unilinalg

Linear algebra for Python — dense and sparse matrices, the classic decompositions (LU, Cholesky, QR, SVD), and fixed-dimension geometric vectors, backed by the native UniLinalg library.

UniLinalg factors and solves through LU with partial pivoting, Cholesky for symmetric positive-definite systems, Householder QR for least squares, and one-sided Jacobi SVD. Matrix.solve's optional refine=True runs one UniAccurate-backed iterative refinement step to recover the last few ULP a plain float64 solve can miss — the other three decompositions don't expose this option through the Python API. CSR sparse matrices cover the mostly-zero case; Vec2/Vec3/Vec4 cover fixed-dimension geometry, distinct from the runtime-sized Matrix.

Install

pip install unilinalg

Prebuilt wheels include the native UniLinalg library for Linux, macOS, and Windows on CPython 3.9–3.14. Installing a wheel needs neither Nim nor a C compiler.

Quick start

import unilinalg

a = unilinalg.Matrix.from_rows([[1.0, 2.0, 1.0],
                                 [2.0, 1.0, 3.0],
                                 [1.0, 1.0, 1.0]])
a.solve([8.0, 13.0, 6.0])                # [1.0000000000000007, 2.0, 2.9999999999999996]
a.solve([8.0, 13.0, 6.0], refine=True)   # [1.0, 2.0, 3.0] -- exact with refinement

spd = unilinalg.Matrix.from_rows([[4.0, 2.0], [2.0, 3.0]])
spd.cholesky().to_rows()                 # [[2.0, 0.0], [1.0, 1.4142135623730951]]

diag = unilinalg.Matrix.from_rows([[2.0, 0.0], [0.0, 5.0]])
u, s, v = diag.svd()
s                                        # [5.0, 2.0]

dense = unilinalg.Matrix.from_rows([[5.0, 0.0, 0.0],
                                     [0.0, 8.0, 3.0],
                                     [0.0, 6.0, 0.0]])
sparse = dense.to_sparse()
sparse.nnz                               # 4
sparse.matvec([1.0, 2.0, 3.0])           # [5.0, 25.0, 12.0]

x, y = unilinalg.Vec3(1.0, 0.0, 0.0), unilinalg.Vec3(0.0, 1.0, 0.0)
x.cross(y)                               # Vec3(0.0, 0.0, 1.0)
unilinalg.Vec2(3.0, 4.0).length          # 5.0

What's included

Category	Python API
Dense matrix	`Matrix` -- construction, indexing, `+`/`-`/`@`/`*`, `transpose`, `almost_equal`
Linear solve	`Matrix.solve` (LU, partial pivoting), `Matrix.determinant`
Decompositions	`Matrix.cholesky`, `Matrix.qr`, `Matrix.svd`
Accurate refinement	`refine=True` on `solve` -- one UniAccurate-backed correction step
Sparse matrix	`Sparse` (CSR) -- `Matrix.to_sparse`, `Sparse.to_dense`, `Sparse.matvec`, `Sparse.nnz`
Fixed-dimension vectors	`Vec2`, `Vec3`, `Vec4` -- arithmetic, `dot`, `length`, `normalize`; `Vec3.cross`; `Vec2.cross2d`/`perp`/`perp_cw`

A numeric-looking element is coerced through float(...), same as a plain Python list of numbers would be — but a singular matrix, a shape mismatch, or a genuinely non-numeric component raises ValueError/TypeError rather than returning a wrong-shaped or silently wrong result.

For an executable tour of the API, see the Python quickstart notebook.

Development

Building from source (contributing, or a platform without a prebuilt wheel) needs a Nim toolchain.

nimble pyLib   # native lib for this platform
cd py
python3 setup.py build_ext --inplace   # build the Cython extension
python3 -m pytest -q                   # test

On Windows, use python instead of python3 (PowerShell and cmd.exe both resolve it; python3 is a POSIX-only convention):

nimble pyLib
cd py
python setup.py build_ext --inplace
python -m pytest -q

Run the build before the test in every case: pytest imports the unilinalg package straight out of this checkout, so it only finds the _core extension once build_ext --inplace has compiled it.

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unilinalg 1.0.0

unilinalg

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