trueskill/PHPSkills/TrueSkill/TruncatedGaussianCorrectionFunctions.php

<?php
namespace Moserware\Skills\TrueSkill;

require_once(dirname(__FILE__) . '/../Numerics/GaussianDistribution.php');

use Moserware\Numerics\GaussianDistribution;

class TruncatedGaussianCorrectionFunctions
{
    // These functions from the bottom of page 4 of the TrueSkill paper.

    /// <summary>
    /// The "V" function where the team performance difference is greater than the draw margin.
    /// </summary>
    /// <remarks>In the reference F# implementation, this is referred to as "the additive
    /// correction of a single-sided truncated Gaussian with unit variance."</remarks>
    /// <param name="teamPerformanceDifference"></param>
    /// <param name="drawMargin">In the paper, it's referred to as just "ε".</param>
    /// <returns></returns>
    public static function vExceedsMarginScaled($teamPerformanceDifference, $drawMargin, $c)
    {
        return self::vExceedsMargin($teamPerformanceDifference/$c, $drawMargin/$c);
    }

    public static function vExceedsMargin($teamPerformanceDifference, $drawMargin)
    {
        $denominator = GaussianDistribution::cumulativeTo($teamPerformanceDifference - $drawMargin);

        if ($denominator < 2.222758749e-162)
        {
            return -$teamPerformanceDifference + $drawMargin;
        }

        return GaussianDistribution::at($teamPerformanceDifference - $drawMargin)/$denominator;
    }

    /// <summary>
    /// The "W" function where the team performance difference is greater than the draw margin.
    /// </summary>
    /// <remarks>In the reference F# implementation, this is referred to as "the multiplicative
    /// correction of a single-sided truncated Gaussian with unit variance."</remarks>
    /// <param name="teamPerformanceDifference"></param>
    /// <param name="drawMargin"></param>
    /// <param name="c"></param>
    /// <returns></returns>
    public static function wExceedsMarginScaled($teamPerformanceDifference, $drawMargin, $c)
    {
        return self::wExceedsMargin($teamPerformanceDifference/$c, $drawMargin/$c);
    }

    public static function wExceedsMargin($teamPerformanceDifference, $drawMargin)
    {
        $denominator = GaussianDistribution::cumulativeTo($teamPerformanceDifference - $drawMargin);

        if ($denominator < 2.222758749e-162)
        {
            if ($teamPerformanceDifference < 0.0)
            {
                return 1.0;
            }
            return 0.0;
        }

        $vWin = self::vExceedsMargin($teamPerformanceDifference, $drawMargin);
        return $vWin*($vWin + $teamPerformanceDifference - $drawMargin);
    }

    // the additive correction of a double-sided truncated Gaussian with unit variance
    public static function vWithinMarginScaled($teamPerformanceDifference, $drawMargin, $c)
    {
        return self::vWithinMargin($teamPerformanceDifference/$c, $drawMargin/$c);
    }
    
    // from F#:
    public static function vWithinMargin($teamPerformanceDifference, $drawMargin)
    {
        $teamPerformanceDifferenceAbsoluteValue = abs($teamPerformanceDifference);
        $denominator =
            GaussianDistribution::cumulativeTo($drawMargin - $teamPerformanceDifferenceAbsoluteValue) -
            GaussianDistribution::cumulativeTo(-$drawMargin - $teamPerformanceDifferenceAbsoluteValue);

        if ($denominator < 2.222758749e-162)
        {
            if ($teamPerformanceDifference < 0.0)
            {
                return -$teamPerformanceDifference - $drawMargin;
            }

            return -$teamPerformanceDifference + $drawMargin;
        }

        $numerator = GaussianDistribution::at(-$drawMargin - $teamPerformanceDifferenceAbsoluteValue) -
                     GaussianDistribution::at($drawMargin - $teamPerformanceDifferenceAbsoluteValue);

        if ($teamPerformanceDifference < 0.0)
        {
            return -$numerator/$denominator;
        }

        return $numerator/$denominator;
    }

    // the multiplicative correction of a double-sided truncated Gaussian with unit variance
    public static function wWithinMarginScaled($teamPerformanceDifference, $drawMargin, $c)
    {
        return self::wWithinMargin($teamPerformanceDifference/$c, $drawMargin/$c);
    }

    // From F#:
    public static function wWithinMargin($teamPerformanceDifference, $drawMargin)
    {
        $teamPerformanceDifferenceAbsoluteValue = abs($teamPerformanceDifference);
        $denominator = GaussianDistribution::cumulativeTo($drawMargin - $teamPerformanceDifferenceAbsoluteValue)
                       -
                       GaussianDistribution::cumulativeTo(-$drawMargin - $teamPerformanceDifferenceAbsoluteValue);

        if ($denominator < 2.222758749e-162)
        {
            return 1.0;
        }

        $vt = self::vWithinMargin($teamPerformanceDifferenceAbsoluteValue, $drawMargin);

        return $vt*$vt +
               (
                   ($drawMargin - $teamPerformanceDifferenceAbsoluteValue)
                   *
                   GaussianDistribution::at(
                       $drawMargin - $teamPerformanceDifferenceAbsoluteValue)
                   - (-$drawMargin - $teamPerformanceDifferenceAbsoluteValue)
                     *
                     GaussianDistribution::at(-$drawMargin - $teamPerformanceDifferenceAbsoluteValue))/$denominator;
    }
}
?>