/lib/phpexcel/PHPExcel/Calculation/Statistical.php
PHP | 3745 lines | 2176 code | 376 blank | 1193 comment | 641 complexity | 36beb73f1383cae74278f2e963c7e9b0 MD5 | raw file
Possible License(s): Apache-2.0, LGPL-2.1, BSD-3-Clause, MIT, GPL-3.0
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- <?php
- /** 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
- *
- * Copyright (c) 2006 - 2015 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 - 2015 PHPExcel (http://www.codeplex.com/PHPExcel)
- * @license http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt LGPL
- * @version ##VERSION##, ##DATE##
- */
- 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;
- }
- /**
- * 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, $q));
- }
- }
- /**
- * Incomplete beta function
- *
- * @author Jaco van Kooten
- * @author Paul Meagher
- *
- * The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992).
- * @param x require 0<=x<=1
- * @param p require p>0
- * @param q require q>0
- * @return 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow
- */
- private static function incompleteBeta($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 cache for logBeta function
- private static $logBetaCacheP = 0.0;
- private static $logBetaCacheQ = 0.0;
- private static $logBetaCacheResult = 0.0;
- /**
- * The natural logarithm of the beta function.
- *
- * @param p require p>0
- * @param q require q>0
- * @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
- * @author Jaco van Kooten
- */
- private static function logBeta($p, $q)
- {
- if ($p != self::$logBetaCacheP || $q != self::$logBetaCacheQ) {
- self::$logBetaCacheP = $p;
- self::$logBetaCacheQ = $q;
- if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) {
- self::$logBetaCacheResult = 0.0;
- } else {
- self::$logBetaCacheResult = self::logGamma($p) + self::logGamma($q) - self::logGamma($p + $q);
- }
- }
- return self::$logBetaCacheResult;
- }
- /**
- * 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;
- }
- /**
- * 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 $logGammaCacheResult = 0.0;
- private static $logGammaCacheX = 0.0;
- private static function logGamma($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::$logGammaCacheX) {
- return self::$logGammaCacheResult;
- }
- $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
- // --------------------------
- $res = MAX_VALUE;
- }
- // ------------------------------
- // Final adjustments and return
- // ------------------------------
- self::$logGammaCacheX = $x;
- self::$logGammaCacheResult = $res;
- return $res;
- }
- //
- // Private implementation of the incomplete Gamma function
- //
- private static function incompleteGamma($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) * $summer;
- }
- //
- // Private implementation of the Gamma function
- //
- private static function gamma($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 / $x));
- }
- /***************************************************************************
- * inverse_ncdf.php
- * -------------------
- * begin : Friday, January 16, 2004
- * copyright : (C) 2004 Michael Nickerson
- * email : nickersonm@yahoo.com
- *
- ***************************************************************************/
- private static function inverseNcdf($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]) * $q + 1);
- }
- // If 0 < p < 1, return a null value
- return PHPExcel_Calculation_Functions::NULL();
- }
- private static function inverseNcdf2($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 $z;
- } // function inverseNcdf2()
- private static function inverseNcdf3($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;
- }
- /**
- * 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();
- }
- /**
- * 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();
- }
- }
- /**
- * 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()
- {
- $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;
- }
- }
- }
- if ($aCount > 0) {
- return $returnValue / $aCount;
- } else {
- return PHPExcel_Calculation_Functions::DIV0();
- }
- }
- /**
- * 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.
- * @param mixed[] $averageArgs Data values
- * @return float
- */
- public static function AVERAGEIF($aArgs, $condition, $averageArgs = array())
- {
- $returnValue = 0;
- $aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
- $averageArgs = PHPExcel_Calculation_Functions::flattenArray($averageArgs);
- if (empty($averageArgs)) {
- $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;
- }
- }
- }
- if ($aCount > 0) {
- return $returnValue / $aCount;
- }
- return PHPExcel_Calculation_Functions::DIV0();
- }
- /**
- * 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();
- }
- /**
- * 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 float $rMin Minimum value
- * @param float $rMax Maximum value
- * @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();
- }
- /**
- * 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();
- }
- /**
- * 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();
- }
- /**
- * 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();
- }
- /**
- * 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();
- }
- /**
- * 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();
- }
- /**
- * 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()
- {
- $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 $returnValue;
- }
- /**
- * 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()
- {
- $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 $returnValue;
- }
- /**
- * 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()
- {
- $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 $returnValue;
- }
- /**
- * 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)
- {
- $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 $returnValue;
- }
- /**
- * COVAR
- *
- * Returns covariance, the average of the products of deviations for each data point pair.
- *
- * @param array of mixed Data Series Y
- * @param array of mixed Data Series X
- * @return float
- */
- public static function COVAR($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);
- return $bestFitLinear->getCovariance();
- }
- /**
- * CRITBINOM
- *
- * Returns the smallest value for which the cumulative binomial distribution is greater
- * than or equal to a criterion value
- *
- * See http://support.microsoft.com/kb/828117/ for details of the algorithm used
- *
- * @param float $trials number of Bernoulli trials
- * @param float $probability probability of a success on each trial
- * @param float $alpha criterion value
- * @return int
- *
- * @todo Warning. This implementation differs from the algorithm detailed on the MS
- * web site in that $CumPGuessMinus1 = $CumPGuess - 1 rather than $CumPGuess - $PGuess
- * This eliminates a potential endless loop error, but may have an adverse affect on the
- * accuracy of the function (although all my tests have so far returned correct results).
- *
- */
- public static function CRITBINOM($trials, $probability, $alpha)
- {
- $trials = floor(PHPExcel_Calculation_Functions::flattenSingleValue($trials));
- $probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
- $alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
- if ((is_numeric($trials)) && (is_numeric($probability)) && (is_numeric($alpha))) {
- if ($trials < 0) {
- return PHPExcel_Calculation_Functions::NaN();
- } elseif (($probability < 0) || ($probability > 1)) {
- return PHPExcel_Calculation_Functions::NaN();
- } elseif (($alpha < 0) || ($alpha > 1)) {
- return PHPExcel_Calculation_Functions::NaN();
- } elseif ($alpha <= 0.5) {
- $t = sqrt(log(1 / ($alpha * $alpha)));
- $trialsApprox = 0 - ($t + (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t));
- } else {
- $t = sqrt(log(1 / pow(1 - $alpha, 2)));
- $trialsApprox = $t - (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t);
- }
- $Guess = floor($trials * $probability + $trialsApprox * sqrt($trials * $probability * (1 - $probability)));
- if ($Guess < 0) {
- $Guess = 0;
- } elseif ($Guess > $trials) {
- $Guess = $trials;
- }
- $TotalUnscaledProbability = $UnscaledPGuess = $UnscaledCumPGuess = 0.0;
- $EssentiallyZero = 10e-12;
- $m = floor($trials * $probability);
- ++$TotalUnscaledProbability;
- if ($m == $Guess) {
- ++$UnscaledPGuess;
- }
- if ($m <= $Guess) {
- ++$UnscaledCumPGuess;
- }
- $Prev…
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