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MatrixTest.php
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<?php
namespace Tensor\Tests;
use Tensor\Tensor;
use Tensor\Vector;
use Tensor\Matrix;
use Tensor\Special;
use Tensor\ArrayLike;
use Tensor\Algebraic;
use Tensor\Arithmetic;
use Tensor\Comparable;
use Tensor\Statistical;
use Tensor\ColumnVector;
use Tensor\Trigonometric;
use Tensor\Reductions\REF;
use Tensor\Reductions\RREF;
use Tensor\Decompositions\LU;
use Tensor\Decompositions\SVD;
use Tensor\Decompositions\Eigen;
use Tensor\Decompositions\Cholesky;
use PHPUnit\Framework\TestCase;
use Generator;
/**
* @covers \Tensor\Matrix
*/
class MatrixTest extends TestCase
{
/**
* The maximum error tolerated due to varying numerical precision.
*
* @var float
*/
protected const MAX_DELTA = 1e-8;
/**
* @test
*/
public function build() : void
{
$matrix = Matrix::build([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$this->assertInstanceOf(Matrix::class, $matrix);
$this->assertInstanceOf(Tensor::class, $matrix);
$this->assertInstanceOf(ArrayLike::class, $matrix);
$this->assertInstanceOf(Arithmetic::class, $matrix);
$this->assertInstanceOf(Comparable::class, $matrix);
$this->assertInstanceOf(Algebraic::class, $matrix);
$this->assertInstanceOf(Trigonometric::class, $matrix);
$this->assertInstanceOf(Statistical::class, $matrix);
$this->assertInstanceOf(Special::class, $matrix);
}
/**
* @test
*/
public function identity() : void
{
$matrix = Matrix::identity(4);
$expected = Matrix::quick([
[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1],
]);
$this->assertEquals($expected, $matrix);
}
/**
* @test
*/
public function zeros() : void
{
$matrix = Matrix::zeros(2, 4);
$expected = Matrix::quick([
[0, 0, 0, 0],
[0, 0, 0, 0],
]);
$this->assertEquals($expected, $matrix);
}
/**
* @test
*/
public function ones() : void
{
$matrix = Matrix::ones(4, 2);
$expected = Matrix::quick([
[1, 1],
[1, 1],
[1, 1],
[1, 1],
]);
$this->assertEquals($expected, $matrix);
}
/**
* @test
*/
public function diagonal() : void
{
$matrix = Matrix::diagonal([0, 1, 4, 5]);
$expected = Matrix::quick([
[0, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 4, 0],
[0, 0, 0, 5],
]);
$this->assertEquals($expected, $matrix);
}
/**
* @test
*/
public function fill() : void
{
$matrix = Matrix::fill(5, 4, 4);
$expected = Matrix::quick([
[5, 5, 5, 5],
[5, 5, 5, 5],
[5, 5, 5, 5],
[5, 5, 5, 5],
]);
$this->assertEquals($expected, $matrix);
}
/**
* @test
*/
public function rand() : void
{
$matrix = Matrix::rand(4, 4);
$this->assertCount(16, $matrix);
}
/**
* @test
*/
public function gaussian() : void
{
$matrix = Matrix::gaussian(3, 3);
$this->assertCount(9, $matrix);
}
/**
* @test
*/
public function poisson() : void
{
$matrix = Matrix::poisson(6, 4, 2.);
$this->assertCount(24, $matrix);
}
/**
* @test
*/
public function uniform() : void
{
$matrix = Matrix::uniform(3, 3);
$this->assertCount(9, $matrix);
}
/**
* @test
*/
public function shape() : void
{
$matrix = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$this->assertEquals([3, 3], $matrix->shape());
}
/**
* @test
*/
public function shapeString() : void
{
$matrix = Matrix::quick([
[22, -17, 12, 16],
[4, 11, -2, 18],
]);
$this->assertEquals('2 x 4', $matrix->shapeString());
}
/**
* @test
* @dataProvider isSquareProvider
*
* @param Matrix $matrix
* @param bool $expected
*/
public function isSquare(Matrix $matrix, $expected) : void
{
$this->assertEquals($expected, $matrix->isSquare());
}
/**
* @return Generator<mixed[]>
*/
public function isSquareProvider() : Generator
{
yield [
Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]),
true,
];
yield [
Matrix::quick([
[22, -17, 12, 16],
[4, 11, -2, 18],
]),
false,
];
}
/**
* @test
*/
public function size() : void
{
$matrix = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$this->assertEquals(9, $matrix->size());
}
/**
* @test
*/
public function m() : void
{
$matrix = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$this->assertEquals(3, $matrix->m());
}
/**
* @test
*/
public function n() : void
{
$matrix = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$this->assertEquals(3, $matrix->n());
}
/**
* @test
*/
public function rowAsVector() : void
{
$a = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$b = $a->rowAsVector(1);
$expected = Vector::quick([4, 11, -2]);
$this->assertEquals($expected, $b);
}
/**
* @test
*/
public function columnAsVector() : void
{
$a = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$b = $a->columnAsVector(1);
$expected = ColumnVector::quick([-17, 11, -6]);
$this->assertEquals($expected, $b);
}
/**
* @test
*/
public function diagonalAsVector() : void
{
$a = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$b = $a->diagonalAsVector();
$expected = Vector::quick([22, 11, -9]);
$this->assertEquals($expected, $b);
}
/**
* @test
*/
public function asArray() : void
{
$matrix = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$expected = [
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
];
$this->assertEquals($expected, $matrix->asArray());
}
/**
* @test
*/
public function asVectors() : void
{
$matrix = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$vectors = $matrix->asVectors();
$expected = [
Vector::quick([22, -17, 12]),
Vector::quick([4, 11, -2]),
Vector::quick([20, -6, -9]),
];
$this->assertEquals($expected, $vectors);
}
/**
* @test
*/
public function asColumnVectors() : void
{
$matrix = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$vectors = $matrix->asColumnVectors();
$expected = [
ColumnVector::quick([22, 4, 20]),
ColumnVector::quick([-17, 11, -6]),
ColumnVector::quick([12, -2, -9]),
];
$this->assertEquals($expected, $vectors);
}
/**
* @test
*/
public function flatten() : void
{
$a = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$b = $a->flatten();
$expected = Vector::quick([22, -17, 12, 4, 11, -2, 20, -6, -9]);
$this->assertEquals($expected, $b);
}
/**
* @test
*/
public function transpose() : void
{
$a = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$b = $a->transpose();
$expected = Matrix::quick([
[22, 4, 20],
[-17, 11, -6],
[12, -2, -9],
]);
$this->assertEquals($expected, $b);
}
/**
* @test
*/
public function inverse() : void
{
$a = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]);
$b = $a->inverse();
$expected = Matrix::quick([
[0.02093549603923048, 0.042436816295737464, 0.018483591097698978],
[0.0007544322897019996, 0.08261033572236892, -0.017351942663145988],
[0.04602036967182196, 0.03923047906450396, -0.05846850245190495],
]);
$this->assertEqualsWithDelta($expected, $b, self::MAX_DELTA);
}
/**
* @test
* @requires extension tensor
*/
public function pseudoinverse() : void
{
$a = Matrix::quick([
[22, -17, 12],
[4, 11, -2],
]);
$b = $a->pseudoinverse();
$expected = Matrix::quick([
[0.03147992432205172, 0.05583000490505223],
[-0.009144418751313844, 0.07003713825239999],
[0.01266554551187723, -0.0031357298016957483],
]);
$this->assertEqualsWithDelta($expected, $b, self::MAX_DELTA);
}
/**
* @test
*/
public function det() : void
{
$a = Matrix::quick([
[4, 6, -12],
[1, 3, 5],
[-10, -1, 14],
]);
$this->assertEqualsWithDelta(-544.0, $a->det(), self::MAX_DELTA);
}
/**
* @test
*/
public function trace() : void
{
$a = Matrix::quick([
[4, 6, -12],
[1, 3, 5],
[-10, -1, 14],
]);
$this->assertEquals(21.0, $a->trace());
}
/**
* @test
* @dataProvider symmetricProvider
*
* @param Matrix $matrix
* @param bool $expected
*/
public function symmetric(Matrix $matrix, $expected) : void
{
$this->assertEquals($expected, $matrix->symmetric());
}
/**
* @return Generator<mixed[]>
*/
public function symmetricProvider() : Generator
{
yield [
Matrix::quick([
[22, -17, 12],
[4, 11, -2],
[20, -6, -9],
]),
false,
];
yield [
Matrix::quick([
[1, 5, 2],
[5, 1, 3],
[2, 3, 1],
]),
true,
];
}
/**
* @test
*/
public function rank() : void
{
$a = Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]);
$this->assertEquals(3, $a->rank());
}
/**
* @test
*/
public function fullRank() : void
{
$a = Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]);
$this->assertTrue($a->fullRank());
}
/**
* @test
*/
public function reciprocal() : void
{
$a = Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]);
$b = $a->reciprocal();
$expected = Matrix::quick([
[0.045454545454545456, -0.058823529411764705, 0.08333333333333333],
[0.25, 0.09090909090909091, -0.5],
[0.05, -0.16666666666666666, -0.1111111111111111],
]);
$this->assertEqualsWithDelta($expected, $b, self::MAX_DELTA);
}
/**
* @test
*/
public function map() : void
{
$a = Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]);
$sign = function ($value) {
return $value >= 0.0 ? 1 : -1;
};
$b = $a->map($sign);
$expected = Matrix::quick([
[1, -1, 1],
[1, 1, -1],
[1, -1, -1],
]);
$this->assertEquals($expected, $b);
}
/**
* @test
*/
public function ref() : void
{
$matrix = Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]);
$ref = $matrix->ref();
$a = Matrix::quick([
[22, -17, 12],
[0, 14.09090909090909, -4.181818181818182],
[0, 0, -17.10322580645161],
]);
$expected = new REF($a, 0);
$this->assertEqualsWithDelta($expected, $ref, self::MAX_DELTA);
}
/**
* @test
*/
public function rref() : void
{
$matrix = Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]);
$rref = $matrix->rref();
$a = Matrix::quick([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1],
]);
$expected = new RREF($a);
$this->assertEqualsWithDelta($expected, $rref, self::MAX_DELTA);
}
/**
* @test
*/
public function lu() : void
{
$matrix = Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]);
$lu = $matrix->lu();
$l = Matrix::quick([
[1.0, 0, 0],
[0.18181818181818182, 1.0, 0],
[0.9090909090909091, 0.6709677419354838, 1.0],
]);
$u = Matrix::quick([
[22, -17, 12],
[0, 14.09090909090909, -4.181818181818182],
[0, 0, -17.10322580645161],
]);
$p = Matrix::quick([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1],
]);
$expected = new LU($l, $u, $p);
$this->assertEqualsWithDelta($expected, $lu, self::MAX_DELTA);
}
/**
* @test
*/
public function cholesky() : void
{
$matrix = Matrix::quick([
[2, -1, 0],
[-1, 2, -1],
[0, -1, 2],
]);
$cholesky = $matrix->cholesky();
$l = Matrix::quick([
[1.4142135623730951, 0, 0],
[-0.7071067811865475, 1.224744871391589, 0],
[0, -0.8164965809277261, 1.1547005383792515],
]);
$expected = new Cholesky($l);
$this->assertEqualsWithDelta($expected, $cholesky, self::MAX_DELTA);
}
/**
* @test
* @requires extension tensor
* @dataProvider eigProvider
*
* @param Matrix $matrix
* @param Eigen $expected
*/
public function eig(Matrix $matrix, Eigen $expected) : void
{
$eig = $matrix->eig(false);
$this->assertEqualsWithDelta($expected, $eig, self::MAX_DELTA);
}
/**
* @return Generator<mixed[]>
*/
public function eigProvider() : Generator
{
yield [
Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]),
new Eigen(
[
-15.096331148319537, 25.108706520450326, 13.9876246278692,
],
Matrix::quick([
[0.25848694820886425, -0.11314537870318066, -0.9593657388523845],
[-0.8622719261400653, -0.17721179605718698, -0.47442924101375483],
[-0.6684472200177011, -0.6126879076802705, -0.42165369894378907],
])
),
];
}
/**
* @test
* @requires extension tensor
*/
public function eigSymmetric() : void
{
$matrix = Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]);
$eig = $matrix->matmul($matrix)->eig(true);
$values = [-366.30071669298195, 335.92000012383926, 1084.3807165691428];
$vectors = Matrix::quick([
[0.5423765325213931, 0.8162941265260668, -0.19872492538460218],
[-0.04667292577741032, 0.26544998308386847, 0.9629942598375911],
[-0.8388380862654284, 0.5130304137961217, -0.1820726765627782],
]);
$expected = new Eigen($values, $vectors);
$this->assertEqualsWithDelta($expected, $eig, self::MAX_DELTA);
}
/**
* @test
* @requires extension tensor
*/
public function svd() : void
{
$matrix = Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]);
$svd = $matrix->svd();
$u = Matrix::quick([
[-0.8436018806559158, 0.4252547343454771, -0.3278631999333884],
[0.08179499775610413, -0.5016868397437385, -0.8611735557772425],
[-0.5307027843302525, -0.7533052009276842, 0.38844025146657923],
]);
$singularValues = [
34.66917512262571, 17.12630582468919, 8.929610580306822,
];
$vT = Matrix::quick([
[-0.8320393250771425, 0.531457514846513, -0.15894486917903863],
[-0.4506078135544562, -0.48043370238236727, 0.7524201326246152],
[-0.3235168618307952, -0.6976649392999047, -0.6392186422366096],
]);
$expected = new SVD($u, $singularValues, $vT);
$this->assertEqualsWithDelta($expected, $svd, self::MAX_DELTA);
}
/**
* @test
*/
public function matmul() : void
{
$a = Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]);
$b = Matrix::quick([
[13],
[11],
[9],
]);
$c = $a->matmul($b);
$expected = Matrix::quick([
[207], [155], [113],
]);
$this->assertEqualsWithDelta($expected, $c, self::MAX_DELTA);
}
/**
* @test
*/
public function dotVector() : void
{
$a = Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]);
$b = Vector::quick([2, 10, -1]);
$c = $a->dot($b);
$expected = ColumnVector::quick([-138, 120, -11]);
$this->assertEqualsWithDelta($expected, $c, self::MAX_DELTA);
}
/**
* @test
*/
public function convolve() : void
{
$a = Matrix::quick([
[3, 27, 66, 29, 42, 5],
[5, 9, 15, 42, 45, 16],
[1, 5, 10, 22, 66, 5],
[0, 1, 4, 9, 10, 22, 2],
[0, 0, 3, 19, 21, 25],
[0, 0, 0, 5, 2, 33, 35],
]);
$b = Matrix::quick([
[0, 0, 1],
[0, 1, 0],
[1, 0, 0],
]);
$c = $a->convolve($b, 1);
$expected = Matrix::quick([
[3, 32, 75, 44, 84, 50],
[32, 76, 49, 94, 72, 82],
[10, 20, 53, 71, 91, 15],
[5, 11, 26, 78, 34, 43],
[1, 4, 12, 29, 48, 27],
[0, 3, 19, 26, 27, 33],
]);
$this->assertEqualsWithDelta($expected, $c, self::MAX_DELTA);
}
/**
* @test
* @dataProvider multiplyProvider
*
* @param Matrix $a
* @param Tensor|float $b
* @param Tensor|float $expected
*/
public function multiply(Matrix $a, $b, $expected) : void
{
$c = $a->multiply($b);
$this->assertEqualsWithDelta($expected, $c, self::MAX_DELTA);
}
/**
* @return Generator<mixed[]>
*/
public function multiplyProvider() : Generator
{
yield [
Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]),
Matrix::quick([
[4, 6, -12],
[1, 3, 5],
[-10, -1, 14],
]),
Matrix::quick([
[88, -102, -144],
[4, 33, -10],
[-200, 6, -126],
]),
];
yield [
Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]),
Vector::quick([2, 10, -1]),
Matrix::quick([
[44, -170, -12],
[8, 110, 2],
[40, -60, 9],
]),
];
yield [
Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]),
ColumnVector::quick([2.5, -1, 4.8]),
Matrix::quick([
[55.0, -42.5, 30.],
[-4, -11, 2],
[96.0, -28.799999999999997, -43.199999999999996],
]),
];
yield [
Matrix::quick([
[22.0, -17.0, 12.0],
[4.0, 11.0, -2.0],
[20.0, -6.0, -9.0],
]),
2.5,
Matrix::quick([
[55, -42.5, 30],
[10.0, 27.5, -5.],
[50, -15, -22.5],
]),
];
}
/**
* @test
* @dataProvider divideProvider