113 lines
3.2 KiB
Plaintext
113 lines
3.2 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_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 = static_cast<T>((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(asymptotic_bessel_large_x_limit(n, x))
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{
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value = factor * asymptotic_bessel_y_large_x_2(static_cast<T>(abs(n)), x);
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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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policies::check_series_iterations<T>("boost::math::bessel_y_n<%1%>(%1%,%1%)", n, pol);
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T mult = 2 * k / x;
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value = mult * current - prev;
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prev = current;
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current = value;
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++k;
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if((mult > 1) && (fabs(current) > 1))
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{
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prev /= current;
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factor /= current;
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value /= current;
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current = 1;
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}
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while(k < n)
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{
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mult = 2 * k / x;
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value = mult * 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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if(fabs(tools::max_value<T>() * factor) < fabs(value))
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return sign(value) * sign(factor) * 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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