<?php

namespace MathPHP\Tests\Probability\Distribution\Continuous;

use MathPHP\Probability\Distribution\Continuous\Normal;

class NormalTest extends \PHPUnit\Framework\TestCase
{
    /**
     * @test         pdf
     * @dataProvider dataProviderForPdf
     * @param        float $x
     * @param        float $μ
     * @param        float $σ
     * @param        float $expected_pdf
     */
    public function testPdf(float $μ, float $σ, float $x, float $expected_pdf)
    {
        // Given
        $normal = new Normal($μ, $σ);

        // When
        $pdf = $normal->pdf($x);

        // Then
        $this->assertEquals($expected_pdf, $pdf, '', 0.0000001);
    }

    /**
     * @return array [μ, σ, x, pdf]
     */
    public function dataProviderForPdf(): array
    {
        return [
            [0, 1, 10, 0],
            [0, 1, 6, 1e-8],
            [0, 1, 5, 0.00000149],
            [0, 1, 4, 0.00013383],
            [0, 1, 3, 0.00443185],
            [0, 1, 2, 0.05399097],
            [0, 1, 1.96, 0.05844094],
            [0, 1, 1.5, 0.1295176],
            [0, 1, 1.1, 0.21785218],
            [0, 1, 1, 0.24197072],
            [0, 1, 0.9, 0.26608525],
            [0, 1, 0.8, 0.28969155],
            [0, 1, 0.7, 0.31225393],
            [0, 1, 0.6, 0.3332246],
            [0, 1, 0.5, 0.35206533],
            [0, 1, 0.4, 0.36827014],
            [0, 1, 0.3, 0.38138782],
            [0, 1, 0.2, 0.39104269],
            [0, 1, 0.1, 0.39695255],
            [0, 1, 0, 0.39894228],
            [0, 1, -0.1, 0.39695255],
            [0, 1, -0.5, 0.35206533],
            [0, 1, -1, 0.24197072],
            [0, 1, -1.96, 0.05844094],
            [0, 1, -2, 0.05399097],
            [0, 1, -3, 0.00443185],
            [0, 1, -4, 0.00013383],
            [0, 1, -5, 0.00000149],
            [0, 1, -6, 1e-8],
            [0, 1, -10, 0],

            [1, 1, 10, 0],
            [1, 1, 6, 0.00000149],
            [1, 1, 5, 0.00013383],
            [1, 1, 4, 0.00443185],
            [1, 1, 3, 0.05399097],
            [1, 1, 2, 0.24197072],
            [1, 1, 1.96, 0.25164434],
            [1, 1, 1.5, 0.35206533],
            [1, 1, 1.1, 0.39695255],
            [1, 1, 1, 0.39894228],
            [1, 1, 0.9, 0.39695255],
            [1, 1, 0.8, 0.39104269],
            [1, 1, 0.7, 0.38138782],
            [1, 1, 0.6, 0.36827014],
            [1, 1, 0.5, 0.35206533],
            [1, 1, 0.4, 0.3332246],
            [1, 1, 0.3, 0.31225393],
            [1, 1, 0.2, 0.28969155],
            [1, 1, 0.1, 0.26608525],
            [1, 1, 0, 0.24197072],
            [1, 1, -0.1, 0.21785218],
            [1, 1, -0.5, 0.1295176],
            [1, 1, -1, 0.05399097],
            [1, 1, -1.96, 0.0049929],
            [1, 1, -2, 0.00443185],
            [1, 1, -3, 0.00013383],
            [1, 1, -4, 0.00000149],
            [1, 1, -5, 1e-8],
            [1, 1, -6, 0],
            [1, 1, -10, 0],

            [3.2, 2.8, 10, 0.00746494],
            [3.2, 2.8, 6, 0.08641812],
            [3.2, 2.8, 5, 0.1158811],
            [3.2, 2.8, 4, 0.13678099],
            [3.2, 2.8, 3, 0.14211638],
            [3.2, 2.8, 2, 0.1299774],
            [3.2, 2.8, 1, 0.10463979],
            [3.2, 2.8, 0, 0.07415341],
            [3.2, 2.8, -1, 0.04625628],
            [3.2, 2.8, -2, 0.02539894],
            [3.2, 2.8, -3, 0.01227625],
            [3.2, 2.8, -4, 0.00522302],
            [3.2, 2.8, -5, 0.00195606],
            [3.2, 2.8, -6, 0.00064483],
            [3.2, 2.8, -10, 0.00000213],

            [72, 15.2, 84, 0.01921876],
            [25, 2, 26, 0.17603266338],
        ];
    }

    /**
     * @test         cdf
     * @dataProvider dataProviderForCdf
     * @param        float $x
     * @param        float $μ
     * @param        float $σ
     * @param        float $expected_cdf
     */
    public function testCdf(float $μ, float $σ, float $x, float $expected_cdf)
    {
        // Given
        $normal = new Normal($μ, $σ);

        // When
        $cdf = $normal->cdf($x);

        // Then
        $this->assertEquals($expected_cdf, $cdf, '', 0.0000001);
    }

    /**
     * @return array [μ, σ, x, cdf]
     */
    public function dataProviderForCdf(): array
    {
        return [
            [0, 1, 10, 1],
            [0, 1, 6, 1],
            [0, 1, 5, 0.99999971],
            [0, 1, 4, 0.99996833],
            [0, 1, 3, 0.9986501],
            [0, 1, 2, 0.97724987],
            [0, 1, 1.96, 0.9750021],
            [0, 1, 1.5, 0.9331928],
            [0, 1, 1.1, 0.86433394],
            [0, 1, 1, 0.84134475],
            [0, 1, 0.9, 0.81593987],
            [0, 1, 0.8, 0.7881446],
            [0, 1, 0.7, 0.75803635],
            [0, 1, 0.6, 0.72574688],
            [0, 1, 0.5, 0.69146246],
            [0, 1, 0.4, 0.65542174],
            [0, 1, 0.31, 0.62171952],
            [0, 1, 0.3, 0.61791142],
            [0, 1, 0.2, 0.57925971],
            [0, 1, 0.1, 0.53982784],
            [0, 1, 0.01, 0.50398936],
            [0, 1, 0.02, 0.50797831],
            [0, 1, 0, 0.5],
            [0, 1, -0.1, 0.46017216],
            [0, 1, -0.31, 0.37828048],
            [0, 1, -0.39, 0.34826827],
            [0, 1, -0.5, 0.30853754],
            [0, 1, -1, 0.15865525],
            [0, 1, -1.96, 0.0249979],
            [0, 1, -2, 0.02275013],
            [0, 1, -2.90, 0.00186581],
            [0, 1, -2.96, 0.0015382],
            [0, 1, -3, 0.0013499],
            [0, 1, -3.09, 0.00100078],
            [0, 1, -4, 0.00003167],
            [0, 1, -5, 2.9e-7],
            [0, 1, -6, 0],
            [0, 1, -10, 0],

            [1, 1, 10, 1],
            [1, 1, 6, 0.99999971],
            [1, 1, 5, 0.99996833],
            [1, 1, 4, 0.9986501],
            [1, 1, 3, 0.97724987],
            [1, 1, 2, 0.84134475],
            [1, 1, 1.96, 0.83147239],
            [1, 1, 1.5, 0.69146246],
            [1, 1, 1.1, 0.53982784],
            [1, 1, 1, 0.5],
            [1, 1, 0.9, 0.46017216],
            [1, 1, 0.8, 0.42074029],
            [1, 1, 0.7, 0.38208858],
            [1, 1, 0.6, 0.34457826],
            [1, 1, 0.5, 0.30853754],
            [1, 1, 0.4, 0.27425312],
            [1, 1, 0.3, 0.24196365],
            [1, 1, 0.2, 0.2118554],
            [1, 1, 0.1, 0.18406013],
            [1, 1, 0, 0.15865525],
            [1, 1, -0.1, 0.13566606],
            [1, 1, -0.5, 0.0668072],
            [1, 1, -1, 0.02275013],
            [1, 1, -1.96, 0.0015382],
            [1, 1, -2, 0.0013499],
            [1, 1, -3, 0.00003167],
            [1, 1, -4, 2.9e-7],
            [1, 1, -5, 0],
            [1, 1, -6, 0],
            [1, 1, -10, 0],

            [3.2, 2.8, 10, 0.99242078],
            [3.2, 2.8, 6, 0.84134475],
            [3.2, 2.8, 5, 0.7398416],
            [3.2, 2.8, 4, 0.61245152],
            [3.2, 2.8, 3, 0.47152834],
            [3.2, 2.8, 2, 0.33411757],
            [3.2, 2.8, 1, 0.21601745],
            [3.2, 2.8, 0, 0.12654895],
            [3.2, 2.8, -1, 0.0668072],
            [3.2, 2.8, -2, 0.03164542],
            [3.2, 2.8, -3, 0.01340457],
            [3.2, 2.8, -4, 0.005064],
            [3.2, 2.8, -5, 0.00170262],
            [3.2, 2.8, -6, 0.00050862],
            [3.2, 2.8, -10, 0.00000121],

            [72, 15.2, 84, 0.7850824],
            [25, 2, 26, 0.69146246],
            [5, 1, 6, 0.84134475],
            [25, 14, 39, 0.84134475],
            [4, 0.3, 3.5, 0.04779035],
            [1, 1.1, 1.3, 0.60746857],
        ];
    }

    /**
     * @test         between
     * @dataProvider dataProviderForBetween
     * @param        float $lower
     * @param        float $upper
     * @param        float $μ
     * @param        float $σ
     * @param        float $probability
     */
    public function testBetween(float $lower, float $upper, float $μ, float $σ, float $probability)
    {
        // Given
        $normal = new Normal($μ, $σ);

        // When
        $between = $normal->between($lower, $upper);

        // Then
        $this->assertEquals($probability, $between, '', 0.00001);
    }

    /**
     * @return array [lower, upper, μ, σ, probability]
     */
    public function dataProviderForBetween(): array
    {
        return [
            [ 5, 7, 6, 1, 0.682689492 ],
            [ -1.95996398454005, 1.95996398454005, 0, 1, .95 ],
        ];
    }

    /**
     * @test         outside
     * @dataProvider dataProviderForOutside
     * @param        float $lower
     * @param        float $upper
     * @param        float $μ
     * @param        float $σ
     * @param        float $probability
     */
    public function testOutside(float $lower, float $upper, float $μ, float $σ, float $probability)
    {
        // Given
        $normal = new Normal($μ, $σ);

        // When
        $outside = $normal->outside($lower, $upper);

        // Then
        $this->assertEquals($probability, $outside, '', 0.00001);
    }

    /**
     * @return array [lower, upper, μ, σ, probability]
     */
    public function dataProviderForOutside(): array
    {
        return [
            [ 5, 7, 6, 2, 0.6170750774519740000000000 ],
            [ -1.64485362695147, 1.64485362695147, 0, 1, 0.1 ],
        ];
    }

    /**
     * @test         above
     * @dataProvider dataProviderForAbove
     * @param        float $x
     * @param        float $μ
     * @param        float $σ
     * @param        float $probability
     */
    public function testAbove(float $x, float $μ, float $σ, float $probability)
    {
        // Given
        $normal = new Normal($μ, $σ);

        // When
        $above = $normal->above($x);

        // Then
        $this->assertEquals($probability, $above, '', 0.00001);
    }

    /**
     * @return array [x, μ, σ, probability]
     */
    public function dataProviderForAbove(): array
    {
        return [
            [ 1.64485362695147, 0, 1, 0.05 ],
            [ 1.95996398454005, 6, 2, 0.97830924 ],
        ];
    }

    /**
     * @test         mean
     * @dataProvider dataProviderForMean
     * @param        float μ
     */
    public function testMean(float $μ)
    {
        // Given
        $σ      = 1.5;
        $normal = new Normal($μ, $σ);

        // When
        $mean = $normal->mean();

        // Then
        $this->assertEquals($μ, $mean);
    }

    /**
     * @test         median
     * @dataProvider dataProviderForMean
     * @param        float μ
     */
    public function testMedian(float $μ)
    {
        // Given
        $σ      = 1.5;
        $normal = new Normal($μ, $σ);

        // When
        $median = $normal->median();

        // Then
        $this->assertEquals($μ, $median);
    }

    /**
     * @test         mode
     * @dataProvider dataProviderForMean
     * @param        float μ
     */
    public function testMode(float $μ)
    {
        // Given
        $σ      = 1.5;
        $normal = new Normal($μ, $σ);

        // When
        $mode = $normal->mode();

        // Then
        $this->assertEquals($μ, $mode);
    }

    /**
     * @return array [μ]
     */
    public function dataProviderForMean(): array
    {
        return [
            [-2],
            [-1],
            [0],
            [1],
            [1.3],
            [2],
            [5],
        ];
    }

    /**
     * @test         variance
     * @dataProvider dataProviderForVariance
     * @param        float $μ
     * @param        float $σ
     * @param        float $expected
     */
    public function testVariance(float $μ, float $σ, float $expected)
    {
        // Given
        $normal = new Normal($μ, $σ);

        // When
        $variance = $normal->variance();

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

    /**
     * @return array [μ, σ, var]
     */
    public function dataProviderForVariance(): array
    {
        return [
            [-2, 1, 1],
            [-1, 2, 4],
            [0, 3, 9],
            [1, 4, 16],
            [1.3, 5, 25],
            [2, 6, 36],
        ];
    }

    /**
     * @test         inverse
     * @dataProvider dataProviderForInverse
     * @param        float $x
     * @param        float $μ
     * @param        float $σ
     * @param        float $inverse
     */
    public function testInverse(float $μ, float $σ, float $x, float $inverse)
    {
        $normal = new Normal($μ, $σ);
        $this->assertEquals($inverse, $normal->inverse($x), '', 0.00001);
    }

    /**
     * @return array [μ, σ, x, inverse]
     */
    public function dataProviderForInverse(): array
    {
        return [
            [0, 1, 1, \INF],
            [0, 1, 0.99, 2.32634787],
            [0, 1, 0.9, 1.28155157],
            [0, 1, 0.8, 0.84162123],
            [0, 1, 0.7, 0.52440051],
            [0, 1, 0.6, 0.2533471],
            [0, 1, 0.51, 0.02506891],
            [0, 1, 0.501, 0.00250663],
            [0, 1, 0.500000005, 1e-8],
            [0, 1, 0.50000000005, 0],
            [0, 1, 0.5, 0],
            [0, 1, 0.49999999995, 0],
            [0, 1, 0.499999995, -1e-8],
            [0, 1, 0.499, -0.00250663],
            [0, 1, 0.49, -0.02506891],
            [0, 1, 0.4, -0.2533471],
            [0, 1, 0.3, -0.52440051],
            [0, 1, 0.2, -0.84162123],
            [0, 1, 0.1, -1.28155157],
            [0, 1, 0.01, -2.32634787],
            [0, 1, 0, -\INF],

            [1, 1, 1, \INF],
            [1, 1, 0.99, 3.32634787],
            [1, 1, 0.9, 2.28155157],
            [1, 1, 0.8, 1.84162123],
            [1, 1, 0.7, 1.52440051],
            [1, 1, 0.6, 1.2533471],
            [1, 1, 0.5, 1],
            [1, 1, 0.4, 0.7466529],
            [1, 1, 0.3, 0.47559949],
            [1, 1, 0.2, 0.15837877],
            [1, 1, 0.1, -0.28155157],
            [1, 1, 0.01, -1.32634787],
            [1, 1, 0, -\INF],

            [3.2, 2.8, 1, \INF],
            [3.2, 2.8, 0.99, 9.71377405],
            [3.2, 2.8, 0.9, 6.78834438],
            [3.2, 2.8, 0.8, 5.55653945],
            [3.2, 2.8, 0.7, 4.66832144],
            [3.2, 2.8, 0.6, 3.90937189],
            [3.2, 2.8, 0.5, 3.2],
            [3.2, 2.8, 0.4, 2.49062811],
            [3.2, 2.8, 0.3, 1.73167856],
            [3.2, 2.8, 0.2, 0.84346055],
            [3.2, 2.8, 0.1, -0.38834438],
            [3.2, 2.8, 0.01, -3.31377405],
            [3.2, 2.8, 0, -\INF],

            [-1, 1, 0, -\INF],
            [-1, 1, 0.1, -2.281552],
            [-1, 1, 0.2, -1.841621],
            [-1, 1, 0.3, -1.524401],
            [-1, 1, 0.4, -1.253347],
            [-1, 1, 0.5, -1],
            [-1, 1, 0.6, -0.7466529],
            [-1, 1, 0.7, -0.4755995],
            [-1, 1, 0.8, -0.1583788],
            [-1, 1, 0.9, 0.2815516],
            [-1, 1, 1, \INF],

            [5, 7, 0, -\INF],
            [5, 7, 0.1, -3.970861],
            [5, 7, 0.2, -0.8913486],
            [5, 7, 0.3, 1.329196],
            [5, 7, 0.4, 3.22657],
            [5, 7, 0.5, 5],
            [5, 7, 0.6, 6.77343],
            [5, 7, 0.7, 8.670804],
            [5, 7, 0.8, 10.89135],
            [5, 7, 0.9, 13.97086],
            [5, 7, 1, \INF],
        ];
    }

    /**
     * @test         Inverse of CDF is x
     * @dataProvider dataProviderForInverseOfCdf
     * @param        float $x
     * @param        float $μ
     * @param        float $σ
     */
    public function testInverseOfCdf(float $μ, float $σ, float $x)
    {
        // Given
        $normal = new Normal($μ, $σ);
        $cdf    = $normal->cdf($x);

        // When
        $inverse_of_cdf = $normal->inverse($cdf);

        // Then
        $this->assertEquals($x, $inverse_of_cdf, '', 0.00001);
    }

    /**
     * @return array [μ, σ, x, cdf]
     */
    public function dataProviderForInverseOfCdf(): array
    {
        return [
            [0, 1, 5, 0.99999971],
            [0, 1, 4, 0.99996833],
            [0, 1, 3, 0.9986501],
            [0, 1, 2, 0.97724987],
            [0, 1, 1.96, 0.9750021],
            [0, 1, 1.5, 0.9331928],
            [0, 1, 1.1, 0.86433394],
            [0, 1, 1, 0.84134475],
            [0, 1, 0.9, 0.81593987],
            [0, 1, 0.8, 0.7881446],
            [0, 1, 0.7, 0.75803635],
            [0, 1, 0.6, 0.72574688],
            [0, 1, 0.5, 0.69146246],
            [0, 1, 0.4, 0.65542174],
            [0, 1, 0.31, 0.62171952],
            [0, 1, 0.3, 0.61791142],
            [0, 1, 0.2, 0.57925971],
            [0, 1, 0.1, 0.53982784],
            [0, 1, 0.01, 0.50398936],
            [0, 1, 0.02, 0.50797831],
            [0, 1, 0, 0.5],
            [0, 1, -0.1, 0.46017216],
            [0, 1, -0.31, 0.37828048],
            [0, 1, -0.39, 0.34826827],
            [0, 1, -0.5, 0.30853754],
            [0, 1, -1, 0.15865525],
            [0, 1, -1.96, 0.0249979],
            [0, 1, -2, 0.02275013],
            [0, 1, -2.90, 0.00186581],
            [0, 1, -2.96, 0.0015382],
            [0, 1, -3, 0.0013499],
            [0, 1, -3.09, 0.00100078],
            [0, 1, -4, 0.00003167],
            [0, 1, -5, 2.9e-7],

            [1, 1, 6, 0.99999971],
            [1, 1, 5, 0.99996833],
            [1, 1, 4, 0.9986501],
            [1, 1, 3, 0.97724987],
            [1, 1, 2, 0.84134475],
            [1, 1, 1.96, 0.83147239],
            [1, 1, 1.5, 0.69146246],
            [1, 1, 1.1, 0.53982784],
            [1, 1, 1, 0.5],
            [1, 1, 0.9, 0.46017216],
            [1, 1, 0.8, 0.42074029],
            [1, 1, 0.7, 0.38208858],
            [1, 1, 0.6, 0.34457826],
            [1, 1, 0.5, 0.30853754],
            [1, 1, 0.4, 0.27425312],
            [1, 1, 0.3, 0.24196365],
            [1, 1, 0.2, 0.2118554],
            [1, 1, 0.1, 0.18406013],
            [1, 1, 0, 0.15865525],
            [1, 1, -0.1, 0.13566606],
            [1, 1, -0.5, 0.0668072],
            [1, 1, -1, 0.02275013],
            [1, 1, -1.96, 0.0015382],
            [1, 1, -2, 0.0013499],
            [1, 1, -3, 0.00003167],
            [1, 1, -4, 2.9e-7],

            [3.2, 2.8, 10, 0.99242078],
            [3.2, 2.8, 6, 0.84134475],
            [3.2, 2.8, 5, 0.7398416],
            [3.2, 2.8, 4, 0.61245152],
            [3.2, 2.8, 3, 0.47152834],
            [3.2, 2.8, 2, 0.33411757],
            [3.2, 2.8, 1, 0.21601745],
            [3.2, 2.8, 0, 0.12654895],
            [3.2, 2.8, -1, 0.0668072],
            [3.2, 2.8, -2, 0.03164542],
            [3.2, 2.8, -3, 0.01340457],
            [3.2, 2.8, -4, 0.005064],
            [3.2, 2.8, -5, 0.00170262],
            [3.2, 2.8, -6, 0.00050862],
            [3.2, 2.8, -10, 0.00000121],

            [72, 15.2, 84, 0.7850824],
            [25, 2, 26, 0.69146246],
            [5, 1, 6, 0.84134475],
            [25, 14, 39, 0.84134475],
            [4, 0.3, 3.5, 0.04779035],
            [1, 1.1, 1.3, 0.60746857],
        ];
    }

    /**
     * @test rand
     */
    public function testRand()
    {
        foreach (range(-3, 3) as $μ) {
            foreach (range(1, 3) as $σ) {
                // Given
                $normal = new Normal($μ, $σ);

                // When
                $random = $normal->rand();

                // Then
                $this->assertTrue(is_numeric($random));
            }
        }
    }
}