circle_bundles.CobirthResult

class circle_bundles.CobirthResult(k_removed, cutoff_weight, removed_edges)[source]

Bases: object

Cobirth event for an edge-driven filtration.

In the edge-driven filtration used here, edges are removed in descending weight order (heaviest first). At each stage we consider the induced subcomplex on the remaining edges (and any higher simplices whose edges are all still present).

A cobirth is the first stage k_removed at which the relevant class becomes a cocycle on the induced complex.

Parameters:

k_removed (int)
cutoff_weight (float)
removed_edges (List[Tuple[int, int]])

k_removed

Number of edges removed at the cobirth stage. 0 means the full complex.

Type:: int

cutoff_weight

Filtration cutoff weight at that stage.

+∞ when k_removed = 0 (no edges removed)
-∞ when k_removed is at least the number of edges (everything removed)

Type:: float

removed_edges

List of canonical edges that were removed up to and including the stage, in the order they were removed (heaviest first).

Type:: List[Tuple[int, int]]

See also

CodeathResult, summarize_edge_driven_persistence

__init__(k_removed, cutoff_weight, removed_edges)

Parameters:

k_removed (int)
cutoff_weight (float)
removed_edges (List[Tuple[int, int]])

Return type:

None

Methods

__init__(k_removed, cutoff_weight, removed_edges)

Attributes

`k_removed`
`cutoff_weight`
`removed_edges`