示例#1
0
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)))
   {
      return bessel_j_small_z_series(v, x, pol);
   }
   
   T j, y;
   bessel_jy(v, x, &j, &y, need_j, pol);
   return j;
}
示例#2
0
文件: bessel.hpp 项目: ANCL/autopilot
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;
}
示例#3
0
T bessel_jn(int n, T x, const Policy& pol)
{
    T value(0), factor, current, prev, next;

    BOOST_MATH_STD_USING

    //
    // Reflection has to come first:
    //
    if (n < 0)
    {
        factor = static_cast<T>((n & 0x1) ? -1 : 1);  // J_{-n}(z) = (-1)^n J_n(z)
        n = -n;
    }
    else
    {
        factor = 1;
    }
    if(x < 0)
    {
        factor *= (n & 0x1) ? -1 : 1;  // J_{n}(-z) = (-1)^n J_n(z)
        x = -x;
    }
    //
    // Special cases:
    //
    if(asymptotic_bessel_large_x_limit(T(n), x))
        return factor * asymptotic_bessel_j_large_x_2<T>(T(n), x);
    if (n == 0)
    {
        return factor * bessel_j0(x);
    }
    if (n == 1)
    {
        return factor * bessel_j1(x);
    }

    if (x == 0)                             // n >= 2
    {
        return static_cast<T>(0);
    }

    BOOST_ASSERT(n > 1);
    T scale = 1;
    if (n < abs(x))                         // forward recurrence
    {
        prev = bessel_j0(x);
        current = bessel_j1(x);
        policies::check_series_iterations<T>("boost::math::bessel_j_n<%1%>(%1%,%1%)", n, pol);
        for (int k = 1; k < n; k++)
        {
            T fact = 2 * k / x;
            //
            // rescale if we would overflow or underflow:
            //
            if((fabs(fact) > 1) && ((tools::max_value<T>() - fabs(prev)) / fabs(fact) < fabs(current)))
            {
                scale /= current;
                prev /= current;
                current = 1;
            }
            value = fact * current - prev;
            prev = current;
            current = value;
        }
    }
    else if((x < 1) || (n > x * x / 4) || (x < 5))
    {
        return factor * bessel_j_small_z_series(T(n), x, pol);
    }
    else                                    // backward recurrence
    {
        T fn;
        int s;                        // fn = J_(n+1) / J_n
        // |x| <= n, fast convergence for continued fraction CF1
        boost::math::detail::CF1_jy(static_cast<T>(n), x, &fn, &s, pol);
        prev = fn;
        current = 1;
        // Check recursion won't go on too far:
        policies::check_series_iterations<T>("boost::math::bessel_j_n<%1%>(%1%,%1%)", n, pol);
        for (int k = n; k > 0; k--)
        {
            T fact = 2 * k / x;
            if((fabs(fact) > 1) && ((tools::max_value<T>() - fabs(prev)) / fabs(fact) < fabs(current)))
            {
                prev /= current;
                scale /= current;
                current = 1;
            }
            next = fact * current - prev;
            prev = current;
            current = next;
        }
        value = bessel_j0(x) / current;       // normalization
        scale = 1 / scale;
    }
    value *= factor;

    if(tools::max_value<T>() * scale < fabs(value))
        return policies::raise_overflow_error<T>("boost::math::bessel_jn<%1%>(%1%,%1%)", 0, pol);

    return value / scale;
}