Persistent Homology¶
See the Gudhi documentation for more information on persistent homology and its applications [gudhi] .
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orbithunter.persistent_homology.orbit_complex(orbit_instance, **kwargs)[source]¶ Wrapper for Gudhi persistent homology package’s PeriodicCubicalComplex
- Parameters
- orbit_instanceOrbit
The orbit for which to compute the complex.
- kwargs :
periodic_dimensions : tuple Contains bools which flag which axes of the orbit’s field are assumed to be periodic for the persistence calculations. Defaults to Orbit defaults.
- Returns
- cubical_complexPeriodicCubicalComplex
-
orbithunter.persistent_homology.orbit_persistence(orbit_instance, **kwargs)[source]¶ Evaluate the persistence of an orbit complex; returns betti numbers and persistence intervals.
- Parameters
- orbit_instanceOrbit
- Returns
- ndarray or list :
NumPy or Gudhi format. Numpy format returns an array of shape (N, 3). Gudhi format is a list whose elements are of the form (int, (float, float)).
- kwargs :
min_persistence : float Minimum persistence interval size for returned values. periodic_dimensions : tuple of bool Flags the dimensions of Orbit.state which are periodic.
Notes
Mainly a convenience function because of how Gudhi structures its output.
-
orbithunter.persistent_homology.persistence_plot(orbit_instance, gudhi_method='diagram', **kwargs)[source]¶ - Parameters
- orbit_instanceOrbit
Iterable of length N that contains elements of length 2 (i.e. N x 2 array) containing the persistence intervals (birth, death)
- gudhi_methodstr
Plotting gudhi_method. Takes one of the following values: ‘diagram’, ‘barcode’, ‘density’.
- kwargs :
kwargs related to gudhi plotting functions. See Gudhi docs for details.
-
orbithunter.persistent_homology.persistence_distance(orbit_or_array, second_orbit_or_array, gudhi_metric='bottleneck', **kwargs)[source]¶ Compute the distance between two Orbits’ persistence diagrams.
- Parameters
- orbit1Orbit
Orbit whose persistence creates the first diagram
- orbit2Orbit
Orbit whose persistence creates the second diagram
- gudhi_metricstr
The persistence diagram distance metric to use. Takes values ‘bottleneck’ and ‘wasserstein’.
- kwargs :
Keyword arguments for orbit persistence and orbit complex computations.