PowerIteration

Implementation of the Power Iteration method for finding (dominant) eigenvalues and the corresponding eigenvectors of a matrix, using the excellent math-php library.

Installation

Install using composer:

$ composer require aboks/power-iteration

Basic usage

<?php
use Aboks\PowerIteration\PowerIteration;
use MathPHP\LinearAlgebra\MatrixFactory;

$power_iteration = new PowerIteration();
$dominant_eigenpair = $power_iteration->getDominantEigenpair(MatrixFactory::create([
    [2, 1],
    [0, 1]
 ]));
var_dump($dominant_eigenpair->getEigenvalue()); // 2
var_dump($dominant_eigenpair->getEigenvector()); // Vector([1, 0]), or a scalar multiple

Advanced usage

Calculating the least dominant eigenpair

In most situations, one is interested in the dominant eigenvalue and its corresponding eigenvector. It is also possible to calculate the least dominant eigenpair however:

<?php
use Aboks\PowerIteration\PowerIteration;
use MathPHP\LinearAlgebra\Matrix;

$power_iteration = new PowerIteration();
$dominant_eigenpair = $power_iteration->getLeastDominantEigenpair(MatrixFactory::create([
    [2, 1],
    [0, 1]
 ]));
var_dump($dominant_eigenpair->getEigenvalue()); // 1
var_dump($dominant_eigenpair->getEigenvector()); // Vector([√2, -√2]), or a scalar multiple

Customizations

Stopping criterion

By default, the power iteration runs for 1000 iterations. The stopping criterion can be altered by passing an instance of StoppingCriterion as the first argument to PowerIteration:

<?php
use Aboks\PowerIteration\PowerIteration;
use Aboks\PowerIteration\StoppingCriterion\MaxIterations;
use Aboks\PowerIteration\StoppingCriterion\EigenvectorTolerance;

new PowerIteration(new MaxIterations(10));           // will stop after 10 iterations
new PowerIteration(new EigenvectorTolerance(0.01));  // will stop when ‖Av - λv‖ < 0.01

Scaling method

To prevent overflow in case of very large eigenvalues (or underflow in case of small eigenvalues), the eigenvector estimates are scaled/normalized after each iteration. The final eigenvector estimate is also scaled using the same method. By default, the estimates are scaled to a unit vector based on the L2-norm. To use a different method, provide an instance of ScalingMethod as a second argument to PowerIteration:

<?php
use Aboks\PowerIteration\PowerIteration;
use Aboks\PowerIteration\ScalingMethod\NormBased;
use Aboks\PowerIteration\Norm\MaxNorm;

new PowerIteration(null, new NormBased(new MaxNorm()));  // will scale to a unit vector based on the max-norm

Running tests

After installing dependencies (including development dependencies) using Composer, run

$ ./vendor/bin/phpunit

from the project root dir.

Contributing

Contributions to this library are very welcome! Please make sure that your changes have sufficient test coverage, and that the code follows PSR-2.

Versioning

This project adheres to Semantic Versioning.

License

The code is released under the MIT license.