tablepress / libraries / vendor / PhpSpreadsheet / Calculation / Engineering / BesselJ.php

BesselJ.php in TablePress – Tables in WordPress made easy 3.4, at libraries/vendor/PhpSpreadsheet/Calculation/Engineering/BesselJ.php

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1	<?php
2
3	namespace TablePress\PhpOffice\PhpSpreadsheet\Calculation\Engineering;
4
5	use TablePress\PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
6	use TablePress\PhpOffice\PhpSpreadsheet\Calculation\Exception;
7	use TablePress\PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
8
9	class BesselJ
10	{
11	use ArrayEnabled;
12
13	/**
14	* BESSELJ.
15	*
16	* Returns the Bessel function
17	*
18	* Excel Function:
19	* BESSELJ(x,ord)
20	*
21	* NOTE: The MS Excel implementation of the BESSELJ function is still not accurate, particularly for higher order
22	* values with x < -8 and x > 8. This code provides a more accurate calculation
23	*
24	* @param mixed $x A float value at which to evaluate the function.
25	* If x is nonnumeric, BESSELJ returns the #VALUE! error value.
26	* Or can be an array of values
27	* @param mixed $ord The integer order of the Bessel function.
28	* If ord is not an integer, it is truncated.
29	* If $ord is nonnumeric, BESSELJ returns the #VALUE! error value.
30	* If $ord < 0, BESSELJ returns the #NUM! error value.
31	* Or can be an array of values
32	*
33	* @return array<mixed>\|float\|string Result, or a string containing an error
34	* If an array of numbers is passed as an argument, then the returned result will also be an array
35	* with the same dimensions
36	*/
37	public static function BESSELJ($x, $ord)
38	{
39	if (is_array($x) \|\| is_array($ord)) {
40	return self::evaluateArrayArguments([self::class, __FUNCTION__], $x, $ord);
41	}
42
43	try {
44	$x = EngineeringValidations::validateFloat($x);
45	$ord = EngineeringValidations::validateInt($ord);
46	} catch (Exception $e) {
47	return $e->getMessage();
48	}
49
50	if ($ord < 0) {
51	return ExcelError::NAN();
52	}
53
54	$fResult = self::calculate($x, $ord);
55
56	return (is_nan($fResult)) ? ExcelError::NAN() : $fResult;
57	}
58
59	private static function calculate(float $x, int $ord): float
60	{
61	switch ($ord) {
62	case 0:
63	return self::besselJ0($x);
64	case 1:
65	return self::besselJ1($x);
66	default:
67	return self::besselJ2($x, $ord);
68	}
69	}
70
71	private static function besselJ0(float $x): float
72	{
73	$ax = abs($x);
74
75	if ($ax < 8.0) {
76	$y = $x * $x;
77	$ans1 = 57568490574.0 + $y * (-13362590354.0 + $y * (651619640.7 + $y * (-11214424.18 + $y
78	* (77392.33017 + $y * (-184.9052456)))));
79	$ans2 = 57568490411.0 + $y * (1029532985.0 + $y * (9494680.718 + $y * (59272.64853 + $y
80	* (267.8532712 + $y * 1.0))));
81
82	return $ans1 / $ans2;
83	}
84
85	$z = 8.0 / $ax;
86	$y = $z * $z;
87	$xx = $ax - 0.785398164;
88	$ans1 = 1.0 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
89	$ans2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y
90	* (0.7621095161e-6 - $y * 0.934935152e-7)));
91
92	return sqrt(0.636619772 / $ax) * (cos($xx) * $ans1 - $z * sin($xx) * $ans2);
93	}
94
95	private static function besselJ1(float $x): float
96	{
97	$ax = abs($x);
98
99	if ($ax < 8.0) {
100	$y = $x * $x;
101	$ans1 = $x * (72362614232.0 + $y * (-7895059235.0 + $y * (242396853.1 + $y
102	* (-2972611.439 + $y * (15704.48260 + $y * (-30.16036606))))));
103	$ans2 = 144725228442.0 + $y * (2300535178.0 + $y * (18583304.74 + $y * (99447.43394 + $y
104	* (376.9991397 + $y * 1.0))));
105
106	return $ans1 / $ans2;
107	}
108
109	$z = 8.0 / $ax;
110	$y = $z * $z;
111	$xx = $ax - 2.356194491;
112
113	$ans1 = 1.0 + $y * (0.183105e-2 + $y * (-0.3516396496e-4 + $y * (0.2457520174e-5 + $y * (-0.240337019e-6))));
114	$ans2 = 0.04687499995 + $y * (-0.2002690873e-3 + $y * (0.8449199096e-5 + $y
115	* (-0.88228987e-6 + $y * 0.105787412e-6)));
116	$ans = sqrt(0.636619772 / $ax) * (cos($xx) * $ans1 - $z * sin($xx) * $ans2);
117
118	return ($x < 0.0) ? -$ans : $ans;
119	}
120
121	private static function besselJ2(float $x, int $ord): float
122	{
123	$ax = abs($x);
124	if ($ax === 0.0) {
125	return 0.0;
126	}
127
128	if ($ax > $ord) {
129	return self::besselj2a($ax, $ord, $x);
130	}
131
132	return self::besselj2b($ax, $ord, $x);
133	}
134
135	private static function besselj2a(float $ax, int $ord, float $x): float
136	{
137	$tox = 2.0 / $ax;
138	$bjm = self::besselJ0($ax);
139	$bj = self::besselJ1($ax);
140	for ($j = 1; $j < $ord; ++$j) {
141	$bjp = $j * $tox * $bj - $bjm;
142	$bjm = $bj;
143	$bj = $bjp;
144	}
145	$ans = $bj;
146
147	return ($x < 0.0 && ($ord % 2) == 1) ? -$ans : $ans;
148	}
149
150	private static function besselj2b(float $ax, int $ord, float $x): float
151	{
152	$tox = 2.0 / $ax;
153	$jsum = false;
154	$bjp = $ans = $sum = 0.0;
155	$bj = 1.0;
156	for ($j = 2 * ($ord + (int) sqrt(40.0 * $ord)); $j > 0; --$j) {
157	$bjm = $j * $tox * $bj - $bjp;
158	$bjp = $bj;
159	$bj = $bjm;
160	if (abs($bj) > 1.0e+10) {
161	$bj *= 1.0e-10;
162	$bjp *= 1.0e-10;
163	$ans *= 1.0e-10;
164	$sum *= 1.0e-10;
165	}
166	if ($jsum === true) {
167	$sum += $bj;
168	}
169	$jsum = $jsum === false;
170	if ($j === $ord) {
171	$ans = $bjp;
172	}
173	}
174	$sum = 2.0 * $sum - $bj;
175	$ans /= $sum;
176
177	return ($x < 0.0 && ($ord % 2) === 1) ? -$ans : $ans;
178	}
179	}
180