Eigen/src/plugins/ArrayCwiseBinaryOps.h - eigen/fuchsia - Git at Google


 /** \returns an expression of the coefficient wise product of \c *this and \a other
   *
   * \sa MatrixBase::cwiseProduct
   */
 template<typename OtherDerived>
 EIGEN_DEVICE_FUNC
 EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)
 operator*(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
 {
   return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)(derived(), other.derived());
 }

 /** \returns an expression of the coefficient wise quotient of \c *this and \a other
   *
   * \sa MatrixBase::cwiseQuotient
   */
 template<typename OtherDerived>
 EIGEN_DEVICE_FUNC
 EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,typename OtherDerived::Scalar>, const Derived, const OtherDerived>
 operator/(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
 {
   return CwiseBinaryOp<internal::scalar_quotient_op<Scalar,typename OtherDerived::Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
 }

 /** \returns an expression of the coefficient-wise min of \c *this and \a other
   *
   * Example: \include Cwise_min.cpp
   * Output: \verbinclude Cwise_min.out
   *
   * \sa max()
   */
 EIGEN_MAKE_CWISE_BINARY_OP(min,min)

 /** \returns an expression of the coefficient-wise min of \c *this and scalar \a other
   *
   * \sa max()
   */
 EIGEN_DEVICE_FUNC
 EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived,
                                         const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >
 #ifdef EIGEN_PARSED_BY_DOXYGEN
 min
 #else
 (min)
 #endif
 (const Scalar &other) const
 {
   return (min)(Derived::PlainObject::Constant(rows(), cols(), other));
 }

 /** \returns an expression of the coefficient-wise max of \c *this and \a other
   *
   * Example: \include Cwise_max.cpp
   * Output: \verbinclude Cwise_max.out
   *
   * \sa min()
   */
 EIGEN_MAKE_CWISE_BINARY_OP(max,max)

 /** \returns an expression of the coefficient-wise max of \c *this and scalar \a other
   *
   * \sa min()
   */
 EIGEN_DEVICE_FUNC
 EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived,
                                         const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >
 #ifdef EIGEN_PARSED_BY_DOXYGEN
 max
 #else
 (max)
 #endif
 (const Scalar &other) const
 {
   return (max)(Derived::PlainObject::Constant(rows(), cols(), other));
 }

 /** \returns an expression of the coefficient-wise power of \c *this 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
   */
 EIGEN_MAKE_CWISE_BINARY_OP(pow,pow)

 #ifndef EIGEN_PARSED_BY_DOXYGEN
 EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(pow,pow)
 #else
 /** \returns an expression of the coefficients of \c *this rasied to the constant power \a exponent
   *
   * \tparam T is the scalar type of \a exponent. It must be compatible with the scalar type of the given expression.
   *
   * This function computes the coefficient-wise power. The function MatrixBase::pow() in the
   * unsupported module MatrixFunctions computes the matrix power.
   *
   * Example: \include Cwise_pow.cpp
   * Output: \verbinclude Cwise_pow.out
   *
   * \sa ArrayBase::pow(ArrayBase), square(), cube(), exp(), log()
   */
 template<typename T>
 const CwiseBinaryOp<internal::scalar_pow_op<Scalar,T>,Derived,Constant<T> > pow(const T& exponent) const;
 #endif


 // TODO code generating macros could be moved to Macros.h and could include generation of documentation
 #define EIGEN_MAKE_CWISE_COMP_OP(OP, COMPARATOR) \
 template<typename OtherDerived> \
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<Scalar, typename OtherDerived::Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived> \
 OP(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
 { \
   return CwiseBinaryOp<internal::scalar_cmp_op<Scalar, typename OtherDerived::Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived>(derived(), other.derived()); \
 }\
 typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> > Cmp ## COMPARATOR ## ReturnType; \
 typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar, internal::cmp_ ## COMPARATOR>, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject>, const Derived > RCmp ## COMPARATOR ## ReturnType; \
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Cmp ## COMPARATOR ## ReturnType \
 OP(const Scalar& s) const { \
   return this->OP(Derived::PlainObject::Constant(rows(), cols(), s)); \
 } \
 EIGEN_DEVICE_FUNC friend EIGEN_STRONG_INLINE const RCmp ## COMPARATOR ## ReturnType \
 OP(const Scalar& s, const Derived& d) { \
   return Derived::PlainObject::Constant(d.rows(), d.cols(), s).OP(d); \
 }

 #define EIGEN_MAKE_CWISE_COMP_R_OP(OP, R_OP, RCOMPARATOR) \
 template<typename OtherDerived> \
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<typename OtherDerived::Scalar, Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived> \
 OP(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
 { \
   return CwiseBinaryOp<internal::scalar_cmp_op<typename OtherDerived::Scalar, Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived>(other.derived(), derived()); \
 } \
 EIGEN_DEVICE_FUNC \
 inline const RCmp ## RCOMPARATOR ## ReturnType \
 OP(const Scalar& s) const { \
   return Derived::PlainObject::Constant(rows(), cols(), s).R_OP(*this); \
 } \
 friend inline const Cmp ## RCOMPARATOR ## ReturnType \
 OP(const Scalar& s, const Derived& d) { \
   return d.R_OP(Derived::PlainObject::Constant(d.rows(), d.cols(), s)); \
 }


 /** \returns an expression of the coefficient-wise \< operator of *this and \a other
   *
   * Example: \include Cwise_less.cpp
   * Output: \verbinclude Cwise_less.out
   *
   * \sa all(), any(), operator>(), operator<=()
   */
 EIGEN_MAKE_CWISE_COMP_OP(operator<, LT)

 /** \returns an expression of the coefficient-wise \<= operator of *this and \a other
   *
   * Example: \include Cwise_less_equal.cpp
   * Output: \verbinclude Cwise_less_equal.out
   *
   * \sa all(), any(), operator>=(), operator<()
   */
 EIGEN_MAKE_CWISE_COMP_OP(operator<=, LE)

 /** \returns an expression of the coefficient-wise \> operator of *this and \a other
   *
   * Example: \include Cwise_greater.cpp
   * Output: \verbinclude Cwise_greater.out
   *
   * \sa all(), any(), operator>=(), operator<()
   */
 EIGEN_MAKE_CWISE_COMP_R_OP(operator>, operator<, LT)

 /** \returns an expression of the coefficient-wise \>= operator of *this and \a other
   *
   * Example: \include Cwise_greater_equal.cpp
   * Output: \verbinclude Cwise_greater_equal.out
   *
   * \sa all(), any(), operator>(), operator<=()
   */
 EIGEN_MAKE_CWISE_COMP_R_OP(operator>=, operator<=, LE)

 /** \returns an expression of the coefficient-wise == operator of *this and \a other
   *
   * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
   * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
   * generally a far better idea to use a fuzzy comparison as provided by isApprox() and
   * isMuchSmallerThan().
   *
   * Example: \include Cwise_equal_equal.cpp
   * Output: \verbinclude Cwise_equal_equal.out
   *
   * \sa all(), any(), isApprox(), isMuchSmallerThan()
   */
 EIGEN_MAKE_CWISE_COMP_OP(operator==, EQ)

 /** \returns an expression of the coefficient-wise != operator of *this and \a other
   *
   * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
   * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
   * generally a far better idea to use a fuzzy comparison as provided by isApprox() and
   * isMuchSmallerThan().
   *
   * Example: \include Cwise_not_equal.cpp
   * Output: \verbinclude Cwise_not_equal.out
   *
   * \sa all(), any(), isApprox(), isMuchSmallerThan()
   */
 EIGEN_MAKE_CWISE_COMP_OP(operator!=, NEQ)


 #undef EIGEN_MAKE_CWISE_COMP_OP
 #undef EIGEN_MAKE_CWISE_COMP_R_OP

 // scalar addition
 #ifndef EIGEN_PARSED_BY_DOXYGEN
 EIGEN_MAKE_SCALAR_BINARY_OP(operator+,sum)
 #else
 /** \returns an expression of \c *this with each coeff incremented by the constant \a scalar
   *
   * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
   *
   * Example: \include Cwise_plus.cpp
   * Output: \verbinclude Cwise_plus.out
   *
   * \sa operator+=(), operator-()
   */
 template<typename T>
 const CwiseBinaryOp<internal::scalar_sum_op<Scalar,T>,Derived,Constant<T> > operator+(const T& scalar) const;
 /** \returns an expression of \a expr with each coeff incremented by the constant \a scalar
   *
   * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
   */
 template<typename T> friend
 const CwiseBinaryOp<internal::scalar_sum_op<T,Scalar>,Constant<T>,Derived> operator+(const T& scalar, const StorageBaseType& expr);
 #endif

 #ifndef EIGEN_PARSED_BY_DOXYGEN
 EIGEN_MAKE_SCALAR_BINARY_OP(operator-,difference)
 #else
 /** \returns an expression of \c *this with each coeff decremented by the constant \a scalar
   *
   * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
   *
   * Example: \include Cwise_minus.cpp
   * Output: \verbinclude Cwise_minus.out
   *
   * \sa operator+=(), operator-()
   */
 template<typename T>
 const CwiseBinaryOp<internal::scalar_difference_op<Scalar,T>,Derived,Constant<T> > operator-(const T& scalar) const;
 /** \returns an expression of the constant matrix of value \a scalar decremented by the coefficients of \a expr
   *
   * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
   */
 template<typename T> friend
 const CwiseBinaryOp<internal::scalar_difference_op<T,Scalar>,Constant<T>,Derived> operator-(const T& scalar, const StorageBaseType& expr);
 #endif


 #ifndef EIGEN_PARSED_BY_DOXYGEN
   EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(operator/,quotient)
 #else
   /**
     * \brief Component-wise division of the scalar \a s by array elements of \a a.
     *
     * \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).
     */
   template<typename T> friend
   inline const CwiseBinaryOp<internal::scalar_quotient_op<T,Scalar>,Constant<T>,Derived>
   operator/(const T& s,const StorageBaseType& a);
 #endif

 /** \returns an expression of the coefficient-wise ^ operator of *this and \a other
  *
  * \warning this operator is for expression of bool only.
  *
  * Example: \include Cwise_boolean_xor.cpp
  * Output: \verbinclude Cwise_boolean_xor.out
  *
  * \sa operator&&(), select()
  */
 template<typename OtherDerived>
 EIGEN_DEVICE_FUNC
 inline const CwiseBinaryOp<internal::scalar_boolean_xor_op, const Derived, const OtherDerived>
 operator^(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
 {
   EIGEN_STATIC_ASSERT((internal::is_same<bool,Scalar>::value && internal::is_same<bool,typename OtherDerived::Scalar>::value),
                       THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL);
   return CwiseBinaryOp<internal::scalar_boolean_xor_op, const Derived, const OtherDerived>(derived(),other.derived());
 }

 // NOTE disabled until we agree on argument order
 #if 0
 /** \cpp11 \returns an expression of the coefficient-wise polygamma function.
   *
   * \specialfunctions_module
   *
   * It returns the \a n -th derivative of the digamma(psi) evaluated at \c *this.
   *
   * \warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x)
   *
   * \sa Eigen::polygamma()
   */
 template<typename DerivedN>
 inline const CwiseBinaryOp<internal::scalar_polygamma_op<Scalar>, const DerivedN, const Derived>
 polygamma(const EIGEN_CURRENT_STORAGE_BASE_CLASS<DerivedN> &n) const
 {
   return CwiseBinaryOp<internal::scalar_polygamma_op<Scalar>, const DerivedN, const Derived>(n.derived(), this->derived());
 }
 #endif

 /** \returns an expression of the coefficient-wise zeta function.
   *
   * \specialfunctions_module
   *
   * It returns the Riemann zeta function of two arguments \c *this and \a q:
   *
   * \param *this 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.
   *
   * This method is an alias for zeta(*this,q);
   *
   * \sa Eigen::zeta()
   */
 template<typename DerivedQ>
 inline const CwiseBinaryOp<internal::scalar_zeta_op<Scalar>, const Derived, const DerivedQ>
 zeta(const EIGEN_CURRENT_STORAGE_BASE_CLASS<DerivedQ> &q) const
 {
   return CwiseBinaryOp<internal::scalar_zeta_op<Scalar>, const Derived, const DerivedQ>(this->derived(), q.derived());
 }

	/** \returns an expression of the coefficient wise product of \c *this and \a other
	*
	* \sa MatrixBase::cwiseProduct
	*/
	template<typename OtherDerived>
	EIGEN_DEVICE_FUNC
	EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)
	operator*(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
	{
	return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)(derived(), other.derived());
	}

	/** \returns an expression of the coefficient wise quotient of \c *this and \a other
	*
	* \sa MatrixBase::cwiseQuotient
	*/
	template<typename OtherDerived>
	EIGEN_DEVICE_FUNC
	EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,typename OtherDerived::Scalar>, const Derived, const OtherDerived>
	operator/(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
	{
	return CwiseBinaryOp<internal::scalar_quotient_op<Scalar,typename OtherDerived::Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
	}

	/** \returns an expression of the coefficient-wise min of \c *this and \a other
	*
	* Example: \include Cwise_min.cpp
	* Output: \verbinclude Cwise_min.out
	*
	* \sa max()
	*/
	EIGEN_MAKE_CWISE_BINARY_OP(min,min)

	/** \returns an expression of the coefficient-wise min of \c *this and scalar \a other
	*
	* \sa max()
	*/
	EIGEN_DEVICE_FUNC
	EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived,
	const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >
	#ifdef EIGEN_PARSED_BY_DOXYGEN
	min
	#else
	(min)
	#endif
	(const Scalar &other) const
	{
	return (min)(Derived::PlainObject::Constant(rows(), cols(), other));
	}

	/** \returns an expression of the coefficient-wise max of \c *this and \a other
	*
	* Example: \include Cwise_max.cpp
	* Output: \verbinclude Cwise_max.out
	*
	* \sa min()
	*/
	EIGEN_MAKE_CWISE_BINARY_OP(max,max)

	/** \returns an expression of the coefficient-wise max of \c *this and scalar \a other
	*
	* \sa min()
	*/
	EIGEN_DEVICE_FUNC
	EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived,
	const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >
	#ifdef EIGEN_PARSED_BY_DOXYGEN
	max
	#else
	(max)
	#endif
	(const Scalar &other) const
	{
	return (max)(Derived::PlainObject::Constant(rows(), cols(), other));
	}

	/** \returns an expression of the coefficient-wise power of \c *this 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
	*/
	EIGEN_MAKE_CWISE_BINARY_OP(pow,pow)

	#ifndef EIGEN_PARSED_BY_DOXYGEN
	EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(pow,pow)
	#else
	/** \returns an expression of the coefficients of \c *this rasied to the constant power \a exponent
	*
	* \tparam T is the scalar type of \a exponent. It must be compatible with the scalar type of the given expression.
	*
	* This function computes the coefficient-wise power. The function MatrixBase::pow() in the
	* unsupported module MatrixFunctions computes the matrix power.
	*
	* Example: \include Cwise_pow.cpp
	* Output: \verbinclude Cwise_pow.out
	*
	* \sa ArrayBase::pow(ArrayBase), square(), cube(), exp(), log()
	*/
	template<typename T>
	const CwiseBinaryOp<internal::scalar_pow_op<Scalar,T>,Derived,Constant<T> > pow(const T& exponent) const;
	#endif


	// TODO code generating macros could be moved to Macros.h and could include generation of documentation
	#define EIGEN_MAKE_CWISE_COMP_OP(OP, COMPARATOR) \
	template<typename OtherDerived> \
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<Scalar, typename OtherDerived::Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived> \
	OP(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
	{ \
	return CwiseBinaryOp<internal::scalar_cmp_op<Scalar, typename OtherDerived::Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived>(derived(), other.derived()); \
	}\
	typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> > Cmp ## COMPARATOR ## ReturnType; \
	typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar, internal::cmp_ ## COMPARATOR>, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject>, const Derived > RCmp ## COMPARATOR ## ReturnType; \
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Cmp ## COMPARATOR ## ReturnType \
	OP(const Scalar& s) const { \
	return this->OP(Derived::PlainObject::Constant(rows(), cols(), s)); \
	} \
	EIGEN_DEVICE_FUNC friend EIGEN_STRONG_INLINE const RCmp ## COMPARATOR ## ReturnType \
	OP(const Scalar& s, const Derived& d) { \
	return Derived::PlainObject::Constant(d.rows(), d.cols(), s).OP(d); \
	}

	#define EIGEN_MAKE_CWISE_COMP_R_OP(OP, R_OP, RCOMPARATOR) \
	template<typename OtherDerived> \
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<typename OtherDerived::Scalar, Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived> \
	OP(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
	{ \
	return CwiseBinaryOp<internal::scalar_cmp_op<typename OtherDerived::Scalar, Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived>(other.derived(), derived()); \
	} \
	EIGEN_DEVICE_FUNC \
	inline const RCmp ## RCOMPARATOR ## ReturnType \
	OP(const Scalar& s) const { \
	return Derived::PlainObject::Constant(rows(), cols(), s).R_OP(*this); \
	} \
	friend inline const Cmp ## RCOMPARATOR ## ReturnType \
	OP(const Scalar& s, const Derived& d) { \
	return d.R_OP(Derived::PlainObject::Constant(d.rows(), d.cols(), s)); \
	}



	/** \returns an expression of the coefficient-wise \< operator of *this and \a other
	*
	* Example: \include Cwise_less.cpp
	* Output: \verbinclude Cwise_less.out
	*
	* \sa all(), any(), operator>(), operator<=()
	*/
	EIGEN_MAKE_CWISE_COMP_OP(operator<, LT)

	/** \returns an expression of the coefficient-wise \<= operator of *this and \a other
	*
	* Example: \include Cwise_less_equal.cpp
	* Output: \verbinclude Cwise_less_equal.out
	*
	* \sa all(), any(), operator>=(), operator<()
	*/
	EIGEN_MAKE_CWISE_COMP_OP(operator<=, LE)

	/** \returns an expression of the coefficient-wise \> operator of *this and \a other
	*
	* Example: \include Cwise_greater.cpp
	* Output: \verbinclude Cwise_greater.out
	*
	* \sa all(), any(), operator>=(), operator<()
	*/
	EIGEN_MAKE_CWISE_COMP_R_OP(operator>, operator<, LT)

	/** \returns an expression of the coefficient-wise \>= operator of *this and \a other
	*
	* Example: \include Cwise_greater_equal.cpp
	* Output: \verbinclude Cwise_greater_equal.out
	*
	* \sa all(), any(), operator>(), operator<=()
	*/
	EIGEN_MAKE_CWISE_COMP_R_OP(operator>=, operator<=, LE)

	/** \returns an expression of the coefficient-wise == operator of *this and \a other
	*
	* \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
	* In order to check for equality between two vectors or matrices with floating-point coefficients, it is
	* generally a far better idea to use a fuzzy comparison as provided by isApprox() and
	* isMuchSmallerThan().
	*
	* Example: \include Cwise_equal_equal.cpp
	* Output: \verbinclude Cwise_equal_equal.out
	*
	* \sa all(), any(), isApprox(), isMuchSmallerThan()
	*/
	EIGEN_MAKE_CWISE_COMP_OP(operator==, EQ)

	/** \returns an expression of the coefficient-wise != operator of *this and \a other
	*
	* \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
	* In order to check for equality between two vectors or matrices with floating-point coefficients, it is
	* generally a far better idea to use a fuzzy comparison as provided by isApprox() and
	* isMuchSmallerThan().
	*
	* Example: \include Cwise_not_equal.cpp
	* Output: \verbinclude Cwise_not_equal.out
	*
	* \sa all(), any(), isApprox(), isMuchSmallerThan()
	*/
	EIGEN_MAKE_CWISE_COMP_OP(operator!=, NEQ)


	#undef EIGEN_MAKE_CWISE_COMP_OP
	#undef EIGEN_MAKE_CWISE_COMP_R_OP

	// scalar addition
	#ifndef EIGEN_PARSED_BY_DOXYGEN
	EIGEN_MAKE_SCALAR_BINARY_OP(operator+,sum)
	#else
	/** \returns an expression of \c *this with each coeff incremented by the constant \a scalar
	*
	* \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
	*
	* Example: \include Cwise_plus.cpp
	* Output: \verbinclude Cwise_plus.out
	*
	* \sa operator+=(), operator-()
	*/
	template<typename T>
	const CwiseBinaryOp<internal::scalar_sum_op<Scalar,T>,Derived,Constant<T> > operator+(const T& scalar) const;
	/** \returns an expression of \a expr with each coeff incremented by the constant \a scalar
	*
	* \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
	*/
	template<typename T> friend
	const CwiseBinaryOp<internal::scalar_sum_op<T,Scalar>,Constant<T>,Derived> operator+(const T& scalar, const StorageBaseType& expr);
	#endif

	#ifndef EIGEN_PARSED_BY_DOXYGEN
	EIGEN_MAKE_SCALAR_BINARY_OP(operator-,difference)
	#else
	/** \returns an expression of \c *this with each coeff decremented by the constant \a scalar
	*
	* \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
	*
	* Example: \include Cwise_minus.cpp
	* Output: \verbinclude Cwise_minus.out
	*
	* \sa operator+=(), operator-()
	*/
	template<typename T>
	const CwiseBinaryOp<internal::scalar_difference_op<Scalar,T>,Derived,Constant<T> > operator-(const T& scalar) const;
	/** \returns an expression of the constant matrix of value \a scalar decremented by the coefficients of \a expr
	*
	* \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
	*/
	template<typename T> friend
	const CwiseBinaryOp<internal::scalar_difference_op<T,Scalar>,Constant<T>,Derived> operator-(const T& scalar, const StorageBaseType& expr);
	#endif


	#ifndef EIGEN_PARSED_BY_DOXYGEN
	EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(operator/,quotient)
	#else
	/**
	* \brief Component-wise division of the scalar \a s by array elements of \a a.
	*
	* \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).
	*/
	template<typename T> friend
	inline const CwiseBinaryOp<internal::scalar_quotient_op<T,Scalar>,Constant<T>,Derived>
	operator/(const T& s,const StorageBaseType& a);
	#endif

	/** \returns an expression of the coefficient-wise ^ operator of *this and \a other
	*
	* \warning this operator is for expression of bool only.
	*
	* Example: \include Cwise_boolean_xor.cpp
	* Output: \verbinclude Cwise_boolean_xor.out
	*
	* \sa operator&&(), select()
	*/
	template<typename OtherDerived>
	EIGEN_DEVICE_FUNC
	inline const CwiseBinaryOp<internal::scalar_boolean_xor_op, const Derived, const OtherDerived>
	operator^(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
	{
	EIGEN_STATIC_ASSERT((internal::is_same<bool,Scalar>::value && internal::is_same<bool,typename OtherDerived::Scalar>::value),
	THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL);
	return CwiseBinaryOp<internal::scalar_boolean_xor_op, const Derived, const OtherDerived>(derived(),other.derived());
	}

	// NOTE disabled until we agree on argument order
	#if 0
	/** \cpp11 \returns an expression of the coefficient-wise polygamma function.
	*
	* \specialfunctions_module
	*
	* It returns the \a n -th derivative of the digamma(psi) evaluated at \c *this.
	*
	* \warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x)
	*
	* \sa Eigen::polygamma()
	*/
	template<typename DerivedN>
	inline const CwiseBinaryOp<internal::scalar_polygamma_op<Scalar>, const DerivedN, const Derived>
	polygamma(const EIGEN_CURRENT_STORAGE_BASE_CLASS<DerivedN> &n) const
	{
	return CwiseBinaryOp<internal::scalar_polygamma_op<Scalar>, const DerivedN, const Derived>(n.derived(), this->derived());
	}
	#endif

	/** \returns an expression of the coefficient-wise zeta function.
	*
	* \specialfunctions_module
	*
	* It returns the Riemann zeta function of two arguments \c *this and \a q:
	*
	* \param *this 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.
	*
	* This method is an alias for zeta(*this,q);
	*
	* \sa Eigen::zeta()
	*/
	template<typename DerivedQ>
	inline const CwiseBinaryOp<internal::scalar_zeta_op<Scalar>, const Derived, const DerivedQ>
	zeta(const EIGEN_CURRENT_STORAGE_BASE_CLASS<DerivedQ> &q) const
	{
	return CwiseBinaryOp<internal::scalar_zeta_op<Scalar>, const Derived, const DerivedQ>(this->derived(), q.derived());
	}