Efficiently compute a 3D matrix of outer products - MATLAB

Question

Suppose I have a matrix of elements like so:

A = reshape(1:25, 5, 5)

A =

 1     6    11    16    21
 2     7    12    17    22
 3     8    13    18    23
          


        

Answer 1

To state the obvious, have you tried a simple for-loop:

[m,n] = size(A);
B = zeros(m,m,n);
for i=1:n
    B(:,:,i) = A(:,i) * A(:,i).';
end

You'll be surprised how competitively fast it is.

Answer 2

This is just a minor improvement over Divakar's answer. It is a little faster because it replaces a 3D-array permute with a 2D-array permute:

B = bsxfun(@times, permute(A, [1 3 2]), permute(A, [3 1 2]));

Answer 3

This -

B = permute(bsxfun(@times,A,permute(A,[3 2 1])),[1 3 2])