Pybind11 Vs Numpy For A Matrix Product

Edit 2 (18 June 2018.) I used the Matrix class proposed in http://pybind11.readthedocs.io/en/stable/advanced/pycpp/numpy.html with a Matrix product that I implemented as follows :

Solution 1:

I don't think the factor would have been drastically improved would I have used intel mkl for the c++ part of the product"

It absolutely would. Matrix-matrix product (GEMM) in MKL and similar libraries is one of the most highly tuned pieces of code ever written. It is in a completely different league than your ad-hoc loops.