Chris@16: 
Chris@16: //  (C) Copyright John Maddock 2006.
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_MATH_SPECIAL_LAGUERRE_HPP
Chris@16: #define BOOST_MATH_SPECIAL_LAGUERRE_HPP
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: #pragma once
Chris@16: #endif
Chris@16: 
Chris@16: #include <boost/math/special_functions/math_fwd.hpp>
Chris@16: #include <boost/math/tools/config.hpp>
Chris@16: #include <boost/math/policies/error_handling.hpp>
Chris@16: 
Chris@16: namespace boost{
Chris@16: namespace math{
Chris@16: 
Chris@16: // Recurrance relation for Laguerre polynomials:
Chris@16: template <class T1, class T2, class T3>
Chris@16: inline typename tools::promote_args<T1, T2, T3>::type  
Chris@16:    laguerre_next(unsigned n, T1 x, T2 Ln, T3 Lnm1)
Chris@16: {
Chris@16:    typedef typename tools::promote_args<T1, T2, T3>::type result_type;
Chris@16:    return ((2 * n + 1 - result_type(x)) * result_type(Ln) - n * result_type(Lnm1)) / (n + 1);
Chris@16: }
Chris@16: 
Chris@16: namespace detail{
Chris@16: 
Chris@16: // Implement Laguerre polynomials via recurrance:
Chris@16: template <class T>
Chris@16: T laguerre_imp(unsigned n, T x)
Chris@16: {
Chris@16:    T p0 = 1;
Chris@16:    T p1 = 1 - x;
Chris@16: 
Chris@16:    if(n == 0)
Chris@16:       return p0;
Chris@16: 
Chris@16:    unsigned c = 1;
Chris@16: 
Chris@16:    while(c < n)
Chris@16:    {
Chris@16:       std::swap(p0, p1);
Chris@16:       p1 = laguerre_next(c, x, p0, p1);
Chris@16:       ++c;
Chris@16:    }
Chris@16:    return p1;
Chris@16: }
Chris@16: 
Chris@16: template <class T, class Policy>
Chris@16: inline typename tools::promote_args<T>::type 
Chris@16: laguerre(unsigned n, T x, const Policy&, const mpl::true_&)
Chris@16: {
Chris@16:    typedef typename tools::promote_args<T>::type result_type;
Chris@16:    typedef typename policies::evaluation<result_type, Policy>::type value_type;
Chris@16:    return policies::checked_narrowing_cast<result_type, Policy>(detail::laguerre_imp(n, static_cast<value_type>(x)), "boost::math::laguerre<%1%>(unsigned, %1%)");
Chris@16: }
Chris@16: 
Chris@16: template <class T>
Chris@16: inline typename tools::promote_args<T>::type 
Chris@16:    laguerre(unsigned n, unsigned m, T x, const mpl::false_&)
Chris@16: {
Chris@16:    return boost::math::laguerre(n, m, x, policies::policy<>());
Chris@16: }
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: template <class T>
Chris@16: inline typename tools::promote_args<T>::type 
Chris@16:    laguerre(unsigned n, T x)
Chris@16: {
Chris@16:    return laguerre(n, x, policies::policy<>());
Chris@16: }
Chris@16: 
Chris@16: // Recurrence for associated polynomials:
Chris@16: template <class T1, class T2, class T3>
Chris@16: inline typename tools::promote_args<T1, T2, T3>::type  
Chris@16:    laguerre_next(unsigned n, unsigned l, T1 x, T2 Pl, T3 Plm1)
Chris@16: {
Chris@16:    typedef typename tools::promote_args<T1, T2, T3>::type result_type;
Chris@16:    return ((2 * n + l + 1 - result_type(x)) * result_type(Pl) - (n + l) * result_type(Plm1)) / (n+1);
Chris@16: }
Chris@16: 
Chris@16: namespace detail{
Chris@16: // Laguerre Associated Polynomial:
Chris@16: template <class T, class Policy>
Chris@16: T laguerre_imp(unsigned n, unsigned m, T x, const Policy& pol)
Chris@16: {
Chris@16:    // Special cases:
Chris@16:    if(m == 0)
Chris@16:       return boost::math::laguerre(n, x, pol);
Chris@16: 
Chris@16:    T p0 = 1;
Chris@16:    
Chris@16:    if(n == 0)
Chris@16:       return p0;
Chris@16: 
Chris@16:    T p1 = m + 1 - x;
Chris@16: 
Chris@16:    unsigned c = 1;
Chris@16: 
Chris@16:    while(c < n)
Chris@16:    {
Chris@16:       std::swap(p0, p1);
Chris@16:       p1 = laguerre_next(c, m, x, p0, p1);
Chris@16:       ++c;
Chris@16:    }
Chris@16:    return p1;
Chris@16: }
Chris@16: 
Chris@16: }
Chris@16: 
Chris@16: template <class T, class Policy>
Chris@16: inline typename tools::promote_args<T>::type 
Chris@16:    laguerre(unsigned n, unsigned m, T x, const Policy& pol)
Chris@16: {
Chris@16:    typedef typename tools::promote_args<T>::type result_type;
Chris@16:    typedef typename policies::evaluation<result_type, Policy>::type value_type;
Chris@16:    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%)");
Chris@16: }
Chris@16: 
Chris@16: template <class T1, class T2>
Chris@16: inline typename laguerre_result<T1, T2>::type 
Chris@16:    laguerre(unsigned n, T1 m, T2 x)
Chris@16: {
Chris@16:    typedef typename policies::is_policy<T2>::type tag_type;
Chris@16:    return detail::laguerre(n, m, x, tag_type());
Chris@16: }
Chris@16: 
Chris@16: } // namespace math
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #endif // BOOST_MATH_SPECIAL_LAGUERRE_HPP
Chris@16: 
Chris@16: 
Chris@16: