rand(M,N);
PSI_conv(s,t) = sum(PSI_sph(:).* conj(PSI_ab(:)));
end
end

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回答（1 个）

Sean de Wolski
Sean de Wolski 2011-6-1

1 个投票

The idea is to minimize the number of computations inside the FOR-loop.
In this case, conj(PSI_ab(:)) doesn't change and thus only needs to be computed once. Why bother generating PSI_sph as an MxN matrix when you could just generate it as a vector and then not need the (:) operation?
M=1000;
N=1000;
PSI_conv = zeros (M,N);
PSI_ab = rand(M,N);
PSI_ab = conj(reshape(PSI_ab,numel(PSI_ab),1));
MN = M*N;
for s = 1 : M % M = 1000
for t = 1 : N % N = 1000
PHI_sph = rand(1,MN); %Edit per Jan's comment and my time test.
PSI_conv(s,t) = PSI_sph*PSI_ab;
end
end

8 个评论
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Jan
Jan 2011-6-1
"rand(1,MN) * PSI_ab" might be faster.
Mehdi
Mehdi 2011-6-1
Thanks Sean and Jan. The idea of removing the repetetive conj operation is definitely a time saver, thanks. I will also try converting matrices to vectors to see how much gain I can get. I was hoping that there is a smart way of leveraging matrix multiplications (like Jan's comment) to avoid one (or both) of the for loops.
Sean de Wolski
Sean de Wolski 2011-6-1
You would be correct. I'm seeing it take around 57% of the time.
t1 = 0;
t2 = 0;
mcol = rand(500*500,1);
mrow = rand(1,500*500);
m2 = rand(500*500,1);
for ii = 1:100;
tic
R1 = mcol.*m2;
t1 = t1+toc;
tic
R2 = mrow*m2;
t2 = t2+toc;
end
t2/t1
%{
ans =
0.55224
0.57016
0.57103
%}
Jan
Jan 2011-6-1
"rand(1,MN)*PSI_ab" is a scalar already, such that SUM can be omitted.
Sean de Wolski
Sean de Wolski 2011-6-1
Dur-da-dur. Time for another coffee :)
Matt Fig
Matt Fig 2011-6-1
Another case where the (or a?) one liner vectorization is slower!
PSI_conv = reshape(sum(bsxfun(@times,rand(M*N,N,M),conj(rand(M*N,1)))),M,N);
Sean de Wolski
Sean de Wolski 2011-6-1
The 1000^4 element matrix must take some serious time to construct. I wonder if a single for-loop and 1000^3 matrix on each iteration would be faster.
Matt Fig
Matt Fig 2011-6-1
I posted a version with BSXFUN in a single loop and it was slower, so I deleted it...

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Mehdi
Mehdi
2011-6-1

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