Setting Up

First, download GUDHI, one of the .tar.gzs on this page with python in its name, save it in the ./gudhi folder, and exit setup.sh to make sure it knows it's there.

Make sure you follow the steps here which are annoying but necessary (unless the GUDHI people updated the library).

Make sure that Boost, CGAL, Eigen, and optionally also Intel TBB are installed on your system. On OS X, I was able to do this all with Homebrew:

$ brew install boost cgal eigen tbb

Also, you need to be running Python>=3.6.

Then,

$ . setup.sh

To test and see if everything worked, try

$ python3 $GUDHI_PATH/example/alpha_complex_from_points_example.py

(note that GUDHI_PATH was set by setup.sh).

Usage

TBD, but the place to look is scripts/alpha_complex_persistent_homology.py.

References

• Math background and survey of software packages: https://arxiv.org/pdf/1506.08903.pdf

• helpful: http://www.dyinglovegrape.com/math/topology_data_1.php < follows http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01249-X/S0273-0979-09-01249-X.pdf

• a textbook: http://www.math.cornell.edu/~hatcher/AT/AT.pdf

• "accessible" textbook, Munkres: http://webmath2.unito.it/paginepersonali/sergio.console/Dispense/Elements%20of%20Algebraic%20Topology%20-%20James%20R.%20Munkres.pdf

• interesting overview of Rips, and feasible approximation: https://arxiv.org/pdf/1203.6786.pdf < by http://donsheehy.net/ < visualized? http://donsheehy.net/cavanna15visualizing.html < nerve of cones: http://donsheehy.net/research/cavanna15geometric.pdf

• net-trees: < original http://sarielhp.org/p/04/lipschitz/lipschitz.pdf < slides http://sarielhp.org/p/04/lipschitz/lips_slides.pdf < sheehy explains http://donsheehy.net/research/jahanseir15cover.pdf