chalc.sixpack.types¶

Implementation of a 6-pack of persistence diagrams.

Classes¶

`SimplexPairings`	Persistence diagram represented by paired and unpaired simplices.
`SixPack`	6-pack of persistence diagrams.

Module Contents¶

class SimplexPairings(paired: collections.abc.Collection[tuple[int, int]] = set(), unpaired: collections.abc.Collection[int] = set())¶

Bases: collections.abc.Collection

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Persistence diagram represented by paired and unpaired simplices.

__bool__() → bool¶: Return true if the diagram is non-empty.

__contains__(feature: object) → bool¶

Return true if a feature is in the diagram.

The feature to check should be either a pair of simplices (int, int) or a single simplex (int).

__eq__(other: object) → bool¶: Check if two diagrams have the same paired and unpaired simplices.

__hash__() → int¶: Return a hash of the persistence diagram.

__iter__() → collections.abc.Iterator[tuple[int, int] | int]¶: Iterate over all features in the diagram.

__len__() → int¶: Return the number of features in the diagram.

__str__() → str¶: Represent the persistence diagram as a string.

property paired: frozenset[tuple[int, int]]¶: Set of indices of paired simplices.

paired_as_matrix() → numpy.ndarray[tuple[int, Literal[2]], numpy.dtype[numpy.int64]]¶: Return a matrix representation of the finite persistence features in the diagram.

property unpaired: frozenset[int]¶: Set of indices of unpaired simplices.

class SixPack( kernel: SimplexPairings | None = None, cokernel: SimplexPairings | None = None, domain: SimplexPairings | None = None, codomain: SimplexPairings | None = None, image: SimplexPairings | None = None, relative: SimplexPairings | None = None, entrance_times: collections.abc.Sequence[float] = [], dimensions: collections.abc.Sequence[int] = [], )¶

Bases: collections.abc.Mapping

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6-pack of persistence diagrams.

__bool__() → bool¶: Return true if any diagram in the 6-pack is non-empty.

__contains__(key: object) → bool¶: Return true if a diagram is in the 6-pack.

__eq__(other: object) → bool¶: Check if two 6-packs of persistence diagrams are identical.

__getitem__(key: DiagramName) → SimplexPairings¶: Access a specific diagram in the 6-pack.

__hash__() → int¶: Return a hash of the 6-pack of persistence diagrams.

__iter__() → collections.abc.Iterator[DiagramName]¶: Iterate over all diagrams in the 6-pack.

__len__() → int¶: Return the number of diagrams in the 6-pack.

property dimensions: numpy.ndarray[tuple[int], numpy.dtype[numpy.int64]]¶: Dimensions of the simplices.

property entrance_times: numpy.ndarray[tuple[int], numpy.dtype[numpy.float64]]¶: Entrance times of the simplices.

classmethod from_file(file: h5py.Group) → SixPack¶

Load a 6-pack of persistence diagrams from a HDF5 file or group.

Parameters:: file – A h5py file or group.

get_matrix(diagram_name: DiagramName, dimension: int) → numpy.ndarray[tuple[int, Literal[2]], numpy.dtype[numpy.float64]]¶

get_matrix(diagram_name: DiagramName, dimension: list[int] | None = None) → list[numpy.ndarray[tuple[int, Literal[2]], numpy.dtype[numpy.float64]]]

Get a specific diagram as a matrix of birth and death times.

Parameters:

diagram_name – One of 'ker', 'cok', 'dom', 'cod', 'im', or 'rel'.
dimension – Dimension(s) of the diagram desired. If a list is provided then a list of matrices is returned, with the order of matrices respecting the order of entries of dim. If dimension is not provided then the returned matrix will contain persistent features from all homological dimensions from zero to max(self.dimensions).

Returns:

An \(m \times 2\) matrix whose rows are a pair of birth and death times, or a list of such matrices.

items() → collections.abc.ItemsView[DiagramName, SimplexPairings]¶: View of the diagrams in the 6-pack.

keys() → collections.abc.KeysView[DiagramName]¶: View of the names of the diagrams in the 6-pack.

classmethod names() → tuple[DiagramName, Ellipsis]¶: Return the names of the diagrams in the 6-pack.

num_features() → int¶: Count the total number of features across all diagrams in the 6-pack.

save(file: h5py.Group) → None¶

Save a 6-pack of persistence diagrams to a HDF5 file or group.

Parameters:: file – A h5py file or group.

threshold(tolerance: float) → SixPack¶: Discard all features with persistence <=tolerance.

values() → collections.abc.ValuesView[SimplexPairings]¶: View of the diagrams in the 6-pack.