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Replace array_search with floating-point filter in Eigenvector::eigenvectors #473

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Merged
markrogoyski merged 2 commits into from
Nov 8, 2023
Merged

Replace array_search with floating-point filter in Eigenvector::eigenvectors #473

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32f8bff
Test Eigenvectors can handle numerical imprecision
Aweptimum Nov 7, 2023
163c0f9
Replace array_search with floating-point filter
Aweptimum Nov 6, 2023
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11 changes: 9 additions & 2 deletions src/LinearAlgebra/Eigenvector.php
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Original file line number Diff line number Diff line change
Expand Up @@ -2,6 +2,7 @@

namespace MathPHP\LinearAlgebra;

use MathPHP\Arithmetic;
use MathPHP\Exception;
use MathPHP\Exception\MatrixException;
use MathPHP\Functions\Map\Single;
Expand Down Expand Up @@ -66,8 +67,14 @@ public static function eigenvectors(NumericMatrix $A, array $eigenvalues = []):
foreach ($eigenvalues as $eigenvalue) {
// If this is a duplicate eigenvalue, and this is the second instance, the first
// pass already found all the vectors.
$key = \array_search($eigenvalue, \array_column($solution_array, 'eigenvalue'));
if (!$key) {
$key = false;
foreach (\array_column($solution_array, 'eigenvalue') as $i => $v) {
if (Arithmetic::almostEqual($v, $eigenvalue, $A->getError())) {
$key = $i;
break;
}
}
if ($key === false) {
$Iλ = MatrixFactory::identity($number)->scalarMultiply($eigenvalue);
$T = $A->subtract($Iλ);

Expand Down
57 changes: 57 additions & 0 deletions tests/LinearAlgebra/Eigen/EigenvectorTest.php
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Expand Up @@ -131,6 +131,63 @@ public function dataProviderForEigenvector(): array
];
}

/**
* @test eigenvector can handle numerical precision errors
* @dataProvider dataProviderForPerturbedEigenvalues
* @param array $A
* @param array $E
* @param array $S
*/
public function testEigenvectorsPerturbedEigenvalues(array $A, array $E, array $S)
{
// Perturb E
foreach ($E as $i => $component) {
$E[$i] = $component + (random_int(-1, 1) * 10**-12);
}

// Given
$A = MatrixFactory::create($A);
$S = MatrixFactory::create($S);

// When
$eigenvectors = Eigenvector::eigenvectors($A, $E);

// Then
$this->assertEqualsWithDelta($S, $eigenvectors, 0.0001);
}

public function dataProviderForPerturbedEigenvalues(): array
{
return [
[ // Matrix has duplicate eigenvalues. One vector is on an axis.
[
[2, 0, 1],
[2, 1, 2],
[3, 0, 4],
],
[5, 1, 1],
[
[1 / \sqrt(14), 0, \M_SQRT1_2],
[2 / \sqrt(14), 1, 0],
[3 / \sqrt(14), 0, -1 * \M_SQRT1_2],
]
],
[ // Matrix has duplicate eigenvalues. no solution on the axis
[
[2, 2, -3],
[2, 5, -6],
[3, 6, -8],
],
[-3, 1, 1],
[
[1 / \sqrt(14), 1 / \M_SQRT3, 5 / \sqrt(42)],
[2 / \sqrt(14), 1 / \M_SQRT3, -4 / \sqrt(42)],
[3 / \sqrt(14), 1 / \M_SQRT3, -1 / \sqrt(42)],
]
],
];
}

/**
* @test eigenvectors throws a BadDataException when the matrix is not square
*/
Expand Down