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103 lines
2.7 KiB
103 lines
2.7 KiB
// 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_YN_HPP |
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#define BOOST_MATH_BESSEL_YN_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_y0.hpp> |
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#include <boost/math/special_functions/detail/bessel_y1.hpp> |
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#include <boost/math/special_functions/detail/bessel_jy_series.hpp> |
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#include <boost/math/policies/error_handling.hpp> |
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// Bessel function of the second kind of integer order |
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// Y_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_yn(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, factor, current, prev; |
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using namespace boost::math::tools; |
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static const char* function = "boost::math::bessel_yn<%1%>(%1%,%1%)"; |
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if ((x == 0) && (n == 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 (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 x must be > 0, complex result not supported.", x, pol); |
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} |
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// |
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// Reflection comes first: |
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// |
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if (n < 0) |
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{ |
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factor = (n & 0x1) ? -1 : 1; // Y_{-n}(z) = (-1)^n Y_n(z) |
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n = -n; |
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} |
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else |
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{ |
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factor = 1; |
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} |
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if(x < policies::get_epsilon<T, Policy>()) |
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{ |
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T scale = 1; |
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value = bessel_yn_small_z(n, x, &scale, pol); |
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if(tools::max_value<T>() * fabs(scale) < fabs(value)) |
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return boost::math::sign(scale) * boost::math::sign(value) * policies::raise_overflow_error<T>(function, 0, pol); |
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value /= scale; |
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} |
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else if (n == 0) |
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{ |
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value = bessel_y0(x, pol); |
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} |
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else if (n == 1) |
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{ |
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value = factor * bessel_y1(x, pol); |
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} |
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else |
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{ |
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prev = bessel_y0(x, pol); |
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current = bessel_y1(x, pol); |
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int k = 1; |
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BOOST_ASSERT(k < n); |
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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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prev /= current; |
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factor /= 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>() * factor < value) |
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return sign(value) * sign(value) * policies::raise_overflow_error<T>(function, 0, pol); |
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value /= factor; |
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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_YN_HPP |
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