news_producer/vendor/markrogoyski/math-php/tests/Number/ComplexTest.php

<?php

namespace MathPHP\Tests\Number;

use MathPHP\Number\Complex;
use MathPHP\Exception;
use MathPHP\Number\ObjectArithmetic;

class ComplexTest extends \PHPUnit\Framework\TestCase
{
    /**
     * @test Interfaces
     */
    public function testObjectArithmeticInterface()
    {
        // Given
        $c = new Complex(1, 2);

        // Then
        $this->assertInstanceOf(ObjectArithmetic::class, $c);
    }

    public function testZeroValue()
    {
        // Given
        $c = Complex::createZeroValue();

        // Then
        $this->assertEquals(0, $c->r);
        $this->assertEquals(0, $c->i);
    }

    /**
     * @test         __toString returns the proper string representation of a complex number
     * @dataProvider dataProviderForToString
     * @param        number $r
     * @param        number $i
     * @param        string $expected
     */
    public function testToString($r, $i, string $expected)
    {
        // Given
        $complex = new Complex($r, $i);

        // When
        $string = $complex->__toString();

        // Then
        $this->assertEquals($expected, $string);
        $this->assertEquals($expected, (string) $complex);
    }

    public function dataProviderForToString(): array
    {
        return [
            [0, 0, '0'],
            [1, 0, '1'],
            [-1, 0, '-1'],
            [0, 1, '1i'],
            [0, -1, '-1i'],
            [1, 1, '1 + 1i'],
            [1, 2, '1 + 2i'],
            [2, 1, '2 + 1i'],
            [2, 2, '2 + 2i'],
            [1, -1, '1 - 1i'],
            [1, -2, '1 - 2i'],
            [2, -1, '2 - 1i'],
            [2, -2, '2 - 2i'],
            [-1, 1, '-1 + 1i'],
            [-1, 2, '-1 + 2i'],
            [-2, 1, '-2 + 1i'],
            [-2, 2, '-2 + 2i'],
            [-1, -1, '-1 - 1i'],
            [-1, -2, '-1 - 2i'],
            [-2, -1, '-2 - 1i'],
            [-2, -2, '-2 - 2i'],
        ];
    }

    /**
     * @test __get returns r and i
     */
    public function testGet()
    {
        // Given
        $r       = 1;
        $i       = 2;
        $complex = new Complex($r, $i);

        // Then
        $this->assertEquals($r, $complex->r);
        $this->assertEquals($i, $complex->i);
    }

    /**
     * @test __get throws an Exception\BadParameterException if a property other than r or i is attempted
     */
    public function testGetException()
    {
        // Given
        $r       = 1;
        $i       = 2;
        $complex = new Complex($r, $i);

        // Then
        $this->expectException(Exception\BadParameterException::class);

        // When
        $z = $complex->z;
    }

    /**
     * @test         complexConjugate returns the expected Complex number
     * @dataProvider dataProviderForComplexConjugate
     * @param        number $r
     * @param        number $i
     */
    public function testComplexConjugate($r, $i)
    {
        // Given
        $c = new Complex($r, $i);

        // When
        $cc = $c->complexConjugate();

        // Then
        $this->assertEquals($c->r, $cc->r);
        $this->assertEquals($c->i, -1 * $cc->i);
    }

    public function dataProviderForComplexConjugate(): array
    {
        return [
            [0, 0],
            [1, 0],
            [0, 1],
            [1, 1],
            [1, 2],
            [3, 7],
        ];
    }

    /**
     * @test         abs returns the expected value
     * @dataProvider dataProviderForAbs
     * @param        number $r
     * @param        number $i
     * @param        number $expected
     */
    public function testAbs($r, $i, $expected)
    {
        // Given
        $c = new Complex($r, $i);

        // When
        $abs = $c->abs();

        // Then
        $this->assertEquals($expected, $abs);
    }

    public function dataProviderForAbs(): array
    {
        return [
            [0, 0, 0],
            [1, 0, 1],
            [0, 1, 1],
            [1, 2, \sqrt(5)],
            [2, 1, \sqrt(5)],
            [2, 2, \sqrt(8)],
            [-1, 0, 1],
            [0, -1, 1],
            [-1, 2, \sqrt(5)],
            [2, -1, \sqrt(5)],
            [-2, -2, \sqrt(8)],
        ];
    }

    /**
     * @test         arg returns the expected value
     * @dataProvider dataProviderForArg
     * @param        number $r
     * @param        number $i
     * @param        number $expected
     */
    public function testArg($r, $i, $expected)
    {
        // Given
        $c = new Complex($r, $i);

        // When
        $arg = $c->arg();

        // Then
        $this->assertEqualsWithDelta($expected, $arg, 0.00000001);
    }

    public function dataProviderForArg(): array
    {
        return [
            [0, 1, \M_PI / 2],
            [0, -1, \M_PI / -2],
            [1, 1, 0.7853981633974483],
            [2, 2, 0.7853981633974483],
            [3, 3, 0.7853981633974483],
            [1, 2, 1.1071487177940904],
            [2, 1, 0.4636476090008061],
            [3, 1.4, 0.4366271598135413],
            [\M_PI, 1, 0.30816907111598496],
            [1, \M_PI, 1.2626272556789115],
            [-1, 1, 2.356194490192345],
            [1, -1, -0.78539816],
            [-1, -1, -2.35619449],
        ];
    }

    /**
     * @test         sqrt returns the expected positive Complex root
     * @dataProvider dataProviderForSqrt
     * @param        number $r
     * @param        number $i
     * @param        number $expected_r
     * @param        number $expected_i
     */
    public function testSqrt($r, $i, $expected_r, $expected_i)
    {
        // Given
        $c = new Complex($r, $i);

        // When
        $sqrt = $c->sqrt();

        // Then
        $this->assertEqualsWithDelta($expected_r, $sqrt->r, 0.00001);
        $this->assertEqualsWithDelta($expected_i, $sqrt->i, 0.00001);
    }

    public function dataProviderForSqrt(): array
    {
        return [
            [8, -6, 3, -1],
            [9, 4, \sqrt((9 + \sqrt(97)) / 2), 2 * (sqrt(2 / (9 + \sqrt(97))))],
            [-4, -6, 1.2671, -2.3676],
            [0, 9, 2.1213203, 2.1213203],
            [10, -6, 3.2910412, -0.9115656],
            [-4, 0, 0, 2],
            [-3, 0, 0, 1.7320508],
            [-2, 0, 0, 1.4142136],
            [-1, 0, 0, 1],
            [0, 0, 0, 0],
        ];
    }

    /**
     * @test         roots returns the expected array of two Complex roots
     * @dataProvider dataProviderForRoots
     * @param        number $r
     * @param        number $i
     * @param        array  $z₁
     * @param        array  $z₂
     */
    public function testRoots($r, $i, array $z₁, array $z₂)
    {
        // Given
        $c = new Complex($r, $i);

        // When
        $roots = $c->roots();

        // Then
        $this->assertEqualsWithDelta($z₁['r'], $roots[0]->r, 0.00001);
        $this->assertEqualsWithDelta($z₁['i'], $roots[0]->i, 0.00001);
        $this->assertEqualsWithDelta($z₂['r'], $roots[1]->r, 0.00001);
        $this->assertEqualsWithDelta($z₂['i'], $roots[1]->i, 0.00001);
    }

    public function dataProviderForRoots(): array
    {
        return [
            [8, -6, ['r' => 3, 'i' => -1], ['r' => -3, 'i' => 1]],
            [9, 4, ['r' => \sqrt((9 + \sqrt(97)) / 2), 'i' => 2 * (sqrt(2 / (9 + \sqrt(97))))], ['r' => -sqrt((9 + \sqrt(97)) / 2), 'i' => -2 * (sqrt(2 / (9 + \sqrt(97))))]],
            [-4, -6, ['r' => 1.2671, 'i' => -2.3676], ['r' => -1.2671, 'i' => 2.3676]],
            [0, 9, ['r' => 2.1213203, 'i' => 2.1213203], ['r' => -2.1213203, 'i' => -2.1213203]],
            [10, -6, ['r' => 3.2910412, 'i' => -0.9115656], ['r' => -3.2910412, 'i' => 0.9115656]],
            [3, 3, ['r' => 1.90298, 'i' => 0.78824], ['r' => -1.90298, 'i' => -0.78824]],
            [-4, 0, ['r' => 0, 'i' => 2], ['r' => 0, 'i' => -2]],
            [-3, 0, ['r' => 0, 'i' => 1.7320508], ['r' => 0, 'i' => -1.7320508]],
            [-2, 0, ['r' => 0, 'i' => 1.4142136], ['r' => 0, 'i' => -1.4142136]],
            [-1, 0, ['r' => 0, 'i' => 1], ['r' => 0, 'i' => -1]],
            [0, 0, ['r' => 0, 'i' => 0], ['r' => 0, 'i' => -0]],
        ];
    }

    /**
     * @test         negate returns the expected complex number with signs negated
     * @dataProvider dataProviderForNegate
     * @param        number $r₁
     * @param        number $i₁
     * @param        number $r₂
     * @param        number $i₂
     */
    public function testNegate($r₁, $i₁, $r₂, $i₂)
    {
        // Given
        $c        = new Complex($r₁, $i₁);
        $expected = new Complex($r₂, $i₂);

        // When
        $negated = $c->negate();

        // Then
        $this->assertTrue($negated->equals($expected));
        $this->assertEquals($expected->r, $negated->r);
        $this->assertEquals($expected->i, $negated->i);
    }

    public function dataProviderForNegate(): array
    {
        return [
            [0, 0, 0, 0],
            [1, 0, -1, 0],
            [0, 1, 0, -1],
            [1, 2, -1, -2],
            [3, 4, -3, -4],
            [-4, -5, 4, 5],
            [-6, 3, 6, -3],
        ];
    }

    /**
     * @test         polarForm returns the expected complex number
     * @dataProvider dataProviderForPolarForm
     * @param        number $r
     * @param        number $i
     * @param        number $expectedR
     * @param        number $expectedθ
     */
    public function testPolarForm($r, $i, $expectedR, $expectedθ)
    {
        // Given
        $c = new Complex($r, $i);

        // When
        [$polarR, $polarθ] = $c->polarForm();

        // Then
        $this->assertEqualsWithDelta($expectedR, $polarR, 0.00001);
        $this->assertEqualsWithDelta($expectedθ, $polarθ, 0.00001);
    }

    /**
     * Test data created with: http://www.analyzemath.com/Calculators/complex_polar_exp.html
     * Python: cmath.polar(complex(5, 2))
     * @return array
     */
    public function dataProviderForPolarForm(): array
    {
        return [
            [5, 2, 5.385164807134504, 0.3805063771123649],
            [49.90, 25.42, 56.00166426098424, 0.4711542560514266],
            [-1, -1, 1.4142135623730951, -2.356194490192345],
            [1, 0, 1, 0],
            [0, 1, 1, 1.5707963267948966],
            [0, 0, 0, 0],
            [\M_PI, 2, 3.724191778237173, 0.5669115049410094],
            [8, 9, 12.041594578792296, 0.844153986113171],
            [814, -54, 815.7891884549587, -0.06624200592698481],
            [-5, -3, 5.830951894845301, -2.601173153319209],
        ];
    }

    /**
     * @test         exp returns the expected complex number
     * @dataProvider dataProviderForExp
     * @param        number $r₁
     * @param        number $i₁
     * @param        number $r₂
     * @param        number $i₂
     */
    public function testExp($r₁, $i₁, $r₂, $i₂)
    {
        // Given
        $c        = new Complex($r₁, $i₁);
        $expected = new Complex($r₂, $i₂);

        // When
        $exp = $c->exp();

        // Then
        $this->assertEqualsWithDelta($expected->r, $exp->r, 0.00001);
        $this->assertEqualsWithDelta($expected->i, $exp->i, 0.00001);
    }

    /**
     * Test data created from wolfram alpha: example: https://www.wolframalpha.com/input/?i=e%5E%281%2B2*i%29
     * @return array
     */
    public function dataProviderForExp(): array
    {
        return [
            [0, \pi(), -1, 0],
            [1, 2, -1.13120438375681363843125525551079471062886799582652575021772191, 2.47172667200481892761693089355166453273619036924100818420075883],
            [5, 0, \exp(5), 0],
        ];
    }

    /**
     * @test         add of two complex numbers returns the expected complex number
     * @dataProvider dataProviderForAdd
     * @param        array  $complex1
     * @param        array  $complex2
     * @param        array  $expected
     */
    public function testAdd(array $complex1, array $complex2, array $expected)
    {
        // Given
        $c1 = new Complex($complex1['r'], $complex1['i']);
        $c2 = new Complex($complex2['r'], $complex2['i']);

        // When
        $result = $c1->add($c2);

        // Then
        $this->assertEquals($expected['r'], $result->r);
        $this->assertEquals($expected['i'], $result->i);
    }

    public function dataProviderForAdd(): array
    {
        return [
            [
                ['r' => 3, 'i' => 2],
                ['r' => 4, 'i' => -3],
                ['r' => 7, 'i' => -1],
            ],
            [
                ['r' => 0, 'i' => 0],
                ['r' => 4, 'i' => -3],
                ['r' => 4, 'i' => -3],
            ],
            [
                ['r' => -3, 'i' => -2],
                ['r' => 4, 'i' => 3],
                ['r' => 1, 'i' => 1],
            ],
            [
                ['r' => 7, 'i' => 6],
                ['r' => 4, 'i' => 4],
                ['r' => 11, 'i' => 10],
            ],
        ];
    }

    /**
     * @test         add of real numbers returns the expected complex number
     * @dataProvider dataProviderForAddReal
     */
    public function testAddReal($complex, $real, $expected)
    {
        // Given
        $c = new Complex($complex['r'], $complex['i']);

        // When
        $result = $c->add($real);

        // Then
        $this->assertEquals($expected['r'], $result->r);
        $this->assertEquals($expected['i'], $result->i);
    }

    public function dataProviderForAddReal()
    {
        return [
            [
                ['r' => 3, 'i' => 2],
                5,
                ['r' => 8, 'i' => 2],
            ],
            [
                ['r' => 0, 'i' => 0],
                5,
                ['r' => 5, 'i' => 0],
            ],
            [
                ['r' => 3, 'i' => 2],
                -2,
                ['r' => 1, 'i' => 2],
            ],
        ];
    }

    /**
     * @test         subtract of two complex numbers returns the expected complex number
     * @dataProvider dataProviderForSubtract
     * @param        array  $complex1
     * @param        array  $complex2
     * @param        array  $expected
     */
    public function testSubtract(array $complex1, array $complex2, array $expected)
    {
        // Given
        $c1 = new Complex($complex1['r'], $complex1['i']);
        $c2 = new Complex($complex2['r'], $complex2['i']);

        // When
        $result = $c1->subtract($c2);

        // Then
        $this->assertEquals($expected['r'], $result->r);
        $this->assertEquals($expected['i'], $result->i);
    }

    public function dataProviderForSubtract(): array
    {
        return [
            [
                ['r' => 3, 'i' => 2],
                ['r' => 4, 'i' => -3],
                ['r' => -1, 'i' => 5],
            ],
            [
                ['r' => 3, 'i' => 2],
                ['r' => 4, 'i' => -3],
                ['r' => -1, 'i' => 5],
            ],
            [
                ['r' => 0, 'i' => 0],
                ['r' => 4, 'i' => -3],
                ['r' => -4, 'i' => 3],
            ],
            [
                ['r' => -3, 'i' => -2],
                ['r' => 4, 'i' => 3],
                ['r' => -7, 'i' => -5],
            ],
            [
                ['r' => 7, 'i' => 6],
                ['r' => 4, 'i' => 4],
                ['r' => 3, 'i' => 2],
            ],
        ];
    }


    /**
     * @test         subtract of real numbers returns the expected complex number
     * @dataProvider dataProviderForSubtractReal
     */
    public function testSubtractReal($complex, $real, $expected)
    {
        // Given
        $c = new Complex($complex['r'], $complex['i']);

        // When
        $result = $c->subtract($real);

        // Then
        $this->assertEquals($expected['r'], $result->r);
        $this->assertEquals($expected['i'], $result->i);
    }

    public function dataProviderForSubtractReal(): array
    {
        return [
            [
                ['r' => 3, 'i' => 2],
                5,
                ['r' => -2, 'i' => 2],
            ],
            [
                ['r' => 0, 'i' => 0],
                5,
                ['r' => -5, 'i' => 0],
            ],
            [
                ['r' => 3, 'i' => 2],
                -2,
                ['r' => 5, 'i' => 2],
            ],
        ];
    }

    /**
     * @test         multiply of two complex numbers returns the expected complex number
     * @dataProvider dataProviderForMultiply
     * @param        array  $complex1
     * @param        array  $complex2
     * @param        array  $expected
     */
    public function testMultiply(array $complex1, array $complex2, array $expected)
    {
        // Given
        $c1 = new Complex($complex1['r'], $complex1['i']);
        $c2 = new Complex($complex2['r'], $complex2['i']);

        // When
        $result = $c1->multiply($c2);

        // Then
        $this->assertEquals($expected['r'], $result->r);
        $this->assertEquals($expected['i'], $result->i);
    }

    public function dataProviderForMultiply(): array
    {
        return [
            [
                ['r' => 3, 'i' => 2],
                ['r' => 1, 'i' => 4],
                ['r' => -5, 'i' => 14],
            ],
            [
                ['r' => 3, 'i' => 13],
                ['r' => 7, 'i' => 17],
                ['r' => -200, 'i' => 142],
            ],
            [
                ['r' => 6, 'i' => 8],
                ['r' => 4, 'i' => -9],
                ['r' => 96, 'i' => -22],
            ],
            [
                ['r' => -56, 'i' => 3],
                ['r' => -84, 'i' => -4],
                ['r' => 4716, 'i' => -28],
            ],
        ];
    }

    /**
     * @test         multiply of real numbers returns the expected complex number
     * @dataProvider dataProviderForMultiplyReal
     */
    public function testMultiplyReal($complex, $real, $expected)
    {
        // Given
        $c = new Complex($complex['r'], $complex['i']);

        // When
        $result = $c->multiply($real);

        // Then
        $this->assertEquals($expected['r'], $result->r);
        $this->assertEquals($expected['i'], $result->i);
    }

    public function dataProviderForMultiplyReal()
    {
        return [
            [
                ['r' => 3, 'i' => 1],
                2,
                ['r' => 6, 'i' => 2],
            ],
            [
                ['r' => 30, 'i' => 13],
                2,
                ['r' => 60, 'i' => 26],
            ],
        ];
    }

    /**
     * @test         divide of two complex numbers returns the expected complex number
     * @dataProvider dataProviderForDivide
     * @param        array  $complex1
     * @param        array  $complex2
     * @param        array  $expected
     */
    public function testDivide(array $complex1, array $complex2, array $expected)
    {
        // Given
        $c1 = new Complex($complex1['r'], $complex1['i']);
        $c2 = new Complex($complex2['r'], $complex2['i']);

        // When
        $result = $c1->divide($c2);

        // Then
        $this->assertEqualsWithDelta($expected['r'], $result->r, 0.00001);
        $this->assertEqualsWithDelta($expected['i'], $result->i, 0.00001);
    }

    public function dataProviderForDivide(): array
    {
        return [
            [
                ['r' => 3, 'i' => 2],
                ['r' => 4, 'i' => -3],
                ['r' => 0.24, 'i' => 0.68],
            ],
            [
                ['r' => 5, 'i' => 5],
                ['r' => 6, 'i' => 2],
                ['r' => 1, 'i' => 1 / 2],
            ],
            [
                ['r' => 6, 'i' => 2],
                ['r' => 7, 'i' => -7],
                ['r' => 2 / 7, 'i' => 4 / 7],
            ],
            [
                ['r' => -56, 'i' => 3],
                ['r' => -84, 'i' => -4],
                ['r' => 69 / 104, 'i' => -7 / 104],
            ],
        ];
    }

    /**
     * @test         divide of real numbers returns the expected complex number
     * @dataProvider dataProviderForDivideReal
     */
    public function testDivideReal($complex, $real, $expected)
    {
        // Given
        $c = new Complex($complex['r'], $complex['i']);

        // When
        $result = $c->divide($real);

        // Then
        $this->assertEquals($expected['r'], $result->r);
        $this->assertEquals($expected['i'], $result->i);
    }

    public function dataProviderForDivideReal()
    {
        return [
            [
                ['r' => 4, 'i' => 1],
                2,
                ['r' => 2, 'i' => 1 / 2],
            ],
            [
                ['r' => 60, 'i' => 9],
                3,
                ['r' => 20, 'i' => 3],
            ],
        ];
    }

    /**
     * @test add throws an Exception\IncorrectTypeException when the argument is not a number or complex number
     */
    public function testComplexAddException()
    {
        // Given
        $complex = new Complex(1, 1);

        // Then
        $this->expectException(Exception\IncorrectTypeException::class);

        // When
        $complex->add("string");
    }

    /**
     * @test subtract throws an Exception\IncorrectTypeException when the argument is not a number or complex number
     */
    public function testComplexSubtractException()
    {
        // Given
        $complex = new Complex(1, 1);

        // Then
        $this->expectException(Exception\IncorrectTypeException::class);

        // When
        $complex->subtract("string");
    }

    /**
     * @test multiply throws an Exception\IncorrectTypeException when the argument is not a number or complex number
     */
    public function testComplexMultiplyException()
    {
        // Given
        $complex = new Complex(1, 1);

        // Then
        $this->expectException(Exception\IncorrectTypeException::class);

        // When
        $complex->multiply("string");
    }

    /**
     * @test divide throws an Exception\IncorrectTypeException when the argument is not a number or complex number
     */
    public function testComplexDivideException()
    {
        // Given
        $complex = new Complex(1, 1);

        // Then
        $this->expectException(Exception\IncorrectTypeException::class);

        // When
        $complex->divide("string");
    }

    /**
     * @test         pow of complex numbers raised to a number returns the expected complex number
     * @dataProvider dataProviderForPowNumber
     * @param        array   $complex1
     * @param        number  $number
     * @param        array   $expected
     */
    public function testPowNumber(array $complex1, $number, array $expected)
    {
        // Given
        $c1 = new Complex($complex1['r'], $complex1['i']);

        // When
        $result = $c1->pow($number);

        // Then
        $this->assertEqualsWithDelta($expected['r'], $result->r, 0.00001);
        $this->assertEqualsWithDelta($expected['i'], $result->i, 0.00001);
    }

    /**
     * https://www.wolframalpha.com/input/?i=%281%2B2*i%29%5E%283%2B4*i%29
     */
    public function dataProviderForPowNumber(): array
    {
        return [
            [
                ['r' => 1, 'i' => 2],
                5,
                ['r' => 41, 'i' => -38],
            ],
            [
                ['r' => 7, 'i' => 13],
                0,
                ['r' => 1, 'i' => 0],
            ],
            [
                ['r' => 0, 'i' => 0],
                0,
                ['r' => 1, 'i' => 0],
            ],
        ];
    }

    /**
     * @test         pow of two complex numbers returns the expected complex number
     * @dataProvider dataProviderForPow
     * @param        array  $complex1
     * @param        array  $complex2
     * @param        array  $expected
     */
    public function testPow(array $complex1, array $complex2, array $expected)
    {
        // Given
        $c1 = new Complex($complex1['r'], $complex1['i']);
        $c2 = new Complex($complex2['r'], $complex2['i']);

        // When
        $result = $c1->pow($c2);

        // Then
        $this->assertEqualsWithDelta($expected['r'], $result->r, 0.00000001);
        $this->assertEqualsWithDelta($expected['i'], $result->i, 0.00000001);
    }

    /**
     * https://www.wolframalpha.com/input/?i=%281%2B2*i%29%5E%283%2B4*i%29
     * R: complex(real=1, imaginary=2)**complex(real=3, imaginary=4)
     * Python: complex(1,2)**complex(3,4)
     */
    public function dataProviderForPow(): array
    {
        return [
            [
                ['r' => 1, 'i' => 2],
                ['r' => 3, 'i' => 4],
                ['r' => 0.12900959407446689407705233965244724409184546447229472777070039, 'i' => 0.033924092905170126697617854622547901540547320222677608399651655],
            ],
            [
                ['r' => 1, 'i' => 2],
                ['r' => 5, 'i' => 0],
                ['r' => 41, 'i' => -38],
            ],
            [
                ['r' => 1, 'i' => 2],
                ['r' => 0, 'i' => 0],
                ['r' => 1, 'i' => 0],
            ],
            [
                ['r' => 2, 'i' => 2],
                ['r' => -2, 'i' => -2],
                ['r' => -0.5251869237872764, 'i' => 0.2928344540350973],
            ],
            [
                ['r' => -2, 'i' => -2],
                ['r' => -2, 'i' => -2],
                ['r' => -9.807565e-04, 'i' => 5.468516e-04],
            ],
            [
                ['r' => 83, 'i' => 24],
                ['r' => 4, 'i' => 6],
                ['r' => -9503538.518957876, 'i' => 3956277.4270916637],
            ],
            [
                ['r' => 2, 'i' => 3],
                ['r' => 4, 'i' => 5],
                ['r' => -0.7530458367485596, 'i' => -0.9864287886477445],
            ],
            [
                ['r' => -2, 'i' => 3],
                ['r' => 4, 'i' => 5],
                ['r' => -0.0027390773950467934, 'i' => 0.0021275418620241996],
            ],
            [
                ['r' => 2, 'i' => -3],
                ['r' => 4, 'i' => 5],
                ['r' => -18175.48769862527, 'i' => 14117.567839250678],
            ],
            [
                ['r' => 2, 'i' => 3],
                ['r' => -4, 'i' => 5],
                ['r' => -3.4315770545555685e-05, 'i' => 2.6654317433786663e-05],
            ],
            [
                ['r' => 2, 'i' => 3],
                ['r' => 4, 'i' => -5],
                ['r' => -18175.48769862527, 'i' => -14117.567839250678],
            ],
            [
                ['r' => 0, 'i' => 0],
                ['r' => 0, 'i' => 0],
                ['r' => 1, 'i' => 0],
            ],
        ];
    }

    /**
     * @test pow IncorrectTypeException
     */
    public function testComplexPowTypeError()
    {
        // Given
        $c = new Complex(1, 2);

        // And
        $nonNumber = 'KaPoW!';

        // Then
        $this->expectException(Exception\IncorrectTypeException::class);

        // When
        $c->pow($nonNumber);
    }

    /**
     * @test         inverse returns the expected complex number
     * @dataProvider dataProviderForInverse
     * @param        number $r
     * @param        number $i
     * @param        number $expected_r
     * @param        number $expected_i
     */
    public function testInverse($r, $i, $expected_r, $expected_i)
    {
        // Given
        $c = new Complex($r, $i);

        // When
        $inverse = $c->inverse();

        // Then
        $this->assertEqualsWithDelta($expected_r, $inverse->r, 0.00001);
        $this->assertEqualsWithDelta($expected_i, $inverse->i, 0.00001);
    }

    public function dataProviderForInverse(): array
    {
        return [
            [1, 0, 1, 0],
            [0, 1, 0, -1],
            [1, 1, 1 / 2, -1 / 2],
            [4, 6, 1 / 13, -3 / 26],
            [-4, 6, -1 / 13, -3 / 26],
            [4, -6, 1 / 13, 3 / 26],
            [-4, -6, -1 / 13, 3 / 26],
        ];
    }

    /**
     * @test inverse throws an Exception\BadDataException when value is 0 + 0i
     */
    public function testInverseException()
    {
        // Given
        $complex = new Complex(0, 0);

        // Then
        $this->expectException(Exception\BadDataException::class);

        // When
        $complex->inverse();
    }

    /**
     * @test         equals returns true if the complex numbers are the same
     * @dataProvider dataProviderForComplexNumbers
     * @param        number $r
     * @param        number $i
     */
    public function testEqualsTrue($r, $i)
    {
        // Given
        $c1 = new Complex($r, $i);
        $c2 = new Complex($r, $i);

        // When
        $isEqual = $c1->Equals($c2);

        // Then
        $this->assertTrue($isEqual);
    }

    /**
     * @test         equals returns false if the complex numbers are different
     * @dataProvider dataProviderForComplexNumbers
     * @param        number $r
     * @param        number $i
     */
    public function testEqualsFalse($r, $i)
    {
        // Given
        $c1 = new Complex($r, $i);
        $c2 = new Complex($r + 1, $i - 1);

        // When
        $isNotEqual = $c1->Equals($c2);

        // Then
        $this->assertFalse($isNotEqual);
    }

    public function dataProviderForComplexNumbers(): array
    {
        return [
            [0, 0],
            [1, 0],
            [0, 1],
            [1, 1],
            [1, 2],
            [2, 1],
            [2, 2],
            [3, 4],
            [5, 3],
            [-1, 0],
            [0, 1],
            [-1, 1],
            [-1, 2],
            [-2, 1],
            [-2, 2],
            [-3, 4],
            [-5, 3],
            [1, 0],
            [0, -1],
            [1, -1],
            [1, -2],
            [2, -1],
            [2, -2],
            [3, -4],
            [5, -3],
            [-1, 0],
            [0, -1],
            [-1, -1],
            [-1, -2],
            [-2, -1],
            [-2, -2],
            [-3, -4],
            [-5, -3],
        ];
    }
}