// Copyright (c) 2006 Xiaogang Zhang, 2015 John Maddock // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) // // History: // XZ wrote the original of this file as part of the Google // Summer of Code 2006. JM modified it to fit into the // Boost.Math conceptual framework better, and to correctly // handle the y < 0 case. // Updated 2015 to use Carlson's latest methods. // #ifndef BOOST_MATH_ELLINT_RC_HPP #define BOOST_MATH_ELLINT_RC_HPP #ifdef _MSC_VER #pragma once #endif #include <boost/math/policies/error_handling.hpp> #include <boost/math/tools/config.hpp> #include <boost/math/special_functions/math_fwd.hpp> #include <boost/math/special_functions/log1p.hpp> #include <boost/math/constants/constants.hpp> #include <iostream> // Carlson's degenerate elliptic integral // R_C(x, y) = R_F(x, y, y) = 0.5 * \int_{0}^{\infty} (t+x)^{-1/2} (t+y)^{-1} dt // Carlson, Numerische Mathematik, vol 33, 1 (1979) namespace boost { namespace math { namespace detail{ template <typename T, typename Policy> T ellint_rc_imp(T x, T y, const Policy& pol) { BOOST_MATH_STD_USING static const char* function = "boost::math::ellint_rc<%1%>(%1%,%1%)"; if(x < 0) { return policies::raise_domain_error<T>(function, "Argument x must be non-negative but got %1%", x, pol); } if(y == 0) { return policies::raise_domain_error<T>(function, "Argument y must not be zero but got %1%", y, pol); } // for y < 0, the integral is singular, return Cauchy principal value T prefix, result; if(y < 0) { prefix = sqrt(x / (x - y)); x = x - y; y = -y; } else prefix = 1; if(x == 0) { result = constants::half_pi<T>() / sqrt(y); } else if(x == y) { result = 1 / sqrt(x); } else if(y > x) { result = atan(sqrt((y - x) / x)) / sqrt(y - x); } else { if(y / x > 0.5) { T arg = sqrt((x - y) / x); result = (boost::math::log1p(arg) - boost::math::log1p(-arg)) / (2 * sqrt(x - y)); } else { result = log((sqrt(x) + sqrt(x - y)) / sqrt(y)) / sqrt(x - y); } } return prefix * result; } } // namespace detail template <class T1, class T2, class Policy> inline typename tools::promote_args<T1, T2>::type ellint_rc(T1 x, T2 y, const Policy& pol) { typedef typename tools::promote_args<T1, T2>::type result_type; typedef typename policies::evaluation<result_type, Policy>::type value_type; return policies::checked_narrowing_cast<result_type, Policy>( detail::ellint_rc_imp( static_cast<value_type>(x), static_cast<value_type>(y), pol), "boost::math::ellint_rc<%1%>(%1%,%1%)"); } template <class T1, class T2> inline typename tools::promote_args<T1, T2>::type ellint_rc(T1 x, T2 y) { return ellint_rc(x, y, policies::policy<>()); } }} // namespaces #endif // BOOST_MATH_ELLINT_RC_HPP