sympy2c: from symbolic expressions to fast C/C++ functions and ODE solvers in Python

TL;DR

sympy2c is a Python package that converts symbolic equations from SymPy into optimized C/C++ code, enabling fast numerical solutions of complex systems like the Einstein-Boltzmann equations in cosmology.

Contribution

It introduces a novel method for generating optimized ODE solvers by exploiting Jacobian sparsity, bridging symbolic development and efficient numerical implementation.

Findings

Achieves significant performance improvements in solving Einstein-Boltzmann equations.

Demonstrates the effectiveness of symbolic transformations for code optimization.

Provides a widely applicable tool for computational physics applications.

Abstract

Computer algebra systems play an important role in science as they facilitate the development of new theoretical models. The resulting symbolic equations are often implemented in a compiled programming language in order to provide fast and portable codes for practical applications. We describe sympy2c, a new Python package designed to bridge the gap between the symbolic development and the numerical implementation of a theoretical model. sympy2c translates symbolic equations implemented in the SymPy Python package to C/C++ code that is optimized using symbolic transformations. The resulting functions can be conveniently used as an extension module in Python. sympy2c is used within the PyCosmo Python package to solve the Einstein-Boltzmann equations, a large system of ODEs describing the evolution of linear perturbations in the Universe. After reviewing the functionalities and usage of sympy2c, we describe its implementation and optimization strategies. This includes, in particular, a novel approach to generate optimized ODE solvers making use of the sparsity of the symbolic Jacobian matrix. We demonstrate its performance using the Einstein-Boltzmann equations as a test case. sympy2c is widely applicable and may prove useful for various areas of computational physics. sympy2c is publicly available at https://cosmology.ethz.ch/research/software-lab/sympy2c.html