persty 1.0.0

Implementation of Minibox and Delauany edges algorithms.

persty - Minibox and Delaunay Edges Algorithms

This package provides an implementation of algorithms for finding the Minibox and Delaunay edges on a finite set of points in d-dimensional space with Chebyshev distance.

Installation

Install it with

>>> pip install persty

For the installation to complete succesfully you need

• setuptools and numpy installed in the current Python environment;
• a C compiler for the module to be built. On Windows download and install Visual Studio community.

To use the functionality of the persty.util submodule it is also necessary to install the gudhi Python package. If you installed conda this can be obtained by running the following command in a terminal window.

>>> conda install -c conda-forge gudhi

Basic usage

import numpy as np
import persty.minibox
import persty.delaunay

np.random.seed(0)
points = np.random.rand(20, 2).tolist()

minibox_edges = persty.minibox.edges(points)
delaunay_edges = persty.delaunay.edges(points)

Computing Persistent Homology

Minibox and Delaunay edges can be used to compute persistent homology in homological dimensions zero and one.

The pesty package provides a wrapper function to generate a gudhi.SimplexTree() object that can be used to compute persistence diagrams of Minibox and Alpha Clique filtrations.

The following code computes the zero and one dimensional persistence diagrams of 100 three-dimensional randomly sampled points in the unit cube.

import numpy as np
import persty.minibox
import persty.util
from scipy.spatial.distance import chebyshev

np.random.seed(0)
points = np.random.rand(100, 3).tolist()
minibox_edges = persty.minibox.edges(points)
simplex_tree = persty.util.make_gudhi_simplex_tree(points,
                                                   minibox_edges,
                                                   max_simplex_dim=2,
                                                   metric=chebyshev)
persistence_diagrams = simplex_tree.persistence(homology_coeff_field=2,
                                                persistence_dim_max=False)

Tests

To check that this package was installed correctly you can run the tests in the test/ directory of this repository.

• Download this repository on you computer by running the following command in a terminal window.

>>> git clone https://github.com/gbeltramo/persty.git

Note

On Windows you can obtain git by installing the chocolatey package manager, and running

>>> choco install git

• In a terminal window move to the persty directory you just downloaded.

• If you do not have the pytest package installed run

>>> pip install pytest

• Finally run

>>> pytest

or

>>> pytest -q

The second option decreases the verbosity of the output of this command.