# hyperpopy: Poisson Hyperplane Model Package
[](https://badge.fury.io/py/hyperpopy)
[](https://www.python.org/downloads/)
[](https://opensource.org/licenses/MIT)
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
```bash
pip install --upgrade hyperpopy
```
## Quick Start
```python
import hyperpopy
import numpy as np
# Calculate the arrival rate of a Poisson hyperplane process
rate_2d = hyperpopy.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 = hyperpopy.plot_hyperplanes_color_2d(
radius=10,
grid_resolution=100,
colorcutoffs=np.array([0.5]),
cmap_list=hyperpopy.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 = hyperpopy.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:
```bash
git clone https://github.com/AlecShelley/hyperpopy.git
cd hyperpopy
pip install -e .
```
## License
This project is licensed under the MIT License - see the [LICENSE](LICENSE) file for details.
## Citation
If you use this package in your research, please cite:
```bibtex
@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](https://github.com/AlecShelley/hyperpopy)
- [PyPI Package](https://pypi.org/project/hyperpopy/)
- [Issue Tracker](https://github.com/AlecShelley/hyperpopy/issues)
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