问题
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.
回答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);
回答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.
回答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
来源：https://stackoverflow.com/questions/2301046/how-to-compute-only-the-diagonal-of-a-matrix-product-in-octave