Viewing file:  BesselJ.php (5.78 KB) -rw-r--r--
Select action/file-type:
 (+) |  (+) |  (+) | Code (+) | Session (+) |  (+) | SDB (+) |  (+) |  (+) |  (+) |  (+) |  (+) |
<?php
namespace PhpOffice\PhpSpreadsheet\Calculation\Engineering;
use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
use PhpOffice\PhpSpreadsheet\Calculation\Exception;
use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
class BesselJ
{
use ArrayEnabled;
/**
* BESSELJ.
*
* Returns the Bessel function
*
* Excel Function:
* BESSELJ(x,ord)
*
* NOTE: The MS Excel implementation of the BESSELJ function is still not accurate, particularly for higher order
* values with x < -8 and x > 8. This code provides a more accurate calculation
*
* @param mixed $x A float value at which to evaluate the function.
* If x is nonnumeric, BESSELJ 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, BESSELJ returns the #VALUE! error value.
* If $ord < 0, BESSELJ returns the #NUM! error value.
* Or can be an array of values
*
* @return array|float|string Result, or a string containing an error
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function BESSELJ($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) {
return ExcelError::NAN();
}
$fResult = self::calculate($x, $ord);
return (is_nan($fResult)) ? ExcelError::NAN() : $fResult;
}
private static function calculate(float $x, int $ord): float
{
// special cases
switch ($ord) {
case 0:
return self::besselJ0($x);
case 1:
return self::besselJ1($x);
}
return self::besselJ2($x, $ord);
}
private static function besselJ0(float $x): float
{
$ax = abs($x);
if ($ax < 8.0) {
$y = $x * $x;
$ans1 = 57568490574.0 + $y * (-13362590354.0 + $y * (651619640.7 + $y * (-11214424.18 + $y *
(77392.33017 + $y * (-184.9052456)))));
$ans2 = 57568490411.0 + $y * (1029532985.0 + $y * (9494680.718 + $y * (59272.64853 + $y *
(267.8532712 + $y * 1.0))));
return $ans1 / $ans2;
}
$z = 8.0 / $ax;
$y = $z * $z;
$xx = $ax - 0.785398164;
$ans1 = 1.0 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
$ans2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y *
(0.7621095161e-6 - $y * 0.934935152e-7)));
return sqrt(0.636619772 / $ax) * (cos($xx) * $ans1 - $z * sin($xx) * $ans2);
}
private static function besselJ1(float $x): float
{
$ax = abs($x);
if ($ax < 8.0) {
$y = $x * $x;
$ans1 = $x * (72362614232.0 + $y * (-7895059235.0 + $y * (242396853.1 + $y *
(-2972611.439 + $y * (15704.48260 + $y * (-30.16036606))))));
$ans2 = 144725228442.0 + $y * (2300535178.0 + $y * (18583304.74 + $y * (99447.43394 + $y *
(376.9991397 + $y * 1.0))));
return $ans1 / $ans2;
}
$z = 8.0 / $ax;
$y = $z * $z;
$xx = $ax - 2.356194491;
$ans1 = 1.0 + $y * (0.183105e-2 + $y * (-0.3516396496e-4 + $y * (0.2457520174e-5 + $y * (-0.240337019e-6))));
$ans2 = 0.04687499995 + $y * (-0.2002690873e-3 + $y * (0.8449199096e-5 + $y *
(-0.88228987e-6 + $y * 0.105787412e-6)));
$ans = sqrt(0.636619772 / $ax) * (cos($xx) * $ans1 - $z * sin($xx) * $ans2);
return ($x < 0.0) ? -$ans : $ans;
}
private static function besselJ2(float $x, int $ord): float
{
$ax = abs($x);
if ($ax === 0.0) {
return 0.0;
}
if ($ax > $ord) {
return self::besselj2a($ax, $ord, $x);
}
return self::besselj2b($ax, $ord, $x);
}
private static function besselj2a(float $ax, int $ord, float $x): float
{
$tox = 2.0 / $ax;
$bjm = self::besselJ0($ax);
$bj = self::besselJ1($ax);
for ($j = 1; $j < $ord; ++$j) {
$bjp = $j * $tox * $bj - $bjm;
$bjm = $bj;
$bj = $bjp;
}
$ans = $bj;
return ($x < 0.0 && ($ord % 2) == 1) ? -$ans : $ans;
}
private static function besselj2b(float $ax, int $ord, float $x): float
{
$tox = 2.0 / $ax;
$jsum = false;
$bjp = $ans = $sum = 0.0;
$bj = 1.0;
for ($j = 2 * ($ord + (int) sqrt(40.0 * $ord)); $j > 0; --$j) {
$bjm = $j * $tox * $bj - $bjp;
$bjp = $bj;
$bj = $bjm;
if (abs($bj) > 1.0e+10) {
$bj *= 1.0e-10;
$bjp *= 1.0e-10;
$ans *= 1.0e-10;
$sum *= 1.0e-10;
}
if ($jsum === true) {
$sum += $bj;
}
$jsum = $jsum === false;
if ($j === $ord) {
$ans = $bjp;
}
}
$sum = 2.0 * $sum - $bj;
$ans /= $sum;
return ($x < 0.0 && ($ord % 2) === 1) ? -$ans : $ans;
}
}
|