text: //=================================================================================================
  /*!
  //  \file blaze/math/adaptors/hermitianmatrix/HermitianProxy.h
  //  \brief Header file for the HermitianProxy class
  //
  //  Copyright (C) 2012-2018 Klaus Iglberger - All Rights Reserved
  //
  //  This file is part of the Blaze library. You can redistribute it and/or modify it under
  //  the terms of the New (Revised) BSD License. Redistribution and use in source and binary
  //  forms, with or without modification, are permitted provided that the following conditions
  //  are met:
  //
  //  1. Redistributions of source code must retain the above copyright notice, this list of
  //     conditions and the following disclaimer.
  //  2. Redistributions in binary form must reproduce the above copyright notice, this list
  //     of conditions and the following disclaimer in the documentation and/or other materials
  //     provided with the distribution.
  //  3. Neither the names of the Blaze development group nor the names of its contributors
  //     may be used to endorse or promote products derived from this software without specific
  //     prior written permission.
  //
  //  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
  //  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  //  OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
  //  SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  //  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
  //  TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
  //  BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  //  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  //  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
  //  DAMAGE.
  */
  //=================================================================================================
  
  #ifndef _BLAZE_MATH_ADAPTORS_HERMITIANMATRIX_HERMITIANPROXY_H_
  #define _BLAZE_MATH_ADAPTORS_HERMITIANMATRIX_HERMITIANPROXY_H_
  
  
  //*************************************************************************************************
  // Includes
  //*************************************************************************************************
  
  #include "../../../math/Aliases.h"
  #include "../../../math/constraints/Expression.h"
  #include "../../../math/constraints/Hermitian.h"
  #include "../../../math/constraints/Lower.h"
  #include "../../../math/constraints/Matrix.h"
  #include "../../../math/constraints/Symmetric.h"
  #include "../../../math/constraints/Upper.h"
  #include "../../../math/Exception.h"
  #include "../../../math/proxy/Proxy.h"
  #include "../../../math/shims/Clear.h"
  #include "../../../math/shims/Conjugate.h"
  #include "../../../math/shims/Invert.h"
  #include "../../../math/shims/IsDefault.h"
  #include "../../../math/shims/IsNaN.h"
  #include "../../../math/shims/IsOne.h"
  #include "../../../math/shims/IsReal.h"
  #include "../../../math/shims/IsZero.h"
  #include "../../../math/shims/Reset.h"
  #include "../../../util/constraints/Const.h"
  #include "../../../util/constraints/Numeric.h"
  #include "../../../util/constraints/Pointer.h"
  #include "../../../util/constraints/Reference.h"
  #include "../../../util/constraints/Volatile.h"
  #include "../../../util/InvalidType.h"
  #include "../../../util/mpl/If.h"
  #include "../../../util/Types.h"
  #include "../../../util/typetraits/IsComplex.h"
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  CLASS DEFINITION
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\brief Access proxy for Hermitian matrices.
  // \ingroup hermitian_matrix
  //
  // The HermitianProxy provides controlled access to the elements of a non-const Hermitian matrix.
  // It guarantees that a modification of element \f$ a_{ij} \f$ of the accessed matrix is also
  // applied to element \f$ a_{ji} \f$. The following example illustrates this by means of a
  // \f$ 3 \times 3 \f$ dense Hermitian matrix:
  
     \code
     // Creating a 3x3 Hermitian dense matrix
     blaze::HermitianMatrix< blaze::DynamicMatrix<int> > A( 3UL );
  
     A(0,2) = -2;  //        (  0 0 -2 )
     A(1,1) =  3;  // => A = (  0 3  5 )
     A(1,2) =  5;  //        ( -2 5  0 )
     \endcode
  */
  template< typename MT >  // Type of the adapted matrix
  class HermitianProxy
     : public Proxy< HermitianProxy<MT> >
  {
   private:
     //**struct BuiltinType**************************************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Auxiliary struct to determine the value type of the represented complex element.
     */
     template< typename T >
     struct BuiltinType { using Type = INVALID_TYPE; };
     /*! \endcond */
     //**********************************************************************************************
  
     //**struct ComplexType**************************************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Auxiliary struct to determine the value type of the represented complex element.
     */
     template< typename T >
     struct ComplexType { using Type = typename T::value_type; };
     /*! \endcond */
     //**********************************************************************************************
  
   public:
     //**Type definitions****************************************************************************
     using RepresentedType = ElementType_t<MT>;      //!< Type of the represented matrix element.
     using Reference       = Reference_t<MT>;        //!< Reference to the represented element.
     using ConstReference  = ConstReference_t<MT>;   //!< Reference-to-const to the represented element.
     using Pointer         = HermitianProxy*;        //!< Pointer to the represented element.
     using ConstPointer    = const HermitianProxy*;  //!< Pointer-to-const to the represented element.
  
     //! Value type of the represented complex element.
     using ValueType = typename If_t< IsComplex_v<RepresentedType>
                                    , ComplexType<RepresentedType>
                                    , BuiltinType<RepresentedType> >::Type;
     //**********************************************************************************************
  
     //**Constructors********************************************************************************
     /*!\name Constructors */
     //@{
     explicit inline HermitianProxy( MT& matrix, size_t row, size_t column );
              inline HermitianProxy( const HermitianProxy& hp );
     //@}
     //**********************************************************************************************
  
     //**Destructor**********************************************************************************
     // No explicitly declared destructor.
     //**********************************************************************************************
  
     //**Assignment operators************************************************************************
     /*!\name Assignment operators */
     //@{
                            inline HermitianProxy& operator= ( const HermitianProxy& hp );
     template< typename T > inline HermitianProxy& operator= ( const T& value );
     template< typename T > inline HermitianProxy& operator+=( const T& value );
     template< typename T > inline HermitianProxy& operator-=( const T& value );
     template< typename T > inline HermitianProxy& operator*=( const T& value );
     template< typename T > inline HermitianProxy& operator/=( const T& value );
     template< typename T > inline HermitianProxy& operator%=( const T& value );
     //@}
     //**********************************************************************************************
  
     //**Access operators****************************************************************************
     /*!\name Access operators */
     //@{
     inline Pointer      operator->() noexcept;
     inline ConstPointer operator->() const noexcept;
     //@}
     //**********************************************************************************************
  
     //**Utility functions***************************************************************************
     /*!\name Utility functions */
     //@{
     inline void reset () const;
     inline void clear () const;
     inline void invert() const;
  
     inline ConstReference get() const noexcept;
     //@}
     //**********************************************************************************************
  
     //**Conversion operator*************************************************************************
     /*!\name Conversion operator */
     //@{
     inline operator ConstReference() const noexcept;
     //@}
     //**********************************************************************************************
  
     //**Complex data access functions***************************************************************
     /*!\name Complex data access functions */
     //@{
     inline ValueType real() const;
     inline void      real( ValueType value ) const;
     inline ValueType imag() const;
     inline void      imag( ValueType value ) const;
     //@}
     //**********************************************************************************************
  
   private:
     //**Member variables****************************************************************************
     /*!\name Member variables */
     //@{
     Reference value1_;     //!< Reference to the first accessed matrix element.
     Reference value2_;     //!< Reference to the second accessed matrix element.
     const bool diagonal_;  //!< Flag for the accessed matrix element.
                            /*!< The flag indicates if the accessed element is a diagonal element.
                                 It is \a true in case the proxy represents an element on the
                                 diagonal. */
     //@}
     //**********************************************************************************************
  
     //**Compile time checks*************************************************************************
     /*! \cond BLAZE_INTERNAL */
     BLAZE_CONSTRAINT_MUST_BE_MATRIX_TYPE              ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_REFERENCE_TYPE       ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_POINTER_TYPE         ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_CONST                ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_VOLATILE             ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_EXPRESSION_TYPE      ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_SYMMETRIC_MATRIX_TYPE( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_HERMITIAN_MATRIX_TYPE( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_LOWER_MATRIX_TYPE    ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_UPPER_MATRIX_TYPE    ( MT );
     BLAZE_CONSTRAINT_MUST_BE_NUMERIC_TYPE             ( RepresentedType );
     /*! \endcond */
     //**********************************************************************************************
  };
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  CONSTRUCTORS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\brief Initialization constructor for a HermitianProxy.
  //
  // \param matrix Reference to the adapted matrix.
  // \param row The row-index of the accessed matrix element.
  // \param column The column-index of the accessed matrix element.
  */
  template< typename MT >  // Type of the adapted matrix
  inline HermitianProxy<MT>::HermitianProxy( MT& matrix, size_t row, size_t column )
     : value1_  ( matrix(row,column) )  // Reference to the first accessed matrix element
     , value2_  ( matrix(column,row) )  // Reference to the second accessed matrix element
     , diagonal_( row == column )       // Flag for the accessed matrix element
  {}
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief The copy constructor for HermitianProxy.
  //
  // \param hp Numeric proxy to be copied.
  */
  template< typename MT >  // Type of the adapted matrix
  inline HermitianProxy<MT>::HermitianProxy( const HermitianProxy& hp )
     : value1_  ( hp.value1_   )  // Reference to the first accessed matrix element
     , value2_  ( hp.value2_   )  // Reference to the second accessed matrix element
     , diagonal_( hp.diagonal_ )  // Flag for the accessed matrix element
  {}
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  OPERATORS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\brief Copy assignment operator for HermitianProxy.
  //
  // \param hp Numeric proxy to be copied.
  // \return Reference to the assigned proxy.
  // \exception std::invalid_argument Invalid assignment to diagonal matrix element.
  //
  // In case the proxy represents a diagonal element and the assigned value does not represent
  // a real number, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT >  // Type of the adapted matrix
  inline HermitianProxy<MT>& HermitianProxy<MT>::operator=( const HermitianProxy& hp )
  {
     using ET = ElementType_t<MT>;
  
     if( IsComplex_v<ET> && diagonal_ && !isReal( hp.value1_ ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to diagonal matrix element" );
     }
  
     value1_ = hp.value1_;
     if( !diagonal_ )
        value2_ = conj( value1_ );
  
     return *this;
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Assignment to the accessed matrix element.
  //
  // \param value The new value of the matrix element.
  // \return Reference to the assigned proxy.
  // \exception std::invalid_argument Invalid assignment to diagonal matrix element.
  //
  // In case the proxy represents a diagonal element and the assigned value does not represent
  // a real number, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT >  // Type of the adapted matrix
  template< typename T >   // Type of the right-hand side value
  inline HermitianProxy<MT>& HermitianProxy<MT>::operator=( const T& value )
  {
     using ET = ElementType_t<MT>;
  
     if( IsComplex_v<ET> && diagonal_ && !isReal( value ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to diagonal matrix element" );
     }
  
     value1_ = value;
     if( !diagonal_ )
        value2_ = conj( value1_ );
  
     return *this;
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Addition assignment to the accessed matrix element.
  //
  // \param value The right-hand side value to be added to the matrix element.
  // \return Reference to the assigned proxy.
  // \exception std::invalid_argument Invalid assignment to diagonal matrix element.
  //
  // In case the proxy represents a diagonal element and the assigned value does not represent
  // a real number, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT >  // Type of the adapted matrix
  template< typename T >   // Type of the right-hand side value
  inline HermitianProxy<MT>& HermitianProxy<MT>::operator+=( const T& value )
  {
     using ET = ElementType_t<MT>;
  
     if( IsComplex_v<ET> && diagonal_ && !isReal( value ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to diagonal matrix element" );
     }
  
     value1_ += value;
     if( !diagonal_ )
        value2_ = conj( value1_ );
  
     return *this;
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Subtraction assignment to the accessed matrix element.
  //
  // \param value The right-hand side value to be subtracted from the matrix element.
  // \return Reference to the assigned proxy.
  // \exception std::invalid_argument Invalid assignment to diagonal matrix element.
  //
  // In case the proxy represents a diagonal element and the assigned value does not represent
  // a real number, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT >  // Type of the adapted matrix
  template< typename T >   // Type of the right-hand side value
  inline HermitianProxy<MT>& HermitianProxy<MT>::operator-=( const T& value )
  {
     using ET = ElementType_t<MT>;
  
     if( IsComplex_v<ET> && diagonal_ && !isReal( value ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to diagonal matrix element" );
     }
  
     value1_ -= value;
     if( !diagonal_ )
        value2_ = conj( value1_ );
  
     return *this;
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Multiplication assignment to the accessed matrix element.
  //
  // \param value The right-hand side value for the multiplication.
  // \return Reference to the assigned proxy.
  // \exception std::invalid_argument Invalid assignment to diagonal matrix element.
  //
  // In case the proxy represents a diagonal element and the assigned value does not represent
  // a real number, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT >  // Type of the adapted matrix
  template< typename T >   // Type of the right-hand side value
  inline HermitianProxy<MT>& HermitianProxy<MT>::operator*=( const T& value )
  {
     using ET = ElementType_t<MT>;
  
     if( IsComplex_v<ET> && diagonal_ && !isReal( value ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to diagonal matrix element" );
     }
  
     value1_ *= value;
     if( !diagonal_ )
        value2_ = conj( value1_ );
  
     return *this;
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Division assignment to the accessed matrix element.
  //
  // \param value The right-hand side value for the division.
  // \return Reference to the assigned proxy.
  // \exception std::invalid_argument Invalid assignment to diagonal matrix element.
  //
  // In case the proxy represents a diagonal element and the assigned value does not represent
  // a real number, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT >  // Type of the adapted matrix
  template< typename T >   // Type of the right-hand side value
  inline HermitianProxy<MT>& HermitianProxy<MT>::operator/=( const T& value )
  {
     using ET = ElementType_t<MT>;
  
     if( IsComplex_v<ET> && diagonal_ && !isReal( value ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to diagonal matrix element" );
     }
  
     value1_ /= value;
     if( !diagonal_ )
        value2_ = conj( value1_ );
  
     return *this;
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Modulo assignment to the accessed matrix element.
  //
  // \param value The right-hand side value for the modulo operation.
  // \return Reference to the assigned proxy.
  // \exception std::invalid_argument Invalid assignment to diagonal matrix element.
  //
  // In case the proxy represents a diagonal element and the assigned value does not represent
  // a real number, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT >  // Type of the adapted matrix
  template< typename T >   // Type of the right-hand side value
  inline HermitianProxy<MT>& HermitianProxy<MT>::operator%=( const T& value )
  {
     using ET = ElementType_t<MT>;
  
     if( IsComplex_v<ET> && diagonal_ && !isReal( value ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to diagonal matrix element" );
     }
  
     value1_ %= value;
     if( !diagonal_ )
        value2_ = conj( value1_ );
  
     return *this;
  }
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ACCESS OPERATORS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\brief Direct access to the represented matrix element.
  //
  // \return Pointer to the represented matrix element.
  */
  template< typename MT >  // Type of the adapted matrix
  inline typename HermitianProxy<MT>::Pointer HermitianProxy<MT>::operator->() noexcept
  {
     return this;
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Direct access to the represented matrix element.
  //
  // \return Pointer to the represented matrix element.
  */
  template< typename MT >  // Type of the adapted matrix
  inline typename HermitianProxy<MT>::ConstPointer HermitianProxy<MT>::operator->() const noexcept
  {
     return this;
  }
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  UTILITY FUNCTIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\brief Reset the represented element to its default initial value.
  //
  // \return void
  //
  // This function resets the element represented by the proxy to its default initial value.
  */
  template< typename MT >  // Type of the adapted matrix
  inline void HermitianProxy<MT>::reset() const
  {
     using blaze::reset;
  
     reset( value1_ );
     if( !diagonal_ )
        reset( value2_ );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Clearing the represented element.
  //
  // \return void
  //
  // This function clears the element represented by the proxy to its default initial state.
  */
  template< typename MT >  // Type of the adapted matrix
  inline void HermitianProxy<MT>::clear() const
  {
     using blaze::clear;
  
     clear( value1_ );
     if( !diagonal_ )
        clear( value2_ );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief In-place inversion of the represented element
  //
  // \return void
  */
  template< typename MT >  // Type of the adapted matrix
  inline void HermitianProxy<MT>::invert() const
  {
     using blaze::invert;
  
     invert( value1_ );
     if( !diagonal_ )
        value2_ = conj( value1_ );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Returning the value of the accessed matrix element.
  //
  // \return Direct/raw reference to the accessed matrix element.
  */
  template< typename MT >  // Type of the adapted matrix
  inline typename HermitianProxy<MT>::ConstReference HermitianProxy<MT>::get() const noexcept
  {
     return value1_;
  }
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  CONVERSION OPERATOR
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\brief Conversion to the accessed matrix element.
  //
  // \return Direct/raw reference to the accessed matrix element.
  */
  template< typename MT >  // Type of the adapted matrix
  inline HermitianProxy<MT>::operator ConstReference() const noexcept
  {
     return get();
  }
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  COMPLEX DATA ACCESS FUNCTIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\brief Returns the real part of the represented complex number.
  //
  // \return The current real part of the represented complex number.
  //
  // In case the proxy represents a complex number, this function returns the current value of its
  // real part.
  */
  template< typename MT >  // Type of the adapted matrix
  inline typename HermitianProxy<MT>::ValueType HermitianProxy<MT>::real() const
  {
     return value1_.real();
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Setting the real part of the represented complex number.
  //
  // \param value The new value for the real part.
  // \return void
  //
  // In case the proxy represents a complex number, this function sets a new value to its real part.
  */
  template< typename MT >  // Type of the adapted matrix
  inline void HermitianProxy<MT>::real( ValueType value ) const
  {
     value1_.real( value );
     if( !diagonal_ )
        value2_.real( value );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Returns the imaginary part of the represented complex number.
  //
  // \return The current imaginary part of the represented complex number.
  //
  // In case the proxy represents a complex number, this function returns the current value of its
  // imaginary part.
  */
  template< typename MT >  // Type of the adapted matrix
  inline typename HermitianProxy<MT>::ValueType HermitianProxy<MT>::imag() const
  {
     return value1_.imag();
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Setting the imaginary part of the represented complex number.
  //
  // \param value The new value for the imaginary part.
  // \return void
  // \exception std::invalid_argument Invalid setting for diagonal matrix element.
  //
  // In case the proxy represents a complex number, this function sets a new value to its imaginary
  // part. In case the proxy represents a diagonal element and the given value is not zero, a
  // \a std::invalid_argument exception is thrown.
  */
  template< typename MT >  // Type of the adapted matrix
  inline void HermitianProxy<MT>::imag( ValueType value ) const
  {
     if( diagonal_ && !isZero( value ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid setting for diagonal matrix element" );
     }
  
     value1_.imag( value );
     if( !diagonal_ )
        value2_.imag( -value );
  }
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  GLOBAL FUNCTIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\name HermitianProxy global functions */
  //@{
  template< typename MT >
  inline void reset( const HermitianProxy<MT>& proxy );
  
  template< typename MT >
  inline void clear( const HermitianProxy<MT>& proxy );
  
  template< typename MT >
  inline void invert( const HermitianProxy<MT>& proxy );
  
  template< bool RF, typename MT >
  inline bool isDefault( const HermitianProxy<MT>& proxy );
  
  template< bool RF, typename MT >
  inline bool isReal( const HermitianProxy<MT>& proxy );
  
  template< bool RF, typename MT >
  inline bool isZero( const HermitianProxy<MT>& proxy );
  
  template< bool RF, typename MT >
  inline bool isOne( const HermitianProxy<MT>& proxy );
  
  template< typename MT >
  inline bool isnan( const HermitianProxy<MT>& proxy );
  //@}
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Resetting the represented element to the default initial values.
  // \ingroup hermitian_matrix
  //
  // \param proxy The given access proxy.
  // \return void
  //
  // This function resets the element represented by the access proxy to its default initial
  // value.
  */
  template< typename MT >
  inline void reset( const HermitianProxy<MT>& proxy )
  {
     proxy.reset();
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Clearing the represented element.
  // \ingroup hermitian_matrix
  //
  // \param proxy The given access proxy.
  // \return void
  //
  // This function clears the element represented by the access proxy to its default initial
  // state.
  */
  template< typename MT >
  inline void clear( const HermitianProxy<MT>& proxy )
  {
     proxy.clear();
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief In-place inversion of the represented element.
  // \ingroup hermitian_matrix
  //
  // \param proxy The given proxy instance.
  // \return void
  */
  template< typename MT >
  inline void invert( const HermitianProxy<MT>& proxy )
  {
     proxy.invert();
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Returns whether the represented element is in default state.
  // \ingroup hermitian_matrix
  //
  // \param proxy The given access proxy
  // \return \a true in case the represented element is in default state, \a false otherwise.
  //
  // This function checks whether the element represented by the access proxy is in default state.
  // In case it is in default state, the function returns \a true, otherwise it returns \a false.
  */
  template< bool RF, typename MT >
  inline bool isDefault( const HermitianProxy<MT>& proxy )
  {
     using blaze::isDefault;
  
     return isDefault<RF>( proxy.get() );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Returns whether the matrix element represents a real number.
  // \ingroup hermitian_matrix
  //
  // \param proxy The given access proxy.
  // \return \a true in case the matrix element represents a real number, \a false otherwise.
  //
  // This function checks whether the element represented by the access proxy represents the a
  // real number. In case the element is of built-in type, the function returns \a true. In case
  // the element is of complex type, the function returns \a true if the imaginary part is equal
  // to 0. Otherwise it returns \a false.
  */
  template< bool RF, typename MT >
  inline bool isReal( const HermitianProxy<MT>& proxy )
  {
     using blaze::isReal;
  
     return isReal<RF>( proxy.get() );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Returns whether the represented element is 0.
  // \ingroup hermitian_matrix
  //
  // \param proxy The given access proxy.
  // \return \a true in case the represented element is 0, \a false otherwise.
  //
  // This function checks whether the element represented by the access proxy represents the numeric
  // value 0. In case it is 0, the function returns \a true, otherwise it returns \a false.
  */
  template< bool RF, typename MT >
  inline bool isZero( const HermitianProxy<MT>& proxy )
  {
     using blaze::isZero;
  
     return isZero<RF>( proxy.get() );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Returns whether the represented element is 1.
  // \ingroup hermitian_matrix
  //
  // \param proxy The given access proxy.
  // \return \a true in case the represented element is 1, \a false otherwise.
  //
  // This function checks whether the element represented by the access proxy represents the numeric
  // value 1. In case it is 1, the function returns \a true, otherwise it returns \a false.
  */
  template< bool RF, typename MT >
  inline bool isOne( const HermitianProxy<MT>& proxy )
  {
     using blaze::isOne;
  
     return isOne<RF>( proxy.get() );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Returns whether the represented element is not a number.
  // \ingroup hermitian_matrix
  //
  // \param proxy The given access proxy.
  // \return \a true in case the represented element is in not a number, \a false otherwise.
  //
  // This function checks whether the element represented by the access proxy is not a number (NaN).
  // In case it is not a number, the function returns \a true, otherwise it returns \a false.
  */
  template< typename MT >
  inline bool isnan( const HermitianProxy<MT>& proxy )
  {
     using blaze::isnan;
  
     return isnan( proxy.get() );
  }
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  