<?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 BesselJ
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{
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use ArrayEnabled;
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/**
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* BESSELJ.
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*
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* Returns the Bessel function
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*
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* Excel Function:
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* BESSELJ(x,ord)
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*
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* NOTE: The MS Excel implementation of the BESSELJ function is still not accurate, particularly for higher order
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* values with x < -8 and x > 8. This code provides a more accurate calculation
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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, BESSELJ 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, BESSELJ returns the #VALUE! error value.
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* If $ord < 0, BESSELJ 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 BESSELJ(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) {
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return ExcelError::NAN();
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}
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$fResult = self::calculate($x, $ord);
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return (is_nan($fResult)) ? ExcelError::NAN() : $fResult;
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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::besselJ0($x),
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1 => self::besselJ1($x),
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default => self::besselJ2($x, $ord),
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};
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}
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private static function besselJ0(float $x): float
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{
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$ax = abs($x);
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if ($ax < 8.0) {
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$y = $x * $x;
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$ans1 = 57568490574.0 + $y * (-13362590354.0 + $y * (651619640.7 + $y * (-11214424.18 + $y
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* (77392.33017 + $y * (-184.9052456)))));
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$ans2 = 57568490411.0 + $y * (1029532985.0 + $y * (9494680.718 + $y * (59272.64853 + $y
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* (267.8532712 + $y * 1.0))));
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return $ans1 / $ans2;
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}
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$z = 8.0 / $ax;
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$y = $z * $z;
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$xx = $ax - 0.785398164;
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$ans1 = 1.0 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
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$ans2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y
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* (0.7621095161e-6 - $y * 0.934935152e-7)));
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return sqrt(0.636619772 / $ax) * (cos($xx) * $ans1 - $z * sin($xx) * $ans2);
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}
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private static function besselJ1(float $x): float
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{
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$ax = abs($x);
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if ($ax < 8.0) {
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$y = $x * $x;
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$ans1 = $x * (72362614232.0 + $y * (-7895059235.0 + $y * (242396853.1 + $y
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* (-2972611.439 + $y * (15704.48260 + $y * (-30.16036606))))));
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$ans2 = 144725228442.0 + $y * (2300535178.0 + $y * (18583304.74 + $y * (99447.43394 + $y
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* (376.9991397 + $y * 1.0))));
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return $ans1 / $ans2;
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}
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$z = 8.0 / $ax;
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$y = $z * $z;
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$xx = $ax - 2.356194491;
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$ans1 = 1.0 + $y * (0.183105e-2 + $y * (-0.3516396496e-4 + $y * (0.2457520174e-5 + $y * (-0.240337019e-6))));
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$ans2 = 0.04687499995 + $y * (-0.2002690873e-3 + $y * (0.8449199096e-5 + $y
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* (-0.88228987e-6 + $y * 0.105787412e-6)));
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$ans = sqrt(0.636619772 / $ax) * (cos($xx) * $ans1 - $z * sin($xx) * $ans2);
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return ($x < 0.0) ? -$ans : $ans;
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}
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private static function besselJ2(float $x, int $ord): float
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{
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$ax = abs($x);
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if ($ax === 0.0) {
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return 0.0;
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}
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if ($ax > $ord) {
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return self::besselj2a($ax, $ord, $x);
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}
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return self::besselj2b($ax, $ord, $x);
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}
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private static function besselj2a(float $ax, int $ord, float $x): float
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{
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$tox = 2.0 / $ax;
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$bjm = self::besselJ0($ax);
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$bj = self::besselJ1($ax);
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for ($j = 1; $j < $ord; ++$j) {
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$bjp = $j * $tox * $bj - $bjm;
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$bjm = $bj;
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$bj = $bjp;
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}
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$ans = $bj;
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return ($x < 0.0 && ($ord % 2) == 1) ? -$ans : $ans;
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}
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private static function besselj2b(float $ax, int $ord, float $x): float
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{
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$tox = 2.0 / $ax;
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$jsum = false;
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$bjp = $ans = $sum = 0.0;
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$bj = 1.0;
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for ($j = 2 * ($ord + (int) sqrt(40.0 * $ord)); $j > 0; --$j) {
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$bjm = $j * $tox * $bj - $bjp;
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$bjp = $bj;
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$bj = $bjm;
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if (abs($bj) > 1.0e+10) {
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$bj *= 1.0e-10;
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$bjp *= 1.0e-10;
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$ans *= 1.0e-10;
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$sum *= 1.0e-10;
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}
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if ($jsum === true) {
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$sum += $bj;
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}
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$jsum = $jsum === false;
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if ($j === $ord) {
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$ans = $bjp;
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}
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}
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$sum = 2.0 * $sum - $bj;
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$ans /= $sum;
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return ($x < 0.0 && ($ord % 2) === 1) ? -$ans : $ans;
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}
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}
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