87 lines
2.3 KiB
Plaintext
87 lines
2.3 KiB
Plaintext
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// Copyright (c) 2006 Xiaogang Zhang
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_BESSEL_KN_HPP
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#define BOOST_MATH_BESSEL_KN_HPP
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <boost/math/special_functions/detail/bessel_k0.hpp>
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#include <boost/math/special_functions/detail/bessel_k1.hpp>
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#include <boost/math/policies/error_handling.hpp>
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// Modified Bessel function of the second kind of integer order
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// K_n(z) is the dominant solution, forward recurrence always OK (though unstable)
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namespace boost { namespace math { namespace detail{
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template <typename T, typename Policy>
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T bessel_kn(int n, T x, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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T value, current, prev;
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using namespace boost::math::tools;
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static const char* function = "boost::math::bessel_kn<%1%>(%1%,%1%)";
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if (x < 0)
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{
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return policies::raise_domain_error<T>(function,
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"Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol);
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}
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if (x == 0)
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{
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return policies::raise_overflow_error<T>(function, 0, pol);
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}
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if (n < 0)
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{
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n = -n; // K_{-n}(z) = K_n(z)
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}
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if (n == 0)
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{
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value = bessel_k0(x, pol);
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}
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else if (n == 1)
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{
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value = bessel_k1(x, pol);
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}
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else
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{
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prev = bessel_k0(x, pol);
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current = bessel_k1(x, pol);
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int k = 1;
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BOOST_ASSERT(k < n);
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T scale = 1;
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do
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{
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T fact = 2 * k / x;
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if((tools::max_value<T>() - fabs(prev)) / fact < fabs(current))
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{
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scale /= current;
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prev /= current;
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current = 1;
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}
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value = fact * current + prev;
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prev = current;
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current = value;
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++k;
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}
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while(k < n);
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if(tools::max_value<T>() * scale < fabs(value))
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return sign(scale) * sign(value) * policies::raise_overflow_error<T>(function, 0, pol);
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value /= scale;
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}
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return value;
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}
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}}} // namespaces
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#endif // BOOST_MATH_BESSEL_KN_HPP
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