special_functions/detail/bessel_kn.hpp

0001 //  Copyright (c) 2006 Xiaogang Zhang
0002 //  Use, modification and distribution are subject to the
0003 //  Boost Software License, Version 1.0. (See accompanying file
0004 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0005
0006 #ifndef BOOST_MATH_BESSEL_KN_HPP
0007 #define BOOST_MATH_BESSEL_KN_HPP
0008
0009 #ifdef _MSC_VER
0010 #pragma once
0011 #endif
0012
0013 #include <boost/math/special_functions/detail/bessel_k0.hpp>
0014 #include <boost/math/special_functions/detail/bessel_k1.hpp>
0015 #include <boost/math/policies/error_handling.hpp>
0016
0017 // Modified Bessel function of the second kind of integer order
0018 // K_n(z) is the dominant solution, forward recurrence always OK (though unstable)
0019
0020 namespace boost { namespace math { namespace detail{
0021
0022 template <typename T, typename Policy>
0023 T bessel_kn(int n, T x, const Policy& pol)
0024 {
0025     BOOST_MATH_STD_USING
0026     T value, current, prev;
0027
0028     using namespace boost::math::tools;
0029
0030     static const char* function = "boost::math::bessel_kn<%1%>(%1%,%1%)";
0031
0032     if (x < 0)
0033     {
0034        return policies::raise_domain_error<T>(function,
0035             "Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol);
0036     }
0037     if (x == 0)
0038     {
0039        return policies::raise_overflow_error<T>(function, nullptr, pol);
0040     }
0041
0042     if (n < 0)
0043     {
0044         n = -n;                             // K_{-n}(z) = K_n(z)
0045     }
0046     if (n == 0)
0047     {
0048         value = bessel_k0(x);
0049     }
0050     else if (n == 1)
0051     {
0052         value = bessel_k1(x);
0053     }
0054     else
0055     {
0056        prev = bessel_k0(x);
0057        current = bessel_k1(x);
0058        int k = 1;
0059        BOOST_MATH_ASSERT(k < n);
0060        T scale = 1;
0061        do
0062        {
0063            T fact = 2 * k / x;
0064            if((tools::max_value<T>() - fabs(prev)) / fact < fabs(current))
0065            {
0066               scale /= current;
0067               prev /= current;
0068               current = 1;
0069            }
0070            value = fact * current + prev;
0071            prev = current;
0072            current = value;
0073            ++k;
0074        }
0075        while(k < n);
0076        if(tools::max_value<T>() * scale < fabs(value))
0077           return sign(scale) * sign(value) * policies::raise_overflow_error<T>(function, nullptr, pol);
0078        value /= scale;
0079     }
0080     return value;
0081 }
0082
0083 }}} // namespaces
0084
0085 #endif // BOOST_MATH_BESSEL_KN_HPP
0086