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markrogoyskimarkrogoyski
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Add unit tests.
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‎tests/LinearAlgebra/Decomposition/LUTest.php‎

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@@ -494,6 +494,167 @@ public function dataProviderForLuDecomposition(): array
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[0, 1, 0, 0],
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],
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],
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// Near-singular matrix with very small determinant
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[
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[
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[1.0, 2.0, 3.0],
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[4.0, 5.0, 6.0],
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[7.0, 8.0, 9.00001]
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],
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[
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[1, 0, 0],
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[0.14285714, 1, 0],
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[0.57142857, 0.5, 1]
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],
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[
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[7.0, 8.0, 9.00001],
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[0, 0.857142857, 1.71428429],
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[0, 0, -5.0e-6]
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],
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[
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[0, 0, 1],
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[1, 0, 0],
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[0, 1, 0]
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]
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],
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// Near-singular 2x2 matrix
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[
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[
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[2.0, 4.0],
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[1.0, 2.00001]
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],
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[
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[1, 0],
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[0.5, 1]
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],
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[
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[2, 4],
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[0, 1.0E-5]
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],
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[
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[1, 0],
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[0, 1]
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]
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],
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// Hilbert matrix (ill-conditioned)
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[
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[
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[1.0, 0.5, 0.3333333333],
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[0.5, 0.3333333333, 0.25],
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[0.3333333333, 0.25, 0.2]
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],
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[
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[1.0, 0, 0],
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[0.5, 1.0, 0],
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[0.3333333333, 1, 1]
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],
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[
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[1.0, 0.5, 0.3333333333],
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[0, 0.08333333, 0.08333333335],
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[0, 0, 0.00555556]
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],
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[
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[1, 0, 0],
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[0, 1, 0],
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[0, 0, 1]
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]
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],
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// Diagonally dominant 3x3
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[
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[
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[10.0, 1.0, 2.0],
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[1.0, 15.0, 3.0],
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[2.0, 1.0, 20.0]
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],
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[
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[1, 0, 0],
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[0.1, 1, 0],
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[0.2, 0.05369128, 1]
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],
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[
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[10.0, 1, 2],
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[0, 14.9, 2.8],
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[0, 0, 19.44966443]
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],
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[
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[1, 0, 0],
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[0, 1, 0],
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[0, 0, 1]
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]
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],
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// Diagonally dominant 4x4
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[
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[
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[20.0, 1.0, 2.0, 3.0],
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[1.0, 25.0, 2.0, 1.0],
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[2.0, 1.0, 30.0, 2.0],
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[3.0, 1.0, 2.0, 35.0]
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],
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[
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[1, 0, 0, 0],
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[0.05, 1, 0, 0],
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[0.1, 0.03607214, 1, 0],
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[0.15, 0.03406814, 0.05500135, 1]
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],
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[
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[20, 1, 2, 3],
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[0, 24.95, 1.9, 0.85],
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[0, 0, 29.73146293, 1.66933868],
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[0, 0, 0, 34.42922621]
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],
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[
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[1, 0, 0, 0],
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[0, 1, 0, 0],
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[0, 0, 1, 0],
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[0, 0, 0, 1]
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]
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],
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// Numerical stability test - large and small numbers
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[
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[
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[1000000.0, 0.000001, 1.0],
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[0.000001, 1000000.0, 1.0],
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[1.0, 1.0, 1000000.0]
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],
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[
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[1, 0, 0],
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[0, 1, 0],
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[0.000001, 1.e-06, 1]
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],
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[
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[1000000, 0.000001, 1],
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[0, 1000000, 1],
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[0, 0, 1.e+06]
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],
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[
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[1, 0, 0],
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[0, 1, 0],
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[0, 0, 1]
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]
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],
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// Numerical stability test - moderate scaling
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[
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[
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[100.0, 0.01, 1.0],
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[0.01, 100.0, 1.0],
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[1.0, 1.0, 100.0]
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],
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[
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[1, 0, 0],
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[0.0001, 1.0, 0],
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[0.01, 0.0099990001, 1]
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],
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[
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[100, 0.01, 1],
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[0, 99.999999, 0.9999],
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[0, 0, 99.980002]
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],
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[
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[1, 0, 0],
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[0, 1, 0],
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[0, 0, 1]
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]
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],
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];
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}
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@@ -562,4 +723,53 @@ public function testLUDecompositionSolveIncorrectTypeError()
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// When
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$LU->solve($b);
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}
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/**
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* @test Permutation matrix verification - P should be orthogonal
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* @dataProvider dataProviderForLUDecomposition
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* @param array $A
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* @throws \Exception
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*/
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public function testPermutationMatrixProperties(array $A)
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{
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// Given
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$A = MatrixFactory::create($A);
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// When
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$LU = $A->luDecomposition();
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// Then - P should be orthogonal (P * P^T = I)
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$P = $LU->P;
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$PT = $P->transpose();
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$PxPT = $P->multiply($PT);
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$I = MatrixFactory::identity($A->getN());
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$this->assertEqualsWithDelta($I->getMatrix(), $PxPT->getMatrix(), 0.0001);
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// And - determinant should be ±1
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$det = abs($P->det());
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$this->assertEqualsWithDelta(1.0, $det, 0.0001);
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}
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/**
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* @test Round-trip accuracy test - solve Ax=b, then verify A*x ≈ b
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* @dataProvider dataProviderForSolve
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* @param array $A
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* @param array $b
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* @throws \Exception
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*/
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public function testRoundTripAccuracy(array $A, array $b)
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{
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// Given
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$A = MatrixFactory::create($A);
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$b_vec = new Vector($b);
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$LU = $A->luDecomposition();
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// When
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$x = $LU->solve($b);
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// Then - A*x should equal b
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$A_times_x = $A->multiply($x);
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$this->assertEqualsWithDelta($b_vec->getVector(), $A_times_x->getColumn(0), 0.0001);
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}
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}

‎tests/LinearAlgebra/Fixture/MatrixDataProvider.php‎

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Original file line numberDiff line numberDiff line change
@@ -5095,6 +5095,37 @@ public function dataProviderForSolve(): array
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[1, 1],
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[1, 0],
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],
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// 3x3 system
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[
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[
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[4, -1, 2],
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[2, 5, -3],
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[-1, 2, 6]
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],
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[7, 1, 8],
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[1.2046783625730995, 0.5321637426900584, 1.3567251461988303]
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],
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// 4x4 system
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[
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[
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[5, 1, 2, 1],
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[1, 4, 1, 2],
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[2, 1, 6, 1],
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[1, 2, 1, 5]
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],
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[12, 11, 16, 13],
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[1.1128608923884515, 1.2598425196850391, 1.8346456692913384, 1.5065616797900263]
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],
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// Diagonally dominant system
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[
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[
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[10, 1, 1],
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[1, 12, 1],
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[1, 1, 15]
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],
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[20, 25, 30],
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[1.643059490084986, 1.7988668555240792, 1.7705382436260622]
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]
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];
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}
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