does eigen have self transpose multiply optimization like H.transpose()*H

Question

I have browsed the tutorial of eigen at https://eigen.tuxfamily.org/dox-devel/group__TutorialMatrixArithmetic.html

it said \"Note: for BLAS users worried about per

Answer 1

You are right, you need to tell Eigen that the result is symmetric this way:

Eigen::MatrixXd H = Eigen::MatrixXd::Random(m,n);
Eigen::MatrixXd Z = Eigen::MatrixXd::Zero(n,n);
Z.template selfadjointView<Eigen::Lower>().rankUpdate(H.transpose());

The last line computes Z += H * H^T within the lower triangular part. The upper part is left unchanged. You want a full matrix, then copy the lower part to the upper one:

Z.template triangularView<Eigen::Upper>() = Z.transpose();

This rankUpdate routine is fully vectorized and comparable to the BLAS equivalent. For small matrices, better perform the full product.

See also the respective doc.