chalc.morphisms.sheaf

Utilities to compute sheaves of persistence modules from chromatic point clouds.

Classes

ChromaticSheaf	Sheaf of persistence modules arising from a coloured point cloud.
PersistenceModuleMorphism	Sparse map in the interval bases of domain and codomain.
SubfiltrationInclusion	Inclusion of a subfiltration with the same vertex set as its parent.

Module Contents

class ChromaticSheaf

Sheaf of persistence modules arising from a coloured point cloud.

property colours: ColourSet

Return all colours in the indexing colour poset.

classmethod from_chromatic_points(

points: numpy.ndarray[tuple[int, int], numpy.dtype[numpy.floating]],

colours: collections.abc.Sequence[int],

max_num_colours: int,

) → ChromaticSheaf

Construct a chromatic sheaf from a coloured point cloud.

property max_num_colours: int

Maximum number of colours to consider at a time.

This determines the height to which we restrict the colour poset.

morphism(source: ColourSet, target: ColourSet) → PersistenceModuleMorphism

Return the morphism of persistence modules between two sets of colours.

The first time a morphism is requested, it has to be constructed by composing morphisms across edges in the Hasse diagram. Intermediate compositions are cached, so future calls to this function are faster.

stalk(colours: ColourSet) → chalc.morphisms.AugmentedPersistenceModule

Return the stalk persistence module over a set of colours.

class PersistenceModuleMorphism

Sparse map in the interval bases of domain and codomain.

map sends module-local source birth indices to one-dimensional int64 arrays of module-local target birth indices, with coefficients in F2. Zero columns are omitted. At a given time, restrict to source and target intervals alive at that time. Nonzero coefficients preserve homological degree and, for source interval [b_s, d_s) and target interval [b_t, d_t), require b_t <= b_s < d_t <= d_s.

__eq__(other: object) → bool

Compare the modules and sparse support arrays by value.

__matmul__(other: PersistenceModuleMorphism) → PersistenceModuleMorphism

Return the composition of composable maps of persistence modules.

__post_init__() → None

Validate generator indices, homological degrees, and interval compatibility.

classmethod identity(module: chalc.morphisms.AugmentedPersistenceModule) → PersistenceModuleMorphism

Identity morphism on a given module.

classmethod zero(source: chalc.morphisms.AugmentedPersistenceModule, target: chalc.morphisms.AugmentedPersistenceModule) → PersistenceModuleMorphism

Return the zero morphism.

class SubfiltrationInclusion(subfiltration: chalc.filtration.Filtration, filtration: chalc.filtration.Filtration)

Bases: chalc.morphisms.FiltrationInclusion

Inclusion of a subfiltration with the same vertex set as its parent.

Both filtrations must use the same vertex labels 0, ..., num_vertices - 1. Filtration times on the subfiltration must agree with those of the parent filtration.

simplex_in_domain(column: tuple[list[int], int, float, list[int]]) → bool

Check if a simplex is in the domain of the inclusion map.

A simplex is identified by its column in the boundary matrix of the filtration. This column has the same format as the columns returned by chalc.filtration.Filtration.boundary_matrix().