Computations for Persistence Modules using GAP

This package is still in alpha development. Features are incomplete, and the API is subject to changes as deemed necessary. pmgap relies heavily on QPA for basic objects and computations involving quiver representations. That is, pmgap specializes the general quiver representations in QPA to commutative grid representations (2D persistence modules) and adds several new functions that are of interest for such representations.

Currently, the following main features are implemented.

1. Objects representing persistence modules over finite commutative grids and functions to work with them.

   • Creation of commutative grids and persistence modules
   • Reading and writing files that represent persistence modules
   • Enumeration of interval persistence modules

2. Computation of the interval-decomposable part of a persistence module, using the algorithm in H. Asashiba, M. Buchet, E. G. Escolar, K. Nakashima, and M. Yoshiwaki. "On Interval Decomposability of 2D Persistence Modules". arXiv:1812.05261. These computations can be performed within GAP, or using the convenience scripts:

   pmgap_interval_decomposable.sh
   

   and

   pmgap_batch_interval_decomposable.sh
   

   provided (installation of utility scripts needed).

3. Computation of the compressed multiplicity and interval-decomposable approximation over 2 x n grids, as introduced in H. Asashiba, E. G. Escolar, K. Nakashima, and M. Yoshiwaki. "On Approximation of 2D Persistence Modules by Interval-decomposables". arXiv:1911.01637 These computations can be performed within GAP, or using the convenience script:

   pmgap_interval_approximation.sh
   

   provided (installation of utility scripts needed).

4. Creation of persistence module over finite finite commutative grid from a bifiltered simplicial complex, using the program

   pmgap_cmplx2repn
   

   (compilation and installation of utility scripts needed).

1. Demo for the paper On Approximation of 2D Persistence Modules by Interval-decomposables (compressed multiplicity and interval-decomposable approximation):

   After completing Install Part 1: GAP package pmgap below, navigate to the demos folder inside a terminal and run

   gap pmgap_demo_interval_approximation.g
   

   to run the demo.

1. Install GAP and its packages, which already includes QPA.

2. Locate and choose a pkg directory where GAP searches for packages. See Section 9.2 "GAP Root Directories" of the GAP manual for more information.

   It can be any pkg/ subdirectory of one of the directories returned by running:

   gap> GAPInfo.RootPaths;
   

   in gap. A typical choice is to use the directory ~/.gap/pkg/.

3. Clone/download this repository as a subfolder in the pkg directory. As an example, all the contents of this repository will be inside ~/.gap/pkg/pmgap-master. Alternatively, a symbolic link can also be used.

4. Run tests by running

   >> gap tst/testall.g
   

   in the pmgap folder, inside the shell (outside of GAP).

5. Compile the documentation by running

   >> gap makedoc.g
   

   in the pmgap folder, inside the shell (outside of GAP).

6. Load the package with

   gap> LoadPackage("pmgap");
   

   inside of GAP. If installed correctly, this should work from any folder.

0. Ensure that the following libraries are installed.

   • Eigen
   • nlohmann/json
   • TCLAP
   • Catch2
   • autoconf
   • automake
   • libtool

   The above requirements may be available using your operating system's package manager. For example, using apt on Ubuntu, the requirements may be satisifed by installing

   • libeigen3-dev
   • nlohmann-json3-dev
   • libtclap-dev
   • catch
   • autoconf
   • automake
   • libtool

   respectively.

   This project used to depend on gyoza, but this dependency has been removed. This project now directly contains code from gyoza.

1. Navigate to this project's folder (as set in step 3 above).

2. Run the following commands, making sure that the previous command succeeds before proceeding to the next one.

   autoreconf --install
   

   ./configure
   

   make
   

   make check
   

   make install
   

1. ./configure complains that "Eigen header not found". [SOLUTION] Try adding Eigen to CPPFLAGS as follows:

   ./configure CPPFLAGS=-I/usr/include/eigen3
   

   or wherever you have installed Eigen.

2. Shared library not found when running c++ utilities. [SOLUTION] Try running

   sudo ldconfig
   

   See also https://stackoverflow.com/questions/480764/linux-error-while-loading-shared-libraries-cannot-open-shared-object-file-no-s

3. make install gives "Permission denied" error. [SOLUTION] Install as

   sudo make install
   

   or use --prefix option with ./configure in order to change the installation directory. See

   ./configure --help
   

   for more details.

Refer to the documentation in the folder doc/ (after compiling the documentation).

• Emerson G. Escolar (main developer)
• Shunsuke Tada