Emulate Blas Interface

[JaredCrean2]

We should emulate the Blas interface for the smallmatvec and smallmatmat functions. Currently we don't have the alpha and beta coefficients. This is a bit annoying for reverse mode, where we often want to update, not overwrite, the output vector.

Source code here.

[JaredCrean2]

I figured out why I didn't add the alpha and beta parameters initially. The Julia generic matrix-vector and matrix-matrix multiplication function doesn't accept them either. See the signature here. The hierarchy is:

• smallmatvec
  • call smallmatvec_kernel! if matrix is small enough
  • call A_mul_B otherwise
    • Call BLAS if possible, doing some some conversion trick for complex valued matrices
    • Call Julia generic algorithm otherwise (matrices that don't appear to be strided in a way that BLAS an accept, or element types that are not supported by BLAS)

We could create a replacement for A_mul_B that also accepts the alpha and beta parameters, but that would require re-implementing the logic inside A_mul_B that sorts out what kinds of matrices can be passed to BLAS or not.

In the interim, I added the alpha and beta parameters to the matrix-matrix multiplication kernels (because I need those for what I am currently working on), and exported them.