Fast way to compute only the diagonal of the square of a matrix

Question

I have an nxm matrix V, of which I compute the square S=V'*V. For my following computations I need only the diagonal of S, so I write s=diag(V'*V). However, this is a bit of a waste, because I'm computing also all the off-diagonal elements. Is there a fast way to compute only the diagonal elements of S? I could use a for loop, of course, but explicit looping isn't the fast way to do stuff in MATLAB.

Answer 1

That's easy:

sum(conj(v).*v,1)

or

sum(abs(v).^2,1)

If the matrix is real, you can simplify to

sum(v.*v,1)

or

sum(v.^2,1)