libstdc++
poly_hermite.tcc
Go to the documentation of this file.
1 // Special functions -*- C++ -*-
2 
3 // Copyright (C) 2006, 2007, 2008, 2009
4 // Free Software Foundation, Inc.
5 //
6 // This file is part of the GNU ISO C++ Library. This library is free
7 // software; you can redistribute it and/or modify it under the
8 // terms of the GNU General Public License as published by the
9 // Free Software Foundation; either version 3, or (at your option)
10 // any later version.
11 //
12 // This library is distributed in the hope that it will be useful,
13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 // GNU General Public License for more details.
16 //
17 // Under Section 7 of GPL version 3, you are granted additional
18 // permissions described in the GCC Runtime Library Exception, version
19 // 3.1, as published by the Free Software Foundation.
20 
21 // You should have received a copy of the GNU General Public License and
22 // a copy of the GCC Runtime Library Exception along with this program;
23 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
24 // <http://www.gnu.org/licenses/>.
25 
26 /** @file tr1/poly_hermite.tcc
27  * This is an internal header file, included by other library headers.
28  * You should not attempt to use it directly.
29  */
30 
31 //
32 // ISO C++ 14882 TR1: 5.2 Special functions
33 //
34 
35 // Written by Edward Smith-Rowland based on:
36 // (1) Handbook of Mathematical Functions,
37 // Ed. Milton Abramowitz and Irene A. Stegun,
38 // Dover Publications, Section 22 pp. 773-802
39 
40 #ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC
41 #define _GLIBCXX_TR1_POLY_HERMITE_TCC 1
42 
43 namespace std
44 {
45 namespace tr1
46 {
47 
48  // [5.2] Special functions
49 
50  // Implementation-space details.
51  namespace __detail
52  {
53 
54  /**
55  * @brief This routine returns the Hermite polynomial
56  * of order n: \f$ H_n(x) \f$ by recursion on n.
57  *
58  * The Hermite polynomial is defined by:
59  * @f[
60  * H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
61  * @f]
62  *
63  * @param __n The order of the Hermite polynomial.
64  * @param __x The argument of the Hermite polynomial.
65  * @return The value of the Hermite polynomial of order n
66  * and argument x.
67  */
68  template<typename _Tp>
69  _Tp
70  __poly_hermite_recursion(const unsigned int __n, const _Tp __x)
71  {
72  // Compute H_0.
73  _Tp __H_0 = 1;
74  if (__n == 0)
75  return __H_0;
76 
77  // Compute H_1.
78  _Tp __H_1 = 2 * __x;
79  if (__n == 1)
80  return __H_1;
81 
82  // Compute H_n.
83  _Tp __H_n, __H_nm1, __H_nm2;
84  unsigned int __i;
85  for (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i)
86  {
87  __H_n = 2 * (__x * __H_nm1 + (__i - 1) * __H_nm2);
88  __H_nm2 = __H_nm1;
89  __H_nm1 = __H_n;
90  }
91 
92  return __H_n;
93  }
94 
95 
96  /**
97  * @brief This routine returns the Hermite polynomial
98  * of order n: \f$ H_n(x) \f$.
99  *
100  * The Hermite polynomial is defined by:
101  * @f[
102  * H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
103  * @f]
104  *
105  * @param __n The order of the Hermite polynomial.
106  * @param __x The argument of the Hermite polynomial.
107  * @return The value of the Hermite polynomial of order n
108  * and argument x.
109  */
110  template<typename _Tp>
111  inline _Tp
112  __poly_hermite(const unsigned int __n, const _Tp __x)
113  {
114  if (__isnan(__x))
116  else
117  return __poly_hermite_recursion(__n, __x);
118  }
119 
120  } // namespace std::tr1::__detail
121 }
122 }
123 
124 #endif // _GLIBCXX_TR1_POLY_HERMITE_TCC