//=================================================================================================
/*!
//  \file blaze/math/adaptors/symmetricmatrix/SparseNonScalar.h
//  \brief SymmetricMatrix specialization for sparse matrices with non-scalar element type
//
//  Copyright (C) 2012-2020 Klaus Iglberger - All Rights Reserved
//
//  This file is part of the Blaze library. You can redistribute it and/or modify it under
//  the terms of the New (Revised) BSD License. Redistribution and use in source and binary
//  forms, with or without modification, are permitted provided that the following conditions
//  are met:
//
//  1. Redistributions of source code must retain the above copyright notice, this list of
//     conditions and the following disclaimer.
//  2. Redistributions in binary form must reproduce the above copyright notice, this list
//     of conditions and the following disclaimer in the documentation and/or other materials
//     provided with the distribution.
//  3. Neither the names of the Blaze development group nor the names of its contributors
//     may be used to endorse or promote products derived from this software without specific
//     prior written permission.
//
//  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
//  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
//  OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
//  SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
//  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
//  TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
//  BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
//  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
//  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
//  DAMAGE.
*/
//=================================================================================================

#ifndef _BLAZE_MATH_ADAPTORS_SYMMETRICMATRIX_SPARSENONSCALAR_H_
#define _BLAZE_MATH_ADAPTORS_SYMMETRICMATRIX_SPARSENONSCALAR_H_


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

#include <iterator>
#include <utility>
#include <vector>
#include <blaze/math/adaptors/symmetricmatrix/BaseTemplate.h>
#include <blaze/math/adaptors/symmetricmatrix/NonScalarProxy.h>
#include <blaze/math/adaptors/symmetricmatrix/SharedValue.h>
#include <blaze/math/Aliases.h>
#include <blaze/math/constraints/Computation.h>
#include <blaze/math/constraints/Hermitian.h>
#include <blaze/math/constraints/Lower.h>
#include <blaze/math/constraints/Resizable.h>
#include <blaze/math/constraints/Scalar.h>
#include <blaze/math/constraints/SparseMatrix.h>
#include <blaze/math/constraints/StorageOrder.h>
#include <blaze/math/constraints/Symmetric.h>
#include <blaze/math/constraints/Transformation.h>
#include <blaze/math/constraints/Upper.h>
#include <blaze/math/constraints/View.h>
#include <blaze/math/Exception.h>
#include <blaze/math/expressions/SparseMatrix.h>
#include <blaze/math/RelaxationFlag.h>
#include <blaze/math/shims/Clear.h>
#include <blaze/math/shims/Conjugate.h>
#include <blaze/math/shims/IsDefault.h>
#include <blaze/math/shims/IsZero.h>
#include <blaze/math/sparse/SparseElement.h>
#include <blaze/math/sparse/SparseMatrix.h>
#include <blaze/math/traits/AddTrait.h>
#include <blaze/math/traits/SchurTrait.h>
#include <blaze/math/traits/SubTrait.h>
#include <blaze/math/typetraits/IsComputation.h>
#include <blaze/math/typetraits/IsScalar.h>
#include <blaze/math/typetraits/IsSquare.h>
#include <blaze/math/typetraits/IsSymmetric.h>
#include <blaze/math/typetraits/RemoveAdaptor.h>
#include <blaze/math/typetraits/Size.h>
#include <blaze/util/Assert.h>
#include <blaze/util/constraints/Const.h>
#include <blaze/util/constraints/Pointer.h>
#include <blaze/util/constraints/Reference.h>
#include <blaze/util/constraints/Volatile.h>
#include <blaze/util/EnableIf.h>
#include <blaze/util/MaybeUnused.h>
#include <blaze/util/mpl/If.h>
#include <blaze/util/StaticAssert.h>
#include <blaze/util/Types.h>


namespace blaze {

//=================================================================================================
//
//  CLASS TEMPLATE SPECIALIZATION FOR SPARSE MATRICES WITH NON-SCALAR ELEMENT TYPE
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Specialization of SymmetricMatrix for sparse matrices with non-scalar element type.
// \ingroup symmetric_matrix
//
// This specialization of SymmetricMatrix adapts the class template to the requirements of sparse
// matrices with non-scalar element type.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
class SymmetricMatrix<MT,SO,false,false>
   : public SparseMatrix< SymmetricMatrix<MT,SO,false,false>, SO >
{
 private:
   //**Type definitions****************************************************************************
   using OT = OppositeType_t<MT>;   //!< Opposite type of the sparse matrix.
   using TT = TransposeType_t<MT>;  //!< Transpose type of the sparse matrix.
   using ET = ElementType_t<MT>;    //!< Element type of the sparse matrix.

   //! Rebound matrix type for shared values.
   using MatrixType = typename MT::template Rebind< SharedValue<ET> >::Other;
   //**********************************************************************************************

 public:
   //**Type definitions****************************************************************************
   using This           = SymmetricMatrix<MT,SO,false,false>;   //!< Type of this SymmetricMatrix instance.
   using BaseType       = SparseMatrix<This,SO>;                //!< Base type of this SymmetricMatrix instance.
   using ResultType     = This;                                 //!< Result type for expression template evaluations.
   using OppositeType   = SymmetricMatrix<OT,!SO,false,false>;  //!< Result type with opposite storage order for expression template evaluations.
   using TransposeType  = SymmetricMatrix<TT,!SO,false,false>;  //!< Transpose type for expression template evaluations.
   using ElementType    = ET;                                   //!< Type of the matrix elements.
   using TagType        = TagType_t<MT>;                        //!< Tag type of this SymmetricMatrix instance.
   using ReturnType     = ReturnType_t<MT>;                     //!< Return type for expression template evaluations.
   using CompositeType  = const This&;                          //!< Data type for composite expression templates.
   using Reference      = NonScalarProxy<MatrixType>;           //!< Reference to a non-constant matrix value.
   using ConstReference = ConstReference_t<MT>;                 //!< Reference to a constant matrix value.
   //**********************************************************************************************

   //**Rebind struct definition********************************************************************
   /*!\brief Rebind mechanism to obtain a SymmetricMatrix with different data/element type.
   */
   template< typename NewType >  // Data type of the other matrix
   struct Rebind {
      //! The type of the other SymmetricMatrix.
      using Other = SymmetricMatrix< typename MT::template Rebind<NewType>::Other >;
   };
   //**********************************************************************************************

   //**Resize struct definition********************************************************************
   /*!\brief Resize mechanism to obtain a SymmetricMatrix with different fixed dimensions.
   */
   template< size_t NewM    // Number of rows of the other matrix
           , size_t NewN >  // Number of columns of the other matrix
   struct Resize {
      //! The type of the other SymmetricMatrix.
      using Other = SymmetricMatrix< typename MT::template Resize<NewM,NewN>::Other >;
   };
   //**********************************************************************************************

   //**SharedElement class definition**************************************************************
   /*!\brief Access proxy for a specific shared element of the sparse symmetric matrix.
   */
   template< typename IteratorType >  // Type of the sparse matrix iterator
   class SharedElement
      : private SparseElement
   {
    public:
      //**Type definitions*************************************************************************
      using ValueType      = ET;                    //!< The value type of the value-index-pair.
      using IndexType      = size_t;                //!< The index type of the value-index-pair.
      using Reference      = ValueType&;            //!< Reference return type.
      using ConstReference = const ValueType&;      //!< Reference-to-const return type.
      using Pointer        = SharedElement*;        //!< Pointer return type.
      using ConstPointer   = const SharedElement*;  //!< Pointer-to-const return type.
      //*******************************************************************************************

      //**Constructor******************************************************************************
      /*!\brief Constructor for the SharedElement class.
      //
      // \param pos Iterator to the current sparse symmetric matrix element.
      */
      inline SharedElement( IteratorType pos )
         : pos_( pos )  // Iterator to the current sparse symmetric matrix element
      {}
      //*******************************************************************************************

      //**Assignment operator**********************************************************************
      /*!\brief Assignment to the symmetric element.
      //
      // \param v The new v of the symmetric element.
      // \return Reference to the assigned symmetric element.
      */
      template< typename T > inline SharedElement& operator=( const T& v ) {
         *pos_->value() = v;
         return *this;
      }
      //*******************************************************************************************

      //**Addition assignment operator*************************************************************
      /*!\brief Addition assignment to the symmetric element.
      //
      // \param v The right-hand side value for the addition.
      // \return Reference to the assigned symmetric element.
      */
      template< typename T > inline SharedElement& operator+=( const T& v ) {
         *pos_->value() += v;
         return *this;
      }
      //*******************************************************************************************

      //**Subtraction assignment operator**********************************************************
      /*!\brief Subtraction assignment to the symmetric element.
      //
      // \param v The right-hand side value for the subtraction.
      // \return Reference to the assigned symmetric element.
      */
      template< typename T > inline SharedElement& operator-=( const T& v ) {
         *pos_->value() -= v;
         return *this;
      }
      //*******************************************************************************************

      //**Multiplication assignment operator*******************************************************
      /*!\brief Multiplication assignment to the symmetric element.
      //
      // \param v The right-hand side value for the multiplication.
      // \return Reference to the assigned symmetric element.
      */
      template< typename T > inline SharedElement& operator*=( const T& v ) {
         *pos_->value() *= v;
         return *this;
      }
      //*******************************************************************************************

      //**Division assignment operator*************************************************************
      /*!\brief Division assignment to the symmetric element.
      //
      // \param v The right-hand side value for the division.
      // \return Reference to the assigned symmetric element.
      */
      template< typename T > inline SharedElement& operator/=( const T& v ) {
         *pos_->value() /= v;
         return *this;
      }
      //*******************************************************************************************

      //**Element access operator******************************************************************
      /*!\brief Direct access to the symmetric element.
      //
      // \return Reference to the value of the symmetric element.
      */
      inline Pointer operator->() {
         return this;
      }
      //*******************************************************************************************

      //**Element access operator******************************************************************
      /*!\brief Direct access to the symmetric element.
      //
      // \return Reference to the value of the symmetric element.
      */
      inline ConstPointer operator->() const {
         return this;
      }
      //*******************************************************************************************

      //**Value function***************************************************************************
      /*!\brief Access to the current value of the symmetric element.
      //
      // \return The current value of the symmetric element.
      */
      inline Reference value() {
         return *pos_->value();
      }
      //*******************************************************************************************

      //**Value function***************************************************************************
      /*!\brief Access to the current value of the symmetric element.
      //
      // \return The current value of the symmetric element.
      */
      inline ConstReference value() const {
         return *pos_->value();
      }
      //*******************************************************************************************

      //**Index function***************************************************************************
      /*!\brief Access to the current index of the symmetric element.
      //
      // \return The current index of the symmetric element.
      */
      inline IndexType index() const {
         return pos_->index();
      }
      //*******************************************************************************************

    private:
      //**Member variables*************************************************************************
      IteratorType pos_;  //!< Iterator to the current sparse symmetric matrix element.
      //*******************************************************************************************
   };
   //**********************************************************************************************

   //**SharedIterator class definition*************************************************************
   /*!\brief Iterator over the elements of the sparse symmetric matrix.
   */
   template< typename SparseElementType  // Type of the underlying sparse elements.
           , typename IteratorType >     // Type of the sparse matrix iterator
   class SharedIterator
   {
    public:
      //**Type definitions*************************************************************************
      using IteratorCategory = std::forward_iterator_tag;  //!< The iterator category.
      using ValueType        = SparseElementType;          //!< Type of the underlying elements.
      using PointerType      = SparseElementType;          //!< Pointer return type.
      using ReferenceType    = SparseElementType;          //!< Reference return type.
      using DifferenceType   = ptrdiff_t;                  //!< Difference between two iterators.

      // 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.
      //*******************************************************************************************

      //**Default constructor**********************************************************************
      /*!\brief Default constructor for the SharedIterator class.
      */
      inline SharedIterator()
         : pos_()  // Iterator to the current sparse symmetric matrix element
      {}
      //*******************************************************************************************

      //**Constructor******************************************************************************
      /*!\brief Constructor for the SharedIterator class.
      //
      // \param pos The initial position of the iterator.
      */
      inline SharedIterator( IteratorType pos )
         : pos_( pos )  // Iterator to the current sparse symmetric matrix element
      {}
      //*******************************************************************************************

      //**Constructor******************************************************************************
      /*!\brief Conversion constructor from different SharedIterator instances.
      //
      // \param it The matrix iterator to be copied.
      */
      template< typename SparseElementType2, typename IteratorType2 >
      inline SharedIterator( const SharedIterator<SparseElementType2,IteratorType2>& it )
         : pos_( it.pos_ )  // Iterator to the current sparse symmetric matrix element
      {}
      //*******************************************************************************************

      //**Prefix increment operator****************************************************************
      /*!\brief Pre-increment operator.
      //
      // \return Reference to the incremented iterator.
      */
      inline SharedIterator& operator++() {
         ++pos_;
         return *this;
      }
      //*******************************************************************************************

      //**Postfix increment operator***************************************************************
      /*!\brief Post-increment operator.
      //
      // \return The previous position of the iterator.
      */
      inline const SharedIterator operator++( int ) {
         const SharedIterator tmp( *this );
         ++(*this);
         return tmp;
      }
      //*******************************************************************************************

      //**Element access operator******************************************************************
      /*!\brief Direct access to the current sparse matrix element.
      //
      // \return Reference to the current sparse matrix element.
      */
      inline ReferenceType operator*() const {
         return ReferenceType( pos_ );
      }
      //*******************************************************************************************

      //**Element access operator******************************************************************
      /*!\brief Direct access to the current sparse matrix element.
      //
      // \return Pointer to the current sparse matrix element.
      */
      inline PointerType operator->() const {
         return PointerType( pos_ );
      }
      //*******************************************************************************************

      //**Equality operator************************************************************************
      /*!\brief Equality comparison between two SharedIterator objects.
      //
      // \param rhs The right-hand side matrix iterator.
      // \return \a true if the iterators refer to the same element, \a false if not.
      */
      inline bool operator==( const SharedIterator& rhs ) const {
         return pos_ == rhs.pos_;
      }
      //*******************************************************************************************

      //**Inequality operator**********************************************************************
      /*!\brief Inequality comparison between two SharedIterator objects.
      //
      // \param rhs The right-hand side matrix iterator.
      // \return \a true if the iterators don't refer to the same element, \a false if they do.
      */
      inline bool operator!=( const SharedIterator& rhs ) const {
         return !( *this == rhs );
      }
      //*******************************************************************************************

      //**Subtraction operator*********************************************************************
      /*!\brief Calculating the number of elements between two iterators.
      //
      // \param rhs The right-hand side iterator.
      // \return The number of elements between the two iterators.
      */
      inline DifferenceType operator-( const SharedIterator& rhs ) const {
         return pos_ - rhs.pos_;
      }
      //*******************************************************************************************

      //**Base function****************************************************************************
      /*!\brief Access to the current position of the iterator.
      //
      // \return The current position of the iterator.
      */
      inline IteratorType base() const {
         return pos_;
      }
      //*******************************************************************************************

    private:
      //**Member variables*************************************************************************
      IteratorType pos_;  //!< Iterator to the current sparse symmetric matrix element.
      //*******************************************************************************************

      //**Friend declarations**********************************************************************
      template< typename SparseElementType2, typename IteratorType2 > friend class SharedIterator;
      //*******************************************************************************************
   };
   //**********************************************************************************************

   //**Type definitions****************************************************************************
   //! Iterator over non-constant elements.
   using Iterator = SharedIterator< SharedElement< Iterator_t<MatrixType> >
                                  , Iterator_t<MatrixType> >;

   //! Iterator over constant elements.
   using ConstIterator = SharedIterator< const SharedElement< ConstIterator_t<MatrixType> >
                                       , ConstIterator_t<MatrixType> >;
   //**********************************************************************************************

   //**Compilation flags***************************************************************************
   //! Compilation switch for the expression template assignment strategy.
   static constexpr bool smpAssignable = false;
   //**********************************************************************************************

   //**Constructors********************************************************************************
   /*!\name Constructors */
   //@{
            inline SymmetricMatrix();
   explicit inline SymmetricMatrix( size_t n );
            inline SymmetricMatrix( size_t n, size_t nonzeros );
            inline SymmetricMatrix( size_t n, const std::vector<size_t>& nonzeros );

   inline SymmetricMatrix( const SymmetricMatrix& m );
   inline SymmetricMatrix( SymmetricMatrix&& m ) noexcept;

   template< typename MT2 > inline SymmetricMatrix( const Matrix<MT2,SO>&  m );
   template< typename MT2 > inline SymmetricMatrix( const Matrix<MT2,!SO>& m );
   //@}
   //**********************************************************************************************

   //**Destructor**********************************************************************************
   /*!\name Destructor */
   //@{
   ~SymmetricMatrix() = default;
   //@}
   //**********************************************************************************************

   //**Data access functions***********************************************************************
   /*!\name Data access functions */
   //@{
   inline Reference      operator()( size_t i, size_t j );
   inline ConstReference operator()( size_t i, size_t j ) const;
   inline Reference      at( size_t i, size_t j );
   inline ConstReference at( size_t i, size_t j ) const;
   inline Iterator       begin ( size_t i );
   inline ConstIterator  begin ( size_t i ) const;
   inline ConstIterator  cbegin( size_t i ) const;
   inline Iterator       end   ( size_t i );
   inline ConstIterator  end   ( size_t i ) const;
   inline ConstIterator  cend  ( size_t i ) const;
   //@}
   //**********************************************************************************************

   //**Assignment operators************************************************************************
   /*!\name Assignment operators */
   //@{
   inline SymmetricMatrix& operator=( const SymmetricMatrix& rhs );
   inline SymmetricMatrix& operator=( SymmetricMatrix&& rhs ) noexcept;

   template< typename MT2 >
   inline auto operator=( const Matrix<MT2,SO>& rhs )
      -> DisableIf_t< IsComputation_v<MT2>, SymmetricMatrix& >;

   template< typename MT2 >
   inline auto operator=( const Matrix<MT2,SO>& rhs )
      -> EnableIf_t< IsComputation_v<MT2>, SymmetricMatrix& >;

   template< typename MT2 >
   inline auto operator=( const Matrix<MT2,!SO>& rhs ) -> SymmetricMatrix&;

   template< typename MT2 >
   inline auto operator+=( const Matrix<MT2,SO>& rhs ) -> SymmetricMatrix&;

   template< typename MT2 >
   inline auto operator+=( const Matrix<MT2,!SO>& rhs ) -> SymmetricMatrix&;

   template< typename MT2 >
   inline auto operator-=( const Matrix<MT2,SO>& rhs ) -> SymmetricMatrix&;

   template< typename MT2 >
   inline auto operator-=( const Matrix<MT2,!SO>& rhs ) -> SymmetricMatrix&;

   template< typename MT2 >
   inline auto operator%=( const Matrix<MT2,SO>& rhs ) -> SymmetricMatrix&;

   template< typename MT2 >
   inline auto operator%=( const Matrix<MT2,!SO>& rhs ) -> SymmetricMatrix&;

   template< typename ST >
   inline auto operator*=( ST rhs ) -> EnableIf_t< IsScalar_v<ST>, SymmetricMatrix& >;

   template< typename ST >
   inline auto operator/=( ST rhs ) -> EnableIf_t< IsScalar_v<ST>, SymmetricMatrix& >;
   //@}
   //**********************************************************************************************

   //**Utility functions***************************************************************************
   /*!\name Utility functions */
   //@{
   inline size_t rows() const noexcept;
   inline size_t columns() const noexcept;
   inline size_t capacity() const noexcept;
   inline size_t capacity( size_t i ) const noexcept;
   inline size_t nonZeros() const;
   inline size_t nonZeros( size_t i ) const;
   inline void   reset();
   inline void   reset( size_t i );
   inline void   clear();
   inline void   resize ( size_t n, bool preserve=true );
   inline void   reserve( size_t nonzeros );
   inline void   reserve( size_t i, size_t nonzeros );
   inline void   trim();
   inline void   trim( size_t i );
   inline void   shrinkToFit();
   inline void   swap( SymmetricMatrix& m ) noexcept;
   //@}
   //**********************************************************************************************

   //**Insertion functions*************************************************************************
   /*!\name Insertion functions */
   //@{
   inline Iterator set     ( size_t i, size_t j, const ElementType& value );
   inline Iterator insert  ( size_t i, size_t j, const ElementType& value );
   inline void     append  ( size_t i, size_t j, const ElementType& value, bool check=false );
   inline void     finalize( size_t i );
   //@}
   //**********************************************************************************************

   //**Erase functions*****************************************************************************
   /*!\name Erase functions */
   //@{
   inline void     erase( size_t i, size_t j );
   inline Iterator erase( size_t i, Iterator pos );
   inline Iterator erase( size_t i, Iterator first, Iterator last );

   template< typename Pred >
   inline void erase( Pred predicate );

   template< typename Pred >
   inline void erase( size_t i, Iterator first, Iterator last, Pred predicate );
   //@}
   //**********************************************************************************************

   //**Lookup functions****************************************************************************
   /*!\name Lookup functions */
   //@{
   inline Iterator      find      ( size_t i, size_t j );
   inline ConstIterator find      ( size_t i, size_t j ) const;
   inline Iterator      lowerBound( size_t i, size_t j );
   inline ConstIterator lowerBound( size_t i, size_t j ) const;
   inline Iterator      upperBound( size_t i, size_t j );
   inline ConstIterator upperBound( size_t i, size_t j ) const;
   //@}
   //**********************************************************************************************

   //**Numeric functions***************************************************************************
   /*!\name Numeric functions */
   //@{
   inline SymmetricMatrix& transpose();
   inline SymmetricMatrix& ctranspose();

   template< typename Other > inline SymmetricMatrix& scale( const Other& scalar );
   //@}
   //**********************************************************************************************

   //**Debugging functions*************************************************************************
   /*!\name Utility functions */
   //@{
   inline bool isIntact() const noexcept;
   //@}
   //**********************************************************************************************

   //**Expression template evaluation functions****************************************************
   /*!\name Expression template evaluation functions */
   //@{
   template< typename Other > inline bool canAlias ( const Other* alias ) const noexcept;
   template< typename Other > inline bool isAliased( const Other* alias ) const noexcept;

   inline bool canSMPAssign() const noexcept;
   //@}
   //**********************************************************************************************

 private:
   //**Expression template evaluation functions****************************************************
   /*!\name Expression template evaluation functions */
   //@{
   template< typename MT2 > void assign( DenseMatrix<MT2,SO>& rhs );
   template< typename MT2 > void assign( const DenseMatrix<MT2,SO>& rhs );
   template< typename MT2 > void assign( SparseMatrix<MT2,SO>& rhs );
   template< typename MT2 > void assign( const SparseMatrix<MT2,SO>& rhs );
   //@}
   //**********************************************************************************************

   //**Member variables****************************************************************************
   /*!\name Member variables */
   //@{
   MatrixType matrix_;  //!< The adapted sparse matrix.
   //@}
   //**********************************************************************************************

   //**Friend declarations*************************************************************************
   template< RelaxationFlag RF, typename MT2, bool SO2, bool DF2, bool SF2 >
   friend bool isDefault( const SymmetricMatrix<MT2,SO2,DF2,SF2>& m );
   //**********************************************************************************************

   //**Compile time checks*************************************************************************
   BLAZE_CONSTRAINT_MUST_BE_SPARSE_MATRIX_TYPE       ( MT );
   BLAZE_CONSTRAINT_MUST_NOT_BE_REFERENCE_TYPE       ( MT );
   BLAZE_CONSTRAINT_MUST_NOT_BE_POINTER_TYPE         ( MT );
   BLAZE_CONSTRAINT_MUST_NOT_BE_CONST                ( MT );
   BLAZE_CONSTRAINT_MUST_NOT_BE_VOLATILE             ( MT );
   BLAZE_CONSTRAINT_MUST_NOT_BE_VIEW_TYPE            ( MT );
   BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE     ( MT );
   BLAZE_CONSTRAINT_MUST_NOT_BE_TRANSFORMATION_TYPE  ( MT );
   BLAZE_CONSTRAINT_MUST_NOT_BE_SYMMETRIC_MATRIX_TYPE( MT );
   BLAZE_CONSTRAINT_MUST_NOT_BE_HERMITIAN_MATRIX_TYPE( MT );
   BLAZE_CONSTRAINT_MUST_NOT_BE_LOWER_MATRIX_TYPE    ( MT );
   BLAZE_CONSTRAINT_MUST_NOT_BE_UPPER_MATRIX_TYPE    ( MT );
   BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( OT, !SO );
   BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( TT, !SO );
   BLAZE_CONSTRAINT_MUST_NOT_BE_SCALAR_TYPE          ( ElementType );
   BLAZE_STATIC_ASSERT( ( Size_v<MT,0UL> == Size_v<MT,1UL> ) );
   //**********************************************************************************************
};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  CONSTRUCTORS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief The default constructor for SymmetricMatrix.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline SymmetricMatrix<MT,SO,false,false>::SymmetricMatrix()
   : matrix_()  // The adapted sparse matrix
{
   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Constructor for a matrix of size \f$ n \times n \f$.
//
// \param n The number of rows and columns of the matrix.
//
// The matrix is initialized to the zero matrix and has no free capacity.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline SymmetricMatrix<MT,SO,false,false>::SymmetricMatrix( size_t n )
   : matrix_( n, n )  // The adapted sparse matrix
{
   BLAZE_CONSTRAINT_MUST_BE_RESIZABLE_TYPE( MT );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Constructor for a matrix of size \f$ n \times n \f$.
//
// \param n The number of rows and columns of the matrix.
// \param nonzeros The number of expected non-zero elements.
//
// The matrix is initialized to the zero matrix.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline SymmetricMatrix<MT,SO,false,false>::SymmetricMatrix( size_t n, size_t nonzeros )
   : matrix_( n, n, nonzeros )  // The adapted sparse matrix
{
   BLAZE_CONSTRAINT_MUST_BE_RESIZABLE_TYPE( MT );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Constructor for a matrix of size \f$ n \times n \f$.
//
// \param n The number of rows and columns of the matrix.
// \param nonzeros The expected number of non-zero elements in each row/column.
//
// The matrix is initialized to the zero matrix and will have the specified capacity in each
// row/column. Note that in case of a row-major matrix the given vector must have at least
// \a m elements, in case of a column-major matrix at least \a n elements.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline SymmetricMatrix<MT,SO,false,false>::SymmetricMatrix( size_t n, const std::vector<size_t>& nonzeros )
   : matrix_( n, n, nonzeros )  // The adapted sparse matrix
{
   BLAZE_CONSTRAINT_MUST_BE_RESIZABLE_TYPE( MT );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief The copy constructor for SymmetricMatrix.
//
// \param m The symmetric matrix to be copied.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline SymmetricMatrix<MT,SO,false,false>::SymmetricMatrix( const SymmetricMatrix& m )
   : matrix_()  // The adapted sparse matrix
{
   using blaze::resize;

   resize( matrix_, m.rows(), m.columns() );
   assign( m );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
   BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief The move constructor for SymmetricMatrix.
//
// \param m The symmetric matrix to be moved into this instance.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline SymmetricMatrix<MT,SO,false,false>::SymmetricMatrix( SymmetricMatrix&& m ) noexcept
   : matrix_( std::move( m.matrix_ ) )  // The adapted sparse matrix
{
   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
   BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Conversion constructor from different matrices with the same storage order.
//
// \param m Matrix to be copied.
// \exception std::invalid_argument Invalid setup of symmetric matrix.
//
// This constructor initializes the symmetric matrix as a copy of the given matrix. In case the
// given matrix is not a symmetric matrix, a \a std::invalid_argument exception is thrown.
*/
template< typename MT     // Type of the adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the foreign matrix
inline SymmetricMatrix<MT,SO,false,false>::SymmetricMatrix( const Matrix<MT2,SO>& m )
   : matrix_()  // The adapted sparse matrix
{
   using blaze::resize;

   using RT  = RemoveAdaptor_t< ResultType_t<MT2> >;
   using Tmp = If_t< IsComputation_v<MT2>, RT, const MT2& >;

   Tmp tmp( *m );

   if( !IsSymmetric_v<MT2> && !isSymmetric( tmp ) ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Invalid setup of symmetric matrix" );
   }

   resize( matrix_, tmp.rows(), tmp.columns() );
   assign( tmp );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
   BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Conversion constructor from different matrices with opposite storage order.
//
// \param m Matrix to be copied.
// \exception std::invalid_argument Invalid setup of symmetric matrix.
//
// This constructor initializes the symmetric matrix as a copy of the given matrix. In case the
// given matrix is not a symmetric matrix, a \a std::invalid_argument exception is thrown.
*/
template< typename MT     // Type of the adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the foreign matrix
inline SymmetricMatrix<MT,SO,false,false>::SymmetricMatrix( const Matrix<MT2,!SO>& m )
   : matrix_()  // The adapted sparse matrix
{
   using blaze::resize;

   using RT  = RemoveAdaptor_t< ResultType_t<MT2> >;
   using Tmp = If_t< IsComputation_v<MT2>, RT, const MT2& >;

   Tmp tmp( *m );

   if( !IsSymmetric_v<MT2> && !isSymmetric( tmp ) ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Invalid setup of symmetric matrix" );
   }

   resize( matrix_, tmp.rows(), tmp.columns() );
   assign( trans( tmp ) );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
   BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
}
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  DATA ACCESS FUNCTIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief 2D-access to the matrix elements.
//
// \param i Access index for the row. The index has to be in the range \f$[0..N-1]\f$.
// \param j Access index for the column. The index has to be in the range \f$[0..N-1]\f$.
// \return Reference to the accessed value.
//
// The function call operator provides access to both elements \f$ a_{ij} \f$ and \f$ a_{ji} \f$.
// In order to preserve the symmetry of the matrix, any modification to one of the elements will
// also be applied to the other element.
//
// Note that 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 indices.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::Reference
   SymmetricMatrix<MT,SO,false,false>::operator()( size_t i, size_t j )
{
   BLAZE_USER_ASSERT( i<rows()   , "Invalid row access index"    );
   BLAZE_USER_ASSERT( j<columns(), "Invalid column access index" );

   return Reference( matrix_, i, j );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief 2D-access to the matrix elements.
//
// \param i Access index for the row. The index has to be in the range \f$[0..N-1]\f$.
// \param j Access index for the column. The index has to be in the range \f$[0..N-1]\f$.
// \return Reference to the accessed value.
//
// The function call operator provides access to both elements \f$ a_{ij} \f$ and \f$ a_{ji} \f$.
// In order to preserve the symmetry of the matrix, any modification to one of the elements will
// also be applied to the other element.
//
// Note that 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 indices.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::ConstReference
   SymmetricMatrix<MT,SO,false,false>::operator()( size_t i, size_t j ) const
{
   BLAZE_USER_ASSERT( i<rows()   , "Invalid row access index"    );
   BLAZE_USER_ASSERT( j<columns(), "Invalid column access index" );

   return *matrix_(i,j);
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Checked access to the matrix elements.
//
// \param i Access index for the row. The index has to be in the range \f$[0..N-1]\f$.
// \param j Access index for the column. The index has to be in the range \f$[0..N-1]\f$.
// \return Reference to the accessed value.
// \exception std::out_of_range Invalid matrix access index.
//
// The function call operator provides access to both the elements at position (i,j) and (j,i).
// In order to preserve the symmetry of the matrix, any modification to one of the elements will
// also be applied to the other element.
//
// Note that in contrast to the subscript operator this function always performs a check of the
// given access indices.
*/
template< typename MT  // Type of the adapted dense matrix
        , bool SO >    // Storage order of the adapted dense matrix
inline typename SymmetricMatrix<MT,SO,false,false>::Reference
   SymmetricMatrix<MT,SO,false,false>::at( size_t i, size_t j )
{
   if( i >= rows() ) {
      BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
   }
   if( j >= columns() ) {
      BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
   }
   return (*this)(i,j);
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Checked access to the matrix elements.
//
// \param i Access index for the row. The index has to be in the range \f$[0..N-1]\f$.
// \param j Access index for the column. The index has to be in the range \f$[0..N-1]\f$.
// \return Reference to the accessed value.
// \exception std::out_of_range Invalid matrix access index.
//
// The function call operator provides access to both the elements at position (i,j) and (j,i).
// In order to preserve the symmetry of the matrix, any modification to one of the elements will
// also be applied to the other element.
//
// Note that in contrast to the subscript operator this function always performs a check of the
// given access indices.
*/
template< typename MT  // Type of the adapted dense matrix
        , bool SO >    // Storage order of the adapted dense matrix
inline typename SymmetricMatrix<MT,SO,false,false>::ConstReference
   SymmetricMatrix<MT,SO,false,false>::at( size_t i, size_t j ) const
{
   if( i >= rows() ) {
      BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
   }
   if( j >= columns() ) {
      BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
   }
   return (*this)(i,j);
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns an iterator to the first element of row/column \a i.
//
// \param i The row/column index.
// \return Iterator to the first element of row/column \a i.
//
// This function returns a row/column iterator to the first element of row/column \a i. In case
// the symmetric matrix adapts a \a rowMajor sparse matrix the function returns an iterator to
// the first element of row \a i, in case it adapts a \a columnMajor sparse matrix the function
// returns an iterator to the first element of column \a i.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::Iterator
   SymmetricMatrix<MT,SO,false,false>::begin( size_t i )
{
   return Iterator( matrix_.begin(i) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns an iterator to the first element of row/column \a i.
//
// \param i The row/column index.
// \return Iterator to the first element of row/column \a i.
//
// This function returns a row/column iterator to the first element of row/column \a i. In case
// the symmetric matrix adapts a \a rowMajor sparse matrix the function returns an iterator to
// the first element of row \a i, in case it adapts a \a columnMajor sparse matrix the function
// returns an iterator to the first element of column \a i.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::ConstIterator
   SymmetricMatrix<MT,SO,false,false>::begin( size_t i ) const
{
   return ConstIterator( matrix_.begin(i) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns an iterator to the first element of row/column \a i.
//
// \param i The row/column index.
// \return Iterator to the first element of row/column \a i.
//
// This function returns a row/column iterator to the first element of row/column \a i. In case
// the symmetric matrix adapts a \a rowMajor sparse matrix the function returns an iterator to
// the first element of row \a i, in case it adapts a \a columnMajor sparse matrix the function
// returns an iterator to the first element of column \a i.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::ConstIterator
   SymmetricMatrix<MT,SO,false,false>::cbegin( size_t i ) const
{
   return ConstIterator( matrix_.cbegin(i) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns an iterator just past the last element of row/column \a i.
//
// \param i The row/column index.
// \return Iterator just past the last element of row/column \a i.
//
// This function returns an row/column iterator just past the last element of row/column \a i.
// In case the symmetric matrix adapts a \a rowMajor sparse matrix the function returns an iterator
// just past the last element of row \a i, in case it adapts a \a columnMajor sparse matrix the
// function returns an iterator just past the last element of column \a i.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::Iterator
   SymmetricMatrix<MT,SO,false,false>::end( size_t i )
{
   return Iterator( matrix_.end(i) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns an iterator just past the last element of row/column \a i.
//
// \param i The row/column index.
// \return Iterator just past the last element of row/column \a i.
//
// This function returns an row/column iterator just past the last element of row/column \a i.
// In case the symmetric matrix adapts a \a rowMajor sparse matrix the function returns an iterator
// just past the last element of row \a i, in case it adapts a \a columnMajor sparse matrix the
// function returns an iterator just past the last element of column \a i.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::ConstIterator
   SymmetricMatrix<MT,SO,false,false>::end( size_t i ) const
{
   return ConstIterator( matrix_.end(i) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns an iterator just past the last element of row/column \a i.
//
// \param i The row/column index.
// \return Iterator just past the last element of row/column \a i.
//
// This function returns an row/column iterator just past the last element of row/column \a i.
// In case the symmetric matrix adapts a \a rowMajor sparse matrix the function returns an iterator
// just past the last element of row \a i, in case it adapts a \a columnMajor sparse matrix the
// function returns an iterator just past the last element of column \a i.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::ConstIterator
   SymmetricMatrix<MT,SO,false,false>::cend( size_t i ) const
{
   return ConstIterator( matrix_.cend(i) );
}
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ASSIGNMENT OPERATORS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Copy assignment operator for SymmetricMatrix.
//
// \param rhs Matrix to be copied.
// \return Reference to the assigned matrix.
//
// If possible and necessary, the matrix is resized according to the given \f$ N \times N \f$
// matrix and initialized as a copy of this matrix.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline SymmetricMatrix<MT,SO,false,false>&
   SymmetricMatrix<MT,SO,false,false>::operator=( const SymmetricMatrix& rhs )
{
   using blaze::resize;

   if( &rhs == this ) return *this;

   resize( matrix_, rhs.rows(), rhs.columns() );
   reset();
   assign( rhs );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
   BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );

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


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Move assignment operator for SymmetricMatrix.
//
// \param rhs The matrix to be moved into this instance.
// \return Reference to the assigned matrix.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline SymmetricMatrix<MT,SO,false,false>&
   SymmetricMatrix<MT,SO,false,false>::operator=( SymmetricMatrix&& rhs ) noexcept
{
   matrix_ = std::move( rhs.matrix_ );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
   BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );

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


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Assignment operator for general matrices.
//
// \param rhs The general matrix to be copied.
// \return Reference to the assigned matrix.
// \exception std::invalid_argument Invalid assignment to symmetric matrix.
// \exception std::invalid_argument Matrix sizes do not match.
//
// If possible and necessary, the matrix is resized according to the given \f$ N \times N \f$
// matrix and initialized as a copy of this matrix. If the matrix cannot be resized accordingly,
// a \a std::invalid_argument exception is thrown. Also note that the given matrix must be a
// symmetric matrix. Otherwise, a \a std::invalid_argument exception is thrown.
*/
template< typename MT     // Type of the adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side matrix
inline auto SymmetricMatrix<MT,SO,false,false>::operator=( const Matrix<MT2,SO>& rhs )
   -> DisableIf_t< IsComputation_v<MT2>, SymmetricMatrix& >
{
   using blaze::resize;

   if( !IsSymmetric_v<MT2> && !isSymmetric( *rhs ) ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to symmetric matrix" );
   }

   if( (*rhs).canAlias( this ) ) {
      SymmetricMatrix tmp( *rhs );
      swap( tmp );
   }
   else {
      resize( matrix_, (*rhs).rows(), (*rhs).columns() );
      reset();
      assign( *rhs );
   }

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
   BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );

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


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Assignment operator for matrix computations.
//
// \param rhs The matrix computation to be copied.
// \return Reference to the assigned matrix.
// \exception std::invalid_argument Invalid assignment to symmetric matrix.
// \exception std::invalid_argument Matrix sizes do not match.
//
// If possible and necessary, the matrix is resized according to the given \f$ N \times N \f$
// matrix and initialized as a copy of this matrix. If the matrix cannot be resized accordingly,
// a \a std::invalid_argument exception is thrown. Also note that the given matrix must be a
// symmetric matrix. Otherwise, a \a std::invalid_argument exception is thrown.
*/
template< typename MT     // Type of the adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side matrix
inline auto SymmetricMatrix<MT,SO,false,false>::operator=( const Matrix<MT2,SO>& rhs )
   -> EnableIf_t< IsComputation_v<MT2>, SymmetricMatrix& >
{
   using blaze::resize;

   if( !IsSquare_v<MT2> && !isSquare( *rhs ) ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to symmetric matrix" );
   }

   const ResultType_t<MT2> tmp( *rhs );

   if( !IsSymmetric_v<MT2> && !isSymmetric( tmp ) ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to symmetric matrix" );
   }

   resize( matrix_, tmp.rows(), tmp.columns() );
   reset();
   assign( tmp );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
   BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );

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


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Assignment operator for matrices with opposite storage order.
//
// \param rhs The right-hand side matrix to be copied.
// \return Reference to the assigned matrix.
// \exception std::invalid_argument Invalid assignment to symmetric matrix.
// \exception std::invalid_argument Matrix sizes do not match.
//
// If possible and necessary, the matrix is resized according to the given \f$ N \times N \f$
// matrix and initialized as a copy of this matrix. If the matrix cannot be resized accordingly,
// a \a std::invalid_argument exception is thrown. Also note that the given matrix must be a
// symmetric matrix. Otherwise, a \a std::invalid_argument exception is thrown.
*/
template< typename MT     // Type of the adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side matrix
inline auto SymmetricMatrix<MT,SO,false,false>::operator=( const Matrix<MT2,!SO>& rhs )
   -> SymmetricMatrix&
{
   return this->operator=( trans( *rhs ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Addition assignment operator for the addition of a matrix (\f$ A+=B \f$).
//
// \param rhs The right-hand side matrix to be added.
// \return Reference to the matrix.
// \exception std::invalid_argument Invalid assignment to symmetric matrix.
//
// In case the current sizes of the two matrices don't match, a \a std::invalid_argument exception
// is thrown. Also note that the result of the addition operation must be a symmetric matrix, i.e.
// the given matrix must be a symmetric matrix. In case the result is not a symmetric matrix, a
// \a std::invalid_argument exception is thrown.
*/
template< typename MT     // Type of the adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side matrix
inline auto SymmetricMatrix<MT,SO,false,false>::operator+=( const Matrix<MT2,SO>& rhs )
   -> SymmetricMatrix&
{
   using blaze::resize;

   using Tmp = AddTrait_t< MT, ResultType_t<MT2> >;

   if( !IsSquare_v<MT2> && !isSquare( *rhs ) ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to symmetric matrix" );
   }

   Tmp tmp( (*this) + *rhs );

   if( !IsSymmetric_v<Tmp> && !isSymmetric( tmp ) ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to symmetric matrix" );
   }

   resize( matrix_, tmp.rows(), tmp.columns() );
   reset();
   assign( tmp );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
   BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );

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


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Addition assignment operator for the addition of a matrix with opposite storage order
//        (\f$ A+=B \f$).
//
// \param rhs The right-hand side matrix to be added.
// \return Reference to the matrix.
// \exception std::invalid_argument Invalid assignment to symmetric matrix.
//
// In case the current sizes of the two matrices don't match, a \a std::invalid_argument exception
// is thrown. Also note that the result of the addition operation must be a symmetric matrix, i.e.
// the given matrix must be a symmetric matrix. In case the result is not a symmetric matrix, a
// \a std::invalid_argument exception is thrown.
*/
template< typename MT     // Type of the adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side matrix
inline auto SymmetricMatrix<MT,SO,false,false>::operator+=( const Matrix<MT2,!SO>& rhs )
   -> SymmetricMatrix&
{
   return this->operator+=( trans( *rhs ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Subtraction assignment operator for the subtraction of a matrix (\f$ A-=B \f$).
//
// \param rhs The right-hand side matrix to be subtracted.
// \return Reference to the matrix.
// \exception std::invalid_argument Invalid assignment to symmetric matrix.
//
// In case the current sizes of the two matrices don't match, a \a std::invalid_argument exception
// is thrown. Also note that the result of the subtraction operation must be a symmetric matrix,
// i.e. the given matrix must be a symmetric matrix. In case the result is not a symmetric matrix,
// a \a std::invalid_argument exception is thrown.
*/
template< typename MT     // Type of the adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side matrix
inline auto SymmetricMatrix<MT,SO,false,false>::operator-=( const Matrix<MT2,SO>& rhs )
   -> SymmetricMatrix&
{
   using blaze::resize;

   using Tmp = SubTrait_t< MT, ResultType_t<MT2> >;

   if( !IsSquare_v<MT2> && !isSquare( *rhs ) ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to symmetric matrix" );
   }

   Tmp tmp( (*this) - *rhs );

   if( !IsSymmetric_v<Tmp> && !isSymmetric( tmp ) ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to symmetric matrix" );
   }

   resize( matrix_, tmp.rows(), tmp.columns() );
   reset();
   assign( tmp );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
   BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );

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


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Subtraction assignment operator for the subtraction of a matrix with opposite storage
//        order (\f$ A-=B \f$).
//
// \param rhs The right-hand side matrix to be subtracted.
// \return Reference to the matrix.
// \exception std::invalid_argument Invalid assignment to symmetric matrix.
//
// In case the current sizes of the two matrices don't match, a \a std::invalid_argument exception
// is thrown. Also note that the result of the subtraction operation must be a symmetric matrix,
// i.e. the given matrix must be a symmetric matrix. In case the result is not a symmetric matrix,
// a \a std::invalid_argument exception is thrown.
*/
template< typename MT     // Type of the adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side matrix
inline auto SymmetricMatrix<MT,SO,false,false>::operator-=( const Matrix<MT2,!SO>& rhs )
   -> SymmetricMatrix&
{
   return this->operator-=( trans( *rhs ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Schur product assignment operator for the multiplication of a matrix (\f$ A\circ=B \f$).
//
// \param rhs The right-hand side matrix for the Schur product.
// \return Reference to the matrix.
// \exception std::invalid_argument Invalid assignment to symmetric matrix.
//
// In case the current sizes of the two matrices don't match, a \a std::invalid_argument exception
// is thrown. Also note that the result of the Schur product operation must be a symmetric matrix,
// i.e. the given matrix must be a symmetric matrix. In case the result is not a symmetric matrix,
// a \a std::invalid_argument exception is thrown.
*/
template< typename MT     // Type of the adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side matrix
inline auto SymmetricMatrix<MT,SO,false,false>::operator%=( const Matrix<MT2,SO>& rhs )
   -> SymmetricMatrix&
{
   using blaze::resize;

   using Tmp = SchurTrait_t< MT, ResultType_t<MT2> >;

   if( !IsSquare_v<MT2> && !isSquare( *rhs ) ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to symmetric matrix" );
   }

   Tmp tmp( (*this) % *rhs );

   if( !IsSymmetric_v<Tmp> && !isSymmetric( tmp ) ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to symmetric matrix" );
   }

   resize( matrix_, tmp.rows(), tmp.columns() );
   reset();
   assign( tmp );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );
   BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );

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


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Schur product assignment operator for the multiplication of a matrix with opposite
//        storage order (\f$ A\circ=B \f$).
//
// \param rhs The right-hand side matrix for the Schur product.
// \return Reference to the matrix.
// \exception std::invalid_argument Invalid assignment to symmetric matrix.
//
// In case the current sizes of the two matrices don't match, a \a std::invalid_argument exception
// is thrown. Also note that the result of the Schur product operation must be a symmetric matrix,
// i.e. the given matrix must be a symmetric matrix. In case the result is not a symmetric matrix,
// a \a std::invalid_argument exception is thrown.
*/
template< typename MT     // Type of the adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side matrix
inline auto SymmetricMatrix<MT,SO,false,false>::operator%=( const Matrix<MT2,!SO>& rhs )
   -> SymmetricMatrix&
{
   return this->operator%=( trans( *rhs ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Multiplication assignment operator for the multiplication between a matrix and
//        a scalar value (\f$ A*=s \f$).
//
// \param rhs The right-hand side scalar value for the multiplication.
// \return Reference to the matrix.
*/
template< typename MT    // Type of the adapted sparse matrix
        , bool SO >      // Storage order of the adapted sparse matrix
template< typename ST >  // Data type of the right-hand side scalar
inline auto SymmetricMatrix<MT,SO,false,false>::operator*=( ST rhs )
   -> EnableIf_t< IsScalar_v<ST>, SymmetricMatrix& >
{
   for( size_t i=0UL; i<rows(); ++i ) {
      const auto last( matrix_.upperBound(i,i) );
      for( auto element=matrix_.begin(i); element!=last; ++element )
         *element->value() *= rhs;
   }

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


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Division assignment operator for the division of a matrix by a scalar value
//        (\f$ A/=s \f$).
//
// \param rhs The right-hand side scalar value for the division.
// \return Reference to the matrix.
*/
template< typename MT    // Type of the adapted sparse matrix
        , bool SO >      // Storage order of the adapted sparse matrix
template< typename ST >  // Data type of the right-hand side scalar
inline auto SymmetricMatrix<MT,SO,false,false>::operator/=( ST rhs )
   -> EnableIf_t< IsScalar_v<ST>, SymmetricMatrix& >
{
   BLAZE_USER_ASSERT( !isZero( rhs ), "Division by zero detected" );

   for( size_t i=0UL; i<rows(); ++i ) {
      const auto last( matrix_.upperBound(i,i) );
      for( auto element=matrix_.begin(i); element!=last; ++element )
         *element->value() /= rhs;
   }

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




//=================================================================================================
//
//  UTILITY FUNCTIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns the current number of rows of the matrix.
//
// \return The number of rows of the matrix.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline size_t SymmetricMatrix<MT,SO,false,false>::rows() const noexcept
{
   return matrix_.rows();
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns the current number of columns of the matrix.
//
// \return The number of columns of the matrix.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline size_t SymmetricMatrix<MT,SO,false,false>::columns() const noexcept
{
   return matrix_.columns();
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns the maximum capacity of the matrix.
//
// \return The capacity of the matrix.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline size_t SymmetricMatrix<MT,SO,false,false>::capacity() const noexcept
{
   return matrix_.capacity();
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns the current capacity of the specified row/column.
//
// \param i The index of the row/column.
// \return The current capacity of row/column \a i.
//
// This function returns the current capacity of the specified row/column. In case the symmetric
// matrix adapts a \a rowMajor sparse matrix the function returns the capacity of row \a i, in
// case it adapts a \a columnMajor sparse matrix the function returns the capacity of column \a i.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline size_t SymmetricMatrix<MT,SO,false,false>::capacity( size_t i ) const noexcept
{
   return matrix_.capacity(i);
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns the total number of non-zero elements in the matrix
//
// \return The number of non-zero elements in the symmetric matrix.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline size_t SymmetricMatrix<MT,SO,false,false>::nonZeros() const
{
   return matrix_.nonZeros();
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns the number of non-zero elements in the specified row/column.
//
// \param i The index of the row/column.
// \return The number of non-zero elements of row/column \a i.
//
// This function returns the current number of non-zero elements in the specified row/column. In
// case the symmetric matrix adapts a \a rowMajor sparse matrix the function returns the number of
// non-zero elements in row \a i, in case it adapts a to \a columnMajor sparse matrix the function
// returns the number of non-zero elements in column \a i.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline size_t SymmetricMatrix<MT,SO,false,false>::nonZeros( size_t i ) const
{
   return matrix_.nonZeros(i);
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Reset to the default initial values.
//
// \return void
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline void SymmetricMatrix<MT,SO,false,false>::reset()
{
   matrix_.reset();
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Reset the specified row \b and column to the default initial values.
//
// \param i The index of the row/column.
// \return void
// \exception std::invalid_argument Invalid row/column access index.
//
// This function resets the values in the specified row \b and column to their default value.
// The following example demonstrates this by means of a \f$ 5 \times 5 \f$ symmetric matrix:

   \code
   using blaze::CompressedMatrix;
   using blaze::StaticVector;
   using blaze::SymmetricMatrix;

   SymmetricMatrix< CompressedMatrix< StaticVector<int,1UL> > > A;

   // Initializing the symmetric matrix A to
   //
   //      ( (    ) (  2 ) (  5 ) ( -4 ) (    ) )
   //      ( (  2 ) (  1 ) ( -3 ) (  7 ) (    ) )
   //  A = ( (  5 ) ( -3 ) (  8 ) ( -1 ) ( -2 ) )
   //      ( ( -4 ) (  7 ) ( -1 ) (    ) ( -6 ) )
   //      ( (    ) (  0 ) ( -2 ) ( -6 ) (  1 ) )
   // ...

   // Resetting the 1st row/column results in the matrix
   //
   //      ( (    ) (    ) (  5 ) ( -4 ) (    ) )
   //      ( (    ) (    ) (    ) (    ) (    ) )
   //  A = ( (  5 ) (    ) (  8 ) ( -1 ) ( -2 ) )
   //      ( ( -4 ) (    ) ( -1 ) (    ) ( -6 ) )
   //      ( (    ) (    ) ( -2 ) ( -6 ) (  1 ) )
   //
   A.reset( 1UL );
   \endcode

// Note that the reset() function has no impact on the capacity of the matrix or row/column.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline void SymmetricMatrix<MT,SO,false,false>::reset( size_t i )
{
   using blaze::erase;

   for( auto it=matrix_.begin(i); it!=matrix_.end(i); ++it )
   {
      const size_t j( it->index() );

      if( i == j )
         continue;

      if( SO ) {
         const Iterator_t<MatrixType> pos( matrix_.find( i, j ) );
         BLAZE_INTERNAL_ASSERT( pos != matrix_.end( j ), "Missing element detected" );
         erase( matrix_, j, pos );
      }
      else {
         const Iterator_t<MatrixType> pos( matrix_.find( j, i ) );
         BLAZE_INTERNAL_ASSERT( pos != matrix_.end( j ), "Missing element detected" );
         erase( matrix_, j, pos );
      }
   }

   matrix_.reset( i );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Clearing the symmetric matrix.
//
// \return void
//
// This function clears the symmetric matrix and returns it to its default state.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline void SymmetricMatrix<MT,SO,false,false>::clear()
{
   using blaze::clear;

   clear( matrix_ );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Changing the size of the symmetric matrix.
//
// \param n The new number of rows and columns of the matrix.
// \param preserve \a true if the old values of the matrix should be preserved, \a false if not.
// \return void
//
// This function resizes the matrix using the given size to \f$ m \times n \f$. During this
// operation, new dynamic memory may be allocated in case the capacity of the matrix is too
// small. Note that this function may invalidate all existing views (submatrices, rows, columns,
// ...) on the matrix if it is used to shrink the matrix. Additionally, the resize operation
// potentially changes all matrix elements. In order to preserve the old matrix values, the
// \a preserve flag can be set to \a true.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
void SymmetricMatrix<MT,SO,false,false>::resize( size_t n, bool preserve )
{
   BLAZE_CONSTRAINT_MUST_BE_RESIZABLE_TYPE( MT );

   MAYBE_UNUSED( preserve );

   BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square symmetric matrix detected" );

   matrix_.resize( n, n, true );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Setting the minimum capacity of the symmetric matrix.
//
// \param nonzeros The new minimum capacity of the symmetric matrix.
// \return void
//
// This function increases the capacity of the symmetric matrix to at least \a nonzeros elements.
// The current values of the matrix elements and the individual capacities of the matrix rows
// are preserved.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline void SymmetricMatrix<MT,SO,false,false>::reserve( size_t nonzeros )
{
   matrix_.reserve( nonzeros );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Setting the minimum capacity of a specific row/column of the symmetric matrix.
//
// \param i The row/column index \f$[0..N-1]\f$.
// \param nonzeros The new minimum capacity of the specified row/column.
// \return void
//
// This function increases the capacity of row/column \a i of the symmetric matrix to at least
// \a nonzeros elements. The current values of the symmetric matrix and all other individual
// row/column capacities are preserved. In case the storage order is set to \a rowMajor, the
// function reserves capacity for row \a i. In case the storage order is set to \a columnMajor,
// the function reserves capacity for column \a i. The index has to be in the range \f$[0..N-1]\f$.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline void SymmetricMatrix<MT,SO,false,false>::reserve( size_t i, size_t nonzeros )
{
   matrix_.reserve( i, nonzeros );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Removing all excessive capacity from all rows/columns.
//
// \return void
//
// The trim() function can be used to reverse the effect of all row/column-specific reserve()
// calls. The function removes all excessive capacity from all rows (in case of a rowMajor
// matrix) or columns (in case of a columnMajor matrix). Note that this function does not
// remove the overall capacity but only reduces the capacity per row/column.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline void SymmetricMatrix<MT,SO,false,false>::trim()
{
   matrix_.trim();
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Removing all excessive capacity of a specific row/column of the symmetric matrix.
//
// \param i The index of the row/column to be trimmed \f$[0..N-1]\f$.
// \return void
//
// This function can be used to reverse the effect of a row/column-specific reserve() call.
// It removes all excessive capacity from the specified row (in case of a rowMajor matrix)
// or column (in case of a columnMajor matrix). The excessive capacity is assigned to the
// subsequent row/column.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline void SymmetricMatrix<MT,SO,false,false>::trim( size_t i )
{
   matrix_.trim( i );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Requesting the removal of unused capacity.
//
// \return void
//
// This function minimizes the capacity of the matrix by removing unused capacity. Please note
// that in case a reallocation occurs, all iterators (including end() iterators), all pointers
// and references to elements of this matrix are invalidated.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline void SymmetricMatrix<MT,SO,false,false>::shrinkToFit()
{
   matrix_.shrinkToFit();
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Swapping the contents of two matrices.
//
// \param m The matrix to be swapped.
// \return void
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline void SymmetricMatrix<MT,SO,false,false>::swap( SymmetricMatrix& m ) noexcept
{
   using std::swap;

   swap( matrix_, m.matrix_ );
}
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  INSERTION FUNCTIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Setting elements of the symmetric matrix.
//
// \param i The row index of the new element. The index has to be in the range \f$[0..N-1]\f$.
// \param j The column index of the new element. The index has to be in the range \f$[0..N-1]\f$.
// \param value The value of the element to be set.
// \return Iterator to the set element.
//
// This function sets the value of both the elements \f$ a_{ij} \f$ and \f$ a_{ji} \f$ of the
// symmetric matrix and returns an iterator to the successfully set element \f$ a_{ij} \f$. In
// case the symmetric matrix already contains the two elements with index \a i and \a j their
// values are modified, else two new elements with the given \a value are inserted.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::Iterator
   SymmetricMatrix<MT,SO,false,false>::set( size_t i, size_t j, const ElementType& value )
{
   SharedValue<ET> shared( value );

   if( i != j )
      matrix_.set( j, i, shared );

   return Iterator( matrix_.set( i, j, shared ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Inserting elements into the symmetric matrix.
//
// \param i The row index of the new element. The index has to be in the range \f$[0..N-1]\f$.
// \param j The column index of the new element. The index has to be in the range \f$[0..N-1]\f$.
// \param value The value of the element to be inserted.
// \return Iterator to the newly inserted element.
// \exception std::invalid_argument Invalid sparse matrix access index.
//
// This function inserts both the elements \f$ a_{ij} \f$ and \f$ a_{ji} \f$ into the symmetric
// matrix and returns an iterator to the successfully inserted element \f$ a_{ij} \f$. However,
// duplicate elements are not allowed. In case the symmetric matrix an element with row index
// \a i and column index \a j, a \a std::invalid_argument exception is thrown.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::Iterator
   SymmetricMatrix<MT,SO,false,false>::insert( size_t i, size_t j, const ElementType& value )
{
   SharedValue<ET> shared( value );

   if( i != j )
      matrix_.insert( j, i, shared );

   return Iterator( matrix_.insert( i, j, shared ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Appending elements to the specified row/column of the symmetric matrix.
//
// \param i The row index of the new element. The index has to be in the range \f$[0..N-1]\f$.
// \param j The column index of the new element. The index has to be in the range \f$[0..N-1]\f$.
// \param value The value of the element to be appended.
// \param check \a true if the new value should be checked for default values, \a false if not.
// \return void
//
// This function both appends the element \f$ a_{ij} \f$ to the specified row/column and inserts
// its according counterpart \f$ a_{ji} \f$ into the symmetric matrix. Since element \f$ a_{ij} \f$
// is appended without any additional memory allocation, it is strictly necessary to keep the
// following preconditions in mind:
//
//  - the index of the new element must be strictly larger than the largest index of non-zero
//    elements in the specified row/column of the sparse matrix
//  - the current number of non-zero elements in the matrix must be smaller than the capacity
//    of the matrix
//
// Ignoring these preconditions might result in undefined behavior! The optional \a check
// parameter specifies whether the new value should be tested for a default value. If the new
// value is a default value (for instance 0 in case of an integral element type) the value is
// not appended. Per default the values are not tested.
//
// Although in addition to element \f$ a_{ij} \f$ a second element \f$ a_{ji} \f$ is inserted into
// the matrix, this function still provides the most efficient way to fill a symmetric matrix with
// values. However, in order to achieve maximum efficiency, the matrix has to be specifically
// prepared with reserve() calls:

   \code
   using blaze::CompressedMatrix;
   using blaze::SymmetricMatrix;
   using blaze::rowMajor;

   // Setup of the symmetric matrix
   //
   //       ( 0 1 3 )
   //   A = ( 1 2 0 )
   //       ( 3 0 0 )

   SymmetricMatrix< CompressedMatrix<double,rowMajor> > A( 3 );

   A.reserve( 5 );         // Reserving enough capacity for 5 non-zero elements
   A.reserve( 0, 2 );      // Reserving two non-zero elements in the first row
   A.reserve( 1, 2 );      // Reserving two non-zero elements in the second row
   A.reserve( 2, 1 );      // Reserving a single non-zero element in the third row
   A.append( 0, 1, 1.0 );  // Appending the value 1 at position (0,1) and (1,0)
   A.append( 1, 1, 2.0 );  // Appending the value 2 at position (1,1)
   A.append( 2, 0, 3.0 );  // Appending the value 3 at position (2,0) and (0,2)
   \endcode

// \note Although append() does not allocate new memory, it still invalidates all iterators
// returned by the end() functions!
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline void SymmetricMatrix<MT,SO,false,false>::append( size_t i, size_t j, const ElementType& value, bool check )
{
   SharedValue<ET> shared( value );

   matrix_.append( i, j, shared, check );
   if( i != j && ( !check || !isDefault<strict>( value ) ) )
      matrix_.insert( j, i, shared );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Finalizing the element insertion of a row/column.
//
// \param i The index of the row/column to be finalized \f$[0..N-1]\f$.
// \return void
//
// This function is part of the low-level interface to efficiently fill a matrix with elements.
// After completion of row/column \a i via the append() function, this function can be called to
// finalize row/column \a i and prepare the next row/column for insertion process via append().
//
// \note Although finalize() does not allocate new memory, it still invalidates all iterators
// returned by the end() functions!
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline void SymmetricMatrix<MT,SO,false,false>::finalize( size_t i )
{
   matrix_.trim( i );
}
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  ERASE FUNCTIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Erasing elements from the symmetric matrix.
//
// \param i The row index of the element to be erased. The index has to be in the range \f$[0..N-1]\f$.
// \param j The column index of the element to be erased. The index has to be in the range \f$[0..N-1]\f$.
// \return void
//
// This function erases both elements \f$ a_{ij} \f$ and \f$ a_{ji} \f$ from the symmetric matrix.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline void SymmetricMatrix<MT,SO,false,false>::erase( size_t i, size_t j )
{
   using blaze::erase;

   erase( matrix_, i, j );
   if( i != j )
      erase( matrix_, j, i );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Erasing elements from the symmetric matrix.
//
// \param i The row/column index of the element to be erased. The index has to be in the range \f$[0..N-1]\f$.
// \param pos Iterator to the element to be erased.
// \return Iterator to the element after the erased element.
//
// This function erases both the specified element and its according symmetric counterpart from
// the symmetric matrix. In case the storage order is set to \a rowMajor the given index \a i
// refers to a row, in case the storage flag is set to \a columnMajor \a i refers to a column.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::Iterator
   SymmetricMatrix<MT,SO,false,false>::erase( size_t i, Iterator pos )
{
   using blaze::erase;

   if( pos == end( i ) )
      return pos;

   const size_t j( pos->index() );

   if( i == j )
      return Iterator( erase( matrix_, i, pos.base() ) );

   if( SO ) {
      BLAZE_INTERNAL_ASSERT( matrix_.find( i, j ) != matrix_.end( j ), "Missing element detected" );
      erase( matrix_, j, matrix_.find( i, j ) );
      return Iterator( erase( matrix_, i, pos.base() ) );
   }
   else {
      BLAZE_INTERNAL_ASSERT( matrix_.find( j, i ) != matrix_.end( j ), "Missing element detected" );
      erase( matrix_, j, matrix_.find( j, i ) );
      return Iterator( erase( matrix_, i, pos.base() ) );
   }
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Erasing a range of elements from the symmetric matrix.
//
// \param i The row/column index of the element to be erased. The index has to be in the range \f$[0..N-1]\f$.
// \param first Iterator to first element to be erased.
// \param last Iterator just past the last element to be erased.
// \return Iterator to the element after the erased element.
//
// This function erases both the range of elements specified by the iterator pair \a first and
// \a last and their according symmetric counterparts from the symmetric matrix. In case the
// storage order is set to \a rowMajor the given index \a i refers to a row, in case the storage
// flag is set to \a columnMajor \a i refers to a column.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::Iterator
   SymmetricMatrix<MT,SO,false,false>::erase( size_t i, Iterator first, Iterator last )
{
   using blaze::erase;

   for( auto it=first; it!=last; ++it )
   {
      const size_t j( it->index() );

      if( i == j )
         continue;

      if( SO ) {
         BLAZE_INTERNAL_ASSERT( matrix_.find( i, j ) != matrix_.end( j ), "Missing element detected" );
         erase( matrix_, i, j );
      }
      else {
         BLAZE_INTERNAL_ASSERT( matrix_.find( j, i ) != matrix_.end( j ), "Missing element detected" );
         erase( matrix_, j, i );
      }
   }

   return Iterator( erase( matrix_, i, first.base(), last.base() ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Erasing specific elements from the symmetric matrix.
//
// \param predicate The unary predicate for the element selection.
// \return void.
//
// This function erases specific elements from the symmetric matrix. The elements are selected
// by the given unary predicate \a predicate, which is expected to accept a single argument of
// the type of the elements and to be pure.
//
// \note The predicate is required to be pure, i.e. to produce deterministic results for elements
// with the same value. The attempt to use an impure predicate leads to undefined behavior!
*/
template< typename MT      // Type of the adapted sparse matrix
        , bool SO >        // Storage order of the adapted sparse matrix
template< typename Pred >  // Type of the unary predicate
inline void SymmetricMatrix<MT,SO,false,false>::erase( Pred predicate )
{
   using blaze::erase;

   erase( matrix_, [predicate=predicate]( const SharedValue<ET>& value ) {
                      return predicate( *value );
                   } );

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


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Erasing specific elements from a range of the symmetric matrix.
//
// \param i The row/column index of the elements to be erased. The index has to be in the range \f$[0..M-1]\f$.
// \param first Iterator to first element of the range.
// \param last Iterator just past the last element of the range.
// \param predicate The unary predicate for the element selection.
// \return void
//
// This function erases specific elements from a range of elements of the symmetric matrix. The
// elements are selected by the given unary predicate \a predicate, which is expected to accept
// a single argument of the type of the elements and to be pure. In case the storage order is
// set to \a rowMajor the function erases a range of elements from row \a i, in case the storage
// flag is set to \a columnMajor the function erases a range of elements from column \a i.
//
// \note The predicate is required to be pure, i.e. to produce deterministic results for elements
// with the same value. The attempt to use an impure predicate leads to undefined behavior!
*/
template< typename MT      // Type of the adapted sparse matrix
        , bool SO >        // Storage order of the adapted sparse matrix
template< typename Pred >  // Type of the unary predicate
inline void
   SymmetricMatrix<MT,SO,false,false>::erase( size_t i, Iterator first, Iterator last, Pred predicate )
{
   using blaze::erase;

   for( auto it=first; it!=last; ++it ) {
      const size_t j( it->index() );
      if( i != j && predicate( it->value() ) ) {
         if( SO )
            erase( matrix_, i, j );
         else
            erase( matrix_, j, i );
      }
   }

   erase( matrix_, i, first.base(), last.base(),
                   [predicate=predicate]( const SharedValue<ET>& value ) {
                      return predicate( *value );
                   } );

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




//=================================================================================================
//
//  LOOKUP FUNCTIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Searches for a specific matrix element.
//
// \param i The row index of the search element. The index has to be in the range \f$[0..N-1]\f$.
// \param j The column index of the search element. The index has to be in the range \f$[0..N-1]\f$.
// \return Iterator to the element in case the index is found, end() iterator otherwise.
//
// This function can be used to check whether a specific element is contained in the symmetric
// matrix. It specifically searches for the element with row index \a i and column index \a j.
// In case the element is found, the function returns an row/column iterator to the element.
// Otherwise an iterator just past the last non-zero element of row \a i or column \a j (the
// end() iterator) is returned. Note that the returned symmetric matrix iterator is subject
// to invalidation due to inserting operations via the function call operator, the set()
// function or the insert() function!
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::Iterator
   SymmetricMatrix<MT,SO,false,false>::find( size_t i, size_t j )
{
   return Iterator( matrix_.find( i, j ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Searches for a specific matrix element.
//
// \param i The row index of the search element. The index has to be in the range \f$[0..N-1]\f$.
// \param j The column index of the search element. The index has to be in the range \f$[0..N-1]\f$.
// \return Iterator to the element in case the index is found, end() iterator otherwise.
//
// This function can be used to check whether a specific element is contained in the symmetric
// matrix. It specifically searches for the element with row index \a i and column index \a j.
// In case the element is found, the function returns an row/column iterator to the element.
// Otherwise an iterator just past the last non-zero element of row \a i or column \a j (the
// end() iterator) is returned. Note that the returned symmetric matrix iterator is subject
// to invalidation due to inserting operations via the function call operator, the set()
// function or the insert() function!
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::ConstIterator
   SymmetricMatrix<MT,SO,false,false>::find( size_t i, size_t j ) const
{
   return ConstIterator( matrix_.find( i, j ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns an iterator to the first index not less then the given index.
//
// \param i The row index of the search element. The index has to be in the range \f$[0..N-1]\f$.
// \param j The column index of the search element. The index has to be in the range \f$[0..N-1]\f$.
// \return Iterator to the first index not less then the given index, end() iterator otherwise.
//
// In case of a row-major matrix, this function returns a row iterator to the first element with
// an index not less then the given column index. In case of a column-major matrix, the function
// returns a column iterator to the first element with an index not less then the given row
// index. In combination with the upperBound() function this function can be used to create a
// pair of iterators specifying a range of indices. Note that the returned symmetric matrix
// iterator is subject to invalidation due to inserting operations via the function call operator,
// the set() function or the insert() function!
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::Iterator
   SymmetricMatrix<MT,SO,false,false>::lowerBound( size_t i, size_t j )
{
   return Iterator( matrix_.lowerBound( i, j ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns an iterator to the first index not less then the given index.
//
// \param i The row index of the search element. The index has to be in the range \f$[0..N-1]\f$.
// \param j The column index of the search element. The index has to be in the range \f$[0..N-1]\f$.
// \return Iterator to the first index not less then the given index, end() iterator otherwise.
//
// In case of a row-major matrix, this function returns a row iterator to the first element with
// an index not less then the given column index. In case of a column-major matrix, the function
// returns a column iterator to the first element with an index not less then the given row
// index. In combination with the upperBound() function this function can be used to create a
// pair of iterators specifying a range of indices. Note that the returned symmetric matrix
// iterator is subject to invalidation due to inserting operations via the function call operator,
// the set() function or the insert() function!
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::ConstIterator
   SymmetricMatrix<MT,SO,false,false>::lowerBound( size_t i, size_t j ) const
{
   return ConstIterator( matrix_.lowerBound( i, j ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns an iterator to the first index greater then the given index.
//
// \param i The row index of the search element. The index has to be in the range \f$[0..N-1]\f$.
// \param j The column index of the search element. The index has to be in the range \f$[0..N-1]\f$.
// \return Iterator to the first index greater then the given index, end() iterator otherwise.
//
// In case of a row-major matrix, this function returns a row iterator to the first element with
// an index greater then the given column index. In case of a column-major matrix, the function
// returns a column iterator to the first element with an index greater then the given row
// index. In combination with the lowerBound() function this function can be used to create a
// pair of iterators specifying a range of indices. Note that the returned symmetric matrix
// iterator is subject to invalidation due to inserting operations via the function call operator,
// the set() function or the insert() function!
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::Iterator
   SymmetricMatrix<MT,SO,false,false>::upperBound( size_t i, size_t j )
{
   return Iterator( matrix_.upperBound( i, j ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns an iterator to the first index greater then the given index.
//
// \param i The row index of the search element. The index has to be in the range \f$[0..N-1]\f$.
// \param j The column index of the search element. The index has to be in the range \f$[0..N-1]\f$.
// \return Iterator to the first index greater then the given index, end() iterator otherwise.
//
// In case of a row-major matrix, this function returns a row iterator to the first element with
// an index greater then the given column index. In case of a column-major matrix, the function
// returns a column iterator to the first element with an index greater then the given row
// index. In combination with the lowerBound() function this function can be used to create a
// pair of iterators specifying a range of indices. Note that the returned symmetric matrix
// iterator is subject to invalidation due to inserting operations via the function call operator,
// the set() function or the insert() function!
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline typename SymmetricMatrix<MT,SO,false,false>::ConstIterator
   SymmetricMatrix<MT,SO,false,false>::upperBound( size_t i, size_t j ) const
{
   return ConstIterator( matrix_.upperBound( i, j ) );
}
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  NUMERIC FUNCTIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief In-place transpose of the symmetric matrix.
//
// \return Reference to the transposed matrix.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline SymmetricMatrix<MT,SO,false,false>& SymmetricMatrix<MT,SO,false,false>::transpose()
{
   return *this;
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief In-place conjugate transpose of the symmetric matrix.
//
// \return Reference to the transposed matrix.
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline SymmetricMatrix<MT,SO,false,false>& SymmetricMatrix<MT,SO,false,false>::ctranspose()
{
   for( size_t i=0UL; i<rows(); ++i ) {
      const auto last( matrix_.upperBound(i,i) );
      for( auto element=matrix_.begin(i); element!=last; ++element )
         conjugate( *element->value() );
   }

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


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Scaling of the matrix by the scalar value \a scalar (\f$ A=B*s \f$).
//
// \param scalar The scalar value for the matrix scaling.
// \return Reference to the matrix.
//
// This function scales the matrix by applying the given scalar value \a scalar to each element
// of the matrix. For built-in and \c complex data types it has the same effect as using the
// multiplication assignment operator:

   \code
   blaze::SymmetricMatrix< blaze::CompressedMatrix< blaze::StaticVector<int,1UL> > > A;
   // ... Resizing and initialization
   A *= 4;        // Scaling of the matrix
   A.scale( 4 );  // Same effect as above
   \endcode
*/
template< typename MT       // Type of the adapted sparse matrix
        , bool SO >         // Storage order of the adapted sparse matrix
template< typename Other >  // Data type of the scalar value
inline SymmetricMatrix<MT,SO,false,false>&
   SymmetricMatrix<MT,SO,false,false>::scale( const Other& scalar )
{
   for( size_t i=0UL; i<rows(); ++i ) {
      const auto last( matrix_.upperBound(i,i) );
      for( auto element=matrix_.begin(i); element!=last; ++element )
         ( *element->value() ).scale( scalar );
   }

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




//=================================================================================================
//
//  DEBUGGING FUNCTIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns whether the invariants of the symmetric matrix are intact.
//
// \return \a true in case the symmetric matrix's invariants are intact, \a false otherwise.
//
// This function checks whether the invariants of the symmetric matrix are intact, i.e. if its
// state is valid. In case the invariants are intact, the function returns \a true, else it
// will return \a false.
*/
template< typename MT  // Type of the adapted dense matrix
        , bool SO >    // Storage order of the adapted dense matrix
inline bool SymmetricMatrix<MT,SO,false,false>::isIntact() const noexcept
{
   using blaze::isIntact;

   return ( isIntact( matrix_ ) && isSymmetric( matrix_ ) );
}
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  EXPRESSION TEMPLATE EVALUATION FUNCTIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns whether the matrix 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 matrix, \a false if not.
//
// This function returns whether the given address can alias with the matrix. 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 adapted sparse matrix
        , bool SO >         // Storage order of the adapted sparse matrix
template< typename Other >  // Data type of the foreign expression
inline bool SymmetricMatrix<MT,SO,false,false>::canAlias( const Other* alias ) const noexcept
{
   return matrix_.canAlias( alias );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns whether the matrix 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 matrix, \a false if not.
//
// This function returns whether the given address is aliased with the matrix. 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 adapted sparse matrix
        , bool SO >         // Storage order of the adapted sparse matrix
template< typename Other >  // Data type of the foreign expression
inline bool SymmetricMatrix<MT,SO,false,false>::isAliased( const Other* alias ) const noexcept
{
   return matrix_.isAliased( alias );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Returns whether the matrix can be used in SMP assignments.
//
// \return \a true in case the matrix can be used in SMP assignments, \a false if not.
//
// This function returns whether the matrix 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 number of
// rows and/or columns of the matrix).
*/
template< typename MT  // Type of the adapted sparse matrix
        , bool SO >    // Storage order of the adapted sparse matrix
inline bool SymmetricMatrix<MT,SO,false,false>::canSMPAssign() const noexcept
{
   return matrix_.canSMPAssign();
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Optimized implementation of the assignment of a temporary dense matrix.
//
// \param rhs The right-hand side dense matrix 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 adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side dense matrix
void SymmetricMatrix<MT,SO,false,false>::assign( DenseMatrix<MT2,SO>& rhs )
{
   BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT2 );

   BLAZE_INTERNAL_ASSERT( rows()    == (*rhs).rows()   , "Invalid number of rows"    );
   BLAZE_INTERNAL_ASSERT( columns() == (*rhs).columns(), "Invalid number of columns" );

   std::vector<size_t> nonzeros( rows(), 0UL );
   size_t sum( 0UL );

   for( size_t i=0UL; i<rows(); ++i ) {
      nonzeros[i] = (*rhs).nonZeros(i);
      sum += nonzeros[i];
   }

   matrix_.reserve( sum );
   for( size_t i=0UL; i<rows(); ++i ) {
      matrix_.reserve( i, nonzeros[i] );
   }

   for( size_t i=0UL; i<rows(); ++i ) {
      for( size_t j=i; j<columns(); ++j ) {
         if( !isDefault( (*rhs)(i,j) ) ) {
            SharedValue<ET> shared;
            *shared = std::move( (*rhs)(i,j) );
            matrix_.append( i, j, shared, false );
            if( i != j )
               matrix_.append( j, i, shared, false );
         }
      }
   }
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Default implementation of the assignment of a dense matrix.
//
// \param rhs The right-hand side dense matrix 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 adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side dense matrix
void SymmetricMatrix<MT,SO,false,false>::assign( const DenseMatrix<MT2,SO>& rhs )
{
   BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT2 );

   BLAZE_INTERNAL_ASSERT( rows()    == (*rhs).rows()   , "Invalid number of rows"    );
   BLAZE_INTERNAL_ASSERT( columns() == (*rhs).columns(), "Invalid number of columns" );

   std::vector<size_t> nonzeros( rows(), 0UL );
   size_t sum( 0UL );

   for( size_t i=0UL; i<rows(); ++i ) {
      nonzeros[i] = (*rhs).nonZeros(i);
      sum += nonzeros[i];
   }

   matrix_.reserve( sum );
   for( size_t i=0UL; i<rows(); ++i ) {
      matrix_.reserve( i, nonzeros[i] );
   }

   for( size_t i=0UL; i<rows(); ++i ) {
      for( size_t j=i; j<columns(); ++j ) {
         if( !isDefault( (*rhs)(i,j) ) ) {
            const SharedValue<ET> shared( (*rhs)(i,j) );
            matrix_.append( i, j, shared, false );
            if( i != j )
               matrix_.append( j, i, shared, false );
         }
      }
   }
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Optimized implementation of the assignment of a temporary sparse matrix.
//
// \param rhs The right-hand side sparse matrix 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 adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side sparse matrix
void SymmetricMatrix<MT,SO,false,false>::assign( SparseMatrix<MT2,SO>& rhs )
{
   BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT2 );

   BLAZE_INTERNAL_ASSERT( rows()    == (*rhs).rows()   , "Invalid number of rows"    );
   BLAZE_INTERNAL_ASSERT( columns() == (*rhs).columns(), "Invalid number of columns" );

   std::vector<size_t> nonzeros( rows(), 0UL );
   size_t sum( 0UL );

   for( size_t i=0UL; i<rows(); ++i ) {
      nonzeros[i] = (*rhs).nonZeros(i);
      sum += nonzeros[i];
   }

   matrix_.reserve( sum );
   for( size_t i=0UL; i<rows(); ++i ) {
      matrix_.reserve( i, nonzeros[i] );
   }

   for( size_t i=0UL; i<rows(); ++i ) {
      for( auto it=(*rhs).lowerBound(i,i); it!=(*rhs).end(i); ++it ) {
         if( !isDefault( it->value() ) ) {
            SharedValue<ET> shared;
            *shared = std::move( it->value() );
            matrix_.append( i, it->index(), shared, false );
            if( i != it->index() )
               matrix_.append( it->index(), i, shared, false );
         }
      }
   }
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Default implementation of the assignment of a sparse matrix.
//
// \param rhs The right-hand side sparse matrix 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 adapted sparse matrix
        , bool SO >       // Storage order of the adapted sparse matrix
template< typename MT2 >  // Type of the right-hand side sparse matrix
void SymmetricMatrix<MT,SO,false,false>::assign( const SparseMatrix<MT2,SO>& rhs )
{
   BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT2 );

   BLAZE_INTERNAL_ASSERT( rows()    == (*rhs).rows()   , "Invalid number of rows"    );
   BLAZE_INTERNAL_ASSERT( columns() == (*rhs).columns(), "Invalid number of columns" );

   std::vector<size_t> nonzeros( rows(), 0UL );
   size_t sum( 0UL );

   for( size_t i=0UL; i<rows(); ++i ) {
      nonzeros[i] = (*rhs).nonZeros(i);
      sum += nonzeros[i];
   }

   matrix_.reserve( sum );
   for( size_t i=0UL; i<rows(); ++i ) {
      matrix_.reserve( i, nonzeros[i] );
   }

   for( size_t i=0UL; i<rows(); ++i ) {
      for( auto it=(*rhs).lowerBound(i,i); it!=(*rhs).end(i); ++it ) {
         if( !isDefault( it->value() ) ) {
            const SharedValue<ET> shared( it->value() );
            matrix_.append( i, it->index(), shared, false );
            if( i != it->index() )
               matrix_.append( it->index(), i, shared, false );
         }
      }
   }
}
/*! \endcond */
//*************************************************************************************************

} // namespace blaze

#endif
