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src/boost/math/special_functions/bessel.hpp  view on Meta::CPAN

#ifndef BOOST_MATH_BESSEL_HPP
#define BOOST_MATH_BESSEL_HPP

#ifdef _MSC_VER
#pragma once
#endif

#include <boost/math/special_functions/detail/bessel_jy.hpp>
#include <boost/math/special_functions/detail/bessel_jn.hpp>
#include <boost/math/special_functions/detail/bessel_yn.hpp>
#include <boost/math/special_functions/detail/bessel_ik.hpp>
#include <boost/math/special_functions/detail/bessel_i0.hpp>
#include <boost/math/special_functions/detail/bessel_i1.hpp>
#include <boost/math/special_functions/detail/bessel_kn.hpp>
#include <boost/math/special_functions/detail/iconv.hpp>
#include <boost/math/special_functions/sin_pi.hpp>
#include <boost/math/special_functions/cos_pi.hpp>
#include <boost/math/special_functions/sinc.hpp>
#include <boost/math/special_functions/trunc.hpp>
#include <boost/math/special_functions/round.hpp>
#include <boost/math/tools/rational.hpp>
#include <boost/math/tools/promotion.hpp>
#include <boost/math/tools/series.hpp>

namespace boost{ namespace math{

namespace detail{

template <class T, class Policy>
struct sph_bessel_j_small_z_series_term
{
   typedef T result_type;

   sph_bessel_j_small_z_series_term(unsigned v_, T x)
      : N(0), v(v_)
   {
      BOOST_MATH_STD_USING
      mult = x / 2;
      term = pow(mult, T(v)) / boost::math::tgamma(v+1+T(0.5f), Policy());
      mult *= -mult;
   }
   T operator()()
   {
      T r = term;
      ++N;
      term *= mult / (N * T(N + v + 0.5f));
      return r;
   }
private:
   unsigned N;
   unsigned v;
   T mult;
   T term;
};

template <class T, class Policy>
inline T sph_bessel_j_small_z_series(unsigned v, T x, const Policy& pol)
{
   BOOST_MATH_STD_USING // ADL of std names
   sph_bessel_j_small_z_series_term<T, Policy> s(v, x);
   boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
   T zero = 0;
   T result = boost::math::tools::sum_series(s, boost::math::policies::get_epsilon<T, Policy>(), max_iter, zero);
#else
   T result = boost::math::tools::sum_series(s, boost::math::policies::get_epsilon<T, Policy>(), max_iter);
#endif
   policies::check_series_iterations<T>("boost::math::sph_bessel_j_small_z_series<%1%>(%1%,%1%)", max_iter, pol);
   return result * sqrt(constants::pi<T>() / 4);
}

template <class T, class Policy>
T cyl_bessel_j_imp(T v, T x, const bessel_no_int_tag& t, const Policy& pol)
{
   BOOST_MATH_STD_USING
   static const char* function = "boost::math::bessel_j<%1%>(%1%,%1%)";
   if(x < 0)
   {
      // better have integer v:
      if(floor(v) == v)
      {
         T r = cyl_bessel_j_imp(v, T(-x), t, pol);
         if(iround(v, pol) & 1)
            r = -r;
         return r;
      }
      else
         return policies::raise_domain_error<T>(
            function,
            "Got x = %1%, but we need x >= 0", x, pol);
   }
   if(x == 0)
      return (v == 0) ? 1 : (v > 0) ? 0 : 
         policies::raise_domain_error<T>(
            function, 
            "Got v = %1%, but require v >= 0 or a negative integer: the result would be complex.", v, pol);
   
   
   if((v >= 0) && ((x < 1) || (v > x * x / 4) || (x < 5)))
   {
      //
      // This series will actually converge rapidly for all small
      // x - say up to x < 20 - but the first few terms are large
      // and divergent which leads to large errors :-(
      //
      return bessel_j_small_z_series(v, x, pol);
   }
   
   T j, y;
   bessel_jy(v, x, &j, &y, need_j, pol);
   return j;
}

template <class T, class Policy>
inline T cyl_bessel_j_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol)
{
   BOOST_MATH_STD_USING  // ADL of std names.
   int ival = detail::iconv(v, pol);
   if((abs(ival) < 200) && (0 == v - ival))
   {
      return bessel_jn(ival/*iround(v, pol)*/, x, pol);
   }
   return cyl_bessel_j_imp(v, x, bessel_no_int_tag(), pol);
}

template <class T, class Policy>
inline T cyl_bessel_j_imp(int v, T x, const bessel_int_tag&, const Policy& pol)
{