Welcome to PersistentLaplacians’s documentation!

Note

This project has not been publicly released yet, so this is preliminary documentation. Check out my website for more information For developing it, I have restricted some of the configurations for usage and installation to my environment. If you want a minor change to setup (e.g. build wheels for Python 3.11), just ask!

Overview

Persistent Laplacians are a persistent version of combinatorial Laplacians, which generalize the well-studied graph Laplacian to simplicial and other complexes, such as path complexes. As with graph Laplacians, we study persistent Laplacians largely through their eigenvalues.

This is a C++ library with Python bindings that computes Persistent Laplacians extremely quickly (orders of magnitude faster than other tools) for a variety of simplicial and non-simplicial complexes. Most importantly, it will compute the persistent Laplacian given any collection of (filtered) boundary matrices.

This project is intended to be user-friendly for two audiences:

  1. Researchers in Topological Data Analysis (TDA), who develop and analyze both theoretical and computational tools.

  2. Researchers with data that could be analyzed with topology. If you use Persistent Homology, it is likely that Persistent Laplacians will be of interest to you!

Source code is available on GitHub.

This project is written and maintained by Ben Jones at Michigan State University.

Acknowledgements:

This project is partially supported by grants xxx.

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