Optimizing a nested loop by summation

Does anyone have a suggestion on how I can optimize this nested loop? Is it possible to do this faster by just using sum? O, L, and W are of arbitrary size.

A = zeros(size(W));

for m = 1:size(O,1)

for pix = 1:NumPixels

A = A + O(m,pix) .* ( L(:,:,m,pix) ./ W ) ./ (sum( sum( L(:,:,m,pix) , 1 ) , 2 ) );

end

end

Answer 1

[Andrei Bobrov]

A = zeros(size(W));
for m = 1:size(O,1)
    for pix = 1:NumPixels
        L1 = L(:,:,m,pix);
        A = A + O(m,pix)* L1./W / sum(L1(:));
    end
end

without loop

s = size(L);
L1 = reshape(L,s(1),s(2),[]);
out = sum(bsxfun(@times,bsxfun(@rdivide,...
                    bsxfun(@rdivide,L1,W),sum(sum(L1,2))),reshape(O,1,1,[])),3);

ADD [8:27MDT 16.12.2011]

s = size(L);
L1 = reshape(L,prod(s(1:2)),[]);
A1 = reshape( bsxfun(@times,L1, 1./(W(:)*sum(L1)))*O(:),s(1),[])

[Kristoffer]

It looks good, but it's only marginally faster and demands more memory.