/wfs-and-reach-examples

Primary LanguageJupyter NotebookOtherNOASSERTION

Data and scripts for geometric feature sizes

Copyright (C) 2022 Parker Edwards

External requirements

  1. Julia. Written and tested with version 1.4.1.
  2. Jupyter notebook
  3. HomologyInferenceWithWeakFeatureSize.jl.
  4. (Optional) If you would like to re-compute bottleneck correspondence solutions, Bertini, parallel version recommended.

Setup

  1. Clone this repository
  2. In a terminal, boot Julia, go to package mode with ]. There are now two options
  3. A - If you are not worried about e.g. HomotopyContinuation.jl in your main Julia environment, you can just run add https://github.com/P-Edwards/HomologyInferenceWithWeakFeatureSize.jl
  4. B - If you are concerned about this. First run activate .. Then run add https://github.com/P-Edwards/HomologyInferenceWithWeakFeatureSize.jl.
  5. (Optional) If you would like to run the butterfly_lfs_sparse example, also add Distances, PersistenceDiagrams, ProgressBars, JLD, CSV, Measures, Plots, DataFrames
  6. B - With option B, a Project.toml file was created. Copy this into any directory with a notebook you would like to run yourself.

Description and Usage

This repository contains data and scripts accompanying the manuscript Computing geometric feature sizes for algebraic manifolds. The directory structure is sorted by example. To recompute Julia-based filtering steps with precomputed solutions, install the first three requirements and:

  1. Start jupyter notebook via terminal with jupyter notebook
  2. Navigate in the browser tab opened to a notebook file in one of the provided directories.

If you would like to check the algebraic computations, each directory for an example which uses Bertini includes a directory bertini_inputs. Each leaf folder contains a file labelled input, and you can run Bertini, say with 12 threads, via mpirun -np 12 bertini input. Follow directions in the notebooks to filter these new solutions.

Large data files

Some data files are too large to store on GitHub. They are instead available for download at https://notredame.box.com/v/feature-size-large-data. For each directory at that link, place the data in the "paper_data" folder for this repository's correspondingly named directory.

Computational warning

Algebraic computations for 3- and 4-bottlenecks for the examples in R^3, i.e. the quartic surface and torus-Clebsch intersection curve, are expensive. The 4-bottlenecks in particular can take a week or more to re-compute with Bertini.

License

This repository is distributed under GPLv3.