# 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:

```
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`

.

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

Install as user:

`pip install pylu --user`

Install as admin:

`sudo pip install pylu`

### From GitHub

As user:

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

As admin, change the last command to

`sudo python setup.py install`

## Dependencies

## License

BSD. Copyright 2016-2017 Juha Jeronen and University of Jyväskylä.

#### Acknowledgement

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