ceph/src/boost/libs/math/include/boost/math/special_functions/detail/bessel_derivatives_linear.hpp

   1 //  Copyright (c) 2013 Anton Bikineev
   2 //  Use, modification and distribution are subject to the
   3 //  Boost Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   5
   6 //
   7 // This is a partial header, do not include on it's own!!!
   8 //
   9 // Linear combination for bessel derivatives are defined here
  10 #ifndef BOOST_MATH_SF_DETAIL_BESSEL_DERIVATIVES_LINEAR_HPP
  11 #define BOOST_MATH_SF_DETAIL_BESSEL_DERIVATIVES_LINEAR_HPP
  12
  13 #ifdef _MSC_VER
  14 #pragma once
  15 #endif
  16
  17 namespace boost{ namespace math{ namespace detail{
  18
  19 template <class T, class Tag, class Policy>
  20 inline T bessel_j_derivative_linear(T v, T x, Tag tag, Policy pol)
  21 {
  22    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;
  23 }
  24
  25 template <class T, class Policy>
  26 inline T bessel_j_derivative_linear(T v, T x, const bessel_int_tag& tag, Policy pol)
  27 {
  28    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;
  29 }
  30
  31 template <class T, class Policy>
  32 inline T sph_bessel_j_derivative_linear(unsigned v, T x, Policy pol)
  33 {
  34    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);
  35 }
  36
  37 template <class T, class Policy>
  38 inline T bessel_i_derivative_linear(T v, T x, Policy pol)
  39 {
  40    T result = boost::math::detail::cyl_bessel_i_imp<T>(v - 1, x, pol);
  41    if(result >= tools::max_value<T>())
  42       return result;  // result is infinite
  43    T result2 = boost::math::detail::cyl_bessel_i_imp<T>(v + 1, x, pol);
  44    if(result2 >= tools::max_value<T>() - result)
  45       return result2;  // result is infinite
  46    return (result + result2) / 2;
  47 }
  48
  49 template <class T, class Tag, class Policy>
  50 inline T bessel_k_derivative_linear(T v, T x, Tag tag, Policy pol)
  51 {
  52    T result = boost::math::detail::cyl_bessel_k_imp<T>(v - 1, x, tag, pol);
  53    if(result >= tools::max_value<T>())
  54       return -result;  // result is infinite
  55    T result2 = boost::math::detail::cyl_bessel_k_imp<T>(v + 1, x, tag, pol);
  56    if(result2 >= tools::max_value<T>() - result)
  57       return -result2;  // result is infinite
  58    return (result + result2) / -2;
  59 }
  60
  61 template <class T, class Policy>
  62 inline T bessel_k_derivative_linear(T v, T x, const bessel_int_tag& tag, Policy pol)
  63 {
  64    return (boost::math::detail::cyl_bessel_k_imp<T>(itrunc(v-1), x, tag, pol) + boost::math::detail::cyl_bessel_k_imp<T>(itrunc(v+1), x, tag, pol)) / -2;
  65 }
  66
  67 template <class T, class Tag, class Policy>
  68 inline T bessel_y_derivative_linear(T v, T x, Tag tag, Policy pol)
  69 {
  70    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;
  71 }
  72
  73 template <class T, class Policy>
  74 inline T bessel_y_derivative_linear(T v, T x, const bessel_int_tag& tag, Policy pol)
  75 {
  76    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;
  77 }
  78
  79 template <class T, class Policy>
  80 inline T sph_neumann_derivative_linear(unsigned v, T x, Policy pol)
  81 {
  82    return (v / x) * boost::math::detail::sph_neumann_imp<T>(v, x, pol) - boost::math::detail::sph_neumann_imp<T>(v+1, x, pol);
  83 }
  84
  85 }}} // namespaces
  86
  87 #endif // BOOST_MATH_SF_DETAIL_BESSEL_DERIVATIVES_LINEAR_HPP