immrax

immrax is a tool for interval analysis and mixed monotone reachability analysis in JAX.

Inclusion function transformations are composable with existing JAX transformations, allowing the use of Automatic Differentiation to learn relationships between inputs and outputs, as well as parallelization and GPU capabilities for quick, accurate reachable set estimation.

For more information, please see the full documentation.

Installation

System Dependencies

immrax depends on the library pypoman, which internally uses pycddlib as a wrapper around the cdd library. For this wrapper to function properly, you must install cdd to your system. On Ubuntu, the relevant packages can be installed with

apt-get install -y libcdd-dev libgmp-dev

On Arch linux, you can use

pacman -S cddlib

Package

immrax is available as a package on PyPI and can be installed with pip.

pip install immrax

We recommend you use a python virtual environment (e.g. through pip, conda, uv, etc.).

Hardware Acceleration

immrax supports hardware acceleration through JAX. You can install the cuda12 or cuda13 extras it supplies directly, or manually choose a different JAX accelerator. (Our development machines are all currently CUDA based; other methods are untested.)

pip install "jax[rocm7-local]"

See the JAX installation guide for further details.

Development

Simply clone this repo to get started with immrax development. We manage dependencies with uv; to create a virtual environment with everything you need run

uv sync

The above comments on system dependencies still apply.

Examples

To test if the installation process worked, run the compare.py example. This should return the outputs of different inclusion functions as well as their runtimes.

uv run examples/compare.py

The additional examples extra contains some dependencies needed for the more complex examples; be sure to also install it if you want to run the others.

Other Tooling

We have a useful (though not yet comprehensive) test suite that can be run with

uv run pytest

Automatic linting and formatting is done with ruff

uv run ruff check # lint all project files, report only
uv run ruff format # autoformat all project files

This repo also ships a tracked git pre-commit hook that runs ruff check --fix and ruff format on staged Python files automatically. Enable it once per clone with

git config core.hooksPath .githooks

The hook is non-blocking: it applies safe fixes and formatting, warns if any unfixable lint issues remain, and lets the commit proceed.

Citation

If you find this library useful, please cite our paper with the following bibtex entry.

@article{immrax,
title = {immrax: A Parallelizable and Differentiable Toolbox for Interval Analysis and Mixed Monotone Reachability in {JAX}},
journal = {IFAC-PapersOnLine},
volume = {58},
number = {11},
pages = {75-80},
year = {2024},
note = {8th IFAC Conference on Analysis and Design of Hybrid Systems ADHS 2024},
issn = {2405-8963},
doi = {https://doi.org/10.1016/j.ifacol.2024.07.428},
url = {https://www.sciencedirect.com/science/article/pii/S2405896324005275},
author = {Akash Harapanahalli and Saber Jafarpour and Samuel Coogan},
keywords = {Interval analysis, Reachability analysis, Automatic differentiation, Parallel computation, Computational tools, Optimal control, Robust control},
abstract = {We present an implementation of interval analysis and mixed monotone interval reachability analysis as function transforms in Python, fully composable with the computational framework JAX. The resulting toolbox inherits several key features from JAX, including computational efficiency through Just-In-Time Compilation, GPU acceleration for quick parallelized computations, and Automatic Differentiability We demonstrate the toolbox’s performance on several case studies, including a reachability problem on a vehicle model controlled by a neural network, and a robust closed-loop optimal control problem for a swinging pendulum.}
}