hyperpopy 0.1.0

Poisson Hyperplane Model Package

hyperpopy: Poisson Hyperplane Model Package

A Python package for working with Poisson hyperplane models, providing tools for analytical calculations, generation, visualization, and Monte Carlo simulation of Poisson hyperplane processes.

Features

• Analytical Calculations: Compute conditional probability functions for color in Poisson hyperplane models
• Generation & Visualization: Generate and plot realizations of the Poisson hyperplane process
• Monte Carlo Simulation: Estimate connectivity distributions and color probabilities
• Probability Landscapes: Visualize conditional probability functions and convergence analysis
• Multi-dimensional Support: Works in 1D, 2D, and 3D spaces

Installation

pip install popy

Quick Start

import popy
import numpy as np

# Calculate the arrival rate of a Poisson hyperplane process
rate_2d = popy.rate(2, 1.0)  # 2D, radius 1.0
print(f"2D Poisson rate: {rate_2d}")

# Generate a 2D visualization of the Poisson hyperplane process
fig = popy.plot_hyperplanes_color_2d(
    radius=10,
    grid_resolution=100,
    colorcutoffs=np.array([0.5]),
    cmap_list=popy.frozen_lake_colors
)

# Calculate color distribution for given points
points = np.array([[0, 0], [1, 0], [0, 1]])
colors = (0, 1, 0)  # Known colors for first two points
color_dist = (0.5, 0.5)  # Equal probability for each color

prob_dist = popy.color_distribution(points, colors, color_dist)
print(f"Color probabilities: {prob_dist}")

Key Functions

Analytical Utilities

• rate(dimension, radius): Calculate Poisson hyperplane arrival rate
• color_distribution(points, colors, color_dist): Compute conditional color probabilities
• hitrate_1d/2d/3d(points): Calculate hit rates for convex hulls
• slash_rates(points): Return rates of hyperplane partitions

Generation & Visualization

• sample_from_ball(dimension, num_points): Sample points from unit ball
• plot_hyperplanes_color_2d(): Generate 2D Poisson hyperplane visualizations
• hyperplane_partition(points, gridpoints): Partition space using hyperplanes

Monte Carlo Simulation

• monte_carlo_hyperplane_partitions(): Estimate connectivity distributions
• plot_mc_colors_with_errorbars(): Plot convergence with error bars
• probability_landscape(): Visualize probability landscapes in 2D/3D

Examples

See the examples/ directory for comprehensive examples including:

• Figure generation from research papers
• Monte Carlo convergence analysis
• Probability landscape visualization
• Chord length statistics

Requirements

• Python 3.8+
• NumPy >= 1.20.0
• SciPy >= 1.7.0
• Matplotlib >= 3.3.0
• scikit-learn >= 1.0.0
• Numba >= 0.50.0

Development

To install in development mode:

git clone https://github.com/AlecShelley/popy.git
cd popy
pip install -e .

License

This project is licensed under the MIT License - see the LICENSE file for details.

Citation

If you use this package in your research, please cite:

@software{hyperpopy2024,
  title={HyperPopy: Poisson Hyperplane Model Package},
  author={Alec Shelley},
  year={2024},
  url={https://github.com/AlecShelley/hyperpopy}
}

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

Links

• GitHub Repository
• PyPI Package
• Issue Tracker