private static function PHPExcel_Calculation_Statistical::_logGamma in Loft Data Grids 7.2

Same name and namespace in other branches

1. 6.2 vendor/phpoffice/phpexcel/Classes/PHPExcel/Calculation/Statistical.php \PHPExcel_Calculation_Statistical::_logGamma()

1 call to PHPExcel_Calculation_Statistical::_logGamma()

PHPExcel_Calculation_Statistical::_logBeta in vendor/phpoffice/phpexcel/Classes/PHPExcel/Calculation/Statistical.php

* The natural logarithm of the beta function. * *

File

vendor/phpoffice/phpexcel/Classes/PHPExcel/Calculation/Statistical.php, line 262

Class

PHPExcel_Calculation_Statistical

PHPExcel_Calculation_Statistical

Code

private static function _logGamma($x) {

  // Log Gamma related constants
  static $lg_d1 = -0.5772156649015329;
  static $lg_d2 = 0.42278433509846713;
  static $lg_d4 = 1.791759469228055;
  static $lg_p1 = array(
    4.945235359296727,
    201.8112620856775,
    2290.8383738313464,
    11319.672059033808,
    28557.246356716354,
    38484.962284437934,
    26377.487876241954,
    7225.813979700288,
  );
  static $lg_p2 = array(
    4.974607845568932,
    542.4138599891071,
    15506.93864978365,
    184793.29044456323,
    1088204.7694688288,
    3338152.96798703,
    5106661.678927353,
    3074109.0548505397,
  );
  static $lg_p4 = array(
    14745.0216605994,
    2426813.3694867045,
    121475557.40450932,
    2663432449.630977,
    29403789566.34554,
    170266573776.5399,
    492612579337.7431,
    560625185622.3951,
  );
  static $lg_q1 = array(
    67.48212550303778,
    1113.3323938571993,
    7738.757056935398,
    27639.870744033407,
    54993.102062261576,
    61611.22180066002,
    36351.2759150194,
    8785.536302431014,
  );
  static $lg_q2 = array(
    183.03283993705926,
    7765.049321445006,
    133190.38279660742,
    1136705.8213219696,
    5267964.117437947,
    13467014.543111017,
    17827365.303532742,
    9533095.591844354,
  );
  static $lg_q4 = array(
    2690.5301758708993,
    639388.5654300093,
    41355999.30241388,
    1120872109.616148,
    14886137286.788137,
    101680358627.24382,
    341747634550.73773,
    446315818741.9713,
  );
  static $lg_c = array(
    -0.001910444077728,
    0.0008417138778129501,
    -0.0005952379913043012,
    0.0007936507935003503,
    -0.0027777777777776816,
    0.08333333333333333,
    0.0057083835261,
  );

  // Rough estimate of the fourth root of logGamma_xBig
  static $lg_frtbig = 2.25E+76;
  static $pnt68 = 0.6796875;
  if ($x == self::$_logGammaCache_x) {
    return self::$_logGammaCache_result;
  }
  $y = $x;
  if ($y > 0.0 && $y <= LOG_GAMMA_X_MAX_VALUE) {
    if ($y <= EPS) {
      $res = -log(y);
    }
    elseif ($y <= 1.5) {

      // ---------------------
      //	EPS .LT. X .LE. 1.5
      // ---------------------
      if ($y < $pnt68) {
        $corr = -log($y);
        $xm1 = $y;
      }
      else {
        $corr = 0.0;
        $xm1 = $y - 1.0;
      }
      if ($y <= 0.5 || $y >= $pnt68) {
        $xden = 1.0;
        $xnum = 0.0;
        for ($i = 0; $i < 8; ++$i) {
          $xnum = $xnum * $xm1 + $lg_p1[$i];
          $xden = $xden * $xm1 + $lg_q1[$i];
        }
        $res = $corr + $xm1 * ($lg_d1 + $xm1 * ($xnum / $xden));
      }
      else {
        $xm2 = $y - 1.0;
        $xden = 1.0;
        $xnum = 0.0;
        for ($i = 0; $i < 8; ++$i) {
          $xnum = $xnum * $xm2 + $lg_p2[$i];
          $xden = $xden * $xm2 + $lg_q2[$i];
        }
        $res = $corr + $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
      }
    }
    elseif ($y <= 4.0) {

      // ---------------------
      //	1.5 .LT. X .LE. 4.0
      // ---------------------
      $xm2 = $y - 2.0;
      $xden = 1.0;
      $xnum = 0.0;
      for ($i = 0; $i < 8; ++$i) {
        $xnum = $xnum * $xm2 + $lg_p2[$i];
        $xden = $xden * $xm2 + $lg_q2[$i];
      }
      $res = $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
    }
    elseif ($y <= 12.0) {

      // ----------------------
      //	4.0 .LT. X .LE. 12.0
      // ----------------------
      $xm4 = $y - 4.0;
      $xden = -1.0;
      $xnum = 0.0;
      for ($i = 0; $i < 8; ++$i) {
        $xnum = $xnum * $xm4 + $lg_p4[$i];
        $xden = $xden * $xm4 + $lg_q4[$i];
      }
      $res = $lg_d4 + $xm4 * ($xnum / $xden);
    }
    else {

      // ---------------------------------
      //	Evaluate for argument .GE. 12.0
      // ---------------------------------
      $res = 0.0;
      if ($y <= $lg_frtbig) {
        $res = $lg_c[6];
        $ysq = $y * $y;
        for ($i = 0; $i < 6; ++$i) {
          $res = $res / $ysq + $lg_c[$i];
        }
      }
      $res /= $y;
      $corr = log($y);
      $res = $res + log(SQRT2PI) - 0.5 * $corr;
      $res += $y * ($corr - 1.0);
    }
  }
  else {

    // --------------------------
    //	Return for bad arguments
    // --------------------------
    $res = MAX_VALUE;
  }

  // ------------------------------
  //	Final adjustments and return
  // ------------------------------
  self::$_logGammaCache_x = $x;
  self::$_logGammaCache_result = $res;
  return $res;
}