blob: ef3be01adec858da20b98d56243e1f82154731ba (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
|
// Special functions -*- C++ -*-
// Copyright (C) 2016-2017 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library. This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
// <http://www.gnu.org/licenses/>.
/** @file bits/sf_gegenbauer.tcc
* This is an internal header file, included by other library headers.
* Do not attempt to use it directly. @headername{cmath}
*/
#ifndef _GLIBCXX_BITS_SF_GEGENBAUER_TCC
#define _GLIBCXX_BITS_SF_GEGENBAUER_TCC 1
#pragma GCC system_header
#include <ext/math_const.h>
namespace std _GLIBCXX_VISIBILITY(default)
{
// Implementation-space details.
namespace __detail
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
/**
* Return the Gegenbauer polynomial @f$ C_n^{\alpha}(x) @f$ of degree @c n
* and real order @f$ \alpha @f$ and argument @c x.
*
* The Gegenbauer polynomials are generated by a three-term recursion relation:
* @f[
* C_n^{\alpha}(x) = \frac{1}{n}\left[ 2x(n+\alpha-1)C_{n-1}^{\alpha}(x)
* - (n+2\alpha-2)C_{n-2}^{\alpha}(x) \right]
* @f]
* and @f$ C_0^{\alpha}(x) = 1 @f$, @f$ C_1^{\alpha}(x) = 2\alpha x @f$.
*
* @tparam _Talpha The real type of the order
* @tparam _Tp The real type of the argument
* @param __n The non-negative integral degree
* @param __alpha The real order
* @param __x The real argument
*/
template<typename _Tp>
_Tp
__gegenbauer_poly(unsigned int __n, _Tp __alpha, _Tp __x)
{
const auto _S_NaN = __gnu_cxx::__quiet_NaN(__x);
if (__isnan(__alpha) || __isnan(__x))
return _S_NaN;
auto _C0 = _Tp{1};
if (__n == 0)
return _C0;
auto _C1 = _Tp{2} * __alpha * __x;
if (__n == 1)
return _C1;
auto _Cn = _Tp{0};
for (unsigned int __nn = 2; __nn <= __n; ++__nn)
{
_Cn = (_Tp{2} * (_Tp{__nn} - _Tp{1} + __alpha) * __x * _C1
- (_Tp{__nn} - _Tp{2} + _Tp{2} * __alpha) * _C0)
/ _Tp(__nn);
_C0 = _C1;
_C1 = _Cn;
}
return _Cn;
}
} // namespace __detail
} // namespace std
#endif // _GLIBCXX_BITS_SF_GEGENBAUER_TCC
|
