当前路径:Classes/PHPExcel/Calculation/Statistical.php <?php /** PHPExcel root directory */ if (!defined('PHPEXCEL_ROOT')) { /** * @ignore */ define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../'); require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php'); } require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/trend/trendClass.php'; /** LOG_GAMMA_X_MAX_VALUE */ define('LOG_GAMMA_X_MAX_VALUE', 2.55e305); /** XMININ */ define('XMININ', 2.23e-308); /** EPS */ define('EPS', 2.22e-16); /** SQRT2PI */ define('SQRT2PI', 2.5066282746310005024157652848110452530069867406099); /** * PHPExcel_Calculation_Statistical * * Copyright (c) 2006 - 2015 PHPExcel * * This library is free software; you can redistribute it and/or * modify it under the terms of the GNU Lesser General Public * License as published by the Free Software Foundation; either * version 2.1 of the License, or (at your option) any later version. * * This library is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public * License along with this library; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA * * @category PHPExcel * @package PHPExcel_Calculation * @copyright Copyright (c) 2006 - 2015 PHPExcel (http://www.codeplex.com/PHPExcel) * @license http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt LGPL * @version ##VERSION##, ##DATE## */ class PHPExcel_Calculation_Statistical { private static function checkTrendArrays(&$array1, &$array2) { if (!is_array($array1)) { $array1 = array($array1); } if (!is_array($array2)) { $array2 = array($array2); } $array1 = PHPExcel_Calculation_Functions::flattenArray($array1); $array2 = PHPExcel_Calculation_Functions::flattenArray($array2); foreach ($array1 as $key => $value) { if ((is_bool($value)) || (is_string($value)) || (is_null($value))) { unset($array1[$key]); unset($array2[$key]); } } foreach ($array2 as $key => $value) { if ((is_bool($value)) || (is_string($value)) || (is_null($value))) { unset($array1[$key]); unset($array2[$key]); } } $array1 = array_merge($array1); $array2 = array_merge($array2); return true; } /** * Beta function. * * @author Jaco van Kooten * * @param p require p>0 * @param q require q>0 * @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow */ private static function beta($p, $q) { if ($p <= 0.0 || $q <= 0.0 || ($p + $q) > LOG_GAMMA_X_MAX_VALUE) { return 0.0; } else { return exp(self::logBeta($p, $q)); } } /** * Incomplete beta function * * @author Jaco van Kooten * @author Paul Meagher * * The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992). * @param x require 0<=x<=1 * @param p require p>0 * @param q require q>0 * @return 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow */ private static function incompleteBeta($x, $p, $q) { if ($x <= 0.0) { return 0.0; } elseif ($x >= 1.0) { return 1.0; } elseif (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) { return 0.0; } $beta_gam = exp((0 - self::logBeta($p, $q)) + $p * log($x) + $q * log(1.0 - $x)); if ($x < ($p + 1.0) / ($p + $q + 2.0)) { return $beta_gam * self::betaFraction($x, $p, $q) / $p; } else { return 1.0 - ($beta_gam * self::betaFraction(1 - $x, $q, $p) / $q); } } // Function cache for logBeta function private static $logBetaCacheP = 0.0; private static $logBetaCacheQ = 0.0; private static $logBetaCacheResult = 0.0; /** * The natural logarithm of the beta function. * * @param p require p>0 * @param q require q>0 * @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow * @author Jaco van Kooten */ private static function logBeta($p, $q) { if ($p != self::$logBetaCacheP || $q != self::$logBetaCacheQ) { self::$logBetaCacheP = $p; self::$logBetaCacheQ = $q; if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) { self::$logBetaCacheResult = 0.0; } else { self::$logBetaCacheResult = self::logGamma($p) + self::logGamma($q) - self::logGamma($p + $q); } } return self::$logBetaCacheResult; } /** * Evaluates of continued fraction part of incomplete beta function. * Based on an idea from Numerical Recipes (W.H. Press et al, 1992). * @author Jaco van Kooten */ private static function betaFraction($x, $p, $q) { $c = 1.0; $sum_pq = $p + $q; $p_plus = $p + 1.0; $p_minus = $p - 1.0; $h = 1.0 - $sum_pq * $x / $p_plus; if (abs($h) < XMININ) { $h = XMININ; } $h = 1.0 / $h; $frac = $h; $m = 1; $delta = 0.0; while ($m <= MAX_ITERATIONS && abs($delta-1.0) > PRECISION) { $m2 = 2 * $m; // even index for d $d = $m * ($q - $m) * $x / ( ($p_minus + $m2) * ($p + $m2)); $h = 1.0 + $d * $h; if (abs($h) < XMININ) { $h = XMININ; } $h = 1.0 / $h; $c = 1.0 + $d / $c; if (abs($c) < XMININ) { $c = XMININ; } $frac *= $h * $c; // odd index for d $d = -($p + $m) * ($sum_pq + $m) * $x / (($p + $m2) * ($p_plus + $m2)); $h = 1.0 + $d * $h; if (abs($h) < XMININ) { $h = XMININ; } $h = 1.0 / $h; $c = 1.0 + $d / $c; if (abs($c) < XMININ) { $c = XMININ; } $delta = $h * $c; $frac *= $delta; ++$m; } return $frac; } /** * logGamma function * * @version 1.1 * @author Jaco van Kooten * * Original author was Jaco van Kooten. Ported to PHP by Paul Meagher. * * The natural logarithm of the gamma function. <br /> * Based on public domain NETLIB (Fortran) code by W. J. Cody and L. Stoltz <br /> * Applied Mathematics Division <br /> * Argonne National Laboratory <br /> * Argonne, IL 60439 <br /> * <p> * References: * <ol> * <li>W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural * Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203.</li> * <li>K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969.</li> * <li>Hart, Et. Al., Computer Approximations, Wiley and sons, New York, 1968.</li> * </ol> * </p> * <p> * From the original documentation: * </p> * <p> * This routine calculates the LOG(GAMMA) function for a positive real argument X. * Computation is based on an algorithm outlined in references 1 and 2. * The program uses rational functions that theoretically approximate LOG(GAMMA) * to at least 18 significant decimal digits. The approximation for X > 12 is from * reference 3, while approximations for X < 12.0 are similar to those in reference * 1, but are unpublished. The accuracy achieved depends on the arithmetic system, * the compiler, the intrinsic functions, and proper selection of the * machine-dependent constants. * </p> * <p> * Error returns: <br /> * The program returns the value XINF for X .LE. 0.0 or when overflow would occur. * The computation is believed to be free of underflow and overflow. * </p> * @return MAX_VALUE for x < 0.0 or when overflow would occur, i.e. x > 2.55E305 */ // Function cache for logGamma private static $logGammaCacheResult = 0.0; private static $logGammaCacheX = 0.0; private static function logGamma($x) { // Log Gamma related constants static $lg_d1 = -0.5772156649015328605195174; static $lg_d2 = 0.4227843350984671393993777; static $lg_d4 = 1.791759469228055000094023; static $lg_p1 = array( 4.945235359296727046734888, 201.8112620856775083915565, 2290.838373831346393026739, 11319.67205903380828685045, 28557.24635671635335736389, 38484.96228443793359990269, 26377.48787624195437963534, 7225.813979700288197698961 ); static $lg_p2 = array( 4.974607845568932035012064, 542.4138599891070494101986, 15506.93864978364947665077, 184793.2904445632425417223, 1088204.76946882876749847, 3338152.967987029735917223, 5106661.678927352456275255, 3074109.054850539556250927 ); static $lg_p4 = array( 14745.02166059939948905062, 2426813.369486704502836312, 121475557.4045093227939592, 2663432449.630976949898078, 29403789566.34553899906876, 170266573776.5398868392998, 492612579337.743088758812, 560625185622.3951465078242 ); static $lg_q1 = array( 67.48212550303777196073036, 1113.332393857199323513008, 7738.757056935398733233834, 27639.87074403340708898585, 54993.10206226157329794414, 61611.22180066002127833352, 36351.27591501940507276287, 8785.536302431013170870835 ); static $lg_q2 = array( 183.0328399370592604055942, 7765.049321445005871323047, 133190.3827966074194402448, 1136705.821321969608938755, 5267964.117437946917577538, 13467014.54311101692290052, 17827365.30353274213975932, 9533095.591844353613395747 ); static $lg_q4 = array( 2690.530175870899333379843, 639388.5654300092398984238, 41355999.30241388052042842, 1120872109.61614794137657, 14886137286.78813811542398, 101680358627.2438228077304, 341747634550.7377132798597, 446315818741.9713286462081 ); static $lg_c = array( -0.001910444077728, 8.4171387781295e-4, -5.952379913043012e-4, 7.93650793500350248e-4, -0.002777777777777681622553, 0.08333333333333333331554247, 0.0057083835261 ); // Rough estimate of the fourth root of logGamma_xBig static $lg_frtbig = 2.25e76; static $pnt68 = 0.6796875; if ($x == self::$logGammaCacheX) { return self::$logGammaCacheResult; } $y = $x; if ($y > 0.0 && $y <= LOG_GAMMA_X_MAX_VALUE) { if ($y <= EPS) { $res = -log(y); } elseif ($y <= 1.5) { // --------------------- // EPS .LT. X .LE. 1.5 // --------------------- if ($y < $pnt68) { $corr = -log($y); $xm1 = $y; } else { $corr = 0.0; $xm1 = $y - 1.0; } if ($y <= 0.5 || $y >= $pnt68) { $xden = 1.0; $xnum = 0.0; for ($i = 0; $i < 8; ++$i) { $xnum = $xnum * $xm1 + $lg_p1[$i]; $xden = $xden * $xm1 + $lg_q1[$i]; } $res = $corr + $xm1 * ($lg_d1 + $xm1 * ($xnum / $xden)); } else { $xm2 = $y - 1.0; $xden = 1.0; $xnum = 0.0; for ($i = 0; $i < 8; ++$i) { $xnum = $xnum * $xm2 + $lg_p2[$i]; $xden = $xden * $xm2 + $lg_q2[$i]; } $res = $corr + $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden)); } } elseif ($y <= 4.0) { // --------------------- // 1.5 .LT. X .LE. 4.0 // --------------------- $xm2 = $y - 2.0; $xden = 1.0; $xnum = 0.0; for ($i = 0; $i < 8; ++$i) { $xnum = $xnum * $xm2 + $lg_p2[$i]; $xden = $xden * $xm2 + $lg_q2[$i]; } $res = $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden)); } elseif ($y <= 12.0) { // ---------------------- // 4.0 .LT. X .LE. 12.0 // ---------------------- $xm4 = $y - 4.0; $xden = -1.0; $xnum = 0.0; for ($i = 0; $i < 8; ++$i) { $xnum = $xnum * $xm4 + $lg_p4[$i]; $xden = $xden * $xm4 + $lg_q4[$i]; } $res = $lg_d4 + $xm4 * ($xnum / $xden); } else { // --------------------------------- // Evaluate for argument .GE. 12.0 // --------------------------------- $res = 0.0; if ($y <= $lg_frtbig) { $res = $lg_c[6]; $ysq = $y * $y; for ($i = 0; $i < 6; ++$i) { $res = $res / $ysq + $lg_c[$i]; } $res /= $y; $corr = log($y); $res = $res + log(SQRT2PI) - 0.5 * $corr; $res += $y * ($corr - 1.0); } } } else { // -------------------------- // Return for bad arguments // -------------------------- $res = MAX_VALUE; } // ------------------------------ // Final adjustments and return // ------------------------------ self::$logGammaCacheX = $x; self::$logGammaCacheResult = $res; return $res; } // // Private implementation of the incomplete Gamma function // private static function incompleteGamma($a, $x) { static $max = 32; $summer = 0; for ($n=0; $n<=$max; ++$n) { $divisor = $a; for ($i=1; $i<=$n; ++$i) { $divisor *= ($a + $i); } $summer += (pow($x, $n) / $divisor); } return pow($x, $a) * exp(0-$x) * $summer; } // // Private implementation of the Gamma function // private static function gamma($data) { if ($data == 0.0) { return 0; } static $p0 = 1.000000000190015; static $p = array( 1 => 76.18009172947146, 2 => -86.50532032941677, 3 => 24.01409824083091, 4 => -1.231739572450155, 5 => 1.208650973866179e-3, 6 => -5.395239384953e-6 ); $y = $x = $data; $tmp = $x + 5.5; $tmp -= ($x + 0.5) * log($tmp); $summer = $p0; for ($j=1; $j<=6; ++$j) { $summer += ($p[$j] / ++$y); } return exp(0 - $tmp + log(SQRT2PI * $summer / $x)); } /*************************************************************************** * inverse_ncdf.php * ------------------- * begin : Friday, January 16, 2004 * copyright : (C) 2004 Michael Nickerson * email : nickersonm@yahoo.com * ***************************************************************************/ private static function inverseNcdf($p) { // Inverse ncdf approximation by Peter J. Acklam, implementation adapted to // PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as // a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html // I have not checked the accuracy of this implementation. Be aware that PHP // will truncate the coeficcients to 14 digits. // You have permission to use and distribute this function freely for // whatever purpose you want, but please show common courtesy and give credit // where credit is due. // Input paramater is $p - probability - where 0 < p < 1. // Coefficients in rational approximations static $a = array( 1 => -3.969683028665376e+01, 2 => 2.209460984245205e+02, 3 => -2.759285104469687e+02, 4 => 1.383577518672690e+02, 5 => -3.066479806614716e+01, 6 => 2.506628277459239e+00 ); static $b = array( 1 => -5.447609879822406e+01, 2 => 1.615858368580409e+02, 3 => -1.556989798598866e+02, 4 => 6.680131188771972e+01, 5 => -1.328068155288572e+01 ); static $c = array( 1 => -7.784894002430293e-03, 2 => -3.223964580411365e-01, 3 => -2.400758277161838e+00, 4 => -2.549732539343734e+00, 5 => 4.374664141464968e+00, 6 => 2.938163982698783e+00 ); static $d = array( 1 => 7.784695709041462e-03, 2 => 3.224671290700398e-01, 3 => 2.445134137142996e+00, 4 => 3.754408661907416e+00 ); // Define lower and upper region break-points. $p_low = 0.02425; //Use lower region approx. below this $p_high = 1 - $p_low; //Use upper region approx. above this if (0 < $p && $p < $p_low) { // Rational approximation for lower region. $q = sqrt(-2 * log($p)); return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) / (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1); } elseif ($p_low <= $p && $p <= $p_high) { // Rational approximation for central region. $q = $p - 0.5; $r = $q * $q; return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q / ((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1); } elseif ($p_high < $p && $p < 1) { // Rational approximation for upper region. $q = sqrt(-2 * log(1 - $p)); return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) / (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1); } // If 0 < p < 1, return a null value return PHPExcel_Calculation_Functions::NULL(); } private static function inverseNcdf2($prob) { // Approximation of inverse standard normal CDF developed by // B. Moro, "The Full Monte," Risk 8(2), Feb 1995, 57-58. $a1 = 2.50662823884; $a2 = -18.61500062529; $a3 = 41.39119773534; $a4 = -25.44106049637; $b1 = -8.4735109309; $b2 = 23.08336743743; $b3 = -21.06224101826; $b4 = 3.13082909833; $c1 = 0.337475482272615; $c2 = 0.976169019091719; $c3 = 0.160797971491821; $c4 = 2.76438810333863E-02; $c5 = 3.8405729373609E-03; $c6 = 3.951896511919E-04; $c7 = 3.21767881768E-05; $c8 = 2.888167364E-07; $c9 = 3.960315187E-07; $y = $prob - 0.5; if (abs($y) < 0.42) { $z = ($y * $y); $z = $y * ((($a4 * $z + $a3) * $z + $a2) * $z + $a1) / (((($b4 * $z + $b3) * $z + $b2) * $z + $b1) * $z + 1); } else { if ($y > 0) { $z = log(-log(1 - $prob)); } else { $z = log(-log($prob)); } $z = $c1 + $z * ($c2 + $z * ($c3 + $z * ($c4 + $z * ($c5 + $z * ($c6 + $z * ($c7 + $z * ($c8 + $z * $c9))))))); if ($y < 0) { $z = -$z; } } return $z; } // function inverseNcdf2() private static function inverseNcdf3($p) { // ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3. // Produces the normal deviate Z corresponding to a given lower // tail area of P; Z is accurate to about 1 part in 10**16. // // This is a PHP version of the original FORTRAN code that can // be found at http://lib.stat.cmu.edu/apstat/ $split1 = 0.425; $split2 = 5; $const1 = 0.180625; $const2 = 1.6; // coefficients for p close to 0.5 $a0 = 3.3871328727963666080; $a1 = 1.3314166789178437745E+2; $a2 = 1.9715909503065514427E+3; $a3 = 1.3731693765509461125E+4; $a4 = 4.5921953931549871457E+4; $a5 = 6.7265770927008700853E+4; $a6 = 3.3430575583588128105E+4; $a7 = 2.5090809287301226727E+3; $b1 = 4.2313330701600911252E+1; $b2 = 6.8718700749205790830E+2; $b3 = 5.3941960214247511077E+3; $b4 = 2.1213794301586595867E+4; $b5 = 3.9307895800092710610E+4; $b6 = 2.8729085735721942674E+4; $b7 = 5.2264952788528545610E+3; // coefficients for p not close to 0, 0.5 or 1. $c0 = 1.42343711074968357734; $c1 = 4.63033784615654529590; $c2 = 5.76949722146069140550; $c3 = 3.64784832476320460504; $c4 = 1.27045825245236838258; $c5 = 2.41780725177450611770E-1; $c6 = 2.27238449892691845833E-2; $c7 = 7.74545014278341407640E-4; $d1 = 2.05319162663775882187; $d2 = 1.67638483018380384940; $d3 = 6.89767334985100004550E-1; $d4 = 1.48103976427480074590E-1; $d5 = 1.51986665636164571966E-2; $d6 = 5.47593808499534494600E-4; $d7 = 1.05075007164441684324E-9; // coefficients for p near 0 or 1. $e0 = 6.65790464350110377720; $e1 = 5.46378491116411436990; $e2 = 1.78482653991729133580; $e3 = 2.96560571828504891230E-1; $e4 = 2.65321895265761230930E-2; $e5 = 1.24266094738807843860E-3; $e6 = 2.71155556874348757815E-5; $e7 = 2.01033439929228813265E-7; $f1 = 5.99832206555887937690E-1; $f2 = 1.36929880922735805310E-1; $f3 = 1.48753612908506148525E-2; $f4 = 7.86869131145613259100E-4; $f5 = 1.84631831751005468180E-5; $f6 = 1.42151175831644588870E-7; $f7 = 2.04426310338993978564E-15; $q = $p - 0.5; // computation for p close to 0.5 if (abs($q) <= split1) { $R = $const1 - $q * $q; $z = $q * ((((((($a7 * $R + $a6) * $R + $a5) * $R + $a4) * $R + $a3) * $R + $a2) * $R + $a1) * $R + $a0) / ((((((($b7 * $R + $b6) * $R + $b5) * $R + $b4) * $R + $b3) * $R + $b2) * $R + $b1) * $R + 1); } else { if ($q < 0) { $R = $p; } else { $R = 1 - $p; } $R = pow(-log($R), 2); // computation for p not close to 0, 0.5 or 1. if ($R <= $split2) { $R = $R - $const2; $z = ((((((($c7 * $R + $c6) * $R + $c5) * $R + $c4) * $R + $c3) * $R + $c2) * $R + $c1) * $R + $c0) / ((((((($d7 * $R + $d6) * $R + $d5) * $R + $d4) * $R + $d3) * $R + $d2) * $R + $d1) * $R + 1); } else { // computation for p near 0 or 1. $R = $R - $split2; $z = ((((((($e7 * $R + $e6) * $R + $e5) * $R + $e4) * $R + $e3) * $R + $e2) * $R + $e1) * $R + $e0) / ((((((($f7 * $R + $f6) * $R + $f5) * $R + $f4) * $R + $f3) * $R + $f2) * $R + $f1) * $R + 1); } if ($q < 0) { $z = -$z; } } return $z; } /** * AVEDEV * * Returns the average of the absolute deviations of data points from their mean. * AVEDEV is a measure of the variability in a data set. * * Excel Function: * AVEDEV(value1[,value2[, ...]]) * * @access public * @category Statistical Functions * @param mixed $arg,... Data values * @return float */ public static function AVEDEV() { $aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args()); // Return value $returnValue = null; $aMean = self::AVERAGE($aArgs); if ($aMean != PHPExcel_Calculation_Functions::DIV0()) { $aCount = 0; foreach ($aArgs as $k => $arg) { if ((is_bool($arg)) && ((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) { $arg = (integer) $arg; } // Is it a numeric value? if ((is_numeric($arg)) && (!is_string($arg))) { if (is_null($returnValue)) { $returnValue = abs($arg - $aMean); } else { $returnValue += abs($arg - $aMean); } ++$aCount; } } // Return if ($aCount == 0) { return PHPExcel_Calculation_Functions::DIV0(); } return $returnValue / $aCount; } return PHPExcel_Calculation_Fun...
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联系电话(Tel):4008-010-151(免长途)
地址:北京市海淀区大恒科技大厦五层 邮编:100080
Floor 5th,Daheng Building,Zhongguancun,Beijing,China,100080
51Aspx.com 版权所有 CopyRight © 2006-2023. 京ICP备09089570号 | 京公网安备11010702000869号