Welcome to sandalwood’s documentation!

sandalwood is a Python library for creating, manipulating, and composing Multivariate Taylor Functions, with high-performance backends for acceleration. It provides a robust framework for working with multivariate Taylor series expansions based on the principles of Differential Algebra (DA).

This library is designed for scientists, engineers, and researchers who need to perform high-order differentiation, integration, and function composition in a computationally efficient manner.

#### Features * Hybrid Multicore Architecture: Seamlessly combines JIT-compiled Python (Numba), vectorized Fortran (COSY Infinity), and GPU-accelerated backends. * Robust Memory Management: Features the CosyIndexPool for O(1) memory allocation and strict CosyScope tracking for complex simulations. * Massive Order Support: Efficiently handles Taylor expansions up to order 128+ with specialized dense-mode multiplication tables. * High-Performance Physics: Includes optimized kernels for Biot-Savart integration and high-order symplectic Map Composition.

User Guide

• Getting Started
  • Installation
  • A Quick-Start Example
  • Running Tests
• Examples & Tutorials
  • Quick Start Guide to sandalwood
  • sandalwood Tutorial: Basic Functionality
  • sandalwood Tutorial: Advanced Functionality
  • TaylorMap Demo
  • sandalwood Tutorial: Convergence and Accuracy
• Working with Taylor Maps
  • Creating a TaylorMap
  • Accessing Components
  • Composing Taylor Maps
  • Inverting Taylor Maps
  • Connection to Differential Equations
  • See Also

API

• sandalwood API Reference
  • sandalwood Package
  • sandalwood.taylor_function Module
  • sandalwood.complex_taylor_function Module
  • sandalwood.taylor_map Module
  • sandalwood.backend Module
  • Elementary Functions
  • Utility Functions

Background

• The Differential Algebraic Method: Theoretical Background for sandalwood
  • Foundational Principles of Differential Algebra
  • The Differential Algebra Data Type: An Implementation Perspective
  • Foundational Citations for Differential Algebra (DA) and COSY INFINITY

Advanced Topics

• Advanced Topics
  • Backends and Performance
  • Future Work
• Performance Optimization in Sandalwood
  • The “Two-Language” Problem
  • 1. “Dense Mode” Architecture
  • 2. Numba JIT Compilation
  • 3. Lazy Materialization
  • 4. Fast Evaluation with Power Caching
  • 5. Vectorized Object Instantiation
  • Summary of Speedups
  • 6. Hybrid Dispatch & Fortran Fast Path
  • 7. Phase 1 Optimizations (Vectorization & Batching)
  • 8. Phase 2 Optimizations (Solver & Batching)
  • 9. Final Benchmark Results
  • 10. Map Composition Optimization (Phase 4)
  • 11. Phase 5 Optimizations (Python Structural)
• COSY Infinity Backend Architecture
  • Architecture Overview
  • Memory Management Architecture
  • Specialized Physics Kernels
  • Memory Management: The “CosyScope”
  • Performance Optimizations
  • Memory Configuration
  • Extending the Backend
• Benchmarking and Performance Analysis
  • Quick Start
  • Benchmarking Modes
  • Methodology
  • Reporting Tools
  • Extending Benchmarks
• AI Agent Tools Integration
  • Architecture
  • Response Envelope Structure
  • Usage
  • API Reference

• Index

• Module Index

• Search Page