text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
  //
  // This Source Code Form is subject to the terms of the Mozilla
  // Public License v. 2.0. If a copy of the MPL was not distributed
  // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  
  #ifndef EIGEN_DENSECOEFFSBASE_H
  #define EIGEN_DENSECOEFFSBASE_H
  
  namespace Eigen {
  
  namespace internal {
  template<typename T> struct add_const_on_value_type_if_arithmetic
  {
    typedef typename conditional<is_arithmetic<T>::value, T, typename add_const_on_value_type<T>::type>::type type;
  };
  }
  
  /** \brief Base class providing read-only coefficient access to matrices and arrays.
    * \ingroup Core_Module
    * \tparam Derived Type of the derived class
    * \tparam #ReadOnlyAccessors Constant indicating read-only access
    *
    * This class defines the \c operator() \c const function and friends, which can be used to read specific
    * entries of a matrix or array.
    * 
    * \sa DenseCoeffsBase<Derived, WriteAccessors>, DenseCoeffsBase<Derived, DirectAccessors>,
    *     \ref TopicClassHierarchy
    */
  template<typename Derived>
  class DenseCoeffsBase<Derived,ReadOnlyAccessors> : public EigenBase<Derived>
  {
    public:
      typedef typename internal::traits<Derived>::StorageKind StorageKind;
      typedef typename internal::traits<Derived>::Index Index;
      typedef typename internal::traits<Derived>::Scalar Scalar;
      typedef typename internal::packet_traits<Scalar>::type PacketScalar;
  
      // Explanation for this CoeffReturnType typedef.
      // - This is the return type of the coeff() method.
      // - The LvalueBit means exactly that we can offer a coeffRef() method, which means exactly that we can get references
      // to coeffs, which means exactly that we can have coeff() return a const reference (as opposed to returning a value).
      // - The is_artihmetic check is required since "const int", "const double", etc. will cause warnings on some systems
      // while the declaration of "const T", where T is a non arithmetic type does not. Always returning "const Scalar&" is
      // not possible, since the underlying expressions might not offer a valid address the reference could be referring to.
      typedef typename internal::conditional<bool(internal::traits<Derived>::Flags&LvalueBit),
                           const Scalar&,
                           typename internal::conditional<internal::is_arithmetic<Scalar>::value, Scalar, const Scalar>::type
                       >::type CoeffReturnType;
  
      typedef typename internal::add_const_on_value_type_if_arithmetic<
                           typename internal::packet_traits<Scalar>::type
                       >::type PacketReturnType;
  
      typedef EigenBase<Derived> Base;
      using Base::rows;
      using Base::cols;
      using Base::size;
      using Base::derived;
  
      EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner) const
      {
        return int(Derived::RowsAtCompileTime) == 1 ? 0
            : int(Derived::ColsAtCompileTime) == 1 ? inner
            : int(Derived::Flags)&RowMajorBit ? outer
            : inner;
      }
  
      EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner) const
      {
        return int(Derived::ColsAtCompileTime) == 1 ? 0
            : int(Derived::RowsAtCompileTime) == 1 ? inner
            : int(Derived::Flags)&RowMajorBit ? inner
            : outer;
      }
  
      /** Short version: don't use this function, use
        * \link operator()(Index,Index) const \endlink instead.
        *
        * Long version: this function is similar to
        * \link operator()(Index,Index) const \endlink, but without the assertion.
        * Use this for limiting the performance cost of debugging code when doing
        * repeated coefficient access. Only use this when it is guaranteed that the
        * parameters \a row and \a col are in range.
        *
        * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
        * function equivalent to \link operator()(Index,Index) const \endlink.
        *
        * \sa operator()(Index,Index) const, coeffRef(Index,Index), coeff(Index) const
        */
      EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const
      {
        eigen_internal_assert(row >= 0 && row < rows()
                          && col >= 0 && col < cols());
        return derived().coeff(row, col);
      }
  
      EIGEN_STRONG_INLINE CoeffReturnType coeffByOuterInner(Index outer, Index inner) const
      {
        return coeff(rowIndexByOuterInner(outer, inner),
                     colIndexByOuterInner(outer, inner));
      }
  
      /** \returns the coefficient at given the given row and column.
        *
        * \sa operator()(Index,Index), operator[](Index)
        */
      EIGEN_STRONG_INLINE CoeffReturnType operator()(Index row, Index col) const
      {
        eigen_assert(row >= 0 && row < rows()
            && col >= 0 && col < cols());
        return derived().coeff(row, col);
      }
  
      /** Short version: don't use this function, use
        * \link operator[](Index) const \endlink instead.
        *
        * Long version: this function is similar to
        * \link operator[](Index) const \endlink, but without the assertion.
        * Use this for limiting the performance cost of debugging code when doing
        * repeated coefficient access. Only use this when it is guaranteed that the
        * parameter \a index is in range.
        *
        * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
        * function equivalent to \link operator[](Index) const \endlink.
        *
        * \sa operator[](Index) const, coeffRef(Index), coeff(Index,Index) const
        */
  
      EIGEN_STRONG_INLINE CoeffReturnType
      coeff(Index index) const
      {
        eigen_internal_assert(index >= 0 && index < size());
        return derived().coeff(index);
      }
  
  
      /** \returns the coefficient at given index.
        *
        * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
        *
        * \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
        * z() const, w() const
        */
  
      EIGEN_STRONG_INLINE CoeffReturnType
      operator[](Index index) const
      {
        #ifndef EIGEN2_SUPPORT
        EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
                            THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
        #endif
        eigen_assert(index >= 0 && index < size());
        return derived().coeff(index);
      }
  
      /** \returns the coefficient at given index.
        *
        * This is synonymous to operator[](Index) const.
        *
        * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
        *
        * \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
        * z() const, w() const
        */
  
      EIGEN_STRONG_INLINE CoeffReturnType
      operator()(Index index) const
      {
        eigen_assert(index >= 0 && index < size());
        return derived().coeff(index);
      }
  
      /** equivalent to operator[](0).  */
  
      EIGEN_STRONG_INLINE CoeffReturnType
      x() const { return (*this)[0]; }
  
      /** equivalent to operator[](1).  */
  
      EIGEN_STRONG_INLINE CoeffReturnType
      y() const { return (*this)[1]; }
  
      /** equivalent to operator[](2).  */
  
      EIGEN_STRONG_INLINE CoeffReturnType
      z() const { return (*this)[2]; }
  
      /** equivalent to operator[](3).  */
  
      EIGEN_STRONG_INLINE CoeffReturnType
      w() const { return (*this)[3]; }
  
      /** \internal
        * \returns the packet of coefficients starting at the given row and column. It is your responsibility
        * to ensure that a packet really starts there. This method is only available on expressions having the
        * PacketAccessBit.
        *
        * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
        * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
        * starting at an address which is a multiple of the packet size.
        */
  
      template<int LoadMode>
      EIGEN_STRONG_INLINE PacketReturnType packet(Index row, Index col) const
      {
        eigen_internal_assert(row >= 0 && row < rows()
                        && col >= 0 && col < cols());
        return derived().template packet<LoadMode>(row,col);
      }
  
  
      /** \internal */
      template<int LoadMode>
      EIGEN_STRONG_INLINE PacketReturnType packetByOuterInner(Index outer, Index inner) const
      {
        return packet<LoadMode>(rowIndexByOuterInner(outer, inner),
                                colIndexByOuterInner(outer, inner));
      }
  
      /** \internal
        * \returns the packet of coefficients starting at the given index. It is your responsibility
        * to ensure that a packet really starts there. This method is only available on expressions having the
        * PacketAccessBit and the LinearAccessBit.
        *
        * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
        * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
        * starting at an address which is a multiple of the packet size.
        */
  
      template<int LoadMode>
      EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
      {
        eigen_internal_assert(index >= 0 && index < size());
        return derived().template packet<LoadMode>(index);
      }
  
    protected:
      // explanation: DenseBase is doing "using ..." on the methods from DenseCoeffsBase.
      // But some methods are only available in the DirectAccess case.
      // So we add dummy methods here with these names, so that "using... " doesn't fail.
      // It's not private so that the child class DenseBase can access them, and it's not public
      // either since it's an implementation detail, so has to be protected.
      void coeffRef();
      void coeffRefByOuterInner();
      void writePacket();
      void writePacketByOuterInner();
      void copyCoeff();
      void copyCoeffByOuterInner();
      void copyPacket();
      void copyPacketByOuterInner();
      void stride();
      void innerStride();
      void outerStride();
      void rowStride();
      void colStride();
  };
  
  /** \brief Base class providing read/write coefficient access to matrices and arrays.
    * \ingroup Core_Module
    * \tparam Derived Type of the derived class
    * \tparam #WriteAccessors Constant indicating read/write access
    *
    * This class defines the non-const \c operator() function and friends, which can be used to write specific
    * entries of a matrix or array. This class inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which
    * defines the const variant for reading specific entries.
    * 
    * \sa DenseCoeffsBase<Derived, DirectAccessors>, \ref TopicClassHierarchy
    */
  template<typename Derived>
  class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
  {
    public:
  
      typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
  
      typedef typename internal::traits<Derived>::StorageKind StorageKind;
      typedef typename internal::traits<Derived>::Index Index;
      typedef typename internal::traits<Derived>::Scalar Scalar;
      typedef typename internal::packet_traits<Scalar>::type PacketScalar;
      typedef typename NumTraits<Scalar>::Real RealScalar;
  
      using Base::coeff;
      using Base::rows;
      using Base::cols;
      using Base::size;
      using Base::derived;
      using Base::rowIndexByOuterInner;
      using Base::colIndexByOuterInner;
      using Base::operator[];
      using Base::operator();
      using Base::x;
      using Base::y;
      using Base::z;
      using Base::w;
  
      /** Short version: don't use this function, use
        * \link operator()(Index,Index) \endlink instead.
        *
        * Long version: this function is similar to
        * \link operator()(Index,Index) \endlink, but without the assertion.
        * Use this for limiting the performance cost of debugging code when doing
        * repeated coefficient access. Only use this when it is guaranteed that the
        * parameters \a row and \a col are in range.
        *
        * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
        * function equivalent to \link operator()(Index,Index) \endlink.
        *
        * \sa operator()(Index,Index), coeff(Index, Index) const, coeffRef(Index)
        */
      EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)
      {
        eigen_internal_assert(row >= 0 && row < rows()
                          && col >= 0 && col < cols());
        return derived().coeffRef(row, col);
      }
  
      EIGEN_STRONG_INLINE Scalar&
      coeffRefByOuterInner(Index outer, Index inner)
      {
        return coeffRef(rowIndexByOuterInner(outer, inner),
                        colIndexByOuterInner(outer, inner));
      }
  
      /** \returns a reference to the coefficient at given the given row and column.
        *
        * \sa operator[](Index)
        */
  
      EIGEN_STRONG_INLINE Scalar&
      operator()(Index row, Index col)
      {
        eigen_assert(row >= 0 && row < rows()
            && col >= 0 && col < cols());
        return derived().coeffRef(row, col);
      }
  
  
      /** Short version: don't use this function, use
        * \link operator[](Index) \endlink instead.
        *
        * Long version: this function is similar to
        * \link operator[](Index) \endlink, but without the assertion.
        * Use this for limiting the performance cost of debugging code when doing
        * repeated coefficient access. Only use this when it is guaranteed that the
        * parameters \a row and \a col are in range.
        *
        * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
        * function equivalent to \link operator[](Index) \endlink.
        *
        * \sa operator[](Index), coeff(Index) const, coeffRef(Index,Index)
        */
  
      EIGEN_STRONG_INLINE Scalar&
      coeffRef(Index index)
      {
        eigen_internal_assert(index >= 0 && index < size());
        return derived().coeffRef(index);
      }
  
      /** \returns a reference to the coefficient at given index.
        *
        * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
        *
        * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
        */
  
      EIGEN_STRONG_INLINE Scalar&
      operator[](Index index)
      {
        #ifndef EIGEN2_SUPPORT
        EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
                            THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
        #endif
        eigen_assert(index >= 0 && index < size());
        return derived().coeffRef(index);
      }
  
      /** \returns a reference to the coefficient at given index.
        *
        * This is synonymous to operator[](Index).
        *
        * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
        *
        * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
        */
  
      EIGEN_STRONG_INLINE Scalar&
      operator()(Index index)
      {
        eigen_assert(index >= 0 && index < size());
        return derived().coeffRef(index);
      }
  
      /** equivalent to operator[](0).  */
  
      EIGEN_STRONG_INLINE Scalar&
      x() { return (*this)[0]; }
  
      /** equivalent to operator[](1).  */
  
      EIGEN_STRONG_INLINE Scalar&
      y() { return (*this)[1]; }
  
      /** equivalent to operator[](2).  */
  
      EIGEN_STRONG_INLINE Scalar&
      z() { return (*this)[2]; }
  
      /** equivalent to operator[](3).  */
  
      EIGEN_STRONG_INLINE Scalar&
      w() { return (*this)[3]; }
  
      /** \internal
        * Stores the given packet of coefficients, at the given row and column of this expression. It is your responsibility
        * to ensure that a packet really starts there. This method is only available on expressions having the
        * PacketAccessBit.
        *
        * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
        * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
        * starting at an address which is a multiple of the packet size.
        */
  
      template<int StoreMode>
      EIGEN_STRONG_INLINE void writePacket
      (Index row, Index col, const typename internal::packet_traits<Scalar>::type& val)
      {
        eigen_internal_assert(row >= 0 && row < rows()
                          && col >= 0 && col < cols());
        derived().template writePacket<StoreMode>(row,col,val);
      }
  
  
      /** \internal */
      template<int StoreMode>
      EIGEN_STRONG_INLINE void writePacketByOuterInner
      (Index outer, Index inner, const typename internal::packet_traits<Scalar>::type& val)
      {
        writePacket<StoreMode>(rowIndexByOuterInner(outer, inner),
                              colIndexByOuterInner(outer, inner),
                              val);
      }
  
      /** \internal
        * Stores the given packet of coefficients, at the given index in this expression. It is your responsibility
        * to ensure that a packet really starts there. This method is only available on expressions having the
        * PacketAccessBit and the LinearAccessBit.
        *
        * The \a LoadMode parameter may have the value \a Aligned or \a Unaligned. Its effect is to select
        * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
        * starting at an address which is a multiple of the packet size.
        */
      template<int StoreMode>
      EIGEN_STRONG_INLINE void writePacket
      (Index index, const typename internal::packet_traits<Scalar>::type& val)
      {
        eigen_internal_assert(index >= 0 && index < size());
        derived().template writePacket<StoreMode>(index,val);
      }
  
  #ifndef EIGEN_PARSED_BY_DOXYGEN
  
      /** \internal Copies the coefficient at position (row,col) of other into *this.
        *
        * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
        * with usual assignments.
        *
        * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
        */
  
      template<typename OtherDerived>
      EIGEN_STRONG_INLINE void copyCoeff(Index row, Index col, const DenseBase<OtherDerived>& other)
      {
        eigen_internal_assert(row >= 0 && row < rows()
                          && col >= 0 && col < cols());
        derived().coeffRef(row, col) = other.derived().coeff(row, col);
      }
  
      /** \internal Copies the coefficient at the given index of other into *this.
        *
        * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
        * with usual assignments.
        *
        * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
        */
  
      template<typename OtherDerived>
      EIGEN_STRONG_INLINE void copyCoeff(Index index, const DenseBase<OtherDerived>& other)
      {
        eigen_internal_assert(index >= 0 && index < size());
        derived().coeffRef(index) = other.derived().coeff(index);
      }
  
  
      template<typename OtherDerived>
      EIGEN_STRONG_INLINE void copyCoeffByOuterInner(Index outer, Index inner, const DenseBase<OtherDerived>& other)
      {
        const Index row = rowIndexByOuterInner(outer,inner);
        const Index col = colIndexByOuterInner(outer,inner);
        // derived() is important here: copyCoeff() may be reimplemented in Derived!
        derived().copyCoeff(row, col, other);
      }
  
      /** \internal Copies the packet at position (row,col) of other into *this.
        *
        * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
        * with usual assignments.
        *
        * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
        */
  
      template<typename OtherDerived, int StoreMode, int LoadMode>
      EIGEN_STRONG_INLINE void copyPacket(Index row, Index col, const DenseBase<OtherDerived>& other)
      {
        eigen_internal_assert(row >= 0 && row < rows()
                          && col >= 0 && col < cols());
        derived().template writePacket<StoreMode>(row, col,
          other.derived().template packet<LoadMode>(row, col));
      }
  
      /** \internal Copies the packet at the given index of other into *this.
        *
        * This method is overridden in SwapWrapper, allowing swap() assignments to share 99% of their code
        * with usual assignments.
        *
        * Outside of this internal usage, this method has probably no usefulness. It is hidden in the public API dox.
        */
  
      template<typename OtherDerived, int StoreMode, int LoadMode>
      EIGEN_STRONG_INLINE void copyPacket(Index index, const DenseBase<OtherDerived>& other)
      {
        eigen_internal_assert(index >= 0 && index < size());
        derived().template writePacket<StoreMode>(index,
          other.derived().template packet<LoadMode>(index));
      }
  
      /** \internal */
      template<typename OtherDerived, int StoreMode, int LoadMode>
      EIGEN_STRONG_INLINE void copyPacketByOuterInner(Index outer, Index inner, const DenseBase<OtherDerived>& other)
      {
        const Index row = rowIndexByOuterInner(outer,inner);
        const Index col = colIndexByOuterInner(outer,inner);
        // derived() is important here: copyCoeff() may be reimplemented in Derived!
        derived().template copyPacket< OtherDerived, StoreMode, LoadMode>(row, col, other);
      }
  #endif
  
  };
  
  /** \brief Base class providing direct read-only coefficient access to matrices and arrays.
    * \ingroup Core_Module
    * \tparam Derived Type of the derived class
    * \tparam #DirectAccessors Constant indicating direct access
    *
    * This class defines functions to work with strides which can be used to access entries directly. This class
    * inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which defines functions to access entries read-only using
    * \c operator() .
    *
    * \sa \ref TopicClassHierarchy
    */
  template<typename Derived>
  class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
  {
    public:
  
      typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
      typedef typename internal::traits<Derived>::Index Index;
      typedef typename internal::traits<Derived>::Scalar Scalar;
      typedef typename NumTraits<Scalar>::Real RealScalar;
  
      using Base::rows;
      using Base::cols;
      using Base::size;
      using Base::derived;
  
      /** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
        *
        * \sa outerStride(), rowStride(), colStride()
        */
      inline Index innerStride() const
      {
        return derived().innerStride();
      }
  
      /** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
        *          in a column-major matrix).
        *
        * \sa innerStride(), rowStride(), colStride()
        */
      inline Index outerStride() const
      {
        return derived().outerStride();
      }
  
      // FIXME shall we remove it ?
      inline Index stride() const
      {
        return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
      }
  
      /** \returns the pointer increment between two consecutive rows.
        *
        * \sa innerStride(), outerStride(), colStride()
        */
      inline Index rowStride() const
      {
        return Derived::IsRowMajor ? outerStride() : innerStride();
      }
  
      /** \returns the pointer increment between two consecutive columns.
        *
        * \sa innerStride(), outerStride(), rowStride()
        */
      inline Index colStride() const
      {
        return Derived::IsRowMajor ? innerStride() : outerStride();
      }
  };
  
  /** \brief Base class providing direct read/write coefficient access to matrices and arrays.
    * \ingroup Core_Module
    * \tparam Derived Type of the derived class
    * \tparam #DirectWriteAccessors Constant indicating direct access
    *
    * This class defines functions to work with strides which can be used to access entries directly. This class
    * inherits DenseCoeffsBase<Derived, WriteAccessors> which defines functions to access entries read/write using
    * \c operator().
    *
    * \sa \ref TopicClassHierarchy
    */
  template<typename Derived>
  class DenseCoeffsBase<Derived, DirectWriteAccessors>
    : public DenseCoeffsBase<Derived, WriteAccessors>
  {
    public:
  
      typedef DenseCoeffsBase<Derived, WriteAccessors> Base;
      typedef typename internal::traits<Derived>::Index Index;
      typedef typename internal::traits<Derived>::Scalar Scalar;
      typedef typename NumTraits<Scalar>::Real RealScalar;
  
      using Base::rows;
      using Base::cols;
      using Base::size;
      using Base::derived;
  
      /** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
        *
        * \sa outerStride(), rowStride(), colStride()
        */
      inline Index innerStride() const
      {
        return derived().innerStride();
      }
  
      /** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
        *          in a column-major matrix).
        *
        * \sa innerStride(), rowStride(), colStride()
        */
      inline Index outerStride() const
      {
        return derived().outerStride();
      }
  
      // FIXME shall we remove it ?
      inline Index stride() const
      {
        return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
      }
  
      /** \returns the pointer increment between two consecutive rows.
        *
        * \sa innerStride(), outerStride(), colStride()
        */
      inline Index rowStride() const
      {
        return Derived::IsRowMajor ? outerStride() : innerStride();
      }
  
      /** \returns the pointer increment between two consecutive columns.
        *
        * \sa innerStride(), outerStride(), rowStride()
        */
      inline Index colStride() const
      {
        return Derived::IsRowMajor ? innerStride() : outerStride();
      }
  };
  
  namespace internal {
  
  template<typename Derived, bool JustReturnZero>
  struct first_aligned_impl
  {
    static inline typename Derived::Index run(const Derived&)
    { return 0; }
  };
  
  template<typename Derived>
  struct first_aligned_impl<Derived, false>
  {
    static inline typename Derived::Index run(const Derived& m)
    {
      return internal::first_aligned(&m.const_cast_derived().coeffRef(0,0), m.size());
    }
  };
  
  /** \internal \returns the index of the first element of the array that is well aligned for vectorization.
    *
    * There is also the variant first_aligned(const Scalar*, Integer) defined in Memory.h. See it for more
    * documentation.
    */
  template<typename Derived>
  static inline typename Derived::Index first_aligned(const Derived& m)
  {
    return first_aligned_impl
            <Derived, (Derived::Flags & AlignedBit) || !(Derived::Flags & DirectAccessBit)>
            ::run(m);
  }
  
  template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
  struct inner_stride_at_compile_time
  {
    enum { ret = traits<Derived>::InnerStrideAtCompileTime };
  };
  
  template<typename Derived>
  struct inner_stride_at_compile_time<Derived, false>
  {
    enum { ret = 0 };
  };
  
  template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
  struct outer_stride_at_compile_time
  {
    enum { ret = traits<Derived>::OuterStrideAtCompileTime };
  };
  
  template<typename Derived>
  struct outer_stride_at_compile_time<Derived, false>
  {
    enum { ret = 0 };
  };
  
  } // end namespace internal
  
  } // end namespace Eigen
  
  #endif // EIGEN_DENSECOEFFSBASE_H
  