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 // Recurrence 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 recurrence:
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
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77