/common/libraries/plugin/phpexcel/PHPExcel/Calculation/Statistical.php
PHP | 4183 lines | 2565 code | 384 blank | 1234 comment | 616 complexity | da7daf734cb14eab3ea98c886bc3f5ab MD5 | raw file
Possible License(s): GPL-2.0, BSD-3-Clause, LGPL-2.1, LGPL-3.0, GPL-3.0, MIT
Large files files are truncated, but you can click here to view the full file
- <?php
- /**
- * PHPExcel
- *
- * Copyright (c) 2006 - 2011 PHPExcel
- *
- * This library is free software; you can redistribute it and/or
- * modify it under the terms of the GNU Lesser General Public
- * License as published by the Free Software Foundation; either
- * version 2.1 of the License, or (at your option) any later version.
- *
- * This library is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- * Lesser General Public License for more details.
- *
- * You should have received a copy of the GNU Lesser General Public
- * License along with this library; if not, write to the Free Software
- * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
- *
- * @category PHPExcel
- * @package PHPExcel_Calculation
- * @copyright Copyright (c) 2006 - 2011 PHPExcel (http://www.codeplex.com/PHPExcel)
- * @license http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt LGPL
- * @version 1.7.6, 2011-02-27
- */
-
- /** PHPExcel root directory */
- if (! defined('PHPEXCEL_ROOT'))
- {
- /**
- * @ignore
- */
- define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
- require (PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
- }
-
- require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/trend/trendClass.php';
-
- /** LOG_GAMMA_X_MAX_VALUE */
- define('LOG_GAMMA_X_MAX_VALUE', 2.55e305);
-
- /** XMININ */
- define('XMININ', 2.23e-308);
-
- /** EPS */
- define('EPS', 2.22e-16);
-
- /** SQRT2PI */
- define('SQRT2PI', 2.5066282746310005024157652848110452530069867406099);
-
- /**
- * PHPExcel_Calculation_Statistical
- *
- * @category PHPExcel
- * @package PHPExcel_Calculation
- * @copyright Copyright (c) 2006 - 2011 PHPExcel (http://www.codeplex.com/PHPExcel)
- */
- class PHPExcel_Calculation_Statistical
- {
-
- private static function _checkTrendArrays(&$array1, &$array2)
- {
- if (! is_array($array1))
- {
- $array1 = array($array1);
- }
- if (! is_array($array2))
- {
- $array2 = array($array2);
- }
-
- $array1 = PHPExcel_Calculation_Functions :: flattenArray($array1);
- $array2 = PHPExcel_Calculation_Functions :: flattenArray($array2);
- foreach ($array1 as $key => $value)
- {
- if ((is_bool($value)) || (is_string($value)) || (is_null($value)))
- {
- unset($array1[$key]);
- unset($array2[$key]);
- }
- }
- foreach ($array2 as $key => $value)
- {
- if ((is_bool($value)) || (is_string($value)) || (is_null($value)))
- {
- unset($array1[$key]);
- unset($array2[$key]);
- }
- }
- $array1 = array_merge($array1);
- $array2 = array_merge($array2);
-
- return True;
- } // function _checkTrendArrays()
-
-
- /**
- * Beta function.
- *
- * @author Jaco van Kooten
- *
- * @param p require p>0
- * @param q require q>0
- * @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
- */
- private static function _beta($p, $q)
- {
- if ($p <= 0.0 || $q <= 0.0 || ($p + $q) > LOG_GAMMA_X_MAX_VALUE)
- {
- return 0.0;
- }
- else
- {
- return exp(self :: _logBeta($p, $q));
- }
- } // function _beta()
-
-
- /**
- * Incomplete beta function
- *
- * @author Jaco van Kooten
- * @author Paul Meagher
- *
- * The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992).
- * @param x require 0<=x<=1
- * @param p require p>0
- * @param q require q>0
- * @return 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow
- */
- private static function _incompleteBeta($x, $p, $q)
- {
- if ($x <= 0.0)
- {
- return 0.0;
- }
- elseif ($x >= 1.0)
- {
- return 1.0;
- }
- elseif (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE))
- {
- return 0.0;
- }
- $beta_gam = exp((0 - self :: _logBeta($p, $q)) + $p * log($x) + $q * log(1.0 - $x));
- if ($x < ($p + 1.0) / ($p + $q + 2.0))
- {
- return $beta_gam * self :: _betaFraction($x, $p, $q) / $p;
- }
- else
- {
- return 1.0 - ($beta_gam * self :: _betaFraction(1 - $x, $q, $p) / $q);
- }
- } // function _incompleteBeta()
-
-
- // Function cache for _logBeta function
- private static $_logBetaCache_p = 0.0;
- private static $_logBetaCache_q = 0.0;
- private static $_logBetaCache_result = 0.0;
-
- /**
- * The natural logarithm of the beta function.
- * @param p require p>0
- * @param q require q>0
- * @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
- * @author Jaco van Kooten
- */
- private static function _logBeta($p, $q)
- {
- if ($p != self :: $_logBetaCache_p || $q != self :: $_logBetaCache_q)
- {
- self :: $_logBetaCache_p = $p;
- self :: $_logBetaCache_q = $q;
- if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE))
- {
- self :: $_logBetaCache_result = 0.0;
- }
- else
- {
- self :: $_logBetaCache_result = self :: _logGamma($p) + self :: _logGamma($q) - self :: _logGamma($p + $q);
- }
- }
- return self :: $_logBetaCache_result;
- } // function _logBeta()
-
-
- /**
- * Evaluates of continued fraction part of incomplete beta function.
- * Based on an idea from Numerical Recipes (W.H. Press et al, 1992).
- * @author Jaco van Kooten
- */
- private static function _betaFraction($x, $p, $q)
- {
- $c = 1.0;
- $sum_pq = $p + $q;
- $p_plus = $p + 1.0;
- $p_minus = $p - 1.0;
- $h = 1.0 - $sum_pq * $x / $p_plus;
- if (abs($h) < XMININ)
- {
- $h = XMININ;
- }
- $h = 1.0 / $h;
- $frac = $h;
- $m = 1;
- $delta = 0.0;
- while ($m <= MAX_ITERATIONS && abs($delta - 1.0) > PRECISION)
- {
- $m2 = 2 * $m;
- // even index for d
- $d = $m * ($q - $m) * $x / (($p_minus + $m2) * ($p + $m2));
- $h = 1.0 + $d * $h;
- if (abs($h) < XMININ)
- {
- $h = XMININ;
- }
- $h = 1.0 / $h;
- $c = 1.0 + $d / $c;
- if (abs($c) < XMININ)
- {
- $c = XMININ;
- }
- $frac *= $h * $c;
- // odd index for d
- $d = - ($p + $m) * ($sum_pq + $m) * $x / (($p + $m2) * ($p_plus + $m2));
- $h = 1.0 + $d * $h;
- if (abs($h) < XMININ)
- {
- $h = XMININ;
- }
- $h = 1.0 / $h;
- $c = 1.0 + $d / $c;
- if (abs($c) < XMININ)
- {
- $c = XMININ;
- }
- $delta = $h * $c;
- $frac *= $delta;
- ++ $m;
- }
- return $frac;
- } // function _betaFraction()
-
-
- /**
- * logGamma function
- *
- * @version 1.1
- * @author Jaco van Kooten
- *
- * Original author was Jaco van Kooten. Ported to PHP by Paul Meagher.
- *
- * The natural logarithm of the gamma function. <br />
- * Based on public domain NETLIB (Fortran) code by W. J. Cody and L. Stoltz <br />
- * Applied Mathematics Division <br />
- * Argonne National Laboratory <br />
- * Argonne, IL 60439 <br />
- * <p>
- * References:
- * <ol>
- * <li>W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural
- * Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203.</li>
- * <li>K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969.</li>
- * <li>Hart, Et. Al., Computer Approximations, Wiley and sons, New York, 1968.</li>
- * </ol>
- * </p>
- * <p>
- * From the original documentation:
- * </p>
- * <p>
- * This routine calculates the LOG(GAMMA) function for a positive real argument X.
- * Computation is based on an algorithm outlined in references 1 and 2.
- * The program uses rational functions that theoretically approximate LOG(GAMMA)
- * to at least 18 significant decimal digits. The approximation for X > 12 is from
- * reference 3, while approximations for X < 12.0 are similar to those in reference
- * 1, but are unpublished. The accuracy achieved depends on the arithmetic system,
- * the compiler, the intrinsic functions, and proper selection of the
- * machine-dependent constants.
- * </p>
- * <p>
- * Error returns: <br />
- * The program returns the value XINF for X .LE. 0.0 or when overflow would occur.
- * The computation is believed to be free of underflow and overflow.
- * </p>
- * @return MAX_VALUE for x < 0.0 or when overflow would occur, i.e. x > 2.55E305
- */
-
- // Function cache for logGamma
- private static $_logGammaCache_result = 0.0;
- private static $_logGammaCache_x = 0.0;
-
- private static function _logGamma($x)
- {
- // Log Gamma related constants
- static $lg_d1 = - 0.5772156649015328605195174;
- static $lg_d2 = 0.4227843350984671393993777;
- static $lg_d4 = 1.791759469228055000094023;
-
- static $lg_p1 = array(4.945235359296727046734888, 201.8112620856775083915565, 2290.838373831346393026739,
- 11319.67205903380828685045, 28557.24635671635335736389, 38484.96228443793359990269,
- 26377.48787624195437963534, 7225.813979700288197698961);
- static $lg_p2 = array(4.974607845568932035012064, 542.4138599891070494101986, 15506.93864978364947665077,
- 184793.2904445632425417223, 1088204.76946882876749847, 3338152.967987029735917223,
- 5106661.678927352456275255, 3074109.054850539556250927);
- static $lg_p4 = array(14745.02166059939948905062, 2426813.369486704502836312, 121475557.4045093227939592,
- 2663432449.630976949898078, 29403789566.34553899906876, 170266573776.5398868392998,
- 492612579337.743088758812, 560625185622.3951465078242);
-
- static $lg_q1 = array(67.48212550303777196073036, 1113.332393857199323513008, 7738.757056935398733233834,
- 27639.87074403340708898585, 54993.10206226157329794414, 61611.22180066002127833352,
- 36351.27591501940507276287, 8785.536302431013170870835);
- static $lg_q2 = array(183.0328399370592604055942, 7765.049321445005871323047, 133190.3827966074194402448,
- 1136705.821321969608938755, 5267964.117437946917577538, 13467014.54311101692290052,
- 17827365.30353274213975932, 9533095.591844353613395747);
- static $lg_q4 = array(2690.530175870899333379843, 639388.5654300092398984238, 41355999.30241388052042842,
- 1120872109.61614794137657, 14886137286.78813811542398, 101680358627.2438228077304,
- 341747634550.7377132798597, 446315818741.9713286462081);
-
- static $lg_c = array(- 0.001910444077728, 8.4171387781295e-4, - 5.952379913043012e-4, 7.93650793500350248e-4,
- - 0.002777777777777681622553, 0.08333333333333333331554247, 0.0057083835261);
-
- // Rough estimate of the fourth root of logGamma_xBig
- static $lg_frtbig = 2.25e76;
- 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 $res;
- } // function _logGamma()
-
-
- //
- // Private implementation of the incomplete Gamma function
- //
- private static function _incompleteGamma($a, $x)
- {
- static $max = 32;
- $summer = 0;
- for($n = 0; $n <= $max; ++ $n)
- {
- $divisor = $a;
- for($i = 1; $i <= $n; ++ $i)
- {
- $divisor *= ($a + $i);
- }
- $summer += (pow($x, $n) / $divisor);
- }
- return pow($x, $a) * exp(0 - $x) * $summer;
- } // function _incompleteGamma()
-
-
- //
- // Private implementation of the Gamma function
- //
- private static function _gamma($data)
- {
- if ($data == 0.0)
- return 0;
-
- static $p0 = 1.000000000190015;
- static $p = array(1 => 76.18009172947146, 2 => - 86.50532032941677, 3 => 24.01409824083091,
- 4 => - 1.231739572450155, 5 => 1.208650973866179e-3, 6 => - 5.395239384953e-6);
-
- $y = $x = $data;
- $tmp = $x + 5.5;
- $tmp -= ($x + 0.5) * log($tmp);
-
- $summer = $p0;
- for($j = 1; $j <= 6; ++ $j)
- {
- $summer += ($p[$j] / ++ $y);
- }
- return exp(0 - $tmp + log(SQRT2PI * $summer / $x));
- } // function _gamma()
-
-
- /***************************************************************************
- * inverse_ncdf.php
- * -------------------
- * begin : Friday, January 16, 2004
- * copyright : (C) 2004 Michael Nickerson
- * email : nickersonm@yahoo.com
- *
- ***************************************************************************/
- private static function _inverse_ncdf($p)
- {
- // Inverse ncdf approximation by Peter J. Acklam, implementation adapted to
- // PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
- // a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
- // I have not checked the accuracy of this implementation. Be aware that PHP
- // will truncate the coeficcients to 14 digits.
-
-
- // You have permission to use and distribute this function freely for
- // whatever purpose you want, but please show common courtesy and give credit
- // where credit is due.
-
-
- // Input paramater is $p - probability - where 0 < p < 1.
-
-
- // Coefficients in rational approximations
- static $a = array(1 => - 3.969683028665376e+01, 2 => 2.209460984245205e+02, 3 => - 2.759285104469687e+02,
- 4 => 1.383577518672690e+02, 5 => - 3.066479806614716e+01, 6 => 2.506628277459239e+00);
-
- static $b = array(1 => - 5.447609879822406e+01, 2 => 1.615858368580409e+02, 3 => - 1.556989798598866e+02,
- 4 => 6.680131188771972e+01, 5 => - 1.328068155288572e+01);
-
- static $c = array(1 => - 7.784894002430293e-03, 2 => - 3.223964580411365e-01, 3 => - 2.400758277161838e+00,
- 4 => - 2.549732539343734e+00, 5 => 4.374664141464968e+00, 6 => 2.938163982698783e+00);
-
- static $d = array(1 => 7.784695709041462e-03, 2 => 3.224671290700398e-01, 3 => 2.445134137142996e+00,
- 4 => 3.754408661907416e+00);
-
- // Define lower and upper region break-points.
- $p_low = 0.02425; //Use lower region approx. below this
- $p_high = 1 - $p_low; //Use upper region approx. above this
-
-
- if (0 < $p && $p < $p_low)
- {
- // Rational approximation for lower region.
- $q = sqrt(- 2 * log($p));
- return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) / (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
- }
- elseif ($p_low <= $p && $p <= $p_high)
- {
- // Rational approximation for central region.
- $q = $p - 0.5;
- $r = $q * $q;
- return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q / ((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1);
- }
- elseif ($p_high < $p && $p < 1)
- {
- // Rational approximation for upper region.
- $q = sqrt(- 2 * log(1 - $p));
- return - ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) / (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
- }
- // If 0 < p < 1, return a null value
- return PHPExcel_Calculation_Functions :: NULL();
- } // function _inverse_ncdf()
-
-
- private static function _inverse_ncdf2($prob)
- {
- // Approximation of inverse standard normal CDF developed by
- // B. Moro, "The Full Monte," Risk 8(2), Feb 1995, 57-58.
-
-
- $a1 = 2.50662823884;
- $a2 = - 18.61500062529;
- $a3 = 41.39119773534;
- $a4 = - 25.44106049637;
-
- $b1 = - 8.4735109309;
- $b2 = 23.08336743743;
- $b3 = - 21.06224101826;
- $b4 = 3.13082909833;
-
- $c1 = 0.337475482272615;
- $c2 = 0.976169019091719;
- $c3 = 0.160797971491821;
- $c4 = 2.76438810333863E-02;
- $c5 = 3.8405729373609E-03;
- $c6 = 3.951896511919E-04;
- $c7 = 3.21767881768E-05;
- $c8 = 2.888167364E-07;
- $c9 = 3.960315187E-07;
-
- $y = $prob - 0.5;
- if (abs($y) < 0.42)
- {
- $z = ($y * $y);
- $z = $y * ((($a4 * $z + $a3) * $z + $a2) * $z + $a1) / (((($b4 * $z + $b3) * $z + $b2) * $z + $b1) * $z + 1);
- }
- else
- {
- if ($y > 0)
- {
- $z = log(- log(1 - $prob));
- }
- else
- {
- $z = log(- log($prob));
- }
- $z = $c1 + $z * ($c2 + $z * ($c3 + $z * ($c4 + $z * ($c5 + $z * ($c6 + $z * ($c7 + $z * ($c8 + $z * $c9)))))));
- if ($y < 0)
- {
- $z = - $z;
- }
- }
- return $z;
- } // function _inverse_ncdf2()
-
-
- private static function _inverse_ncdf3($p)
- {
- // ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3.
- // Produces the normal deviate Z corresponding to a given lower
- // tail area of P; Z is accurate to about 1 part in 10**16.
- //
- // This is a PHP version of the original FORTRAN code that can
- // be found at http://lib.stat.cmu.edu/apstat/
- $split1 = 0.425;
- $split2 = 5;
- $const1 = 0.180625;
- $const2 = 1.6;
-
- // coefficients for p close to 0.5
- $a0 = 3.3871328727963666080;
- $a1 = 1.3314166789178437745E+2;
- $a2 = 1.9715909503065514427E+3;
- $a3 = 1.3731693765509461125E+4;
- $a4 = 4.5921953931549871457E+4;
- $a5 = 6.7265770927008700853E+4;
- $a6 = 3.3430575583588128105E+4;
- $a7 = 2.5090809287301226727E+3;
-
- $b1 = 4.2313330701600911252E+1;
- $b2 = 6.8718700749205790830E+2;
- $b3 = 5.3941960214247511077E+3;
- $b4 = 2.1213794301586595867E+4;
- $b5 = 3.9307895800092710610E+4;
- $b6 = 2.8729085735721942674E+4;
- $b7 = 5.2264952788528545610E+3;
-
- // coefficients for p not close to 0, 0.5 or 1.
- $c0 = 1.42343711074968357734;
- $c1 = 4.63033784615654529590;
- $c2 = 5.76949722146069140550;
- $c3 = 3.64784832476320460504;
- $c4 = 1.27045825245236838258;
- $c5 = 2.41780725177450611770E-1;
- $c6 = 2.27238449892691845833E-2;
- $c7 = 7.74545014278341407640E-4;
-
- $d1 = 2.05319162663775882187;
- $d2 = 1.67638483018380384940;
- $d3 = 6.89767334985100004550E-1;
- $d4 = 1.48103976427480074590E-1;
- $d5 = 1.51986665636164571966E-2;
- $d6 = 5.47593808499534494600E-4;
- $d7 = 1.05075007164441684324E-9;
-
- // coefficients for p near 0 or 1.
- $e0 = 6.65790464350110377720;
- $e1 = 5.46378491116411436990;
- $e2 = 1.78482653991729133580;
- $e3 = 2.96560571828504891230E-1;
- $e4 = 2.65321895265761230930E-2;
- $e5 = 1.24266094738807843860E-3;
- $e6 = 2.71155556874348757815E-5;
- $e7 = 2.01033439929228813265E-7;
-
- $f1 = 5.99832206555887937690E-1;
- $f2 = 1.36929880922735805310E-1;
- $f3 = 1.48753612908506148525E-2;
- $f4 = 7.86869131145613259100E-4;
- $f5 = 1.84631831751005468180E-5;
- $f6 = 1.42151175831644588870E-7;
- $f7 = 2.04426310338993978564E-15;
-
- $q = $p - 0.5;
-
- // computation for p close to 0.5
- if (abs($q) <= split1)
- {
- $R = $const1 - $q * $q;
- $z = $q * ((((((($a7 * $R + $a6) * $R + $a5) * $R + $a4) * $R + $a3) * $R + $a2) * $R + $a1) * $R + $a0) / ((((((($b7 * $R + $b6) * $R + $b5) * $R + $b4) * $R + $b3) * $R + $b2) * $R + $b1) * $R + 1);
- }
- else
- {
- if ($q < 0)
- {
- $R = $p;
- }
- else
- {
- $R = 1 - $p;
- }
- $R = pow(- log($R), 2);
-
- // computation for p not close to 0, 0.5 or 1.
- If ($R <= $split2)
- {
- $R = $R - $const2;
- $z = ((((((($c7 * $R + $c6) * $R + $c5) * $R + $c4) * $R + $c3) * $R + $c2) * $R + $c1) * $R + $c0) / ((((((($d7 * $R + $d6) * $R + $d5) * $R + $d4) * $R + $d3) * $R + $d2) * $R + $d1) * $R + 1);
- }
- else
- {
- // computation for p near 0 or 1.
- $R = $R - $split2;
- $z = ((((((($e7 * $R + $e6) * $R + $e5) * $R + $e4) * $R + $e3) * $R + $e2) * $R + $e1) * $R + $e0) / ((((((($f7 * $R + $f6) * $R + $f5) * $R + $f4) * $R + $f3) * $R + $f2) * $R + $f1) * $R + 1);
- }
- if ($q < 0)
- {
- $z = - $z;
- }
- }
- return $z;
- } // function _inverse_ncdf3()
-
-
- /**
- * AVEDEV
- *
- * Returns the average of the absolute deviations of data points from their mean.
- * AVEDEV is a measure of the variability in a data set.
- *
- * Excel Function:
- * AVEDEV(value1[,value2[, ...]])
- *
- * @access public
- * @category Statistical Functions
- * @param mixed $arg,... Data values
- * @return float
- */
- public static function AVEDEV()
- {
- $aArgs = PHPExcel_Calculation_Functions :: flattenArrayIndexed(func_get_args());
-
- // Return value
- $returnValue = null;
-
- $aMean = self :: AVERAGE($aArgs);
- if ($aMean != PHPExcel_Calculation_Functions :: DIV0())
- {
- $aCount = 0;
- foreach ($aArgs as $k => $arg)
- {
- if ((is_bool($arg)) && ((! PHPExcel_Calculation_Functions :: isCellValue($k)) || (PHPExcel_Calculation_Functions :: getCompatibilityMode() == PHPExcel_Calculation_Functions :: COMPATIBILITY_OPENOFFICE)))
- {
- $arg = (integer) $arg;
- }
- // Is it a numeric value?
- if ((is_numeric($arg)) && (! is_string($arg)))
- {
- if (is_null($returnValue))
- {
- $returnValue = abs($arg - $aMean);
- }
- else
- {
- $returnValue += abs($arg - $aMean);
- }
- ++ $aCount;
- }
- }
-
- // Return
- if ($aCount == 0)
- {
- return PHPExcel_Calculation_Functions :: DIV0();
- }
- return $returnValue / $aCount;
- }
- return PHPExcel_Calculation_Functions :: NaN();
- } // function AVEDEV()
-
-
- /**
- * AVERAGE
- *
- * Returns the average (arithmetic mean) of the arguments
- *
- * Excel Function:
- * AVERAGE(value1[,value2[, ...]])
- *
- * @access public
- * @category Statistical Functions
- * @param mixed $arg,... Data values
- * @return float
- */
- public static function AVERAGE()
- {
- $returnValue = $aCount = 0;
-
- // Loop through arguments
- foreach (PHPExcel_Calculation_Functions :: flattenArrayIndexed(func_get_args()) as $k => $arg)
- {
- if ((is_bool($arg)) && ((! PHPExcel_Calculation_Functions :: isCellValue($k)) || (PHPExcel_Calculation_Functions :: getCompatibilityMode() == PHPExcel_Calculation_Functions :: COMPATIBILITY_OPENOFFICE)))
- {
- $arg = (integer) $arg;
- }
- // Is it a numeric value?
- if ((is_numeric($arg)) && (! is_string($arg)))
- {
- if (is_null($returnValue))
- {
- $returnValue = $arg;
- }
- else
- {
- $returnValue += $arg;
- }
- ++ $aCount;
- }
- }
-
- // Return
- if ($aCount > 0)
- {
- return $returnValue / $aCount;
- }
- else
- {
- return PHPExcel_Calculation_Functions :: DIV0();
- }
- } // function AVERAGE()
-
-
- /**
- * AVERAGEA
- *
- * Returns the average of its arguments, including numbers, text, and logical values
- *
- * Excel Function:
- * AVERAGEA(value1[,value2[, ...]])
- *
- * @access public
- * @category Statistical Functions
- * @param mixed $arg,... Data values
- * @return float
- */
- public static function AVERAGEA()
- {
- // Return value
- $returnValue = null;
-
- $aCount = 0;
- // Loop through arguments
- foreach (PHPExcel_Calculation_Functions :: flattenArrayIndexed(func_get_args()) as $k => $arg)
- {
- if ((is_bool($arg)) && (! PHPExcel_Calculation_Functions :: isMatrixValue($k)))
- {
- }
- else
- {
- if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != ''))))
- {
- if (is_bool($arg))
- {
- $arg = (integer) $arg;
- }
- elseif (is_string($arg))
- {
- $arg = 0;
- }
- if (is_null($returnValue))
- {
- $returnValue = $arg;
- }
- else
- {
- $returnValue += $arg;
- }
- ++ $aCount;
- }
- }
- }
-
- // Return
- if ($aCount > 0)
- {
- return $returnValue / $aCount;
- }
- else
- {
- return PHPExcel_Calculation_Functions :: DIV0();
- }
- } // function AVERAGEA()
-
-
- /**
- * AVERAGEIF
- *
- * Returns the average value from a range of cells that contain numbers within the list of arguments
- *
- * Excel Function:
- * AVERAGEIF(value1[,value2[, ...]],condition)
- *
- * @access public
- * @category Mathematical and Trigonometric Functions
- * @param mixed $arg,... Data values
- * @param string $condition The criteria that defines which cells will be checked.
- * @return float
- */
- public static function AVERAGEIF($aArgs, $condition, $averageArgs = array())
- {
- // Return value
- $returnValue = 0;
-
- $aArgs = PHPExcel_Calculation_Functions :: flattenArray($aArgs);
- $averageArgs = PHPExcel_Calculation_Functions :: flattenArray($averageArgs);
- if (count($averageArgs) == 0)
- {
- $averageArgs = $aArgs;
- }
- $condition = PHPExcel_Calculation_Functions :: _ifCondition($condition);
- // Loop through arguments
- $aCount = 0;
- foreach ($aArgs as $key => $arg)
- {
- if (! is_numeric($arg))
- {
- $arg = PHPExcel_Calculation :: _wrapResult(strtoupper($arg));
- }
- $testCondition = '=' . $arg . $condition;
- if (PHPExcel_Calculation :: getInstance()->_calculateFormulaValue($testCondition))
- {
- if ((is_null($returnValue)) || ($arg > $returnValue))
- {
- $returnValue += $arg;
- ++ $aCount;
- }
- }
- }
-
- // Return
- if ($aCount > 0)
- {
- return $returnValue / $aCount;
- }
- else
- {
- return PHPExcel_Calculation_Functions :: DIV0();
- }
- } // function AVERAGEIF()
-
-
- /**
- * BETADIST
- *
- * Returns the beta distribution.
- *
- * @param float $value Value at which you want to evaluate the distribution
- * @param float $alpha Parameter to the distribution
- * @param float $beta Parameter to the distribution
- * @param boolean $cumulative
- * @return float
- *
- */
- public static function BETADIST($value, $alpha, $beta, $rMin = 0, $rMax = 1)
- {
- $value = PHPExcel_Calculation_Functions :: flattenSingleValue($value);
- $alpha = PHPExcel_Calculation_Functions :: flattenSingleValue($alpha);
- $beta = PHPExcel_Calculation_Functions :: flattenSingleValue($beta);
- $rMin = PHPExcel_Calculation_Functions :: flattenSingleValue($rMin);
- $rMax = PHPExcel_Calculation_Functions :: flattenSingleValue($rMax);
-
- if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax)))
- {
- if (($value < $rMin) || ($value > $rMax) || ($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax))
- {
- return PHPExcel_Calculation_Functions :: NaN();
- }
- if ($rMin > $rMax)
- {
- $tmp = $rMin;
- $rMin = $rMax;
- $rMax = $tmp;
- }
- $value -= $rMin;
- $value /= ($rMax - $rMin);
- return self :: _incompleteBeta($value, $alpha, $beta);
- }
- return PHPExcel_Calculation_Functions :: VALUE();
- } // function BETADIST()
-
-
- /**
- * BETAINV
- *
- * Returns the inverse of the beta distribution.
- *
- * @param float $probability Probability at which you want to evaluate the distribution
- * @param float $alpha Parameter to the distribution
- * @param float $beta Parameter to the distribution
- * @param boolean $cumulative
- * @return float
- *
- */
- public static function BETAINV($probability, $alpha, $beta, $rMin = 0, $rMax = 1)
- {
- $probability = PHPExcel_Calculation_Functions :: flattenSingleValue($probability);
- $alpha = PHPExcel_Calculation_Functions :: flattenSingleValue($alpha);
- $beta = PHPExcel_Calculation_Functions :: flattenSingleValue($beta);
- $rMin = PHPExcel_Calculation_Functions :: flattenSingleValue($rMin);
- $rMax = PHPExcel_Calculation_Functions :: flattenSingleValue($rMax);
-
- if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax)))
- {
- if (($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax) || ($probability <= 0) || ($probability > 1))
- {
- return PHPExcel_Calculation_Functions :: NaN();
- }
- if ($rMin > $rMax)
- {
- $tmp = $rMin;
- $rMin = $rMax;
- $rMax = $tmp;
- }
- $a = 0;
- $b = 2;
-
- $i = 0;
- while ((($b - $a) > PRECISION) && ($i ++ < MAX_ITERATIONS))
- {
- $guess = ($a + $b) / 2;
- $result = self :: BETADIST($guess, $alpha, $beta);
- if (($result == $probability) || ($result == 0))
- {
- $b = $a;
- }
- elseif ($result > $probability)
- {
- $b = $guess;
- }
- else
- {
- $a = $guess;
- }
- }
- if ($i == MAX_ITERATIONS)
- {
- return PHPExcel_Calculation_Functions :: NA();
- }
- return round($rMin + $guess * ($rMax - $rMin), 12);
- }
- return PHPExcel_Calculation_Functions :: VALUE();
- } // function BETAINV()
-
-
- /**
- * BINOMDIST
- *
- * Returns the individual term binomial distribution probability. Use BINOMDIST in problems with
- * a fixed number of tests or trials, when the outcomes of any trial are only success or failure,
- * when trials are independent, and when the probability of success is constant throughout the
- * experiment. For example, BINOMDIST can calculate the probability that two of the next three
- * babies born are male.
- *
- * @param float $value Number of successes in trials
- * @param float $trials Number of trials
- * @param float $probability Probability of success on each trial
- * @param boolean $cumulative
- * @return float
- *
- * @todo Cumulative distribution function
- *
- */
- public static function BINOMDIST($value, $trials, $probability, $cumulative)
- {
- $value = floor(PHPExcel_Calculation_Functions :: flattenSingleValue($value));
- $trials = floor(PHPExcel_Calculation_Functions :: flattenSingleValue($trials));
- $probability = PHPExcel_Calculation_Functions :: flattenSingleValue($probability);
-
- if ((is_numeric($value)) && (is_numeric($trials)) && (is_numeric($probability)))
- {
- if (($value < 0) || ($value > $trials))
- {
- return PHPExcel_Calculation_Functions :: NaN();
- }
- if (($probability < 0) || ($probability > 1))
- {
- return PHPExcel_Calculation_Functions :: NaN();
- }
- if ((is_numeric($cumulative)) || (is_bool($cumulative)))
- {
- if ($cumulative)
- {
- $summer = 0;
- for($i = 0; $i <= $value; ++ $i)
- {
- $summer += PHPExcel_Calculation_MathTrig :: COMBIN($trials, $i) * pow($probability, $i) * pow(1 - $probability, $trials - $i);
- }
- return $summer;
- }
- else
- {
- return PHPExcel_Calculation_MathTrig :: COMBIN($trials, $value) * pow($probability, $value) * pow(1 - $probability, $trials - $value);
- }
- }
- }
- return PHPExcel_Calculation_Functions :: VALUE();
- } // function BINOMDIST()
-
-
- /**
- * CHIDIST
- *
- * Returns the one-tailed probability of the chi-squared distribution.
- *
- * @param float $value Value for the function
- * @param float $degrees degrees of freedom
- * @return float
- */
- public static function CHIDIST($value, $degrees)
- {
- $value = PHPExcel_Calculation_Functions :: flattenSingleValue($value);
- $degrees = floor(PHPExcel_Calculation_Functions :: flattenSingleValue($degrees));
-
- if ((is_numeric($value)) && (is_numeric($degrees)))
- {
- if ($degrees < 1)
- {
- return PHPExcel_Calculation_Functions :: NaN();
- }
- if ($value < 0)
- {
- if (PHPExcel_Calculation_Functions :: getCompatibilityMode() == PHPExcel_Calculation_Functions :: COMPATIBILITY_GNUMERIC)
- {
- return 1;
- }
- return PHPExcel_Calculation_Functions :: NaN();
- }
- return 1 - (self :: _incompleteGamma($degrees / 2, $value / 2) / self :: _gamma($degrees / 2));
- }
- return PHPExcel_Calculation_Functions :: VALUE();
- } // function CHIDIST()
-
-
- /**
- * CHIINV
- *
- * Returns the one-tailed probability of the chi-squared distribution.
- *
- * @param float $probability Probability for the function
- * @param float $degrees degrees of freedom
- * @return float
- */
- public static function CHIINV($probability, $degrees)
- {
- $probability = PHPExcel_Calculation_Functions :: flattenSingleValue($probability);
- $degrees = floor(PHPExcel_Calculation_Functions :: flattenSingleValue($degrees));
-
- if ((is_numeric($probability)) && (is_numeric($degrees)))
- {
-
- $xLo = 100;
- $xHi = 0;
-
- $x = $xNew = 1;
- $dx = 1;
- $i = 0;
-
- while ((abs($dx) > PRECISION) && ($i ++ < MAX_ITERATIONS))
- {
- // Apply Newton-Raphson step
- $result = self :: CHIDIST($x, $degrees);
- $error = $result - $probability;
- if ($error == 0.0)
- {
- $dx = 0;
- }
- elseif ($error < 0.0)
- {
- $xLo = $x;
- }
- else
- {
- $xHi = $x;
- }
- // Avoid division by zero
- if ($result != 0.0)
- {
- $dx = $error / $result;
- $xNew = $x - $dx;
- }
- // If the NR fails to converge (which for example may be the
- // case if the initial guess is too rough) we apply a bisection
- // step to determine a more narrow interval around the root.
- if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0))
- {
- $xNew = ($xLo + $xHi) / 2;
- $dx = $xNew - $x;
- }
- $x = $xNew;
- }
- if ($i == MAX_ITERATIONS)
- {
- return PHPExcel_Calculation_Functions :: NA();
- }
- return round($x, 12);
- }
- return PHPExcel_Calculation_Functions :: VALUE();
- } // function CHIINV()
-
-
- /**
- * CONFIDENCE
- *
- * Returns the confidence interval for a population mean
- *
- * @param float $alpha
- * @param float $stdDev Standard Deviation
- * @param float $size
- * @return float
- *
- */
- public static function CONFIDENCE($alpha, $stdDev, $size)
- {
- $alpha = PHPExcel_Calculation_Functions :: flattenSingleValue($alpha);
- $stdDev = PHPExcel_Calculation_Functions :: flattenSingleValue($stdDev);
- $size = floor(PHPExcel_Calculation_Functions :: flattenSingleValue($size));
-
- if ((is_numeric($alpha)) && (is_numeric($stdDev)) && (is_numeric($size)))
- {
- if (($alpha <= 0) || ($alpha >= 1))
- {
- return PHPExcel_Calculation_Functions :: NaN();
- }
- if (($stdDev <= 0) || ($size < 1))
- {
- return PHPExcel_Calculation_Functions :: NaN();
- }
- return self :: NORMSINV(1 - $alpha / 2) * $stdDev / sqrt($size);
- }
- return PHPExcel_Calculation_Functions :: VALUE();
- } // function CONFIDENCE()
-
-
- /**
- * CORREL
- *
- * Returns covariance, the average of the products of deviations for each data point pair.
- *
- * @param array of mixed Data Series Y
- * @param array of mixed Data Series X
- * @return float
- */
- public static function CORREL($yValues, $xValues = null)
- {
- if ((is_null($xValues)) || (! is_array($yValues)) || (! is_array($xValues)))
- {
- return PHPExcel_Calculation_Functions :: VALUE();
- }
- if (! self :: _checkTrendArrays($yValues, $xValues))
- {
- return PHPExcel_Calculation_Functions :: VALUE();
- }
- $yValueCount = count($yValues);
- $xValueCount = count($xValues);
-
- if (($yValueCount == 0) || ($yValueCount != $xValueCount))
- {
- return PHPExcel_Calculation_Functions :: NA();
- }
- elseif ($yValueCount == 1)
- {
- return PHPExcel_Calculation_Functions :: DIV0();
- }
-
- $bestFitLinear = trendClass :: calculate(trendClass :: TREND_LINEAR, $yValues, $xValues);
- return $bestFitLinear->getCorrelation();
- } // function CORREL()
-
-
- /**
- * COUNT
- *
- * Counts the number of cells that contain numbers within the list of arguments
- *
- * Excel Function:
- * COUNT(value1[,value2[, ...]])
- *
- * @access public
- * @category Statistical Functions
- * @param mixed $arg,... Data values
- * @return int
- */
- public static function COUNT()
- {
- // Return value
- $returnValue = 0;
-
- // Loop through arguments
- $aArgs = PHPExcel_Calculation_Functions :: flattenArrayIndexed(func_get_args());
- foreach ($aArgs as $k => $arg)
- {
- if ((is_bool($arg)) && ((! PHPExcel_Calculation_Functions :: isCellValue($k)) || (PHPExcel_Calculation_Functions :: getCompatibilityMode() == PHPExcel_Calculation_Functions :: COMPATIBILITY_OPENOFFICE)))
- {
- $arg = (integer) $arg;
- }
- // Is it a numeric value?
- if ((is_numeric($arg)) && (! is_string($arg)))
- {
- ++ $returnValue;
- }
- }
-
- // Return
- return $returnValue;
- } // function COUNT()
-
-
- /**
- * COUNTA
- *
- * Counts the number of cells that are not empty within the list of arguments
- *
- * Excel Function:
- * COUNTA(value1[,value2[, ...]])
- *
- * @access public
- * @category Statistical Functions
- * @param mixed $arg,... Data values
- * @return int
- */
- public static function COUNTA()
- {
- // Return value
- $returnValue = 0;
-
- // Loop through arguments
- $aArgs = PHPExcel_Calculation_Functions :: flattenArray(func_get_args());
- foreach ($aArgs as $arg)
- {
- // Is it a numeric, boolean or string value?
- if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != ''))))
- {
- ++ $returnValue;
- }
- }
-
- // Return
- return $returnValue;
- } // function COUNTA()
-
-
- /**
- * COUNTBLANK
- *
- * Counts the number of empty cells within the list of arguments
- *
- * Excel Function:
- * COUNTBLANK(value1[,value2[, ...]])
- *
- * @access public
- * @category Statistical Functions
- * @param mixed $arg,... Data values
- * @return int
- */
- public static function COUNTBLANK()
- {
- // Return value
- $returnValue = 0;
-
- // Loop through arguments
- $aArgs = PHPExcel_Calculation_Functions :: flattenArray(func_get_args());
- foreach ($aArgs as $arg)
- {
- // Is it a blank cell?
- if ((is_null($arg)) || ((is_string($arg)) && ($arg == '')))
- {
- ++ $returnValue;
- }
- }
-
- // Return
- return $returnValue;
- } // function COUNTBLANK()
-
-
- /**
- * COUNTIF
- *
- * Counts the number of cells that contain numbers within the list of arguments
- *
- * Excel Function:
- * COUNTIF(value1[,value2[, ...]],condition)
- *
- * @access public
- * @category Statistical Functions
- * @param mixed $arg,... Data values
- * @param string $condition The criteria that defines which cells will be counted.
- * @return int
- */
- public static function COUNTIF($aArgs, $condition)
- {
- // Return value
- $returnValue = 0;
-
- $aArgs = PHPExcel_Calculation_Functions :: flattenArray($aArgs);
- $condition = PHPExcel_Calculation_Functions :: _ifCondition($condition);
- // Loop through arguments
- foreach ($aArgs as $arg)
- {
- if (! is_numeric($arg))
- {
- $arg = PHPExcel_Calculation :: _wrapResult(strtoupper($arg));
- }
- $testCondition = '=' . $arg . $condition;
- if (PHPExcel_Calculation :: getInstance()->_calculateFormulaValue($testCondition))
- {
- // Is it a value within our criteria
- ++ $returnValue;
- }
- }
-
- // Return
- return $returnValue;
- } // function COUNTIF()
-
-
- /**
- * COVAR
- *
- * Returns covariance, the average of the products of deviations for each data point pair.
- *
- * @param array of mixed Data Series Y
- * @param array of mixed Data Series X
- * @return float
- */
- public static function COVAR($yValues, $xValues)
- {
- if (! self :: _checkTrendArrays($yValues, $xValues))
- {
- return PHPExcel_Calculation_Functions :: VALUE();
- }
- $yValueCount = count($yValues);
- $xValueCount = count($xValues);
-
- if (($yValueCount == 0) || ($yValueCount != $xValueCount))
- {
- return PHPExcel_Calculation_Functions :: NA();
- }
- elseif ($yValueCount == 1)
- {
- return PHPExcel_Calculation_Functions :: DIV0();
- }
-
- $bestFitLinear = trendClass :: calculate(trendClass :: TREND_LINEAR, $yValues, $xValues);
- re…
Large files files are truncated, but you can click here to view the full file