poly_hermite.tcc

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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

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