cleanup BLAS detection

[soumith]

PyTorch and Caffe2 use the following libraries as preferred for BLAS/LAPACK capabilities:

• MKL - first preference in unified build system

• Eigen - 2nd preference in unified build system, but first preference if ATen is not being compiled

• PyTorch finds OpenBLAS, Accelerate, cblas if MKL is not found -- finding OpenBLAS is useful for PPC64

• I have to explore what Caffe2 does if Eigen is not found

There are however additional subtelities.
MKL and Eigen are not used JUST for BLAS/LAPACK, but also for additional functionality:

• MKL for FFT, VML in pytorch
• Eigen for implementing caffe2 operators

Additionally, we also use fortran-blas interface in pytorch, cblas interface in Caffe2 (if not Eigen), and eigen::MatrixMap interface if Eigen is found and CAFFE2_USE_EIGEN_FOR_BLAS is set.

Cleanup plan:

• separate what it means to detect MKL / Eigen from what it means to detect BLAS capabilities
  • Find MKL at a single entry point across PyTorch, Caffe2, and if it's found, set a USE_BLAS="mkl" with BLAS_INCLUDE and BLAS_LIBRARIES variables set to MKL paths. This is in addition to setting MKL_FOUND
  • [Should we] Find Eigen by default (unless USE_EIGEN=OFF (which we can set via setup.py) and use it for everything (building caffe2 operators etc.) except BLAS (i.e. only not set CAFFE2_USE_EIGEN_FOR_BLAS). If MKL was not found, use Eigen for BLAS as well cc: @Yangqing for guidance.
  • On PPC64 and OSX, should we prefer OpenBLAS and Accelerate respectively (instead of Eigen) for the BLAS capabilities? cc: @Yangqing

cc @malfet @seemethere @walterddr @jianyuh @nikitaved @pearu @mruberry @heitorschueroff

[Yangqing]

Thanks! Pasting replies from internal chat here:

• re "Eigen - 2nd preference, but first preference in caffe2 if ATen is not being compiled" - we can do MKL as first preference to be consistent, and use MKL if it is found.
• C2 actually needs Eigen for its vectorization work, although if we do not use Eigen for BLAS (aka, not -DBLAS=Eigen), then simple inclusion is all needed (header-only).
• on PPC and OSX - yes.

In general, it sounds reasonable to use the BLAS found by CMake first, and use Eigen as the last option if others are not found.

[orionr]

FYI, the fallback to Eigen from MKL roughly matches what is being done at https://github.com/pytorch/pytorch/blob/master/cmake/Dependencies.cmake#L73-L77 so makes sense.