# Universal Hyperbolic Geometry (UHG)

A PyTorch library for hyperbolic deep learning using pure UHG principles.

## Features

- Pure projective geometry implementation
- No differential geometry or manifold concepts
- Cross-ratio preservation
- Projective transformations
- Graph neural networks
- Optimizers and samplers

## Quick Start

```python
import torch
import uhg

# Create points in projective space
x = torch.randn(10, 3)
y = torch.randn(10, 3)

# Initialize UHG
uhg_proj = uhg.ProjectiveUHG()

# Transform points
x_proj = uhg_proj.transform(x)
y_proj = uhg_proj.transform(y)

# Compute projective distance
dist = uhg_proj.proj_dist(x_proj, y_proj)

# Compute cross-ratio
cr = uhg_proj.cross_ratio(x_proj[0], x_proj[1], x_proj[2], x_proj[3])
```

## Installation

```bash
pip install uhg
```

## Documentation

For detailed documentation, visit [uhg.readthedocs.io](https://uhg.readthedocs.io). 