88 lines
2.9 KiB
Plaintext
88 lines
2.9 KiB
Plaintext
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// Copyright (c) 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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#ifndef BOOST_MATH_ELLINT_HL_HPP
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#define BOOST_MATH_ELLINT_HL_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/special_functions/math_fwd.hpp>
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#include <boost/math/special_functions/ellint_rj.hpp>
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#include <boost/math/special_functions/ellint_rj.hpp>
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#include <boost/math/special_functions/ellint_1.hpp>
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#include <boost/math/special_functions/jacobi_zeta.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/math/policies/error_handling.hpp>
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#include <boost/math/tools/workaround.hpp>
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// Elliptic integral the Jacobi Zeta function.
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namespace boost { namespace math {
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namespace detail{
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// Elliptic integral - Jacobi Zeta
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template <typename T, typename Policy>
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T heuman_lambda_imp(T phi, T k, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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using namespace boost::math::tools;
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using namespace boost::math::constants;
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const char* function = "boost::math::heuman_lambda<%1%>(%1%, %1%)";
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if(fabs(k) > 1)
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return policies::raise_domain_error<T>(function, "We require |k| <= 1 but got k = %1%", k, pol);
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T result;
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T sinp = sin(phi);
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T cosp = cos(phi);
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T s2 = sinp * sinp;
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T k2 = k * k;
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T kp = 1 - k2;
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T delta = sqrt(1 - (kp * s2));
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if(fabs(phi) <= constants::half_pi<T>())
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{
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result = kp * sinp * cosp / (delta * constants::half_pi<T>());
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result *= ellint_rf_imp(T(0), kp, T(1), pol) + k2 * ellint_rj(T(0), kp, T(1), T(1 - k2 / (delta * delta)), pol) / (3 * delta * delta);
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}
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else
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{
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T rkp = sqrt(kp);
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T ratio;
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if(rkp == 1)
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{
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return policies::raise_domain_error<T>(function, "When 1-k^2 == 1 then phi must be < Pi/2, but got phi = %1%", phi, pol);
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}
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else
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ratio = ellint_f_imp(phi, rkp, pol) / ellint_k_imp(rkp, pol);
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result = ratio + ellint_k_imp(k, pol) * jacobi_zeta_imp(phi, rkp, pol) / constants::half_pi<T>();
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}
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return result;
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}
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} // detail
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template <class T1, class T2, class Policy>
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inline typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi, 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>(detail::heuman_lambda_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::heuman_lambda<%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 heuman_lambda(T1 k, T2 phi)
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{
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return boost::math::heuman_lambda(k, phi, policies::policy<>());
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}
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}} // namespaces
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#endif // BOOST_MATH_ELLINT_D_HPP
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