MATLAB: Find maximum intermediate product in matrix multiplication

MATLABmatrix productmaximumvectorised

Hello,
I am in need of an efficient solution for the following problem…
For the matrix product C = A × B, where A is an n x m matrix, and B is an m x p matrix, each element [i,j] in the matrix product C is given by the sum of m products,
C_{i,j} = sum[ A_{ i, k} .* B_{ k, j}]_( k=1,…, m)
I need to find a similar function, that gives the matrix C as the maximum of m products,
C_{i,j} = max[ A_{ i, k} .* B_{ k, j}]_( k=1,…, m)
Actually, I need to find the index k that corresponds to the maximum in each case.
I have found a way to do this using loops, but it is way too slow for what I need. I also found an ugly solution using the kronecker product, but it is also too slow. My matrices, although sparse, are also quite large (m=n~1000 and p<1000).
I have been thinking about this for two weeks, but I haven't found a good solution!
Cheers, Ben

Best Answer

Another way using a loop, which avoids the potentially large intermediate result if the dimensions happen to be large.
function K = maxtimes(A,B)
AT = A.'; % gets the product data contiguous in memory
K = zeros(size(A,1),size(B,2));
for j=1:size(B,2)
    [~,k] = max(AT.*B(:,j)); % Uses implicit array expansion
    K(:,j) = k(:);
end
end
If this still isn't fast enough, you may need to resort to a mex routine.
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