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Diffstat (limited to 'boost/math/special_functions/heuman_lambda.hpp')
-rw-r--r-- | boost/math/special_functions/heuman_lambda.hpp | 87 |
1 files changed, 87 insertions, 0 deletions
diff --git a/boost/math/special_functions/heuman_lambda.hpp b/boost/math/special_functions/heuman_lambda.hpp new file mode 100644 index 0000000000..6389443ee4 --- /dev/null +++ b/boost/math/special_functions/heuman_lambda.hpp @@ -0,0 +1,87 @@ +// 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_HL_HPP +#define BOOST_MATH_ELLINT_HL_HPP + +#ifdef _MSC_VER +#pragma once +#endif + +#include <boost/math/special_functions/math_fwd.hpp> +#include <boost/math/special_functions/ellint_rj.hpp> +#include <boost/math/special_functions/ellint_rj.hpp> +#include <boost/math/special_functions/ellint_1.hpp> +#include <boost/math/special_functions/jacobi_zeta.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 heuman_lambda_imp(T phi, T k, const Policy& pol) +{ + BOOST_MATH_STD_USING + using namespace boost::math::tools; + using namespace boost::math::constants; + + const char* function = "boost::math::heuman_lambda<%1%>(%1%, %1%)"; + + if(fabs(k) > 1) + return policies::raise_domain_error<T>(function, "We require |k| <= 1 but got k = %1%", k, pol); + + T result; + T sinp = sin(phi); + T cosp = cos(phi); + T s2 = sinp * sinp; + T k2 = k * k; + T kp = 1 - k2; + T delta = sqrt(1 - (kp * s2)); + if(fabs(phi) <= constants::half_pi<T>()) + { + result = kp * sinp * cosp / (delta * constants::half_pi<T>()); + 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); + } + else + { + T rkp = sqrt(kp); + T ratio; + if(rkp == 1) + { + return policies::raise_domain_error<T>(function, "When 1-k^2 == 1 then phi must be < Pi/2, but got phi = %1%", phi, pol); + } + else + ratio = ellint_f_imp(phi, rkp, pol) / ellint_k_imp(rkp, pol); + result = ratio + ellint_k_imp(k, pol) * jacobi_zeta_imp(phi, rkp, pol) / constants::half_pi<T>(); + } + return result; +} + +} // detail + +template <class T1, class T2, class Policy> +inline typename tools::promote_args<T1, T2>::type heuman_lambda(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::heuman_lambda_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::heuman_lambda<%1%>(%1%,%1%)"); +} + +template <class T1, class T2> +inline typename tools::promote_args<T1, T2>::type heuman_lambda(T1 k, T2 phi) +{ + return boost::math::heuman_lambda(k, phi, policies::policy<>()); +} + +}} // namespaces + +#endif // BOOST_MATH_ELLINT_D_HPP + |