Eigen/src/Core/GlobalFunctions.h - mirror - 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()); \
     } \
   };

 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(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(exp,scalar_exp_op,exponential,\sa ArrayBase::exp)
   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::log)
   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)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op,square root,\sa ArrayBase::sqrt DOXCOMMA MatrixBase::cwiseSqrt)
   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(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)

   /** \returns an expression of the coefficient-wise power of \a x to the given constant \a exponent.
     *
     * \sa ArrayBase::pow()
     */
   template<typename Derived>
   inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar>, const Derived>
   pow(const Eigen::ArrayBase<Derived>& x, const typename Derived::Scalar& exponent) {
     return x.derived().pow(exponent);
   }

   /** \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()
     */
   template<typename Derived,typename ExponentDerived>
   inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_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_binary_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.
     * Beaware that the scalar type of the input scalar \a x and the exponents \a exponents must be the same.
     *
     * Example: \include Cwise_scalar_power_array.cpp
     * Output: \verbinclude Cwise_scalar_power_array.out
     *
     * \sa ArrayBase::pow()
     */
   template<typename Derived>
   inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename Derived::Scalar>, const typename Derived::ConstantReturnType, const Derived>
   pow(const typename Derived::Scalar& x, const Eigen::ArrayBase<Derived>& exponents)
   {
     typename Derived::ConstantReturnType constant_x(exponents.rows(), exponents.cols(), x);
     return Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename Derived::Scalar>, const typename Derived::ConstantReturnType, const Derived>(
       constant_x,
       exponents.derived()
     );
   }

   /**
     * \brief Component-wise division of a scalar by array elements.
     **/
   template <typename Derived>
   inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>
     operator/(const typename Derived::Scalar& s, const Eigen::ArrayBase<Derived>& a)
   {
     return Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>(
       a.derived(),
       Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>(s)
     );
   }

   /** \cpp11 \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays.
     *
     * This function computes the coefficient-wise incomplete gamma function.
     *
     * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
     * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar
     * type T to be supported.
     *
     * \sa Eigen::igammac(), Eigen::lgamma()
     */
   template<typename Derived,typename ExponentDerived>
   inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
   igamma(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x)
   {
     return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
       a.derived(),
       x.derived()
     );
   }

   /** \cpp11 \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays.
     *
     * This function computes the coefficient-wise complementary incomplete gamma function.
     *
     * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
     * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar
     * type T to be supported.
     *
     * \sa Eigen::igamma(), Eigen::lgamma()
     */
   template<typename Derived,typename ExponentDerived>
   inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
   igammac(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x)
   {
     return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
       a.derived(),
       x.derived()
     );
   }

   /** \cpp11 \returns an expression of the coefficient-wise polygamma(\a n, \a x) to the given arrays.
     *
     * It returns the \a n -th derivative of the digamma(psi) evaluated at \c x.
     *
     * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
     * or float/double in non c++11 mode, the user has to provide implementations of polygamma(T,T) for any scalar
     * type T to be supported.
     *
     * \sa Eigen::digamma()
     */
   // * \warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x)
   // * \sa ArrayBase::polygamma()
   template<typename DerivedN,typename DerivedX>
   inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX>
   polygamma(const Eigen::ArrayBase<DerivedN>& n, const Eigen::ArrayBase<DerivedX>& x)
   {
     return Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX>(
       n.derived(),
       x.derived()
     );
   }

   /** \cpp11 \returns an expression of the coefficient-wise betainc(\a x, \a a, \a b) to the given arrays.
     *
     * This function computes the regularized incomplete beta function (integral).
     *
     * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
     * or float/double in non c++11 mode, the user has to provide implementations of betainc(T,T,T) for any scalar
     * type T to be supported.
     *
     * \sa Eigen::betainc(), Eigen::lgamma()
     */
   template<typename ArgADerived, typename ArgBDerived, typename ArgXDerived>
   inline const Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived>
   betainc(const Eigen::ArrayBase<ArgADerived>& a, const Eigen::ArrayBase<ArgBDerived>& b, const Eigen::ArrayBase<ArgXDerived>& x)
   {
     return Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived>(
       a.derived(),
       b.derived(),
       x.derived()
     );
   }


   /** \returns an expression of the coefficient-wise zeta(\a x, \a q) to the given arrays.
     *
     * It returns the Riemann zeta function of two arguments \a x and \a q:
     *
     * \param x is the exposent, it must be > 1
     * \param q is the shift, it must be > 0
     *
     * \note This function supports only float and double scalar types. To support other scalar types, the user has
     * to provide implementations of zeta(T,T) for any scalar type T to be supported.
     *
     * \sa ArrayBase::zeta()
     */
   template<typename DerivedX,typename DerivedQ>
   inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>
   zeta(const Eigen::ArrayBase<DerivedX>& x, const Eigen::ArrayBase<DerivedQ>& q)
   {
     return Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>(
       x.derived(),
       q.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()); \
	} \
	};

	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(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(exp,scalar_exp_op,exponential,\sa ArrayBase::exp)
	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::log)
	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)
	EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op,square root,\sa ArrayBase::sqrt DOXCOMMA MatrixBase::cwiseSqrt)
	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(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)

	/** \returns an expression of the coefficient-wise power of \a x to the given constant \a exponent.
	*
	* \sa ArrayBase::pow()
	*/
	template<typename Derived>
	inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar>, const Derived>
	pow(const Eigen::ArrayBase<Derived>& x, const typename Derived::Scalar& exponent) {
	return x.derived().pow(exponent);
	}

	/** \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()
	*/
	template<typename Derived,typename ExponentDerived>
	inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_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_binary_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.
	* Beaware that the scalar type of the input scalar \a x and the exponents \a exponents must be the same.
	*
	* Example: \include Cwise_scalar_power_array.cpp
	* Output: \verbinclude Cwise_scalar_power_array.out
	*
	* \sa ArrayBase::pow()
	*/
	template<typename Derived>
	inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename Derived::Scalar>, const typename Derived::ConstantReturnType, const Derived>
	pow(const typename Derived::Scalar& x, const Eigen::ArrayBase<Derived>& exponents)
	{
	typename Derived::ConstantReturnType constant_x(exponents.rows(), exponents.cols(), x);
	return Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename Derived::Scalar>, const typename Derived::ConstantReturnType, const Derived>(
	constant_x,
	exponents.derived()
	);
	}

	/**
	* \brief Component-wise division of a scalar by array elements.
	**/
	template <typename Derived>
	inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>
	operator/(const typename Derived::Scalar& s, const Eigen::ArrayBase<Derived>& a)
	{
	return Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>(
	a.derived(),
	Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>(s)
	);
	}

	/** \cpp11 \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays.
	*
	* This function computes the coefficient-wise incomplete gamma function.
	*
	* \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
	* or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar
	* type T to be supported.
	*
	* \sa Eigen::igammac(), Eigen::lgamma()
	*/
	template<typename Derived,typename ExponentDerived>
	inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
	igamma(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x)
	{
	return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
	a.derived(),
	x.derived()
	);
	}

	/** \cpp11 \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays.
	*
	* This function computes the coefficient-wise complementary incomplete gamma function.
	*
	* \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
	* or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar
	* type T to be supported.
	*
	* \sa Eigen::igamma(), Eigen::lgamma()
	*/
	template<typename Derived,typename ExponentDerived>
	inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
	igammac(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x)
	{
	return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
	a.derived(),
	x.derived()
	);
	}

	/** \cpp11 \returns an expression of the coefficient-wise polygamma(\a n, \a x) to the given arrays.
	*
	* It returns the \a n -th derivative of the digamma(psi) evaluated at \c x.
	*
	* \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
	* or float/double in non c++11 mode, the user has to provide implementations of polygamma(T,T) for any scalar
	* type T to be supported.
	*
	* \sa Eigen::digamma()
	*/
	// * \warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x)
	// * \sa ArrayBase::polygamma()
	template<typename DerivedN,typename DerivedX>
	inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX>
	polygamma(const Eigen::ArrayBase<DerivedN>& n, const Eigen::ArrayBase<DerivedX>& x)
	{
	return Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX>(
	n.derived(),
	x.derived()
	);
	}

	/** \cpp11 \returns an expression of the coefficient-wise betainc(\a x, \a a, \a b) to the given arrays.
	*
	* This function computes the regularized incomplete beta function (integral).
	*
	* \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
	* or float/double in non c++11 mode, the user has to provide implementations of betainc(T,T,T) for any scalar
	* type T to be supported.
	*
	* \sa Eigen::betainc(), Eigen::lgamma()
	*/
	template<typename ArgADerived, typename ArgBDerived, typename ArgXDerived>
	inline const Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived>
	betainc(const Eigen::ArrayBase<ArgADerived>& a, const Eigen::ArrayBase<ArgBDerived>& b, const Eigen::ArrayBase<ArgXDerived>& x)
	{
	return Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived>(
	a.derived(),
	b.derived(),
	x.derived()
	);
	}


	/** \returns an expression of the coefficient-wise zeta(\a x, \a q) to the given arrays.
	*
	* It returns the Riemann zeta function of two arguments \a x and \a q:
	*
	* \param x is the exposent, it must be > 1
	* \param q is the shift, it must be > 0
	*
	* \note This function supports only float and double scalar types. To support other scalar types, the user has
	* to provide implementations of zeta(T,T) for any scalar type T to be supported.
	*
	* \sa ArrayBase::zeta()
	*/
	template<typename DerivedX,typename DerivedQ>
	inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>
	zeta(const Eigen::ArrayBase<DerivedX>& x, const Eigen::ArrayBase<DerivedQ>& q)
	{
	return Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>(
	x.derived(),
	q.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