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139 lines
3.6 KiB
139 lines
3.6 KiB
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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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// Recurrance 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 recurrance: |
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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 mpl::true_&) |
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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 mpl::false_&) |
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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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