181 lines
7.0 KiB
Plaintext
181 lines
7.0 KiB
Plaintext
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// Copyright John Maddock 2012.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_HANKEL_HPP
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#define BOOST_MATH_HANKEL_HPP
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#include <boost/math/special_functions/math_fwd.hpp>
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#include <boost/math/special_functions/bessel.hpp>
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namespace boost{ namespace math{
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namespace detail{
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template <class T, class Policy>
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std::complex<T> hankel_imp(T v, T x, const bessel_no_int_tag&, const Policy& pol, int sign)
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{
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BOOST_MATH_STD_USING
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static const char* function = "boost::math::cyl_hankel_1<%1%>(%1%,%1%)";
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if(x < 0)
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{
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bool isint_v = floor(v) == v;
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T j, y;
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bessel_jy(v, -x, &j, &y, need_j | need_y, pol);
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std::complex<T> cx(x), cv(v);
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std::complex<T> j_result, y_result;
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if(isint_v)
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{
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int s = (iround(v) & 1) ? -1 : 1;
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j_result = j * s;
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y_result = T(s) * (y - (2 / constants::pi<T>()) * (log(-x) - log(cx)) * j);
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}
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else
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{
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j_result = pow(cx, v) * pow(-cx, -v) * j;
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T p1 = pow(-x, v);
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std::complex<T> p2 = pow(cx, v);
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y_result = p1 * y / p2
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+ (p2 / p1 - p1 / p2) * j / tan(constants::pi<T>() * v);
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}
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// multiply y_result by i:
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y_result = std::complex<T>(-sign * y_result.imag(), sign * y_result.real());
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return j_result + y_result;
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}
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if(x == 0)
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{
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if(v == 0)
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{
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// J is 1, Y is -INF
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return std::complex<T>(1, sign * -policies::raise_overflow_error<T>(function, 0, pol));
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}
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else
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{
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// At least one of J and Y is complex infinity:
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return std::complex<T>(policies::raise_overflow_error<T>(function, 0, pol), sign * policies::raise_overflow_error<T>(function, 0, pol));
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}
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}
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T j, y;
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bessel_jy(v, x, &j, &y, need_j | need_y, pol);
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return std::complex<T>(j, sign * y);
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}
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template <class T, class Policy>
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std::complex<T> hankel_imp(int v, T x, const bessel_int_tag&, const Policy& pol, int sign);
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template <class T, class Policy>
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inline std::complex<T> hankel_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol, int sign)
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{
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BOOST_MATH_STD_USING // ADL of std names.
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int ival = detail::iconv(v, pol);
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if(0 == v - ival)
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{
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return hankel_imp(ival, x, bessel_int_tag(), pol, sign);
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}
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return hankel_imp(v, x, bessel_no_int_tag(), pol, sign);
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}
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template <class T, class Policy>
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inline std::complex<T> hankel_imp(int v, T x, const bessel_int_tag&, const Policy& pol, int sign)
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{
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BOOST_MATH_STD_USING
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if((std::abs(v) < 200) && (x > 0))
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return std::complex<T>(bessel_jn(v, x, pol), sign * bessel_yn(v, x, pol));
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return hankel_imp(static_cast<T>(v), x, bessel_no_int_tag(), pol, sign);
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}
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template <class T, class Policy>
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inline std::complex<T> sph_hankel_imp(T v, T x, const Policy& pol, int sign)
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{
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BOOST_MATH_STD_USING
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return constants::root_half_pi<T>() * hankel_imp(v + 0.5f, x, bessel_no_int_tag(), pol, sign) / sqrt(std::complex<T>(x));
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}
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} // namespace detail
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template <class T1, class T2, class Policy>
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inline std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_1(T1 v, T2 x, const Policy& pol)
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{
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BOOST_FPU_EXCEPTION_GUARD
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typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
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typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
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typedef typename policies::evaluation<result_type, Policy>::type value_type;
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return policies::checked_narrowing_cast<std::complex<result_type>, Policy>(detail::hankel_imp<value_type>(v, static_cast<value_type>(x), tag_type(), pol, 1), "boost::math::cyl_hankel_1<%1%>(%1%,%1%)");
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}
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template <class T1, class T2>
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inline std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_1(T1 v, T2 x)
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{
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return cyl_hankel_1(v, x, policies::policy<>());
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}
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template <class T1, class T2, class Policy>
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inline std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> cyl_hankel_2(T1 v, T2 x, const Policy& pol)
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{
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BOOST_FPU_EXCEPTION_GUARD
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typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
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typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
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typedef typename policies::evaluation<result_type, Policy>::type value_type;
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return policies::checked_narrowing_cast<std::complex<result_type>, Policy>(detail::hankel_imp<value_type>(v, static_cast<value_type>(x), tag_type(), pol, -1), "boost::math::cyl_hankel_1<%1%>(%1%,%1%)");
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}
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template <class T1, class T2>
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inline std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> cyl_hankel_2(T1 v, T2 x)
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{
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return cyl_hankel_2(v, x, policies::policy<>());
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}
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template <class T1, class T2, class Policy>
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inline std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_1(T1 v, T2 x, const Policy&)
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{
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BOOST_FPU_EXCEPTION_GUARD
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typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
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typedef typename policies::evaluation<result_type, Policy>::type value_type;
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typedef typename policies::normalise<
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Policy,
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policies::promote_float<false>,
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policies::promote_double<false>,
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policies::discrete_quantile<>,
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policies::assert_undefined<> >::type forwarding_policy;
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return policies::checked_narrowing_cast<std::complex<result_type>, Policy>(detail::sph_hankel_imp<value_type>(static_cast<value_type>(v), static_cast<value_type>(x), forwarding_policy(), 1), "boost::math::sph_hankel_1<%1%>(%1%,%1%)");
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}
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template <class T1, class T2>
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inline std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_1(T1 v, T2 x)
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{
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return sph_hankel_1(v, x, policies::policy<>());
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}
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template <class T1, class T2, class Policy>
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inline std::complex<typename detail::bessel_traits<T1, T2, Policy>::result_type> sph_hankel_2(T1 v, T2 x, const Policy&)
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{
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BOOST_FPU_EXCEPTION_GUARD
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typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
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typedef typename policies::evaluation<result_type, Policy>::type value_type;
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typedef typename policies::normalise<
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Policy,
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policies::promote_float<false>,
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policies::promote_double<false>,
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policies::discrete_quantile<>,
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policies::assert_undefined<> >::type forwarding_policy;
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return policies::checked_narrowing_cast<std::complex<result_type>, Policy>(detail::sph_hankel_imp<value_type>(static_cast<value_type>(v), static_cast<value_type>(x), forwarding_policy(), -1), "boost::math::sph_hankel_1<%1%>(%1%,%1%)");
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}
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template <class T1, class T2>
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inline std::complex<typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type> sph_hankel_2(T1 v, T2 x)
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{
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return sph_hankel_2(v, x, policies::policy<>());
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}
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}} // namespaces
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#endif // BOOST_MATH_HANKEL_HPP
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