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<?php
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/**
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* PHPExcel
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*
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* Copyright (c) 2006 - 2013 PHPExcel
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*
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* @category PHPExcel
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* @package PHPExcel_Calculation
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* @copyright Copyright (c) 2006 - 2013 PHPExcel (http://www.codeplex.com/PHPExcel)
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* @license http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt LGPL
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* @version ##VERSION##, ##DATE##
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*/
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/** PHPExcel root directory */
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if (!defined('PHPEXCEL_ROOT')) {
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/**
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* @ignore
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*/
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define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
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require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
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}
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require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/trend/trendClass.php';
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/** LOG_GAMMA_X_MAX_VALUE */
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define('LOG_GAMMA_X_MAX_VALUE', 2.55e305);
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/** XMININ */
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define('XMININ', 2.23e-308);
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/** EPS */
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define('EPS', 2.22e-16);
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/** SQRT2PI */
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define('SQRT2PI', 2.5066282746310005024157652848110452530069867406099);
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/**
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* PHPExcel_Calculation_Statistical
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*
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* @category PHPExcel
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* @package PHPExcel_Calculation
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* @copyright Copyright (c) 2006 - 2013 PHPExcel (http://www.codeplex.com/PHPExcel)
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*/
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class PHPExcel_Calculation_Statistical {
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private static function _checkTrendArrays(&$array1,&$array2) {
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if (!is_array($array1)) { $array1 = array($array1); }
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if (!is_array($array2)) { $array2 = array($array2); }
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$array1 = PHPExcel_Calculation_Functions::flattenArray($array1);
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$array2 = PHPExcel_Calculation_Functions::flattenArray($array2);
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foreach($array1 as $key => $value) {
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if ((is_bool($value)) || (is_string($value)) || (is_null($value))) {
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unset($array1[$key]);
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unset($array2[$key]);
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}
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}
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foreach($array2 as $key => $value) {
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if ((is_bool($value)) || (is_string($value)) || (is_null($value))) {
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unset($array1[$key]);
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unset($array2[$key]);
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}
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}
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$array1 = array_merge($array1);
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$array2 = array_merge($array2);
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return True;
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} // function _checkTrendArrays()
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/**
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* Beta function.
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*
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* @author Jaco van Kooten
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*
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* @param p require p>0
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* @param q require q>0
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* @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
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*/
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private static function _beta($p, $q) {
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if ($p <= 0.0 || $q <= 0.0 || ($p + $q) > LOG_GAMMA_X_MAX_VALUE) {
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return 0.0;
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} else {
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return exp(self::_logBeta($p, $q));
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}
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} // function _beta()
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/**
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* Incomplete beta function
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*
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* @author Jaco van Kooten
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* @author Paul Meagher
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*
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* The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992).
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* @param x require 0<=x<=1
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* @param p require p>0
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* @param q require q>0
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* @return 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow
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*/
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private static function _incompleteBeta($x, $p, $q) {
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if ($x <= 0.0) {
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return 0.0;
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} elseif ($x >= 1.0) {
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return 1.0;
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} elseif (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) {
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return 0.0;
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}
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$beta_gam = exp((0 - self::_logBeta($p, $q)) + $p * log($x) + $q * log(1.0 - $x));
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if ($x < ($p + 1.0) / ($p + $q + 2.0)) {
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return $beta_gam * self::_betaFraction($x, $p, $q) / $p;
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} else {
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return 1.0 - ($beta_gam * self::_betaFraction(1 - $x, $q, $p) / $q);
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}
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} // function _incompleteBeta()
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// Function cache for _logBeta function
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private static $_logBetaCache_p = 0.0;
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private static $_logBetaCache_q = 0.0;
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private static $_logBetaCache_result = 0.0;
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/**
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* The natural logarithm of the beta function.
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*
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* @param p require p>0
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* @param q require q>0
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* @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
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* @author Jaco van Kooten
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*/
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private static function _logBeta($p, $q) {
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if ($p != self::$_logBetaCache_p || $q != self::$_logBetaCache_q) {
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self::$_logBetaCache_p = $p;
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self::$_logBetaCache_q = $q;
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if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) {
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self::$_logBetaCache_result = 0.0;
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} else {
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self::$_logBetaCache_result = self::_logGamma($p) + self::_logGamma($q) - self::_logGamma($p + $q);
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}
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}
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return self::$_logBetaCache_result;
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} // function _logBeta()
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/**
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* Evaluates of continued fraction part of incomplete beta function.
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* Based on an idea from Numerical Recipes (W.H. Press et al, 1992).
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* @author Jaco van Kooten
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*/
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private static function _betaFraction($x, $p, $q) {
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$c = 1.0;
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$sum_pq = $p + $q;
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$p_plus = $p + 1.0;
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$p_minus = $p - 1.0;
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$h = 1.0 - $sum_pq * $x / $p_plus;
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if (abs($h) < XMININ) {
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$h = XMININ;
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}
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$h = 1.0 / $h;
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$frac = $h;
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$m = 1;
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$delta = 0.0;
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while ($m <= MAX_ITERATIONS && abs($delta-1.0) > PRECISION ) {
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$m2 = 2 * $m;
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// even index for d
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$d = $m * ($q - $m) * $x / ( ($p_minus + $m2) * ($p + $m2));
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$h = 1.0 + $d * $h;
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if (abs($h) < XMININ) {
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$h = XMININ;
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}
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$h = 1.0 / $h;
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$c = 1.0 + $d / $c;
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if (abs($c) < XMININ) {
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$c = XMININ;
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}
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$frac *= $h * $c;
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// odd index for d
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$d = -($p + $m) * ($sum_pq + $m) * $x / (($p + $m2) * ($p_plus + $m2));
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$h = 1.0 + $d * $h;
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if (abs($h) < XMININ) {
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$h = XMININ;
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}
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$h = 1.0 / $h;
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$c = 1.0 + $d / $c;
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if (abs($c) < XMININ) {
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$c = XMININ;
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}
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$delta = $h * $c;
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$frac *= $delta;
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++$m;
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}
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return $frac;
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} // function _betaFraction()
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/**
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* logGamma function
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*
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* @version 1.1
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* @author Jaco van Kooten
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*
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* Original author was Jaco van Kooten. Ported to PHP by Paul Meagher.
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*
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* The natural logarithm of the gamma function. <br />
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* Based on public domain NETLIB (Fortran) code by W. J. Cody and L. Stoltz <br />
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* Applied Mathematics Division <br />
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* Argonne National Laboratory <br />
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* Argonne, IL 60439 <br />
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* <p>
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* References:
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* <ol>
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* <li>W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural
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* Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203.</li>
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* <li>K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969.</li>
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* <li>Hart, Et. Al., Computer Approximations, Wiley and sons, New York, 1968.</li>
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* </ol>
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* </p>
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* <p>
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* From the original documentation:
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* </p>
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* <p>
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* This routine calculates the LOG(GAMMA) function for a positive real argument X.
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* Computation is based on an algorithm outlined in references 1 and 2.
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* The program uses rational functions that theoretically approximate LOG(GAMMA)
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* to at least 18 significant decimal digits. The approximation for X > 12 is from
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* reference 3, while approximations for X < 12.0 are similar to those in reference
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* 1, but are unpublished. The accuracy achieved depends on the arithmetic system,
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* the compiler, the intrinsic functions, and proper selection of the
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* machine-dependent constants.
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* </p>
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* <p>
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* Error returns: <br />
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* The program returns the value XINF for X .LE. 0.0 or when overflow would occur.
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* The computation is believed to be free of underflow and overflow.
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* </p>
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* @return MAX_VALUE for x < 0.0 or when overflow would occur, i.e. x > 2.55E305
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*/
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// Function cache for logGamma
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private static $_logGammaCache_result = 0.0;
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private static $_logGammaCache_x = 0.0;
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private static function _logGamma($x) {
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// Log Gamma related constants
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static $lg_d1 = -0.5772156649015328605195174;
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static $lg_d2 = 0.4227843350984671393993777;
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static $lg_d4 = 1.791759469228055000094023;
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static $lg_p1 = array( 4.945235359296727046734888,
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201.8112620856775083915565,
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2290.838373831346393026739,
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11319.67205903380828685045,
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28557.24635671635335736389,
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38484.96228443793359990269,
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26377.48787624195437963534,
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7225.813979700288197698961 );
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static $lg_p2 = array( 4.974607845568932035012064,
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542.4138599891070494101986,
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15506.93864978364947665077,
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184793.2904445632425417223,
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1088204.76946882876749847,
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3338152.967987029735917223,
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5106661.678927352456275255,
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3074109.054850539556250927 );
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static $lg_p4 = array( 14745.02166059939948905062,
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2426813.369486704502836312,
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121475557.4045093227939592,
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2663432449.630976949898078,
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29403789566.34553899906876,
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170266573776.5398868392998,
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492612579337.743088758812,
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560625185622.3951465078242 );
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static $lg_q1 = array( 67.48212550303777196073036,
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1113.332393857199323513008,
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7738.757056935398733233834,
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27639.87074403340708898585,
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54993.10206226157329794414,
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61611.22180066002127833352,
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36351.27591501940507276287,
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8785.536302431013170870835 );
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static $lg_q2 = array( 183.0328399370592604055942,
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7765.049321445005871323047,
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133190.3827966074194402448,
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1136705.821321969608938755,
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5267964.117437946917577538,
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13467014.54311101692290052,
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17827365.30353274213975932,
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9533095.591844353613395747 );
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static $lg_q4 = array( 2690.530175870899333379843,
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639388.5654300092398984238,
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41355999.30241388052042842,
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1120872109.61614794137657,
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14886137286.78813811542398,
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101680358627.2438228077304,
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341747634550.7377132798597,
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446315818741.9713286462081 );
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static $lg_c = array( -0.001910444077728,
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8.4171387781295e-4,
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-5.952379913043012e-4,
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7.93650793500350248e-4,
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-0.002777777777777681622553,
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0.08333333333333333331554247,
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0.0057083835261 );
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326 |
// Rough estimate of the fourth root of logGamma_xBig
|
|
|
327 |
static $lg_frtbig = 2.25e76;
|
|
|
328 |
static $pnt68 = 0.6796875;
|
|
|
329 |
|
|
|
330 |
|
|
|
331 |
if ($x == self::$_logGammaCache_x) {
|
|
|
332 |
return self::$_logGammaCache_result;
|
|
|
333 |
}
|
|
|
334 |
$y = $x;
|
|
|
335 |
if ($y > 0.0 && $y <= LOG_GAMMA_X_MAX_VALUE) {
|
|
|
336 |
if ($y <= EPS) {
|
|
|
337 |
$res = -log(y);
|
|
|
338 |
} elseif ($y <= 1.5) {
|
|
|
339 |
// ---------------------
|
|
|
340 |
// EPS .LT. X .LE. 1.5
|
|
|
341 |
// ---------------------
|
|
|
342 |
if ($y < $pnt68) {
|
|
|
343 |
$corr = -log($y);
|
|
|
344 |
$xm1 = $y;
|
|
|
345 |
} else {
|
|
|
346 |
$corr = 0.0;
|
|
|
347 |
$xm1 = $y - 1.0;
|
|
|
348 |
}
|
|
|
349 |
if ($y <= 0.5 || $y >= $pnt68) {
|
|
|
350 |
$xden = 1.0;
|
|
|
351 |
$xnum = 0.0;
|
|
|
352 |
for ($i = 0; $i < 8; ++$i) {
|
|
|
353 |
$xnum = $xnum * $xm1 + $lg_p1[$i];
|
|
|
354 |
$xden = $xden * $xm1 + $lg_q1[$i];
|
|
|
355 |
}
|
|
|
356 |
$res = $corr + $xm1 * ($lg_d1 + $xm1 * ($xnum / $xden));
|
|
|
357 |
} else {
|
|
|
358 |
$xm2 = $y - 1.0;
|
|
|
359 |
$xden = 1.0;
|
|
|
360 |
$xnum = 0.0;
|
|
|
361 |
for ($i = 0; $i < 8; ++$i) {
|
|
|
362 |
$xnum = $xnum * $xm2 + $lg_p2[$i];
|
|
|
363 |
$xden = $xden * $xm2 + $lg_q2[$i];
|
|
|
364 |
}
|
|
|
365 |
$res = $corr + $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
|
|
|
366 |
}
|
|
|
367 |
} elseif ($y <= 4.0) {
|
|
|
368 |
// ---------------------
|
|
|
369 |
// 1.5 .LT. X .LE. 4.0
|
|
|
370 |
// ---------------------
|
|
|
371 |
$xm2 = $y - 2.0;
|
|
|
372 |
$xden = 1.0;
|
|
|
373 |
$xnum = 0.0;
|
|
|
374 |
for ($i = 0; $i < 8; ++$i) {
|
|
|
375 |
$xnum = $xnum * $xm2 + $lg_p2[$i];
|
|
|
376 |
$xden = $xden * $xm2 + $lg_q2[$i];
|
|
|
377 |
}
|
|
|
378 |
$res = $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
|
|
|
379 |
} elseif ($y <= 12.0) {
|
|
|
380 |
// ----------------------
|
|
|
381 |
// 4.0 .LT. X .LE. 12.0
|
|
|
382 |
// ----------------------
|
|
|
383 |
$xm4 = $y - 4.0;
|
|
|
384 |
$xden = -1.0;
|
|
|
385 |
$xnum = 0.0;
|
|
|
386 |
for ($i = 0; $i < 8; ++$i) {
|
|
|
387 |
$xnum = $xnum * $xm4 + $lg_p4[$i];
|
|
|
388 |
$xden = $xden * $xm4 + $lg_q4[$i];
|
|
|
389 |
}
|
|
|
390 |
$res = $lg_d4 + $xm4 * ($xnum / $xden);
|
|
|
391 |
} else {
|
|
|
392 |
// ---------------------------------
|
|
|
393 |
// Evaluate for argument .GE. 12.0
|
|
|
394 |
// ---------------------------------
|
|
|
395 |
$res = 0.0;
|
|
|
396 |
if ($y <= $lg_frtbig) {
|
|
|
397 |
$res = $lg_c[6];
|
|
|
398 |
$ysq = $y * $y;
|
|
|
399 |
for ($i = 0; $i < 6; ++$i)
|
|
|
400 |
$res = $res / $ysq + $lg_c[$i];
|
|
|
401 |
}
|
|
|
402 |
$res /= $y;
|
|
|
403 |
$corr = log($y);
|
|
|
404 |
$res = $res + log(SQRT2PI) - 0.5 * $corr;
|
|
|
405 |
$res += $y * ($corr - 1.0);
|
|
|
406 |
}
|
|
|
407 |
} else {
|
|
|
408 |
// --------------------------
|
|
|
409 |
// Return for bad arguments
|
|
|
410 |
// --------------------------
|
|
|
411 |
$res = MAX_VALUE;
|
|
|
412 |
}
|
|
|
413 |
// ------------------------------
|
|
|
414 |
// Final adjustments and return
|
|
|
415 |
// ------------------------------
|
|
|
416 |
self::$_logGammaCache_x = $x;
|
|
|
417 |
self::$_logGammaCache_result = $res;
|
|
|
418 |
return $res;
|
|
|
419 |
} // function _logGamma()
|
|
|
420 |
|
|
|
421 |
|
|
|
422 |
//
|
|
|
423 |
// Private implementation of the incomplete Gamma function
|
|
|
424 |
//
|
|
|
425 |
private static function _incompleteGamma($a,$x) {
|
|
|
426 |
static $max = 32;
|
|
|
427 |
$summer = 0;
|
|
|
428 |
for ($n=0; $n<=$max; ++$n) {
|
|
|
429 |
$divisor = $a;
|
|
|
430 |
for ($i=1; $i<=$n; ++$i) {
|
|
|
431 |
$divisor *= ($a + $i);
|
|
|
432 |
}
|
|
|
433 |
$summer += (pow($x,$n) / $divisor);
|
|
|
434 |
}
|
|
|
435 |
return pow($x,$a) * exp(0-$x) * $summer;
|
|
|
436 |
} // function _incompleteGamma()
|
|
|
437 |
|
|
|
438 |
|
|
|
439 |
//
|
|
|
440 |
// Private implementation of the Gamma function
|
|
|
441 |
//
|
|
|
442 |
private static function _gamma($data) {
|
|
|
443 |
if ($data == 0.0) return 0;
|
|
|
444 |
|
|
|
445 |
static $p0 = 1.000000000190015;
|
|
|
446 |
static $p = array ( 1 => 76.18009172947146,
|
|
|
447 |
2 => -86.50532032941677,
|
|
|
448 |
3 => 24.01409824083091,
|
|
|
449 |
4 => -1.231739572450155,
|
|
|
450 |
5 => 1.208650973866179e-3,
|
|
|
451 |
6 => -5.395239384953e-6
|
|
|
452 |
);
|
|
|
453 |
|
|
|
454 |
$y = $x = $data;
|
|
|
455 |
$tmp = $x + 5.5;
|
|
|
456 |
$tmp -= ($x + 0.5) * log($tmp);
|
|
|
457 |
|
|
|
458 |
$summer = $p0;
|
|
|
459 |
for ($j=1;$j<=6;++$j) {
|
|
|
460 |
$summer += ($p[$j] / ++$y);
|
|
|
461 |
}
|
|
|
462 |
return exp(0 - $tmp + log(SQRT2PI * $summer / $x));
|
|
|
463 |
} // function _gamma()
|
|
|
464 |
|
|
|
465 |
|
|
|
466 |
/***************************************************************************
|
|
|
467 |
* inverse_ncdf.php
|
|
|
468 |
* -------------------
|
|
|
469 |
* begin : Friday, January 16, 2004
|
|
|
470 |
* copyright : (C) 2004 Michael Nickerson
|
|
|
471 |
* email : nickersonm@yahoo.com
|
|
|
472 |
*
|
|
|
473 |
***************************************************************************/
|
|
|
474 |
private static function _inverse_ncdf($p) {
|
|
|
475 |
// Inverse ncdf approximation by Peter J. Acklam, implementation adapted to
|
|
|
476 |
// PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
|
|
|
477 |
// a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
|
|
|
478 |
// I have not checked the accuracy of this implementation. Be aware that PHP
|
|
|
479 |
// will truncate the coeficcients to 14 digits.
|
|
|
480 |
|
|
|
481 |
// You have permission to use and distribute this function freely for
|
|
|
482 |
// whatever purpose you want, but please show common courtesy and give credit
|
|
|
483 |
// where credit is due.
|
|
|
484 |
|
|
|
485 |
// Input paramater is $p - probability - where 0 < p < 1.
|
|
|
486 |
|
|
|
487 |
// Coefficients in rational approximations
|
|
|
488 |
static $a = array( 1 => -3.969683028665376e+01,
|
|
|
489 |
2 => 2.209460984245205e+02,
|
|
|
490 |
3 => -2.759285104469687e+02,
|
|
|
491 |
4 => 1.383577518672690e+02,
|
|
|
492 |
5 => -3.066479806614716e+01,
|
|
|
493 |
6 => 2.506628277459239e+00
|
|
|
494 |
);
|
|
|
495 |
|
|
|
496 |
static $b = array( 1 => -5.447609879822406e+01,
|
|
|
497 |
2 => 1.615858368580409e+02,
|
|
|
498 |
3 => -1.556989798598866e+02,
|
|
|
499 |
4 => 6.680131188771972e+01,
|
|
|
500 |
5 => -1.328068155288572e+01
|
|
|
501 |
);
|
|
|
502 |
|
|
|
503 |
static $c = array( 1 => -7.784894002430293e-03,
|
|
|
504 |
2 => -3.223964580411365e-01,
|
|
|
505 |
3 => -2.400758277161838e+00,
|
|
|
506 |
4 => -2.549732539343734e+00,
|
|
|
507 |
5 => 4.374664141464968e+00,
|
|
|
508 |
6 => 2.938163982698783e+00
|
|
|
509 |
);
|
|
|
510 |
|
|
|
511 |
static $d = array( 1 => 7.784695709041462e-03,
|
|
|
512 |
2 => 3.224671290700398e-01,
|
|
|
513 |
3 => 2.445134137142996e+00,
|
|
|
514 |
4 => 3.754408661907416e+00
|
|
|
515 |
);
|
|
|
516 |
|
|
|
517 |
// Define lower and upper region break-points.
|
|
|
518 |
$p_low = 0.02425; //Use lower region approx. below this
|
|
|
519 |
$p_high = 1 - $p_low; //Use upper region approx. above this
|
|
|
520 |
|
|
|
521 |
if (0 < $p && $p < $p_low) {
|
|
|
522 |
// Rational approximation for lower region.
|
|
|
523 |
$q = sqrt(-2 * log($p));
|
|
|
524 |
return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
|
|
|
525 |
(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
|
|
|
526 |
} elseif ($p_low <= $p && $p <= $p_high) {
|
|
|
527 |
// Rational approximation for central region.
|
|
|
528 |
$q = $p - 0.5;
|
|
|
529 |
$r = $q * $q;
|
|
|
530 |
return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q /
|
|
|
531 |
((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1);
|
|
|
532 |
} elseif ($p_high < $p && $p < 1) {
|
|
|
533 |
// Rational approximation for upper region.
|
|
|
534 |
$q = sqrt(-2 * log(1 - $p));
|
|
|
535 |
return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
|
|
|
536 |
(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
|
|
|
537 |
}
|
|
|
538 |
// If 0 < p < 1, return a null value
|
|
|
539 |
return PHPExcel_Calculation_Functions::NULL();
|
|
|
540 |
} // function _inverse_ncdf()
|
|
|
541 |
|
|
|
542 |
|
|
|
543 |
private static function _inverse_ncdf2($prob) {
|
|
|
544 |
// Approximation of inverse standard normal CDF developed by
|
|
|
545 |
// B. Moro, "The Full Monte," Risk 8(2), Feb 1995, 57-58.
|
|
|
546 |
|
|
|
547 |
$a1 = 2.50662823884;
|
|
|
548 |
$a2 = -18.61500062529;
|
|
|
549 |
$a3 = 41.39119773534;
|
|
|
550 |
$a4 = -25.44106049637;
|
|
|
551 |
|
|
|
552 |
$b1 = -8.4735109309;
|
|
|
553 |
$b2 = 23.08336743743;
|
|
|
554 |
$b3 = -21.06224101826;
|
|
|
555 |
$b4 = 3.13082909833;
|
|
|
556 |
|
|
|
557 |
$c1 = 0.337475482272615;
|
|
|
558 |
$c2 = 0.976169019091719;
|
|
|
559 |
$c3 = 0.160797971491821;
|
|
|
560 |
$c4 = 2.76438810333863E-02;
|
|
|
561 |
$c5 = 3.8405729373609E-03;
|
|
|
562 |
$c6 = 3.951896511919E-04;
|
|
|
563 |
$c7 = 3.21767881768E-05;
|
|
|
564 |
$c8 = 2.888167364E-07;
|
|
|
565 |
$c9 = 3.960315187E-07;
|
|
|
566 |
|
|
|
567 |
$y = $prob - 0.5;
|
|
|
568 |
if (abs($y) < 0.42) {
|
|
|
569 |
$z = ($y * $y);
|
|
|
570 |
$z = $y * ((($a4 * $z + $a3) * $z + $a2) * $z + $a1) / (((($b4 * $z + $b3) * $z + $b2) * $z + $b1) * $z + 1);
|
|
|
571 |
} else {
|
|
|
572 |
if ($y > 0) {
|
|
|
573 |
$z = log(-log(1 - $prob));
|
|
|
574 |
} else {
|
|
|
575 |
$z = log(-log($prob));
|
|
|
576 |
}
|
|
|
577 |
$z = $c1 + $z * ($c2 + $z * ($c3 + $z * ($c4 + $z * ($c5 + $z * ($c6 + $z * ($c7 + $z * ($c8 + $z * $c9)))))));
|
|
|
578 |
if ($y < 0) {
|
|
|
579 |
$z = -$z;
|
|
|
580 |
}
|
|
|
581 |
}
|
|
|
582 |
return $z;
|
|
|
583 |
} // function _inverse_ncdf2()
|
|
|
584 |
|
|
|
585 |
|
|
|
586 |
private static function _inverse_ncdf3($p) {
|
|
|
587 |
// ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3.
|
|
|
588 |
// Produces the normal deviate Z corresponding to a given lower
|
|
|
589 |
// tail area of P; Z is accurate to about 1 part in 10**16.
|
|
|
590 |
//
|
|
|
591 |
// This is a PHP version of the original FORTRAN code that can
|
|
|
592 |
// be found at http://lib.stat.cmu.edu/apstat/
|
|
|
593 |
$split1 = 0.425;
|
|
|
594 |
$split2 = 5;
|
|
|
595 |
$const1 = 0.180625;
|
|
|
596 |
$const2 = 1.6;
|
|
|
597 |
|
|
|
598 |
// coefficients for p close to 0.5
|
|
|
599 |
$a0 = 3.3871328727963666080;
|
|
|
600 |
$a1 = 1.3314166789178437745E+2;
|
|
|
601 |
$a2 = 1.9715909503065514427E+3;
|
|
|
602 |
$a3 = 1.3731693765509461125E+4;
|
|
|
603 |
$a4 = 4.5921953931549871457E+4;
|
|
|
604 |
$a5 = 6.7265770927008700853E+4;
|
|
|
605 |
$a6 = 3.3430575583588128105E+4;
|
|
|
606 |
$a7 = 2.5090809287301226727E+3;
|
|
|
607 |
|
|
|
608 |
$b1 = 4.2313330701600911252E+1;
|
|
|
609 |
$b2 = 6.8718700749205790830E+2;
|
|
|
610 |
$b3 = 5.3941960214247511077E+3;
|
|
|
611 |
$b4 = 2.1213794301586595867E+4;
|
|
|
612 |
$b5 = 3.9307895800092710610E+4;
|
|
|
613 |
$b6 = 2.8729085735721942674E+4;
|
|
|
614 |
$b7 = 5.2264952788528545610E+3;
|
|
|
615 |
|
|
|
616 |
// coefficients for p not close to 0, 0.5 or 1.
|
|
|
617 |
$c0 = 1.42343711074968357734;
|
|
|
618 |
$c1 = 4.63033784615654529590;
|
|
|
619 |
$c2 = 5.76949722146069140550;
|
|
|
620 |
$c3 = 3.64784832476320460504;
|
|
|
621 |
$c4 = 1.27045825245236838258;
|
|
|
622 |
$c5 = 2.41780725177450611770E-1;
|
|
|
623 |
$c6 = 2.27238449892691845833E-2;
|
|
|
624 |
$c7 = 7.74545014278341407640E-4;
|
|
|
625 |
|
|
|
626 |
$d1 = 2.05319162663775882187;
|
|
|
627 |
$d2 = 1.67638483018380384940;
|
|
|
628 |
$d3 = 6.89767334985100004550E-1;
|
|
|
629 |
$d4 = 1.48103976427480074590E-1;
|
|
|
630 |
$d5 = 1.51986665636164571966E-2;
|
|
|
631 |
$d6 = 5.47593808499534494600E-4;
|
|
|
632 |
$d7 = 1.05075007164441684324E-9;
|
|
|
633 |
|
|
|
634 |
// coefficients for p near 0 or 1.
|
|
|
635 |
$e0 = 6.65790464350110377720;
|
|
|
636 |
$e1 = 5.46378491116411436990;
|
|
|
637 |
$e2 = 1.78482653991729133580;
|
|
|
638 |
$e3 = 2.96560571828504891230E-1;
|
|
|
639 |
$e4 = 2.65321895265761230930E-2;
|
|
|
640 |
$e5 = 1.24266094738807843860E-3;
|
|
|
641 |
$e6 = 2.71155556874348757815E-5;
|
|
|
642 |
$e7 = 2.01033439929228813265E-7;
|
|
|
643 |
|
|
|
644 |
$f1 = 5.99832206555887937690E-1;
|
|
|
645 |
$f2 = 1.36929880922735805310E-1;
|
|
|
646 |
$f3 = 1.48753612908506148525E-2;
|
|
|
647 |
$f4 = 7.86869131145613259100E-4;
|
|
|
648 |
$f5 = 1.84631831751005468180E-5;
|
|
|
649 |
$f6 = 1.42151175831644588870E-7;
|
|
|
650 |
$f7 = 2.04426310338993978564E-15;
|
|
|
651 |
|
|
|
652 |
$q = $p - 0.5;
|
|
|
653 |
|
|
|
654 |
// computation for p close to 0.5
|
|
|
655 |
if (abs($q) <= split1) {
|
|
|
656 |
$R = $const1 - $q * $q;
|
|
|
657 |
$z = $q * ((((((($a7 * $R + $a6) * $R + $a5) * $R + $a4) * $R + $a3) * $R + $a2) * $R + $a1) * $R + $a0) /
|
|
|
658 |
((((((($b7 * $R + $b6) * $R + $b5) * $R + $b4) * $R + $b3) * $R + $b2) * $R + $b1) * $R + 1);
|
|
|
659 |
} else {
|
|
|
660 |
if ($q < 0) {
|
|
|
661 |
$R = $p;
|
|
|
662 |
} else {
|
|
|
663 |
$R = 1 - $p;
|
|
|
664 |
}
|
|
|
665 |
$R = pow(-log($R),2);
|
|
|
666 |
|
|
|
667 |
// computation for p not close to 0, 0.5 or 1.
|
|
|
668 |
If ($R <= $split2) {
|
|
|
669 |
$R = $R - $const2;
|
|
|
670 |
$z = ((((((($c7 * $R + $c6) * $R + $c5) * $R + $c4) * $R + $c3) * $R + $c2) * $R + $c1) * $R + $c0) /
|
|
|
671 |
((((((($d7 * $R + $d6) * $R + $d5) * $R + $d4) * $R + $d3) * $R + $d2) * $R + $d1) * $R + 1);
|
|
|
672 |
} else {
|
|
|
673 |
// computation for p near 0 or 1.
|
|
|
674 |
$R = $R - $split2;
|
|
|
675 |
$z = ((((((($e7 * $R + $e6) * $R + $e5) * $R + $e4) * $R + $e3) * $R + $e2) * $R + $e1) * $R + $e0) /
|
|
|
676 |
((((((($f7 * $R + $f6) * $R + $f5) * $R + $f4) * $R + $f3) * $R + $f2) * $R + $f1) * $R + 1);
|
|
|
677 |
}
|
|
|
678 |
if ($q < 0) {
|
|
|
679 |
$z = -$z;
|
|
|
680 |
}
|
|
|
681 |
}
|
|
|
682 |
return $z;
|
|
|
683 |
} // function _inverse_ncdf3()
|
|
|
684 |
|
|
|
685 |
|
|
|
686 |
/**
|
|
|
687 |
* AVEDEV
|
|
|
688 |
*
|
|
|
689 |
* Returns the average of the absolute deviations of data points from their mean.
|
|
|
690 |
* AVEDEV is a measure of the variability in a data set.
|
|
|
691 |
*
|
|
|
692 |
* Excel Function:
|
|
|
693 |
* AVEDEV(value1[,value2[, ...]])
|
|
|
694 |
*
|
|
|
695 |
* @access public
|
|
|
696 |
* @category Statistical Functions
|
|
|
697 |
* @param mixed $arg,... Data values
|
|
|
698 |
* @return float
|
|
|
699 |
*/
|
|
|
700 |
public static function AVEDEV() {
|
|
|
701 |
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
702 |
|
|
|
703 |
// Return value
|
|
|
704 |
$returnValue = null;
|
|
|
705 |
|
|
|
706 |
$aMean = self::AVERAGE($aArgs);
|
|
|
707 |
if ($aMean != PHPExcel_Calculation_Functions::DIV0()) {
|
|
|
708 |
$aCount = 0;
|
|
|
709 |
foreach ($aArgs as $k => $arg) {
|
|
|
710 |
if ((is_bool($arg)) &&
|
|
|
711 |
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
|
|
|
712 |
$arg = (integer) $arg;
|
|
|
713 |
}
|
|
|
714 |
// Is it a numeric value?
|
|
|
715 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
716 |
if (is_null($returnValue)) {
|
|
|
717 |
$returnValue = abs($arg - $aMean);
|
|
|
718 |
} else {
|
|
|
719 |
$returnValue += abs($arg - $aMean);
|
|
|
720 |
}
|
|
|
721 |
++$aCount;
|
|
|
722 |
}
|
|
|
723 |
}
|
|
|
724 |
|
|
|
725 |
// Return
|
|
|
726 |
if ($aCount == 0) {
|
|
|
727 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
728 |
}
|
|
|
729 |
return $returnValue / $aCount;
|
|
|
730 |
}
|
|
|
731 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
732 |
} // function AVEDEV()
|
|
|
733 |
|
|
|
734 |
|
|
|
735 |
/**
|
|
|
736 |
* AVERAGE
|
|
|
737 |
*
|
|
|
738 |
* Returns the average (arithmetic mean) of the arguments
|
|
|
739 |
*
|
|
|
740 |
* Excel Function:
|
|
|
741 |
* AVERAGE(value1[,value2[, ...]])
|
|
|
742 |
*
|
|
|
743 |
* @access public
|
|
|
744 |
* @category Statistical Functions
|
|
|
745 |
* @param mixed $arg,... Data values
|
|
|
746 |
* @return float
|
|
|
747 |
*/
|
|
|
748 |
public static function AVERAGE() {
|
|
|
749 |
$returnValue = $aCount = 0;
|
|
|
750 |
|
|
|
751 |
// Loop through arguments
|
|
|
752 |
foreach (PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args()) as $k => $arg) {
|
|
|
753 |
if ((is_bool($arg)) &&
|
|
|
754 |
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
|
|
|
755 |
$arg = (integer) $arg;
|
|
|
756 |
}
|
|
|
757 |
// Is it a numeric value?
|
|
|
758 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
759 |
if (is_null($returnValue)) {
|
|
|
760 |
$returnValue = $arg;
|
|
|
761 |
} else {
|
|
|
762 |
$returnValue += $arg;
|
|
|
763 |
}
|
|
|
764 |
++$aCount;
|
|
|
765 |
}
|
|
|
766 |
}
|
|
|
767 |
|
|
|
768 |
// Return
|
|
|
769 |
if ($aCount > 0) {
|
|
|
770 |
return $returnValue / $aCount;
|
|
|
771 |
} else {
|
|
|
772 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
773 |
}
|
|
|
774 |
} // function AVERAGE()
|
|
|
775 |
|
|
|
776 |
|
|
|
777 |
/**
|
|
|
778 |
* AVERAGEA
|
|
|
779 |
*
|
|
|
780 |
* Returns the average of its arguments, including numbers, text, and logical values
|
|
|
781 |
*
|
|
|
782 |
* Excel Function:
|
|
|
783 |
* AVERAGEA(value1[,value2[, ...]])
|
|
|
784 |
*
|
|
|
785 |
* @access public
|
|
|
786 |
* @category Statistical Functions
|
|
|
787 |
* @param mixed $arg,... Data values
|
|
|
788 |
* @return float
|
|
|
789 |
*/
|
|
|
790 |
public static function AVERAGEA() {
|
|
|
791 |
// Return value
|
|
|
792 |
$returnValue = null;
|
|
|
793 |
|
|
|
794 |
$aCount = 0;
|
|
|
795 |
// Loop through arguments
|
|
|
796 |
foreach (PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args()) as $k => $arg) {
|
|
|
797 |
if ((is_bool($arg)) &&
|
|
|
798 |
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
|
799 |
} else {
|
|
|
800 |
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
|
|
|
801 |
if (is_bool($arg)) {
|
|
|
802 |
$arg = (integer) $arg;
|
|
|
803 |
} elseif (is_string($arg)) {
|
|
|
804 |
$arg = 0;
|
|
|
805 |
}
|
|
|
806 |
if (is_null($returnValue)) {
|
|
|
807 |
$returnValue = $arg;
|
|
|
808 |
} else {
|
|
|
809 |
$returnValue += $arg;
|
|
|
810 |
}
|
|
|
811 |
++$aCount;
|
|
|
812 |
}
|
|
|
813 |
}
|
|
|
814 |
}
|
|
|
815 |
|
|
|
816 |
// Return
|
|
|
817 |
if ($aCount > 0) {
|
|
|
818 |
return $returnValue / $aCount;
|
|
|
819 |
} else {
|
|
|
820 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
821 |
}
|
|
|
822 |
} // function AVERAGEA()
|
|
|
823 |
|
|
|
824 |
|
|
|
825 |
/**
|
|
|
826 |
* AVERAGEIF
|
|
|
827 |
*
|
|
|
828 |
* Returns the average value from a range of cells that contain numbers within the list of arguments
|
|
|
829 |
*
|
|
|
830 |
* Excel Function:
|
|
|
831 |
* AVERAGEIF(value1[,value2[, ...]],condition)
|
|
|
832 |
*
|
|
|
833 |
* @access public
|
|
|
834 |
* @category Mathematical and Trigonometric Functions
|
|
|
835 |
* @param mixed $arg,... Data values
|
|
|
836 |
* @param string $condition The criteria that defines which cells will be checked.
|
|
|
837 |
* @param mixed[] $averageArgs Data values
|
|
|
838 |
* @return float
|
|
|
839 |
*/
|
|
|
840 |
public static function AVERAGEIF($aArgs,$condition,$averageArgs = array()) {
|
|
|
841 |
// Return value
|
|
|
842 |
$returnValue = 0;
|
|
|
843 |
|
|
|
844 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
|
|
|
845 |
$averageArgs = PHPExcel_Calculation_Functions::flattenArray($averageArgs);
|
|
|
846 |
if (empty($averageArgs)) {
|
|
|
847 |
$averageArgs = $aArgs;
|
|
|
848 |
}
|
|
|
849 |
$condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
|
|
|
850 |
// Loop through arguments
|
|
|
851 |
$aCount = 0;
|
|
|
852 |
foreach ($aArgs as $key => $arg) {
|
|
|
853 |
if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
|
|
|
854 |
$testCondition = '='.$arg.$condition;
|
|
|
855 |
if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
|
|
|
856 |
if ((is_null($returnValue)) || ($arg > $returnValue)) {
|
|
|
857 |
$returnValue += $arg;
|
|
|
858 |
++$aCount;
|
|
|
859 |
}
|
|
|
860 |
}
|
|
|
861 |
}
|
|
|
862 |
|
|
|
863 |
// Return
|
|
|
864 |
if ($aCount > 0) {
|
|
|
865 |
return $returnValue / $aCount;
|
|
|
866 |
} else {
|
|
|
867 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
868 |
}
|
|
|
869 |
} // function AVERAGEIF()
|
|
|
870 |
|
|
|
871 |
|
|
|
872 |
/**
|
|
|
873 |
* BETADIST
|
|
|
874 |
*
|
|
|
875 |
* Returns the beta distribution.
|
|
|
876 |
*
|
|
|
877 |
* @param float $value Value at which you want to evaluate the distribution
|
|
|
878 |
* @param float $alpha Parameter to the distribution
|
|
|
879 |
* @param float $beta Parameter to the distribution
|
|
|
880 |
* @param boolean $cumulative
|
|
|
881 |
* @return float
|
|
|
882 |
*
|
|
|
883 |
*/
|
|
|
884 |
public static function BETADIST($value,$alpha,$beta,$rMin=0,$rMax=1) {
|
|
|
885 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
886 |
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
|
|
|
887 |
$beta = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
|
|
|
888 |
$rMin = PHPExcel_Calculation_Functions::flattenSingleValue($rMin);
|
|
|
889 |
$rMax = PHPExcel_Calculation_Functions::flattenSingleValue($rMax);
|
|
|
890 |
|
|
|
891 |
if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
|
|
|
892 |
if (($value < $rMin) || ($value > $rMax) || ($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax)) {
|
|
|
893 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
894 |
}
|
|
|
895 |
if ($rMin > $rMax) {
|
|
|
896 |
$tmp = $rMin;
|
|
|
897 |
$rMin = $rMax;
|
|
|
898 |
$rMax = $tmp;
|
|
|
899 |
}
|
|
|
900 |
$value -= $rMin;
|
|
|
901 |
$value /= ($rMax - $rMin);
|
|
|
902 |
return self::_incompleteBeta($value,$alpha,$beta);
|
|
|
903 |
}
|
|
|
904 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
905 |
} // function BETADIST()
|
|
|
906 |
|
|
|
907 |
|
|
|
908 |
/**
|
|
|
909 |
* BETAINV
|
|
|
910 |
*
|
|
|
911 |
* Returns the inverse of the beta distribution.
|
|
|
912 |
*
|
|
|
913 |
* @param float $probability Probability at which you want to evaluate the distribution
|
|
|
914 |
* @param float $alpha Parameter to the distribution
|
|
|
915 |
* @param float $beta Parameter to the distribution
|
|
|
916 |
* @param float $rMin Minimum value
|
|
|
917 |
* @param float $rMax Maximum value
|
|
|
918 |
* @param boolean $cumulative
|
|
|
919 |
* @return float
|
|
|
920 |
*
|
|
|
921 |
*/
|
|
|
922 |
public static function BETAINV($probability,$alpha,$beta,$rMin=0,$rMax=1) {
|
|
|
923 |
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
|
924 |
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
|
|
|
925 |
$beta = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
|
|
|
926 |
$rMin = PHPExcel_Calculation_Functions::flattenSingleValue($rMin);
|
|
|
927 |
$rMax = PHPExcel_Calculation_Functions::flattenSingleValue($rMax);
|
|
|
928 |
|
|
|
929 |
if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
|
|
|
930 |
if (($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax) || ($probability <= 0) || ($probability > 1)) {
|
|
|
931 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
932 |
}
|
|
|
933 |
if ($rMin > $rMax) {
|
|
|
934 |
$tmp = $rMin;
|
|
|
935 |
$rMin = $rMax;
|
|
|
936 |
$rMax = $tmp;
|
|
|
937 |
}
|
|
|
938 |
$a = 0;
|
|
|
939 |
$b = 2;
|
|
|
940 |
|
|
|
941 |
$i = 0;
|
|
|
942 |
while ((($b - $a) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
|
|
|
943 |
$guess = ($a + $b) / 2;
|
|
|
944 |
$result = self::BETADIST($guess, $alpha, $beta);
|
|
|
945 |
if (($result == $probability) || ($result == 0)) {
|
|
|
946 |
$b = $a;
|
|
|
947 |
} elseif ($result > $probability) {
|
|
|
948 |
$b = $guess;
|
|
|
949 |
} else {
|
|
|
950 |
$a = $guess;
|
|
|
951 |
}
|
|
|
952 |
}
|
|
|
953 |
if ($i == MAX_ITERATIONS) {
|
|
|
954 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
955 |
}
|
|
|
956 |
return round($rMin + $guess * ($rMax - $rMin),12);
|
|
|
957 |
}
|
|
|
958 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
959 |
} // function BETAINV()
|
|
|
960 |
|
|
|
961 |
|
|
|
962 |
/**
|
|
|
963 |
* BINOMDIST
|
|
|
964 |
*
|
|
|
965 |
* Returns the individual term binomial distribution probability. Use BINOMDIST in problems with
|
|
|
966 |
* a fixed number of tests or trials, when the outcomes of any trial are only success or failure,
|
|
|
967 |
* when trials are independent, and when the probability of success is constant throughout the
|
|
|
968 |
* experiment. For example, BINOMDIST can calculate the probability that two of the next three
|
|
|
969 |
* babies born are male.
|
|
|
970 |
*
|
|
|
971 |
* @param float $value Number of successes in trials
|
|
|
972 |
* @param float $trials Number of trials
|
|
|
973 |
* @param float $probability Probability of success on each trial
|
|
|
974 |
* @param boolean $cumulative
|
|
|
975 |
* @return float
|
|
|
976 |
*
|
|
|
977 |
* @todo Cumulative distribution function
|
|
|
978 |
*
|
|
|
979 |
*/
|
|
|
980 |
public static function BINOMDIST($value, $trials, $probability, $cumulative) {
|
|
|
981 |
$value = floor(PHPExcel_Calculation_Functions::flattenSingleValue($value));
|
|
|
982 |
$trials = floor(PHPExcel_Calculation_Functions::flattenSingleValue($trials));
|
|
|
983 |
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
|
984 |
|
|
|
985 |
if ((is_numeric($value)) && (is_numeric($trials)) && (is_numeric($probability))) {
|
|
|
986 |
if (($value < 0) || ($value > $trials)) {
|
|
|
987 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
988 |
}
|
|
|
989 |
if (($probability < 0) || ($probability > 1)) {
|
|
|
990 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
991 |
}
|
|
|
992 |
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
|
|
|
993 |
if ($cumulative) {
|
|
|
994 |
$summer = 0;
|
|
|
995 |
for ($i = 0; $i <= $value; ++$i) {
|
|
|
996 |
$summer += PHPExcel_Calculation_MathTrig::COMBIN($trials,$i) * pow($probability,$i) * pow(1 - $probability,$trials - $i);
|
|
|
997 |
}
|
|
|
998 |
return $summer;
|
|
|
999 |
} else {
|
|
|
1000 |
return PHPExcel_Calculation_MathTrig::COMBIN($trials,$value) * pow($probability,$value) * pow(1 - $probability,$trials - $value) ;
|
|
|
1001 |
}
|
|
|
1002 |
}
|
|
|
1003 |
}
|
|
|
1004 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1005 |
} // function BINOMDIST()
|
|
|
1006 |
|
|
|
1007 |
|
|
|
1008 |
/**
|
|
|
1009 |
* CHIDIST
|
|
|
1010 |
*
|
|
|
1011 |
* Returns the one-tailed probability of the chi-squared distribution.
|
|
|
1012 |
*
|
|
|
1013 |
* @param float $value Value for the function
|
|
|
1014 |
* @param float $degrees degrees of freedom
|
|
|
1015 |
* @return float
|
|
|
1016 |
*/
|
|
|
1017 |
public static function CHIDIST($value, $degrees) {
|
|
|
1018 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
1019 |
$degrees = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));
|
|
|
1020 |
|
|
|
1021 |
if ((is_numeric($value)) && (is_numeric($degrees))) {
|
|
|
1022 |
if ($degrees < 1) {
|
|
|
1023 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1024 |
}
|
|
|
1025 |
if ($value < 0) {
|
|
|
1026 |
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
|
|
|
1027 |
return 1;
|
|
|
1028 |
}
|
|
|
1029 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1030 |
}
|
|
|
1031 |
return 1 - (self::_incompleteGamma($degrees/2,$value/2) / self::_gamma($degrees/2));
|
|
|
1032 |
}
|
|
|
1033 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1034 |
} // function CHIDIST()
|
|
|
1035 |
|
|
|
1036 |
|
|
|
1037 |
/**
|
|
|
1038 |
* CHIINV
|
|
|
1039 |
*
|
|
|
1040 |
* Returns the one-tailed probability of the chi-squared distribution.
|
|
|
1041 |
*
|
|
|
1042 |
* @param float $probability Probability for the function
|
|
|
1043 |
* @param float $degrees degrees of freedom
|
|
|
1044 |
* @return float
|
|
|
1045 |
*/
|
|
|
1046 |
public static function CHIINV($probability, $degrees) {
|
|
|
1047 |
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
|
1048 |
$degrees = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));
|
|
|
1049 |
|
|
|
1050 |
if ((is_numeric($probability)) && (is_numeric($degrees))) {
|
|
|
1051 |
|
|
|
1052 |
$xLo = 100;
|
|
|
1053 |
$xHi = 0;
|
|
|
1054 |
|
|
|
1055 |
$x = $xNew = 1;
|
|
|
1056 |
$dx = 1;
|
|
|
1057 |
$i = 0;
|
|
|
1058 |
|
|
|
1059 |
while ((abs($dx) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
|
|
|
1060 |
// Apply Newton-Raphson step
|
|
|
1061 |
$result = self::CHIDIST($x, $degrees);
|
|
|
1062 |
$error = $result - $probability;
|
|
|
1063 |
if ($error == 0.0) {
|
|
|
1064 |
$dx = 0;
|
|
|
1065 |
} elseif ($error < 0.0) {
|
|
|
1066 |
$xLo = $x;
|
|
|
1067 |
} else {
|
|
|
1068 |
$xHi = $x;
|
|
|
1069 |
}
|
|
|
1070 |
// Avoid division by zero
|
|
|
1071 |
if ($result != 0.0) {
|
|
|
1072 |
$dx = $error / $result;
|
|
|
1073 |
$xNew = $x - $dx;
|
|
|
1074 |
}
|
|
|
1075 |
// If the NR fails to converge (which for example may be the
|
|
|
1076 |
// case if the initial guess is too rough) we apply a bisection
|
|
|
1077 |
// step to determine a more narrow interval around the root.
|
|
|
1078 |
if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0)) {
|
|
|
1079 |
$xNew = ($xLo + $xHi) / 2;
|
|
|
1080 |
$dx = $xNew - $x;
|
|
|
1081 |
}
|
|
|
1082 |
$x = $xNew;
|
|
|
1083 |
}
|
|
|
1084 |
if ($i == MAX_ITERATIONS) {
|
|
|
1085 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
1086 |
}
|
|
|
1087 |
return round($x,12);
|
|
|
1088 |
}
|
|
|
1089 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1090 |
} // function CHIINV()
|
|
|
1091 |
|
|
|
1092 |
|
|
|
1093 |
/**
|
|
|
1094 |
* CONFIDENCE
|
|
|
1095 |
*
|
|
|
1096 |
* Returns the confidence interval for a population mean
|
|
|
1097 |
*
|
|
|
1098 |
* @param float $alpha
|
|
|
1099 |
* @param float $stdDev Standard Deviation
|
|
|
1100 |
* @param float $size
|
|
|
1101 |
* @return float
|
|
|
1102 |
*
|
|
|
1103 |
*/
|
|
|
1104 |
public static function CONFIDENCE($alpha,$stdDev,$size) {
|
|
|
1105 |
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
|
|
|
1106 |
$stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
|
|
|
1107 |
$size = floor(PHPExcel_Calculation_Functions::flattenSingleValue($size));
|
|
|
1108 |
|
|
|
1109 |
if ((is_numeric($alpha)) && (is_numeric($stdDev)) && (is_numeric($size))) {
|
|
|
1110 |
if (($alpha <= 0) || ($alpha >= 1)) {
|
|
|
1111 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1112 |
}
|
|
|
1113 |
if (($stdDev <= 0) || ($size < 1)) {
|
|
|
1114 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1115 |
}
|
|
|
1116 |
return self::NORMSINV(1 - $alpha / 2) * $stdDev / sqrt($size);
|
|
|
1117 |
}
|
|
|
1118 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1119 |
} // function CONFIDENCE()
|
|
|
1120 |
|
|
|
1121 |
|
|
|
1122 |
/**
|
|
|
1123 |
* CORREL
|
|
|
1124 |
*
|
|
|
1125 |
* Returns covariance, the average of the products of deviations for each data point pair.
|
|
|
1126 |
*
|
|
|
1127 |
* @param array of mixed Data Series Y
|
|
|
1128 |
* @param array of mixed Data Series X
|
|
|
1129 |
* @return float
|
|
|
1130 |
*/
|
|
|
1131 |
public static function CORREL($yValues,$xValues=null) {
|
|
|
1132 |
if ((is_null($xValues)) || (!is_array($yValues)) || (!is_array($xValues))) {
|
|
|
1133 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1134 |
}
|
|
|
1135 |
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
|
1136 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1137 |
}
|
|
|
1138 |
$yValueCount = count($yValues);
|
|
|
1139 |
$xValueCount = count($xValues);
|
|
|
1140 |
|
|
|
1141 |
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
|
1142 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
1143 |
} elseif ($yValueCount == 1) {
|
|
|
1144 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
1145 |
}
|
|
|
1146 |
|
|
|
1147 |
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
|
1148 |
return $bestFitLinear->getCorrelation();
|
|
|
1149 |
} // function CORREL()
|
|
|
1150 |
|
|
|
1151 |
|
|
|
1152 |
/**
|
|
|
1153 |
* COUNT
|
|
|
1154 |
*
|
|
|
1155 |
* Counts the number of cells that contain numbers within the list of arguments
|
|
|
1156 |
*
|
|
|
1157 |
* Excel Function:
|
|
|
1158 |
* COUNT(value1[,value2[, ...]])
|
|
|
1159 |
*
|
|
|
1160 |
* @access public
|
|
|
1161 |
* @category Statistical Functions
|
|
|
1162 |
* @param mixed $arg,... Data values
|
|
|
1163 |
* @return int
|
|
|
1164 |
*/
|
|
|
1165 |
public static function COUNT() {
|
|
|
1166 |
// Return value
|
|
|
1167 |
$returnValue = 0;
|
|
|
1168 |
|
|
|
1169 |
// Loop through arguments
|
|
|
1170 |
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
1171 |
foreach ($aArgs as $k => $arg) {
|
|
|
1172 |
if ((is_bool($arg)) &&
|
|
|
1173 |
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
|
|
|
1174 |
$arg = (integer) $arg;
|
|
|
1175 |
}
|
|
|
1176 |
// Is it a numeric value?
|
|
|
1177 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
1178 |
++$returnValue;
|
|
|
1179 |
}
|
|
|
1180 |
}
|
|
|
1181 |
|
|
|
1182 |
// Return
|
|
|
1183 |
return $returnValue;
|
|
|
1184 |
} // function COUNT()
|
|
|
1185 |
|
|
|
1186 |
|
|
|
1187 |
/**
|
|
|
1188 |
* COUNTA
|
|
|
1189 |
*
|
|
|
1190 |
* Counts the number of cells that are not empty within the list of arguments
|
|
|
1191 |
*
|
|
|
1192 |
* Excel Function:
|
|
|
1193 |
* COUNTA(value1[,value2[, ...]])
|
|
|
1194 |
*
|
|
|
1195 |
* @access public
|
|
|
1196 |
* @category Statistical Functions
|
|
|
1197 |
* @param mixed $arg,... Data values
|
|
|
1198 |
* @return int
|
|
|
1199 |
*/
|
|
|
1200 |
public static function COUNTA() {
|
|
|
1201 |
// Return value
|
|
|
1202 |
$returnValue = 0;
|
|
|
1203 |
|
|
|
1204 |
// Loop through arguments
|
|
|
1205 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
1206 |
foreach ($aArgs as $arg) {
|
|
|
1207 |
// Is it a numeric, boolean or string value?
|
|
|
1208 |
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
|
|
|
1209 |
++$returnValue;
|
|
|
1210 |
}
|
|
|
1211 |
}
|
|
|
1212 |
|
|
|
1213 |
// Return
|
|
|
1214 |
return $returnValue;
|
|
|
1215 |
} // function COUNTA()
|
|
|
1216 |
|
|
|
1217 |
|
|
|
1218 |
/**
|
|
|
1219 |
* COUNTBLANK
|
|
|
1220 |
*
|
|
|
1221 |
* Counts the number of empty cells within the list of arguments
|
|
|
1222 |
*
|
|
|
1223 |
* Excel Function:
|
|
|
1224 |
* COUNTBLANK(value1[,value2[, ...]])
|
|
|
1225 |
*
|
|
|
1226 |
* @access public
|
|
|
1227 |
* @category Statistical Functions
|
|
|
1228 |
* @param mixed $arg,... Data values
|
|
|
1229 |
* @return int
|
|
|
1230 |
*/
|
|
|
1231 |
public static function COUNTBLANK() {
|
|
|
1232 |
// Return value
|
|
|
1233 |
$returnValue = 0;
|
|
|
1234 |
|
|
|
1235 |
// Loop through arguments
|
|
|
1236 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
1237 |
foreach ($aArgs as $arg) {
|
|
|
1238 |
// Is it a blank cell?
|
|
|
1239 |
if ((is_null($arg)) || ((is_string($arg)) && ($arg == ''))) {
|
|
|
1240 |
++$returnValue;
|
|
|
1241 |
}
|
|
|
1242 |
}
|
|
|
1243 |
|
|
|
1244 |
// Return
|
|
|
1245 |
return $returnValue;
|
|
|
1246 |
} // function COUNTBLANK()
|
|
|
1247 |
|
|
|
1248 |
|
|
|
1249 |
/**
|
|
|
1250 |
* COUNTIF
|
|
|
1251 |
*
|
|
|
1252 |
* Counts the number of cells that contain numbers within the list of arguments
|
|
|
1253 |
*
|
|
|
1254 |
* Excel Function:
|
|
|
1255 |
* COUNTIF(value1[,value2[, ...]],condition)
|
|
|
1256 |
*
|
|
|
1257 |
* @access public
|
|
|
1258 |
* @category Statistical Functions
|
|
|
1259 |
* @param mixed $arg,... Data values
|
|
|
1260 |
* @param string $condition The criteria that defines which cells will be counted.
|
|
|
1261 |
* @return int
|
|
|
1262 |
*/
|
|
|
1263 |
public static function COUNTIF($aArgs,$condition) {
|
|
|
1264 |
// Return value
|
|
|
1265 |
$returnValue = 0;
|
|
|
1266 |
|
|
|
1267 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
|
|
|
1268 |
$condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
|
|
|
1269 |
// Loop through arguments
|
|
|
1270 |
foreach ($aArgs as $arg) {
|
|
|
1271 |
if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
|
|
|
1272 |
$testCondition = '='.$arg.$condition;
|
|
|
1273 |
if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
|
|
|
1274 |
// Is it a value within our criteria
|
|
|
1275 |
++$returnValue;
|
|
|
1276 |
}
|
|
|
1277 |
}
|
|
|
1278 |
|
|
|
1279 |
// Return
|
|
|
1280 |
return $returnValue;
|
|
|
1281 |
} // function COUNTIF()
|
|
|
1282 |
|
|
|
1283 |
|
|
|
1284 |
/**
|
|
|
1285 |
* COVAR
|
|
|
1286 |
*
|
|
|
1287 |
* Returns covariance, the average of the products of deviations for each data point pair.
|
|
|
1288 |
*
|
|
|
1289 |
* @param array of mixed Data Series Y
|
|
|
1290 |
* @param array of mixed Data Series X
|
|
|
1291 |
* @return float
|
|
|
1292 |
*/
|
|
|
1293 |
public static function COVAR($yValues,$xValues) {
|
|
|
1294 |
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
|
1295 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1296 |
}
|
|
|
1297 |
$yValueCount = count($yValues);
|
|
|
1298 |
$xValueCount = count($xValues);
|
|
|
1299 |
|
|
|
1300 |
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
|
1301 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
1302 |
} elseif ($yValueCount == 1) {
|
|
|
1303 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
1304 |
}
|
|
|
1305 |
|
|
|
1306 |
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
|
1307 |
return $bestFitLinear->getCovariance();
|
|
|
1308 |
} // function COVAR()
|
|
|
1309 |
|
|
|
1310 |
|
|
|
1311 |
/**
|
|
|
1312 |
* CRITBINOM
|
|
|
1313 |
*
|
|
|
1314 |
* Returns the smallest value for which the cumulative binomial distribution is greater
|
|
|
1315 |
* than or equal to a criterion value
|
|
|
1316 |
*
|
|
|
1317 |
* See http://support.microsoft.com/kb/828117/ for details of the algorithm used
|
|
|
1318 |
*
|
|
|
1319 |
* @param float $trials number of Bernoulli trials
|
|
|
1320 |
* @param float $probability probability of a success on each trial
|
|
|
1321 |
* @param float $alpha criterion value
|
|
|
1322 |
* @return int
|
|
|
1323 |
*
|
|
|
1324 |
* @todo Warning. This implementation differs from the algorithm detailed on the MS
|
|
|
1325 |
* web site in that $CumPGuessMinus1 = $CumPGuess - 1 rather than $CumPGuess - $PGuess
|
|
|
1326 |
* This eliminates a potential endless loop error, but may have an adverse affect on the
|
|
|
1327 |
* accuracy of the function (although all my tests have so far returned correct results).
|
|
|
1328 |
*
|
|
|
1329 |
*/
|
|
|
1330 |
public static function CRITBINOM($trials, $probability, $alpha) {
|
|
|
1331 |
$trials = floor(PHPExcel_Calculation_Functions::flattenSingleValue($trials));
|
|
|
1332 |
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
|
1333 |
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
|
|
|
1334 |
|
|
|
1335 |
if ((is_numeric($trials)) && (is_numeric($probability)) && (is_numeric($alpha))) {
|
|
|
1336 |
if ($trials < 0) {
|
|
|
1337 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1338 |
}
|
|
|
1339 |
if (($probability < 0) || ($probability > 1)) {
|
|
|
1340 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1341 |
}
|
|
|
1342 |
if (($alpha < 0) || ($alpha > 1)) {
|
|
|
1343 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1344 |
}
|
|
|
1345 |
if ($alpha <= 0.5) {
|
|
|
1346 |
$t = sqrt(log(1 / ($alpha * $alpha)));
|
|
|
1347 |
$trialsApprox = 0 - ($t + (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t));
|
|
|
1348 |
} else {
|
|
|
1349 |
$t = sqrt(log(1 / pow(1 - $alpha,2)));
|
|
|
1350 |
$trialsApprox = $t - (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t);
|
|
|
1351 |
}
|
|
|
1352 |
$Guess = floor($trials * $probability + $trialsApprox * sqrt($trials * $probability * (1 - $probability)));
|
|
|
1353 |
if ($Guess < 0) {
|
|
|
1354 |
$Guess = 0;
|
|
|
1355 |
} elseif ($Guess > $trials) {
|
|
|
1356 |
$Guess = $trials;
|
|
|
1357 |
}
|
|
|
1358 |
|
|
|
1359 |
$TotalUnscaledProbability = $UnscaledPGuess = $UnscaledCumPGuess = 0.0;
|
|
|
1360 |
$EssentiallyZero = 10e-12;
|
|
|
1361 |
|
|
|
1362 |
$m = floor($trials * $probability);
|
|
|
1363 |
++$TotalUnscaledProbability;
|
|
|
1364 |
if ($m == $Guess) { ++$UnscaledPGuess; }
|
|
|
1365 |
if ($m <= $Guess) { ++$UnscaledCumPGuess; }
|
|
|
1366 |
|
|
|
1367 |
$PreviousValue = 1;
|
|
|
1368 |
$Done = False;
|
|
|
1369 |
$k = $m + 1;
|
|
|
1370 |
while ((!$Done) && ($k <= $trials)) {
|
|
|
1371 |
$CurrentValue = $PreviousValue * ($trials - $k + 1) * $probability / ($k * (1 - $probability));
|
|
|
1372 |
$TotalUnscaledProbability += $CurrentValue;
|
|
|
1373 |
if ($k == $Guess) { $UnscaledPGuess += $CurrentValue; }
|
|
|
1374 |
if ($k <= $Guess) { $UnscaledCumPGuess += $CurrentValue; }
|
|
|
1375 |
if ($CurrentValue <= $EssentiallyZero) { $Done = True; }
|
|
|
1376 |
$PreviousValue = $CurrentValue;
|
|
|
1377 |
++$k;
|
|
|
1378 |
}
|
|
|
1379 |
|
|
|
1380 |
$PreviousValue = 1;
|
|
|
1381 |
$Done = False;
|
|
|
1382 |
$k = $m - 1;
|
|
|
1383 |
while ((!$Done) && ($k >= 0)) {
|
|
|
1384 |
$CurrentValue = $PreviousValue * $k + 1 * (1 - $probability) / (($trials - $k) * $probability);
|
|
|
1385 |
$TotalUnscaledProbability += $CurrentValue;
|
|
|
1386 |
if ($k == $Guess) { $UnscaledPGuess += $CurrentValue; }
|
|
|
1387 |
if ($k <= $Guess) { $UnscaledCumPGuess += $CurrentValue; }
|
|
|
1388 |
if ($CurrentValue <= $EssentiallyZero) { $Done = True; }
|
|
|
1389 |
$PreviousValue = $CurrentValue;
|
|
|
1390 |
--$k;
|
|
|
1391 |
}
|
|
|
1392 |
|
|
|
1393 |
$PGuess = $UnscaledPGuess / $TotalUnscaledProbability;
|
|
|
1394 |
$CumPGuess = $UnscaledCumPGuess / $TotalUnscaledProbability;
|
|
|
1395 |
|
|
|
1396 |
// $CumPGuessMinus1 = $CumPGuess - $PGuess;
|
|
|
1397 |
$CumPGuessMinus1 = $CumPGuess - 1;
|
|
|
1398 |
|
|
|
1399 |
while (True) {
|
|
|
1400 |
if (($CumPGuessMinus1 < $alpha) && ($CumPGuess >= $alpha)) {
|
|
|
1401 |
return $Guess;
|
|
|
1402 |
} elseif (($CumPGuessMinus1 < $alpha) && ($CumPGuess < $alpha)) {
|
|
|
1403 |
$PGuessPlus1 = $PGuess * ($trials - $Guess) * $probability / $Guess / (1 - $probability);
|
|
|
1404 |
$CumPGuessMinus1 = $CumPGuess;
|
|
|
1405 |
$CumPGuess = $CumPGuess + $PGuessPlus1;
|
|
|
1406 |
$PGuess = $PGuessPlus1;
|
|
|
1407 |
++$Guess;
|
|
|
1408 |
} elseif (($CumPGuessMinus1 >= $alpha) && ($CumPGuess >= $alpha)) {
|
|
|
1409 |
$PGuessMinus1 = $PGuess * $Guess * (1 - $probability) / ($trials - $Guess + 1) / $probability;
|
|
|
1410 |
$CumPGuess = $CumPGuessMinus1;
|
|
|
1411 |
$CumPGuessMinus1 = $CumPGuessMinus1 - $PGuess;
|
|
|
1412 |
$PGuess = $PGuessMinus1;
|
|
|
1413 |
--$Guess;
|
|
|
1414 |
}
|
|
|
1415 |
}
|
|
|
1416 |
}
|
|
|
1417 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1418 |
} // function CRITBINOM()
|
|
|
1419 |
|
|
|
1420 |
|
|
|
1421 |
/**
|
|
|
1422 |
* DEVSQ
|
|
|
1423 |
*
|
|
|
1424 |
* Returns the sum of squares of deviations of data points from their sample mean.
|
|
|
1425 |
*
|
|
|
1426 |
* Excel Function:
|
|
|
1427 |
* DEVSQ(value1[,value2[, ...]])
|
|
|
1428 |
*
|
|
|
1429 |
* @access public
|
|
|
1430 |
* @category Statistical Functions
|
|
|
1431 |
* @param mixed $arg,... Data values
|
|
|
1432 |
* @return float
|
|
|
1433 |
*/
|
|
|
1434 |
public static function DEVSQ() {
|
|
|
1435 |
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
1436 |
|
|
|
1437 |
// Return value
|
|
|
1438 |
$returnValue = null;
|
|
|
1439 |
|
|
|
1440 |
$aMean = self::AVERAGE($aArgs);
|
|
|
1441 |
if ($aMean != PHPExcel_Calculation_Functions::DIV0()) {
|
|
|
1442 |
$aCount = -1;
|
|
|
1443 |
foreach ($aArgs as $k => $arg) {
|
|
|
1444 |
// Is it a numeric value?
|
|
|
1445 |
if ((is_bool($arg)) &&
|
|
|
1446 |
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
|
|
|
1447 |
$arg = (integer) $arg;
|
|
|
1448 |
}
|
|
|
1449 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
1450 |
if (is_null($returnValue)) {
|
|
|
1451 |
$returnValue = pow(($arg - $aMean),2);
|
|
|
1452 |
} else {
|
|
|
1453 |
$returnValue += pow(($arg - $aMean),2);
|
|
|
1454 |
}
|
|
|
1455 |
++$aCount;
|
|
|
1456 |
}
|
|
|
1457 |
}
|
|
|
1458 |
|
|
|
1459 |
// Return
|
|
|
1460 |
if (is_null($returnValue)) {
|
|
|
1461 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1462 |
} else {
|
|
|
1463 |
return $returnValue;
|
|
|
1464 |
}
|
|
|
1465 |
}
|
|
|
1466 |
return self::NA();
|
|
|
1467 |
} // function DEVSQ()
|
|
|
1468 |
|
|
|
1469 |
|
|
|
1470 |
/**
|
|
|
1471 |
* EXPONDIST
|
|
|
1472 |
*
|
|
|
1473 |
* Returns the exponential distribution. Use EXPONDIST to model the time between events,
|
|
|
1474 |
* such as how long an automated bank teller takes to deliver cash. For example, you can
|
|
|
1475 |
* use EXPONDIST to determine the probability that the process takes at most 1 minute.
|
|
|
1476 |
*
|
|
|
1477 |
* @param float $value Value of the function
|
|
|
1478 |
* @param float $lambda The parameter value
|
|
|
1479 |
* @param boolean $cumulative
|
|
|
1480 |
* @return float
|
|
|
1481 |
*/
|
|
|
1482 |
public static function EXPONDIST($value, $lambda, $cumulative) {
|
|
|
1483 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
1484 |
$lambda = PHPExcel_Calculation_Functions::flattenSingleValue($lambda);
|
|
|
1485 |
$cumulative = PHPExcel_Calculation_Functions::flattenSingleValue($cumulative);
|
|
|
1486 |
|
|
|
1487 |
if ((is_numeric($value)) && (is_numeric($lambda))) {
|
|
|
1488 |
if (($value < 0) || ($lambda < 0)) {
|
|
|
1489 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1490 |
}
|
|
|
1491 |
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
|
|
|
1492 |
if ($cumulative) {
|
|
|
1493 |
return 1 - exp(0-$value*$lambda);
|
|
|
1494 |
} else {
|
|
|
1495 |
return $lambda * exp(0-$value*$lambda);
|
|
|
1496 |
}
|
|
|
1497 |
}
|
|
|
1498 |
}
|
|
|
1499 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1500 |
} // function EXPONDIST()
|
|
|
1501 |
|
|
|
1502 |
|
|
|
1503 |
/**
|
|
|
1504 |
* FISHER
|
|
|
1505 |
*
|
|
|
1506 |
* Returns the Fisher transformation at x. This transformation produces a function that
|
|
|
1507 |
* is normally distributed rather than skewed. Use this function to perform hypothesis
|
|
|
1508 |
* testing on the correlation coefficient.
|
|
|
1509 |
*
|
|
|
1510 |
* @param float $value
|
|
|
1511 |
* @return float
|
|
|
1512 |
*/
|
|
|
1513 |
public static function FISHER($value) {
|
|
|
1514 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
1515 |
|
|
|
1516 |
if (is_numeric($value)) {
|
|
|
1517 |
if (($value <= -1) || ($value >= 1)) {
|
|
|
1518 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1519 |
}
|
|
|
1520 |
return 0.5 * log((1+$value)/(1-$value));
|
|
|
1521 |
}
|
|
|
1522 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1523 |
} // function FISHER()
|
|
|
1524 |
|
|
|
1525 |
|
|
|
1526 |
/**
|
|
|
1527 |
* FISHERINV
|
|
|
1528 |
*
|
|
|
1529 |
* Returns the inverse of the Fisher transformation. Use this transformation when
|
|
|
1530 |
* analyzing correlations between ranges or arrays of data. If y = FISHER(x), then
|
|
|
1531 |
* FISHERINV(y) = x.
|
|
|
1532 |
*
|
|
|
1533 |
* @param float $value
|
|
|
1534 |
* @return float
|
|
|
1535 |
*/
|
|
|
1536 |
public static function FISHERINV($value) {
|
|
|
1537 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
1538 |
|
|
|
1539 |
if (is_numeric($value)) {
|
|
|
1540 |
return (exp(2 * $value) - 1) / (exp(2 * $value) + 1);
|
|
|
1541 |
}
|
|
|
1542 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1543 |
} // function FISHERINV()
|
|
|
1544 |
|
|
|
1545 |
|
|
|
1546 |
/**
|
|
|
1547 |
* FORECAST
|
|
|
1548 |
*
|
|
|
1549 |
* Calculates, or predicts, a future value by using existing values. The predicted value is a y-value for a given x-value.
|
|
|
1550 |
*
|
|
|
1551 |
* @param float Value of X for which we want to find Y
|
|
|
1552 |
* @param array of mixed Data Series Y
|
|
|
1553 |
* @param array of mixed Data Series X
|
|
|
1554 |
* @return float
|
|
|
1555 |
*/
|
|
|
1556 |
public static function FORECAST($xValue,$yValues,$xValues) {
|
|
|
1557 |
$xValue = PHPExcel_Calculation_Functions::flattenSingleValue($xValue);
|
|
|
1558 |
if (!is_numeric($xValue)) {
|
|
|
1559 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1560 |
}
|
|
|
1561 |
|
|
|
1562 |
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
|
1563 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1564 |
}
|
|
|
1565 |
$yValueCount = count($yValues);
|
|
|
1566 |
$xValueCount = count($xValues);
|
|
|
1567 |
|
|
|
1568 |
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
|
1569 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
1570 |
} elseif ($yValueCount == 1) {
|
|
|
1571 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
1572 |
}
|
|
|
1573 |
|
|
|
1574 |
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
|
1575 |
return $bestFitLinear->getValueOfYForX($xValue);
|
|
|
1576 |
} // function FORECAST()
|
|
|
1577 |
|
|
|
1578 |
|
|
|
1579 |
/**
|
|
|
1580 |
* GAMMADIST
|
|
|
1581 |
*
|
|
|
1582 |
* Returns the gamma distribution.
|
|
|
1583 |
*
|
|
|
1584 |
* @param float $value Value at which you want to evaluate the distribution
|
|
|
1585 |
* @param float $a Parameter to the distribution
|
|
|
1586 |
* @param float $b Parameter to the distribution
|
|
|
1587 |
* @param boolean $cumulative
|
|
|
1588 |
* @return float
|
|
|
1589 |
*
|
|
|
1590 |
*/
|
|
|
1591 |
public static function GAMMADIST($value,$a,$b,$cumulative) {
|
|
|
1592 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
1593 |
$a = PHPExcel_Calculation_Functions::flattenSingleValue($a);
|
|
|
1594 |
$b = PHPExcel_Calculation_Functions::flattenSingleValue($b);
|
|
|
1595 |
|
|
|
1596 |
if ((is_numeric($value)) && (is_numeric($a)) && (is_numeric($b))) {
|
|
|
1597 |
if (($value < 0) || ($a <= 0) || ($b <= 0)) {
|
|
|
1598 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1599 |
}
|
|
|
1600 |
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
|
|
|
1601 |
if ($cumulative) {
|
|
|
1602 |
return self::_incompleteGamma($a,$value / $b) / self::_gamma($a);
|
|
|
1603 |
} else {
|
|
|
1604 |
return (1 / (pow($b,$a) * self::_gamma($a))) * pow($value,$a-1) * exp(0-($value / $b));
|
|
|
1605 |
}
|
|
|
1606 |
}
|
|
|
1607 |
}
|
|
|
1608 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1609 |
} // function GAMMADIST()
|
|
|
1610 |
|
|
|
1611 |
|
|
|
1612 |
/**
|
|
|
1613 |
* GAMMAINV
|
|
|
1614 |
*
|
|
|
1615 |
* Returns the inverse of the beta distribution.
|
|
|
1616 |
*
|
|
|
1617 |
* @param float $probability Probability at which you want to evaluate the distribution
|
|
|
1618 |
* @param float $alpha Parameter to the distribution
|
|
|
1619 |
* @param float $beta Parameter to the distribution
|
|
|
1620 |
* @return float
|
|
|
1621 |
*
|
|
|
1622 |
*/
|
|
|
1623 |
public static function GAMMAINV($probability,$alpha,$beta) {
|
|
|
1624 |
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
|
1625 |
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
|
|
|
1626 |
$beta = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
|
|
|
1627 |
|
|
|
1628 |
if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta))) {
|
|
|
1629 |
if (($alpha <= 0) || ($beta <= 0) || ($probability < 0) || ($probability > 1)) {
|
|
|
1630 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1631 |
}
|
|
|
1632 |
|
|
|
1633 |
$xLo = 0;
|
|
|
1634 |
$xHi = $alpha * $beta * 5;
|
|
|
1635 |
|
|
|
1636 |
$x = $xNew = 1;
|
|
|
1637 |
$error = $pdf = 0;
|
|
|
1638 |
$dx = 1024;
|
|
|
1639 |
$i = 0;
|
|
|
1640 |
|
|
|
1641 |
while ((abs($dx) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
|
|
|
1642 |
// Apply Newton-Raphson step
|
|
|
1643 |
$error = self::GAMMADIST($x, $alpha, $beta, True) - $probability;
|
|
|
1644 |
if ($error < 0.0) {
|
|
|
1645 |
$xLo = $x;
|
|
|
1646 |
} else {
|
|
|
1647 |
$xHi = $x;
|
|
|
1648 |
}
|
|
|
1649 |
$pdf = self::GAMMADIST($x, $alpha, $beta, False);
|
|
|
1650 |
// Avoid division by zero
|
|
|
1651 |
if ($pdf != 0.0) {
|
|
|
1652 |
$dx = $error / $pdf;
|
|
|
1653 |
$xNew = $x - $dx;
|
|
|
1654 |
}
|
|
|
1655 |
// If the NR fails to converge (which for example may be the
|
|
|
1656 |
// case if the initial guess is too rough) we apply a bisection
|
|
|
1657 |
// step to determine a more narrow interval around the root.
|
|
|
1658 |
if (($xNew < $xLo) || ($xNew > $xHi) || ($pdf == 0.0)) {
|
|
|
1659 |
$xNew = ($xLo + $xHi) / 2;
|
|
|
1660 |
$dx = $xNew - $x;
|
|
|
1661 |
}
|
|
|
1662 |
$x = $xNew;
|
|
|
1663 |
}
|
|
|
1664 |
if ($i == MAX_ITERATIONS) {
|
|
|
1665 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
1666 |
}
|
|
|
1667 |
return $x;
|
|
|
1668 |
}
|
|
|
1669 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1670 |
} // function GAMMAINV()
|
|
|
1671 |
|
|
|
1672 |
|
|
|
1673 |
/**
|
|
|
1674 |
* GAMMALN
|
|
|
1675 |
*
|
|
|
1676 |
* Returns the natural logarithm of the gamma function.
|
|
|
1677 |
*
|
|
|
1678 |
* @param float $value
|
|
|
1679 |
* @return float
|
|
|
1680 |
*/
|
|
|
1681 |
public static function GAMMALN($value) {
|
|
|
1682 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
1683 |
|
|
|
1684 |
if (is_numeric($value)) {
|
|
|
1685 |
if ($value <= 0) {
|
|
|
1686 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1687 |
}
|
|
|
1688 |
return log(self::_gamma($value));
|
|
|
1689 |
}
|
|
|
1690 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1691 |
} // function GAMMALN()
|
|
|
1692 |
|
|
|
1693 |
|
|
|
1694 |
/**
|
|
|
1695 |
* GEOMEAN
|
|
|
1696 |
*
|
|
|
1697 |
* Returns the geometric mean of an array or range of positive data. For example, you
|
|
|
1698 |
* can use GEOMEAN to calculate average growth rate given compound interest with
|
|
|
1699 |
* variable rates.
|
|
|
1700 |
*
|
|
|
1701 |
* Excel Function:
|
|
|
1702 |
* GEOMEAN(value1[,value2[, ...]])
|
|
|
1703 |
*
|
|
|
1704 |
* @access public
|
|
|
1705 |
* @category Statistical Functions
|
|
|
1706 |
* @param mixed $arg,... Data values
|
|
|
1707 |
* @return float
|
|
|
1708 |
*/
|
|
|
1709 |
public static function GEOMEAN() {
|
|
|
1710 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
1711 |
|
|
|
1712 |
$aMean = PHPExcel_Calculation_MathTrig::PRODUCT($aArgs);
|
|
|
1713 |
if (is_numeric($aMean) && ($aMean > 0)) {
|
|
|
1714 |
$aCount = self::COUNT($aArgs) ;
|
|
|
1715 |
if (self::MIN($aArgs) > 0) {
|
|
|
1716 |
return pow($aMean, (1 / $aCount));
|
|
|
1717 |
}
|
|
|
1718 |
}
|
|
|
1719 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1720 |
} // GEOMEAN()
|
|
|
1721 |
|
|
|
1722 |
|
|
|
1723 |
/**
|
|
|
1724 |
* GROWTH
|
|
|
1725 |
*
|
|
|
1726 |
* Returns values along a predicted emponential trend
|
|
|
1727 |
*
|
|
|
1728 |
* @param array of mixed Data Series Y
|
|
|
1729 |
* @param array of mixed Data Series X
|
|
|
1730 |
* @param array of mixed Values of X for which we want to find Y
|
|
|
1731 |
* @param boolean A logical value specifying whether to force the intersect to equal 0.
|
|
|
1732 |
* @return array of float
|
|
|
1733 |
*/
|
|
|
1734 |
public static function GROWTH($yValues,$xValues=array(),$newValues=array(),$const=True) {
|
|
|
1735 |
$yValues = PHPExcel_Calculation_Functions::flattenArray($yValues);
|
|
|
1736 |
$xValues = PHPExcel_Calculation_Functions::flattenArray($xValues);
|
|
|
1737 |
$newValues = PHPExcel_Calculation_Functions::flattenArray($newValues);
|
|
|
1738 |
$const = (is_null($const)) ? True : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
|
|
|
1739 |
|
|
|
1740 |
$bestFitExponential = trendClass::calculate(trendClass::TREND_EXPONENTIAL,$yValues,$xValues,$const);
|
|
|
1741 |
if (empty($newValues)) {
|
|
|
1742 |
$newValues = $bestFitExponential->getXValues();
|
|
|
1743 |
}
|
|
|
1744 |
|
|
|
1745 |
$returnArray = array();
|
|
|
1746 |
foreach($newValues as $xValue) {
|
|
|
1747 |
$returnArray[0][] = $bestFitExponential->getValueOfYForX($xValue);
|
|
|
1748 |
}
|
|
|
1749 |
|
|
|
1750 |
return $returnArray;
|
|
|
1751 |
} // function GROWTH()
|
|
|
1752 |
|
|
|
1753 |
|
|
|
1754 |
/**
|
|
|
1755 |
* HARMEAN
|
|
|
1756 |
*
|
|
|
1757 |
* Returns the harmonic mean of a data set. The harmonic mean is the reciprocal of the
|
|
|
1758 |
* arithmetic mean of reciprocals.
|
|
|
1759 |
*
|
|
|
1760 |
* Excel Function:
|
|
|
1761 |
* HARMEAN(value1[,value2[, ...]])
|
|
|
1762 |
*
|
|
|
1763 |
* @access public
|
|
|
1764 |
* @category Statistical Functions
|
|
|
1765 |
* @param mixed $arg,... Data values
|
|
|
1766 |
* @return float
|
|
|
1767 |
*/
|
|
|
1768 |
public static function HARMEAN() {
|
|
|
1769 |
// Return value
|
|
|
1770 |
$returnValue = PHPExcel_Calculation_Functions::NA();
|
|
|
1771 |
|
|
|
1772 |
// Loop through arguments
|
|
|
1773 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
1774 |
if (self::MIN($aArgs) < 0) {
|
|
|
1775 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1776 |
}
|
|
|
1777 |
$aCount = 0;
|
|
|
1778 |
foreach ($aArgs as $arg) {
|
|
|
1779 |
// Is it a numeric value?
|
|
|
1780 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
1781 |
if ($arg <= 0) {
|
|
|
1782 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1783 |
}
|
|
|
1784 |
if (is_null($returnValue)) {
|
|
|
1785 |
$returnValue = (1 / $arg);
|
|
|
1786 |
} else {
|
|
|
1787 |
$returnValue += (1 / $arg);
|
|
|
1788 |
}
|
|
|
1789 |
++$aCount;
|
|
|
1790 |
}
|
|
|
1791 |
}
|
|
|
1792 |
|
|
|
1793 |
// Return
|
|
|
1794 |
if ($aCount > 0) {
|
|
|
1795 |
return 1 / ($returnValue / $aCount);
|
|
|
1796 |
} else {
|
|
|
1797 |
return $returnValue;
|
|
|
1798 |
}
|
|
|
1799 |
} // function HARMEAN()
|
|
|
1800 |
|
|
|
1801 |
|
|
|
1802 |
/**
|
|
|
1803 |
* HYPGEOMDIST
|
|
|
1804 |
*
|
|
|
1805 |
* Returns the hypergeometric distribution. HYPGEOMDIST returns the probability of a given number of
|
|
|
1806 |
* sample successes, given the sample size, population successes, and population size.
|
|
|
1807 |
*
|
|
|
1808 |
* @param float $sampleSuccesses Number of successes in the sample
|
|
|
1809 |
* @param float $sampleNumber Size of the sample
|
|
|
1810 |
* @param float $populationSuccesses Number of successes in the population
|
|
|
1811 |
* @param float $populationNumber Population size
|
|
|
1812 |
* @return float
|
|
|
1813 |
*
|
|
|
1814 |
*/
|
|
|
1815 |
public static function HYPGEOMDIST($sampleSuccesses, $sampleNumber, $populationSuccesses, $populationNumber) {
|
|
|
1816 |
$sampleSuccesses = floor(PHPExcel_Calculation_Functions::flattenSingleValue($sampleSuccesses));
|
|
|
1817 |
$sampleNumber = floor(PHPExcel_Calculation_Functions::flattenSingleValue($sampleNumber));
|
|
|
1818 |
$populationSuccesses = floor(PHPExcel_Calculation_Functions::flattenSingleValue($populationSuccesses));
|
|
|
1819 |
$populationNumber = floor(PHPExcel_Calculation_Functions::flattenSingleValue($populationNumber));
|
|
|
1820 |
|
|
|
1821 |
if ((is_numeric($sampleSuccesses)) && (is_numeric($sampleNumber)) && (is_numeric($populationSuccesses)) && (is_numeric($populationNumber))) {
|
|
|
1822 |
if (($sampleSuccesses < 0) || ($sampleSuccesses > $sampleNumber) || ($sampleSuccesses > $populationSuccesses)) {
|
|
|
1823 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1824 |
}
|
|
|
1825 |
if (($sampleNumber <= 0) || ($sampleNumber > $populationNumber)) {
|
|
|
1826 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1827 |
}
|
|
|
1828 |
if (($populationSuccesses <= 0) || ($populationSuccesses > $populationNumber)) {
|
|
|
1829 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1830 |
}
|
|
|
1831 |
return PHPExcel_Calculation_MathTrig::COMBIN($populationSuccesses,$sampleSuccesses) *
|
|
|
1832 |
PHPExcel_Calculation_MathTrig::COMBIN($populationNumber - $populationSuccesses,$sampleNumber - $sampleSuccesses) /
|
|
|
1833 |
PHPExcel_Calculation_MathTrig::COMBIN($populationNumber,$sampleNumber);
|
|
|
1834 |
}
|
|
|
1835 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1836 |
} // function HYPGEOMDIST()
|
|
|
1837 |
|
|
|
1838 |
|
|
|
1839 |
/**
|
|
|
1840 |
* INTERCEPT
|
|
|
1841 |
*
|
|
|
1842 |
* Calculates the point at which a line will intersect the y-axis by using existing x-values and y-values.
|
|
|
1843 |
*
|
|
|
1844 |
* @param array of mixed Data Series Y
|
|
|
1845 |
* @param array of mixed Data Series X
|
|
|
1846 |
* @return float
|
|
|
1847 |
*/
|
|
|
1848 |
public static function INTERCEPT($yValues,$xValues) {
|
|
|
1849 |
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
|
1850 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1851 |
}
|
|
|
1852 |
$yValueCount = count($yValues);
|
|
|
1853 |
$xValueCount = count($xValues);
|
|
|
1854 |
|
|
|
1855 |
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
|
1856 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
1857 |
} elseif ($yValueCount == 1) {
|
|
|
1858 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
1859 |
}
|
|
|
1860 |
|
|
|
1861 |
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
|
1862 |
return $bestFitLinear->getIntersect();
|
|
|
1863 |
} // function INTERCEPT()
|
|
|
1864 |
|
|
|
1865 |
|
|
|
1866 |
/**
|
|
|
1867 |
* KURT
|
|
|
1868 |
*
|
|
|
1869 |
* Returns the kurtosis of a data set. Kurtosis characterizes the relative peakedness
|
|
|
1870 |
* or flatness of a distribution compared with the normal distribution. Positive
|
|
|
1871 |
* kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a
|
|
|
1872 |
* relatively flat distribution.
|
|
|
1873 |
*
|
|
|
1874 |
* @param array Data Series
|
|
|
1875 |
* @return float
|
|
|
1876 |
*/
|
|
|
1877 |
public static function KURT() {
|
|
|
1878 |
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
1879 |
$mean = self::AVERAGE($aArgs);
|
|
|
1880 |
$stdDev = self::STDEV($aArgs);
|
|
|
1881 |
|
|
|
1882 |
if ($stdDev > 0) {
|
|
|
1883 |
$count = $summer = 0;
|
|
|
1884 |
// Loop through arguments
|
|
|
1885 |
foreach ($aArgs as $k => $arg) {
|
|
|
1886 |
if ((is_bool($arg)) &&
|
|
|
1887 |
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
|
1888 |
} else {
|
|
|
1889 |
// Is it a numeric value?
|
|
|
1890 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
1891 |
$summer += pow((($arg - $mean) / $stdDev),4) ;
|
|
|
1892 |
++$count;
|
|
|
1893 |
}
|
|
|
1894 |
}
|
|
|
1895 |
}
|
|
|
1896 |
|
|
|
1897 |
// Return
|
|
|
1898 |
if ($count > 3) {
|
|
|
1899 |
return $summer * ($count * ($count+1) / (($count-1) * ($count-2) * ($count-3))) - (3 * pow($count-1,2) / (($count-2) * ($count-3)));
|
|
|
1900 |
}
|
|
|
1901 |
}
|
|
|
1902 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
1903 |
} // function KURT()
|
|
|
1904 |
|
|
|
1905 |
|
|
|
1906 |
/**
|
|
|
1907 |
* LARGE
|
|
|
1908 |
*
|
|
|
1909 |
* Returns the nth largest value in a data set. You can use this function to
|
|
|
1910 |
* select a value based on its relative standing.
|
|
|
1911 |
*
|
|
|
1912 |
* Excel Function:
|
|
|
1913 |
* LARGE(value1[,value2[, ...]],entry)
|
|
|
1914 |
*
|
|
|
1915 |
* @access public
|
|
|
1916 |
* @category Statistical Functions
|
|
|
1917 |
* @param mixed $arg,... Data values
|
|
|
1918 |
* @param int $entry Position (ordered from the largest) in the array or range of data to return
|
|
|
1919 |
* @return float
|
|
|
1920 |
*
|
|
|
1921 |
*/
|
|
|
1922 |
public static function LARGE() {
|
|
|
1923 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
1924 |
|
|
|
1925 |
// Calculate
|
|
|
1926 |
$entry = floor(array_pop($aArgs));
|
|
|
1927 |
|
|
|
1928 |
if ((is_numeric($entry)) && (!is_string($entry))) {
|
|
|
1929 |
$mArgs = array();
|
|
|
1930 |
foreach ($aArgs as $arg) {
|
|
|
1931 |
// Is it a numeric value?
|
|
|
1932 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
1933 |
$mArgs[] = $arg;
|
|
|
1934 |
}
|
|
|
1935 |
}
|
|
|
1936 |
$count = self::COUNT($mArgs);
|
|
|
1937 |
$entry = floor(--$entry);
|
|
|
1938 |
if (($entry < 0) || ($entry >= $count) || ($count == 0)) {
|
|
|
1939 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
1940 |
}
|
|
|
1941 |
rsort($mArgs);
|
|
|
1942 |
return $mArgs[$entry];
|
|
|
1943 |
}
|
|
|
1944 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1945 |
} // function LARGE()
|
|
|
1946 |
|
|
|
1947 |
|
|
|
1948 |
/**
|
|
|
1949 |
* LINEST
|
|
|
1950 |
*
|
|
|
1951 |
* Calculates the statistics for a line by using the "least squares" method to calculate a straight line that best fits your data,
|
|
|
1952 |
* and then returns an array that describes the line.
|
|
|
1953 |
*
|
|
|
1954 |
* @param array of mixed Data Series Y
|
|
|
1955 |
* @param array of mixed Data Series X
|
|
|
1956 |
* @param boolean A logical value specifying whether to force the intersect to equal 0.
|
|
|
1957 |
* @param boolean A logical value specifying whether to return additional regression statistics.
|
|
|
1958 |
* @return array
|
|
|
1959 |
*/
|
|
|
1960 |
public static function LINEST($yValues, $xValues = NULL, $const = TRUE, $stats = FALSE) {
|
|
|
1961 |
$const = (is_null($const)) ? TRUE : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
|
|
|
1962 |
$stats = (is_null($stats)) ? FALSE : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($stats);
|
|
|
1963 |
if (is_null($xValues)) $xValues = range(1,count(PHPExcel_Calculation_Functions::flattenArray($yValues)));
|
|
|
1964 |
|
|
|
1965 |
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
|
1966 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
1967 |
}
|
|
|
1968 |
$yValueCount = count($yValues);
|
|
|
1969 |
$xValueCount = count($xValues);
|
|
|
1970 |
|
|
|
1971 |
|
|
|
1972 |
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
|
1973 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
1974 |
} elseif ($yValueCount == 1) {
|
|
|
1975 |
return 0;
|
|
|
1976 |
}
|
|
|
1977 |
|
|
|
1978 |
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues,$const);
|
|
|
1979 |
if ($stats) {
|
|
|
1980 |
return array( array( $bestFitLinear->getSlope(),
|
|
|
1981 |
$bestFitLinear->getSlopeSE(),
|
|
|
1982 |
$bestFitLinear->getGoodnessOfFit(),
|
|
|
1983 |
$bestFitLinear->getF(),
|
|
|
1984 |
$bestFitLinear->getSSRegression(),
|
|
|
1985 |
),
|
|
|
1986 |
array( $bestFitLinear->getIntersect(),
|
|
|
1987 |
$bestFitLinear->getIntersectSE(),
|
|
|
1988 |
$bestFitLinear->getStdevOfResiduals(),
|
|
|
1989 |
$bestFitLinear->getDFResiduals(),
|
|
|
1990 |
$bestFitLinear->getSSResiduals()
|
|
|
1991 |
)
|
|
|
1992 |
);
|
|
|
1993 |
} else {
|
|
|
1994 |
return array( $bestFitLinear->getSlope(),
|
|
|
1995 |
$bestFitLinear->getIntersect()
|
|
|
1996 |
);
|
|
|
1997 |
}
|
|
|
1998 |
} // function LINEST()
|
|
|
1999 |
|
|
|
2000 |
|
|
|
2001 |
/**
|
|
|
2002 |
* LOGEST
|
|
|
2003 |
*
|
|
|
2004 |
* Calculates an exponential curve that best fits the X and Y data series,
|
|
|
2005 |
* and then returns an array that describes the line.
|
|
|
2006 |
*
|
|
|
2007 |
* @param array of mixed Data Series Y
|
|
|
2008 |
* @param array of mixed Data Series X
|
|
|
2009 |
* @param boolean A logical value specifying whether to force the intersect to equal 0.
|
|
|
2010 |
* @param boolean A logical value specifying whether to return additional regression statistics.
|
|
|
2011 |
* @return array
|
|
|
2012 |
*/
|
|
|
2013 |
public static function LOGEST($yValues,$xValues=null,$const=True,$stats=False) {
|
|
|
2014 |
$const = (is_null($const)) ? True : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
|
|
|
2015 |
$stats = (is_null($stats)) ? False : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($stats);
|
|
|
2016 |
if (is_null($xValues)) $xValues = range(1,count(PHPExcel_Calculation_Functions::flattenArray($yValues)));
|
|
|
2017 |
|
|
|
2018 |
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
|
2019 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2020 |
}
|
|
|
2021 |
$yValueCount = count($yValues);
|
|
|
2022 |
$xValueCount = count($xValues);
|
|
|
2023 |
|
|
|
2024 |
foreach($yValues as $value) {
|
|
|
2025 |
if ($value <= 0.0) {
|
|
|
2026 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2027 |
}
|
|
|
2028 |
}
|
|
|
2029 |
|
|
|
2030 |
|
|
|
2031 |
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
|
2032 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
2033 |
} elseif ($yValueCount == 1) {
|
|
|
2034 |
return 1;
|
|
|
2035 |
}
|
|
|
2036 |
|
|
|
2037 |
$bestFitExponential = trendClass::calculate(trendClass::TREND_EXPONENTIAL,$yValues,$xValues,$const);
|
|
|
2038 |
if ($stats) {
|
|
|
2039 |
return array( array( $bestFitExponential->getSlope(),
|
|
|
2040 |
$bestFitExponential->getSlopeSE(),
|
|
|
2041 |
$bestFitExponential->getGoodnessOfFit(),
|
|
|
2042 |
$bestFitExponential->getF(),
|
|
|
2043 |
$bestFitExponential->getSSRegression(),
|
|
|
2044 |
),
|
|
|
2045 |
array( $bestFitExponential->getIntersect(),
|
|
|
2046 |
$bestFitExponential->getIntersectSE(),
|
|
|
2047 |
$bestFitExponential->getStdevOfResiduals(),
|
|
|
2048 |
$bestFitExponential->getDFResiduals(),
|
|
|
2049 |
$bestFitExponential->getSSResiduals()
|
|
|
2050 |
)
|
|
|
2051 |
);
|
|
|
2052 |
} else {
|
|
|
2053 |
return array( $bestFitExponential->getSlope(),
|
|
|
2054 |
$bestFitExponential->getIntersect()
|
|
|
2055 |
);
|
|
|
2056 |
}
|
|
|
2057 |
} // function LOGEST()
|
|
|
2058 |
|
|
|
2059 |
|
|
|
2060 |
/**
|
|
|
2061 |
* LOGINV
|
|
|
2062 |
*
|
|
|
2063 |
* Returns the inverse of the normal cumulative distribution
|
|
|
2064 |
*
|
|
|
2065 |
* @param float $probability
|
|
|
2066 |
* @param float $mean
|
|
|
2067 |
* @param float $stdDev
|
|
|
2068 |
* @return float
|
|
|
2069 |
*
|
|
|
2070 |
* @todo Try implementing P J Acklam's refinement algorithm for greater
|
|
|
2071 |
* accuracy if I can get my head round the mathematics
|
|
|
2072 |
* (as described at) http://home.online.no/~pjacklam/notes/invnorm/
|
|
|
2073 |
*/
|
|
|
2074 |
public static function LOGINV($probability, $mean, $stdDev) {
|
|
|
2075 |
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
|
2076 |
$mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
|
|
|
2077 |
$stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
|
|
|
2078 |
|
|
|
2079 |
if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
|
|
|
2080 |
if (($probability < 0) || ($probability > 1) || ($stdDev <= 0)) {
|
|
|
2081 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2082 |
}
|
|
|
2083 |
return exp($mean + $stdDev * self::NORMSINV($probability));
|
|
|
2084 |
}
|
|
|
2085 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2086 |
} // function LOGINV()
|
|
|
2087 |
|
|
|
2088 |
|
|
|
2089 |
/**
|
|
|
2090 |
* LOGNORMDIST
|
|
|
2091 |
*
|
|
|
2092 |
* Returns the cumulative lognormal distribution of x, where ln(x) is normally distributed
|
|
|
2093 |
* with parameters mean and standard_dev.
|
|
|
2094 |
*
|
|
|
2095 |
* @param float $value
|
|
|
2096 |
* @param float $mean
|
|
|
2097 |
* @param float $stdDev
|
|
|
2098 |
* @return float
|
|
|
2099 |
*/
|
|
|
2100 |
public static function LOGNORMDIST($value, $mean, $stdDev) {
|
|
|
2101 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
2102 |
$mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
|
|
|
2103 |
$stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
|
|
|
2104 |
|
|
|
2105 |
if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
|
|
|
2106 |
if (($value <= 0) || ($stdDev <= 0)) {
|
|
|
2107 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2108 |
}
|
|
|
2109 |
return self::NORMSDIST((log($value) - $mean) / $stdDev);
|
|
|
2110 |
}
|
|
|
2111 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2112 |
} // function LOGNORMDIST()
|
|
|
2113 |
|
|
|
2114 |
|
|
|
2115 |
/**
|
|
|
2116 |
* MAX
|
|
|
2117 |
*
|
|
|
2118 |
* MAX returns the value of the element of the values passed that has the highest value,
|
|
|
2119 |
* with negative numbers considered smaller than positive numbers.
|
|
|
2120 |
*
|
|
|
2121 |
* Excel Function:
|
|
|
2122 |
* MAX(value1[,value2[, ...]])
|
|
|
2123 |
*
|
|
|
2124 |
* @access public
|
|
|
2125 |
* @category Statistical Functions
|
|
|
2126 |
* @param mixed $arg,... Data values
|
|
|
2127 |
* @return float
|
|
|
2128 |
*/
|
|
|
2129 |
public static function MAX() {
|
|
|
2130 |
// Return value
|
|
|
2131 |
$returnValue = null;
|
|
|
2132 |
|
|
|
2133 |
// Loop through arguments
|
|
|
2134 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
2135 |
foreach ($aArgs as $arg) {
|
|
|
2136 |
// Is it a numeric value?
|
|
|
2137 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
2138 |
if ((is_null($returnValue)) || ($arg > $returnValue)) {
|
|
|
2139 |
$returnValue = $arg;
|
|
|
2140 |
}
|
|
|
2141 |
}
|
|
|
2142 |
}
|
|
|
2143 |
|
|
|
2144 |
// Return
|
|
|
2145 |
if(is_null($returnValue)) {
|
|
|
2146 |
return 0;
|
|
|
2147 |
}
|
|
|
2148 |
return $returnValue;
|
|
|
2149 |
} // function MAX()
|
|
|
2150 |
|
|
|
2151 |
|
|
|
2152 |
/**
|
|
|
2153 |
* MAXA
|
|
|
2154 |
*
|
|
|
2155 |
* Returns the greatest value in a list of arguments, including numbers, text, and logical values
|
|
|
2156 |
*
|
|
|
2157 |
* Excel Function:
|
|
|
2158 |
* MAXA(value1[,value2[, ...]])
|
|
|
2159 |
*
|
|
|
2160 |
* @access public
|
|
|
2161 |
* @category Statistical Functions
|
|
|
2162 |
* @param mixed $arg,... Data values
|
|
|
2163 |
* @return float
|
|
|
2164 |
*/
|
|
|
2165 |
public static function MAXA() {
|
|
|
2166 |
// Return value
|
|
|
2167 |
$returnValue = null;
|
|
|
2168 |
|
|
|
2169 |
// Loop through arguments
|
|
|
2170 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
2171 |
foreach ($aArgs as $arg) {
|
|
|
2172 |
// Is it a numeric value?
|
|
|
2173 |
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
|
|
|
2174 |
if (is_bool($arg)) {
|
|
|
2175 |
$arg = (integer) $arg;
|
|
|
2176 |
} elseif (is_string($arg)) {
|
|
|
2177 |
$arg = 0;
|
|
|
2178 |
}
|
|
|
2179 |
if ((is_null($returnValue)) || ($arg > $returnValue)) {
|
|
|
2180 |
$returnValue = $arg;
|
|
|
2181 |
}
|
|
|
2182 |
}
|
|
|
2183 |
}
|
|
|
2184 |
|
|
|
2185 |
// Return
|
|
|
2186 |
if(is_null($returnValue)) {
|
|
|
2187 |
return 0;
|
|
|
2188 |
}
|
|
|
2189 |
return $returnValue;
|
|
|
2190 |
} // function MAXA()
|
|
|
2191 |
|
|
|
2192 |
|
|
|
2193 |
/**
|
|
|
2194 |
* MAXIF
|
|
|
2195 |
*
|
|
|
2196 |
* Counts the maximum value within a range of cells that contain numbers within the list of arguments
|
|
|
2197 |
*
|
|
|
2198 |
* Excel Function:
|
|
|
2199 |
* MAXIF(value1[,value2[, ...]],condition)
|
|
|
2200 |
*
|
|
|
2201 |
* @access public
|
|
|
2202 |
* @category Mathematical and Trigonometric Functions
|
|
|
2203 |
* @param mixed $arg,... Data values
|
|
|
2204 |
* @param string $condition The criteria that defines which cells will be checked.
|
|
|
2205 |
* @return float
|
|
|
2206 |
*/
|
|
|
2207 |
public static function MAXIF($aArgs,$condition,$sumArgs = array()) {
|
|
|
2208 |
// Return value
|
|
|
2209 |
$returnValue = null;
|
|
|
2210 |
|
|
|
2211 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
|
|
|
2212 |
$sumArgs = PHPExcel_Calculation_Functions::flattenArray($sumArgs);
|
|
|
2213 |
if (empty($sumArgs)) {
|
|
|
2214 |
$sumArgs = $aArgs;
|
|
|
2215 |
}
|
|
|
2216 |
$condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
|
|
|
2217 |
// Loop through arguments
|
|
|
2218 |
foreach ($aArgs as $key => $arg) {
|
|
|
2219 |
if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
|
|
|
2220 |
$testCondition = '='.$arg.$condition;
|
|
|
2221 |
if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
|
|
|
2222 |
if ((is_null($returnValue)) || ($arg > $returnValue)) {
|
|
|
2223 |
$returnValue = $arg;
|
|
|
2224 |
}
|
|
|
2225 |
}
|
|
|
2226 |
}
|
|
|
2227 |
|
|
|
2228 |
// Return
|
|
|
2229 |
return $returnValue;
|
|
|
2230 |
} // function MAXIF()
|
|
|
2231 |
|
|
|
2232 |
|
|
|
2233 |
/**
|
|
|
2234 |
* MEDIAN
|
|
|
2235 |
*
|
|
|
2236 |
* Returns the median of the given numbers. The median is the number in the middle of a set of numbers.
|
|
|
2237 |
*
|
|
|
2238 |
* Excel Function:
|
|
|
2239 |
* MEDIAN(value1[,value2[, ...]])
|
|
|
2240 |
*
|
|
|
2241 |
* @access public
|
|
|
2242 |
* @category Statistical Functions
|
|
|
2243 |
* @param mixed $arg,... Data values
|
|
|
2244 |
* @return float
|
|
|
2245 |
*/
|
|
|
2246 |
public static function MEDIAN() {
|
|
|
2247 |
// Return value
|
|
|
2248 |
$returnValue = PHPExcel_Calculation_Functions::NaN();
|
|
|
2249 |
|
|
|
2250 |
$mArgs = array();
|
|
|
2251 |
// Loop through arguments
|
|
|
2252 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
2253 |
foreach ($aArgs as $arg) {
|
|
|
2254 |
// Is it a numeric value?
|
|
|
2255 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
2256 |
$mArgs[] = $arg;
|
|
|
2257 |
}
|
|
|
2258 |
}
|
|
|
2259 |
|
|
|
2260 |
$mValueCount = count($mArgs);
|
|
|
2261 |
if ($mValueCount > 0) {
|
|
|
2262 |
sort($mArgs,SORT_NUMERIC);
|
|
|
2263 |
$mValueCount = $mValueCount / 2;
|
|
|
2264 |
if ($mValueCount == floor($mValueCount)) {
|
|
|
2265 |
$returnValue = ($mArgs[$mValueCount--] + $mArgs[$mValueCount]) / 2;
|
|
|
2266 |
} else {
|
|
|
2267 |
$mValueCount == floor($mValueCount);
|
|
|
2268 |
$returnValue = $mArgs[$mValueCount];
|
|
|
2269 |
}
|
|
|
2270 |
}
|
|
|
2271 |
|
|
|
2272 |
// Return
|
|
|
2273 |
return $returnValue;
|
|
|
2274 |
} // function MEDIAN()
|
|
|
2275 |
|
|
|
2276 |
|
|
|
2277 |
/**
|
|
|
2278 |
* MIN
|
|
|
2279 |
*
|
|
|
2280 |
* MIN returns the value of the element of the values passed that has the smallest value,
|
|
|
2281 |
* with negative numbers considered smaller than positive numbers.
|
|
|
2282 |
*
|
|
|
2283 |
* Excel Function:
|
|
|
2284 |
* MIN(value1[,value2[, ...]])
|
|
|
2285 |
*
|
|
|
2286 |
* @access public
|
|
|
2287 |
* @category Statistical Functions
|
|
|
2288 |
* @param mixed $arg,... Data values
|
|
|
2289 |
* @return float
|
|
|
2290 |
*/
|
|
|
2291 |
public static function MIN() {
|
|
|
2292 |
// Return value
|
|
|
2293 |
$returnValue = null;
|
|
|
2294 |
|
|
|
2295 |
// Loop through arguments
|
|
|
2296 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
2297 |
foreach ($aArgs as $arg) {
|
|
|
2298 |
// Is it a numeric value?
|
|
|
2299 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
2300 |
if ((is_null($returnValue)) || ($arg < $returnValue)) {
|
|
|
2301 |
$returnValue = $arg;
|
|
|
2302 |
}
|
|
|
2303 |
}
|
|
|
2304 |
}
|
|
|
2305 |
|
|
|
2306 |
// Return
|
|
|
2307 |
if(is_null($returnValue)) {
|
|
|
2308 |
return 0;
|
|
|
2309 |
}
|
|
|
2310 |
return $returnValue;
|
|
|
2311 |
} // function MIN()
|
|
|
2312 |
|
|
|
2313 |
|
|
|
2314 |
/**
|
|
|
2315 |
* MINA
|
|
|
2316 |
*
|
|
|
2317 |
* Returns the smallest value in a list of arguments, including numbers, text, and logical values
|
|
|
2318 |
*
|
|
|
2319 |
* Excel Function:
|
|
|
2320 |
* MINA(value1[,value2[, ...]])
|
|
|
2321 |
*
|
|
|
2322 |
* @access public
|
|
|
2323 |
* @category Statistical Functions
|
|
|
2324 |
* @param mixed $arg,... Data values
|
|
|
2325 |
* @return float
|
|
|
2326 |
*/
|
|
|
2327 |
public static function MINA() {
|
|
|
2328 |
// Return value
|
|
|
2329 |
$returnValue = null;
|
|
|
2330 |
|
|
|
2331 |
// Loop through arguments
|
|
|
2332 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
2333 |
foreach ($aArgs as $arg) {
|
|
|
2334 |
// Is it a numeric value?
|
|
|
2335 |
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
|
|
|
2336 |
if (is_bool($arg)) {
|
|
|
2337 |
$arg = (integer) $arg;
|
|
|
2338 |
} elseif (is_string($arg)) {
|
|
|
2339 |
$arg = 0;
|
|
|
2340 |
}
|
|
|
2341 |
if ((is_null($returnValue)) || ($arg < $returnValue)) {
|
|
|
2342 |
$returnValue = $arg;
|
|
|
2343 |
}
|
|
|
2344 |
}
|
|
|
2345 |
}
|
|
|
2346 |
|
|
|
2347 |
// Return
|
|
|
2348 |
if(is_null($returnValue)) {
|
|
|
2349 |
return 0;
|
|
|
2350 |
}
|
|
|
2351 |
return $returnValue;
|
|
|
2352 |
} // function MINA()
|
|
|
2353 |
|
|
|
2354 |
|
|
|
2355 |
/**
|
|
|
2356 |
* MINIF
|
|
|
2357 |
*
|
|
|
2358 |
* Returns the minimum value within a range of cells that contain numbers within the list of arguments
|
|
|
2359 |
*
|
|
|
2360 |
* Excel Function:
|
|
|
2361 |
* MINIF(value1[,value2[, ...]],condition)
|
|
|
2362 |
*
|
|
|
2363 |
* @access public
|
|
|
2364 |
* @category Mathematical and Trigonometric Functions
|
|
|
2365 |
* @param mixed $arg,... Data values
|
|
|
2366 |
* @param string $condition The criteria that defines which cells will be checked.
|
|
|
2367 |
* @return float
|
|
|
2368 |
*/
|
|
|
2369 |
public static function MINIF($aArgs,$condition,$sumArgs = array()) {
|
|
|
2370 |
// Return value
|
|
|
2371 |
$returnValue = null;
|
|
|
2372 |
|
|
|
2373 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
|
|
|
2374 |
$sumArgs = PHPExcel_Calculation_Functions::flattenArray($sumArgs);
|
|
|
2375 |
if (empty($sumArgs)) {
|
|
|
2376 |
$sumArgs = $aArgs;
|
|
|
2377 |
}
|
|
|
2378 |
$condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
|
|
|
2379 |
// Loop through arguments
|
|
|
2380 |
foreach ($aArgs as $key => $arg) {
|
|
|
2381 |
if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
|
|
|
2382 |
$testCondition = '='.$arg.$condition;
|
|
|
2383 |
if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
|
|
|
2384 |
if ((is_null($returnValue)) || ($arg < $returnValue)) {
|
|
|
2385 |
$returnValue = $arg;
|
|
|
2386 |
}
|
|
|
2387 |
}
|
|
|
2388 |
}
|
|
|
2389 |
|
|
|
2390 |
// Return
|
|
|
2391 |
return $returnValue;
|
|
|
2392 |
} // function MINIF()
|
|
|
2393 |
|
|
|
2394 |
|
|
|
2395 |
//
|
|
|
2396 |
// Special variant of array_count_values that isn't limited to strings and integers,
|
|
|
2397 |
// but can work with floating point numbers as values
|
|
|
2398 |
//
|
|
|
2399 |
private static function _modeCalc($data) {
|
|
|
2400 |
$frequencyArray = array();
|
|
|
2401 |
foreach($data as $datum) {
|
|
|
2402 |
$found = False;
|
|
|
2403 |
foreach($frequencyArray as $key => $value) {
|
|
|
2404 |
if ((string) $value['value'] == (string) $datum) {
|
|
|
2405 |
++$frequencyArray[$key]['frequency'];
|
|
|
2406 |
$found = True;
|
|
|
2407 |
break;
|
|
|
2408 |
}
|
|
|
2409 |
}
|
|
|
2410 |
if (!$found) {
|
|
|
2411 |
$frequencyArray[] = array('value' => $datum,
|
|
|
2412 |
'frequency' => 1 );
|
|
|
2413 |
}
|
|
|
2414 |
}
|
|
|
2415 |
|
|
|
2416 |
foreach($frequencyArray as $key => $value) {
|
|
|
2417 |
$frequencyList[$key] = $value['frequency'];
|
|
|
2418 |
$valueList[$key] = $value['value'];
|
|
|
2419 |
}
|
|
|
2420 |
array_multisort($frequencyList, SORT_DESC, $valueList, SORT_ASC, SORT_NUMERIC, $frequencyArray);
|
|
|
2421 |
|
|
|
2422 |
if ($frequencyArray[0]['frequency'] == 1) {
|
|
|
2423 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
2424 |
}
|
|
|
2425 |
return $frequencyArray[0]['value'];
|
|
|
2426 |
} // function _modeCalc()
|
|
|
2427 |
|
|
|
2428 |
|
|
|
2429 |
/**
|
|
|
2430 |
* MODE
|
|
|
2431 |
*
|
|
|
2432 |
* Returns the most frequently occurring, or repetitive, value in an array or range of data
|
|
|
2433 |
*
|
|
|
2434 |
* Excel Function:
|
|
|
2435 |
* MODE(value1[,value2[, ...]])
|
|
|
2436 |
*
|
|
|
2437 |
* @access public
|
|
|
2438 |
* @category Statistical Functions
|
|
|
2439 |
* @param mixed $arg,... Data values
|
|
|
2440 |
* @return float
|
|
|
2441 |
*/
|
|
|
2442 |
public static function MODE() {
|
|
|
2443 |
// Return value
|
|
|
2444 |
$returnValue = PHPExcel_Calculation_Functions::NA();
|
|
|
2445 |
|
|
|
2446 |
// Loop through arguments
|
|
|
2447 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
2448 |
|
|
|
2449 |
$mArgs = array();
|
|
|
2450 |
foreach ($aArgs as $arg) {
|
|
|
2451 |
// Is it a numeric value?
|
|
|
2452 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
2453 |
$mArgs[] = $arg;
|
|
|
2454 |
}
|
|
|
2455 |
}
|
|
|
2456 |
|
|
|
2457 |
if (!empty($mArgs)) {
|
|
|
2458 |
return self::_modeCalc($mArgs);
|
|
|
2459 |
}
|
|
|
2460 |
|
|
|
2461 |
// Return
|
|
|
2462 |
return $returnValue;
|
|
|
2463 |
} // function MODE()
|
|
|
2464 |
|
|
|
2465 |
|
|
|
2466 |
/**
|
|
|
2467 |
* NEGBINOMDIST
|
|
|
2468 |
*
|
|
|
2469 |
* Returns the negative binomial distribution. NEGBINOMDIST returns the probability that
|
|
|
2470 |
* there will be number_f failures before the number_s-th success, when the constant
|
|
|
2471 |
* probability of a success is probability_s. This function is similar to the binomial
|
|
|
2472 |
* distribution, except that the number of successes is fixed, and the number of trials is
|
|
|
2473 |
* variable. Like the binomial, trials are assumed to be independent.
|
|
|
2474 |
*
|
|
|
2475 |
* @param float $failures Number of Failures
|
|
|
2476 |
* @param float $successes Threshold number of Successes
|
|
|
2477 |
* @param float $probability Probability of success on each trial
|
|
|
2478 |
* @return float
|
|
|
2479 |
*
|
|
|
2480 |
*/
|
|
|
2481 |
public static function NEGBINOMDIST($failures, $successes, $probability) {
|
|
|
2482 |
$failures = floor(PHPExcel_Calculation_Functions::flattenSingleValue($failures));
|
|
|
2483 |
$successes = floor(PHPExcel_Calculation_Functions::flattenSingleValue($successes));
|
|
|
2484 |
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
|
2485 |
|
|
|
2486 |
if ((is_numeric($failures)) && (is_numeric($successes)) && (is_numeric($probability))) {
|
|
|
2487 |
if (($failures < 0) || ($successes < 1)) {
|
|
|
2488 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2489 |
}
|
|
|
2490 |
if (($probability < 0) || ($probability > 1)) {
|
|
|
2491 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2492 |
}
|
|
|
2493 |
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
|
|
|
2494 |
if (($failures + $successes - 1) <= 0) {
|
|
|
2495 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2496 |
}
|
|
|
2497 |
}
|
|
|
2498 |
return (PHPExcel_Calculation_MathTrig::COMBIN($failures + $successes - 1,$successes - 1)) * (pow($probability,$successes)) * (pow(1 - $probability,$failures)) ;
|
|
|
2499 |
}
|
|
|
2500 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2501 |
} // function NEGBINOMDIST()
|
|
|
2502 |
|
|
|
2503 |
|
|
|
2504 |
/**
|
|
|
2505 |
* NORMDIST
|
|
|
2506 |
*
|
|
|
2507 |
* Returns the normal distribution for the specified mean and standard deviation. This
|
|
|
2508 |
* function has a very wide range of applications in statistics, including hypothesis
|
|
|
2509 |
* testing.
|
|
|
2510 |
*
|
|
|
2511 |
* @param float $value
|
|
|
2512 |
* @param float $mean Mean Value
|
|
|
2513 |
* @param float $stdDev Standard Deviation
|
|
|
2514 |
* @param boolean $cumulative
|
|
|
2515 |
* @return float
|
|
|
2516 |
*
|
|
|
2517 |
*/
|
|
|
2518 |
public static function NORMDIST($value, $mean, $stdDev, $cumulative) {
|
|
|
2519 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
2520 |
$mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
|
|
|
2521 |
$stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
|
|
|
2522 |
|
|
|
2523 |
if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
|
|
|
2524 |
if ($stdDev < 0) {
|
|
|
2525 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2526 |
}
|
|
|
2527 |
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
|
|
|
2528 |
if ($cumulative) {
|
|
|
2529 |
return 0.5 * (1 + PHPExcel_Calculation_Engineering::_erfVal(($value - $mean) / ($stdDev * sqrt(2))));
|
|
|
2530 |
} else {
|
|
|
2531 |
return (1 / (SQRT2PI * $stdDev)) * exp(0 - (pow($value - $mean,2) / (2 * ($stdDev * $stdDev))));
|
|
|
2532 |
}
|
|
|
2533 |
}
|
|
|
2534 |
}
|
|
|
2535 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2536 |
} // function NORMDIST()
|
|
|
2537 |
|
|
|
2538 |
|
|
|
2539 |
/**
|
|
|
2540 |
* NORMINV
|
|
|
2541 |
*
|
|
|
2542 |
* Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.
|
|
|
2543 |
*
|
|
|
2544 |
* @param float $value
|
|
|
2545 |
* @param float $mean Mean Value
|
|
|
2546 |
* @param float $stdDev Standard Deviation
|
|
|
2547 |
* @return float
|
|
|
2548 |
*
|
|
|
2549 |
*/
|
|
|
2550 |
public static function NORMINV($probability,$mean,$stdDev) {
|
|
|
2551 |
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
|
2552 |
$mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
|
|
|
2553 |
$stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
|
|
|
2554 |
|
|
|
2555 |
if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
|
|
|
2556 |
if (($probability < 0) || ($probability > 1)) {
|
|
|
2557 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2558 |
}
|
|
|
2559 |
if ($stdDev < 0) {
|
|
|
2560 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2561 |
}
|
|
|
2562 |
return (self::_inverse_ncdf($probability) * $stdDev) + $mean;
|
|
|
2563 |
}
|
|
|
2564 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2565 |
} // function NORMINV()
|
|
|
2566 |
|
|
|
2567 |
|
|
|
2568 |
/**
|
|
|
2569 |
* NORMSDIST
|
|
|
2570 |
*
|
|
|
2571 |
* Returns the standard normal cumulative distribution function. The distribution has
|
|
|
2572 |
* a mean of 0 (zero) and a standard deviation of one. Use this function in place of a
|
|
|
2573 |
* table of standard normal curve areas.
|
|
|
2574 |
*
|
|
|
2575 |
* @param float $value
|
|
|
2576 |
* @return float
|
|
|
2577 |
*/
|
|
|
2578 |
public static function NORMSDIST($value) {
|
|
|
2579 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
2580 |
|
|
|
2581 |
return self::NORMDIST($value, 0, 1, True);
|
|
|
2582 |
} // function NORMSDIST()
|
|
|
2583 |
|
|
|
2584 |
|
|
|
2585 |
/**
|
|
|
2586 |
* NORMSINV
|
|
|
2587 |
*
|
|
|
2588 |
* Returns the inverse of the standard normal cumulative distribution
|
|
|
2589 |
*
|
|
|
2590 |
* @param float $value
|
|
|
2591 |
* @return float
|
|
|
2592 |
*/
|
|
|
2593 |
public static function NORMSINV($value) {
|
|
|
2594 |
return self::NORMINV($value, 0, 1);
|
|
|
2595 |
} // function NORMSINV()
|
|
|
2596 |
|
|
|
2597 |
|
|
|
2598 |
/**
|
|
|
2599 |
* PERCENTILE
|
|
|
2600 |
*
|
|
|
2601 |
* Returns the nth percentile of values in a range..
|
|
|
2602 |
*
|
|
|
2603 |
* Excel Function:
|
|
|
2604 |
* PERCENTILE(value1[,value2[, ...]],entry)
|
|
|
2605 |
*
|
|
|
2606 |
* @access public
|
|
|
2607 |
* @category Statistical Functions
|
|
|
2608 |
* @param mixed $arg,... Data values
|
|
|
2609 |
* @param float $entry Percentile value in the range 0..1, inclusive.
|
|
|
2610 |
* @return float
|
|
|
2611 |
*/
|
|
|
2612 |
public static function PERCENTILE() {
|
|
|
2613 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
2614 |
|
|
|
2615 |
// Calculate
|
|
|
2616 |
$entry = array_pop($aArgs);
|
|
|
2617 |
|
|
|
2618 |
if ((is_numeric($entry)) && (!is_string($entry))) {
|
|
|
2619 |
if (($entry < 0) || ($entry > 1)) {
|
|
|
2620 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2621 |
}
|
|
|
2622 |
$mArgs = array();
|
|
|
2623 |
foreach ($aArgs as $arg) {
|
|
|
2624 |
// Is it a numeric value?
|
|
|
2625 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
2626 |
$mArgs[] = $arg;
|
|
|
2627 |
}
|
|
|
2628 |
}
|
|
|
2629 |
$mValueCount = count($mArgs);
|
|
|
2630 |
if ($mValueCount > 0) {
|
|
|
2631 |
sort($mArgs);
|
|
|
2632 |
$count = self::COUNT($mArgs);
|
|
|
2633 |
$index = $entry * ($count-1);
|
|
|
2634 |
$iBase = floor($index);
|
|
|
2635 |
if ($index == $iBase) {
|
|
|
2636 |
return $mArgs[$index];
|
|
|
2637 |
} else {
|
|
|
2638 |
$iNext = $iBase + 1;
|
|
|
2639 |
$iProportion = $index - $iBase;
|
|
|
2640 |
return $mArgs[$iBase] + (($mArgs[$iNext] - $mArgs[$iBase]) * $iProportion) ;
|
|
|
2641 |
}
|
|
|
2642 |
}
|
|
|
2643 |
}
|
|
|
2644 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2645 |
} // function PERCENTILE()
|
|
|
2646 |
|
|
|
2647 |
|
|
|
2648 |
/**
|
|
|
2649 |
* PERCENTRANK
|
|
|
2650 |
*
|
|
|
2651 |
* Returns the rank of a value in a data set as a percentage of the data set.
|
|
|
2652 |
*
|
|
|
2653 |
* @param array of number An array of, or a reference to, a list of numbers.
|
|
|
2654 |
* @param number The number whose rank you want to find.
|
|
|
2655 |
* @param number The number of significant digits for the returned percentage value.
|
|
|
2656 |
* @return float
|
|
|
2657 |
*/
|
|
|
2658 |
public static function PERCENTRANK($valueSet,$value,$significance=3) {
|
|
|
2659 |
$valueSet = PHPExcel_Calculation_Functions::flattenArray($valueSet);
|
|
|
2660 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
2661 |
$significance = (is_null($significance)) ? 3 : (integer) PHPExcel_Calculation_Functions::flattenSingleValue($significance);
|
|
|
2662 |
|
|
|
2663 |
foreach($valueSet as $key => $valueEntry) {
|
|
|
2664 |
if (!is_numeric($valueEntry)) {
|
|
|
2665 |
unset($valueSet[$key]);
|
|
|
2666 |
}
|
|
|
2667 |
}
|
|
|
2668 |
sort($valueSet,SORT_NUMERIC);
|
|
|
2669 |
$valueCount = count($valueSet);
|
|
|
2670 |
if ($valueCount == 0) {
|
|
|
2671 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2672 |
}
|
|
|
2673 |
|
|
|
2674 |
$valueAdjustor = $valueCount - 1;
|
|
|
2675 |
if (($value < $valueSet[0]) || ($value > $valueSet[$valueAdjustor])) {
|
|
|
2676 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
2677 |
}
|
|
|
2678 |
|
|
|
2679 |
$pos = array_search($value,$valueSet);
|
|
|
2680 |
if ($pos === False) {
|
|
|
2681 |
$pos = 0;
|
|
|
2682 |
$testValue = $valueSet[0];
|
|
|
2683 |
while ($testValue < $value) {
|
|
|
2684 |
$testValue = $valueSet[++$pos];
|
|
|
2685 |
}
|
|
|
2686 |
--$pos;
|
|
|
2687 |
$pos += (($value - $valueSet[$pos]) / ($testValue - $valueSet[$pos]));
|
|
|
2688 |
}
|
|
|
2689 |
|
|
|
2690 |
return round($pos / $valueAdjustor,$significance);
|
|
|
2691 |
} // function PERCENTRANK()
|
|
|
2692 |
|
|
|
2693 |
|
|
|
2694 |
/**
|
|
|
2695 |
* PERMUT
|
|
|
2696 |
*
|
|
|
2697 |
* Returns the number of permutations for a given number of objects that can be
|
|
|
2698 |
* selected from number objects. A permutation is any set or subset of objects or
|
|
|
2699 |
* events where internal order is significant. Permutations are different from
|
|
|
2700 |
* combinations, for which the internal order is not significant. Use this function
|
|
|
2701 |
* for lottery-style probability calculations.
|
|
|
2702 |
*
|
|
|
2703 |
* @param int $numObjs Number of different objects
|
|
|
2704 |
* @param int $numInSet Number of objects in each permutation
|
|
|
2705 |
* @return int Number of permutations
|
|
|
2706 |
*/
|
|
|
2707 |
public static function PERMUT($numObjs,$numInSet) {
|
|
|
2708 |
$numObjs = PHPExcel_Calculation_Functions::flattenSingleValue($numObjs);
|
|
|
2709 |
$numInSet = PHPExcel_Calculation_Functions::flattenSingleValue($numInSet);
|
|
|
2710 |
|
|
|
2711 |
if ((is_numeric($numObjs)) && (is_numeric($numInSet))) {
|
|
|
2712 |
$numInSet = floor($numInSet);
|
|
|
2713 |
if ($numObjs < $numInSet) {
|
|
|
2714 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2715 |
}
|
|
|
2716 |
return round(PHPExcel_Calculation_MathTrig::FACT($numObjs) / PHPExcel_Calculation_MathTrig::FACT($numObjs - $numInSet));
|
|
|
2717 |
}
|
|
|
2718 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2719 |
} // function PERMUT()
|
|
|
2720 |
|
|
|
2721 |
|
|
|
2722 |
/**
|
|
|
2723 |
* POISSON
|
|
|
2724 |
*
|
|
|
2725 |
* Returns the Poisson distribution. A common application of the Poisson distribution
|
|
|
2726 |
* is predicting the number of events over a specific time, such as the number of
|
|
|
2727 |
* cars arriving at a toll plaza in 1 minute.
|
|
|
2728 |
*
|
|
|
2729 |
* @param float $value
|
|
|
2730 |
* @param float $mean Mean Value
|
|
|
2731 |
* @param boolean $cumulative
|
|
|
2732 |
* @return float
|
|
|
2733 |
*
|
|
|
2734 |
*/
|
|
|
2735 |
public static function POISSON($value, $mean, $cumulative) {
|
|
|
2736 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
2737 |
$mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
|
|
|
2738 |
|
|
|
2739 |
if ((is_numeric($value)) && (is_numeric($mean))) {
|
|
|
2740 |
if (($value <= 0) || ($mean <= 0)) {
|
|
|
2741 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2742 |
}
|
|
|
2743 |
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
|
|
|
2744 |
if ($cumulative) {
|
|
|
2745 |
$summer = 0;
|
|
|
2746 |
for ($i = 0; $i <= floor($value); ++$i) {
|
|
|
2747 |
$summer += pow($mean,$i) / PHPExcel_Calculation_MathTrig::FACT($i);
|
|
|
2748 |
}
|
|
|
2749 |
return exp(0-$mean) * $summer;
|
|
|
2750 |
} else {
|
|
|
2751 |
return (exp(0-$mean) * pow($mean,$value)) / PHPExcel_Calculation_MathTrig::FACT($value);
|
|
|
2752 |
}
|
|
|
2753 |
}
|
|
|
2754 |
}
|
|
|
2755 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2756 |
} // function POISSON()
|
|
|
2757 |
|
|
|
2758 |
|
|
|
2759 |
/**
|
|
|
2760 |
* QUARTILE
|
|
|
2761 |
*
|
|
|
2762 |
* Returns the quartile of a data set.
|
|
|
2763 |
*
|
|
|
2764 |
* Excel Function:
|
|
|
2765 |
* QUARTILE(value1[,value2[, ...]],entry)
|
|
|
2766 |
*
|
|
|
2767 |
* @access public
|
|
|
2768 |
* @category Statistical Functions
|
|
|
2769 |
* @param mixed $arg,... Data values
|
|
|
2770 |
* @param int $entry Quartile value in the range 1..3, inclusive.
|
|
|
2771 |
* @return float
|
|
|
2772 |
*/
|
|
|
2773 |
public static function QUARTILE() {
|
|
|
2774 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
2775 |
|
|
|
2776 |
// Calculate
|
|
|
2777 |
$entry = floor(array_pop($aArgs));
|
|
|
2778 |
|
|
|
2779 |
if ((is_numeric($entry)) && (!is_string($entry))) {
|
|
|
2780 |
$entry /= 4;
|
|
|
2781 |
if (($entry < 0) || ($entry > 1)) {
|
|
|
2782 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2783 |
}
|
|
|
2784 |
return self::PERCENTILE($aArgs,$entry);
|
|
|
2785 |
}
|
|
|
2786 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2787 |
} // function QUARTILE()
|
|
|
2788 |
|
|
|
2789 |
|
|
|
2790 |
/**
|
|
|
2791 |
* RANK
|
|
|
2792 |
*
|
|
|
2793 |
* Returns the rank of a number in a list of numbers.
|
|
|
2794 |
*
|
|
|
2795 |
* @param number The number whose rank you want to find.
|
|
|
2796 |
* @param array of number An array of, or a reference to, a list of numbers.
|
|
|
2797 |
* @param mixed Order to sort the values in the value set
|
|
|
2798 |
* @return float
|
|
|
2799 |
*/
|
|
|
2800 |
public static function RANK($value,$valueSet,$order=0) {
|
|
|
2801 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
2802 |
$valueSet = PHPExcel_Calculation_Functions::flattenArray($valueSet);
|
|
|
2803 |
$order = (is_null($order)) ? 0 : (integer) PHPExcel_Calculation_Functions::flattenSingleValue($order);
|
|
|
2804 |
|
|
|
2805 |
foreach($valueSet as $key => $valueEntry) {
|
|
|
2806 |
if (!is_numeric($valueEntry)) {
|
|
|
2807 |
unset($valueSet[$key]);
|
|
|
2808 |
}
|
|
|
2809 |
}
|
|
|
2810 |
|
|
|
2811 |
if ($order == 0) {
|
|
|
2812 |
rsort($valueSet,SORT_NUMERIC);
|
|
|
2813 |
} else {
|
|
|
2814 |
sort($valueSet,SORT_NUMERIC);
|
|
|
2815 |
}
|
|
|
2816 |
$pos = array_search($value,$valueSet);
|
|
|
2817 |
if ($pos === False) {
|
|
|
2818 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
2819 |
}
|
|
|
2820 |
|
|
|
2821 |
return ++$pos;
|
|
|
2822 |
} // function RANK()
|
|
|
2823 |
|
|
|
2824 |
|
|
|
2825 |
/**
|
|
|
2826 |
* RSQ
|
|
|
2827 |
*
|
|
|
2828 |
* Returns the square of the Pearson product moment correlation coefficient through data points in known_y's and known_x's.
|
|
|
2829 |
*
|
|
|
2830 |
* @param array of mixed Data Series Y
|
|
|
2831 |
* @param array of mixed Data Series X
|
|
|
2832 |
* @return float
|
|
|
2833 |
*/
|
|
|
2834 |
public static function RSQ($yValues,$xValues) {
|
|
|
2835 |
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
|
2836 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2837 |
}
|
|
|
2838 |
$yValueCount = count($yValues);
|
|
|
2839 |
$xValueCount = count($xValues);
|
|
|
2840 |
|
|
|
2841 |
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
|
2842 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
2843 |
} elseif ($yValueCount == 1) {
|
|
|
2844 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
2845 |
}
|
|
|
2846 |
|
|
|
2847 |
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
|
2848 |
return $bestFitLinear->getGoodnessOfFit();
|
|
|
2849 |
} // function RSQ()
|
|
|
2850 |
|
|
|
2851 |
|
|
|
2852 |
/**
|
|
|
2853 |
* SKEW
|
|
|
2854 |
*
|
|
|
2855 |
* Returns the skewness of a distribution. Skewness characterizes the degree of asymmetry
|
|
|
2856 |
* of a distribution around its mean. Positive skewness indicates a distribution with an
|
|
|
2857 |
* asymmetric tail extending toward more positive values. Negative skewness indicates a
|
|
|
2858 |
* distribution with an asymmetric tail extending toward more negative values.
|
|
|
2859 |
*
|
|
|
2860 |
* @param array Data Series
|
|
|
2861 |
* @return float
|
|
|
2862 |
*/
|
|
|
2863 |
public static function SKEW() {
|
|
|
2864 |
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
2865 |
$mean = self::AVERAGE($aArgs);
|
|
|
2866 |
$stdDev = self::STDEV($aArgs);
|
|
|
2867 |
|
|
|
2868 |
$count = $summer = 0;
|
|
|
2869 |
// Loop through arguments
|
|
|
2870 |
foreach ($aArgs as $k => $arg) {
|
|
|
2871 |
if ((is_bool($arg)) &&
|
|
|
2872 |
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
|
2873 |
} else {
|
|
|
2874 |
// Is it a numeric value?
|
|
|
2875 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
2876 |
$summer += pow((($arg - $mean) / $stdDev),3) ;
|
|
|
2877 |
++$count;
|
|
|
2878 |
}
|
|
|
2879 |
}
|
|
|
2880 |
}
|
|
|
2881 |
|
|
|
2882 |
// Return
|
|
|
2883 |
if ($count > 2) {
|
|
|
2884 |
return $summer * ($count / (($count-1) * ($count-2)));
|
|
|
2885 |
}
|
|
|
2886 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
2887 |
} // function SKEW()
|
|
|
2888 |
|
|
|
2889 |
|
|
|
2890 |
/**
|
|
|
2891 |
* SLOPE
|
|
|
2892 |
*
|
|
|
2893 |
* Returns the slope of the linear regression line through data points in known_y's and known_x's.
|
|
|
2894 |
*
|
|
|
2895 |
* @param array of mixed Data Series Y
|
|
|
2896 |
* @param array of mixed Data Series X
|
|
|
2897 |
* @return float
|
|
|
2898 |
*/
|
|
|
2899 |
public static function SLOPE($yValues,$xValues) {
|
|
|
2900 |
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
|
2901 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2902 |
}
|
|
|
2903 |
$yValueCount = count($yValues);
|
|
|
2904 |
$xValueCount = count($xValues);
|
|
|
2905 |
|
|
|
2906 |
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
|
2907 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
2908 |
} elseif ($yValueCount == 1) {
|
|
|
2909 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
2910 |
}
|
|
|
2911 |
|
|
|
2912 |
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
|
2913 |
return $bestFitLinear->getSlope();
|
|
|
2914 |
} // function SLOPE()
|
|
|
2915 |
|
|
|
2916 |
|
|
|
2917 |
/**
|
|
|
2918 |
* SMALL
|
|
|
2919 |
*
|
|
|
2920 |
* Returns the nth smallest value in a data set. You can use this function to
|
|
|
2921 |
* select a value based on its relative standing.
|
|
|
2922 |
*
|
|
|
2923 |
* Excel Function:
|
|
|
2924 |
* SMALL(value1[,value2[, ...]],entry)
|
|
|
2925 |
*
|
|
|
2926 |
* @access public
|
|
|
2927 |
* @category Statistical Functions
|
|
|
2928 |
* @param mixed $arg,... Data values
|
|
|
2929 |
* @param int $entry Position (ordered from the smallest) in the array or range of data to return
|
|
|
2930 |
* @return float
|
|
|
2931 |
*/
|
|
|
2932 |
public static function SMALL() {
|
|
|
2933 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
2934 |
|
|
|
2935 |
// Calculate
|
|
|
2936 |
$entry = array_pop($aArgs);
|
|
|
2937 |
|
|
|
2938 |
if ((is_numeric($entry)) && (!is_string($entry))) {
|
|
|
2939 |
$mArgs = array();
|
|
|
2940 |
foreach ($aArgs as $arg) {
|
|
|
2941 |
// Is it a numeric value?
|
|
|
2942 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
2943 |
$mArgs[] = $arg;
|
|
|
2944 |
}
|
|
|
2945 |
}
|
|
|
2946 |
$count = self::COUNT($mArgs);
|
|
|
2947 |
$entry = floor(--$entry);
|
|
|
2948 |
if (($entry < 0) || ($entry >= $count) || ($count == 0)) {
|
|
|
2949 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2950 |
}
|
|
|
2951 |
sort($mArgs);
|
|
|
2952 |
return $mArgs[$entry];
|
|
|
2953 |
}
|
|
|
2954 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2955 |
} // function SMALL()
|
|
|
2956 |
|
|
|
2957 |
|
|
|
2958 |
/**
|
|
|
2959 |
* STANDARDIZE
|
|
|
2960 |
*
|
|
|
2961 |
* Returns a normalized value from a distribution characterized by mean and standard_dev.
|
|
|
2962 |
*
|
|
|
2963 |
* @param float $value Value to normalize
|
|
|
2964 |
* @param float $mean Mean Value
|
|
|
2965 |
* @param float $stdDev Standard Deviation
|
|
|
2966 |
* @return float Standardized value
|
|
|
2967 |
*/
|
|
|
2968 |
public static function STANDARDIZE($value,$mean,$stdDev) {
|
|
|
2969 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
2970 |
$mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
|
|
|
2971 |
$stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
|
|
|
2972 |
|
|
|
2973 |
if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
|
|
|
2974 |
if ($stdDev <= 0) {
|
|
|
2975 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
2976 |
}
|
|
|
2977 |
return ($value - $mean) / $stdDev ;
|
|
|
2978 |
}
|
|
|
2979 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
2980 |
} // function STANDARDIZE()
|
|
|
2981 |
|
|
|
2982 |
|
|
|
2983 |
/**
|
|
|
2984 |
* STDEV
|
|
|
2985 |
*
|
|
|
2986 |
* Estimates standard deviation based on a sample. The standard deviation is a measure of how
|
|
|
2987 |
* widely values are dispersed from the average value (the mean).
|
|
|
2988 |
*
|
|
|
2989 |
* Excel Function:
|
|
|
2990 |
* STDEV(value1[,value2[, ...]])
|
|
|
2991 |
*
|
|
|
2992 |
* @access public
|
|
|
2993 |
* @category Statistical Functions
|
|
|
2994 |
* @param mixed $arg,... Data values
|
|
|
2995 |
* @return float
|
|
|
2996 |
*/
|
|
|
2997 |
public static function STDEV() {
|
|
|
2998 |
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
2999 |
|
|
|
3000 |
// Return value
|
|
|
3001 |
$returnValue = null;
|
|
|
3002 |
|
|
|
3003 |
$aMean = self::AVERAGE($aArgs);
|
|
|
3004 |
if (!is_null($aMean)) {
|
|
|
3005 |
$aCount = -1;
|
|
|
3006 |
foreach ($aArgs as $k => $arg) {
|
|
|
3007 |
if ((is_bool($arg)) &&
|
|
|
3008 |
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
|
|
|
3009 |
$arg = (integer) $arg;
|
|
|
3010 |
}
|
|
|
3011 |
// Is it a numeric value?
|
|
|
3012 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
3013 |
if (is_null($returnValue)) {
|
|
|
3014 |
$returnValue = pow(($arg - $aMean),2);
|
|
|
3015 |
} else {
|
|
|
3016 |
$returnValue += pow(($arg - $aMean),2);
|
|
|
3017 |
}
|
|
|
3018 |
++$aCount;
|
|
|
3019 |
}
|
|
|
3020 |
}
|
|
|
3021 |
|
|
|
3022 |
// Return
|
|
|
3023 |
if (($aCount > 0) && ($returnValue >= 0)) {
|
|
|
3024 |
return sqrt($returnValue / $aCount);
|
|
|
3025 |
}
|
|
|
3026 |
}
|
|
|
3027 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
3028 |
} // function STDEV()
|
|
|
3029 |
|
|
|
3030 |
|
|
|
3031 |
/**
|
|
|
3032 |
* STDEVA
|
|
|
3033 |
*
|
|
|
3034 |
* Estimates standard deviation based on a sample, including numbers, text, and logical values
|
|
|
3035 |
*
|
|
|
3036 |
* Excel Function:
|
|
|
3037 |
* STDEVA(value1[,value2[, ...]])
|
|
|
3038 |
*
|
|
|
3039 |
* @access public
|
|
|
3040 |
* @category Statistical Functions
|
|
|
3041 |
* @param mixed $arg,... Data values
|
|
|
3042 |
* @return float
|
|
|
3043 |
*/
|
|
|
3044 |
public static function STDEVA() {
|
|
|
3045 |
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
3046 |
|
|
|
3047 |
// Return value
|
|
|
3048 |
$returnValue = null;
|
|
|
3049 |
|
|
|
3050 |
$aMean = self::AVERAGEA($aArgs);
|
|
|
3051 |
if (!is_null($aMean)) {
|
|
|
3052 |
$aCount = -1;
|
|
|
3053 |
foreach ($aArgs as $k => $arg) {
|
|
|
3054 |
if ((is_bool($arg)) &&
|
|
|
3055 |
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
|
3056 |
} else {
|
|
|
3057 |
// Is it a numeric value?
|
|
|
3058 |
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
|
|
|
3059 |
if (is_bool($arg)) {
|
|
|
3060 |
$arg = (integer) $arg;
|
|
|
3061 |
} elseif (is_string($arg)) {
|
|
|
3062 |
$arg = 0;
|
|
|
3063 |
}
|
|
|
3064 |
if (is_null($returnValue)) {
|
|
|
3065 |
$returnValue = pow(($arg - $aMean),2);
|
|
|
3066 |
} else {
|
|
|
3067 |
$returnValue += pow(($arg - $aMean),2);
|
|
|
3068 |
}
|
|
|
3069 |
++$aCount;
|
|
|
3070 |
}
|
|
|
3071 |
}
|
|
|
3072 |
}
|
|
|
3073 |
|
|
|
3074 |
// Return
|
|
|
3075 |
if (($aCount > 0) && ($returnValue >= 0)) {
|
|
|
3076 |
return sqrt($returnValue / $aCount);
|
|
|
3077 |
}
|
|
|
3078 |
}
|
|
|
3079 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
3080 |
} // function STDEVA()
|
|
|
3081 |
|
|
|
3082 |
|
|
|
3083 |
/**
|
|
|
3084 |
* STDEVP
|
|
|
3085 |
*
|
|
|
3086 |
* Calculates standard deviation based on the entire population
|
|
|
3087 |
*
|
|
|
3088 |
* Excel Function:
|
|
|
3089 |
* STDEVP(value1[,value2[, ...]])
|
|
|
3090 |
*
|
|
|
3091 |
* @access public
|
|
|
3092 |
* @category Statistical Functions
|
|
|
3093 |
* @param mixed $arg,... Data values
|
|
|
3094 |
* @return float
|
|
|
3095 |
*/
|
|
|
3096 |
public static function STDEVP() {
|
|
|
3097 |
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
3098 |
|
|
|
3099 |
// Return value
|
|
|
3100 |
$returnValue = null;
|
|
|
3101 |
|
|
|
3102 |
$aMean = self::AVERAGE($aArgs);
|
|
|
3103 |
if (!is_null($aMean)) {
|
|
|
3104 |
$aCount = 0;
|
|
|
3105 |
foreach ($aArgs as $k => $arg) {
|
|
|
3106 |
if ((is_bool($arg)) &&
|
|
|
3107 |
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
|
|
|
3108 |
$arg = (integer) $arg;
|
|
|
3109 |
}
|
|
|
3110 |
// Is it a numeric value?
|
|
|
3111 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
3112 |
if (is_null($returnValue)) {
|
|
|
3113 |
$returnValue = pow(($arg - $aMean),2);
|
|
|
3114 |
} else {
|
|
|
3115 |
$returnValue += pow(($arg - $aMean),2);
|
|
|
3116 |
}
|
|
|
3117 |
++$aCount;
|
|
|
3118 |
}
|
|
|
3119 |
}
|
|
|
3120 |
|
|
|
3121 |
// Return
|
|
|
3122 |
if (($aCount > 0) && ($returnValue >= 0)) {
|
|
|
3123 |
return sqrt($returnValue / $aCount);
|
|
|
3124 |
}
|
|
|
3125 |
}
|
|
|
3126 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
3127 |
} // function STDEVP()
|
|
|
3128 |
|
|
|
3129 |
|
|
|
3130 |
/**
|
|
|
3131 |
* STDEVPA
|
|
|
3132 |
*
|
|
|
3133 |
* Calculates standard deviation based on the entire population, including numbers, text, and logical values
|
|
|
3134 |
*
|
|
|
3135 |
* Excel Function:
|
|
|
3136 |
* STDEVPA(value1[,value2[, ...]])
|
|
|
3137 |
*
|
|
|
3138 |
* @access public
|
|
|
3139 |
* @category Statistical Functions
|
|
|
3140 |
* @param mixed $arg,... Data values
|
|
|
3141 |
* @return float
|
|
|
3142 |
*/
|
|
|
3143 |
public static function STDEVPA() {
|
|
|
3144 |
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
3145 |
|
|
|
3146 |
// Return value
|
|
|
3147 |
$returnValue = null;
|
|
|
3148 |
|
|
|
3149 |
$aMean = self::AVERAGEA($aArgs);
|
|
|
3150 |
if (!is_null($aMean)) {
|
|
|
3151 |
$aCount = 0;
|
|
|
3152 |
foreach ($aArgs as $k => $arg) {
|
|
|
3153 |
if ((is_bool($arg)) &&
|
|
|
3154 |
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
|
3155 |
} else {
|
|
|
3156 |
// Is it a numeric value?
|
|
|
3157 |
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
|
|
|
3158 |
if (is_bool($arg)) {
|
|
|
3159 |
$arg = (integer) $arg;
|
|
|
3160 |
} elseif (is_string($arg)) {
|
|
|
3161 |
$arg = 0;
|
|
|
3162 |
}
|
|
|
3163 |
if (is_null($returnValue)) {
|
|
|
3164 |
$returnValue = pow(($arg - $aMean),2);
|
|
|
3165 |
} else {
|
|
|
3166 |
$returnValue += pow(($arg - $aMean),2);
|
|
|
3167 |
}
|
|
|
3168 |
++$aCount;
|
|
|
3169 |
}
|
|
|
3170 |
}
|
|
|
3171 |
}
|
|
|
3172 |
|
|
|
3173 |
// Return
|
|
|
3174 |
if (($aCount > 0) && ($returnValue >= 0)) {
|
|
|
3175 |
return sqrt($returnValue / $aCount);
|
|
|
3176 |
}
|
|
|
3177 |
}
|
|
|
3178 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
3179 |
} // function STDEVPA()
|
|
|
3180 |
|
|
|
3181 |
|
|
|
3182 |
/**
|
|
|
3183 |
* STEYX
|
|
|
3184 |
*
|
|
|
3185 |
* Returns the standard error of the predicted y-value for each x in the regression.
|
|
|
3186 |
*
|
|
|
3187 |
* @param array of mixed Data Series Y
|
|
|
3188 |
* @param array of mixed Data Series X
|
|
|
3189 |
* @return float
|
|
|
3190 |
*/
|
|
|
3191 |
public static function STEYX($yValues,$xValues) {
|
|
|
3192 |
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
|
3193 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
3194 |
}
|
|
|
3195 |
$yValueCount = count($yValues);
|
|
|
3196 |
$xValueCount = count($xValues);
|
|
|
3197 |
|
|
|
3198 |
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
|
3199 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
3200 |
} elseif ($yValueCount == 1) {
|
|
|
3201 |
return PHPExcel_Calculation_Functions::DIV0();
|
|
|
3202 |
}
|
|
|
3203 |
|
|
|
3204 |
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
|
3205 |
return $bestFitLinear->getStdevOfResiduals();
|
|
|
3206 |
} // function STEYX()
|
|
|
3207 |
|
|
|
3208 |
|
|
|
3209 |
/**
|
|
|
3210 |
* TDIST
|
|
|
3211 |
*
|
|
|
3212 |
* Returns the probability of Student's T distribution.
|
|
|
3213 |
*
|
|
|
3214 |
* @param float $value Value for the function
|
|
|
3215 |
* @param float $degrees degrees of freedom
|
|
|
3216 |
* @param float $tails number of tails (1 or 2)
|
|
|
3217 |
* @return float
|
|
|
3218 |
*/
|
|
|
3219 |
public static function TDIST($value, $degrees, $tails) {
|
|
|
3220 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
3221 |
$degrees = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));
|
|
|
3222 |
$tails = floor(PHPExcel_Calculation_Functions::flattenSingleValue($tails));
|
|
|
3223 |
|
|
|
3224 |
if ((is_numeric($value)) && (is_numeric($degrees)) && (is_numeric($tails))) {
|
|
|
3225 |
if (($value < 0) || ($degrees < 1) || ($tails < 1) || ($tails > 2)) {
|
|
|
3226 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
3227 |
}
|
|
|
3228 |
// tdist, which finds the probability that corresponds to a given value
|
|
|
3229 |
// of t with k degrees of freedom. This algorithm is translated from a
|
|
|
3230 |
// pascal function on p81 of "Statistical Computing in Pascal" by D
|
|
|
3231 |
// Cooke, A H Craven & G M Clark (1985: Edward Arnold (Pubs.) Ltd:
|
|
|
3232 |
// London). The above Pascal algorithm is itself a translation of the
|
|
|
3233 |
// fortran algoritm "AS 3" by B E Cooper of the Atlas Computer
|
|
|
3234 |
// Laboratory as reported in (among other places) "Applied Statistics
|
|
|
3235 |
// Algorithms", editied by P Griffiths and I D Hill (1985; Ellis
|
|
|
3236 |
// Horwood Ltd.; W. Sussex, England).
|
|
|
3237 |
$tterm = $degrees;
|
|
|
3238 |
$ttheta = atan2($value,sqrt($tterm));
|
|
|
3239 |
$tc = cos($ttheta);
|
|
|
3240 |
$ts = sin($ttheta);
|
|
|
3241 |
$tsum = 0;
|
|
|
3242 |
|
|
|
3243 |
if (($degrees % 2) == 1) {
|
|
|
3244 |
$ti = 3;
|
|
|
3245 |
$tterm = $tc;
|
|
|
3246 |
} else {
|
|
|
3247 |
$ti = 2;
|
|
|
3248 |
$tterm = 1;
|
|
|
3249 |
}
|
|
|
3250 |
|
|
|
3251 |
$tsum = $tterm;
|
|
|
3252 |
while ($ti < $degrees) {
|
|
|
3253 |
$tterm *= $tc * $tc * ($ti - 1) / $ti;
|
|
|
3254 |
$tsum += $tterm;
|
|
|
3255 |
$ti += 2;
|
|
|
3256 |
}
|
|
|
3257 |
$tsum *= $ts;
|
|
|
3258 |
if (($degrees % 2) == 1) { $tsum = M_2DIVPI * ($tsum + $ttheta); }
|
|
|
3259 |
$tValue = 0.5 * (1 + $tsum);
|
|
|
3260 |
if ($tails == 1) {
|
|
|
3261 |
return 1 - abs($tValue);
|
|
|
3262 |
} else {
|
|
|
3263 |
return 1 - abs((1 - $tValue) - $tValue);
|
|
|
3264 |
}
|
|
|
3265 |
}
|
|
|
3266 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
3267 |
} // function TDIST()
|
|
|
3268 |
|
|
|
3269 |
|
|
|
3270 |
/**
|
|
|
3271 |
* TINV
|
|
|
3272 |
*
|
|
|
3273 |
* Returns the one-tailed probability of the chi-squared distribution.
|
|
|
3274 |
*
|
|
|
3275 |
* @param float $probability Probability for the function
|
|
|
3276 |
* @param float $degrees degrees of freedom
|
|
|
3277 |
* @return float
|
|
|
3278 |
*/
|
|
|
3279 |
public static function TINV($probability, $degrees) {
|
|
|
3280 |
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
|
3281 |
$degrees = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));
|
|
|
3282 |
|
|
|
3283 |
if ((is_numeric($probability)) && (is_numeric($degrees))) {
|
|
|
3284 |
$xLo = 100;
|
|
|
3285 |
$xHi = 0;
|
|
|
3286 |
|
|
|
3287 |
$x = $xNew = 1;
|
|
|
3288 |
$dx = 1;
|
|
|
3289 |
$i = 0;
|
|
|
3290 |
|
|
|
3291 |
while ((abs($dx) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
|
|
|
3292 |
// Apply Newton-Raphson step
|
|
|
3293 |
$result = self::TDIST($x, $degrees, 2);
|
|
|
3294 |
$error = $result - $probability;
|
|
|
3295 |
if ($error == 0.0) {
|
|
|
3296 |
$dx = 0;
|
|
|
3297 |
} elseif ($error < 0.0) {
|
|
|
3298 |
$xLo = $x;
|
|
|
3299 |
} else {
|
|
|
3300 |
$xHi = $x;
|
|
|
3301 |
}
|
|
|
3302 |
// Avoid division by zero
|
|
|
3303 |
if ($result != 0.0) {
|
|
|
3304 |
$dx = $error / $result;
|
|
|
3305 |
$xNew = $x - $dx;
|
|
|
3306 |
}
|
|
|
3307 |
// If the NR fails to converge (which for example may be the
|
|
|
3308 |
// case if the initial guess is too rough) we apply a bisection
|
|
|
3309 |
// step to determine a more narrow interval around the root.
|
|
|
3310 |
if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0)) {
|
|
|
3311 |
$xNew = ($xLo + $xHi) / 2;
|
|
|
3312 |
$dx = $xNew - $x;
|
|
|
3313 |
}
|
|
|
3314 |
$x = $xNew;
|
|
|
3315 |
}
|
|
|
3316 |
if ($i == MAX_ITERATIONS) {
|
|
|
3317 |
return PHPExcel_Calculation_Functions::NA();
|
|
|
3318 |
}
|
|
|
3319 |
return round($x,12);
|
|
|
3320 |
}
|
|
|
3321 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
3322 |
} // function TINV()
|
|
|
3323 |
|
|
|
3324 |
|
|
|
3325 |
/**
|
|
|
3326 |
* TREND
|
|
|
3327 |
*
|
|
|
3328 |
* Returns values along a linear trend
|
|
|
3329 |
*
|
|
|
3330 |
* @param array of mixed Data Series Y
|
|
|
3331 |
* @param array of mixed Data Series X
|
|
|
3332 |
* @param array of mixed Values of X for which we want to find Y
|
|
|
3333 |
* @param boolean A logical value specifying whether to force the intersect to equal 0.
|
|
|
3334 |
* @return array of float
|
|
|
3335 |
*/
|
|
|
3336 |
public static function TREND($yValues,$xValues=array(),$newValues=array(),$const=True) {
|
|
|
3337 |
$yValues = PHPExcel_Calculation_Functions::flattenArray($yValues);
|
|
|
3338 |
$xValues = PHPExcel_Calculation_Functions::flattenArray($xValues);
|
|
|
3339 |
$newValues = PHPExcel_Calculation_Functions::flattenArray($newValues);
|
|
|
3340 |
$const = (is_null($const)) ? True : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
|
|
|
3341 |
|
|
|
3342 |
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues,$const);
|
|
|
3343 |
if (empty($newValues)) {
|
|
|
3344 |
$newValues = $bestFitLinear->getXValues();
|
|
|
3345 |
}
|
|
|
3346 |
|
|
|
3347 |
$returnArray = array();
|
|
|
3348 |
foreach($newValues as $xValue) {
|
|
|
3349 |
$returnArray[0][] = $bestFitLinear->getValueOfYForX($xValue);
|
|
|
3350 |
}
|
|
|
3351 |
|
|
|
3352 |
return $returnArray;
|
|
|
3353 |
} // function TREND()
|
|
|
3354 |
|
|
|
3355 |
|
|
|
3356 |
/**
|
|
|
3357 |
* TRIMMEAN
|
|
|
3358 |
*
|
|
|
3359 |
* Returns the mean of the interior of a data set. TRIMMEAN calculates the mean
|
|
|
3360 |
* taken by excluding a percentage of data points from the top and bottom tails
|
|
|
3361 |
* of a data set.
|
|
|
3362 |
*
|
|
|
3363 |
* Excel Function:
|
|
|
3364 |
* TRIMEAN(value1[,value2[, ...]],$discard)
|
|
|
3365 |
*
|
|
|
3366 |
* @access public
|
|
|
3367 |
* @category Statistical Functions
|
|
|
3368 |
* @param mixed $arg,... Data values
|
|
|
3369 |
* @param float $discard Percentage to discard
|
|
|
3370 |
* @return float
|
|
|
3371 |
*/
|
|
|
3372 |
public static function TRIMMEAN() {
|
|
|
3373 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
3374 |
|
|
|
3375 |
// Calculate
|
|
|
3376 |
$percent = array_pop($aArgs);
|
|
|
3377 |
|
|
|
3378 |
if ((is_numeric($percent)) && (!is_string($percent))) {
|
|
|
3379 |
if (($percent < 0) || ($percent > 1)) {
|
|
|
3380 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
3381 |
}
|
|
|
3382 |
$mArgs = array();
|
|
|
3383 |
foreach ($aArgs as $arg) {
|
|
|
3384 |
// Is it a numeric value?
|
|
|
3385 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
3386 |
$mArgs[] = $arg;
|
|
|
3387 |
}
|
|
|
3388 |
}
|
|
|
3389 |
$discard = floor(self::COUNT($mArgs) * $percent / 2);
|
|
|
3390 |
sort($mArgs);
|
|
|
3391 |
for ($i=0; $i < $discard; ++$i) {
|
|
|
3392 |
array_pop($mArgs);
|
|
|
3393 |
array_shift($mArgs);
|
|
|
3394 |
}
|
|
|
3395 |
return self::AVERAGE($mArgs);
|
|
|
3396 |
}
|
|
|
3397 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
3398 |
} // function TRIMMEAN()
|
|
|
3399 |
|
|
|
3400 |
|
|
|
3401 |
/**
|
|
|
3402 |
* VARFunc
|
|
|
3403 |
*
|
|
|
3404 |
* Estimates variance based on a sample.
|
|
|
3405 |
*
|
|
|
3406 |
* Excel Function:
|
|
|
3407 |
* VAR(value1[,value2[, ...]])
|
|
|
3408 |
*
|
|
|
3409 |
* @access public
|
|
|
3410 |
* @category Statistical Functions
|
|
|
3411 |
* @param mixed $arg,... Data values
|
|
|
3412 |
* @return float
|
|
|
3413 |
*/
|
|
|
3414 |
public static function VARFunc() {
|
|
|
3415 |
// Return value
|
|
|
3416 |
$returnValue = PHPExcel_Calculation_Functions::DIV0();
|
|
|
3417 |
|
|
|
3418 |
$summerA = $summerB = 0;
|
|
|
3419 |
|
|
|
3420 |
// Loop through arguments
|
|
|
3421 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
3422 |
$aCount = 0;
|
|
|
3423 |
foreach ($aArgs as $arg) {
|
|
|
3424 |
if (is_bool($arg)) { $arg = (integer) $arg; }
|
|
|
3425 |
// Is it a numeric value?
|
|
|
3426 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
3427 |
$summerA += ($arg * $arg);
|
|
|
3428 |
$summerB += $arg;
|
|
|
3429 |
++$aCount;
|
|
|
3430 |
}
|
|
|
3431 |
}
|
|
|
3432 |
|
|
|
3433 |
// Return
|
|
|
3434 |
if ($aCount > 1) {
|
|
|
3435 |
$summerA *= $aCount;
|
|
|
3436 |
$summerB *= $summerB;
|
|
|
3437 |
$returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
|
|
|
3438 |
}
|
|
|
3439 |
return $returnValue;
|
|
|
3440 |
} // function VARFunc()
|
|
|
3441 |
|
|
|
3442 |
|
|
|
3443 |
/**
|
|
|
3444 |
* VARA
|
|
|
3445 |
*
|
|
|
3446 |
* Estimates variance based on a sample, including numbers, text, and logical values
|
|
|
3447 |
*
|
|
|
3448 |
* Excel Function:
|
|
|
3449 |
* VARA(value1[,value2[, ...]])
|
|
|
3450 |
*
|
|
|
3451 |
* @access public
|
|
|
3452 |
* @category Statistical Functions
|
|
|
3453 |
* @param mixed $arg,... Data values
|
|
|
3454 |
* @return float
|
|
|
3455 |
*/
|
|
|
3456 |
public static function VARA() {
|
|
|
3457 |
// Return value
|
|
|
3458 |
$returnValue = PHPExcel_Calculation_Functions::DIV0();
|
|
|
3459 |
|
|
|
3460 |
$summerA = $summerB = 0;
|
|
|
3461 |
|
|
|
3462 |
// Loop through arguments
|
|
|
3463 |
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
3464 |
$aCount = 0;
|
|
|
3465 |
foreach ($aArgs as $k => $arg) {
|
|
|
3466 |
if ((is_string($arg)) &&
|
|
|
3467 |
(PHPExcel_Calculation_Functions::isValue($k))) {
|
|
|
3468 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
3469 |
} elseif ((is_string($arg)) &&
|
|
|
3470 |
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
|
3471 |
} else {
|
|
|
3472 |
// Is it a numeric value?
|
|
|
3473 |
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
|
|
|
3474 |
if (is_bool($arg)) {
|
|
|
3475 |
$arg = (integer) $arg;
|
|
|
3476 |
} elseif (is_string($arg)) {
|
|
|
3477 |
$arg = 0;
|
|
|
3478 |
}
|
|
|
3479 |
$summerA += ($arg * $arg);
|
|
|
3480 |
$summerB += $arg;
|
|
|
3481 |
++$aCount;
|
|
|
3482 |
}
|
|
|
3483 |
}
|
|
|
3484 |
}
|
|
|
3485 |
|
|
|
3486 |
// Return
|
|
|
3487 |
if ($aCount > 1) {
|
|
|
3488 |
$summerA *= $aCount;
|
|
|
3489 |
$summerB *= $summerB;
|
|
|
3490 |
$returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
|
|
|
3491 |
}
|
|
|
3492 |
return $returnValue;
|
|
|
3493 |
} // function VARA()
|
|
|
3494 |
|
|
|
3495 |
|
|
|
3496 |
/**
|
|
|
3497 |
* VARP
|
|
|
3498 |
*
|
|
|
3499 |
* Calculates variance based on the entire population
|
|
|
3500 |
*
|
|
|
3501 |
* Excel Function:
|
|
|
3502 |
* VARP(value1[,value2[, ...]])
|
|
|
3503 |
*
|
|
|
3504 |
* @access public
|
|
|
3505 |
* @category Statistical Functions
|
|
|
3506 |
* @param mixed $arg,... Data values
|
|
|
3507 |
* @return float
|
|
|
3508 |
*/
|
|
|
3509 |
public static function VARP() {
|
|
|
3510 |
// Return value
|
|
|
3511 |
$returnValue = PHPExcel_Calculation_Functions::DIV0();
|
|
|
3512 |
|
|
|
3513 |
$summerA = $summerB = 0;
|
|
|
3514 |
|
|
|
3515 |
// Loop through arguments
|
|
|
3516 |
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
3517 |
$aCount = 0;
|
|
|
3518 |
foreach ($aArgs as $arg) {
|
|
|
3519 |
if (is_bool($arg)) { $arg = (integer) $arg; }
|
|
|
3520 |
// Is it a numeric value?
|
|
|
3521 |
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
|
3522 |
$summerA += ($arg * $arg);
|
|
|
3523 |
$summerB += $arg;
|
|
|
3524 |
++$aCount;
|
|
|
3525 |
}
|
|
|
3526 |
}
|
|
|
3527 |
|
|
|
3528 |
// Return
|
|
|
3529 |
if ($aCount > 0) {
|
|
|
3530 |
$summerA *= $aCount;
|
|
|
3531 |
$summerB *= $summerB;
|
|
|
3532 |
$returnValue = ($summerA - $summerB) / ($aCount * $aCount);
|
|
|
3533 |
}
|
|
|
3534 |
return $returnValue;
|
|
|
3535 |
} // function VARP()
|
|
|
3536 |
|
|
|
3537 |
|
|
|
3538 |
/**
|
|
|
3539 |
* VARPA
|
|
|
3540 |
*
|
|
|
3541 |
* Calculates variance based on the entire population, including numbers, text, and logical values
|
|
|
3542 |
*
|
|
|
3543 |
* Excel Function:
|
|
|
3544 |
* VARPA(value1[,value2[, ...]])
|
|
|
3545 |
*
|
|
|
3546 |
* @access public
|
|
|
3547 |
* @category Statistical Functions
|
|
|
3548 |
* @param mixed $arg,... Data values
|
|
|
3549 |
* @return float
|
|
|
3550 |
*/
|
|
|
3551 |
public static function VARPA() {
|
|
|
3552 |
// Return value
|
|
|
3553 |
$returnValue = PHPExcel_Calculation_Functions::DIV0();
|
|
|
3554 |
|
|
|
3555 |
$summerA = $summerB = 0;
|
|
|
3556 |
|
|
|
3557 |
// Loop through arguments
|
|
|
3558 |
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
3559 |
$aCount = 0;
|
|
|
3560 |
foreach ($aArgs as $k => $arg) {
|
|
|
3561 |
if ((is_string($arg)) &&
|
|
|
3562 |
(PHPExcel_Calculation_Functions::isValue($k))) {
|
|
|
3563 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
3564 |
} elseif ((is_string($arg)) &&
|
|
|
3565 |
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
|
3566 |
} else {
|
|
|
3567 |
// Is it a numeric value?
|
|
|
3568 |
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
|
|
|
3569 |
if (is_bool($arg)) {
|
|
|
3570 |
$arg = (integer) $arg;
|
|
|
3571 |
} elseif (is_string($arg)) {
|
|
|
3572 |
$arg = 0;
|
|
|
3573 |
}
|
|
|
3574 |
$summerA += ($arg * $arg);
|
|
|
3575 |
$summerB += $arg;
|
|
|
3576 |
++$aCount;
|
|
|
3577 |
}
|
|
|
3578 |
}
|
|
|
3579 |
}
|
|
|
3580 |
|
|
|
3581 |
// Return
|
|
|
3582 |
if ($aCount > 0) {
|
|
|
3583 |
$summerA *= $aCount;
|
|
|
3584 |
$summerB *= $summerB;
|
|
|
3585 |
$returnValue = ($summerA - $summerB) / ($aCount * $aCount);
|
|
|
3586 |
}
|
|
|
3587 |
return $returnValue;
|
|
|
3588 |
} // function VARPA()
|
|
|
3589 |
|
|
|
3590 |
|
|
|
3591 |
/**
|
|
|
3592 |
* WEIBULL
|
|
|
3593 |
*
|
|
|
3594 |
* Returns the Weibull distribution. Use this distribution in reliability
|
|
|
3595 |
* analysis, such as calculating a device's mean time to failure.
|
|
|
3596 |
*
|
|
|
3597 |
* @param float $value
|
|
|
3598 |
* @param float $alpha Alpha Parameter
|
|
|
3599 |
* @param float $beta Beta Parameter
|
|
|
3600 |
* @param boolean $cumulative
|
|
|
3601 |
* @return float
|
|
|
3602 |
*
|
|
|
3603 |
*/
|
|
|
3604 |
public static function WEIBULL($value, $alpha, $beta, $cumulative) {
|
|
|
3605 |
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
3606 |
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
|
|
|
3607 |
$beta = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
|
|
|
3608 |
|
|
|
3609 |
if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta))) {
|
|
|
3610 |
if (($value < 0) || ($alpha <= 0) || ($beta <= 0)) {
|
|
|
3611 |
return PHPExcel_Calculation_Functions::NaN();
|
|
|
3612 |
}
|
|
|
3613 |
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
|
|
|
3614 |
if ($cumulative) {
|
|
|
3615 |
return 1 - exp(0 - pow($value / $beta,$alpha));
|
|
|
3616 |
} else {
|
|
|
3617 |
return ($alpha / pow($beta,$alpha)) * pow($value,$alpha - 1) * exp(0 - pow($value / $beta,$alpha));
|
|
|
3618 |
}
|
|
|
3619 |
}
|
|
|
3620 |
}
|
|
|
3621 |
return PHPExcel_Calculation_Functions::VALUE();
|
|
|
3622 |
} // function WEIBULL()
|
|
|
3623 |
|
|
|
3624 |
|
|
|
3625 |
/**
|
|
|
3626 |
* ZTEST
|
|
|
3627 |
*
|
|
|
3628 |
* Returns the Weibull distribution. Use this distribution in reliability
|
|
|
3629 |
* analysis, such as calculating a device's mean time to failure.
|
|
|
3630 |
*
|
|
|
3631 |
* @param float $dataSet
|
|
|
3632 |
* @param float $m0 Alpha Parameter
|
|
|
3633 |
* @param float $sigma Beta Parameter
|
|
|
3634 |
* @param boolean $cumulative
|
|
|
3635 |
* @return float
|
|
|
3636 |
*
|
|
|
3637 |
*/
|
|
|
3638 |
public static function ZTEST($dataSet, $m0, $sigma = NULL) {
|
|
|
3639 |
$dataSet = PHPExcel_Calculation_Functions::flattenArrayIndexed($dataSet);
|
|
|
3640 |
$m0 = PHPExcel_Calculation_Functions::flattenSingleValue($m0);
|
|
|
3641 |
$sigma = PHPExcel_Calculation_Functions::flattenSingleValue($sigma);
|
|
|
3642 |
|
|
|
3643 |
if (is_null($sigma)) {
|
|
|
3644 |
$sigma = self::STDEV($dataSet);
|
|
|
3645 |
}
|
|
|
3646 |
$n = count($dataSet);
|
|
|
3647 |
|
|
|
3648 |
return 1 - self::NORMSDIST((self::AVERAGE($dataSet) - $m0)/($sigma/SQRT($n)));
|
|
|
3649 |
} // function ZTEST()
|
|
|
3650 |
|
|
|
3651 |
} // class PHPExcel_Calculation_Statistical
|