00001 // Special functions -*- C++ -*- 00002 00003 // Copyright (C) 2006, 2007, 2008 00004 // Free Software Foundation, Inc. 00005 // 00006 // This file is part of the GNU ISO C++ Library. This library is free 00007 // software; you can redistribute it and/or modify it under the 00008 // terms of the GNU General Public License as published by the 00009 // Free Software Foundation; either version 2, or (at your option) 00010 // any later version. 00011 // 00012 // This library is distributed in the hope that it will be useful, 00013 // but WITHOUT ANY WARRANTY; without even the implied warranty of 00014 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 00015 // GNU General Public License for more details. 00016 // 00017 // You should have received a copy of the GNU General Public License along 00018 // with this library; see the file COPYING. If not, write to the Free 00019 // Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, 00020 // USA. 00021 // 00022 // As a special exception, you may use this file as part of a free software 00023 // library without restriction. Specifically, if other files instantiate 00024 // templates or use macros or inline functions from this file, or you compile 00025 // this file and link it with other files to produce an executable, this 00026 // file does not by itself cause the resulting executable to be covered by 00027 // the GNU General Public License. This exception does not however 00028 // invalidate any other reasons why the executable file might be covered by 00029 // the GNU General Public License. 00030 00031 /** @file tr1/poly_hermite.tcc 00032 * This is an internal header file, included by other library headers. 00033 * You should not attempt to use it directly. 00034 */ 00035 00036 // 00037 // ISO C++ 14882 TR1: 5.2 Special functions 00038 // 00039 00040 // Written by Edward Smith-Rowland based on: 00041 // (1) Handbook of Mathematical Functions, 00042 // Ed. Milton Abramowitz and Irene A. Stegun, 00043 // Dover Publications, Section 22 pp. 773-802 00044 00045 #ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC 00046 #define _GLIBCXX_TR1_POLY_HERMITE_TCC 1 00047 00048 namespace std 00049 { 00050 namespace tr1 00051 { 00052 00053 // [5.2] Special functions 00054 00055 // Implementation-space details. 00056 namespace __detail 00057 { 00058 00059 /** 00060 * @brief This routine returns the Hermite polynomial 00061 * of order n: \f$ H_n(x) \f$ by recursion on n. 00062 * 00063 * The Hermite polynomial is defined by: 00064 * @f[ 00065 * H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2} 00066 * @f] 00067 * 00068 * @param __n The order of the Hermite polynomial. 00069 * @param __x The argument of the Hermite polynomial. 00070 * @return The value of the Hermite polynomial of order n 00071 * and argument x. 00072 */ 00073 template<typename _Tp> 00074 _Tp 00075 __poly_hermite_recursion(const unsigned int __n, const _Tp __x) 00076 { 00077 // Compute H_0. 00078 _Tp __H_0 = 1; 00079 if (__n == 0) 00080 return __H_0; 00081 00082 // Compute H_1. 00083 _Tp __H_1 = 2 * __x; 00084 if (__n == 1) 00085 return __H_1; 00086 00087 // Compute H_n. 00088 _Tp __H_n, __H_nm1, __H_nm2; 00089 unsigned int __i; 00090 for (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i) 00091 { 00092 __H_n = 2 * (__x * __H_nm1 + (__i - 1) * __H_nm2); 00093 __H_nm2 = __H_nm1; 00094 __H_nm1 = __H_n; 00095 } 00096 00097 return __H_n; 00098 } 00099 00100 00101 /** 00102 * @brief This routine returns the Hermite polynomial 00103 * of order n: \f$ H_n(x) \f$. 00104 * 00105 * The Hermite polynomial is defined by: 00106 * @f[ 00107 * H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2} 00108 * @f] 00109 * 00110 * @param __n The order of the Hermite polynomial. 00111 * @param __x The argument of the Hermite polynomial. 00112 * @return The value of the Hermite polynomial of order n 00113 * and argument x. 00114 */ 00115 template<typename _Tp> 00116 inline _Tp 00117 __poly_hermite(const unsigned int __n, const _Tp __x) 00118 { 00119 if (__isnan(__x)) 00120 return std::numeric_limits<_Tp>::quiet_NaN(); 00121 else 00122 return __poly_hermite_recursion(__n, __x); 00123 } 00124 00125 } // namespace std::tr1::__detail 00126 } 00127 } 00128 00129 #endif // _GLIBCXX_TR1_POLY_HERMITE_TCC