//=================================================================================================
/*!
//  \file blaze/math/adaptors/HermitianMatrix.h
//  \brief Header file for the implementation of a Hermitian matrix adaptor
//
//  Copyright (C) 2012-2020 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_H_
#define _BLAZE_MATH_ADAPTORS_HERMITIANMATRIX_H_


//*************************************************************************************************
// Includes
//*************************************************************************************************

#include <blaze/math/Aliases.h>
#include <blaze/math/adaptors/hermitianmatrix/BaseTemplate.h>
#include <blaze/math/adaptors/hermitianmatrix/Dense.h>
#include <blaze/math/adaptors/hermitianmatrix/Sparse.h>
#include <blaze/math/constraints/BLASCompatible.h>
#include <blaze/math/constraints/RequiresEvaluation.h>
#include <blaze/math/Exception.h>
#include <blaze/math/Forward.h>
#include <blaze/math/InversionFlag.h>
#include <blaze/math/RelaxationFlag.h>
#include <blaze/math/shims/Conjugate.h>
#include <blaze/math/shims/IsDefault.h>
#include <blaze/math/shims/IsDivisor.h>
#include <blaze/math/shims/IsReal.h>
#include <blaze/math/traits/AddTrait.h>
#include <blaze/math/traits/DeclDiagTrait.h>
#include <blaze/math/traits/DeclHermTrait.h>
#include <blaze/math/traits/DeclLowTrait.h>
#include <blaze/math/traits/DeclStrLowTrait.h>
#include <blaze/math/traits/DeclStrUppTrait.h>
#include <blaze/math/traits/DeclSymTrait.h>
#include <blaze/math/traits/DeclUniLowTrait.h>
#include <blaze/math/traits/DeclUniUppTrait.h>
#include <blaze/math/traits/DeclUppTrait.h>
#include <blaze/math/traits/DivTrait.h>
#include <blaze/math/traits/KronTrait.h>
#include <blaze/math/traits/MapTrait.h>
#include <blaze/math/traits/MultTrait.h>
#include <blaze/math/traits/RepeatTrait.h>
#include <blaze/math/traits/SchurTrait.h>
#include <blaze/math/traits/SubmatrixTrait.h>
#include <blaze/math/traits/SubTrait.h>
#include <blaze/math/typetraits/HasConstDataAccess.h>
#include <blaze/math/typetraits/HighType.h>
#include <blaze/math/typetraits/IsAdaptor.h>
#include <blaze/math/typetraits/IsAligned.h>
#include <blaze/math/typetraits/IsContiguous.h>
#include <blaze/math/typetraits/IsDiagonal.h>
#include <blaze/math/typetraits/IsHermitian.h>
#include <blaze/math/typetraits/IsMatrix.h>
#include <blaze/math/typetraits/IsPadded.h>
#include <blaze/math/typetraits/IsRestricted.h>
#include <blaze/math/typetraits/IsScalar.h>
#include <blaze/math/typetraits/IsSquare.h>
#include <blaze/math/typetraits/IsStrictlyLower.h>
#include <blaze/math/typetraits/IsStrictlyUpper.h>
#include <blaze/math/typetraits/IsSymmetric.h>
#include <blaze/math/typetraits/IsUniform.h>
#include <blaze/math/typetraits/IsZero.h>
#include <blaze/math/typetraits/LowType.h>
#include <blaze/math/typetraits/MaxSize.h>
#include <blaze/math/typetraits/RemoveAdaptor.h>
#include <blaze/math/typetraits/Size.h>
#include <blaze/math/typetraits/StorageOrder.h>
#include <blaze/math/typetraits/UnderlyingScalar.h>
#include <blaze/math/typetraits/YieldsHermitian.h>
#include <blaze/math/typetraits/YieldsIdentity.h>
#include <blaze/math/typetraits/YieldsSymmetric.h>
#include <blaze/util/algorithms/Min.h>
#include <blaze/util/Assert.h>
#include <blaze/util/EnableIf.h>
#include <blaze/util/IntegralConstant.h>
#include <blaze/util/MaybeUnused.h>
#include <blaze/util/typetraits/IsBuiltin.h>
#include <blaze/util/typetraits/IsComplex.h>


namespace blaze {

//=================================================================================================
//
//  HERMITIANMATRIX OPERATORS
//
//=================================================================================================

//*************************************************************************************************
/*!\name HermitianMatrix operators */
//@{
template< RelaxationFlag RF, typename MT, bool SO, bool DF >
bool isDefault( const HermitianMatrix<MT,SO,DF>& m );

template< typename MT, bool SO, bool DF >
bool isIntact( const HermitianMatrix<MT,SO,DF>& m );

template< typename MT, bool SO, bool DF >
void swap( HermitianMatrix<MT,SO,DF>& a, HermitianMatrix<MT,SO,DF>& b ) noexcept;
//@}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Returns whether the given Hermitian matrix is in default state.
// \ingroup hermitian_matrix
//
// \param m The Hermitian matrix to be tested for its default state.
// \return \a true in case the given matrix is component-wise zero, \a false otherwise.
//
// This function checks whether the matrix is in default state. For instance, in case the
// matrix is instantiated for a built-in integral or floating point data type, the function
// returns \a true in case all matrix elements are 0 and \a false in case any matrix element
// is not 0. The following example demonstrates the use of the \a isDefault function:

   \code
   blaze::HermitianMatrix<int> A;
   // ... Resizing and initialization
   if( isDefault( A ) ) { ... }
   \endcode

// Optionally, it is possible to switch between strict semantics (blaze::strict) and relaxed
// semantics (blaze::relaxed):

   \code
   if( isDefault<relaxed>( A ) ) { ... }
   \endcode
*/
template< RelaxationFlag RF  // Relaxation flag
        , typename MT        // Type of the adapted matrix
        , bool SO            // Storage order of the adapted matrix
        , bool DF >          // Density flag
inline bool isDefault( const HermitianMatrix<MT,SO,DF>& m )
{
   if( Size_v<MT,0UL> == DefaultSize_v )
      return m.rows() == 0UL;
   else return isStrictlyLower<RF>( m );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Returns whether the invariants of the given Hermitian matrix are intact.
// \ingroup hermitian_matrix
//
// \param m The Hermitian matrix to be tested.
// \return \a true in case the given matrix's invariants are intact, \a false otherwise.
//
// This function checks whether the invariants of the Hermitian matrix are intact, i.e. if its
// state is valid. In case the invariants are intact, the function returns \a true, else it
// will return \a false. The following example demonstrates the use of the \a isIntact()
// function:

   \code
   using blaze::DynamicMatrix;
   using blaze::HermitianMatrix;

   HermitianMatrix< DynamicMatrix<int> > A;
   // ... Resizing and initialization
   if( isIntact( A ) ) { ... }
   \endcode
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF >    // Density flag
inline bool isIntact( const HermitianMatrix<MT,SO,DF>& m )
{
   return m.isIntact();
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Swapping the contents of two matrices.
// \ingroup hermitian_matrix
//
// \param a The first matrix to be swapped.
// \param b The second matrix to be swapped.
// \return void
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF >    // Density flag
inline void swap( HermitianMatrix<MT,SO,DF>& a, HermitianMatrix<MT,SO,DF>& b ) noexcept
{
   a.swap( b );
}
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief In-place inversion of the given Hermitian dense matrix.
// \ingroup hermitian_matrix
//
// \param m The Hermitian dense matrix to be inverted.
// \return void
// \exception std::invalid_argument Inversion of singular matrix failed.
//
// This function inverts the given Hermitian dense matrix by means of the specified matrix
// inversion algorithm \c IF. The The inversion fails if the given matrix is singular and not
// invertible. In this case a \a std::invalid_argument exception is thrown.
//
// \note The matrix inversion can only be used for dense matrices with \c float, \c double,
// \c complex<float> or \c complex<double> element type. The attempt to call the function with
// matrices of any other element type results in a compile time error!
//
// \note This function can only be used if a fitting LAPACK library is available and linked to
// the executable. Otherwise a linker error will be created.
//
// \note This function does only provide the basic exception safety guarantee, i.e. in case of an
// exception \a m may already have been modified.
*/
template< InversionFlag IF  // Inversion algorithm
        , typename MT       // Type of the dense matrix
        , bool SO >         // Storage order of the dense matrix
inline void invert( HermitianMatrix<MT,SO,true>& m )
{
   BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<MT> );

   if( IF == asUniLower || IF == asUniUpper ) {
      BLAZE_INTERNAL_ASSERT( isIdentity( m ), "Violation of preconditions detected" );
      return;
   }

   constexpr InversionFlag flag( ( IF == byLU || IF == byLDLT || IF == byLDLH ||
                                   IF == asGeneral || IF == asSymmetric || IF == asHermitian )
                                 ? ( byLDLH )
                                 : ( ( IF == byLLH )
                                     ?( byLLH )
                                     :( asDiagonal ) ) );

   MT tmp( m.matrix_ );
   invert<flag>( tmp );
   m.matrix_ = std::move( tmp );

   BLAZE_INTERNAL_ASSERT( isIntact( m ), "Broken invariant detected" );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by setting a single element of an Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param mat The target Hermitian matrix.
// \param i The row index of the element to be set.
// \param j The column index of the element to be set.
// \param value The value to be set to the element.
// \return \a true in case the operation would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT    // Type of the adapted matrix
        , bool SO        // Storage order of the adapted matrix
        , bool DF        // Density flag
        , typename ET >  // Type of the element
inline bool trySet( const HermitianMatrix<MT,SO,DF>& mat, size_t i, size_t j, const ET& value )
{
   BLAZE_INTERNAL_ASSERT( i < (*mat).rows(), "Invalid row access index" );
   BLAZE_INTERNAL_ASSERT( j < (*mat).columns(), "Invalid column access index" );

   MAYBE_UNUSED( mat );

   return ( i != j || isReal( value ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by setting a range of elements of an Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param mat The target Hermitian matrix.
// \param row The index of the first row of the range to be multiplied.
// \param column The index of the first column of the range to be multiplied.
// \param m The number of rows of the range to be multiplied.
// \param n The number of columns of the range to be multiplied.
// \param value The value to be set to the range of elements.
// \return \a true in case the operation would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT    // Type of the adapted matrix
        , bool SO        // Storage order of the adapted matrix
        , bool DF        // Density flag
        , typename ET >  // Type of the element
BLAZE_ALWAYS_INLINE bool
   trySet( const HermitianMatrix<MT,SO,DF>& mat, size_t row, size_t column, size_t m, size_t n, const ET& value )
{
   BLAZE_INTERNAL_ASSERT( row <= (*mat).rows(), "Invalid row access index" );
   BLAZE_INTERNAL_ASSERT( column <= (*mat).columns(), "Invalid column access index" );
   BLAZE_INTERNAL_ASSERT( row + m <= (*mat).rows(), "Invalid number of rows" );
   BLAZE_INTERNAL_ASSERT( column + n <= (*mat).columns(), "Invalid number of columns" );

   MAYBE_UNUSED( mat );

   return ( m == 0UL ) ||
          ( n == 0UL ) ||
          ( row >= column + n ) ||
          ( column >= row + m ) ||
          isReal( value );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by adding to a single element of an Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param mat The target Hermitian matrix.
// \param i The row index of the element to be modified.
// \param j The column index of the element to be modified.
// \param value The value to be added to the element.
// \return \a true in case the operation would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT    // Type of the adapted matrix
        , bool SO        // Storage order of the adapted matrix
        , bool DF        // Density flag
        , typename ET >  // Type of the element
inline bool tryAdd( const HermitianMatrix<MT,SO,DF>& mat, size_t i, size_t j, const ET& value )
{
   return trySet( mat, i, j, value );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by adding to a range of elements of an Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param mat The target Hermitian matrix.
// \param row The index of the first row of the range to be multiplied.
// \param column The index of the first column of the range to be multiplied.
// \param m The number of rows of the range to be multiplied.
// \param n The number of columns of the range to be multiplied.
// \param value The value to be added to the range of elements.
// \return \a true in case the operation would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT    // Type of the adapted matrix
        , bool SO        // Storage order of the adapted matrix
        , bool DF        // Density flag
        , typename ET >  // Type of the element
BLAZE_ALWAYS_INLINE bool
   tryAdd( const HermitianMatrix<MT,SO,DF>& mat, size_t row, size_t column, size_t m, size_t n, const ET& value )
{
   return trySet( mat, row, column, m, n, value );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by subtracting from a single element of an Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param mat The target Hermitian matrix.
// \param i The row index of the element to be modified.
// \param j The column index of the element to be modified.
// \param value The value to be subtracted from the element.
// \return \a true in case the operation would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT    // Type of the adapted matrix
        , bool SO        // Storage order of the adapted matrix
        , bool DF        // Density flag
        , typename ET >  // Type of the element
inline bool trySub( const HermitianMatrix<MT,SO,DF>& mat, size_t i, size_t j, const ET& value )
{
   return trySet( mat, i, j, value );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by subtracting from a range of elements of an Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param mat The target Hermitian matrix.
// \param row The index of the first row of the range to be multiplied.
// \param column The index of the first column of the range to be multiplied.
// \param m The number of rows of the range to be multiplied.
// \param n The number of columns of the range to be multiplied.
// \param value The value to be subtracted from the range of elements.
// \return \a true in case the operation would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT    // Type of the adapted matrix
        , bool SO        // Storage order of the adapted matrix
        , bool DF        // Density flag
        , typename ET >  // Type of the element
BLAZE_ALWAYS_INLINE bool
   trySub( const HermitianMatrix<MT,SO,DF>& mat, size_t row, size_t column, size_t m, size_t n, const ET& value )
{
   return trySet( mat, row, column, m, n, value );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by scaling a single element of an Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param mat The target Hermitian matrix.
// \param i The row index of the element to be modified.
// \param j The column index of the element to be modified.
// \param value The factor for the element.
// \return \a true in case the operation would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT    // Type of the adapted matrix
        , bool SO        // Storage order of the adapted matrix
        , bool DF        // Density flag
        , typename ET >  // Type of the element
inline bool tryMult( const HermitianMatrix<MT,SO,DF>& mat, size_t i, size_t j, const ET& value )
{
   return trySet( mat, i, j, value );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by scaling a range of elements of an Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param mat The target Hermitian matrix.
// \param row The index of the first row of the range to be multiplied.
// \param column The index of the first column of the range to be multiplied.
// \param m The number of rows of the range to be multiplied.
// \param n The number of columns of the range to be multiplied.
// \param value The factor for the elements.
// \return \a true in case the operation would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT    // Type of the adapted matrix
        , bool SO        // Storage order of the adapted matrix
        , bool DF        // Density flag
        , typename ET >  // Type of the element
BLAZE_ALWAYS_INLINE bool
   tryMult( const HermitianMatrix<MT,SO,DF>& mat, size_t row, size_t column, size_t m, size_t n, const ET& value )
{
   return trySet( mat, row, column, m, n, value );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by scaling a single element of an Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param mat The target Hermitian matrix.
// \param i The row index of the element to be modified.
// \param j The column index of the element to be modified.
// \param value The divisor for the element.
// \return \a true in case the operation would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT    // Type of the adapted matrix
        , bool SO        // Storage order of the adapted matrix
        , bool DF        // Density flag
        , typename ET >  // Type of the element
inline bool tryDiv( const HermitianMatrix<MT,SO,DF>& mat, size_t i, size_t j, const ET& value )
{
   return trySet( mat, i, j, value );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by scaling a range of elements of an Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param mat The target Hermitian matrix.
// \param row The index of the first row of the range to be multiplied.
// \param column The index of the first column of the range to be multiplied.
// \param m The number of rows of the range to be multiplied.
// \param n The number of columns of the range to be multiplied.
// \param value The divisor for the elements.
// \return \a true in case the operation would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT    // Type of the adapted matrix
        , bool SO        // Storage order of the adapted matrix
        , bool DF        // Density flag
        , typename ET >  // Type of the element
BLAZE_ALWAYS_INLINE bool
   tryDiv( const HermitianMatrix<MT,SO,DF>& mat, size_t row, size_t column, size_t m, size_t n, const ET& value )
{
   return trySet( mat, row, column, m, n, value );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the assignment of a vector to a Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side vector to be assigned.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT    // Type of the adapted matrix
        , bool SO        // Storage order of the adapted matrix
        , bool DF        // Density flag
        , typename VT >  // Type of the right-hand side vector
inline bool tryAssign( const HermitianMatrix<MT,SO,DF>& lhs,
                       const Vector<VT,false>& rhs, size_t row, size_t column )
{
   BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( VT );

   BLAZE_INTERNAL_ASSERT( row <= lhs.rows(), "Invalid row access index" );
   BLAZE_INTERNAL_ASSERT( column <= lhs.columns(), "Invalid column access index" );
   BLAZE_INTERNAL_ASSERT( row + (*rhs).size() <= lhs.rows(), "Invalid number of rows" );

   MAYBE_UNUSED( lhs );

   using ET = ElementType_t< HermitianMatrix<MT,SO,DF> >;

   return ( IsBuiltin_v<ET> ||
            column < row ||
            (*rhs).size() <= column - row ||
            isReal( (*rhs)[column-row] ) );

   return true;
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the assignment of a vector to a Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side vector to be assigned.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT    // Type of the adapted matrix
        , bool SO        // Storage order of the adapted matrix
        , bool DF        // Density flag
        , typename VT >  // Type of the right-hand side vector
inline bool tryAssign( const HermitianMatrix<MT,SO,DF>& lhs,
                       const Vector<VT,true>& rhs, size_t row, size_t column )
{
   BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( VT );

   BLAZE_INTERNAL_ASSERT( row <= lhs.rows(), "Invalid row access index" );
   BLAZE_INTERNAL_ASSERT( column <= lhs.columns(), "Invalid column access index" );
   BLAZE_INTERNAL_ASSERT( column + (*rhs).size() <= lhs.columns(), "Invalid number of columns" );

   MAYBE_UNUSED( lhs );

   using ET = ElementType_t< HermitianMatrix<MT,SO,DF> >;

   return ( IsBuiltin_v<ET> ||
            row < column ||
            (*rhs).size() <= row - column ||
            isReal( (*rhs)[row-column] ) );

   return true;
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the assignment of a dense vector to the band of
//        a Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side dense vector to be assigned.
// \param band The index of the band the right-hand side vector is assigned to.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF      // Density flag
        , typename VT  // Type of the right-hand side dense vector
        , bool TF >    // Transpose flag of the right-hand side dense vector
inline bool tryAssign( const HermitianMatrix<MT,SO,DF>& lhs, const DenseVector<VT,TF>& rhs,
                       ptrdiff_t band, size_t row, size_t column )
{
   BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( VT );

   BLAZE_INTERNAL_ASSERT( row <= lhs.rows(), "Invalid row access index" );
   BLAZE_INTERNAL_ASSERT( column <= lhs.columns(), "Invalid column access index" );
   BLAZE_INTERNAL_ASSERT( row + (*rhs).size() <= lhs.rows(), "Invalid number of rows" );
   BLAZE_INTERNAL_ASSERT( column + (*rhs).size() <= lhs.columns(), "Invalid number of columns" );

   MAYBE_UNUSED( lhs, row, column );

   if( band == 0L ) {
      for( size_t i=0UL; i<(*rhs).size(); ++i ) {
         if( !isReal( (*rhs)[i] ) )
            return false;
      }
   }

   return true;
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the assignment of a sparse vector to the band of
//        a Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side sparse vector to be assigned.
// \param band The index of the band the right-hand side vector is assigned to.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF      // Density flag
        , typename VT  // Type of the right-hand side sparse vector
        , bool TF >    // Transpose flag of the right-hand side sparse vector
inline bool tryAssign( const HermitianMatrix<MT,SO,DF>& lhs, const SparseVector<VT,TF>& rhs,
                       ptrdiff_t band, size_t row, size_t column )
{
   BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( VT );

   BLAZE_INTERNAL_ASSERT( row <= lhs.rows(), "Invalid row access index" );
   BLAZE_INTERNAL_ASSERT( column <= lhs.columns(), "Invalid column access index" );
   BLAZE_INTERNAL_ASSERT( row + (*rhs).size() <= lhs.rows(), "Invalid number of rows" );
   BLAZE_INTERNAL_ASSERT( column + (*rhs).size() <= lhs.columns(), "Invalid number of columns" );

   MAYBE_UNUSED( lhs, row, column );

   if( band == 0L ) {
      for( const auto& element : *rhs ) {
         if( !isReal( element.value() ) )
            return false;
      }
   }

   return true;
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the assignment of a matrix to a Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side matrix to be assigned.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT1  // Type of the adapted matrix
        , bool SO1      // Storage order of the adapted matrix
        , bool DF       // Density flag
        , typename MT2  // Type of the right-hand side matrix
        , bool SO2 >    // Storage order of the right-hand side matrix
inline bool tryAssign( const HermitianMatrix<MT1,SO1,DF>& lhs,
                       const Matrix<MT2,SO2>& rhs, size_t row, size_t column )
{
   BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( MT2 );

   BLAZE_INTERNAL_ASSERT( row <= lhs.rows(), "Invalid row access index" );
   BLAZE_INTERNAL_ASSERT( column <= lhs.columns(), "Invalid column access index" );
   BLAZE_INTERNAL_ASSERT( row + (*rhs).rows() <= lhs.rows(), "Invalid number of rows" );
   BLAZE_INTERNAL_ASSERT( column + (*rhs).columns() <= lhs.columns(), "Invalid number of columns" );

   MAYBE_UNUSED( lhs );

   const size_t M( (*rhs).rows()    );
   const size_t N( (*rhs).columns() );

   if( ( row + M <= column ) || ( column + N <= row ) )
      return true;

   const bool   lower( row > column );
   const size_t size ( min( row + M, column + N ) - ( lower ? row : column ) );

   if( size < 2UL )
      return true;

   const size_t subrow( lower ? 0UL : column - row );
   const size_t subcol( lower ? row - column : 0UL );

   return isHermitian( submatrix( *rhs, subrow, subcol, size, size ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the addition assignment of a vector to a Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side vector to be added.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF      // Density flag
        , typename VT  // Type of the right-hand side vector
        , bool TF >    // Transpose flag of the right-hand side vector
inline bool tryAddAssign( const HermitianMatrix<MT,SO,DF>& lhs,
                          const Vector<VT,TF>& rhs, size_t row, size_t column )
{
   return tryAssign( lhs, *rhs, row, column );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the addition assignment of a vector to the band of
//        a Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side vector to be added.
// \param band The index of the band the right-hand side vector is assigned to.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF      // Density flag
        , typename VT  // Type of the right-hand side vector
        , bool TF >    // Transpose flag of the right-hand side vector
inline bool tryAddAssign( const HermitianMatrix<MT,SO,DF>& lhs, const Vector<VT,TF>& rhs,
                          ptrdiff_t band, size_t row, size_t column )
{
   return tryAssign( lhs, *rhs, band, row, column );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the addition assignment of a matrix to a Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side matrix to be added.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT1  // Type of the adapted matrix
        , bool SO1      // Storage order of the adapted matrix
        , bool DF       // Density flag
        , typename MT2  // Type of the right-hand side matrix
        , bool SO2 >    // Storage order of the right-hand side matrix
inline bool tryAddAssign( const HermitianMatrix<MT1,SO1,DF>& lhs,
                          const Matrix<MT2,SO2>& rhs, size_t row, size_t column )
{
   return tryAssign( lhs, *rhs, row, column );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the subtraction assignment of a vector to a Hermitian
//        matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side vector to be subtracted.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF      // Density flag
        , typename VT  // Type of the right-hand side vector
        , bool TF >    // Transpose flag of the right-hand side vector
inline bool trySubAssign( const HermitianMatrix<MT,SO,DF>& lhs,
                          const Vector<VT,TF>& rhs, size_t row, size_t column )
{
   return tryAssign( lhs, *rhs, row, column );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the subtraction assignment of a vector to the band of
//        a Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side vector to be subtracted.
// \param band The index of the band the right-hand side vector is assigned to.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF      // Density flag
        , typename VT  // Type of the right-hand side vector
        , bool TF >    // Transpose flag of the right-hand side vector
inline bool trySubAssign( const HermitianMatrix<MT,SO,DF>& lhs, const Vector<VT,TF>& rhs,
                          ptrdiff_t band, size_t row, size_t column )
{
   return tryAssign( lhs, *rhs, band, row, column );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the subtraction assignment of a matrix to a Hermitian
//        matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side matrix to be subtracted.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT1  // Type of the adapted matrix
        , bool SO1      // Storage order of the adapted matrix
        , bool DF       // Density flag
        , typename MT2  // Type of the right-hand side matrix
        , bool SO2 >    // Storage order of the right-hand side matrix
inline bool trySubAssign( const HermitianMatrix<MT1,SO1,DF>& lhs,
                          const Matrix<MT2,SO2>& rhs, size_t row, size_t column )
{
   return tryAssign( lhs, *rhs, row, column );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the multiplication assignment of a vector to a Hermitian
//        matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side vector to be multiplied.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF      // Density flag
        , typename VT  // Type of the right-hand side vector
        , bool TF >    // Transpose flag of the right-hand side vector
inline bool tryMultAssign( const HermitianMatrix<MT,SO,DF>& lhs,
                           const Vector<VT,TF>& rhs, size_t row, size_t column )
{
   return tryAssign( lhs, *rhs, row, column );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the multiplication assignment of a vector to the band
//        of a Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side vector to be multiplied.
// \param band The index of the band the right-hand side vector is assigned to.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF      // Density flag
        , typename VT  // Type of the right-hand side vector
        , bool TF >    // Transpose flag of the right-hand side vector
inline bool tryMultAssign( const HermitianMatrix<MT,SO,DF>& lhs, const Vector<VT,TF>& rhs,
                           ptrdiff_t band, size_t row, size_t column )
{
   return tryAssign( lhs, *rhs, band, row, column );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the Schur product assignment of a matrix to a Hermitian
//        matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side matrix for the Schur product.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT1  // Type of the adapted matrix
        , bool SO1      // Storage order of the adapted matrix
        , bool DF       // Density flag
        , typename MT2  // Type of the right-hand side matrix
        , bool SO2 >    // Storage order of the right-hand side matrix
inline bool trySchurAssign( const HermitianMatrix<MT1,SO1,DF>& lhs,
                            const Matrix<MT2,SO2>& rhs, size_t row, size_t column )
{
   return tryAssign( lhs, *rhs, row, column );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the division assignment of a vector to a Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side vector divisor.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF      // Density flag
        , typename VT  // Type of the right-hand side vector
        , bool TF >    // Transpose flag of the right-hand side vector
inline bool tryDivAssign( const HermitianMatrix<MT,SO,DF>& lhs,
                          const Vector<VT,TF>& rhs, size_t row, size_t column )
{
   return tryAssign( lhs, *rhs, row, column );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Predict invariant violations by the division assignment of a vector to the band of
//        a Hermitian matrix.
// \ingroup hermitian_matrix
//
// \param lhs The target left-hand side Hermitian matrix.
// \param rhs The right-hand side vector divisor.
// \param band The index of the band the right-hand side vector is assigned to.
// \param row The row index of the first element to be modified.
// \param column The column index of the first element to be modified.
// \return \a true in case the assignment would be successful, \a false if not.
//
// This function must \b NOT be called explicitly! It is used internally for the performance
// optimized evaluation of expression templates. Calling this function explicitly might result
// in erroneous results and/or in compilation errors. Instead of using this function use the
// assignment operator.
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF      // Density flag
        , typename VT  // Type of the right-hand side vector
        , bool TF >    // Transpose flag of the right-hand side vector
inline bool tryDivAssign( const HermitianMatrix<MT,SO,DF>& lhs, const Vector<VT,TF>& rhs,
                          ptrdiff_t band, size_t row, size_t column )
{
   return tryAssign( lhs, *rhs, band, row, column );
}
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  SIZE SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct Size< HermitianMatrix<MT,SO,DF>, 0UL >
   : public Size<MT,0UL>
{};

template< typename MT, bool SO, bool DF >
struct Size< HermitianMatrix<MT,SO,DF>, 1UL >
   : public Size<MT,1UL>
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  MAXSIZE SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct MaxSize< HermitianMatrix<MT,SO,DF>, 0UL >
   : public MaxSize<MT,0UL>
{};

template< typename MT, bool SO, bool DF >
struct MaxSize< HermitianMatrix<MT,SO,DF>, 1UL >
   : public MaxSize<MT,1UL>
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ISSQUARE SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct IsSquare< HermitianMatrix<MT,SO,DF> >
   : public TrueType
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ISUNIFORM SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct IsUniform< HermitianMatrix<MT,SO,DF> >
   : public IsUniform<MT>
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ISSYMMETRIC SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct IsSymmetric< HermitianMatrix<MT,SO,DF> >
   : public IsBuiltin< ElementType_t<MT> >
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ISHERMITIAN SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct IsHermitian< HermitianMatrix<MT,SO,DF> >
   : public TrueType
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ISSTRICTLYLOWER SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct IsStrictlyLower< HermitianMatrix<MT,SO,DF> >
   : public IsZero<MT>
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ISSTRICTLYUPPER SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct IsStrictlyUpper< HermitianMatrix<MT,SO,DF> >
   : public IsZero<MT>
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ISADAPTOR SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct IsAdaptor< HermitianMatrix<MT,SO,DF> >
   : public TrueType
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ISRESTRICTED SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct IsRestricted< HermitianMatrix<MT,SO,DF> >
   : public TrueType
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  HASCONSTDATAACCESS SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO >
struct HasConstDataAccess< HermitianMatrix<MT,SO,true> >
   : public TrueType
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ISALIGNED SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct IsAligned< HermitianMatrix<MT,SO,DF> >
   : public IsAligned<MT>
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ISCONTIGUOUS SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct IsContiguous< HermitianMatrix<MT,SO,DF> >
   : public IsContiguous<MT>
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ISPADDED SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct IsPadded< HermitianMatrix<MT,SO,DF> >
   : public IsPadded<MT>
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  REMOVEADAPTOR SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct RemoveAdaptor< HermitianMatrix<MT,SO,DF> >
{
   using Type = MT;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ADDTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename T1, typename T2 >
struct AddTraitEval1< T1, T2
                    , EnableIf_t< IsMatrix_v<T1> &&
                                  IsMatrix_v<T2> &&
                                  ( ( IsHermitian_v<T1> && !IsSymmetric_v<T1> &&
                                      IsHermitian_v<T2> && !IsSymmetric_v<T2> ) ||
                                    ( IsHermitian_v<T1> && !IsSymmetric_v<T1> &&
                                      IsSymmetric_v<T2> && !IsComplex_v< UnderlyingScalar_t<T2> > ) ||
                                    ( IsSymmetric_v<T1> && !IsComplex_v< UnderlyingScalar_t<T1> > &&
                                      IsHermitian_v<T2> && !IsSymmetric_v<T2> ) ) &&
                                  !( IsUniform_v<T1> && IsUniform_v<T2> ) &&
                                  !( IsZero_v<T1> || IsZero_v<T2> ) > >
{
   using Type = HermitianMatrix< typename AddTraitEval2<T1,T2>::Type >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  SUBTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename T1, typename T2 >
struct SubTraitEval1< T1, T2
                    , EnableIf_t< IsMatrix_v<T1> &&
                                  IsMatrix_v<T2> &&
                                  ( ( IsHermitian_v<T1> && !IsSymmetric_v<T1> &&
                                      IsHermitian_v<T2> && !IsSymmetric_v<T2> ) ||
                                    ( IsHermitian_v<T1> && !IsSymmetric_v<T1> &&
                                      IsSymmetric_v<T2> && !IsComplex_v< UnderlyingScalar_t<T2> > ) ||
                                    ( IsSymmetric_v<T1> && !IsComplex_v< UnderlyingScalar_t<T1> > &&
                                      IsHermitian_v<T2> && !IsSymmetric_v<T2> ) ) &&
                                  !( IsZero_v<T1> || IsZero_v<T2> ) > >
{
   using Type = HermitianMatrix< typename SubTraitEval2<T1,T2>::Type >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  SCHURTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename T1, typename T2 >
struct SchurTraitEval1< T1, T2
                      , EnableIf_t< IsMatrix_v<T1> &&
                                    IsMatrix_v<T2> &&
                                    ( IsHermitian_v<T1> && IsHermitian_v<T2> ) &&
                                    !( IsSymmetric_v<T1> && IsSymmetric_v<T2> ) &&
                                    !( IsDiagonal_v<T1> || IsZero_v<T1> ) &&
                                    !( IsDiagonal_v<T2> || IsZero_v<T2> ) > >
{
   using Type = HermitianMatrix< typename SchurTraitEval2<T1,T2>::Type >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  MULTTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename T1, typename T2 >
struct MultTraitEval1< T1, T2
                     , EnableIf_t< IsMatrix_v<T1> &&
                                   IsScalar_v<T2> &&
                                   ( IsHermitian_v<T1> && !IsSymmetric_v<T1> && !IsUniform_v<T1> ) > >
{
   using Type = HermitianMatrix< typename MultTraitEval2<T1,T2>::Type >;
};

template< typename T1, typename T2 >
struct MultTraitEval1< T1, T2
                     , EnableIf_t< IsScalar_v<T1> &&
                                   IsMatrix_v<T2> &&
                                   ( IsHermitian_v<T2> && !IsSymmetric_v<T2> && !IsUniform_v<T2> ) > >
{
   using Type = HermitianMatrix< typename MultTraitEval2<T1,T2>::Type >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  KRONTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename T1, typename T2 >
struct KronTraitEval1< T1, T2
                     , EnableIf_t< IsMatrix_v<T1> &&
                                   IsMatrix_v<T2> &&
                                   ( IsHermitian_v<T1> && IsHermitian_v<T2> ) &&
                                   !( IsSymmetric_v<T1> && IsSymmetric_v<T2> ) &&
                                   !( IsZero_v<T1> || IsZero_v<T2> ) > >
{
   using Type = HermitianMatrix< typename KronTraitEval2<T1,T2>::Type >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  DIVTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename T1, typename T2 >
struct DivTraitEval1< T1, T2
                    , EnableIf_t< IsHermitian_v<T1> && !IsSymmetric_v<T1> && IsScalar_v<T2> > >
{
   using Type = HermitianMatrix< typename DivTraitEval2<T1,T2>::Type >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  MAPTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename T, typename OP >
struct UnaryMapTraitEval1< T, OP
                         , EnableIf_t< YieldsHermitian_v<OP,T> &&
                                       !YieldsSymmetric_v<OP,T> &&
                                       !YieldsIdentity_v<OP,T> > >
{
   using Type = HermitianMatrix< typename UnaryMapTraitEval2<T,OP>::Type, StorageOrder_v<T> >;
};
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename T1, typename T2, typename OP >
struct BinaryMapTraitEval1< T1, T2, OP
                          , EnableIf_t< YieldsHermitian_v<OP,T1,T2> &&
                                        !YieldsSymmetric_v<OP,T1,T2> &&
                                        !YieldsIdentity_v<OP,T1,T2> > >
{
   using Type = HermitianMatrix< typename BinaryMapTraitEval2<T1,T2,OP>::Type >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  REPEATTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename T, size_t R0, size_t R1 >
struct RepeatTraitEval1< T, R0, R1, inf
                       , EnableIf_t< R0 != inf && R1 != inf && R0 == R1 &&
                                     IsHermitian_v<T> && !IsSymmetric_v<T> > >
{
   using Type = HermitianMatrix< typename RepeatTraitEval2<T,R0,R1,inf>::Type >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  DECLSYMTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct DeclSymTrait< HermitianMatrix<MT,SO,DF> >
{
   using Type = SymmetricMatrix<MT,SO,DF>;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  DECLHERMTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct DeclHermTrait< HermitianMatrix<MT,SO,DF> >
{
   using Type = HermitianMatrix<MT,SO,DF>;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  DECLLOWTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct DeclLowTrait< HermitianMatrix<MT,SO,DF> >
{
   using Type = DiagonalMatrix<MT,SO,DF>;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  DECLUNILOWTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct DeclUniLowTrait< HermitianMatrix<MT,SO,DF> >
{
   using Type = IdentityMatrix< ElementType_t<MT>, SO >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  DECLSTRLOWTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct DeclStrLowTrait< HermitianMatrix<MT,SO,DF> >
{
   using Type = ZeroMatrix< ElementType_t<MT>, SO >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  DECLUPPTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct DeclUppTrait< HermitianMatrix<MT,SO,DF> >
{
   using Type = DiagonalMatrix<MT,SO,DF>;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  DECLUNIUPPTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct DeclUniUppTrait< HermitianMatrix<MT,SO,DF> >
{
   using Type = IdentityMatrix< ElementType_t<MT>, SO >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  DECLSTRUPPTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct DeclStrUppTrait< HermitianMatrix<MT,SO,DF> >
{
   using Type = ZeroMatrix< ElementType_t<MT>, SO >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  DECLDIAGTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, bool SO, bool DF >
struct DeclDiagTrait< HermitianMatrix<MT,SO,DF> >
{
   using Type = DiagonalMatrix<MT,SO,DF>;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  HIGHTYPE SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT1, bool SO1, bool DF1, typename MT2, bool SO2, bool DF2 >
struct HighType< HermitianMatrix<MT1,SO1,DF1>, HermitianMatrix<MT2,SO2,DF2> >
{
   using Type = HermitianMatrix< typename HighType<MT1,MT2>::Type >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  LOWTYPE SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT1, bool SO1, bool DF1, typename MT2, bool SO2, bool DF2 >
struct LowType< HermitianMatrix<MT1,SO1,DF1>, HermitianMatrix<MT2,SO2,DF2> >
{
   using Type = HermitianMatrix< typename LowType<MT1,MT2>::Type >;
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  SUBMATRIXTRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename MT, size_t I, size_t N >
struct SubmatrixTraitEval1< MT, I, I, N, N
                          , EnableIf_t< I != inf && N != inf &&
                                        IsHermitian_v<MT> &&
                                        !IsSymmetric_v<MT> > >
{
   using Type = HermitianMatrix< typename SubmatrixTraitEval2<MT,I,I,N,N>::Type >;
};
/*! \endcond */
//*************************************************************************************************

} // namespace blaze

#endif
