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Diffstat (limited to 'boost/math/special_functions/jacobi_zeta.hpp')
-rw-r--r-- | boost/math/special_functions/jacobi_zeta.hpp | 74 |
1 files changed, 74 insertions, 0 deletions
diff --git a/boost/math/special_functions/jacobi_zeta.hpp b/boost/math/special_functions/jacobi_zeta.hpp new file mode 100644 index 0000000000..a3fa54746e --- /dev/null +++ b/boost/math/special_functions/jacobi_zeta.hpp @@ -0,0 +1,74 @@ +// 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 + |