// (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 | |