Does MATLAB optimize diag(A*B)?

Question

Say I have two very big matrices A (M-by-N) and B (N-by-M). I need the diagonal of A*B. Computing the full A*B requires M

Answer 1

Actually, you can do this faster than a for loop using the wonders of bsxfun:

diag4 = sum(bsxfun(@times,A,B.'),2)

This about twice as fast as the explicit for loop on my machine for large matrices (2,000-by-2,000 and bigger) and is faster for matrices larger than about 500-by-500.

Note that all of these methods will produce numerically different results because of the different orders of summation and multiplication.