Asked by Maximilian
on 11 Dec 2012

Hi guys,

does anybody have an idea how I could speed up the following loop:

Havg = zeros(1, length(Gsum)); for k=1:K Havg = Havg + circshift(Gsum, [0 numBlocks*M*(k-1)]); end

Here, length(Gsum)=280000 and K=1200. NumBlocks equals 10 and M=14. This loop is very slow. However, I did not find a way to use the MATLAB-specific vector processing to speed it up.

How can I speed up the loop, e.g. with MATLABs powerful vector processing?

Regards, Max

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Answer by Matt J
on 11 Dec 2012

Accepted answer

If Gsum is sparse, there may be better ways than the following fft-based method:

numBlocks=10; M=14; N=length(Gsum); K=1200;

f=@(t) mod(t-1,N)+1; shifts = f(1:numBlocks*M:numBlocks*M*(K-1)+1); comb=accumarray(shifts.',1,[N,1]).'; Havg=ifft(fft(Gsum).*fft(comb),'symmetric');

Maximilian
on 12 Dec 2012

Thank you for this fft-based idea. The code works well and much faster than the original version.

Answer by Roger Stafford
on 11 Dec 2012

As your code is now, you are performing 280,000 X 1,200 = 336,000,000 additions. You can cut down the number of flops by a factor of about 1/333 with the use of matlab's 'cumsum' function.

p = 140; q = 2000; r = 1200; Havg = reshape(Gsum,p,q); Havg = cumsum([zeros(p,1),Havg,Havg(:,1:r-1)],2); Havg = reshape(Havg(:,r+1:r+q)-Havg(:,1:q),1,[]);

It should be noted, however, that the above reduction in the number of flops comes at the cost of increased round-off error accumulated by 'cumsum' over q+r = 3200 steps in each of the 140 rows in the next-to-last line.

Roger Stafford

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## 2 Comments

## José-Luis (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/56286#comment_116564

How slow is very slow? I assume Gsum is a row vector?

## Matt J (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/56286#comment_116577

Is Gsum sparse?