FG_Multi: library for computing a discrete gradient on multivariate data
FG_Multi is a library to compute a discrete gradient on multiparameter filtrations, i.e., filtrations defined by a vector-valued function. It can compute a Forman gradient on a simplicial complex (up to 3 dimensions) with multiple scalar values defined at its vertices. This library uses an incidence-based data structure for compactly encoding the relations among vertices, edges, and triangles. The computation of the Forman gradient relies on homotopic expansion.
The source code and additional information can be found on
(1) A Discrete Morse-Based Approach to Multivariate Data Analysis by Federico Iuricich, Sara Scaramuccia, Claudia Landi, and Leila De Floriani in SIGGRAPH ASIA 2016 Symposium on Visualization, pages 1-8, 2016.
(2) Computing multiparameter persistent homology through a discrete Morse-based approach by Sara Scaramuccia, Federico Iuricich, Leila De Floriani, and Claudia Landi in Computational Geometry, 89, 2020.