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115 lines
3.2 KiB
115 lines
3.2 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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// |
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// History: |
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// XZ wrote the original of this file as part of the Google |
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// Summer of Code 2006. JM modified it to fit into the |
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// Boost.Math conceptual framework better, and to correctly |
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// handle the y < 0 case. |
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// |
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#ifndef BOOST_MATH_ELLINT_RC_HPP |
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#define BOOST_MATH_ELLINT_RC_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/policies/error_handling.hpp> |
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#include <boost/math/tools/config.hpp> |
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#include <boost/math/special_functions/math_fwd.hpp> |
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// Carlson's degenerate elliptic integral |
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// R_C(x, y) = R_F(x, y, y) = 0.5 * \int_{0}^{\infty} (t+x)^{-1/2} (t+y)^{-1} dt |
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// Carlson, Numerische Mathematik, vol 33, 1 (1979) |
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namespace boost { namespace math { namespace detail{ |
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template <typename T, typename Policy> |
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T ellint_rc_imp(T x, T y, const Policy& pol) |
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{ |
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T value, S, u, lambda, tolerance, prefix; |
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unsigned long k; |
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BOOST_MATH_STD_USING |
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using namespace boost::math::tools; |
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static const char* function = "boost::math::ellint_rc<%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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"Argument x must be non-negative but got %1%", x, pol); |
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} |
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if(y == 0) |
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{ |
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return policies::raise_domain_error<T>(function, |
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"Argument y must not be zero but got %1%", y, pol); |
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} |
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// error scales as the 6th power of tolerance |
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tolerance = pow(4 * tools::epsilon<T>(), T(1) / 6); |
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// for y < 0, the integral is singular, return Cauchy principal value |
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if (y < 0) |
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{ |
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prefix = sqrt(x / (x - y)); |
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x = x - y; |
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y = -y; |
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} |
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else |
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prefix = 1; |
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// duplication: |
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k = 1; |
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do |
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{ |
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u = (x + y + y) / 3; |
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S = y / u - 1; // 1 - x / u = 2 * S |
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if (2 * abs(S) < tolerance) |
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break; |
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T sx = sqrt(x); |
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T sy = sqrt(y); |
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lambda = 2 * sx * sy + y; |
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x = (x + lambda) / 4; |
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y = (y + lambda) / 4; |
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++k; |
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}while(k < policies::get_max_series_iterations<Policy>()); |
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// Check to see if we gave up too soon: |
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policies::check_series_iterations<T>(function, k, pol); |
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// Taylor series expansion to the 5th order |
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value = (1 + S * S * (T(3) / 10 + S * (T(1) / 7 + S * (T(3) / 8 + S * T(9) / 22)))) / sqrt(u); |
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return value * prefix; |
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} |
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} // namespace detail |
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template <class T1, class T2, class Policy> |
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inline typename tools::promote_args<T1, T2>::type |
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ellint_rc(T1 x, T2 y, const Policy& pol) |
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{ |
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typedef typename tools::promote_args<T1, T2>::type result_type; |
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typedef typename policies::evaluation<result_type, Policy>::type value_type; |
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return policies::checked_narrowing_cast<result_type, Policy>( |
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detail::ellint_rc_imp( |
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static_cast<value_type>(x), |
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static_cast<value_type>(y), pol), "boost::math::ellint_rc<%1%>(%1%,%1%)"); |
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} |
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template <class T1, class T2> |
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inline typename tools::promote_args<T1, T2>::type |
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ellint_rc(T1 x, T2 y) |
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{ |
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return ellint_rc(x, y, policies::policy<>()); |
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} |
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}} // namespaces |
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#endif // BOOST_MATH_ELLINT_RC_HPP |
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