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Diffstat (limited to 'admin/survey/excel/PHPExcel/Calculation/Statistical.php')
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1 files changed, 3644 insertions, 0 deletions
diff --git a/admin/survey/excel/PHPExcel/Calculation/Statistical.php b/admin/survey/excel/PHPExcel/Calculation/Statistical.php new file mode 100644 index 0000000..b2a4f43 --- /dev/null +++ b/admin/survey/excel/PHPExcel/Calculation/Statistical.php @@ -0,0 +1,3644 @@ +<?php
+/**
+ * PHPExcel
+ *
+ * Copyright (c) 2006 - 2012 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 - 2012 PHPExcel (http://www.codeplex.com/PHPExcel)
+ * @license http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt LGPL
+ * @version 1.7.8, 2012-10-12
+ */
+
+
+/** 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 - 2012 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 (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;
+ }
+ }
+ }
+
+ // 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);
+ return $bestFitLinear->getCovariance();
+ } // function COVAR()
+
+
+ /**
+ * 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();
+ }
+ if (($probability < 0) || ($probability > 1)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if (($alpha < 0) || ($alpha > 1)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if ($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; }
+
+ $PreviousValue = 1;
+ $Done = False;
+ $k = $m + 1;
+ while ((!$Done) && ($k <= $trials)) {
+ $CurrentValue = $PreviousValue * ($trials - $k + 1) * $probability / ($k * (1 - $probability));
+ $TotalUnscaledProbability += $CurrentValue;
+ if ($k == $Guess) { $UnscaledPGuess += $CurrentValue; }
+ if ($k <= $Guess) { $UnscaledCumPGuess += $CurrentValue; }
+ if ($CurrentValue <= $EssentiallyZero) { $Done = True; }
+ $PreviousValue = $CurrentValue;
+ ++$k;
+ }
+
+ $PreviousValue = 1;
+ $Done = False;
+ $k = $m - 1;
+ while ((!$Done) && ($k >= 0)) {
+ $CurrentValue = $PreviousValue * $k + 1 * (1 - $probability) / (($trials - $k) * $probability);
+ $TotalUnscaledProbability += $CurrentValue;
+ if ($k == $Guess) { $UnscaledPGuess += $CurrentValue; }
+ if ($k <= $Guess) { $UnscaledCumPGuess += $CurrentValue; }
+ if ($CurrentValue <= $EssentiallyZero) { $Done = True; }
+ $PreviousValue = $CurrentValue;
+ --$k;
+ }
+
+ $PGuess = $UnscaledPGuess / $TotalUnscaledProbability;
+ $CumPGuess = $UnscaledCumPGuess / $TotalUnscaledProbability;
+
+// $CumPGuessMinus1 = $CumPGuess - $PGuess;
+ $CumPGuessMinus1 = $CumPGuess - 1;
+
+ while (True) {
+ if (($CumPGuessMinus1 < $alpha) && ($CumPGuess >= $alpha)) {
+ return $Guess;
+ } elseif (($CumPGuessMinus1 < $alpha) && ($CumPGuess < $alpha)) {
+ $PGuessPlus1 = $PGuess * ($trials - $Guess) * $probability / $Guess / (1 - $probability);
+ $CumPGuessMinus1 = $CumPGuess;
+ $CumPGuess = $CumPGuess + $PGuessPlus1;
+ $PGuess = $PGuessPlus1;
+ ++$Guess;
+ } elseif (($CumPGuessMinus1 >= $alpha) && ($CumPGuess >= $alpha)) {
+ $PGuessMinus1 = $PGuess * $Guess * (1 - $probability) / ($trials - $Guess + 1) / $probability;
+ $CumPGuess = $CumPGuessMinus1;
+ $CumPGuessMinus1 = $CumPGuessMinus1 - $PGuess;
+ $PGuess = $PGuessMinus1;
+ --$Guess;
+ }
+ }
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function CRITBINOM()
+
+
+ /**
+ * DEVSQ
+ *
+ * Returns the sum of squares of deviations of data points from their sample mean.
+ *
+ * Excel Function:
+ * DEVSQ(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function DEVSQ() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
+
+ // Return value
+ $returnValue = null;
+
+ $aMean = self::AVERAGE($aArgs);
+ if ($aMean != PHPExcel_Calculation_Functions::DIV0()) {
+ $aCount = -1;
+ foreach ($aArgs as $k => $arg) {
+ // Is it a numeric value?
+ if ((is_bool($arg)) &&
+ ((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
+ $arg = (integer) $arg;
+ }
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ if (is_null($returnValue)) {
+ $returnValue = pow(($arg - $aMean),2);
+ } else {
+ $returnValue += pow(($arg - $aMean),2);
+ }
+ ++$aCount;
+ }
+ }
+
+ // Return
+ if (is_null($returnValue)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ } else {
+ return $returnValue;
+ }
+ }
+ return self::NA();
+ } // function DEVSQ()
+
+
+ /**
+ * EXPONDIST
+ *
+ * Returns the exponential distribution. Use EXPONDIST to model the time between events,
+ * such as how long an automated bank teller takes to deliver cash. For example, you can
+ * use EXPONDIST to determine the probability that the process takes at most 1 minute.
+ *
+ * @param float $value Value of the function
+ * @param float $lambda The parameter value
+ * @param boolean $cumulative
+ * @return float
+ */
+ public static function EXPONDIST($value, $lambda, $cumulative) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+ $lambda = PHPExcel_Calculation_Functions::flattenSingleValue($lambda);
+ $cumulative = PHPExcel_Calculation_Functions::flattenSingleValue($cumulative);
+
+ if ((is_numeric($value)) && (is_numeric($lambda))) {
+ if (($value < 0) || ($lambda < 0)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
+ if ($cumulative) {
+ return 1 - exp(0-$value*$lambda);
+ } else {
+ return $lambda * exp(0-$value*$lambda);
+ }
+ }
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function EXPONDIST()
+
+
+ /**
+ * FISHER
+ *
+ * Returns the Fisher transformation at x. This transformation produces a function that
+ * is normally distributed rather than skewed. Use this function to perform hypothesis
+ * testing on the correlation coefficient.
+ *
+ * @param float $value
+ * @return float
+ */
+ public static function FISHER($value) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+
+ if (is_numeric($value)) {
+ if (($value <= -1) || ($value >= 1)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ return 0.5 * log((1+$value)/(1-$value));
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function FISHER()
+
+
+ /**
+ * FISHERINV
+ *
+ * Returns the inverse of the Fisher transformation. Use this transformation when
+ * analyzing correlations between ranges or arrays of data. If y = FISHER(x), then
+ * FISHERINV(y) = x.
+ *
+ * @param float $value
+ * @return float
+ */
+ public static function FISHERINV($value) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+
+ if (is_numeric($value)) {
+ return (exp(2 * $value) - 1) / (exp(2 * $value) + 1);
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function FISHERINV()
+
+
+ /**
+ * FORECAST
+ *
+ * Calculates, or predicts, a future value by using existing values. The predicted value is a y-value for a given x-value.
+ *
+ * @param float Value of X for which we want to find Y
+ * @param array of mixed Data Series Y
+ * @param array of mixed Data Series X
+ * @return float
+ */
+ public static function FORECAST($xValue,$yValues,$xValues) {
+ $xValue = PHPExcel_Calculation_Functions::flattenSingleValue($xValue);
+ if (!is_numeric($xValue)) {
+ return PHPExcel_Calculation_Functions::VALUE();
+ }
+
+ if (!self::_checkTrendArrays($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 $bestFitLinear->getValueOfYForX($xValue);
+ } // function FORECAST()
+
+
+ /**
+ * GAMMADIST
+ *
+ * Returns the gamma distribution.
+ *
+ * @param float $value Value at which you want to evaluate the distribution
+ * @param float $a Parameter to the distribution
+ * @param float $b Parameter to the distribution
+ * @param boolean $cumulative
+ * @return float
+ *
+ */
+ public static function GAMMADIST($value,$a,$b,$cumulative) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+ $a = PHPExcel_Calculation_Functions::flattenSingleValue($a);
+ $b = PHPExcel_Calculation_Functions::flattenSingleValue($b);
+
+ if ((is_numeric($value)) && (is_numeric($a)) && (is_numeric($b))) {
+ if (($value < 0) || ($a <= 0) || ($b <= 0)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
+ if ($cumulative) {
+ return self::_incompleteGamma($a,$value / $b) / self::_gamma($a);
+ } else {
+ return (1 / (pow($b,$a) * self::_gamma($a))) * pow($value,$a-1) * exp(0-($value / $b));
+ }
+ }
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function GAMMADIST()
+
+
+ /**
+ * GAMMAINV
+ *
+ * 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 $beta Parameter to the distribution
+ * @return float
+ *
+ */
+ public static function GAMMAINV($probability,$alpha,$beta) {
+ $probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
+ $alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
+ $beta = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
+
+ if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta))) {
+ if (($alpha <= 0) || ($beta <= 0) || ($probability < 0) || ($probability > 1)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+
+ $xLo = 0;
+ $xHi = $alpha * $beta * 5;
+
+ $x = $xNew = 1;
+ $error = $pdf = 0;
+ $dx = 1024;
+ $i = 0;
+
+ while ((abs($dx) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
+ // Apply Newton-Raphson step
+ $error = self::GAMMADIST($x, $alpha, $beta, True) - $probability;
+ if ($error < 0.0) {
+ $xLo = $x;
+ } else {
+ $xHi = $x;
+ }
+ $pdf = self::GAMMADIST($x, $alpha, $beta, False);
+ // Avoid division by zero
+ if ($pdf != 0.0) {
+ $dx = $error / $pdf;
+ $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 > $xHi) || ($pdf == 0.0)) {
+ $xNew = ($xLo + $xHi) / 2;
+ $dx = $xNew - $x;
+ }
+ $x = $xNew;
+ }
+ if ($i == MAX_ITERATIONS) {
+ return PHPExcel_Calculation_Functions::NA();
+ }
+ return $x;
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function GAMMAINV()
+
+
+ /**
+ * GAMMALN
+ *
+ * Returns the natural logarithm of the gamma function.
+ *
+ * @param float $value
+ * @return float
+ */
+ public static function GAMMALN($value) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+
+ if (is_numeric($value)) {
+ if ($value <= 0) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ return log(self::_gamma($value));
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function GAMMALN()
+
+
+ /**
+ * GEOMEAN
+ *
+ * Returns the geometric mean of an array or range of positive data. For example, you
+ * can use GEOMEAN to calculate average growth rate given compound interest with
+ * variable rates.
+ *
+ * Excel Function:
+ * GEOMEAN(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function GEOMEAN() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+
+ $aMean = PHPExcel_Calculation_MathTrig::PRODUCT($aArgs);
+ if (is_numeric($aMean) && ($aMean > 0)) {
+ $aCount = self::COUNT($aArgs) ;
+ if (self::MIN($aArgs) > 0) {
+ return pow($aMean, (1 / $aCount));
+ }
+ }
+ return PHPExcel_Calculation_Functions::NaN();
+ } // GEOMEAN()
+
+
+ /**
+ * GROWTH
+ *
+ * Returns values along a predicted emponential trend
+ *
+ * @param array of mixed Data Series Y
+ * @param array of mixed Data Series X
+ * @param array of mixed Values of X for which we want to find Y
+ * @param boolean A logical value specifying whether to force the intersect to equal 0.
+ * @return array of float
+ */
+ public static function GROWTH($yValues,$xValues=array(),$newValues=array(),$const=True) {
+ $yValues = PHPExcel_Calculation_Functions::flattenArray($yValues);
+ $xValues = PHPExcel_Calculation_Functions::flattenArray($xValues);
+ $newValues = PHPExcel_Calculation_Functions::flattenArray($newValues);
+ $const = (is_null($const)) ? True : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
+
+ $bestFitExponential = trendClass::calculate(trendClass::TREND_EXPONENTIAL,$yValues,$xValues,$const);
+ if (empty($newValues)) {
+ $newValues = $bestFitExponential->getXValues();
+ }
+
+ $returnArray = array();
+ foreach($newValues as $xValue) {
+ $returnArray[0][] = $bestFitExponential->getValueOfYForX($xValue);
+ }
+
+ return $returnArray;
+ } // function GROWTH()
+
+
+ /**
+ * HARMEAN
+ *
+ * Returns the harmonic mean of a data set. The harmonic mean is the reciprocal of the
+ * arithmetic mean of reciprocals.
+ *
+ * Excel Function:
+ * HARMEAN(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function HARMEAN() {
+ // Return value
+ $returnValue = PHPExcel_Calculation_Functions::NA();
+
+ // Loop through arguments
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+ if (self::MIN($aArgs) < 0) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ $aCount = 0;
+ foreach ($aArgs as $arg) {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ if ($arg <= 0) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if (is_null($returnValue)) {
+ $returnValue = (1 / $arg);
+ } else {
+ $returnValue += (1 / $arg);
+ }
+ ++$aCount;
+ }
+ }
+
+ // Return
+ if ($aCount > 0) {
+ return 1 / ($returnValue / $aCount);
+ } else {
+ return $returnValue;
+ }
+ } // function HARMEAN()
+
+
+ /**
+ * HYPGEOMDIST
+ *
+ * Returns the hypergeometric distribution. HYPGEOMDIST returns the probability of a given number of
+ * sample successes, given the sample size, population successes, and population size.
+ *
+ * @param float $sampleSuccesses Number of successes in the sample
+ * @param float $sampleNumber Size of the sample
+ * @param float $populationSuccesses Number of successes in the population
+ * @param float $populationNumber Population size
+ * @return float
+ *
+ */
+ public static function HYPGEOMDIST($sampleSuccesses, $sampleNumber, $populationSuccesses, $populationNumber) {
+ $sampleSuccesses = floor(PHPExcel_Calculation_Functions::flattenSingleValue($sampleSuccesses));
+ $sampleNumber = floor(PHPExcel_Calculation_Functions::flattenSingleValue($sampleNumber));
+ $populationSuccesses = floor(PHPExcel_Calculation_Functions::flattenSingleValue($populationSuccesses));
+ $populationNumber = floor(PHPExcel_Calculation_Functions::flattenSingleValue($populationNumber));
+
+ if ((is_numeric($sampleSuccesses)) && (is_numeric($sampleNumber)) && (is_numeric($populationSuccesses)) && (is_numeric($populationNumber))) {
+ if (($sampleSuccesses < 0) || ($sampleSuccesses > $sampleNumber) || ($sampleSuccesses > $populationSuccesses)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if (($sampleNumber <= 0) || ($sampleNumber > $populationNumber)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if (($populationSuccesses <= 0) || ($populationSuccesses > $populationNumber)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ return PHPExcel_Calculation_MathTrig::COMBIN($populationSuccesses,$sampleSuccesses) *
+ PHPExcel_Calculation_MathTrig::COMBIN($populationNumber - $populationSuccesses,$sampleNumber - $sampleSuccesses) /
+ PHPExcel_Calculation_MathTrig::COMBIN($populationNumber,$sampleNumber);
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function HYPGEOMDIST()
+
+
+ /**
+ * INTERCEPT
+ *
+ * Calculates the point at which a line will intersect the y-axis by using existing x-values and y-values.
+ *
+ * @param array of mixed Data Series Y
+ * @param array of mixed Data Series X
+ * @return float
+ */
+ public static function INTERCEPT($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->getIntersect();
+ } // function INTERCEPT()
+
+
+ /**
+ * KURT
+ *
+ * Returns the kurtosis of a data set. Kurtosis characterizes the relative peakedness
+ * or flatness of a distribution compared with the normal distribution. Positive
+ * kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a
+ * relatively flat distribution.
+ *
+ * @param array Data Series
+ * @return float
+ */
+ public static function KURT() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
+ $mean = self::AVERAGE($aArgs);
+ $stdDev = self::STDEV($aArgs);
+
+ if ($stdDev > 0) {
+ $count = $summer = 0;
+ // Loop through arguments
+ foreach ($aArgs as $k => $arg) {
+ if ((is_bool($arg)) &&
+ (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
+ } else {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ $summer += pow((($arg - $mean) / $stdDev),4) ;
+ ++$count;
+ }
+ }
+ }
+
+ // Return
+ if ($count > 3) {
+ return $summer * ($count * ($count+1) / (($count-1) * ($count-2) * ($count-3))) - (3 * pow($count-1,2) / (($count-2) * ($count-3)));
+ }
+ }
+ return PHPExcel_Calculation_Functions::DIV0();
+ } // function KURT()
+
+
+ /**
+ * LARGE
+ *
+ * Returns the nth largest value in a data set. You can use this function to
+ * select a value based on its relative standing.
+ *
+ * Excel Function:
+ * LARGE(value1[,value2[, ...]],entry)
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @param int $entry Position (ordered from the largest) in the array or range of data to return
+ * @return float
+ *
+ */
+ public static function LARGE() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+
+ // Calculate
+ $entry = floor(array_pop($aArgs));
+
+ if ((is_numeric($entry)) && (!is_string($entry))) {
+ $mArgs = array();
+ foreach ($aArgs as $arg) {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ $mArgs[] = $arg;
+ }
+ }
+ $count = self::COUNT($mArgs);
+ $entry = floor(--$entry);
+ if (($entry < 0) || ($entry >= $count) || ($count == 0)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ rsort($mArgs);
+ return $mArgs[$entry];
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function LARGE()
+
+
+ /**
+ * LINEST
+ *
+ * Calculates the statistics for a line by using the "least squares" method to calculate a straight line that best fits your data,
+ * and then returns an array that describes the line.
+ *
+ * @param array of mixed Data Series Y
+ * @param array of mixed Data Series X
+ * @param boolean A logical value specifying whether to force the intersect to equal 0.
+ * @param boolean A logical value specifying whether to return additional regression statistics.
+ * @return array
+ */
+ public static function LINEST($yValues,$xValues=null,$const=True,$stats=False) {
+ $const = (is_null($const)) ? True : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
+ $stats = (is_null($stats)) ? False : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($stats);
+ if (is_null($xValues)) $xValues = range(1,count(PHPExcel_Calculation_Functions::flattenArray($yValues)));
+
+ 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 0;
+ }
+
+ $bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues,$const);
+ if ($stats) {
+ return array( array( $bestFitLinear->getSlope(),
+ $bestFitLinear->getSlopeSE(),
+ $bestFitLinear->getGoodnessOfFit(),
+ $bestFitLinear->getF(),
+ $bestFitLinear->getSSRegression(),
+ ),
+ array( $bestFitLinear->getIntersect(),
+ $bestFitLinear->getIntersectSE(),
+ $bestFitLinear->getStdevOfResiduals(),
+ $bestFitLinear->getDFResiduals(),
+ $bestFitLinear->getSSResiduals()
+ )
+ );
+ } else {
+ return array( $bestFitLinear->getSlope(),
+ $bestFitLinear->getIntersect()
+ );
+ }
+ } // function LINEST()
+
+
+ /**
+ * LOGEST
+ *
+ * Calculates an exponential curve that best fits the X and Y data series,
+ * and then returns an array that describes the line.
+ *
+ * @param array of mixed Data Series Y
+ * @param array of mixed Data Series X
+ * @param boolean A logical value specifying whether to force the intersect to equal 0.
+ * @param boolean A logical value specifying whether to return additional regression statistics.
+ * @return array
+ */
+ public static function LOGEST($yValues,$xValues=null,$const=True,$stats=False) {
+ $const = (is_null($const)) ? True : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
+ $stats = (is_null($stats)) ? False : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($stats);
+ if (is_null($xValues)) $xValues = range(1,count(PHPExcel_Calculation_Functions::flattenArray($yValues)));
+
+ if (!self::_checkTrendArrays($yValues,$xValues)) {
+ return PHPExcel_Calculation_Functions::VALUE();
+ }
+ $yValueCount = count($yValues);
+ $xValueCount = count($xValues);
+
+ foreach($yValues as $value) {
+ if ($value <= 0.0) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ }
+
+
+ if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
+ return PHPExcel_Calculation_Functions::NA();
+ } elseif ($yValueCount == 1) {
+ return 1;
+ }
+
+ $bestFitExponential = trendClass::calculate(trendClass::TREND_EXPONENTIAL,$yValues,$xValues,$const);
+ if ($stats) {
+ return array( array( $bestFitExponential->getSlope(),
+ $bestFitExponential->getSlopeSE(),
+ $bestFitExponential->getGoodnessOfFit(),
+ $bestFitExponential->getF(),
+ $bestFitExponential->getSSRegression(),
+ ),
+ array( $bestFitExponential->getIntersect(),
+ $bestFitExponential->getIntersectSE(),
+ $bestFitExponential->getStdevOfResiduals(),
+ $bestFitExponential->getDFResiduals(),
+ $bestFitExponential->getSSResiduals()
+ )
+ );
+ } else {
+ return array( $bestFitExponential->getSlope(),
+ $bestFitExponential->getIntersect()
+ );
+ }
+ } // function LOGEST()
+
+
+ /**
+ * LOGINV
+ *
+ * Returns the inverse of the normal cumulative distribution
+ *
+ * @param float $value
+ * @return float
+ *
+ * @todo Try implementing P J Acklam's refinement algorithm for greater
+ * accuracy if I can get my head round the mathematics
+ * (as described at) http://home.online.no/~pjacklam/notes/invnorm/
+ */
+ public static function LOGINV($probability, $mean, $stdDev) {
+ $probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
+ $mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
+ $stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
+
+ if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
+ if (($probability < 0) || ($probability > 1) || ($stdDev <= 0)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ return exp($mean + $stdDev * self::NORMSINV($probability));
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function LOGINV()
+
+
+ /**
+ * LOGNORMDIST
+ *
+ * Returns the cumulative lognormal distribution of x, where ln(x) is normally distributed
+ * with parameters mean and standard_dev.
+ *
+ * @param float $value
+ * @return float
+ */
+ public static function LOGNORMDIST($value, $mean, $stdDev) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+ $mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
+ $stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
+
+ if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
+ if (($value <= 0) || ($stdDev <= 0)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ return self::NORMSDIST((log($value) - $mean) / $stdDev);
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function LOGNORMDIST()
+
+
+ /**
+ * MAX
+ *
+ * MAX returns the value of the element of the values passed that has the highest value,
+ * with negative numbers considered smaller than positive numbers.
+ *
+ * Excel Function:
+ * MAX(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function MAX() {
+ // Return value
+ $returnValue = null;
+
+ // Loop through arguments
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+ foreach ($aArgs as $arg) {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ if ((is_null($returnValue)) || ($arg > $returnValue)) {
+ $returnValue = $arg;
+ }
+ }
+ }
+
+ // Return
+ if(is_null($returnValue)) {
+ return 0;
+ }
+ return $returnValue;
+ } // function MAX()
+
+
+ /**
+ * MAXA
+ *
+ * Returns the greatest value in a list of arguments, including numbers, text, and logical values
+ *
+ * Excel Function:
+ * MAXA(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function MAXA() {
+ // Return value
+ $returnValue = null;
+
+ // Loop through arguments
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+ foreach ($aArgs as $arg) {
+ // Is it a numeric value?
+ if ((is_numeric($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)) || ($arg > $returnValue)) {
+ $returnValue = $arg;
+ }
+ }
+ }
+
+ // Return
+ if(is_null($returnValue)) {
+ return 0;
+ }
+ return $returnValue;
+ } // function MAXA()
+
+
+ /**
+ * MAXIF
+ *
+ * Counts the maximum value within a range of cells that contain numbers within the list of arguments
+ *
+ * Excel Function:
+ * MAXIF(value1[,value2[, ...]],condition)
+ *
+ * @access public
+ * @category Mathematical and Trigonometric Functions
+ * @param mixed $arg,... Data values
+ * @param string $condition The criteria that defines which cells will be checked.
+ * @return float
+ */
+ public static function MAXIF($aArgs,$condition,$sumArgs = array()) {
+ // Return value
+ $returnValue = null;
+
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
+ $sumArgs = PHPExcel_Calculation_Functions::flattenArray($sumArgs);
+ if (empty($sumArgs)) {
+ $sumArgs = $aArgs;
+ }
+ $condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
+ // Loop through arguments
+ 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;
+ }
+ }
+ }
+
+ // Return
+ return $returnValue;
+ } // function MAXIF()
+
+
+ /**
+ * MEDIAN
+ *
+ * Returns the median of the given numbers. The median is the number in the middle of a set of numbers.
+ *
+ * Excel Function:
+ * MEDIAN(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function MEDIAN() {
+ // Return value
+ $returnValue = PHPExcel_Calculation_Functions::NaN();
+
+ $mArgs = array();
+ // Loop through arguments
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+ foreach ($aArgs as $arg) {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ $mArgs[] = $arg;
+ }
+ }
+
+ $mValueCount = count($mArgs);
+ if ($mValueCount > 0) {
+ sort($mArgs,SORT_NUMERIC);
+ $mValueCount = $mValueCount / 2;
+ if ($mValueCount == floor($mValueCount)) {
+ $returnValue = ($mArgs[$mValueCount--] + $mArgs[$mValueCount]) / 2;
+ } else {
+ $mValueCount == floor($mValueCount);
+ $returnValue = $mArgs[$mValueCount];
+ }
+ }
+
+ // Return
+ return $returnValue;
+ } // function MEDIAN()
+
+
+ /**
+ * MIN
+ *
+ * MIN returns the value of the element of the values passed that has the smallest value,
+ * with negative numbers considered smaller than positive numbers.
+ *
+ * Excel Function:
+ * MIN(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function MIN() {
+ // Return value
+ $returnValue = null;
+
+ // Loop through arguments
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+ foreach ($aArgs as $arg) {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ if ((is_null($returnValue)) || ($arg < $returnValue)) {
+ $returnValue = $arg;
+ }
+ }
+ }
+
+ // Return
+ if(is_null($returnValue)) {
+ return 0;
+ }
+ return $returnValue;
+ } // function MIN()
+
+
+ /**
+ * MINA
+ *
+ * Returns the smallest value in a list of arguments, including numbers, text, and logical values
+ *
+ * Excel Function:
+ * MINA(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function MINA() {
+ // Return value
+ $returnValue = null;
+
+ // Loop through arguments
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+ foreach ($aArgs as $arg) {
+ // Is it a numeric value?
+ if ((is_numeric($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)) || ($arg < $returnValue)) {
+ $returnValue = $arg;
+ }
+ }
+ }
+
+ // Return
+ if(is_null($returnValue)) {
+ return 0;
+ }
+ return $returnValue;
+ } // function MINA()
+
+
+ /**
+ * MINIF
+ *
+ * Returns the minimum value within a range of cells that contain numbers within the list of arguments
+ *
+ * Excel Function:
+ * MINIF(value1[,value2[, ...]],condition)
+ *
+ * @access public
+ * @category Mathematical and Trigonometric Functions
+ * @param mixed $arg,... Data values
+ * @param string $condition The criteria that defines which cells will be checked.
+ * @return float
+ */
+ public static function MINIF($aArgs,$condition,$sumArgs = array()) {
+ // Return value
+ $returnValue = null;
+
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
+ $sumArgs = PHPExcel_Calculation_Functions::flattenArray($sumArgs);
+ if (empty($sumArgs)) {
+ $sumArgs = $aArgs;
+ }
+ $condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
+ // Loop through arguments
+ 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;
+ }
+ }
+ }
+
+ // Return
+ return $returnValue;
+ } // function MINIF()
+
+
+ //
+ // Special variant of array_count_values that isn't limited to strings and integers,
+ // but can work with floating point numbers as values
+ //
+ private static function _modeCalc($data) {
+ $frequencyArray = array();
+ foreach($data as $datum) {
+ $found = False;
+ foreach($frequencyArray as $key => $value) {
+ if ((string) $value['value'] == (string) $datum) {
+ ++$frequencyArray[$key]['frequency'];
+ $found = True;
+ break;
+ }
+ }
+ if (!$found) {
+ $frequencyArray[] = array('value' => $datum,
+ 'frequency' => 1 );
+ }
+ }
+
+ foreach($frequencyArray as $key => $value) {
+ $frequencyList[$key] = $value['frequency'];
+ $valueList[$key] = $value['value'];
+ }
+ array_multisort($frequencyList, SORT_DESC, $valueList, SORT_ASC, SORT_NUMERIC, $frequencyArray);
+
+ if ($frequencyArray[0]['frequency'] == 1) {
+ return PHPExcel_Calculation_Functions::NA();
+ }
+ return $frequencyArray[0]['value'];
+ } // function _modeCalc()
+
+
+ /**
+ * MODE
+ *
+ * Returns the most frequently occurring, or repetitive, value in an array or range of data
+ *
+ * Excel Function:
+ * MODE(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function MODE() {
+ // Return value
+ $returnValue = PHPExcel_Calculation_Functions::NA();
+
+ // Loop through arguments
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+
+ $mArgs = array();
+ foreach ($aArgs as $arg) {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ $mArgs[] = $arg;
+ }
+ }
+
+ if (!empty($mArgs)) {
+ return self::_modeCalc($mArgs);
+ }
+
+ // Return
+ return $returnValue;
+ } // function MODE()
+
+
+ /**
+ * NEGBINOMDIST
+ *
+ * Returns the negative binomial distribution. NEGBINOMDIST returns the probability that
+ * there will be number_f failures before the number_s-th success, when the constant
+ * probability of a success is probability_s. This function is similar to the binomial
+ * distribution, except that the number of successes is fixed, and the number of trials is
+ * variable. Like the binomial, trials are assumed to be independent.
+ *
+ * @param float $failures Number of Failures
+ * @param float $successes Threshold number of Successes
+ * @param float $probability Probability of success on each trial
+ * @return float
+ *
+ */
+ public static function NEGBINOMDIST($failures, $successes, $probability) {
+ $failures = floor(PHPExcel_Calculation_Functions::flattenSingleValue($failures));
+ $successes = floor(PHPExcel_Calculation_Functions::flattenSingleValue($successes));
+ $probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
+
+ if ((is_numeric($failures)) && (is_numeric($successes)) && (is_numeric($probability))) {
+ if (($failures < 0) || ($successes < 1)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if (($probability < 0) || ($probability > 1)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
+ if (($failures + $successes - 1) <= 0) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ }
+ return (PHPExcel_Calculation_MathTrig::COMBIN($failures + $successes - 1,$successes - 1)) * (pow($probability,$successes)) * (pow(1 - $probability,$failures)) ;
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function NEGBINOMDIST()
+
+
+ /**
+ * NORMDIST
+ *
+ * Returns the normal distribution for the specified mean and standard deviation. This
+ * function has a very wide range of applications in statistics, including hypothesis
+ * testing.
+ *
+ * @param float $value
+ * @param float $mean Mean Value
+ * @param float $stdDev Standard Deviation
+ * @param boolean $cumulative
+ * @return float
+ *
+ */
+ public static function NORMDIST($value, $mean, $stdDev, $cumulative) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+ $mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
+ $stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
+
+ if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
+ if ($stdDev < 0) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
+ if ($cumulative) {
+ return 0.5 * (1 + PHPExcel_Calculation_Engineering::_erfVal(($value - $mean) / ($stdDev * sqrt(2))));
+ } else {
+ return (1 / (SQRT2PI * $stdDev)) * exp(0 - (pow($value - $mean,2) / (2 * ($stdDev * $stdDev))));
+ }
+ }
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function NORMDIST()
+
+
+ /**
+ * NORMINV
+ *
+ * Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.
+ *
+ * @param float $value
+ * @param float $mean Mean Value
+ * @param float $stdDev Standard Deviation
+ * @return float
+ *
+ */
+ public static function NORMINV($probability,$mean,$stdDev) {
+ $probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
+ $mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
+ $stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
+
+ if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
+ if (($probability < 0) || ($probability > 1)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if ($stdDev < 0) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ return (self::_inverse_ncdf($probability) * $stdDev) + $mean;
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function NORMINV()
+
+
+ /**
+ * NORMSDIST
+ *
+ * Returns the standard normal cumulative distribution function. The distribution has
+ * a mean of 0 (zero) and a standard deviation of one. Use this function in place of a
+ * table of standard normal curve areas.
+ *
+ * @param float $value
+ * @return float
+ */
+ public static function NORMSDIST($value) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+
+ return self::NORMDIST($value, 0, 1, True);
+ } // function NORMSDIST()
+
+
+ /**
+ * NORMSINV
+ *
+ * Returns the inverse of the standard normal cumulative distribution
+ *
+ * @param float $value
+ * @return float
+ */
+ public static function NORMSINV($value) {
+ return self::NORMINV($value, 0, 1);
+ } // function NORMSINV()
+
+
+ /**
+ * PERCENTILE
+ *
+ * Returns the nth percentile of values in a range..
+ *
+ * Excel Function:
+ * PERCENTILE(value1[,value2[, ...]],entry)
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @param float $entry Percentile value in the range 0..1, inclusive.
+ * @return float
+ */
+ public static function PERCENTILE() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+
+ // Calculate
+ $entry = array_pop($aArgs);
+
+ if ((is_numeric($entry)) && (!is_string($entry))) {
+ if (($entry < 0) || ($entry > 1)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ $mArgs = array();
+ foreach ($aArgs as $arg) {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ $mArgs[] = $arg;
+ }
+ }
+ $mValueCount = count($mArgs);
+ if ($mValueCount > 0) {
+ sort($mArgs);
+ $count = self::COUNT($mArgs);
+ $index = $entry * ($count-1);
+ $iBase = floor($index);
+ if ($index == $iBase) {
+ return $mArgs[$index];
+ } else {
+ $iNext = $iBase + 1;
+ $iProportion = $index - $iBase;
+ return $mArgs[$iBase] + (($mArgs[$iNext] - $mArgs[$iBase]) * $iProportion) ;
+ }
+ }
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function PERCENTILE()
+
+
+ /**
+ * PERCENTRANK
+ *
+ * Returns the rank of a value in a data set as a percentage of the data set.
+ *
+ * @param array of number An array of, or a reference to, a list of numbers.
+ * @param number The number whose rank you want to find.
+ * @param number The number of significant digits for the returned percentage value.
+ * @return float
+ */
+ public static function PERCENTRANK($valueSet,$value,$significance=3) {
+ $valueSet = PHPExcel_Calculation_Functions::flattenArray($valueSet);
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+ $significance = (is_null($significance)) ? 3 : (integer) PHPExcel_Calculation_Functions::flattenSingleValue($significance);
+
+ foreach($valueSet as $key => $valueEntry) {
+ if (!is_numeric($valueEntry)) {
+ unset($valueSet[$key]);
+ }
+ }
+ sort($valueSet,SORT_NUMERIC);
+ $valueCount = count($valueSet);
+ if ($valueCount == 0) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+
+ $valueAdjustor = $valueCount - 1;
+ if (($value < $valueSet[0]) || ($value > $valueSet[$valueAdjustor])) {
+ return PHPExcel_Calculation_Functions::NA();
+ }
+
+ $pos = array_search($value,$valueSet);
+ if ($pos === False) {
+ $pos = 0;
+ $testValue = $valueSet[0];
+ while ($testValue < $value) {
+ $testValue = $valueSet[++$pos];
+ }
+ --$pos;
+ $pos += (($value - $valueSet[$pos]) / ($testValue - $valueSet[$pos]));
+ }
+
+ return round($pos / $valueAdjustor,$significance);
+ } // function PERCENTRANK()
+
+
+ /**
+ * PERMUT
+ *
+ * Returns the number of permutations for a given number of objects that can be
+ * selected from number objects. A permutation is any set or subset of objects or
+ * events where internal order is significant. Permutations are different from
+ * combinations, for which the internal order is not significant. Use this function
+ * for lottery-style probability calculations.
+ *
+ * @param int $numObjs Number of different objects
+ * @param int $numInSet Number of objects in each permutation
+ * @return int Number of permutations
+ */
+ public static function PERMUT($numObjs,$numInSet) {
+ $numObjs = PHPExcel_Calculation_Functions::flattenSingleValue($numObjs);
+ $numInSet = PHPExcel_Calculation_Functions::flattenSingleValue($numInSet);
+
+ if ((is_numeric($numObjs)) && (is_numeric($numInSet))) {
+ $numInSet = floor($numInSet);
+ if ($numObjs < $numInSet) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ return round(PHPExcel_Calculation_MathTrig::FACT($numObjs) / PHPExcel_Calculation_MathTrig::FACT($numObjs - $numInSet));
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function PERMUT()
+
+
+ /**
+ * POISSON
+ *
+ * Returns the Poisson distribution. A common application of the Poisson distribution
+ * is predicting the number of events over a specific time, such as the number of
+ * cars arriving at a toll plaza in 1 minute.
+ *
+ * @param float $value
+ * @param float $mean Mean Value
+ * @param boolean $cumulative
+ * @return float
+ *
+ */
+ public static function POISSON($value, $mean, $cumulative) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+ $mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
+
+ if ((is_numeric($value)) && (is_numeric($mean))) {
+ if (($value <= 0) || ($mean <= 0)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
+ if ($cumulative) {
+ $summer = 0;
+ for ($i = 0; $i <= floor($value); ++$i) {
+ $summer += pow($mean,$i) / PHPExcel_Calculation_MathTrig::FACT($i);
+ }
+ return exp(0-$mean) * $summer;
+ } else {
+ return (exp(0-$mean) * pow($mean,$value)) / PHPExcel_Calculation_MathTrig::FACT($value);
+ }
+ }
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function POISSON()
+
+
+ /**
+ * QUARTILE
+ *
+ * Returns the quartile of a data set.
+ *
+ * Excel Function:
+ * QUARTILE(value1[,value2[, ...]],entry)
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @param int $entry Quartile value in the range 1..3, inclusive.
+ * @return float
+ */
+ public static function QUARTILE() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+
+ // Calculate
+ $entry = floor(array_pop($aArgs));
+
+ if ((is_numeric($entry)) && (!is_string($entry))) {
+ $entry /= 4;
+ if (($entry < 0) || ($entry > 1)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ return self::PERCENTILE($aArgs,$entry);
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function QUARTILE()
+
+
+ /**
+ * RANK
+ *
+ * Returns the rank of a number in a list of numbers.
+ *
+ * @param number The number whose rank you want to find.
+ * @param array of number An array of, or a reference to, a list of numbers.
+ * @param mixed Order to sort the values in the value set
+ * @return float
+ */
+ public static function RANK($value,$valueSet,$order=0) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+ $valueSet = PHPExcel_Calculation_Functions::flattenArray($valueSet);
+ $order = (is_null($order)) ? 0 : (integer) PHPExcel_Calculation_Functions::flattenSingleValue($order);
+
+ foreach($valueSet as $key => $valueEntry) {
+ if (!is_numeric($valueEntry)) {
+ unset($valueSet[$key]);
+ }
+ }
+
+ if ($order == 0) {
+ rsort($valueSet,SORT_NUMERIC);
+ } else {
+ sort($valueSet,SORT_NUMERIC);
+ }
+ $pos = array_search($value,$valueSet);
+ if ($pos === False) {
+ return PHPExcel_Calculation_Functions::NA();
+ }
+
+ return ++$pos;
+ } // function RANK()
+
+
+ /**
+ * RSQ
+ *
+ * Returns the square of the Pearson product moment correlation coefficient through data points in known_y's and known_x's.
+ *
+ * @param array of mixed Data Series Y
+ * @param array of mixed Data Series X
+ * @return float
+ */
+ public static function RSQ($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->getGoodnessOfFit();
+ } // function RSQ()
+
+
+ /**
+ * SKEW
+ *
+ * Returns the skewness of a distribution. Skewness characterizes the degree of asymmetry
+ * of a distribution around its mean. Positive skewness indicates a distribution with an
+ * asymmetric tail extending toward more positive values. Negative skewness indicates a
+ * distribution with an asymmetric tail extending toward more negative values.
+ *
+ * @param array Data Series
+ * @return float
+ */
+ public static function SKEW() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
+ $mean = self::AVERAGE($aArgs);
+ $stdDev = self::STDEV($aArgs);
+
+ $count = $summer = 0;
+ // Loop through arguments
+ foreach ($aArgs as $k => $arg) {
+ if ((is_bool($arg)) &&
+ (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
+ } else {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ $summer += pow((($arg - $mean) / $stdDev),3) ;
+ ++$count;
+ }
+ }
+ }
+
+ // Return
+ if ($count > 2) {
+ return $summer * ($count / (($count-1) * ($count-2)));
+ }
+ return PHPExcel_Calculation_Functions::DIV0();
+ } // function SKEW()
+
+
+ /**
+ * SLOPE
+ *
+ * Returns the slope of the linear regression line through data points in known_y's and known_x's.
+ *
+ * @param array of mixed Data Series Y
+ * @param array of mixed Data Series X
+ * @return float
+ */
+ public static function SLOPE($yValues,$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->getSlope();
+ } // function SLOPE()
+
+
+ /**
+ * SMALL
+ *
+ * Returns the nth smallest value in a data set. You can use this function to
+ * select a value based on its relative standing.
+ *
+ * Excel Function:
+ * SMALL(value1[,value2[, ...]],entry)
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @param int $entry Position (ordered from the smallest) in the array or range of data to return
+ * @return float
+ */
+ public static function SMALL() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+
+ // Calculate
+ $entry = array_pop($aArgs);
+
+ if ((is_numeric($entry)) && (!is_string($entry))) {
+ $mArgs = array();
+ foreach ($aArgs as $arg) {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ $mArgs[] = $arg;
+ }
+ }
+ $count = self::COUNT($mArgs);
+ $entry = floor(--$entry);
+ if (($entry < 0) || ($entry >= $count) || ($count == 0)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ sort($mArgs);
+ return $mArgs[$entry];
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function SMALL()
+
+
+ /**
+ * STANDARDIZE
+ *
+ * Returns a normalized value from a distribution characterized by mean and standard_dev.
+ *
+ * @param float $value Value to normalize
+ * @param float $mean Mean Value
+ * @param float $stdDev Standard Deviation
+ * @return float Standardized value
+ */
+ public static function STANDARDIZE($value,$mean,$stdDev) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+ $mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
+ $stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
+
+ if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
+ if ($stdDev <= 0) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ return ($value - $mean) / $stdDev ;
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function STANDARDIZE()
+
+
+ /**
+ * STDEV
+ *
+ * Estimates standard deviation based on a sample. The standard deviation is a measure of how
+ * widely values are dispersed from the average value (the mean).
+ *
+ * Excel Function:
+ * STDEV(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function STDEV() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
+
+ // Return value
+ $returnValue = null;
+
+ $aMean = self::AVERAGE($aArgs);
+ if (!is_null($aMean)) {
+ $aCount = -1;
+ foreach ($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)) {
+ $returnValue = pow(($arg - $aMean),2);
+ } else {
+ $returnValue += pow(($arg - $aMean),2);
+ }
+ ++$aCount;
+ }
+ }
+
+ // Return
+ if (($aCount > 0) && ($returnValue >= 0)) {
+ return sqrt($returnValue / $aCount);
+ }
+ }
+ return PHPExcel_Calculation_Functions::DIV0();
+ } // function STDEV()
+
+
+ /**
+ * STDEVA
+ *
+ * Estimates standard deviation based on a sample, including numbers, text, and logical values
+ *
+ * Excel Function:
+ * STDEVA(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function STDEVA() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
+
+ // Return value
+ $returnValue = null;
+
+ $aMean = self::AVERAGEA($aArgs);
+ if (!is_null($aMean)) {
+ $aCount = -1;
+ foreach ($aArgs as $k => $arg) {
+ if ((is_bool($arg)) &&
+ (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
+ } else {
+ // Is it a numeric value?
+ if ((is_numeric($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)) {
+ $returnValue = pow(($arg - $aMean),2);
+ } else {
+ $returnValue += pow(($arg - $aMean),2);
+ }
+ ++$aCount;
+ }
+ }
+ }
+
+ // Return
+ if (($aCount > 0) && ($returnValue >= 0)) {
+ return sqrt($returnValue / $aCount);
+ }
+ }
+ return PHPExcel_Calculation_Functions::DIV0();
+ } // function STDEVA()
+
+
+ /**
+ * STDEVP
+ *
+ * Calculates standard deviation based on the entire population
+ *
+ * Excel Function:
+ * STDEVP(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function STDEVP() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
+
+ // Return value
+ $returnValue = null;
+
+ $aMean = self::AVERAGE($aArgs);
+ if (!is_null($aMean)) {
+ $aCount = 0;
+ foreach ($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)) {
+ $returnValue = pow(($arg - $aMean),2);
+ } else {
+ $returnValue += pow(($arg - $aMean),2);
+ }
+ ++$aCount;
+ }
+ }
+
+ // Return
+ if (($aCount > 0) && ($returnValue >= 0)) {
+ return sqrt($returnValue / $aCount);
+ }
+ }
+ return PHPExcel_Calculation_Functions::DIV0();
+ } // function STDEVP()
+
+
+ /**
+ * STDEVPA
+ *
+ * Calculates standard deviation based on the entire population, including numbers, text, and logical values
+ *
+ * Excel Function:
+ * STDEVPA(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function STDEVPA() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
+
+ // Return value
+ $returnValue = null;
+
+ $aMean = self::AVERAGEA($aArgs);
+ if (!is_null($aMean)) {
+ $aCount = 0;
+ foreach ($aArgs as $k => $arg) {
+ if ((is_bool($arg)) &&
+ (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
+ } else {
+ // Is it a numeric value?
+ if ((is_numeric($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)) {
+ $returnValue = pow(($arg - $aMean),2);
+ } else {
+ $returnValue += pow(($arg - $aMean),2);
+ }
+ ++$aCount;
+ }
+ }
+ }
+
+ // Return
+ if (($aCount > 0) && ($returnValue >= 0)) {
+ return sqrt($returnValue / $aCount);
+ }
+ }
+ return PHPExcel_Calculation_Functions::DIV0();
+ } // function STDEVPA()
+
+
+ /**
+ * STEYX
+ *
+ * Returns the standard error of the predicted y-value for each x in the regression.
+ *
+ * @param array of mixed Data Series Y
+ * @param array of mixed Data Series X
+ * @return float
+ */
+ public static function STEYX($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->getStdevOfResiduals();
+ } // function STEYX()
+
+
+ /**
+ * TDIST
+ *
+ * Returns the probability of Student's T distribution.
+ *
+ * @param float $value Value for the function
+ * @param float $degrees degrees of freedom
+ * @param float $tails number of tails (1 or 2)
+ * @return float
+ */
+ public static function TDIST($value, $degrees, $tails) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+ $degrees = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));
+ $tails = floor(PHPExcel_Calculation_Functions::flattenSingleValue($tails));
+
+ if ((is_numeric($value)) && (is_numeric($degrees)) && (is_numeric($tails))) {
+ if (($value < 0) || ($degrees < 1) || ($tails < 1) || ($tails > 2)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ // tdist, which finds the probability that corresponds to a given value
+ // of t with k degrees of freedom. This algorithm is translated from a
+ // pascal function on p81 of "Statistical Computing in Pascal" by D
+ // Cooke, A H Craven & G M Clark (1985: Edward Arnold (Pubs.) Ltd:
+ // London). The above Pascal algorithm is itself a translation of the
+ // fortran algoritm "AS 3" by B E Cooper of the Atlas Computer
+ // Laboratory as reported in (among other places) "Applied Statistics
+ // Algorithms", editied by P Griffiths and I D Hill (1985; Ellis
+ // Horwood Ltd.; W. Sussex, England).
+ $tterm = $degrees;
+ $ttheta = atan2($value,sqrt($tterm));
+ $tc = cos($ttheta);
+ $ts = sin($ttheta);
+ $tsum = 0;
+
+ if (($degrees % 2) == 1) {
+ $ti = 3;
+ $tterm = $tc;
+ } else {
+ $ti = 2;
+ $tterm = 1;
+ }
+
+ $tsum = $tterm;
+ while ($ti < $degrees) {
+ $tterm *= $tc * $tc * ($ti - 1) / $ti;
+ $tsum += $tterm;
+ $ti += 2;
+ }
+ $tsum *= $ts;
+ if (($degrees % 2) == 1) { $tsum = M_2DIVPI * ($tsum + $ttheta); }
+ $tValue = 0.5 * (1 + $tsum);
+ if ($tails == 1) {
+ return 1 - abs($tValue);
+ } else {
+ return 1 - abs((1 - $tValue) - $tValue);
+ }
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function TDIST()
+
+
+ /**
+ * TINV
+ *
+ * Returns the one-tailed probability of the chi-squared distribution.
+ *
+ * @param float $probability Probability for the function
+ * @param float $degrees degrees of freedom
+ * @return float
+ */
+ public static function TINV($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
+ $result = self::TDIST($x, $degrees, 2);
+ $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($x,12);
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function TINV()
+
+
+ /**
+ * TREND
+ *
+ * Returns values along a linear trend
+ *
+ * @param array of mixed Data Series Y
+ * @param array of mixed Data Series X
+ * @param array of mixed Values of X for which we want to find Y
+ * @param boolean A logical value specifying whether to force the intersect to equal 0.
+ * @return array of float
+ */
+ public static function TREND($yValues,$xValues=array(),$newValues=array(),$const=True) {
+ $yValues = PHPExcel_Calculation_Functions::flattenArray($yValues);
+ $xValues = PHPExcel_Calculation_Functions::flattenArray($xValues);
+ $newValues = PHPExcel_Calculation_Functions::flattenArray($newValues);
+ $const = (is_null($const)) ? True : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
+
+ $bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues,$const);
+ if (empty($newValues)) {
+ $newValues = $bestFitLinear->getXValues();
+ }
+
+ $returnArray = array();
+ foreach($newValues as $xValue) {
+ $returnArray[0][] = $bestFitLinear->getValueOfYForX($xValue);
+ }
+
+ return $returnArray;
+ } // function TREND()
+
+
+ /**
+ * TRIMMEAN
+ *
+ * Returns the mean of the interior of a data set. TRIMMEAN calculates the mean
+ * taken by excluding a percentage of data points from the top and bottom tails
+ * of a data set.
+ *
+ * Excel Function:
+ * TRIMEAN(value1[,value2[, ...]],$discard)
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @param float $discard Percentage to discard
+ * @return float
+ */
+ public static function TRIMMEAN() {
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+
+ // Calculate
+ $percent = array_pop($aArgs);
+
+ if ((is_numeric($percent)) && (!is_string($percent))) {
+ if (($percent < 0) || ($percent > 1)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ $mArgs = array();
+ foreach ($aArgs as $arg) {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ $mArgs[] = $arg;
+ }
+ }
+ $discard = floor(self::COUNT($mArgs) * $percent / 2);
+ sort($mArgs);
+ for ($i=0; $i < $discard; ++$i) {
+ array_pop($mArgs);
+ array_shift($mArgs);
+ }
+ return self::AVERAGE($mArgs);
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function TRIMMEAN()
+
+
+ /**
+ * VARFunc
+ *
+ * Estimates variance based on a sample.
+ *
+ * Excel Function:
+ * VAR(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function VARFunc() {
+ // Return value
+ $returnValue = PHPExcel_Calculation_Functions::DIV0();
+
+ $summerA = $summerB = 0;
+
+ // Loop through arguments
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+ $aCount = 0;
+ foreach ($aArgs as $arg) {
+ if (is_bool($arg)) { $arg = (integer) $arg; }
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ $summerA += ($arg * $arg);
+ $summerB += $arg;
+ ++$aCount;
+ }
+ }
+
+ // Return
+ if ($aCount > 1) {
+ $summerA *= $aCount;
+ $summerB *= $summerB;
+ $returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
+ }
+ return $returnValue;
+ } // function VARFunc()
+
+
+ /**
+ * VARA
+ *
+ * Estimates variance based on a sample, including numbers, text, and logical values
+ *
+ * Excel Function:
+ * VARA(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function VARA() {
+ // Return value
+ $returnValue = PHPExcel_Calculation_Functions::DIV0();
+
+ $summerA = $summerB = 0;
+
+ // Loop through arguments
+ $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
+ $aCount = 0;
+ foreach ($aArgs as $k => $arg) {
+ if ((is_string($arg)) &&
+ (PHPExcel_Calculation_Functions::isValue($k))) {
+ return PHPExcel_Calculation_Functions::VALUE();
+ } elseif ((is_string($arg)) &&
+ (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
+ } else {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
+ if (is_bool($arg)) {
+ $arg = (integer) $arg;
+ } elseif (is_string($arg)) {
+ $arg = 0;
+ }
+ $summerA += ($arg * $arg);
+ $summerB += $arg;
+ ++$aCount;
+ }
+ }
+ }
+
+ // Return
+ if ($aCount > 1) {
+ $summerA *= $aCount;
+ $summerB *= $summerB;
+ $returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
+ }
+ return $returnValue;
+ } // function VARA()
+
+
+ /**
+ * VARP
+ *
+ * Calculates variance based on the entire population
+ *
+ * Excel Function:
+ * VARP(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function VARP() {
+ // Return value
+ $returnValue = PHPExcel_Calculation_Functions::DIV0();
+
+ $summerA = $summerB = 0;
+
+ // Loop through arguments
+ $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
+ $aCount = 0;
+ foreach ($aArgs as $arg) {
+ if (is_bool($arg)) { $arg = (integer) $arg; }
+ // Is it a numeric value?
+ if ((is_numeric($arg)) && (!is_string($arg))) {
+ $summerA += ($arg * $arg);
+ $summerB += $arg;
+ ++$aCount;
+ }
+ }
+
+ // Return
+ if ($aCount > 0) {
+ $summerA *= $aCount;
+ $summerB *= $summerB;
+ $returnValue = ($summerA - $summerB) / ($aCount * $aCount);
+ }
+ return $returnValue;
+ } // function VARP()
+
+
+ /**
+ * VARPA
+ *
+ * Calculates variance based on the entire population, including numbers, text, and logical values
+ *
+ * Excel Function:
+ * VARPA(value1[,value2[, ...]])
+ *
+ * @access public
+ * @category Statistical Functions
+ * @param mixed $arg,... Data values
+ * @return float
+ */
+ public static function VARPA() {
+ // Return value
+ $returnValue = PHPExcel_Calculation_Functions::DIV0();
+
+ $summerA = $summerB = 0;
+
+ // Loop through arguments
+ $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
+ $aCount = 0;
+ foreach ($aArgs as $k => $arg) {
+ if ((is_string($arg)) &&
+ (PHPExcel_Calculation_Functions::isValue($k))) {
+ return PHPExcel_Calculation_Functions::VALUE();
+ } elseif ((is_string($arg)) &&
+ (!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
+ } else {
+ // Is it a numeric value?
+ if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
+ if (is_bool($arg)) {
+ $arg = (integer) $arg;
+ } elseif (is_string($arg)) {
+ $arg = 0;
+ }
+ $summerA += ($arg * $arg);
+ $summerB += $arg;
+ ++$aCount;
+ }
+ }
+ }
+
+ // Return
+ if ($aCount > 0) {
+ $summerA *= $aCount;
+ $summerB *= $summerB;
+ $returnValue = ($summerA - $summerB) / ($aCount * $aCount);
+ }
+ return $returnValue;
+ } // function VARPA()
+
+
+ /**
+ * WEIBULL
+ *
+ * Returns the Weibull distribution. Use this distribution in reliability
+ * analysis, such as calculating a device's mean time to failure.
+ *
+ * @param float $value
+ * @param float $alpha Alpha Parameter
+ * @param float $beta Beta Parameter
+ * @param boolean $cumulative
+ * @return float
+ *
+ */
+ public static function WEIBULL($value, $alpha, $beta, $cumulative) {
+ $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
+ $alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
+ $beta = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
+
+ if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta))) {
+ if (($value < 0) || ($alpha <= 0) || ($beta <= 0)) {
+ return PHPExcel_Calculation_Functions::NaN();
+ }
+ if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
+ if ($cumulative) {
+ return 1 - exp(0 - pow($value / $beta,$alpha));
+ } else {
+ return ($alpha / pow($beta,$alpha)) * pow($value,$alpha - 1) * exp(0 - pow($value / $beta,$alpha));
+ }
+ }
+ }
+ return PHPExcel_Calculation_Functions::VALUE();
+ } // function WEIBULL()
+
+
+ /**
+ * ZTEST
+ *
+ * Returns the Weibull distribution. Use this distribution in reliability
+ * analysis, such as calculating a device's mean time to failure.
+ *
+ * @param float $value
+ * @param float $alpha Alpha Parameter
+ * @param float $beta Beta Parameter
+ * @param boolean $cumulative
+ * @return float
+ *
+ */
+ public static function ZTEST($dataSet, $m0, $sigma=null) {
+ $dataSet = PHPExcel_Calculation_Functions::flattenArrayIndexed($dataSet);
+ $m0 = PHPExcel_Calculation_Functions::flattenSingleValue($m0);
+ $sigma = PHPExcel_Calculation_Functions::flattenSingleValue($sigma);
+
+ if (is_null($sigma)) {
+ $sigma = self::STDEV($dataSet);
+ }
+ $n = count($dataSet);
+
+ return 1 - self::NORMSDIST((self::AVERAGE($dataSet) - $m0)/($sigma/SQRT($n)));
+ } // function ZTEST()
+
+} // class PHPExcel_Calculation_Statistical
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