ceph/src/boost/libs/math/include/boost/math/special_functions/hermite.hpp

   1
   2 //  (C) Copyright John Maddock 2006.
   3 //  Use, modification and distribution are subject to the
   4 //  Boost Software License, Version 1.0. (See accompanying file
   5 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   6
   7 #ifndef BOOST_MATH_SPECIAL_HERMITE_HPP
   8 #define BOOST_MATH_SPECIAL_HERMITE_HPP
   9
  10 #ifdef _MSC_VER
  11 #pragma once
  12 #endif
  13
  14 #include <boost/math/special_functions/math_fwd.hpp>
  15 #include <boost/math/tools/config.hpp>
  16 #include <boost/math/policies/error_handling.hpp>
  17
  18 namespace boost{
  19 namespace math{
  20
  21 // Recurrance relation for Hermite polynomials:
  22 template <class T1, class T2, class T3>
  23 inline typename tools::promote_args<T1, T2, T3>::type
  24    hermite_next(unsigned n, T1 x, T2 Hn, T3 Hnm1)
  25 {
  26    return (2 * x * Hn - 2 * n * Hnm1);
  27 }
  28
  29 namespace detail{
  30
  31 // Implement Hermite polynomials via recurrance:
  32 template <class T>
  33 T hermite_imp(unsigned n, T x)
  34 {
  35    T p0 = 1;
  36    T p1 = 2 * x;
  37
  38    if(n == 0)
  39       return p0;
  40
  41    unsigned c = 1;
  42
  43    while(c < n)
  44    {
  45       std::swap(p0, p1);
  46       p1 = hermite_next(c, x, p0, p1);
  47       ++c;
  48    }
  49    return p1;
  50 }
  51
  52 } // namespace detail
  53
  54 template <class T, class Policy>
  55 inline typename tools::promote_args<T>::type
  56    hermite(unsigned n, T x, const Policy&)
  57 {
  58    typedef typename tools::promote_args<T>::type result_type;
  59    typedef typename policies::evaluation<result_type, Policy>::type value_type;
  60    return policies::checked_narrowing_cast<result_type, Policy>(detail::hermite_imp(n, static_cast<value_type>(x)), "boost::math::hermite<%1%>(unsigned, %1%)");
  61 }
  62
  63 template <class T>
  64 inline typename tools::promote_args<T>::type
  65    hermite(unsigned n, T x)
  66 {
  67    return boost::math::hermite(n, x, policies::policy<>());
  68 }
  69
  70 } // namespace math
  71 } // namespace boost
  72
  73 #endif // BOOST_MATH_SPECIAL_HERMITE_HPP
  74
  75
  76