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Statistical.php
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Statistical.php
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<?php
/**
* PHPExcel
*
* Copyright (c) 2006 - 2012 PHPExcel
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*
* @category PHPExcel
* @package PHPExcel_Calculation
* @copyright Copyright (c) 2006 - 2012 PHPExcel (http://www.codeplex.com/PHPExcel)
* @license http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt LGPL
* @version ##VERSION##, ##DATE##
*/
/** PHPExcel root directory */
if (!defined('PHPEXCEL_ROOT')) {
/**
* @ignore
*/
define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
}
require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/trend/trendClass.php';
/** LOG_GAMMA_X_MAX_VALUE */
define('LOG_GAMMA_X_MAX_VALUE', 2.55e305);
/** XMININ */
define('XMININ', 2.23e-308);
/** EPS */
define('EPS', 2.22e-16);
/** SQRT2PI */
define('SQRT2PI', 2.5066282746310005024157652848110452530069867406099);
/**
* PHPExcel_Calculation_Statistical
*
* @category PHPExcel
* @package PHPExcel_Calculation
* @copyright Copyright (c) 2006 - 2012 PHPExcel (http://www.codeplex.com/PHPExcel)
*/
class PHPExcel_Calculation_Statistical {
private static function _checkTrendArrays(&$array1,&$array2) {
if (!is_array($array1)) { $array1 = array($array1); }
if (!is_array($array2)) { $array2 = array($array2); }
$array1 = PHPExcel_Calculation_Functions::flattenArray($array1);
$array2 = PHPExcel_Calculation_Functions::flattenArray($array2);
foreach($array1 as $key => $value) {
if ((is_bool($value)) || (is_string($value)) || (is_null($value))) {
unset($array1[$key]);
unset($array2[$key]);
}
}
foreach($array2 as $key => $value) {
if ((is_bool($value)) || (is_string($value)) || (is_null($value))) {
unset($array1[$key]);
unset($array2[$key]);
}
}
$array1 = array_merge($array1);
$array2 = array_merge($array2);
return True;
} // function _checkTrendArrays()
/**
* Beta function.
*
* @author Jaco van Kooten
*
* @param p require p>0
* @param q require q>0
* @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
*/
private static function _beta($p, $q) {
if ($p <= 0.0 || $q <= 0.0 || ($p + $q) > LOG_GAMMA_X_MAX_VALUE) {
return 0.0;
} else {
return exp(self::_logBeta($p, $q));
}
} // function _beta()
/**
* Incomplete beta function
*
* @author Jaco van Kooten
* @author Paul Meagher
*
* The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992).
* @param x require 0<=x<=1
* @param p require p>0
* @param q require q>0
* @return 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow
*/
private static function _incompleteBeta($x, $p, $q) {
if ($x <= 0.0) {
return 0.0;
} elseif ($x >= 1.0) {
return 1.0;
} elseif (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) {
return 0.0;
}
$beta_gam = exp((0 - self::_logBeta($p, $q)) + $p * log($x) + $q * log(1.0 - $x));
if ($x < ($p + 1.0) / ($p + $q + 2.0)) {
return $beta_gam * self::_betaFraction($x, $p, $q) / $p;
} else {
return 1.0 - ($beta_gam * self::_betaFraction(1 - $x, $q, $p) / $q);
}
} // function _incompleteBeta()
// Function cache for _logBeta function
private static $_logBetaCache_p = 0.0;
private static $_logBetaCache_q = 0.0;
private static $_logBetaCache_result = 0.0;
/**
* The natural logarithm of the beta function.
*
* @param p require p>0
* @param q require q>0
* @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
* @author Jaco van Kooten
*/
private static function _logBeta($p, $q) {
if ($p != self::$_logBetaCache_p || $q != self::$_logBetaCache_q) {
self::$_logBetaCache_p = $p;
self::$_logBetaCache_q = $q;
if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) {
self::$_logBetaCache_result = 0.0;
} else {
self::$_logBetaCache_result = self::_logGamma($p) + self::_logGamma($q) - self::_logGamma($p + $q);
}
}
return self::$_logBetaCache_result;
} // function _logBeta()
/**
* Evaluates of continued fraction part of incomplete beta function.
* Based on an idea from Numerical Recipes (W.H. Press et al, 1992).
* @author Jaco van Kooten
*/
private static function _betaFraction($x, $p, $q) {
$c = 1.0;
$sum_pq = $p + $q;
$p_plus = $p + 1.0;
$p_minus = $p - 1.0;
$h = 1.0 - $sum_pq * $x / $p_plus;
if (abs($h) < XMININ) {
$h = XMININ;
}
$h = 1.0 / $h;
$frac = $h;
$m = 1;
$delta = 0.0;
while ($m <= MAX_ITERATIONS && abs($delta-1.0) > PRECISION ) {
$m2 = 2 * $m;
// even index for d
$d = $m * ($q - $m) * $x / ( ($p_minus + $m2) * ($p + $m2));
$h = 1.0 + $d * $h;
if (abs($h) < XMININ) {
$h = XMININ;
}
$h = 1.0 / $h;
$c = 1.0 + $d / $c;
if (abs($c) < XMININ) {
$c = XMININ;
}
$frac *= $h * $c;
// odd index for d
$d = -($p + $m) * ($sum_pq + $m) * $x / (($p + $m2) * ($p_plus + $m2));
$h = 1.0 + $d * $h;
if (abs($h) < XMININ) {
$h = XMININ;
}
$h = 1.0 / $h;
$c = 1.0 + $d / $c;
if (abs($c) < XMININ) {
$c = XMININ;
}
$delta = $h * $c;
$frac *= $delta;
++$m;
}
return $frac;
} // function _betaFraction()
/**
* logGamma function
*
* @version 1.1
* @author Jaco van Kooten
*
* Original author was Jaco van Kooten. Ported to PHP by Paul Meagher.
*
* The natural logarithm of the gamma function. <br />
* Based on public domain NETLIB (Fortran) code by W. J. Cody and L. Stoltz <br />
* Applied Mathematics Division <br />
* Argonne National Laboratory <br />
* Argonne, IL 60439 <br />
* <p>
* References:
* <ol>
* <li>W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural
* Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203.</li>
* <li>K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969.</li>
* <li>Hart, Et. Al., Computer Approximations, Wiley and sons, New York, 1968.</li>
* </ol>
* </p>
* <p>
* From the original documentation:
* </p>
* <p>
* This routine calculates the LOG(GAMMA) function for a positive real argument X.
* Computation is based on an algorithm outlined in references 1 and 2.
* The program uses rational functions that theoretically approximate LOG(GAMMA)
* to at least 18 significant decimal digits. The approximation for X > 12 is from
* reference 3, while approximations for X < 12.0 are similar to those in reference
* 1, but are unpublished. The accuracy achieved depends on the arithmetic system,
* the compiler, the intrinsic functions, and proper selection of the
* machine-dependent constants.
* </p>
* <p>
* Error returns: <br />
* The program returns the value XINF for X .LE. 0.0 or when overflow would occur.
* The computation is believed to be free of underflow and overflow.
* </p>
* @return MAX_VALUE for x < 0.0 or when overflow would occur, i.e. x > 2.55E305
*/
// Function cache for logGamma
private static $_logGammaCache_result = 0.0;
private static $_logGammaCache_x = 0.0;
private static function _logGamma($x) {
// Log Gamma related constants
static $lg_d1 = -0.5772156649015328605195174;
static $lg_d2 = 0.4227843350984671393993777;
static $lg_d4 = 1.791759469228055000094023;
static $lg_p1 = array( 4.945235359296727046734888,
201.8112620856775083915565,
2290.838373831346393026739,
11319.67205903380828685045,
28557.24635671635335736389,
38484.96228443793359990269,
26377.48787624195437963534,
7225.813979700288197698961 );
static $lg_p2 = array( 4.974607845568932035012064,
542.4138599891070494101986,
15506.93864978364947665077,
184793.2904445632425417223,
1088204.76946882876749847,
3338152.967987029735917223,
5106661.678927352456275255,
3074109.054850539556250927 );
static $lg_p4 = array( 14745.02166059939948905062,
2426813.369486704502836312,
121475557.4045093227939592,
2663432449.630976949898078,
29403789566.34553899906876,
170266573776.5398868392998,
492612579337.743088758812,
560625185622.3951465078242 );
static $lg_q1 = array( 67.48212550303777196073036,
1113.332393857199323513008,
7738.757056935398733233834,
27639.87074403340708898585,
54993.10206226157329794414,
61611.22180066002127833352,
36351.27591501940507276287,
8785.536302431013170870835 );
static $lg_q2 = array( 183.0328399370592604055942,
7765.049321445005871323047,
133190.3827966074194402448,
1136705.821321969608938755,
5267964.117437946917577538,
13467014.54311101692290052,
17827365.30353274213975932,
9533095.591844353613395747 );
static $lg_q4 = array( 2690.530175870899333379843,
639388.5654300092398984238,
41355999.30241388052042842,
1120872109.61614794137657,
14886137286.78813811542398,
101680358627.2438228077304,
341747634550.7377132798597,
446315818741.9713286462081 );
static $lg_c = array( -0.001910444077728,
8.4171387781295e-4,
-5.952379913043012e-4,
7.93650793500350248e-4,
-0.002777777777777681622553,
0.08333333333333333331554247,
0.0057083835261 );
// Rough estimate of the fourth root of logGamma_xBig
static $lg_frtbig = 2.25e76;
static $pnt68 = 0.6796875;
if ($x == self::$_logGammaCache_x) {
return self::$_logGammaCache_result;
}
$y = $x;
if ($y > 0.0 && $y <= LOG_GAMMA_X_MAX_VALUE) {
if ($y <= EPS) {
$res = -log(y);
} elseif ($y <= 1.5) {
// ---------------------
// EPS .LT. X .LE. 1.5
// ---------------------
if ($y < $pnt68) {
$corr = -log($y);
$xm1 = $y;
} else {
$corr = 0.0;
$xm1 = $y - 1.0;
}
if ($y <= 0.5 || $y >= $pnt68) {
$xden = 1.0;
$xnum = 0.0;
for ($i = 0; $i < 8; ++$i) {
$xnum = $xnum * $xm1 + $lg_p1[$i];
$xden = $xden * $xm1 + $lg_q1[$i];
}
$res = $corr + $xm1 * ($lg_d1 + $xm1 * ($xnum / $xden));
} else {
$xm2 = $y - 1.0;
$xden = 1.0;
$xnum = 0.0;
for ($i = 0; $i < 8; ++$i) {
$xnum = $xnum * $xm2 + $lg_p2[$i];
$xden = $xden * $xm2 + $lg_q2[$i];
}
$res = $corr + $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
}
} elseif ($y <= 4.0) {
// ---------------------
// 1.5 .LT. X .LE. 4.0
// ---------------------
$xm2 = $y - 2.0;
$xden = 1.0;
$xnum = 0.0;
for ($i = 0; $i < 8; ++$i) {
$xnum = $xnum * $xm2 + $lg_p2[$i];
$xden = $xden * $xm2 + $lg_q2[$i];
}
$res = $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
} elseif ($y <= 12.0) {
// ----------------------
// 4.0 .LT. X .LE. 12.0
// ----------------------
$xm4 = $y - 4.0;
$xden = -1.0;
$xnum = 0.0;
for ($i = 0; $i < 8; ++$i) {
$xnum = $xnum * $xm4 + $lg_p4[$i];
$xden = $xden * $xm4 + $lg_q4[$i];
}
$res = $lg_d4 + $xm4 * ($xnum / $xden);
} else {
// ---------------------------------
// Evaluate for argument .GE. 12.0
// ---------------------------------
$res = 0.0;
if ($y <= $lg_frtbig) {
$res = $lg_c[6];
$ysq = $y * $y;
for ($i = 0; $i < 6; ++$i)
$res = $res / $ysq + $lg_c[$i];
}
$res /= $y;
$corr = log($y);
$res = $res + log(SQRT2PI) - 0.5 * $corr;
$res += $y * ($corr - 1.0);
}
} else {
// --------------------------
// Return for bad arguments
// --------------------------
$res = MAX_VALUE;
}
// ------------------------------
// Final adjustments and return
// ------------------------------
self::$_logGammaCache_x = $x;
self::$_logGammaCache_result = $res;
return $res;
} // function _logGamma()
//
// Private implementation of the incomplete Gamma function
//
private static function _incompleteGamma($a,$x) {
static $max = 32;
$summer = 0;
for ($n=0; $n<=$max; ++$n) {
$divisor = $a;
for ($i=1; $i<=$n; ++$i) {
$divisor *= ($a + $i);
}
$summer += (pow($x,$n) / $divisor);
}
return pow($x,$a) * exp(0-$x) * $summer;
} // function _incompleteGamma()
//
// Private implementation of the Gamma function
//
private static function _gamma($data) {
if ($data == 0.0) return 0;
static $p0 = 1.000000000190015;
static $p = array ( 1 => 76.18009172947146,
2 => -86.50532032941677,
3 => 24.01409824083091,
4 => -1.231739572450155,
5 => 1.208650973866179e-3,
6 => -5.395239384953e-6
);
$y = $x = $data;
$tmp = $x + 5.5;
$tmp -= ($x + 0.5) * log($tmp);
$summer = $p0;
for ($j=1;$j<=6;++$j) {
$summer += ($p[$j] / ++$y);
}
return exp(0 - $tmp + log(SQRT2PI * $summer / $x));
} // function _gamma()
/***************************************************************************
* inverse_ncdf.php
* -------------------
* begin : Friday, January 16, 2004
* copyright : (C) 2004 Michael Nickerson
* email : nickersonm@yahoo.com
*
***************************************************************************/
private static function _inverse_ncdf($p) {
// Inverse ncdf approximation by Peter J. Acklam, implementation adapted to
// PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
// a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
// I have not checked the accuracy of this implementation. Be aware that PHP
// will truncate the coeficcients to 14 digits.
// You have permission to use and distribute this function freely for
// whatever purpose you want, but please show common courtesy and give credit
// where credit is due.
// Input paramater is $p - probability - where 0 < p < 1.
// Coefficients in rational approximations
static $a = array( 1 => -3.969683028665376e+01,
2 => 2.209460984245205e+02,
3 => -2.759285104469687e+02,
4 => 1.383577518672690e+02,
5 => -3.066479806614716e+01,
6 => 2.506628277459239e+00
);
static $b = array( 1 => -5.447609879822406e+01,
2 => 1.615858368580409e+02,
3 => -1.556989798598866e+02,
4 => 6.680131188771972e+01,
5 => -1.328068155288572e+01
);
static $c = array( 1 => -7.784894002430293e-03,
2 => -3.223964580411365e-01,
3 => -2.400758277161838e+00,
4 => -2.549732539343734e+00,
5 => 4.374664141464968e+00,
6 => 2.938163982698783e+00
);
static $d = array( 1 => 7.784695709041462e-03,
2 => 3.224671290700398e-01,
3 => 2.445134137142996e+00,
4 => 3.754408661907416e+00
);
// Define lower and upper region break-points.
$p_low = 0.02425; //Use lower region approx. below this
$p_high = 1 - $p_low; //Use upper region approx. above this
if (0 < $p && $p < $p_low) {
// Rational approximation for lower region.
$q = sqrt(-2 * log($p));
return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
} elseif ($p_low <= $p && $p <= $p_high) {
// Rational approximation for central region.
$q = $p - 0.5;
$r = $q * $q;
return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q /
((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1);
} elseif ($p_high < $p && $p < 1) {
// Rational approximation for upper region.
$q = sqrt(-2 * log(1 - $p));
return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
}
// If 0 < p < 1, return a null value
return PHPExcel_Calculation_Functions::NULL();
} // function _inverse_ncdf()
private static function _inverse_ncdf2($prob) {
// Approximation of inverse standard normal CDF developed by
// B. Moro, "The Full Monte," Risk 8(2), Feb 1995, 57-58.
$a1 = 2.50662823884;
$a2 = -18.61500062529;
$a3 = 41.39119773534;
$a4 = -25.44106049637;
$b1 = -8.4735109309;
$b2 = 23.08336743743;
$b3 = -21.06224101826;
$b4 = 3.13082909833;
$c1 = 0.337475482272615;
$c2 = 0.976169019091719;
$c3 = 0.160797971491821;
$c4 = 2.76438810333863E-02;
$c5 = 3.8405729373609E-03;
$c6 = 3.951896511919E-04;
$c7 = 3.21767881768E-05;
$c8 = 2.888167364E-07;
$c9 = 3.960315187E-07;
$y = $prob - 0.5;
if (abs($y) < 0.42) {
$z = ($y * $y);
$z = $y * ((($a4 * $z + $a3) * $z + $a2) * $z + $a1) / (((($b4 * $z + $b3) * $z + $b2) * $z + $b1) * $z + 1);
} else {
if ($y > 0) {
$z = log(-log(1 - $prob));
} else {
$z = log(-log($prob));
}
$z = $c1 + $z * ($c2 + $z * ($c3 + $z * ($c4 + $z * ($c5 + $z * ($c6 + $z * ($c7 + $z * ($c8 + $z * $c9)))))));
if ($y < 0) {
$z = -$z;
}
}
return $z;
} // function _inverse_ncdf2()
private static function _inverse_ncdf3($p) {
// ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3.
// Produces the normal deviate Z corresponding to a given lower
// tail area of P; Z is accurate to about 1 part in 10**16.
//
// This is a PHP version of the original FORTRAN code that can
// be found at http://lib.stat.cmu.edu/apstat/
$split1 = 0.425;
$split2 = 5;
$const1 = 0.180625;
$const2 = 1.6;
// coefficients for p close to 0.5
$a0 = 3.3871328727963666080;
$a1 = 1.3314166789178437745E+2;
$a2 = 1.9715909503065514427E+3;
$a3 = 1.3731693765509461125E+4;
$a4 = 4.5921953931549871457E+4;
$a5 = 6.7265770927008700853E+4;
$a6 = 3.3430575583588128105E+4;
$a7 = 2.5090809287301226727E+3;
$b1 = 4.2313330701600911252E+1;
$b2 = 6.8718700749205790830E+2;
$b3 = 5.3941960214247511077E+3;
$b4 = 2.1213794301586595867E+4;
$b5 = 3.9307895800092710610E+4;
$b6 = 2.8729085735721942674E+4;
$b7 = 5.2264952788528545610E+3;
// coefficients for p not close to 0, 0.5 or 1.
$c0 = 1.42343711074968357734;
$c1 = 4.63033784615654529590;
$c2 = 5.76949722146069140550;
$c3 = 3.64784832476320460504;
$c4 = 1.27045825245236838258;
$c5 = 2.41780725177450611770E-1;
$c6 = 2.27238449892691845833E-2;
$c7 = 7.74545014278341407640E-4;
$d1 = 2.05319162663775882187;
$d2 = 1.67638483018380384940;
$d3 = 6.89767334985100004550E-1;
$d4 = 1.48103976427480074590E-1;
$d5 = 1.51986665636164571966E-2;
$d6 = 5.47593808499534494600E-4;
$d7 = 1.05075007164441684324E-9;
// coefficients for p near 0 or 1.
$e0 = 6.65790464350110377720;
$e1 = 5.46378491116411436990;
$e2 = 1.78482653991729133580;
$e3 = 2.96560571828504891230E-1;
$e4 = 2.65321895265761230930E-2;
$e5 = 1.24266094738807843860E-3;
$e6 = 2.71155556874348757815E-5;
$e7 = 2.01033439929228813265E-7;
$f1 = 5.99832206555887937690E-1;
$f2 = 1.36929880922735805310E-1;
$f3 = 1.48753612908506148525E-2;
$f4 = 7.86869131145613259100E-4;
$f5 = 1.84631831751005468180E-5;
$f6 = 1.42151175831644588870E-7;
$f7 = 2.04426310338993978564E-15;
$q = $p - 0.5;
// computation for p close to 0.5
if (abs($q) <= split1) {
$R = $const1 - $q * $q;
$z = $q * ((((((($a7 * $R + $a6) * $R + $a5) * $R + $a4) * $R + $a3) * $R + $a2) * $R + $a1) * $R + $a0) /
((((((($b7 * $R + $b6) * $R + $b5) * $R + $b4) * $R + $b3) * $R + $b2) * $R + $b1) * $R + 1);
} else {
if ($q < 0) {
$R = $p;
} else {
$R = 1 - $p;
}
$R = pow(-log($R),2);
// computation for p not close to 0, 0.5 or 1.
If ($R <= $split2) {
$R = $R - $const2;
$z = ((((((($c7 * $R + $c6) * $R + $c5) * $R + $c4) * $R + $c3) * $R + $c2) * $R + $c1) * $R + $c0) /
((((((($d7 * $R + $d6) * $R + $d5) * $R + $d4) * $R + $d3) * $R + $d2) * $R + $d1) * $R + 1);
} else {
// computation for p near 0 or 1.
$R = $R - $split2;
$z = ((((((($e7 * $R + $e6) * $R + $e5) * $R + $e4) * $R + $e3) * $R + $e2) * $R + $e1) * $R + $e0) /
((((((($f7 * $R + $f6) * $R + $f5) * $R + $f4) * $R + $f3) * $R + $f2) * $R + $f1) * $R + 1);
}
if ($q < 0) {
$z = -$z;
}
}
return $z;
} // function _inverse_ncdf3()
/**
* AVEDEV
*
* Returns the average of the absolute deviations of data points from their mean.
* AVEDEV is a measure of the variability in a data set.
*
* Excel Function:
* AVEDEV(value1[,value2[, ...]])
*
* @access public
* @category Statistical Functions
* @param mixed $arg,... Data values
* @return float
*/
public static function AVEDEV() {
$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
// Return value
$returnValue = null;
$aMean = self::AVERAGE($aArgs);
if ($aMean != PHPExcel_Calculation_Functions::DIV0()) {
$aCount = 0;
foreach ($aArgs as $k => $arg) {
if ((is_bool($arg)) &&
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
$arg = (integer) $arg;
}
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
if (is_null($returnValue)) {
$returnValue = abs($arg - $aMean);
} else {
$returnValue += abs($arg - $aMean);
}
++$aCount;
}
}
// Return
if ($aCount == 0) {
return PHPExcel_Calculation_Functions::DIV0();
}
return $returnValue / $aCount;
}
return PHPExcel_Calculation_Functions::NaN();
} // function AVEDEV()
/**
* AVERAGE
*
* Returns the average (arithmetic mean) of the arguments
*
* Excel Function:
* AVERAGE(value1[,value2[, ...]])
*
* @access public
* @category Statistical Functions
* @param mixed $arg,... Data values
* @return float
*/
public static function AVERAGE() {
$returnValue = $aCount = 0;
// Loop through arguments
foreach (PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args()) as $k => $arg) {
if ((is_bool($arg)) &&
((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
$arg = (integer) $arg;
}
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
if (is_null($returnValue)) {
$returnValue = $arg;
} else {
$returnValue += $arg;
}
++$aCount;
}
}
// Return
if ($aCount > 0) {
return $returnValue / $aCount;
} else {
return PHPExcel_Calculation_Functions::DIV0();
}
} // function AVERAGE()
/**
* AVERAGEA
*
* Returns the average of its arguments, including numbers, text, and logical values
*
* Excel Function:
* AVERAGEA(value1[,value2[, ...]])
*
* @access public
* @category Statistical Functions
* @param mixed $arg,... Data values
* @return float
*/
public static function AVERAGEA() {
// Return value
$returnValue = null;
$aCount = 0;
// Loop through arguments
foreach (PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args()) as $k => $arg) {
if ((is_bool($arg)) &&
(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
} else {
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
if (is_bool($arg)) {
$arg = (integer) $arg;
} elseif (is_string($arg)) {
$arg = 0;
}
if (is_null($returnValue)) {
$returnValue = $arg;
} else {
$returnValue += $arg;
}
++$aCount;
}
}
}
// Return
if ($aCount > 0) {
return $returnValue / $aCount;
} else {
return PHPExcel_Calculation_Functions::DIV0();
}
} // function AVERAGEA()
/**
* AVERAGEIF
*
* Returns the average value from a range of cells that contain numbers within the list of arguments
*
* Excel Function:
* AVERAGEIF(value1[,value2[, ...]],condition)
*
* @access public
* @category Mathematical and Trigonometric Functions
* @param mixed $arg,... Data values
* @param string $condition The criteria that defines which cells will be checked.
* @return float
*/
public static function AVERAGEIF($aArgs,$condition,$averageArgs = array()) {
// Return value
$returnValue = 0;
$aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
$averageArgs = PHPExcel_Calculation_Functions::flattenArray($averageArgs);
if (empty($averageArgs)) {
$averageArgs = $aArgs;
}
$condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
// Loop through arguments
$aCount = 0;
foreach ($aArgs as $key => $arg) {
if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
$testCondition = '='.$arg.$condition;
if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
if ((is_null($returnValue)) || ($arg > $returnValue)) {
$returnValue += $arg;
++$aCount;
}
}
}
// Return
if ($aCount > 0) {
return $returnValue / $aCount;
} else {
return PHPExcel_Calculation_Functions::DIV0();
}
} // function AVERAGEIF()
/**
* BETADIST
*
* Returns the beta distribution.
*
* @param float $value Value at which you want to evaluate the distribution
* @param float $alpha Parameter to the distribution
* @param float $beta Parameter to the distribution
* @param boolean $cumulative
* @return float
*
*/
public static function BETADIST($value,$alpha,$beta,$rMin=0,$rMax=1) {
$value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
$beta = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
$rMin = PHPExcel_Calculation_Functions::flattenSingleValue($rMin);
$rMax = PHPExcel_Calculation_Functions::flattenSingleValue($rMax);
if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
if (($value < $rMin) || ($value > $rMax) || ($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax)) {
return PHPExcel_Calculation_Functions::NaN();
}
if ($rMin > $rMax) {
$tmp = $rMin;
$rMin = $rMax;
$rMax = $tmp;
}
$value -= $rMin;
$value /= ($rMax - $rMin);
return self::_incompleteBeta($value,$alpha,$beta);
}
return PHPExcel_Calculation_Functions::VALUE();
} // function BETADIST()
/**
* BETAINV
*
* Returns the inverse of the beta distribution.
*
* @param float $probability Probability at which you want to evaluate the distribution
* @param float $alpha Parameter to the distribution
* @param float $beta Parameter to the distribution
* @param boolean $cumulative
* @return float
*
*/
public static function BETAINV($probability,$alpha,$beta,$rMin=0,$rMax=1) {
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
$alpha = PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
$beta = PHPExcel_Calculation_Functions::flattenSingleValue($beta);
$rMin = PHPExcel_Calculation_Functions::flattenSingleValue($rMin);
$rMax = PHPExcel_Calculation_Functions::flattenSingleValue($rMax);
if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
if (($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax) || ($probability <= 0) || ($probability > 1)) {
return PHPExcel_Calculation_Functions::NaN();
}
if ($rMin > $rMax) {
$tmp = $rMin;
$rMin = $rMax;
$rMax = $tmp;
}
$a = 0;
$b = 2;
$i = 0;
while ((($b - $a) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
$guess = ($a + $b) / 2;
$result = self::BETADIST($guess, $alpha, $beta);
if (($result == $probability) || ($result == 0)) {
$b = $a;
} elseif ($result > $probability) {
$b = $guess;
} else {
$a = $guess;
}
}
if ($i == MAX_ITERATIONS) {
return PHPExcel_Calculation_Functions::NA();
}
return round($rMin + $guess * ($rMax - $rMin),12);
}
return PHPExcel_Calculation_Functions::VALUE();
} // function BETAINV()
/**
* BINOMDIST
*
* Returns the individual term binomial distribution probability. Use BINOMDIST in problems with
* a fixed number of tests or trials, when the outcomes of any trial are only success or failure,
* when trials are independent, and when the probability of success is constant throughout the
* experiment. For example, BINOMDIST can calculate the probability that two of the next three
* babies born are male.
*
* @param float $value Number of successes in trials
* @param float $trials Number of trials
* @param float $probability Probability of success on each trial
* @param boolean $cumulative
* @return float
*
* @todo Cumulative distribution function
*
*/
public static function BINOMDIST($value, $trials, $probability, $cumulative) {
$value = floor(PHPExcel_Calculation_Functions::flattenSingleValue($value));
$trials = floor(PHPExcel_Calculation_Functions::flattenSingleValue($trials));
$probability = PHPExcel_Calculation_Functions::flattenSingleValue($probability);
if ((is_numeric($value)) && (is_numeric($trials)) && (is_numeric($probability))) {
if (($value < 0) || ($value > $trials)) {
return PHPExcel_Calculation_Functions::NaN();
}
if (($probability < 0) || ($probability > 1)) {
return PHPExcel_Calculation_Functions::NaN();
}
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
if ($cumulative) {
$summer = 0;
for ($i = 0; $i <= $value; ++$i) {
$summer += PHPExcel_Calculation_MathTrig::COMBIN($trials,$i) * pow($probability,$i) * pow(1 - $probability,$trials - $i);
}
return $summer;
} else {
return PHPExcel_Calculation_MathTrig::COMBIN($trials,$value) * pow($probability,$value) * pow(1 - $probability,$trials - $value) ;
}
}
}