How can I use the MATLAB vector processing instead of this for loop?

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

[José-Luis]

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

[Matt J]

Is Gsum sparse?

Answer 1

[Matt J]

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]

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

Answer 2

[Roger Stafford]

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