mirror of
https://github.com/furyfire/trueskill.git
synced 2025-11-04 10:12:28 +01:00
267 lines
8.7 KiB
PHP
267 lines
8.7 KiB
PHP
<?php
|
|
/**
|
|
* Computes Gaussian values.
|
|
*
|
|
* PHP version 5
|
|
*
|
|
* @category Math
|
|
* @package PHPSkills
|
|
* @author Jeff Moser <jeff@moserware.com>
|
|
* @copyright 2010 Jeff Moser
|
|
*/
|
|
|
|
namespace Moserware\Numerics;
|
|
|
|
require_once(dirname(__FILE__) . "/basicmath.php");
|
|
|
|
class GaussianDistribution
|
|
{
|
|
private $_mean;
|
|
private $_standardDeviation;
|
|
|
|
// Precision and PrecisionMean are used because they make multiplying and dividing simpler
|
|
// (the the accompanying math paper for more details)
|
|
private $_precision;
|
|
private $_precisionMean;
|
|
private $_variance;
|
|
|
|
function __construct($mean = 0.0, $standardDeviation = 1.0)
|
|
{
|
|
$this->_mean = $mean;
|
|
$this->_standardDeviation = $standardDeviation;
|
|
$this->_variance = square($standardDeviation);
|
|
$this->_precision = 1.0/$this->_variance;
|
|
$this->_precisionMean = $this->_precision*$this->_mean;
|
|
}
|
|
|
|
public function getMean()
|
|
{
|
|
return $this->_mean;
|
|
}
|
|
|
|
public function getVariance()
|
|
{
|
|
return $this->_variance;
|
|
}
|
|
|
|
public function getStandardDeviation()
|
|
{
|
|
return $this->_standardDeviation;
|
|
}
|
|
|
|
public function getPrecision()
|
|
{
|
|
return $this->_precision;
|
|
}
|
|
|
|
public function getPrecisionMean()
|
|
{
|
|
return $this->_precisionMean;
|
|
}
|
|
|
|
public function getNormalizationConstant()
|
|
{
|
|
// Great derivation of this is at http://www.astro.psu.edu/~mce/A451_2/A451/downloads/notes0.pdf
|
|
return 1.0/(sqrt(2*M_PI)*$this->_standardDeviation);
|
|
}
|
|
|
|
public function __clone()
|
|
{
|
|
$result = new GaussianDistribution();
|
|
$result->_mean = $this->_mean;
|
|
$result->_standardDeviation = $this->_standardDeviation;
|
|
$result->_variance = $this->_variance;
|
|
$result->_precision = $this->_precision;
|
|
$result->_precisionMean = $this->_precisionMean;
|
|
return $result;
|
|
}
|
|
|
|
public static function fromPrecisionMean($precisionMean, $precision)
|
|
{
|
|
$result = new GaussianDistribution();
|
|
$result->_precision = $precision;
|
|
$result->_precisionMean = $precisionMean;
|
|
|
|
if($precision != 0)
|
|
{
|
|
$result->_variance = 1.0/$precision;
|
|
$result->_standardDeviation = sqrt($result->_variance);
|
|
$result->_mean = $result->_precisionMean/$result->_precision;
|
|
}
|
|
else
|
|
{
|
|
$result->_variance = \INF;
|
|
$result->_standardDeviation = \INF;
|
|
$result->_mean = \NAN;
|
|
}
|
|
return $result;
|
|
}
|
|
|
|
// For details, see http://www.tina-vision.net/tina-knoppix/tina-memo/2003-003.pdf
|
|
// for multiplication, the precision mean ones are easier to write :)
|
|
public static function multiply(GaussianDistribution $left, GaussianDistribution $right)
|
|
{
|
|
return GaussianDistribution::fromPrecisionMean($left->_precisionMean + $right->_precisionMean, $left->_precision + $right->_precision);
|
|
}
|
|
|
|
// Computes the absolute difference between two Gaussians
|
|
public static function absoluteDifference(GaussianDistribution $left, GaussianDistribution $right)
|
|
{
|
|
return max(
|
|
abs($left->_precisionMean - $right->_precisionMean),
|
|
sqrt(abs($left->_precision - $right->_precision)));
|
|
}
|
|
|
|
// Computes the absolute difference between two Gaussians
|
|
public static function subtract(GaussianDistribution $left, GaussianDistribution $right)
|
|
{
|
|
return absoluteDifference($left, $right);
|
|
}
|
|
|
|
public static function logProductNormalization(GaussianDistribution $left, GaussianDistribution $right)
|
|
{
|
|
if (($left->_precision == 0) || ($right->_precision == 0))
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
$varianceSum = $left->_variance + $right->_variance;
|
|
$meanDifference = $left->_mean - $right->_mean;
|
|
|
|
$logSqrt2Pi = log(sqrt(2*M_PI));
|
|
return -$logSqrt2Pi - (log($varianceSum)/2.0) - (square($meanDifference)/(2.0*$varianceSum));
|
|
}
|
|
|
|
public static function divide(GaussianDistribution $numerator, GaussianDistribution $denominator)
|
|
{
|
|
return GaussianDistribution::fromPrecisionMean($numerator->_precisionMean - $denominator->_precisionMean,
|
|
$numerator->_precision - $denominator->_precision);
|
|
}
|
|
|
|
public static function logRatioNormalization(GaussianDistribution $numerator, GaussianDistribution $denominator)
|
|
{
|
|
if (($numerator->_precision == 0) || ($denominator->_precision == 0))
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
$varianceDifference = $denominator->_variance - $numerator->_variance;
|
|
$meanDifference = $numerator->_mean - $denominator->_mean;
|
|
|
|
$logSqrt2Pi = log(sqrt(2*M_PI));
|
|
|
|
return log($denominator->_variance) + $logSqrt2Pi - log($varianceDifference)/2.0 +
|
|
square($meanDifference)/(2*$varianceDifference);
|
|
}
|
|
|
|
public static function at($x, $mean = 0.0, $standardDeviation = 1.0)
|
|
{
|
|
// See http://mathworld.wolfram.com/NormalDistribution.html
|
|
// 1 -(x-mean)^2 / (2*stdDev^2)
|
|
// P(x) = ------------------- * e
|
|
// stdDev * sqrt(2*pi)
|
|
|
|
$multiplier = 1.0/($standardDeviation*sqrt(2*M_PI));
|
|
$expPart = exp((-1.0*square($x - $mean))/(2*square($standardDeviation)));
|
|
$result = $multiplier*$expPart;
|
|
return $result;
|
|
}
|
|
|
|
public static function cumulativeTo($x, $mean = 0.0, $standardDeviation = 1.0)
|
|
{
|
|
$invsqrt2 = -0.707106781186547524400844362104;
|
|
$result = GaussianDistribution::errorFunctionCumulativeTo($invsqrt2*$x);
|
|
return 0.5*$result;
|
|
}
|
|
|
|
private static function errorFunctionCumulativeTo($x)
|
|
{
|
|
// Derived from page 265 of Numerical Recipes 3rd Edition
|
|
$z = abs($x);
|
|
|
|
$t = 2.0/(2.0 + $z);
|
|
$ty = 4*$t - 2;
|
|
|
|
$coefficients = array(
|
|
-1.3026537197817094,
|
|
6.4196979235649026e-1,
|
|
1.9476473204185836e-2,
|
|
-9.561514786808631e-3,
|
|
-9.46595344482036e-4,
|
|
3.66839497852761e-4,
|
|
4.2523324806907e-5,
|
|
-2.0278578112534e-5,
|
|
-1.624290004647e-6,
|
|
1.303655835580e-6,
|
|
1.5626441722e-8,
|
|
-8.5238095915e-8,
|
|
6.529054439e-9,
|
|
5.059343495e-9,
|
|
-9.91364156e-10,
|
|
-2.27365122e-10,
|
|
9.6467911e-11,
|
|
2.394038e-12,
|
|
-6.886027e-12,
|
|
8.94487e-13,
|
|
3.13092e-13,
|
|
-1.12708e-13,
|
|
3.81e-16,
|
|
7.106e-15,
|
|
-1.523e-15,
|
|
-9.4e-17,
|
|
1.21e-16,
|
|
-2.8e-17 );
|
|
|
|
$ncof = count($coefficients);
|
|
$d = 0.0;
|
|
$dd = 0.0;
|
|
|
|
for ($j = $ncof - 1; $j > 0; $j--)
|
|
{
|
|
$tmp = $d;
|
|
$d = $ty*$d - $dd + $coefficients[$j];
|
|
$dd = $tmp;
|
|
}
|
|
|
|
$ans = $t*exp(-$z*$z + 0.5*($coefficients[0] + $ty*$d) - $dd);
|
|
return ($x >= 0.0) ? $ans : (2.0 - $ans);
|
|
}
|
|
|
|
private static function inverseErrorFunctionCumulativeTo($p)
|
|
{
|
|
// From page 265 of numerical recipes
|
|
|
|
if ($p >= 2.0)
|
|
{
|
|
return -100;
|
|
}
|
|
if ($p <= 0.0)
|
|
{
|
|
return 100;
|
|
}
|
|
|
|
$pp = ($p < 1.0) ? $p : 2 - $p;
|
|
$t = sqrt(-2*log($pp/2.0)); // Initial guess
|
|
$x = -0.70711*((2.30753 + $t*0.27061)/(1.0 + $t*(0.99229 + $t*0.04481)) - $t);
|
|
|
|
for ($j = 0; $j < 2; $j++)
|
|
{
|
|
$err = GaussianDistribution::errorFunctionCumulativeTo($x) - $pp;
|
|
$x += $err/(1.12837916709551257*exp(-square($x)) - $x*$err); // Halley
|
|
}
|
|
|
|
return ($p < 1.0) ? $x : -$x;
|
|
}
|
|
|
|
public static function inverseCumulativeTo($x, $mean = 0.0, $standardDeviation = 1.0)
|
|
{
|
|
// From numerical recipes, page 320
|
|
return $mean - sqrt(2)*$standardDeviation*GaussianDistribution::inverseErrorFunctionCumulativeTo(2*$x);
|
|
}
|
|
|
|
public function __toString()
|
|
{
|
|
return 'mean=' . $this->_mean . ' standardDeviation=' . $this->_standardDeviation;
|
|
}
|
|
}
|
|
?>
|