PersistenceDiagram class

class PersistenceDiagram
__init__(dimension)

Initializes : an empty( no points ) PersistenceDiagram object and sets the dimension attribute( must be integer ) e.g.:

dia = PersistenceDiagram( 1 )
__init__(dimension, point_seq)

Initializes PersistenceDiagram of specified dimension from the given sequence seq of tuples, e.g.:

dia = PersistenceDiagram( 1, (1,2) )

The tuples must have at least 2 elements (birth, death). If there is a third element, it is stored as extra data associated to a point.

append(p)

Adds point p to the persistence diagram.

dimension

Dimension of the persistence diagram. Must be an integer. Must be set at initialization.

__iter__()

Iterator over the points in the persistence diagram, e.g.:

for p in dia: print p
__len__()
Returns:The number of points in the diagram.

Utility functions for persistence diagrams

init_diagrams(persistence, filtration[, eval = lambda s: s.data[, data = lambda i: None]])

Initializes a collection of PersistenceDiagram instances from persistence and filtration. Optional eval can determine how to extract birth and death values from a simplex. For example, if filtration was filled using fill_alpha_complex(), the data contains a pair (value, critical). We can extract the value from the tuple:

init_diagrams(persistence, filtration, lambda s: s.data[0])

Optional data argument can return arbitrary data to associate with each point, given an node of persistence.

bottleneck_distance(dia1, dia2)

Calculates the bottleneck distance between the two persistence diagrams.

wasserstein_distance(dia1, dia2, p)

Calculates the p-th Wasserstein distance between the two persistence diagrams.