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