Multiply matrix columns into a vector in Eigen

Question

I would like to multiply the columns of matrix A to vector v and finally get the sum of each column. I use Eigen library and coded as follows:

for (int j = 0 ; j< A.cols(); j++)
    C.col(j).noalias() = V.cwiseProduct(A.col(j));
V2 = C.colwise().sum();

However, it is still slow. I also used the following products but these are even slower.

1. C = A * V.asDiagonal();
2. C = A.array().rowwise() * V.transpose().array();

Any idea?

Answer 1

Hm... what you're looking for is a plain standard vector-matrix product:

V2.noalias() = V.transpose() * A;

The .noalias() is optional, it's only here to save you one temporary.

If you really need the intermediate matrix C , then your two options should be equally fast as your hand-crafted for loop provided that you correct them to make them compute the same thing:

C = V.asDiagonal() * A;
C = A.array().colwise() * V.array();

And don't forget to enable compiler optimizations, eg -O3 -march=native .