text: //=================================================================================================
  /*!
  //  \file blaze/math/adaptors/strictlylowermatrix/Dense.h
  //  \brief StrictlyLowerMatrix specialization for dense matrices
  //
  //  Copyright (C) 2012-2018 Klaus Iglberger - All Rights Reserved
  //
  //  This file is part of the Blaze library. You can redistribute it and/or modify it under
  //  the terms of the New (Revised) BSD License. Redistribution and use in source and binary
  //  forms, with or without modification, are permitted provided that the following conditions
  //  are met:
  //
  //  1. Redistributions of source code must retain the above copyright notice, this list of
  //     conditions and the following disclaimer.
  //  2. Redistributions in binary form must reproduce the above copyright notice, this list
  //     of conditions and the following disclaimer in the documentation and/or other materials
  //     provided with the distribution.
  //  3. Neither the names of the Blaze development group nor the names of its contributors
  //     may be used to endorse or promote products derived from this software without specific
  //     prior written permission.
  //
  //  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
  //  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  //  OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
  //  SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  //  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
  //  TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
  //  BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  //  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  //  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
  //  DAMAGE.
  */
  //=================================================================================================
  
  #ifndef _BLAZE_MATH_ADAPTORS_STRICTLYLOWERMATRIX_DENSE_H_
  #define _BLAZE_MATH_ADAPTORS_STRICTLYLOWERMATRIX_DENSE_H_
  
  
  //*************************************************************************************************
  // Includes
  //*************************************************************************************************
  
  #include <iterator>
  #include <utility>
  #include "../../../math/adaptors/Forward.h"
  #include "../../../math/adaptors/strictlylowermatrix/BaseTemplate.h"
  #include "../../../math/adaptors/strictlylowermatrix/StrictlyLowerProxy.h"
  #include "../../../math/Aliases.h"
  #include "../../../math/constraints/DenseMatrix.h"
  #include "../../../math/constraints/Expression.h"
  #include "../../../math/constraints/Hermitian.h"
  #include "../../../math/constraints/Lower.h"
  #include "../../../math/constraints/Resizable.h"
  #include "../../../math/constraints/Square.h"
  #include "../../../math/constraints/Static.h"
  #include "../../../math/constraints/StorageOrder.h"
  #include "../../../math/constraints/Symmetric.h"
  #include "../../../math/constraints/Upper.h"
  #include "../../../math/dense/DenseMatrix.h"
  #include "../../../math/dense/InitializerMatrix.h"
  #include "../../../math/Exception.h"
  #include "../../../math/expressions/DenseMatrix.h"
  #include "../../../math/InitializerList.h"
  #include "../../../math/shims/Clear.h"
  #include "../../../math/shims/IsDefault.h"
  #include "../../../math/shims/IsZero.h"
  #include "../../../math/typetraits/IsComputation.h"
  #include "../../../math/typetraits/IsResizable.h"
  #include "../../../math/typetraits/IsSquare.h"
  #include "../../../math/typetraits/IsStrictlyLower.h"
  #include "../../../math/typetraits/IsUniTriangular.h"
  #include "../../../math/typetraits/Size.h"
  #include "../../../math/views/Submatrix.h"
  #include "../../../system/Inline.h"
  #include "../../../util/Assert.h"
  #include "../../../util/constraints/Const.h"
  #include "../../../util/constraints/Pointer.h"
  #include "../../../util/constraints/Reference.h"
  #include "../../../util/constraints/Vectorizable.h"
  #include "../../../util/constraints/Volatile.h"
  #include "../../../util/DisableIf.h"
  #include "../../../util/EnableIf.h"
  #include "../../../util/FalseType.h"
  #include "../../../util/StaticAssert.h"
  #include "../../../util/TrueType.h"
  #include "../../../util/Types.h"
  #include "../../../util/Unused.h"
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  CLASS TEMPLATE SPECIALIZATION FOR DENSE MATRICES
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Specialization of StrictlyLowerMatrix for dense matrices.
  // \ingroup strictly_lower_matrix
  //
  // This specialization of StrictlyLowerMatrix adapts the class template to the requirements of
  // dense matrices.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  class StrictlyLowerMatrix<MT,SO,true>
     : public DenseMatrix< StrictlyLowerMatrix<MT,SO,true>, SO >
  {
   private:
     //**Type definitions****************************************************************************
     using OT = OppositeType_t<MT>;   //!< Opposite type of the dense matrix.
     using TT = TransposeType_t<MT>;  //!< Transpose type of the dense matrix.
     using ET = ElementType_t<MT>;    //!< Element type of the dense matrix.
     //**********************************************************************************************
  
   public:
     //**Type definitions****************************************************************************
     using This           = StrictlyLowerMatrix<MT,SO,true>;   //!< Type of this StrictlyLowerMatrix instance.
     using BaseType       = DenseMatrix<This,SO>;              //!< Base type of this StrictlyLowerMatrix instance.
     using ResultType     = This;                              //!< Result type for expression template evaluations.
     using OppositeType   = StrictlyLowerMatrix<OT,!SO,true>;  //!< Result type with opposite storage order for expression template evaluations.
     using TransposeType  = StrictlyUpperMatrix<TT,!SO,true>;  //!< Transpose type for expression template evaluations.
     using ElementType    = ET;                                //!< Type of the matrix elements.
     using SIMDType       = SIMDType_t<MT>;                    //!< SIMD type of the matrix elements.
     using ReturnType     = ReturnType_t<MT>;                  //!< Return type for expression template evaluations.
     using CompositeType  = const This&;                       //!< Data type for composite expression templates.
     using Reference      = StrictlyLowerProxy<MT>;            //!< Reference to a non-constant matrix value.
     using ConstReference = ConstReference_t<MT>;              //!< Reference to a constant matrix value.
     using Pointer        = Pointer_t<MT>;                     //!< Pointer to a non-constant matrix value.
     using ConstPointer   = ConstPointer_t<MT>;                //!< Pointer to a constant matrix value.
     using ConstIterator  = ConstIterator_t<MT>;               //!< Iterator over constant elements.
     //**********************************************************************************************
  
     //**Rebind struct definition********************************************************************
     /*!\brief Rebind mechanism to obtain a StrictlyLowerMatrix with different data/element type.
     */
     template< typename NewType >  // Data type of the other matrix
     struct Rebind {
        //! The type of the other StrictlyLowerMatrix.
        using Other = StrictlyLowerMatrix< typename MT::template Rebind<NewType>::Other >;
     };
     //**********************************************************************************************
  
     //**Resize struct definition********************************************************************
     /*!\brief Resize mechanism to obtain a StrictlyLowerMatrix 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 StrictlyLowerMatrix.
        using Other = StrictlyLowerMatrix< typename MT::template Resize<NewM,NewN>::Other >;
     };
     //**********************************************************************************************
  
     //**Iterator class definition*******************************************************************
     /*!\brief Iterator over the non-constant elements of the dense strictly lower matrix.
     */
     class Iterator
     {
      public:
        //**Type definitions*************************************************************************
        using IteratorCategory = std::random_access_iterator_tag;  //!< The iterator category.
        using ValueType        = ElementType_t<MT>;                //!< Type of the underlying elements.
        using PointerType      = StrictlyLowerProxy<MT>;           //!< Pointer return type.
        using ReferenceType    = StrictlyLowerProxy<MT>;           //!< 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.
        //*******************************************************************************************
  
        //**Constructor******************************************************************************
        /*!\brief Default constructor of the Iterator class.
        */
        inline Iterator() noexcept
           : matrix_( nullptr )  // Reference to the adapted dense matrix
           , row_   ( 0UL )      // The current row index of the iterator
           , column_( 0UL )      // The current column index of the iterator
        {}
        //*******************************************************************************************
  
        //**Constructor******************************************************************************
        /*!\brief Constructor for the Iterator class.
        //
        // \param matrix The adapted matrix.
        // \param row Initial row index of the iterator.
        // \param column Initial column index of the iterator.
        */
        inline Iterator( MT& matrix, size_t row, size_t column ) noexcept
           : matrix_( &matrix )  // Reference to the adapted dense matrix
           , row_   ( row     )  // The current row-index of the iterator
           , column_( column  )  // The current column-index of the iterator
        {}
        //*******************************************************************************************
  
        //**Addition assignment operator*************************************************************
        /*!\brief Addition assignment operator.
        //
        // \param inc The increment of the iterator.
        // \return The incremented iterator.
        */
        inline Iterator& operator+=( size_t inc ) noexcept {
           ( SO )?( row_ += inc ):( column_ += inc );
           return *this;
        }
        //*******************************************************************************************
  
        //**Subtraction assignment operator**********************************************************
        /*!\brief Subtraction assignment operator.
        //
        // \param dec The decrement of the iterator.
        // \return The decremented iterator.
        */
        inline Iterator& operator-=( size_t dec ) noexcept {
           ( SO )?( row_ -= dec ):( column_ -= dec );
           return *this;
        }
        //*******************************************************************************************
  
        //**Prefix increment operator****************************************************************
        /*!\brief Pre-increment operator.
        //
        // \return Reference to the incremented iterator.
        */
        inline Iterator& operator++() noexcept {
           ( SO )?( ++row_ ):( ++column_ );
           return *this;
        }
        //*******************************************************************************************
  
        //**Postfix increment operator***************************************************************
        /*!\brief Post-increment operator.
        //
        // \return The previous position of the iterator.
        */
        inline const Iterator operator++( int ) noexcept {
           const Iterator tmp( *this );
           ++(*this);
           return tmp;
        }
        //*******************************************************************************************
  
        //**Prefix decrement operator****************************************************************
        /*!\brief Pre-decrement operator.
        //
        // \return Reference to the decremented iterator.
        */
        inline Iterator& operator--() noexcept {
           ( SO )?( --row_ ):( --column_ );
           return *this;
        }
        //*******************************************************************************************
  
        //**Postfix decrement operator***************************************************************
        /*!\brief Post-decrement operator.
        //
        // \return The previous position of the iterator.
        */
        inline const Iterator operator--( int ) noexcept {
           const Iterator tmp( *this );
           --(*this);
           return tmp;
        }
        //*******************************************************************************************
  
        //**Element access operator******************************************************************
        /*!\brief Direct access to the element at the current iterator position.
        //
        // \return The resulting value.
        */
        inline ReferenceType operator*() const {
           return ReferenceType( *matrix_, row_, column_ );
        }
        //*******************************************************************************************
  
        //**Element access operator******************************************************************
        /*!\brief Direct access to the element at the current iterator position.
        //
        // \return The resulting value.
        */
        inline PointerType operator->() const {
           return PointerType( *matrix_, row_, column_ );
        }
        //*******************************************************************************************
  
        //**Load function****************************************************************************
        /*!\brief Load of a SIMD element at the current iterator position.
        //
        // \return The loaded SIMD element.
        //
        // This function performs a load of the current SIMD element at the current iterator
        // position. 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.
        */
        inline SIMDType load() const {
           return (*matrix_).load(row_,column_);
        }
        //*******************************************************************************************
  
        //**Loada function***************************************************************************
        /*!\brief Aligned load of a SIMD element at the current iterator position.
        //
        // \return The loaded SIMD element.
        //
        // This function performs an aligned load of the current SIMD element at the current
        // iterator position. 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.
        */
        inline SIMDType loada() const {
           return (*matrix_).loada(row_,column_);
        }
        //*******************************************************************************************
  
        //**Loadu function***************************************************************************
        /*!\brief Unaligned load of a SIMD element at the current iterator position.
        //
        // \return The loaded SIMD element.
        //
        // This function performs an unaligned load of the current SIMD element at the current
        // iterator position. 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.
        */
        inline SIMDType loadu() const {
           return (*matrix_).loadu(row_,column_);
        }
        //*******************************************************************************************
  
        //**Conversion operator**********************************************************************
        /*!\brief Conversion to an iterator over constant elements.
        //
        // \return An iterator over constant elements.
        */
        inline operator ConstIterator() const {
           if( SO )
              return matrix_->begin( column_ ) + row_;
           else
              return matrix_->begin( row_ ) + column_;
        }
        //*******************************************************************************************
  
        //**Equality operator************************************************************************
        /*!\brief Equality comparison between two Iterator objects.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the iterators refer to the same element, \a false if not.
        */
        friend inline bool operator==( const Iterator& lhs, const Iterator& rhs ) noexcept {
           return ( SO )?( lhs.row_ == rhs.row_ ):( lhs.column_ == rhs.column_ );
        }
        //*******************************************************************************************
  
        //**Equality operator************************************************************************
        /*!\brief Equality comparison between a Iterator and a ConstIterator.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the iterators refer to the same element, \a false if not.
        */
        friend inline bool operator==( const Iterator& lhs, const ConstIterator& rhs ) {
           return ( ConstIterator( lhs ) == rhs );
        }
        //*******************************************************************************************
  
        //**Equality operator************************************************************************
        /*!\brief Equality comparison between a ConstIterator and a Iterator.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the iterators refer to the same element, \a false if not.
        */
        friend inline bool operator==( const ConstIterator& lhs, const Iterator& rhs ) {
           return ( lhs == ConstIterator( rhs ) );
        }
        //*******************************************************************************************
  
        //**Inequality operator**********************************************************************
        /*!\brief Inequality comparison between two Iterator objects.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the iterators don't refer to the same element, \a false if they do.
        */
        friend inline bool operator!=( const Iterator& lhs, const Iterator& rhs ) noexcept {
           return ( SO )?( lhs.row_ != rhs.row_ ):( lhs.column_ != rhs.column_ );
        }
        //*******************************************************************************************
  
        //**Inequality operator**********************************************************************
        /*!\brief Inequality comparison between a Iterator and ConstIterator.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the iterators don't refer to the same element, \a false if they do.
        */
        friend inline bool operator!=( const Iterator& lhs, const ConstIterator& rhs ) {
           return ( ConstIterator( lhs ) != rhs );
        }
        //*******************************************************************************************
  
        //**Inequality operator**********************************************************************
        /*!\brief Inequality comparison between a ConstIterator and Iterator.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the iterators don't refer to the same element, \a false if they do.
        */
        friend inline bool operator!=( const ConstIterator& lhs, const Iterator& rhs ) {
           return ( lhs != ConstIterator( rhs ) );
        }
        //*******************************************************************************************
  
        //**Less-than operator***********************************************************************
        /*!\brief Less-than comparison between two Iterator objects.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is smaller, \a false if not.
        */
        friend inline bool operator<( const Iterator& lhs, const Iterator& rhs ) noexcept {
           return ( SO )?( lhs.row_ < rhs.row_ ):( lhs.column_ < rhs.column_ );
        }
        //*******************************************************************************************
  
        //**Less-than operator***********************************************************************
        /*!\brief Less-than comparison between a Iterator and a ConstIterator.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is smaller, \a false if not.
        */
        friend inline bool operator<( const Iterator& lhs, const ConstIterator& rhs ) {
           return ( ConstIterator( lhs ) < rhs );
        }
        //*******************************************************************************************
  
        //**Less-than operator***********************************************************************
        /*!\brief Less-than comparison between a ConstIterator and a Iterator.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is smaller, \a false if not.
        */
        friend inline bool operator<( const ConstIterator& lhs, const Iterator& rhs ) {
           return ( lhs < ConstIterator( rhs ) );
        }
        //*******************************************************************************************
  
        //**Greater-than operator********************************************************************
        /*!\brief Greater-than comparison between two Iterator objects.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is greater, \a false if not.
        */
        friend inline bool operator>( const Iterator& lhs, const Iterator& rhs ) noexcept {
           return ( SO )?( lhs.row_ > rhs.row_ ):( lhs.column_ > rhs.column_ );
        }
        //*******************************************************************************************
  
        //**Greater-than operator********************************************************************
        /*!\brief Greater-than comparison between a Iterator and a ConstIterator.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is greater, \a false if not.
        */
        friend inline bool operator>( const Iterator& lhs, const ConstIterator& rhs ) {
           return ( ConstIterator( lhs ) > rhs );
        }
        //*******************************************************************************************
  
        //**Greater-than operator********************************************************************
        /*!\brief Greater-than comparison between a ConstIterator and a Iterator.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is greater, \a false if not.
        */
        friend inline bool operator>( const ConstIterator& lhs, const Iterator& rhs ) {
           return ( lhs > ConstIterator( rhs ) );
        }
        //*******************************************************************************************
  
        //**Less-or-equal-than operator**************************************************************
        /*!\brief Less-than comparison between two Iterator objects.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is smaller or equal, \a false if not.
        */
        friend inline bool operator<=( const Iterator& lhs, const Iterator& rhs ) noexcept {
           return ( SO )?( lhs.row_ <= rhs.row_ ):( lhs.column_ <= rhs.column_ );
        }
        //*******************************************************************************************
  
        //**Less-or-equal-than operator**************************************************************
        /*!\brief Less-than comparison between a Iterator and a ConstIterator.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is smaller or equal, \a false if not.
        */
        friend inline bool operator<=( const Iterator& lhs, const ConstIterator& rhs ) {
           return ( ConstIterator( lhs ) <= rhs );
        }
        //*******************************************************************************************
  
        //**Less-or-equal-than operator**************************************************************
        /*!\brief Less-than comparison between a ConstIterator and a Iterator.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is smaller or equal, \a false if not.
        */
        friend inline bool operator<=( const ConstIterator& lhs, const Iterator& rhs ) {
           return ( lhs <= ConstIterator( rhs ) );
        }
        //*******************************************************************************************
  
        //**Greater-or-equal-than operator***********************************************************
        /*!\brief Greater-than comparison between two Iterator objects.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is greater or equal, \a false if not.
        */
        friend inline bool operator>=( const Iterator& lhs, const Iterator& rhs ) noexcept {
           return ( SO )?( lhs.row_ >= rhs.row_ ):( lhs.column_ >= rhs.column_ );
        }
        //*******************************************************************************************
  
        //**Greater-or-equal-than operator***********************************************************
        /*!\brief Greater-than comparison between a Iterator and a ConstIterator.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is greater or equal, \a false if not.
        */
        friend inline bool operator>=( const Iterator& lhs, const ConstIterator& rhs ) {
           return ( ConstIterator( lhs ) >= rhs );
        }
        //*******************************************************************************************
  
        //**Greater-or-equal-than operator***********************************************************
        /*!\brief Greater-than comparison between two Iterator objects.
        //
        // \param lhs The left-hand side iterator.
        // \param rhs The right-hand side iterator.
        // \return \a true if the left-hand side iterator is greater or equal, \a false if not.
        */
        friend inline bool operator>=( const ConstIterator& lhs, const Iterator& rhs ) {
           return ( lhs >= ConstIterator( 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 Iterator& rhs ) const noexcept {
           return ( SO )?( row_ - rhs.row_ ):( column_ - rhs.column_ );
        }
        //*******************************************************************************************
  
        //**Addition operator************************************************************************
        /*!\brief Addition between a Iterator and an integral value.
        //
        // \param it The iterator to be incremented.
        // \param inc The number of elements the iterator is incremented.
        // \return The incremented iterator.
        */
        friend inline const Iterator operator+( const Iterator& it, size_t inc ) noexcept {
           if( SO )
              return Iterator( *it.matrix_, it.row_ + inc, it.column_ );
           else
              return Iterator( *it.matrix_, it.row_, it.column_ + inc );
        }
        //*******************************************************************************************
  
        //**Addition operator************************************************************************
        /*!\brief Addition between an integral value and a Iterator.
        //
        // \param inc The number of elements the iterator is incremented.
        // \param it The iterator to be incremented.
        // \return The incremented iterator.
        */
        friend inline const Iterator operator+( size_t inc, const Iterator& it ) noexcept {
           if( SO )
              return Iterator( *it.matrix_, it.row_ + inc, it.column_ );
           else
              return Iterator( *it.matrix_, it.row_, it.column_ + inc );
        }
        //*******************************************************************************************
  
        //**Subtraction operator*********************************************************************
        /*!\brief Subtraction between a Iterator and an integral value.
        //
        // \param it The iterator to be decremented.
        // \param dec The number of elements the iterator is decremented.
        // \return The decremented iterator.
        */
        friend inline const Iterator operator-( const Iterator& it, size_t dec ) noexcept {
           if( SO )
              return Iterator( *it.matrix_, it.row_ - dec, it.column_ );
           else
              return Iterator( *it.matrix_, it.row_, it.column_ - dec );
        }
        //*******************************************************************************************
  
      private:
        //**Member variables*************************************************************************
        MT*    matrix_;  //!< Reference to the adapted dense matrix.
        size_t row_;     //!< The current row-index of the iterator.
        size_t column_;  //!< The current column-index of the iterator.
        //*******************************************************************************************
     };
     //**********************************************************************************************
  
     //**Compilation flags***************************************************************************
     //! Compilation switch for the expression template evaluation strategy.
     static constexpr bool simdEnabled = MT::simdEnabled;
  
     //! Compilation switch for the expression template assignment strategy.
     static constexpr bool smpAssignable = MT::smpAssignable;
     //**********************************************************************************************
  
     //**Constructors********************************************************************************
     /*!\name Constructors */
     //@{
                             explicit inline StrictlyLowerMatrix();
     template< typename A1 > explicit inline StrictlyLowerMatrix( const A1& a1 );
                             explicit inline StrictlyLowerMatrix( size_t n, const ElementType& init );
  
     explicit inline StrictlyLowerMatrix( initializer_list< initializer_list<ElementType> > list );
  
     template< typename Other >
     explicit inline StrictlyLowerMatrix( size_t n, const Other* array );
  
     template< typename Other, size_t N >
     explicit inline StrictlyLowerMatrix( const Other (&array)[N][N] );
  
     explicit inline StrictlyLowerMatrix( ElementType* ptr, size_t n );
     explicit inline StrictlyLowerMatrix( ElementType* ptr, size_t n, size_t nn );
  
     inline StrictlyLowerMatrix( const StrictlyLowerMatrix& m );
     inline StrictlyLowerMatrix( StrictlyLowerMatrix&& m ) noexcept;
     //@}
     //**********************************************************************************************
  
     //**Destructor**********************************************************************************
     // No explicitly declared destructor.
     //**********************************************************************************************
  
     //**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 ConstPointer   data  () const noexcept;
     inline ConstPointer   data  ( size_t i ) const noexcept;
     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 StrictlyLowerMatrix& operator=( const ElementType& rhs );
     inline StrictlyLowerMatrix& operator=( initializer_list< initializer_list<ElementType> > list );
  
     template< typename Other, size_t N >
     inline StrictlyLowerMatrix& operator=( const Other (&array)[N][N] );
  
     inline StrictlyLowerMatrix& operator=( const StrictlyLowerMatrix& rhs );
     inline StrictlyLowerMatrix& operator=( StrictlyLowerMatrix&& rhs ) noexcept;
  
     template< typename MT2, bool SO2 >
     inline auto operator=( const Matrix<MT2,SO2>& rhs )
        -> DisableIf_t< IsComputation_v<MT2>, StrictlyLowerMatrix& >;
  
     template< typename MT2, bool SO2 >
     inline auto operator=( const Matrix<MT2,SO2>& rhs )
        -> EnableIf_t< IsComputation_v<MT2>, StrictlyLowerMatrix& >;
  
     template< typename MT2, bool SO2 >
     inline auto operator+=( const Matrix<MT2,SO2>& rhs )
        -> DisableIf_t< IsComputation_v<MT2>, StrictlyLowerMatrix& >;
  
     template< typename MT2, bool SO2 >
     inline auto operator+=( const Matrix<MT2,SO2>& rhs )
        -> EnableIf_t< IsComputation_v<MT2>, StrictlyLowerMatrix& >;
  
     template< typename MT2, bool SO2 >
     inline auto operator-=( const Matrix<MT2,SO2>& rhs )
        -> DisableIf_t< IsComputation_v<MT2>, StrictlyLowerMatrix& >;
  
     template< typename MT2, bool SO2 >
     inline auto operator-=( const Matrix<MT2,SO2>& rhs )
        -> EnableIf_t< IsComputation_v<MT2>, StrictlyLowerMatrix& >;
  
     template< typename MT2, bool SO2 >
     inline auto operator%=( const Matrix<MT2,SO2>& rhs ) -> StrictlyLowerMatrix&;
  
     template< typename ST >
     inline auto operator*=( ST rhs ) -> EnableIf_t< IsNumeric_v<ST>, StrictlyLowerMatrix& >;
  
     template< typename ST >
     inline auto operator/=( ST rhs ) -> EnableIf_t< IsNumeric_v<ST>, StrictlyLowerMatrix& >;
     //@}
     //**********************************************************************************************
  
     //**Utility functions***************************************************************************
     /*!\name Utility functions */
     //@{
     inline size_t rows() const noexcept;
     inline size_t columns() const noexcept;
     inline size_t spacing() 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();
            void   resize ( size_t n, bool preserve=true );
     inline void   extend ( size_t n, bool preserve=true );
     inline void   reserve( size_t elements );
     inline void   shrinkToFit();
     inline void   swap( StrictlyLowerMatrix& m ) noexcept;
  
     static inline constexpr size_t maxNonZeros() noexcept;
     static inline constexpr size_t maxNonZeros( size_t n ) noexcept;
     //@}
     //**********************************************************************************************
  
     //**Numeric functions***************************************************************************
     /*!\name Numeric functions */
     //@{
     template< typename Other > inline StrictlyLowerMatrix& scale( const Other& scalar );
     //@}
     //**********************************************************************************************
  
     //**Debugging functions*************************************************************************
     /*!\name Debugging 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 isAligned   () const noexcept;
     inline bool canSMPAssign() const noexcept;
  
     BLAZE_ALWAYS_INLINE SIMDType load ( size_t i, size_t j ) const noexcept;
     BLAZE_ALWAYS_INLINE SIMDType loada( size_t i, size_t j ) const noexcept;
     BLAZE_ALWAYS_INLINE SIMDType loadu( size_t i, size_t j ) const noexcept;
     //@}
     //**********************************************************************************************
  
   private:
     //**Construction functions**********************************************************************
     /*!\name Construction functions */
     //@{
     inline const MT construct( size_t n                , TrueType  );
     inline const MT construct( const ElementType& value, FalseType );
  
     template< typename MT2, bool SO2, typename T >
     inline const MT construct( const Matrix<MT2,SO2>& m, T );
     //@}
     //**********************************************************************************************
  
     //**Member variables****************************************************************************
     /*!\name Member variables */
     //@{
     MT matrix_;  //!< The adapted dense matrix.
     //@}
     //**********************************************************************************************
  
     //**Friend declarations*************************************************************************
     template< typename MT2, bool SO2, bool DF2 >
     friend MT2& derestrict( StrictlyLowerMatrix<MT2,SO2,DF2>& m );
     //**********************************************************************************************
  
     //**Compile time checks*************************************************************************
     BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE        ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_REFERENCE_TYPE       ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_POINTER_TYPE         ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_CONST                ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_VOLATILE             ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_EXPRESSION_TYPE      ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_SYMMETRIC_MATRIX_TYPE( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_HERMITIAN_MATRIX_TYPE( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_LOWER_MATRIX_TYPE    ( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_UPPER_MATRIX_TYPE    ( MT );
     BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( OT, !SO );
     BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER( TT, !SO );
     BLAZE_STATIC_ASSERT( ( Size_v<MT,0UL> == Size_v<MT,1UL> ) );
     //**********************************************************************************************
  };
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  CONSTRUCTORS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief The default constructor for StrictlyLowerMatrix.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline StrictlyLowerMatrix<MT,SO,true>::StrictlyLowerMatrix()
     : matrix_()  // The adapted dense matrix
  {
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower matrix detected" );
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Single argument constructor for a strictly lower matrix.
  //
  // \param a1 The single constructor argument.
  // \exception std::invalid_argument Invalid setup of strictly lower matrix.
  //
  // This constructor constructs the strictly lower matrix based on the given argument and the
  // type of the underlying matrix \a MT:
  //  - in case the given argument is a matrix, the strictly lower matrix is initialized as a copy
  //    of the given matrix.
  //  - in case the given argument is not a matrix and the underlying matrix of type \a MT is
  //    resizable, the given argument \a a1 specifies the number of rows and columns of the
  //    strictly lower matrix.
  //  - in case the given argument is not a matrix and the underlying matrix of type \a MT is
  //    a matrix with fixed size, the given argument \a a1 specifies the initial value of the
  //    lower elements.
  */
  template< typename MT    // Type of the adapted dense matrix
          , bool SO >      // Storage order of the adapted dense matrix
  template< typename A1 >  // Type of the constructor argument
  inline StrictlyLowerMatrix<MT,SO,true>::StrictlyLowerMatrix( const A1& a1 )
     : matrix_( construct( a1, typename IsResizable<MT>::Type() ) )  // The adapted dense matrix
  {
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower matrix detected" );
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Constructor for a \f$ n \times n \f$ matrix with initialized lower elements.
  //
  // \param n The number of rows and columns of the matrix.
  // \param init The initial value of the lower matrix elements.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline StrictlyLowerMatrix<MT,SO,true>::StrictlyLowerMatrix( size_t n, const ElementType& init )
     : matrix_( n, n, ElementType() )  // The adapted dense matrix
  {
     BLAZE_CONSTRAINT_MUST_BE_RESIZABLE_TYPE( MT );
  
     if( SO ) {
        for( size_t j=0UL; j<columns(); ++j ) {
           for( size_t i=j+1UL; i<rows(); ++i )
              matrix_(i,j) = init;
        }
     }
     else {
        for( size_t i=0UL; i<rows(); ++i ) {
           for( size_t j=0UL; j<i; ++j )
              matrix_(i,j) = init;
        }
     }
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower matrix detected" );
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief List initialization of all matrix elements.
  //
  // \param list The initializer list.
  // \exception std::invalid_argument Invalid setup of strictly lower matrix.
  //
  // This constructor provides the option to explicitly initialize the elements of the strictly
  // lower matrix by means of an initializer list:
  
     \code
     using blaze::rowMajor;
  
     blaze::StrictlyLowerMatrix< blaze::StaticMatrix<int,3,3,rowMajor> > A{ { },
                                                                            { 2 },
                                                                            { 4, 5 } };
     \endcode
  
  // The matrix is sized according to the size of the initializer list and all matrix elements are
  // initialized with the values from the given list. Missing values are initialized with default
  // values. In case the matrix cannot be resized and the dimensions of the initializer list don't
  // match or if the given list does not represent a strictly lower matrix, a \a std::invalid_argument
  // exception is thrown.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline StrictlyLowerMatrix<MT,SO,true>::StrictlyLowerMatrix( initializer_list< initializer_list<ElementType> > list )
     : matrix_( list )  // The adapted dense matrix
  {
     if( !isStrictlyLower( matrix_ ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid setup of strictly lower matrix" );
     }
  
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Array initialization of all strictly lower matrix elements.
  //
  // \param n The number of rows and columns of the matrix.
  // \param array Dynamic array for the initialization.
  // \exception std::invalid_argument Invalid setup of strictly lower matrix.
  //
  // This constructor offers the option to directly initialize the elements of the strictly lower
  // matrix with a dynamic array:
  
     \code
     using blaze::rowMajor;
  
     int* array = new int[16];
     // ... Initialization of the dynamic array
     blaze::StrictlyLowerMatrix< blaze::DynamicMatrix<int,rowMajor> > v( 4UL, array );
     delete[] array;
     \endcode
  
  // The matrix is sized accoring to the given size of the array and initialized with the values
  // from the given array. Note that it is expected that the given \a array has at least \a n by
  // \a n elements. Providing an array with less elements results in undefined behavior! Also,
  // in case the given array does not represent a strictly lower triangular matrix, a
  // \a std::invalid_argument exception is thrown.
  */
  template< typename MT       // Type of the adapted dense matrix
          , bool SO >         // Storage order of the adapted dense matrix
  template< typename Other >  // Data type of the initialization array
  inline StrictlyLowerMatrix<MT,SO,true>::StrictlyLowerMatrix( size_t n, const Other* array )
     : matrix_( n, n, array )  // The adapted dense matrix
  {
     if( !isStrictlyLower( matrix_ ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid setup of strictly lower matrix" );
     }
  
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Array initialization of all strictly lower matrix elements.
  //
  // \param array \f$ N \times N \f$ dimensional array for the initialization.
  // \exception std::invalid_argument Invalid setup of strictly lower matrix.
  //
  // This constructor offers the option to directly initialize the elements of the strictly lower
  // matrix with a static array:
  
     \code
     using blaze::rowMajor;
  
     const int init[3][3] = { {  },
                              { 2 },
                              { 4, 5 } };
     blaze::StrictlyLowerMatrix< blaze::StaticMatrix<int,3,3,rowMajor> > A( init );
     \endcode
  
  // The matrix is initialized with the values from the given array. Missing values are initialized
  // with default values. In case the given array does not represent a strictly lower triangular
  // matrix, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT     // Type of the adapted dense matrix
          , bool SO >       // Storage order of the adapted dense matrix
  template< typename Other  // Data type of the initialization array
          , size_t N >      // Number of rows and columns of the initialization array
  inline StrictlyLowerMatrix<MT,SO,true>::StrictlyLowerMatrix( const Other (&array)[N][N] )
     : matrix_( array )  // The adapted dense matrix
  {
     if( !isStrictlyLower( matrix_ ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid setup of strictly lower matrix" );
     }
  
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Constructor for a strictly lower custom matrix of size \f$ n \times n \f$.
  //
  // \param ptr The array of elements to be used by the matrix.
  // \param n The number of rows and columns of the array of elements.
  // \exception std::invalid_argument Invalid setup of strictly lower custom matrix.
  //
  // This constructor creates an unpadded strictly lower custom matrix of size \f$ n \times n \f$:
  
     \code
     using blaze::StrictlyLowerMatrix;
     using blaze::CustomMatrix;
     using blaze::unaligned;
     using blaze::unpadded;
  
     std::vector<int> memory( 9UL );
     StrictlyLowerMatrix< CustomMatrix<int,unaligned,unpadded> > A( memory.data(), 3UL );
     \endcode
  
  // The construction fails if ...
  //
  //  - ... the passed pointer is \c nullptr;
  //  - ... the alignment flag \a AF is set to \a aligned, but the passed pointer is not properly
  //    aligned according to the available instruction set (SSE, AVX, ...);
  //  - ... the values in the given array do not represent a strictly lower triangular matrix.
  //
  // In all failure cases a \a std::invalid_argument exception is thrown.
  //
  // \note This constructor is \b NOT available for padded strictly lower custom matrices!
  // \note The strictly lower custom matrix does \b NOT take responsibility for the given array of
  // elements!
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline StrictlyLowerMatrix<MT,SO,true>::StrictlyLowerMatrix( ElementType* ptr, size_t n )
     : matrix_( ptr, n, n )  // The adapted dense matrix
  {
     if( !isStrictlyLower( matrix_ ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid setup of strictly lower matrix" );
     }
  
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Constructor for a strictly lower custom matrix of size \f$ n \times n \f$.
  //
  // \param ptr The array of elements to be used by the matrix.
  // \param n The number of rows and columns of the array of elements.
  // \param nn The total number of elements between two rows/columns.
  // \exception std::invalid_argument Invalid setup of strictly lower custom matrix.
  //
  // This constructor creates a strictly lower custom matrix of size \f$ n \times n \f$:
  
     \code
     using blaze::StrictlyLowerMatrix;
     using blaze::CustomMatrix;
     using blaze::unaligned;
     using blaze::padded;
  
     std::vector<int> memory( 24UL );
     StrictlyLowerMatrix< CustomMatrix<int,unaligned,padded> > A( memory.data(), 3UL, 8UL );
     \endcode
  
  // The construction fails if ...
  //
  //  - ... the passed pointer is \c nullptr;
  //  - ... the alignment flag \a AF is set to \a aligned, but the passed pointer is not properly
  //    aligned according to the available instruction set (SSE, AVX, ...);
  //  - ... the specified spacing \a nn is insufficient for the given data type \a Type and the
  //    available instruction set;
  //  - ... the values in the given array do not represent a strictly lower triangular matrix.
  //
  // In all failure cases a \a std::invalid_argument exception is thrown.
  //
  // \note The matrix does \b NOT take responsibility for the given array of elements!
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline StrictlyLowerMatrix<MT,SO,true>::StrictlyLowerMatrix( ElementType* ptr, size_t n, size_t nn )
     : matrix_( ptr, n, n, nn )  // The adapted dense matrix
  {
     if( !isStrictlyLower( matrix_ ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid setup of strictly lower matrix" );
     }
  
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief The copy constructor for StrictlyLowerMatrix.
  //
  // \param m The strictly lower matrix to be copied.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline StrictlyLowerMatrix<MT,SO,true>::StrictlyLowerMatrix( const StrictlyLowerMatrix& m )
     : matrix_( m.matrix_ )  // The adapted dense matrix
  {
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower matrix detected" );
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief The move constructor for StrictlyLowerMatrix.
  //
  // \param m The strictly lower matrix to be moved into this instance.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline StrictlyLowerMatrix<MT,SO,true>::StrictlyLowerMatrix( StrictlyLowerMatrix&& m ) noexcept
     : matrix_( std::move( m.matrix_ ) )  // The adapted dense matrix
  {
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower 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.
  // \exception std::invalid_argument Invalid assignment to upper matrix element.
  //
  // The function call operator provides access to the elements at position (i,j). The attempt
  // to assign to an element on the diagonal or in the upper part of the matrix (i.e. above the
  // diagonal) will result in a \a std::invalid_argument exception.
  //
  // 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 dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline typename StrictlyLowerMatrix<MT,SO,true>::Reference
     StrictlyLowerMatrix<MT,SO,true>::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.
  // \exception std::invalid_argument Invalid assignment to upper matrix element.
  //
  // The function call operator provides access to the elements at position (i,j). The attempt
  // to assign to an element on the diagonal or in the upper part of the matrix (i.e. above the
  // diagonal) will result in a \a std::invalid_argument exception.
  //
  // 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 dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline typename StrictlyLowerMatrix<MT,SO,true>::ConstReference
     StrictlyLowerMatrix<MT,SO,true>::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.
  // \exception std::invalid_argument Invalid assignment to upper matrix element.
  //
  // The function call operator provides access to the elements at position (i,j). The attempt
  // to assign to an element on the diagonal or in the upper part of the matrix (i.e. above the
  // diagonal) will result in a \a std::invalid_argument exception.
  //
  // 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 StrictlyLowerMatrix<MT,SO,true>::Reference
     StrictlyLowerMatrix<MT,SO,true>::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.
  // \exception std::invalid_argument Invalid assignment to upper matrix element.
  //
  // The function call operator provides access to the elements at position (i,j). The attempt
  // to assign to an element on the diagonal or in the upper part of the matrix (i.e. above the
  // diagonal) will result in a \a std::invalid_argument exception.
  //
  // 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 StrictlyLowerMatrix<MT,SO,true>::ConstReference
     StrictlyLowerMatrix<MT,SO,true>::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 Low-level data access to the matrix elements.
  //
  // \return Pointer to the internal element storage.
  //
  // This function returns a pointer to the internal storage of the strictly lower matrix. Note
  // that you can NOT assume that all matrix elements lie adjacent to each other! The strictly
  // lower matrix may use techniques such as padding to improve the alignment of the data. Whereas
  // the number of elements within a row/column are given by the \c rows() and \c columns() member
  // functions, respectively, the total number of elements including padding is given by the
  // \c spacing() member function.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline typename StrictlyLowerMatrix<MT,SO,true>::ConstPointer
     StrictlyLowerMatrix<MT,SO,true>::data() const noexcept
  {
     return matrix_.data();
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Low-level data access to the matrix elements of row/column \a i.
  //
  // \param i The row/column index.
  // \return Pointer to the internal element storage.
  //
  // This function returns a pointer to the internal storage for the elements in row/column \a i.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline typename StrictlyLowerMatrix<MT,SO,true>::ConstPointer
     StrictlyLowerMatrix<MT,SO,true>::data( size_t i ) const noexcept
  {
     return matrix_.data(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 strictly lower matrix adapts a \a rowMajor dense matrix the function returns an iterator
  // to the first element of row \a i, in case it adapts a \a columnMajor dense matrix the function
  // returns an iterator to the first element of column \a i.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline typename StrictlyLowerMatrix<MT,SO,true>::Iterator
     StrictlyLowerMatrix<MT,SO,true>::begin( size_t i )
  {
     if( SO )
        return Iterator( matrix_, 0UL, i );
     else
        return Iterator( matrix_, i, 0UL );
  }
  /*! \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 strictly lower matrix adapts a \a rowMajor dense matrix the function returns an iterator
  // to the first element of row \a i, in case it adapts a \a columnMajor dense matrix the function
  // returns an iterator to the first element of column \a i.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline typename StrictlyLowerMatrix<MT,SO,true>::ConstIterator
     StrictlyLowerMatrix<MT,SO,true>::begin( size_t i ) const
  {
     return 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 strictly lower matrix adapts a \a rowMajor dense matrix the function returns an iterator
  // to the first element of row \a i, in case it adapts a \a columnMajor dense matrix the function
  // returns an iterator to the first element of column \a i.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline typename StrictlyLowerMatrix<MT,SO,true>::ConstIterator
     StrictlyLowerMatrix<MT,SO,true>::cbegin( size_t i ) const
  {
     return 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 strictly lower matrix adapts a \a rowMajor dense matrix the function returns an
  // iterator just past the last element of row \a i, in case it adapts a \a columnMajor dense
  // matrix the function returns an iterator just past the last element of column \a i.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline typename StrictlyLowerMatrix<MT,SO,true>::Iterator
     StrictlyLowerMatrix<MT,SO,true>::end( size_t i )
  {
     if( SO )
        return Iterator( matrix_, rows(), i );
     else
        return Iterator( matrix_, i, columns() );
  }
  /*! \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 strictly lower matrix adapts a \a rowMajor dense matrix the function returns an
  // iterator just past the last element of row \a i, in case it adapts a \a columnMajor dense
  // matrix the function returns an iterator just past the last element of column \a i.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline typename StrictlyLowerMatrix<MT,SO,true>::ConstIterator
     StrictlyLowerMatrix<MT,SO,true>::end( size_t i ) const
  {
     return 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 strictly lower matrix adapts a \a rowMajor dense matrix the function returns an
  // iterator just past the last element of row \a i, in case it adapts a \a columnMajor dense
  // matrix the function returns an iterator just past the last element of column \a i.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline typename StrictlyLowerMatrix<MT,SO,true>::ConstIterator
     StrictlyLowerMatrix<MT,SO,true>::cend( size_t i ) const
  {
     return matrix_.cend(i);
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  ASSIGNMENT OPERATORS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Homogenous assignment to all lower matrix elements.
  //
  // \param rhs Scalar value to be assigned to the lower matrix elements.
  // \return Reference to the assigned matrix.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline StrictlyLowerMatrix<MT,SO,true>&
     StrictlyLowerMatrix<MT,SO,true>::operator=( const ElementType& rhs )
  {
     if( SO ) {
        for( size_t j=0UL; j<columns(); ++j )
           for( size_t i=j+1UL; i<rows(); ++i )
              matrix_(i,j) = rhs;
     }
     else {
        for( size_t i=1UL; i<rows(); ++i )
           for( size_t j=0UL; j<i; ++j )
              matrix_(i,j) = rhs;
     }
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief List assignment to all matrix elements.
  //
  // \param list The initializer list.
  // \exception std::invalid_argument Invalid assignment to strictly lower matrix.
  //
  // This assignment operator offers the option to directly assign to all elements of the strictly
  // lower matrix by means of an initializer list:
  
     \code
     using blaze::rowMajor;
  
     blaze::StrictlyLowerMatrix< blaze::StaticMatrix<int,3UL,3UL,rowMajor> > A;
     A = { { },
           { 2 },
           { 4, 5 } };
     \endcode
  
  // The matrix is resized according to the size of the initializer list and all matrix elements
  // are assigned the values from the given list. Missing values are assigned default values. In
  // case the matrix cannot be resized and the dimensions of the initializer list don't match or
  // if the given list does not represent a strictly lower matrix, a \a std::invalid_argument
  // exception is thrown.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline StrictlyLowerMatrix<MT,SO,true>&
     StrictlyLowerMatrix<MT,SO,true>::operator=( initializer_list< initializer_list<ElementType> > list )
  {
     const InitializerMatrix<ElementType> tmp( list, list.size() );
  
     if( !isStrictlyLower( tmp ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to strictly lower matrix" );
     }
  
     matrix_ = list;
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower matrix detected" );
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Array assignment to all strictly lower matrix elements.
  //
  // \param array \f$ N \times N \f$ dimensional array for the assignment.
  // \return Reference to the assigned matrix.
  // \exception std::invalid_argument Invalid assignment to strictly lower matrix.
  //
  // This assignment operator offers the option to directly set all elements of the strictly lower
  // matrix:
  
     \code
     using blaze::rowMajor;
  
     const int init[3][3] = { { },
                              { 2 },
                              { 4, 5 } };
     blaze::StrictlyLowerMatrix< blaze::StaticMatrix<int,3UL,3UL,rowMajor> > A;
     A = init;
     \endcode
  
  // The matrix is assigned the values from the given array. Missing values are initialized with
  // default values. In case the given array does not represent a strictly lower triangular matrix,
  // a \a std::invalid_argument exception is thrown.
  */
  template< typename MT     // Type of the adapted dense matrix
          , bool SO >       // Storage order of the adapted dense matrix
  template< typename Other  // Data type of the initialization array
          , size_t N >      // Number of rows and columns of the initialization array
  inline StrictlyLowerMatrix<MT,SO,true>&
     StrictlyLowerMatrix<MT,SO,true>::operator=( const Other (&array)[N][N] )
  {
     MT tmp( array );
  
     if( !isStrictlyLower( tmp ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to strictly lower matrix" );
     }
  
     matrix_ = std::move( tmp );
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower matrix detected" );
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Copy assignment operator for StrictlyLowerMatrix.
  //
  // \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 dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline StrictlyLowerMatrix<MT,SO,true>&
     StrictlyLowerMatrix<MT,SO,true>::operator=( const StrictlyLowerMatrix& rhs )
  {
     matrix_ = rhs.matrix_;
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower matrix detected" );
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Move assignment operator for StrictlyLowerMatrix.
  //
  // \param rhs The matrix to be moved into this instance.
  // \return Reference to the assigned matrix.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline StrictlyLowerMatrix<MT,SO,true>&
     StrictlyLowerMatrix<MT,SO,true>::operator=( StrictlyLowerMatrix&& rhs ) noexcept
  {
     matrix_ = std::move( rhs.matrix_ );
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower 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 strictly lower 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. If the matrix cannot be resized accordingly,
  // a \a std::invalid_argument exception is thrown. Also note that the given matrix must be a
  // strictly lower matrix. Otherwise, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT   // Type of the adapted dense matrix
          , bool SO >     // Storage order of the adapted dense matrix
  template< typename MT2  // Type of the right-hand side matrix
          , bool SO2 >    // Storage order of the right-hand side matrix
  inline auto StrictlyLowerMatrix<MT,SO,true>::operator=( const Matrix<MT2,SO2>& rhs )
     -> DisableIf_t< IsComputation_v<MT2>, StrictlyLowerMatrix& >
  {
     if( IsUniTriangular_v<MT2> ||
         ( !IsStrictlyLower_v<MT2> && !isStrictlyLower( ~rhs ) ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to strictly lower matrix" );
     }
  
     matrix_ = decllow( ~rhs );
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower 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 strictly lower 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. If the matrix cannot be resized accordingly,
  // a \a std::invalid_argument exception is thrown. Also note that the given matrix must be a
  // strictly lower matrix. Otherwise, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT   // Type of the adapted dense matrix
          , bool SO >     // Storage order of the adapted dense matrix
  template< typename MT2  // Type of the right-hand side matrix
          , bool SO2 >    // Storage order of the right-hand side matrix
  inline auto StrictlyLowerMatrix<MT,SO,true>::operator=( const Matrix<MT2,SO2>& rhs )
     -> EnableIf_t< IsComputation_v<MT2>, StrictlyLowerMatrix& >
  {
     if( IsUniTriangular_v<MT2> || ( !IsSquare_v<MT2> && !isSquare( ~rhs ) ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to strictly lower matrix" );
     }
  
     if( IsStrictlyLower_v<MT2> ) {
        matrix_ = ~rhs;
     }
     else {
        MT tmp( ~rhs );
  
        if( !isStrictlyLower( tmp ) ) {
           BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to strictly lower matrix" );
        }
  
        matrix_ = std::move( tmp );
     }
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower matrix detected" );
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Addition assignment operator for the addition of a general matrix (\f$ A+=B \f$).
  //
  // \param rhs The right-hand side general matrix to be added.
  // \return Reference to the matrix.
  // \exception std::invalid_argument Invalid assignment to strictly lower 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 strictly
  // lower matrix, i.e. the given matrix must be a strictly lower matrix. In case the result is
  // not a strictly lower matrix, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT   // Type of the adapted dense matrix
          , bool SO >     // Storage order of the adapted dense matrix
  template< typename MT2  // Type of the right-hand side matrix
          , bool SO2 >    // Storage order of the right-hand side matrix
  inline auto StrictlyLowerMatrix<MT,SO,true>::operator+=( const Matrix<MT2,SO2>& rhs )
     -> DisableIf_t< IsComputation_v<MT2>, StrictlyLowerMatrix& >
  {
     if( IsUniTriangular_v<MT2> ||
        ( !IsStrictlyLower_v<MT2> && !isStrictlyLower( ~rhs ) ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to strictly lower matrix" );
     }
  
     matrix_ += decllow( ~rhs );
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower 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 computation (\f$ A+=B \f$).
  //
  // \param rhs The right-hand side matrix computation to be added.
  // \return Reference to the matrix.
  // \exception std::invalid_argument Invalid assignment to strictly lower 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 strictly
  // lower matrix, i.e. the given matrix must be a strictly lower matrix. In case the result is
  // not a strictly lower matrix, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT   // Type of the adapted dense matrix
          , bool SO >     // Storage order of the adapted dense matrix
  template< typename MT2  // Type of the right-hand side matrix
          , bool SO2 >    // Storage order of the right-hand side matrix
  inline auto StrictlyLowerMatrix<MT,SO,true>::operator+=( const Matrix<MT2,SO2>& rhs )
     -> EnableIf_t< IsComputation_v<MT2>, StrictlyLowerMatrix& >
  {
     if( IsUniTriangular_v<MT2> || ( !IsSquare_v<MT2> && !isSquare( ~rhs ) ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to strictly lower matrix" );
     }
  
     if( IsStrictlyLower_v<MT2> ) {
        matrix_ += ~rhs;
     }
     else {
        const ResultType_t<MT2> tmp( ~rhs );
  
        if( !isStrictlyLower( tmp ) ) {
           BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to strictly lower matrix" );
        }
  
        matrix_ += decllow( tmp );
     }
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower matrix detected" );
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Subtraction assignment operator for the subtraction of a general matrix (\f$ A-=B \f$).
  //
  // \param rhs The right-hand side general matrix to be subtracted.
  // \return Reference to the matrix.
  // \exception std::invalid_argument Invalid assignment to strictly lower 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 strictly
  // lower matrix, i.e. the given matrix must be a strictly lower matrix. In case the result is not
  // a strictly lower matrix, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT   // Type of the adapted dense matrix
          , bool SO >     // Storage order of the adapted dense matrix
  template< typename MT2  // Type of the right-hand side matrix
          , bool SO2 >    // Storage order of the right-hand side matrix
  inline auto StrictlyLowerMatrix<MT,SO,true>::operator-=( const Matrix<MT2,SO2>& rhs )
     -> DisableIf_t< IsComputation_v<MT2>, StrictlyLowerMatrix& >
  {
     if( IsUniTriangular_v<MT2> ||
        ( !IsStrictlyLower_v<MT2> && !isStrictlyLower( ~rhs ) ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to strictly lower matrix" );
     }
  
     matrix_ -= decllow( ~rhs );
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower 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 computation (\f$ A-=B \f$).
  //
  // \param rhs The right-hand side matrix computation to be subtracted.
  // \return Reference to the matrix.
  // \exception std::invalid_argument Invalid assignment to strictly lower 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 strictly
  // lower matrix, i.e. the given matrix must be a strictly lower matrix. In case the result is not
  // a strictly lower matrix, a \a std::invalid_argument exception is thrown.
  */
  template< typename MT   // Type of the adapted dense matrix
          , bool SO >     // Storage order of the adapted dense matrix
  template< typename MT2  // Type of the right-hand side matrix
          , bool SO2 >    // Storage order of the right-hand side matrix
  inline auto StrictlyLowerMatrix<MT,SO,true>::operator-=( const Matrix<MT2,SO2>& rhs )
     -> EnableIf_t< IsComputation_v<MT2>, StrictlyLowerMatrix& >
  {
     if( IsUniTriangular_v<MT2> || ( !IsSquare_v<MT2> && !isSquare( ~rhs ) ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to strictly lower matrix" );
     }
  
     if( IsStrictlyLower_v<MT2> ) {
        matrix_ -= ~rhs;
     }
     else {
        const ResultType_t<MT2> tmp( ~rhs );
  
        if( !isStrictlyLower( tmp ) ) {
           BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to strictly lower matrix" );
        }
  
        matrix_ -= decllow( tmp );
     }
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower 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 (\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 strictly lower matrix.
  //
  // In case the current sizes of the two matrices don't match, a \a std::invalid_argument exception
  // is thrown.
  */
  template< typename MT   // Type of the adapted dense matrix
          , bool SO >     // Storage order of the adapted dense matrix
  template< typename MT2  // Type of the right-hand side matrix
          , bool SO2 >    // Storage order of the right-hand side matrix
  inline auto StrictlyLowerMatrix<MT,SO,true>::operator%=( const Matrix<MT2,SO2>& rhs )
     -> StrictlyLowerMatrix&
  {
     if( !IsSquare_v<MT2> && !isSquare( ~rhs ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid assignment to strictly lower matrix" );
     }
  
     matrix_ %= ~rhs;
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower matrix detected" );
     BLAZE_INTERNAL_ASSERT( isIntact(), "Broken invariant detected" );
  
     return *this;
  }
  /*! \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 dense matrix
          , bool SO >      // Storage order of the adapted dense matrix
  template< typename ST >  // Data type of the right-hand side scalar
  inline auto StrictlyLowerMatrix<MT,SO,true>::operator*=( ST rhs )
     -> EnableIf_t< IsNumeric_v<ST>, StrictlyLowerMatrix& >
  {
     matrix_ *= rhs;
     return *this;
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \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 dense matrix
          , bool SO >      // Storage order of the adapted dense matrix
  template< typename ST >  // Data type of the right-hand side scalar
  inline auto StrictlyLowerMatrix<MT,SO,true>::operator/=( ST rhs )
     -> EnableIf_t< IsNumeric_v<ST>, StrictlyLowerMatrix& >
  {
     BLAZE_USER_ASSERT( !isZero( rhs ), "Division by zero detected" );
  
     matrix_ /= 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 dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline size_t StrictlyLowerMatrix<MT,SO,true>::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 dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline size_t StrictlyLowerMatrix<MT,SO,true>::columns() const noexcept
  {
     return matrix_.columns();
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns the spacing between the beginning of two rows/columns.
  //
  // \return The spacing between the beginning of two rows/columns.
  //
  // This function returns the spacing between the beginning of two rows/columns, i.e. the total
  // number of elements of a row/column. In case the strictly lower matrix adapts a \a rowMajor
  // dense matrix the function returns the spacing between two rows, in case it adapts a
  // \a columnMajor dense matrix the function returns the spacing between two columns.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline size_t StrictlyLowerMatrix<MT,SO,true>::spacing() const noexcept
  {
     return matrix_.spacing();
  }
  /*! \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 dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline size_t StrictlyLowerMatrix<MT,SO,true>::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 strictly
  // lower matrix adapts a \a rowMajor dense matrix the function returns the capacity of row \a i,
  // in case it adapts a \a columnMajor dense matrix the function returns the capacity of column
  // \a i.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline size_t StrictlyLowerMatrix<MT,SO,true>::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 strictly lower matrix.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline size_t StrictlyLowerMatrix<MT,SO,true>::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 strictly lower matrix adapts a \a rowMajor dense matrix the function returns the
  // number of non-zero elements in row \a i, in case it adapts a to \a columnMajor dense matrix
  // the function returns the number of non-zero elements in column \a i.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline size_t StrictlyLowerMatrix<MT,SO,true>::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 dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline void StrictlyLowerMatrix<MT,SO,true>::reset()
  {
     using blaze::clear;
  
     if( SO ) {
        for( size_t j=0UL; j<columns(); ++j )
           for( size_t i=j+1UL; i<rows(); ++i )
              clear( matrix_(i,j) );
     }
     else {
        for( size_t i=1UL; i<rows(); ++i )
           for( size_t j=0UL; j<i; ++j )
              clear( matrix_(i,j) );
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Reset the specified row/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/column to their default value. In case
  // the storage order is set to \a rowMajor the function resets the values in row \a i, in case
  // the storage order is set to \a columnMajor the function resets the values in column \a i.
  // Note that the reset() function has no impact on the capacity of the matrix or row/column.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline void StrictlyLowerMatrix<MT,SO,true>::reset( size_t i )
  {
     using blaze::clear;
  
     if( SO ) {
        for( size_t j=i+1UL; j<rows(); ++j )
           clear( matrix_(j,i) );
     }
     else {
        for( size_t j=0UL; j<i; ++j )
           clear( matrix_(i,j) );
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Clearing the strictly lower matrix.
  //
  // \return void
  //
  // This function clears the matrix and returns it to its default state. The function has the same
  // effect as calling clear() on the adapted matrix of type \a MT: In case of a resizable matrix
  // (for instance DynamicMatrix or HybridMatrix) the number of rows and columns will be set to 0,
  // whereas in case of a fixed-size matrix (for instance StaticMatrix) only the elements will be
  // reset to their default state.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline void StrictlyLowerMatrix<MT,SO,true>::clear()
  {
     using blaze::clear;
  
     if( IsResizable_v<MT> ) {
        clear( matrix_ );
     }
     else {
        reset();
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Changing the size of the strictly lower 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
  //
  // In case the strictly lower matrix adapts a resizable matrix, this function resizes the matrix
  // using the given size to \f$ n \times n \f$. During this operation, new dynamic memory may
  // be allocated in case the capacity of the matrix is too small. Note that this function may
  // invalidate all existing views (submatrices, rows, columns, ...) on the matrix if it is used to
  // shrink the matrix. Additionally, the resize operation potentially changes all matrix elements.
  // In order to preserve the old matrix values, the \a preserve flag can be set to \a true. Also
  // note that in case the size of the matrix is increased, only the new elements on the diagonal
  // and in the upper part of the matrix are initialized.\n
  // The following example illustrates the resize operation of a \f$ 3 \times 3 \f$ matrix to a
  // \f$ 4 \times 4 \f$ matrix. The new, uninitialized elements are marked with \a x:
  
                                \f[
                                \left(\begin{array}{*{3}{c}}
                                1 & 0 & 0 \\
                                2 & 1 & 0 \\
                                3 & 4 & 1 \\
                                \end{array}\right)
  
                                \Longrightarrow
  
                                \left(\begin{array}{*{4}{c}}
                                1 & 0 & 0 & 0 \\
                                2 & 1 & 0 & 0 \\
                                3 & 4 & 1 & 0 \\
                                x & x & x & 1 \\
                                \end{array}\right)
                                \f]
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  void StrictlyLowerMatrix<MT,SO,true>::resize( size_t n, bool preserve )
  {
     BLAZE_CONSTRAINT_MUST_BE_RESIZABLE_TYPE( MT );
  
     UNUSED_PARAMETER( preserve );
  
     BLAZE_INTERNAL_ASSERT( isSquare( matrix_ ), "Non-square strictly lower matrix detected" );
  
     const size_t oldsize( matrix_.rows() );
  
     matrix_.resize( n, n, true );
  
     if( n > oldsize )
     {
        const size_t increment( n - oldsize );
        submatrix( matrix_, 0UL, oldsize, n, increment ).reset();
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Extending the size of the matrix.
  //
  // \param n Number of additional rows and columns.
  // \param preserve \a true if the old values of the matrix should be preserved, \a false if not.
  // \return void
  //
  // This function increases the matrix size by \a n rows and \a n columns. During this operation,
  // new dynamic memory may be allocated in case the capacity of the matrix is too small. Therefore
  // this function potentially changes all matrix elements. In order to preserve the old matrix
  // values, the \a preserve flag can be set to \a true. The new elements are default initialized.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline void StrictlyLowerMatrix<MT,SO,true>::extend( size_t n, bool preserve )
  {
     BLAZE_CONSTRAINT_MUST_BE_RESIZABLE_TYPE( MT );
  
     UNUSED_PARAMETER( preserve );
  
     resize( rows() + n, true );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Setting the minimum capacity of the matrix.
  //
  // \param elements The new minimum capacity of the strictly lower matrix.
  // \return void
  //
  // This function increases the capacity of the strictly lower matrix to at least \a elements
  // elements. The current values of the matrix elements are preserved.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline void StrictlyLowerMatrix<MT,SO,true>::reserve( size_t elements )
  {
     matrix_.reserve( elements );
  }
  /*! \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 dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline void StrictlyLowerMatrix<MT,SO,true>::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 dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline void StrictlyLowerMatrix<MT,SO,true>::swap( StrictlyLowerMatrix& m ) noexcept
  {
     using std::swap;
  
     swap( matrix_, m.matrix_ );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns the maximum number of non-zero values for a strictly lower triangular matrix.
  //
  // \return The maximum number of non-zero values.
  //
  // This function returns the maximum possible number of non-zero values for a strictly lower
  // triangular matrix with fixed-size adapted matrix of type \a MT. Note that this function
  // can only be called in case the adapted dense matrix is a fixed-size matrix (as for instance
  // StaticMatrix). The attempt to call this function in case the adapted matrix is resizable
  // matrix will result in a compile time error.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline constexpr size_t StrictlyLowerMatrix<MT,SO,true>::maxNonZeros() noexcept
  {
     BLAZE_CONSTRAINT_MUST_BE_STATIC_TYPE( MT );
  
     return maxNonZeros( Size_v<MT,0UL> );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns the maximum number of non-zero values for a strictly lower triangular matrix.
  //
  // \param n The number of rows and columns of the matrix.
  // \return The maximum number of non-zero values.
  //
  // This function returns the maximum possible number of non-zero values for a strictly lower
  // triangular matrix of the given number of rows and columns.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline constexpr size_t StrictlyLowerMatrix<MT,SO,true>::maxNonZeros( size_t n ) noexcept
  {
     return ( ( n - 1UL ) * n ) / 2UL;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  NUMERIC FUNCTIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \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::StrictlyLowerMatrix< blaze::DynamicMatrix<int> > 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 dense matrix
          , bool SO >         // Storage order of the adapted dense matrix
  template< typename Other >  // Data type of the scalar value
  inline StrictlyLowerMatrix<MT,SO,true>&
     StrictlyLowerMatrix<MT,SO,true>::scale( const Other& scalar )
  {
     matrix_.scale( scalar );
     return *this;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  DEBUGGING FUNCTIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns whether the invariants of the strictly lower matrix are intact.
  //
  // \return \a true in case the strictly lower matrix's invariants are intact, \a false otherwise.
  //
  // This function checks whether the invariants of the strictly lower 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 StrictlyLowerMatrix<MT,SO,true>::isIntact() const noexcept
  {
     using blaze::isIntact;
  
     return ( isIntact( matrix_ ) && isStrictlyLower( 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 dense matrix
          , bool SO >         // Storage order of the adapted dense matrix
  template< typename Other >  // Data type of the foreign expression
  inline bool StrictlyLowerMatrix<MT,SO,true>::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 dense matrix
          , bool SO >         // Storage order of the adapted dense matrix
  template< typename Other >  // Data type of the foreign expression
  inline bool StrictlyLowerMatrix<MT,SO,true>::isAliased( const Other* alias ) const noexcept
  {
     return matrix_.isAliased( alias );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Returns whether the matrix is properly aligned in memory.
  //
  // \return \a true in case the matrix is aligned, \a false if not.
  //
  // This function returns whether the matrix is guaranteed to be properly aligned in memory, i.e.
  // whether the beginning and the end of each row/column of the matrix are guaranteed to conform
  // to the alignment restrictions of the element type \a Type.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline bool StrictlyLowerMatrix<MT,SO,true>::isAligned() const noexcept
  {
     return matrix_.isAligned();
  }
  /*! \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 dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline bool StrictlyLowerMatrix<MT,SO,true>::canSMPAssign() const noexcept
  {
     return matrix_.canSMPAssign();
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Load of a SIMD element of the matrix.
  //
  // \param i Access index for the row. The index has to be in the range [0..M-1].
  // \param j Access index for the column. The index has to be in the range [0..N-1].
  // \return The loaded SIMD element.
  //
  // This function performs a load of a specific SIMD element of the strictly lower matrix.
  // The row index must be smaller than the number of rows and the column index must be smaller
  // than the number of columns. Additionally, the column index (in case of a row-major matrix)
  // or the row index (in case of a column-major matrix) must be a multiple of the number of
  // values inside the SIMD element. 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.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  BLAZE_ALWAYS_INLINE typename StrictlyLowerMatrix<MT,SO,true>::SIMDType
     StrictlyLowerMatrix<MT,SO,true>::load( size_t i, size_t j ) const noexcept
  {
     return matrix_.load( i, j );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Aligned load of a SIMD element of the matrix.
  //
  // \param i Access index for the row. The index has to be in the range [0..M-1].
  // \param j Access index for the column. The index has to be in the range [0..N-1].
  // \return The loaded SIMD element.
  //
  // This function performs an aligned load of a specific SIMD element of the strictly lower
  // matrix. The row index must be smaller than the number of rows and the column index must be
  // smaller than the number of columns. Additionally, the column index (in case of a row-major
  // matrix) or the row index (in case of a column-major matrix) must be a multiple of the number
  // of values inside the SIMD element. 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.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  BLAZE_ALWAYS_INLINE typename StrictlyLowerMatrix<MT,SO,true>::SIMDType
     StrictlyLowerMatrix<MT,SO,true>::loada( size_t i, size_t j ) const noexcept
  {
     return matrix_.loada( i, j );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Unaligned load of a SIMD element of the matrix.
  //
  // \param i Access index for the row. The index has to be in the range [0..M-1].
  // \param j Access index for the column. The index has to be in the range [0..N-1].
  // \return The loaded SIMD element.
  //
  // This function performs an unaligned load of a specific SIMD element of the strictly lower
  // matrix. The row index must be smaller than the number of rows and the column index must be
  // smaller than the number of columns. Additionally, the column index (in case of a row-major
  // matrix) or the row index (in case of a column-major matrix) must be a multiple of the number
  // of values inside the SIMD element. 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.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  BLAZE_ALWAYS_INLINE typename StrictlyLowerMatrix<MT,SO,true>::SIMDType
     StrictlyLowerMatrix<MT,SO,true>::loadu( size_t i, size_t j ) const noexcept
  {
     return matrix_.loadu( i, j );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  CONSTRUCTION FUNCTIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Constructing a resizable matrix of size \f$ n \times n \f$.
  //
  // \param n The number of rows and columns of the matrix.
  // \return The newly constructed matrix.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline const MT StrictlyLowerMatrix<MT,SO,true>::construct( size_t n, TrueType )
  {
     BLAZE_CONSTRAINT_MUST_BE_RESIZABLE_TYPE( MT );
  
     return MT( n, n, ElementType() );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Constructing a fixed-size matrix with homogeneously initialized lower elements.
  //
  // \param init The initial value of the lower matrix elements.
  // \return The newly constructed matrix.
  */
  template< typename MT  // Type of the adapted dense matrix
          , bool SO >    // Storage order of the adapted dense matrix
  inline const MT StrictlyLowerMatrix<MT,SO,true>::construct( const ElementType& init, FalseType )
  {
     BLAZE_CONSTRAINT_MUST_NOT_BE_RESIZABLE_TYPE( MT );
     BLAZE_CONSTRAINT_MUST_BE_SQUARE_MATRIX_TYPE( MT );
  
     MT tmp;
  
     if( SO ) {
        for( size_t j=0UL; j<tmp.columns(); ++j ) {
           for( size_t i=j+1UL; i<tmp.rows(); ++i )
              tmp(i,j) = init;
        }
     }
     else {
        for( size_t i=0UL; i<tmp.rows(); ++i ) {
           for( size_t j=0UL; j<i; ++j )
              tmp(i,j) = init;
        }
     }
  
     return tmp;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Constructing a matrix as a copy from another matrix.
  //
  // \param m Matrix to be copied.
  // \exception std::invalid_argument Invalid setup of strictly lower matrix.
  // \return The newly constructed matrix.
  //
  // In case the given matrix is not a strictly lower matrix, a \a std::invalid_argument exception
  // is thrown.
  */
  template< typename MT   // Type of the adapted dense matrix
          , bool SO >     // Storage order of the adapted dense matrix
  template< typename MT2  // Type of the foreign matrix
          , bool SO2      // Storage order of the foreign matrix
          , typename T >  // Type of the third argument
  inline const MT StrictlyLowerMatrix<MT,SO,true>::construct( const Matrix<MT2,SO2>& m, T )
  {
     const MT tmp( ~m );
  
     if( IsUniTriangular_v<MT2> ||
         ( !IsStrictlyLower_v<MT2> && !isStrictlyLower( tmp ) ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid setup of strictly lower matrix" );
     }
  
     return tmp;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  