| // 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 |
| |