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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_LAGUERRE_HPP | |
8 | #define BOOST_MATH_SPECIAL_LAGUERRE_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 Laguerre polynomials: | |
22 | template <class T1, class T2, class T3> | |
23 | inline typename tools::promote_args<T1, T2, T3>::type | |
24 | laguerre_next(unsigned n, T1 x, T2 Ln, T3 Lnm1) | |
25 | { | |
26 | typedef typename tools::promote_args<T1, T2, T3>::type result_type; | |
27 | return ((2 * n + 1 - result_type(x)) * result_type(Ln) - n * result_type(Lnm1)) / (n + 1); | |
28 | } | |
29 | ||
30 | namespace detail{ | |
31 | ||
32 | // Implement Laguerre polynomials via recurrance: | |
33 | template <class T> | |
34 | T laguerre_imp(unsigned n, T x) | |
35 | { | |
36 | T p0 = 1; | |
37 | T p1 = 1 - x; | |
38 | ||
39 | if(n == 0) | |
40 | return p0; | |
41 | ||
42 | unsigned c = 1; | |
43 | ||
44 | while(c < n) | |
45 | { | |
46 | std::swap(p0, p1); | |
47 | p1 = laguerre_next(c, x, p0, p1); | |
48 | ++c; | |
49 | } | |
50 | return p1; | |
51 | } | |
52 | ||
53 | template <class T, class Policy> | |
54 | inline typename tools::promote_args<T>::type | |
55 | laguerre(unsigned n, T x, const Policy&, const mpl::true_&) | |
56 | { | |
57 | typedef typename tools::promote_args<T>::type result_type; | |
58 | typedef typename policies::evaluation<result_type, Policy>::type value_type; | |
59 | return policies::checked_narrowing_cast<result_type, Policy>(detail::laguerre_imp(n, static_cast<value_type>(x)), "boost::math::laguerre<%1%>(unsigned, %1%)"); | |
60 | } | |
61 | ||
62 | template <class T> | |
63 | inline typename tools::promote_args<T>::type | |
64 | laguerre(unsigned n, unsigned m, T x, const mpl::false_&) | |
65 | { | |
66 | return boost::math::laguerre(n, m, x, policies::policy<>()); | |
67 | } | |
68 | ||
69 | } // namespace detail | |
70 | ||
71 | template <class T> | |
72 | inline typename tools::promote_args<T>::type | |
73 | laguerre(unsigned n, T x) | |
74 | { | |
75 | return laguerre(n, x, policies::policy<>()); | |
76 | } | |
77 | ||
78 | // Recurrence for associated polynomials: | |
79 | template <class T1, class T2, class T3> | |
80 | inline typename tools::promote_args<T1, T2, T3>::type | |
81 | laguerre_next(unsigned n, unsigned l, T1 x, T2 Pl, T3 Plm1) | |
82 | { | |
83 | typedef typename tools::promote_args<T1, T2, T3>::type result_type; | |
84 | return ((2 * n + l + 1 - result_type(x)) * result_type(Pl) - (n + l) * result_type(Plm1)) / (n+1); | |
85 | } | |
86 | ||
87 | namespace detail{ | |
88 | // Laguerre Associated Polynomial: | |
89 | template <class T, class Policy> | |
90 | T laguerre_imp(unsigned n, unsigned m, T x, const Policy& pol) | |
91 | { | |
92 | // Special cases: | |
93 | if(m == 0) | |
94 | return boost::math::laguerre(n, x, pol); | |
95 | ||
96 | T p0 = 1; | |
97 | ||
98 | if(n == 0) | |
99 | return p0; | |
100 | ||
101 | T p1 = m + 1 - x; | |
102 | ||
103 | unsigned c = 1; | |
104 | ||
105 | while(c < n) | |
106 | { | |
107 | std::swap(p0, p1); | |
108 | p1 = laguerre_next(c, m, x, p0, p1); | |
109 | ++c; | |
110 | } | |
111 | return p1; | |
112 | } | |
113 | ||
114 | } | |
115 | ||
116 | template <class T, class Policy> | |
117 | inline typename tools::promote_args<T>::type | |
118 | laguerre(unsigned n, unsigned m, T x, const Policy& pol) | |
119 | { | |
120 | typedef typename tools::promote_args<T>::type result_type; | |
121 | typedef typename policies::evaluation<result_type, Policy>::type value_type; | |
122 | return policies::checked_narrowing_cast<result_type, Policy>(detail::laguerre_imp(n, m, static_cast<value_type>(x), pol), "boost::math::laguerre<%1%>(unsigned, unsigned, %1%)"); | |
123 | } | |
124 | ||
125 | template <class T1, class T2> | |
126 | inline typename laguerre_result<T1, T2>::type | |
127 | laguerre(unsigned n, T1 m, T2 x) | |
128 | { | |
129 | typedef typename policies::is_policy<T2>::type tag_type; | |
130 | return detail::laguerre(n, m, x, tag_type()); | |
131 | } | |
132 | ||
133 | } // namespace math | |
134 | } // namespace boost | |
135 | ||
136 | #endif // BOOST_MATH_SPECIAL_LAGUERRE_HPP | |
137 | ||
138 | ||
139 |