MuRiT

MuRiT (Multiparameter-Rips Transform) computes pathwise persistent homology for a multifiltered clique complex. It implements the pathwise Vietoris–Rips transformations of (Neumann et al., 2022), letting you probe multi-parameter persistence with the speed and memory footprint of Ripser.

What it does

• Multi-parameter input – describe a clique complex via a CSV listing 1-simplices with their generator antichains in \(\mathbb{R}^k\); incomparable generators per edge are supported and automatically pruned to a minimal antichain.
• Pathwise persistence – specify a coordinatewise non-decreasing path through \(\mathbb{R}^k\); MuRiT reduces the multifiltration to a one-dimensional auxiliary matrix and feeds it to Ripser, translating interval endpoints back to filtration vectors.
• Multi-path orchestration – pass a .paths file to process many paths in one run; outputs are written per path (*_pathNN.aux, *_pathNN.ripser).
• Ripser integration – --ripser uses ripser from PATH; --ripser <path> uses an explicit binary.
• Parallel execution – auxiliary matrix generation is fully multithreaded with deterministic output order.

Typical workflow

murit \
  --complex examples/figure8.csv \
  --path examples/figure8.paths \
  --ripser --dim 1

figure8.csv specifies the complex:

N,k
9,2
0,1,"[[0,0]]"
1,2,"[[0,0]]"
...

figure8.paths lists one JSON path literal per line:

[[0,0],[1,0],[1,1]]
[[0,0],[0,1],[1,1]]

MuRiT writes figure8_path01.ripser, figure8_path02.ripser, … with Ripser output translated back to filtration vectors.

When to use it

• Exploring multi-parameter filtrations by sweeping many paths before committing to heavier multi-persistence computations.
• Benchmarking time-varying or multi-modal datasets where several parameters interact.
• Automating feature-stability studies across many paths through the same complex.

Learn more and cite

• Source code & releases: github.com/tdalife/murit
• Preprint: Maximilian Neumann et al. “MuRiT: Efficient Computation of Pathwise Persistence Barcodes in Multi-Filtered Flag Complexes via Vietoris-Rips Transformations,” arXiv:2207.03394.