Getting Started#

Python Installation#

If you have a system compatible with any of the compiled binary wheels listed here, you can just install via pip install petls.

Otherwise, to install from source, there are the following dependencies:

  • CMake >= 3.16.3

  • Python >= 3.10

  • pytest

If you intend to use the Alpha complex from Gudhi, you will also need the following dependencies at the time of installation:

  • Boost >= 1.78.0

  • CGAL >= 4.11

There are three ways to install from source:

  1. If you do not have a system compatible with any of the pre-compiled binaries on PyPI, then pip install petls should still install from source.

  2. Clone the GitHub repository and from the project root run pip install .

  3. Clone the GitHub repository and from the project root run:

    mkdir build
cd build
cmake ..
make
sudo make install

C++ Installation#

Dependencies:

  • CMake >= 3.16.3

  • Eigen 3.4

Note

This project downloads and compiles Eigen 3.4 for internal usage (some features new to 3.4 are used), but to call PETLS functions you must pass in Eigen matrices, so you must have access to your own version of Eigen 3. You likely do not need Eigen 3.4 to use this library.

If you intend to use the Alpha complex from Gudhi, you will also need the following dependencies at the time of installation:

  • Boost >= 1.78.0

  • CGAL >= 4.11

There is one way to install from source. From the project root:

cd cpp
mkdir build
cd build
cmake ..
make
sudo make install

Usage#

Suppose you have the following filtered simplicial complex:

Dimension 0:

  • point a, added at filtration = 0

  • point b, added at filtration = 1

  • point c, added at filtration = 2

Dimension 1:

  • line (a,b), added at filtration = 3

  • line (b,c), added at filtration = 4

  • line (a,c), added at filtration = 5

Dimension 2:

  • triangle (a,b,c), added at filtration = 5

You can create the persistent Laplacians and compute the spectra:

Python

import numpy as np
import petls


# boundary matrices
d1 = np.array([[-1,0,-1],
             [1,-1,0],
             [0,1,1]])
d2 = np.array([[1],[1],[-1]])
boundaries = [d1,d2]

filtrations = [[0,1,2],   # dim 0 filtrations
               [3,4,5],    # dim 1 filtrations
               [5]]        # dim 2 filtrations

complex = petls.Complex(boundaries, fsiltrations)
print(complex.spectra())

C++

#include "petls.hpp"
#include <Eigen/Dense>
#include <vector>
#include <iostream>

SparseMatrixInt d1(3,3);
SparseMatrixInt d2(3,1);
d1.coeffRef(0,0) = -1;
d1.coeffRef(0,1) = 0;
d1.coeffRef(0,2) = -1;
d1.coeffRef(1,0) = 1;
d1.coeffRef(1,1) = -1;
d1.coeffRef(1,2) = 0;
d1.coeffRef(2,0) = 0;
d1.coeffRef(2,1) = 1;
d1.coeffRef(2,2) = 1;

d2.coeffRef(0,0) = 1;
d2.coeffRef(1,0) = 1;
d2.coeffRef(2,0) = -1;

std::vector<filtration_type> c0_filtrations = {0.0, 1.0, 2.0};
std::vector<filtration_type> c1_filtrations = {3.0, 4.0, 5.0};
std::vector<filtration_type> c2_filtrations = {5.0};

std::vector<SparseMatrixInt> boundaries;
boundaries.push_back(d1);
boundaries.push_back(d2);

std::vector<std::vector<filtration_type>> filtrations;
filtrations.push_back(c0_filtrations);
filtrations.push_back(c1_filtrations);
filtrations.push_back(c2_filtrations);

petls::Complex complex(boundaries,filtrations);
std::cout << complex.spectra() << std::endl;