visualizer / vendor / phpoffice / phpspreadsheet / src / PhpSpreadsheet / Calculation / Statistical.php

Statistical.php in Visualizer – Tables & Charts Manager with Built-in AI Generator 3.9.4, at vendor/phpoffice/phpspreadsheet/src/PhpSpreadsheet/Calculation/Statistical.php

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1	<?php
2
3	namespace PhpOffice\PhpSpreadsheet\Calculation;
4
5	use PhpOffice\PhpSpreadsheet\Shared\Trend\Trend;
6
7	class Statistical
8	{
9	const LOG_GAMMA_X_MAX_VALUE = 2.55e305;
10	const XMININ = 2.23e-308;
11	const EPS = 2.22e-16;
12	const MAX_VALUE = 1.2e308;
13	const MAX_ITERATIONS = 256;
14	const SQRT2PI = 2.5066282746310005024157652848110452530069867406099;
15
16	private static function checkTrendArrays(&$array1, &$array2)
17	{
18	if (!is_array($array1)) {
19	$array1 = [$array1];
20	}
21	if (!is_array($array2)) {
22	$array2 = [$array2];
23	}
24
25	$array1 = Functions::flattenArray($array1);
26	$array2 = Functions::flattenArray($array2);
27	foreach ($array1 as $key => $value) {
28	if ((is_bool($value)) \|\| (is_string($value)) \|\| ($value === null)) {
29	unset($array1[$key], $array2[$key]);
30	}
31	}
32	foreach ($array2 as $key => $value) {
33	if ((is_bool($value)) \|\| (is_string($value)) \|\| ($value === null)) {
34	unset($array1[$key], $array2[$key]);
35	}
36	}
37	$array1 = array_merge($array1);
38	$array2 = array_merge($array2);
39
40	return true;
41	}
42
43	/**
44	* Incomplete beta function.
45	*
46	* @author Jaco van Kooten
47	* @author Paul Meagher
48	*
49	* The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992).
50	*
51	* @param mixed $x require 0<=x<=1
52	* @param mixed $p require p>0
53	* @param mixed $q require q>0
54	*
55	* @return float 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow
56	*/
57	private static function incompleteBeta($x, $p, $q)
58	{
59	if ($x <= 0.0) {
60	return 0.0;
61	} elseif ($x >= 1.0) {
62	return 1.0;
63	} elseif (($p <= 0.0) \|\| ($q <= 0.0) \|\| (($p + $q) > self::LOG_GAMMA_X_MAX_VALUE)) {
64	return 0.0;
65	}
66	$beta_gam = exp((0 - self::logBeta($p, $q)) + $p * log($x) + $q * log(1.0 - $x));
67	if ($x < ($p + 1.0) / ($p + $q + 2.0)) {
68	return $beta_gam * self::betaFraction($x, $p, $q) / $p;
69	}
70
71	return 1.0 - ($beta_gam * self::betaFraction(1 - $x, $q, $p) / $q);
72	}
73
74	// Function cache for logBeta function
75	private static $logBetaCacheP = 0.0;
76
77	private static $logBetaCacheQ = 0.0;
78
79	private static $logBetaCacheResult = 0.0;
80
81	/**
82	* The natural logarithm of the beta function.
83	*
84	* @param mixed $p require p>0
85	* @param mixed $q require q>0
86	*
87	* @return float 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
88	*
89	* @author Jaco van Kooten
90	*/
91	private static function logBeta($p, $q)
92	{
93	if ($p != self::$logBetaCacheP \|\| $q != self::$logBetaCacheQ) {
94	self::$logBetaCacheP = $p;
95	self::$logBetaCacheQ = $q;
96	if (($p <= 0.0) \|\| ($q <= 0.0) \|\| (($p + $q) > self::LOG_GAMMA_X_MAX_VALUE)) {
97	self::$logBetaCacheResult = 0.0;
98	} else {
99	self::$logBetaCacheResult = self::logGamma($p) + self::logGamma($q) - self::logGamma($p + $q);
100	}
101	}
102
103	return self::$logBetaCacheResult;
104	}
105
106	/**
107	* Evaluates of continued fraction part of incomplete beta function.
108	* Based on an idea from Numerical Recipes (W.H. Press et al, 1992).
109	*
110	* @author Jaco van Kooten
111	*
112	* @param mixed $x
113	* @param mixed $p
114	* @param mixed $q
115	*
116	* @return float
117	*/
118	private static function betaFraction($x, $p, $q)
119	{
120	$c = 1.0;
121	$sum_pq = $p + $q;
122	$p_plus = $p + 1.0;
123	$p_minus = $p - 1.0;
124	$h = 1.0 - $sum_pq * $x / $p_plus;
125	if (abs($h) < self::XMININ) {
126	$h = self::XMININ;
127	}
128	$h = 1.0 / $h;
129	$frac = $h;
130	$m = 1;
131	$delta = 0.0;
132	while ($m <= self::MAX_ITERATIONS && abs($delta - 1.0) > Functions::PRECISION) {
133	$m2 = 2 * $m;
134	// even index for d
135	$d = $m * ($q - $m) * $x / (($p_minus + $m2) * ($p + $m2));
136	$h = 1.0 + $d * $h;
137	if (abs($h) < self::XMININ) {
138	$h = self::XMININ;
139	}
140	$h = 1.0 / $h;
141	$c = 1.0 + $d / $c;
142	if (abs($c) < self::XMININ) {
143	$c = self::XMININ;
144	}
145	$frac = $h $c;
146	// odd index for d
147	$d = -($p + $m) * ($sum_pq + $m) * $x / (($p + $m2) * ($p_plus + $m2));
148	$h = 1.0 + $d * $h;
149	if (abs($h) < self::XMININ) {
150	$h = self::XMININ;
151	}
152	$h = 1.0 / $h;
153	$c = 1.0 + $d / $c;
154	if (abs($c) < self::XMININ) {
155	$c = self::XMININ;
156	}
157	$delta = $h * $c;
158	$frac *= $delta;
159	++$m;
160	}
161
162	return $frac;
163	}
164
165	/**
166	* logGamma function.
167	*
168	* @version 1.1
169	*
170	* @author Jaco van Kooten
171	*
172	* Original author was Jaco van Kooten. Ported to PHP by Paul Meagher.
173	*
174	* The natural logarithm of the gamma function. <br />
175	* Based on public domain NETLIB (Fortran) code by W. J. Cody and L. Stoltz <br />
176	* Applied Mathematics Division <br />
177	* Argonne National Laboratory <br />
178	* Argonne, IL 60439 <br />
179	* <p>
180	* References:
181	* <ol>
182	* <li>W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural
183	* Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203.</li>
184	* <li>K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969.</li>
185	* <li>Hart, Et. Al., Computer Approximations, Wiley and sons, New York, 1968.</li>
186	* </ol>
187	* </p>
188	* <p>
189	* From the original documentation:
190	* </p>
191	* <p>
192	* This routine calculates the LOG(GAMMA) function for a positive real argument X.
193	* Computation is based on an algorithm outlined in references 1 and 2.
194	* The program uses rational functions that theoretically approximate LOG(GAMMA)
195	* to at least 18 significant decimal digits. The approximation for X > 12 is from
196	* reference 3, while approximations for X < 12.0 are similar to those in reference
197	* 1, but are unpublished. The accuracy achieved depends on the arithmetic system,
198	* the compiler, the intrinsic functions, and proper selection of the
199	* machine-dependent constants.
200	* </p>
201	* <p>
202	* Error returns: <br />
203	* The program returns the value XINF for X .LE. 0.0 or when overflow would occur.
204	* The computation is believed to be free of underflow and overflow.
205	* </p>
206	*
207	* @return float MAX_VALUE for x < 0.0 or when overflow would occur, i.e. x > 2.55E305
208	*/
209
210	// Function cache for logGamma
211	private static $logGammaCacheResult = 0.0;
212
213	private static $logGammaCacheX = 0.0;
214
215	private static function logGamma($x)
216	{
217	// Log Gamma related constants
218	static $lg_d1 = -0.5772156649015328605195174;
219	static $lg_d2 = 0.4227843350984671393993777;
220	static $lg_d4 = 1.791759469228055000094023;
221
222	static $lg_p1 = [
223	4.945235359296727046734888,
224	201.8112620856775083915565,
225	2290.838373831346393026739,
226	11319.67205903380828685045,
227	28557.24635671635335736389,
228	38484.96228443793359990269,
229	26377.48787624195437963534,
230	7225.813979700288197698961,
231	];
232	static $lg_p2 = [
233	4.974607845568932035012064,
234	542.4138599891070494101986,
235	15506.93864978364947665077,
236	184793.2904445632425417223,
237	1088204.76946882876749847,
238	3338152.967987029735917223,
239	5106661.678927352456275255,
240	3074109.054850539556250927,
241	];
242	static $lg_p4 = [
243	14745.02166059939948905062,
244	2426813.369486704502836312,
245	121475557.4045093227939592,
246	2663432449.630976949898078,
247	29403789566.34553899906876,
248	170266573776.5398868392998,
249	492612579337.743088758812,
250	560625185622.3951465078242,
251	];
252	static $lg_q1 = [
253	67.48212550303777196073036,
254	1113.332393857199323513008,
255	7738.757056935398733233834,
256	27639.87074403340708898585,
257	54993.10206226157329794414,
258	61611.22180066002127833352,
259	36351.27591501940507276287,
260	8785.536302431013170870835,
261	];
262	static $lg_q2 = [
263	183.0328399370592604055942,
264	7765.049321445005871323047,
265	133190.3827966074194402448,
266	1136705.821321969608938755,
267	5267964.117437946917577538,
268	13467014.54311101692290052,
269	17827365.30353274213975932,
270	9533095.591844353613395747,
271	];
272	static $lg_q4 = [
273	2690.530175870899333379843,
274	639388.5654300092398984238,
275	41355999.30241388052042842,
276	1120872109.61614794137657,
277	14886137286.78813811542398,
278	101680358627.2438228077304,
279	341747634550.7377132798597,
280	446315818741.9713286462081,
281	];
282	static $lg_c = [
283	-0.001910444077728,
284	8.4171387781295e-4,
285	-5.952379913043012e-4,
286	7.93650793500350248e-4,
287	-0.002777777777777681622553,
288	0.08333333333333333331554247,
289	0.0057083835261,
290	];
291
292	// Rough estimate of the fourth root of logGamma_xBig
293	static $lg_frtbig = 2.25e76;
294	static $pnt68 = 0.6796875;
295
296	if ($x == self::$logGammaCacheX) {
297	return self::$logGammaCacheResult;
298	}
299	$y = $x;
300	if ($y > 0.0 && $y <= self::LOG_GAMMA_X_MAX_VALUE) {
301	if ($y <= self::EPS) {
302	$res = -log($y);
303	} elseif ($y <= 1.5) {
304	// ---------------------
305	// EPS .LT. X .LE. 1.5
306	// ---------------------
307	if ($y < $pnt68) {
308	$corr = -log($y);
309	$xm1 = $y;
310	} else {
311	$corr = 0.0;
312	$xm1 = $y - 1.0;
313	}
314	if ($y <= 0.5 \|\| $y >= $pnt68) {
315	$xden = 1.0;
316	$xnum = 0.0;
317	for ($i = 0; $i < 8; ++$i) {
318	$xnum = $xnum * $xm1 + $lg_p1[$i];
319	$xden = $xden * $xm1 + $lg_q1[$i];
320	}
321	$res = $corr + $xm1 * ($lg_d1 + $xm1 * ($xnum / $xden));
322	} else {
323	$xm2 = $y - 1.0;
324	$xden = 1.0;
325	$xnum = 0.0;
326	for ($i = 0; $i < 8; ++$i) {
327	$xnum = $xnum * $xm2 + $lg_p2[$i];
328	$xden = $xden * $xm2 + $lg_q2[$i];
329	}
330	$res = $corr + $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
331	}
332	} elseif ($y <= 4.0) {
333	// ---------------------
334	// 1.5 .LT. X .LE. 4.0
335	// ---------------------
336	$xm2 = $y - 2.0;
337	$xden = 1.0;
338	$xnum = 0.0;
339	for ($i = 0; $i < 8; ++$i) {
340	$xnum = $xnum * $xm2 + $lg_p2[$i];
341	$xden = $xden * $xm2 + $lg_q2[$i];
342	}
343	$res = $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
344	} elseif ($y <= 12.0) {
345	// ----------------------
346	// 4.0 .LT. X .LE. 12.0
347	// ----------------------
348	$xm4 = $y - 4.0;
349	$xden = -1.0;
350	$xnum = 0.0;
351	for ($i = 0; $i < 8; ++$i) {
352	$xnum = $xnum * $xm4 + $lg_p4[$i];
353	$xden = $xden * $xm4 + $lg_q4[$i];
354	}
355	$res = $lg_d4 + $xm4 * ($xnum / $xden);
356	} else {
357	// ---------------------------------
358	// Evaluate for argument .GE. 12.0
359	// ---------------------------------
360	$res = 0.0;
361	if ($y <= $lg_frtbig) {
362	$res = $lg_c[6];
363	$ysq = $y * $y;
364	for ($i = 0; $i < 6; ++$i) {
365	$res = $res / $ysq + $lg_c[$i];
366	}
367	$res /= $y;
368	$corr = log($y);
369	$res = $res + log(self::SQRT2PI) - 0.5 * $corr;
370	$res += $y * ($corr - 1.0);
371	}
372	}
373	} else {
374	// --------------------------
375	// Return for bad arguments
376	// --------------------------
377	$res = self::MAX_VALUE;
378	}
379	// ------------------------------
380	// Final adjustments and return
381	// ------------------------------
382	self::$logGammaCacheX = $x;
383	self::$logGammaCacheResult = $res;
384
385	return $res;
386	}
387
388	//
389	// Private implementation of the incomplete Gamma function
390	//
391	private static function incompleteGamma($a, $x)
392	{
393	static $max = 32;
394	$summer = 0;
395	for ($n = 0; $n <= $max; ++$n) {
396	$divisor = $a;
397	for ($i = 1; $i <= $n; ++$i) {
398	$divisor *= ($a + $i);
399	}
400	$summer += (pow($x, $n) / $divisor);
401	}
402
403	return pow($x, $a) * exp(0 - $x) * $summer;
404	}
405
406	//
407	// Private implementation of the Gamma function
408	//
409	private static function gamma($data)
410	{
411	if ($data == 0.0) {
412	return 0;
413	}
414
415	static $p0 = 1.000000000190015;
416	static $p = [
417	1 => 76.18009172947146,
418	2 => -86.50532032941677,
419	3 => 24.01409824083091,
420	4 => -1.231739572450155,
421	5 => 1.208650973866179e-3,
422	6 => -5.395239384953e-6,
423	];
424
425	$y = $x = $data;
426	$tmp = $x + 5.5;
427	$tmp -= ($x + 0.5) * log($tmp);
428
429	$summer = $p0;
430	for ($j = 1; $j <= 6; ++$j) {
431	$summer += ($p[$j] / ++$y);
432	}
433
434	return exp(0 - $tmp + log(self::SQRT2PI * $summer / $x));
435	}
436
437	/*
438	* inverse_ncdf.php
439	* -------------------
440	* begin : Friday, January 16, 2004
441	* copyright : (C) 2004 Michael Nickerson
442	* email : nickersonm@yahoo.com
443	*
444	*/
445	private static function inverseNcdf($p)
446	{
447	// Inverse ncdf approximation by Peter J. Acklam, implementation adapted to
448	// PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
449	// a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
450	// I have not checked the accuracy of this implementation. Be aware that PHP
451	// will truncate the coeficcients to 14 digits.
452
453	// You have permission to use and distribute this function freely for
454	// whatever purpose you want, but please show common courtesy and give credit
455	// where credit is due.
456
457	// Input paramater is $p - probability - where 0 < p < 1.
458
459	// Coefficients in rational approximations
460	static $a = [
461	1 => -3.969683028665376e+01,
462	2 => 2.209460984245205e+02,
463	3 => -2.759285104469687e+02,
464	4 => 1.383577518672690e+02,
465	5 => -3.066479806614716e+01,
466	6 => 2.506628277459239e+00,
467	];
468
469	static $b = [
470	1 => -5.447609879822406e+01,
471	2 => 1.615858368580409e+02,
472	3 => -1.556989798598866e+02,
473	4 => 6.680131188771972e+01,
474	5 => -1.328068155288572e+01,
475	];
476
477	static $c = [
478	1 => -7.784894002430293e-03,
479	2 => -3.223964580411365e-01,
480	3 => -2.400758277161838e+00,
481	4 => -2.549732539343734e+00,
482	5 => 4.374664141464968e+00,
483	6 => 2.938163982698783e+00,
484	];
485
486	static $d = [
487	1 => 7.784695709041462e-03,
488	2 => 3.224671290700398e-01,
489	3 => 2.445134137142996e+00,
490	4 => 3.754408661907416e+00,
491	];
492
493	// Define lower and upper region break-points.
494	$p_low = 0.02425; //Use lower region approx. below this
495	$p_high = 1 - $p_low; //Use upper region approx. above this
496
497	if (0 < $p && $p < $p_low) {
498	// Rational approximation for lower region.
499	$q = sqrt(-2 * log($p));
500
501	return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
502	(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
503	} elseif ($p_low <= $p && $p <= $p_high) {
504	// Rational approximation for central region.
505	$q = $p - 0.5;
506	$r = $q * $q;
507
508	return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q /
509	((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1);
510	} elseif ($p_high < $p && $p < 1) {
511	// Rational approximation for upper region.
512	$q = sqrt(-2 * log(1 - $p));
513
514	return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
515	(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
516	}
517	// If 0 < p < 1, return a null value
518	return Functions::NULL();
519	}
520
521	/**
522	* AVEDEV.
523	*
524	* Returns the average of the absolute deviations of data points from their mean.
525	* AVEDEV is a measure of the variability in a data set.
526	*
527	* Excel Function:
528	* AVEDEV(value1[,value2[, ...]])
529	*
530	* @category Statistical Functions
531	*
532	* @param mixed ...$args Data values
533	*
534	* @return float
535	*/
536	public static function AVEDEV(...$args)
537	{
538	$aArgs = Functions::flattenArrayIndexed($args);
539
540	// Return value
541	$returnValue = null;
542
543	$aMean = self::AVERAGE($aArgs);
544	if ($aMean != Functions::DIV0()) {
545	$aCount = 0;
546	foreach ($aArgs as $k => $arg) {
547	if ((is_bool($arg)) &&
548	((!Functions::isCellValue($k)) \|\| (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) {
549	$arg = (int) $arg;
550	}
551	// Is it a numeric value?
552	if ((is_numeric($arg)) && (!is_string($arg))) {
553	if ($returnValue === null) {
554	$returnValue = abs($arg - $aMean);
555	} else {
556	$returnValue += abs($arg - $aMean);
557	}
558	++$aCount;
559	}
560	}
561
562	// Return
563	if ($aCount == 0) {
564	return Functions::DIV0();
565	}
566
567	return $returnValue / $aCount;
568	}
569
570	return Functions::NAN();
571	}
572
573	/**
574	* AVERAGE.
575	*
576	* Returns the average (arithmetic mean) of the arguments
577	*
578	* Excel Function:
579	* AVERAGE(value1[,value2[, ...]])
580	*
581	* @category Statistical Functions
582	*
583	* @param mixed ...$args Data values
584	*
585	* @return float
586	*/
587	public static function AVERAGE(...$args)
588	{
589	$returnValue = $aCount = 0;
590
591	// Loop through arguments
592	foreach (Functions::flattenArrayIndexed($args) as $k => $arg) {
593	if ((is_bool($arg)) &&
594	((!Functions::isCellValue($k)) \|\| (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) {
595	$arg = (int) $arg;
596	}
597	// Is it a numeric value?
598	if ((is_numeric($arg)) && (!is_string($arg))) {
599	if ($returnValue === null) {
600	$returnValue = $arg;
601	} else {
602	$returnValue += $arg;
603	}
604	++$aCount;
605	}
606	}
607
608	// Return
609	if ($aCount > 0) {
610	return $returnValue / $aCount;
611	}
612
613	return Functions::DIV0();
614	}
615
616	/**
617	* AVERAGEA.
618	*
619	* Returns the average of its arguments, including numbers, text, and logical values
620	*
621	* Excel Function:
622	* AVERAGEA(value1[,value2[, ...]])
623	*
624	* @category Statistical Functions
625	*
626	* @param mixed ...$args Data values
627	*
628	* @return float
629	*/
630	public static function AVERAGEA(...$args)
631	{
632	$returnValue = null;
633
634	$aCount = 0;
635	// Loop through arguments
636	foreach (Functions::flattenArrayIndexed($args) as $k => $arg) {
637	if ((is_bool($arg)) &&
638	(!Functions::isMatrixValue($k))) {
639	} else {
640	if ((is_numeric($arg)) \|\| (is_bool($arg)) \|\| ((is_string($arg) && ($arg != '')))) {
641	if (is_bool($arg)) {
642	$arg = (int) $arg;
643	} elseif (is_string($arg)) {
644	$arg = 0;
645	}
646	if ($returnValue === null) {
647	$returnValue = $arg;
648	} else {
649	$returnValue += $arg;
650	}
651	++$aCount;
652	}
653	}
654	}
655
656	if ($aCount > 0) {
657	return $returnValue / $aCount;
658	}
659
660	return Functions::DIV0();
661	}
662
663	/**
664	* AVERAGEIF.
665	*
666	* Returns the average value from a range of cells that contain numbers within the list of arguments
667	*
668	* Excel Function:
669	* AVERAGEIF(value1[,value2[, ...]],condition)
670	*
671	* @category Mathematical and Trigonometric Functions
672	*
673	* @param mixed $aArgs Data values
674	* @param string $condition the criteria that defines which cells will be checked
675	* @param mixed[] $averageArgs Data values
676	*
677	* @return float
678	*/
679	public static function AVERAGEIF($aArgs, $condition, $averageArgs = [])
680	{
681	$returnValue = 0;
682
683	$aArgs = Functions::flattenArray($aArgs);
684	$averageArgs = Functions::flattenArray($averageArgs);
685	if (empty($averageArgs)) {
686	$averageArgs = $aArgs;
687	}
688	$condition = Functions::ifCondition($condition);
689	// Loop through arguments
690	$aCount = 0;
691	foreach ($aArgs as $key => $arg) {
692	if (!is_numeric($arg)) {
693	$arg = Calculation::wrapResult(strtoupper($arg));
694	}
695	$testCondition = '=' . $arg . $condition;
696	if (Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
697	if (($returnValue === null) \|\| ($arg > $returnValue)) {
698	$returnValue += $arg;
699	++$aCount;
700	}
701	}
702	}
703
704	if ($aCount > 0) {
705	return $returnValue / $aCount;
706	}
707
708	return Functions::DIV0();
709	}
710
711	/**
712	* BETADIST.
713	*
714	* Returns the beta distribution.
715	*
716	* @param float $value Value at which you want to evaluate the distribution
717	* @param float $alpha Parameter to the distribution
718	* @param float $beta Parameter to the distribution
719	* @param mixed $rMin
720	* @param mixed $rMax
721	*
722	* @return float
723	*/
724	public static function BETADIST($value, $alpha, $beta, $rMin = 0, $rMax = 1)
725	{
726	$value = Functions::flattenSingleValue($value);
727	$alpha = Functions::flattenSingleValue($alpha);
728	$beta = Functions::flattenSingleValue($beta);
729	$rMin = Functions::flattenSingleValue($rMin);
730	$rMax = Functions::flattenSingleValue($rMax);
731
732	if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
733	if (($value < $rMin) \|\| ($value > $rMax) \|\| ($alpha <= 0) \|\| ($beta <= 0) \|\| ($rMin == $rMax)) {
734	return Functions::NAN();
735	}
736	if ($rMin > $rMax) {
737	$tmp = $rMin;
738	$rMin = $rMax;
739	$rMax = $tmp;
740	}
741	$value -= $rMin;
742	$value /= ($rMax - $rMin);
743
744	return self::incompleteBeta($value, $alpha, $beta);
745	}
746
747	return Functions::VALUE();
748	}
749
750	/**
751	* BETAINV.
752	*
753	* Returns the inverse of the beta distribution.
754	*
755	* @param float $probability Probability at which you want to evaluate the distribution
756	* @param float $alpha Parameter to the distribution
757	* @param float $beta Parameter to the distribution
758	* @param float $rMin Minimum value
759	* @param float $rMax Maximum value
760	*
761	* @return float
762	*/
763	public static function BETAINV($probability, $alpha, $beta, $rMin = 0, $rMax = 1)
764	{
765	$probability = Functions::flattenSingleValue($probability);
766	$alpha = Functions::flattenSingleValue($alpha);
767	$beta = Functions::flattenSingleValue($beta);
768	$rMin = Functions::flattenSingleValue($rMin);
769	$rMax = Functions::flattenSingleValue($rMax);
770
771	if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
772	if (($alpha <= 0) \|\| ($beta <= 0) \|\| ($rMin == $rMax) \|\| ($probability <= 0) \|\| ($probability > 1)) {
773	return Functions::NAN();
774	}
775	if ($rMin > $rMax) {
776	$tmp = $rMin;
777	$rMin = $rMax;
778	$rMax = $tmp;
779	}
780	$a = 0;
781	$b = 2;
782
783	$i = 0;
784	while ((($b - $a) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) {
785	$guess = ($a + $b) / 2;
786	$result = self::BETADIST($guess, $alpha, $beta);
787	if (($result == $probability) \|\| ($result == 0)) {
788	$b = $a;
789	} elseif ($result > $probability) {
790	$b = $guess;
791	} else {
792	$a = $guess;
793	}
794	}
795	if ($i == self::MAX_ITERATIONS) {
796	return Functions::NA();
797	}
798
799	return round($rMin + $guess * ($rMax - $rMin), 12);
800	}
801
802	return Functions::VALUE();
803	}
804
805	/**
806	* BINOMDIST.
807	*
808	* Returns the individual term binomial distribution probability. Use BINOMDIST in problems with
809	* a fixed number of tests or trials, when the outcomes of any trial are only success or failure,
810	* when trials are independent, and when the probability of success is constant throughout the
811	* experiment. For example, BINOMDIST can calculate the probability that two of the next three
812	* babies born are male.
813	*
814	* @param float $value Number of successes in trials
815	* @param float $trials Number of trials
816	* @param float $probability Probability of success on each trial
817	* @param bool $cumulative
818	*
819	* @return float
820	*
821	* @todo Cumulative distribution function
822	*/
823	public static function BINOMDIST($value, $trials, $probability, $cumulative)
824	{
825	$value = floor(Functions::flattenSingleValue($value));
826	$trials = floor(Functions::flattenSingleValue($trials));
827	$probability = Functions::flattenSingleValue($probability);
828
829	if ((is_numeric($value)) && (is_numeric($trials)) && (is_numeric($probability))) {
830	if (($value < 0) \|\| ($value > $trials)) {
831	return Functions::NAN();
832	}
833	if (($probability < 0) \|\| ($probability > 1)) {
834	return Functions::NAN();
835	}
836	if ((is_numeric($cumulative)) \|\| (is_bool($cumulative))) {
837	if ($cumulative) {
838	$summer = 0;
839	for ($i = 0; $i <= $value; ++$i) {
840	$summer += MathTrig::COMBIN($trials, $i) * pow($probability, $i) * pow(1 - $probability, $trials - $i);
841	}
842
843	return $summer;
844	}
845
846	return MathTrig::COMBIN($trials, $value) * pow($probability, $value) * pow(1 - $probability, $trials - $value);
847	}
848	}
849
850	return Functions::VALUE();
851	}
852
853	/**
854	* CHIDIST.
855	*
856	* Returns the one-tailed probability of the chi-squared distribution.
857	*
858	* @param float $value Value for the function
859	* @param float $degrees degrees of freedom
860	*
861	* @return float
862	*/
863	public static function CHIDIST($value, $degrees)
864	{
865	$value = Functions::flattenSingleValue($value);
866	$degrees = floor(Functions::flattenSingleValue($degrees));
867
868	if ((is_numeric($value)) && (is_numeric($degrees))) {
869	if ($degrees < 1) {
870	return Functions::NAN();
871	}
872	if ($value < 0) {
873	if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
874	return 1;
875	}
876
877	return Functions::NAN();
878	}
879
880	return 1 - (self::incompleteGamma($degrees / 2, $value / 2) / self::gamma($degrees / 2));
881	}
882
883	return Functions::VALUE();
884	}
885
886	/**
887	* CHIINV.
888	*
889	* Returns the one-tailed probability of the chi-squared distribution.
890	*
891	* @param float $probability Probability for the function
892	* @param float $degrees degrees of freedom
893	*
894	* @return float
895	*/
896	public static function CHIINV($probability, $degrees)
897	{
898	$probability = Functions::flattenSingleValue($probability);
899	$degrees = floor(Functions::flattenSingleValue($degrees));
900
901	if ((is_numeric($probability)) && (is_numeric($degrees))) {
902	$xLo = 100;
903	$xHi = 0;
904
905	$x = $xNew = 1;
906	$dx = 1;
907	$i = 0;
908
909	while ((abs($dx) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) {
910	// Apply Newton-Raphson step
911	$result = self::CHIDIST($x, $degrees);
912	$error = $result - $probability;
913	if ($error == 0.0) {
914	$dx = 0;
915	} elseif ($error < 0.0) {
916	$xLo = $x;
917	} else {
918	$xHi = $x;
919	}
920	// Avoid division by zero
921	if ($result != 0.0) {
922	$dx = $error / $result;
923	$xNew = $x - $dx;
924	}
925	// If the NR fails to converge (which for example may be the
926	// case if the initial guess is too rough) we apply a bisection
927	// step to determine a more narrow interval around the root.
928	if (($xNew < $xLo) \|\| ($xNew > $xHi) \|\| ($result == 0.0)) {
929	$xNew = ($xLo + $xHi) / 2;
930	$dx = $xNew - $x;
931	}
932	$x = $xNew;
933	}
934	if ($i == self::MAX_ITERATIONS) {
935	return Functions::NA();
936	}
937
938	return round($x, 12);
939	}
940
941	return Functions::VALUE();
942	}
943
944	/**
945	* CONFIDENCE.
946	*
947	* Returns the confidence interval for a population mean
948	*
949	* @param float $alpha
950	* @param float $stdDev Standard Deviation
951	* @param float $size
952	*
953	* @return float
954	*/
955	public static function CONFIDENCE($alpha, $stdDev, $size)
956	{
957	$alpha = Functions::flattenSingleValue($alpha);
958	$stdDev = Functions::flattenSingleValue($stdDev);
959	$size = floor(Functions::flattenSingleValue($size));
960
961	if ((is_numeric($alpha)) && (is_numeric($stdDev)) && (is_numeric($size))) {
962	if (($alpha <= 0) \|\| ($alpha >= 1)) {
963	return Functions::NAN();
964	}
965	if (($stdDev <= 0) \|\| ($size < 1)) {
966	return Functions::NAN();
967	}
968
969	return self::NORMSINV(1 - $alpha / 2) * $stdDev / sqrt($size);
970	}
971
972	return Functions::VALUE();
973	}
974
975	/**
976	* CORREL.
977	*
978	* Returns covariance, the average of the products of deviations for each data point pair.
979	*
980	* @param mixed $yValues array of mixed Data Series Y
981	* @param null\|mixed $xValues array of mixed Data Series X
982	*
983	* @return float
984	*/
985	public static function CORREL($yValues, $xValues = null)
986	{
987	if (($xValues === null) \|\| (!is_array($yValues)) \|\| (!is_array($xValues))) {
988	return Functions::VALUE();
989	}
990	if (!self::checkTrendArrays($yValues, $xValues)) {
991	return Functions::VALUE();
992	}
993	$yValueCount = count($yValues);
994	$xValueCount = count($xValues);
995
996	if (($yValueCount == 0) \|\| ($yValueCount != $xValueCount)) {
997	return Functions::NA();
998	} elseif ($yValueCount == 1) {
999	return Functions::DIV0();
1000	}
1001
1002	$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
1003
1004	return $bestFitLinear->getCorrelation();
1005	}
1006
1007	/**
1008	* COUNT.
1009	*
1010	* Counts the number of cells that contain numbers within the list of arguments
1011	*
1012	* Excel Function:
1013	* COUNT(value1[,value2[, ...]])
1014	*
1015	* @category Statistical Functions
1016	*
1017	* @param mixed ...$args Data values
1018	*
1019	* @return int
1020	*/
1021	public static function COUNT(...$args)
1022	{
1023	$returnValue = 0;
1024
1025	// Loop through arguments
1026	$aArgs = Functions::flattenArrayIndexed($args);
1027	foreach ($aArgs as $k => $arg) {
1028	if ((is_bool($arg)) &&
1029	((!Functions::isCellValue($k)) \|\| (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) {
1030	$arg = (int) $arg;
1031	}
1032	// Is it a numeric value?
1033	if ((is_numeric($arg)) && (!is_string($arg))) {
1034	++$returnValue;
1035	}
1036	}
1037
1038	return $returnValue;
1039	}
1040
1041	/**
1042	* COUNTA.
1043	*
1044	* Counts the number of cells that are not empty within the list of arguments
1045	*
1046	* Excel Function:
1047	* COUNTA(value1[,value2[, ...]])
1048	*
1049	* @category Statistical Functions
1050	*
1051	* @param mixed ...$args Data values
1052	*
1053	* @return int
1054	*/
1055	public static function COUNTA(...$args)
1056	{
1057	$returnValue = 0;
1058
1059	// Loop through arguments
1060	$aArgs = Functions::flattenArray($args);
1061	foreach ($aArgs as $arg) {
1062	// Is it a numeric, boolean or string value?
1063	if ((is_numeric($arg)) \|\| (is_bool($arg)) \|\| ((is_string($arg) && ($arg != '')))) {
1064	++$returnValue;
1065	}
1066	}
1067
1068	return $returnValue;
1069	}
1070
1071	/**
1072	* COUNTBLANK.
1073	*
1074	* Counts the number of empty cells within the list of arguments
1075	*
1076	* Excel Function:
1077	* COUNTBLANK(value1[,value2[, ...]])
1078	*
1079	* @category Statistical Functions
1080	*
1081	* @param mixed ...$args Data values
1082	*
1083	* @return int
1084	*/
1085	public static function COUNTBLANK(...$args)
1086	{
1087	$returnValue = 0;
1088
1089	// Loop through arguments
1090	$aArgs = Functions::flattenArray($args);
1091	foreach ($aArgs as $arg) {
1092	// Is it a blank cell?
1093	if (($arg === null) \|\| ((is_string($arg)) && ($arg == ''))) {
1094	++$returnValue;
1095	}
1096	}
1097
1098	return $returnValue;
1099	}
1100
1101	/**
1102	* COUNTIF.
1103	*
1104	* Counts the number of cells that contain numbers within the list of arguments
1105	*
1106	* Excel Function:
1107	* COUNTIF(value1[,value2[, ...]],condition)
1108	*
1109	* @category Statistical Functions
1110	*
1111	* @param mixed $aArgs Data values
1112	* @param string $condition the criteria that defines which cells will be counted
1113	*
1114	* @return int
1115	*/
1116	public static function COUNTIF($aArgs, $condition)
1117	{
1118	$returnValue = 0;
1119
1120	$aArgs = Functions::flattenArray($aArgs);
1121	$condition = Functions::ifCondition($condition);
1122	// Loop through arguments
1123	foreach ($aArgs as $arg) {
1124	if (!is_numeric($arg)) {
1125	$arg = Calculation::wrapResult(strtoupper($arg));
1126	}
1127	$testCondition = '=' . $arg . $condition;
1128	if (Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
1129	// Is it a value within our criteria
1130	++$returnValue;
1131	}
1132	}
1133
1134	return $returnValue;
1135	}
1136
1137	/**
1138	* COVAR.
1139	*
1140	* Returns covariance, the average of the products of deviations for each data point pair.
1141	*
1142	* @param mixed $yValues array of mixed Data Series Y
1143	* @param mixed $xValues array of mixed Data Series X
1144	*
1145	* @return float
1146	*/
1147	public static function COVAR($yValues, $xValues)
1148	{
1149	if (!self::checkTrendArrays($yValues, $xValues)) {
1150	return Functions::VALUE();
1151	}
1152	$yValueCount = count($yValues);
1153	$xValueCount = count($xValues);
1154
1155	if (($yValueCount == 0) \|\| ($yValueCount != $xValueCount)) {
1156	return Functions::NA();
1157	} elseif ($yValueCount == 1) {
1158	return Functions::DIV0();
1159	}
1160
1161	$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
1162
1163	return $bestFitLinear->getCovariance();
1164	}
1165
1166	/**
1167	* CRITBINOM.
1168	*
1169	* Returns the smallest value for which the cumulative binomial distribution is greater
1170	* than or equal to a criterion value
1171	*
1172	* See https://support.microsoft.com/en-us/help/828117/ for details of the algorithm used
1173	*
1174	* @param float $trials number of Bernoulli trials
1175	* @param float $probability probability of a success on each trial
1176	* @param float $alpha criterion value
1177	*
1178	* @return int
1179	*
1180	* @todo Warning. This implementation differs from the algorithm detailed on the MS
1181	* web site in that $CumPGuessMinus1 = $CumPGuess - 1 rather than $CumPGuess - $PGuess
1182	* This eliminates a potential endless loop error, but may have an adverse affect on the
1183	* accuracy of the function (although all my tests have so far returned correct results).
1184	*/
1185	public static function CRITBINOM($trials, $probability, $alpha)
1186	{
1187	$trials = floor(Functions::flattenSingleValue($trials));
1188	$probability = Functions::flattenSingleValue($probability);
1189	$alpha = Functions::flattenSingleValue($alpha);
1190
1191	if ((is_numeric($trials)) && (is_numeric($probability)) && (is_numeric($alpha))) {
1192	if ($trials < 0) {
1193	return Functions::NAN();
1194	} elseif (($probability < 0) \|\| ($probability > 1)) {
1195	return Functions::NAN();
1196	} elseif (($alpha < 0) \|\| ($alpha > 1)) {
1197	return Functions::NAN();
1198	} elseif ($alpha <= 0.5) {
1199	$t = sqrt(log(1 / ($alpha * $alpha)));
1200	$trialsApprox = 0 - ($t + (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t));
1201	} else {
1202	$t = sqrt(log(1 / pow(1 - $alpha, 2)));
1203	$trialsApprox = $t - (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t);
1204	}
1205	$Guess = floor($trials * $probability + $trialsApprox * sqrt($trials * $probability * (1 - $probability)));
1206	if ($Guess < 0) {
1207	$Guess = 0;
1208	} elseif ($Guess > $trials) {
1209	$Guess = $trials;
1210	}
1211
1212	$TotalUnscaledProbability = $UnscaledPGuess = $UnscaledCumPGuess = 0.0;
1213	$EssentiallyZero = 10e-12;
1214
1215	$m = floor($trials * $probability);
1216	++$TotalUnscaledProbability;
1217	if ($m == $Guess) {
1218	++$UnscaledPGuess;
1219	}
1220	if ($m <= $Guess) {
1221	++$UnscaledCumPGuess;
1222	}
1223
1224	$PreviousValue = 1;
1225	$Done = false;
1226	$k = $m + 1;
1227	while ((!$Done) && ($k <= $trials)) {
1228	$CurrentValue = $PreviousValue * ($trials - $k + 1) * $probability / ($k * (1 - $probability));
1229	$TotalUnscaledProbability += $CurrentValue;
1230	if ($k == $Guess) {
1231	$UnscaledPGuess += $CurrentValue;
1232	}
1233	if ($k <= $Guess) {
1234	$UnscaledCumPGuess += $CurrentValue;
1235	}
1236	if ($CurrentValue <= $EssentiallyZero) {
1237	$Done = true;
1238	}
1239	$PreviousValue = $CurrentValue;
1240	++$k;
1241	}
1242
1243	$PreviousValue = 1;
1244	$Done = false;
1245	$k = $m - 1;
1246	while ((!$Done) && ($k >= 0)) {
1247	$CurrentValue = $PreviousValue * $k + 1 * (1 - $probability) / (($trials - $k) * $probability);
1248	$TotalUnscaledProbability += $CurrentValue;
1249	if ($k == $Guess) {
1250	$UnscaledPGuess += $CurrentValue;
1251	}
1252	if ($k <= $Guess) {
1253	$UnscaledCumPGuess += $CurrentValue;
1254	}
1255	if ($CurrentValue <= $EssentiallyZero) {
1256	$Done = true;
1257	}
1258	$PreviousValue = $CurrentValue;
1259	--$k;
1260	}
1261
1262	$PGuess = $UnscaledPGuess / $TotalUnscaledProbability;
1263	$CumPGuess = $UnscaledCumPGuess / $TotalUnscaledProbability;
1264
1265	$CumPGuessMinus1 = $CumPGuess - 1;
1266
1267	while (true) {
1268	if (($CumPGuessMinus1 < $alpha) && ($CumPGuess >= $alpha)) {
1269	return $Guess;
1270	} elseif (($CumPGuessMinus1 < $alpha) && ($CumPGuess < $alpha)) {
1271	$PGuessPlus1 = $PGuess * ($trials - $Guess) * $probability / $Guess / (1 - $probability);
1272	$CumPGuessMinus1 = $CumPGuess;
1273	$CumPGuess = $CumPGuess + $PGuessPlus1;
1274	$PGuess = $PGuessPlus1;
1275	++$Guess;
1276	} elseif (($CumPGuessMinus1 >= $alpha) && ($CumPGuess >= $alpha)) {
1277	$PGuessMinus1 = $PGuess * $Guess * (1 - $probability) / ($trials - $Guess + 1) / $probability;
1278	$CumPGuess = $CumPGuessMinus1;
1279	$CumPGuessMinus1 = $CumPGuessMinus1 - $PGuess;
1280	$PGuess = $PGuessMinus1;
1281	--$Guess;
1282	}
1283	}
1284	}
1285
1286	return Functions::VALUE();
1287	}
1288
1289	/**
1290	* DEVSQ.
1291	*
1292	* Returns the sum of squares of deviations of data points from their sample mean.
1293	*
1294	* Excel Function:
1295	* DEVSQ(value1[,value2[, ...]])
1296	*
1297	* @category Statistical Functions
1298	*
1299	* @param mixed ...$args Data values
1300	*
1301	* @return float
1302	*/
1303	public static function DEVSQ(...$args)
1304	{
1305	$aArgs = Functions::flattenArrayIndexed($args);
1306
1307	// Return value
1308	$returnValue = null;
1309
1310	$aMean = self::AVERAGE($aArgs);
1311	if ($aMean != Functions::DIV0()) {
1312	$aCount = -1;
1313	foreach ($aArgs as $k => $arg) {
1314	// Is it a numeric value?
1315	if ((is_bool($arg)) &&
1316	((!Functions::isCellValue($k)) \|\|
1317	(Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) {
1318	$arg = (int) $arg;
1319	}
1320	if ((is_numeric($arg)) && (!is_string($arg))) {
1321	if ($returnValue === null) {
1322	$returnValue = pow(($arg - $aMean), 2);
1323	} else {
1324	$returnValue += pow(($arg - $aMean), 2);
1325	}
1326	++$aCount;
1327	}
1328	}
1329
1330	// Return
1331	if ($returnValue === null) {
1332	return Functions::NAN();
1333	}
1334
1335	return $returnValue;
1336	}
1337
1338	return self::NA();
1339	}
1340
1341	/**
1342	* EXPONDIST.
1343	*
1344	* Returns the exponential distribution. Use EXPONDIST to model the time between events,
1345	* such as how long an automated bank teller takes to deliver cash. For example, you can
1346	* use EXPONDIST to determine the probability that the process takes at most 1 minute.
1347	*
1348	* @param float $value Value of the function
1349	* @param float $lambda The parameter value
1350	* @param bool $cumulative
1351	*
1352	* @return float
1353	*/
1354	public static function EXPONDIST($value, $lambda, $cumulative)
1355	{
1356	$value = Functions::flattenSingleValue($value);
1357	$lambda = Functions::flattenSingleValue($lambda);
1358	$cumulative = Functions::flattenSingleValue($cumulative);
1359
1360	if ((is_numeric($value)) && (is_numeric($lambda))) {
1361	if (($value < 0) \|\| ($lambda < 0)) {
1362	return Functions::NAN();
1363	}
1364	if ((is_numeric($cumulative)) \|\| (is_bool($cumulative))) {
1365	if ($cumulative) {
1366	return 1 - exp(0 - $value * $lambda);
1367	}
1368
1369	return $lambda * exp(0 - $value * $lambda);
1370	}
1371	}
1372
1373	return Functions::VALUE();
1374	}
1375
1376	/**
1377	* FISHER.
1378	*
1379	* Returns the Fisher transformation at x. This transformation produces a function that
1380	* is normally distributed rather than skewed. Use this function to perform hypothesis
1381	* testing on the correlation coefficient.
1382	*
1383	* @param float $value
1384	*
1385	* @return float
1386	*/
1387	public static function FISHER($value)
1388	{
1389	$value = Functions::flattenSingleValue($value);
1390
1391	if (is_numeric($value)) {
1392	if (($value <= -1) \|\| ($value >= 1)) {
1393	return Functions::NAN();
1394	}
1395
1396	return 0.5 * log((1 + $value) / (1 - $value));
1397	}
1398
1399	return Functions::VALUE();
1400	}
1401
1402	/**
1403	* FISHERINV.
1404	*
1405	* Returns the inverse of the Fisher transformation. Use this transformation when
1406	* analyzing correlations between ranges or arrays of data. If y = FISHER(x), then
1407	* FISHERINV(y) = x.
1408	*
1409	* @param float $value
1410	*
1411	* @return float
1412	*/
1413	public static function FISHERINV($value)
1414	{
1415	$value = Functions::flattenSingleValue($value);
1416
1417	if (is_numeric($value)) {
1418	return (exp(2 * $value) - 1) / (exp(2 * $value) + 1);
1419	}
1420
1421	return Functions::VALUE();
1422	}
1423
1424	/**
1425	* FORECAST.
1426	*
1427	* Calculates, or predicts, a future value by using existing values. The predicted value is a y-value for a given x-value.
1428	*
1429	* @param float $xValue Value of X for which we want to find Y
1430	* @param mixed $yValues array of mixed Data Series Y
1431	* @param mixed $xValues of mixed Data Series X
1432	*
1433	* @return float
1434	*/
1435	public static function FORECAST($xValue, $yValues, $xValues)
1436	{
1437	$xValue = Functions::flattenSingleValue($xValue);
1438	if (!is_numeric($xValue)) {
1439	return Functions::VALUE();
1440	} elseif (!self::checkTrendArrays($yValues, $xValues)) {
1441	return Functions::VALUE();
1442	}
1443	$yValueCount = count($yValues);
1444	$xValueCount = count($xValues);
1445
1446	if (($yValueCount == 0) \|\| ($yValueCount != $xValueCount)) {
1447	return Functions::NA();
1448	} elseif ($yValueCount == 1) {
1449	return Functions::DIV0();
1450	}
1451
1452	$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
1453
1454	return $bestFitLinear->getValueOfYForX($xValue);
1455	}
1456
1457	/**
1458	* GAMMADIST.
1459	*
1460	* Returns the gamma distribution.
1461	*
1462	* @param float $value Value at which you want to evaluate the distribution
1463	* @param float $a Parameter to the distribution
1464	* @param float $b Parameter to the distribution
1465	* @param bool $cumulative
1466	*
1467	* @return float
1468	*/
1469	public static function GAMMADIST($value, $a, $b, $cumulative)
1470	{
1471	$value = Functions::flattenSingleValue($value);
1472	$a = Functions::flattenSingleValue($a);
1473	$b = Functions::flattenSingleValue($b);
1474
1475	if ((is_numeric($value)) && (is_numeric($a)) && (is_numeric($b))) {
1476	if (($value < 0) \|\| ($a <= 0) \|\| ($b <= 0)) {
1477	return Functions::NAN();
1478	}
1479	if ((is_numeric($cumulative)) \|\| (is_bool($cumulative))) {
1480	if ($cumulative) {
1481	return self::incompleteGamma($a, $value / $b) / self::gamma($a);
1482	}
1483
1484	return (1 / (pow($b, $a) * self::gamma($a))) * pow($value, $a - 1) * exp(0 - ($value / $b));
1485	}
1486	}
1487
1488	return Functions::VALUE();
1489	}
1490
1491	/**
1492	* GAMMAINV.
1493	*
1494	* Returns the inverse of the beta distribution.
1495	*
1496	* @param float $probability Probability at which you want to evaluate the distribution
1497	* @param float $alpha Parameter to the distribution
1498	* @param float $beta Parameter to the distribution
1499	*
1500	* @return float
1501	*/
1502	public static function GAMMAINV($probability, $alpha, $beta)
1503	{
1504	$probability = Functions::flattenSingleValue($probability);
1505	$alpha = Functions::flattenSingleValue($alpha);
1506	$beta = Functions::flattenSingleValue($beta);
1507
1508	if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta))) {
1509	if (($alpha <= 0) \|\| ($beta <= 0) \|\| ($probability < 0) \|\| ($probability > 1)) {
1510	return Functions::NAN();
1511	}
1512
1513	$xLo = 0;
1514	$xHi = $alpha * $beta * 5;
1515
1516	$x = $xNew = 1;
1517	$error = $pdf = 0;
1518	$dx = 1024;
1519	$i = 0;
1520
1521	while ((abs($dx) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) {
1522	// Apply Newton-Raphson step
1523	$error = self::GAMMADIST($x, $alpha, $beta, true) - $probability;
1524	if ($error < 0.0) {
1525	$xLo = $x;
1526	} else {
1527	$xHi = $x;
1528	}
1529	$pdf = self::GAMMADIST($x, $alpha, $beta, false);
1530	// Avoid division by zero
1531	if ($pdf != 0.0) {
1532	$dx = $error / $pdf;
1533	$xNew = $x - $dx;
1534	}
1535	// If the NR fails to converge (which for example may be the
1536	// case if the initial guess is too rough) we apply a bisection
1537	// step to determine a more narrow interval around the root.
1538	if (($xNew < $xLo) \|\| ($xNew > $xHi) \|\| ($pdf == 0.0)) {
1539	$xNew = ($xLo + $xHi) / 2;
1540	$dx = $xNew - $x;
1541	}
1542	$x = $xNew;
1543	}
1544	if ($i == self::MAX_ITERATIONS) {
1545	return Functions::NA();
1546	}
1547
1548	return $x;
1549	}
1550
1551	return Functions::VALUE();
1552	}
1553
1554	/**
1555	* GAMMALN.
1556	*
1557	* Returns the natural logarithm of the gamma function.
1558	*
1559	* @param float $value
1560	*
1561	* @return float
1562	*/
1563	public static function GAMMALN($value)
1564	{
1565	$value = Functions::flattenSingleValue($value);
1566
1567	if (is_numeric($value)) {
1568	if ($value <= 0) {
1569	return Functions::NAN();
1570	}
1571
1572	return log(self::gamma($value));
1573	}
1574
1575	return Functions::VALUE();
1576	}
1577
1578	/**
1579	* GEOMEAN.
1580	*
1581	* Returns the geometric mean of an array or range of positive data. For example, you
1582	* can use GEOMEAN to calculate average growth rate given compound interest with
1583	* variable rates.
1584	*
1585	* Excel Function:
1586	* GEOMEAN(value1[,value2[, ...]])
1587	*
1588	* @category Statistical Functions
1589	*
1590	* @param mixed ...$args Data values
1591	*
1592	* @return float
1593	*/
1594	public static function GEOMEAN(...$args)
1595	{
1596	$aArgs = Functions::flattenArray($args);
1597
1598	$aMean = MathTrig::PRODUCT($aArgs);
1599	if (is_numeric($aMean) && ($aMean > 0)) {
1600	$aCount = self::COUNT($aArgs);
1601	if (self::MIN($aArgs) > 0) {
1602	return pow($aMean, (1 / $aCount));
1603	}
1604	}
1605
1606	return Functions::NAN();
1607	}
1608
1609	/**
1610	* GROWTH.
1611	*
1612	* Returns values along a predicted emponential Trend
1613	*
1614	* @param mixed[] $yValues Data Series Y
1615	* @param mixed[] $xValues Data Series X
1616	* @param mixed[] $newValues Values of X for which we want to find Y
1617	* @param bool $const a logical value specifying whether to force the intersect to equal 0
1618	*
1619	* @return array of float
1620	*/
1621	public static function GROWTH($yValues, $xValues = [], $newValues = [], $const = true)
1622	{
1623	$yValues = Functions::flattenArray($yValues);
1624	$xValues = Functions::flattenArray($xValues);
1625	$newValues = Functions::flattenArray($newValues);
1626	$const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const);
1627
1628	$bestFitExponential = Trend::calculate(Trend::TREND_EXPONENTIAL, $yValues, $xValues, $const);
1629	if (empty($newValues)) {
1630	$newValues = $bestFitExponential->getXValues();
1631	}
1632
1633	$returnArray = [];
1634	foreach ($newValues as $xValue) {
1635	$returnArray[0][] = $bestFitExponential->getValueOfYForX($xValue);
1636	}
1637
1638	return $returnArray;
1639	}
1640
1641	/**
1642	* HARMEAN.
1643	*
1644	* Returns the harmonic mean of a data set. The harmonic mean is the reciprocal of the
1645	* arithmetic mean of reciprocals.
1646	*
1647	* Excel Function:
1648	* HARMEAN(value1[,value2[, ...]])
1649	*
1650	* @category Statistical Functions
1651	*
1652	* @param mixed ...$args Data values
1653	*
1654	* @return float
1655	*/
1656	public static function HARMEAN(...$args)
1657	{
1658	// Return value
1659	$returnValue = Functions::NA();
1660
1661	// Loop through arguments
1662	$aArgs = Functions::flattenArray($args);
1663	if (self::MIN($aArgs) < 0) {
1664	return Functions::NAN();
1665	}
1666	$aCount = 0;
1667	foreach ($aArgs as $arg) {
1668	// Is it a numeric value?
1669	if ((is_numeric($arg)) && (!is_string($arg))) {
1670	if ($arg <= 0) {
1671	return Functions::NAN();
1672	}
1673	if ($returnValue === null) {
1674	$returnValue = (1 / $arg);
1675	} else {
1676	$returnValue += (1 / $arg);
1677	}
1678	++$aCount;
1679	}
1680	}
1681
1682	// Return
1683	if ($aCount > 0) {
1684	return 1 / ($returnValue / $aCount);
1685	}
1686
1687	return $returnValue;
1688	}
1689
1690	/**
1691	* HYPGEOMDIST.
1692	*
1693	* Returns the hypergeometric distribution. HYPGEOMDIST returns the probability of a given number of
1694	* sample successes, given the sample size, population successes, and population size.
1695	*
1696	* @param float $sampleSuccesses Number of successes in the sample
1697	* @param float $sampleNumber Size of the sample
1698	* @param float $populationSuccesses Number of successes in the population
1699	* @param float $populationNumber Population size
1700	*
1701	* @return float
1702	*/
1703	public static function HYPGEOMDIST($sampleSuccesses, $sampleNumber, $populationSuccesses, $populationNumber)
1704	{
1705	$sampleSuccesses = floor(Functions::flattenSingleValue($sampleSuccesses));
1706	$sampleNumber = floor(Functions::flattenSingleValue($sampleNumber));
1707	$populationSuccesses = floor(Functions::flattenSingleValue($populationSuccesses));
1708	$populationNumber = floor(Functions::flattenSingleValue($populationNumber));
1709
1710	if ((is_numeric($sampleSuccesses)) && (is_numeric($sampleNumber)) && (is_numeric($populationSuccesses)) && (is_numeric($populationNumber))) {
1711	if (($sampleSuccesses < 0) \|\| ($sampleSuccesses > $sampleNumber) \|\| ($sampleSuccesses > $populationSuccesses)) {
1712	return Functions::NAN();
1713	}
1714	if (($sampleNumber <= 0) \|\| ($sampleNumber > $populationNumber)) {
1715	return Functions::NAN();
1716	}
1717	if (($populationSuccesses <= 0) \|\| ($populationSuccesses > $populationNumber)) {
1718	return Functions::NAN();
1719	}
1720
1721	return MathTrig::COMBIN($populationSuccesses, $sampleSuccesses) *
1722	MathTrig::COMBIN($populationNumber - $populationSuccesses, $sampleNumber - $sampleSuccesses) /
1723	MathTrig::COMBIN($populationNumber, $sampleNumber);
1724	}
1725
1726	return Functions::VALUE();
1727	}
1728
1729	/**
1730	* INTERCEPT.
1731	*
1732	* Calculates the point at which a line will intersect the y-axis by using existing x-values and y-values.
1733	*
1734	* @param mixed[] $yValues Data Series Y
1735	* @param mixed[] $xValues Data Series X
1736	*
1737	* @return float
1738	*/
1739	public static function INTERCEPT($yValues, $xValues)
1740	{
1741	if (!self::checkTrendArrays($yValues, $xValues)) {
1742	return Functions::VALUE();
1743	}
1744	$yValueCount = count($yValues);
1745	$xValueCount = count($xValues);
1746
1747	if (($yValueCount == 0) \|\| ($yValueCount != $xValueCount)) {
1748	return Functions::NA();
1749	} elseif ($yValueCount == 1) {
1750	return Functions::DIV0();
1751	}
1752
1753	$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
1754
1755	return $bestFitLinear->getIntersect();
1756	}
1757
1758	/**
1759	* KURT.
1760	*
1761	* Returns the kurtosis of a data set. Kurtosis characterizes the relative peakedness
1762	* or flatness of a distribution compared with the normal distribution. Positive
1763	* kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a
1764	* relatively flat distribution.
1765	*
1766	* @param array ...$args Data Series
1767	*
1768	* @return float
1769	*/
1770	public static function KURT(...$args)
1771	{
1772	$aArgs = Functions::flattenArrayIndexed($args);
1773	$mean = self::AVERAGE($aArgs);
1774	$stdDev = self::STDEV($aArgs);
1775
1776	if ($stdDev > 0) {
1777	$count = $summer = 0;
1778	// Loop through arguments
1779	foreach ($aArgs as $k => $arg) {
1780	if ((is_bool($arg)) &&
1781	(!Functions::isMatrixValue($k))) {
1782	} else {
1783	// Is it a numeric value?
1784	if ((is_numeric($arg)) && (!is_string($arg))) {
1785	$summer += pow((($arg - $mean) / $stdDev), 4);
1786	++$count;
1787	}
1788	}
1789	}
1790
1791	// Return
1792	if ($count > 3) {
1793	return $summer * ($count * ($count + 1) / (($count - 1) * ($count - 2) * ($count - 3))) - (3 * pow($count - 1, 2) / (($count - 2) * ($count - 3)));
1794	}
1795	}
1796
1797	return Functions::DIV0();
1798	}
1799
1800	/**
1801	* LARGE.
1802	*
1803	* Returns the nth largest value in a data set. You can use this function to
1804	* select a value based on its relative standing.
1805	*
1806	* Excel Function:
1807	* LARGE(value1[,value2[, ...]],entry)
1808	*
1809	* @category Statistical Functions
1810	*
1811	* @param mixed $args Data values
1812	* @param int $entry Position (ordered from the largest) in the array or range of data to return
1813	*
1814	* @return float
1815	*/
1816	public static function LARGE(...$args)
1817	{
1818	$aArgs = Functions::flattenArray($args);
1819
1820	// Calculate
1821	$entry = floor(array_pop($aArgs));
1822
1823	if ((is_numeric($entry)) && (!is_string($entry))) {
1824	$mArgs = [];
1825	foreach ($aArgs as $arg) {
1826	// Is it a numeric value?
1827	if ((is_numeric($arg)) && (!is_string($arg))) {
1828	$mArgs[] = $arg;
1829	}
1830	}
1831	$count = self::COUNT($mArgs);
1832	$entry = floor(--$entry);
1833	if (($entry < 0) \|\| ($entry >= $count) \|\| ($count == 0)) {
1834	return Functions::NAN();
1835	}
1836	rsort($mArgs);
1837
1838	return $mArgs[$entry];
1839	}
1840
1841	return Functions::VALUE();
1842	}
1843
1844	/**
1845	* LINEST.
1846	*
1847	* Calculates the statistics for a line by using the "least squares" method to calculate a straight line that best fits your data,
1848	* and then returns an array that describes the line.
1849	*
1850	* @param mixed[] $yValues Data Series Y
1851	* @param null\|mixed[] $xValues Data Series X
1852	* @param bool $const a logical value specifying whether to force the intersect to equal 0
1853	* @param bool $stats a logical value specifying whether to return additional regression statistics
1854	*
1855	* @return array
1856	*/
1857	public static function LINEST($yValues, $xValues = null, $const = true, $stats = false)
1858	{
1859	$const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const);
1860	$stats = ($stats === null) ? false : (bool) Functions::flattenSingleValue($stats);
1861	if ($xValues === null) {
1862	$xValues = range(1, count(Functions::flattenArray($yValues)));
1863	}
1864
1865	if (!self::checkTrendArrays($yValues, $xValues)) {
1866	return Functions::VALUE();
1867	}
1868	$yValueCount = count($yValues);
1869	$xValueCount = count($xValues);
1870
1871	if (($yValueCount == 0) \|\| ($yValueCount != $xValueCount)) {
1872	return Functions::NA();
1873	} elseif ($yValueCount == 1) {
1874	return 0;
1875	}
1876
1877	$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues, $const);
1878	if ($stats) {
1879	return [
1880	[
1881	$bestFitLinear->getSlope(),
1882	$bestFitLinear->getSlopeSE(),
1883	$bestFitLinear->getGoodnessOfFit(),
1884	$bestFitLinear->getF(),
1885	$bestFitLinear->getSSRegression(),
1886	],
1887	[
1888	$bestFitLinear->getIntersect(),
1889	$bestFitLinear->getIntersectSE(),
1890	$bestFitLinear->getStdevOfResiduals(),
1891	$bestFitLinear->getDFResiduals(),
1892	$bestFitLinear->getSSResiduals(),
1893	],
1894	];
1895	}
1896
1897	return [
1898	$bestFitLinear->getSlope(),
1899	$bestFitLinear->getIntersect(),
1900	];
1901	}
1902
1903	/**
1904	* LOGEST.
1905	*
1906	* Calculates an exponential curve that best fits the X and Y data series,
1907	* and then returns an array that describes the line.
1908	*
1909	* @param mixed[] $yValues Data Series Y
1910	* @param null\|mixed[] $xValues Data Series X
1911	* @param bool $const a logical value specifying whether to force the intersect to equal 0
1912	* @param bool $stats a logical value specifying whether to return additional regression statistics
1913	*
1914	* @return array
1915	*/
1916	public static function LOGEST($yValues, $xValues = null, $const = true, $stats = false)
1917	{
1918	$const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const);
1919	$stats = ($stats === null) ? false : (bool) Functions::flattenSingleValue($stats);
1920	if ($xValues === null) {
1921	$xValues = range(1, count(Functions::flattenArray($yValues)));
1922	}
1923
1924	if (!self::checkTrendArrays($yValues, $xValues)) {
1925	return Functions::VALUE();
1926	}
1927	$yValueCount = count($yValues);
1928	$xValueCount = count($xValues);
1929
1930	foreach ($yValues as $value) {
1931	if ($value <= 0.0) {
1932	return Functions::NAN();
1933	}
1934	}
1935
1936	if (($yValueCount == 0) \|\| ($yValueCount != $xValueCount)) {
1937	return Functions::NA();
1938	} elseif ($yValueCount == 1) {
1939	return 1;
1940	}
1941
1942	$bestFitExponential = Trend::calculate(Trend::TREND_EXPONENTIAL, $yValues, $xValues, $const);
1943	if ($stats) {
1944	return [
1945	[
1946	$bestFitExponential->getSlope(),
1947	$bestFitExponential->getSlopeSE(),
1948	$bestFitExponential->getGoodnessOfFit(),
1949	$bestFitExponential->getF(),
1950	$bestFitExponential->getSSRegression(),
1951	],
1952	[
1953	$bestFitExponential->getIntersect(),
1954	$bestFitExponential->getIntersectSE(),
1955	$bestFitExponential->getStdevOfResiduals(),
1956	$bestFitExponential->getDFResiduals(),
1957	$bestFitExponential->getSSResiduals(),
1958	],
1959	];
1960	}
1961
1962	return [
1963	$bestFitExponential->getSlope(),
1964	$bestFitExponential->getIntersect(),
1965	];
1966	}
1967
1968	/**
1969	* LOGINV.
1970	*
1971	* Returns the inverse of the normal cumulative distribution
1972	*
1973	* @param float $probability
1974	* @param float $mean
1975	* @param float $stdDev
1976	*
1977	* @return float
1978	*
1979	* @todo Try implementing P J Acklam's refinement algorithm for greater
1980	* accuracy if I can get my head round the mathematics
1981	* (as described at) http://home.online.no/~pjacklam/notes/invnorm/
1982	*/
1983	public static function LOGINV($probability, $mean, $stdDev)
1984	{
1985	$probability = Functions::flattenSingleValue($probability);
1986	$mean = Functions::flattenSingleValue($mean);
1987	$stdDev = Functions::flattenSingleValue($stdDev);
1988
1989	if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
1990	if (($probability < 0) \|\| ($probability > 1) \|\| ($stdDev <= 0)) {
1991	return Functions::NAN();
1992	}
1993
1994	return exp($mean + $stdDev * self::NORMSINV($probability));
1995	}
1996
1997	return Functions::VALUE();
1998	}
1999
2000	/**
2001	* LOGNORMDIST.
2002	*
2003	* Returns the cumulative lognormal distribution of x, where ln(x) is normally distributed
2004	* with parameters mean and standard_dev.
2005	*
2006	* @param float $value
2007	* @param float $mean
2008	* @param float $stdDev
2009	*
2010	* @return float
2011	*/
2012	public static function LOGNORMDIST($value, $mean, $stdDev)
2013	{
2014	$value = Functions::flattenSingleValue($value);
2015	$mean = Functions::flattenSingleValue($mean);
2016	$stdDev = Functions::flattenSingleValue($stdDev);
2017
2018	if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
2019	if (($value <= 0) \|\| ($stdDev <= 0)) {
2020	return Functions::NAN();
2021	}
2022
2023	return self::NORMSDIST((log($value) - $mean) / $stdDev);
2024	}
2025
2026	return Functions::VALUE();
2027	}
2028
2029	/**
2030	* MAX.
2031	*
2032	* MAX returns the value of the element of the values passed that has the highest value,
2033	* with negative numbers considered smaller than positive numbers.
2034	*
2035	* Excel Function:
2036	* MAX(value1[,value2[, ...]])
2037	*
2038	* @category Statistical Functions
2039	*
2040	* @param mixed ...$args Data values
2041	*
2042	* @return float
2043	*/
2044	public static function MAX(...$args)
2045	{
2046	$returnValue = null;
2047
2048	// Loop through arguments
2049	$aArgs = Functions::flattenArray($args);
2050	foreach ($aArgs as $arg) {
2051	// Is it a numeric value?
2052	if ((is_numeric($arg)) && (!is_string($arg))) {
2053	if (($returnValue === null) \|\| ($arg > $returnValue)) {
2054	$returnValue = $arg;
2055	}
2056	}
2057	}
2058
2059	if ($returnValue === null) {
2060	return 0;
2061	}
2062
2063	return $returnValue;
2064	}
2065
2066	/**
2067	* MAXA.
2068	*
2069	* Returns the greatest value in a list of arguments, including numbers, text, and logical values
2070	*
2071	* Excel Function:
2072	* MAXA(value1[,value2[, ...]])
2073	*
2074	* @category Statistical Functions
2075	*
2076	* @param mixed ...$args Data values
2077	*
2078	* @return float
2079	*/
2080	public static function MAXA(...$args)
2081	{
2082	$returnValue = null;
2083
2084	// Loop through arguments
2085	$aArgs = Functions::flattenArray($args);
2086	foreach ($aArgs as $arg) {
2087	// Is it a numeric value?
2088	if ((is_numeric($arg)) \|\| (is_bool($arg)) \|\| ((is_string($arg) && ($arg != '')))) {
2089	if (is_bool($arg)) {
2090	$arg = (int) $arg;
2091	} elseif (is_string($arg)) {
2092	$arg = 0;
2093	}
2094	if (($returnValue === null) \|\| ($arg > $returnValue)) {
2095	$returnValue = $arg;
2096	}
2097	}
2098	}
2099
2100	if ($returnValue === null) {
2101	return 0;
2102	}
2103
2104	return $returnValue;
2105	}
2106
2107	/**
2108	* MAXIF.
2109	*
2110	* Counts the maximum value within a range of cells that contain numbers within the list of arguments
2111	*
2112	* Excel Function:
2113	* MAXIF(value1[,value2[, ...]],condition)
2114	*
2115	* @category Mathematical and Trigonometric Functions
2116	*
2117	* @param mixed $aArgs Data values
2118	* @param string $condition the criteria that defines which cells will be checked
2119	* @param mixed $sumArgs
2120	*
2121	* @return float
2122	*/
2123	public static function MAXIF($aArgs, $condition, $sumArgs = [])
2124	{
2125	$returnValue = null;
2126
2127	$aArgs = Functions::flattenArray($aArgs);
2128	$sumArgs = Functions::flattenArray($sumArgs);
2129	if (empty($sumArgs)) {
2130	$sumArgs = $aArgs;
2131	}
2132	$condition = Functions::ifCondition($condition);
2133	// Loop through arguments
2134	foreach ($aArgs as $key => $arg) {
2135	if (!is_numeric($arg)) {
2136	$arg = Calculation::wrapResult(strtoupper($arg));
2137	}
2138	$testCondition = '=' . $arg . $condition;
2139	if (Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
2140	if (($returnValue === null) \|\| ($arg > $returnValue)) {
2141	$returnValue = $arg;
2142	}
2143	}
2144	}
2145
2146	return $returnValue;
2147	}
2148
2149	/**
2150	* MEDIAN.
2151	*
2152	* Returns the median of the given numbers. The median is the number in the middle of a set of numbers.
2153	*
2154	* Excel Function:
2155	* MEDIAN(value1[,value2[, ...]])
2156	*
2157	* @category Statistical Functions
2158	*
2159	* @param mixed ...$args Data values
2160	*
2161	* @return float
2162	*/
2163	public static function MEDIAN(...$args)
2164	{
2165	$returnValue = Functions::NAN();
2166
2167	$mArgs = [];
2168	// Loop through arguments
2169	$aArgs = Functions::flattenArray($args);
2170	foreach ($aArgs as $arg) {
2171	// Is it a numeric value?
2172	if ((is_numeric($arg)) && (!is_string($arg))) {
2173	$mArgs[] = $arg;
2174	}
2175	}
2176
2177	$mValueCount = count($mArgs);
2178	if ($mValueCount > 0) {
2179	sort($mArgs, SORT_NUMERIC);
2180	$mValueCount = $mValueCount / 2;
2181	if ($mValueCount == floor($mValueCount)) {
2182	$returnValue = ($mArgs[$mValueCount--] + $mArgs[$mValueCount]) / 2;
2183	} else {
2184	$mValueCount = floor($mValueCount);
2185	$returnValue = $mArgs[$mValueCount];
2186	}
2187	}
2188
2189	return $returnValue;
2190	}
2191
2192	/**
2193	* MIN.
2194	*
2195	* MIN returns the value of the element of the values passed that has the smallest value,
2196	* with negative numbers considered smaller than positive numbers.
2197	*
2198	* Excel Function:
2199	* MIN(value1[,value2[, ...]])
2200	*
2201	* @category Statistical Functions
2202	*
2203	* @param mixed ...$args Data values
2204	*
2205	* @return float
2206	*/
2207	public static function MIN(...$args)
2208	{
2209	$returnValue = null;
2210
2211	// Loop through arguments
2212	$aArgs = Functions::flattenArray($args);
2213	foreach ($aArgs as $arg) {
2214	// Is it a numeric value?
2215	if ((is_numeric($arg)) && (!is_string($arg))) {
2216	if (($returnValue === null) \|\| ($arg < $returnValue)) {
2217	$returnValue = $arg;
2218	}
2219	}
2220	}
2221
2222	if ($returnValue === null) {
2223	return 0;
2224	}
2225
2226	return $returnValue;
2227	}
2228
2229	/**
2230	* MINA.
2231	*
2232	* Returns the smallest value in a list of arguments, including numbers, text, and logical values
2233	*
2234	* Excel Function:
2235	* MINA(value1[,value2[, ...]])
2236	*
2237	* @category Statistical Functions
2238	*
2239	* @param mixed ...$args Data values
2240	*
2241	* @return float
2242	*/
2243	public static function MINA(...$args)
2244	{
2245	$returnValue = null;
2246
2247	// Loop through arguments
2248	$aArgs = Functions::flattenArray($args);
2249	foreach ($aArgs as $arg) {
2250	// Is it a numeric value?
2251	if ((is_numeric($arg)) \|\| (is_bool($arg)) \|\| ((is_string($arg) && ($arg != '')))) {
2252	if (is_bool($arg)) {
2253	$arg = (int) $arg;
2254	} elseif (is_string($arg)) {
2255	$arg = 0;
2256	}
2257	if (($returnValue === null) \|\| ($arg < $returnValue)) {
2258	$returnValue = $arg;
2259	}
2260	}
2261	}
2262
2263	if ($returnValue === null) {
2264	return 0;
2265	}
2266
2267	return $returnValue;
2268	}
2269
2270	/**
2271	* MINIF.
2272	*
2273	* Returns the minimum value within a range of cells that contain numbers within the list of arguments
2274	*
2275	* Excel Function:
2276	* MINIF(value1[,value2[, ...]],condition)
2277	*
2278	* @category Mathematical and Trigonometric Functions
2279	*
2280	* @param mixed $aArgs Data values
2281	* @param string $condition the criteria that defines which cells will be checked
2282	* @param mixed $sumArgs
2283	*
2284	* @return float
2285	*/
2286	public static function MINIF($aArgs, $condition, $sumArgs = [])
2287	{
2288	$returnValue = null;
2289
2290	$aArgs = Functions::flattenArray($aArgs);
2291	$sumArgs = Functions::flattenArray($sumArgs);
2292	if (empty($sumArgs)) {
2293	$sumArgs = $aArgs;
2294	}
2295	$condition = Functions::ifCondition($condition);
2296	// Loop through arguments
2297	foreach ($aArgs as $key => $arg) {
2298	if (!is_numeric($arg)) {
2299	$arg = Calculation::wrapResult(strtoupper($arg));
2300	}
2301	$testCondition = '=' . $arg . $condition;
2302	if (Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
2303	if (($returnValue === null) \|\| ($arg < $returnValue)) {
2304	$returnValue = $arg;
2305	}
2306	}
2307	}
2308
2309	return $returnValue;
2310	}
2311
2312	//
2313	// Special variant of array_count_values that isn't limited to strings and integers,
2314	// but can work with floating point numbers as values
2315	//
2316	private static function modeCalc($data)
2317	{
2318	$frequencyArray = [];
2319	foreach ($data as $datum) {
2320	$found = false;
2321	foreach ($frequencyArray as $key => $value) {
2322	if ((string) $value['value'] == (string) $datum) {
2323	++$frequencyArray[$key]['frequency'];
2324	$found = true;
2325
2326	break;
2327	}
2328	}
2329	if (!$found) {
2330	$frequencyArray[] = [
2331	'value' => $datum,
2332	'frequency' => 1,
2333	];
2334	}
2335	}
2336
2337	foreach ($frequencyArray as $key => $value) {
2338	$frequencyList[$key] = $value['frequency'];
2339	$valueList[$key] = $value['value'];
2340	}
2341	array_multisort($frequencyList, SORT_DESC, $valueList, SORT_ASC, SORT_NUMERIC, $frequencyArray);
2342
2343	if ($frequencyArray[0]['frequency'] == 1) {
2344	return Functions::NA();
2345	}
2346
2347	return $frequencyArray[0]['value'];
2348	}
2349
2350	/**
2351	* MODE.
2352	*
2353	* Returns the most frequently occurring, or repetitive, value in an array or range of data
2354	*
2355	* Excel Function:
2356	* MODE(value1[,value2[, ...]])
2357	*
2358	* @category Statistical Functions
2359	*
2360	* @param mixed ...$args Data values
2361	*
2362	* @return float
2363	*/
2364	public static function MODE(...$args)
2365	{
2366	$returnValue = Functions::NA();
2367
2368	// Loop through arguments
2369	$aArgs = Functions::flattenArray($args);
2370
2371	$mArgs = [];
2372	foreach ($aArgs as $arg) {
2373	// Is it a numeric value?
2374	if ((is_numeric($arg)) && (!is_string($arg))) {
2375	$mArgs[] = $arg;
2376	}
2377	}
2378
2379	if (!empty($mArgs)) {
2380	return self::modeCalc($mArgs);
2381	}
2382
2383	return $returnValue;
2384	}
2385
2386	/**
2387	* NEGBINOMDIST.
2388	*
2389	* Returns the negative binomial distribution. NEGBINOMDIST returns the probability that
2390	* there will be number_f failures before the number_s-th success, when the constant
2391	* probability of a success is probability_s. This function is similar to the binomial
2392	* distribution, except that the number of successes is fixed, and the number of trials is
2393	* variable. Like the binomial, trials are assumed to be independent.
2394	*
2395	* @param float $failures Number of Failures
2396	* @param float $successes Threshold number of Successes
2397	* @param float $probability Probability of success on each trial
2398	*
2399	* @return float
2400	*/
2401	public static function NEGBINOMDIST($failures, $successes, $probability)
2402	{
2403	$failures = floor(Functions::flattenSingleValue($failures));
2404	$successes = floor(Functions::flattenSingleValue($successes));
2405	$probability = Functions::flattenSingleValue($probability);
2406
2407	if ((is_numeric($failures)) && (is_numeric($successes)) && (is_numeric($probability))) {
2408	if (($failures < 0) \|\| ($successes < 1)) {
2409	return Functions::NAN();
2410	} elseif (($probability < 0) \|\| ($probability > 1)) {
2411	return Functions::NAN();
2412	}
2413	if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
2414	if (($failures + $successes - 1) <= 0) {
2415	return Functions::NAN();
2416	}
2417	}
2418
2419	return (MathTrig::COMBIN($failures + $successes - 1, $successes - 1)) * (pow($probability, $successes)) * (pow(1 - $probability, $failures));
2420	}
2421
2422	return Functions::VALUE();
2423	}
2424
2425	/**
2426	* NORMDIST.
2427	*
2428	* Returns the normal distribution for the specified mean and standard deviation. This
2429	* function has a very wide range of applications in statistics, including hypothesis
2430	* testing.
2431	*
2432	* @param float $value
2433	* @param float $mean Mean Value
2434	* @param float $stdDev Standard Deviation
2435	* @param bool $cumulative
2436	*
2437	* @return float
2438	*/
2439	public static function NORMDIST($value, $mean, $stdDev, $cumulative)
2440	{
2441	$value = Functions::flattenSingleValue($value);
2442	$mean = Functions::flattenSingleValue($mean);
2443	$stdDev = Functions::flattenSingleValue($stdDev);
2444
2445	if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
2446	if ($stdDev < 0) {
2447	return Functions::NAN();
2448	}
2449	if ((is_numeric($cumulative)) \|\| (is_bool($cumulative))) {
2450	if ($cumulative) {
2451	return 0.5 * (1 + Engineering::erfVal(($value - $mean) / ($stdDev * sqrt(2))));
2452	}
2453
2454	return (1 / (self::SQRT2PI * $stdDev)) * exp(0 - (pow($value - $mean, 2) / (2 * ($stdDev * $stdDev))));
2455	}
2456	}
2457
2458	return Functions::VALUE();
2459	}
2460
2461	/**
2462	* NORMINV.
2463	*
2464	* Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.
2465	*
2466	* @param float $probability
2467	* @param float $mean Mean Value
2468	* @param float $stdDev Standard Deviation
2469	*
2470	* @return float
2471	*/
2472	public static function NORMINV($probability, $mean, $stdDev)
2473	{
2474	$probability = Functions::flattenSingleValue($probability);
2475	$mean = Functions::flattenSingleValue($mean);
2476	$stdDev = Functions::flattenSingleValue($stdDev);
2477
2478	if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
2479	if (($probability < 0) \|\| ($probability > 1)) {
2480	return Functions::NAN();
2481	}
2482	if ($stdDev < 0) {
2483	return Functions::NAN();
2484	}
2485
2486	return (self::inverseNcdf($probability) * $stdDev) + $mean;
2487	}
2488
2489	return Functions::VALUE();
2490	}
2491
2492	/**
2493	* NORMSDIST.
2494	*
2495	* Returns the standard normal cumulative distribution function. The distribution has
2496	* a mean of 0 (zero) and a standard deviation of one. Use this function in place of a
2497	* table of standard normal curve areas.
2498	*
2499	* @param float $value
2500	*
2501	* @return float
2502	*/
2503	public static function NORMSDIST($value)
2504	{
2505	$value = Functions::flattenSingleValue($value);
2506
2507	return self::NORMDIST($value, 0, 1, true);
2508	}
2509
2510	/**
2511	* NORMSINV.
2512	*
2513	* Returns the inverse of the standard normal cumulative distribution
2514	*
2515	* @param float $value
2516	*
2517	* @return float
2518	*/
2519	public static function NORMSINV($value)
2520	{
2521	return self::NORMINV($value, 0, 1);
2522	}
2523
2524	/**
2525	* PERCENTILE.
2526	*
2527	* Returns the nth percentile of values in a range..
2528	*
2529	* Excel Function:
2530	* PERCENTILE(value1[,value2[, ...]],entry)
2531	*
2532	* @category Statistical Functions
2533	*
2534	* @param mixed $args Data values
2535	* @param float $entry Percentile value in the range 0..1, inclusive.
2536	*
2537	* @return float
2538	*/
2539	public static function PERCENTILE(...$args)
2540	{
2541	$aArgs = Functions::flattenArray($args);
2542
2543	// Calculate
2544	$entry = array_pop($aArgs);
2545
2546	if ((is_numeric($entry)) && (!is_string($entry))) {
2547	if (($entry < 0) \|\| ($entry > 1)) {
2548	return Functions::NAN();
2549	}
2550	$mArgs = [];
2551	foreach ($aArgs as $arg) {
2552	// Is it a numeric value?
2553	if ((is_numeric($arg)) && (!is_string($arg))) {
2554	$mArgs[] = $arg;
2555	}
2556	}
2557	$mValueCount = count($mArgs);
2558	if ($mValueCount > 0) {
2559	sort($mArgs);
2560	$count = self::COUNT($mArgs);
2561	$index = $entry * ($count - 1);
2562	$iBase = floor($index);
2563	if ($index == $iBase) {
2564	return $mArgs[$index];
2565	}
2566	$iNext = $iBase + 1;
2567	$iProportion = $index - $iBase;
2568
2569	return $mArgs[$iBase] + (($mArgs[$iNext] - $mArgs[$iBase]) * $iProportion);
2570	}
2571	}
2572
2573	return Functions::VALUE();
2574	}
2575
2576	/**
2577	* PERCENTRANK.
2578	*
2579	* Returns the rank of a value in a data set as a percentage of the data set.
2580	*
2581	* @param float[] $valueSet An array of, or a reference to, a list of numbers
2582	* @param int $value the number whose rank you want to find
2583	* @param int $significance the number of significant digits for the returned percentage value
2584	*
2585	* @return float
2586	*/
2587	public static function PERCENTRANK($valueSet, $value, $significance = 3)
2588	{
2589	$valueSet = Functions::flattenArray($valueSet);
2590	$value = Functions::flattenSingleValue($value);
2591	$significance = ($significance === null) ? 3 : (int) Functions::flattenSingleValue($significance);
2592
2593	foreach ($valueSet as $key => $valueEntry) {
2594	if (!is_numeric($valueEntry)) {
2595	unset($valueSet[$key]);
2596	}
2597	}
2598	sort($valueSet, SORT_NUMERIC);
2599	$valueCount = count($valueSet);
2600	if ($valueCount == 0) {
2601	return Functions::NAN();
2602	}
2603
2604	$valueAdjustor = $valueCount - 1;
2605	if (($value < $valueSet[0]) \|\| ($value > $valueSet[$valueAdjustor])) {
2606	return Functions::NA();
2607	}
2608
2609	$pos = array_search($value, $valueSet);
2610	if ($pos === false) {
2611	$pos = 0;
2612	$testValue = $valueSet[0];
2613	while ($testValue < $value) {
2614	$testValue = $valueSet[++$pos];
2615	}
2616	--$pos;
2617	$pos += (($value - $valueSet[$pos]) / ($testValue - $valueSet[$pos]));
2618	}
2619
2620	return round($pos / $valueAdjustor, $significance);
2621	}
2622
2623	/**
2624	* PERMUT.
2625	*
2626	* Returns the number of permutations for a given number of objects that can be
2627	* selected from number objects. A permutation is any set or subset of objects or
2628	* events where internal order is significant. Permutations are different from
2629	* combinations, for which the internal order is not significant. Use this function
2630	* for lottery-style probability calculations.
2631	*
2632	* @param int $numObjs Number of different objects
2633	* @param int $numInSet Number of objects in each permutation
2634	*
2635	* @return int Number of permutations
2636	*/
2637	public static function PERMUT($numObjs, $numInSet)
2638	{
2639	$numObjs = Functions::flattenSingleValue($numObjs);
2640	$numInSet = Functions::flattenSingleValue($numInSet);
2641
2642	if ((is_numeric($numObjs)) && (is_numeric($numInSet))) {
2643	$numInSet = floor($numInSet);
2644	if ($numObjs < $numInSet) {
2645	return Functions::NAN();
2646	}
2647
2648	return round(MathTrig::FACT($numObjs) / MathTrig::FACT($numObjs - $numInSet));
2649	}
2650
2651	return Functions::VALUE();
2652	}
2653
2654	/**
2655	* POISSON.
2656	*
2657	* Returns the Poisson distribution. A common application of the Poisson distribution
2658	* is predicting the number of events over a specific time, such as the number of
2659	* cars arriving at a toll plaza in 1 minute.
2660	*
2661	* @param float $value
2662	* @param float $mean Mean Value
2663	* @param bool $cumulative
2664	*
2665	* @return float
2666	*/
2667	public static function POISSON($value, $mean, $cumulative)
2668	{
2669	$value = Functions::flattenSingleValue($value);
2670	$mean = Functions::flattenSingleValue($mean);
2671
2672	if ((is_numeric($value)) && (is_numeric($mean))) {
2673	if (($value < 0) \|\| ($mean <= 0)) {
2674	return Functions::NAN();
2675	}
2676	if ((is_numeric($cumulative)) \|\| (is_bool($cumulative))) {
2677	if ($cumulative) {
2678	$summer = 0;
2679	$floor = floor($value);
2680	for ($i = 0; $i <= $floor; ++$i) {
2681	$summer += pow($mean, $i) / MathTrig::FACT($i);
2682	}
2683
2684	return exp(0 - $mean) * $summer;
2685	}
2686
2687	return (exp(0 - $mean) * pow($mean, $value)) / MathTrig::FACT($value);
2688	}
2689	}
2690
2691	return Functions::VALUE();
2692	}
2693
2694	/**
2695	* QUARTILE.
2696	*
2697	* Returns the quartile of a data set.
2698	*
2699	* Excel Function:
2700	* QUARTILE(value1[,value2[, ...]],entry)
2701	*
2702	* @category Statistical Functions
2703	*
2704	* @param mixed $args Data values
2705	* @param int $entry Quartile value in the range 1..3, inclusive.
2706	*
2707	* @return float
2708	*/
2709	public static function QUARTILE(...$args)
2710	{
2711	$aArgs = Functions::flattenArray($args);
2712
2713	// Calculate
2714	$entry = floor(array_pop($aArgs));
2715
2716	if ((is_numeric($entry)) && (!is_string($entry))) {
2717	$entry /= 4;
2718	if (($entry < 0) \|\| ($entry > 1)) {
2719	return Functions::NAN();
2720	}
2721
2722	return self::PERCENTILE($aArgs, $entry);
2723	}
2724
2725	return Functions::VALUE();
2726	}
2727
2728	/**
2729	* RANK.
2730	*
2731	* Returns the rank of a number in a list of numbers.
2732	*
2733	* @param int $value the number whose rank you want to find
2734	* @param float[] $valueSet An array of, or a reference to, a list of numbers
2735	* @param int $order Order to sort the values in the value set
2736	*
2737	* @return float
2738	*/
2739	public static function RANK($value, $valueSet, $order = 0)
2740	{
2741	$value = Functions::flattenSingleValue($value);
2742	$valueSet = Functions::flattenArray($valueSet);
2743	$order = ($order === null) ? 0 : (int) Functions::flattenSingleValue($order);
2744
2745	foreach ($valueSet as $key => $valueEntry) {
2746	if (!is_numeric($valueEntry)) {
2747	unset($valueSet[$key]);
2748	}
2749	}
2750
2751	if ($order == 0) {
2752	rsort($valueSet, SORT_NUMERIC);
2753	} else {
2754	sort($valueSet, SORT_NUMERIC);
2755	}
2756	$pos = array_search($value, $valueSet);
2757	if ($pos === false) {
2758	return Functions::NA();
2759	}
2760
2761	return ++$pos;
2762	}
2763
2764	/**
2765	* RSQ.
2766	*
2767	* Returns the square of the Pearson product moment correlation coefficient through data points in known_y's and known_x's.
2768	*
2769	* @param mixed[] $yValues Data Series Y
2770	* @param mixed[] $xValues Data Series X
2771	*
2772	* @return float
2773	*/
2774	public static function RSQ($yValues, $xValues)
2775	{
2776	if (!self::checkTrendArrays($yValues, $xValues)) {
2777	return Functions::VALUE();
2778	}
2779	$yValueCount = count($yValues);
2780	$xValueCount = count($xValues);
2781
2782	if (($yValueCount == 0) \|\| ($yValueCount != $xValueCount)) {
2783	return Functions::NA();
2784	} elseif ($yValueCount == 1) {
2785	return Functions::DIV0();
2786	}
2787
2788	$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
2789
2790	return $bestFitLinear->getGoodnessOfFit();
2791	}
2792
2793	/**
2794	* SKEW.
2795	*
2796	* Returns the skewness of a distribution. Skewness characterizes the degree of asymmetry
2797	* of a distribution around its mean. Positive skewness indicates a distribution with an
2798	* asymmetric tail extending toward more positive values. Negative skewness indicates a
2799	* distribution with an asymmetric tail extending toward more negative values.
2800	*
2801	* @param array ...$args Data Series
2802	*
2803	* @return float
2804	*/
2805	public static function SKEW(...$args)
2806	{
2807	$aArgs = Functions::flattenArrayIndexed($args);
2808	$mean = self::AVERAGE($aArgs);
2809	$stdDev = self::STDEV($aArgs);
2810
2811	$count = $summer = 0;
2812	// Loop through arguments
2813	foreach ($aArgs as $k => $arg) {
2814	if ((is_bool($arg)) &&
2815	(!Functions::isMatrixValue($k))) {
2816	} else {
2817	// Is it a numeric value?
2818	if ((is_numeric($arg)) && (!is_string($arg))) {
2819	$summer += pow((($arg - $mean) / $stdDev), 3);
2820	++$count;
2821	}
2822	}
2823	}
2824
2825	if ($count > 2) {
2826	return $summer * ($count / (($count - 1) * ($count - 2)));
2827	}
2828
2829	return Functions::DIV0();
2830	}
2831
2832	/**
2833	* SLOPE.
2834	*
2835	* Returns the slope of the linear regression line through data points in known_y's and known_x's.
2836	*
2837	* @param mixed[] $yValues Data Series Y
2838	* @param mixed[] $xValues Data Series X
2839	*
2840	* @return float
2841	*/
2842	public static function SLOPE($yValues, $xValues)
2843	{
2844	if (!self::checkTrendArrays($yValues, $xValues)) {
2845	return Functions::VALUE();
2846	}
2847	$yValueCount = count($yValues);
2848	$xValueCount = count($xValues);
2849
2850	if (($yValueCount == 0) \|\| ($yValueCount != $xValueCount)) {
2851	return Functions::NA();
2852	} elseif ($yValueCount == 1) {
2853	return Functions::DIV0();
2854	}
2855
2856	$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
2857
2858	return $bestFitLinear->getSlope();
2859	}
2860
2861	/**
2862	* SMALL.
2863	*
2864	* Returns the nth smallest value in a data set. You can use this function to
2865	* select a value based on its relative standing.
2866	*
2867	* Excel Function:
2868	* SMALL(value1[,value2[, ...]],entry)
2869	*
2870	* @category Statistical Functions
2871	*
2872	* @param mixed $args Data values
2873	* @param int $entry Position (ordered from the smallest) in the array or range of data to return
2874	*
2875	* @return float
2876	*/
2877	public static function SMALL(...$args)
2878	{
2879	$aArgs = Functions::flattenArray($args);
2880
2881	// Calculate
2882	$entry = array_pop($aArgs);
2883
2884	if ((is_numeric($entry)) && (!is_string($entry))) {
2885	$mArgs = [];
2886	foreach ($aArgs as $arg) {
2887	// Is it a numeric value?
2888	if ((is_numeric($arg)) && (!is_string($arg))) {
2889	$mArgs[] = $arg;
2890	}
2891	}
2892	$count = self::COUNT($mArgs);
2893	$entry = floor(--$entry);
2894	if (($entry < 0) \|\| ($entry >= $count) \|\| ($count == 0)) {
2895	return Functions::NAN();
2896	}
2897	sort($mArgs);
2898
2899	return $mArgs[$entry];
2900	}
2901
2902	return Functions::VALUE();
2903	}
2904
2905	/**
2906	* STANDARDIZE.
2907	*
2908	* Returns a normalized value from a distribution characterized by mean and standard_dev.
2909	*
2910	* @param float $value Value to normalize
2911	* @param float $mean Mean Value
2912	* @param float $stdDev Standard Deviation
2913	*
2914	* @return float Standardized value
2915	*/
2916	public static function STANDARDIZE($value, $mean, $stdDev)
2917	{
2918	$value = Functions::flattenSingleValue($value);
2919	$mean = Functions::flattenSingleValue($mean);
2920	$stdDev = Functions::flattenSingleValue($stdDev);
2921
2922	if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) {
2923	if ($stdDev <= 0) {
2924	return Functions::NAN();
2925	}
2926
2927	return ($value - $mean) / $stdDev;
2928	}
2929
2930	return Functions::VALUE();
2931	}
2932
2933	/**
2934	* STDEV.
2935	*
2936	* Estimates standard deviation based on a sample. The standard deviation is a measure of how
2937	* widely values are dispersed from the average value (the mean).
2938	*
2939	* Excel Function:
2940	* STDEV(value1[,value2[, ...]])
2941	*
2942	* @category Statistical Functions
2943	*
2944	* @param mixed ...$args Data values
2945	*
2946	* @return float
2947	*/
2948	public static function STDEV(...$args)
2949	{
2950	$aArgs = Functions::flattenArrayIndexed($args);
2951
2952	// Return value
2953	$returnValue = null;
2954
2955	$aMean = self::AVERAGE($aArgs);
2956	if ($aMean !== null) {
2957	$aCount = -1;
2958	foreach ($aArgs as $k => $arg) {
2959	if ((is_bool($arg)) &&
2960	((!Functions::isCellValue($k)) \|\| (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) {
2961	$arg = (int) $arg;
2962	}
2963	// Is it a numeric value?
2964	if ((is_numeric($arg)) && (!is_string($arg))) {
2965	if ($returnValue === null) {
2966	$returnValue = pow(($arg - $aMean), 2);
2967	} else {
2968	$returnValue += pow(($arg - $aMean), 2);
2969	}
2970	++$aCount;
2971	}
2972	}
2973
2974	// Return
2975	if (($aCount > 0) && ($returnValue >= 0)) {
2976	return sqrt($returnValue / $aCount);
2977	}
2978	}
2979
2980	return Functions::DIV0();
2981	}
2982
2983	/**
2984	* STDEVA.
2985	*
2986	* Estimates standard deviation based on a sample, including numbers, text, and logical values
2987	*
2988	* Excel Function:
2989	* STDEVA(value1[,value2[, ...]])
2990	*
2991	* @category Statistical Functions
2992	*
2993	* @param mixed ...$args Data values
2994	*
2995	* @return float
2996	*/
2997	public static function STDEVA(...$args)
2998	{
2999	$aArgs = Functions::flattenArrayIndexed($args);
3000
3001	$returnValue = null;
3002
3003	$aMean = self::AVERAGEA($aArgs);
3004	if ($aMean !== null) {
3005	$aCount = -1;
3006	foreach ($aArgs as $k => $arg) {
3007	if ((is_bool($arg)) &&
3008	(!Functions::isMatrixValue($k))) {
3009	} else {
3010	// Is it a numeric value?
3011	if ((is_numeric($arg)) \|\| (is_bool($arg)) \|\| ((is_string($arg) & ($arg != '')))) {
3012	if (is_bool($arg)) {
3013	$arg = (int) $arg;
3014	} elseif (is_string($arg)) {
3015	$arg = 0;
3016	}
3017	if ($returnValue === null) {
3018	$returnValue = pow(($arg - $aMean), 2);
3019	} else {
3020	$returnValue += pow(($arg - $aMean), 2);
3021	}
3022	++$aCount;
3023	}
3024	}
3025	}
3026
3027	if (($aCount > 0) && ($returnValue >= 0)) {
3028	return sqrt($returnValue / $aCount);
3029	}
3030	}
3031
3032	return Functions::DIV0();
3033	}
3034
3035	/**
3036	* STDEVP.
3037	*
3038	* Calculates standard deviation based on the entire population
3039	*
3040	* Excel Function:
3041	* STDEVP(value1[,value2[, ...]])
3042	*
3043	* @category Statistical Functions
3044	*
3045	* @param mixed ...$args Data values
3046	*
3047	* @return float
3048	*/
3049	public static function STDEVP(...$args)
3050	{
3051	$aArgs = Functions::flattenArrayIndexed($args);
3052
3053	$returnValue = null;
3054
3055	$aMean = self::AVERAGE($aArgs);
3056	if ($aMean !== null) {
3057	$aCount = 0;
3058	foreach ($aArgs as $k => $arg) {
3059	if ((is_bool($arg)) &&
3060	((!Functions::isCellValue($k)) \|\| (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) {
3061	$arg = (int) $arg;
3062	}
3063	// Is it a numeric value?
3064	if ((is_numeric($arg)) && (!is_string($arg))) {
3065	if ($returnValue === null) {
3066	$returnValue = pow(($arg - $aMean), 2);
3067	} else {
3068	$returnValue += pow(($arg - $aMean), 2);
3069	}
3070	++$aCount;
3071	}
3072	}
3073
3074	if (($aCount > 0) && ($returnValue >= 0)) {
3075	return sqrt($returnValue / $aCount);
3076	}
3077	}
3078
3079	return Functions::DIV0();
3080	}
3081
3082	/**
3083	* STDEVPA.
3084	*
3085	* Calculates standard deviation based on the entire population, including numbers, text, and logical values
3086	*
3087	* Excel Function:
3088	* STDEVPA(value1[,value2[, ...]])
3089	*
3090	* @category Statistical Functions
3091	*
3092	* @param mixed ...$args Data values
3093	*
3094	* @return float
3095	*/
3096	public static function STDEVPA(...$args)
3097	{
3098	$aArgs = Functions::flattenArrayIndexed($args);
3099
3100	$returnValue = null;
3101
3102	$aMean = self::AVERAGEA($aArgs);
3103	if ($aMean !== null) {
3104	$aCount = 0;
3105	foreach ($aArgs as $k => $arg) {
3106	if ((is_bool($arg)) &&
3107	(!Functions::isMatrixValue($k))) {
3108	} else {
3109	// Is it a numeric value?
3110	if ((is_numeric($arg)) \|\| (is_bool($arg)) \|\| ((is_string($arg) & ($arg != '')))) {
3111	if (is_bool($arg)) {
3112	$arg = (int) $arg;
3113	} elseif (is_string($arg)) {
3114	$arg = 0;
3115	}
3116	if ($returnValue === null) {
3117	$returnValue = pow(($arg - $aMean), 2);
3118	} else {
3119	$returnValue += pow(($arg - $aMean), 2);
3120	}
3121	++$aCount;
3122	}
3123	}
3124	}
3125
3126	if (($aCount > 0) && ($returnValue >= 0)) {
3127	return sqrt($returnValue / $aCount);
3128	}
3129	}
3130
3131	return Functions::DIV0();
3132	}
3133
3134	/**
3135	* STEYX.
3136	*
3137	* Returns the standard error of the predicted y-value for each x in the regression.
3138	*
3139	* @param mixed[] $yValues Data Series Y
3140	* @param mixed[] $xValues Data Series X
3141	*
3142	* @return float
3143	*/
3144	public static function STEYX($yValues, $xValues)
3145	{
3146	if (!self::checkTrendArrays($yValues, $xValues)) {
3147	return Functions::VALUE();
3148	}
3149	$yValueCount = count($yValues);
3150	$xValueCount = count($xValues);
3151
3152	if (($yValueCount == 0) \|\| ($yValueCount != $xValueCount)) {
3153	return Functions::NA();
3154	} elseif ($yValueCount == 1) {
3155	return Functions::DIV0();
3156	}
3157
3158	$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues);
3159
3160	return $bestFitLinear->getStdevOfResiduals();
3161	}
3162
3163	/**
3164	* TDIST.
3165	*
3166	* Returns the probability of Student's T distribution.
3167	*
3168	* @param float $value Value for the function
3169	* @param float $degrees degrees of freedom
3170	* @param float $tails number of tails (1 or 2)
3171	*
3172	* @return float
3173	*/
3174	public static function TDIST($value, $degrees, $tails)
3175	{
3176	$value = Functions::flattenSingleValue($value);
3177	$degrees = floor(Functions::flattenSingleValue($degrees));
3178	$tails = floor(Functions::flattenSingleValue($tails));
3179
3180	if ((is_numeric($value)) && (is_numeric($degrees)) && (is_numeric($tails))) {
3181	if (($value < 0) \|\| ($degrees < 1) \|\| ($tails < 1) \|\| ($tails > 2)) {
3182	return Functions::NAN();
3183	}
3184	// tdist, which finds the probability that corresponds to a given value
3185	// of t with k degrees of freedom. This algorithm is translated from a
3186	// pascal function on p81 of "Statistical Computing in Pascal" by D
3187	// Cooke, A H Craven & G M Clark (1985: Edward Arnold (Pubs.) Ltd:
3188	// London). The above Pascal algorithm is itself a translation of the
3189	// fortran algoritm "AS 3" by B E Cooper of the Atlas Computer
3190	// Laboratory as reported in (among other places) "Applied Statistics
3191	// Algorithms", editied by P Griffiths and I D Hill (1985; Ellis
3192	// Horwood Ltd.; W. Sussex, England).
3193	$tterm = $degrees;
3194	$ttheta = atan2($value, sqrt($tterm));
3195	$tc = cos($ttheta);
3196	$ts = sin($ttheta);
3197	$tsum = 0;
3198
3199	if (($degrees % 2) == 1) {
3200	$ti = 3;
3201	$tterm = $tc;
3202	} else {
3203	$ti = 2;
3204	$tterm = 1;
3205	}
3206
3207	$tsum = $tterm;
3208	while ($ti < $degrees) {
3209	$tterm = $tc $tc * ($ti - 1) / $ti;
3210	$tsum += $tterm;
3211	$ti += 2;
3212	}
3213	$tsum *= $ts;
3214	if (($degrees % 2) == 1) {
3215	$tsum = Functions::M_2DIVPI * ($tsum + $ttheta);
3216	}
3217	$tValue = 0.5 * (1 + $tsum);
3218	if ($tails == 1) {
3219	return 1 - abs($tValue);
3220	}
3221
3222	return 1 - abs((1 - $tValue) - $tValue);
3223	}
3224
3225	return Functions::VALUE();
3226	}
3227
3228	/**
3229	* TINV.
3230	*
3231	* Returns the one-tailed probability of the chi-squared distribution.
3232	*
3233	* @param float $probability Probability for the function
3234	* @param float $degrees degrees of freedom
3235	*
3236	* @return float
3237	*/
3238	public static function TINV($probability, $degrees)
3239	{
3240	$probability = Functions::flattenSingleValue($probability);
3241	$degrees = floor(Functions::flattenSingleValue($degrees));
3242
3243	if ((is_numeric($probability)) && (is_numeric($degrees))) {
3244	$xLo = 100;
3245	$xHi = 0;
3246
3247	$x = $xNew = 1;
3248	$dx = 1;
3249	$i = 0;
3250
3251	while ((abs($dx) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) {
3252	// Apply Newton-Raphson step
3253	$result = self::TDIST($x, $degrees, 2);
3254	$error = $result - $probability;
3255	if ($error == 0.0) {
3256	$dx = 0;
3257	} elseif ($error < 0.0) {
3258	$xLo = $x;
3259	} else {
3260	$xHi = $x;
3261	}
3262	// Avoid division by zero
3263	if ($result != 0.0) {
3264	$dx = $error / $result;
3265	$xNew = $x - $dx;
3266	}
3267	// If the NR fails to converge (which for example may be the
3268	// case if the initial guess is too rough) we apply a bisection
3269	// step to determine a more narrow interval around the root.
3270	if (($xNew < $xLo) \|\| ($xNew > $xHi) \|\| ($result == 0.0)) {
3271	$xNew = ($xLo + $xHi) / 2;
3272	$dx = $xNew - $x;
3273	}
3274	$x = $xNew;
3275	}
3276	if ($i == self::MAX_ITERATIONS) {
3277	return Functions::NA();
3278	}
3279
3280	return round($x, 12);
3281	}
3282
3283	return Functions::VALUE();
3284	}
3285
3286	/**
3287	* TREND.
3288	*
3289	* Returns values along a linear Trend
3290	*
3291	* @param mixed[] $yValues Data Series Y
3292	* @param mixed[] $xValues Data Series X
3293	* @param mixed[] $newValues Values of X for which we want to find Y
3294	* @param bool $const a logical value specifying whether to force the intersect to equal 0
3295	*
3296	* @return array of float
3297	*/
3298	public static function TREND($yValues, $xValues = [], $newValues = [], $const = true)
3299	{
3300	$yValues = Functions::flattenArray($yValues);
3301	$xValues = Functions::flattenArray($xValues);
3302	$newValues = Functions::flattenArray($newValues);
3303	$const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const);
3304
3305	$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues, $const);
3306	if (empty($newValues)) {
3307	$newValues = $bestFitLinear->getXValues();
3308	}
3309
3310	$returnArray = [];
3311	foreach ($newValues as $xValue) {
3312	$returnArray[0][] = $bestFitLinear->getValueOfYForX($xValue);
3313	}
3314
3315	return $returnArray;
3316	}
3317
3318	/**
3319	* TRIMMEAN.
3320	*
3321	* Returns the mean of the interior of a data set. TRIMMEAN calculates the mean
3322	* taken by excluding a percentage of data points from the top and bottom tails
3323	* of a data set.
3324	*
3325	* Excel Function:
3326	* TRIMEAN(value1[,value2[, ...]], $discard)
3327	*
3328	* @category Statistical Functions
3329	*
3330	* @param mixed $args Data values
3331	* @param float $discard Percentage to discard
3332	*
3333	* @return float
3334	*/
3335	public static function TRIMMEAN(...$args)
3336	{
3337	$aArgs = Functions::flattenArray($args);
3338
3339	// Calculate
3340	$percent = array_pop($aArgs);
3341
3342	if ((is_numeric($percent)) && (!is_string($percent))) {
3343	if (($percent < 0) \|\| ($percent > 1)) {
3344	return Functions::NAN();
3345	}
3346	$mArgs = [];
3347	foreach ($aArgs as $arg) {
3348	// Is it a numeric value?
3349	if ((is_numeric($arg)) && (!is_string($arg))) {
3350	$mArgs[] = $arg;
3351	}
3352	}
3353	$discard = floor(self::COUNT($mArgs) * $percent / 2);
3354	sort($mArgs);
3355	for ($i = 0; $i < $discard; ++$i) {
3356	array_pop($mArgs);
3357	array_shift($mArgs);
3358	}
3359
3360	return self::AVERAGE($mArgs);
3361	}
3362
3363	return Functions::VALUE();
3364	}
3365
3366	/**
3367	* VARFunc.
3368	*
3369	* Estimates variance based on a sample.
3370	*
3371	* Excel Function:
3372	* VAR(value1[,value2[, ...]])
3373	*
3374	* @category Statistical Functions
3375	*
3376	* @param mixed ...$args Data values
3377	*
3378	* @return float
3379	*/
3380	public static function VARFunc(...$args)
3381	{
3382	$returnValue = Functions::DIV0();
3383
3384	$summerA = $summerB = 0;
3385
3386	// Loop through arguments
3387	$aArgs = Functions::flattenArray($args);
3388	$aCount = 0;
3389	foreach ($aArgs as $arg) {
3390	if (is_bool($arg)) {
3391	$arg = (int) $arg;
3392	}
3393	// Is it a numeric value?
3394	if ((is_numeric($arg)) && (!is_string($arg))) {
3395	$summerA += ($arg * $arg);
3396	$summerB += $arg;
3397	++$aCount;
3398	}
3399	}
3400
3401	if ($aCount > 1) {
3402	$summerA *= $aCount;
3403	$summerB *= $summerB;
3404	$returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
3405	}
3406
3407	return $returnValue;
3408	}
3409
3410	/**
3411	* VARA.
3412	*
3413	* Estimates variance based on a sample, including numbers, text, and logical values
3414	*
3415	* Excel Function:
3416	* VARA(value1[,value2[, ...]])
3417	*
3418	* @category Statistical Functions
3419	*
3420	* @param mixed ...$args Data values
3421	*
3422	* @return float
3423	*/
3424	public static function VARA(...$args)
3425	{
3426	$returnValue = Functions::DIV0();
3427
3428	$summerA = $summerB = 0;
3429
3430	// Loop through arguments
3431	$aArgs = Functions::flattenArrayIndexed($args);
3432	$aCount = 0;
3433	foreach ($aArgs as $k => $arg) {
3434	if ((is_string($arg)) &&
3435	(Functions::isValue($k))) {
3436	return Functions::VALUE();
3437	} elseif ((is_string($arg)) &&
3438	(!Functions::isMatrixValue($k))) {
3439	} else {
3440	// Is it a numeric value?
3441	if ((is_numeric($arg)) \|\| (is_bool($arg)) \|\| ((is_string($arg) & ($arg != '')))) {
3442	if (is_bool($arg)) {
3443	$arg = (int) $arg;
3444	} elseif (is_string($arg)) {
3445	$arg = 0;
3446	}
3447	$summerA += ($arg * $arg);
3448	$summerB += $arg;
3449	++$aCount;
3450	}
3451	}
3452	}
3453
3454	if ($aCount > 1) {
3455	$summerA *= $aCount;
3456	$summerB *= $summerB;
3457	$returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1));
3458	}
3459
3460	return $returnValue;
3461	}
3462
3463	/**
3464	* VARP.
3465	*
3466	* Calculates variance based on the entire population
3467	*
3468	* Excel Function:
3469	* VARP(value1[,value2[, ...]])
3470	*
3471	* @category Statistical Functions
3472	*
3473	* @param mixed ...$args Data values
3474	*
3475	* @return float
3476	*/
3477	public static function VARP(...$args)
3478	{
3479	// Return value
3480	$returnValue = Functions::DIV0();
3481
3482	$summerA = $summerB = 0;
3483
3484	// Loop through arguments
3485	$aArgs = Functions::flattenArray($args);
3486	$aCount = 0;
3487	foreach ($aArgs as $arg) {
3488	if (is_bool($arg)) {
3489	$arg = (int) $arg;
3490	}
3491	// Is it a numeric value?
3492	if ((is_numeric($arg)) && (!is_string($arg))) {
3493	$summerA += ($arg * $arg);
3494	$summerB += $arg;
3495	++$aCount;
3496	}
3497	}
3498
3499	if ($aCount > 0) {
3500	$summerA *= $aCount;
3501	$summerB *= $summerB;
3502	$returnValue = ($summerA - $summerB) / ($aCount * $aCount);
3503	}
3504
3505	return $returnValue;
3506	}
3507
3508	/**
3509	* VARPA.
3510	*
3511	* Calculates variance based on the entire population, including numbers, text, and logical values
3512	*
3513	* Excel Function:
3514	* VARPA(value1[,value2[, ...]])
3515	*
3516	* @category Statistical Functions
3517	*
3518	* @param mixed ...$args Data values
3519	*
3520	* @return float
3521	*/
3522	public static function VARPA(...$args)
3523	{
3524	$returnValue = Functions::DIV0();
3525
3526	$summerA = $summerB = 0;
3527
3528	// Loop through arguments
3529	$aArgs = Functions::flattenArrayIndexed($args);
3530	$aCount = 0;
3531	foreach ($aArgs as $k => $arg) {
3532	if ((is_string($arg)) &&
3533	(Functions::isValue($k))) {
3534	return Functions::VALUE();
3535	} elseif ((is_string($arg)) &&
3536	(!Functions::isMatrixValue($k))) {
3537	} else {
3538	// Is it a numeric value?
3539	if ((is_numeric($arg)) \|\| (is_bool($arg)) \|\| ((is_string($arg) & ($arg != '')))) {
3540	if (is_bool($arg)) {
3541	$arg = (int) $arg;
3542	} elseif (is_string($arg)) {
3543	$arg = 0;
3544	}
3545	$summerA += ($arg * $arg);
3546	$summerB += $arg;
3547	++$aCount;
3548	}
3549	}
3550	}
3551
3552	if ($aCount > 0) {
3553	$summerA *= $aCount;
3554	$summerB *= $summerB;
3555	$returnValue = ($summerA - $summerB) / ($aCount * $aCount);
3556	}
3557
3558	return $returnValue;
3559	}
3560
3561	/**
3562	* WEIBULL.
3563	*
3564	* Returns the Weibull distribution. Use this distribution in reliability
3565	* analysis, such as calculating a device's mean time to failure.
3566	*
3567	* @param float $value
3568	* @param float $alpha Alpha Parameter
3569	* @param float $beta Beta Parameter
3570	* @param bool $cumulative
3571	*
3572	* @return float
3573	*/
3574	public static function WEIBULL($value, $alpha, $beta, $cumulative)
3575	{
3576	$value = Functions::flattenSingleValue($value);
3577	$alpha = Functions::flattenSingleValue($alpha);
3578	$beta = Functions::flattenSingleValue($beta);
3579
3580	if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta))) {
3581	if (($value < 0) \|\| ($alpha <= 0) \|\| ($beta <= 0)) {
3582	return Functions::NAN();
3583	}
3584	if ((is_numeric($cumulative)) \|\| (is_bool($cumulative))) {
3585	if ($cumulative) {
3586	return 1 - exp(0 - pow($value / $beta, $alpha));
3587	}
3588
3589	return ($alpha / pow($beta, $alpha)) * pow($value, $alpha - 1) * exp(0 - pow($value / $beta, $alpha));
3590	}
3591	}
3592
3593	return Functions::VALUE();
3594	}
3595
3596	/**
3597	* ZTEST.
3598	*
3599	* Returns the Weibull distribution. Use this distribution in reliability
3600	* analysis, such as calculating a device's mean time to failure.
3601	*
3602	* @param float $dataSet
3603	* @param float $m0 Alpha Parameter
3604	* @param float $sigma Beta Parameter
3605	*
3606	* @return float
3607	*/
3608	public static function ZTEST($dataSet, $m0, $sigma = null)
3609	{
3610	$dataSet = Functions::flattenArrayIndexed($dataSet);
3611	$m0 = Functions::flattenSingleValue($m0);
3612	$sigma = Functions::flattenSingleValue($sigma);
3613
3614	if ($sigma === null) {
3615	$sigma = self::STDEV($dataSet);
3616	}
3617	$n = count($dataSet);
3618
3619	return 1 - self::NORMSDIST((self::AVERAGE($dataSet) - $m0) / ($sigma / sqrt($n)));
3620	}
3621	}
3622