ceph/src/boost/libs/math/include/boost/math/special_functions/hankel.hpp

   1 // Copyright John Maddock 2012.
   2 // Use, modification and distribution are subject to the
   3 // Boost Software License, Version 1.0.
   4 // (See accompanying file LICENSE_1_0.txt
   5 // or copy at http://www.boost.org/LICENSE_1_0.txt)
   6
   7 #ifndef BOOST_MATH_HANKEL_HPP
   8 #define BOOST_MATH_HANKEL_HPP
   9
  10 #include <boost/math/special_functions/math_fwd.hpp>
  11 #include <boost/math/special_functions/bessel.hpp>
  12
  13 namespace boost{ namespace math{
  14
  15 namespace detail{
  16
  17 template <class T, class Policy>
  18 std::complex<T> hankel_imp(T v, T x, const bessel_no_int_tag&, const Policy& pol, int sign)
  19 {
  20    BOOST_MATH_STD_USING
  21    static const char* function = "boost::math::cyl_hankel_1<%1%>(%1%,%1%)";
  22
  23    if(x < 0)
  24    {
  25       bool isint_v = floor(v) == v;
  26       T j, y;
  27       bessel_jy(v, -x, &j, &y, need_j | need_y, pol);
  28       std::complex<T> cx(x), cv(v);
  29       std::complex<T> j_result, y_result;
  30       if(isint_v)
  31       {
  32          int s = (iround(v) & 1) ? -1 : 1;
  33          j_result = j * s;
  34          y_result = T(s) * (y - (2 / constants::pi<T>()) * (log(-x) - log(cx)) * j);
  35       }
  36       else
  37       {
  38          j_result = pow(cx, v) * pow(-cx, -v) * j;
  39          T p1 = pow(-x, v);
  40          std::complex<T> p2 = pow(cx, v);
  41          y_result = p1 * y / p2
  42             + (p2 / p1 - p1 / p2) * j / tan(constants::pi<T>() * v);
  43       }
  44       // multiply y_result by i:
  45       y_result = std::complex<T>(-sign * y_result.imag(), sign * y_result.real());
  46       return j_result + y_result;
  47    }
  48
  49    if(x == 0)
  50    {
  51       if(v == 0)
  52       {
  53          // J is 1, Y is -INF
  54          return std::complex<T>(1, sign * -policies::raise_overflow_error<T>(function, 0, pol));
  55       }
  56       else
  57       {
  58          // At least one of J and Y is complex infinity:
  59          return std::complex<T>(policies::raise_overflow_error<T>(function, 0, pol), sign * policies::raise_overflow_error<T>(function, 0, pol));
  60       }
  61    }
  62
  63    T j, y;
  64    bessel_jy(v, x, &j, &y, need_j | need_y, pol);
  65    return std::complex<T>(j, sign * y);
  66 }
  67
  68 template <class T, class Policy>
  69 std::complex<T> hankel_imp(int v, T x, const bessel_int_tag&, const Policy& pol, int sign);
  70
  71 template <class T, class Policy>
  72 inline std::complex<T> hankel_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol, int sign)
  73 {
  74    BOOST_MATH_STD_USING  // ADL of std names.
  75    int ival = detail::iconv(v, pol);
  76    if(0 == v - ival)
  77    {
  78       return hankel_imp(ival, x, bessel_int_tag(), pol, sign);
  79    }
  80    return hankel_imp(v, x, bessel_no_int_tag(), pol, sign);
  81 }
  82
  83 template <class T, class Policy>
  84 inline std::complex<T> hankel_imp(int v, T x, const bessel_int_tag&, const Policy& pol, int sign)
  85 {
  86    BOOST_MATH_STD_USING
  87    if((std::abs(v) < 200) && (x > 0))
  88       return std::complex<T>(bessel_jn(v, x, pol), sign * bessel_yn(v, x, pol));
  89    return hankel_imp(static_cast<T>(v), x, bessel_no_int_tag(), pol, sign);
  90 }
  91
  92 template <class T, class Policy>
  93 inline std::complex<T> sph_hankel_imp(T v, T x, const Policy& pol, int sign)
  94 {
  95    BOOST_MATH_STD_USING
  96    return constants::root_half_pi<T>() * hankel_imp(v + 0.5f, x, bessel_no_int_tag(), pol, sign) / sqrt(std::complex<T>(x));
  97 }
  98
  99 } // namespace detail
 100
 101 template <class T1, class T2, class Policy>
 102 inline std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_1(T1 v, T2 x, const Policy& pol)
 103 {
 104    BOOST_FPU_EXCEPTION_GUARD
 105    typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
 106    typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
 107    typedef typename policies::evaluation<result_type, Policy>::type value_type;
 108    return policies::checked_narrowing_cast<std::complex<result_type>, Policy>(detail::hankel_imp<value_type>(v, static_cast<value_type>(x), tag_type(), pol, 1), "boost::math::cyl_hankel_1<%1%>(%1%,%1%)");
 109 }
 110
 111 template <class T1, class T2>
 112 inline std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_1(T1 v, T2 x)
 113 {
 114    return cyl_hankel_1(v, x, policies::policy<>());
 115 }
 116
 117 template <class T1, class T2, class Policy>
 118 inline std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_2(T1 v, T2 x, const Policy& pol)
 119 {
 120    BOOST_FPU_EXCEPTION_GUARD
 121    typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
 122    typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
 123    typedef typename policies::evaluation<result_type, Policy>::type value_type;
 124    return policies::checked_narrowing_cast<std::complex<result_type>, Policy>(detail::hankel_imp<value_type>(v, static_cast<value_type>(x), tag_type(), pol, -1), "boost::math::cyl_hankel_1<%1%>(%1%,%1%)");
 125 }
 126
 127 template <class T1, class T2>
 128 inline std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_2(T1 v, T2 x)
 129 {
 130    return cyl_hankel_2(v, x, policies::policy<>());
 131 }
 132
 133 template <class T1, class T2, class Policy>
 134 inline std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_1(T1 v, T2 x, const Policy&)
 135 {
 136    BOOST_FPU_EXCEPTION_GUARD
 137    typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
 138    typedef typename policies::evaluation<result_type, Policy>::type value_type;
 139    typedef typename policies::normalise<
 140       Policy,
 141       policies::promote_float<false>,
 142       policies::promote_double<false>,
 143       policies::discrete_quantile<>,
 144       policies::assert_undefined<> >::type forwarding_policy;
 145
 146    return policies::checked_narrowing_cast<std::complex<result_type>, Policy>(detail::sph_hankel_imp<value_type>(static_cast<value_type>(v), static_cast<value_type>(x), forwarding_policy(), 1), "boost::math::sph_hankel_1<%1%>(%1%,%1%)");
 147 }
 148
 149 template <class T1, class T2>
 150 inline std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_1(T1 v, T2 x)
 151 {
 152    return sph_hankel_1(v, x, policies::policy<>());
 153 }
 154
 155 template <class T1, class T2, class Policy>
 156 inline std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_2(T1 v, T2 x, const Policy&)
 157 {
 158    BOOST_FPU_EXCEPTION_GUARD
 159    typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
 160    typedef typename policies::evaluation<result_type, Policy>::type value_type;
 161    typedef typename policies::normalise<
 162       Policy,
 163       policies::promote_float<false>,
 164       policies::promote_double<false>,
 165       policies::discrete_quantile<>,
 166       policies::assert_undefined<> >::type forwarding_policy;
 167
 168    return policies::checked_narrowing_cast<std::complex<result_type>, Policy>(detail::sph_hankel_imp<value_type>(static_cast<value_type>(v), static_cast<value_type>(x), forwarding_policy(), -1), "boost::math::sph_hankel_1<%1%>(%1%,%1%)");
 169 }
 170
 171 template <class T1, class T2>
 172 inline std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_2(T1 v, T2 x)
 173 {
 174    return sph_hankel_2(v, x, policies::policy<>());
 175 }
 176
 177 }} // namespaces
 178
 179 #endif // BOOST_MATH_HANKEL_HPP
 180