Fix using BLAS for all compatible cases of memory layout #1419
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Lost in the recent workspace refactor.
We compute A B -> C with matrices A, B, C With the blas (cblas) interface it supports matrices that adhere to certain criteria. They should be contiguous on one dimension (stride=1). We glance a little at how numpy does this to try to catch all cases. In short, we accept A, B contiguous on either axis (row or column major). We use the case where C is (weakly) row major, but if it is column major we transpose A, B, C => A^t, B^t, C^t so that we are back to the C row major case. (Weakly = contiguous with stride=1 on that inner dimension, but stride for the other dimension can be larger; to differentiate from strictly whole array contiguous.) Minor change to the gemv function, no functional change, only updating due to the refactoring of blas layout functions. Fixes #1278
If we have a matrix of dimension say 5 x 5, BLAS requires the leading stride to be >= 5. Smaller cases are possible for read-only array views in ndarray(broadcasting and custom strides). In this case we mark the array as not BLAS compatible
Using cblas we can simplify this further to a more satisfying translation (from ndarray to BLAS), much simpler logic. Avoids creating and handling an extra layer of array views.
Add a crate with a mock blas implementation, so that we can assert that cblas_sgemm etc are called (depending on memory layout).
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With the blas (cblas) interface it supports matrices that adhere to certain
criteria. They should be contiguous on one dimension (stride=1).
We glance a little at how numpy does this to try to catch all cases.
Compute A B -> C:
We require for BLAS compatibility that: A, B, C are
"weakly" contiguous (stride=1) in their fastest dimension, but it can be
either first or second axis (either rowmajor/"c" or colmajor/"f").
The "normal case" is CblasRowMajor for cblas. Select CblasRowMajor /
CblasColMajor to fit C's memory order.
Apply transpose to A, B as needed if they differ from row major. If C
is CblasColMajor then transpose both A, B (again!)
(Weakly = contiguous with stride=1 on that fastest axis, but stride for the
other axis can be arbitrary large; to differentiate from strictly whole
array contiguous.)
A first commit simplified and corrected the logic, while still using
ndarray's reversed axes. But a further commit simplified it even further, to
a satisfying little function in
mat_mul_implas the final result.I have kept both states (both commits) because I think the first version is
a useful guide if we would ever go to use plain BLAS instead of CBLAS(?).
Fixes #1278