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: 
Chris@102: #ifndef BOOST_MATH_ELLINT_JZ_HPP
Chris@102: #define BOOST_MATH_ELLINT_JZ_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_1.hpp>
Chris@102: #include <boost/math/special_functions/ellint_rj.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 jacobi_zeta_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:     bool invert = false;
Chris@102:     if(phi < 0)
Chris@102:     {
Chris@102:        phi = fabs(phi);
Chris@102:        invert = true;
Chris@102:     }
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:     if(k == 1)
Chris@102:        result = sinp * (boost::math::sign)(cosp);  // We get here by simplifying JacobiZeta[w, 1] in Mathematica, and the fact that 0 <= phi.
Chris@102:     else
Chris@102:        result = k2 * sinp * cosp * sqrt(1 - k2 * s2) * ellint_rj_imp(T(0), kp, T(1), T(1 - k2 * s2), pol) / (3 * ellint_k_imp(k, pol));
Chris@102:     return invert ? T(-result) : 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 jacobi_zeta(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::jacobi_zeta_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::jacobi_zeta<%1%>(%1%,%1%)");
Chris@102: }
Chris@102: 
Chris@102: template <class T1, class T2>
Chris@102: inline typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi)
Chris@102: {
Chris@102:    return boost::math::jacobi_zeta(k, phi, policies::policy<>());
Chris@102: }
Chris@102: 
Chris@102: }} // namespaces
Chris@102: 
Chris@102: #endif // BOOST_MATH_ELLINT_D_HPP
Chris@102: