How can I vectorize this loop?

Question

Michael on 30 Jul 2014

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https://uk.mathworks.com/matlabcentral/answers/144084-how-can-i-vectorize-this-loop

Edited: Andrei Bobrov on 30 Jul 2014

Accepted Answer: Jian Wei

I am trying to remove a loop from my code without using repmat.

A and B are matrices that have the same number of rows, say m. Otherwise they have arbitrary column size.

Let

The loop I want to vectorize.

k = size(A, 2);
l = size(B, 2);
     for t = 1:m
        ARP = ARP + A(t,:)' * B(t,:)
     end

Which is a sum of matrices size (kX1)X(1Xl) = kXl. I actually want the average so:

ARP = (1/m) * ARP

So far I have tried using repmat which balloons up the size of my matrices and in fact fails when the matrices get largish.

%Create copies of A stacked on top of each other to a depth of l
exA = repmat(A, l, 1);                     % (m * k)Xl
%Reshape it so that exA has each column of A cloned k times
exA = reshape(exA, m, k * l);              % mX(k * l)
%Create copies of B stacked next to each other to a width k
exB = repmat(B, 1, k);                     % mX(l * k)
%Both matrices are now m X k*l so we can element-wise multiply
%and take the mean of the rows.
ARP = mean(exA .* exB, 1);   % 1X(k * l)
ARP = reshape(ARP, l, k)';

I am also aware that repmat can be replaced in vectorizations with bsxfun, although it is not clear how to implement bsxfun in this case. I appreciate any help that gets me to an optimized solution and also illustrates techniques for vectorization that I can study for similar problems.

Thanks in advance Mike