| // Copyright (c) 2015 John Maddock |
| // Use, modification and distribution are subject to the |
| // Boost Software License, Version 1.0. (See accompanying file |
| // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) |
| // |
| |
| #ifndef BOOST_MATH_ELLINT_JZ_HPP |
| #define BOOST_MATH_ELLINT_JZ_HPP |
| |
| #ifdef _MSC_VER |
| #pragma once |
| #endif |
| |
| #include <boost/math/special_functions/math_fwd.hpp> |
| #include <boost/math/special_functions/ellint_1.hpp> |
| #include <boost/math/special_functions/ellint_rj.hpp> |
| #include <boost/math/constants/constants.hpp> |
| #include <boost/math/policies/error_handling.hpp> |
| #include <boost/math/tools/workaround.hpp> |
| |
| // Elliptic integral the Jacobi Zeta function. |
| |
| namespace boost { namespace math { |
| |
| namespace detail{ |
| |
| // Elliptic integral - Jacobi Zeta |
| template <typename T, typename Policy> |
| T jacobi_zeta_imp(T phi, T k, const Policy& pol) |
| { |
| BOOST_MATH_STD_USING |
| using namespace boost::math::tools; |
| using namespace boost::math::constants; |
| |
| bool invert = false; |
| if(phi < 0) |
| { |
| phi = fabs(phi); |
| invert = true; |
| } |
| |
| T result; |
| T sinp = sin(phi); |
| T cosp = cos(phi); |
| T s2 = sinp * sinp; |
| T k2 = k * k; |
| T kp = 1 - k2; |
| if(k == 1) |
| result = sinp * (boost::math::sign)(cosp); // We get here by simplifying JacobiZeta[w, 1] in Mathematica, and the fact that 0 <= phi. |
| else |
| 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)); |
| return invert ? T(-result) : result; |
| } |
| |
| } // detail |
| |
| template <class T1, class T2, class Policy> |
| inline typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi, const Policy& pol) |
| { |
| typedef typename tools::promote_args<T1, T2>::type result_type; |
| typedef typename policies::evaluation<result_type, Policy>::type value_type; |
| 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%)"); |
| } |
| |
| template <class T1, class T2> |
| inline typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi) |
| { |
| return boost::math::jacobi_zeta(k, phi, policies::policy<>()); |
| } |
| |
| }} // namespaces |
| |
| #endif // BOOST_MATH_ELLINT_D_HPP |
| |