pylu 1.0.0

Small nogil-compatible linear equation system solver

PyLU

Small nogil-compatible Cython-based solver for linear equation systems A x = b.

We use semantic versioning.

For my stance on AI contributions, see the collaboration guidelines.

Introduction

The algorithm is LU decomposition with partial pivoting (row swaps). The code requires only NumPy and Cython.

The main use case for PyLU (over numpy.linalg.solve) is solving many small systems inside a nogil block in Cython code, without requiring SciPy (for its cython_lapack module).

Python and Cython interfaces are provided. The API is designed to be as simple to use as possible.

The arrays are stored using the C memory layout.

A rudimentary banded solver is also provided, based on detecting the band structure (if any) from the initial full LU decomposition. For cases where L and U have small bandwidth, this makes the O(n**2) solve step run faster. The LU decomposition still costs O(n**3), so this is useful only if the system is small, and the same matrix is needed for a large number of different RHS vectors. (This can be the case e.g. in integration of ODE systems with a constant-in-time mass matrix.)

Examples

Basic usage:

import numpy as np
import pylu

A = np.random.random( (5,5) )
b = np.random.random( 5 )

x = pylu.solve( A, b )

For a complete tour, see the test suite.

The main item of interest, however, is the Cython API in dgesv.pxd. The main differences to the Python API are:

• Function names end with _c.
• Explicit sizes must be provided, since the arrays are accessed via raw pointers.
• The result array x must be allocated by the caller, and passed in as an argument. See dgesv.pyx for examples on how to do this in NumPy.

Installation

From PyPI

pip install pylu

From source

git clone https://github.com/Technologicat/pylu.git
cd pylu
pip install .

For maximum performance on your machine, build with architecture-specific optimizations:

CFLAGS="-march=native" pip install --no-build-isolation .

Pre-built wheels from PyPI use generic -O2 because -march=native bakes in the instruction set of the build machine — a wheel built with AVX-512 would crash on a CPU without it. Building from source avoids this and lets the compiler target your specific hardware.

Development setup

PyLU uses meson-python as its build backend and PDM for dependency management.

git clone https://github.com/Technologicat/pylu.git
cd pylu
pdm install
pip install --no-build-isolation -e .

The --no-build-isolation flag is required for editable installs with meson-python. Normally pip builds in a temporary isolated venv, but meson-python's editable mode needs the build dependencies (Cython, NumPy, meson) to remain available in the environment for on-import rebuilds.

Note on editable installs: meson-python editable installs rebuild the Cython extension on import via a redirect .pth file. After modifying .pyx or .pxd files, re-run pip install --no-build-isolation -e . to rebuild. Alternatively, use a non-editable install (pip install .) and reinstall after changes.

Dependencies

• NumPy ≥ 1.25
• Cython ≥ 3.0 (build-time only)

Requires Python ≥ 3.11.

License

BSD. Copyright 2016–2026 Juha Jeronen, University of Jyväskylä, and JAMK University of Applied Sciences.

Acknowledgement

This work was financially supported by the Jenny and Antti Wihuri Foundation.