Boost C++ Libraries

boost/math/special_functions/detail/bessel_derivatives_linear.hpp

//  Copyright (c) 2013 Anton Bikineev
//  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)

//
// This is a partial header, do not include on it's own!!!
//
// Linear combination for bessel derivatives are defined here
#ifndef BOOST_MATH_SF_DETAIL_BESSEL_DERIVATIVES_LINEAR_HPP
#define BOOST_MATH_SF_DETAIL_BESSEL_DERIVATIVES_LINEAR_HPP
#include <iostream>
#ifdef _MSC_VER
#pragma once
#endif

namespace boost{ namespace math{ namespace detail{

template <class T, class Tag, class Policy>
inline T bessel_j_derivative_linear(T v, T x, Tag tag, Policy pol)
{
   return (boost::math::detail::cyl_bessel_j_imp<T>(v-1, x, tag, pol) - boost::math::detail::cyl_bessel_j_imp<T>(v+1, x, tag, pol)) / 2;
}

template <class T, class Policy>
inline T bessel_j_derivative_linear(T v, T x, const bessel_int_tag& tag, Policy pol)
{
   return (boost::math::detail::cyl_bessel_j_imp<T>(itrunc(v-1), x, tag, pol) - boost::math::detail::cyl_bessel_j_imp<T>(itrunc(v+1), x, tag, pol)) / 2;
}

template <class T, class Policy>
inline T sph_bessel_j_derivative_linear(unsigned v, T x, Policy pol)
{
   return (v / x) * boost::math::detail::sph_bessel_j_imp<T>(v, x, pol) - boost::math::detail::sph_bessel_j_imp<T>(v+1, x, pol);
}

template <class T, class Policy>
inline T bessel_i_derivative_linear(T v, T x, Policy pol)
{
   T result = boost::math::detail::cyl_bessel_i_imp<T>(v - 1, x, pol);
   if(result >= tools::max_value<T>())
      return result;  // result is infinite
   // Both experimentally, and based on https://www.wolframalpha.com/input?i=BesselI%5Bv%2C+x%5D%2FBesselI%5Bv%2B2%2C+x%5D
   // I[v + 1, x] < I[v-1, x], so this can't overflow:
   T result2 = boost::math::detail::cyl_bessel_i_imp<T>(v + 1, x, pol);

   return result / 2 + result2 / 2;
}

template <class T, class Tag, class Policy>
inline T bessel_k_derivative_linear(T v, T x, Tag tag, Policy pol)
{
   T result = boost::math::detail::cyl_bessel_k_imp<T>(v - 1, x, tag, pol);
   if(result >= tools::max_value<T>())
      return -result;  // result is infinite
   T result2 = boost::math::detail::cyl_bessel_k_imp<T>(v + 1, x, tag, pol);
   if(result2 >= tools::max_value<T>() + result)
      return -boost::math::policies::raise_overflow_error<T>("cyl_bessel_k_prime<%1>", 0, pol);  // result is infinite
   result /= -2;
   result2 /= -2;
   return result + result2;
}

template <class T, class Policy>
inline T bessel_k_derivative_linear(T v, T x, const bessel_int_tag& tag, Policy pol)
{
   T result = boost::math::detail::cyl_bessel_k_imp<T>(itrunc(v - 1), x, tag, pol);
   if (result >= tools::max_value<T>())
      return -result;  // result is infinite
   T result2 = boost::math::detail::cyl_bessel_k_imp<T>(itrunc(v + 1), x, tag, pol);
   if (result2 >= tools::max_value<T>() + result)
      return -boost::math::policies::raise_overflow_error<T>("cyl_bessel_k_prime<%1>", 0, pol);  // result is infinite
   result /= -2;
   result2 /= -2;
   return result + result2;
}

template <class T, class Policy>
inline T bessel_k_derivative_linear(T v, T x, const bessel_maybe_int_tag&, Policy pol)
{
   using std::floor;
   if (floor(v) == v)
      return bessel_k_derivative_linear(v, x, bessel_int_tag(), pol);
   return bessel_k_derivative_linear(v, x, bessel_no_int_tag(), pol);
}

template <class T, class Tag, class Policy>
inline T bessel_y_derivative_linear(T v, T x, Tag tag, Policy pol)
{
   return (boost::math::detail::cyl_neumann_imp<T>(v-1, x, tag, pol) - boost::math::detail::cyl_neumann_imp<T>(v+1, x, tag, pol)) / 2;
}

template <class T, class Policy>
inline T bessel_y_derivative_linear(T v, T x, const bessel_int_tag& tag, Policy pol)
{
   return (boost::math::detail::cyl_neumann_imp<T>(itrunc(v-1), x, tag, pol) - boost::math::detail::cyl_neumann_imp<T>(itrunc(v+1), x, tag, pol)) / 2;
}

template <class T, class Policy>
inline T sph_neumann_derivative_linear(unsigned v, T x, Policy pol)
{
   return (v / x) * boost::math::detail::sph_neumann_imp<T>(v, x, pol) - boost::math::detail::sph_neumann_imp<T>(v+1, x, pol);
}

}}} // namespaces

#endif // BOOST_MATH_SF_DETAIL_BESSEL_DERIVATIVES_LINEAR_HPP