php-ml/tests/Phpml/Math/LinearAlgebra/EigenDecompositionTest.php

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<?php
declare(strict_types=1);
namespace Phpml\Tests\Math\LinearAlgebra;
use Phpml\Math\LinearAlgebra\EigenvalueDecomposition;
use Phpml\Math\Matrix;
use PHPUnit\Framework\TestCase;
class EigenDecompositionTest extends TestCase
{
public function testSymmetricMatrixEigenPairs(): void
{
// Acceptable error
$epsilon = 0.001;
// First a simple example whose result is known and given in
// http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf
$matrix = [
[0.616555556, 0.615444444],
[0.614444444, 0.716555556],
];
$knownEigvalues = [0.0490833989, 1.28402771];
$knownEigvectors = [[-0.735178656, 0.677873399], [-0.677873399, -0.735178656]];
$decomp = new EigenvalueDecomposition($matrix);
$eigVectors = $decomp->getEigenvectors();
$eigValues = $decomp->getRealEigenvalues();
$this->assertEquals($knownEigvalues, $eigValues, '', $epsilon);
$this->assertEquals($knownEigvectors, $eigVectors, '', $epsilon);
// Secondly, generate a symmetric square matrix
// and test for A.v=λ.v
//
// (We, for now, omit non-symmetric matrices whose eigenvalues can be complex numbers)
$len = 3;
$A = array_fill(0, $len, array_fill(0, $len, 0.0));
2017-09-02 19:41:06 +00:00
$seed = microtime(true) * 1000;
srand((int) $seed);
for ($i = 0; $i < $len; ++$i) {
for ($k = 0; $k < $len; ++$k) {
if ($i > $k) {
$A[$i][$k] = $A[$k][$i];
} else {
$A[$i][$k] = random_int(0, 10);
}
}
}
$decomp = new EigenvalueDecomposition($A);
$eigValues = $decomp->getRealEigenvalues();
$eigVectors = $decomp->getEigenvectors();
foreach ($eigValues as $index => $lambda) {
$m1 = new Matrix($A);
$m2 = (new Matrix($eigVectors[$index]))->transpose();
// A.v=λ.v
$leftSide = $m1->multiply($m2)->toArray();
$rightSide = $m2->multiplyByScalar($lambda)->toArray();
$this->assertEquals($leftSide, $rightSide, '', $epsilon);
}
}
}