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<?php
namespace PhpOffice\PhpSpreadsheet\Calculation\Statistical\Distributions;
use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
use PhpOffice\PhpSpreadsheet\Calculation\Exception;
use PhpOffice\PhpSpreadsheet\Calculation\Functions;
use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
class ChiSquared
{
use ArrayEnabled;
private const MAX_ITERATIONS = 256;
private const EPS = 2.22e-16;
/**
* CHIDIST.
*
* Returns the one-tailed probability of the chi-squared distribution.
*
* @param mixed $value Float value for which we want the probability
* Or can be an array of values
* @param mixed $degrees Integer degrees of freedom
* Or can be an array of values
*
* @return array|float|string
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function distributionRightTail($value, $degrees)
{
if (is_array($value) || is_array($degrees)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $value, $degrees);
}
try {
$value = DistributionValidations::validateFloat($value);
$degrees = DistributionValidations::validateInt($degrees);
} catch (Exception $e) {
return $e->getMessage();
}
if ($degrees < 1) {
return ExcelError::NAN();
}
if ($value < 0) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
return 1;
}
return ExcelError::NAN();
}
return 1 - (Gamma::incompleteGamma($degrees / 2, $value / 2) / Gamma::gammaValue($degrees / 2));
}
/**
* CHIDIST.
*
* Returns the one-tailed probability of the chi-squared distribution.
*
* @param mixed $value Float value for which we want the probability
* Or can be an array of values
* @param mixed $degrees Integer degrees of freedom
* Or can be an array of values
* @param mixed $cumulative Boolean value indicating if we want the cdf (true) or the pdf (false)
* Or can be an array of values
*
* @return array|float|string
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function distributionLeftTail($value, $degrees, $cumulative)
{
if (is_array($value) || is_array($degrees) || is_array($cumulative)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $value, $degrees, $cumulative);
}
try {
$value = DistributionValidations::validateFloat($value);
$degrees = DistributionValidations::validateInt($degrees);
$cumulative = DistributionValidations::validateBool($cumulative);
} catch (Exception $e) {
return $e->getMessage();
}
if ($degrees < 1) {
return ExcelError::NAN();
}
if ($value < 0) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
return 1;
}
return ExcelError::NAN();
}
if ($cumulative === true) {
return 1 - self::distributionRightTail($value, $degrees);
}
return ($value ** (($degrees / 2) - 1) * exp(-$value / 2)) /
((2 ** ($degrees / 2)) * Gamma::gammaValue($degrees / 2));
}
/**
* CHIINV.
*
* Returns the inverse of the right-tailed probability of the chi-squared distribution.
*
* @param mixed $probability Float probability at which you want to evaluate the distribution
* Or can be an array of values
* @param mixed $degrees Integer degrees of freedom
* Or can be an array of values
*
* @return array|float|string
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function inverseRightTail($probability, $degrees)
{
if (is_array($probability) || is_array($degrees)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $probability, $degrees);
}
try {
$probability = DistributionValidations::validateProbability($probability);
$degrees = DistributionValidations::validateInt($degrees);
} catch (Exception $e) {
return $e->getMessage();
}
if ($degrees < 1) {
return ExcelError::NAN();
}
$callback = function ($value) use ($degrees) {
return 1 - (Gamma::incompleteGamma($degrees / 2, $value / 2)
/ Gamma::gammaValue($degrees / 2));
};
$newtonRaphson = new NewtonRaphson($callback);
return $newtonRaphson->execute($probability);
}
/**
* CHIINV.
*
* Returns the inverse of the left-tailed probability of the chi-squared distribution.
*
* @param mixed $probability Float probability at which you want to evaluate the distribution
* Or can be an array of values
* @param mixed $degrees Integer degrees of freedom
* Or can be an array of values
*
* @return array|float|string
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function inverseLeftTail($probability, $degrees)
{
if (is_array($probability) || is_array($degrees)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $probability, $degrees);
}
try {
$probability = DistributionValidations::validateProbability($probability);
$degrees = DistributionValidations::validateInt($degrees);
} catch (Exception $e) {
return $e->getMessage();
}
if ($degrees < 1) {
return ExcelError::NAN();
}
return self::inverseLeftTailCalculation($probability, $degrees);
}
/**
* CHITEST.
*
* Uses the chi-square test to calculate the probability that the differences between two supplied data sets
* (of observed and expected frequencies), are likely to be simply due to sampling error,
* or if they are likely to be real.
*
* @param mixed $actual an array of observed frequencies
* @param mixed $expected an array of expected frequencies
*
* @return float|string
*/
public static function test($actual, $expected)
{
$rows = count($actual);
$actual = Functions::flattenArray($actual);
$expected = Functions::flattenArray($expected);
$columns = count($actual) / $rows;
$countActuals = count($actual);
$countExpected = count($expected);
if ($countActuals !== $countExpected || $countActuals === 1) {
return ExcelError::NAN();
}
$result = 0.0;
for ($i = 0; $i < $countActuals; ++$i) {
if ($expected[$i] == 0.0) {
return ExcelError::DIV0();
} elseif ($expected[$i] < 0.0) {
return ExcelError::NAN();
}
$result += (($actual[$i] - $expected[$i]) ** 2) / $expected[$i];
}
$degrees = self::degrees($rows, $columns);
$result = Functions::scalar(self::distributionRightTail($result, $degrees));
return $result;
}
protected static function degrees(int $rows, int $columns): int
{
if ($rows === 1) {
return $columns - 1;
} elseif ($columns === 1) {
return $rows - 1;
}
return ($columns - 1) * ($rows - 1);
}
private static function inverseLeftTailCalculation(float $probability, int $degrees): float
{
// bracket the root
$min = 0;
$sd = sqrt(2.0 * $degrees);
$max = 2 * $sd;
$s = -1;
while ($s * self::pchisq($max, $degrees) > $probability * $s) {
$min = $max;
$max += 2 * $sd;
}
// Find root using bisection
$chi2 = 0.5 * ($min + $max);
while (($max - $min) > self::EPS * $chi2) {
if ($s * self::pchisq($chi2, $degrees) > $probability * $s) {
$min = $chi2;
} else {
$max = $chi2;
}
$chi2 = 0.5 * ($min + $max);
}
return $chi2;
}
private static function pchisq($chi2, $degrees)
{
return self::gammp($degrees, 0.5 * $chi2);
}
private static function gammp($n, $x)
{
if ($x < 0.5 * $n + 1) {
return self::gser($n, $x);
}
return 1 - self::gcf($n, $x);
}
// Return the incomplete gamma function P(n/2,x) evaluated by
// series representation. Algorithm from numerical recipe.
// Assume that n is a positive integer and x>0, won't check arguments.
// Relative error controlled by the eps parameter
private static function gser($n, $x)
{
/** @var float */
$gln = Gamma::ln($n / 2);
$a = 0.5 * $n;
$ap = $a;
$sum = 1.0 / $a;
$del = $sum;
for ($i = 1; $i < 101; ++$i) {
++$ap;
$del = $del * $x / $ap;
$sum += $del;
if ($del < $sum * self::EPS) {
break;
}
}
return $sum * exp(-$x + $a * log($x) - $gln);
}
// Return the incomplete gamma function Q(n/2,x) evaluated by
// its continued fraction representation. Algorithm from numerical recipe.
// Assume that n is a postive integer and x>0, won't check arguments.
// Relative error controlled by the eps parameter
private static function gcf($n, $x)
{
/** @var float */
$gln = Gamma::ln($n / 2);
$a = 0.5 * $n;
$b = $x + 1 - $a;
$fpmin = 1.e-300;
$c = 1 / $fpmin;
$d = 1 / $b;
$h = $d;
for ($i = 1; $i < 101; ++$i) {
$an = -$i * ($i - $a);
$b += 2;
$d = $an * $d + $b;
if (abs($d) < $fpmin) {
$d = $fpmin;
}
$c = $b + $an / $c;
if (abs($c) < $fpmin) {
$c = $fpmin;
}
$d = 1 / $d;
$del = $d * $c;
$h = $h * $del;
if (abs($del - 1) < self::EPS) {
break;
}
}
return $h * exp(-$x + $a * log($x) - $gln);
}
}
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