codes instead of 'for' loops to speed up

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Coo Boo
Coo Boo 2012-8-18
Hi to all,
I have 3 'for' loop which make the excutation to be time-consuming. Is there any way to speed up? The code is:
...
for i= 0:P
for j=0:P
ss=0;
for k=P:N-1
ss=ss+x(k-j+1,1)*x(k-i+1,1);
end
R(i+1,j+1)=ss;
end
end
...
Thanks,

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采纳的回答

Jan
Jan 2012-8-18
as Matt has mentioned already, the question does not contain enough information to be answered exhaustively. The simple approach to vectorize the innermost loop is most likely not efficient:
for i = 0:P
for j = 0:P
R(i+1, j+1) = sum(x(P-j+1:N-j, 1) .* x(P-i+1:N-i, 1));
end
end
Now the creation of the intermediate vectors x(P-j+1:N-j, 1) takes too much time - but this is a guess only, which I cannot prove due to the missing details in the question.
But you could try to store one of the vectors in a temporary variable:
for i = 0:P
t1 = x(P-i+1:N-i, 1);
for j = 0:P
R(i+1, j+1) = sum(x(P-j+1:N-j, 1) .* t1);
end
end
Then you should exploit the symmetric structure of the result:
for i = 0:P
t1 = x(P-i+1:N-i, 1);
R(i+1, i+1) = sum(t1 .* t1); % Diagonal element
for j = i+1:P
t2 = sum(x(P-j+1:N-j, 1) .* t1);
R(i+1, j+1) = t2;
R(j+1, i+1) = t2;
end
end
Again: I cannot test this code. Please post requests for optimizing code always with a set of usual test data. Most likely the SUM(vector1 .* vector2) approach is slower than a lean and clean loop. Therefore I assume that exploiting the symmetry is a more useful strategy.
Omitting the 2nd index in "x(k, 1)" saves time, if x is a vector. But perhaps x is a function and the 2nd input is important.

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