Vectorizing/speeding up bsxfun multiplication-loop

I have a situation that looks like this:

C=zeros(1440,181,8);

for i=1:8
C(:,:,i)=sum(bsxfun(@times,A(:,:,31:end),reshape(B(:,i),1,1,[])),3);
end

Where A is of size=1440x181x2251 and B size=2221x8.

What I want to do is simply perform an element wise multiplication between A(:,:,31:end) and all the rows of the i’th column in B and then store the summation of the third dimension of this in C depending on the address of i. This seemingly simple command is destroying the runtime of my script and I can’t really figure out how to speed it up by avoiding the for loop. I tried replacing the for loop by a parfor to do several loops at the same time but I immediately run out of memory when I try that so it doesn’t work.

Any suggestions?

Thanks

Answer 1

[Roger Stafford]

You can try these to see which, if either, is faster than your current method:

   C = reshape(reshape(A(:,:,31:end),[],2221)*B,1440,181,8);

or

   C = reshape(reshape(A(1440*181*30+1:end),[],2221)*B,1440,181,8);

They should both give the same result as your code. The idea here is to convert to two-dimensional matrix multiplication and then reshape the result back to a three dimensional array, with the hope that Mathworks' matrix multiplication is more efficient than the combined action of 'sum' and 'bsxfun'.

[PetterS]

The first suggestion works like a dream! Thank you so much.

(the second one was also faster than my version but it caused a huge memory usage spike of about 10 Gb to run which I can’t afford)