[eigen] Matrix-matrix multiplication is slow compared to openBlas

[Oleg Shirokobrod <oleg.shirokobrod@xxxxxxxxx>]

Hi,

I have compared calculation of two expressions with Eigen and Eigen with openBlas backend (EIGEN_USE_BLAS)

1. MatrixXd AY = A*Y; where MatrixXd A[2048x2048], MatrixXd Y[2048x110]
2. Y.noalias() = A.adjoint() * X; where MatrixXd X[2048x110]

In Eq.1 I do not use noalias() because this is initialization of a declared matrix..

Calculation with openBlas is approximately 3 times faster.

I used
Intel(R) Core (TM) i5-3470 CPU @ 3.20 GHz; RAM 8 GB; 64 bit OS, x64 based processor;

Windows 10 Pro

MSVS 2015. O2, AVX options.

Eigen 3.3.3

Results:

1. openBlas = 0.028532 s; Eigen = 0.083807 s

2. openBlas = 0.028888 s; Eigen = 0.077522 s

Are these results expected or they should be better?

Thanks,

Oleg Shirokobrod