108 lines
4.1 KiB
C++
108 lines
4.1 KiB
C++
// 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
|