text: //=================================================================================================
  /*!
  //  \file blaze/math/views/band/Dense.h
  //  \brief Band specialization for dense matrices
  //
  //  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_VIEWS_BAND_DENSE_H_
  #define _BLAZE_MATH_VIEWS_BAND_DENSE_H_
  
  
  //*************************************************************************************************
  // Includes
  //*************************************************************************************************
  
  #include <algorithm>
  #include <iterator>
  #include <blaze/math/Aliases.h>
  #include <blaze/math/constraints/Computation.h>
  #include <blaze/math/constraints/DenseMatrix.h>
  #include <blaze/math/constraints/DenseVector.h>
  #include <blaze/math/constraints/MatMatMultExpr.h>
  #include <blaze/math/constraints/RequiresEvaluation.h>
  #include <blaze/math/constraints/TransExpr.h>
  #include <blaze/math/constraints/TransposeFlag.h>
  #include <blaze/math/constraints/UniTriangular.h>
  #include <blaze/math/dense/InitializerVector.h>
  #include <blaze/math/Exception.h>
  #include <blaze/math/expressions/DenseVector.h>
  #include <blaze/math/expressions/SparseVector.h>
  #include <blaze/math/expressions/View.h>
  #include <blaze/math/InitializerList.h>
  #include <blaze/math/shims/Clear.h>
  #include <blaze/math/shims/IsDefault.h>
  #include <blaze/math/shims/PrevMultiple.h>
  #include <blaze/math/shims/Reset.h>
  #include <blaze/math/traits/BandTrait.h>
  #include <blaze/math/traits/CrossTrait.h>
  #include <blaze/math/typetraits/HasMutableDataAccess.h>
  #include <blaze/math/typetraits/IsColumnMajorMatrix.h>
  #include <blaze/math/typetraits/IsExpression.h>
  #include <blaze/math/typetraits/IsLower.h>
  #include <blaze/math/typetraits/IsRestricted.h>
  #include <blaze/math/typetraits/IsRowMajorMatrix.h>
  #include <blaze/math/typetraits/IsSparseMatrix.h>
  #include <blaze/math/typetraits/IsSparseVector.h>
  #include <blaze/math/typetraits/IsStrictlyLower.h>
  #include <blaze/math/typetraits/IsStrictlyUpper.h>
  #include <blaze/math/typetraits/IsTriangular.h>
  #include <blaze/math/typetraits/IsUniLower.h>
  #include <blaze/math/typetraits/IsUniUpper.h>
  #include <blaze/math/typetraits/IsUpper.h>
  #include <blaze/math/typetraits/RequiresEvaluation.h>
  #include <blaze/math/views/band/BandData.h>
  #include <blaze/math/views/band/BaseTemplate.h>
  #include <blaze/math/views/Check.h>
  #include <blaze/system/Thresholds.h>
  #include <blaze/util/algorithms/Min.h>
  #include <blaze/util/Assert.h>
  #include <blaze/util/constraints/Pointer.h>
  #include <blaze/util/constraints/Reference.h>
  #include <blaze/util/mpl/If.h>
  #include <blaze/util/TypeList.h>
  #include <blaze/util/Types.h>
  #include <blaze/util/typetraits/IsConst.h>
  #include <blaze/util/typetraits/IsReference.h>
  #include <blaze/util/typetraits/RemoveReference.h>
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  CLASS TEMPLATE SPECIALIZATION FOR DENSE MATRICES
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Specialization of Band for dense matrices.
  // \ingroup views
  //
  // This specialization of Band adapts the class template to the requirements of dense matrices.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  class Band<MT,TF,true,false,CBAs...>
     : public View< DenseVector< Band<MT,TF,true,false,CBAs...>, TF > >
     , private BandData<CBAs...>
  {
   private:
     //**Type definitions****************************************************************************
     using RT       = ResultType_t<MT>;                     //!< Result type of the dense matrix expression.
     using DataType = BandData<CBAs...>;                    //!< The type of the BandData base class.
     using Operand  = If_t< IsExpression_v<MT>, MT, MT& >;  //!< Composite data type of the dense matrix expression.
     //**********************************************************************************************
  
   public:
     //**Type definitions****************************************************************************
     //! Type of this Band instance.
     using This = Band<MT,TF,true,false,CBAs...>;
  
     using BaseType      = DenseVector<This,TF>;         //!< Base type of this Band instance.
     using ViewedType    = MT;                           //!< The type viewed by this Band instance.
     using ResultType    = BandTrait_t<RT,CBAs...>;      //!< Result type for expression template evaluations.
     using TransposeType = TransposeType_t<ResultType>;  //!< Transpose type for expression template evaluations.
     using ElementType   = ElementType_t<MT>;            //!< Type of the band elements.
     using ReturnType    = ReturnType_t<MT>;             //!< Return type for expression template evaluations
  
     //! Data type for composite expression templates.
     using CompositeType = If_t< RequiresEvaluation_v<MT>, const ResultType, const Band& >;
  
     //! Reference to a constant band value.
     using ConstReference = ConstReference_t<MT>;
  
     //! Reference to a non-constant band value.
     using Reference = If_t< IsConst_v<MT>, ConstReference, Reference_t<MT> >;
  
     //! Pointer to a constant band value.
     using ConstPointer = ConstPointer_t<MT>;
  
     //! Pointer to a non-constant band value.
     using Pointer = If_t< IsConst_v<MT> || !HasMutableDataAccess_v<MT>, ConstPointer, Pointer_t<MT> >;
     //**********************************************************************************************
  
     //**BandIterator class definition***************************************************************
     /*!\brief Iterator over the elements of the dense band.
     */
     template< typename MatrixType      // Type of the dense matrix
             , typename IteratorType >  // Type of the dense matrix iterator
     class BandIterator
     {
      public:
        //**Type definitions*************************************************************************
        //! The iterator category.
        using IteratorCategory = typename std::iterator_traits<IteratorType>::iterator_category;
  
        //! Type of the underlying elements.
        using ValueType = typename std::iterator_traits<IteratorType>::value_type;
  
        //! Pointer return type.
        using PointerType = typename std::iterator_traits<IteratorType>::pointer;
  
        //! Reference return type.
        using ReferenceType = typename std::iterator_traits<IteratorType>::reference;
  
        //! Difference between two iterators.
        using DifferenceType = typename std::iterator_traits<IteratorType>::difference_type;
  
        // STL iterator requirements
        using iterator_category = IteratorCategory;  //!< The iterator category.
        using value_type        = ValueType;         //!< Type of the underlying elements.
        using pointer           = PointerType;       //!< Pointer return type.
        using reference         = ReferenceType;     //!< Reference return type.
        using difference_type   = DifferenceType;    //!< Difference between two iterators.
        //*******************************************************************************************
  
        //**Constructor******************************************************************************
        /*!\brief Default constructor of the BandIterator class.
        */
        inline BandIterator() noexcept
           : matrix_( nullptr )  // The dense matrix containing the band
           , row_   ( 0UL )      // The current row index
           , column_( 0UL )      // The current column index
           , pos_   (     )      // Iterator to the current dense element
        {}
        //*******************************************************************************************
  
        //**Constructor******************************************************************************
        /*!\brief Constructor of the BandIterator class.
        //
        // \param matrix The matrix containing the band.
        // \param rowIndex The initial row index.
        // \param columnIndex The initial column index.
        */
        inline BandIterator( MatrixType& matrix, size_t rowIndex, size_t columnIndex ) noexcept
           : matrix_( &matrix     )  // The dense matrix containing the band
           , row_   ( rowIndex    )  // The current row index
           , column_( columnIndex )  // The current column index
           , pos_   (             )  // Iterator to the current dense element
        {
           if( IsRowMajorMatrix_v<MatrixType> && row_ != matrix_->rows() )
              pos_ = matrix_->begin( row_ ) + column_;
           else if( IsColumnMajorMatrix_v<MatrixType> && column_ != matrix_->columns() )
              pos_ = matrix_->begin( column_ ) + row_;
        }
        //*******************************************************************************************
  
        //**Constructor******************************************************************************
        /*!\brief Conversion constructor from different BandIterator instances.
        //
        // \param it The band iterator to be copied.
        */
        template< typename MatrixType2, typename IteratorType2 >
        inline BandIterator( const BandIterator<MatrixType2,IteratorType2>& it ) noexcept
           : matrix_( it.matrix_ )  // The dense matrix containing the band
           , row_   ( it.row_    )  // The current row index
           , column_( it.column_ )  // The current column index
           , pos_   ( it.pos_    )  // Iterator to the current dense element
        {}
        //*******************************************************************************************
  
        //**Addition assignment operator*************************************************************
        /*!\brief Addition assignment operator.
        //
        // \param inc The increment of the iterator.
        // \return The incremented iterator.
        */
        inline BandIterator& operator+=( size_t inc ) noexcept {
           using blaze::reset;
  
           row_    += inc;
           column_ += inc;
  
           if( IsRowMajorMatrix_v<MatrixType> && row_ != matrix_->rows() )
              pos_ = matrix_->begin( row_ ) + column_;
           else if( IsColumnMajorMatrix_v<MatrixType> && column_ != matrix_->columns() )
              pos_ = matrix_->begin( column_ ) + row_;
           else reset( pos_ );
  
           return *this;
        }
        //*******************************************************************************************
  
        //**Subtraction assignment operator**********************************************************
        /*!\brief Subtraction assignment operator.
        //
        // \param dec The decrement of the iterator.
        // \return The decremented iterator.
        */
        inline BandIterator& operator-=( size_t dec ) noexcept {
           using blaze::reset;
  
           row_    -= dec;
           column_ -= dec;
  
           if( IsRowMajorMatrix_v<MatrixType> && row_ != matrix_->rows() )
              pos_ = matrix_->begin( row_ ) + column_;
           else if( IsColumnMajorMatrix_v<MatrixType> && column_ != matrix_->columns() )
              pos_ = matrix_->begin( column_ ) + row_;
           else reset( pos_ );
  
           return *this;
        }
        //*******************************************************************************************
  
        //**Prefix increment operator****************************************************************
        /*!\brief Pre-increment operator.
        //
        // \return Reference to the incremented iterator.
        */
        inline BandIterator& operator++() noexcept {
           using blaze::reset;
  
           ++row_;
           ++column_;
  
           if( IsRowMajorMatrix_v<MatrixType> && row_ != matrix_->rows() )
              pos_ = matrix_->begin( row_ ) + column_;
           else if( IsColumnMajorMatrix_v<MatrixType> && column_ != matrix_->columns() )
              pos_ = matrix_->begin( column_ ) + row_;
           else reset( pos_ );
  
           return *this;
        }
        //*******************************************************************************************
  
        //**Postfix increment operator***************************************************************
        /*!\brief Post-increment operator.
        //
        // \return The previous position of the iterator.
        */
        inline const BandIterator operator++( int ) noexcept {
           const BandIterator tmp( *this );
           ++(*this);
           return tmp;
        }
        //*******************************************************************************************
  
        //**Prefix decrement operator****************************************************************
        /*!\brief Pre-decrement operator.
        //
        // \return Reference to the decremented iterator.
        */
        inline BandIterator& operator--() noexcept {
           using blaze::reset;
  
           --row_;
           --column_;
  
           if( IsRowMajorMatrix_v<MatrixType> && row_ != matrix_->rows() )
              pos_ = matrix_->begin( row_ ) + column_;
           else if( IsColumnMajorMatrix_v<MatrixType> && column_ != matrix_->columns() )
              pos_ = matrix_->begin( column_ ) + row_;
           else reset( pos_ );
  
           return *this;
        }
        //*******************************************************************************************
  
        //**Postfix decrement operator***************************************************************
        /*!\brief Post-decrement operator.
        //
        // \return The previous position of the iterator.
        */
        inline const BandIterator operator--( int ) noexcept {
           const BandIterator tmp( *this );
           --(*this);
           return tmp;
        }
        //*******************************************************************************************
  
        //**Subscript operator***********************************************************************
        /*!\brief Direct access to the dense band elements.
        //
        // \param index Access index.
        // \return Reference to the accessed value.
        */
        inline ReferenceType operator[]( size_t index ) const {
           BLAZE_USER_ASSERT( row_   +index < matrix_->rows()   , "Invalid access index detected" );
           BLAZE_USER_ASSERT( column_+index < matrix_->columns(), "Invalid access index detected" );
           const IteratorType pos( IsRowMajorMatrix_v<MatrixType>
                                 ? matrix_->begin( row_+index ) + column_ + index
                                 : matrix_->begin( column_+index ) + row_ + index );
           return *pos;
        }
        //*******************************************************************************************
  
        //**Element access operator******************************************************************
        /*!\brief Direct access to the dense band element at the current iterator position.
        //
        // \return Reference to the current value.
        */
        inline ReferenceType operator*() const {
           return *pos_;
        }
        //*******************************************************************************************
  
        //**Element access operator******************************************************************
        /*!\brief Direct access to the dense band element at the current iterator position.
        //
        // \return Pointer to the dense band element at the current iterator position.
        */
        inline PointerType operator->() const {
           return pos_;
        }
        //*******************************************************************************************
  
        //**Equality operator************************************************************************
        /*!\brief Equality comparison between two BandIterator objects.
        //
        // \param rhs The right-hand side band iterator.
        // \return \a true if the iterators refer to the same element, \a false if not.
        */
        template< typename MatrixType2, typename IteratorType2 >
        inline bool operator==( const BandIterator<MatrixType2,IteratorType2>& rhs ) const noexcept {
           return row_ == rhs.row_;
        }
        //*******************************************************************************************
  
        //**Inequality operator**********************************************************************
        /*!\brief Inequality comparison between two BandIterator objects.
        //
        // \param rhs The right-hand side band iterator.
        // \return \a true if the iterators don't refer to the same element, \a false if they do.
        */
        template< typename MatrixType2, typename IteratorType2 >
        inline bool operator!=( const BandIterator<MatrixType2,IteratorType2>& rhs ) const noexcept {
           return !( *this == rhs );
        }
        //*******************************************************************************************
  
        //**Less-than operator***********************************************************************
        /*!\brief Less-than comparison between two BandIterator objects.
        //
        // \param rhs The right-hand side band iterator.
        // \return \a true if the left-hand side iterator is smaller, \a false if not.
        */
        template< typename MatrixType2, typename IteratorType2 >
        inline bool operator<( const BandIterator<MatrixType2,IteratorType2>& rhs ) const noexcept {
           return row_ < rhs.row_;
        }
        //*******************************************************************************************
  
        //**Greater-than operator********************************************************************
        /*!\brief Greater-than comparison between two BandIterator objects.
        //
        // \param rhs The right-hand side band iterator.
        // \return \a true if the left-hand side iterator is greater, \a false if not.
        */
        template< typename MatrixType2, typename IteratorType2 >
        inline bool operator>( const BandIterator<MatrixType2,IteratorType2>& rhs ) const noexcept {
           return row_ > rhs.row_;
        }
        //*******************************************************************************************
  
        //**Less-or-equal-than operator**************************************************************
        /*!\brief Less-than comparison between two BandIterator objects.
        //
        // \param rhs The right-hand side band iterator.
        // \return \a true if the left-hand side iterator is smaller or equal, \a false if not.
        */
        template< typename MatrixType2, typename IteratorType2 >
        inline bool operator<=( const BandIterator<MatrixType2,IteratorType2>& rhs ) const noexcept {
           return row_ <= rhs.row_;
        }
        //*******************************************************************************************
  
        //**Greater-or-equal-than operator***********************************************************
        /*!\brief Greater-than comparison between two BandIterator objects.
        //
        // \param rhs The right-hand side band iterator.
        // \return \a true if the left-hand side iterator is greater or equal, \a false if not.
        */
        template< typename MatrixType2, typename IteratorType2 >
        inline bool operator>=( const BandIterator<MatrixType2,IteratorType2>& rhs ) const noexcept {
           return row_ >= rhs.row_;
        }
        //*******************************************************************************************
  
        //**Subtraction operator*********************************************************************
        /*!\brief Calculating the number of elements between two band iterators.
        //
        // \param rhs The right-hand side band iterator.
        // \return The number of elements between the two band iterators.
        */
        inline DifferenceType operator-( const BandIterator& rhs ) const noexcept {
           return row_ - rhs.row_;
        }
        //*******************************************************************************************
  
        //**Addition operator************************************************************************
        /*!\brief Addition between a BandIterator and an integral value.
        //
        // \param it The iterator to be incremented.
        // \param inc The number of elements the iterator is incremented.
        // \return The incremented iterator.
        */
        friend inline const BandIterator operator+( const BandIterator& it, size_t inc ) noexcept {
           return BandIterator( *it.matrix_, it.row_+inc, it.column_+inc );
        }
        //*******************************************************************************************
  
        //**Addition operator************************************************************************
        /*!\brief Addition between an integral value and a BandIterator.
        //
        // \param inc The number of elements the iterator is incremented.
        // \param it The iterator to be incremented.
        // \return The incremented iterator.
        */
        friend inline const BandIterator operator+( size_t inc, const BandIterator& it ) noexcept {
           return BandIterator( *it.matrix_, it.row_+inc, it.column_+inc );
        }
        //*******************************************************************************************
  
        //**Subtraction operator*********************************************************************
        /*!\brief Subtraction between a BandIterator and an integral value.
        //
        // \param it The iterator to be decremented.
        // \param inc The number of elements the iterator is decremented.
        // \return The decremented iterator.
        */
        friend inline const BandIterator operator-( const BandIterator& it, size_t dec ) noexcept {
           return BandIterator( *it.matrix_, it.row_-dec, it.column_-dec );
        }
        //*******************************************************************************************
  
      private:
        //**Member variables*************************************************************************
        MatrixType*  matrix_;  //!< The dense matrix containing the band.
        size_t       row_;     //!< The current row index.
        size_t       column_;  //!< The current column index.
        IteratorType pos_;     //!< Iterator to the current dense element.
        //*******************************************************************************************
  
        //**Friend declarations**********************************************************************
        template< typename MatrixType2, typename IteratorType2 > friend class BandIterator;
        //*******************************************************************************************
     };
     //**********************************************************************************************
  
     //**Type definitions****************************************************************************
     //! Iterator over constant elements.
     using ConstIterator = BandIterator< const MT, ConstIterator_t<MT> >;
  
     //! Iterator over non-constant elements.
     using Iterator = If_t< IsConst_v<MT>, ConstIterator, BandIterator< MT, Iterator_t<MT> > >;
     //**********************************************************************************************
  
     //**Compilation flags***************************************************************************
     //! Compilation switch for the expression template evaluation strategy.
     static constexpr bool simdEnabled = false;
  
     //! Compilation switch for the expression template assignment strategy.
     static constexpr bool smpAssignable = MT::smpAssignable;
  
     //! Compilation switch for the expression template evaluation strategy.
     static constexpr bool compileTimeArgs = DataType::compileTimeArgs;
     //**********************************************************************************************
  
     //**Constructors********************************************************************************
     /*!\name Constructors */
     //@{
     template< typename... RBAs >
     explicit inline Band( MT& matrix, RBAs... args );
  
     Band( const Band& ) = default;
     //@}
     //**********************************************************************************************
  
     //**Destructor**********************************************************************************
     /*!\name Destructor */
     //@{
     ~Band() = default;
     //@}
     //**********************************************************************************************
  
     //**Data access functions***********************************************************************
     /*!\name Data access functions */
     //@{
     inline Reference      operator[]( size_t index );
     inline ConstReference operator[]( size_t index ) const;
     inline Reference      at( size_t index );
     inline ConstReference at( size_t index ) const;
     inline Pointer        data  () noexcept;
     inline ConstPointer   data  () const noexcept;
     inline Iterator       begin ();
     inline ConstIterator  begin () const;
     inline ConstIterator  cbegin() const;
     inline Iterator       end   ();
     inline ConstIterator  end   () const;
     inline ConstIterator  cend  () const;
     //@}
     //**********************************************************************************************
  
     //**Assignment operators************************************************************************
     /*!\name Assignment operators */
     //@{
     inline Band& operator=( const ElementType& rhs );
     inline Band& operator=( initializer_list<ElementType> list );
     inline Band& operator=( const Band& rhs );
  
     template< typename VT > inline Band& operator= ( const Vector<VT,TF>& rhs );
     template< typename VT > inline Band& operator+=( const Vector<VT,TF>& rhs );
     template< typename VT > inline Band& operator-=( const Vector<VT,TF>& rhs );
     template< typename VT > inline Band& operator*=( const Vector<VT,TF>& rhs );
     template< typename VT > inline Band& operator/=( const DenseVector<VT,TF>&  rhs );
     template< typename VT > inline Band& operator%=( const Vector<VT,TF>& rhs );
     //@}
     //**********************************************************************************************
  
     //**Utility functions***************************************************************************
     /*!\name Utility functions */
     //@{
     using DataType::band;
     using DataType::row;
     using DataType::column;
  
     inline MT&       operand() noexcept;
     inline const MT& operand() const noexcept;
  
     inline size_t size() const noexcept;
     inline size_t spacing() const noexcept;
     inline size_t capacity() const noexcept;
     inline size_t nonZeros() const;
     inline void   reset();
     //@}
     //**********************************************************************************************
  
     //**Numeric functions***************************************************************************
     /*!\name Numeric functions */
     //@{
     template< typename Other > inline Band& scale( const Other& scalar );
     //@}
     //**********************************************************************************************
  
     //**Expression template evaluation functions****************************************************
     /*!\name Expression template evaluation functions */
     //@{
     template< typename Other >
     inline bool canAlias( const Other* alias ) const noexcept;
  
     template< typename MT2, ptrdiff_t... CBAs2 >
     inline bool canAlias( const Band<MT2,TF,true,false,CBAs2...>* alias ) const noexcept;
  
     template< typename Other >
     inline bool isAliased( const Other* alias ) const noexcept;
  
     template< typename MT2, ptrdiff_t... CBAs2 >
     inline bool isAliased( const Band<MT2,TF,true,false,CBAs2...>* alias ) const noexcept;
  
     inline bool isAligned   () const noexcept;
     inline bool canSMPAssign() const noexcept;
  
     template< typename VT > inline void assign    ( const DenseVector <VT,TF>& rhs );
     template< typename VT > inline void assign    ( const SparseVector<VT,TF>& rhs );
     template< typename VT > inline void addAssign ( const DenseVector <VT,TF>& rhs );
     template< typename VT > inline void addAssign ( const SparseVector<VT,TF>& rhs );
     template< typename VT > inline void subAssign ( const DenseVector <VT,TF>& rhs );
     template< typename VT > inline void subAssign ( const SparseVector<VT,TF>& rhs );
     template< typename VT > inline void multAssign( const DenseVector <VT,TF>& rhs );
     template< typename VT > inline void multAssign( const SparseVector<VT,TF>& rhs );
     template< typename VT > inline void divAssign ( const DenseVector <VT,TF>& rhs );
     //@}
     //**********************************************************************************************
  
   private:
     //**Member variables****************************************************************************
     /*!\name Member variables */
     //@{
     Operand matrix_;  //!< The matrix containing the band.
     //@}
     //**********************************************************************************************
  
     //**Friend declarations*************************************************************************
     template< typename MT2, bool TF2, bool DF2, bool MF2, ptrdiff_t... CBAs2 > friend class Band;
     //**********************************************************************************************
  
     //**Compile time checks*************************************************************************
     BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE   ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_TRANSEXPR_TYPE  ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_POINTER_TYPE    ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_REFERENCE_TYPE  ( MT );
     //**********************************************************************************************
  };
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  CONSTRUCTORS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Constructor for bands on dense matrices.
  //
  // \param matrix The matrix containing the band.
  // \param args The runtime band arguments.
  // \exception std::invalid_argument Invalid band access index.
  //
  // By default, the provided band arguments are checked at runtime. In case the band is not
  // properly specified (i.e. if the specified index does not correspond to a valid band in the
  // given matrix) a \a std::invalid_argument exception is thrown. The checks can be skipped by
  // providing the optional \a blaze::unchecked argument.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename... RBAs >   // Runtime band arguments
  inline Band<MT,TF,true,false,CBAs...>::Band( MT& matrix, RBAs... args )
     : DataType( args... )  // Base class initialization
     , matrix_ ( matrix  )  // The matrix containing the band
  {
     if( !Contains_v< TypeList<RBAs...>, Unchecked > ) {
        if( ( band() > 0L && column() >= matrix.columns() ) ||
            ( band() < 0L && row() >= matrix.rows() ) ) {
           BLAZE_THROW_INVALID_ARGUMENT( "Invalid band access index" );
        }
     }
     else {
        BLAZE_USER_ASSERT( band() <= 0L || column() < matrix.columns(), "Invalid band access index" );
        BLAZE_USER_ASSERT( band() >= 0L || row() < matrix.rows(), "Invalid band access index" );
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  DATA ACCESS FUNCTIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Subscript operator for the direct access to the band elements.
  //
  // \param index Access index. The index must be smaller than the number of matrix columns.
  // \return Reference to the accessed value.
  //
  // This function only performs an index check in case BLAZE_USER_ASSERT() is active. In contrast,
  // the at() function is guaranteed to perform a check of the given access index.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline typename Band<MT,TF,true,false,CBAs...>::Reference
     Band<MT,TF,true,false,CBAs...>::operator[]( size_t index )
  {
     BLAZE_USER_ASSERT( index < size(), "Invalid band access index" );
     return matrix_(row()+index,column()+index);
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Subscript operator for the direct access to the band elements.
  //
  // \param index Access index. The index must be smaller than the number of matrix columns.
  // \return Reference to the accessed value.
  //
  // This function only performs an index check in case BLAZE_USER_ASSERT() is active. In contrast,
  // the at() function is guaranteed to perform a check of the given access index.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline typename Band<MT,TF,true,false,CBAs...>::ConstReference
     Band<MT,TF,true,false,CBAs...>::operator[]( size_t index ) const
  {
     BLAZE_USER_ASSERT( index < size(), "Invalid band access index" );
     return const_cast<const MT&>( matrix_ )(row()+index,column()+index);
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Checked access to the band elements.
  //
  // \param index Access index. The index must be smaller than the number of matrix columns.
  // \return Reference to the accessed value.
  // \exception std::out_of_range Invalid band access index.
  //
  // In contrast to the subscript operator this function always performs a check of the given
  // access index.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline typename Band<MT,TF,true,false,CBAs...>::Reference
     Band<MT,TF,true,false,CBAs...>::at( size_t index )
  {
     if( index >= size() ) {
        BLAZE_THROW_OUT_OF_RANGE( "Invalid band access index" );
     }
     return (*this)[index];
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Checked access to the band elements.
  //
  // \param index Access index. The index must be smaller than the number of matrix columns.
  // \return Reference to the accessed value.
  // \exception std::out_of_range Invalid band access index.
  //
  // In contrast to the subscript operator this function always performs a check of the given
  // access index.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline typename Band<MT,TF,true,false,CBAs...>::ConstReference
     Band<MT,TF,true,false,CBAs...>::at( size_t index ) const
  {
     if( index >= size() ) {
        BLAZE_THROW_OUT_OF_RANGE( "Invalid band access index" );
     }
     return (*this)[index];
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Low-level data access to the band elements.
  //
  // \return Pointer to the internal element storage.
  //
  // This function returns a pointer to the internal storage of the dense band. Note that you
  // can NOT assume that the band elements lie adjacent to each other!
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline typename Band<MT,TF,true,false,CBAs...>::Pointer
     Band<MT,TF,true,false,CBAs...>::data() noexcept
  {
     if( IsRowMajorMatrix_v<MT> )
        return matrix_.data() + row() * matrix_.spacing() + column();
     else
        return matrix_.data() + row() + column() * matrix_.spacing();
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Low-level data access to the row elements.
  //
  // \return Pointer to the internal element storage.
  //
  // This function returns a pointer to the internal storage of the dense band. Note that you
  // can NOT assume that the band elements lie adjacent to each other!
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline typename Band<MT,TF,true,false,CBAs...>::ConstPointer
     Band<MT,TF,true,false,CBAs...>::data() const noexcept
  {
     if( IsRowMajorMatrix_v<MT> )
        return matrix_.data() + row() * matrix_.spacing() + column();
     else
        return matrix_.data() + row() + column() * matrix_.spacing();
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns an iterator to the first element of the band.
  //
  // \return Iterator to the first element of the band.
  //
  // This function returns an iterator to the first element of the band.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline typename Band<MT,TF,true,false,CBAs...>::Iterator
     Band<MT,TF,true,false,CBAs...>::begin()
  {
     return Iterator( matrix_, row(), column() );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns an iterator to the first element of the band.
  //
  // \return Iterator to the first element of the band.
  //
  // This function returns an iterator to the first element of the band.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline typename Band<MT,TF,true,false,CBAs...>::ConstIterator
     Band<MT,TF,true,false,CBAs...>::begin() const
  {
     return ConstIterator( matrix_, row(), column() );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns an iterator to the first element of the band.
  //
  // \return Iterator to the first element of the band.
  //
  // This function returns an iterator to the first element of the band.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline typename Band<MT,TF,true,false,CBAs...>::ConstIterator
     Band<MT,TF,true,false,CBAs...>::cbegin() const
  {
     return ConstIterator( matrix_, row(), column() );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns an iterator just past the last element of the band.
  //
  // \return Iterator just past the last element of the band.
  //
  // This function returns an iterator just past the last element of the band.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline typename Band<MT,TF,true,false,CBAs...>::Iterator
     Band<MT,TF,true,false,CBAs...>::end()
  {
     const size_t n( size() );
     return Iterator( matrix_, row()+n, column()+n );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns an iterator just past the last element of the band.
  //
  // \return Iterator just past the last element of the band.
  //
  // This function returns an iterator just past the last element of the band.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline typename Band<MT,TF,true,false,CBAs...>::ConstIterator
     Band<MT,TF,true,false,CBAs...>::end() const
  {
     const size_t n( size() );
     return ConstIterator( matrix_, row()+n, column()+n );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns an iterator just past the last element of the band.
  //
  // \return Iterator just past the last element of the band.
  //
  // This function returns an iterator just past the last element of the band.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline typename Band<MT,TF,true,false,CBAs...>::ConstIterator
     Band<MT,TF,true,false,CBAs...>::cend() const
  {
     const size_t n( size() );
     return ConstIterator( matrix_, row()+n, column()+n );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ASSIGNMENT OPERATORS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Homogenous assignment to all band elements.
  //
  // \param rhs Scalar value to be assigned to all band elements.
  // \return Reference to the assigned band.
  //
  // This function homogeneously assigns the given value to all elements of the band. Note that in
  // case the underlying dense matrix is a lower/upper matrix only lower/upper and diagonal elements
  // of the underlying matrix are modified.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline Band<MT,TF,true,false,CBAs...>&
     Band<MT,TF,true,false,CBAs...>::operator=( const ElementType& rhs )
  {
     decltype(auto) left( derestrict( matrix_ ) );
  
     if( ( IsLower_v<MT> && column() > 0UL ) ||
         ( ( IsUniLower_v<MT> || IsStrictlyLower_v<MT> ) && row() == 0UL ) ||
         ( IsUpper_v<MT> && row() > 0UL ) ||
         ( ( IsUniUpper_v<MT> || IsStrictlyUpper_v<MT> ) && column() == 0UL ) )
        return *this;
  
     const size_t n( size() );
     for( size_t i=0UL; i<n; ++i ) {
        if( !IsRestricted_v<MT> || IsTriangular_v<MT> || trySet( matrix_, row()+i, column()+i, rhs ) )
           left(row()+i,column()+i) = rhs;
     }
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief List assignment to all band elements.
  //
  // \param list The initializer list.
  // \exception std::invalid_argument Invalid assignment to band.
  // \exception std::invalid_argument Invalid assignment to restricted matrix.
  //
  // This assignment operator offers the option to directly assign to all elements of the dense
  // band by means of an initializer list. The band elements are assigned the values from the given
  // initializer list. Missing values are reset to their default state. Note that in case the size
  // of the initializer list exceeds the size of the band, a \a std::invalid_argument exception is
  // thrown. Also, if the underlying matrix \a MT is restricted and the assignment would violate an
  // invariant of the matrix, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline Band<MT,TF,true,false,CBAs...>&
     Band<MT,TF,true,false,CBAs...>::operator=( initializer_list<ElementType> list )
  {
     if( list.size() > size() ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to band" );
     }
  
     if( IsRestricted_v<MT> ) {
        const InitializerVector<ElementType,false> tmp( list, size() );
        if( !tryAssign( matrix_, tmp, band(), row(), column() ) ) {
           BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to restricted matrix" );
        }
     }
  
     decltype(auto) left( derestrict( *this ) );
  
     std::fill( std::copy( list.begin(), list.end(), left.begin() ), left.end(), ElementType() );
  
     BLAZE_INTERNAL_ASSERT( isIntact( matrix_ ), "Invariant violation detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Copy assignment operator for Band.
  //
  // \param rhs Dense band to be copied.
  // \return Reference to the assigned band.
  // \exception std::invalid_argument Band sizes do not match.
  // \exception std::invalid_argument Invalid assignment to restricted matrix.
  //
  // In case the current sizes of the two bands don't match, a \a std::invalid_argument exception
  // is thrown. Also, if the underlying matrix \a MT is a lower or upper triangular matrix and the
  // assignment would violate its lower or upper property, respectively, a \a std::invalid_argument
  // exception is thrown.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline Band<MT,TF,true,false,CBAs...>&
     Band<MT,TF,true,false,CBAs...>::operator=( const Band& rhs )
  {
     if( &rhs == this ) return *this;
  
     if( size() != rhs.size() ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Band sizes do not match" );
     }
  
     if( !tryAssign( matrix_, rhs, band(), row(), column() ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to restricted matrix" );
     }
  
     decltype(auto) left( derestrict( *this ) );
  
     if( IsExpression_v<MT> && rhs.canAlias( this ) ) {
        const ResultType tmp( rhs );
        smpAssign( left, tmp );
     }
     else {
        smpAssign( left, rhs );
     }
  
     BLAZE_INTERNAL_ASSERT( isIntact( matrix_ ), "Invariant violation detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Assignment operator for different vectors.
  //
  // \param rhs Vector to be assigned.
  // \return Reference to the assigned band.
  // \exception std::invalid_argument Vector sizes do not match.
  // \exception std::invalid_argument Invalid assignment to restricted matrix.
  //
  // In case the current sizes of the two vectors don't match, a \a std::invalid_argument exception
  // is thrown. Also, if the underlying matrix \a MT is a lower or upper triangular matrix and the
  // assignment would violate its lower or upper property, respectively, a \a std::invalid_argument
  // exception is thrown.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side vector
  inline Band<MT,TF,true,false,CBAs...>&
     Band<MT,TF,true,false,CBAs...>::operator=( const Vector<VT,TF>& rhs )
  {
     BLAZE_CONSTRAINT_MUST_BE_VECTOR_WITH_TRANSPOSE_FLAG( ResultType_t<VT>, TF );
     BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( ResultType_t<VT> );
  
     if( size() != (~rhs).size() ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Vector sizes do not match" );
     }
  
     using Right = If_t< IsRestricted_v<MT>, CompositeType_t<VT>, const VT& >;
     Right right( ~rhs );
  
     if( !tryAssign( matrix_, right, band(), row(), column() ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to restricted matrix" );
     }
  
     decltype(auto) left( derestrict( *this ) );
  
     if( IsReference_v<Right> && right.canAlias( this ) ) {
        const ResultType_t<VT> tmp( right );
        smpAssign( left, tmp );
     }
     else {
        if( IsSparseVector_v<VT> )
           reset();
        smpAssign( left, right );
     }
  
     BLAZE_INTERNAL_ASSERT( isIntact( matrix_ ), "Invariant violation detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Addition assignment operator for the addition of a vector (\f$ \vec{a}+=\vec{b} \f$).
  //
  // \param rhs The right-hand side vector to be added to the dense band.
  // \return Reference to the assigned band.
  // \exception std::invalid_argument Vector sizes do not match.
  // \exception std::invalid_argument Invalid assignment to restricted matrix.
  //
  // In case the current sizes of the two vectors don't match, a \a std::invalid_argument exception
  // is thrown. Also, if the underlying matrix \a MT is a lower or upper triangular matrix and the
  // assignment would violate its lower or upper property, respectively, a \a std::invalid_argument
  // exception is thrown.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side vector
  inline Band<MT,TF,true,false,CBAs...>&
     Band<MT,TF,true,false,CBAs...>::operator+=( const Vector<VT,TF>& rhs )
  {
     BLAZE_CONSTRAINT_MUST_BE_VECTOR_WITH_TRANSPOSE_FLAG( ResultType_t<VT>, TF );
     BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( ResultType_t<VT> );
  
     if( size() != (~rhs).size() ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Vector sizes do not match" );
     }
  
     using Right = If_t< IsRestricted_v<MT>, CompositeType_t<VT>, const VT& >;
     Right right( ~rhs );
  
     if( !tryAddAssign( matrix_, right, band(), row(), column() ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to restricted matrix" );
     }
  
     decltype(auto) left( derestrict( *this ) );
  
     if( IsReference_v<Right> && right.canAlias( this ) ) {
        const ResultType_t<VT> tmp( right );
        smpAddAssign( left, tmp );
     }
     else {
        smpAddAssign( left, right );
     }
  
     BLAZE_INTERNAL_ASSERT( isIntact( matrix_ ), "Invariant violation detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Subtraction assignment operator for the subtraction of a vector (\f$ \vec{a}-=\vec{b} \f$).
  //
  // \param rhs The right-hand side vector to be subtracted from the dense band.
  // \return Reference to the assigned band.
  // \exception std::invalid_argument Vector sizes do not match.
  // \exception std::invalid_argument Invalid assignment to restricted matrix.
  //
  // In case the current sizes of the two vectors don't match, a \a std::invalid_argument exception
  // is thrown. Also, if the underlying matrix \a MT is a lower or upper triangular matrix and the
  // assignment would violate its lower or upper property, respectively, a \a std::invalid_argument
  // exception is thrown.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side vector
  inline Band<MT,TF,true,false,CBAs...>&
     Band<MT,TF,true,false,CBAs...>::operator-=( const Vector<VT,TF>& rhs )
  {
     BLAZE_CONSTRAINT_MUST_BE_VECTOR_WITH_TRANSPOSE_FLAG( ResultType_t<VT>, TF );
     BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( ResultType_t<VT> );
  
     if( size() != (~rhs).size() ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Vector sizes do not match" );
     }
  
     using Right = If_t< IsRestricted_v<MT>, CompositeType_t<VT>, const VT& >;
     Right right( ~rhs );
  
     if( !trySubAssign( matrix_, right, band(), row(), column() ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to restricted matrix" );
     }
  
     decltype(auto) left( derestrict( *this ) );
  
     if( IsReference_v<Right> && right.canAlias( this ) ) {
        const ResultType_t<VT> tmp( right );
        smpSubAssign( left, tmp );
     }
     else {
        smpSubAssign( left, right );
     }
  
     BLAZE_INTERNAL_ASSERT( isIntact( matrix_ ), "Invariant violation detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Multiplication assignment operator for the multiplication of a vector
  //        (\f$ \vec{a}*=\vec{b} \f$).
  //
  // \param rhs The right-hand side vector to be multiplied with the dense band.
  // \return Reference to the assigned band.
  // \exception std::invalid_argument Vector sizes do not match.
  // \exception std::invalid_argument Invalid assignment to restricted matrix.
  //
  // In case the current sizes of the two vectors don't match, a \a std::invalid_argument exception
  // is thrown.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side vector
  inline Band<MT,TF,true,false,CBAs...>&
     Band<MT,TF,true,false,CBAs...>::operator*=( const Vector<VT,TF>& rhs )
  {
     BLAZE_CONSTRAINT_MUST_BE_DENSE_VECTOR_TYPE( ResultType );
     BLAZE_CONSTRAINT_MUST_BE_VECTOR_WITH_TRANSPOSE_FLAG( ResultType, TF );
     BLAZE_CONSTRAINT_MUST_BE_VECTOR_WITH_TRANSPOSE_FLAG( ResultType_t<VT>, TF );
     BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( ResultType );
     BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( ResultType_t<VT> );
  
     if( size() != (~rhs).size() ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Vector sizes do not match" );
     }
  
     using Right = If_t< IsRestricted_v<MT>, CompositeType_t<VT>, const VT& >;
     Right right( ~rhs );
  
     if( !tryMultAssign( matrix_, right, band(), row(), column() ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to restricted matrix" );
     }
  
     decltype(auto) left( derestrict( *this ) );
  
     if( IsReference_v<Right> && right.canAlias( this ) ) {
        const ResultType_t<VT> tmp( right );
        smpMultAssign( left, tmp );
     }
     else {
        smpMultAssign( left, right );
     }
  
     BLAZE_INTERNAL_ASSERT( isIntact( matrix_ ), "Invariant violation detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Division assignment operator for the division of a dense vector (\f$ \vec{a}/=\vec{b} \f$).
  //
  // \param rhs The right-hand side dense vector divisor.
  // \return Reference to the assigned row.
  // \exception std::invalid_argument Vector sizes do not match.
  // \exception std::invalid_argument Invalid assignment to restricted matrix.
  //
  // In case the current sizes of the two vectors don't match, a \a std::invalid_argument exception
  // is thrown.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side dense vector
  inline Band<MT,TF,true,false,CBAs...>&
     Band<MT,TF,true,false,CBAs...>::operator/=( const DenseVector<VT,TF>& rhs )
  {
     BLAZE_CONSTRAINT_MUST_BE_VECTOR_WITH_TRANSPOSE_FLAG( ResultType_t<VT>, TF );
     BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( ResultType_t<VT> );
  
     if( size() != (~rhs).size() ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Vector sizes do not match" );
     }
  
     using Right = If_t< IsRestricted_v<MT>, CompositeType_t<VT>, const VT& >;
     Right right( ~rhs );
  
     if( !tryDivAssign( matrix_, right, band(), row(), column() ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to restricted matrix" );
     }
  
     decltype(auto) left( derestrict( *this ) );
  
     if( IsReference_v<Right> && right.canAlias( this ) ) {
        const ResultType_t<VT> tmp( right );
        smpDivAssign( left, tmp );
     }
     else {
        smpDivAssign( left, right );
     }
  
     BLAZE_INTERNAL_ASSERT( isIntact( matrix_ ), "Invariant violation detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Cross product assignment operator for the multiplication of a vector
  //        (\f$ \vec{a}\times=\vec{b} \f$).
  //
  // \param rhs The right-hand side vector for the cross product.
  // \return Reference to the assigned row.
  // \exception std::invalid_argument Invalid vector size for cross product.
  // \exception std::invalid_argument Invalid assignment to restricted matrix.
  //
  // In case the current size of any of the two vectors is not equal to 3, a \a std::invalid_argument
  // exception is thrown.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side vector
  inline Band<MT,TF,true,false,CBAs...>&
     Band<MT,TF,true,false,CBAs...>::operator%=( const Vector<VT,TF>& rhs )
  {
     using blaze::assign;
  
     BLAZE_CONSTRAINT_MUST_BE_VECTOR_WITH_TRANSPOSE_FLAG( ResultType_t<VT>, TF );
     BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( ResultType_t<VT> );
  
     using CrossType = CrossTrait_t< ResultType, ResultType_t<VT> >;
  
     BLAZE_CONSTRAINT_MUST_BE_DENSE_VECTOR_TYPE( CrossType );
     BLAZE_CONSTRAINT_MUST_BE_VECTOR_WITH_TRANSPOSE_FLAG( CrossType, TF );
     BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( CrossType );
  
     if( size() != 3UL || (~rhs).size() != 3UL ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid vector size for cross product" );
     }
  
     const CrossType right( *this % (~rhs) );
  
     if( !tryAssign( matrix_, right, band(), row(), column() ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to restricted matrix" );
     }
  
     decltype(auto) left( derestrict( *this ) );
  
     assign( left, right );
  
     BLAZE_INTERNAL_ASSERT( isIntact( matrix_ ), "Invariant violation detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  UTILITY FUNCTIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns the matrix containing the band.
  //
  // \return The matrix containing the band.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline MT& Band<MT,TF,true,false,CBAs...>::operand() noexcept
  {
     return matrix_;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns the matrix containing the band.
  //
  // \return The matrix containing the band.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline const MT& Band<MT,TF,true,false,CBAs...>::operand() const noexcept
  {
     return matrix_;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns the current size/dimension of the band.
  //
  // \return The size of the band.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline size_t Band<MT,TF,true,false,CBAs...>::size() const noexcept
  {
     return min( matrix_.rows() - row(), matrix_.columns() - column() );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns the minimum capacity of the band.
  //
  // \return The minimum capacity of the band.
  //
  // This function returns the minimum capacity of the band, which corresponds to the current size
  // plus padding.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline size_t Band<MT,TF,true,false,CBAs...>::spacing() const noexcept
  {
     return size();
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns the maximum capacity of the dense band.
  //
  // \return The maximum capacity of the dense band.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline size_t Band<MT,TF,true,false,CBAs...>::capacity() const noexcept
  {
     return size();
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns the number of non-zero elements in the band.
  //
  // \return The number of non-zero elements in the band.
  //
  // Note that the number of non-zero elements is always less than or equal to the current number
  // of columns of the matrix containing the band.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline size_t Band<MT,TF,true,false,CBAs...>::nonZeros() const
  {
     const size_t n( size() );
     size_t nonzeros( 0UL );
  
     for( size_t i=0UL; i<n; ++i )
        if( !isDefault( matrix_(row()+i,column()+i) ) )
           ++nonzeros;
  
     return nonzeros;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Reset to the default initial values.
  //
  // \return void
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline void Band<MT,TF,true,false,CBAs...>::reset()
  {
     using blaze::clear;
  
     if( ( IsLower_v<MT> && column() > 0UL ) ||
         ( ( IsUniLower_v<MT> || IsStrictlyLower_v<MT> ) && row() == 0UL ) ||
         ( IsUpper_v<MT> && row() > 0UL ) ||
         ( ( IsUniUpper_v<MT> || IsStrictlyUpper_v<MT> ) && column() == 0UL ) )
        return;
  
     const size_t n( size() );
     for( size_t i=0UL; i<n; ++i )
        clear( matrix_(row()+i,column()+i) );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  NUMERIC FUNCTIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Scaling of the band by the scalar value \a scalar (\f$ \vec{a}=\vec{b}*s \f$).
  //
  // \param scalar The scalar value for the band scaling.
  // \return Reference to the dense band.
  //
  // This function scales the band by applying the given scalar value \a scalar to each element
  // of the band. For built-in and \c complex data types it has the same effect as using the
  // multiplication assignment operator. Note that the function cannot be used to scale a band
  // on a lower or upper unitriangular matrix. The attempt to scale such a band results in a
  // compile time error!
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename Other >     // Data type of the scalar value
  inline Band<MT,TF,true,false,CBAs...>&
     Band<MT,TF,true,false,CBAs...>::scale( const Other& scalar )
  {
     BLAZE_CONSTRAINT_MUST_NOT_BE_UNITRIANGULAR_MATRIX_TYPE( MT );
  
     if( ( IsLower_v<MT>         && column() >  0UL ) ||
         ( IsStrictlyLower_v<MT> && row()    == 0UL ) ||
         ( IsUpper_v<MT>         && row()    >  0UL ) ||
         ( IsStrictlyUpper_v<MT> && column() == 0UL ) )
        return *this;
  
     const size_t n( size() );
     for( size_t i=0UL; i<n; ++i ) {
        matrix_(row()+i,column()+i) *= scalar;
     }
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  EXPRESSION TEMPLATE EVALUATION FUNCTIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns whether the dense band can alias with the given address \a alias.
  //
  // \param alias The alias to be checked.
  // \return \a true in case the alias corresponds to this dense band, \a false if not.
  //
  // This function returns whether the given address can alias with the dense band. In contrast
  // to the isAliased() function this function is allowed to use compile time expressions to
  // optimize the evaluation.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename Other >     // Data type of the foreign expression
  inline bool Band<MT,TF,true,false,CBAs...>::canAlias( const Other* alias ) const noexcept
  {
     return matrix_.isAliased( &unview( *alias ) );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns whether the dense band can alias with the given dense band \a alias.
  //
  // \param alias The alias to be checked.
  // \return \a true in case the alias corresponds to this dense band, \a false if not.
  //
  // This function returns whether the given address can alias with the dense band. In contrast
  // to the isAliased() function this function is allowed to use compile time expressions to
  // optimize the evaluation.
  */
  template< typename MT           // Type of the dense matrix
          , bool TF               // Transpose flag
          , ptrdiff_t... CBAs >   // Compile time band arguments
  template< typename MT2          // Matrix type of the foreign dense band
          , ptrdiff_t... CBAs2 >  // Compile time band arguments of the foreign dense band
  inline bool
     Band<MT,TF,true,false,CBAs...>::canAlias( const Band<MT2,TF,true,false,CBAs2...>* alias ) const noexcept
  {
     return matrix_.isAliased( &alias->matrix_ ) && ( band() == alias->band() );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns whether the dense band is aliased with the given address \a alias.
  //
  // \param alias The alias to be checked.
  // \return \a true in case the alias corresponds to this dense band, \a false if not.
  //
  // This function returns whether the given address is aliased with the dense band. In contrast
  // to the canAlias() function this function is not allowed to use compile time expressions to
  // optimize the evaluation.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename Other >     // Data type of the foreign expression
  inline bool Band<MT,TF,true,false,CBAs...>::isAliased( const Other* alias ) const noexcept
  {
     return matrix_.isAliased( &unview( *alias ) );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns whether the dense band is aliased with the given dense band \a alias.
  //
  // \param alias The alias to be checked.
  // \return \a true in case the alias corresponds to this dense band, \a false if not.
  //
  // This function returns whether the given address is aliased with the dense band. In contrast
  // to the canAlias() function this function is not allowed to use compile time expressions to
  // optimize the evaluation.
  */
  template< typename MT           // Type of the dense matrix
          , bool TF               // Transpose flag
          , ptrdiff_t... CBAs >   // Compile time band arguments
  template< typename MT2          // Matrix type of the foreign dense band
          , ptrdiff_t... CBAs2 >  // Compile time band arguments of the foreign dense band
  inline bool
     Band<MT,TF,true,false,CBAs...>::isAliased( const Band<MT2,TF,true,false,CBAs2...>* alias ) const noexcept
  {
     return matrix_.isAliased( &alias->matrix_ ) && ( band() == alias->band() );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns whether the dense band is properly aligned in memory.
  //
  // \return \a true in case the dense band is aligned, \a false if not.
  //
  // This function returns whether the dense band is guaranteed to be properly aligned in memory,
  // i.e. whether the beginning and the end of the dense band are guaranteed to conform to the
  // alignment restrictions of the element type \a Type.
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline bool Band<MT,TF,true,false,CBAs...>::isAligned() const noexcept
  {
     return false;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns whether the dense band can be used in SMP assignments.
  //
  // \return \a true in case the dense band can be used in SMP assignments, \a false if not.
  //
  // This function returns whether the dense band can be used in SMP assignments. In contrast to
  // the \a smpAssignable member enumeration, which is based solely on compile time information,
  // this function additionally provides runtime information (as for instance the current size
  // of the dense band).
  */
  template< typename MT          // Type of the dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  inline bool Band<MT,TF,true,false,CBAs...>::canSMPAssign() const noexcept
  {
     return ( size() > SMP_DVECASSIGN_THRESHOLD );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Default implementation of the assignment of a dense vector.
  //
  // \param rhs The right-hand side dense vector to be assigned.
  // \return void
  //
  // 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 dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side dense vector
  inline void Band<MT,TF,true,false,CBAs...>::assign( const DenseVector<VT,TF>& rhs )
  {
     BLAZE_INTERNAL_ASSERT( size() == (~rhs).size(), "Invalid vector sizes" );
  
     const size_t ipos( prevMultiple( (~rhs).size(), 2UL ) );
     BLAZE_INTERNAL_ASSERT( ipos <= (~rhs).size(), "Invalid end calculation" );
  
     for( size_t i=0UL; i<ipos; i+=2UL ) {
        matrix_(row()+i    ,column()+i    ) = (~rhs)[i    ];
        matrix_(row()+i+1UL,column()+i+1UL) = (~rhs)[i+1UL];
     }
     if( ipos < (~rhs).size() ) {
        matrix_(row()+ipos,column()+ipos) = (~rhs)[ipos];
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Default implementation of the assignment of a sparse vector.
  //
  // \param rhs The right-hand side sparse vector to be assigned.
  // \return void
  //
  // 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 dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side sparse vector
  inline void Band<MT,TF,true,false,CBAs...>::assign( const SparseVector<VT,TF>& rhs )
  {
     BLAZE_INTERNAL_ASSERT( size() == (~rhs).size(), "Invalid vector sizes" );
  
     for( ConstIterator_t<VT> element=(~rhs).begin(); element!=(~rhs).end(); ++element ) {
        const size_t index( element->index() );
        matrix_(row()+index,column()+index) = element->value();
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Default implementation of the addition assignment of a dense vector.
  //
  // \param rhs The right-hand side dense vector to be added.
  // \return void
  //
  // 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 dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side dense vector
  inline void Band<MT,TF,true,false,CBAs...>::addAssign( const DenseVector<VT,TF>& rhs )
  {
     BLAZE_INTERNAL_ASSERT( size() == (~rhs).size(), "Invalid vector sizes" );
  
     const size_t ipos( prevMultiple( (~rhs).size(), 2UL ) );
     BLAZE_INTERNAL_ASSERT( ipos <= (~rhs).size(), "Invalid end calculation" );
  
     for( size_t i=0UL; i<ipos; i+=2UL ) {
        matrix_(row()+i    ,column()+i    ) += (~rhs)[i    ];
        matrix_(row()+i+1UL,column()+i+1UL) += (~rhs)[i+1UL];
     }
     if( ipos < (~rhs).size() ) {
        matrix_(row()+ipos,column()+ipos) += (~rhs)[ipos];
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Default implementation of the addition assignment of a sparse vector.
  //
  // \param rhs The right-hand side sparse vector to be added.
  // \return void
  //
  // 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 dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side sparse vector
  inline void Band<MT,TF,true,false,CBAs...>::addAssign( const SparseVector<VT,TF>& rhs )
  {
     BLAZE_INTERNAL_ASSERT( size() == (~rhs).size(), "Invalid vector sizes" );
  
     for( ConstIterator_t<VT> element=(~rhs).begin(); element!=(~rhs).end(); ++element ) {
        const size_t index( element->index() );
        matrix_(row()+index,column()+index) += element->value();
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Default implementation of the subtraction assignment of a dense vector.
  //
  // \param rhs The right-hand side dense vector to be subtracted.
  // \return void
  //
  // 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 dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side dense vector
  inline void Band<MT,TF,true,false,CBAs...>::subAssign( const DenseVector<VT,TF>& rhs )
  {
     BLAZE_INTERNAL_ASSERT( size() == (~rhs).size(), "Invalid vector sizes" );
  
     const size_t ipos( prevMultiple( (~rhs).size(), 2UL ) );
     BLAZE_INTERNAL_ASSERT( ipos <= (~rhs).size(), "Invalid end calculation" );
  
     for( size_t i=0UL; i<ipos; i+=2UL ) {
        matrix_(row()+i    ,column()+i    ) -= (~rhs)[i    ];
        matrix_(row()+i+1UL,column()+i+1UL) -= (~rhs)[i+1UL];
     }
     if( ipos < (~rhs).size() ) {
        matrix_(row()+ipos,column()+ipos) -= (~rhs)[ipos];
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Default implementation of the subtraction assignment of a sparse vector.
  //
  // \param rhs The right-hand side sparse vector to be subtracted.
  // \return void
  //
  // 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 dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side sparse vector
  inline void Band<MT,TF,true,false,CBAs...>::subAssign( const SparseVector<VT,TF>& rhs )
  {
     BLAZE_INTERNAL_ASSERT( size() == (~rhs).size(), "Invalid vector sizes" );
  
     for( ConstIterator_t<VT> element=(~rhs).begin(); element!=(~rhs).end(); ++element ) {
        const size_t index( element->index() );
        matrix_(row()+index,column()+index) -= element->value();
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Default implementation of the multiplication assignment of a dense vector.
  //
  // \param rhs The right-hand side dense vector to be multiplied.
  // \return void
  //
  // 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 dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side dense vector
  inline void Band<MT,TF,true,false,CBAs...>::multAssign( const DenseVector<VT,TF>& rhs )
  {
     BLAZE_INTERNAL_ASSERT( size() == (~rhs).size(), "Invalid vector sizes" );
  
     const size_t ipos( prevMultiple( (~rhs).size(), 2UL ) );
     BLAZE_INTERNAL_ASSERT( ipos <= (~rhs).size(), "Invalid end calculation" );
  
     for( size_t i=0UL; i<ipos; i+=2UL ) {
        matrix_(row()+i    ,column()+i    ) *= (~rhs)[i    ];
        matrix_(row()+i+1UL,column()+i+1UL) *= (~rhs)[i+1UL];
     }
     if( ipos < (~rhs).size() ) {
        matrix_(row()+ipos,column()+ipos) *= (~rhs)[ipos];
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Default implementation of the multiplication assignment of a sparse vector.
  //
  // \param rhs The right-hand side sparse vector to be multiplied.
  // \return void
  //
  // 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 dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side sparse vector
  inline void Band<MT,TF,true,false,CBAs...>::multAssign( const SparseVector<VT,TF>& rhs )
  {
     using blaze::reset;
  
     BLAZE_INTERNAL_ASSERT( size() == (~rhs).size(), "Invalid vector sizes" );
  
     size_t i( 0UL );
  
     for( ConstIterator_t<VT> element=(~rhs).begin(); element!=(~rhs).end(); ++element ) {
        const size_t index( element->index() );
        for( ; i<index; ++i )
           reset( matrix_(row()+i,column()+i) );
        matrix_(row()+index,column()+index) *= element->value();
        ++i;
     }
  
     for( ; i<size(); ++i ) {
        reset( matrix_(row()+i,column()+i) );
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Default implementation of the division assignment of a dense vector.
  //
  // \param rhs The right-hand side dense vector divisor.
  // \return void
  //
  // 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 dense matrix
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  template< typename VT >        // Type of the right-hand side dense vector
  inline void Band<MT,TF,true,false,CBAs...>::divAssign( const DenseVector<VT,TF>& rhs )
  {
     BLAZE_INTERNAL_ASSERT( size() == (~rhs).size(), "Invalid vector sizes" );
  
     const size_t ipos( prevMultiple( (~rhs).size(), 2UL ) );
     BLAZE_INTERNAL_ASSERT( ipos <= (~rhs).size(), "Invalid end calculation" );
  
     for( size_t i=0UL; i<ipos; i+=2UL ) {
        matrix_(row()+i    ,column()+i    ) /= (~rhs)[i    ];
        matrix_(row()+i+1UL,column()+i+1UL) /= (~rhs)[i+1UL];
     }
     if( ipos < (~rhs).size() ) {
        matrix_(row()+ipos,column()+ipos) /= (~rhs)[ipos];
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  CLASS TEMPLATE SPECIALIZATION FOR DENSE MATRIX MULTIPLICATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Specialization of Band for dense matrix multiplications.
  // \ingroup views
  //
  // This specialization of Band adapts the class template to the requirements of dense matrix
  // multiplications.
  */
  template< typename MT          // Type of the dense matrix multiplication
          , bool TF              // Transpose flag
          , ptrdiff_t... CBAs >  // Compile time band arguments
  class Band<MT,TF,true,true,CBAs...>
     : public View< DenseVector< Band<MT,TF,true,true,CBAs...>, TF > >
     , private BandData<CBAs...>
     , private Computation
  {
   private:
     //**Type definitions****************************************************************************
     //! The type of the BandData base class.
     using DataType = BandData<CBAs...>;
  
     //! The type of the left-hand side matrix operand.
     using LeftOperand = RemoveReference_t< LeftOperand_t<MT> >;
  
     //! The type of the right-hand side matrix operand.
     using RightOperand = RemoveReference_t< RightOperand_t<MT> >;
     //**********************************************************************************************
  
   public:
     //**Type definitions****************************************************************************
     //! Type of this Band instance.
     using This = Band<MT,TF,true,true,CBAs...>;
  
     //! Base type of this Band instance.
     using BaseType = DenseVector<This,TF>;
  
     //! The type viewed by this Band instance.
     using ViewedType = MT;
  
     //! Result type for expression template evaluations.
     using ResultType = BandTrait_t<ResultType_t<MT>,CBAs...>;
  
     using TransposeType = TransposeType_t<ResultType>;  //!< Transpose type for expression template evaluations.
     using ElementType   = ElementType_t<ResultType>;    //!< Resulting element type.
     using ReturnType    = ReturnType_t<MT>;             //!< Return type for expression template evaluations.
  
     //! Data type for composite expression templates.
     using CompositeType = If_t< RequiresEvaluation_v<LeftOperand> ||
                                 RequiresEvaluation_v<RightOperand>
                               , const ResultType, const Band& >;
  
     //! Type for the assignment of the left-hand side matrix operand.
     using LT = If_t< IsSparseMatrix_v<LeftOperand> && IsColumnMajorMatrix_v<LeftOperand>
                    , ResultType_t<LeftOperand>
                    , CompositeType_t<LeftOperand> >;
  
     //! Type for the assignment of the right-hand side matrix operand.
     using RT = If_t< IsSparseMatrix_v<RightOperand> && IsRowMajorMatrix_v<RightOperand>
                    , ResultType_t<RightOperand>
                    , CompositeType_t<RightOperand> >;
     //**********************************************************************************************
  
     //**Compilation flags***************************************************************************
     //! Compilation switch for the expression template evaluation strategy.
     static constexpr bool simdEnabled = false;
  
     //! Compilation switch for the expression template assignment strategy.
     static constexpr bool smpAssignable = false;
  
     //! Compilation switch for the expression template evaluation strategy.
     static constexpr bool compileTimeArgs = DataType::compileTimeArgs;
     //**********************************************************************************************
  
     //**Constructor*********************************************************************************
     /*!\brief Constructor for bands on dense matrix multiplications.
     //
     // \param mmm The matrix multiplication containing the band.
     // \param args The runtime band arguments.
     // \exception std::invalid_argument Invalid band access index.
     */
     template< typename... RBAs >  // Runtime band arguments
     explicit inline Band( const MT& mmm, RBAs... args )
        : DataType( args... )  // Base class initialization
        , matrix_ ( mmm )      // The matrix multiplication containing the band
     {
        if( !Contains_v< TypeList<RBAs...>, Unchecked > ) {
           if( ( band() > 0L && column() >= mmm.columns() ) ||
               ( band() < 0L && row() >= mmm.rows() ) ) {
              BLAZE_THROW_INVALID_ARGUMENT( "Invalid band access index" );
           }
        }
        else {
           BLAZE_USER_ASSERT( band() <= 0L || column() < mmm.columns(), "Invalid band access index" );
           BLAZE_USER_ASSERT( band() >= 0L || row() < mmm.rows(), "Invalid band access index" );
        }
     }
     //**********************************************************************************************
  
     //**Subscript operator**************************************************************************
     /*!\brief Subscript operator for the direct access to the vector elements.
     //
     // \param index Access index. The index has to be in the range \f$[0..N-1]\f$.
     // \return The resulting value.
     */
     inline ReturnType operator[]( size_t index ) const {
        BLAZE_INTERNAL_ASSERT( index < size(), "Invalid vector access index" );
        return matrix_(row()+index,column()+index);
     }
     //**********************************************************************************************
  
     //**At function*********************************************************************************
     /*!\brief Checked access to the vector elements.
     //
     // \param index Access index. The index has to be in the range \f$[0..N-1]\f$.
     // \return The resulting value.
     // \exception std::out_of_range Invalid vector access index.
     */
     inline ReturnType at( size_t index ) const {
        if( index >= size() ) {
           BLAZE_THROW_OUT_OF_RANGE( "Invalid vector access index" );
        }
        return (*this)[index];
     }
     //**********************************************************************************************
  
     //**Size function*******************************************************************************
     /*!\brief Returns the current size/dimension of the vector.
     //
     // \return The size of the vector.
     */
     inline size_t size() const noexcept {
        return min( matrix_.rows() - row(), matrix_.columns() - column() );
     }
     //**********************************************************************************************
  
     //**********************************************************************************************
     using DataType::band;
     using DataType::row;
     using DataType::column;
     //**********************************************************************************************
  
     //**Operand access******************************************************************************
     /*!\brief Returns the matrix multiplication expression containing the band.
     //
     // \return The matrix multiplication expression containing the band.
     */
     inline const MT& operand() const noexcept {
        return matrix_;
     }
     //**********************************************************************************************
  
     //**********************************************************************************************
     /*!\brief Returns whether the expression can alias with the given address \a alias.
     //
     // \param alias The alias to be checked.
     // \return \a true in case the expression can alias, \a false otherwise.
     */
     template< typename T >
     inline bool canAlias( const T* alias ) const noexcept {
        return matrix_.isAliased( &unview( *alias ) );
     }
     //**********************************************************************************************
  
     //**********************************************************************************************
     /*!\brief Returns whether the expression is aliased with the given address \a alias.
     //
     // \param alias The alias to be checked.
     // \return \a true in case an alias effect is detected, \a false otherwise.
     */
     template< typename T >
     inline bool isAliased( const T* alias ) const noexcept {
        return matrix_.isAliased( &unview( *alias ) );
     }
     //**********************************************************************************************
  
     //**********************************************************************************************
     /*!\brief Returns whether the operands of the expression are properly aligned in memory.
     //
     // \return \a true in case the operands are aligned, \a false if not.
     */
     constexpr bool isAligned() const noexcept {
        return false;
     }
     //**********************************************************************************************
  
   private:
     //**Member variables****************************************************************************
     MT matrix_;  //!< The matrix multiplication containing the band.
     //**********************************************************************************************
  
     //**Assignment to dense vectors*****************************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Assignment of a band view on a dense matrix multiplication to a dense vector.
     // \ingroup dense_vector
     //
     // \param lhs The target left-hand side dense vector.
     // \param rhs The right-hand side band view to be assigned.
     // \return void
     //
     // This function implements the performance optimized assignment of a band view on a dense
     // matrix multiplication to a dense vector.
     */
     template< typename VT >  // Type of the target dense vector
     friend inline void assign( DenseVector<VT,TF>& lhs, const Band& rhs )
     {
        using blaze::row;
        using blaze::column;
  
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).size() == rhs.size(), "Invalid vector sizes" );
  
        LT A( serial( rhs.operand().leftOperand()  ) );
        RT B( serial( rhs.operand().rightOperand() ) );
  
        const size_t n( rhs.size() );
        for( size_t i=0UL; i<n; ++i ) {
           (~lhs)[i] = row( A, rhs.row()+i, unchecked ) * column( B, rhs.column()+i, unchecked );
        }
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Assignment to sparse vectors****************************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Assignment of a band view on a dense matrix multiplication to a sparse vector.
     // \ingroup dense_vector
     //
     // \param lhs The target left-hand side sparse vector.
     // \param rhs The right-hand side band view to be assigned.
     // \return void
     //
     // This function implements the performance optimized assignment of a band view on a dense
     // matrix multiplication to a sparse vector.
     */
     template< typename VT >  // Type of the target sparse vector
     friend inline void assign( SparseVector<VT,TF>& lhs, const Band& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_CONSTRAINT_MUST_BE_DENSE_VECTOR_TYPE( ResultType );
        BLAZE_CONSTRAINT_MUST_BE_VECTOR_WITH_TRANSPOSE_FLAG( ResultType, TF );
        BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( ResultType );
  
        BLAZE_INTERNAL_ASSERT( (~lhs).size() == rhs.size(), "Invalid vector sizes" );
  
        const ResultType tmp( serial( rhs ) );
        assign( ~lhs, tmp );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Addition assignment to dense vectors********************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Addition assignment of a band view on a dense matrix multiplication to a dense vector.
     // \ingroup dense_vector
     //
     // \param lhs The target left-hand side dense vector.
     // \param rhs The right-hand side band view to be added.
     // \return void
     //
     // This function implements the performance optimized addition assignment of a band view on a
     // dense matrix multiplication to a dense vector.
     */
     template< typename VT >  // Type of the target dense vector
     friend inline void addAssign( DenseVector<VT,TF>& lhs, const Band& rhs )
     {
        using blaze::row;
        using blaze::column;
  
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).size() == rhs.size(), "Invalid vector sizes" );
  
        LT A( serial( rhs.operand().leftOperand()  ) );
        RT B( serial( rhs.operand().rightOperand() ) );
  
        const size_t n( rhs.size() );
        for( size_t i=0UL; i<n; ++i ) {
           (~lhs)[i] += row( A, rhs.row()+i, unchecked ) * column( B, rhs.column()+i, unchecked );
        }
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Addition assignment to sparse vectors*******************************************************
     // No special implementation for the addition assignment to sparse vectors.
     //**********************************************************************************************
  
     //**Subtraction assignment to dense vectors*****************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Subtraction assignment of a band view on a dense matrix multiplication to a dense vector.
     // \ingroup dense_vector
     //
     // \param lhs The target left-hand side dense vector.
     // \param rhs The right-hand side band view to be subtracted.
     // \return void
     //
     // This function implements the performance optimized subtraction assignment of a band view
     // on a dense matrix multiplication to a dense vector.
     */
     template< typename VT >  // Type of the target dense vector
     friend inline void subAssign( DenseVector<VT,TF>& lhs, const Band& rhs )
     {
        using blaze::row;
        using blaze::column;
  
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).size() == rhs.size(), "Invalid vector sizes" );
  
        LT A( serial( rhs.operand().leftOperand()  ) );
        RT B( serial( rhs.operand().rightOperand() ) );
  
        const size_t n( rhs.size() );
        for( size_t i=0UL; i<n; ++i ) {
           (~lhs)[i] -= row( A, rhs.row()+i, unchecked ) * column( B, rhs.column()+i, unchecked );
        }
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Subtraction assignment to sparse vectors****************************************************
     // No special implementation for the subtraction assignment to sparse vectors.
     //**********************************************************************************************
  
     //**Multiplication assignment to dense vectors**************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Multiplication assignment of a band view on a dense matrix multiplication to a
     //        dense vector.
     // \ingroup dense_vector
     //
     // \param lhs The target left-hand side dense vector.
     // \param rhs The right-hand side band view to be multiplied.
     // \return void
     //
     // This function implements the performance optimized multiplication assignment of a band view
     // on a dense matrix multiplication to a dense vector.
     */
     template< typename VT >  // Type of the target dense vector
     friend inline void multAssign( DenseVector<VT,TF>& lhs, const Band& rhs )
     {
        using blaze::row;
        using blaze::column;
  
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).size() == rhs.size(), "Invalid vector sizes" );
  
        LT A( serial( rhs.operand().leftOperand()  ) );
        RT B( serial( rhs.operand().rightOperand() ) );
  
        const size_t n( rhs.size() );
        for( size_t i=0UL; i<n; ++i ) {
           (~lhs)[i] *= row( A, rhs.row()+i, unchecked ) * column( B, rhs.column()+i, unchecked );
        }
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Multiplication assignment to sparse vectors*************************************************
     // No special implementation for the multiplication assignment to sparse vectors.
     //**********************************************************************************************
  
     //**Division assignment to dense vectors********************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Division assignment of a band view on a dense matrix multiplication to a dense vector.
     // \ingroup dense_vector
     //
     // \param lhs The target left-hand side dense vector.
     // \param rhs The right-hand side band view divisor.
     // \return void
     //
     // This function implements the performance optimized division assignment of a band view on a
     // dense matrix multiplication to a dense vector.
     */
     template< typename VT >  // Type of the target dense vector
     friend inline void divAssign( DenseVector<VT,TF>& lhs, const Band& rhs )
     {
        using blaze::row;
        using blaze::column;
  
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).size() == rhs.size(), "Invalid vector sizes" );
  
        LT A( serial( rhs.operand().leftOperand()  ) );
        RT B( serial( rhs.operand().rightOperand() ) );
  
        const size_t n( rhs.size() );
        for( size_t i=0UL; i<n; ++i ) {
           (~lhs)[i] /= row( A, rhs.row()+i, unchecked ) * column( B, rhs.column()+i, unchecked );
        }
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Division assignment to sparse vectors*******************************************************
     // No special implementation for the division assignment to sparse vectors.
     //**********************************************************************************************
  
     //**Compile time checks*************************************************************************
     /*! \cond BLAZE_INTERNAL */
     BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE  ( MT );
     BLAZE_CONSTRAINT_MUST_BE_MATMATMULTEXPR_TYPE( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_POINTER_TYPE   ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_REFERENCE_TYPE ( MT );
     /*! \endcond */
     //**********************************************************************************************
  };
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  