poly_hermite.tcc

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00001 // Special functions -*- C++ -*-
00002 
00003 // Copyright (C) 2006, 2007, 2008, 2009
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 3, 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 // Under Section 7 of GPL version 3, you are granted additional
00018 // permissions described in the GCC Runtime Library Exception, version
00019 // 3.1, as published by the Free Software Foundation.
00020 
00021 // You should have received a copy of the GNU General Public License and
00022 // a copy of the GCC Runtime Library Exception along with this program;
00023 // see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
00024 // <http://www.gnu.org/licenses/>.
00025 
00026 /** @file tr1/poly_hermite.tcc
00027  *  This is an internal header file, included by other library headers.
00028  *  You should not attempt to use it directly.
00029  */
00030 
00031 //
00032 // ISO C++ 14882 TR1: 5.2  Special functions
00033 //
00034 
00035 // Written by Edward Smith-Rowland based on:
00036 //   (1) Handbook of Mathematical Functions,
00037 //       Ed. Milton Abramowitz and Irene A. Stegun,
00038 //       Dover Publications, Section 22 pp. 773-802
00039 
00040 #ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC
00041 #define _GLIBCXX_TR1_POLY_HERMITE_TCC 1
00042 
00043 namespace std
00044 {
00045 namespace tr1
00046 {
00047 
00048   // [5.2] Special functions
00049 
00050   // Implementation-space details.
00051   namespace __detail
00052   {
00053 
00054     /**
00055      *   @brief This routine returns the Hermite polynomial
00056      *          of order n: \f$ H_n(x) \f$ by recursion on n.
00057      * 
00058      *   The Hermite polynomial is defined by:
00059      *   @f[
00060      *     H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
00061      *   @f]
00062      *
00063      *   @param __n The order of the Hermite polynomial.
00064      *   @param __x The argument of the Hermite polynomial.
00065      *   @return The value of the Hermite polynomial of order n
00066      *           and argument x.
00067      */
00068     template<typename _Tp>
00069     _Tp
00070     __poly_hermite_recursion(const unsigned int __n, const _Tp __x)
00071     {
00072       //  Compute H_0.
00073       _Tp __H_0 = 1;
00074       if (__n == 0)
00075         return __H_0;
00076 
00077       //  Compute H_1.
00078       _Tp __H_1 = 2 * __x;
00079       if (__n == 1)
00080         return __H_1;
00081 
00082       //  Compute H_n.
00083       _Tp __H_n, __H_nm1, __H_nm2;
00084       unsigned int __i;
00085       for  (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i)
00086         {
00087           __H_n = 2 * (__x * __H_nm1 + (__i - 1) * __H_nm2);
00088           __H_nm2 = __H_nm1;
00089           __H_nm1 = __H_n;
00090         }
00091 
00092       return __H_n;
00093     }
00094 
00095 
00096     /**
00097      *   @brief This routine returns the Hermite polynomial
00098      *          of order n: \f$ H_n(x) \f$.
00099      * 
00100      *   The Hermite polynomial is defined by:
00101      *   @f[
00102      *     H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
00103      *   @f]
00104      *
00105      *   @param __n The order of the Hermite polynomial.
00106      *   @param __x The argument of the Hermite polynomial.
00107      *   @return The value of the Hermite polynomial of order n
00108      *           and argument x.
00109      */
00110     template<typename _Tp>
00111     inline _Tp
00112     __poly_hermite(const unsigned int __n, const _Tp __x)
00113     {
00114       if (__isnan(__x))
00115         return std::numeric_limits<_Tp>::quiet_NaN();
00116       else
00117         return __poly_hermite_recursion(__n, __x);
00118     }
00119 
00120   } // namespace std::tr1::__detail
00121 }
00122 }
00123 
00124 #endif // _GLIBCXX_TR1_POLY_HERMITE_TCC

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