115 lines
3.2 KiB
Plaintext
115 lines
3.2 KiB
Plaintext
// Copyright (c) 2006 Xiaogang Zhang, 2015 John Maddock
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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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// Updated 2015 to use Carlson's latest methods.
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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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#include <boost/math/special_functions/log1p.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <iostream>
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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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BOOST_MATH_STD_USING
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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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// for y < 0, the integral is singular, return Cauchy principal value
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T prefix, result;
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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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if(x == 0)
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{
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result = constants::half_pi<T>() / sqrt(y);
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}
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else if(x == y)
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{
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result = 1 / sqrt(x);
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}
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else if(y > x)
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{
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result = atan(sqrt((y - x) / x)) / sqrt(y - x);
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}
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else
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{
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if(y / x > 0.5)
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{
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T arg = sqrt((x - y) / x);
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result = (boost::math::log1p(arg) - boost::math::log1p(-arg)) / (2 * sqrt(x - y));
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}
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else
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{
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result = log((sqrt(x) + sqrt(x - y)) / sqrt(y)) / sqrt(x - y);
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}
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}
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return prefix * result;
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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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