3652 lines
107 KiB
PHP
3652 lines
107 KiB
PHP
<?php
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/**
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* PHPExcel
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*
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* Copyright (c) 2006 - 2014 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 - 2014 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 - 2014 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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// Rough estimate of the fourth root of logGamma_xBig
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static $lg_frtbig = 2.25e76;
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static $pnt68 = 0.6796875;
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if ($x == self::$_logGammaCache_x) {
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return self::$_logGammaCache_result;
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}
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$y = $x;
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if ($y > 0.0 && $y <= LOG_GAMMA_X_MAX_VALUE) {
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if ($y <= EPS) {
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$res = -log(y);
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} elseif ($y <= 1.5) {
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// ---------------------
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// EPS .LT. X .LE. 1.5
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// ---------------------
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if ($y < $pnt68) {
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$corr = -log($y);
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$xm1 = $y;
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} else {
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$corr = 0.0;
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$xm1 = $y - 1.0;
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}
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if ($y <= 0.5 || $y >= $pnt68) {
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$xden = 1.0;
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$xnum = 0.0;
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for ($i = 0; $i < 8; ++$i) {
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$xnum = $xnum * $xm1 + $lg_p1[$i];
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$xden = $xden * $xm1 + $lg_q1[$i];
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}
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$res = $corr + $xm1 * ($lg_d1 + $xm1 * ($xnum / $xden));
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} else {
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$xm2 = $y - 1.0;
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$xden = 1.0;
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$xnum = 0.0;
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for ($i = 0; $i < 8; ++$i) {
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$xnum = $xnum * $xm2 + $lg_p2[$i];
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$xden = $xden * $xm2 + $lg_q2[$i];
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}
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$res = $corr + $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
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}
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} elseif ($y <= 4.0) {
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// ---------------------
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// 1.5 .LT. X .LE. 4.0
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// ---------------------
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$xm2 = $y - 2.0;
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$xden = 1.0;
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$xnum = 0.0;
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for ($i = 0; $i < 8; ++$i) {
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$xnum = $xnum * $xm2 + $lg_p2[$i];
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$xden = $xden * $xm2 + $lg_q2[$i];
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}
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$res = $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
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} elseif ($y <= 12.0) {
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// ----------------------
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// 4.0 .LT. X .LE. 12.0
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// ----------------------
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$xm4 = $y - 4.0;
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$xden = -1.0;
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$xnum = 0.0;
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for ($i = 0; $i < 8; ++$i) {
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$xnum = $xnum * $xm4 + $lg_p4[$i];
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$xden = $xden * $xm4 + $lg_q4[$i];
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}
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$res = $lg_d4 + $xm4 * ($xnum / $xden);
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} else {
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// ---------------------------------
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// Evaluate for argument .GE. 12.0
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// ---------------------------------
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$res = 0.0;
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if ($y <= $lg_frtbig) {
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$res = $lg_c[6];
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$ysq = $y * $y;
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for ($i = 0; $i < 6; ++$i)
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$res = $res / $ysq + $lg_c[$i];
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}
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$res /= $y;
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$corr = log($y);
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$res = $res + log(SQRT2PI) - 0.5 * $corr;
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$res += $y * ($corr - 1.0);
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}
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} else {
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// --------------------------
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// Return for bad arguments
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// --------------------------
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$res = MAX_VALUE;
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}
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// ------------------------------
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// Final adjustments and return
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// ------------------------------
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self::$_logGammaCache_x = $x;
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self::$_logGammaCache_result = $res;
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return $res;
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} // function _logGamma()
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//
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// Private implementation of the incomplete Gamma function
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//
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private static function _incompleteGamma($a,$x) {
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static $max = 32;
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$summer = 0;
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for ($n=0; $n<=$max; ++$n) {
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$divisor = $a;
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for ($i=1; $i<=$n; ++$i) {
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$divisor *= ($a + $i);
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}
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$summer += (pow($x,$n) / $divisor);
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}
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return pow($x,$a) * exp(0-$x) * $summer;
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} // function _incompleteGamma()
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|
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//
|
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// Private implementation of the Gamma function
|
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//
|
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private static function _gamma($data) {
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if ($data == 0.0) return 0;
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|
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static $p0 = 1.000000000190015;
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static $p = array ( 1 => 76.18009172947146,
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2 => -86.50532032941677,
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3 => 24.01409824083091,
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4 => -1.231739572450155,
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5 => 1.208650973866179e-3,
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6 => -5.395239384953e-6
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);
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$y = $x = $data;
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$tmp = $x + 5.5;
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$tmp -= ($x + 0.5) * log($tmp);
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$summer = $p0;
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for ($j=1;$j<=6;++$j) {
|
|
$summer += ($p[$j] / ++$y);
|
|
}
|
|
return exp(0 - $tmp + log(SQRT2PI * $summer / $x));
|
|
} // function _gamma()
|
|
|
|
|
|
/***************************************************************************
|
|
* inverse_ncdf.php
|
|
* -------------------
|
|
* begin : Friday, January 16, 2004
|
|
* copyright : (C) 2004 Michael Nickerson
|
|
* email : nickersonm@yahoo.com
|
|
*
|
|
***************************************************************************/
|
|
private static function _inverse_ncdf($p) {
|
|
// Inverse ncdf approximation by Peter J. Acklam, implementation adapted to
|
|
// PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
|
|
// a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
|
|
// I have not checked the accuracy of this implementation. Be aware that PHP
|
|
// will truncate the coeficcients to 14 digits.
|
|
|
|
// You have permission to use and distribute this function freely for
|
|
// whatever purpose you want, but please show common courtesy and give credit
|
|
// where credit is due.
|
|
|
|
// Input paramater is $p - probability - where 0 < p < 1.
|
|
|
|
// Coefficients in rational approximations
|
|
static $a = array( 1 => -3.969683028665376e+01,
|
|
2 => 2.209460984245205e+02,
|
|
3 => -2.759285104469687e+02,
|
|
4 => 1.383577518672690e+02,
|
|
5 => -3.066479806614716e+01,
|
|
6 => 2.506628277459239e+00
|
|
);
|
|
|
|
static $b = array( 1 => -5.447609879822406e+01,
|
|
2 => 1.615858368580409e+02,
|
|
3 => -1.556989798598866e+02,
|
|
4 => 6.680131188771972e+01,
|
|
5 => -1.328068155288572e+01
|
|
);
|
|
|
|
static $c = array( 1 => -7.784894002430293e-03,
|
|
2 => -3.223964580411365e-01,
|
|
3 => -2.400758277161838e+00,
|
|
4 => -2.549732539343734e+00,
|
|
5 => 4.374664141464968e+00,
|
|
6 => 2.938163982698783e+00
|
|
);
|
|
|
|
static $d = array( 1 => 7.784695709041462e-03,
|
|
2 => 3.224671290700398e-01,
|
|
3 => 2.445134137142996e+00,
|
|
4 => 3.754408661907416e+00
|
|
);
|
|
|
|
// Define lower and upper region break-points.
|
|
$p_low = 0.02425; //Use lower region approx. below this
|
|
$p_high = 1 - $p_low; //Use upper region approx. above this
|
|
|
|
if (0 < $p && $p < $p_low) {
|
|
// Rational approximation for lower region.
|
|
$q = sqrt(-2 * log($p));
|
|
return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
|
|
(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
|
|
} elseif ($p_low <= $p && $p <= $p_high) {
|
|
// Rational approximation for central region.
|
|
$q = $p - 0.5;
|
|
$r = $q * $q;
|
|
return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q /
|
|
((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1);
|
|
} elseif ($p_high < $p && $p < 1) {
|
|
// Rational approximation for upper region.
|
|
$q = sqrt(-2 * log(1 - $p));
|
|
return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
|
|
(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
|
|
}
|
|
// If 0 < p < 1, return a null value
|
|
return PHPExcel_Calculation_Functions::NULL();
|
|
} // function _inverse_ncdf()
|
|
|
|
|
|
private static function _inverse_ncdf2($prob) {
|
|
// Approximation of inverse standard normal CDF developed by
|
|
// B. Moro, "The Full Monte," Risk 8(2), Feb 1995, 57-58.
|
|
|
|
$a1 = 2.50662823884;
|
|
$a2 = -18.61500062529;
|
|
$a3 = 41.39119773534;
|
|
$a4 = -25.44106049637;
|
|
|
|
$b1 = -8.4735109309;
|
|
$b2 = 23.08336743743;
|
|
$b3 = -21.06224101826;
|
|
$b4 = 3.13082909833;
|
|
|
|
$c1 = 0.337475482272615;
|
|
$c2 = 0.976169019091719;
|
|
$c3 = 0.160797971491821;
|
|
$c4 = 2.76438810333863E-02;
|
|
$c5 = 3.8405729373609E-03;
|
|
$c6 = 3.951896511919E-04;
|
|
$c7 = 3.21767881768E-05;
|
|
$c8 = 2.888167364E-07;
|
|
$c9 = 3.960315187E-07;
|
|
|
|
$y = $prob - 0.5;
|
|
if (abs($y) < 0.42) {
|
|
$z = ($y * $y);
|
|
$z = $y * ((($a4 * $z + $a3) * $z + $a2) * $z + $a1) / (((($b4 * $z + $b3) * $z + $b2) * $z + $b1) * $z + 1);
|
|
} else {
|
|
if ($y > 0) {
|
|
$z = log(-log(1 - $prob));
|
|
} else {
|
|
$z = log(-log($prob));
|
|
}
|
|
$z = $c1 + $z * ($c2 + $z * ($c3 + $z * ($c4 + $z * ($c5 + $z * ($c6 + $z * ($c7 + $z * ($c8 + $z * $c9)))))));
|
|
if ($y < 0) {
|
|
$z = -$z;
|
|
}
|
|
}
|
|
return $z;
|
|
} // function _inverse_ncdf2()
|
|
|
|
|
|
private static function _inverse_ncdf3($p) {
|
|
// ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3.
|
|
// Produces the normal deviate Z corresponding to a given lower
|
|
// tail area of P; Z is accurate to about 1 part in 10**16.
|
|
//
|
|
// This is a PHP version of the original FORTRAN code that can
|
|
// be found at http://lib.stat.cmu.edu/apstat/
|
|
$split1 = 0.425;
|
|
$split2 = 5;
|
|
$const1 = 0.180625;
|
|
$const2 = 1.6;
|
|
|
|
// coefficients for p close to 0.5
|
|
$a0 = 3.3871328727963666080;
|
|
$a1 = 1.3314166789178437745E+2;
|
|
$a2 = 1.9715909503065514427E+3;
|
|
$a3 = 1.3731693765509461125E+4;
|
|
$a4 = 4.5921953931549871457E+4;
|
|
$a5 = 6.7265770927008700853E+4;
|
|
$a6 = 3.3430575583588128105E+4;
|
|
$a7 = 2.5090809287301226727E+3;
|
|
|
|
$b1 = 4.2313330701600911252E+1;
|
|
$b2 = 6.8718700749205790830E+2;
|
|
$b3 = 5.3941960214247511077E+3;
|
|
$b4 = 2.1213794301586595867E+4;
|
|
$b5 = 3.9307895800092710610E+4;
|
|
$b6 = 2.8729085735721942674E+4;
|
|
$b7 = 5.2264952788528545610E+3;
|
|
|
|
// coefficients for p not close to 0, 0.5 or 1.
|
|
$c0 = 1.42343711074968357734;
|
|
$c1 = 4.63033784615654529590;
|
|
$c2 = 5.76949722146069140550;
|
|
$c3 = 3.64784832476320460504;
|
|
$c4 = 1.27045825245236838258;
|
|
$c5 = 2.41780725177450611770E-1;
|
|
$c6 = 2.27238449892691845833E-2;
|
|
$c7 = 7.74545014278341407640E-4;
|
|
|
|
$d1 = 2.05319162663775882187;
|
|
$d2 = 1.67638483018380384940;
|
|
$d3 = 6.89767334985100004550E-1;
|
|
$d4 = 1.48103976427480074590E-1;
|
|
$d5 = 1.51986665636164571966E-2;
|
|
$d6 = 5.47593808499534494600E-4;
|
|
$d7 = 1.05075007164441684324E-9;
|
|
|
|
// coefficients for p near 0 or 1.
|
|
$e0 = 6.65790464350110377720;
|
|
$e1 = 5.46378491116411436990;
|
|
$e2 = 1.78482653991729133580;
|
|
$e3 = 2.96560571828504891230E-1;
|
|
$e4 = 2.65321895265761230930E-2;
|
|
$e5 = 1.24266094738807843860E-3;
|
|
$e6 = 2.71155556874348757815E-5;
|
|
$e7 = 2.01033439929228813265E-7;
|
|
|
|
$f1 = 5.99832206555887937690E-1;
|
|
$f2 = 1.36929880922735805310E-1;
|
|
$f3 = 1.48753612908506148525E-2;
|
|
$f4 = 7.86869131145613259100E-4;
|
|
$f5 = 1.84631831751005468180E-5;
|
|
$f6 = 1.42151175831644588870E-7;
|
|
$f7 = 2.04426310338993978564E-15;
|
|
|
|
$q = $p - 0.5;
|
|
|
|
// computation for p close to 0.5
|
|
if (abs($q) <= split1) {
|
|
$R = $const1 - $q * $q;
|
|
$z = $q * ((((((($a7 * $R + $a6) * $R + $a5) * $R + $a4) * $R + $a3) * $R + $a2) * $R + $a1) * $R + $a0) /
|
|
((((((($b7 * $R + $b6) * $R + $b5) * $R + $b4) * $R + $b3) * $R + $b2) * $R + $b1) * $R + 1);
|
|
} else {
|
|
if ($q < 0) {
|
|
$R = $p;
|
|
} else {
|
|
$R = 1 - $p;
|
|
}
|
|
$R = pow(-log($R),2);
|
|
|
|
// computation for p not close to 0, 0.5 or 1.
|
|
If ($R <= $split2) {
|
|
$R = $R - $const2;
|
|
$z = ((((((($c7 * $R + $c6) * $R + $c5) * $R + $c4) * $R + $c3) * $R + $c2) * $R + $c1) * $R + $c0) /
|
|
((((((($d7 * $R + $d6) * $R + $d5) * $R + $d4) * $R + $d3) * $R + $d2) * $R + $d1) * $R + 1);
|
|
} else {
|
|
// computation for p near 0 or 1.
|
|
$R = $R - $split2;
|
|
$z = ((((((($e7 * $R + $e6) * $R + $e5) * $R + $e4) * $R + $e3) * $R + $e2) * $R + $e1) * $R + $e0) /
|
|
((((((($f7 * $R + $f6) * $R + $f5) * $R + $f4) * $R + $f3) * $R + $f2) * $R + $f1) * $R + 1);
|
|
}
|
|
if ($q < 0) {
|
|
$z = -$z;
|
|
}
|
|
}
|
|
return $z;
|
|
} // function _inverse_ncdf3()
|
|
|
|
|
|
/**
|
|
* AVEDEV
|
|
*
|
|
* Returns the average of the absolute deviations of data points from their mean.
|
|
* AVEDEV is a measure of the variability in a data set.
|
|
*
|
|
* Excel Function:
|
|
* AVEDEV(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function AVEDEV() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
$aMean = self::AVERAGE($aArgs);
|
|
if ($aMean != PHPExcel_Calculation_Functions::DIV0()) {
|
|
$aCount = 0;
|
|
foreach ($aArgs as $k => $arg) {
|
|
if ((is_bool($arg)) &&
|
|
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
|
|
$arg = (integer) $arg;
|
|
}
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
if (is_null($returnValue)) {
|
|
$returnValue = abs($arg - $aMean);
|
|
} else {
|
|
$returnValue += abs($arg - $aMean);
|
|
}
|
|
++$aCount;
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if ($aCount == 0) {
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
}
|
|
return $returnValue / $aCount;
|
|
}
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
} // function AVEDEV()
|
|
|
|
|
|
/**
|
|
* AVERAGE
|
|
*
|
|
* Returns the average (arithmetic mean) of the arguments
|
|
*
|
|
* Excel Function:
|
|
* AVERAGE(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function AVERAGE() {
|
|
$returnValue = $aCount = 0;
|
|
|
|
// Loop through arguments
|
|
foreach (PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args()) as $k => $arg) {
|
|
if ((is_bool($arg)) &&
|
|
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
|
|
$arg = (integer) $arg;
|
|
}
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
if (is_null($returnValue)) {
|
|
$returnValue = $arg;
|
|
} else {
|
|
$returnValue += $arg;
|
|
}
|
|
++$aCount;
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if ($aCount > 0) {
|
|
return $returnValue / $aCount;
|
|
} else {
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
}
|
|
} // function AVERAGE()
|
|
|
|
|
|
/**
|
|
* AVERAGEA
|
|
*
|
|
* Returns the average of its arguments, including numbers, text, and logical values
|
|
*
|
|
* Excel Function:
|
|
* AVERAGEA(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function AVERAGEA() {
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
$aCount = 0;
|
|
// Loop through arguments
|
|
foreach (PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args()) as $k => $arg) {
|
|
if ((is_bool($arg)) &&
|
|
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
} else {
|
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
|
|
if (is_bool($arg)) {
|
|
$arg = (integer) $arg;
|
|
} elseif (is_string($arg)) {
|
|
$arg = 0;
|
|
}
|
|
if (is_null($returnValue)) {
|
|
$returnValue = $arg;
|
|
} else {
|
|
$returnValue += $arg;
|
|
}
|
|
++$aCount;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if ($aCount > 0) {
|
|
return $returnValue / $aCount;
|
|
} else {
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
}
|
|
} // function AVERAGEA()
|
|
|
|
|
|
/**
|
|
* AVERAGEIF
|
|
*
|
|
* Returns the average value from a range of cells that contain numbers within the list of arguments
|
|
*
|
|
* Excel Function:
|
|
* AVERAGEIF(value1[,value2[, ...]],condition)
|
|
*
|
|
* @access public
|
|
* @category Mathematical and Trigonometric Functions
|
|
* @param mixed $arg,... Data values
|
|
* @param string $condition The criteria that defines which cells will be checked.
|
|
* @param mixed[] $averageArgs Data values
|
|
* @return float
|
|
*/
|
|
public static function AVERAGEIF($aArgs,$condition,$averageArgs = array()) {
|
|
// Return value
|
|
$returnValue = 0;
|
|
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
|
|
$averageArgs = PHPExcel_Calculation_Functions::flattenArray($averageArgs);
|
|
if (empty($averageArgs)) {
|
|
$averageArgs = $aArgs;
|
|
}
|
|
$condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
|
|
// Loop through arguments
|
|
$aCount = 0;
|
|
foreach ($aArgs as $key => $arg) {
|
|
if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
|
|
$testCondition = '='.$arg.$condition;
|
|
if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
|
|
if ((is_null($returnValue)) || ($arg > $returnValue)) {
|
|
$returnValue += $arg;
|
|
++$aCount;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if ($aCount > 0) {
|
|
return $returnValue / $aCount;
|
|
} else {
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
}
|
|
} // function AVERAGEIF()
|
|
|
|
|
|
/**
|
|
* BETADIST
|
|
*
|
|
* Returns the beta distribution.
|
|
*
|
|
* @param float $value Value at which you want to evaluate the distribution
|
|
* @param float $alpha Parameter to the distribution
|
|
* @param float $beta Parameter to the distribution
|
|
* @param boolean $cumulative
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function BETADIST($value,$alpha,$beta,$rMin=0,$rMax=1) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
|
|
$beta = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
|
|
$rMin = PHPExcel_Calculation_Functions::flattenSingleValue($rMin);
|
|
$rMax = PHPExcel_Calculation_Functions::flattenSingleValue($rMax);
|
|
|
|
if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
|
|
if (($value < $rMin) || ($value > $rMax) || ($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if ($rMin > $rMax) {
|
|
$tmp = $rMin;
|
|
$rMin = $rMax;
|
|
$rMax = $tmp;
|
|
}
|
|
$value -= $rMin;
|
|
$value /= ($rMax - $rMin);
|
|
return self::_incompleteBeta($value,$alpha,$beta);
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function BETADIST()
|
|
|
|
|
|
/**
|
|
* BETAINV
|
|
*
|
|
* Returns the inverse of the beta distribution.
|
|
*
|
|
* @param float $probability Probability at which you want to evaluate the distribution
|
|
* @param float $alpha Parameter to the distribution
|
|
* @param float $beta Parameter to the distribution
|
|
* @param float $rMin Minimum value
|
|
* @param float $rMax Maximum value
|
|
* @param boolean $cumulative
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function BETAINV($probability,$alpha,$beta,$rMin=0,$rMax=1) {
|
|
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
|
|
$beta = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
|
|
$rMin = PHPExcel_Calculation_Functions::flattenSingleValue($rMin);
|
|
$rMax = PHPExcel_Calculation_Functions::flattenSingleValue($rMax);
|
|
|
|
if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
|
|
if (($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax) || ($probability <= 0) || ($probability > 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if ($rMin > $rMax) {
|
|
$tmp = $rMin;
|
|
$rMin = $rMax;
|
|
$rMax = $tmp;
|
|
}
|
|
$a = 0;
|
|
$b = 2;
|
|
|
|
$i = 0;
|
|
while ((($b - $a) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
|
|
$guess = ($a + $b) / 2;
|
|
$result = self::BETADIST($guess, $alpha, $beta);
|
|
if (($result == $probability) || ($result == 0)) {
|
|
$b = $a;
|
|
} elseif ($result > $probability) {
|
|
$b = $guess;
|
|
} else {
|
|
$a = $guess;
|
|
}
|
|
}
|
|
if ($i == MAX_ITERATIONS) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
}
|
|
return round($rMin + $guess * ($rMax - $rMin),12);
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function BETAINV()
|
|
|
|
|
|
/**
|
|
* BINOMDIST
|
|
*
|
|
* Returns the individual term binomial distribution probability. Use BINOMDIST in problems with
|
|
* a fixed number of tests or trials, when the outcomes of any trial are only success or failure,
|
|
* when trials are independent, and when the probability of success is constant throughout the
|
|
* experiment. For example, BINOMDIST can calculate the probability that two of the next three
|
|
* babies born are male.
|
|
*
|
|
* @param float $value Number of successes in trials
|
|
* @param float $trials Number of trials
|
|
* @param float $probability Probability of success on each trial
|
|
* @param boolean $cumulative
|
|
* @return float
|
|
*
|
|
* @todo Cumulative distribution function
|
|
*
|
|
*/
|
|
public static function BINOMDIST($value, $trials, $probability, $cumulative) {
|
|
$value = floor(PHPExcel_Calculation_Functions::flattenSingleValue($value));
|
|
$trials = floor(PHPExcel_Calculation_Functions::flattenSingleValue($trials));
|
|
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
|
|
if ((is_numeric($value)) && (is_numeric($trials)) && (is_numeric($probability))) {
|
|
if (($value < 0) || ($value > $trials)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if (($probability < 0) || ($probability > 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
|
|
if ($cumulative) {
|
|
$summer = 0;
|
|
for ($i = 0; $i <= $value; ++$i) {
|
|
$summer += PHPExcel_Calculation_MathTrig::COMBIN($trials,$i) * pow($probability,$i) * pow(1 - $probability,$trials - $i);
|
|
}
|
|
return $summer;
|
|
} else {
|
|
return PHPExcel_Calculation_MathTrig::COMBIN($trials,$value) * pow($probability,$value) * pow(1 - $probability,$trials - $value) ;
|
|
}
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function BINOMDIST()
|
|
|
|
|
|
/**
|
|
* CHIDIST
|
|
*
|
|
* Returns the one-tailed probability of the chi-squared distribution.
|
|
*
|
|
* @param float $value Value for the function
|
|
* @param float $degrees degrees of freedom
|
|
* @return float
|
|
*/
|
|
public static function CHIDIST($value, $degrees) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
$degrees = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));
|
|
|
|
if ((is_numeric($value)) && (is_numeric($degrees))) {
|
|
if ($degrees < 1) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if ($value < 0) {
|
|
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
|
|
return 1;
|
|
}
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
return 1 - (self::_incompleteGamma($degrees/2,$value/2) / self::_gamma($degrees/2));
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function CHIDIST()
|
|
|
|
|
|
/**
|
|
* CHIINV
|
|
*
|
|
* Returns the one-tailed probability of the chi-squared distribution.
|
|
*
|
|
* @param float $probability Probability for the function
|
|
* @param float $degrees degrees of freedom
|
|
* @return float
|
|
*/
|
|
public static function CHIINV($probability, $degrees) {
|
|
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
$degrees = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));
|
|
|
|
if ((is_numeric($probability)) && (is_numeric($degrees))) {
|
|
|
|
$xLo = 100;
|
|
$xHi = 0;
|
|
|
|
$x = $xNew = 1;
|
|
$dx = 1;
|
|
$i = 0;
|
|
|
|
while ((abs($dx) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
|
|
// Apply Newton-Raphson step
|
|
$result = self::CHIDIST($x, $degrees);
|
|
$error = $result - $probability;
|
|
if ($error == 0.0) {
|
|
$dx = 0;
|
|
} elseif ($error < 0.0) {
|
|
$xLo = $x;
|
|
} else {
|
|
$xHi = $x;
|
|
}
|
|
// Avoid division by zero
|
|
if ($result != 0.0) {
|
|
$dx = $error / $result;
|
|
$xNew = $x - $dx;
|
|
}
|
|
// If the NR fails to converge (which for example may be the
|
|
// case if the initial guess is too rough) we apply a bisection
|
|
// step to determine a more narrow interval around the root.
|
|
if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0)) {
|
|
$xNew = ($xLo + $xHi) / 2;
|
|
$dx = $xNew - $x;
|
|
}
|
|
$x = $xNew;
|
|
}
|
|
if ($i == MAX_ITERATIONS) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
}
|
|
return round($x,12);
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function CHIINV()
|
|
|
|
|
|
/**
|
|
* CONFIDENCE
|
|
*
|
|
* Returns the confidence interval for a population mean
|
|
*
|
|
* @param float $alpha
|
|
* @param float $stdDev Standard Deviation
|
|
* @param float $size
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function CONFIDENCE($alpha,$stdDev,$size) {
|
|
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
|
|
$stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
|
|
$size = floor(PHPExcel_Calculation_Functions::flattenSingleValue($size));
|
|
|
|
if ((is_numeric($alpha)) && (is_numeric($stdDev)) && (is_numeric($size))) {
|
|
if (($alpha <= 0) || ($alpha >= 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if (($stdDev <= 0) || ($size < 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
return self::NORMSINV(1 - $alpha / 2) * $stdDev / sqrt($size);
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function CONFIDENCE()
|
|
|
|
|
|
/**
|
|
* CORREL
|
|
*
|
|
* Returns covariance, the average of the products of deviations for each data point pair.
|
|
*
|
|
* @param array of mixed Data Series Y
|
|
* @param array of mixed Data Series X
|
|
* @return float
|
|
*/
|
|
public static function CORREL($yValues,$xValues=null) {
|
|
if ((is_null($xValues)) || (!is_array($yValues)) || (!is_array($xValues))) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
}
|
|
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
}
|
|
$yValueCount = count($yValues);
|
|
$xValueCount = count($xValues);
|
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
} elseif ($yValueCount == 1) {
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
}
|
|
|
|
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
return $bestFitLinear->getCorrelation();
|
|
} // function CORREL()
|
|
|
|
|
|
/**
|
|
* COUNT
|
|
*
|
|
* Counts the number of cells that contain numbers within the list of arguments
|
|
*
|
|
* Excel Function:
|
|
* COUNT(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return int
|
|
*/
|
|
public static function COUNT() {
|
|
// Return value
|
|
$returnValue = 0;
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
foreach ($aArgs as $k => $arg) {
|
|
if ((is_bool($arg)) &&
|
|
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
|
|
$arg = (integer) $arg;
|
|
}
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
++$returnValue;
|
|
}
|
|
}
|
|
|
|
// Return
|
|
return $returnValue;
|
|
} // function COUNT()
|
|
|
|
|
|
/**
|
|
* COUNTA
|
|
*
|
|
* Counts the number of cells that are not empty within the list of arguments
|
|
*
|
|
* Excel Function:
|
|
* COUNTA(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return int
|
|
*/
|
|
public static function COUNTA() {
|
|
// Return value
|
|
$returnValue = 0;
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a numeric, boolean or string value?
|
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
|
|
++$returnValue;
|
|
}
|
|
}
|
|
|
|
// Return
|
|
return $returnValue;
|
|
} // function COUNTA()
|
|
|
|
|
|
/**
|
|
* COUNTBLANK
|
|
*
|
|
* Counts the number of empty cells within the list of arguments
|
|
*
|
|
* Excel Function:
|
|
* COUNTBLANK(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return int
|
|
*/
|
|
public static function COUNTBLANK() {
|
|
// Return value
|
|
$returnValue = 0;
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a blank cell?
|
|
if ((is_null($arg)) || ((is_string($arg)) && ($arg == ''))) {
|
|
++$returnValue;
|
|
}
|
|
}
|
|
|
|
// Return
|
|
return $returnValue;
|
|
} // function COUNTBLANK()
|
|
|
|
|
|
/**
|
|
* COUNTIF
|
|
*
|
|
* Counts the number of cells that contain numbers within the list of arguments
|
|
*
|
|
* Excel Function:
|
|
* COUNTIF(value1[,value2[, ...]],condition)
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @param string $condition The criteria that defines which cells will be counted.
|
|
* @return int
|
|
*/
|
|
public static function COUNTIF($aArgs,$condition) {
|
|
// Return value
|
|
$returnValue = 0;
|
|
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
|
|
$condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
|
|
// Loop through arguments
|
|
foreach ($aArgs as $arg) {
|
|
if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
|
|
$testCondition = '='.$arg.$condition;
|
|
if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
|
|
// Is it a value within our criteria
|
|
++$returnValue;
|
|
}
|
|
}
|
|
|
|
// Return
|
|
return $returnValue;
|
|
} // function COUNTIF()
|
|
|
|
|
|
/**
|
|
* COVAR
|
|
*
|
|
* Returns covariance, the average of the products of deviations for each data point pair.
|
|
*
|
|
* @param array of mixed Data Series Y
|
|
* @param array of mixed Data Series X
|
|
* @return float
|
|
*/
|
|
public static function COVAR($yValues,$xValues) {
|
|
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
}
|
|
$yValueCount = count($yValues);
|
|
$xValueCount = count($xValues);
|
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
} elseif ($yValueCount == 1) {
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
}
|
|
|
|
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
return $bestFitLinear->getCovariance();
|
|
} // function COVAR()
|
|
|
|
|
|
/**
|
|
* CRITBINOM
|
|
*
|
|
* Returns the smallest value for which the cumulative binomial distribution is greater
|
|
* than or equal to a criterion value
|
|
*
|
|
* See http://support.microsoft.com/kb/828117/ for details of the algorithm used
|
|
*
|
|
* @param float $trials number of Bernoulli trials
|
|
* @param float $probability probability of a success on each trial
|
|
* @param float $alpha criterion value
|
|
* @return int
|
|
*
|
|
* @todo Warning. This implementation differs from the algorithm detailed on the MS
|
|
* web site in that $CumPGuessMinus1 = $CumPGuess - 1 rather than $CumPGuess - $PGuess
|
|
* This eliminates a potential endless loop error, but may have an adverse affect on the
|
|
* accuracy of the function (although all my tests have so far returned correct results).
|
|
*
|
|
*/
|
|
public static function CRITBINOM($trials, $probability, $alpha) {
|
|
$trials = floor(PHPExcel_Calculation_Functions::flattenSingleValue($trials));
|
|
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
|
|
|
|
if ((is_numeric($trials)) && (is_numeric($probability)) && (is_numeric($alpha))) {
|
|
if ($trials < 0) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if (($probability < 0) || ($probability > 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if (($alpha < 0) || ($alpha > 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if ($alpha <= 0.5) {
|
|
$t = sqrt(log(1 / ($alpha * $alpha)));
|
|
$trialsApprox = 0 - ($t + (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t));
|
|
} else {
|
|
$t = sqrt(log(1 / pow(1 - $alpha,2)));
|
|
$trialsApprox = $t - (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t);
|
|
}
|
|
$Guess = floor($trials * $probability + $trialsApprox * sqrt($trials * $probability * (1 - $probability)));
|
|
if ($Guess < 0) {
|
|
$Guess = 0;
|
|
} elseif ($Guess > $trials) {
|
|
$Guess = $trials;
|
|
}
|
|
|
|
$TotalUnscaledProbability = $UnscaledPGuess = $UnscaledCumPGuess = 0.0;
|
|
$EssentiallyZero = 10e-12;
|
|
|
|
$m = floor($trials * $probability);
|
|
++$TotalUnscaledProbability;
|
|
if ($m == $Guess) { ++$UnscaledPGuess; }
|
|
if ($m <= $Guess) { ++$UnscaledCumPGuess; }
|
|
|
|
$PreviousValue = 1;
|
|
$Done = False;
|
|
$k = $m + 1;
|
|
while ((!$Done) && ($k <= $trials)) {
|
|
$CurrentValue = $PreviousValue * ($trials - $k + 1) * $probability / ($k * (1 - $probability));
|
|
$TotalUnscaledProbability += $CurrentValue;
|
|
if ($k == $Guess) { $UnscaledPGuess += $CurrentValue; }
|
|
if ($k <= $Guess) { $UnscaledCumPGuess += $CurrentValue; }
|
|
if ($CurrentValue <= $EssentiallyZero) { $Done = True; }
|
|
$PreviousValue = $CurrentValue;
|
|
++$k;
|
|
}
|
|
|
|
$PreviousValue = 1;
|
|
$Done = False;
|
|
$k = $m - 1;
|
|
while ((!$Done) && ($k >= 0)) {
|
|
$CurrentValue = $PreviousValue * $k + 1 * (1 - $probability) / (($trials - $k) * $probability);
|
|
$TotalUnscaledProbability += $CurrentValue;
|
|
if ($k == $Guess) { $UnscaledPGuess += $CurrentValue; }
|
|
if ($k <= $Guess) { $UnscaledCumPGuess += $CurrentValue; }
|
|
if ($CurrentValue <= $EssentiallyZero) { $Done = True; }
|
|
$PreviousValue = $CurrentValue;
|
|
--$k;
|
|
}
|
|
|
|
$PGuess = $UnscaledPGuess / $TotalUnscaledProbability;
|
|
$CumPGuess = $UnscaledCumPGuess / $TotalUnscaledProbability;
|
|
|
|
// $CumPGuessMinus1 = $CumPGuess - $PGuess;
|
|
$CumPGuessMinus1 = $CumPGuess - 1;
|
|
|
|
while (True) {
|
|
if (($CumPGuessMinus1 < $alpha) && ($CumPGuess >= $alpha)) {
|
|
return $Guess;
|
|
} elseif (($CumPGuessMinus1 < $alpha) && ($CumPGuess < $alpha)) {
|
|
$PGuessPlus1 = $PGuess * ($trials - $Guess) * $probability / $Guess / (1 - $probability);
|
|
$CumPGuessMinus1 = $CumPGuess;
|
|
$CumPGuess = $CumPGuess + $PGuessPlus1;
|
|
$PGuess = $PGuessPlus1;
|
|
++$Guess;
|
|
} elseif (($CumPGuessMinus1 >= $alpha) && ($CumPGuess >= $alpha)) {
|
|
$PGuessMinus1 = $PGuess * $Guess * (1 - $probability) / ($trials - $Guess + 1) / $probability;
|
|
$CumPGuess = $CumPGuessMinus1;
|
|
$CumPGuessMinus1 = $CumPGuessMinus1 - $PGuess;
|
|
$PGuess = $PGuessMinus1;
|
|
--$Guess;
|
|
}
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function CRITBINOM()
|
|
|
|
|
|
/**
|
|
* DEVSQ
|
|
*
|
|
* Returns the sum of squares of deviations of data points from their sample mean.
|
|
*
|
|
* Excel Function:
|
|
* DEVSQ(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function DEVSQ() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
$aMean = self::AVERAGE($aArgs);
|
|
if ($aMean != PHPExcel_Calculation_Functions::DIV0()) {
|
|
$aCount = -1;
|
|
foreach ($aArgs as $k => $arg) {
|
|
// Is it a numeric value?
|
|
if ((is_bool($arg)) &&
|
|
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
|
|
$arg = (integer) $arg;
|
|
}
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
if (is_null($returnValue)) {
|
|
$returnValue = pow(($arg - $aMean),2);
|
|
} else {
|
|
$returnValue += pow(($arg - $aMean),2);
|
|
}
|
|
++$aCount;
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if (is_null($returnValue)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
} else {
|
|
return $returnValue;
|
|
}
|
|
}
|
|
return self::NA();
|
|
} // function DEVSQ()
|
|
|
|
|
|
/**
|
|
* EXPONDIST
|
|
*
|
|
* Returns the exponential distribution. Use EXPONDIST to model the time between events,
|
|
* such as how long an automated bank teller takes to deliver cash. For example, you can
|
|
* use EXPONDIST to determine the probability that the process takes at most 1 minute.
|
|
*
|
|
* @param float $value Value of the function
|
|
* @param float $lambda The parameter value
|
|
* @param boolean $cumulative
|
|
* @return float
|
|
*/
|
|
public static function EXPONDIST($value, $lambda, $cumulative) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
$lambda = PHPExcel_Calculation_Functions::flattenSingleValue($lambda);
|
|
$cumulative = PHPExcel_Calculation_Functions::flattenSingleValue($cumulative);
|
|
|
|
if ((is_numeric($value)) && (is_numeric($lambda))) {
|
|
if (($value < 0) || ($lambda < 0)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
|
|
if ($cumulative) {
|
|
return 1 - exp(0-$value*$lambda);
|
|
} else {
|
|
return $lambda * exp(0-$value*$lambda);
|
|
}
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function EXPONDIST()
|
|
|
|
|
|
/**
|
|
* FISHER
|
|
*
|
|
* Returns the Fisher transformation at x. This transformation produces a function that
|
|
* is normally distributed rather than skewed. Use this function to perform hypothesis
|
|
* testing on the correlation coefficient.
|
|
*
|
|
* @param float $value
|
|
* @return float
|
|
*/
|
|
public static function FISHER($value) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
|
if (is_numeric($value)) {
|
|
if (($value <= -1) || ($value >= 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
return 0.5 * log((1+$value)/(1-$value));
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function FISHER()
|
|
|
|
|
|
/**
|
|
* FISHERINV
|
|
*
|
|
* Returns the inverse of the Fisher transformation. Use this transformation when
|
|
* analyzing correlations between ranges or arrays of data. If y = FISHER(x), then
|
|
* FISHERINV(y) = x.
|
|
*
|
|
* @param float $value
|
|
* @return float
|
|
*/
|
|
public static function FISHERINV($value) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
|
if (is_numeric($value)) {
|
|
return (exp(2 * $value) - 1) / (exp(2 * $value) + 1);
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function FISHERINV()
|
|
|
|
|
|
/**
|
|
* FORECAST
|
|
*
|
|
* Calculates, or predicts, a future value by using existing values. The predicted value is a y-value for a given x-value.
|
|
*
|
|
* @param float Value of X for which we want to find Y
|
|
* @param array of mixed Data Series Y
|
|
* @param array of mixed Data Series X
|
|
* @return float
|
|
*/
|
|
public static function FORECAST($xValue,$yValues,$xValues) {
|
|
$xValue = PHPExcel_Calculation_Functions::flattenSingleValue($xValue);
|
|
if (!is_numeric($xValue)) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
}
|
|
|
|
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
}
|
|
$yValueCount = count($yValues);
|
|
$xValueCount = count($xValues);
|
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
} elseif ($yValueCount == 1) {
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
}
|
|
|
|
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
return $bestFitLinear->getValueOfYForX($xValue);
|
|
} // function FORECAST()
|
|
|
|
|
|
/**
|
|
* GAMMADIST
|
|
*
|
|
* Returns the gamma distribution.
|
|
*
|
|
* @param float $value Value at which you want to evaluate the distribution
|
|
* @param float $a Parameter to the distribution
|
|
* @param float $b Parameter to the distribution
|
|
* @param boolean $cumulative
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function GAMMADIST($value,$a,$b,$cumulative) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
$a = PHPExcel_Calculation_Functions::flattenSingleValue($a);
|
|
$b = PHPExcel_Calculation_Functions::flattenSingleValue($b);
|
|
|
|
if ((is_numeric($value)) && (is_numeric($a)) && (is_numeric($b))) {
|
|
if (($value < 0) || ($a <= 0) || ($b <= 0)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
|
|
if ($cumulative) {
|
|
return self::_incompleteGamma($a,$value / $b) / self::_gamma($a);
|
|
} else {
|
|
return (1 / (pow($b,$a) * self::_gamma($a))) * pow($value,$a-1) * exp(0-($value / $b));
|
|
}
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function GAMMADIST()
|
|
|
|
|
|
/**
|
|
* GAMMAINV
|
|
*
|
|
* Returns the inverse of the beta distribution.
|
|
*
|
|
* @param float $probability Probability at which you want to evaluate the distribution
|
|
* @param float $alpha Parameter to the distribution
|
|
* @param float $beta Parameter to the distribution
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function GAMMAINV($probability,$alpha,$beta) {
|
|
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
|
|
$beta = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
|
|
|
|
if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta))) {
|
|
if (($alpha <= 0) || ($beta <= 0) || ($probability < 0) || ($probability > 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
|
|
$xLo = 0;
|
|
$xHi = $alpha * $beta * 5;
|
|
|
|
$x = $xNew = 1;
|
|
$error = $pdf = 0;
|
|
$dx = 1024;
|
|
$i = 0;
|
|
|
|
while ((abs($dx) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
|
|
// Apply Newton-Raphson step
|
|
$error = self::GAMMADIST($x, $alpha, $beta, True) - $probability;
|
|
if ($error < 0.0) {
|
|
$xLo = $x;
|
|
} else {
|
|
$xHi = $x;
|
|
}
|
|
$pdf = self::GAMMADIST($x, $alpha, $beta, False);
|
|
// Avoid division by zero
|
|
if ($pdf != 0.0) {
|
|
$dx = $error / $pdf;
|
|
$xNew = $x - $dx;
|
|
}
|
|
// If the NR fails to converge (which for example may be the
|
|
// case if the initial guess is too rough) we apply a bisection
|
|
// step to determine a more narrow interval around the root.
|
|
if (($xNew < $xLo) || ($xNew > $xHi) || ($pdf == 0.0)) {
|
|
$xNew = ($xLo + $xHi) / 2;
|
|
$dx = $xNew - $x;
|
|
}
|
|
$x = $xNew;
|
|
}
|
|
if ($i == MAX_ITERATIONS) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
}
|
|
return $x;
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function GAMMAINV()
|
|
|
|
|
|
/**
|
|
* GAMMALN
|
|
*
|
|
* Returns the natural logarithm of the gamma function.
|
|
*
|
|
* @param float $value
|
|
* @return float
|
|
*/
|
|
public static function GAMMALN($value) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
|
if (is_numeric($value)) {
|
|
if ($value <= 0) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
return log(self::_gamma($value));
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function GAMMALN()
|
|
|
|
|
|
/**
|
|
* GEOMEAN
|
|
*
|
|
* Returns the geometric mean of an array or range of positive data. For example, you
|
|
* can use GEOMEAN to calculate average growth rate given compound interest with
|
|
* variable rates.
|
|
*
|
|
* Excel Function:
|
|
* GEOMEAN(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function GEOMEAN() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
|
$aMean = PHPExcel_Calculation_MathTrig::PRODUCT($aArgs);
|
|
if (is_numeric($aMean) && ($aMean > 0)) {
|
|
$aCount = self::COUNT($aArgs) ;
|
|
if (self::MIN($aArgs) > 0) {
|
|
return pow($aMean, (1 / $aCount));
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
} // GEOMEAN()
|
|
|
|
|
|
/**
|
|
* GROWTH
|
|
*
|
|
* Returns values along a predicted emponential trend
|
|
*
|
|
* @param array of mixed Data Series Y
|
|
* @param array of mixed Data Series X
|
|
* @param array of mixed Values of X for which we want to find Y
|
|
* @param boolean A logical value specifying whether to force the intersect to equal 0.
|
|
* @return array of float
|
|
*/
|
|
public static function GROWTH($yValues,$xValues=array(),$newValues=array(),$const=True) {
|
|
$yValues = PHPExcel_Calculation_Functions::flattenArray($yValues);
|
|
$xValues = PHPExcel_Calculation_Functions::flattenArray($xValues);
|
|
$newValues = PHPExcel_Calculation_Functions::flattenArray($newValues);
|
|
$const = (is_null($const)) ? True : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
|
|
|
|
$bestFitExponential = trendClass::calculate(trendClass::TREND_EXPONENTIAL,$yValues,$xValues,$const);
|
|
if (empty($newValues)) {
|
|
$newValues = $bestFitExponential->getXValues();
|
|
}
|
|
|
|
$returnArray = array();
|
|
foreach($newValues as $xValue) {
|
|
$returnArray[0][] = $bestFitExponential->getValueOfYForX($xValue);
|
|
}
|
|
|
|
return $returnArray;
|
|
} // function GROWTH()
|
|
|
|
|
|
/**
|
|
* HARMEAN
|
|
*
|
|
* Returns the harmonic mean of a data set. The harmonic mean is the reciprocal of the
|
|
* arithmetic mean of reciprocals.
|
|
*
|
|
* Excel Function:
|
|
* HARMEAN(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function HARMEAN() {
|
|
// Return value
|
|
$returnValue = PHPExcel_Calculation_Functions::NA();
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
if (self::MIN($aArgs) < 0) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
$aCount = 0;
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
if ($arg <= 0) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if (is_null($returnValue)) {
|
|
$returnValue = (1 / $arg);
|
|
} else {
|
|
$returnValue += (1 / $arg);
|
|
}
|
|
++$aCount;
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if ($aCount > 0) {
|
|
return 1 / ($returnValue / $aCount);
|
|
} else {
|
|
return $returnValue;
|
|
}
|
|
} // function HARMEAN()
|
|
|
|
|
|
/**
|
|
* HYPGEOMDIST
|
|
*
|
|
* Returns the hypergeometric distribution. HYPGEOMDIST returns the probability of a given number of
|
|
* sample successes, given the sample size, population successes, and population size.
|
|
*
|
|
* @param float $sampleSuccesses Number of successes in the sample
|
|
* @param float $sampleNumber Size of the sample
|
|
* @param float $populationSuccesses Number of successes in the population
|
|
* @param float $populationNumber Population size
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function HYPGEOMDIST($sampleSuccesses, $sampleNumber, $populationSuccesses, $populationNumber) {
|
|
$sampleSuccesses = floor(PHPExcel_Calculation_Functions::flattenSingleValue($sampleSuccesses));
|
|
$sampleNumber = floor(PHPExcel_Calculation_Functions::flattenSingleValue($sampleNumber));
|
|
$populationSuccesses = floor(PHPExcel_Calculation_Functions::flattenSingleValue($populationSuccesses));
|
|
$populationNumber = floor(PHPExcel_Calculation_Functions::flattenSingleValue($populationNumber));
|
|
|
|
if ((is_numeric($sampleSuccesses)) && (is_numeric($sampleNumber)) && (is_numeric($populationSuccesses)) && (is_numeric($populationNumber))) {
|
|
if (($sampleSuccesses < 0) || ($sampleSuccesses > $sampleNumber) || ($sampleSuccesses > $populationSuccesses)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if (($sampleNumber <= 0) || ($sampleNumber > $populationNumber)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if (($populationSuccesses <= 0) || ($populationSuccesses > $populationNumber)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
return PHPExcel_Calculation_MathTrig::COMBIN($populationSuccesses,$sampleSuccesses) *
|
|
PHPExcel_Calculation_MathTrig::COMBIN($populationNumber - $populationSuccesses,$sampleNumber - $sampleSuccesses) /
|
|
PHPExcel_Calculation_MathTrig::COMBIN($populationNumber,$sampleNumber);
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function HYPGEOMDIST()
|
|
|
|
|
|
/**
|
|
* INTERCEPT
|
|
*
|
|
* Calculates the point at which a line will intersect the y-axis by using existing x-values and y-values.
|
|
*
|
|
* @param array of mixed Data Series Y
|
|
* @param array of mixed Data Series X
|
|
* @return float
|
|
*/
|
|
public static function INTERCEPT($yValues,$xValues) {
|
|
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
}
|
|
$yValueCount = count($yValues);
|
|
$xValueCount = count($xValues);
|
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
} elseif ($yValueCount == 1) {
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
}
|
|
|
|
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
return $bestFitLinear->getIntersect();
|
|
} // function INTERCEPT()
|
|
|
|
|
|
/**
|
|
* KURT
|
|
*
|
|
* Returns the kurtosis of a data set. Kurtosis characterizes the relative peakedness
|
|
* or flatness of a distribution compared with the normal distribution. Positive
|
|
* kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a
|
|
* relatively flat distribution.
|
|
*
|
|
* @param array Data Series
|
|
* @return float
|
|
*/
|
|
public static function KURT() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
$mean = self::AVERAGE($aArgs);
|
|
$stdDev = self::STDEV($aArgs);
|
|
|
|
if ($stdDev > 0) {
|
|
$count = $summer = 0;
|
|
// Loop through arguments
|
|
foreach ($aArgs as $k => $arg) {
|
|
if ((is_bool($arg)) &&
|
|
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
} else {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
$summer += pow((($arg - $mean) / $stdDev),4) ;
|
|
++$count;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if ($count > 3) {
|
|
return $summer * ($count * ($count+1) / (($count-1) * ($count-2) * ($count-3))) - (3 * pow($count-1,2) / (($count-2) * ($count-3)));
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
} // function KURT()
|
|
|
|
|
|
/**
|
|
* LARGE
|
|
*
|
|
* Returns the nth largest value in a data set. You can use this function to
|
|
* select a value based on its relative standing.
|
|
*
|
|
* Excel Function:
|
|
* LARGE(value1[,value2[, ...]],entry)
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @param int $entry Position (ordered from the largest) in the array or range of data to return
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function LARGE() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
|
// Calculate
|
|
$entry = floor(array_pop($aArgs));
|
|
|
|
if ((is_numeric($entry)) && (!is_string($entry))) {
|
|
$mArgs = array();
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
$mArgs[] = $arg;
|
|
}
|
|
}
|
|
$count = self::COUNT($mArgs);
|
|
$entry = floor(--$entry);
|
|
if (($entry < 0) || ($entry >= $count) || ($count == 0)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
rsort($mArgs);
|
|
return $mArgs[$entry];
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function LARGE()
|
|
|
|
|
|
/**
|
|
* LINEST
|
|
*
|
|
* Calculates the statistics for a line by using the "least squares" method to calculate a straight line that best fits your data,
|
|
* and then returns an array that describes the line.
|
|
*
|
|
* @param array of mixed Data Series Y
|
|
* @param array of mixed Data Series X
|
|
* @param boolean A logical value specifying whether to force the intersect to equal 0.
|
|
* @param boolean A logical value specifying whether to return additional regression statistics.
|
|
* @return array
|
|
*/
|
|
public static function LINEST($yValues, $xValues = NULL, $const = TRUE, $stats = FALSE) {
|
|
$const = (is_null($const)) ? TRUE : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
|
|
$stats = (is_null($stats)) ? FALSE : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($stats);
|
|
if (is_null($xValues)) $xValues = range(1,count(PHPExcel_Calculation_Functions::flattenArray($yValues)));
|
|
|
|
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
}
|
|
$yValueCount = count($yValues);
|
|
$xValueCount = count($xValues);
|
|
|
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
} elseif ($yValueCount == 1) {
|
|
return 0;
|
|
}
|
|
|
|
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues,$const);
|
|
if ($stats) {
|
|
return array( array( $bestFitLinear->getSlope(),
|
|
$bestFitLinear->getSlopeSE(),
|
|
$bestFitLinear->getGoodnessOfFit(),
|
|
$bestFitLinear->getF(),
|
|
$bestFitLinear->getSSRegression(),
|
|
),
|
|
array( $bestFitLinear->getIntersect(),
|
|
$bestFitLinear->getIntersectSE(),
|
|
$bestFitLinear->getStdevOfResiduals(),
|
|
$bestFitLinear->getDFResiduals(),
|
|
$bestFitLinear->getSSResiduals()
|
|
)
|
|
);
|
|
} else {
|
|
return array( $bestFitLinear->getSlope(),
|
|
$bestFitLinear->getIntersect()
|
|
);
|
|
}
|
|
} // function LINEST()
|
|
|
|
|
|
/**
|
|
* LOGEST
|
|
*
|
|
* Calculates an exponential curve that best fits the X and Y data series,
|
|
* and then returns an array that describes the line.
|
|
*
|
|
* @param array of mixed Data Series Y
|
|
* @param array of mixed Data Series X
|
|
* @param boolean A logical value specifying whether to force the intersect to equal 0.
|
|
* @param boolean A logical value specifying whether to return additional regression statistics.
|
|
* @return array
|
|
*/
|
|
public static function LOGEST($yValues,$xValues=null,$const=True,$stats=False) {
|
|
$const = (is_null($const)) ? True : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
|
|
$stats = (is_null($stats)) ? False : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($stats);
|
|
if (is_null($xValues)) $xValues = range(1,count(PHPExcel_Calculation_Functions::flattenArray($yValues)));
|
|
|
|
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
}
|
|
$yValueCount = count($yValues);
|
|
$xValueCount = count($xValues);
|
|
|
|
foreach($yValues as $value) {
|
|
if ($value <= 0.0) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
}
|
|
|
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
} elseif ($yValueCount == 1) {
|
|
return 1;
|
|
}
|
|
|
|
$bestFitExponential = trendClass::calculate(trendClass::TREND_EXPONENTIAL,$yValues,$xValues,$const);
|
|
if ($stats) {
|
|
return array( array( $bestFitExponential->getSlope(),
|
|
$bestFitExponential->getSlopeSE(),
|
|
$bestFitExponential->getGoodnessOfFit(),
|
|
$bestFitExponential->getF(),
|
|
$bestFitExponential->getSSRegression(),
|
|
),
|
|
array( $bestFitExponential->getIntersect(),
|
|
$bestFitExponential->getIntersectSE(),
|
|
$bestFitExponential->getStdevOfResiduals(),
|
|
$bestFitExponential->getDFResiduals(),
|
|
$bestFitExponential->getSSResiduals()
|
|
)
|
|
);
|
|
} else {
|
|
return array( $bestFitExponential->getSlope(),
|
|
$bestFitExponential->getIntersect()
|
|
);
|
|
}
|
|
} // function LOGEST()
|
|
|
|
|
|
/**
|
|
* LOGINV
|
|
*
|
|
* Returns the inverse of the normal cumulative distribution
|
|
*
|
|
* @param float $probability
|
|
* @param float $mean
|
|
* @param float $stdDev
|
|
* @return float
|
|
*
|
|
* @todo Try implementing P J Acklam's refinement algorithm for greater
|
|
* accuracy if I can get my head round the mathematics
|
|
* (as described at) http://home.online.no/~pjacklam/notes/invnorm/
|
|
*/
|
|
public static function LOGINV($probability, $mean, $stdDev) {
|
|
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
$mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
|
|
$stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
|
|
|
|
if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
|
|
if (($probability < 0) || ($probability > 1) || ($stdDev <= 0)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
return exp($mean + $stdDev * self::NORMSINV($probability));
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function LOGINV()
|
|
|
|
|
|
/**
|
|
* LOGNORMDIST
|
|
*
|
|
* Returns the cumulative lognormal distribution of x, where ln(x) is normally distributed
|
|
* with parameters mean and standard_dev.
|
|
*
|
|
* @param float $value
|
|
* @param float $mean
|
|
* @param float $stdDev
|
|
* @return float
|
|
*/
|
|
public static function LOGNORMDIST($value, $mean, $stdDev) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
$mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
|
|
$stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
|
|
|
|
if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
|
|
if (($value <= 0) || ($stdDev <= 0)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
return self::NORMSDIST((log($value) - $mean) / $stdDev);
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function LOGNORMDIST()
|
|
|
|
|
|
/**
|
|
* MAX
|
|
*
|
|
* MAX returns the value of the element of the values passed that has the highest value,
|
|
* with negative numbers considered smaller than positive numbers.
|
|
*
|
|
* Excel Function:
|
|
* MAX(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function MAX() {
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
if ((is_null($returnValue)) || ($arg > $returnValue)) {
|
|
$returnValue = $arg;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if(is_null($returnValue)) {
|
|
return 0;
|
|
}
|
|
return $returnValue;
|
|
} // function MAX()
|
|
|
|
|
|
/**
|
|
* MAXA
|
|
*
|
|
* Returns the greatest value in a list of arguments, including numbers, text, and logical values
|
|
*
|
|
* Excel Function:
|
|
* MAXA(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function MAXA() {
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
|
|
if (is_bool($arg)) {
|
|
$arg = (integer) $arg;
|
|
} elseif (is_string($arg)) {
|
|
$arg = 0;
|
|
}
|
|
if ((is_null($returnValue)) || ($arg > $returnValue)) {
|
|
$returnValue = $arg;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if(is_null($returnValue)) {
|
|
return 0;
|
|
}
|
|
return $returnValue;
|
|
} // function MAXA()
|
|
|
|
|
|
/**
|
|
* MAXIF
|
|
*
|
|
* Counts the maximum value within a range of cells that contain numbers within the list of arguments
|
|
*
|
|
* Excel Function:
|
|
* MAXIF(value1[,value2[, ...]],condition)
|
|
*
|
|
* @access public
|
|
* @category Mathematical and Trigonometric Functions
|
|
* @param mixed $arg,... Data values
|
|
* @param string $condition The criteria that defines which cells will be checked.
|
|
* @return float
|
|
*/
|
|
public static function MAXIF($aArgs,$condition,$sumArgs = array()) {
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
|
|
$sumArgs = PHPExcel_Calculation_Functions::flattenArray($sumArgs);
|
|
if (empty($sumArgs)) {
|
|
$sumArgs = $aArgs;
|
|
}
|
|
$condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
|
|
// Loop through arguments
|
|
foreach ($aArgs as $key => $arg) {
|
|
if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
|
|
$testCondition = '='.$arg.$condition;
|
|
if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
|
|
if ((is_null($returnValue)) || ($arg > $returnValue)) {
|
|
$returnValue = $arg;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
return $returnValue;
|
|
} // function MAXIF()
|
|
|
|
|
|
/**
|
|
* MEDIAN
|
|
*
|
|
* Returns the median of the given numbers. The median is the number in the middle of a set of numbers.
|
|
*
|
|
* Excel Function:
|
|
* MEDIAN(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function MEDIAN() {
|
|
// Return value
|
|
$returnValue = PHPExcel_Calculation_Functions::NaN();
|
|
|
|
$mArgs = array();
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
$mArgs[] = $arg;
|
|
}
|
|
}
|
|
|
|
$mValueCount = count($mArgs);
|
|
if ($mValueCount > 0) {
|
|
sort($mArgs,SORT_NUMERIC);
|
|
$mValueCount = $mValueCount / 2;
|
|
if ($mValueCount == floor($mValueCount)) {
|
|
$returnValue = ($mArgs[$mValueCount--] + $mArgs[$mValueCount]) / 2;
|
|
} else {
|
|
$mValueCount == floor($mValueCount);
|
|
$returnValue = $mArgs[$mValueCount];
|
|
}
|
|
}
|
|
|
|
// Return
|
|
return $returnValue;
|
|
} // function MEDIAN()
|
|
|
|
|
|
/**
|
|
* MIN
|
|
*
|
|
* MIN returns the value of the element of the values passed that has the smallest value,
|
|
* with negative numbers considered smaller than positive numbers.
|
|
*
|
|
* Excel Function:
|
|
* MIN(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function MIN() {
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
if ((is_null($returnValue)) || ($arg < $returnValue)) {
|
|
$returnValue = $arg;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if(is_null($returnValue)) {
|
|
return 0;
|
|
}
|
|
return $returnValue;
|
|
} // function MIN()
|
|
|
|
|
|
/**
|
|
* MINA
|
|
*
|
|
* Returns the smallest value in a list of arguments, including numbers, text, and logical values
|
|
*
|
|
* Excel Function:
|
|
* MINA(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function MINA() {
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
|
|
if (is_bool($arg)) {
|
|
$arg = (integer) $arg;
|
|
} elseif (is_string($arg)) {
|
|
$arg = 0;
|
|
}
|
|
if ((is_null($returnValue)) || ($arg < $returnValue)) {
|
|
$returnValue = $arg;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if(is_null($returnValue)) {
|
|
return 0;
|
|
}
|
|
return $returnValue;
|
|
} // function MINA()
|
|
|
|
|
|
/**
|
|
* MINIF
|
|
*
|
|
* Returns the minimum value within a range of cells that contain numbers within the list of arguments
|
|
*
|
|
* Excel Function:
|
|
* MINIF(value1[,value2[, ...]],condition)
|
|
*
|
|
* @access public
|
|
* @category Mathematical and Trigonometric Functions
|
|
* @param mixed $arg,... Data values
|
|
* @param string $condition The criteria that defines which cells will be checked.
|
|
* @return float
|
|
*/
|
|
public static function MINIF($aArgs,$condition,$sumArgs = array()) {
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
|
|
$sumArgs = PHPExcel_Calculation_Functions::flattenArray($sumArgs);
|
|
if (empty($sumArgs)) {
|
|
$sumArgs = $aArgs;
|
|
}
|
|
$condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
|
|
// Loop through arguments
|
|
foreach ($aArgs as $key => $arg) {
|
|
if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
|
|
$testCondition = '='.$arg.$condition;
|
|
if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
|
|
if ((is_null($returnValue)) || ($arg < $returnValue)) {
|
|
$returnValue = $arg;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
return $returnValue;
|
|
} // function MINIF()
|
|
|
|
|
|
//
|
|
// Special variant of array_count_values that isn't limited to strings and integers,
|
|
// but can work with floating point numbers as values
|
|
//
|
|
private static function _modeCalc($data) {
|
|
$frequencyArray = array();
|
|
foreach($data as $datum) {
|
|
$found = False;
|
|
foreach($frequencyArray as $key => $value) {
|
|
if ((string) $value['value'] == (string) $datum) {
|
|
++$frequencyArray[$key]['frequency'];
|
|
$found = True;
|
|
break;
|
|
}
|
|
}
|
|
if (!$found) {
|
|
$frequencyArray[] = array('value' => $datum,
|
|
'frequency' => 1 );
|
|
}
|
|
}
|
|
|
|
foreach($frequencyArray as $key => $value) {
|
|
$frequencyList[$key] = $value['frequency'];
|
|
$valueList[$key] = $value['value'];
|
|
}
|
|
array_multisort($frequencyList, SORT_DESC, $valueList, SORT_ASC, SORT_NUMERIC, $frequencyArray);
|
|
|
|
if ($frequencyArray[0]['frequency'] == 1) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
}
|
|
return $frequencyArray[0]['value'];
|
|
} // function _modeCalc()
|
|
|
|
|
|
/**
|
|
* MODE
|
|
*
|
|
* Returns the most frequently occurring, or repetitive, value in an array or range of data
|
|
*
|
|
* Excel Function:
|
|
* MODE(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function MODE() {
|
|
// Return value
|
|
$returnValue = PHPExcel_Calculation_Functions::NA();
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
|
$mArgs = array();
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
$mArgs[] = $arg;
|
|
}
|
|
}
|
|
|
|
if (!empty($mArgs)) {
|
|
return self::_modeCalc($mArgs);
|
|
}
|
|
|
|
// Return
|
|
return $returnValue;
|
|
} // function MODE()
|
|
|
|
|
|
/**
|
|
* NEGBINOMDIST
|
|
*
|
|
* Returns the negative binomial distribution. NEGBINOMDIST returns the probability that
|
|
* there will be number_f failures before the number_s-th success, when the constant
|
|
* probability of a success is probability_s. This function is similar to the binomial
|
|
* distribution, except that the number of successes is fixed, and the number of trials is
|
|
* variable. Like the binomial, trials are assumed to be independent.
|
|
*
|
|
* @param float $failures Number of Failures
|
|
* @param float $successes Threshold number of Successes
|
|
* @param float $probability Probability of success on each trial
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function NEGBINOMDIST($failures, $successes, $probability) {
|
|
$failures = floor(PHPExcel_Calculation_Functions::flattenSingleValue($failures));
|
|
$successes = floor(PHPExcel_Calculation_Functions::flattenSingleValue($successes));
|
|
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
|
|
if ((is_numeric($failures)) && (is_numeric($successes)) && (is_numeric($probability))) {
|
|
if (($failures < 0) || ($successes < 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if (($probability < 0) || ($probability > 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
|
|
if (($failures + $successes - 1) <= 0) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
}
|
|
return (PHPExcel_Calculation_MathTrig::COMBIN($failures + $successes - 1,$successes - 1)) * (pow($probability,$successes)) * (pow(1 - $probability,$failures)) ;
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function NEGBINOMDIST()
|
|
|
|
|
|
/**
|
|
* NORMDIST
|
|
*
|
|
* Returns the normal distribution for the specified mean and standard deviation. This
|
|
* function has a very wide range of applications in statistics, including hypothesis
|
|
* testing.
|
|
*
|
|
* @param float $value
|
|
* @param float $mean Mean Value
|
|
* @param float $stdDev Standard Deviation
|
|
* @param boolean $cumulative
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function NORMDIST($value, $mean, $stdDev, $cumulative) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
$mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
|
|
$stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
|
|
|
|
if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
|
|
if ($stdDev < 0) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
|
|
if ($cumulative) {
|
|
return 0.5 * (1 + PHPExcel_Calculation_Engineering::_erfVal(($value - $mean) / ($stdDev * sqrt(2))));
|
|
} else {
|
|
return (1 / (SQRT2PI * $stdDev)) * exp(0 - (pow($value - $mean,2) / (2 * ($stdDev * $stdDev))));
|
|
}
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function NORMDIST()
|
|
|
|
|
|
/**
|
|
* NORMINV
|
|
*
|
|
* Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.
|
|
*
|
|
* @param float $value
|
|
* @param float $mean Mean Value
|
|
* @param float $stdDev Standard Deviation
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function NORMINV($probability,$mean,$stdDev) {
|
|
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
$mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
|
|
$stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
|
|
|
|
if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
|
|
if (($probability < 0) || ($probability > 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if ($stdDev < 0) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
return (self::_inverse_ncdf($probability) * $stdDev) + $mean;
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function NORMINV()
|
|
|
|
|
|
/**
|
|
* NORMSDIST
|
|
*
|
|
* Returns the standard normal cumulative distribution function. The distribution has
|
|
* a mean of 0 (zero) and a standard deviation of one. Use this function in place of a
|
|
* table of standard normal curve areas.
|
|
*
|
|
* @param float $value
|
|
* @return float
|
|
*/
|
|
public static function NORMSDIST($value) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
|
|
return self::NORMDIST($value, 0, 1, True);
|
|
} // function NORMSDIST()
|
|
|
|
|
|
/**
|
|
* NORMSINV
|
|
*
|
|
* Returns the inverse of the standard normal cumulative distribution
|
|
*
|
|
* @param float $value
|
|
* @return float
|
|
*/
|
|
public static function NORMSINV($value) {
|
|
return self::NORMINV($value, 0, 1);
|
|
} // function NORMSINV()
|
|
|
|
|
|
/**
|
|
* PERCENTILE
|
|
*
|
|
* Returns the nth percentile of values in a range..
|
|
*
|
|
* Excel Function:
|
|
* PERCENTILE(value1[,value2[, ...]],entry)
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @param float $entry Percentile value in the range 0..1, inclusive.
|
|
* @return float
|
|
*/
|
|
public static function PERCENTILE() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
|
// Calculate
|
|
$entry = array_pop($aArgs);
|
|
|
|
if ((is_numeric($entry)) && (!is_string($entry))) {
|
|
if (($entry < 0) || ($entry > 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
$mArgs = array();
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
$mArgs[] = $arg;
|
|
}
|
|
}
|
|
$mValueCount = count($mArgs);
|
|
if ($mValueCount > 0) {
|
|
sort($mArgs);
|
|
$count = self::COUNT($mArgs);
|
|
$index = $entry * ($count-1);
|
|
$iBase = floor($index);
|
|
if ($index == $iBase) {
|
|
return $mArgs[$index];
|
|
} else {
|
|
$iNext = $iBase + 1;
|
|
$iProportion = $index - $iBase;
|
|
return $mArgs[$iBase] + (($mArgs[$iNext] - $mArgs[$iBase]) * $iProportion) ;
|
|
}
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function PERCENTILE()
|
|
|
|
|
|
/**
|
|
* PERCENTRANK
|
|
*
|
|
* Returns the rank of a value in a data set as a percentage of the data set.
|
|
*
|
|
* @param array of number An array of, or a reference to, a list of numbers.
|
|
* @param number The number whose rank you want to find.
|
|
* @param number The number of significant digits for the returned percentage value.
|
|
* @return float
|
|
*/
|
|
public static function PERCENTRANK($valueSet,$value,$significance=3) {
|
|
$valueSet = PHPExcel_Calculation_Functions::flattenArray($valueSet);
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
$significance = (is_null($significance)) ? 3 : (integer) PHPExcel_Calculation_Functions::flattenSingleValue($significance);
|
|
|
|
foreach($valueSet as $key => $valueEntry) {
|
|
if (!is_numeric($valueEntry)) {
|
|
unset($valueSet[$key]);
|
|
}
|
|
}
|
|
sort($valueSet,SORT_NUMERIC);
|
|
$valueCount = count($valueSet);
|
|
if ($valueCount == 0) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
|
|
$valueAdjustor = $valueCount - 1;
|
|
if (($value < $valueSet[0]) || ($value > $valueSet[$valueAdjustor])) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
}
|
|
|
|
$pos = array_search($value,$valueSet);
|
|
if ($pos === False) {
|
|
$pos = 0;
|
|
$testValue = $valueSet[0];
|
|
while ($testValue < $value) {
|
|
$testValue = $valueSet[++$pos];
|
|
}
|
|
--$pos;
|
|
$pos += (($value - $valueSet[$pos]) / ($testValue - $valueSet[$pos]));
|
|
}
|
|
|
|
return round($pos / $valueAdjustor,$significance);
|
|
} // function PERCENTRANK()
|
|
|
|
|
|
/**
|
|
* PERMUT
|
|
*
|
|
* Returns the number of permutations for a given number of objects that can be
|
|
* selected from number objects. A permutation is any set or subset of objects or
|
|
* events where internal order is significant. Permutations are different from
|
|
* combinations, for which the internal order is not significant. Use this function
|
|
* for lottery-style probability calculations.
|
|
*
|
|
* @param int $numObjs Number of different objects
|
|
* @param int $numInSet Number of objects in each permutation
|
|
* @return int Number of permutations
|
|
*/
|
|
public static function PERMUT($numObjs,$numInSet) {
|
|
$numObjs = PHPExcel_Calculation_Functions::flattenSingleValue($numObjs);
|
|
$numInSet = PHPExcel_Calculation_Functions::flattenSingleValue($numInSet);
|
|
|
|
if ((is_numeric($numObjs)) && (is_numeric($numInSet))) {
|
|
$numInSet = floor($numInSet);
|
|
if ($numObjs < $numInSet) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
return round(PHPExcel_Calculation_MathTrig::FACT($numObjs) / PHPExcel_Calculation_MathTrig::FACT($numObjs - $numInSet));
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function PERMUT()
|
|
|
|
|
|
/**
|
|
* POISSON
|
|
*
|
|
* Returns the Poisson distribution. A common application of the Poisson distribution
|
|
* is predicting the number of events over a specific time, such as the number of
|
|
* cars arriving at a toll plaza in 1 minute.
|
|
*
|
|
* @param float $value
|
|
* @param float $mean Mean Value
|
|
* @param boolean $cumulative
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function POISSON($value, $mean, $cumulative) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
$mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
|
|
|
|
if ((is_numeric($value)) && (is_numeric($mean))) {
|
|
if (($value <= 0) || ($mean <= 0)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
|
|
if ($cumulative) {
|
|
$summer = 0;
|
|
for ($i = 0; $i <= floor($value); ++$i) {
|
|
$summer += pow($mean,$i) / PHPExcel_Calculation_MathTrig::FACT($i);
|
|
}
|
|
return exp(0-$mean) * $summer;
|
|
} else {
|
|
return (exp(0-$mean) * pow($mean,$value)) / PHPExcel_Calculation_MathTrig::FACT($value);
|
|
}
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function POISSON()
|
|
|
|
|
|
/**
|
|
* QUARTILE
|
|
*
|
|
* Returns the quartile of a data set.
|
|
*
|
|
* Excel Function:
|
|
* QUARTILE(value1[,value2[, ...]],entry)
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @param int $entry Quartile value in the range 1..3, inclusive.
|
|
* @return float
|
|
*/
|
|
public static function QUARTILE() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
|
// Calculate
|
|
$entry = floor(array_pop($aArgs));
|
|
|
|
if ((is_numeric($entry)) && (!is_string($entry))) {
|
|
$entry /= 4;
|
|
if (($entry < 0) || ($entry > 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
return self::PERCENTILE($aArgs,$entry);
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function QUARTILE()
|
|
|
|
|
|
/**
|
|
* RANK
|
|
*
|
|
* Returns the rank of a number in a list of numbers.
|
|
*
|
|
* @param number The number whose rank you want to find.
|
|
* @param array of number An array of, or a reference to, a list of numbers.
|
|
* @param mixed Order to sort the values in the value set
|
|
* @return float
|
|
*/
|
|
public static function RANK($value,$valueSet,$order=0) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
$valueSet = PHPExcel_Calculation_Functions::flattenArray($valueSet);
|
|
$order = (is_null($order)) ? 0 : (integer) PHPExcel_Calculation_Functions::flattenSingleValue($order);
|
|
|
|
foreach($valueSet as $key => $valueEntry) {
|
|
if (!is_numeric($valueEntry)) {
|
|
unset($valueSet[$key]);
|
|
}
|
|
}
|
|
|
|
if ($order == 0) {
|
|
rsort($valueSet,SORT_NUMERIC);
|
|
} else {
|
|
sort($valueSet,SORT_NUMERIC);
|
|
}
|
|
$pos = array_search($value,$valueSet);
|
|
if ($pos === False) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
}
|
|
|
|
return ++$pos;
|
|
} // function RANK()
|
|
|
|
|
|
/**
|
|
* RSQ
|
|
*
|
|
* Returns the square of the Pearson product moment correlation coefficient through data points in known_y's and known_x's.
|
|
*
|
|
* @param array of mixed Data Series Y
|
|
* @param array of mixed Data Series X
|
|
* @return float
|
|
*/
|
|
public static function RSQ($yValues,$xValues) {
|
|
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
}
|
|
$yValueCount = count($yValues);
|
|
$xValueCount = count($xValues);
|
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
} elseif ($yValueCount == 1) {
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
}
|
|
|
|
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
return $bestFitLinear->getGoodnessOfFit();
|
|
} // function RSQ()
|
|
|
|
|
|
/**
|
|
* SKEW
|
|
*
|
|
* Returns the skewness of a distribution. Skewness characterizes the degree of asymmetry
|
|
* of a distribution around its mean. Positive skewness indicates a distribution with an
|
|
* asymmetric tail extending toward more positive values. Negative skewness indicates a
|
|
* distribution with an asymmetric tail extending toward more negative values.
|
|
*
|
|
* @param array Data Series
|
|
* @return float
|
|
*/
|
|
public static function SKEW() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
$mean = self::AVERAGE($aArgs);
|
|
$stdDev = self::STDEV($aArgs);
|
|
|
|
$count = $summer = 0;
|
|
// Loop through arguments
|
|
foreach ($aArgs as $k => $arg) {
|
|
if ((is_bool($arg)) &&
|
|
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
} else {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
$summer += pow((($arg - $mean) / $stdDev),3) ;
|
|
++$count;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if ($count > 2) {
|
|
return $summer * ($count / (($count-1) * ($count-2)));
|
|
}
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
} // function SKEW()
|
|
|
|
|
|
/**
|
|
* SLOPE
|
|
*
|
|
* Returns the slope of the linear regression line through data points in known_y's and known_x's.
|
|
*
|
|
* @param array of mixed Data Series Y
|
|
* @param array of mixed Data Series X
|
|
* @return float
|
|
*/
|
|
public static function SLOPE($yValues,$xValues) {
|
|
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
}
|
|
$yValueCount = count($yValues);
|
|
$xValueCount = count($xValues);
|
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
} elseif ($yValueCount == 1) {
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
}
|
|
|
|
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
return $bestFitLinear->getSlope();
|
|
} // function SLOPE()
|
|
|
|
|
|
/**
|
|
* SMALL
|
|
*
|
|
* Returns the nth smallest value in a data set. You can use this function to
|
|
* select a value based on its relative standing.
|
|
*
|
|
* Excel Function:
|
|
* SMALL(value1[,value2[, ...]],entry)
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @param int $entry Position (ordered from the smallest) in the array or range of data to return
|
|
* @return float
|
|
*/
|
|
public static function SMALL() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
|
// Calculate
|
|
$entry = array_pop($aArgs);
|
|
|
|
if ((is_numeric($entry)) && (!is_string($entry))) {
|
|
$mArgs = array();
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
$mArgs[] = $arg;
|
|
}
|
|
}
|
|
$count = self::COUNT($mArgs);
|
|
$entry = floor(--$entry);
|
|
if (($entry < 0) || ($entry >= $count) || ($count == 0)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
sort($mArgs);
|
|
return $mArgs[$entry];
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function SMALL()
|
|
|
|
|
|
/**
|
|
* STANDARDIZE
|
|
*
|
|
* Returns a normalized value from a distribution characterized by mean and standard_dev.
|
|
*
|
|
* @param float $value Value to normalize
|
|
* @param float $mean Mean Value
|
|
* @param float $stdDev Standard Deviation
|
|
* @return float Standardized value
|
|
*/
|
|
public static function STANDARDIZE($value,$mean,$stdDev) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
$mean = PHPExcel_Calculation_Functions::flattenSingleValue($mean);
|
|
$stdDev = PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
|
|
|
|
if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
|
|
if ($stdDev <= 0) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
return ($value - $mean) / $stdDev ;
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function STANDARDIZE()
|
|
|
|
|
|
/**
|
|
* STDEV
|
|
*
|
|
* Estimates standard deviation based on a sample. The standard deviation is a measure of how
|
|
* widely values are dispersed from the average value (the mean).
|
|
*
|
|
* Excel Function:
|
|
* STDEV(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function STDEV() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
$aMean = self::AVERAGE($aArgs);
|
|
if (!is_null($aMean)) {
|
|
$aCount = -1;
|
|
foreach ($aArgs as $k => $arg) {
|
|
if ((is_bool($arg)) &&
|
|
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
|
|
$arg = (integer) $arg;
|
|
}
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
if (is_null($returnValue)) {
|
|
$returnValue = pow(($arg - $aMean),2);
|
|
} else {
|
|
$returnValue += pow(($arg - $aMean),2);
|
|
}
|
|
++$aCount;
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if (($aCount > 0) && ($returnValue >= 0)) {
|
|
return sqrt($returnValue / $aCount);
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
} // function STDEV()
|
|
|
|
|
|
/**
|
|
* STDEVA
|
|
*
|
|
* Estimates standard deviation based on a sample, including numbers, text, and logical values
|
|
*
|
|
* Excel Function:
|
|
* STDEVA(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function STDEVA() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
$aMean = self::AVERAGEA($aArgs);
|
|
if (!is_null($aMean)) {
|
|
$aCount = -1;
|
|
foreach ($aArgs as $k => $arg) {
|
|
if ((is_bool($arg)) &&
|
|
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
} else {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
|
|
if (is_bool($arg)) {
|
|
$arg = (integer) $arg;
|
|
} elseif (is_string($arg)) {
|
|
$arg = 0;
|
|
}
|
|
if (is_null($returnValue)) {
|
|
$returnValue = pow(($arg - $aMean),2);
|
|
} else {
|
|
$returnValue += pow(($arg - $aMean),2);
|
|
}
|
|
++$aCount;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if (($aCount > 0) && ($returnValue >= 0)) {
|
|
return sqrt($returnValue / $aCount);
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
} // function STDEVA()
|
|
|
|
|
|
/**
|
|
* STDEVP
|
|
*
|
|
* Calculates standard deviation based on the entire population
|
|
*
|
|
* Excel Function:
|
|
* STDEVP(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function STDEVP() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
$aMean = self::AVERAGE($aArgs);
|
|
if (!is_null($aMean)) {
|
|
$aCount = 0;
|
|
foreach ($aArgs as $k => $arg) {
|
|
if ((is_bool($arg)) &&
|
|
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
|
|
$arg = (integer) $arg;
|
|
}
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
if (is_null($returnValue)) {
|
|
$returnValue = pow(($arg - $aMean),2);
|
|
} else {
|
|
$returnValue += pow(($arg - $aMean),2);
|
|
}
|
|
++$aCount;
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if (($aCount > 0) && ($returnValue >= 0)) {
|
|
return sqrt($returnValue / $aCount);
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
} // function STDEVP()
|
|
|
|
|
|
/**
|
|
* STDEVPA
|
|
*
|
|
* Calculates standard deviation based on the entire population, including numbers, text, and logical values
|
|
*
|
|
* Excel Function:
|
|
* STDEVPA(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function STDEVPA() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
|
|
// Return value
|
|
$returnValue = null;
|
|
|
|
$aMean = self::AVERAGEA($aArgs);
|
|
if (!is_null($aMean)) {
|
|
$aCount = 0;
|
|
foreach ($aArgs as $k => $arg) {
|
|
if ((is_bool($arg)) &&
|
|
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
} else {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
|
|
if (is_bool($arg)) {
|
|
$arg = (integer) $arg;
|
|
} elseif (is_string($arg)) {
|
|
$arg = 0;
|
|
}
|
|
if (is_null($returnValue)) {
|
|
$returnValue = pow(($arg - $aMean),2);
|
|
} else {
|
|
$returnValue += pow(($arg - $aMean),2);
|
|
}
|
|
++$aCount;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if (($aCount > 0) && ($returnValue >= 0)) {
|
|
return sqrt($returnValue / $aCount);
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
} // function STDEVPA()
|
|
|
|
|
|
/**
|
|
* STEYX
|
|
*
|
|
* Returns the standard error of the predicted y-value for each x in the regression.
|
|
*
|
|
* @param array of mixed Data Series Y
|
|
* @param array of mixed Data Series X
|
|
* @return float
|
|
*/
|
|
public static function STEYX($yValues,$xValues) {
|
|
if (!self::_checkTrendArrays($yValues,$xValues)) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
}
|
|
$yValueCount = count($yValues);
|
|
$xValueCount = count($xValues);
|
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
} elseif ($yValueCount == 1) {
|
|
return PHPExcel_Calculation_Functions::DIV0();
|
|
}
|
|
|
|
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
|
|
return $bestFitLinear->getStdevOfResiduals();
|
|
} // function STEYX()
|
|
|
|
|
|
/**
|
|
* TDIST
|
|
*
|
|
* Returns the probability of Student's T distribution.
|
|
*
|
|
* @param float $value Value for the function
|
|
* @param float $degrees degrees of freedom
|
|
* @param float $tails number of tails (1 or 2)
|
|
* @return float
|
|
*/
|
|
public static function TDIST($value, $degrees, $tails) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
$degrees = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));
|
|
$tails = floor(PHPExcel_Calculation_Functions::flattenSingleValue($tails));
|
|
|
|
if ((is_numeric($value)) && (is_numeric($degrees)) && (is_numeric($tails))) {
|
|
if (($value < 0) || ($degrees < 1) || ($tails < 1) || ($tails > 2)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
// tdist, which finds the probability that corresponds to a given value
|
|
// of t with k degrees of freedom. This algorithm is translated from a
|
|
// pascal function on p81 of "Statistical Computing in Pascal" by D
|
|
// Cooke, A H Craven & G M Clark (1985: Edward Arnold (Pubs.) Ltd:
|
|
// London). The above Pascal algorithm is itself a translation of the
|
|
// fortran algoritm "AS 3" by B E Cooper of the Atlas Computer
|
|
// Laboratory as reported in (among other places) "Applied Statistics
|
|
// Algorithms", editied by P Griffiths and I D Hill (1985; Ellis
|
|
// Horwood Ltd.; W. Sussex, England).
|
|
$tterm = $degrees;
|
|
$ttheta = atan2($value,sqrt($tterm));
|
|
$tc = cos($ttheta);
|
|
$ts = sin($ttheta);
|
|
$tsum = 0;
|
|
|
|
if (($degrees % 2) == 1) {
|
|
$ti = 3;
|
|
$tterm = $tc;
|
|
} else {
|
|
$ti = 2;
|
|
$tterm = 1;
|
|
}
|
|
|
|
$tsum = $tterm;
|
|
while ($ti < $degrees) {
|
|
$tterm *= $tc * $tc * ($ti - 1) / $ti;
|
|
$tsum += $tterm;
|
|
$ti += 2;
|
|
}
|
|
$tsum *= $ts;
|
|
if (($degrees % 2) == 1) { $tsum = M_2DIVPI * ($tsum + $ttheta); }
|
|
$tValue = 0.5 * (1 + $tsum);
|
|
if ($tails == 1) {
|
|
return 1 - abs($tValue);
|
|
} else {
|
|
return 1 - abs((1 - $tValue) - $tValue);
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function TDIST()
|
|
|
|
|
|
/**
|
|
* TINV
|
|
*
|
|
* Returns the one-tailed probability of the chi-squared distribution.
|
|
*
|
|
* @param float $probability Probability for the function
|
|
* @param float $degrees degrees of freedom
|
|
* @return float
|
|
*/
|
|
public static function TINV($probability, $degrees) {
|
|
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
|
|
$degrees = floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));
|
|
|
|
if ((is_numeric($probability)) && (is_numeric($degrees))) {
|
|
$xLo = 100;
|
|
$xHi = 0;
|
|
|
|
$x = $xNew = 1;
|
|
$dx = 1;
|
|
$i = 0;
|
|
|
|
while ((abs($dx) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
|
|
// Apply Newton-Raphson step
|
|
$result = self::TDIST($x, $degrees, 2);
|
|
$error = $result - $probability;
|
|
if ($error == 0.0) {
|
|
$dx = 0;
|
|
} elseif ($error < 0.0) {
|
|
$xLo = $x;
|
|
} else {
|
|
$xHi = $x;
|
|
}
|
|
// Avoid division by zero
|
|
if ($result != 0.0) {
|
|
$dx = $error / $result;
|
|
$xNew = $x - $dx;
|
|
}
|
|
// If the NR fails to converge (which for example may be the
|
|
// case if the initial guess is too rough) we apply a bisection
|
|
// step to determine a more narrow interval around the root.
|
|
if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0)) {
|
|
$xNew = ($xLo + $xHi) / 2;
|
|
$dx = $xNew - $x;
|
|
}
|
|
$x = $xNew;
|
|
}
|
|
if ($i == MAX_ITERATIONS) {
|
|
return PHPExcel_Calculation_Functions::NA();
|
|
}
|
|
return round($x,12);
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function TINV()
|
|
|
|
|
|
/**
|
|
* TREND
|
|
*
|
|
* Returns values along a linear trend
|
|
*
|
|
* @param array of mixed Data Series Y
|
|
* @param array of mixed Data Series X
|
|
* @param array of mixed Values of X for which we want to find Y
|
|
* @param boolean A logical value specifying whether to force the intersect to equal 0.
|
|
* @return array of float
|
|
*/
|
|
public static function TREND($yValues,$xValues=array(),$newValues=array(),$const=True) {
|
|
$yValues = PHPExcel_Calculation_Functions::flattenArray($yValues);
|
|
$xValues = PHPExcel_Calculation_Functions::flattenArray($xValues);
|
|
$newValues = PHPExcel_Calculation_Functions::flattenArray($newValues);
|
|
$const = (is_null($const)) ? True : (boolean) PHPExcel_Calculation_Functions::flattenSingleValue($const);
|
|
|
|
$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues,$const);
|
|
if (empty($newValues)) {
|
|
$newValues = $bestFitLinear->getXValues();
|
|
}
|
|
|
|
$returnArray = array();
|
|
foreach($newValues as $xValue) {
|
|
$returnArray[0][] = $bestFitLinear->getValueOfYForX($xValue);
|
|
}
|
|
|
|
return $returnArray;
|
|
} // function TREND()
|
|
|
|
|
|
/**
|
|
* TRIMMEAN
|
|
*
|
|
* Returns the mean of the interior of a data set. TRIMMEAN calculates the mean
|
|
* taken by excluding a percentage of data points from the top and bottom tails
|
|
* of a data set.
|
|
*
|
|
* Excel Function:
|
|
* TRIMEAN(value1[,value2[, ...]],$discard)
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @param float $discard Percentage to discard
|
|
* @return float
|
|
*/
|
|
public static function TRIMMEAN() {
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
|
|
// Calculate
|
|
$percent = array_pop($aArgs);
|
|
|
|
if ((is_numeric($percent)) && (!is_string($percent))) {
|
|
if (($percent < 0) || ($percent > 1)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
$mArgs = array();
|
|
foreach ($aArgs as $arg) {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
$mArgs[] = $arg;
|
|
}
|
|
}
|
|
$discard = floor(self::COUNT($mArgs) * $percent / 2);
|
|
sort($mArgs);
|
|
for ($i=0; $i < $discard; ++$i) {
|
|
array_pop($mArgs);
|
|
array_shift($mArgs);
|
|
}
|
|
return self::AVERAGE($mArgs);
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function TRIMMEAN()
|
|
|
|
|
|
/**
|
|
* VARFunc
|
|
*
|
|
* Estimates variance based on a sample.
|
|
*
|
|
* Excel Function:
|
|
* VAR(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function VARFunc() {
|
|
// Return value
|
|
$returnValue = PHPExcel_Calculation_Functions::DIV0();
|
|
|
|
$summerA = $summerB = 0;
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
$aCount = 0;
|
|
foreach ($aArgs as $arg) {
|
|
if (is_bool($arg)) { $arg = (integer) $arg; }
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
$summerA += ($arg * $arg);
|
|
$summerB += $arg;
|
|
++$aCount;
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if ($aCount > 1) {
|
|
$summerA *= $aCount;
|
|
$summerB *= $summerB;
|
|
$returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
|
|
}
|
|
return $returnValue;
|
|
} // function VARFunc()
|
|
|
|
|
|
/**
|
|
* VARA
|
|
*
|
|
* Estimates variance based on a sample, including numbers, text, and logical values
|
|
*
|
|
* Excel Function:
|
|
* VARA(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function VARA() {
|
|
// Return value
|
|
$returnValue = PHPExcel_Calculation_Functions::DIV0();
|
|
|
|
$summerA = $summerB = 0;
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
$aCount = 0;
|
|
foreach ($aArgs as $k => $arg) {
|
|
if ((is_string($arg)) &&
|
|
(PHPExcel_Calculation_Functions::isValue($k))) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} elseif ((is_string($arg)) &&
|
|
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
} else {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
|
|
if (is_bool($arg)) {
|
|
$arg = (integer) $arg;
|
|
} elseif (is_string($arg)) {
|
|
$arg = 0;
|
|
}
|
|
$summerA += ($arg * $arg);
|
|
$summerB += $arg;
|
|
++$aCount;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if ($aCount > 1) {
|
|
$summerA *= $aCount;
|
|
$summerB *= $summerB;
|
|
$returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
|
|
}
|
|
return $returnValue;
|
|
} // function VARA()
|
|
|
|
|
|
/**
|
|
* VARP
|
|
*
|
|
* Calculates variance based on the entire population
|
|
*
|
|
* Excel Function:
|
|
* VARP(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function VARP() {
|
|
// Return value
|
|
$returnValue = PHPExcel_Calculation_Functions::DIV0();
|
|
|
|
$summerA = $summerB = 0;
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
|
|
$aCount = 0;
|
|
foreach ($aArgs as $arg) {
|
|
if (is_bool($arg)) { $arg = (integer) $arg; }
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) && (!is_string($arg))) {
|
|
$summerA += ($arg * $arg);
|
|
$summerB += $arg;
|
|
++$aCount;
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if ($aCount > 0) {
|
|
$summerA *= $aCount;
|
|
$summerB *= $summerB;
|
|
$returnValue = ($summerA - $summerB) / ($aCount * $aCount);
|
|
}
|
|
return $returnValue;
|
|
} // function VARP()
|
|
|
|
|
|
/**
|
|
* VARPA
|
|
*
|
|
* Calculates variance based on the entire population, including numbers, text, and logical values
|
|
*
|
|
* Excel Function:
|
|
* VARPA(value1[,value2[, ...]])
|
|
*
|
|
* @access public
|
|
* @category Statistical Functions
|
|
* @param mixed $arg,... Data values
|
|
* @return float
|
|
*/
|
|
public static function VARPA() {
|
|
// Return value
|
|
$returnValue = PHPExcel_Calculation_Functions::DIV0();
|
|
|
|
$summerA = $summerB = 0;
|
|
|
|
// Loop through arguments
|
|
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
|
|
$aCount = 0;
|
|
foreach ($aArgs as $k => $arg) {
|
|
if ((is_string($arg)) &&
|
|
(PHPExcel_Calculation_Functions::isValue($k))) {
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} elseif ((is_string($arg)) &&
|
|
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
|
|
} else {
|
|
// Is it a numeric value?
|
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) {
|
|
if (is_bool($arg)) {
|
|
$arg = (integer) $arg;
|
|
} elseif (is_string($arg)) {
|
|
$arg = 0;
|
|
}
|
|
$summerA += ($arg * $arg);
|
|
$summerB += $arg;
|
|
++$aCount;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Return
|
|
if ($aCount > 0) {
|
|
$summerA *= $aCount;
|
|
$summerB *= $summerB;
|
|
$returnValue = ($summerA - $summerB) / ($aCount * $aCount);
|
|
}
|
|
return $returnValue;
|
|
} // function VARPA()
|
|
|
|
|
|
/**
|
|
* WEIBULL
|
|
*
|
|
* Returns the Weibull distribution. Use this distribution in reliability
|
|
* analysis, such as calculating a device's mean time to failure.
|
|
*
|
|
* @param float $value
|
|
* @param float $alpha Alpha Parameter
|
|
* @param float $beta Beta Parameter
|
|
* @param boolean $cumulative
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function WEIBULL($value, $alpha, $beta, $cumulative) {
|
|
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
|
|
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
|
|
$beta = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
|
|
|
|
if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta))) {
|
|
if (($value < 0) || ($alpha <= 0) || ($beta <= 0)) {
|
|
return PHPExcel_Calculation_Functions::NaN();
|
|
}
|
|
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
|
|
if ($cumulative) {
|
|
return 1 - exp(0 - pow($value / $beta,$alpha));
|
|
} else {
|
|
return ($alpha / pow($beta,$alpha)) * pow($value,$alpha - 1) * exp(0 - pow($value / $beta,$alpha));
|
|
}
|
|
}
|
|
}
|
|
return PHPExcel_Calculation_Functions::VALUE();
|
|
} // function WEIBULL()
|
|
|
|
|
|
/**
|
|
* ZTEST
|
|
*
|
|
* Returns the Weibull distribution. Use this distribution in reliability
|
|
* analysis, such as calculating a device's mean time to failure.
|
|
*
|
|
* @param float $dataSet
|
|
* @param float $m0 Alpha Parameter
|
|
* @param float $sigma Beta Parameter
|
|
* @param boolean $cumulative
|
|
* @return float
|
|
*
|
|
*/
|
|
public static function ZTEST($dataSet, $m0, $sigma = NULL) {
|
|
$dataSet = PHPExcel_Calculation_Functions::flattenArrayIndexed($dataSet);
|
|
$m0 = PHPExcel_Calculation_Functions::flattenSingleValue($m0);
|
|
$sigma = PHPExcel_Calculation_Functions::flattenSingleValue($sigma);
|
|
|
|
if (is_null($sigma)) {
|
|
$sigma = self::STDEV($dataSet);
|
|
}
|
|
$n = count($dataSet);
|
|
|
|
return 1 - self::NORMSDIST((self::AVERAGE($dataSet) - $m0)/($sigma/SQRT($n)));
|
|
} // function ZTEST()
|
|
|
|
} // class PHPExcel_Calculation_Statistical
|