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124 lines
3.4 KiB
124 lines
3.4 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_JN_HPP |
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#define BOOST_MATH_BESSEL_JN_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_j0.hpp> |
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#include <boost/math/special_functions/detail/bessel_j1.hpp> |
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#include <boost/math/special_functions/detail/bessel_jy.hpp> |
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#include <boost/math/special_functions/detail/bessel_jy_asym.hpp> |
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#include <boost/math/special_functions/detail/bessel_jy_series.hpp> |
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// Bessel function of the first kind of integer order |
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// J_n(z) is the minimal solution |
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// n < abs(z), forward recurrence stable and usable |
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// n >= abs(z), forward recurrence unstable, use Miller's algorithm |
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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_jn(int n, T x, const Policy& pol) |
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{ |
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T value(0), factor, current, prev, next; |
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BOOST_MATH_STD_USING |
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// |
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// Reflection has to come 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; // J_{-n}(z) = (-1)^n J_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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// |
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// Special cases: |
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// |
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if (n == 0) |
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{ |
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return factor * bessel_j0(x); |
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} |
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if (n == 1) |
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{ |
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return factor * bessel_j1(x); |
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} |
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if (x == 0) // n >= 2 |
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{ |
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return static_cast<T>(0); |
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} |
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typedef typename bessel_asymptotic_tag<T, Policy>::type tag_type; |
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if(fabs(x) > asymptotic_bessel_j_limit<T>(n, tag_type())) |
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return factor * asymptotic_bessel_j_large_x_2<T>(n, x); |
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BOOST_ASSERT(n > 1); |
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T scale = 1; |
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if (n < abs(x)) // forward recurrence |
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{ |
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prev = bessel_j0(x); |
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current = bessel_j1(x); |
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for (int k = 1; k < n; k++) |
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{ |
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T fact = 2 * k / x; |
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if((tools::max_value<T>() - fabs(prev)) / fabs(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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} |
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} |
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else if(x < 1) |
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{ |
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return factor * bessel_j_small_z_series(T(n), x, pol); |
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} |
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else // backward recurrence |
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{ |
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T fn; int s; // fn = J_(n+1) / J_n |
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// |x| <= n, fast convergence for continued fraction CF1 |
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boost::math::detail::CF1_jy(static_cast<T>(n), x, &fn, &s, pol); |
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prev = fn; |
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current = 1; |
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for (int k = n; k > 0; k--) |
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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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scale /= current; |
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current = 1; |
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} |
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next = fact * current - prev; |
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prev = current; |
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current = next; |
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} |
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value = bessel_j0(x) / current; // normalization |
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scale = 1 / scale; |
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} |
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value *= factor; |
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if(tools::max_value<T>() * scale < fabs(value)) |
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return policies::raise_overflow_error<T>("boost::math::bessel_jn<%1%>(%1%,%1%)", 0, pol); |
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return value / scale; |
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} |
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}}} // namespaces |
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#endif // BOOST_MATH_BESSEL_JN_HPP |
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