Comparing Matrix Elements pairwise without looping in Matlab

Question

I encountered the following Problem in Matlab:

I have a matrix A, and I want to compare its elements pairwise to a large number of other matrices (B1, B2, B3, etc.) elements. Finally, I want to sum the larger elements, weighted by weights (w1, w2, w3, etc.).

I am trying to calculate the following sum:

S= w1 .* (max(A,B1)) + w2 .* (max(A,B2)) + w3 .* (max(A,B3)) ... etc.

I wrote a loop over the index numbers of B and w, but this approach is very slow.

Is there a nice way to write a faster code for this problem, not using loops?

Thanks for your help

Answer 1

Given:

w = rand(1,10);
A = rand(5,5);
B1 = rand(5,5);
B2 = rand(5,5);
...
B10 = rand(5,5);

The first thing to do is to put all of the B matrices into a 3-dimensional array:

B = cat(3, B1, B2, ..., B10);

Since max is vectorized, the max between A and the individual B's is:

S = max(A,B);

In order to apply the weights, we have to reshape them into the 3rd dimension to multiply the correct max:

w = reshape(w, 1, 1, 10);   % or permute(w, [1 3 2]);
S = w.*S;

Then to take the sum, we just tell sum to operate in the 3rd dimension:

S = sum(S, 3);