[
{
"path": ".github/workflows/build_docs.yml",
"content": "name: Build docs\n\non:\n push:\n branches:\n - main\n\njobs:\n build:\n strategy:\n matrix:\n python-version: [ 3.11 ]\n os: [ ubuntu-latest ]\n runs-on: ${{ matrix.os }}\n steps:\n - name: Checkout code\n uses: actions/checkout@v2\n\n - name: Install the latest version of uv\n uses: astral-sh/setup-uv@v7\n with:\n python-version: ${{ matrix.python-version }}\n\n - name: Install dependencies\n run: |\n uv run echo done\n\n - name: Build docs\n run: |\n uv run mkdocs build\n\n - name: Upload docs\n uses: actions/upload-artifact@v4\n with:\n name: docs\n path: site # where `mkdocs build` puts the built site\n"
},
{
"path": ".github/workflows/release.yml",
"content": "name: Release\n\non:\n push:\n branches:\n - main\n\njobs:\n build:\n runs-on: ubuntu-latest\n steps:\n - name: Release\n uses: patrick-kidger/action_update_python_project@v8\n with:\n python-version: \"3.11\"\n # Uninstall and reinstall pytest to work around the fact that it doesn't get put into `bin` otherwise.\n test-script: |\n cp -r ${{ github.workspace }}/tests ./tests\n cp ${{ github.workspace }}/pyproject.toml ./pyproject.toml\n uv pip uninstall pytest\n uv sync --no-install-project --inexact\n uv run --no-sync pytest\n pypi-token: ${{ secrets.pypi_token }}\n github-user: patrick-kidger\n github-token: ${{ github.token }}\n"
},
{
"path": ".github/workflows/run_tests.yml",
"content": "name: Run tests\n\non:\n pull_request:\n\njobs:\n run-test:\n strategy:\n matrix:\n python-version: [ 3.11 ]\n os: [ ubuntu-latest ]\n fail-fast: false\n runs-on: ${{ matrix.os }}\n steps:\n - name: Checkout code\n uses: actions/checkout@v2\n\n - name: Install the latest version of uv\n uses: astral-sh/setup-uv@v7\n with:\n python-version: ${{ matrix.python-version }}\n\n - name: Install dependencies\n run: |\n uv run echo done\n\n - name: Checks with pre-commit\n run: |\n uv run prek run --all-files\n\n - name: Test with pytest\n run: |\n uv run python -m tests\n\n - name: Check that documentation can be built.\n run: |\n uv run mkdocs build\n"
},
{
"path": ".gitignore",
"content": "**/__pycache__\n**/.ipynb_checkpoints\n*.egg-info/\nbuild/\ndist/\nsite/\nexamples/data\n.all_objects.cache\n.pymon\n.idea\n.venv\nuv.lock\n"
},
{
"path": ".pre-commit-config.yaml",
"content": "fail_fast: true\nrepos:\n - repo: meta\n hooks:\n - id: check-hooks-apply\n - id: check-useless-excludes\n - repo: https://github.com/pre-commit/pre-commit-hooks\n rev: v4.4.0\n hooks:\n - id: trailing-whitespace\n exclude: \\.md$\n - id: check-toml\n - id: mixed-line-ending\n - repo: local\n hooks:\n - id: sort-pyproject\n name: sort pyproject\n files: ^pyproject\\.toml$\n language: system\n entry: uv run -- toml-sort -i --sort-table-keys --sort-inline-tables\n - id: ruff-format\n name: ruff format\n types_or: [python, pyi, jupyter, toml]\n language: system\n entry: uv run -- ruff format --\n require_serial: true\n - id: ruff-lint\n name: ruff lint\n types_or: [python, pyi, jupyter, toml]\n language: system\n entry: uv run -- ruff check --fix --\n require_serial: true\n - id: pyright\n name: pyright\n types_or: [python]\n language: system\n entry: uv run -- pyright\n require_serial: true\n"
},
{
"path": "CONTRIBUTING.md",
"content": "# Contributing\n\nContributions (pull requests) are very welcome! Here's how to get started.\n\n---\n\n### Getting started\n\n[We assume that you have `uv` installed.](https://docs.astral.sh/uv/) Now fork the library on GitHub. Then clone and install the library:\n\n```bash\ngit clone https://github.com/your-username-here/lineax.git\ncd lineax\nuv run prek install # Creates a local venv + installs dependencies + installs pre-commit hooks.\n```\n\n---\n\n### If you're making changes to the code\n\nNow make your changes. Make sure to include additional tests if necessary. Next verify the tests all pass:\n\n```bash\nuv run python -m tests\n```\n\nThen push your changes back to your fork of the repository:\n\n```bash\ngit push\n```\n\nFinally, open a pull request on GitHub!\n\n---\n\n### If you're making changes to the documentation\n\nMake your changes. You can then build the documentation by doing\n\n```bash\nuv run mkdocs serve\n```\n\nYou can then see your local copy of the documentation by navigating to `localhost:8000` in a web browser.\n"
},
{
"path": "LICENSE",
"content": " Apache License\n Version 2.0, January 2004\n http://www.apache.org/licenses/\n\n TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION\n\n 1. Definitions.\n\n \"License\" shall mean the terms and conditions for use, reproduction,\n and distribution as defined by Sections 1 through 9 of this document.\n\n \"Licensor\" shall mean the copyright owner or entity authorized by\n the copyright owner that is granting the License.\n\n \"Legal Entity\" shall mean the union of the acting entity and all\n other entities that control, are controlled by, or are under common\n control with that entity. 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We also recommend that a\n file or class name and description of purpose be included on the\n same \"printed page\" as the copyright notice for easier\n identification within third-party archives.\n\n Copyright [yyyy] [name of copyright owner]\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n"
},
{
"path": "README.md",
"content": "
Lineax
\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 3.10+, JAX 0.4.38+, and [Equinox](https://github.com/patrick-kidger/equinox) 0.11.10+.\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## See also: other libraries in the JAX ecosystem\n\n**Always useful** \n[Equinox](https://github.com/patrick-kidger/equinox): neural networks and everything not already in core JAX! \n[jaxtyping](https://github.com/patrick-kidger/jaxtyping): type annotations for shape/dtype of arrays. \n\n**Deep learning** \n[Optax](https://github.com/deepmind/optax): first-order gradient (SGD, Adam, ...) optimisers. \n[Orbax](https://github.com/google/orbax): checkpointing (async/multi-host/multi-device). \n[Levanter](https://github.com/stanford-crfm/levanter): scalable+reliable training of foundation models (e.g. LLMs). \n[paramax](https://github.com/danielward27/paramax): parameterizations and constraints for PyTrees. \n\n**Scientific computing** \n[Diffrax](https://github.com/patrick-kidger/diffrax): numerical differential equation solvers. \n[Optimistix](https://github.com/patrick-kidger/optimistix): root finding, minimisation, fixed points, and least squares. \n[BlackJAX](https://github.com/blackjax-devs/blackjax): probabilistic+Bayesian sampling. \n[sympy2jax](https://github.com/patrick-kidger/sympy2jax): SymPy<->JAX conversion; train symbolic expressions via gradient descent. \n[PySR](https://github.com/milesCranmer/PySR): symbolic regression. (Non-JAX honourable mention!) \n\n**Awesome JAX** \n[Awesome JAX](https://github.com/n2cholas/awesome-jax): a longer list of other JAX projects. \n"
},
{
"path": "benchmarks/gmres_fails_safely.py",
"content": "# Copyright 2023 Google LLC\n#\n# Licensed under the Apache License, Version 2.0 (the \"License\");\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n# http://www.apache.org/licenses/LICENSE-2.0\n#\n# Unless required by applicable law or agreed to in writing, software\n# distributed under the License is distributed on an \"AS IS\" BASIS,\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n# limitations under the License.\n\nimport functools as ft\n\nimport equinox as eqx\nimport equinox.internal as eqxi\nimport jax\nimport jax.numpy as jnp\nimport jax.random as jr\nimport jax.scipy as jsp\nimport lineax as lx\n\n\ngetkey = eqxi.GetKey()\n\n\ndef tree_allclose(x, y, *, rtol=1e-5, atol=1e-8):\n return eqx.tree_equal(x, y, typematch=True, rtol=rtol, atol=atol)\n\n\njax.config.update(\"jax_enable_x64\", True)\n\n\ndef make_problem(mat_size: int, *, key):\n mat = jr.normal(key, (mat_size, mat_size))\n true_x = jr.normal(key, (mat_size,))\n b = mat @ true_x\n op = lx.MatrixLinearOperator(mat)\n return mat, op, b, true_x\n\n\ndef benchmark_jax(mat_size: int, *, key):\n mat, _, b, true_x = make_problem(mat_size, key=key)\n\n solve_with_jax = ft.partial(\n jsp.sparse.linalg.gmres, tol=1e-5, solve_method=\"batched\"\n )\n gmres_jit = jax.jit(solve_with_jax)\n jax_soln, info = gmres_jit(mat, b)\n\n # info == 0.0 implies that the solve has succeeded.\n returned_failed = jnp.all(info != 0.0)\n actually_failed = not tree_allclose(jax_soln, true_x, atol=1e-4, rtol=1e-4)\n\n assert actually_failed\n\n captured_failure = returned_failed & actually_failed\n return captured_failure\n\n\ndef benchmark_lx(mat_size: int, *, key):\n _, op, b, true_x = make_problem(mat_size, key=key)\n\n lx_soln = lx.linear_solve(op, b, lx.GMRES(atol=1e-5, rtol=1e-5), throw=False)\n\n returned_failed = jnp.all(lx_soln.result != lx.RESULTS.successful)\n actually_failed = not tree_allclose(lx_soln.value, true_x, atol=1e-4, rtol=1e-4)\n\n assert actually_failed\n\n captured_failure = returned_failed & actually_failed\n return captured_failure\n\n\nlx_failed_safely = 0\njax_failed_safely = 0\n\nfor _ in range(100):\n key = getkey()\n jax_captured_failure = benchmark_jax(100, key=key)\n lx_captured_failure = benchmark_lx(100, key=key)\n\n jax_failed_safely = jax_failed_safely + jax_captured_failure\n lx_failed_safely = lx_failed_safely + lx_captured_failure\n\nprint(f\"JAX failed safely {jax_failed_safely} out of 100 times\")\nprint(f\"Lineax failed safely {lx_failed_safely} out of 100 times\")\n"
},
{
"path": "benchmarks/lstsq_gradients.py",
"content": "# Copyright 2023 Google LLC\n#\n# Licensed under the Apache License, Version 2.0 (the \"License\");\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n# http://www.apache.org/licenses/LICENSE-2.0\n#\n# Unless required by applicable law or agreed to in writing, software\n# distributed under the License is distributed on an \"AS IS\" BASIS,\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n# limitations under the License.\n\n# Core JAX has some numerical issues with their lstsq gradients.\n# See https://github.com/google/jax/issues/14868\n# This demonstrates that we don't have the same issue!\n\nimport sys\n\nimport jax\nimport jax.numpy as jnp\nimport lineax as lx\n\n\nsys.path.append(\"../tests\")\nfrom helpers import finite_difference_jvp # pyright: ignore\n\n\na_primal = (jnp.eye(3),)\na_tangent = (jnp.zeros((3, 3)),)\n\n\ndef jax_solve(a):\n sol, _, _, _ = jnp.linalg.lstsq(a, jnp.arange(3)) # pyright: ignore\n return sol\n\n\ndef lx_solve(a):\n op = lx.MatrixLinearOperator(a)\n return lx.linear_solve(op, jnp.arange(3)).value\n\n\n_, true_jvp = finite_difference_jvp(jax_solve, a_primal, a_tangent)\n_, jax_jvp = jax.jvp(jax_solve, a_primal, a_tangent)\n_, lx_jvp = jax.jvp(lx_solve, a_primal, a_tangent)\nassert jnp.isnan(jax_jvp).all()\nassert jnp.allclose(true_jvp, lx_jvp)\n"
},
{
"path": "benchmarks/solver_speeds.py",
"content": "# Copyright 2023 Google LLC\n#\n# Licensed under the Apache License, Version 2.0 (the \"License\");\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n# http://www.apache.org/licenses/LICENSE-2.0\n#\n# Unless required by applicable law or agreed to in writing, software\n# distributed under the License is distributed on an \"AS IS\" BASIS,\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n# limitations under the License.\n\nimport functools as ft\nimport sys\nimport timeit\n\nimport equinox as eqx\nimport equinox.internal as eqxi\nimport jax\nimport jax.numpy as jnp\nimport jax.random as jr\nimport jax.scipy as jsp\nimport lineax as lx\n\n\nsys.path.append(\"../tests\")\nfrom helpers import construct_matrix, has_tag # pyright: ignore[reportMissingImports]\n\n\ngetkey = eqxi.GetKey()\n\n\ndef tree_allclose(x, y, *, rtol=1e-5, atol=1e-8):\n return eqx.tree_equal(x, y, typematch=True, rtol=rtol, atol=atol)\n\n\njax.config.update(\"jax_enable_x64\", True)\n\nif jax.config.jax_enable_x64: # pyright: ignore\n tol = 1e-12\nelse:\n tol = 1e-6\n\n\ndef base_wrapper(a, b, solver):\n op = lx.MatrixLinearOperator(\n a,\n (\n lx.positive_semidefinite_tag,\n lx.symmetric_tag,\n lx.diagonal_tag,\n lx.tridiagonal_tag,\n ),\n )\n out = lx.linear_solve(op, b, solver, throw=False)\n return out.value\n\n\ndef jax_svd(a, b):\n out, _, _, _ = jnp.linalg.lstsq(a, b) # pyright: ignore\n return out\n\n\ndef jax_gmres(a, b):\n out, _ = jsp.sparse.linalg.gmres(a, b, tol=tol)\n return out\n\n\ndef jax_bicgstab(a, b):\n out, _ = jsp.sparse.linalg.bicgstab(a, b, tol=tol)\n return out\n\n\ndef jax_cg(a, b):\n out, _ = jsp.sparse.linalg.cg(a, b, tol=tol)\n return out\n\n\ndef jax_lu(matrix, vector):\n return jsp.linalg.lu_solve(jsp.linalg.lu_factor(matrix), vector)\n\n\ndef jax_cholesky(matrix, vector):\n return jsp.linalg.cho_solve(jsp.linalg.cho_factor(matrix), vector)\n\n\ndef jax_tridiagonal(matrix, vector):\n dl = jnp.append(0.0, matrix.diagonal(-1))\n d = matrix.diagonal(0)\n du = jnp.append(matrix.diagonal(1), 0.0)\n return jax.lax.linalg.tridiagonal_solve(dl, d, du, vector[:, None])[:, 0]\n\n\nnamed_solvers = [\n (\"LU\", \"LU\", lx.LU(), jax_lu, ()),\n (\"QR\", \"SVD\", lx.QR(), jax_svd, ()),\n (\"SVD\", \"SVD\", lx.SVD(), jax_svd, ()),\n (\n \"Cholesky\",\n \"Cholesky\",\n lx.Cholesky(),\n jax_cholesky,\n lx.positive_semidefinite_tag,\n ),\n (\"Diagonal\", \"None\", lx.Diagonal(), None, lx.diagonal_tag),\n (\n \"Tridiagonal\",\n \"Tridiagonal\",\n lx.Tridiagonal(),\n jax_tridiagonal,\n lx.tridiagonal_tag,\n ),\n (\n \"CG\",\n \"CG\",\n lx.CG(atol=tol, rtol=tol, stabilise_every=None),\n jax_cg,\n lx.positive_semidefinite_tag,\n ),\n (\n \"GMRES\",\n \"GMRES\",\n lx.GMRES(atol=1, rtol=1),\n jax_gmres,\n (),\n ),\n (\n \"BiCGStab\",\n \"BiCGStab\",\n lx.BiCGStab(atol=tol, rtol=tol),\n jax_bicgstab,\n (),\n ),\n]\n\n\ndef create_problem(solver, tags, size=3):\n (matrix,) = construct_matrix(getkey, solver, tags, size=size)\n true_x = jr.normal(getkey(), (size,))\n b = matrix @ true_x\n return matrix, true_x, b\n\n\ndef create_easy_iterative_problem(size, tags):\n matrix = jr.normal(getkey(), (size, size)) / size + 2 * jnp.eye(size)\n true_x = jr.normal(getkey(), (size,))\n if has_tag(tags, lx.positive_semidefinite_tag):\n matrix = matrix.T @ matrix\n b = matrix @ true_x\n return matrix, true_x, b\n\n\ndef test_solvers(vmap_size, mat_size):\n for lx_name, jax_name, _lx_solver, jax_solver, tags in named_solvers:\n lx_solver = ft.partial(base_wrapper, solver=_lx_solver)\n if vmap_size == 1:\n if isinstance(_lx_solver, (lx.CG, lx.GMRES, lx.BiCGStab)):\n matrix, true_x, b = create_easy_iterative_problem(mat_size, tags)\n else:\n matrix, true_x, b = create_problem(lx_solver, tags, size=mat_size)\n else:\n if isinstance(_lx_solver, (lx.CG, lx.GMRES, lx.BiCGStab)):\n matrix, true_x, b = eqx.filter_vmap(\n create_easy_iterative_problem,\n axis_size=vmap_size,\n out_axes=eqx.if_array(0),\n )(mat_size, tags)\n else:\n matrix, true_x, b = create_problem(lx_solver, tags, size=mat_size)\n _create_problem = ft.partial(create_problem, size=mat_size)\n matrix, true_x, b = eqx.filter_vmap(\n _create_problem, axis_size=vmap_size, out_axes=eqx.if_array(0)\n )(lx_solver, tags)\n\n lx_solver = jax.vmap(lx_solver)\n if jax_solver is not None:\n jax_solver = jax.vmap(jax_solver)\n\n lx_solver = jax.jit(lx_solver)\n bench_lx = ft.partial(lx_solver, matrix, b)\n\n if vmap_size == 1:\n batch_msg = \"problem\"\n else:\n batch_msg = f\"batch of {vmap_size} problems\"\n\n lx_soln = bench_lx()\n if tree_allclose(lx_soln, true_x, atol=1e-4, rtol=1e-4):\n lx_solve_time = timeit.timeit(bench_lx, number=1)\n\n print(\n f\"Lineax's {lx_name} solved {batch_msg} of \"\n f\"size {mat_size} in {lx_solve_time} seconds.\"\n )\n else:\n fail_time = timeit.timeit(bench_lx, number=1)\n err = jnp.abs(lx_soln - true_x).max()\n print(\n f\"Lineax's {lx_name} failed to solve {batch_msg} of \"\n f\"size {mat_size} with error {err} in {fail_time} seconds\"\n )\n if jax_solver is None:\n print(\"JAX has no equivalent solver. \\n\")\n\n else:\n jax_solver = jax.jit(jax_solver)\n bench_jax = ft.partial(jax_solver, matrix, b)\n jax_soln = bench_jax()\n if tree_allclose(jax_soln, true_x, atol=1e-4, rtol=1e-4):\n jax_solve_time = timeit.timeit(bench_jax, number=1)\n print(\n f\"JAX's {jax_name} solved {batch_msg} of \"\n f\"size {mat_size} in {jax_solve_time} seconds. \\n\"\n )\n else:\n fail_time = timeit.timeit(bench_jax, number=1)\n err = jnp.abs(jax_soln - true_x).max()\n print(\n f\"JAX's {jax_name} failed to solve {batch_msg} of \"\n f\"size {mat_size} with error {err} in {fail_time} seconds. \\n\"\n )\n\n\nfor vmap_size, mat_size in [(1, 50), (1000, 50)]:\n test_solvers(vmap_size, mat_size)\n"
},
{
"path": "docs/.htaccess",
"content": "ErrorDocument 404 /jaxtyping/404.html\n"
},
{
"path": "docs/_overrides/partials/source.html",
"content": "{% import \"partials/language.html\" as lang with context %}\n\n