Delaunay-Čech filtrations

This package provides functions for computing the smallest enclosing ball radius (miniball radius) of sets of three points in two and three dimensions and four points in three dimensions.

These are used to produce Delaunay-Čech filtrations, which can be used to compute Čech persistence diagrams of points in two and three dimensions.

Wrappers are provided for computing Čech persistence diagrams with gudhi for points in two and three dimensional space.

Installation

The setuptools, numpy, scipy, and gudhi Python packages are prerequisites for using this package.

The last one can be installed with conda running

>>> conda install -c conda-forge gudhi

You'll also need pybind11, cmake and a C++ compiler in order to install this package. It is recommended to install both pybind11 and cmake via conda.

>>> conda install -c anaconda cmake
>>> conda install -c conda-forge pybind11

Finally run the following command to build and install this Python package

>>> pip install delcechfiltr

If the command above fails to build this package, tehn you might want to clone this repository to a directory delcechfiltr/ on your computer and run

>>> cd /<path>/<to>/<cloned>/<repo>/delcechfiltr/
>>> python setup.py install

which outputs more information on the errors causing the build to fail.

Windows. After installing conda, run the above commands within an Anaconda prompt. For the C++ compiler install Visual Studio community.

Basic usage

import numpy as np
import delcechfiltr.dgms

n, d = 20, 3
np.random.seed(0)
pts = np.random.rand(n, d)

dgm_H0_cech1, dgm_H1_cech1                        = delcechfiltr.dgms.cech(pts, persistence_dim_max=False)
dgm_H0_cech2, dgm_H1_cech2, dgm_H2_cech2          = delcechfiltr.dgms.cech(pts, persistence_dim_max=True)
dgm_H0_delcech1, dgm_H1_delcech1                  = delcechfiltr.dgms.delcech_3D(pts, persistence_dim_max=False)
dgm_H0_delcech2, dgm_H1_delcech2, dgm_H2_delcech2 = delcechfiltr.dgms.delcech_3D(pts, persistence_dim_max=True)