chalc.chromatic¶

Module containing geometry routines to compute chromatic Delaunay filtrations.

Functions¶

`alpha`(…)	Compute the chromatic alpha filtration of a coloured point cloud.
`delaunay`(…)	Compute the chromatic Delaunay triangulation of a coloured point cloud in Euclidean space.
`delcech`(…)	Compute the chromatic Delaunay--Čech filtration of a coloured point cloud.
`delrips`(…)	Compute the chromatic Delaunay--Rips filtration of a coloured point cloud.

Module Contents¶

alpha( points: numpy.ndarray[tuple[M, N], numpy.dtype[numpy.float64]], colours: numpy.ndarray[tuple[M, Literal[1]], numpy.dtype[numpy.uint16]], max_num_threads: int = 0, ) → chalc.filtration.Filtration¶

alpha(points: numpy.ndarray[tuple[M, N], numpy.dtype[numpy.float64]], colours: list[int], max_num_threads: int = 0) → chalc.filtration.Filtration

Compute the chromatic alpha filtration of a coloured point cloud.

Parameters:

points – Numpy matrix whose columns are points in the point cloud.
colours – List or numpy array of integers describing the colours of the points.
max_num_threads – Hint for maximum number of parallel threads to use. If non-positive, the number of threads to use is automatically determined by the threading library (Intel OneAPI TBB). Note that this may be less than the number of available CPU cores depending on the number of points and the system load.

Returns:

The chromatic alpha filtration.

Raises:

ValueError – If any value in colours is >= MaxColoursChromatic or < 0, or if the length of colours does not match the number of points.
RuntimeError – If the dimension of the point cloud + the number of colours is too large for computations to run without overflowing.

Notes

chalc.chromatic.delcech() has the same 6-pack of persistent homology, and often has slightly better performance.

See also

delrips(), delcech()

delaunay( points: numpy.ndarray[tuple[M, N], numpy.dtype[numpy.float64]], colours: numpy.ndarray[tuple[M, Literal[1]], numpy.dtype[numpy.uint16]], parallel: bool = True, ) → chalc.filtration.Filtration¶

delaunay(points: numpy.ndarray[tuple[M, N], numpy.dtype[numpy.float64]], colours: list[int], parallel: bool = True) → chalc.filtration.Filtration

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

Parameters:

points – Numpy matrix whose columns are points in the point cloud.
colours – List or numpy array of integers describing the colours of the points.
parallel – If true, use parallel computation during the spatial sorting phase of the triangulation.

Raises:

ValueError – If any value in colours is >= MaxColoursChromatic or < 0, or if the length of colours does not match the number of points.
RuntimeError – If the dimension of the point cloud + the number of colours is too large for computations to run without overflowing.

Returns:

The Delaunay triangulation.

delcech( points: numpy.ndarray[tuple[M, N], numpy.dtype[numpy.float64]], colours: numpy.ndarray[tuple[M, Literal[1]], numpy.dtype[numpy.uint16]], max_num_threads: int = 0, ) → chalc.filtration.Filtration¶

delcech(points: numpy.ndarray[tuple[M, N], numpy.dtype[numpy.float64]], colours: list[int], max_num_threads: int = 0) → chalc.filtration.Filtration

Compute the chromatic Delaunay–Čech filtration of a coloured point cloud.

Parameters:

points – Numpy matrix whose columns are points in the point cloud.
colours – List or numpy array of integers describing the colours of the points.
max_num_threads – Hint for maximum number of parallel threads to use. If non-positive, the number of threads to use is automatically determined by the threading library (Intel OneAPI TBB). Note that this may be less than the number of available CPU cores depending on the number of points and the system load.

Returns:

The chromatic Delaunay–Čech filtration.

Raises:

ValueError – If any value in colours is >= MaxColoursChromatic or < 0, or if the length of colours does not match the number of points.
RuntimeError – If the dimension of the point cloud + the number of colours is too large for computations to run without overflowing.

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. Despite the different filtration values, it has the same persistent homology as the chromatic alpha filtration.

See also

alpha(), delrips()

delrips( points: numpy.ndarray[tuple[M, N], numpy.dtype[numpy.float64]], colours: numpy.ndarray[tuple[M, Literal[1]], numpy.dtype[numpy.uint16]], max_num_threads: int = 0, ) → chalc.filtration.Filtration¶

delrips(points: numpy.ndarray[tuple[M, N], numpy.dtype[numpy.float64]], colours: list[int], max_num_threads: int = 0) → chalc.filtration.Filtration

Compute the chromatic Delaunay–Rips filtration of a coloured point cloud.

Parameters:

points – Numpy matrix whose columns are points in the point cloud.
colours – List or numpy array of integers describing the colours of the points.
max_num_threads – Hint for maximum number of parallel threads to use. If non-positive, the number of threads to use is automatically determined by the threading library (Intel OneAPI TBB). Note that this may be less than the number of available CPU cores depending on the number of points and the system load.

Returns:

The chromatic Delaunay–Rips filtration.

Raises:

ValueError – If any value in colours is >= MaxColoursChromatic or < 0, or if the length of colours does not match the number of points.
RuntimeError – If the dimension of the point cloud + the number of colours is too large for computations to run without overflowing.

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.

See also

alpha(), delcech()