chromatic#
Overview#
Module containing geometry routines to compute chromatic Delaunay filtrations.
 MaxColoursChromatic#
Maximum number of colours that can be handled by the methods in this module.
 Type:
Functions#
Computes the chromatic alpha filtration of a coloured point cloud. 

Returns the chromatic Delaunay triangulation of a coloured point cloud in Euclidean space. 

Returns the chromatic DelaunayČech filtration of a coloured point cloud. 

Computes the chromatic DelaunayRips filtration of a coloured point cloud. 
Details#
 alpha(x, colours)#
Computes the chromatic alpha filtration of a coloured point cloud.
 Parameters:
 Returns:
The chromatic alpha filtration and a boolean flag to indicate if numerical issues were encountered. In case of numerical issues, a warning is also raised.
 Raises:
ValueError – If any value in
colours
is >=MaxColoursChromatic
or < 0, or if the length ofcolours
does not match the number of points. Return type:
Notes
This function is included for pedantic reasons. For most purposes you should instead consider using
chalc.chromatic.delcech()
, which is faster to compute, more numerically stable, and has the same persistent homology.
 delaunay(x, colours)#
Returns the chromatic Delaunay triangulation of a coloured point cloud in Euclidean space.
 Parameters:
 Raises:
ValueError – If any value in
colours
is >=MaxColoursChromatic
or < 0, or if the length ofcolours
does not match the number of points. Returns:
The Delaunay triangulation.
 Return type:
 delcech(x, colours)#
Returns the chromatic Delaunay–Čech filtration of a coloured point cloud.
 Parameters:
 Returns:
The chromatic Delaunay–Čech filtration and a boolean flag to indicate if numerical issues were encountered. In case of numerical issues, a warning is also raised.
 Raises:
ValueError – If any value in
colours
is >=MaxColoursChromatic
or < 0, or if the length ofcolours
does not match the number of points. Return type:
Notes
The chromatic Delaunay–Čech filtration of the point cloud has the same set of simplices as the chromatic alpha filtration, but with Čech filtration times.
 delrips(x, colours)#
Computes the chromatic Delaunay–Rips filtration of a coloured point cloud.
 Parameters:
 Returns:
The chromatic Delaunay–Rips filtration and a boolean flag to indicate if numerical issues were encountered. In case of numerical issues, a warning is also raised.
 Raises:
ValueError – If any value in
colours
is >=MaxColoursChromatic
or < 0, or if the length ofcolours
does not match the number of points. Return type:
Notes
The chromatic Delaunay–Rips filtration of the point cloud has the same set of simplices as the chromatic alpha filtration, but with Vietoris–Rips filtration times. The convention used is that the filtration time of a simplex is half the maximum edge length in that simplex. With this convention, the chromatic Delaunay–Rips filtration and chromatic alpha filtration have the same persistence diagrams in degree zero.