| |
| // (C) Copyright John Maddock 2006. |
| // Use, modification and distribution are subject to the |
| // Boost Software License, Version 1.0. (See accompanying file |
| // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) |
| |
| #ifndef BOOST_MATH_SPECIAL_LAGUERRE_HPP |
| #define BOOST_MATH_SPECIAL_LAGUERRE_HPP |
| |
| #ifdef _MSC_VER |
| #pragma once |
| #endif |
| |
| #include <boost/math/special_functions/math_fwd.hpp> |
| #include <boost/math/tools/config.hpp> |
| #include <boost/math/policies/error_handling.hpp> |
| |
| namespace boost{ |
| namespace math{ |
| |
| // Recurrance relation for Laguerre polynomials: |
| template <class T1, class T2, class T3> |
| inline typename tools::promote_args<T1, T2, T3>::type |
| laguerre_next(unsigned n, T1 x, T2 Ln, T3 Lnm1) |
| { |
| typedef typename tools::promote_args<T1, T2, T3>::type result_type; |
| return ((2 * n + 1 - result_type(x)) * result_type(Ln) - n * result_type(Lnm1)) / (n + 1); |
| } |
| |
| namespace detail{ |
| |
| // Implement Laguerre polynomials via recurrance: |
| template <class T> |
| T laguerre_imp(unsigned n, T x) |
| { |
| T p0 = 1; |
| T p1 = 1 - x; |
| |
| if(n == 0) |
| return p0; |
| |
| unsigned c = 1; |
| |
| while(c < n) |
| { |
| std::swap(p0, p1); |
| p1 = laguerre_next(c, x, p0, p1); |
| ++c; |
| } |
| return p1; |
| } |
| |
| template <class T, class Policy> |
| inline typename tools::promote_args<T>::type |
| laguerre(unsigned n, T x, const Policy&, const mpl::true_&) |
| { |
| typedef typename tools::promote_args<T>::type result_type; |
| typedef typename policies::evaluation<result_type, Policy>::type value_type; |
| return policies::checked_narrowing_cast<result_type, Policy>(detail::laguerre_imp(n, static_cast<value_type>(x)), "boost::math::laguerre<%1%>(unsigned, %1%)"); |
| } |
| |
| template <class T> |
| inline typename tools::promote_args<T>::type |
| laguerre(unsigned n, unsigned m, T x, const mpl::false_&) |
| { |
| return boost::math::laguerre(n, m, x, policies::policy<>()); |
| } |
| |
| } // namespace detail |
| |
| template <class T> |
| inline typename tools::promote_args<T>::type |
| laguerre(unsigned n, T x) |
| { |
| return laguerre(n, x, policies::policy<>()); |
| } |
| |
| // Recurrence for associated polynomials: |
| template <class T1, class T2, class T3> |
| inline typename tools::promote_args<T1, T2, T3>::type |
| laguerre_next(unsigned n, unsigned l, T1 x, T2 Pl, T3 Plm1) |
| { |
| typedef typename tools::promote_args<T1, T2, T3>::type result_type; |
| return ((2 * n + l + 1 - result_type(x)) * result_type(Pl) - (n + l) * result_type(Plm1)) / (n+1); |
| } |
| |
| namespace detail{ |
| // Laguerre Associated Polynomial: |
| template <class T, class Policy> |
| T laguerre_imp(unsigned n, unsigned m, T x, const Policy& pol) |
| { |
| // Special cases: |
| if(m == 0) |
| return boost::math::laguerre(n, x, pol); |
| |
| T p0 = 1; |
| |
| if(n == 0) |
| return p0; |
| |
| T p1 = m + 1 - x; |
| |
| unsigned c = 1; |
| |
| while(c < n) |
| { |
| std::swap(p0, p1); |
| p1 = laguerre_next(c, m, x, p0, p1); |
| ++c; |
| } |
| return p1; |
| } |
| |
| } |
| |
| template <class T, class Policy> |
| inline typename tools::promote_args<T>::type |
| laguerre(unsigned n, unsigned m, T x, const Policy& pol) |
| { |
| typedef typename tools::promote_args<T>::type result_type; |
| typedef typename policies::evaluation<result_type, Policy>::type value_type; |
| 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%)"); |
| } |
| |
| template <class T1, class T2> |
| inline typename laguerre_result<T1, T2>::type |
| laguerre(unsigned n, T1 m, T2 x) |
| { |
| typedef typename policies::is_policy<T2>::type tag_type; |
| return detail::laguerre(n, m, x, tag_type()); |
| } |
| |
| } // namespace math |
| } // namespace boost |
| |
| #endif // BOOST_MATH_SPECIAL_LAGUERRE_HPP |
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