| Name | lineax JSON |
| Version |
0.0.5
JSON |
| download |
| home_page | None |
| Summary | Linear solvers in JAX and Equinox. |
| upload_time | 2024-04-14 17:20:19 |
| maintainer | None |
| docs_url | None |
| author | None |
| requires_python | ~=3.9 |
| license | Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. Definitions. "License" shall mean the terms and conditions for use, reproduction, and distribution as defined by Sections 1 through 9 of this document. "Licensor" shall mean the copyright owner or entity authorized by the copyright owner that is granting the License. "Legal Entity" shall mean the union of the acting entity and all other entities that control, are controlled by, or are under common control with that entity. For the purposes of this definition, "control" means (i) the power, direct or indirect, to cause the direction or management of such entity, whether by contract or otherwise, or (ii) ownership of fifty percent (50%) or more of the outstanding shares, or (iii) beneficial ownership of such entity. "You" (or "Your") shall mean an individual or Legal Entity exercising permissions granted by this License. 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While redistributing the Work or Derivative Works thereof, You may choose to offer, and charge a fee for, acceptance of support, warranty, indemnity, or other liability obligations and/or rights consistent with this License. However, in accepting such obligations, You may act only on Your own behalf and on Your sole responsibility, not on behalf of any other Contributor, and only if You agree to indemnify, defend, and hold each Contributor harmless for any liability incurred by, or claims asserted against, such Contributor by reason of your accepting any such warranty or additional liability. END OF TERMS AND CONDITIONS APPENDIX: How to apply the Apache License to your work. To apply the Apache License to your work, attach the following boilerplate notice, with the fields enclosed by brackets "[]" replaced with your own identifying information. (Don't include the brackets!) The text should be enclosed in the appropriate comment syntax for the file format. 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| keywords |
deep-learning
equinox
jax
least-squares
linear-solvers
neural-networks
numerical-methods
|
| VCS |
 |
| bugtrack_url |
|
| requirements |
No requirements were recorded.
|
| Travis-CI |
No Travis.
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| coveralls test coverage |
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|
<h1 align='center'>Lineax</h1>
Lineax is a [JAX](https://github.com/google/jax) library for linear solves and linear least squares. That is, Lineax provides routines that solve for $x$ in $Ax = b$. (Even when $A$ may be ill-posed or rectangular.)
Features include:
- PyTree-valued matrices and vectors;
- General linear operators for Jacobians, transposes, etc.;
- Efficient linear least squares (e.g. QR solvers);
- Numerically stable gradients through linear least squares;
- Support for structured (e.g. symmetric) matrices;
- Improved compilation times;
- Improved runtime of some algorithms;
- Support for both real-valued and complex-valued inputs;
- All the benefits of working with JAX: autodiff, autoparallelism, GPU/TPU support, etc.
## Installation
```bash
pip install lineax
```
Requires Python 3.9+, JAX 0.4.13+, and [Equinox](https://github.com/patrick-kidger/equinox) 0.11.0+.
## Documentation
Available at [https://docs.kidger.site/lineax](https://docs.kidger.site/lineax).
## Quick examples
Lineax can solve a least squares problem with an explicit matrix operator:
```python
import jax.random as jr
import lineax as lx
matrix_key, vector_key = jr.split(jr.PRNGKey(0))
matrix = jr.normal(matrix_key, (10, 8))
vector = jr.normal(vector_key, (10,))
operator = lx.MatrixLinearOperator(matrix)
solution = lx.linear_solve(operator, vector, solver=lx.QR())
```
or Lineax can solve a problem without ever materializing a matrix, as done in this
quadratic solve:
```python
import jax
import lineax as lx
key = jax.random.PRNGKey(0)
y = jax.random.normal(key, (10,))
def quadratic_fn(y, args):
return jax.numpy.sum((y - 1)**2)
gradient_fn = jax.grad(quadratic_fn)
hessian = lx.JacobianLinearOperator(gradient_fn, y, tags=lx.positive_semidefinite_tag)
solver = lx.CG(rtol=1e-6, atol=1e-6)
out = lx.linear_solve(hessian, gradient_fn(y, args=None), solver)
minimum = y - out.value
```
## Citation
If you found this library to be useful in academic work, then please cite: ([arXiv link](https://arxiv.org/abs/2311.17283))
```bibtex
@article{lineax2023,
title={Lineax: unified linear solves and linear least-squares in JAX and Equinox},
author={Jason Rader and Terry Lyons and Patrick Kidger},
journal={
AI for science workshop at Neural Information Processing Systems 2023,
arXiv:2311.17283
},
year={2023},
}
```
(Also consider starring the project on GitHub.)
## Finally
### See also: other libraries in the JAX ecosystem
[jaxtyping](https://github.com/google/jaxtyping): type annotations for shape/dtype of arrays.
[Equinox](https://github.com/patrick-kidger/equinox): neural networks.
[Optax](https://github.com/deepmind/optax): first-order gradient (SGD, Adam, ...) optimisers.
[Diffrax](https://github.com/patrick-kidger/diffrax): numerical differential equation solvers.
[Optimistix](https://github.com/patrick-kidger/optimistix): root finding, minimisation, fixed points, and least squares.
[BlackJAX](https://github.com/blackjax-devs/blackjax): probabilistic+Bayesian sampling.
[Orbax](https://github.com/google/orbax): checkpointing (async/multi-host/multi-device).
[sympy2jax](https://github.com/google/sympy2jax): SymPy<->JAX conversion; train symbolic expressions via gradient descent.
[Eqxvision](https://github.com/paganpasta/eqxvision): computer vision models.
[Levanter](https://github.com/stanford-crfm/levanter): scalable+reliable training of foundation models (e.g. LLMs).
[PySR](https://github.com/milesCranmer/PySR): symbolic regression. (Non-JAX honourable mention!)
### Disclaimer
This is not an official Google product.
Raw data
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"description": "<h1 align='center'>Lineax</h1>\n\nLineax is a [JAX](https://github.com/google/jax) library for linear solves and linear least squares. That is, Lineax provides routines that solve for $x$ in $Ax = b$. (Even when $A$ may be ill-posed or rectangular.)\n\nFeatures include:\n- PyTree-valued matrices and vectors;\n- General linear operators for Jacobians, transposes, etc.;\n- Efficient linear least squares (e.g. QR solvers);\n- Numerically stable gradients through linear least squares;\n- Support for structured (e.g. symmetric) matrices;\n- Improved compilation times;\n- Improved runtime of some algorithms;\n- Support for both real-valued and complex-valued inputs;\n- All the benefits of working with JAX: autodiff, autoparallelism, GPU/TPU support, etc.\n\n## Installation\n\n```bash\npip install lineax\n```\n\nRequires Python 3.9+, JAX 0.4.13+, and [Equinox](https://github.com/patrick-kidger/equinox) 0.11.0+.\n\n## Documentation\n\nAvailable at [https://docs.kidger.site/lineax](https://docs.kidger.site/lineax).\n\n## Quick examples\n\nLineax can solve a least squares problem with an explicit matrix operator:\n\n```python\nimport jax.random as jr\nimport lineax as lx\n\nmatrix_key, vector_key = jr.split(jr.PRNGKey(0))\nmatrix = jr.normal(matrix_key, (10, 8))\nvector = jr.normal(vector_key, (10,))\noperator = lx.MatrixLinearOperator(matrix)\nsolution = lx.linear_solve(operator, vector, solver=lx.QR())\n```\n\nor Lineax can solve a problem without ever materializing a matrix, as done in this\nquadratic solve:\n\n```python\nimport jax\nimport lineax as lx\n\nkey = jax.random.PRNGKey(0)\ny = jax.random.normal(key, (10,))\n\ndef quadratic_fn(y, args):\n return jax.numpy.sum((y - 1)**2)\n\ngradient_fn = jax.grad(quadratic_fn)\nhessian = lx.JacobianLinearOperator(gradient_fn, y, tags=lx.positive_semidefinite_tag)\nsolver = lx.CG(rtol=1e-6, atol=1e-6)\nout = lx.linear_solve(hessian, gradient_fn(y, args=None), solver)\nminimum = y - out.value\n```\n\n## Citation\n\nIf you found this library to be useful in academic work, then please cite: ([arXiv link](https://arxiv.org/abs/2311.17283))\n\n```bibtex\n@article{lineax2023,\n title={Lineax: unified linear solves and linear least-squares in JAX and Equinox},\n author={Jason Rader and Terry Lyons and Patrick Kidger},\n journal={\n AI for science workshop at Neural Information Processing Systems 2023,\n arXiv:2311.17283\n },\n year={2023},\n}\n```\n\n(Also consider starring the project on GitHub.)\n\n## Finally\n\n### See also: other libraries in the JAX ecosystem\n\n[jaxtyping](https://github.com/google/jaxtyping): type annotations for shape/dtype of arrays.\n\n[Equinox](https://github.com/patrick-kidger/equinox): neural networks.\n\n[Optax](https://github.com/deepmind/optax): first-order gradient (SGD, Adam, ...) optimisers.\n\n[Diffrax](https://github.com/patrick-kidger/diffrax): numerical differential equation solvers.\n\n[Optimistix](https://github.com/patrick-kidger/optimistix): root finding, minimisation, fixed points, and least squares.\n\n[BlackJAX](https://github.com/blackjax-devs/blackjax): probabilistic+Bayesian sampling.\n\n[Orbax](https://github.com/google/orbax): checkpointing (async/multi-host/multi-device).\n\n[sympy2jax](https://github.com/google/sympy2jax): SymPy<->JAX conversion; train symbolic expressions via gradient descent.\n\n[Eqxvision](https://github.com/paganpasta/eqxvision): computer vision models.\n\n[Levanter](https://github.com/stanford-crfm/levanter): scalable+reliable training of foundation models (e.g. LLMs).\n\n[PySR](https://github.com/milesCranmer/PySR): symbolic regression. (Non-JAX honourable mention!)\n\n### Disclaimer\n\nThis is not an official Google product.\n",
"bugtrack_url": null,
"license": "Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. Definitions. \"License\" shall mean the terms and conditions for use, reproduction, and distribution as defined by Sections 1 through 9 of this document. \"Licensor\" shall mean the copyright owner or entity authorized by the copyright owner that is granting the License. \"Legal Entity\" shall mean the union of the acting entity and all other entities that control, are controlled by, or are under common control with that entity. For the purposes of this definition, \"control\" means (i) the power, direct or indirect, to cause the direction or management of such entity, whether by contract or otherwise, or (ii) ownership of fifty percent (50%) or more of the outstanding shares, or (iii) beneficial ownership of such entity. \"You\" (or \"Your\") shall mean an individual or Legal Entity exercising permissions granted by this License. \"Source\" form shall mean the preferred form for making modifications, including but not limited to software source code, documentation source, and configuration files. \"Object\" form shall mean any form resulting from mechanical transformation or translation of a Source form, including but not limited to compiled object code, generated documentation, and conversions to other media types. \"Work\" shall mean the work of authorship, whether in Source or Object form, made available under the License, as indicated by a copyright notice that is included in or attached to the work (an example is provided in the Appendix below). \"Derivative Works\" shall mean any work, whether in Source or Object form, that is based on (or derived from) the Work and for which the editorial revisions, annotations, elaborations, or other modifications represent, as a whole, an original work of authorship. For the purposes of this License, Derivative Works shall not include works that remain separable from, or merely link (or bind by name) to the interfaces of, the Work and Derivative Works thereof. \"Contribution\" shall mean any work of authorship, including the original version of the Work and any modifications or additions to that Work or Derivative Works thereof, that is intentionally submitted to Licensor for inclusion in the Work by the copyright owner or by an individual or Legal Entity authorized to submit on behalf of the copyright owner. For the purposes of this definition, \"submitted\" means any form of electronic, verbal, or written communication sent to the Licensor or its representatives, including but not limited to communication on electronic mailing lists, source code control systems, and issue tracking systems that are managed by, or on behalf of, the Licensor for the purpose of discussing and improving the Work, but excluding communication that is conspicuously marked or otherwise designated in writing by the copyright owner as \"Not a Contribution.\" \"Contributor\" shall mean Licensor and any individual or Legal Entity on behalf of whom a Contribution has been received by Licensor and subsequently incorporated within the Work. 2. Grant of Copyright License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable copyright license to reproduce, prepare Derivative Works of, publicly display, publicly perform, sublicense, and distribute the Work and such Derivative Works in Source or Object form. 3. Grant of Patent License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable (except as stated in this section) patent license to make, have made, use, offer to sell, sell, import, and otherwise transfer the Work, where such license applies only to those patent claims licensable by such Contributor that are necessarily infringed by their Contribution(s) alone or by combination of their Contribution(s) with the Work to which such Contribution(s) was submitted. If You institute patent litigation against any entity (including a cross-claim or counterclaim in a lawsuit) alleging that the Work or a Contribution incorporated within the Work constitutes direct or contributory patent infringement, then any patent licenses granted to You under this License for that Work shall terminate as of the date such litigation is filed. 4. Redistribution. You may reproduce and distribute copies of the Work or Derivative Works thereof in any medium, with or without modifications, and in Source or Object form, provided that You meet the following conditions: (a) You must give any other recipients of the Work or Derivative Works a copy of this License; and (b) You must cause any modified files to carry prominent notices stating that You changed the files; and (c) You must retain, in the Source form of any Derivative Works that You distribute, all copyright, patent, trademark, and attribution notices from the Source form of the Work, excluding those notices that do not pertain to any part of the Derivative Works; and (d) If the Work includes a \"NOTICE\" text file as part of its distribution, then any Derivative Works that You distribute must include a readable copy of the attribution notices contained within such NOTICE file, excluding those notices that do not pertain to any part of the Derivative Works, in at least one of the following places: within a NOTICE text file distributed as part of the Derivative Works; within the Source form or documentation, if provided along with the Derivative Works; or, within a display generated by the Derivative Works, if and wherever such third-party notices normally appear. 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You are solely responsible for determining the appropriateness of using or redistributing the Work and assume any risks associated with Your exercise of permissions under this License. 8. Limitation of Liability. In no event and under no legal theory, whether in tort (including negligence), contract, or otherwise, unless required by applicable law (such as deliberate and grossly negligent acts) or agreed to in writing, shall any Contributor be liable to You for damages, including any direct, indirect, special, incidental, or consequential damages of any character arising as a result of this License or out of the use or inability to use the Work (including but not limited to damages for loss of goodwill, work stoppage, computer failure or malfunction, or any and all other commercial damages or losses), even if such Contributor has been advised of the possibility of such damages. 9. Accepting Warranty or Additional Liability. 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