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// 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)
//
#ifndef BOOST_MATH_BESSEL_DERIVATIVES_HPP
#define BOOST_MATH_BESSEL_DERIVATIVES_HPP
#ifdef _MSC_VER
# pragma once
#endif
#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/math/special_functions/bessel.hpp>
#include <boost/math/special_functions/detail/bessel_jy_derivatives_asym.hpp>
#include <boost/math/special_functions/detail/bessel_jy_derivatives_series.hpp>
#include <boost/math/special_functions/detail/bessel_derivatives_linear.hpp>
namespace boost{ namespace math{
namespace detail{
template <class Tag, class T, class Policy>
inline T cyl_bessel_j_prime_imp(T v, T x, const Policy& pol)
{
static const char* const function = "boost::math::cyl_bessel_j_prime<%1%>(%1%,%1%)";
BOOST_MATH_STD_USING
//
// Prevent complex result:
//
if (x < 0 && floor(v) != v)
return boost::math::policies::raise_domain_error<T>(
function,
"Got x = %1%, but function requires x >= 0", x, pol);
//
// Special cases for x == 0:
//
if (x == 0)
{
if (v == 1)
return 0.5;
else if (v == -1)
return -0.5;
else if (floor(v) == v || v > 1)
return 0;
else return boost::math::policies::raise_domain_error<T>(
function,
"Got x = %1%, but function is indeterminate for this order", x, pol);
}
//
// Special case for large x: use asymptotic expansion:
//
if (boost::math::detail::asymptotic_bessel_derivative_large_x_limit(v, x))
return boost::math::detail::asymptotic_bessel_j_derivative_large_x_2(v, x);
//
// Special case for small x: use Taylor series:
//
if ((abs(x) < 5) || (abs(v) > x * x / 4))
{
bool inversed = false;
if (floor(v) == v && v < 0)
{
v = -v;
if (itrunc(v, pol) & 1)
inversed = true;
}
T r = boost::math::detail::bessel_j_derivative_small_z_series(v, x, pol);
return inversed ? T(-r) : r;
}
//
// Special case for v == 0:
//
if (v == 0)
return -boost::math::detail::cyl_bessel_j_imp<T>(1, x, Tag(), pol);
//
// Default case:
//
return boost::math::detail::bessel_j_derivative_linear(v, x, Tag(), pol);
}
template <class T, class Policy>
inline T sph_bessel_j_prime_imp(unsigned v, T x, const Policy& pol)
{
static const char* const function = "boost::math::sph_bessel_prime<%1%>(%1%,%1%)";
//
// Prevent complex result:
//
if (x < 0)
return boost::math::policies::raise_domain_error<T>(
function,
"Got x = %1%, but function requires x >= 0.", x, pol);
//
// Special case for v == 0:
//
if (v == 0)
return (x == 0) ? boost::math::policies::raise_overflow_error<T>(function, 0, pol)
: static_cast<T>(-boost::math::detail::sph_bessel_j_imp<T>(1, x, pol));
//
// Special case for x == 0 and v > 0:
//
if (x == 0)
return boost::math::policies::raise_domain_error<T>(
function,
"Got x = %1%, but function is indeterminate for this order", x, pol);
//
// Default case:
//
return boost::math::detail::sph_bessel_j_derivative_linear(v, x, pol);
}
template <class T, class Policy>
inline T cyl_bessel_i_prime_imp(T v, T x, const Policy& pol)
{
static const char* const function = "boost::math::cyl_bessel_i_prime<%1%>(%1%,%1%)";
BOOST_MATH_STD_USING
//
// Prevent complex result:
//
if (x < 0 && floor(v) != v)
return boost::math::policies::raise_domain_error<T>(
function,
"Got x = %1%, but function requires x >= 0", x, pol);
//
// Special cases for x == 0:
//
if (x == 0)
{
if (v == 1 || v == -1)
return 0.5;
else if (floor(v) == v || v > 1)
return 0;
else return boost::math::policies::raise_domain_error<T>(
function,
"Got x = %1%, but function is indeterminate for this order", x, pol);
}
//
// Special case for v == 0:
//
if (v == 0)
return boost::math::detail::cyl_bessel_i_imp<T>(1, x, pol);
//
// Default case:
//
return boost::math::detail::bessel_i_derivative_linear(v, x, pol);
}
template <class Tag, class T, class Policy>
inline T cyl_bessel_k_prime_imp(T v, T x, const Policy& pol)
{
//
// Prevent complex and indeterminate results:
//
if (x <= 0)
return boost::math::policies::raise_domain_error<T>(
"boost::math::cyl_bessel_k_prime<%1%>(%1%,%1%)",
"Got x = %1%, but function requires x > 0", x, pol);
//
// Special case for v == 0:
//
if (v == 0)
return -boost::math::detail::cyl_bessel_k_imp<T>(1, x, Tag(), pol);
//
// Default case:
//
return boost::math::detail::bessel_k_derivative_linear(v, x, Tag(), pol);
}
template <class Tag, class T, class Policy>
inline T cyl_neumann_prime_imp(T v, T x, const Policy& pol)
{
BOOST_MATH_STD_USING
//
// Prevent complex and indeterminate results:
//
if (x <= 0)
return boost::math::policies::raise_domain_error<T>(
"boost::math::cyl_neumann_prime<%1%>(%1%,%1%)",
"Got x = %1%, but function requires x > 0", x, pol);
//
// Special case for large x: use asymptotic expansion:
//
if (boost::math::detail::asymptotic_bessel_derivative_large_x_limit(v, x))
return boost::math::detail::asymptotic_bessel_y_derivative_large_x_2(v, x);
//
// Special case for small x: use Taylor series:
//
if (v > 0 && floor(v) != v)
{
const T eps = boost::math::policies::get_epsilon<T, Policy>();
if (log(eps / 2) > v * log((x * x) / (v * 4)))
return boost::math::detail::bessel_y_derivative_small_z_series(v, x, pol);
}
//
// Special case for v == 0:
//
if (v == 0)
return -boost::math::detail::cyl_neumann_imp<T>(1, x, Tag(), pol);
//
// Default case:
//
return boost::math::detail::bessel_y_derivative_linear(v, x, Tag(), pol);
}
template <class T, class Policy>
inline T sph_neumann_prime_imp(unsigned v, T x, const Policy& pol)
{
//
// Prevent complex and indeterminate result:
//
if (x <= 0)
return boost::math::policies::raise_domain_error<T>(
"boost::math::sph_neumann_prime<%1%>(%1%,%1%)",
"Got x = %1%, but function requires x > 0.", x, pol);
//
// Special case for v == 0:
//
if (v == 0)
return -boost::math::detail::sph_neumann_imp<T>(1, x, pol);
//
// Default case:
//
return boost::math::detail::sph_neumann_derivative_linear(v, x, pol);
}
} // namespace detail
template <class T1, class T2, class Policy>
inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j_prime(T1 v, T2 x, const Policy& /* pol */)
{
BOOST_FPU_EXCEPTION_GUARD
typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
typedef typename policies::evaluation<result_type, Policy>::type value_type;
typedef typename policies::normalise<
Policy,
policies::promote_float<false>,
policies::promote_double<false>,
policies::discrete_quantile<>,
policies::assert_undefined<> >::type forwarding_policy;
return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_bessel_j_prime_imp<tag_type, value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::cyl_bessel_j_prime<%1%,%1%>(%1%,%1%)");
}
template <class T1, class T2>
inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j_prime(T1 v, T2 x)
{
return cyl_bessel_j_prime(v, x, policies::policy<>());
}
template <class T, class Policy>
inline typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel_prime(unsigned v, T x, const Policy& /* pol */)
{
BOOST_FPU_EXCEPTION_GUARD
typedef typename detail::bessel_traits<T, T, Policy>::result_type result_type;
typedef typename policies::evaluation<result_type, Policy>::type value_type;
typedef typename policies::normalise<
Policy,
policies::promote_float<false>,
policies::promote_double<false>,
policies::discrete_quantile<>,
policies::assert_undefined<> >::type forwarding_policy;
return policies::checked_narrowing_cast<result_type, Policy>(detail::sph_bessel_j_prime_imp<value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::sph_bessel_j_prime<%1%>(%1%,%1%)");
}
template <class T>
inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel_prime(unsigned v, T x)
{
return sph_bessel_prime(v, x, policies::policy<>());
}
template <class T1, class T2, class Policy>
inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i_prime(T1 v, T2 x, const Policy& /* pol */)
{
BOOST_FPU_EXCEPTION_GUARD
typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
typedef typename policies::evaluation<result_type, Policy>::type value_type;
typedef typename policies::normalise<
Policy,
policies::promote_float<false>,
policies::promote_double<false>,
policies::discrete_quantile<>,
policies::assert_undefined<> >::type forwarding_policy;
return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_bessel_i_prime_imp<value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::cyl_bessel_i_prime<%1%>(%1%,%1%)");
}
template <class T1, class T2>
inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i_prime(T1 v, T2 x)
{
return cyl_bessel_i_prime(v, x, policies::policy<>());
}
template <class T1, class T2, class Policy>
inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k_prime(T1 v, T2 x, const Policy& /* pol */)
{
BOOST_FPU_EXCEPTION_GUARD
typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
typedef typename policies::evaluation<result_type, Policy>::type value_type;
typedef typename policies::normalise<
Policy,
policies::promote_float<false>,
policies::promote_double<false>,
policies::discrete_quantile<>,
policies::assert_undefined<> >::type forwarding_policy;
return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_bessel_k_prime_imp<tag_type, value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::cyl_bessel_k_prime<%1%,%1%>(%1%,%1%)");
}
template <class T1, class T2>
inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k_prime(T1 v, T2 x)
{
return cyl_bessel_k_prime(v, x, policies::policy<>());
}
template <class T1, class T2, class Policy>
inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann_prime(T1 v, T2 x, const Policy& /* pol */)
{
BOOST_FPU_EXCEPTION_GUARD
typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
typedef typename policies::evaluation<result_type, Policy>::type value_type;
typedef typename policies::normalise<
Policy,
policies::promote_float<false>,
policies::promote_double<false>,
policies::discrete_quantile<>,
policies::assert_undefined<> >::type forwarding_policy;
return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_neumann_prime_imp<tag_type, value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::cyl_neumann_prime<%1%,%1%>(%1%,%1%)");
}
template <class T1, class T2>
inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann_prime(T1 v, T2 x)
{
return cyl_neumann_prime(v, x, policies::policy<>());
}
template <class T, class Policy>
inline typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann_prime(unsigned v, T x, const Policy& /* pol */)
{
BOOST_FPU_EXCEPTION_GUARD
typedef typename detail::bessel_traits<T, T, Policy>::result_type result_type;
typedef typename policies::evaluation<result_type, Policy>::type value_type;
typedef typename policies::normalise<
Policy,
policies::promote_float<false>,
policies::promote_double<false>,
policies::discrete_quantile<>,
policies::assert_undefined<> >::type forwarding_policy;
return policies::checked_narrowing_cast<result_type, Policy>(detail::sph_neumann_prime_imp<value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::sph_neumann_prime<%1%>(%1%,%1%)");
}
template <class T>
inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann_prime(unsigned v, T x)
{
return sph_neumann_prime(v, x, policies::policy<>());
}
} // namespace math
} // namespace boost
#endif // BOOST_MATH_BESSEL_DERIVATIVES_HPP
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