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https://github.com/technologicat/pylu

Small nogil-compatible linear equation system solver
https://github.com/technologicat/pylu

cython linear-equations numerical numpy python python2 python27 python3 python34 solver

Last synced: 27 days ago
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Small nogil-compatible linear equation system solver

Host: GitHub
URL: https://github.com/technologicat/pylu
Owner: Technologicat
License: bsd-2-clause
Created: 2017-04-07T12:47:33.000Z (over 7 years ago)
Default Branch: master
Last Pushed: 2017-04-25T12:59:00.000Z (over 7 years ago)
Last Synced: 2024-10-15T02:05:02.059Z (about 1 month ago)
Topics: cython, linear-equations, numerical, numpy, python, python2, python27, python3, python34, solver
Language: Python
Homepage:
Size: 123 KB
Stars: 0
Watchers: 3
Forks: 0
Open Issues: 0
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE.md

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README

# PyLU

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

## 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:

```python
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 [`pylu_test.py`](test/pylu_test.py).

The main item of interest, however, is the Cython API in [`dgesv.pxd`](pylu/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`](pylu/dgesv.pyx) for examples on how to do this in NumPy.

## Installation

### From PyPI

Install as user:

```bash
pip install pylu --user
```

Install as admin:

```bash
sudo pip install pylu
```

### From GitHub

As user:

```bash
git clone https://github.com/Technologicat/pylu.git
cd pylu
python setup.py install --user
```

As admin, change the last command to

```bash
sudo python setup.py install
```

## Dependencies

- [NumPy](http://www.numpy.org)
- [Cython](http://www.cython.org)

## License

#### Acknowledgement

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