[Numpy-discussion] Optimisation of matrix multiplication

[Andrew Nelson]

On 30 January 2018 at 17:22, Andrew Nelson <andyfaff at gmail.com> wrote:

> Hi all,
> I have a matrix multiplication that I'd like to optimize.
>
> I have a matrix `a` (dtype=complex) with shape (N, M, 2, 2). I'd like to
> do the following multiplication:
>
> a[:, 0] @ a[:, 1] @ ... @ a[:, M-1]
>
> where the first dimension, N, is element wise (and hopefully vectorisable)
> and M>=2. So for each row do M-1 matrix multiplications of 2x2 matrices.
> The output should have shape (N, 2, 2).
>
> What would be the best way of going about this?
>

I should add that at the moment I have 4 (N, M) arrays and am doing the
matrix multiplication in a for loop over `range(0, M)`, in an unrolled
fashion for each of the 4 elements.
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