Get positive/negative simplex of a persistence pair #110
Description
Hello,
currently, one can get a pair of filtration values, or a cocyle, but sometimes it is convenient to have access to something kind of intermediate: the 2 simplices that create and kill the topological feature, and whose filtration values are precisely the bounds of the interval. Since you already output diagrams dimension by dimension, the simplices could be represented by a numpy array of vertex indices. The main issue is how to represent infinite intervals, either with a fake simplex (make all its vertices -1?), or output them in a separate array of different shape.
As another variant, sometimes for flag complexes we do not quite want the simplex, but only the edge of maximal length of the simplex, i.e. we want to know not just the filtration values at the extremities of the interval, but also where they come from (i.e. which edge). Dimension 0 is a bit inconvenient since vertices do not have a corresponding edge... See http://gudhi.gforge.inria.fr/python/latest/simplex_tree_ref.html#gudhi.SimplexTree.flag_persistence_generators for the interface used by another library.
This is related to #86, but I don't think I am asking for the same thing exactly.