This package provides an interface for construction of Hodge and Bochner Laplacian matrices from the set of simplices.
HodgeLaplacians uses sparse matrices dok_matrix and csr_matrix from scipy.sparse module. Eigenvalues and eigenvectors are computed using Scipy ARPACK algorithm.
HodgeLaplacian class currently provides
Output:
- Boundary operator matrices
- Hodge and Bochner Laplacians
- Combinatorial Forman-Ricci curvature
- Eigenvectors and Eigenvalues of Laplacians
- Higher order heat kernels and diffusion
Input:
- List of simplices
- Symplex tree with filtration values (GUDHI format)
pip3 install hodgelaplaciansfrom hodgelaplacians import HodgeLaplacians
simplices = ((1,2,3), (2,3), (1,2,4), (6,3))
hl = HodgeLaplacians(simplices)
L1 = hl.getHodgeLaplacian(1)Full example output is available in the Jupyter notebook.
This repository also contains Dockerfile based on Ubuntu 18.04 which contains basic python dependencies as well as installation of Gudhi library.
To run this repository with Dockerfile (all C++ and Python dependencies pre-loaded) on Gitpod type
or simply press https://gitpod.io/#https://github.com/tsitsvero/hodgelaplacians.
After you have launched the workspace, you can simply launch the Jupyter Lab (please run "jupyter lab --ip 127.0.0.1" instead of just "jupyter lab") to play with examples and tutorials.
See video instructions embedded on a single page.
- Numpy
- Scipy
There are many tools available on Topological Data Analysis.
Here just a few introductory blog posts
There is a wiki page with a list of TDA packages.
- Random walks on simplicial complexes
- Tutorials on spectral theory of simplicial complexes
- Tutorials with point cloud examples