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7270696
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2011-09-01T13:02:55.357
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2011-09-01T13:02:55.357
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2017-05-23T11:47:57.147
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2
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Here is a solution (similar to what was done <a href="https://stackoverflow.com/questions/1745299/multiply-a-3d-matrix-with-a-2d-matrix/1745587#1745587">here</a>) that computes the result in a single matrix-multiplication operation, although it involves heavy manipulation of the matrices to put them into desired shape. I then compare it to the simple for-loop computation (which I admit is a lot more readable) <pre><code>%# 3D matrices A = rand(4,2,3); B = rand(2,5,3); [m n p] = size(A); [n q p] = size(B); %# single matrix-multiplication operation (computes more products than needed) AA = reshape(permute(A,[2 1 3]), [n m*p])'; %'# cat(1,A(:,:,1),...,A(:,:,p)) BB = reshape(B, [n q*p]); %# cat(2,B(:,:,1),...,B(:,:,p)) CC = AA * BB; [mp qp] = size(CC); %# only keep "blocks" on the diagonal yy = repmat(1:qp, [m 1]); xx = bsxfun(@plus, repmat(1:m,[1 q])', 0:m:mp-1); %' idx = sub2ind(size(CC), xx(:), yy(:)); CC = reshape(CC(idx), [m q p]); %# compare against FOR-LOOP solution C = zeros(m,q,p); for i=1:p C(:,:,i) = A(:,:,i) * B(:,:,i); end isequal(C,CC) </code></pre> Note that the above is performing more multiplications than needed, but sometimes <a href="http://undocumentedmatlab.com/blog/matrix-processing-performance/" rel="nofollow noreferrer">"Anyone who adds, detracts (from execution time)"</a>. Sadly this is not the case, as the FOR-loop is much faster here :) My point was to show that vectorization is not easy, and that loop-based solutions are not always bad...
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singulars
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1. POTensor contraction in Matlab
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