reusable einsum expressions

[jcmgray]

Essentially, I'm using opt_einsum for some tensor network calculations, and a significant proportion of time is spent in contract_path, even for relatively large sized tensors and pre-calculated paths.

Specifically, a huge number of contractions with the same indices and shapes are performed over and over again and I already cache these using the path from contract_path. However, it seems even with the path supplied, a large amount of time is spent parsing the input, in can_blas, parse_einsum_input etc.

My suggestion would be something like:

shapes = [(2, 3), (3, 4), (4, 5)]
my_expr = einsum_expression("ab,bc,cd->ad", *shapes)

for _ in many_repeats:
    ...
    x, y, z = (rand(s) for s in shapes)
    out = my_expr(x, y, z)
    ...

I.e. it would only accept arrays of the same dimensions (and probably an out argument) and would otherwise skip all parsing, using a contraction_list stored within the function.

Anyway, I'm about to knock something up to test for myself, but thought it might be of more general interest.

[dgasmith]

This would be great to have in the framework. I think perhaps the best approach is to break this loop into a separate function that can be called without a lot of checking.