<?php
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namespace PhpOffice\PhpSpreadsheet\Calculation\Engineering;
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use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
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use PhpOffice\PhpSpreadsheet\Calculation\Exception;
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use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
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class BesselK
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{
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use ArrayEnabled;
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/**
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* BESSELK.
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*
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* Returns the modified Bessel function Kn(x), which is equivalent to the Bessel functions evaluated
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* for purely imaginary arguments.
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*
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* Excel Function:
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* BESSELK(x,ord)
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*
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* @param mixed $x A float value at which to evaluate the function.
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* If x is nonnumeric, BESSELK returns the #VALUE! error value.
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* Or can be an array of values
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* @param mixed $ord The integer order of the Bessel function.
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* If ord is not an integer, it is truncated.
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* If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
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* If $ord < 0, BESSELKI returns the #NUM! error value.
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* Or can be an array of values
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*
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* @return array|float|string Result, or a string containing an error
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* If an array of numbers is passed as an argument, then the returned result will also be an array
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* with the same dimensions
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*/
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public static function BESSELK(mixed $x, mixed $ord): array|string|float
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{
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if (is_array($x) || is_array($ord)) {
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return self::evaluateArrayArguments([self::class, __FUNCTION__], $x, $ord);
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}
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try {
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$x = EngineeringValidations::validateFloat($x);
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$ord = EngineeringValidations::validateInt($ord);
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} catch (Exception $e) {
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return $e->getMessage();
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}
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if (($ord < 0) || ($x <= 0.0)) {
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return ExcelError::NAN();
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}
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$fBk = self::calculate($x, $ord);
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return (is_nan($fBk)) ? ExcelError::NAN() : $fBk;
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}
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private static function calculate(float $x, int $ord): float
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{
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return match ($ord) {
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0 => self::besselK0($x),
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1 => self::besselK1($x),
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default => self::besselK2($x, $ord),
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};
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}
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/**
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* Mollify Phpstan.
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*
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* @codeCoverageIgnore
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*/
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private static function callBesselI(float $x, int $ord): float
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{
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$rslt = BesselI::BESSELI($x, $ord);
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if (!is_float($rslt)) {
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throw new Exception('Unexpected array or string');
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}
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return $rslt;
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}
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private static function besselK0(float $x): float
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{
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if ($x <= 2) {
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$fNum2 = $x * 0.5;
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$y = ($fNum2 * $fNum2);
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return -log($fNum2) * self::callBesselI($x, 0)
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+ (-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y
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* (0.10750e-3 + $y * 0.74e-5))))));
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}
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$y = 2 / $x;
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return exp(-$x) / sqrt($x)
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* (1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y
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* (0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3))))));
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}
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private static function besselK1(float $x): float
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{
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if ($x <= 2) {
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$fNum2 = $x * 0.5;
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$y = ($fNum2 * $fNum2);
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return log($fNum2) * self::callBesselI($x, 1)
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+ (1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y
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* (-0.110404e-2 + $y * (-0.4686e-4))))))) / $x;
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}
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$y = 2 / $x;
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return exp(-$x) / sqrt($x)
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* (1.25331414 + $y * (0.23498619 + $y * (-0.3655620e-1 + $y * (0.1504268e-1 + $y * (-0.780353e-2 + $y
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* (0.325614e-2 + $y * (-0.68245e-3)))))));
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}
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private static function besselK2(float $x, int $ord): float
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{
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$fTox = 2 / $x;
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$fBkm = self::besselK0($x);
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$fBk = self::besselK1($x);
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for ($n = 1; $n < $ord; ++$n) {
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$fBkp = $fBkm + $n * $fTox * $fBk;
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$fBkm = $fBk;
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$fBk = $fBkp;
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}
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return $fBk;
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}
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}
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