unilinalg
Linear algebra for Python — dense and sparse matrices, the classic decompositions (LU, Cholesky, QR, SVD, symmetric eigenpairs), 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 3.10–3.14. 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, Matrix.symmetric_eigen |
| 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.
Links
- Source, Nim API, C ABI, and design records: https://github.com/lituus-lab/UniLinalg
- Issues: https://github.com/lituus-lab/UniLinalg/issues
- License: Apache-2.0
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.
1 maintainer
Metadata
1 maintainer
Release files for unilinalg 1.1.0
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