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
xmust be allocated by the caller, and passed in as an argument. Seedgesv.pyxfor 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 # creates venv, installs dev deps
pip install --no-build-isolation -e . # editable install (needs venv activated)
The --no-build-isolation flag is required for editable installs with meson-python — the on-import rebuild mechanism needs build dependencies (Cython, NumPy, meson, ninja) to remain available in the environment, not just in a throwaway build-time overlay.
PATH note: The meson-python editable loader needs meson and ninja on PATH. If you get rebuild errors, ensure the venv's bin/ is on the path:
export PATH="$(pwd)/.venv/bin:$PATH"
Note on editable installs: After modifying .pyx or .pxd files, the next import auto-rebuilds the Cython extension — no manual reinstall step needed. For a clean non-editable build, use pip install . and reinstall after changes.
Dependencies
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.
1 maintainer
Metadata
1 maintainer
Release files for pylu 1.1.0
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