Vectorizing a funky matrix multiplication

I have two matrices H and W, where H is Nx1873 and W is 262144xN (N is a small integer, usually 10-20). I multiply these matrices using the following code:

comp = zeros([512 512 1873 N]);
for i = 1:N
    comp(:,:,:,i) = reshape(W(:,i)*H(i,:),[512 512 1873]);
end

Is there a way to vectorize this operation?

[Matt J]

If N is a small integer, vectorization will probably not make much difference.

Also, the operation itself seems like a bad idea. I don't know what you're planning to do with all of those outer products comp(:,:,:,i), but in most situations there are efficient ways to manipulate outer-products without computing them directly. They consume a lot of memory in spite of containing very little information.

Answer 1

[Matt J]

 Wr=reshape(W,[],1,N);
 Hr=reshape(H.',1,[],N);

 comp=reshape( bsxfun(@times, Wr,Hr), 512,512,[]);

[Matt J]

If N is a small integer, vectorization will probably not make much difference.

Also, the operation itself seems like a bad idea. I don't know what you're planning to do with all of those outer products comp(:,:,:,i), but in most situations there are efficient ways to manipulate outer-products without computing them directly. They consume a lot of memory in spite of containing very little information.

[David Thibodeaux]

I'm using H and W as outputs of either nnmf() or lsqnonneg(), and creating matrices that represent each of the N components individually for my original 512x512x1873 dataset. I use this to create movies where each component can be color coded, to aid in visualizing my data. I'm not sure how else I can organize the data, since I need to again matrix multiply it by my colormap as a final step, and visualize all components at once for each timepoint.

Thanks for your answer, I will try it ans see if there is any improvement!