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Rigid transforms + Lie groups for JAX
| Date | Stars |
|---|---|
| 2026-07-24 | 337 |
| 2026-07-25 | 337 |
| 2026-07-28 | 337 |
| 2026-07-30 | 337 |
| 2026-08-06 | 337 |
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# jaxlie
[](https://codecov.io/gh/brentyi/jaxlie)
[](https://pypi.org/project/jaxlie)
**[ [API reference](https://brentyi.github.io/jaxlie) ]** **[
[PyPI](https://pypi.org/project/jaxlie/) ]**
`jaxlie` is a library containing implementations of Lie groups commonly used for
rigid body transformations, targeted at computer vision & robotics
applications written in JAX. Heavily inspired by the C++ library
[Sophus](https://github.com/strasdat/Sophus).
We implement Lie groups as high-level (data)classes:
<table>
<thead>
<tr>
<th>Group</th>
<th>Description</th>
<th>Parameterization</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td><code>jaxlie.<strong>SO2</strong></code></td>
<td>Rotations in 2D.</td>
<td><em>(real, imaginary):</em> unit complex (∈ S<sup>1</sup>)</td>
</tr>
<tr>
<td><code>jaxlie.<strong>SE2</strong></code></td>
<td>Proper rigid transforms in 2D.</td>
<td><em>(real, imaginary, x, y):</em> unit complex & translation</td>
</tr>
<tr>
<td><code>jaxlie.<strong>SO3</strong></code></td>
<td>Rotations in 3D.</td>
<td><em>(qw, qx, qy, qz):</em> wxyz quaternion (∈ S<sup>3</sup>)</td>
</tr>
<tr>
<td><code>jaxlie.<strong>SE3</strong></code></td>
<td>Proper rigid transforms in 3D.</td>
<td><em>(qw, qx, qy, qz, x, y, z):</em> wxyz quaternion & translation</td>
</tr>
</tbody>
</table>
Where each group supports:
- Forward- and reverse-mode AD-friendly **`exp()`**, **`log()`**,
**`adjoint()`**, **`apply()`**, **`multiply()`**, **`inverse()`**,
**`identity()`**, **`from_matrix()`**, and **`as_matrix()`** operations. (see
[./examples/se3_example.py](./examples/se3_basics.py))
- Taylor approximations near singularities.
- Helpers for optimization on manifolds (see
[./examples/se3_optimization.py](./examples/se3_optimization.py),
<code>jaxlie.<strong>manifold.\*</strong></code>).
- Compatibility with standard JAX function transformations. (see
[./examples/vmap_example.py](./examples/vmap_example.py))
- Broadcasting for leading axes.
- (Un)flattening as pytree nodes.
- Serialization using [flax](https://github.com/google/flax).
We also implement various common utilities for things like uniform random
sampling (**`sample_uniform()`**) and converting from/to Euler angles (in the
`SO3` class).
---
### Install (Python >=3.7)
```bash
# Python 3.6 releases also exist, but are no longer being updated.
pip install jaxlie
```
---
### Misc
`jaxlie` was originally written when I was learning about Lie groups for our IROS 2021 paper
([link](https://github.com/brentyi/dfgo)):
```
@inproceedings{yi2021iros,
author={Brent Yi and Michelle Lee and Alina Kloss and Roberto Mart\'in-Mart\'in and Jeannette Bohg},
title = {Differentiable Factor Graph Optimization for Learning Smoothers},
year = 2021,
BOOKTITLE = {2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}
}
```
Excerpt of 3,342 characters
Read on GitHubWould you bet a product on this? Bounded 0–100 and slow moving.
matched fp:a73280356cc57f99, topic:computer-vision, readme:computer vision
matched fp:a73280356cc57f99, topic:jax
matched fp:a73280356cc57f99, topic:robotics, readme:robotics