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test and cs fixes

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Dennis Eichhorn 2020-05-09 17:27:03 +02:00
parent 9bed188175
commit 2070985e32
12 changed files with 252 additions and 129 deletions
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159
Math/Functions/Beta.php Normal file
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@ -0,0 +1,159 @@
<?php
/**
* Orange Management
*
* PHP Version 7.4
*
* @package phpOMS\Math\Functions
* @copyright Dennis Eichhorn
* @license OMS License 1.0
* @version 1.0.0
* @link https://orange-management.org
*/
declare(strict_types=1);
namespace phpOMS\Math\Functions;
/**
* Beta function
*
* @package phpOMS\Math\Functions
* @license OMS License 1.0
* @link https://orange-management.org
* @since 1.0.0
*/
final class Beta
{
/**
* Constructor.
*
* @since 1.0.0
* @codeCoverageIgnore
*/
private function __construct()
{
}
/**
* Incomplete beta function
*
* @param float $x Value
* @param float $p p
* @param float $q q
*
* @return float
*
* @since 1.0.0
*/
public static function incompleteBeta(float $x, float $p, float $q) : float
{
if ($x < 0.0) {
return 0.0;
} elseif ($x >= 1.0) {
return 1.0;
} elseif ($p <= 0.0 || $q >= 0.0 || $p + $q > 10000000000.0) {
return 0.0;
}
$bGamma = \exp(-self::logBeta($p, $q)) + $p * \log($x) + $q * \log(1.0 - $x);
return $x < ($p + 1.0) / ($p + $q + 2.0)
? $bGamma * self::betaFraction($x, $p, $q) / $p
: 1.0 - $bGamma * self::betaFraction(1 - $x, $q, $p) / $q;
}
/**
* Fraction of the incomplete beta function
*
* @param float $x Value
* @param float $p p
* @param float $q q
*
* @see JSci
* @author Jaco van Kooten
* @license LGPL 2.1
*/
private static function betaFraction(float $x, float $p, float $q) : float
{
$c = 1.0;
$pqSum = $p + $q;
$pPlus = $p + 1.0;
$pMinus = $p - 1.0;
$h = 1.0 - $pqSum * $x / $pPlus;
if (\abs($h) < 2.23e-308) {
$h = 2.23e-308;
}
$h = 1.0 / $h;
$frac = $h;
$m = 1;
$delta = 0.0;
do {
$m2 = 2 * $m;
$d = $m * ($q - $m) * $x / (($pMinus + $m2) * ($p + $m2));
$h = 1.0 + $d * $h;
if (\abs($h) < 2.23e-308) {
$h = 2.23e-308;
}
$h = 1.0 / $h;
$c = 1.0 + $d / $c;
if (\abs($c) < 2.23e-308) {
$c = 2.23e-308;
}
$frac *= $h * $c;
$d = -($p + $m) * ($pqSum + $m) * $x / (($p + $m2) * ($pPlus + $m2));
$h = 1.0 + $d * $h;
if (\abs($h) < 2.23e-308) {
$h = 2.23e-308;
}
$h = 1.0 / $h;
$c = 1.0 + $d / $c;
if (\abs($c) < 2.23e-308) {
$c = 2.23e-308;
}
$delta = $h * $c;
$frac *= $delta;
++$m;
} while ($m < 1000000000 && \abs($delta - 1.0) > 8.88e-16);
return $frac;
}
/**
* Log of Beta
*
* @param float $p p
* @param float $q q
*
* @return float
*
* @since 1.0.0
*/
public static function logBeta(float $p, float $q) : float
{
return $p <= 0.0 || $q <= 0.0 || $p + $q > 10000000000.0
? 0.0
: Gamma::logGamma($p) + Gamma::logGamma($q) - Gamma::logGamma($p + $q);
}
/**
* Beta
*
* @param float $p p
* @param float $q q
*
* @return float
*
* @since 1.0.0
*/
public static function beta(float $p, float $q) : float
{
return \exp(self::logBeta($p, $q));
}
}

38
Math/Functions/Gamma.php
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@ -48,7 +48,7 @@ final class Gamma
/**
* Calculate gamma with Lanczos approximation
*
* @param mixed $z Value
* @param int|float $z Value
*
* @return float
*
@ -74,7 +74,7 @@ final class Gamma
/**
* Calculate gamma with Stirling approximation
*
* @param mixed $x Value
* @param int|float $x Value
*
* @return float
*
@ -88,7 +88,7 @@ final class Gamma
/**
* Calculate gamma with Spouge approximation
*
* @param mixed $z Value
* @param int|float $z Value
*
* @return float
*
@ -114,6 +114,38 @@ final class Gamma
return $accm / $z;
}
/**
* Log of the gamma function
*
* @param int|float $z Value
*
* @return float
*
* @see Book: Numerical Recipes - 9780521406895
*
* @since 1.0.0
*/
public static function logGamma($z) : float
{
static $approx = [
76.18009172947146,-86.50532032941677,
24.01409824083091,-1.231739572450155,
0.1208650973866179e-2,-0.5395239384953e-5
];
$y = $z;
$x = $z;
$temp = $x + 5.5 - ($x + 0.5) * \log($x + 5.5);
$sum = 1.000000000190015;
for ($i = 0; $i < 6; ++$i) {
$sum += $approx[$i] / ++$y;
}
return -$temp + \log(\sqrt(2 * \M_PI * $sum / $x));
}
/**
* Calculate gamma function value.
*

17
Math/Stochastic/Distribution/BetaDistribution.php
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@ -13,6 +13,7 @@
declare(strict_types=1);
namespace phpOMS\Math\Stochastic\Distribution;
use phpOMS\Math\Functions\Beta;
use phpOMS\Math\Functions\Functions;
/**
@ -149,4 +150,20 @@ final class BetaDistribution
return 1 + $sum;
}
/**
* Get cummulative distribution function.
*
* @param float $x Value
* @param float $alpha Alpha
* @param float $beta Beta
*
* @return float
*
* @since 1.0.0
*/
public static function getCdf(float $x, float $alpha, float $beta) : float
{
return Beta::incompleteBeta($x, $alpha, $beta);
}
}

4
Math/Stochastic/Distribution/HypergeometricDistribution.php
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@ -141,7 +141,7 @@ final class HypergeometricDistribution
}
/**
* Hypergeometric-Distribution
* Get cummulative distribution function.
*
* @param int $sampleSuccesses Amount of sample successes
* @param int $samples Sample size
@ -152,7 +152,7 @@ final class HypergeometricDistribution
*
* @since 1.0.0
*/
public static function dist(int $sampleSuccesses, int $samples, int $populationSuccesses, int $population) : float
public static function getCdf(int $sampleSuccesses, int $samples, int $populationSuccesses, int $population) : float
{
// Each multiplication calculates the total amount of possible group combinations based on a total amount of items.
return (int) (\round(Functions::fact($populationSuccesses) / Functions::fact($populationSuccesses - $sampleSuccesses)) / Functions::fact($sampleSuccesses)

12
Math/Stochastic/Distribution/LaplaceDistribution.php
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@ -28,7 +28,7 @@ final class LaplaceDistribution
* Get probability density function.
*
* @param float $x Value x
* @param float $mu Value mu
* @param float $mu Mean
* @param float $b Value b
*
* @return float
@ -44,7 +44,7 @@ final class LaplaceDistribution
* Get cumulative distribution function.
*
* @param float $x Value x
* @param float $mu Value mu
* @param float $mu Mean
* @param float $b Value b
*
* @return float
@ -59,7 +59,7 @@ final class LaplaceDistribution
/**
* Get mode.
*
* @param float $mu Value mu
* @param float $mu Mean
*
* @return float
*
@ -73,7 +73,7 @@ final class LaplaceDistribution
/**
* Get expected value.
*
* @param float $mu Value mu
* @param float $mu Mean
*
* @return float
*
@ -87,7 +87,7 @@ final class LaplaceDistribution
/**
* Get median.
*
* @param float $mu Value mu
* @param float $mu Mean
*
* @return float
*
@ -130,7 +130,7 @@ final class LaplaceDistribution
* Get moment generating function.
*
* @param float $t Valute t
* @param float $mu Value mu
* @param float $mu Mean
* @param float $b Value b
*
* @return float

24
Math/Stochastic/Distribution/LogNormalDistribution.php
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@ -13,6 +13,8 @@
declare(strict_types=1);
namespace phpOMS\Math\Stochastic\Distribution;
use phpOMS\Math\Functions\Functions;
/**
* Log-normal distribution.
*
@ -27,7 +29,7 @@ final class LogNormalDistribution
* Get probability density function.
*
* @param float $x Value x
* @param float $mu Mu
* @param float $mu Mean
* @param float $sigma Sigma
*
* @return float
@ -43,7 +45,7 @@ final class LogNormalDistribution
/**
* Get expected value.
*
* @param float $mu Mu
* @param float $mu Mean
* @param float $sigma Sigma = standard deviation
*
* @return float
@ -58,7 +60,7 @@ final class LogNormalDistribution
/**
* Get median.
*
* @param float $mu Mu
* @param float $mu Mean
*
* @return float
*
@ -72,7 +74,7 @@ final class LogNormalDistribution
/**
* Get mode.
*
* @param float $mu Mu
* @param float $mu Mean
* @param float $sigma Sigma
*
* @return float
@ -87,7 +89,7 @@ final class LogNormalDistribution
/**
* Get variance.
*
* @param float $mu Mu
* @param float $mu Mean
* @param float $sigma Sigma
*
* @return float
@ -102,7 +104,7 @@ final class LogNormalDistribution
/**
* Get standard deviation.
*
* @param float $mu Mu
* @param float $mu Mean
* @param float $sigma Sigma
*
* @return float
@ -145,7 +147,7 @@ final class LogNormalDistribution
/**
* Get entrpoy.
*
* @param float $mu Mu
* @param float $mu Mean
* @param float $sigma Sigma
*
* @return float
@ -175,9 +177,9 @@ final class LogNormalDistribution
}
/**
* Log-Normal-Distribution
* Get cummulative distribution function.
*
* @param float $value Value
* @param float $x Value
* @param float $mean Mean
* @param float $standardDeviation Standard deviation
*
@ -185,8 +187,8 @@ final class LogNormalDistribution
*
* @since 1.0.0
*/
public static function dist(float $value, float $mean, float $standardDeviation) : float
public static function getCdf(float $x, float $mean, float $standardDeviation) : float
{
return NormalDistribution::dist((\log($value) - $mean) / $standardDeviation, 0.0, 1.0, true);
return 0.5 + 0.5 * Functions::getErf((\log($x) - $mean) / (\sqrt(2) * $standardDeviation));
}
}

10
Math/Stochastic/Distribution/LogisticDistribution.php
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@ -27,7 +27,7 @@ final class LogisticDistribution
* Get probability density function.
*
* @param float $x Value x
* @param float $mu Mu location
* @param float $mu Mean
* @param float $s s scale
*
* @return float
@ -44,7 +44,7 @@ final class LogisticDistribution
* Get cummulative distribution function.
*
* @param float $x Value x
* @param float $mu Mu location
* @param float $mu Mean
* @param float $s s scale
*
* @return float
@ -59,7 +59,7 @@ final class LogisticDistribution
/**
* Get mode.
*
* @param float $mu Value mu
* @param float $mu Mean
*
* @return float
*
@ -73,7 +73,7 @@ final class LogisticDistribution
/**
* Get expected value.
*
* @param float $mu Value mu
* @param float $mu Mean
*
* @return float
*
@ -87,7 +87,7 @@ final class LogisticDistribution
/**
* Get median.
*
* @param float $mu Value mu
* @param float $mu Mean
*
* @return float
*

57
Math/Stochastic/Distribution/NormalDistribution.php
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@ -76,7 +76,7 @@ final class NormalDistribution
* Get probability density function.
*
* @param float $x Value x
* @param float $mu Value mu
* @param float $mu Mean
* @param float $sig Sigma
*
* @return float
@ -89,10 +89,10 @@ final class NormalDistribution
}
/**
* Get probability density function.
* Get cummulative distribution function.
*
* @param float $x Value x
* @param float $mu Value mu
* @param float $mu Mean
* @param float $sig Sigma
*
* @return float
@ -101,35 +101,13 @@ final class NormalDistribution
*/
public static function getCdf(float $x, float $mu, float $sig) : float
{
return 1 / 2 * (1 + self::erf(($x - $mu) / ($sig * \sqrt(2))));
}
/**
* Error function approximation
*
* @param float $x Value x
*
* @return float
*
* @todo: compare with Functions::getErf($x);
*
* @since 1.0.0
*/
private static function erf(float $x) : float
{
if ($x < 0) {
return -self::erf(-$x);
}
$a = 8 * (\M_PI - 3) / (3 * \M_PI * (4 - \M_PI));
return \sqrt(1 - \exp(-($x ** 2) * (4 / \M_PI + $a * $x ** 2) / (1 + $a * $x ** 2)));
return 1 / 2 * (1 + Functions::getErf(($x - $mu) / ($sig * \sqrt(2))));
}
/**
* Get mode.
*
* @param float $mu Value mu
* @param float $mu Mean
*
* @return float
*
@ -143,7 +121,7 @@ final class NormalDistribution
/**
* Get expected value.
*
* @param float $mu Value mu
* @param float $mu Mean
*
* @return float
*
@ -157,7 +135,7 @@ final class NormalDistribution
/**
* Get median.
*
* @param float $mu Value mu
* @param float $mu Mean
*
* @return float
*
@ -200,7 +178,7 @@ final class NormalDistribution
* Get moment generating function.
*
* @param float $t Value t
* @param float $mu Value mu
* @param float $mu Mean
* @param float $sig Sigma
*
* @return float
@ -249,23 +227,4 @@ final class NormalDistribution
{
return 0;
}
/**
* Normal-Distribution
*
* @param float $value Value
* @param float $mean Mean
* @param float $standardDeviation Standard deviation
* @param bool $isCumulative Cumulative
*
* @return float
*
* @since 1.0.0
*/
public static function dist(float $value, float $mean, float $standardDeviation, bool $isCumulative = true) : float
{
return $isCumulative
? 0.5 * (1 + Functions::getErf(($value - $mean) / $standardDeviation * \sqrt(2)))
: 1 / (\sqrt(2 * \M_PI) * $standardDeviation) * \exp (-\pow($value - $mean, 2) / (2 * $standardDeviation * $standardDeviation));
}
}

27
Math/Stochastic/Distribution/PoissonDistribution.php
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@ -191,31 +191,4 @@ final class PoissonDistribution
{
return \pow($lambda, -1);
}
/**
* Poisson-Distribution
*
* @param float $value Value
* @param float $mean Mean
* @param bool $isCumulative Cumulative
*
* @return float
*
* @since 1.0.0
*/
public static function dist(float $value, float $mean, bool $isCumulative = true) : float
{
if (!$isCumulative) {
return \exp(-$mean) * \pow($mean, $value) / Functions::fact((int) \floor($value));
}
$sum = 0.0;
$limit = \floor($value);
for ($i = 0; $i <= $limit; ++$i) {
$sum += \pow($mean, $i) / Functions::fact($i);
}
return \exp(-$mean) * $sum;
}
}

10
Math/Stochastic/Distribution/TDistribution.php
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@ -161,9 +161,9 @@ final class TDistribution
}
/**
* T-Distribution
* Get cummulative distribution function.
*
* @param float $value Value
* @param float $x Value
* @param int $degrees Degrees of freedom
* @param int $tails Tails (1 or 2)
*
@ -171,9 +171,9 @@ final class TDistribution
*
* @since 1.0.0
*/
public static function dist(float $value, int $degrees, int $tails = 2) : float
public static function getCdf(float $x, int $degrees, int $tails = 2) : float
{
if ($value < 0.0 || $degrees < 1 || $tails < 1 || $tails > 2) {
if ($x < 0.0 || $degrees < 1 || $tails < 1 || $tails > 2) {
return 0.0;
}
@ -182,7 +182,7 @@ final class TDistribution
* Ellis Horwood Ltd.; W. Sussex, England
*/
$term = $degrees;
$theta = \atan2($value, \sqrt($term));
$theta = \atan2($x, \sqrt($term));
$cos = \cos($theta);
$sin = \sin($theta);
$sum = 0.0;

19
Math/Stochastic/Distribution/WeibullDistribution.php
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@ -101,23 +101,4 @@ final class WeibullDistribution
return $gamma * (1 - 1 / $k) + \log($lambda / $k) + 1;
}
/**
* Weibull-Distribution
*
* @param float $value Value
* @param float $alpha Alpha
* @param float $beta Beta
* @param bool $isCumulative Cumulative
*
* @return float
*
* @since 1.0.0
*/
public static function dist(float $value, float $alpha, float $beta, bool $isCumulative = true) : float
{
return $isCumulative
? 1 - \exp(-\pow($value / $beta, $alpha))
: $alpha / \pow($beta, $alpha) * \pow($value, $alpha - 1) * \exp(-\pow($value / $beta, $alpha));
}
}

4
Math/Stochastic/Distribution/ZTest.php
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@ -79,7 +79,7 @@ final class ZTest
{
$sigma ??= MeasureOfDispersion::standardDeviationSample($data);
return 1 - NormalDistribution::dist((Average::arithmeticMean($data) - $value) / ($sigma / \sqrt(\count($data))), 0.0, 1.0, true);
return 1 - NormalDistribution::getCdf((Average::arithmeticMean($data) - $value) / ($sigma / \sqrt(\count($data))), 0.0, 1.0, true);
}
/**
@ -96,6 +96,6 @@ final class ZTest
*/
public static function zTestingValues(float $value, float $mean, int $dataSize, float $sigma) : float
{
return 1 - NormalDistribution::dist(($mean - $value) / ($sigma / \sqrt($dataSize)), 0.0, 1.0, true);
return 1 - NormalDistribution::getCdf(($mean - $value) / ($sigma / \sqrt($dataSize)), 0.0, 1.0, true);
}
}