about nested for loop

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t g
t g 2012-5-19
i have three matrices A,B,C of size N*N. and I have a nested for loop code as given here,
D=0;
for i=1:N
for j=1:N
for k=1:N
for l=1:N
D = D + A(k,l) * B(i,j) * C(i,k) * C(j,l);
end
end
end
end
Now for a large value of N (say N=500), this code is taking a lot of time to execute. I want to know what is the procedure to improve this code so that it executes faster.
thanks in advance for any help.

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回答（2 个）

Teja Muppirala
Teja Muppirala 2012-5-20
D=sum(sum(B.*(C*A*C')))
Walter Roberson
Walter Roberson 2012-5-19
B(i,j) * C(i,k) can be calculated at the "for k" level. Call that BC. Then you have simplified to
for l=1:N
D = D + BC * A(k,l) * C(j,l);
end
and that can be vectorized along l without a loop.
D = D + BC * sum(A(k,:) .* C(j,:));
After that you may be able to make further optimizations.
Can you rewrite what you are doing in terms of matrix multiplication?

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