Search system for lapack and blas first before looking into numpy

If you look for the system LAPACK first, you risk linking against an unoptimised version of this library, even if a better version is installed along with NumPy.

Wouldn't it be more sensible to do the inverse? Try NumPy's and, if it is not there, then fallback to the system's?

It was looking at numpy before but it did not really check if those libraries were available. So it was failing when it couldn't find mkl. Why should numpy have a better version anyway?

Well - NumPy, presumably, is linked against optimised versions of BLAS and LAPACK in a nice distro (ATLAS or OpenBLAS being the most common). Following it up makes good sense in my view. The problem before was there was no fallback whereas it should as you proposed. I'm just wondering about the order. IMO, we should follow NumPy's where possible.

There is another point: we shouldn't have two versions of the same library loaded into memory, if we can. That can lead to unexpected side effects (like differences in precision when comparing implementations available in this package against NumPy equivalents).