coperto 0.1.7

Filtration of quotient Vietoris Rips fast and exact.

Coperto

Fast and exact persistent homology via quotient Vietoris-Rips filtrations.

Installation

pip install coperto

Usage

import numpy as np
import coperto
# Generate a simple point cloud (e.g. 100 points on a noisy circle)
theta = np.linspace(0, 2 * np.pi, 100)
data = np.column_stack([np.cos(theta), np.sin(theta)]) + 0.05 * np.random.randn(100, 2)
# Compute persistent homology up to dimension 1 (H0 = components, H1 = loops)
barcodes = coperto.persistent_homology(data, max_dim=1)
# Each entry is (dimension, birth, death)
for dim, birth, death in barcodes:
    print(f"H{dim}: [{birth:.3f}, {death:.3f})")

Parameters for persistent_homology:

Parameter	Default	Description
data	—	NumPy array of shape (n_points, n_dims)
max_dim	1	Maximum homological dimension to compute
greedy	True	Use greedy linkage (faster); set False for exact tie-breaking
use_128bit	False	Use 128-bit arithmetic in the persistence computation
Returns: list of (dim, birth, death) tuples.

Note: use_128bit=True is only available on Linux and macOS. Windows does not support 128-bit integers (__int128). Passing use_128bit=True on Windows will raise a RuntimeError.

Reproducing the paper benchmarks

Clone the repository and run the benchmark script from the examples directory:

git clone https://github.com/antonio-leitao/coperto.git
cd coperto
uv run python examples/main.py

Results are saved to examples/results/main_benchmark.csv. The benchmark compares Coperto against Ripser on ten datasets: C. elegans, Vicsek, Klein bottle (400 and 900 points), Dragon (1k and 2k), HIV1, O(3) (1024 and 2048), and PBMC3k.