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1 2// (C) Copyright John Maddock 2006.3// Use, modification and distribution are subject to the4// Boost Software License, Version 1.0. (See accompanying file5// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)6 7#ifndef BOOST_MATH_SPECIAL_LAGUERRE_HPP8#define BOOST_MATH_SPECIAL_LAGUERRE_HPP9 10#ifdef _MSC_VER11#pragma once12#endif13 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 18namespace boost{19namespace math{20 21// Recurrence relation for Laguerre polynomials:22template <class T1, class T2, class T3>23inline 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 30namespace detail{31 32// Implement Laguerre polynomials via recurrence:33template <class T>34T 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 53template <class T, class Policy>54inline typename tools::promote_args<T>::type 55laguerre(unsigned n, T x, const Policy&, const std::true_type&)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 62template <class T>63inline typename tools::promote_args<T>::type 64 laguerre(unsigned n, unsigned m, T x, const std::false_type&)65{66 return boost::math::laguerre(n, m, x, policies::policy<>());67}68 69} // namespace detail70 71template <class T>72inline 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:79template <class T1, class T2, class T3>80inline 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 87namespace detail{88// Laguerre Associated Polynomial:89template <class T, class Policy>90T 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 = static_cast<T>(laguerre_next(c, m, x, p0, p1));109 ++c;110 }111 return p1;112}113 114}115 116template <class T, class Policy>117inline 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 125template <class T1, class T2>126inline 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 math134} // namespace boost135 136#endif // BOOST_MATH_SPECIAL_LAGUERRE_HPP137 138 139 140