The PerformantPathHomology uses MATLAB's symbolic toolbox and hence both MATLAB and the toolbox are required to run some of the scripts.
In order to run flagser please ensure that you have make, cmake and a C++14 compiler.
Then run the setup script which will download both of these libraries with git and build flagser:
./setup.sh
├── 📁 lib - External libraries, written by other authors
│ ├── 📁 flagser - flagser software, for computing homology of directed flag complex
│ └── 📁 pathhomology - Performant path homology computation
├── 📁 mat - MATALB .mat files storing the results of experiments + computations
├── 📁 src - Source MATLAB files for reproducing data + figures
│ ├── 📁 experiments - Data collection scripts for experiments section
│ ├── 📁 plot - Script for converting experimental data into plots
│ ├── 📁 util - Utility functions used in other scripts
│ └── 🗎 compute_Q.m - Script for computing q_{m,l} matrix in explicit bounds
├── 🗎 README.md - This file
└── 🗎 setup.sh - Setup script for importing and building libraries
Many of the plotting scripts, as well as compute_Q.m, begin with a switch on the MODE variable.
The two valid values are nreg for non-regular path homology and dflag for directed flag complex homology.
This variable should be set prior to running the script.
The experiments folder contains all of the scripts which run the experiments described in Appendix B.
The relation between the scripts and the experiment numbers in the paper is shown below.
Each of these experiments outputs its results as .mat file in the mat directory.
| Experiment Number | Script |
|---|---|
| 1 | lower_betti1_check.m |
| 2 | upper_betti1_check.m |
| 3 | lower_betti1_dflag_check.m |
| 4 | upper_betti1_dflag_check.m |
???_betti1_plot.m- These scripts take the data from the experiments and return best fits of the boundaries.???_bound_analysis.m- These scripts produce figures for the purpose of analysing the utility of the explicit bounds, developed in Appendix A.mean_plotter.m- This script draws the illustrative figures in Appendix B.normal_goodness_2.m- This script runs the normal distribution goodness-of-fit tests which are discussed in Appendix B.