TDA4j is a library for persistent homology and related techniques of computational and applied topology, for Scala and the JVM, with interfaces for MATLAB, Java and the command line. It continues the libraries of the Computational Topology workgroup at Stanford (JavaPlex and its predecessors).
import scala.language.experimental.modularity
import org.appliedtopology.tda4j.*
val points = Array.tabulate(40)(i => Array(math.cos(i * 0.16), math.sin(i * 0.16)))
val diagram = Persistence(points) // the Vietoris-Rips diagram in degrees 0, 1 and 2
diagram.dim(1).longest // the loop, with a cycle that goes around it
What it offers
- Many complexes: Vietoris-Rips, Čech, alpha, sparse Rips, witness, distance-to-measure, Dowker and cubical complexes, and simplicial sets for spaces you build yourself, down to classifying spaces of finite groups.
- Any coefficients: every engine works over any prime field or the reals. The default is the field with 17 elements, where signs and odd torsion are visible.
- Representatives: every bar comes with a chain that witnesses it: a cycle, which shows where a feature is, or on request a cocycle, what circular and toroidal coordinates are built from.
- Several engines for the same computation, from a reference implementation to Ripser's algorithm and specialized engines for images and alpha complexes, checked against each other.
- Long computations that can be advanced in steps and read at any scale while they run.
Where to start
- The user guide, starting with the quickstart.
- The tutorials: one question and one data set each, worked through to the answer.
- The developer's guide, for how the library is built.
- The API documentation: org.appliedtopology.tda4j.
For persistent homology itself, we recommend the book Topological Data Analysis with Applications by Gunnar Carlsson and Mikael Vejdemo-Johansson, and the survey Topology and Data by Gunnar Carlsson.
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