MATLAB: Get the diagonal without calculating the explicit matrix

Question

Dear all:

I am trying to calculate a diagonal of a matrix (denoted A), which is formed by multiplying two large-dimensional matrices (denoted as B*C).

A naive way to do it is: first, calculating explicitly A = B*C, then get diagonal out from A. However, the first step takes forever to run due to the high-dimension of B and C. But the only thing I need is the diagonal of A.

Another straightforward way in my mind is: I could create a loop by calculating each element of the diagonal of A one by one. It will surely save a lot of time, but I am not sure if this is the most efficient way.

I am wondering if anyone knows a faster/smarter way to calculate it.

Thank you very much in advance!

Best,

Long

Answer 1

Assuming B*C results in a square matrix,

diagonal=sum(B.' .* C, 1);