// Copyright John Maddock 2012. // 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_HANKEL_HPP #define BOOST_MATH_HANKEL_HPP #include #include namespace boost{ namespace math{ namespace detail{ template std::complex hankel_imp(T v, T x, const bessel_no_int_tag&, const Policy& pol, int sign) { BOOST_MATH_STD_USING static const char* function = "boost::math::cyl_hankel_1<%1%>(%1%,%1%)"; if(x < 0) { bool isint_v = floor(v) == v; T j, y; bessel_jy(v, -x, &j, &y, need_j | need_y, pol); std::complex cx(x), cv(v); std::complex j_result, y_result; if(isint_v) { int s = (iround(v) & 1) ? -1 : 1; j_result = j * s; y_result = T(s) * (y - (2 / constants::pi()) * (log(-x) - log(cx)) * j); } else { j_result = pow(cx, v) * pow(-cx, -v) * j; T p1 = pow(-x, v); std::complex p2 = pow(cx, v); y_result = p1 * y / p2 + (p2 / p1 - p1 / p2) * j / tan(constants::pi() * v); } // multiply y_result by i: y_result = std::complex(-sign * y_result.imag(), sign * y_result.real()); return j_result + y_result; } if(x == 0) { if(v == 0) { // J is 1, Y is -INF return std::complex(1, sign * -policies::raise_overflow_error(function, 0, pol)); } else { // At least one of J and Y is complex infinity: return std::complex(policies::raise_overflow_error(function, 0, pol), sign * policies::raise_overflow_error(function, 0, pol)); } } T j, y; bessel_jy(v, x, &j, &y, need_j | need_y, pol); return std::complex(j, sign * y); } template std::complex hankel_imp(int v, T x, const bessel_int_tag&, const Policy& pol, int sign); template inline std::complex hankel_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol, int sign) { BOOST_MATH_STD_USING // ADL of std names. int ival = detail::iconv(v, pol); if(0 == v - ival) { return hankel_imp(ival, x, bessel_int_tag(), pol, sign); } return hankel_imp(v, x, bessel_no_int_tag(), pol, sign); } template inline std::complex hankel_imp(int v, T x, const bessel_int_tag&, const Policy& pol, int sign) { BOOST_MATH_STD_USING if((std::abs(v) < 200) && (x > 0)) return std::complex(bessel_jn(v, x, pol), sign * bessel_yn(v, x, pol)); return hankel_imp(static_cast(v), x, bessel_no_int_tag(), pol, sign); } template inline std::complex sph_hankel_imp(T v, T x, const Policy& pol, int sign) { BOOST_MATH_STD_USING return constants::root_half_pi() * hankel_imp(v + 0.5f, x, bessel_no_int_tag(), pol, sign) / sqrt(std::complex(x)); } } // namespace detail template inline std::complex::result_type> cyl_hankel_1(T1 v, T2 x, const Policy& pol) { BOOST_FPU_EXCEPTION_GUARD typedef typename detail::bessel_traits::result_type result_type; typedef typename detail::bessel_traits::optimisation_tag tag_type; typedef typename policies::evaluation::type value_type; return policies::checked_narrowing_cast, Policy>(detail::hankel_imp(v, static_cast(x), tag_type(), pol, 1), "boost::math::cyl_hankel_1<%1%>(%1%,%1%)"); } template inline std::complex >::result_type> cyl_hankel_1(T1 v, T2 x) { return cyl_hankel_1(v, x, policies::policy<>()); } template inline std::complex::result_type> cyl_hankel_2(T1 v, T2 x, const Policy& pol) { BOOST_FPU_EXCEPTION_GUARD typedef typename detail::bessel_traits::result_type result_type; typedef typename detail::bessel_traits::optimisation_tag tag_type; typedef typename policies::evaluation::type value_type; return policies::checked_narrowing_cast, Policy>(detail::hankel_imp(v, static_cast(x), tag_type(), pol, -1), "boost::math::cyl_hankel_1<%1%>(%1%,%1%)"); } template inline std::complex >::result_type> cyl_hankel_2(T1 v, T2 x) { return cyl_hankel_2(v, x, policies::policy<>()); } template inline std::complex::result_type> sph_hankel_1(T1 v, T2 x, const Policy&) { BOOST_FPU_EXCEPTION_GUARD typedef typename detail::bessel_traits::result_type result_type; typedef typename policies::evaluation::type value_type; typedef typename policies::normalise< Policy, policies::promote_float, policies::promote_double, policies::discrete_quantile<>, policies::assert_undefined<> >::type forwarding_policy; return policies::checked_narrowing_cast, Policy>(detail::sph_hankel_imp(static_cast(v), static_cast(x), forwarding_policy(), 1), "boost::math::sph_hankel_1<%1%>(%1%,%1%)"); } template inline std::complex >::result_type> sph_hankel_1(T1 v, T2 x) { return sph_hankel_1(v, x, policies::policy<>()); } template inline std::complex::result_type> sph_hankel_2(T1 v, T2 x, const Policy&) { BOOST_FPU_EXCEPTION_GUARD typedef typename detail::bessel_traits::result_type result_type; typedef typename policies::evaluation::type value_type; typedef typename policies::normalise< Policy, policies::promote_float, policies::promote_double, policies::discrete_quantile<>, policies::assert_undefined<> >::type forwarding_policy; return policies::checked_narrowing_cast, Policy>(detail::sph_hankel_imp(static_cast(v), static_cast(x), forwarding_policy(), -1), "boost::math::sph_hankel_1<%1%>(%1%,%1%)"); } template inline std::complex >::result_type> sph_hankel_2(T1 v, T2 x) { return sph_hankel_2(v, x, policies::policy<>()); } }} // namespaces #endif // BOOST_MATH_HANKEL_HPP