Allow repeated and unmatched output indices?

[davidweichiang]

Although the original einsum doesn't allow it, it would be convenient if:

• einsum('i->ii', torch.tensor([1., 2.])) returns torch.tensor([[1., 0.], [0., 2.]]) (that is, it's like torch.diag_embed)
• einsum('->i', torch.tensor(1.) returns torch.tensor([1.]) (that is, it's like torch.unsqueeze)

I can imagine that the second proposal is more controversial than the first one.

[bdusell]

I think the first one is a reasonable extension of the syntax. Are there any other possible interpretations of the i->ii syntax, like being equivalent to input[:, None] * input[None, :]? What would be the result of einsum('ijk->iik', x)?

I think the second one can be worked around easily with an unsqueeze on the return value of einsum. I think most people would consider it an error to use a variable on the RHS that isn't declared on the LHS, but I suppose it's a matter of taste.

[davidweichiang]

Hm, I suppose an argument against i->ii is that it's not the inverse of ii->i (trace).