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