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
hermite_next(unsigned n,T1 x,T2 Hn,T3 Hnm1)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>
hermite_imp(unsigned n,T x)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
hermite(unsigned n,T x,const Policy &)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
hermite(unsigned n,T x)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 
77