Move Bessel function calculations from the Engineering class to a dedicated Engineering\Bessel<x> classes (#1846)
* Move Bessel function calculations from the Engineering class to a dedicated Engineering\Bessel class Retain the original methods in the Engineering class as stubs for BC, but deprecate them. They will be removed for PHPSpreadsheet v2 * Some refactoring of the Bessel calculation logic * Fix callable for ConvertUOM()
This commit is contained in:
Mark Baker
GitHub
parent
17f405cf62
commit
2aa4a28863
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@ -363,22 +363,22 @@ class Calculation
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],
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'BESSELI' => [
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'category' => Category::CATEGORY_ENGINEERING,
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'functionCall' => [Engineering::class, 'BESSELI'],
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'functionCall' => [Engineering\BesselI::class, 'BESSELI'],
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'argumentCount' => '2',
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],
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'BESSELJ' => [
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'category' => Category::CATEGORY_ENGINEERING,
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'functionCall' => [Engineering::class, 'BESSELJ'],
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'functionCall' => [Engineering\BesselJ::class, 'BESSELJ'],
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'argumentCount' => '2',
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],
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'BESSELK' => [
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'category' => Category::CATEGORY_ENGINEERING,
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'functionCall' => [Engineering::class, 'BESSELK'],
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'functionCall' => [Engineering\BesselK::class, 'BESSELK'],
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'argumentCount' => '2',
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],
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'BESSELY' => [
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'category' => Category::CATEGORY_ENGINEERING,
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'functionCall' => [Engineering::class, 'BESSELY'],
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'functionCall' => [Engineering\BesselY::class, 'BESSELY'],
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'argumentCount' => '2',
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],
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'BETADIST' => [
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@ -594,7 +594,7 @@ class Calculation
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],
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'CONVERT' => [
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'category' => Category::CATEGORY_ENGINEERING,
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'functionCall' => [Engineering::class, 'CONVERTUOM'],
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'functionCall' => [Engineering\ConvertUOM::class, 'CONVERT'],
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'argumentCount' => '3',
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],
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'CORREL' => [
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@ -4,6 +4,7 @@ namespace PhpOffice\PhpSpreadsheet\Calculation;
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use Complex\Complex;
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use Complex\Exception as ComplexException;
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use PhpOffice\PhpSpreadsheet\Calculation\Engineering\Bessel;
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use PhpOffice\PhpSpreadsheet\Calculation\Engineering\ConvertUOM;
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class Engineering
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@ -73,6 +74,8 @@ class Engineering
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* Excel Function:
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* BESSELI(x,ord)
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*
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* @Deprecated 2.0.0 Use the BESSELI() method in the Engineering\BesselI class instead
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*
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* @param float $x The value at which to evaluate the function.
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* If x is nonnumeric, BESSELI returns the #VALUE! error value.
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* @param int $ord The order of the Bessel function.
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@ -84,38 +87,7 @@ class Engineering
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*/
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public static function BESSELI($x, $ord)
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{
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$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
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$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
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if ((is_numeric($x)) && (is_numeric($ord))) {
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$ord = floor($ord);
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if ($ord < 0) {
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return Functions::NAN();
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}
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if (abs($x) <= 30) {
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$fResult = $fTerm = ($x / 2) ** $ord / MathTrig::FACT($ord);
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$ordK = 1;
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$fSqrX = ($x * $x) / 4;
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do {
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$fTerm *= $fSqrX;
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$fTerm /= ($ordK * ($ordK + $ord));
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$fResult += $fTerm;
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} while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
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} else {
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$f_2_PI = 2 * M_PI;
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$fXAbs = abs($x);
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$fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs);
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if (($ord & 1) && ($x < 0)) {
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$fResult = -$fResult;
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}
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}
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return (is_nan($fResult)) ? Functions::NAN() : $fResult;
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}
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return Functions::VALUE();
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return Engineering\BesselI::BESSELI($x, $ord);
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}
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/**
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@ -126,6 +98,8 @@ class Engineering
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* Excel Function:
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* BESSELJ(x,ord)
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*
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* @Deprecated 2.0.0 Use the BESSELJ() method in the Engineering\BesselJ class instead
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*
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* @param float $x The 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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* @param int $ord The order of the Bessel function. If n is not an integer, it is truncated.
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@ -136,76 +110,7 @@ class Engineering
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*/
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public static function BESSELJ($x, $ord)
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{
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$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
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$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
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if ((is_numeric($x)) && (is_numeric($ord))) {
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$ord = floor($ord);
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if ($ord < 0) {
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return Functions::NAN();
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}
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$fResult = 0;
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if (abs($x) <= 30) {
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$fResult = $fTerm = ($x / 2) ** $ord / MathTrig::FACT($ord);
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$ordK = 1;
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$fSqrX = ($x * $x) / -4;
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do {
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$fTerm *= $fSqrX;
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$fTerm /= ($ordK * ($ordK + $ord));
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$fResult += $fTerm;
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} while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
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} else {
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$f_PI_DIV_2 = M_PI / 2;
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$f_PI_DIV_4 = M_PI / 4;
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$fXAbs = abs($x);
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$fResult = sqrt(Functions::M_2DIVPI / $fXAbs) * cos($fXAbs - $ord * $f_PI_DIV_2 - $f_PI_DIV_4);
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if (($ord & 1) && ($x < 0)) {
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$fResult = -$fResult;
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}
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}
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return (is_nan($fResult)) ? Functions::NAN() : $fResult;
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}
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return Functions::VALUE();
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}
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private static function besselK0($fNum)
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{
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if ($fNum <= 2) {
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$fNum2 = $fNum * 0.5;
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$y = ($fNum2 * $fNum2);
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$fRet = -log($fNum2) * self::BESSELI($fNum, 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 + $y * 0.74e-5))))));
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} else {
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$y = 2 / $fNum;
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$fRet = exp(-$fNum) / sqrt($fNum) *
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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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return $fRet;
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}
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private static function besselK1($fNum)
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{
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if ($fNum <= 2) {
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$fNum2 = $fNum * 0.5;
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$y = ($fNum2 * $fNum2);
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$fRet = log($fNum2) * self::BESSELI($fNum, 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))))))) / $fNum;
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} else {
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$y = 2 / $fNum;
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$fRet = exp(-$fNum) / sqrt($fNum) *
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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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return $fRet;
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return Engineering\BesselJ::BESSELJ($x, $ord);
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}
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/**
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@ -217,6 +122,8 @@ class Engineering
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* Excel Function:
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* BESSELK(x,ord)
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*
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* @Deprecated 2.0.0 Use the BESSELK() method in the Engineering\BesselK class instead
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*
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* @param float $x The 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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* @param int $ord The order of the Bessel function. If n is not an integer, it is truncated.
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@ -227,73 +134,7 @@ class Engineering
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*/
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public static function BESSELK($x, $ord)
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{
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$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
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$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
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if ((is_numeric($x)) && (is_numeric($ord))) {
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if (($ord < 0) || ($x == 0.0)) {
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return Functions::NAN();
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}
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switch (floor($ord)) {
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case 0:
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$fBk = self::besselK0($x);
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break;
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case 1:
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$fBk = self::besselK1($x);
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break;
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default:
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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 = $fBkp;
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}
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}
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return (is_nan($fBk)) ? Functions::NAN() : $fBk;
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}
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return Functions::VALUE();
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}
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private static function besselY0($fNum)
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{
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if ($fNum < 8.0) {
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$y = ($fNum * $fNum);
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$f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733))));
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$f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y))));
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$fRet = $f1 / $f2 + 0.636619772 * self::BESSELJ($fNum, 0) * log($fNum);
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} else {
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$z = 8.0 / $fNum;
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$y = ($z * $z);
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$xx = $fNum - 0.785398164;
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$f1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
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$f2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7))));
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$fRet = sqrt(0.636619772 / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
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}
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return $fRet;
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}
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private static function besselY1($fNum)
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{
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if ($fNum < 8.0) {
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$y = ($fNum * $fNum);
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$f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y *
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(-0.4237922726e7 + $y * 0.8511937935e4)))));
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$f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
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(0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
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$fRet = $f1 / $f2 + 0.636619772 * (self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
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} else {
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$fRet = sqrt(0.636619772 / $fNum) * sin($fNum - 2.356194491);
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}
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return $fRet;
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return Engineering\BesselK::BESSELK($x, $ord);
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}
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/**
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@ -304,48 +145,19 @@ class Engineering
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* Excel Function:
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* BESSELY(x,ord)
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*
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* @Deprecated 2.0.0 Use the BESSELY() method in the Engineering\BesselY class instead
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*
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* @param float $x The 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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* If x is nonnumeric, BESSELY returns the #VALUE! error value.
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* @param int $ord The order of the Bessel function. If n 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, BESSELK returns the #NUM! error value.
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* If $ord is nonnumeric, BESSELY returns the #VALUE! error value.
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* If $ord < 0, BESSELY returns the #NUM! error value.
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*
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* @return float|string Result, or a string containing an error
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*/
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public static function BESSELY($x, $ord)
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{
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$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
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$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
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if ((is_numeric($x)) && (is_numeric($ord))) {
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if (($ord < 0) || ($x == 0.0)) {
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return Functions::NAN();
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}
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switch (floor($ord)) {
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case 0:
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$fBy = self::besselY0($x);
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break;
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case 1:
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$fBy = self::besselY1($x);
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break;
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default:
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$fTox = 2 / $x;
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$fBym = self::besselY0($x);
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$fBy = self::besselY1($x);
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for ($n = 1; $n < $ord; ++$n) {
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$fByp = $n * $fTox * $fBy - $fBym;
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$fBym = $fBy;
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$fBy = $fByp;
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}
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}
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return (is_nan($fBy)) ? Functions::NAN() : $fBy;
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}
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return Functions::VALUE();
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return Engineering\BesselY::BESSELY($x, $ord);
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}
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/**
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@ -1882,7 +1694,7 @@ class Engineering
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* getConversionGroups
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* Returns a list of the different conversion groups for UOM conversions.
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*
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* @Deprecated Use the getConversionCategories() method in the ConvertUOM class instead
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* @Deprecated 2.0.0 Use the getConversionCategories() method in the Engineering\ConvertUOM class instead
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*
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* @return array
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*/
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@ -0,0 +1,72 @@
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<?php
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namespace PhpOffice\PhpSpreadsheet\Calculation\Engineering;
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use PhpOffice\PhpSpreadsheet\Calculation\Functions;
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use PhpOffice\PhpSpreadsheet\Calculation\MathTrig;
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class BesselI
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{
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/**
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* BESSELI.
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*
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* Returns the modified Bessel function In(x), which is equivalent to the Bessel function evaluated
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* for purely imaginary arguments
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*
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* Excel Function:
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* BESSELI(x,ord)
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*
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* @param float $x The value at which to evaluate the function.
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* If x is nonnumeric, BESSELI returns the #VALUE! error value.
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* @param int $ord The 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, BESSELI returns the #VALUE! error value.
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* If $ord < 0, BESSELI returns the #NUM! error value.
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*
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* @return float|string Result, or a string containing an error
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*/
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public static function BESSELI($x, $ord)
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{
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$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
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$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
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if ((is_numeric($x)) && (is_numeric($ord))) {
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$ord = (int) floor($ord);
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if ($ord < 0) {
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return Functions::NAN();
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}
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$fResult = self::calculate($x, $ord);
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return (is_nan($fResult)) ? Functions::NAN() : $fResult;
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}
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return Functions::VALUE();
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}
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private static function calculate(float $x, int $ord): float
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{
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if (abs($x) <= 30) {
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$fResult = $fTerm = ($x / 2) ** $ord / MathTrig::FACT($ord);
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$ordK = 1;
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$fSqrX = ($x * $x) / 4;
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do {
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$fTerm *= $fSqrX;
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$fTerm /= ($ordK * ($ordK + $ord));
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$fResult += $fTerm;
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} while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
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return $fResult;
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}
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$f_2_PI = 2 * M_PI;
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$fXAbs = abs($x);
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$fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs);
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if (($ord & 1) && ($x < 0)) {
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$fResult = -$fResult;
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}
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return $fResult;
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}
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}
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@ -0,0 +1,71 @@
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<?php
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namespace PhpOffice\PhpSpreadsheet\Calculation\Engineering;
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use PhpOffice\PhpSpreadsheet\Calculation\Functions;
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use PhpOffice\PhpSpreadsheet\Calculation\MathTrig;
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class BesselJ
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{
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/**
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* BESSELJ.
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*
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||||
* Returns the Bessel function
|
||||
*
|
||||
* Excel Function:
|
||||
* BESSELJ(x,ord)
|
||||
*
|
||||
* @param float $x The value at which to evaluate the function.
|
||||
* If x is nonnumeric, BESSELJ returns the #VALUE! error value.
|
||||
* @param int $ord The order of the Bessel function. If n is not an integer, it is truncated.
|
||||
* If $ord is nonnumeric, BESSELJ returns the #VALUE! error value.
|
||||
* If $ord < 0, BESSELJ returns the #NUM! error value.
|
||||
*
|
||||
* @return float|string Result, or a string containing an error
|
||||
*/
|
||||
public static function BESSELJ($x, $ord)
|
||||
{
|
||||
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
|
||||
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
|
||||
|
||||
if ((is_numeric($x)) && (is_numeric($ord))) {
|
||||
$ord = (int) floor($ord);
|
||||
if ($ord < 0) {
|
||||
return Functions::NAN();
|
||||
}
|
||||
|
||||
$fResult = self::calculate($x, $ord);
|
||||
|
||||
return (is_nan($fResult)) ? Functions::NAN() : $fResult;
|
||||
}
|
||||
|
||||
return Functions::VALUE();
|
||||
}
|
||||
|
||||
private static function calculate(float $x, int $ord): float
|
||||
{
|
||||
if (abs($x) <= 30) {
|
||||
$fResult = $fTerm = ($x / 2) ** $ord / MathTrig::FACT($ord);
|
||||
$ordK = 1;
|
||||
$fSqrX = ($x * $x) / -4;
|
||||
do {
|
||||
$fTerm *= $fSqrX;
|
||||
$fTerm /= ($ordK * ($ordK + $ord));
|
||||
$fResult += $fTerm;
|
||||
} while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
|
||||
|
||||
return $fResult;
|
||||
}
|
||||
|
||||
$f_PI_DIV_2 = M_PI / 2;
|
||||
$f_PI_DIV_4 = M_PI / 4;
|
||||
|
||||
$fXAbs = abs($x);
|
||||
$fResult = sqrt(Functions::M_2DIVPI / $fXAbs) * cos($fXAbs - $ord * $f_PI_DIV_2 - $f_PI_DIV_4);
|
||||
if (($ord & 1) && ($x < 0)) {
|
||||
$fResult = -$fResult;
|
||||
}
|
||||
|
||||
return $fResult;
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,104 @@
|
|||
<?php
|
||||
|
||||
namespace PhpOffice\PhpSpreadsheet\Calculation\Engineering;
|
||||
|
||||
use PhpOffice\PhpSpreadsheet\Calculation\Functions;
|
||||
|
||||
class BesselK
|
||||
{
|
||||
/**
|
||||
* 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 float $x The value at which to evaluate the function.
|
||||
* If x is nonnumeric, BESSELK returns the #VALUE! error value.
|
||||
* @param int $ord The order of the Bessel function. If n is not an integer, it is truncated.
|
||||
* If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
|
||||
* If $ord < 0, BESSELK returns the #NUM! error value.
|
||||
*
|
||||
* @return float|string Result, or a string containing an error
|
||||
*/
|
||||
public static function BESSELK($x, $ord)
|
||||
{
|
||||
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
|
||||
$ord = ($ord === null) ? 0 : Functions::flattenSingleValue($ord);
|
||||
|
||||
if ((is_numeric($x)) && (is_numeric($ord))) {
|
||||
if (($ord < 0) || ($x == 0.0)) {
|
||||
return Functions::NAN();
|
||||
}
|
||||
|
||||
switch (floor($ord)) {
|
||||
case 0:
|
||||
$fBk = self::besselK0($x);
|
||||
|
||||
break;
|
||||
case 1:
|
||||
$fBk = self::besselK1($x);
|
||||
|
||||
break;
|
||||
default:
|
||||
$fBk = self::besselK2($x, $ord);
|
||||
}
|
||||
|
||||
return (is_nan($fBk)) ? Functions::NAN() : $fBk;
|
||||
}
|
||||
|
||||
return Functions::VALUE();
|
||||
}
|
||||
|
||||
private static function besselK0(float $fNum): float
|
||||
{
|
||||
if ($fNum <= 2) {
|
||||
$fNum2 = $fNum * 0.5;
|
||||
$y = ($fNum2 * $fNum2);
|
||||
|
||||
return -log($fNum2) * BesselI::BESSELI($fNum, 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 / $fNum;
|
||||
|
||||
return exp(-$fNum) / sqrt($fNum) *
|
||||
(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 $fNum): float
|
||||
{
|
||||
if ($fNum <= 2) {
|
||||
$fNum2 = $fNum * 0.5;
|
||||
$y = ($fNum2 * $fNum2);
|
||||
|
||||
return log($fNum2) * BesselI::BESSELI($fNum, 1) +
|
||||
(1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y *
|
||||
(-0.110404e-2 + $y * (-0.4686e-4))))))) / $fNum;
|
||||
}
|
||||
|
||||
$y = 2 / $fNum;
|
||||
|
||||
return exp(-$fNum) / sqrt($fNum) *
|
||||
(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)
|
||||
{
|
||||
$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;
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,104 @@
|
|||
<?php
|
||||
|
||||
namespace PhpOffice\PhpSpreadsheet\Calculation\Engineering;
|
||||
|
||||
use PhpOffice\PhpSpreadsheet\Calculation\Functions;
|
||||
|
||||
class BesselY
|
||||
{
|
||||
/**
|
||||
* BESSELY.
|
||||
*
|
||||
* Returns the Bessel function, which is also called the Weber function or the Neumann function.
|
||||
*
|
||||
* Excel Function:
|
||||
* BESSELY(x,ord)
|
||||
*
|
||||
* @param float $x The value at which to evaluate the function.
|
||||
* If x is nonnumeric, BESSELY returns the #VALUE! error value.
|
||||
* @param int $ord The order of the Bessel function. If n is not an integer, it is truncated.
|
||||
* If $ord is nonnumeric, BESSELY returns the #VALUE! error value.
|
||||
* If $ord < 0, BESSELY returns the #NUM! error value.
|
||||
*
|
||||
* @return float|string Result, or a string containing an error
|
||||
*/
|
||||
public static function BESSELY($x, $ord)
|
||||
{
|
||||
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
|
||||
$ord = ($ord === null) ? 0 : Functions::flattenSingleValue($ord);
|
||||
|
||||
if ((is_numeric($x)) && (is_numeric($ord))) {
|
||||
if (($ord < 0) || ($x == 0.0)) {
|
||||
return Functions::NAN();
|
||||
}
|
||||
|
||||
switch (floor($ord)) {
|
||||
case 0:
|
||||
$fBy = self::besselY0($x);
|
||||
|
||||
break;
|
||||
case 1:
|
||||
$fBy = self::besselY1($x);
|
||||
|
||||
break;
|
||||
default:
|
||||
$fBy = self::besselY2($x, $ord);
|
||||
}
|
||||
|
||||
return (is_nan($fBy)) ? Functions::NAN() : $fBy;
|
||||
}
|
||||
|
||||
return Functions::VALUE();
|
||||
}
|
||||
|
||||
private static function besselY0(float $fNum): float
|
||||
{
|
||||
if ($fNum < 8.0) {
|
||||
$y = ($fNum * $fNum);
|
||||
$f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y *
|
||||
(-86327.92757 + $y * 228.4622733))));
|
||||
$f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y *
|
||||
(47447.26470 + $y * (226.1030244 + $y))));
|
||||
|
||||
return $f1 / $f2 + 0.636619772 * BesselJ::BESSELJ($fNum, 0) * log($fNum);
|
||||
}
|
||||
|
||||
$z = 8.0 / $fNum;
|
||||
$y = ($z * $z);
|
||||
$xx = $fNum - 0.785398164;
|
||||
$f1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
|
||||
$f2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y *
|
||||
(-0.934945152e-7))));
|
||||
|
||||
return sqrt(0.636619772 / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
|
||||
}
|
||||
|
||||
private static function besselY1(float $fNum): float
|
||||
{
|
||||
if ($fNum < 8.0) {
|
||||
$y = ($fNum * $fNum);
|
||||
$f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y *
|
||||
(0.7349264551e9 + $y * (-0.4237922726e7 + $y * 0.8511937935e4)))));
|
||||
$f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
|
||||
(0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
|
||||
|
||||
return $f1 / $f2 + 0.636619772 * (BesselJ::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
|
||||
}
|
||||
|
||||
return sqrt(0.636619772 / $fNum) * sin($fNum - 2.356194491);
|
||||
}
|
||||
|
||||
private static function besselY2(float $x, int $ord)
|
||||
{
|
||||
$fTox = 2 / $x;
|
||||
$fBym = self::besselY0($x);
|
||||
$fBy = self::besselY1($x);
|
||||
for ($n = 1; $n < $ord; ++$n) {
|
||||
$fByp = $n * $fTox * $fBy - $fBym;
|
||||
$fBym = $fBy;
|
||||
$fBy = $fByp;
|
||||
}
|
||||
|
||||
return $fBy;
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue