Currently, our implementation of the matmul ufunc is intelligent, and is able to pass appropriate transpose flags to BLAS to handle transposed contiguous arrays.

For A, B, and C as contiguous 2D arrays, the inner loop is intelligent enough to map np.matmul(B.T, A.T, out=C.T) to np.matmul(A, B, out=C):

However when the out argument is omitted, the ufunc machinery pre-allocates out with "C" memory ordering, which is not the "F" ordering that C.T has. Ideally, we'd be able to allocate our array such that we can make o_c_blasable or o_f_blasable true as necessary.

As part of @seberg's ufunc work, it would be great if ufuncs could be involved in the output allocation machinery.