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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,95 @@ | ||
| //====================================================================================================================== | ||
| /* | ||
| Kyosu - Complex Without Complexes | ||
| Copyright: KYOSU Contributors & Maintainers | ||
| SPDX-License-Identifier: BSL-1.0 | ||
| */ | ||
| //====================================================================================================================== | ||
| #pragma once | ||
|
|
||
| #include <kyosu/details/invoke.hpp> | ||
| #include <eve/module/bessel.hpp> | ||
|
|
||
| namespace kyosu::tags | ||
| { | ||
| struct callable_cyl_bessel_i: eve::elementwise | ||
| { | ||
| using callable_tag_type = callable_cyl_bessel_i; | ||
|
|
||
| KYOSU_DEFERS_CALLABLE(cyl_bessel_i_); | ||
|
|
||
| template<eve::floating_scalar_value N, eve::floating_ordered_value T> | ||
| static KYOSU_FORCEINLINE auto deferred_call(auto, N nu, T const& v) noexcept | ||
| { | ||
| auto fnu = callable_cyl_bessel_i{}; | ||
| return fnu(nu, complex(v)); | ||
| } | ||
|
|
||
| template<eve::floating_scalar_value N, eve::floating_ordered_value T, typename R> | ||
| static KYOSU_FORCEINLINE auto deferred_call(auto, N nu, T const& v, R& is) noexcept | ||
| { | ||
| auto fnu = callable_cyl_bessel_i{}; | ||
| return fnu(nu, complex(v), is); | ||
| } | ||
|
|
||
| template<typename N, typename T> | ||
| KYOSU_FORCEINLINE auto operator()(N const & target0, T const& target1) const noexcept | ||
| -> decltype(eve::tag_invoke(*this, target0, target1)) | ||
| { | ||
| return eve::tag_invoke(*this, target0, target1); | ||
| } | ||
|
|
||
| template<typename N, typename T, typename R> | ||
| KYOSU_FORCEINLINE auto operator()(N const & target0, T const& target1, R & out0) const noexcept | ||
| -> decltype(eve::tag_invoke(*this, target0, target1, out0)) | ||
| { | ||
| return eve::tag_invoke(*this, target0, target1, out0); | ||
| } | ||
|
|
||
| template<typename... T> | ||
| eve::unsupported_call<callable_cyl_bessel_i(T&&...)> operator()(T&&... x) const | ||
| requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete; | ||
| }; | ||
| } | ||
|
|
||
| namespace kyosu | ||
| { | ||
| //====================================================================================================================== | ||
| //! @addtogroup functions | ||
| //! @{ | ||
| //! @var cyl_bessel_i | ||
| //! @brief Computes the Modified Bessel functions of the first kind. | ||
| //! | ||
| //! @code | ||
| //! #include <kyosu/functions.hpp> | ||
| //! @endcode | ||
| //! | ||
| //! @groupheader{Callable Signatures} | ||
| //! | ||
| //! @code | ||
| //! namespace kyosu | ||
| //! { | ||
| //! template<eve::floating_ordered_value, kyosu::concepts::cayley_dickson T> | ||
| //! constexpr auto cyl_bessel_i(N nu, T z) noexcept; | ||
| //! | ||
| //! template<eve::floating_ordered_value, eve::floating_ordered_value T> | ||
| //! constexpr T cyl_bessel_i(N n, T z) noexcept; | ||
| //! } | ||
| //! @endcode | ||
| //! | ||
| //! **Parameters** | ||
| //! | ||
| //! * `nu`: order of the function. | ||
| //! * `z`: Value to process. | ||
| //! | ||
| //! **Return value** | ||
| //! | ||
| //! * returns \f$I_\nu(z)\f$. | ||
| //! | ||
| //! @groupheader{Example} | ||
| //! | ||
| //! @godbolt{doc/cyl_bessel_i.cpp} | ||
| //! @} | ||
| //====================================================================================================================== | ||
| inline constexpr tags::callable_cyl_bessel_i cyl_bessel_i = {}; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,97 @@ | ||
| //====================================================================================================================== | ||
| /* | ||
| Kyosu - Complex Without Complexes | ||
| Copyright: KYOSU Contributors & Maintainers | ||
| SPDX-License-Identifier: BSL-1.0 | ||
| */ | ||
| //====================================================================================================================== | ||
| #pragma once | ||
|
|
||
| #include <kyosu/details/invoke.hpp> | ||
| #include <eve/module/bessel.hpp> | ||
|
|
||
| namespace kyosu::tags | ||
| { | ||
| struct callable_cyl_bessel_ik: eve::elementwise | ||
| { | ||
| using callable_tag_type = callable_cyl_bessel_ik; | ||
|
|
||
| KYOSU_DEFERS_CALLABLE(cyl_bessel_ik_); | ||
|
|
||
| template<eve::floating_scalar_value N, eve::floating_ordered_value T, typename R> | ||
| static KYOSU_FORCEINLINE auto deferred_call(auto, N nu, T const& v, R& js, R& ys) noexcept | ||
| requires(concepts::complex<decltype(js[0])> && concepts::complex<decltype(ys[0])>) | ||
| { | ||
| auto fnu = callable_cyl_bessel_ik{}; | ||
| return fnu(nu, complex(v), js, ys); | ||
| } | ||
|
|
||
| template<typename N, typename T, typename R> | ||
| KYOSU_FORCEINLINE auto operator()(N const & target0, T const& target1, R& output1, R& output2) const noexcept | ||
| -> decltype(eve::tag_invoke(*this, target0, target1, output1, output2)) | ||
| { | ||
| return eve::tag_invoke(*this, target0, target1, output1, output2); | ||
| } | ||
|
|
||
| template<typename... T> | ||
| eve::unsupported_call<callable_cyl_bessel_ik(T&&...)> operator()(T&&... x) const | ||
| requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete; | ||
| }; | ||
| } | ||
|
|
||
| namespace kyosu | ||
| { | ||
| //====================================================================================================================== | ||
| //! @addtogroup functions | ||
| //! @{ | ||
| //! @var cyl_bessel_ikr | ||
| //! @brief Computes the Bessel functions of the first kind J and Y, | ||
| //! \f$ J_{\nu}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+\nu +1)}} | ||
| //! {\left({x \over 2}\right)}^{2p+\nu }\f$ | ||
| //! extended to the complex plane. | ||
| //! | ||
| //! It is the solution of \f$ x^{2}y''+xy'+(x^2-\nu^2)y=0\f$ for which | ||
| //! \f$ y(0) = 0\f$ if \f$\nu \ne 0\f$ else \f$1\f$. | ||
| //! | ||
| //! @code | ||
| //! #include <kyosu/functions.hpp> | ||
| //! @endcode | ||
| //! | ||
| //! @groupheader{Callable Signatures} | ||
| //! | ||
| //! @code | ||
| //! namespace kyosu | ||
| //! { | ||
| //! template<eve::floating_scalar_ordered_value N, eve::floating_ordered_value T, complexRange R> | ||
| //! constexpr auto cyl_bessel_ikr(N nu, T z, R& js, R& ys) noexcept; | ||
| //! | ||
| //! template<eve::floating_scalar_ordered_value N, conceots::kyosu::complex Z, complexRange R> | ||
| //! constexpr T cyl_bessel_ikr(N n, Z z, R& js, R& ys) noexcept; | ||
| //! } | ||
| //! @endcode | ||
| //! | ||
| //! **Parameters** | ||
| //! | ||
| //! * `nu`: scalar order of the function not necessarily integral. | ||
| //! * `z`: Value to process. | ||
| //! * `js: range able to contain int(nu)+1 complex values (of type complex_t<T> or Z respectively) | ||
| //! * `ys: range able to contain int(nu)+1 complex values (of type complex_t<T> or Z respectively) | ||
| //! | ||
| //! **Return value** | ||
| //! | ||
| //! * returns the kumi pair \f$\{J_\nu(z), Y_\nu(z)\}f$ of complex values. | ||
| //! | ||
| //! *Ouput values | ||
| //! | ||
| //! * on output js contains the values of \f$((J_{\nu_0+i})_{i = 0\cdot n}\f$ | ||
| //! * on output ys contains the values of \f$((Y_{\nu_0+i})_{i = 0\cdot n}\f$ | ||
| //! | ||
| //! where \f$\nu_0\f$ is the fractional part of \f$\nu\f$ (\f$0 \le\nu_0\lt 0\f$ and \f$\nu = \nu_0+n\f$. | ||
| //! | ||
| //! @groupheader{Example} | ||
| //! | ||
| //! @godbolt{doc/cyl_bessel_ikr.cpp} | ||
| //! @} | ||
| //====================================================================================================================== | ||
| inline constexpr tags::callable_cyl_bessel_ik cyl_bessel_ik = {}; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,96 @@ | ||
| //====================================================================================================================== | ||
| /* | ||
| Kyosu - Complex Without Complexes | ||
| Copyright: KYOSU Contributors & Maintainers | ||
| SPDX-License-Identifier: BSL-1.0 | ||
| */ | ||
| //====================================================================================================================== | ||
| #pragma once | ||
|
|
||
| #include <kyosu/details/invoke.hpp> | ||
| #include <eve/module/bessel.hpp> | ||
|
|
||
| namespace kyosu::tags | ||
| { | ||
| struct callable_cyl_bessel_k: eve::elementwise | ||
| { | ||
| using callable_tag_type = callable_cyl_bessel_k; | ||
|
|
||
| KYOSU_DEFERS_CALLABLE(cyl_bessel_k_); | ||
|
|
||
| template<eve::floating_scalar_value N, eve::floating_ordered_value T> | ||
| static KYOSU_FORCEINLINE auto deferred_call(auto, N nu, T const& v) noexcept | ||
| { | ||
| auto fnu = callable_cyl_bessel_k{}; | ||
| return fnu(nu, complex(v)); | ||
| } | ||
|
|
||
|
|
||
| template<eve::floating_scalar_value N, eve::floating_ordered_value T, typename R> | ||
| static KYOSU_FORCEINLINE auto deferred_call(auto, N nu, T const& v, R& ks) noexcept | ||
| { | ||
| auto fnu = callable_cyl_bessel_k{}; | ||
| return fnu(nu, complex(v), ks); | ||
| } | ||
|
|
||
| template<typename N, typename T> | ||
| KYOSU_FORCEINLINE auto operator()(N const & target0, T const& target1) const noexcept | ||
| -> decltype(eve::tag_invoke(*this, target0, target1)) | ||
| { | ||
| return eve::tag_invoke(*this, target0, target1); | ||
| } | ||
|
|
||
| template<typename N, typename T, typename R> | ||
| KYOSU_FORCEINLINE auto operator()(N const & target0, T const& target1, R & out0) const noexcept | ||
| -> decltype(eve::tag_invoke(*this, target0, target1, out0)) | ||
| { | ||
| return eve::tag_invoke(*this, target0, target1, out0); | ||
| } | ||
|
|
||
| template<typename... T> | ||
| eve::unsupported_call<callable_cyl_bessel_k(T&&...)> operator()(T&&... x) const | ||
| requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete; | ||
| }; | ||
| } | ||
|
|
||
| namespace kyosu | ||
| { | ||
| //====================================================================================================================== | ||
| //! @addtogroup functions | ||
| //! @{ | ||
| //! @var cyl_bessel_k | ||
| //! @brief Computes the Modified Bessel functions of the second kind. | ||
| //! | ||
| //! @code | ||
| //! #include <kyosu/functions.hpp> | ||
| //! @endcode | ||
| //! | ||
| //! @groupheader{Callable Signatures} | ||
| //! | ||
| //! @code | ||
| //! namespace kyosu | ||
| //! { | ||
| //! template<eve::floating_ordered_value, kyosu::concepts::cayley_dickson T> | ||
| //! constexpr auto cyl_bessel_k(N nu, T z) noexcept; | ||
| //! | ||
| //! template<eve::floating_ordered_value, eve::floating_ordered_value T> | ||
| //! constexpr T cyl_bessel_k(N n, T z) noexcept; | ||
| //! } | ||
| //! @endcode | ||
| //! | ||
| //! **Parameters** | ||
| //! | ||
| //! * `nu`: order of the function. | ||
| //! * `z`: Value to process. | ||
| //! | ||
| //! **Return value** | ||
| //! | ||
| //! * returns \f$K_\nu(z)\f$. | ||
| //! | ||
| //! @groupheader{Example} | ||
| //! | ||
| //! @godbolt{doc/cyl_bessel_k.cpp} | ||
| //! @} | ||
| //====================================================================================================================== | ||
| inline constexpr tags::callable_cyl_bessel_k cyl_bessel_k = {}; | ||
| } |
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