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<?php
namespace PhpOffice\PhpSpreadsheet\Calculation;
use PhpOffice\PhpSpreadsheet\Shared\Trend\Trend;
class Statistical
{
const LOG_GAMMA_X_MAX_VALUE = 2.55e305;
const XMININ = 2.23e-308;
const EPS = 2.22e-16;
const MAX_VALUE = 1.2e308;
const MAX_ITERATIONS = 256;
const SQRT2PI = 2.5066282746310005024157652848110452530069867406099;
private static function checkTrendArrays(&$array1, &$array2)
{
if (!is_array($array1)) {
$array1 = [$array1];
}
if (!is_array($array2)) {
$array2 = [$array2];
}
$array1 = Functions::flattenArray($array1);
$array2 = Functions::flattenArray($array2);
foreach ($array1 as $key => $value) {
if ((is_bool($value)) || (is_string($value)) || ($value === null)) {
unset($array1[$key], $array2[$key]);
}
}
foreach ($array2 as $key => $value) {
if ((is_bool($value)) || (is_string($value)) || ($value === null)) {
unset($array1[$key], $array2[$key]);
}
}
$array1 = array_merge($array1);
$array2 = array_merge($array2);
return true;
}
/**
* 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 mixed $x require 0<=x<=1
* @param mixed $p require p>0
* @param mixed $q require q>0
*
* @return float 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow
*/
private static function incompleteBeta($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) > self::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) / $p;
}
return 1.0 - ($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 mixed $p require p>0
* @param mixed $q require q>0
*
* @return float 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
*
* @author Jaco van Kooten
*/
private static function logBeta($p, $q)
{
if ($p != self::$logBetaCacheP || $q != self::$logBetaCacheQ) {
self::$logBetaCacheP = $p;
self::$logBetaCacheQ = $q;
if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > self::LOG_GAMMA_X_MAX_VALUE)) {
self::$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
*
* @param mixed $x
* @param mixed $p
* @param mixed $q
*
* @return float
*/
private static function betaFraction($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) < self::XMININ) {
$h = self::XMININ;
}
$h = 1.0 / $h;
$frac = $h;
$m = 1;
$delta = 0.0;
while ($m <= self::MAX_ITERATIONS && abs($delta - 1.0) > Functions::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) < self::XMININ) {
$h = self::XMININ;
}
$h = 1.0 / $h;
$c = 1.0 + $d / $c;
if (abs($c) < self::XMININ) {
$c = self::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) < self::XMININ) {
$h = self::XMININ;
}
$h = 1.0 / $h;
$c = 1.0 + $d / $c;
if (abs($c) < self::XMININ) {
$c = self::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 float 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 = [
4.945235359296727046734888,
201.8112620856775083915565,
2290.838373831346393026739,
11319.67205903380828685045,
28557.24635671635335736389,
38484.96228443793359990269,
26377.48787624195437963534,
7225.813979700288197698961,
];
static $lg_p2 = [
4.974607845568932035012064,
542.4138599891070494101986,
15506.93864978364947665077,
184793.2904445632425417223,
1088204.76946882876749847,
3338152.967987029735917223,
5106661.678927352456275255,
3074109.054850539556250927,
];
static $lg_p4 = [
14745.02166059939948905062,
2426813.369486704502836312,
121475557.4045093227939592,
2663432449.630976949898078,
29403789566.34553899906876,
170266573776.5398868392998,
492612579337.743088758812,
560625185622.3951465078242,
];
static $lg_q1 = [
67.48212550303777196073036,
1113.332393857199323513008,
7738.757056935398733233834,
27639.87074403340708898585,
54993.10206226157329794414,
61611.22180066002127833352,
36351.27591501940507276287,
8785.536302431013170870835,
];
static $lg_q2 = [
183.0328399370592604055942,
7765.049321445005871323047,
133190.3827966074194402448,
1136705.821321969608938755,
5267964.117437946917577538,
13467014.54311101692290052,
17827365.30353274213975932,
9533095.591844353613395747,
];
static $lg_q4 = [
2690.530175870899333379843,
639388.5654300092398984238,
41355999.30241388052042842,
1120872109.61614794137657,
14886137286.78813811542398,
101680358627.2438228077304,
341747634550.7377132798597,
446315818741.9713286462081,
];
static $lg_c = [
-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 && $y <= self::LOG_GAMMA_X_MAX_VALUE) {
if ($y <= self::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(self::SQRT2PI) - 0.5 * $corr;
$res += $y * ($corr - 1.0);
}
}
} else {
// --------------------------
// Return for bad arguments
// --------------------------
$res = self::MAX_VALUE;
}
// ------------------------------
// Final adjustments and return
// ------------------------------
self::$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 = [
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(self::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 = [
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 = [
1 => -5.447609879822406e+01,
2 => 1.615858368580409e+02,
3 => -1.556989798598866e+02,
4 => 6.680131188771972e+01,
5 => -1.328068155288572e+01,
];
static $c = [
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 = [
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]) * $q + 1);
}
// If 0 < p < 1, return a null value
return Functions::NULL();
}
/**
* AVEDEV.
*
* Returns the average of the absolute deviations of data points from their mean.
* AVEDEV is a measure of the variability in a data set.
*
* Excel Function:
* AVEDEV(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function AVEDEV(...$args)
{
$aArgs = Functions::flattenArrayIndexed($args);
// Return value
$returnValue = null;
$aMean = self::AVERAGE($aArgs);
if ($aMean != Functions::DIV0()) {
$aCount = 0;
foreach ($aArgs as $k => $arg) {
if ((is_bool($arg)) &&
((!Functions::isCellValue($k)) || (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) {
$arg = (int) $arg;
}
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
if ($returnValue === null) {
$returnValue = abs($arg - $aMean);
} else {
$returnValue += abs($arg - $aMean);
}
++$aCount;
}
}
// Return
if ($aCount == 0) {
return Functions::DIV0();
}
return $returnValue / $aCount;
}
return Functions::NAN();
}
/**
* AVERAGE.
*
* Returns the average (arithmetic mean) of the arguments
*
* Excel Function:
* AVERAGE(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function AVERAGE(...$args)
{
$returnValue = $aCount = 0;
// Loop through arguments
foreach (Functions::flattenArrayIndexed($args) as $k => $arg) {
if ((is_bool($arg)) &&
((!Functions::isCellValue($k)) || (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) {
$arg = (int) $arg;
}
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
if ($returnValue === null) {
$returnValue = $arg;
} else {
$returnValue += $arg;
}
++$aCount;
}
}
// Return
if ($aCount > 0) {
return $returnValue / $aCount;
}
return Functions::DIV0();
}
/**
* AVERAGEA.
*
* Returns the average of its arguments, including numbers, text, and logical values
*
* Excel Function:
* AVERAGEA(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function AVERAGEA(...$args)
{
$returnValue = null;
$aCount = 0;
// Loop through arguments
foreach (Functions::flattenArrayIndexed($args) as $k => $arg) {
if ((is_bool($arg)) &&
(!Functions::isMatrixValue($k))) {
} else {
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
if (is_bool($arg)) {
$arg = (int) $arg;
} elseif (is_string($arg)) {
$arg = 0;
}
if ($returnValue === null) {
$returnValue = $arg;
} else {
$returnValue += $arg;
}
++$aCount;
}
}
}
if ($aCount > 0) {
return $returnValue / $aCount;
}
return Functions::DIV0();
}
/**
* AVERAGEIF.
*
* Returns the average value from a range of cells that contain numbers within the list of arguments
*
* Excel Function:
* AVERAGEIF(value1[,value2[, ...]],condition)
*
* @category Mathematical and Trigonometric Functions
*
* @param mixed $aArgs 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 = [])
{
$returnValue = 0;
$aArgs = Functions::flattenArray($aArgs);
$averageArgs = Functions::flattenArray($averageArgs);
if (empty($averageArgs)) {
$averageArgs = $aArgs;
}
$condition = Functions::ifCondition($condition);
// Loop through arguments
$aCount = 0;
foreach ($aArgs as $key => $arg) {
if (!is_numeric($arg)) {
$arg = Calculation::wrapResult(strtoupper($arg));
}
$testCondition = '=' . $arg . $condition;
if (Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
if (($returnValue === null) || ($arg > $returnValue)) {
$returnValue += $arg;
++$aCount;
}
}
}
if ($aCount > 0) {
return $returnValue / $aCount;
}
return Functions::DIV0();
}
/**
* 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 mixed $rMin
* @param mixed $rMax
*
* @return float
*/
public static function BETADIST($value, $alpha, $beta, $rMin = 0, $rMax = 1)
{
$value = Functions::flattenSingleValue($value);
$alpha = Functions::flattenSingleValue($alpha);
$beta = Functions::flattenSingleValue($beta);
$rMin = Functions::flattenSingleValue($rMin);
$rMax = Functions::flattenSingleValue($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 == $rMax)) {
return Functions::NAN();
}
if ($rMin > $rMax) {
$tmp = $rMin;
$rMin = $rMax;
$rMax = $tmp;
}
$value -= $rMin;
$value /= ($rMax - $rMin);
return self::incompleteBeta($value, $alpha, $beta);
}
return Functions::VALUE();
}
/**
* 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 $rMax Maximum value
*
* @return float
*/
public static function BETAINV($probability, $alpha, $beta, $rMin = 0, $rMax = 1)
{
$probability = Functions::flattenSingleValue($probability);
$alpha = Functions::flattenSingleValue($alpha);
$beta = Functions::flattenSingleValue($beta);
$rMin = Functions::flattenSingleValue($rMin);
$rMax = Functions::flattenSingleValue($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) || ($probability > 1)) {
return Functions::NAN();
}
if ($rMin > $rMax) {
$tmp = $rMin;
$rMin = $rMax;
$rMax = $tmp;
}
$a = 0;
$b = 2;
$i = 0;
while ((($b - $a) > Functions::PRECISION) && ($i++ < self::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 == self::MAX_ITERATIONS) {
return Functions::NA();
}
return round($rMin + $guess * ($rMax - $rMin), 12);
}
return Functions::VALUE();
}
/**
* 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 bool $cumulative
*
* @return float
*
* @todo Cumulative distribution function
*/
public static function BINOMDIST($value, $trials, $probability, $cumulative)
{
$value = floor(Functions::flattenSingleValue($value));
$trials = floor(Functions::flattenSingleValue($trials));
$probability = Functions::flattenSingleValue($probability);
if ((is_numeric($value)) && (is_numeric($trials)) && (is_numeric($probability))) {
if (($value < 0) || ($value > $trials)) {
return Functions::NAN();
}
if (($probability < 0) || ($probability > 1)) {
return Functions::NAN();
}
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
if ($cumulative) {
$summer = 0;
for ($i = 0; $i <= $value; ++$i) {
$summer += MathTrig::COMBIN($trials, $i) * pow($probability, $i) * pow(1 - $probability, $trials - $i);
}
return $summer;
}
return MathTrig::COMBIN($trials, $value) * pow($probability, $value) * pow(1 - $probability, $trials - $value);
}
}
return Functions::VALUE();
}
/**
* 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)
{
$value = Functions::flattenSingleValue($value);
$degrees = floor(Functions::flattenSingleValue($degrees));
if ((is_numeric($value)) && (is_numeric($degrees))) {
if ($degrees < 1) {
return Functions::NAN();
}
if ($value < 0) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
return 1;
}
return Functions::NAN();
}
return 1 - (self::incompleteGamma($degrees / 2, $value / 2) / self::gamma($degrees / 2));
}
return Functions::VALUE();
}
/**
* 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)
{
$probability = Functions::flattenSingleValue($probability);
$degrees = floor(Functions::flattenSingleValue($degrees));
if ((is_numeric($probability)) && (is_numeric($degrees))) {
$xLo = 100;
$xHi = 0;
$x = $xNew = 1;
$dx = 1;
$i = 0;
while ((abs($dx) > Functions::PRECISION) && ($i++ < self::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 == self::MAX_ITERATIONS) {
return Functions::NA();
}
return round($x, 12);
}
return Functions::VALUE();
}
/**
* 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)
{
$alpha = Functions::flattenSingleValue($alpha);
$stdDev = Functions::flattenSingleValue($stdDev);
$size = floor(Functions::flattenSingleValue($size));
if ((is_numeric($alpha)) && (is_numeric($stdDev)) && (is_numeric($size))) {
if (($alpha <= 0) || ($alpha >= 1)) {
return Functions::NAN();
}
if (($stdDev <= 0) || ($size < 1)) {
return Functions::NAN();
}
return self::NORMSINV(1 - $alpha / 2) * $stdDev / sqrt($size);
}
return Functions::VALUE();
}
/**
* CORREL.
*
* Returns covariance, the average of the products of deviations for each data point pair.
*
* @param mixed $yValues array of mixed Data Series Y
* @param null|mixed $xValues array of mixed Data Series X
*
* @return float
*/
public static function CORREL($yValues, $xValues = null)
{
if (($xValues === null) || (!is_array($yValues)) || (!is_array($xValues))) {
return Functions::VALUE();
}
if (!self::checkTrendArrays($yValues, $xValues)) {
return Functions::VALUE();
}
$yValueCount = count($yValues);
$xValueCount = count($xValues);
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
return Functions::NA();
} elseif ($yValueCount == 1) {
return Functions::DIV0();
}
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
return $bestFitLinear->getCorrelation();
}
/**
* COUNT.
*
* Counts the number of cells that contain numbers within the list of arguments
*
* Excel Function:
* COUNT(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return int
*/
public static function COUNT(...$args)
{
$returnValue = 0;
// Loop through arguments
$aArgs = Functions::flattenArrayIndexed($args);
foreach ($aArgs as $k => $arg) {
if ((is_bool($arg)) &&
((!Functions::isCellValue($k)) || (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) {
$arg = (int) $arg;
}
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
++$returnValue;
}
}
return $returnValue;
}
/**
* COUNTA.
*
* Counts the number of cells that are not empty within the list of arguments
*
* Excel Function:
* COUNTA(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return int
*/
public static function COUNTA(...$args)
{
$returnValue = 0;
// Loop through arguments
$aArgs = Functions::flattenArray($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 $returnValue;
}
/**
* COUNTBLANK.
*
* Counts the number of empty cells within the list of arguments
*
* Excel Function:
* COUNTBLANK(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return int
*/
public static function COUNTBLANK(...$args)
{
$returnValue = 0;
// Loop through arguments
$aArgs = Functions::flattenArray($args);
foreach ($aArgs as $arg) {
// Is it a blank cell?
if (($arg === null) || ((is_string($arg)) && ($arg == ''))) {
++$returnValue;
}
}
return $returnValue;
}
/**
* COUNTIF.
*
* Counts the number of cells that contain numbers within the list of arguments
*
* Excel Function:
* COUNTIF(value1[,value2[, ...]],condition)
*
* @category Statistical Functions
*
* @param mixed $aArgs Data values
* @param string $condition the criteria that defines which cells will be counted
*
* @return int
*/
public static function COUNTIF($aArgs, $condition)
{
$returnValue = 0;
$aArgs = Functions::flattenArray($aArgs);
$condition = Functions::ifCondition($condition);
// Loop through arguments
foreach ($aArgs as $arg) {
if (!is_numeric($arg)) {
$arg = Calculation::wrapResult(strtoupper($arg));
}
$testCondition = '=' . $arg . $condition;
if (Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
// Is it a value within our criteria
++$returnValue;
}
}
return $returnValue;
}
/**
* COVAR.
*
* Returns covariance, the average of the products of deviations for each data point pair.
*
* @param mixed $yValues array of mixed Data Series Y
* @param mixed $xValues array of mixed Data Series X
*
* @return float
*/
public static function COVAR($yValues, $xValues)
{
if (!self::checkTrendArrays($yValues, $xValues)) {
return Functions::VALUE();
}
$yValueCount = count($yValues);
$xValueCount = count($xValues);
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
return Functions::NA();
} elseif ($yValueCount == 1) {
return Functions::DIV0();
}
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
return $bestFitLinear->getCovariance();
}
/**
* CRITBINOM.
*
* Returns the smallest value for which the cumulative binomial distribution is greater
* than or equal to a criterion value
*
* See https://support.microsoft.com/en-us/help/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)
{
$trials = floor(Functions::flattenSingleValue($trials));
$probability = Functions::flattenSingleValue($probability);
$alpha = Functions::flattenSingleValue($alpha);
if ((is_numeric($trials)) && (is_numeric($probability)) && (is_numeric($alpha))) {
if ($trials < 0) {
return Functions::NAN();
} elseif (($probability < 0) || ($probability > 1)) {
return Functions::NAN();
} elseif (($alpha < 0) || ($alpha > 1)) {
return Functions::NAN();
} elseif ($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 = $CumPGuess - 1;
while (true) {
if (($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 Functions::VALUE();
}
/**
* DEVSQ.
*
* Returns the sum of squares of deviations of data points from their sample mean.
*
* Excel Function:
* DEVSQ(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function DEVSQ(...$args)
{
$aArgs = Functions::flattenArrayIndexed($args);
// Return value
$returnValue = null;
$aMean = self::AVERAGE($aArgs);
if ($aMean != Functions::DIV0()) {
$aCount = -1;
foreach ($aArgs as $k => $arg) {
// Is it a numeric value?
if ((is_bool($arg)) &&
((!Functions::isCellValue($k)) ||
(Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) {
$arg = (int) $arg;
}
if ((is_numeric($arg)) && (!is_string($arg))) {
if ($returnValue === null) {
$returnValue = pow(($arg - $aMean), 2);
} else {
$returnValue += pow(($arg - $aMean), 2);
}
++$aCount;
}
}
// Return
if ($returnValue === null) {
return Functions::NAN();
}
return $returnValue;
}
return self::NA();
}
/**
* 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 bool $cumulative
*
* @return float
*/
public static function EXPONDIST($value, $lambda, $cumulative)
{
$value = Functions::flattenSingleValue($value);
$lambda = Functions::flattenSingleValue($lambda);
$cumulative = Functions::flattenSingleValue($cumulative);
if ((is_numeric($value)) && (is_numeric($lambda))) {
if (($value < 0) || ($lambda < 0)) {
return Functions::NAN();
}
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
if ($cumulative) {
return 1 - exp(0 - $value * $lambda);
}
return $lambda * exp(0 - $value * $lambda);
}
}
return Functions::VALUE();
}
/**
* 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)
{
$value = Functions::flattenSingleValue($value);
if (is_numeric($value)) {
if (($value <= -1) || ($value >= 1)) {
return Functions::NAN();
}
return 0.5 * log((1 + $value) / (1 - $value));
}
return Functions::VALUE();
}
/**
* 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)
{
$value = Functions::flattenSingleValue($value);
if (is_numeric($value)) {
return (exp(2 * $value) - 1) / (exp(2 * $value) + 1);
}
return Functions::VALUE();
}
/**
* 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 $xValue Value of X for which we want to find Y
* @param mixed $yValues array of mixed Data Series Y
* @param mixed $xValues of mixed Data Series X
*
* @return float
*/
public static function FORECAST($xValue, $yValues, $xValues)
{
$xValue = Functions::flattenSingleValue($xValue);
if (!is_numeric($xValue)) {
return Functions::VALUE();
} elseif (!self::checkTrendArrays($yValues, $xValues)) {
return Functions::VALUE();
}
$yValueCount = count($yValues);
$xValueCount = count($xValues);
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
return Functions::NA();
} elseif ($yValueCount == 1) {
return Functions::DIV0();
}
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
return $bestFitLinear->getValueOfYForX($xValue);
}
/**
* 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 bool $cumulative
*
* @return float
*/
public static function GAMMADIST($value, $a, $b, $cumulative)
{
$value = Functions::flattenSingleValue($value);
$a = Functions::flattenSingleValue($a);
$b = Functions::flattenSingleValue($b);
if ((is_numeric($value)) && (is_numeric($a)) && (is_numeric($b))) {
if (($value < 0) || ($a <= 0) || ($b <= 0)) {
return Functions::NAN();
}
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
if ($cumulative) {
return self::incompleteGamma($a, $value / $b) / self::gamma($a);
}
return (1 / (pow($b, $a) * self::gamma($a))) * pow($value, $a - 1) * exp(0 - ($value / $b));
}
}
return Functions::VALUE();
}
/**
* 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)
{
$probability = Functions::flattenSingleValue($probability);
$alpha = Functions::flattenSingleValue($alpha);
$beta = Functions::flattenSingleValue($beta);
if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta))) {
if (($alpha <= 0) || ($beta <= 0) || ($probability < 0) || ($probability > 1)) {
return Functions::NAN();
}
$xLo = 0;
$xHi = $alpha * $beta * 5;
$x = $xNew = 1;
$error = $pdf = 0;
$dx = 1024;
$i = 0;
while ((abs($dx) > Functions::PRECISION) && ($i++ < self::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 == self::MAX_ITERATIONS) {
return Functions::NA();
}
return $x;
}
return Functions::VALUE();
}
/**
* GAMMALN.
*
* Returns the natural logarithm of the gamma function.
*
* @param float $value
*
* @return float
*/
public static function GAMMALN($value)
{
$value = Functions::flattenSingleValue($value);
if (is_numeric($value)) {
if ($value <= 0) {
return Functions::NAN();
}
return log(self::gamma($value));
}
return Functions::VALUE();
}
/**
* GEOMEAN.
*
* Returns the geometric mean of an array or range of positive data. For example, you
* can use GEOMEAN to calculate average growth rate given compound interest with
* variable rates.
*
* Excel Function:
* GEOMEAN(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function GEOMEAN(...$args)
{
$aArgs = Functions::flattenArray($args);
$aMean = MathTrig::PRODUCT($aArgs);
if (is_numeric($aMean) && ($aMean > 0)) {
$aCount = self::COUNT($aArgs);
if (self::MIN($aArgs) > 0) {
return pow($aMean, (1 / $aCount));
}
}
return Functions::NAN();
}
/**
* GROWTH.
*
* Returns values along a predicted emponential Trend
*
* @param mixed[] $yValues Data Series Y
* @param mixed[] $xValues Data Series X
* @param mixed[] $newValues Values of X for which we want to find Y
* @param bool $const a logical value specifying whether to force the intersect to equal 0
*
* @return array of float
*/
public static function GROWTH($yValues, $xValues = [], $newValues = [], $const = true)
{
$yValues = Functions::flattenArray($yValues);
$xValues = Functions::flattenArray($xValues);
$newValues = Functions::flattenArray($newValues);
$const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const);
$bestFitExponential = Trend::calculate(Trend::TREND_EXPONENTIAL, $yValues, $xValues, $const);
if (empty($newValues)) {
$newValues = $bestFitExponential->getXValues();
}
$returnArray = [];
foreach ($newValues as $xValue) {
$returnArray[0][] = $bestFitExponential->getValueOfYForX($xValue);
}
return $returnArray;
}
/**
* HARMEAN.
*
* Returns the harmonic mean of a data set. The harmonic mean is the reciprocal of the
* arithmetic mean of reciprocals.
*
* Excel Function:
* HARMEAN(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function HARMEAN(...$args)
{
// Return value
$returnValue = Functions::NA();
// Loop through arguments
$aArgs = Functions::flattenArray($args);
if (self::MIN($aArgs) < 0) {
return Functions::NAN();
}
$aCount = 0;
foreach ($aArgs as $arg) {
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
if ($arg <= 0) {
return Functions::NAN();
}
if ($returnValue === null) {
$returnValue = (1 / $arg);
} else {
$returnValue += (1 / $arg);
}
++$aCount;
}
}
// Return
if ($aCount > 0) {
return 1 / ($returnValue / $aCount);
}
return $returnValue;
}
/**
* 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)
{
$sampleSuccesses = floor(Functions::flattenSingleValue($sampleSuccesses));
$sampleNumber = floor(Functions::flattenSingleValue($sampleNumber));
$populationSuccesses = floor(Functions::flattenSingleValue($populationSuccesses));
$populationNumber = floor(Functions::flattenSingleValue($populationNumber));
if ((is_numeric($sampleSuccesses)) && (is_numeric($sampleNumber)) && (is_numeric($populationSuccesses)) && (is_numeric($populationNumber))) {
if (($sampleSuccesses < 0) || ($sampleSuccesses > $sampleNumber) || ($sampleSuccesses > $populationSuccesses)) {
return Functions::NAN();
}
if (($sampleNumber <= 0) || ($sampleNumber > $populationNumber)) {
return Functions::NAN();
}
if (($populationSuccesses <= 0) || ($populationSuccesses > $populationNumber)) {
return Functions::NAN();
}
return MathTrig::COMBIN($populationSuccesses, $sampleSuccesses) *
MathTrig::COMBIN($populationNumber - $populationSuccesses, $sampleNumber - $sampleSuccesses) /
MathTrig::COMBIN($populationNumber, $sampleNumber);
}
return Functions::VALUE();
}
/**
* INTERCEPT.
*
* Calculates the point at which a line will intersect the y-axis by using existing x-values and y-values.
*
* @param mixed[] $yValues Data Series Y
* @param mixed[] $xValues Data Series X
*
* @return float
*/
public static function INTERCEPT($yValues, $xValues)
{
if (!self::checkTrendArrays($yValues, $xValues)) {
return Functions::VALUE();
}
$yValueCount = count($yValues);
$xValueCount = count($xValues);
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
return Functions::NA();
} elseif ($yValueCount == 1) {
return Functions::DIV0();
}
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
return $bestFitLinear->getIntersect();
}
/**
* KURT.
*
* Returns the kurtosis of a data set. Kurtosis characterizes the relative peakedness
* or flatness of a distribution compared with the normal distribution. Positive
* kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a
* relatively flat distribution.
*
* @param array ...$args Data Series
*
* @return float
*/
public static function KURT(...$args)
{
$aArgs = Functions::flattenArrayIndexed($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)) &&
(!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 Functions::DIV0();
}
/**
* 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)
*
* @category Statistical Functions
*
* @param mixed $args Data values
* @param int $entry Position (ordered from the largest) in the array or range of data to return
*
* @return float
*/
public static function LARGE(...$args)
{
$aArgs = Functions::flattenArray($args);
// Calculate
$entry = floor(array_pop($aArgs));
if ((is_numeric($entry)) && (!is_string($entry))) {
$mArgs = [];
foreach ($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 Functions::NAN();
}
rsort($mArgs);
return $mArgs[$entry];
}
return Functions::VALUE();
}
/**
* 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 mixed[] $yValues Data Series Y
* @param null|mixed[] $xValues Data Series X
* @param bool $const a logical value specifying whether to force the intersect to equal 0
* @param bool $stats a logical value specifying whether to return additional regression statistics
*
* @return array
*/
public static function LINEST($yValues, $xValues = null, $const = true, $stats = false)
{
$const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const);
$stats = ($stats === null) ? false : (bool) Functions::flattenSingleValue($stats);
if ($xValues === null) {
$xValues = range(1, count(Functions::flattenArray($yValues)));
}
if (!self::checkTrendArrays($yValues, $xValues)) {
return Functions::VALUE();
}
$yValueCount = count($yValues);
$xValueCount = count($xValues);
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
return Functions::NA();
} elseif ($yValueCount == 1) {
return 0;
}
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues, $const);
if ($stats) {
return [
[
$bestFitLinear->getSlope(),
$bestFitLinear->getSlopeSE(),
$bestFitLinear->getGoodnessOfFit(),
$bestFitLinear->getF(),
$bestFitLinear->getSSRegression(),
],
[
$bestFitLinear->getIntersect(),
$bestFitLinear->getIntersectSE(),
$bestFitLinear->getStdevOfResiduals(),
$bestFitLinear->getDFResiduals(),
$bestFitLinear->getSSResiduals(),
],
];
}
return [
$bestFitLinear->getSlope(),
$bestFitLinear->getIntersect(),
];
}
/**
* LOGEST.
*
* Calculates an exponential curve that best fits the X and Y data series,
* and then returns an array that describes the line.
*
* @param mixed[] $yValues Data Series Y
* @param null|mixed[] $xValues Data Series X
* @param bool $const a logical value specifying whether to force the intersect to equal 0
* @param bool $stats a logical value specifying whether to return additional regression statistics
*
* @return array
*/
public static function LOGEST($yValues, $xValues = null, $const = true, $stats = false)
{
$const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const);
$stats = ($stats === null) ? false : (bool) Functions::flattenSingleValue($stats);
if ($xValues === null) {
$xValues = range(1, count(Functions::flattenArray($yValues)));
}
if (!self::checkTrendArrays($yValues, $xValues)) {
return Functions::VALUE();
}
$yValueCount = count($yValues);
$xValueCount = count($xValues);
foreach ($yValues as $value) {
if ($value <= 0.0) {
return Functions::NAN();
}
}
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
return Functions::NA();
} elseif ($yValueCount == 1) {
return 1;
}
$bestFitExponential = Trend::calculate(Trend::TREND_EXPONENTIAL, $yValues, $xValues, $const);
if ($stats) {
return [
[
$bestFitExponential->getSlope(),
$bestFitExponential->getSlopeSE(),
$bestFitExponential->getGoodnessOfFit(),
$bestFitExponential->getF(),
$bestFitExponential->getSSRegression(),
],
[
$bestFitExponential->getIntersect(),
$bestFitExponential->getIntersectSE(),
$bestFitExponential->getStdevOfResiduals(),
$bestFitExponential->getDFResiduals(),
$bestFitExponential->getSSResiduals(),
],
];
}
return [
$bestFitExponential->getSlope(),
$bestFitExponential->getIntersect(),
];
}
/**
* 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)
{
$probability = Functions::flattenSingleValue($probability);
$mean = Functions::flattenSingleValue($mean);
$stdDev = Functions::flattenSingleValue($stdDev);
if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
if (($probability < 0) || ($probability > 1) || ($stdDev <= 0)) {
return Functions::NAN();
}
return exp($mean + $stdDev * self::NORMSINV($probability));
}
return Functions::VALUE();
}
/**
* 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)
{
$value = Functions::flattenSingleValue($value);
$mean = Functions::flattenSingleValue($mean);
$stdDev = Functions::flattenSingleValue($stdDev);
if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
if (($value <= 0) || ($stdDev <= 0)) {
return Functions::NAN();
}
return self::NORMSDIST((log($value) - $mean) / $stdDev);
}
return Functions::VALUE();
}
/**
* MAX.
*
* MAX returns the value of the element of the values passed that has the highest value,
* with negative numbers considered smaller than positive numbers.
*
* Excel Function:
* MAX(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function MAX(...$args)
{
$returnValue = null;
// Loop through arguments
$aArgs = Functions::flattenArray($args);
foreach ($aArgs as $arg) {
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
if (($returnValue === null) || ($arg > $returnValue)) {
$returnValue = $arg;
}
}
}
if ($returnValue === null) {
return 0;
}
return $returnValue;
}
/**
* MAXA.
*
* Returns the greatest value in a list of arguments, including numbers, text, and logical values
*
* Excel Function:
* MAXA(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function MAXA(...$args)
{
$returnValue = null;
// Loop through arguments
$aArgs = Functions::flattenArray($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 = (int) $arg;
} elseif (is_string($arg)) {
$arg = 0;
}
if (($returnValue === null) || ($arg > $returnValue)) {
$returnValue = $arg;
}
}
}
if ($returnValue === null) {
return 0;
}
return $returnValue;
}
/**
* MAXIF.
*
* Counts the maximum value within a range of cells that contain numbers within the list of arguments
*
* Excel Function:
* MAXIF(value1[,value2[, ...]],condition)
*
* @category Mathematical and Trigonometric Functions
*
* @param mixed $aArgs Data values
* @param string $condition the criteria that defines which cells will be checked
* @param mixed $sumArgs
*
* @return float
*/
public static function MAXIF($aArgs, $condition, $sumArgs = [])
{
$returnValue = null;
$aArgs = Functions::flattenArray($aArgs);
$sumArgs = Functions::flattenArray($sumArgs);
if (empty($sumArgs)) {
$sumArgs = $aArgs;
}
$condition = Functions::ifCondition($condition);
// Loop through arguments
foreach ($aArgs as $key => $arg) {
if (!is_numeric($arg)) {
$arg = Calculation::wrapResult(strtoupper($arg));
}
$testCondition = '=' . $arg . $condition;
if (Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
if (($returnValue === null) || ($arg > $returnValue)) {
$returnValue = $arg;
}
}
}
return $returnValue;
}
/**
* MEDIAN.
*
* Returns the median of the given numbers. The median is the number in the middle of a set of numbers.
*
* Excel Function:
* MEDIAN(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function MEDIAN(...$args)
{
$returnValue = Functions::NAN();
$mArgs = [];
// Loop through arguments
$aArgs = Functions::flattenArray($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 $returnValue;
}
/**
* MIN.
*
* MIN returns the value of the element of the values passed that has the smallest value,
* with negative numbers considered smaller than positive numbers.
*
* Excel Function:
* MIN(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function MIN(...$args)
{
$returnValue = null;
// Loop through arguments
$aArgs = Functions::flattenArray($args);
foreach ($aArgs as $arg) {
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
if (($returnValue === null) || ($arg < $returnValue)) {
$returnValue = $arg;
}
}
}
if ($returnValue === null) {
return 0;
}
return $returnValue;
}
/**
* MINA.
*
* Returns the smallest value in a list of arguments, including numbers, text, and logical values
*
* Excel Function:
* MINA(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function MINA(...$args)
{
$returnValue = null;
// Loop through arguments
$aArgs = Functions::flattenArray($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 = (int) $arg;
} elseif (is_string($arg)) {
$arg = 0;
}
if (($returnValue === null) || ($arg < $returnValue)) {
$returnValue = $arg;
}
}
}
if ($returnValue === null) {
return 0;
}
return $returnValue;
}
/**
* MINIF.
*
* Returns the minimum value within a range of cells that contain numbers within the list of arguments
*
* Excel Function:
* MINIF(value1[,value2[, ...]],condition)
*
* @category Mathematical and Trigonometric Functions
*
* @param mixed $aArgs Data values
* @param string $condition the criteria that defines which cells will be checked
* @param mixed $sumArgs
*
* @return float
*/
public static function MINIF($aArgs, $condition, $sumArgs = [])
{
$returnValue = null;
$aArgs = Functions::flattenArray($aArgs);
$sumArgs = Functions::flattenArray($sumArgs);
if (empty($sumArgs)) {
$sumArgs = $aArgs;
}
$condition = Functions::ifCondition($condition);
// Loop through arguments
foreach ($aArgs as $key => $arg) {
if (!is_numeric($arg)) {
$arg = Calculation::wrapResult(strtoupper($arg));
}
$testCondition = '=' . $arg . $condition;
if (Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
if (($returnValue === null) || ($arg < $returnValue)) {
$returnValue = $arg;
}
}
}
return $returnValue;
}
//
// Special variant of array_count_values that isn't limited to strings and integers,
// but can work with floating point numbers as values
//
private static function modeCalc($data)
{
$frequencyArray = [];
foreach ($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[] = [
'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 Functions::NA();
}
return $frequencyArray[0]['value'];
}
/**
* MODE.
*
* Returns the most frequently occurring, or repetitive, value in an array or range of data
*
* Excel Function:
* MODE(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function MODE(...$args)
{
$returnValue = Functions::NA();
// Loop through arguments
$aArgs = Functions::flattenArray($args);
$mArgs = [];
foreach ($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 $returnValue;
}
/**
* 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)
{
$failures = floor(Functions::flattenSingleValue($failures));
$successes = floor(Functions::flattenSingleValue($successes));
$probability = Functions::flattenSingleValue($probability);
if ((is_numeric($failures)) && (is_numeric($successes)) && (is_numeric($probability))) {
if (($failures < 0) || ($successes < 1)) {
return Functions::NAN();
} elseif (($probability < 0) || ($probability > 1)) {
return Functions::NAN();
}
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
if (($failures + $successes - 1) <= 0) {
return Functions::NAN();
}
}
return (MathTrig::COMBIN($failures + $successes - 1, $successes - 1)) * (pow($probability, $successes)) * (pow(1 - $probability, $failures));
}
return Functions::VALUE();
}
/**
* 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 bool $cumulative
*
* @return float
*/
public static function NORMDIST($value, $mean, $stdDev, $cumulative)
{
$value = Functions::flattenSingleValue($value);
$mean = Functions::flattenSingleValue($mean);
$stdDev = Functions::flattenSingleValue($stdDev);
if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
if ($stdDev < 0) {
return Functions::NAN();
}
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
if ($cumulative) {
return 0.5 * (1 + Engineering::erfVal(($value - $mean) / ($stdDev * sqrt(2))));
}
return (1 / (self::SQRT2PI * $stdDev)) * exp(0 - (pow($value - $mean, 2) / (2 * ($stdDev * $stdDev))));
}
}
return Functions::VALUE();
}
/**
* NORMINV.
*
* Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.
*
* @param float $probability
* @param float $mean Mean Value
* @param float $stdDev Standard Deviation
*
* @return float
*/
public static function NORMINV($probability, $mean, $stdDev)
{
$probability = Functions::flattenSingleValue($probability);
$mean = Functions::flattenSingleValue($mean);
$stdDev = Functions::flattenSingleValue($stdDev);
if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
if (($probability < 0) || ($probability > 1)) {
return Functions::NAN();
}
if ($stdDev < 0) {
return Functions::NAN();
}
return (self::inverseNcdf($probability) * $stdDev) + $mean;
}
return Functions::VALUE();
}
/**
* 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)
{
$value = Functions::flattenSingleValue($value);
return self::NORMDIST($value, 0, 1, true);
}
/**
* 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);
}
/**
* PERCENTILE.
*
* Returns the nth percentile of values in a range..
*
* Excel Function:
* PERCENTILE(value1[,value2[, ...]],entry)
*
* @category Statistical Functions
*
* @param mixed $args Data values
* @param float $entry Percentile value in the range 0..1, inclusive.
*
* @return float
*/
public static function PERCENTILE(...$args)
{
$aArgs = Functions::flattenArray($args);
// Calculate
$entry = array_pop($aArgs);
if ((is_numeric($entry)) && (!is_string($entry))) {
if (($entry < 0) || ($entry > 1)) {
return Functions::NAN();
}
$mArgs = [];
foreach ($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];
}
$iNext = $iBase + 1;
$iProportion = $index - $iBase;
return $mArgs[$iBase] + (($mArgs[$iNext] - $mArgs[$iBase]) * $iProportion);
}
}
return Functions::VALUE();
}
/**
* PERCENTRANK.
*
* Returns the rank of a value in a data set as a percentage of the data set.
*
* @param float[] $valueSet An array of, or a reference to, a list of numbers
* @param int $value the number whose rank you want to find
* @param int $significance the number of significant digits for the returned percentage value
*
* @return float
*/
public static function PERCENTRANK($valueSet, $value, $significance = 3)
{
$valueSet = Functions::flattenArray($valueSet);
$value = Functions::flattenSingleValue($value);
$significance = ($significance === null) ? 3 : (int) 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 Functions::NAN();
}
$valueAdjustor = $valueCount - 1;
if (($value < $valueSet[0]) || ($value > $valueSet[$valueAdjustor])) {
return 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);
}
/**
* 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)
{
$numObjs = Functions::flattenSingleValue($numObjs);
$numInSet = Functions::flattenSingleValue($numInSet);
if ((is_numeric($numObjs)) && (is_numeric($numInSet))) {
$numInSet = floor($numInSet);
if ($numObjs < $numInSet) {
return Functions::NAN();
}
return round(MathTrig::FACT($numObjs) / MathTrig::FACT($numObjs - $numInSet));
}
return Functions::VALUE();
}
/**
* 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 bool $cumulative
*
* @return float
*/
public static function POISSON($value, $mean, $cumulative)
{
$value = Functions::flattenSingleValue($value);
$mean = Functions::flattenSingleValue($mean);
if ((is_numeric($value)) && (is_numeric($mean))) {
if (($value < 0) || ($mean <= 0)) {
return Functions::NAN();
}
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
if ($cumulative) {
$summer = 0;
$floor = floor($value);
for ($i = 0; $i <= $floor; ++$i) {
$summer += pow($mean, $i) / MathTrig::FACT($i);
}
return exp(0 - $mean) * $summer;
}
return (exp(0 - $mean) * pow($mean, $value)) / MathTrig::FACT($value);
}
}
return Functions::VALUE();
}
/**
* QUARTILE.
*
* Returns the quartile of a data set.
*
* Excel Function:
* QUARTILE(value1[,value2[, ...]],entry)
*
* @category Statistical Functions
*
* @param mixed $args Data values
* @param int $entry Quartile value in the range 1..3, inclusive.
*
* @return float
*/
public static function QUARTILE(...$args)
{
$aArgs = Functions::flattenArray($args);
// Calculate
$entry = floor(array_pop($aArgs));
if ((is_numeric($entry)) && (!is_string($entry))) {
$entry /= 4;
if (($entry < 0) || ($entry > 1)) {
return Functions::NAN();
}
return self::PERCENTILE($aArgs, $entry);
}
return Functions::VALUE();
}
/**
* RANK.
*
* Returns the rank of a number in a list of numbers.
*
* @param int $value the number whose rank you want to find
* @param float[] $valueSet An array of, or a reference to, a list of numbers
* @param int $order Order to sort the values in the value set
*
* @return float
*/
public static function RANK($value, $valueSet, $order = 0)
{
$value = Functions::flattenSingleValue($value);
$valueSet = Functions::flattenArray($valueSet);
$order = ($order === null) ? 0 : (int) 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 Functions::NA();
}
return ++$pos;
}
/**
* RSQ.
*
* Returns the square of the Pearson product moment correlation coefficient through data points in known_y's and known_x's.
*
* @param mixed[] $yValues Data Series Y
* @param mixed[] $xValues Data Series X
*
* @return float
*/
public static function RSQ($yValues, $xValues)
{
if (!self::checkTrendArrays($yValues, $xValues)) {
return Functions::VALUE();
}
$yValueCount = count($yValues);
$xValueCount = count($xValues);
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
return Functions::NA();
} elseif ($yValueCount == 1) {
return Functions::DIV0();
}
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
return $bestFitLinear->getGoodnessOfFit();
}
/**
* SKEW.
*
* Returns the skewness of a distribution. Skewness characterizes the degree of asymmetry
* of a distribution around its mean. Positive skewness indicates a distribution with an
* asymmetric tail extending toward more positive values. Negative skewness indicates a
* distribution with an asymmetric tail extending toward more negative values.
*
* @param array ...$args Data Series
*
* @return float
*/
public static function SKEW(...$args)
{
$aArgs = Functions::flattenArrayIndexed($args);
$mean = self::AVERAGE($aArgs);
$stdDev = self::STDEV($aArgs);
$count = $summer = 0;
// Loop through arguments
foreach ($aArgs as $k => $arg) {
if ((is_bool($arg)) &&
(!Functions::isMatrixValue($k))) {
} else {
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
$summer += pow((($arg - $mean) / $stdDev), 3);
++$count;
}
}
}
if ($count > 2) {
return $summer * ($count / (($count - 1) * ($count - 2)));
}
return Functions::DIV0();
}
/**
* SLOPE.
*
* Returns the slope of the linear regression line through data points in known_y's and known_x's.
*
* @param mixed[] $yValues Data Series Y
* @param mixed[] $xValues Data Series X
*
* @return float
*/
public static function SLOPE($yValues, $xValues)
{
if (!self::checkTrendArrays($yValues, $xValues)) {
return Functions::VALUE();
}
$yValueCount = count($yValues);
$xValueCount = count($xValues);
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
return Functions::NA();
} elseif ($yValueCount == 1) {
return Functions::DIV0();
}
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
return $bestFitLinear->getSlope();
}
/**
* 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)
*
* @category Statistical Functions
*
* @param mixed $args Data values
* @param int $entry Position (ordered from the smallest) in the array or range of data to return
*
* @return float
*/
public static function SMALL(...$args)
{
$aArgs = Functions::flattenArray($args);
// Calculate
$entry = array_pop($aArgs);
if ((is_numeric($entry)) && (!is_string($entry))) {
$mArgs = [];
foreach ($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 Functions::NAN();
}
sort($mArgs);
return $mArgs[$entry];
}
return Functions::VALUE();
}
/**
* 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)
{
$value = Functions::flattenSingleValue($value);
$mean = Functions::flattenSingleValue($mean);
$stdDev = Functions::flattenSingleValue($stdDev);
if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
if ($stdDev <= 0) {
return Functions::NAN();
}
return ($value - $mean) / $stdDev;
}
return Functions::VALUE();
}
/**
* STDEV.
*
* Estimates standard deviation based on a sample. The standard deviation is a measure of how
* widely values are dispersed from the average value (the mean).
*
* Excel Function:
* STDEV(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function STDEV(...$args)
{
$aArgs = Functions::flattenArrayIndexed($args);
// Return value
$returnValue = null;
$aMean = self::AVERAGE($aArgs);
if ($aMean !== null) {
$aCount = -1;
foreach ($aArgs as $k => $arg) {
if ((is_bool($arg)) &&
((!Functions::isCellValue($k)) || (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) {
$arg = (int) $arg;
}
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
if ($returnValue === null) {
$returnValue = pow(($arg - $aMean), 2);
} else {
$returnValue += pow(($arg - $aMean), 2);
}
++$aCount;
}
}
// Return
if (($aCount > 0) && ($returnValue >= 0)) {
return sqrt($returnValue / $aCount);
}
}
return Functions::DIV0();
}
/**
* STDEVA.
*
* Estimates standard deviation based on a sample, including numbers, text, and logical values
*
* Excel Function:
* STDEVA(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function STDEVA(...$args)
{
$aArgs = Functions::flattenArrayIndexed($args);
$returnValue = null;
$aMean = self::AVERAGEA($aArgs);
if ($aMean !== null) {
$aCount = -1;
foreach ($aArgs as $k => $arg) {
if ((is_bool($arg)) &&
(!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 = (int) $arg;
} elseif (is_string($arg)) {
$arg = 0;
}
if ($returnValue === null) {
$returnValue = pow(($arg - $aMean), 2);
} else {
$returnValue += pow(($arg - $aMean), 2);
}
++$aCount;
}
}
}
if (($aCount > 0) && ($returnValue >= 0)) {
return sqrt($returnValue / $aCount);
}
}
return Functions::DIV0();
}
/**
* STDEVP.
*
* Calculates standard deviation based on the entire population
*
* Excel Function:
* STDEVP(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function STDEVP(...$args)
{
$aArgs = Functions::flattenArrayIndexed($args);
$returnValue = null;
$aMean = self::AVERAGE($aArgs);
if ($aMean !== null) {
$aCount = 0;
foreach ($aArgs as $k => $arg) {
if ((is_bool($arg)) &&
((!Functions::isCellValue($k)) || (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) {
$arg = (int) $arg;
}
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
if ($returnValue === null) {
$returnValue = pow(($arg - $aMean), 2);
} else {
$returnValue += pow(($arg - $aMean), 2);
}
++$aCount;
}
}
if (($aCount > 0) && ($returnValue >= 0)) {
return sqrt($returnValue / $aCount);
}
}
return Functions::DIV0();
}
/**
* STDEVPA.
*
* Calculates standard deviation based on the entire population, including numbers, text, and logical values
*
* Excel Function:
* STDEVPA(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function STDEVPA(...$args)
{
$aArgs = Functions::flattenArrayIndexed($args);
$returnValue = null;
$aMean = self::AVERAGEA($aArgs);
if ($aMean !== null) {
$aCount = 0;
foreach ($aArgs as $k => $arg) {
if ((is_bool($arg)) &&
(!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 = (int) $arg;
} elseif (is_string($arg)) {
$arg = 0;
}
if ($returnValue === null) {
$returnValue = pow(($arg - $aMean), 2);
} else {
$returnValue += pow(($arg - $aMean), 2);
}
++$aCount;
}
}
}
if (($aCount > 0) && ($returnValue >= 0)) {
return sqrt($returnValue / $aCount);
}
}
return Functions::DIV0();
}
/**
* STEYX.
*
* Returns the standard error of the predicted y-value for each x in the regression.
*
* @param mixed[] $yValues Data Series Y
* @param mixed[] $xValues Data Series X
*
* @return float
*/
public static function STEYX($yValues, $xValues)
{
if (!self::checkTrendArrays($yValues, $xValues)) {
return Functions::VALUE();
}
$yValueCount = count($yValues);
$xValueCount = count($xValues);
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
return Functions::NA();
} elseif ($yValueCount == 1) {
return Functions::DIV0();
}
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
return $bestFitLinear->getStdevOfResiduals();
}
/**
* 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)
{
$value = Functions::flattenSingleValue($value);
$degrees = floor(Functions::flattenSingleValue($degrees));
$tails = floor(Functions::flattenSingleValue($tails));
if ((is_numeric($value)) && (is_numeric($degrees)) && (is_numeric($tails))) {
if (($value < 0) || ($degrees < 1) || ($tails < 1) || ($tails > 2)) {
return 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) {
$tsum = Functions::M_2DIVPI * ($tsum + $ttheta);
}
$tValue = 0.5 * (1 + $tsum);
if ($tails == 1) {
return 1 - abs($tValue);
}
return 1 - abs((1 - $tValue) - $tValue);
}
return Functions::VALUE();
}
/**
* 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)
{
$probability = Functions::flattenSingleValue($probability);
$degrees = floor(Functions::flattenSingleValue($degrees));
if ((is_numeric($probability)) && (is_numeric($degrees))) {
$xLo = 100;
$xHi = 0;
$x = $xNew = 1;
$dx = 1;
$i = 0;
while ((abs($dx) > Functions::PRECISION) && ($i++ < self::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 == self::MAX_ITERATIONS) {
return Functions::NA();
}
return round($x, 12);
}
return Functions::VALUE();
}
/**
* TREND.
*
* Returns values along a linear Trend
*
* @param mixed[] $yValues Data Series Y
* @param mixed[] $xValues Data Series X
* @param mixed[] $newValues Values of X for which we want to find Y
* @param bool $const a logical value specifying whether to force the intersect to equal 0
*
* @return array of float
*/
public static function TREND($yValues, $xValues = [], $newValues = [], $const = true)
{
$yValues = Functions::flattenArray($yValues);
$xValues = Functions::flattenArray($xValues);
$newValues = Functions::flattenArray($newValues);
$const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const);
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues, $const);
if (empty($newValues)) {
$newValues = $bestFitLinear->getXValues();
}
$returnArray = [];
foreach ($newValues as $xValue) {
$returnArray[0][] = $bestFitLinear->getValueOfYForX($xValue);
}
return $returnArray;
}
/**
* 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)
*
* @category Statistical Functions
*
* @param mixed $args Data values
* @param float $discard Percentage to discard
*
* @return float
*/
public static function TRIMMEAN(...$args)
{
$aArgs = Functions::flattenArray($args);
// Calculate
$percent = array_pop($aArgs);
if ((is_numeric($percent)) && (!is_string($percent))) {
if (($percent < 0) || ($percent > 1)) {
return Functions::NAN();
}
$mArgs = [];
foreach ($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($mArgs);
}
return Functions::VALUE();
}
/**
* VARFunc.
*
* Estimates variance based on a sample.
*
* Excel Function:
* VAR(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function VARFunc(...$args)
{
$returnValue = Functions::DIV0();
$summerA = $summerB = 0;
// Loop through arguments
$aArgs = Functions::flattenArray($args);
$aCount = 0;
foreach ($aArgs as $arg) {
if (is_bool($arg)) {
$arg = (int) $arg;
}
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
$summerA += ($arg * $arg);
$summerB += $arg;
++$aCount;
}
}
if ($aCount > 1) {
$summerA *= $aCount;
$summerB *= $summerB;
$returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
}
return $returnValue;
}
/**
* VARA.
*
* Estimates variance based on a sample, including numbers, text, and logical values
*
* Excel Function:
* VARA(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function VARA(...$args)
{
$returnValue = Functions::DIV0();
$summerA = $summerB = 0;
// Loop through arguments
$aArgs = Functions::flattenArrayIndexed($args);
$aCount = 0;
foreach ($aArgs as $k => $arg) {
if ((is_string($arg)) &&
(Functions::isValue($k))) {
return Functions::VALUE();
} elseif ((is_string($arg)) &&
(!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 = (int) $arg;
} elseif (is_string($arg)) {
$arg = 0;
}
$summerA += ($arg * $arg);
$summerB += $arg;
++$aCount;
}
}
}
if ($aCount > 1) {
$summerA *= $aCount;
$summerB *= $summerB;
$returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
}
return $returnValue;
}
/**
* VARP.
*
* Calculates variance based on the entire population
*
* Excel Function:
* VARP(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function VARP(...$args)
{
// Return value
$returnValue = Functions::DIV0();
$summerA = $summerB = 0;
// Loop through arguments
$aArgs = Functions::flattenArray($args);
$aCount = 0;
foreach ($aArgs as $arg) {
if (is_bool($arg)) {
$arg = (int) $arg;
}
// Is it a numeric value?
if ((is_numeric($arg)) && (!is_string($arg))) {
$summerA += ($arg * $arg);
$summerB += $arg;
++$aCount;
}
}
if ($aCount > 0) {
$summerA *= $aCount;
$summerB *= $summerB;
$returnValue = ($summerA - $summerB) / ($aCount * $aCount);
}
return $returnValue;
}
/**
* VARPA.
*
* Calculates variance based on the entire population, including numbers, text, and logical values
*
* Excel Function:
* VARPA(value1[,value2[, ...]])
*
* @category Statistical Functions
*
* @param mixed ...$args Data values
*
* @return float
*/
public static function VARPA(...$args)
{
$returnValue = Functions::DIV0();
$summerA = $summerB = 0;
// Loop through arguments
$aArgs = Functions::flattenArrayIndexed($args);
$aCount = 0;
foreach ($aArgs as $k => $arg) {
if ((is_string($arg)) &&
(Functions::isValue($k))) {
return Functions::VALUE();
} elseif ((is_string($arg)) &&
(!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 = (int) $arg;
} elseif (is_string($arg)) {
$arg = 0;
}
$summerA += ($arg * $arg);
$summerB += $arg;
++$aCount;
}
}
}
if ($aCount > 0) {
$summerA *= $aCount;
$summerB *= $summerB;
$returnValue = ($summerA - $summerB) / ($aCount * $aCount);
}
return $returnValue;
}
/**
* 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 bool $cumulative
*
* @return float
*/
public static function WEIBULL($value, $alpha, $beta, $cumulative)
{
$value = Functions::flattenSingleValue($value);
$alpha = Functions::flattenSingleValue($alpha);
$beta = Functions::flattenSingleValue($beta);
if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta))) {
if (($value < 0) || ($alpha <= 0) || ($beta <= 0)) {
return Functions::NAN();
}
if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
if ($cumulative) {
return 1 - exp(0 - pow($value / $beta, $alpha));
}
return ($alpha / pow($beta, $alpha)) * pow($value, $alpha - 1) * exp(0 - pow($value / $beta, $alpha));
}
}
return Functions::VALUE();
}
/**
* 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 $sigma Beta Parameter
*
* @return float
*/
public static function ZTEST($dataSet, $m0, $sigma = null)
{
$dataSet = Functions::flattenArrayIndexed($dataSet);
$m0 = Functions::flattenSingleValue($m0);
$sigma = Functions::flattenSingleValue($sigma);
if ($sigma === null) {
$sigma = self::STDEV($dataSet);
}
$n = count($dataSet);
return 1 - self::NORMSDIST((self::AVERAGE($dataSet) - $m0) / ($sigma / sqrt($n)));
}
}