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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,151 @@ | ||
| //====================================================================================================================== | ||
| /* | ||
| Kyosu - Complex Without Complexes | ||
| Copyright: KYOSU Contributors & Maintainers | ||
| SPDX-License-Identifier: BSL-1.0 | ||
| */ | ||
| //====================================================================================================================== | ||
| #pragma once | ||
| #include "eve/traits/as_logical.hpp" | ||
| #include <kyosu/details/callable.hpp> | ||
| #include <kyosu/bessel.hpp> | ||
|
|
||
|
|
||
| namespace kyosu | ||
| { | ||
|
|
||
| template<typename Options> | ||
| struct bessel_h_t : eve::strict_elementwise_callable<bessel_h_t, Options, eve::spherical_option, eve::cylindrical_option, kind_1_option, kind_2_option> | ||
| { | ||
| template<eve::scalar_value N, typename Z> | ||
| requires(concepts::real<Z> || concepts::cayley_dickson<Z>) | ||
| KYOSU_FORCEINLINE constexpr auto operator()(N const& n, Z const & z) const noexcept | ||
| { | ||
| constexpr int Kind = Options::contains(kind_2) ? 2 : 1; | ||
| if constexpr(concepts::complex<Z> ) | ||
| { | ||
| if constexpr(eve::integral_scalar_value<N>) | ||
| { | ||
| if constexpr(Options::contains(eve::spherical)) | ||
| { | ||
| if (eve::is_ltz(n)) | ||
| { | ||
| using u_t = eve::underlying_type_t<Z>; | ||
| return _::sb_hr<Kind>(u_t(n), z); | ||
| } | ||
| else | ||
| return _::sb_hn<Kind>(n, z); | ||
| } | ||
| else | ||
| return _::cb_hn<Kind>(n, z); | ||
| } | ||
| else if constexpr( eve::floating_scalar_value<N>) | ||
| { | ||
| if constexpr(Options::contains(eve::spherical)) | ||
| return _::sb_hr<Kind>(n, z); | ||
| else | ||
| return _::cb_hr<Kind>(n, z); | ||
| } | ||
| } | ||
| else | ||
| return _::cayley_extend_rev(*this, n, z); | ||
| } | ||
|
|
||
| template<eve::scalar_value N, typename Z, std::size_t S> | ||
| requires(concepts::real<Z> || concepts::complex<Z>) | ||
| KYOSU_FORCEINLINE constexpr auto operator()(N const& n, Z const & z, std::span<Z, S> hs) const noexcept | ||
| { | ||
| constexpr int Kind = Options::contains(kind_2) ? 2 : 1; | ||
| if constexpr(eve::integral_scalar_value<N>) | ||
| { | ||
| if constexpr(Options::contains(eve::spherical)) | ||
| { | ||
| if (eve::is_ltz(n)) | ||
| { | ||
| using u_t = eve::underlying_type_t<Z>; | ||
| return _::sb_hr(u_t(n), z, hs); | ||
| } | ||
| else | ||
| return _::sb_hn<Kind>(n, z, hs); | ||
| } | ||
| else | ||
| return _::cb_hn<Kind>(n, z, hs); | ||
| } | ||
| else | ||
| { | ||
| if constexpr(Options::contains(eve::spherical)) | ||
| return _::sb_hr<Kind>(n, z, hs); | ||
| else | ||
| return _::cb_hr<Kind>(n, z, hs); | ||
| } | ||
| } | ||
|
|
||
| KYOSU_CALLABLE_OBJECT(bessel_h_t, bessel_h_); | ||
| }; | ||
|
|
||
| //====================================================================================================================== | ||
| //! @addtogroup functions | ||
| //! @{ | ||
| //! @var bessel_h | ||
| //! @brief Computes the spherical or cylindrical Hankel functions, | ||
| //! extended to the complex plane and cayley_dickson algebras. | ||
| //! | ||
| //! @code | ||
| //! #include <kyosu/functions.hpp> | ||
| //! @endcode | ||
| //! | ||
| //! @groupheader{Callable Signatures} | ||
| //! | ||
| //! @code | ||
| //! namespace kyosu | ||
| //! { | ||
| //! template<eve;scalar_value N, kyosu::concepts::cayley_dickson T> constexpr auto bessel_h(N n, T z) noexcept; //1 | ||
| //! template<eve;scalar_value N, kyosu::concepts::real T> constexpr T bessel_h(N n, T z) noexcept; //1 | ||
| //! template<eve;scalar_value N, kyosu::concepts::complex T, size_t S> constexpr auto bessel_h(N n, T z, std::span<Z, S> chs) noexcept; //2 | ||
| //! template<eve;scalar_value N, kyosu::concepts::real T, size_t S> constexpr T bessel_h(N n, T z, std::span<Z, S> chs) noexcept; //2 | ||
| //! | ||
| //! template<eve;scalar_value N, kyosu::concepts::cayley_dickson T> constexpr auto bessel_h[spherical](N n, T z) noexcept; //3 | ||
| //! template<eve;scalar_value N, kyosu::concepts::real T> constexpr T bessel_h[spherical](N n, T z) noexcept; //3 | ||
| //! template<eve;scalar_value N, kyosu::concepts::complex T, size_t S> constexpr auto bessel_h[spherical](N n, T z, std::span<Z, S> shs) noexcept; //4 | ||
| //! template<eve;scalar_value N, kyosu::concepts::real T, size_t S> constexpr T bessel_h[spherical](N n, T z, std::span<Z, S> shs) noexcept; //4 | ||
| //! | ||
| //! template<eve;scalar_value N, kyosu::concepts::cayley_dickson T> constexpr auto bessel_h[kind_2](/*any previous overloads*/) noexcept; //5 | ||
| //! template<eve;scalar_value N, kyosu::concepts::cayley_dickson T> constexpr auto bessel_h[kind_2][spherical](/*any previous overloads*/) noexcept; //6 | ||
| //! } | ||
| //! @endcode | ||
| //! | ||
| //! **Parameters** | ||
| //! | ||
| //! * `n`: scalar order (integral or floating) | ||
| //! * `z`: Value to process. | ||
| //! * `shs`, `chs` : std::span of T | ||
| //! | ||
| //! **Return value** | ||
| //! | ||
| //! 1. returns \f$H_n\f$(z) (cylindrical first kind). | ||
| //! 2. Same as 1, but chs is filled by the lesser orders. | ||
| //! 3. returns \f$h_n\f$(z) (spherical). | ||
| //! 4. Same as 3, but shs is filled by the lesser orders. | ||
| //! 5. Same as 1., 2., 3., 4. but returns second kind Hankel functions values. | ||
| //! 6. Same as 1., 2., 3., 4. but returns second kind spherical Hankel functions values. | ||
| //! | ||
| //! @note | ||
| //! * Let \f$ i = \lfloor |n| \rfloor \f$ and \f$ j=|n|-i\f$. If \f$n\f$ is | ||
| //! positive the lesser order are \f$(\pm j, \pm(j+1), \dots, \pm(j+i)) \f$ | ||
| //! with \f$+\f$ sign if \f$n\f$ is positive and \f$-\f$ sign if \f$n\f$ is negative. | ||
| //! * The span parameters are filled according the minimum of their allocated size and \f$i\f$. | ||
| //! * `cylindical` and `kind_1` options can be used and their results are identical to the regular call (no option). | ||
| //! | ||
| //! @groupheader{External references} | ||
| //! * [Wolfram MathWorld: Hankel Function](https://mathworld.wolfram.com/HankelFunction.html) | ||
| //! * [Wikipedia: Bessel function](https://en.wikipedia.org/wiki/Bessel_function) | ||
| //! * [DLMF: Bessel functions](https://dlmf.nist.gov/10.2) | ||
| //! | ||
| //! @groupheader{Example} | ||
| //! @godbolt{doc/bessel_h.cpp} | ||
| //====================================================================================================================== | ||
| inline constexpr auto bessel_h = eve::functor<bessel_h_t>; | ||
| //====================================================================================================================== | ||
| //! @} | ||
| //====================================================================================================================== | ||
| } |
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