IdentityTensorMap optimization

[Chenqitrg]

Hi,

The current identity tensor map is dense. Would it be possible to define an identity tensor map struct such that the contraction can be optimized?

[lkdvos]

It is definitely possible to do this, and we have discussed something like this before in the context of fusing legs, but this has never really showed up as a real performance bottleneck in the applications. In principle this is not too hard to implement, but it becomes annoying to handle dispatch for the combination of many different tensor types. As a concrete example, consider just implementing *. Handling TensorMap, DiagonalTensorMap, IdentityTensorMap, BraidingTensor, and making sure all combinations go to the correct methods is a bit of a headache.

Simultaneously, often it is possible to completely avoid this operation, for example because our factorizations directly act on multi-leg tensors. Could you elaborate a bit on the concrete usecase you have in mind?

[Chenqitrg]

Thanks for your reply. The motivation for me is not numerically. Just curious that since there is already DiagonalTensorMap, and maybe having IdentityTensorMap is more symmetric and natural.

[Chenqitrg]

Another thing is to get rid of the edge case more naturally in MPS cache. Adding the identity to the boundary can get rid of many special cases.

[lkdvos]

I think the trade off there isn't great, the multiplication doesn't actually cost you all that much, while you would lose type stability in the cache because now not every environment has the same type. Additionally, our window MPS needs to have a non-identity there, which now again requires to handle special cases. While I am definitely sympathetic to adding this at some point, it often is quite a bit of code effort and maintenance for very low returns on investment