petls-pytorch 1.0.0

GPU-native Persistent Topological Laplacians in PyTorch

PETLS-PyTorch

A PyTorch-native implementation of persistent topological Laplacians, based on the public PETLS API, PETLS documentation, and the algorithms described in the PETLS paper.

The goal of this project is to make PETLS-style computations easier to use in Python and PyTorch workflows, especially when downstream code already works with torch tensors or CUDA devices. The original C++/pybind11 PETLS implementation remains the reference for correctness.

Quick Start

import petls_torch

# Alpha complex from point cloud
alpha = petls_torch.Alpha(points=[[0, 0], [1, 0], [0.5, 1]], max_dim=2)
eigs = alpha.spectra(0, 0.0, 1.0)

# Rips complex from distance matrix
rips = petls_torch.Rips(distances=[[0, 1, 1], [1, 0, 1], [1, 1, 0]], max_dim=2)

# Directed flag complex from .flag file
dflag = petls_torch.dFlag("graph.flag", max_dim=3)

# Sheaf Laplacian
sst = petls_torch.sheaf_simplex_tree(st, extra_data, restriction)
psl = petls_torch.PersistentSheafLaplacian(sst)

Relationship to PETLS

petls_torch is an independent PyTorch-native implementation of the PETLS methods and public API behavior, with attribution to the original PETLS paper and project. Correctness tests compare against the original implementation using shared inputs and the default tolerances used in this repository.

This project is based on the public PETLS API, PETLS documentation, and the algorithms described in the PETLS paper. No source code from the original PETLS implementation is included in this repository.

API Coverage

Original PETLS API	PyTorch API	Status
Complex	Complex	Implemented
Alpha	Alpha	Implemented
Rips	Rips	Implemented
dFlag	dFlag	Implemented
sheaf_simplex_tree	sheaf_simplex_tree	Implemented
PersistentSheafLaplacian	PersistentSheafLaplacian	Implemented
Profile, timer	Profile, Timer	Implemented
summaries, plot_summary	summaries, plot_summary	Implemented
up_Algorithms enum	up_Algorithms enum	Implemented
eigvalsh_wrapper, sparse_wrapper, matrix_is_diagonal	Same	Implemented
flipped optimization	flipped + get_L_top_dim_flipped	Implemented
nonzero_spectra()	nonzero_spectra()	Implemented
store_L(), store_spectra(), store_spectra_summary()	Same	Implemented
time_to_csv()	time_to_csv()	Implemented

Benchmark Notes

The benchmark results below are included to give a sense of current runtime behavior on one local machine. They should be read as preliminary measurements, not as a comprehensive performance study.

The benchmark suite uses the same synthetic datasets, filtrations, and matrix sizes for both packages. The shared benchmark runner is parameterized with --package petls or --package petls_torch.

Hardware

• CPU: Intel i7-14700K
• GPU: NVIDIA RTX 4070 Ti 12GB
• PyTorch 2.x with CUDA 12.x

Quick Preset

Configuration: torus n=500 plus sphere n=300, max_dim=2, 8 filtrations per dataset.

Package	Device	Total Time	Mean Trial	Mean Build	Mean Eigs
petls	CPU	8.29 s	172.6 ms	15.2 ms	157.4 ms
petls_torch	CPU	1.82 s	37.9 ms	4.8 ms	33.1 ms
petls_torch	CUDA	1.85 s	38.5 ms	4.7 ms	33.8 ms

On this workload, the PyTorch implementation is about 4.5x faster than the reference PETLS run on the same CPU. The CUDA timing is similar to the CPU timing for this preset, which suggests that eigendecomposition and data sizes are still small enough that GPU overhead can offset part of the benefit.

Medium Workload

Configuration: torus n=500, max_dim=3, 16 filtrations.

Package	Device	Total Time	Mean Trial	Max Matrix	Status
petls	CPU	> 300 s	unavailable	unavailable	Reached benchmark timeout
petls_torch	CUDA	8.80 s	137.5 ms	5990 x 5990	Completed

For this larger dense-eigendecomposition workload, the PyTorch/CUDA path completed within the benchmark timeout. The PETLS CPU run reached the configured 300-second timeout in this test configuration.

Operation Breakdown

Quick preset timings:

petls (CPU)          : build=15.2 ms  eigs=157.4 ms
petls_torch (CPU)    : build=4.8 ms   eigs=33.1 ms
petls_torch (CUDA)   : build=4.7 ms   eigs=33.8 ms

In these measurements, most time is spent in eigendecomposition. The PyTorch implementation benefits from PyTorch's dense linear algebra backends on CPU and from CUDA support on larger matrix workloads.

Running Benchmarks

# Original PETLS
cd /path/to/workspace
python -m benchmark_shared --preset quick --package petls --algorithm eigvalsh

# PETLS-PyTorch on CUDA
python -m benchmark_shared --preset quick --package petls_torch --algorithm eigvalsh --device cuda

# PETLS-PyTorch on CPU
python -m benchmark_shared --preset quick --package petls_torch --algorithm eigvalsh --device cpu

# Custom single run
python -m benchmark_shared \
    --dataset torus --n_points 2000 --complex alpha --max_dim 3 \
    --package petls_torch --algorithm eigvalsh

Installation

pip install petls-pytorch

Dependencies:

• torch
• numpy
• scipy
• gudhi
• pyflagser
• tadasets for benchmarks

Test Suite

cd PETLS-PYTORCH
pytest tests/ -v

The test suite covers core functionality, Rips complexes, alpha complexes, directed flag complexes, sheaf support, eigenvalue utilities, and I/O helpers.

Citation

If you use petls_torch in research, please cite both this PyTorch implementation and the original PETLS paper.

PETLS-PyTorch

@software{marston2026petlstorch,
  title        = {PETLS-PyTorch: A PyTorch-native implementation of persistent topological Laplacians},
  author       = {Marston, Sumner K.},
  year         = {2026},
  publisher    = {Sylverity Research},
  url          = {https://github.com/Sylverity/petls-pytorch}
}

Original PETLS paper

@misc{jones2025petlspersistenttopologicallaplacian,
    title={PETLS: PErsistent Topological Laplacian Software},
    author={Benjamin Jones and Guo-Wei Wei},
    year={2025},
    eprint={2508.11560},
    archivePrefix={arXiv},
    primaryClass={math.AT},
    url={https://arxiv.org/abs/2508.11560},
}

This project is an independent PyTorch-native implementation based on the public PETLS API, PETLS documentation, and the PETLS paper. No source code from the original PETLS implementation is included in this repository.

• Original PETLS repository: https://github.com/bdjones13/PETLS
• PETLS documentation: https://www.benjones-math.com/software/PETLS/
• PETLS paper: https://arxiv.org/abs/2508.11560