# HPFRACC - High-Performance Fractional Calculus Library
[](https://badge.fury.io/py/hpfracc)
[](https://opensource.org/licenses/MIT)
[](https://www.python.org/downloads/)
[](https://hpfracc.readthedocs.io/)
## 👨💻 **Author & Developer**
**Davian R. Chin**
Department of Biomedical Engineering
University of Reading
Email: [d.r.chin@pgr.reading.ac.uk](mailto:d.r.chin@pgr.reading.ac.uk)
GitHub: [@dave2k77](https://github.com/dave2k77)
## 🚀 **Overview**
HPFRACC (High-Performance Fractional Calculus Library) is a comprehensive Python library that provides high-performance implementations of fractional calculus operations, advanced numerical methods, and machine learning integration with fractional derivatives.
## ✨ **Key Features**
### 🔬 **Core Fractional Calculus**
- **Multiple Definitions**: Riemann-Liouville, Caputo, Grünwald-Letnikov, and more
- **High-Performance Algorithms**: Optimized implementations for speed and accuracy
- **GPU Acceleration**: CUDA support for large-scale computations
- **Advanced Methods**: Mellin transforms, fractional differential equations, and special functions
### 🤖 **Machine Learning Integration**
- **Multi-Backend Support**: Seamless integration with PyTorch, JAX, and NUMBA
- **Fractional Neural Networks**: Core networks with fractional calculus integration
- **Fractional Attention Mechanisms**: Multi-head attention with fractional derivatives
- **Graph Neural Networks**: Fractional GNN architectures for graph learning tasks
- **Comprehensive ML Components**: Loss functions, optimizers, and layers (in development)
### 🎯 **Performance & Usability**
- **Cross-Platform**: Windows, macOS, and Linux support
- **Extensive Documentation**: Comprehensive guides and examples
- **Active Development**: Regular updates and improvements
- **Research-Ready**: Designed for academic and industrial applications
## 🏗️ **Architecture**
### **Multi-Backend Support**
HPFRACC provides a unified interface across multiple computation backends:
- **PyTorch**: Full-featured deep learning with GPU acceleration
- **JAX**: High-performance numerical computing with automatic differentiation
- **NUMBA**: JIT compilation for CPU optimization
### **Core Components**
- **Backend Management**: Automatic detection and seamless switching between backends
- **Unified Tensor Operations**: Consistent API across all backends
- **Fractional Calculus Integration**: Built-in fractional derivatives in all ML components
## 📦 **Installation**
### **Basic Installation**
```bash
pip install hpfracc
```
### **Full Installation with ML Dependencies**
```bash
pip install hpfracc[ml]
```
### **Development Installation**
```bash
git clone https://github.com/dave2k77/hpfracc.git
cd hpfracc
pip install -e .
```
## 🚀 **Quick Start**
### **Basic Fractional Calculus**
```python
from hpfracc import FractionalOrder, riemann_liouville
# Create fractional order
alpha = FractionalOrder(0.5)
# Compute fractional derivative
result = riemann_liouville(function, t, alpha)
```
### **Multi-Backend Neural Networks**
```python
from hpfracc.ml import BackendType, FractionalNeuralNetwork
from hpfracc.core.definitions import FractionalOrder
# Create network with JAX backend
network = FractionalNeuralNetwork(
input_size=10,
hidden_sizes=[32, 16],
output_size=2,
fractional_order=FractionalOrder(0.5),
backend=BackendType.JAX
)
# Forward pass with fractional derivatives
output = network(input_data, use_fractional=True, method="RL")
```
### **Fractional Attention Mechanism**
```python
from hpfracc.ml import FractionalAttention
# Create attention with fractional calculus
attention = FractionalAttention(
d_model=64,
n_heads=8,
fractional_order=FractionalOrder(0.5),
backend=BackendType.TORCH
)
# Apply fractional attention
output = attention(input_sequence, method="RL")
```
### **Fractional Graph Neural Networks**
```python
from hpfracc.ml import FractionalGNNFactory, BackendType
from hpfracc.core.definitions import FractionalOrder
# Create GNN with fractional calculus
gnn = FractionalGNNFactory.create_model(
model_type='gcn', # Options: 'gcn', 'gat', 'sage', 'unet'
input_dim=16,
hidden_dim=32,
output_dim=4,
fractional_order=FractionalOrder(0.5),
backend=BackendType.JAX
)
# Forward pass on graph data
output = gnn(node_features, edge_index)
```
## 🔧 **Current Status**
### **✅ Fully Working**
- **Core Fractional Calculus**: All mathematical operations and algorithms
- **Backend Management**: Seamless switching between PyTorch, JAX, and NUMBA
- **Core Neural Networks**: FractionalNeuralNetwork with multi-backend support
- **Attention Mechanisms**: FractionalAttention with fractional derivatives
- **Tensor Operations**: Unified API across all backends
- **Graph Neural Networks**: Complete GNN architectures (GCN, GAT, GraphSAGE, U-Net)
### **🚧 In Development**
- **Advanced Layers**: Conv1D, Conv2D, LSTM, Transformer layers
- **Loss Functions**: Comprehensive loss function library
- **Optimizers**: Fractional gradient-based optimizers
### **📋 Planned Features**
- **Advanced ML Components**: Complete layer and optimizer library
- **Performance Optimization**: Backend-specific optimizations
- **Research Tools**: Benchmarking and analysis utilities
- **Extended GNN Support**: Additional graph neural network architectures and graph types
## 📚 **Documentation**
- **User Guide**: [docs/user_guide.md](docs/user_guide.md)
- **API Reference**: [docs/api_reference.md](docs/api_reference.md)
- **Examples**: [examples/](examples/) directory
- **Development Guide**: [README_DEV.md](README_DEV.md)
## 🤝 **Contributing**
We welcome contributions! Please see our [Contributing Guidelines](CONTRIBUTING.md) and [Development Guide](README_DEV.md) for details.
### **Development Setup**
```bash
# Clone repository
git clone https://github.com/dave2k77/hpfracc.git
cd hpfracc
# Create virtual environment
conda create -n hpfracc_dev python=3.9
conda activate hpfracc_dev
# Install development dependencies
pip install -e .[dev]
```
## 📄 **License**
This project is licensed under the MIT License - see the [LICENSE](LICENSE) file for details.
## 🙏 **Acknowledgments**
- **University of Reading**: Department of Biomedical Engineering
- **Open Source Community**: Contributors and maintainers
- **Research Community**: Academic and industrial partners
## 📞 **Contact**
- **Email**: [d.r.chin@pgr.reading.ac.uk](mailto:d.r.chin@pgr.reading.ac.uk)
- **GitHub**: [@dave2k77](https://github.com/dave2k77)
- **Project**: [HPFRACC Repository](https://github.com/dave2k77/hpfracc)
---
**HPFRACC** - Advancing fractional calculus through high-performance computing and machine learning integration.
Raw data
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"description": "# HPFRACC - High-Performance Fractional Calculus Library\r\n\r\n[](https://badge.fury.io/py/hpfracc)\r\n[](https://opensource.org/licenses/MIT)\r\n[](https://www.python.org/downloads/)\r\n[](https://hpfracc.readthedocs.io/)\r\n\r\n## \ud83d\udc68\u200d\ud83d\udcbb **Author & Developer**\r\n\r\n**Davian R. Chin** \r\nDepartment of Biomedical Engineering \r\nUniversity of Reading \r\nEmail: [d.r.chin@pgr.reading.ac.uk](mailto:d.r.chin@pgr.reading.ac.uk) \r\nGitHub: [@dave2k77](https://github.com/dave2k77)\r\n\r\n## \ud83d\ude80 **Overview**\r\n\r\nHPFRACC (High-Performance Fractional Calculus Library) is a comprehensive Python library that provides high-performance implementations of fractional calculus operations, advanced numerical methods, and machine learning integration with fractional derivatives.\r\n\r\n## \u2728 **Key Features**\r\n\r\n### \ud83d\udd2c **Core Fractional Calculus**\r\n- **Multiple Definitions**: Riemann-Liouville, Caputo, Gr\u00fcnwald-Letnikov, and more\r\n- **High-Performance Algorithms**: Optimized implementations for speed and accuracy\r\n- **GPU Acceleration**: CUDA support for large-scale computations\r\n- **Advanced Methods**: Mellin transforms, fractional differential equations, and special functions\r\n\r\n### \ud83e\udd16 **Machine Learning Integration**\r\n- **Multi-Backend Support**: Seamless integration with PyTorch, JAX, and NUMBA\r\n- **Fractional Neural Networks**: Core networks with fractional calculus integration\r\n- **Fractional Attention Mechanisms**: Multi-head attention with fractional derivatives\r\n- **Graph Neural Networks**: Fractional GNN architectures for graph learning tasks\r\n- **Comprehensive ML Components**: Loss functions, optimizers, and layers (in development)\r\n\r\n### \ud83c\udfaf **Performance & Usability**\r\n- **Cross-Platform**: Windows, macOS, and Linux support\r\n- **Extensive Documentation**: Comprehensive guides and examples\r\n- **Active Development**: Regular updates and improvements\r\n- **Research-Ready**: Designed for academic and industrial applications\r\n\r\n## \ud83c\udfd7\ufe0f **Architecture**\r\n\r\n### **Multi-Backend Support**\r\nHPFRACC provides a unified interface across multiple computation backends:\r\n\r\n- **PyTorch**: Full-featured deep learning with GPU acceleration\r\n- **JAX**: High-performance numerical computing with automatic differentiation\r\n- **NUMBA**: JIT compilation for CPU optimization\r\n\r\n### **Core Components**\r\n- **Backend Management**: Automatic detection and seamless switching between backends\r\n- **Unified Tensor Operations**: Consistent API across all backends\r\n- **Fractional Calculus Integration**: Built-in fractional derivatives in all ML components\r\n\r\n## \ud83d\udce6 **Installation**\r\n\r\n### **Basic Installation**\r\n```bash\r\npip install hpfracc\r\n```\r\n\r\n### **Full Installation with ML Dependencies**\r\n```bash\r\npip install hpfracc[ml]\r\n```\r\n\r\n### **Development Installation**\r\n```bash\r\ngit clone https://github.com/dave2k77/hpfracc.git\r\ncd hpfracc\r\npip install -e .\r\n```\r\n\r\n## \ud83d\ude80 **Quick Start**\r\n\r\n### **Basic Fractional Calculus**\r\n```python\r\nfrom hpfracc import FractionalOrder, riemann_liouville\r\n\r\n# Create fractional order\r\nalpha = FractionalOrder(0.5)\r\n\r\n# Compute fractional derivative\r\nresult = riemann_liouville(function, t, alpha)\r\n```\r\n\r\n### **Multi-Backend Neural Networks**\r\n```python\r\nfrom hpfracc.ml import BackendType, FractionalNeuralNetwork\r\nfrom hpfracc.core.definitions import FractionalOrder\r\n\r\n# Create network with JAX backend\r\nnetwork = FractionalNeuralNetwork(\r\n input_size=10,\r\n hidden_sizes=[32, 16],\r\n output_size=2,\r\n fractional_order=FractionalOrder(0.5),\r\n backend=BackendType.JAX\r\n)\r\n\r\n# Forward pass with fractional derivatives\r\noutput = network(input_data, use_fractional=True, method=\"RL\")\r\n```\r\n\r\n### **Fractional Attention Mechanism**\r\n```python\r\nfrom hpfracc.ml import FractionalAttention\r\n\r\n# Create attention with fractional calculus\r\nattention = FractionalAttention(\r\n d_model=64,\r\n n_heads=8,\r\n fractional_order=FractionalOrder(0.5),\r\n backend=BackendType.TORCH\r\n)\r\n\r\n# Apply fractional attention\r\noutput = attention(input_sequence, method=\"RL\")\r\n```\r\n\r\n### **Fractional Graph Neural Networks**\r\n```python\r\nfrom hpfracc.ml import FractionalGNNFactory, BackendType\r\nfrom hpfracc.core.definitions import FractionalOrder\r\n\r\n# Create GNN with fractional calculus\r\ngnn = FractionalGNNFactory.create_model(\r\n model_type='gcn', # Options: 'gcn', 'gat', 'sage', 'unet'\r\n input_dim=16,\r\n hidden_dim=32,\r\n output_dim=4,\r\n fractional_order=FractionalOrder(0.5),\r\n backend=BackendType.JAX\r\n)\r\n\r\n# Forward pass on graph data\r\noutput = gnn(node_features, edge_index)\r\n```\r\n\r\n## \ud83d\udd27 **Current Status**\r\n\r\n### **\u2705 Fully Working**\r\n- **Core Fractional Calculus**: All mathematical operations and algorithms\r\n- **Backend Management**: Seamless switching between PyTorch, JAX, and NUMBA\r\n- **Core Neural Networks**: FractionalNeuralNetwork with multi-backend support\r\n- **Attention Mechanisms**: FractionalAttention with fractional derivatives\r\n- **Tensor Operations**: Unified API across all backends\r\n- **Graph Neural Networks**: Complete GNN architectures (GCN, GAT, GraphSAGE, U-Net)\r\n\r\n### **\ud83d\udea7 In Development**\r\n- **Advanced Layers**: Conv1D, Conv2D, LSTM, Transformer layers\r\n- **Loss Functions**: Comprehensive loss function library\r\n- **Optimizers**: Fractional gradient-based optimizers\r\n\r\n### **\ud83d\udccb Planned Features**\r\n- **Advanced ML Components**: Complete layer and optimizer library\r\n- **Performance Optimization**: Backend-specific optimizations\r\n- **Research Tools**: Benchmarking and analysis utilities\r\n- **Extended GNN Support**: Additional graph neural network architectures and graph types\r\n\r\n## \ud83d\udcda **Documentation**\r\n\r\n- **User Guide**: [docs/user_guide.md](docs/user_guide.md)\r\n- **API Reference**: [docs/api_reference.md](docs/api_reference.md)\r\n- **Examples**: [examples/](examples/) directory\r\n- **Development Guide**: [README_DEV.md](README_DEV.md)\r\n\r\n## \ud83e\udd1d **Contributing**\r\n\r\nWe welcome contributions! 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