This is something, but I bet there are other ways too. This is about 10x faster on my hardware/version, but only about 2-3x faster on the web version.
% array size parameters
pagesz = [10 10];
npages = 10;
wa = 10;
% build test arrays
A = rand(npages,wa);
B = rand(pagesz(1),pagesz(2),npages);
% METHOD 1
tic
c = 0;
for j = 1:wa
d = 0;
for k = 1:npages
d = d+A(k,j)*B(:,:,k);
end
c = c+d;
end
toc
% METHOD 2
tic
c2 = sum(B.*permute(sum(A,2),[3 2 1]),3);
toc
% error metric (should be approximately zero)
immse(c,c2)
% METHOD 3 (Chunru's proposal)
tic
c3 = 0;
for j = 1:wa
c3 = c3 + sum(reshape(A(:, j), 1, 1, []).*B, 3);
end
toc
% error metric (should be approximately zero)
immse(c,c3)
While Chunru's proposal might not be generally as fast as what I proposed, it preserves the order of operations, and so the accumulated error will be smaller.
