Eigen/src/Core/GlobalFunctions.h - eigen - Git at Google

 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2010-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
 // Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

 #ifndef EIGEN_GLOBAL_FUNCTIONS_H
 #define EIGEN_GLOBAL_FUNCTIONS_H

 #ifdef EIGEN_PARSED_BY_DOXYGEN

 #define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \
   /** \returns an expression of the coefficient-wise DOC_OP of \a x

     DOC_DETAILS

     \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_##NAME">Math functions</a>, class CwiseUnaryOp
     */ \
   template<typename Derived> \
   inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
   NAME(const Eigen::ArrayBase<Derived>& x);

 #else

 #define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \
   template<typename Derived> \
   inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
   (NAME)(const Eigen::ArrayBase<Derived>& x) { \
     return Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived>(x.derived()); \
   }

 #endif // EIGEN_PARSED_BY_DOXYGEN

 #define EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(NAME,FUNCTOR) \
   \
   template<typename Derived> \
   struct NAME##_retval<ArrayBase<Derived> > \
   { \
     typedef const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> type; \
   }; \
   template<typename Derived> \
   struct NAME##_impl<ArrayBase<Derived> > \
   { \
     static inline typename NAME##_retval<ArrayBase<Derived> >::type run(const Eigen::ArrayBase<Derived>& x) \
     { \
       return typename NAME##_retval<ArrayBase<Derived> >::type(x.derived()); \
     } \
   };

 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"

 namespace Eigen
 {
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real,scalar_real_op,real part,\sa ArrayBase::real)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag,scalar_imag_op,imaginary part,\sa ArrayBase::imag)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(conj,scalar_conjugate_op,complex conjugate,\sa ArrayBase::conjugate)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(inverse,scalar_inverse_op,inverse,\sa ArrayBase::inverse)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sin,scalar_sin_op,sine,\sa ArrayBase::sin)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cos,scalar_cos_op,cosine,\sa ArrayBase::cos)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tan,scalar_tan_op,tangent,\sa ArrayBase::tan)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atan,scalar_atan_op,arc-tangent,\sa ArrayBase::atan)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asin,scalar_asin_op,arc-sine,\sa ArrayBase::asin)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acos,scalar_acos_op,arc-consine,\sa ArrayBase::acos)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sinh,scalar_sinh_op,hyperbolic sine,\sa ArrayBase::sinh)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cosh,scalar_cosh_op,hyperbolic cosine,\sa ArrayBase::cosh)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tanh,scalar_tanh_op,hyperbolic tangent,\sa ArrayBase::tanh)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asinh,scalar_asinh_op,inverse hyperbolic sine,\sa ArrayBase::asinh)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acosh,scalar_acosh_op,inverse hyperbolic cosine,\sa ArrayBase::acosh)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atanh,scalar_atanh_op,inverse hyperbolic tangent,\sa ArrayBase::atanh)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(logistic,scalar_logistic_op,logistic function,\sa ArrayBase::logistic)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(lgamma,scalar_lgamma_op,natural logarithm of the gamma function,\sa ArrayBase::lgamma)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(digamma,scalar_digamma_op,derivative of lgamma,\sa ArrayBase::digamma)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf,scalar_erf_op,error function,\sa ArrayBase::erf)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc,scalar_erfc_op,complement error function,\sa ArrayBase::erfc)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ndtri,scalar_ndtri_op,inverse normal distribution function,\sa ArrayBase::ndtri)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op,exponential,\sa ArrayBase::exp)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(expm1,scalar_expm1_op,exponential of a value minus 1,\sa ArrayBase::expm1)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op,natural logarithm,\sa Eigen::log10 DOXCOMMA ArrayBase::log)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log1p,scalar_log1p_op,natural logarithm of 1 plus the value,\sa ArrayBase::log1p)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10,scalar_log10_op,base 10 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log10)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log2,scalar_log2_op,base 2 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log2)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs,scalar_abs_op,absolute value,\sa ArrayBase::abs DOXCOMMA MatrixBase::cwiseAbs)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs2,scalar_abs2_op,squared absolute value,\sa ArrayBase::abs2 DOXCOMMA MatrixBase::cwiseAbs2)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(arg,scalar_arg_op,complex argument,\sa ArrayBase::arg DOXCOMMA MatrixBase::cwiseArg)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(carg, scalar_carg_op, complex argument, \sa ArrayBase::carg DOXCOMMA MatrixBase::cwiseCArg)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op,square root,\sa ArrayBase::sqrt DOXCOMMA MatrixBase::cwiseSqrt)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rsqrt,scalar_rsqrt_op,reciprocal square root,\sa ArrayBase::rsqrt)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(square,scalar_square_op,square (power 2),\sa Eigen::abs2 DOXCOMMA Eigen::pow DOXCOMMA ArrayBase::square)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cube,scalar_cube_op,cube (power 3),\sa Eigen::pow DOXCOMMA ArrayBase::cube)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rint,scalar_rint_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(round,scalar_round_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(floor,scalar_floor_op,nearest integer not greater than the giben value,\sa Eigen::ceil DOXCOMMA ArrayBase::floor)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ceil,scalar_ceil_op,nearest integer not less than the giben value,\sa Eigen::floor DOXCOMMA ArrayBase::ceil)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isnan,scalar_isnan_op,not-a-number test,\sa Eigen::isinf DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isnan)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isinf,scalar_isinf_op,infinite value test,\sa Eigen::isnan DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isinf)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isfinite,scalar_isfinite_op,finite value test,\sa Eigen::isinf DOXCOMMA Eigen::isnan DOXCOMMA ArrayBase::isfinite)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sign,scalar_sign_op,sign (or 0),\sa ArrayBase::sign)

   template <typename Derived, typename ScalarExponent>
   using GlobalUnaryPowReturnType = std::enable_if_t<
       !internal::is_arithmetic<typename NumTraits<Derived>::Real>::value &&
           internal::is_arithmetic<typename NumTraits<ScalarExponent>::Real>::value,
       CwiseUnaryOp<internal::scalar_unary_pow_op<typename Derived::Scalar, ScalarExponent>, const Derived> >;

   /** \returns an expression of the coefficient-wise power of \a x to the given constant \a exponent.
    *
    * \tparam ScalarExponent is the scalar type of \a exponent. It must be compatible with the scalar type of the given
    * expression (\c Derived::Scalar).
    *
    * \sa ArrayBase::pow()
    *
    * \relates ArrayBase
    */
 #ifdef EIGEN_PARSED_BY_DOXYGEN
   template <typename Derived, typename ScalarExponent>
   EIGEN_DEVICE_FUNC inline const GlobalUnaryPowReturnType<Derived, ScalarExponent> pow(
       const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent);
 #else
   template <typename Derived, typename ScalarExponent>
   EIGEN_DEVICE_FUNC inline const GlobalUnaryPowReturnType<Derived, ScalarExponent> pow(
       const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent) {
     return GlobalUnaryPowReturnType<Derived, ScalarExponent>(
         x.derived(), internal::scalar_unary_pow_op<typename Derived::Scalar, ScalarExponent>(exponent));
   }
 #endif

   /** \returns an expression of the coefficient-wise power of \a x to the given array of \a exponents.
     *
     * This function computes the coefficient-wise power.
     *
     * Example: \include Cwise_array_power_array.cpp
     * Output: \verbinclude Cwise_array_power_array.out
     *
     * \sa ArrayBase::pow()
     *
     * \relates ArrayBase
     */
   template<typename Derived,typename ExponentDerived>
   inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>
   pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<ExponentDerived>& exponents)
   {
     return Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>(
       x.derived(),
       exponents.derived()
     );
   }

   /** \returns an expression of the coefficient-wise power of the scalar \a x to the given array of \a exponents.
     *
     * This function computes the coefficient-wise power between a scalar and an array of exponents.
     *
     * \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar).
     *
     * Example: \include Cwise_scalar_power_array.cpp
     * Output: \verbinclude Cwise_scalar_power_array.out
     *
     * \sa ArrayBase::pow()
     *
     * \relates ArrayBase
     */
 #ifdef EIGEN_PARSED_BY_DOXYGEN
   template<typename Scalar,typename Derived>
   inline const CwiseBinaryOp<internal::scalar_pow_op<Scalar,Derived::Scalar>,Constant<Scalar>,Derived>
   pow(const Scalar& x,const Eigen::ArrayBase<Derived>& x);
 #else
   template <typename Scalar, typename Derived>
   EIGEN_DEVICE_FUNC inline
     const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg<typename Derived::Scalar
                                                  EIGEN_COMMA Scalar EIGEN_COMMA
                                                  EIGEN_SCALAR_BINARY_SUPPORTED(pow,Scalar,typename Derived::Scalar)>::type,Derived,pow)
   pow(const Scalar& x, const Eigen::ArrayBase<Derived>& exponents) {
     typedef typename internal::promote_scalar_arg<typename Derived::Scalar,Scalar,
                                                   EIGEN_SCALAR_BINARY_SUPPORTED(pow,Scalar,typename Derived::Scalar)>::type PromotedScalar;
     return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedScalar,Derived,pow)(
            typename internal::plain_constant_type<Derived,PromotedScalar>::type(exponents.derived().rows(), exponents.derived().cols(), internal::scalar_constant_op<PromotedScalar>(x)), exponents.derived());
   }
 #endif

   /** \returns an expression of the coefficient-wise atan2(\a x, \a y). \a x and \a y must be of the same type.
     *
     * This function computes the coefficient-wise atan2().
     *
     * \sa ArrayBase::atan2()
     *
     * \relates ArrayBase
     */
   template <typename LhsDerived, typename RhsDerived>
   inline const std::enable_if_t<
       std::is_same<typename LhsDerived::Scalar, typename RhsDerived::Scalar>::value,
       Eigen::CwiseBinaryOp<Eigen::internal::scalar_atan2_op<typename LhsDerived::Scalar, typename RhsDerived::Scalar>, const LhsDerived, const RhsDerived>
       >
   atan2(const Eigen::ArrayBase<LhsDerived>& x, const Eigen::ArrayBase<RhsDerived>& exponents) {
     return Eigen::CwiseBinaryOp<Eigen::internal::scalar_atan2_op<typename LhsDerived::Scalar, typename RhsDerived::Scalar>, const LhsDerived, const RhsDerived>(
       x.derived(),
       exponents.derived()
     );
   }

   namespace internal
   {
     EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)
     EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(imag,scalar_imag_op)
     EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs2,scalar_abs2_op)
   }
 }

 // TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random, internal::isApprox...)

 #endif // EIGEN_GLOBAL_FUNCTIONS_H
	// This file is part of Eigen, a lightweight C++ template library
	// for linear algebra.
	//
	// Copyright (C) 2010-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
	// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
	//
	// This Source Code Form is subject to the terms of the Mozilla
	// Public License v. 2.0. If a copy of the MPL was not distributed
	// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

	#ifndef EIGEN_GLOBAL_FUNCTIONS_H
	#define EIGEN_GLOBAL_FUNCTIONS_H

	#ifdef EIGEN_PARSED_BY_DOXYGEN

	#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \
	/** \returns an expression of the coefficient-wise DOC_OP of \a x

	DOC_DETAILS

	\sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_##NAME">Math functions</a>, class CwiseUnaryOp
	*/ \
	template<typename Derived> \
	inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
	NAME(const Eigen::ArrayBase<Derived>& x);

	#else

	#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \
	template<typename Derived> \
	inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
	(NAME)(const Eigen::ArrayBase<Derived>& x) { \
	return Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived>(x.derived()); \
	}

	#endif // EIGEN_PARSED_BY_DOXYGEN

	#define EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(NAME,FUNCTOR) \
	\
	template<typename Derived> \
	struct NAME##_retval<ArrayBase<Derived> > \
	{ \
	typedef const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> type; \
	}; \
	template<typename Derived> \
	struct NAME##_impl<ArrayBase<Derived> > \
	{ \
	static inline typename NAME##_retval<ArrayBase<Derived> >::type run(const Eigen::ArrayBase<Derived>& x) \
	{ \
	return typename NAME##_retval<ArrayBase<Derived> >::type(x.derived()); \
	} \
	};

	// IWYU pragma: private
	#include "./InternalHeaderCheck.h"

	namespace Eigen
	{
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real,scalar_real_op,real part,\sa ArrayBase::real)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag,scalar_imag_op,imaginary part,\sa ArrayBase::imag)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(conj,scalar_conjugate_op,complex conjugate,\sa ArrayBase::conjugate)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(inverse,scalar_inverse_op,inverse,\sa ArrayBase::inverse)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sin,scalar_sin_op,sine,\sa ArrayBase::sin)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cos,scalar_cos_op,cosine,\sa ArrayBase::cos)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tan,scalar_tan_op,tangent,\sa ArrayBase::tan)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atan,scalar_atan_op,arc-tangent,\sa ArrayBase::atan)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asin,scalar_asin_op,arc-sine,\sa ArrayBase::asin)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acos,scalar_acos_op,arc-consine,\sa ArrayBase::acos)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sinh,scalar_sinh_op,hyperbolic sine,\sa ArrayBase::sinh)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cosh,scalar_cosh_op,hyperbolic cosine,\sa ArrayBase::cosh)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tanh,scalar_tanh_op,hyperbolic tangent,\sa ArrayBase::tanh)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asinh,scalar_asinh_op,inverse hyperbolic sine,\sa ArrayBase::asinh)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acosh,scalar_acosh_op,inverse hyperbolic cosine,\sa ArrayBase::acosh)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atanh,scalar_atanh_op,inverse hyperbolic tangent,\sa ArrayBase::atanh)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(logistic,scalar_logistic_op,logistic function,\sa ArrayBase::logistic)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(lgamma,scalar_lgamma_op,natural logarithm of the gamma function,\sa ArrayBase::lgamma)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(digamma,scalar_digamma_op,derivative of lgamma,\sa ArrayBase::digamma)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf,scalar_erf_op,error function,\sa ArrayBase::erf)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc,scalar_erfc_op,complement error function,\sa ArrayBase::erfc)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ndtri,scalar_ndtri_op,inverse normal distribution function,\sa ArrayBase::ndtri)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op,exponential,\sa ArrayBase::exp)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(expm1,scalar_expm1_op,exponential of a value minus 1,\sa ArrayBase::expm1)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op,natural logarithm,\sa Eigen::log10 DOXCOMMA ArrayBase::log)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log1p,scalar_log1p_op,natural logarithm of 1 plus the value,\sa ArrayBase::log1p)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10,scalar_log10_op,base 10 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log10)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log2,scalar_log2_op,base 2 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log2)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs,scalar_abs_op,absolute value,\sa ArrayBase::abs DOXCOMMA MatrixBase::cwiseAbs)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs2,scalar_abs2_op,squared absolute value,\sa ArrayBase::abs2 DOXCOMMA MatrixBase::cwiseAbs2)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(arg,scalar_arg_op,complex argument,\sa ArrayBase::arg DOXCOMMA MatrixBase::cwiseArg)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(carg, scalar_carg_op, complex argument, \sa ArrayBase::carg DOXCOMMA MatrixBase::cwiseCArg)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op,square root,\sa ArrayBase::sqrt DOXCOMMA MatrixBase::cwiseSqrt)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rsqrt,scalar_rsqrt_op,reciprocal square root,\sa ArrayBase::rsqrt)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(square,scalar_square_op,square (power 2),\sa Eigen::abs2 DOXCOMMA Eigen::pow DOXCOMMA ArrayBase::square)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cube,scalar_cube_op,cube (power 3),\sa Eigen::pow DOXCOMMA ArrayBase::cube)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rint,scalar_rint_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(round,scalar_round_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(floor,scalar_floor_op,nearest integer not greater than the giben value,\sa Eigen::ceil DOXCOMMA ArrayBase::floor)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ceil,scalar_ceil_op,nearest integer not less than the giben value,\sa Eigen::floor DOXCOMMA ArrayBase::ceil)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isnan,scalar_isnan_op,not-a-number test,\sa Eigen::isinf DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isnan)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isinf,scalar_isinf_op,infinite value test,\sa Eigen::isnan DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isinf)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isfinite,scalar_isfinite_op,finite value test,\sa Eigen::isinf DOXCOMMA Eigen::isnan DOXCOMMA ArrayBase::isfinite)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sign,scalar_sign_op,sign (or 0),\sa ArrayBase::sign)

	template <typename Derived, typename ScalarExponent>
	using GlobalUnaryPowReturnType = std::enable_if_t<
	!internal::is_arithmetic<typename NumTraits<Derived>::Real>::value &&
	internal::is_arithmetic<typename NumTraits<ScalarExponent>::Real>::value,
	CwiseUnaryOp<internal::scalar_unary_pow_op<typename Derived::Scalar, ScalarExponent>, const Derived> >;

	/** \returns an expression of the coefficient-wise power of \a x to the given constant \a exponent.
	*
	* \tparam ScalarExponent is the scalar type of \a exponent. It must be compatible with the scalar type of the given
	* expression (\c Derived::Scalar).
	*
	* \sa ArrayBase::pow()
	*
	* \relates ArrayBase
	*/
	#ifdef EIGEN_PARSED_BY_DOXYGEN
	template <typename Derived, typename ScalarExponent>
	EIGEN_DEVICE_FUNC inline const GlobalUnaryPowReturnType<Derived, ScalarExponent> pow(
	const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent);
	#else
	template <typename Derived, typename ScalarExponent>
	EIGEN_DEVICE_FUNC inline const GlobalUnaryPowReturnType<Derived, ScalarExponent> pow(
	const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent) {
	return GlobalUnaryPowReturnType<Derived, ScalarExponent>(
	x.derived(), internal::scalar_unary_pow_op<typename Derived::Scalar, ScalarExponent>(exponent));
	}
	#endif

	/** \returns an expression of the coefficient-wise power of \a x to the given array of \a exponents.
	*
	* This function computes the coefficient-wise power.
	*
	* Example: \include Cwise_array_power_array.cpp
	* Output: \verbinclude Cwise_array_power_array.out
	*
	* \sa ArrayBase::pow()
	*
	* \relates ArrayBase
	*/
	template<typename Derived,typename ExponentDerived>
	inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>
	pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<ExponentDerived>& exponents)
	{
	return Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>(
	x.derived(),
	exponents.derived()
	);
	}

	/** \returns an expression of the coefficient-wise power of the scalar \a x to the given array of \a exponents.
	*
	* This function computes the coefficient-wise power between a scalar and an array of exponents.
	*
	* \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar).
	*
	* Example: \include Cwise_scalar_power_array.cpp
	* Output: \verbinclude Cwise_scalar_power_array.out
	*
	* \sa ArrayBase::pow()
	*
	* \relates ArrayBase
	*/
	#ifdef EIGEN_PARSED_BY_DOXYGEN
	template<typename Scalar,typename Derived>
	inline const CwiseBinaryOp<internal::scalar_pow_op<Scalar,Derived::Scalar>,Constant<Scalar>,Derived>
	pow(const Scalar& x,const Eigen::ArrayBase<Derived>& x);
	#else
	template <typename Scalar, typename Derived>
	EIGEN_DEVICE_FUNC inline
	const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg<typename Derived::Scalar
	EIGEN_COMMA Scalar EIGEN_COMMA
	EIGEN_SCALAR_BINARY_SUPPORTED(pow,Scalar,typename Derived::Scalar)>::type,Derived,pow)
	pow(const Scalar& x, const Eigen::ArrayBase<Derived>& exponents) {
	typedef typename internal::promote_scalar_arg<typename Derived::Scalar,Scalar,
	EIGEN_SCALAR_BINARY_SUPPORTED(pow,Scalar,typename Derived::Scalar)>::type PromotedScalar;
	return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedScalar,Derived,pow)(
	typename internal::plain_constant_type<Derived,PromotedScalar>::type(exponents.derived().rows(), exponents.derived().cols(), internal::scalar_constant_op<PromotedScalar>(x)), exponents.derived());
	}
	#endif

	/** \returns an expression of the coefficient-wise atan2(\a x, \a y). \a x and \a y must be of the same type.
	*
	* This function computes the coefficient-wise atan2().
	*
	* \sa ArrayBase::atan2()
	*
	* \relates ArrayBase
	*/
	template <typename LhsDerived, typename RhsDerived>
	inline const std::enable_if_t<
	std::is_same<typename LhsDerived::Scalar, typename RhsDerived::Scalar>::value,
	Eigen::CwiseBinaryOp<Eigen::internal::scalar_atan2_op<typename LhsDerived::Scalar, typename RhsDerived::Scalar>, const LhsDerived, const RhsDerived>
	>
	atan2(const Eigen::ArrayBase<LhsDerived>& x, const Eigen::ArrayBase<RhsDerived>& exponents) {
	return Eigen::CwiseBinaryOp<Eigen::internal::scalar_atan2_op<typename LhsDerived::Scalar, typename RhsDerived::Scalar>, const LhsDerived, const RhsDerived>(
	x.derived(),
	exponents.derived()
	);
	}

	namespace internal
	{
	EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)
	EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(imag,scalar_imag_op)
	EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs2,scalar_abs2_op)
	}
	}

	// TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random, internal::isApprox...)

	#endif // EIGEN_GLOBAL_FUNCTIONS_H