Will giotto-tda support extended persistence?

[ulupo]

Extended persistence (nicely explained by Tim Hosgood in this paper: https://arxiv.org/abs/1609.00920) allows to obtain persistence diagrams in which not only do we not have infinite deaths, but we also replace these infinities with finite values yielding more information. A nice example appears in the PersLay paper: https://arxiv.org/abs/1904.09378.

Personally, I think this would be a great addition. There are two main obstacles:

1. Backends: ripser does not yet support extended persistence -- though GUDHI does.
2. All diagram processing components in giotto-tda heavily rely on the assumption that there be no entries below the diagonal.

1 means that, until ripser (or rather, the version of the backend code contained in ripser.py) support extended persistence, we might have to use the GUDHI backend even for Vietoris-Rips when we want extended persistence. This can be done, in principle. 2 is a bit more thorny and will involve more difficult decisions and refactoring.