boost/math/special_functions/heuman_lambda.hpp
// 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