text: //=================================================================================================
  /*!
  //  \file blaze/math/expressions/SMatDMatSubExpr.h
  //  \brief Header file for the sparse matrix/dense matrix subtraction expression
  //
  //  Copyright (C) 2012-2018 Klaus Iglberger - All Rights Reserved
  //
  //  This file is part of the Blaze library. You can redistribute it and/or modify it under
  //  the terms of the New (Revised) BSD License. Redistribution and use in source and binary
  //  forms, with or without modification, are permitted provided that the following conditions
  //  are met:
  //
  //  1. Redistributions of source code must retain the above copyright notice, this list of
  //     conditions and the following disclaimer.
  //  2. Redistributions in binary form must reproduce the above copyright notice, this list
  //     of conditions and the following disclaimer in the documentation and/or other materials
  //     provided with the distribution.
  //  3. Neither the names of the Blaze development group nor the names of its contributors
  //     may be used to endorse or promote products derived from this software without specific
  //     prior written permission.
  //
  //  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
  //  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  //  OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
  //  SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  //  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
  //  TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
  //  BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  //  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  //  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
  //  DAMAGE.
  */
  //=================================================================================================
  
  #ifndef _BLAZE_MATH_EXPRESSIONS_SMATDMATSUBEXPR_H_
  #define _BLAZE_MATH_EXPRESSIONS_SMATDMATSUBEXPR_H_
  
  
  //*************************************************************************************************
  // Includes
  //*************************************************************************************************
  
  #include <blaze/math/Aliases.h>
  #include <blaze/math/constraints/DenseMatrix.h>
  #include <blaze/math/constraints/MatMatSubExpr.h>
  #include <blaze/math/constraints/RequiresEvaluation.h>
  #include <blaze/math/constraints/SparseMatrix.h>
  #include <blaze/math/constraints/StorageOrder.h>
  #include <blaze/math/Exception.h>
  #include <blaze/math/expressions/Computation.h>
  #include <blaze/math/expressions/DenseMatrix.h>
  #include <blaze/math/expressions/Forward.h>
  #include <blaze/math/expressions/MatMatSubExpr.h>
  #include <blaze/math/shims/Serial.h>
  #include <blaze/math/traits/SubExprTrait.h>
  #include <blaze/math/traits/SubTrait.h>
  #include <blaze/math/typetraits/IsExpression.h>
  #include <blaze/math/typetraits/IsHermitian.h>
  #include <blaze/math/typetraits/IsLower.h>
  #include <blaze/math/typetraits/IsStrictlyLower.h>
  #include <blaze/math/typetraits/IsStrictlyUpper.h>
  #include <blaze/math/typetraits/IsSymmetric.h>
  #include <blaze/math/typetraits/IsTemporary.h>
  #include <blaze/math/typetraits/IsUniLower.h>
  #include <blaze/math/typetraits/IsUniUpper.h>
  #include <blaze/math/typetraits/IsUpper.h>
  #include <blaze/math/typetraits/Size.h>
  #include <blaze/util/Assert.h>
  #include <blaze/util/EnableIf.h>
  #include <blaze/util/FunctionTrace.h>
  #include <blaze/util/mpl/And.h>
  #include <blaze/util/mpl/If.h>
  #include <blaze/util/mpl/Maximum.h>
  #include <blaze/util/Types.h>
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  CLASS SMATDMATSUBEXPR
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\brief Expression object for sparse matrix-dense matrix subtractions.
  // \ingroup dense_matrix_expression
  //
  // The SMatDMatSubExpr class represents the compile time expression for subtractions between
  // a sparse matrix and a dense matrix with identical storage order.
  */
  template< typename MT1  // Type of the left-hand side sparse matrix
          , typename MT2  // Type of the right-hand side dense matrix
          , bool SO >     // Storage order
  class SMatDMatSubExpr
     : public MatMatSubExpr< DenseMatrix< SMatDMatSubExpr<MT1,MT2,SO>, SO > >
     , private Computation
  {
   private:
     //**Type definitions****************************************************************************
     using RT1 = ResultType_<MT1>;  //!< Result type of the left-hand side sparse matrix expression.
     using RT2 = ResultType_<MT2>;  //!< Result type of the right-hand side dense matrix expression.
     using RN1 = ReturnType_<MT1>;  //!< Return type of the left-hand side sparse matrix expression.
     using RN2 = ReturnType_<MT2>;  //!< Return type of the right-hand side dense matrix expression.
     //**********************************************************************************************
  
     //**Return type evaluation**********************************************************************
     //! Compilation switch for the selection of the subscript operator return type.
     /*! The \a returnExpr compile time constant expression is a compilation switch for the
         selection of the \a ReturnType. If either matrix operand returns a temporary vector
         or matrix, \a returnExpr will be set to \a false and the subscript operator will
         return it's result by value. Otherwise \a returnExpr will be set to \a true and
         the subscript operator may return it's result as an expression. */
     enum : bool { returnExpr = !IsTemporary<RN1>::value && !IsTemporary<RN2>::value };
  
     //! Expression return type for the subscript operator.
     using ExprReturnType = SubExprTrait_<RN1,RN2>;
     //**********************************************************************************************
  
     //**Parallel evaluation strategy****************************************************************
     /*! \cond BLAZE_INTERNAL */
     //! Helper structure for the explicit application of the SFINAE principle.
     /*! The UseSMPAssign struct is a helper struct for the selection of the parallel evaluation
         strategy. In case at least one of the two matrix operands is not SMP assignable, \a value
         is set to 1 and the expression specific evaluation strategy is selected. Otherwise \a value
         is set to 0 and the default strategy is chosen. */
     template< typename MT >
     struct UseSMPAssign {
        enum : bool { value = ( !MT1::smpAssignable || !MT2::smpAssignable ) };
     };
     /*! \endcond */
     //**********************************************************************************************
  
   public:
     //**Type definitions****************************************************************************
     using This          = SMatDMatSubExpr<MT1,MT2,SO>;  //!< Type of this SMatDMatSubExpr instance.
     using ResultType    = SubTrait_<RT1,RT2>;           //!< Result type for expression template evaluations.
     using OppositeType  = OppositeType_<ResultType>;    //!< Result type with opposite storage order for expression template evaluations.
     using TransposeType = TransposeType_<ResultType>;   //!< Transpose type for expression template evaluations.
     using ElementType   = ElementType_<ResultType>;     //!< Resulting element type.
  
     //! Return type for expression template evaluations.
     using ReturnType = const IfTrue_< returnExpr, ExprReturnType, ElementType >;
  
     //! Data type for composite expression templates.
     using CompositeType = const ResultType;
  
     //! Composite type of the left-hand side dense matrix expression.
     using LeftOperand = If_< IsExpression<MT1>, const MT1, const MT1& >;
  
     //! Composite type of the right-hand side sparse matrix expression.
     using RightOperand = If_< IsExpression<MT2>, const MT2, const MT2& >;
     //**********************************************************************************************
  
     //**Compilation flags***************************************************************************
     //! Compilation switch for the expression template evaluation strategy.
     enum : bool { simdEnabled = false };
  
     //! Compilation switch for the expression template assignment strategy.
     enum : bool { smpAssignable = false };
     //**********************************************************************************************
  
     //**Constructor*********************************************************************************
     /*!\brief Constructor for the SMatDMatSubExpr class.
     //
     // \param lhs The left-hand side sparse matrix operand of the addition expression.
     // \param rhs The right-hand side dense matrix operand of the addition expression.
     */
     explicit inline SMatDMatSubExpr( const MT1& lhs, const MT2& rhs ) noexcept
        : lhs_( lhs )  // Left-hand side sparse matrix of the subtraction expression
        , rhs_( rhs )  // Right-hand side dense matrix of the subtraction expression
     {
        BLAZE_INTERNAL_ASSERT( lhs.rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( lhs.columns() == rhs.columns(), "Invalid number of columns" );
     }
     //**********************************************************************************************
  
     //**Access operator*****************************************************************************
     /*!\brief 2D-access to the matrix elements.
     //
     // \param i Access index for the row. The index has to be in the range \f$[0..M-1]\f$.
     // \param j Access index for the column. The index has to be in the range \f$[0..N-1]\f$.
     // \return The resulting value.
     */
     inline ReturnType operator()( size_t i, size_t j ) const {
        BLAZE_INTERNAL_ASSERT( i < lhs_.rows()   , "Invalid row access index"    );
        BLAZE_INTERNAL_ASSERT( j < lhs_.columns(), "Invalid column access index" );
        return lhs_(i,j) - rhs_(i,j);
     }
     //**********************************************************************************************
  
     //**At function*********************************************************************************
     /*!\brief Checked access to the matrix elements.
     //
     // \param i Access index for the row. The index has to be in the range \f$[0..M-1]\f$.
     // \param j Access index for the column. The index has to be in the range \f$[0..N-1]\f$.
     // \return The resulting value.
     // \exception std::out_of_range Invalid matrix access index.
     */
     inline ReturnType at( size_t i, size_t j ) const {
        if( i >= lhs_.rows() ) {
           BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
        }
        if( j >= lhs_.columns() ) {
           BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
        }
        return (*this)(i,j);
     }
     //**********************************************************************************************
  
     //**Rows function*******************************************************************************
     /*!\brief Returns the current number of rows of the matrix.
     //
     // \return The number of rows of the matrix.
     */
     inline size_t rows() const noexcept {
        return lhs_.rows();
     }
     //**********************************************************************************************
  
     //**Columns function****************************************************************************
     /*!\brief Returns the current number of columns of the matrix.
     //
     // \return The number of columns of the matrix.
     */
     inline size_t columns() const noexcept {
        return lhs_.columns();
     }
     //**********************************************************************************************
  
     //**Left operand access*************************************************************************
     /*!\brief Returns the left-hand side sparse matrix operand.
     //
     // \return The left-hand side sparse matrix operand.
     */
     inline LeftOperand leftOperand() const noexcept {
        return lhs_;
     }
     //**********************************************************************************************
  
     //**Right operand access************************************************************************
     /*!\brief Returns the right-hand side dense matrix operand.
     //
     // \return The right-hand side dense matrix operand.
     */
     inline RightOperand rightOperand() const noexcept {
        return rhs_;
     }
     //**********************************************************************************************
  
     //**********************************************************************************************
     /*!\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 ( lhs_.canAlias( alias ) ) ||
               ( IsExpression<MT2>::value && rhs_.canAlias( 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 lhs_.isAliased( alias ) || rhs_.isAliased( alias );
     }
     //**********************************************************************************************
  
   private:
     //**Member variables****************************************************************************
     LeftOperand  lhs_;  //!< Left-hand side sparse matrix of the subtraction expression.
     RightOperand rhs_;  //!< Right-hand side dense matrix of the subtraction expression.
     //**********************************************************************************************
  
     //**Assignment to dense matrices****************************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Assignment of a sparse matrix-dense matrix subtraction to a dense matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side subtraction expression to be assigned.
     // \return void
     //
     // This function implements the performance optimized assignment of a sparse matrix-dense
     // matrix subtraction expression to a dense matrix.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline void assign( DenseMatrix<MT,SO2>& lhs, const SMatDMatSubExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        assign   ( ~lhs, -rhs.rhs_ );
        addAssign( ~lhs,  rhs.lhs_ );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Assignment to sparse matrices***************************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Assignment of a sparse matrix-dense matrix subtraction to a sparse matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side sparse matrix.
     // \param rhs The right-hand side subtraction expression to be assigned.
     // \return void
     //
     // This function implements the performance optimized assignment of a sparse matrix-dense
     // matrix subtraction expression to a sparse matrix.
     */
     template< typename MT  // Type of the target sparse matrix
             , bool SO2 >   // Storage order of the target sparse matrix
     friend inline void assign( SparseMatrix<MT,SO2>& lhs, const SMatDMatSubExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        using TmpType = IfTrue_< SO == SO2, ResultType, OppositeType >;
  
        BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( ResultType );
        BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( OppositeType );
        BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( ResultType, SO );
        BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( OppositeType, !SO );
        BLAZE_CONSTRAINT_MATRICES_MUST_HAVE_SAME_STORAGE_ORDER( MT, TmpType );
        BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( TmpType );
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        const TmpType tmp( serial( rhs ) );
        assign( ~lhs, tmp );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Addition assignment to dense matrices*******************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Addition assignment of a sparse matrix-dense matrix subtraction to a dense matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side subtraction expression to be added.
     // \return void
     //
     // This function implements the performance optimized addition assignment of a sparse matrix-
     // dense matrix subtraction expression to a dense matrix.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline void addAssign( DenseMatrix<MT,SO2>& lhs, const SMatDMatSubExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        subAssign( ~lhs, rhs.rhs_ );
        addAssign( ~lhs, rhs.lhs_ );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Addition assignment to sparse matrices******************************************************
     // No special implementation for the addition assignment to sparse matrices.
     //**********************************************************************************************
  
     //**Subtraction assignment to dense matrices****************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Subtraction assignment of a sparse matrix-dense matrix subtraction to a dense matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side subtraction expression to be subtracted.
     // \return void
     //
     // This function implements the performance optimized subtraction assignment of a sparse matrix-
     // dense matrix subtraction expression to a dense matrix.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline void subAssign( DenseMatrix<MT,SO2>& lhs, const SMatDMatSubExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        addAssign( ~lhs, rhs.rhs_ );
        subAssign( ~lhs, rhs.lhs_ );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Subtraction assignment to sparse matrices***************************************************
     // No special implementation for the subtraction assignment to sparse matrices.
     //**********************************************************************************************
  
     //**Schur product assignment to dense matrices**************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief Schur product assignment of a sparse matrix-dense matrix subtraction to a dense
     //        matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side subtraction expression for the Schur product.
     // \return void
     //
     // This function implements the performance optimized Schur product assignment of a sparse
     // matrix-dense matrix subtraction expression to a dense matrix.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline void schurAssign( DenseMatrix<MT,SO2>& lhs, const SMatDMatSubExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( ResultType );
        BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( ResultType, SO );
        BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( ResultType );
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        const ResultType tmp( serial( rhs ) );
        schurAssign( ~lhs, tmp );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**Schur product assignment to sparse matrices*************************************************
     // No special implementation for the Schur product assignment to sparse matrices.
     //**********************************************************************************************
  
     //**Multiplication assignment to dense matrices*************************************************
     // No special implementation for the multiplication assignment to dense matrices.
     //**********************************************************************************************
  
     //**Multiplication assignment to sparse matrices************************************************
     // No special implementation for the multiplication assignment to sparse matrices.
     //**********************************************************************************************
  
     //**SMP assignment to dense matrices*************************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief SMP assignment of a sparse matrix-dense matrix subtraction to a dense matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side subtraction expression to be assigned.
     // \return void
     //
     // This function implements the performance optimized SMP assignment of a sparse matrix-dense
     // matrix subtraction expression to a dense matrix. Due to the explicit application of the
     // SFINAE principle, this function can only be selected by the compiler in case the expression
     // specific parallel evaluation strategy is selected.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline EnableIf_< UseSMPAssign<MT> >
        smpAssign( DenseMatrix<MT,SO2>& lhs, const SMatDMatSubExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        smpAssign   ( ~lhs, -rhs.rhs_ );
        smpAddAssign( ~lhs,  rhs.lhs_ );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**SMP assignment to sparse matrices***********************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief SMP assignment of a sparse matrix-dense matrix subtraction to a sparse matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side sparse matrix.
     // \param rhs The right-hand side subtraction expression to be assigned.
     // \return void
     //
     // This function implements the performance optimized SMP assignment of a sparse matrix-dense
     // matrix subtraction expression to a sparse matrix. Due to the explicit application of the
     // SFINAE principle, this function can only be selected by the compiler in case the expression
     // specific parallel evaluation strategy is selected.
     */
     template< typename MT  // Type of the target sparse matrix
             , bool SO2 >   // Storage order of the target sparse matrix
     friend inline EnableIf_< UseSMPAssign<MT> >
        smpAssign( SparseMatrix<MT,SO2>& lhs, const SMatDMatSubExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        using TmpType = IfTrue_< SO == SO2, ResultType, OppositeType >;
  
        BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( ResultType );
        BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( OppositeType );
        BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( ResultType, SO );
        BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( OppositeType, !SO );
        BLAZE_CONSTRAINT_MATRICES_MUST_HAVE_SAME_STORAGE_ORDER( MT, TmpType );
        BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( TmpType );
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        const TmpType tmp( rhs );
        smpAssign( ~lhs, tmp );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**SMP addition assignment to dense matrices***************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief SMP addition assignment of a sparse matrix-dense matrix subtraction to a dense matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side subtraction expression to be added.
     // \return void
     //
     // This function implements the performance optimized SMP addition assignment of a sparse matrix-
     // dense matrix subtraction expression to a dense matrix. Due to the explicit application of the
     // SFINAE principle, this function can only be selected by the compiler in case the expression
     // specific parallel evaluation strategy is selected.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline EnableIf_< UseSMPAssign<MT> >
        smpAddAssign( DenseMatrix<MT,SO2>& lhs, const SMatDMatSubExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        smpSubAssign( ~lhs, rhs.rhs_ );
        smpAddAssign( ~lhs, rhs.lhs_ );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**SMP addition assignment to sparse matrices**************************************************
     // No special implementation for the SMP addition assignment to sparse matrices.
     //**********************************************************************************************
  
     //**SMP subtraction assignment to dense matrices************************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief SMP subtraction assignment of a sparse matrix-dense matrix subtraction to a dense matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side subtraction expression to be subtracted.
     // \return void
     //
     // This function implements the performance optimized SMP subtraction assignment of a sparse
     // matrix-dense matrix subtraction expression to a dense matrix. Due to the explicit application
     // of the SFINAE principle, this function can only be selected by the compiler in case the
     // expression specific parallel evaluation strategy is selected.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline EnableIf_< UseSMPAssign<MT> >
        smpSubAssign( DenseMatrix<MT,SO2>& lhs, const SMatDMatSubExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        smpAddAssign( ~lhs, rhs.rhs_ );
        smpSubAssign( ~lhs, rhs.lhs_ );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**SMP subtraction assignment to sparse matrices***********************************************
     // No special implementation for the SMP subtraction assignment to sparse matrices.
     //**********************************************************************************************
  
     //**SMP Schur product assignment to dense matrices**********************************************
     /*! \cond BLAZE_INTERNAL */
     /*!\brief SMP Schur product assignment of a sparse matrix-dense matrix subtraction to a dense
     //        matrix.
     // \ingroup dense_matrix
     //
     // \param lhs The target left-hand side dense matrix.
     // \param rhs The right-hand side subtraction expression for the Schur product.
     // \return void
     //
     // This function implements the performance optimized SMP Schur product assignment of a sparse
     // matrix-dense matrix subtraction expression to a dense matrix. Due to the explicit application
     // of the SFINAE principle, this function can only be selected by the compiler in case the
     // expression specific parallel evaluation strategy is selected.
     */
     template< typename MT  // Type of the target dense matrix
             , bool SO2 >   // Storage order of the target dense matrix
     friend inline EnableIf_< UseSMPAssign<MT> >
        smpSchurAssign( DenseMatrix<MT,SO2>& lhs, const SMatDMatSubExpr& rhs )
     {
        BLAZE_FUNCTION_TRACE;
  
        BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( ResultType );
        BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( ResultType, SO );
        BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( ResultType );
  
        BLAZE_INTERNAL_ASSERT( (~lhs).rows()    == rhs.rows()   , "Invalid number of rows"    );
        BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
  
        const ResultType tmp( rhs );
        smpSchurAssign( ~lhs, tmp );
     }
     /*! \endcond */
     //**********************************************************************************************
  
     //**SMP Schur product assignment to sparse matrices*********************************************
     // No special implementation for the SMP Schur product assignment to sparse matrices.
     //**********************************************************************************************
  
     //**SMP multiplication assignment to dense matrices*********************************************
     // No special implementation for the SMP multiplication assignment to dense matrices.
     //**********************************************************************************************
  
     //**SMP multiplication assignment to sparse matrices********************************************
     // No special implementation for the SMP multiplication assignment to sparse matrices.
     //**********************************************************************************************
  
     //**Compile time checks*************************************************************************
     /*! \cond BLAZE_INTERNAL */
     BLAZE_CONSTRAINT_MUST_BE_SPARSE_MATRIX_TYPE( MT1 );
     BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE ( MT2 );
     BLAZE_CONSTRAINT_MATRICES_MUST_HAVE_SAME_STORAGE_ORDER( MT1, MT2 );
     BLAZE_CONSTRAINT_MUST_FORM_VALID_MATMATSUBEXPR( MT1, MT2 );
     /*! \endcond */
     //**********************************************************************************************
  };
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  GLOBAL BINARY ARITHMETIC OPERATORS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\brief Subtraction operator for the subtraction of a sparse matrix and a dense matrix with
  //        identical storage order (\f$ A=B+C \f$).
  // \ingroup dense_matrix
  //
  // \param lhs The left-hand side sparse matrix for the matrix subtraction.
  // \param rhs The right-hand side dense matrix to be subtracted from the sparse matrix.
  // \return The difference of the two matrices.
  // \exception std::invalid_argument Matrix sizes do not match.
  //
  // This operator represents the subtraction of a sparse matrix and a dense matrix with identical
  // storage order:
  
     \code
     using blaze::rowMajor;
  
     blaze::CompressedMatrix<double,rowMajor> A;
     blaze::DynamicMatrix<double,rowMajor> B, C;
     // ... Resizing and initialization
     C = A - B;
     \endcode
  
  // The operator returns an expression representing a dense matrix of the higher-order element
  // type of the two involved matrix element types \a MT1::ElementType and \a MT2::ElementType.
  // Both matrix types \a MT1 and \a MT2 as well as the two element types \a MT1::ElementType
  // and \a MT2::ElementType have to be supported by the SubTrait class template.\n
  // In case the current sizes of the two given matrices don't match, a \a std::invalid_argument
  // is thrown.
  */
  template< typename MT1  // Type of the left-hand side sparse matrix
          , typename MT2  // Type of the right-hand side dense matrix
          , bool SO >     // Storage order
  inline decltype(auto)
     operator-( const SparseMatrix<MT1,SO>& lhs, const DenseMatrix<MT2,SO>& rhs )
  {
     BLAZE_FUNCTION_TRACE;
  
     if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
     }
  
     using ReturnType = const SMatDMatSubExpr<MT1,MT2,SO>;
     return ReturnType( ~lhs, ~rhs );
  }
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  GLOBAL RESTRUCTURING BINARY ARITHMETIC OPERATORS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Addition operator for the addition of a sparse matrix-dense matrix subtraction
  //        expression and a dense matrix (\f$ A=(B-C)+D \f$).
  // \ingroup dense_matrix
  //
  // \param lhs The left-hand side sparse matrix-dense matrix subtraction.
  // \param rhs The right-hand side dense matrix.
  // \return The sum of the two matrices.
  //
  // This operator implements a performance optimized treatment of the addition of a sparse
  // matrix-dense matrix subtraction expression to a dense matrix.
  */
  template< typename MT1  // Type of the sparse matrix of the left-hand side expression
          , typename MT2  // Type of the dense matrix of the left-hand side expression
          , bool SO1      // Storage order of the left-hand side expression
          , typename MT3  // Type of the right-hand side dense matrix
          , bool SO2 >    // Storage order of the right-hand side dense matrix
  inline decltype(auto)
     operator+( const SMatDMatSubExpr<MT1,MT2,SO1>& lhs, const DenseMatrix<MT3,SO2>& rhs )
  {
     BLAZE_FUNCTION_TRACE;
  
     return ( (~rhs) - lhs.rightOperand() ) + lhs.leftOperand();
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Subtraction operator for the subtraction of a sparse matrix-dense matrix subtraction
  //        expression and a dense matrix (\f$ A=(B-C)-D \f$).
  // \ingroup dense_matrix
  //
  // \param lhs The left-hand side sparse matrix-dense matrix subtraction.
  // \param rhs The right-hand side dense matrix.
  // \return The difference of the two matrices.
  //
  // This operator implements a performance optimized treatment of the subtraction of a sparse
  // matrix-dense matrix subtraction expression and a dense matrix.
  */
  template< typename MT1  // Type of the sparse matrix of the left-hand side expression
          , typename MT2  // Type of the dense matrix of the left-hand side expression
          , bool SO1      // Storage order of the left-hand side expression
          , typename MT3  // Type of the right-hand side dense matrix
          , bool SO2 >    // Storage order of the right-hand side dense matrix
  inline decltype(auto)
     operator-( const SMatDMatSubExpr<MT1,MT2,SO1>& lhs, const DenseMatrix<MT3,SO2>& rhs )
  {
     BLAZE_FUNCTION_TRACE;
  
     return lhs.leftOperand() - ( lhs.rightOperand() + (~rhs) );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  SIZE SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct Size< SMatDMatSubExpr<MT1,MT2,SO>, 0UL >
     : public Maximum< Size<MT1,0UL>, Size<MT2,0UL> >
  {};
  
  template< typename MT1, typename MT2, bool SO >
  struct Size< SMatDMatSubExpr<MT1,MT2,SO>, 1UL >
     : public Maximum< Size<MT1,1UL>, Size<MT2,1UL> >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISSYMMETRIC SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsSymmetric< SMatDMatSubExpr<MT1,MT2,SO> >
     : public And< IsSymmetric<MT1>, IsSymmetric<MT2> >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISHERMITIAN SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsHermitian< SMatDMatSubExpr<MT1,MT2,SO> >
     : public And< IsHermitian<MT1>, IsHermitian<MT2> >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISLOWER SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsLower< SMatDMatSubExpr<MT1,MT2,SO> >
     : public And< IsLower<MT1>, IsLower<MT2> >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISUNILOWER SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsUniLower< SMatDMatSubExpr<MT1,MT2,SO> >
     : public And< IsUniLower<MT1>, IsStrictlyLower<MT2> >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISSTRICTLYLOWER SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsStrictlyLower< SMatDMatSubExpr<MT1,MT2,SO> >
     : public And< IsStrictlyLower<MT1>, IsStrictlyLower<MT2> >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISUPPER SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsUpper< SMatDMatSubExpr<MT1,MT2,SO> >
     : public And< IsUpper<MT1>, IsUpper<MT2> >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISUNIUPPER SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsUniUpper< SMatDMatSubExpr<MT1,MT2,SO> >
     : public And< IsUniUpper<MT1>, IsStrictlyUpper<MT2> >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ISSTRICTLYUPPER SPECIALIZATIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  template< typename MT1, typename MT2, bool SO >
  struct IsStrictlyUpper< SMatDMatSubExpr<MT1,MT2,SO> >
     : public And< IsStrictlyUpper<MT1>, IsStrictlyUpper<MT2> >
  {};
  /*! \endcond */
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  