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.

Luis Mendo · Accepted Answer · 2015-07-30 08:01:26Z

5

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)

answered Jul 30, 2015 at 8:01

Luis Mendo

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3 Comments

DeltaIV Over a year ago

:) thanks, man - I was sure this would be answered by you. You're my official bsxfun guru! I like the third one because it's basically the definition of matrix product. I actually needed the diagonal as a column vector, so I modifed it to sum(v.*v,1)', but apart from that it was perfect!!

kkuilla Over a year ago

@DeltaIV Would be interesting to see how much faster that is compared to your original solution.

Luis Mendo Over a year ago

@DeltaIV Thanks! No bsxfun needed here, though :-)

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