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Copy pathxcomplex.hpp
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264 lines (234 loc) · 8.23 KB
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/***************************************************************************
* Copyright (c) Johan Mabille, Sylvain Corlay and Wolf Vollprecht *
* Copyright (c) QuantStack *
* *
* Distributed under the terms of the BSD 3-Clause License. *
* *
* The full license is in the file LICENSE, distributed with this software. *
****************************************************************************/
#ifndef XTENSOR_COMPLEX_HPP
#define XTENSOR_COMPLEX_HPP
#include <type_traits>
#include <utility>
#include <xtl/xcomplex.hpp>
#include "../core/xexpression.hpp"
#include "../generators/xbuilder.hpp"
#include "../views/xoffset_view.hpp"
namespace xt
{
/**
* @defgroup xt_xcomplex Complex numbers
*
* Defined in ``xtensor/xcomplex.hpp``
*/
/******************************
* real and imag declarations *
******************************/
template <class E>
decltype(auto) real(E&& e) noexcept;
template <class E>
decltype(auto) imag(E&& e) noexcept;
/********************************
* real and imag implementation *
********************************/
namespace detail
{
template <bool iscomplex = true>
struct complex_helper
{
template <class E>
inline static auto real(E&& e) noexcept
{
using real_type = typename std::decay_t<E>::value_type::value_type;
return xoffset_view<xclosure_t<E>, real_type, 0>(std::forward<E>(e));
}
template <class E>
inline static auto imag(E&& e) noexcept
{
using real_type = typename std::decay_t<E>::value_type::value_type;
return xoffset_view<xclosure_t<E>, real_type, sizeof(real_type)>(std::forward<E>(e));
}
};
template <>
struct complex_helper<false>
{
template <class E>
inline static decltype(auto) real(E&& e) noexcept
{
return std::forward<E>(e);
}
template <class E>
inline static auto imag(E&& e) noexcept
{
return zeros<typename std::decay_t<E>::value_type>(e.shape());
}
};
template <bool isexpression = true>
struct complex_expression_helper
{
template <class E>
inline static decltype(auto) real(E&& e) noexcept
{
return detail::complex_helper<xtl::is_complex<typename std::decay_t<E>::value_type>::value>::real(
std::forward<E>(e)
);
}
template <class E>
inline static decltype(auto) imag(E&& e) noexcept
{
return detail::complex_helper<xtl::is_complex<typename std::decay_t<E>::value_type>::value>::imag(
std::forward<E>(e)
);
}
};
template <>
struct complex_expression_helper<false>
{
template <class E>
inline static decltype(auto) real(E&& e) noexcept
{
return xtl::forward_real(std::forward<E>(e));
}
template <class E>
inline static decltype(auto) imag(E&& e) noexcept
{
return xtl::forward_imag(std::forward<E>(e));
}
};
}
/**
* Return an xt::xexpression representing the real part of the given expression.
*
* The returned expression either hold a const reference to @p e or a copy
* depending on whether @p e is an lvalue or an rvalue.
*
* @ingroup xt_xcomplex
* @tparam e The xt::xexpression
*/
template <class E>
inline decltype(auto) real(E&& e) noexcept
{
return detail::complex_expression_helper<is_xexpression<std::decay_t<E>>::value>::real(std::forward<E>(e
));
}
/**
* Return an xt::xexpression representing the imaginary part of the given expression.
*
* The returned expression either hold a const reference to @p e or a copy
* depending on whether @p e is an lvalue or an rvalue.
*
* @ingroup xt_xcomplex
* @tparam e The xt::xexpression
*/
template <class E>
inline decltype(auto) imag(E&& e) noexcept
{
return detail::complex_expression_helper<is_xexpression<std::decay_t<E>>::value>::imag(std::forward<E>(e
));
}
#define UNARY_COMPLEX_FUNCTOR(NS, NAME) \
struct NAME##_fun \
{ \
template <class T> \
constexpr auto operator()(const T& t) const \
{ \
using NS::NAME; \
return NAME(t); \
} \
\
template <class B> \
constexpr auto simd_apply(const B& t) const \
{ \
using NS::NAME; \
return NAME(t); \
} \
}
namespace math
{
namespace detail
{
template <class T>
constexpr std::complex<T> conj_impl(const std::complex<T>& c)
{
return std::complex<T>(c.real(), -c.imag());
}
template <class T>
constexpr std::complex<T> conj_impl(const T& real)
{
return std::complex<T>(real, 0);
}
#ifdef XTENSOR_USE_XSIMD
template <class T, class A>
xsimd::complex_batch_type_t<xsimd::batch<T, A>> conj_impl(const xsimd::batch<T, A>& z)
{
return xsimd::conj(z);
}
#endif
}
UNARY_COMPLEX_FUNCTOR(std, norm);
UNARY_COMPLEX_FUNCTOR(std, arg);
UNARY_COMPLEX_FUNCTOR(detail, conj_impl);
}
#undef UNARY_COMPLEX_FUNCTOR
/**
* Return an xt::xfunction evaluating to the complex conjugate of the given expression.
*
* @ingroup xt_xcomplex
* @param e the xt::xexpression
*/
template <class E>
inline auto conj(E&& e) noexcept
{
using functor = math::conj_impl_fun;
using type = xfunction<functor, const_xclosure_t<E>>;
return type(functor(), std::forward<E>(e));
}
/**
* Calculates the phase angle (in radians) elementwise for the complex numbers in @p e.
*
* @ingroup xt_xcomplex
* @param e the xt::xexpression
*/
template <class E>
inline auto arg(E&& e) noexcept
{
using functor = math::arg_fun;
using type = xfunction<functor, const_xclosure_t<E>>;
return type(functor(), std::forward<E>(e));
}
/**
* Calculates the phase angle elementwise for the complex numbers in @p e.
*
* Note that this function might be slightly less performant than xt::arg.
*
* @ingroup xt_xcomplex
* @param e the xt::xexpression
* @param deg calculate angle in degrees instead of radians
*/
template <class E>
inline auto angle(E&& e, bool deg = false) noexcept
{
using value_type = xtl::complex_value_type_t<typename std::decay_t<E>::value_type>;
value_type multiplier = 1.0;
if (deg)
{
multiplier = value_type(180) / numeric_constants<value_type>::PI;
}
return arg(std::forward<E>(e)) * std::move(multiplier);
}
/**
* Calculates the squared magnitude elementwise for the complex numbers in @p e.
*
* Equivalent to ``xt::pow(xt::real(e), 2) + xt::pow(xt::imag(e), 2)``.
* @ingroup xt_xcomplex
* @param e the xt::xexpression
*/
template <class E>
inline auto norm(E&& e) noexcept
{
using functor = math::norm_fun;
using type = xfunction<functor, const_xclosure_t<E>>;
return type(functor(), std::forward<E>(e));
}
}
#endif