Chris@102: //  Copyright (c) 2015 John Maddock
Chris@102: //  Use, modification and distribution are subject to the
Chris@102: //  Boost Software License, Version 1.0. (See accompanying file
Chris@102: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@102: 
Chris@102: #ifndef BOOST_MATH_ELLINT_HL_HPP
Chris@102: #define BOOST_MATH_ELLINT_HL_HPP
Chris@102: 
Chris@102: #ifdef _MSC_VER
Chris@102: #pragma once
Chris@102: #endif
Chris@102: 
Chris@102: #include <boost/math/special_functions/math_fwd.hpp>
Chris@102: #include <boost/math/special_functions/ellint_rj.hpp>
Chris@102: #include <boost/math/special_functions/ellint_rj.hpp>
Chris@102: #include <boost/math/special_functions/ellint_1.hpp>
Chris@102: #include <boost/math/special_functions/jacobi_zeta.hpp>
Chris@102: #include <boost/math/constants/constants.hpp>
Chris@102: #include <boost/math/policies/error_handling.hpp>
Chris@102: #include <boost/math/tools/workaround.hpp>
Chris@102: 
Chris@102: // Elliptic integral the Jacobi Zeta function.
Chris@102: 
Chris@102: namespace boost { namespace math { 
Chris@102:    
Chris@102: namespace detail{
Chris@102: 
Chris@102: // Elliptic integral - Jacobi Zeta
Chris@102: template <typename T, typename Policy>
Chris@102: T heuman_lambda_imp(T phi, T k, const Policy& pol)
Chris@102: {
Chris@102:     BOOST_MATH_STD_USING
Chris@102:     using namespace boost::math::tools;
Chris@102:     using namespace boost::math::constants;
Chris@102: 
Chris@102:     const char* function = "boost::math::heuman_lambda<%1%>(%1%, %1%)";
Chris@102: 
Chris@102:     if(fabs(k) > 1)
Chris@102:        return policies::raise_domain_error<T>(function, "We require |k| <= 1 but got k = %1%", k, pol);
Chris@102: 
Chris@102:     T result;
Chris@102:     T sinp = sin(phi);
Chris@102:     T cosp = cos(phi);
Chris@102:     T s2 = sinp * sinp;
Chris@102:     T k2 = k * k;
Chris@102:     T kp = 1 - k2;
Chris@102:     T delta = sqrt(1 - (kp * s2));
Chris@102:     if(fabs(phi) <= constants::half_pi<T>())
Chris@102:     {
Chris@102:        result = kp * sinp * cosp / (delta * constants::half_pi<T>());
Chris@102:        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);
Chris@102:     }
Chris@102:     else
Chris@102:     {
Chris@102:        T rkp = sqrt(kp);
Chris@102:        T ratio;
Chris@102:        if(rkp == 1)
Chris@102:        {
Chris@102:           return policies::raise_domain_error<T>(function, "When 1-k^2 == 1 then phi must be < Pi/2, but got phi = %1%", phi, pol);
Chris@102:        }
Chris@102:        else
Chris@102:           ratio = ellint_f_imp(phi, rkp, pol) / ellint_k_imp(rkp, pol);
Chris@102:        result = ratio + ellint_k_imp(k, pol) * jacobi_zeta_imp(phi, rkp, pol) / constants::half_pi<T>();
Chris@102:     }
Chris@102:     return result;
Chris@102: }
Chris@102: 
Chris@102: } // detail
Chris@102: 
Chris@102: template <class T1, class T2, class Policy>
Chris@102: inline typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi, const Policy& pol)
Chris@102: {
Chris@102:    typedef typename tools::promote_args<T1, T2>::type result_type;
Chris@102:    typedef typename policies::evaluation<result_type, Policy>::type value_type;
Chris@102:    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%)");
Chris@102: }
Chris@102: 
Chris@102: template <class T1, class T2>
Chris@102: inline typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi)
Chris@102: {
Chris@102:    return boost::math::heuman_lambda(k, phi, policies::policy<>());
Chris@102: }
Chris@102: 
Chris@102: }} // namespaces
Chris@102: 
Chris@102: #endif // BOOST_MATH_ELLINT_D_HPP
Chris@102: