[Numpy-discussion] Is there a better way to write a stacked matrix multiplication

[Charles R Harris]

On Thu, Oct 26, 2017 at 12:11 PM, Daniele Nicolodi <daniele at grinta.net>
wrote:

> Hello,
>
> is there a better way to write the dot product between a stack of
> matrices?  In my case I need to compute
>
> y = A.T @ inv(B) @ A
>
> with A a 3x1 matrix and B a 3x3 matrix, N times, with N in the few
> hundred thousands range.  I thus "vectorize" the thing using stack of
> matrices, so that A is a Nx3x1 matrix and B is Nx3x3 and I can write:
>
> y = np.matmul(np.transpose(A, (0, 2, 1)), np.matmul(inv(B), A))
>
> which I guess could be also written (in Python 3.6 and later):
>
> y = np.transpose(A, (0, 2, 1)) @ inv(B) @ A
>
> and I obtain a Nx1x1 y matrix which I can collapse to the vector I need
> with np.squeeze().
>
> However, the need for the second argument of np.transpose() seems odd to
> me, because all other functions handle transparently the matrix stacking.
>
> Am I missing something?  Is there a more natural matrix arrangement that
> I could use to obtain the same results more naturally?


There has been discussion of adding a operator for transposing the matrices
in a stack, but no resolution at this point. However, if you have a stack
of vectors (not matrices) you can turn then into transposed matrices like
`A[..., None, :]`, so `A[..., None, :] @ inv(B) @ A[..., None]`  and then
squeeze.

Another option is to use einsum.

Chuck
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