How to compute only the diagonal of a matrix produ

Question

Is there a way in Octave to compute and store only the diagonal of a matrix product?

Basically like doing: vector = diag(A*B);

I don't care about any of the values of A*B except those on the diagonal. The matrix sizes are around 80k x 12 and 12 x 80k, so even if I didn't care about the speed/extra memory it simply wont fit in RAM.

Strange, since Octave is a package for huge data sets and diagonals are very important, so it should be possible.

Answer 1

The first element in the diagonal is the scalar product of the first row of A with the first column of B. The second element in the diagonal is the scalar product of the second row of A with the second column of B.

In other words:

vector = sum(A.*B',2);

Answer 2

This is how you could do it in MATLAB (probably similar to Octave syntax):

vector = sum(A.*B',2);

This will compute only the resulting diagonal of the operation A*B as a column vector vector.

Answer 3

actually I think it's the dot product of the first row of A with the first column of B... the second diagonal element is the dot product of the second row and the second column... etc