diff --git a/Eigen/src/Core/Assign.h b/Eigen/src/Core/Assign.h
index 96451a9e7..017331ccb 100644
--- a/Eigen/src/Core/Assign.h
+++ b/Eigen/src/Core/Assign.h
@@ -499,7 +499,8 @@ EIGEN_STRONG_INLINE Derived& DenseBase<Derived>
   enum{
     SameType = internal::is_same<typename Derived::Scalar,typename OtherDerived::Scalar>::value
   };
-  
+
+  EIGEN_STATIC_ASSERT_LVALUE(Derived)
   EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
   EIGEN_STATIC_ASSERT(SameType,YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
 
diff --git a/Eigen/src/Core/DenseBase.h b/Eigen/src/Core/DenseBase.h
index bdd1291cf..1d7ceb9a0 100644
--- a/Eigen/src/Core/DenseBase.h
+++ b/Eigen/src/Core/DenseBase.h
@@ -501,8 +501,6 @@ template<typename Derived> class DenseBase
        * Only do it when debugging Eigen, as this borders on paranoiac and could slow compilation down
        */
 #ifdef EIGEN_INTERNAL_DEBUGGING
-      EIGEN_STATIC_ASSERT(internal::are_flags_consistent<Flags>::ret,
-                          INVALID_MATRIXBASE_TEMPLATE_PARAMETERS)
       EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, int(IsRowMajor))
                         && EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, int(!IsRowMajor))),
                           INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION)
diff --git a/Eigen/src/Core/DenseCoeffsBase.h b/Eigen/src/Core/DenseCoeffsBase.h
index 13c93c392..ddc834304 100644
--- a/Eigen/src/Core/DenseCoeffsBase.h
+++ b/Eigen/src/Core/DenseCoeffsBase.h
@@ -554,19 +554,90 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
 
 };
 
-/** \brief Base class providing direct coefficient access to matrices and arrays.
+/** \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, WriteAccessors> which defines functions to access entries using 
+  * 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, WriteAccessors>
+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 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, 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:
 
diff --git a/Eigen/src/Core/Map.h b/Eigen/src/Core/Map.h
index d163e371a..0321f6669 100644
--- a/Eigen/src/Core/Map.h
+++ b/Eigen/src/Core/Map.h
@@ -80,8 +80,9 @@
 namespace internal {
 template<typename PlainObjectType, int MapOptions, typename StrideType>
 struct traits<Map<PlainObjectType, MapOptions, StrideType> >
-  : public traits<PlainObjectType>
+  : public traits<typename internal::remove_const<PlainObjectType>::type>
 {
+  typedef traits<typename internal::remove_const<PlainObjectType>::type> TraitsBase;
   typedef typename PlainObjectType::Index Index;
   typedef typename PlainObjectType::Scalar Scalar;
   enum {
@@ -101,13 +102,15 @@ struct traits<Map<PlainObjectType, MapOptions, StrideType> >
                            || HasNoOuterStride
                            || ( OuterStrideAtCompileTime!=Dynamic
                            && ((static_cast<int>(sizeof(Scalar))*OuterStrideAtCompileTime)%16)==0 ) ),
-    Flags0 = traits<PlainObjectType>::Flags,
+    Flags0 = TraitsBase::Flags,
     Flags1 = IsAligned ? (int(Flags0) | AlignedBit) : (int(Flags0) & ~AlignedBit),
-    Flags2 = HasNoStride ? int(Flags1) : int(Flags1 & ~LinearAccessBit),
-    Flags = KeepsPacketAccess ? int(Flags2) : (int(Flags2) & ~PacketAccessBit)
+    Flags2 = (bool(HasNoStride) || bool(PlainObjectType::IsVectorAtCompileTime))
+           ? int(Flags1) : int(Flags1 & ~LinearAccessBit),
+    Flags3 = internal::is_const<PlainObjectType>::value ? (int(Flags2) & ~LvalueBit) : int(Flags2),
+    Flags = KeepsPacketAccess ? int(Flags3) : (int(Flags3) & ~PacketAccessBit)
   };
 private:
-  enum { Options }; // Expressions don't support Options
+  enum { Options }; // Expressions don't have Options
 };
 }
 
@@ -120,6 +123,9 @@ template<typename PlainObjectType, int MapOptions, typename StrideType> class Ma
 
     EIGEN_DENSE_PUBLIC_INTERFACE(Map)
 
+    typedef typename Base::PointerType PointerType;
+
+
     inline Index innerStride() const
     {
       return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
@@ -138,7 +144,7 @@ template<typename PlainObjectType, int MapOptions, typename StrideType> class Ma
       * \param data pointer to the array to map
       * \param stride optional Stride object, passing the strides.
       */
-    inline Map(const Scalar* data, const StrideType& stride = StrideType())
+    inline Map(PointerType data, const StrideType& stride = StrideType())
       : Base(data), m_stride(stride)
     {
       PlainObjectType::Base::_check_template_params();
@@ -150,7 +156,7 @@ template<typename PlainObjectType, int MapOptions, typename StrideType> class Ma
       * \param size the size of the vector expression
       * \param stride optional Stride object, passing the strides.
       */
-    inline Map(const Scalar* data, Index size, const StrideType& stride = StrideType())
+    inline Map(PointerType data, Index size, const StrideType& stride = StrideType())
       : Base(data, size), m_stride(stride)
     {
       PlainObjectType::Base::_check_template_params();
@@ -163,7 +169,7 @@ template<typename PlainObjectType, int MapOptions, typename StrideType> class Ma
       * \param cols the number of columns of the matrix expression
       * \param stride optional Stride object, passing the strides.
       */
-    inline Map(const Scalar* data, Index rows, Index cols, const StrideType& stride = StrideType())
+    inline Map(PointerType data, Index rows, Index cols, const StrideType& stride = StrideType())
       : Base(data, rows, cols), m_stride(stride)
     {
       PlainObjectType::Base::_check_template_params();
diff --git a/Eigen/src/Core/MapBase.h b/Eigen/src/Core/MapBase.h
index 5fab85ed7..435d9c09d 100644
--- a/Eigen/src/Core/MapBase.h
+++ b/Eigen/src/Core/MapBase.h
@@ -26,6 +26,11 @@
 #ifndef EIGEN_MAPBASE_H
 #define EIGEN_MAPBASE_H
 
+#define EIGEN_STATIC_ASSERT_LINEAR_ACCESS(Derived) \
+      EIGEN_STATIC_ASSERT(int(internal::traits<Derived>::Flags) & LinearAccessBit, \
+                          YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT)
+
+
 /** \class MapBase
   * \ingroup Core_Module
   *
@@ -33,7 +38,7 @@
   *
   * \sa class Map, class Block
   */
-template<typename Derived> class MapBase
+template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
   : public internal::dense_xpr_base<Derived>::type
 {
   public:
@@ -45,12 +50,16 @@ template<typename Derived> class MapBase
       SizeAtCompileTime = Base::SizeAtCompileTime
     };
 
-
     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;
+    typedef typename internal::conditional<
+                         int(internal::traits<Derived>::Flags) & LvalueBit,
+                         Scalar *,
+                         const Scalar *>::type
+                     PointerType;
 
     using Base::derived;
 //    using Base::RowsAtCompileTime;
@@ -63,10 +72,6 @@ template<typename Derived> class MapBase
     using Base::Flags;
     using Base::IsRowMajor;
 
-    using Base::CoeffReadCost;
-
-//    using Base::derived;
-    using Base::const_cast_derived;
     using Base::rows;
     using Base::cols;
     using Base::size;
@@ -74,11 +79,6 @@ template<typename Derived> class MapBase
     using Base::coeffRef;
     using Base::lazyAssign;
     using Base::eval;
-//    using Base::operator=;
-    using Base::operator+=;
-    using Base::operator-=;
-    using Base::operator*=;
-    using Base::operator/=;
 
     using Base::innerStride;
     using Base::outerStride;
@@ -98,28 +98,27 @@ template<typename Derived> class MapBase
       * \sa innerStride(), outerStride()
       */
     inline const Scalar* data() const { return m_data; }
-    inline Scalar* data() { return const_cast<Scalar*>(m_data); }
 
     inline const Scalar& coeff(Index row, Index col) const
     {
       return m_data[col * colStride() + row * rowStride()];
     }
 
-    inline Scalar& coeffRef(Index row, Index col)
-    {
-      return const_cast<Scalar*>(m_data)[col * colStride() + row * rowStride()];
-    }
-
     inline const Scalar& coeff(Index index) const
     {
-      eigen_assert(Derived::IsVectorAtCompileTime || (internal::traits<Derived>::Flags & LinearAccessBit));
+      EIGEN_STATIC_ASSERT_LINEAR_ACCESS(Derived)
       return m_data[index * innerStride()];
     }
 
-    inline Scalar& coeffRef(Index index)
+    inline const Scalar& coeffRef(Index row, Index col) const
     {
-      eigen_assert(Derived::IsVectorAtCompileTime || (internal::traits<Derived>::Flags & LinearAccessBit));
-      return const_cast<Scalar*>(m_data)[index * innerStride()];
+      return this->m_data[col * colStride() + row * rowStride()];
+    }
+
+    inline const Scalar& coeffRef(Index index) const
+    {
+      EIGEN_STATIC_ASSERT_LINEAR_ACCESS(Derived)
+      return this->m_data[index * innerStride()];
     }
 
     template<int LoadMode>
@@ -132,30 +131,17 @@ template<typename Derived> class MapBase
     template<int LoadMode>
     inline PacketScalar packet(Index index) const
     {
+      EIGEN_STATIC_ASSERT_LINEAR_ACCESS(Derived)
       return internal::ploadt<PacketScalar, LoadMode>(m_data + index * innerStride());
     }
 
-    template<int StoreMode>
-    inline void writePacket(Index row, Index col, const PacketScalar& x)
-    {
-      internal::pstoret<Scalar, PacketScalar, StoreMode>
-               (const_cast<Scalar*>(m_data) + (col * colStride() + row * rowStride()), x);
-    }
-
-    template<int StoreMode>
-    inline void writePacket(Index index, const PacketScalar& x)
-    {
-      internal::pstoret<Scalar, PacketScalar, StoreMode>
-        (const_cast<Scalar*>(m_data) + index * innerStride(), x);
-    }
-
-    inline MapBase(const Scalar* data) : m_data(data), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
+    inline MapBase(PointerType data) : m_data(data), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
     {
       EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
       checkSanity();
     }
 
-    inline MapBase(const Scalar* data, Index size)
+    inline MapBase(PointerType data, Index size)
             : m_data(data),
               m_rows(RowsAtCompileTime == Dynamic ? size : Index(RowsAtCompileTime)),
               m_cols(ColsAtCompileTime == Dynamic ? size : Index(ColsAtCompileTime))
@@ -166,7 +152,7 @@ template<typename Derived> class MapBase
       checkSanity();
     }
 
-    inline MapBase(const Scalar* data, Index rows, Index cols)
+    inline MapBase(PointerType data, Index rows, Index cols)
             : m_data(data), m_rows(rows), m_cols(cols)
     {
       eigen_assert( (data == 0)
@@ -175,14 +161,6 @@ template<typename Derived> class MapBase
       checkSanity();
     }
 
-    Derived& operator=(const MapBase& other)
-    {
-      Base::operator=(other);
-      return derived();
-    }
-
-    using Base::operator=;
-
   protected:
 
     void checkSanity() const
@@ -194,9 +172,76 @@ template<typename Derived> class MapBase
         && "data is not aligned");
     }
 
-    const Scalar* EIGEN_RESTRICT m_data;
+    PointerType EIGEN_RESTRICT m_data;
     const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
     const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
 };
 
+template<typename Derived> class MapBase<Derived, WriteAccessors>
+  : public MapBase<Derived, ReadOnlyAccessors>
+{
+  public:
+
+    typedef MapBase<Derived, ReadOnlyAccessors> Base;
+
+    typedef typename Base::Scalar Scalar;
+    typedef typename Base::PacketScalar PacketScalar;
+    typedef typename Base::Index Index;
+    typedef typename Base::PointerType PointerType;
+
+    using Base::derived;
+    using Base::rows;
+    using Base::cols;
+    using Base::size;
+    using Base::coeff;
+    using Base::coeffRef;
+
+    using Base::innerStride;
+    using Base::outerStride;
+    using Base::rowStride;
+    using Base::colStride;
+
+    inline const Scalar* data() const { return this->m_data; }
+    inline Scalar* data() { return this->m_data; } // no const-cast here so non-const-correct code will give a compile error
+
+    inline Scalar& coeffRef(Index row, Index col)
+    {
+      return this->m_data[col * colStride() + row * rowStride()];
+    }
+
+    inline Scalar& coeffRef(Index index)
+    {
+      EIGEN_STATIC_ASSERT_LINEAR_ACCESS(Derived)
+      return this->m_data[index * innerStride()];
+    }
+
+    template<int StoreMode>
+    inline void writePacket(Index row, Index col, const PacketScalar& x)
+    {
+      internal::pstoret<Scalar, PacketScalar, StoreMode>
+               (this->m_data + (col * colStride() + row * rowStride()), x);
+    }
+
+    template<int StoreMode>
+    inline void writePacket(Index index, const PacketScalar& x)
+    {
+      EIGEN_STATIC_ASSERT_LINEAR_ACCESS(Derived)
+      internal::pstoret<Scalar, PacketScalar, StoreMode>
+                (this->m_data + index * innerStride(), x);
+    }
+
+    inline MapBase(PointerType data) : Base(data) {}
+    inline MapBase(PointerType data, Index size) : Base(data, size) {}
+    inline MapBase(PointerType data, Index rows, Index cols) : Base(data, rows, cols) {}
+
+    Derived& operator=(const MapBase& other)
+    {
+      Base::Base::operator=(other);
+      return derived();
+    }
+
+    using Base::Base::operator=;
+};
+
+
 #endif // EIGEN_MAPBASE_H
diff --git a/Eigen/src/Core/PlainObjectBase.h b/Eigen/src/Core/PlainObjectBase.h
index 6bb42f1c9..4df262d16 100644
--- a/Eigen/src/Core/PlainObjectBase.h
+++ b/Eigen/src/Core/PlainObjectBase.h
@@ -66,10 +66,15 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
     using Base::IsVectorAtCompileTime;
     using Base::Flags;
 
+    typedef typename internal::add_const<Derived>::type ConstDerived;
     friend  class Eigen::Map<Derived, Unaligned>;
-    typedef class Eigen::Map<Derived, Unaligned>  UnalignedMapType;
+    typedef class Eigen::Map<Derived, Unaligned>  MapType;
+    friend  class Eigen::Map<ConstDerived, Unaligned>;
+    typedef class Eigen::Map<ConstDerived, Unaligned> ConstMapType;
     friend  class Eigen::Map<Derived, Aligned>;
-    typedef class Eigen::Map<Derived, Aligned>    AlignedMapType;
+    typedef class Eigen::Map<Derived, Aligned> AlignedMapType;
+    friend  class Eigen::Map<ConstDerived, Aligned>;
+    typedef class Eigen::Map<ConstDerived, Aligned> ConstAlignedMapType;
 
   protected:
     DenseStorage<Scalar, Base::MaxSizeAtCompileTime, Base::RowsAtCompileTime, Base::ColsAtCompileTime, Options> m_storage;
@@ -376,29 +381,29 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
       * \see class Map
       */
     //@{
-    inline static const UnalignedMapType Map(const Scalar* data)
-    { return UnalignedMapType(data); }
-    inline static UnalignedMapType Map(Scalar* data)
-    { return UnalignedMapType(data); }
-    inline static const UnalignedMapType Map(const Scalar* data, Index size)
-    { return UnalignedMapType(data, size); }
-    inline static UnalignedMapType Map(Scalar* data, Index size)
-    { return UnalignedMapType(data, size); }
-    inline static const UnalignedMapType Map(const Scalar* data, Index rows, Index cols)
-    { return UnalignedMapType(data, rows, cols); }
-    inline static UnalignedMapType Map(Scalar* data, Index rows, Index cols)
-    { return UnalignedMapType(data, rows, cols); }
+    inline static const ConstMapType Map(const Scalar* data)
+    { return ConstMapType(data); }
+    inline static MapType Map(Scalar* data)
+    { return MapType(data); }
+    inline static const ConstMapType Map(const Scalar* data, Index size)
+    { return ConstMapType(data, size); }
+    inline static MapType Map(Scalar* data, Index size)
+    { return MapType(data, size); }
+    inline static const ConstMapType Map(const Scalar* data, Index rows, Index cols)
+    { return ConstMapType(data, rows, cols); }
+    inline static MapType Map(Scalar* data, Index rows, Index cols)
+    { return MapType(data, rows, cols); }
 
-    inline static const AlignedMapType MapAligned(const Scalar* data)
-    { return AlignedMapType(data); }
+    inline static const ConstAlignedMapType MapAligned(const Scalar* data)
+    { return ConstAlignedMapType(data); }
     inline static AlignedMapType MapAligned(Scalar* data)
     { return AlignedMapType(data); }
-    inline static const AlignedMapType MapAligned(const Scalar* data, Index size)
-    { return AlignedMapType(data, size); }
+    inline static const ConstAlignedMapType MapAligned(const Scalar* data, Index size)
+    { return ConstAlignedMapType(data, size); }
     inline static AlignedMapType MapAligned(Scalar* data, Index size)
     { return AlignedMapType(data, size); }
-    inline static const AlignedMapType MapAligned(const Scalar* data, Index rows, Index cols)
-    { return AlignedMapType(data, rows, cols); }
+    inline static const ConstAlignedMapType MapAligned(const Scalar* data, Index rows, Index cols)
+    { return ConstAlignedMapType(data, rows, cols); }
     inline static AlignedMapType MapAligned(Scalar* data, Index rows, Index cols)
     { return AlignedMapType(data, rows, cols); }
     //@}
diff --git a/Eigen/src/Core/SelfAdjointView.h b/Eigen/src/Core/SelfAdjointView.h
index 564895143..dd1757aea 100644
--- a/Eigen/src/Core/SelfAdjointView.h
+++ b/Eigen/src/Core/SelfAdjointView.h
@@ -80,7 +80,7 @@ template<typename MatrixType, unsigned int UpLo> class SelfAdjointView
     typedef typename MatrixType::PlainObject PlainObject;
 
     inline SelfAdjointView(const MatrixType& matrix) : m_matrix(matrix)
-    { eigen_assert(internal::are_flags_consistent<Mode>::ret); }
+    {}
 
     inline Index rows() const { return m_matrix.rows(); }
     inline Index cols() const { return m_matrix.cols(); }
diff --git a/Eigen/src/Core/TriangularMatrix.h b/Eigen/src/Core/TriangularMatrix.h
index ba0f2741e..328aac611 100644
--- a/Eigen/src/Core/TriangularMatrix.h
+++ b/Eigen/src/Core/TriangularMatrix.h
@@ -181,7 +181,7 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView
     };
 
     inline TriangularView(const MatrixType& matrix) : m_matrix(matrix)
-    { eigen_assert(internal::are_flags_consistent<Mode>::ret); }
+    {}
 
     inline Index rows() const { return m_matrix.rows(); }
     inline Index cols() const { return m_matrix.cols(); }
diff --git a/Eigen/src/Core/products/SelfadjointProduct.h b/Eigen/src/Core/products/SelfadjointProduct.h
index c6a5287b5..0bf5b72fc 100644
--- a/Eigen/src/Core/products/SelfadjointProduct.h
+++ b/Eigen/src/Core/products/SelfadjointProduct.h
@@ -53,7 +53,7 @@ SelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>
     MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor, UpLo>
     ::run(_expression().cols(), actualU.cols(),
           &actualU.coeff(0,0), actualU.outerStride(), &actualU.coeff(0,0), actualU.outerStride(),
-          const_cast<Scalar*>(_expression().data()), _expression().outerStride(), actualAlpha);
+          _expression().const_cast_derived().data(), _expression().outerStride(), actualAlpha);
 
   return *this;
 }
diff --git a/Eigen/src/Core/products/SelfadjointRank2Update.h b/Eigen/src/Core/products/SelfadjointRank2Update.h
index d81c568b7..7d91f04a5 100644
--- a/Eigen/src/Core/products/SelfadjointRank2Update.h
+++ b/Eigen/src/Core/products/SelfadjointRank2Update.h
@@ -91,7 +91,7 @@ SelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>
     typename internal::remove_all<typename internal::conj_expr_if<IsRowMajor ^ UBlasTraits::NeedToConjugate,_ActualUType>::type>::type,
     typename internal::remove_all<typename internal::conj_expr_if<IsRowMajor ^ VBlasTraits::NeedToConjugate,_ActualVType>::type>::type,
     (IsRowMajor ? int(UpLo==Upper ? Lower : Upper) : UpLo)>
-    ::run(const_cast<Scalar*>(_expression().data()),_expression().outerStride(),actualU,actualV,actualAlpha);
+    ::run(_expression().const_cast_derived().data(),_expression().outerStride(),actualU,actualV,actualAlpha);
 
   return *this;
 }
diff --git a/Eigen/src/Core/products/TriangularMatrixVector.h b/Eigen/src/Core/products/TriangularMatrixVector.h
index 894a42b6c..3694be73a 100644
--- a/Eigen/src/Core/products/TriangularMatrixVector.h
+++ b/Eigen/src/Core/products/TriangularMatrixVector.h
@@ -46,11 +46,11 @@ struct product_triangular_matrix_vector<Index,Mode,LhsScalar,ConjLhs,RhsScalar,C
     
     static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;
 
-    typedef Map<Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;
+    typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;
     const LhsMap lhs(_lhs,rows,cols,OuterStride<>(lhsStride));
     typename conj_expr_if<ConjLhs,LhsMap>::type cjLhs(lhs);
     
-    typedef Map<Matrix<RhsScalar,Dynamic,1>, 0, InnerStride<> > RhsMap;
+    typedef Map<const Matrix<RhsScalar,Dynamic,1>, 0, InnerStride<> > RhsMap;
     const RhsMap rhs(_rhs,cols,InnerStride<>(rhsIncr));
     typename conj_expr_if<ConjRhs,RhsMap>::type cjRhs(rhs);
 
@@ -100,11 +100,11 @@ struct product_triangular_matrix_vector<Index,Mode,LhsScalar,ConjLhs,RhsScalar,C
     
     static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;
 
-    typedef Map<Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;
+    typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;
     const LhsMap lhs(_lhs,rows,cols,OuterStride<>(lhsStride));
     typename conj_expr_if<ConjLhs,LhsMap>::type cjLhs(lhs);
 
-    typedef Map<Matrix<RhsScalar,Dynamic,1> > RhsMap;
+    typedef Map<const Matrix<RhsScalar,Dynamic,1> > RhsMap;
     const RhsMap rhs(_rhs,cols);
     typename conj_expr_if<ConjRhs,RhsMap>::type cjRhs(rhs);
 
diff --git a/Eigen/src/Core/products/TriangularSolverVector.h b/Eigen/src/Core/products/TriangularSolverVector.h
index 16184abb5..0342bb356 100644
--- a/Eigen/src/Core/products/TriangularSolverVector.h
+++ b/Eigen/src/Core/products/TriangularSolverVector.h
@@ -48,7 +48,7 @@ struct triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Con
   };
   static void run(Index size, const LhsScalar* _lhs, Index lhsStride, RhsScalar* rhs)
   {
-    typedef Map<Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;
+    typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;
     const LhsMap lhs(_lhs,size,size,OuterStride<>(lhsStride));
     typename internal::conditional<
                           Conjugate,
@@ -84,7 +84,7 @@ struct triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Con
         Index i = IsLower ? pi+k : pi-k-1;
         Index s = IsLower ? pi   : i+1;
         if (k>0)
-          rhs[i] -= (cjLhs.row(i).segment(s,k).transpose().cwiseProduct(Map<Matrix<RhsScalar,Dynamic,1> >(rhs+s,k))).sum();
+          rhs[i] -= (cjLhs.row(i).segment(s,k).transpose().cwiseProduct(Map<const Matrix<RhsScalar,Dynamic,1> >(rhs+s,k))).sum();
         
         if(!(Mode & UnitDiag))
           rhs[i] /= cjLhs(i,i);
@@ -102,7 +102,7 @@ struct triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Con
   };
   static void run(Index size, const LhsScalar* _lhs, Index lhsStride, RhsScalar* rhs)
   {
-    typedef Map<Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;
+    typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;
     const LhsMap lhs(_lhs,size,size,OuterStride<>(lhsStride));
     typename internal::conditional<Conjugate,
                                    const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,
diff --git a/Eigen/src/Core/util/Constants.h b/Eigen/src/Core/util/Constants.h
index 99b4f3319..03cadc107 100644
--- a/Eigen/src/Core/util/Constants.h
+++ b/Eigen/src/Core/util/Constants.h
@@ -128,8 +128,10 @@ const unsigned int LinearAccessBit = 0x10;
   * Means the expression has a coeffRef() method, i.e. is writable as its individual coefficients are directly addressable.
   * This rules out read-only expressions.
   *
-  * Note that DirectAccessBit implies LvalueBit, but the converse is false: LvalueBit doesn't imply DirectAccessBit because
-  * DirectAccessBit means that the whole memory layout is a plain strided array.
+  * Note that DirectAccessBit and LvalueBit are mutually orthogonal, as there are examples of expression having one but note
+  * the other:
+  *   \li writable expressions that don't have a very simple memory layout as a strided array, have LvalueBit but not DirectAccessBit
+  *   \li Map-to-const expressions, for example Map<const Matrix>, have DirectAccessBit but not LvalueBit
   *
   * Expressions having LvalueBit also have their coeff() method returning a const reference instead of returning a new value.
   */
@@ -137,14 +139,12 @@ const unsigned int LvalueBit = 0x20;
 
 /** \ingroup flags
   *
-  * Means that the underlying array of coefficients can be directly accessed. This means two things.
-  * 
-  * First, this means LvalueBit, i.e. this means that the expression has a coeffRef() method, i.e. is writable as its
-  * individual coefficients are directly addressable. This rules out read-only expressions.
-  *
-  * Second, the memory layout of the array of coefficients must be exactly the natural one suggested by rows(), cols(),
+  * Means that the underlying array of coefficients can be directly accessed as a plain strided array. The memory layout
+  * of the array of coefficients must be exactly the natural one suggested by rows(), cols(),
   * outerStride(), innerStride(), and the RowMajorBit. This rules out expressions such as Diagonal, whose coefficients,
   * though referencable, do not have such a regular memory layout.
+  *
+  * See the comment on LvalueBit for an explanation of how LvalueBit and DirectAccessBit are mutually orthogonal.
   */
 const unsigned int DirectAccessBit = 0x40;
 
@@ -242,7 +242,7 @@ enum {
 };
 
 enum AccessorLevels {
-  ReadOnlyAccessors, WriteAccessors, DirectAccessors
+  ReadOnlyAccessors, WriteAccessors, DirectAccessors, DirectWriteAccessors
 };
 
 enum DecompositionOptions {
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 0d0b905ea..c84401fa8 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -33,16 +33,26 @@ template<typename Derived> struct has_direct_access
 {
   enum { ret = (traits<Derived>::Flags & DirectAccessBit) ? 1 : 0 };
 };
+
+template<typename Derived> struct accessors_level
+{
+  enum { has_direct_access = (traits<Derived>::Flags & DirectAccessBit) ? 1 : 0,
+         has_write_access = (traits<Derived>::Flags & LvalueBit) ? 1 : 0,
+         value = has_direct_access ? (has_write_access ? DirectWriteAccessors : DirectAccessors)
+                                   : (has_write_access ? WriteAccessors       : ReadOnlyAccessors)
+  };
+};
+
 } // end namespace internal
 
 template<typename T> struct NumTraits;
 
 template<typename Derived> struct EigenBase;
 template<typename Derived> class DenseBase;
+
+
 template<typename Derived,
-         AccessorLevels Level = (internal::traits<Derived>::Flags & DirectAccessBit) ? DirectAccessors
-                              : (internal::traits<Derived>::Flags & LvalueBit) ? WriteAccessors
-                              : ReadOnlyAccessors>
+         int Level = internal::accessors_level<Derived>::value >
 class DenseCoeffsBase;
 
 template<typename _Scalar, int _Rows, int _Cols,
@@ -86,6 +96,9 @@ template<typename MatrixType, int Index> class Diagonal;
 template<int SizeAtCompileTime, int MaxSizeAtCompileTime = SizeAtCompileTime> class PermutationMatrix;
 template<int SizeAtCompileTime, int MaxSizeAtCompileTime = SizeAtCompileTime> class Transpositions;
 
+template<typename Derived,
+         int Level = internal::accessors_level<Derived>::has_write_access ? WriteAccessors : ReadOnlyAccessors
+> class MapBase;
 template<int InnerStrideAtCompileTime, int OuterStrideAtCompileTime> class Stride;
 template<typename MatrixType, int MapOptions=Unaligned, typename StrideType = Stride<0,0> > class Map;
 
diff --git a/Eigen/src/Core/util/StaticAssert.h b/Eigen/src/Core/util/StaticAssert.h
index dbdf8b209..3637b7c0a 100644
--- a/Eigen/src/Core/util/StaticAssert.h
+++ b/Eigen/src/Core/util/StaticAssert.h
@@ -93,6 +93,8 @@
         THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS,
         YOU_CANNOT_MIX_ARRAYS_AND_MATRICES,
         YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION,
+        YOU_ARE_TRYING_TO_WRITE_INTO_A_READ_ONLY_EXPRESSION,
+        YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT,
         THIS_METHOD_IS_ONLY_FOR_1x1_EXPRESSIONS
       };
     };
@@ -183,4 +185,8 @@
                           (TYPE::ColsAtCompileTime == 1 || TYPE::ColsAtCompileTime == Dynamic), \
                           THIS_METHOD_IS_ONLY_FOR_1x1_EXPRESSIONS)
 
+#define EIGEN_STATIC_ASSERT_LVALUE(Derived) \
+      EIGEN_STATIC_ASSERT(int(internal::traits<Derived>::Flags) & LvalueBit, \
+                          YOU_ARE_TRYING_TO_WRITE_INTO_A_READ_ONLY_EXPRESSION)
+
 #endif // EIGEN_STATIC_ASSERT_H
diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h
index ea43aa91e..46ade2ba1 100644
--- a/Eigen/src/Core/util/XprHelper.h
+++ b/Eigen/src/Core/util/XprHelper.h
@@ -333,11 +333,6 @@ template<typename T, int n=1, typename PlainObject = typename eval<T>::type> str
   >::type type;
 };
 
-template<unsigned int Flags> struct are_flags_consistent
-{
-  enum { ret = EIGEN_IMPLIES(bool(Flags&DirectAccessBit), bool(Flags&LvalueBit)) };
-};
-
 template<typename Derived, typename XprKind = typename traits<Derived>::XprKind>
 struct dense_xpr_base
 {
diff --git a/Eigen/src/Geometry/Quaternion.h b/Eigen/src/Geometry/Quaternion.h
index afbeef26c..2c4098fc1 100644
--- a/Eigen/src/Geometry/Quaternion.h
+++ b/Eigen/src/Geometry/Quaternion.h
@@ -298,6 +298,42 @@ traits<Quaternion<_Scalar> >
 };
 }
 
+/** \brief Quaternion expression mapping a constant memory buffer
+  *
+  * \param _Scalar the type of the Quaternion coefficients
+  * \param PacketAccess see class Map
+  *
+  * This is a specialization of class Map for Quaternion. This class allows to view
+  * a 4 scalar memory buffer as an Eigen's Quaternion object.
+  *
+  * \sa class Map, class Quaternion, class QuaternionBase
+  */
+template<typename _Scalar, int PacketAccess>
+class Map<const Quaternion<_Scalar>, PacketAccess >
+  : public QuaternionBase<Map<const Quaternion<_Scalar>, PacketAccess> >
+{
+    typedef QuaternionBase<Map<Quaternion<_Scalar>, PacketAccess> > Base;
+
+  public:
+    typedef _Scalar Scalar;
+    typedef typename internal::traits<Map>::Coefficients Coefficients;
+    EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Map)
+    using Base::operator*=;
+
+    /** Constructs a Mapped Quaternion object from the pointer \a coeffs
+      *
+      * The pointer \a coeffs must reference the four coeffecients of Quaternion in the following order:
+      * \code *coeffs == {x, y, z, w} \endcode
+      *
+      * If the template parameter PacketAccess is set to Aligned, then the pointer coeffs must be aligned. */
+    EIGEN_STRONG_INLINE Map(const Scalar* coeffs) : m_coeffs(coeffs) {}
+
+    inline const Coefficients& coeffs() const { return m_coeffs;}
+
+  protected:
+    const Coefficients m_coeffs;
+};
+
 /** \brief Expression of a quaternion from a memory buffer
   *
   * \param _Scalar the type of the Quaternion coefficients
@@ -326,10 +362,10 @@ class Map<Quaternion<_Scalar>, PacketAccess >
       * \code *coeffs == {x, y, z, w} \endcode
       *
       * If the template parameter PacketAccess is set to Aligned, then the pointer coeffs must be aligned. */
-    EIGEN_STRONG_INLINE Map(const Scalar* coeffs) : m_coeffs(coeffs) {}
+    EIGEN_STRONG_INLINE Map(Scalar* coeffs) : m_coeffs(coeffs) {}
 
-    inline Coefficients& coeffs() { return m_coeffs;}
-    inline const Coefficients& coeffs() const { return m_coeffs;}
+    inline Coefficients& coeffs() { return m_coeffs; }
+    inline const Coefficients& coeffs() const { return m_coeffs; }
 
   protected:
     Coefficients m_coeffs;
diff --git a/Eigen/src/Sparse/SparseSelfAdjointView.h b/Eigen/src/Sparse/SparseSelfAdjointView.h
index 60136e9f7..3749c604a 100644
--- a/Eigen/src/Sparse/SparseSelfAdjointView.h
+++ b/Eigen/src/Sparse/SparseSelfAdjointView.h
@@ -75,7 +75,6 @@ template<typename MatrixType, unsigned int UpLo> class SparseSelfAdjointView
 
     inline SparseSelfAdjointView(const MatrixType& matrix) : m_matrix(matrix)
     {
-      eigen_assert(internal::are_flags_consistent<UpLo>::ret);
       eigen_assert(rows()==cols() && "SelfAdjointView is only for squared matrices");
     }
 
diff --git a/test/map.cpp b/test/map.cpp
index aa954167a..99f88b966 100644
--- a/test/map.cpp
+++ b/test/map.cpp
@@ -22,6 +22,10 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
+#ifndef EIGEN_NO_STATIC_ASSERT
+#define EIGEN_NO_STATIC_ASSERT // turn static asserts into runtime asserts in order to check them
+#endif
+
 #include "main.h"
 
 template<typename VectorType> void map_class_vector(const VectorType& m)
@@ -110,15 +114,34 @@ template<typename VectorType> void map_static_methods(const VectorType& m)
   delete[] array3;
 }
 
+template<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)
+{
+  typedef typename PlainObjectType::Index Index;
+  typedef typename PlainObjectType::Scalar Scalar;
+
+  // there's a lot that we can't test here while still having this test compile!
+  // the only possible approach would be to run a script trying to compile stuff and checking that it fails.
+  // CMake can help with that.
+
+  // verify that map-to-const don't have LvalueBit
+  typedef typename internal::add_const<PlainObjectType>::type ConstPlainObjectType;
+  VERIFY( !(internal::traits<Map<ConstPlainObjectType> >::Flags & LvalueBit) );
+  VERIFY( !(internal::traits<Map<ConstPlainObjectType, Aligned> >::Flags & LvalueBit) );
+  VERIFY( !(Map<ConstPlainObjectType>::Flags & LvalueBit) );
+  VERIFY( !(Map<ConstPlainObjectType, Aligned>::Flags & LvalueBit) );
+}
 
 void test_map()
 {
   for(int i = 0; i < g_repeat; i++) {
     CALL_SUBTEST_1( map_class_vector(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST_1( check_const_correctness(Matrix<float, 1, 1>()) );
     CALL_SUBTEST_2( map_class_vector(Vector4d()) );
+    CALL_SUBTEST_2( check_const_correctness(Matrix4d()) );
     CALL_SUBTEST_3( map_class_vector(RowVector4f()) );
     CALL_SUBTEST_4( map_class_vector(VectorXcf(8)) );
     CALL_SUBTEST_5( map_class_vector(VectorXi(12)) );
+    CALL_SUBTEST_5( check_const_correctness(VectorXi(12)) );
 
     CALL_SUBTEST_1( map_class_matrix(Matrix<float, 1, 1>()) );
     CALL_SUBTEST_2( map_class_matrix(Matrix4d()) );