Multiparameter Persistence Landscapes

Python scripts for the computation of multiparameter persistence landscapes for 2 parameter persistence modules from the .rivet files computed by RIVET. The scripts make use of the pyrivet package (a Python API for interacting with RIVET).

• multiparameter_landscape.py Defines a multiparameter_landscape class initialised with a .rivet file corresponding to a 2 parameter persistence module.
• multiparameter_landscape_plotting.py Defines functions to plot landscapes and produce interactive plots of 2D point clouds and their associated multiparameter landscapes.
• one_parameter_classes.py Defines functions to plot landscapes and produce interactive plots of 2D point clouds and their associated multiparameter landscapes.
• one_parameter_plotting.py Defines functions to plot one parameter landscapes and produce interactive plots of 2D point clouds and their associated single parameter barcodes and landscapes.
• matching_distance.py, hera.py, barcode.py, rank.py, rivet.py scripts taken from pyrivet.

For those unfamiliar with persistent homology see these introductory slides which give an intuitive introduction. The slides also provide an introduction as to how one can use multiparameter persistence to filter out noise.

Example Usage

We include a jupyter notebook displaying the interactive plotting capability of the scripts in this repository.

The interactive plots in the notebook are built upon a visualization library Bokeh, and a number of software packages developed by the Topological Data Analysis community.

• One parameter persistence computations are run using Ripser founded by Ulrich Bauer
• Two parameter persistence computations are run using RIVET founded by Michael Lesnick and Matthew Wright
• This notebook was written by Oliver Vipond