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1 | // Copyright (c) 2006 Xiaogang Zhang, 2015 John Maddock |
2 | // Use, modification and distribution are subject to the | |
3 | // Boost Software License, Version 1.0. (See accompanying file | |
4 | // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) | |
5 | // | |
6 | // History: | |
7 | // XZ wrote the original of this file as part of the Google | |
8 | // Summer of Code 2006. JM modified it to fit into the | |
9 | // Boost.Math conceptual framework better, and to correctly | |
10 | // handle the y < 0 case. | |
11 | // Updated 2015 to use Carlson's latest methods. | |
12 | // | |
13 | ||
14 | #ifndef BOOST_MATH_ELLINT_RC_HPP | |
15 | #define BOOST_MATH_ELLINT_RC_HPP | |
16 | ||
17 | #ifdef _MSC_VER | |
18 | #pragma once | |
19 | #endif | |
20 | ||
21 | #include <boost/math/policies/error_handling.hpp> | |
22 | #include <boost/math/tools/config.hpp> | |
23 | #include <boost/math/special_functions/math_fwd.hpp> | |
24 | #include <boost/math/special_functions/log1p.hpp> | |
25 | #include <boost/math/constants/constants.hpp> | |
26 | #include <iostream> | |
27 | ||
28 | // Carlson's degenerate elliptic integral | |
29 | // R_C(x, y) = R_F(x, y, y) = 0.5 * \int_{0}^{\infty} (t+x)^{-1/2} (t+y)^{-1} dt | |
30 | // Carlson, Numerische Mathematik, vol 33, 1 (1979) | |
31 | ||
32 | namespace boost { namespace math { namespace detail{ | |
33 | ||
34 | template <typename T, typename Policy> | |
35 | T ellint_rc_imp(T x, T y, const Policy& pol) | |
36 | { | |
37 | BOOST_MATH_STD_USING | |
38 | ||
39 | static const char* function = "boost::math::ellint_rc<%1%>(%1%,%1%)"; | |
40 | ||
41 | if(x < 0) | |
42 | { | |
43 | return policies::raise_domain_error<T>(function, | |
44 | "Argument x must be non-negative but got %1%", x, pol); | |
45 | } | |
46 | if(y == 0) | |
47 | { | |
48 | return policies::raise_domain_error<T>(function, | |
49 | "Argument y must not be zero but got %1%", y, pol); | |
50 | } | |
51 | ||
52 | // for y < 0, the integral is singular, return Cauchy principal value | |
53 | T prefix, result; | |
54 | if(y < 0) | |
55 | { | |
56 | prefix = sqrt(x / (x - y)); | |
57 | x = x - y; | |
58 | y = -y; | |
59 | } | |
60 | else | |
61 | prefix = 1; | |
62 | ||
63 | if(x == 0) | |
64 | { | |
65 | result = constants::half_pi<T>() / sqrt(y); | |
66 | } | |
67 | else if(x == y) | |
68 | { | |
69 | result = 1 / sqrt(x); | |
70 | } | |
71 | else if(y > x) | |
72 | { | |
73 | result = atan(sqrt((y - x) / x)) / sqrt(y - x); | |
74 | } | |
75 | else | |
76 | { | |
77 | if(y / x > 0.5) | |
78 | { | |
79 | T arg = sqrt((x - y) / x); | |
20effc67 | 80 | result = (boost::math::log1p(arg, pol) - boost::math::log1p(-arg, pol)) / (2 * sqrt(x - y)); |
7c673cae FG |
81 | } |
82 | else | |
83 | { | |
84 | result = log((sqrt(x) + sqrt(x - y)) / sqrt(y)) / sqrt(x - y); | |
85 | } | |
86 | } | |
87 | return prefix * result; | |
88 | } | |
89 | ||
90 | } // namespace detail | |
91 | ||
92 | template <class T1, class T2, class Policy> | |
93 | inline typename tools::promote_args<T1, T2>::type | |
94 | ellint_rc(T1 x, T2 y, const Policy& pol) | |
95 | { | |
96 | typedef typename tools::promote_args<T1, T2>::type result_type; | |
97 | typedef typename policies::evaluation<result_type, Policy>::type value_type; | |
98 | return policies::checked_narrowing_cast<result_type, Policy>( | |
99 | detail::ellint_rc_imp( | |
100 | static_cast<value_type>(x), | |
101 | static_cast<value_type>(y), pol), "boost::math::ellint_rc<%1%>(%1%,%1%)"); | |
102 | } | |
103 | ||
104 | template <class T1, class T2> | |
105 | inline typename tools::promote_args<T1, T2>::type | |
106 | ellint_rc(T1 x, T2 y) | |
107 | { | |
108 | return ellint_rc(x, y, policies::policy<>()); | |
109 | } | |
110 | ||
111 | }} // namespaces | |
112 | ||
113 | #endif // BOOST_MATH_ELLINT_RC_HPP | |
114 |