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