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// (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 #include #include namespace boost{ namespace math{ // Recurrence relation for Laguerre polynomials: template inline typename tools::promote_args::type laguerre_next(unsigned n, T1 x, T2 Ln, T3 Lnm1) { typedef typename tools::promote_args::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 recurrence: template 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 inline typename tools::promote_args::type laguerre(unsigned n, T x, const Policy&, const std::true_type&) { typedef typename tools::promote_args::type result_type; typedef typename policies::evaluation::type value_type; return policies::checked_narrowing_cast(detail::laguerre_imp(n, static_cast(x)), "boost::math::laguerre<%1%>(unsigned, %1%)"); } template inline typename tools::promote_args::type laguerre(unsigned n, unsigned m, T x, const std::false_type&) { return boost::math::laguerre(n, m, x, policies::policy<>()); } } // namespace detail template inline typename tools::promote_args::type laguerre(unsigned n, T x) { return laguerre(n, x, policies::policy<>()); } // Recurrence for associated polynomials: template inline typename tools::promote_args::type laguerre_next(unsigned n, unsigned l, T1 x, T2 Pl, T3 Plm1) { typedef typename tools::promote_args::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 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 = static_cast(laguerre_next(c, m, x, p0, p1)); ++c; } return p1; } } template inline typename tools::promote_args::type laguerre(unsigned n, unsigned m, T x, const Policy& pol) { typedef typename tools::promote_args::type result_type; typedef typename policies::evaluation::type value_type; return policies::checked_narrowing_cast(detail::laguerre_imp(n, m, static_cast(x), pol), "boost::math::laguerre<%1%>(unsigned, unsigned, %1%)"); } template inline typename laguerre_result::type laguerre(unsigned n, T1 m, T2 x) { typedef typename policies::is_policy::type tag_type; return detail::laguerre(n, m, x, tag_type()); } } // namespace math } // namespace boost #endif // BOOST_MATH_SPECIAL_LAGUERRE_HPP