125 lines
3.6 KiB
C++
125 lines
3.6 KiB
C++
// Special functions -*- C++ -*-
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// Copyright (C) 2006-2014 Free Software Foundation, Inc.
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//
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// This file is part of the GNU ISO C++ Library. This library is free
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// software; you can redistribute it and/or modify it under the
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// terms of the GNU General Public License as published by the
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// Free Software Foundation; either version 3, or (at your option)
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// any later version.
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//
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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//
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// Under Section 7 of GPL version 3, you are granted additional
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// permissions described in the GCC Runtime Library Exception, version
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// 3.1, as published by the Free Software Foundation.
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// You should have received a copy of the GNU General Public License and
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// a copy of the GCC Runtime Library Exception along with this program;
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// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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// <http://www.gnu.org/licenses/>.
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/** @file tr1/poly_hermite.tcc
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* This is an internal header file, included by other library headers.
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* Do not attempt to use it directly. @headername{tr1/cmath}
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*/
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//
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// ISO C++ 14882 TR1: 5.2 Special functions
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//
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// Written by Edward Smith-Rowland based on:
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// (1) Handbook of Mathematical Functions,
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// Ed. Milton Abramowitz and Irene A. Stegun,
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// Dover Publications, Section 22 pp. 773-802
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#ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC
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#define _GLIBCXX_TR1_POLY_HERMITE_TCC 1
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namespace std _GLIBCXX_VISIBILITY(default)
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{
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namespace tr1
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{
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// [5.2] Special functions
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// Implementation-space details.
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namespace __detail
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{
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_GLIBCXX_BEGIN_NAMESPACE_VERSION
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/**
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* @brief This routine returns the Hermite polynomial
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* of order n: \f$ H_n(x) \f$ by recursion on n.
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*
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* The Hermite polynomial is defined by:
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* @f[
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* H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
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* @f]
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*
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* @param __n The order of the Hermite polynomial.
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* @param __x The argument of the Hermite polynomial.
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* @return The value of the Hermite polynomial of order n
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* and argument x.
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*/
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template<typename _Tp>
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_Tp
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__poly_hermite_recursion(unsigned int __n, _Tp __x)
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{
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// Compute H_0.
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_Tp __H_0 = 1;
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if (__n == 0)
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return __H_0;
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// Compute H_1.
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_Tp __H_1 = 2 * __x;
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if (__n == 1)
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return __H_1;
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// Compute H_n.
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_Tp __H_n, __H_nm1, __H_nm2;
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unsigned int __i;
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for (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i)
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{
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__H_n = 2 * (__x * __H_nm1 - (__i - 1) * __H_nm2);
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__H_nm2 = __H_nm1;
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__H_nm1 = __H_n;
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}
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return __H_n;
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}
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/**
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* @brief This routine returns the Hermite polynomial
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* of order n: \f$ H_n(x) \f$.
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*
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* The Hermite polynomial is defined by:
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* @f[
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* H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
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* @f]
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*
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* @param __n The order of the Hermite polynomial.
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* @param __x The argument of the Hermite polynomial.
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* @return The value of the Hermite polynomial of order n
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* and argument x.
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*/
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template<typename _Tp>
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inline _Tp
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__poly_hermite(unsigned int __n, _Tp __x)
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{
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if (__isnan(__x))
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return std::numeric_limits<_Tp>::quiet_NaN();
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else
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return __poly_hermite_recursion(__n, __x);
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}
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_GLIBCXX_END_NAMESPACE_VERSION
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} // namespace std::tr1::__detail
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}
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}
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#endif // _GLIBCXX_TR1_POLY_HERMITE_TCC
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