trueskill/tests/Numerics/MatrixTest.php

<?php namespace DNW\Skills\Tests\Numerics;

use DNW\Skills\Numerics\IdentityMatrix;
use DNW\Skills\Numerics\Matrix;
use DNW\Skills\Numerics\SquareMatrix;
use DNW\Skills\Tests\TestCase;

class MatrixTest extends TestCase
{
    public function testTwoByTwoDeterminant()
    {
        $a = new SquareMatrix(1, 2,
                              3, 4);

        $this->assertEquals(-2, $a->getDeterminant());

        $b = new SquareMatrix(3, 4,
                              5, 6);

        $this->assertEquals(-2, $b->getDeterminant());

        $c = new SquareMatrix(1, 1,
                              1, 1);

        $this->assertEquals(0, $c->getDeterminant());

        $d = new SquareMatrix(12, 15,
                              17, 21);

        $this->assertEquals(12 * 21 - 15 * 17, $d->getDeterminant());
    }

    public function testThreeByThreeDeterminant()
    {
        $a = new SquareMatrix(1, 2, 3,
                              4, 5, 6,
                              7, 8, 9);

        $this->assertEquals(0, $a->getDeterminant());

        $pi = new SquareMatrix(3, 1, 4,
                               1, 5, 9,
                               2, 6, 5);

        // Verified against http://www.wolframalpha.com/input/?i=determinant+%7B%7B3%2C1%2C4%7D%2C%7B1%2C5%2C9%7D%2C%7B2%2C6%2C5%7D%7D
        $this->assertEquals(-90, $pi->getDeterminant());
    }

    public function testFourByFourDeterminant()
    {
        $a = new SquareMatrix( 1,  2,  3,  4,
                               5,  6,  7,  8,
                               9, 10, 11, 12,
                              13, 14, 15, 16);

        $this->assertEquals(0, $a->getDeterminant());

        $pi = new SquareMatrix(3, 1, 4, 1,
                               5, 9, 2, 6,
                               5, 3, 5, 8,
                               9, 7, 9, 3);

        // Verified against http://www.wolframalpha.com/input/?i=determinant+%7B+%7B3%2C1%2C4%2C1%7D%2C+%7B5%2C9%2C2%2C6%7D%2C+%7B5%2C3%2C5%2C8%7D%2C+%7B9%2C7%2C9%2C3%7D%7D
        $this->assertEquals(98, $pi->getDeterminant());
    }

    public function testEightByEightDeterminant()
    {
        $a = new SquareMatrix( 1,  2,  3,  4,  5,  6,  7,  8,
                               9, 10, 11, 12, 13, 14, 15, 16,
                              17, 18, 19, 20, 21, 22, 23, 24,
                              25, 26, 27, 28, 29, 30, 31, 32,
                              33, 34, 35, 36, 37, 38, 39, 40,
                              41, 42, 32, 44, 45, 46, 47, 48,
                              49, 50, 51, 52, 53, 54, 55, 56,
                              57, 58, 59, 60, 61, 62, 63, 64);

        $this->assertEquals(0, $a->getDeterminant());

        $pi = new SquareMatrix(3, 1, 4, 1, 5, 9, 2, 6,
                               5, 3, 5, 8, 9, 7, 9, 3,
                               2, 3, 8, 4, 6, 2, 6, 4,
                               3, 3, 8, 3, 2, 7, 9, 5,
                               0, 2, 8, 8, 4, 1, 9, 7,
                               1, 6, 9, 3, 9, 9, 3, 7,
                               5, 1, 0, 5, 8, 2, 0, 9,
                               7, 4, 9, 4, 4, 5, 9, 2);

        // Verified against http://www.wolframalpha.com/input/?i=det+%7B%7B3%2C1%2C4%2C1%2C5%2C9%2C2%2C6%7D%2C%7B5%2C3%2C5%2C8%2C9%2C7%2C9%2C3%7D%2C%7B2%2C3%2C8%2C4%2C6%2C2%2C6%2C4%7D%2C%7B3%2C3%2C8%2C3%2C2%2C7%2C9%2C5%7D%2C%7B0%2C2%2C8%2C8%2C4%2C1%2C9%2C7%7D%2C%7B1%2C6%2C9%2C3%2C9%2C9%2C3%2C7%7D%2C%7B5%2C1%2C0%2C5%2C8%2C2%2C0%2C9%7D%2C%7B7%2C4%2C9%2C4%2C4%2C5%2C9%2C2%7D%7D
        $this->assertEquals(1378143, $pi->getDeterminant());
    }

    public function testEquals()
    {
        $a = new SquareMatrix(1, 2,
                              3, 4);

        $b = new SquareMatrix(1, 2,
                              3, 4);

        $this->assertTrue($a->equals($b));

        $c = Matrix::fromRowsColumns(2, 3,
                                     1, 2, 3,
                                     4, 5, 6);

        $d = Matrix::fromRowsColumns(2, 3,
                                     1, 2, 3,
                                     4, 5, 6);

        $this->assertTrue($c->equals($d));

        $e = Matrix::fromRowsColumns(3, 2,
                                     1, 4,
                                     2, 5,
                                     3, 6);

        $f = $e->getTranspose();
        $this->assertTrue($d->equals($f));

        // Test rounding (thanks to nsp on GitHub for finding this case)
        $g = new SquareMatrix(1, 2.00000000000001,
                              3, 4);

        $h = new SquareMatrix(1, 2,
                              3, 4);

        $this->assertTrue($g->equals($h));
    }

    public function testAdjugate()
    {
        // From Wikipedia: http://en.wikipedia.org/wiki/Adjugate_matrix
        $a = new SquareMatrix(1, 2,
                              3, 4);

        $b = new SquareMatrix( 4, -2,
                              -3,  1);

        $this->assertTrue($b->equals($a->getAdjugate()));


        $c = new SquareMatrix(-3, 2, -5,
                              -1, 0, -2,
                               3, -4, 1);

        $d = new SquareMatrix(-8, 18, -4,
                              -5, 12, -1,
                               4, -6,  2);

        $this->assertTrue($d->equals($c->getAdjugate()));
    }

    public function testInverse()
    {
        // see http://www.mathwords.com/i/inverse_of_a_matrix.htm
        $a = new SquareMatrix(4, 3,
                              3, 2);

        $b = new SquareMatrix(-2,  3,
                               3, -4);

        $aInverse = $a->getInverse();
        $this->assertTrue($b->equals($aInverse));

        $identity2x2 = new IdentityMatrix(2);

        $aaInverse = Matrix::multiply($a, $aInverse);
        $this->assertTrue($identity2x2->equals($aaInverse));

        $c = new SquareMatrix(1, 2, 3,
                              0, 4, 5,
                              1, 0, 6);

        $cInverse = $c->getInverse();
        $d = Matrix::scalarMultiply((1.0 / 22), new SquareMatrix(24, -12, -2,
                                                                  5,   3, -5,
                                                                 -4,   2,  4));


        $this->assertTrue($d->equals($cInverse));
        $identity3x3 = new IdentityMatrix(3);

        $ccInverse = Matrix::multiply($c, $cInverse);
        $this->assertTrue($identity3x3->equals($ccInverse));
    }
}