sync with mainline

18 files changed, 475 insertions, 224 deletions

diff --git a/Eigen/Core b/Eigen/Core
index c8fcb1c09..3dce6422f 100644
--- a/Eigen/Core
+++ b/Eigen/Core
@@ -200,6 +200,7 @@ namespace Eigen {
 #include "src/Core/products/TriangularMatrixMatrix.h"
 #include "src/Core/products/TriangularSolverMatrix.h"
 #include "src/Core/BandMatrix.h"
+#include "src/Core/ExpressionMaker.h"
 
 } // namespace Eigen
 
diff --git a/Eigen/Sparse b/Eigen/Sparse
index a8888daa3..96bd61419 100644
--- a/Eigen/Sparse
+++ b/Eigen/Sparse
@@ -110,6 +110,7 @@ namespace Eigen {
 #include "src/Sparse/SparseLLT.h"
 #include "src/Sparse/SparseLDLT.h"
 #include "src/Sparse/SparseLU.h"
+#include "src/Sparse/SparseExpressionMaker.h"
 
 #ifdef EIGEN_CHOLMOD_SUPPORT
 # include "src/Sparse/CholmodSupport.h"
diff --git a/Eigen/src/Core/Block.h b/Eigen/src/Core/Block.h
index cebfeaf75..5fffdcb01 100644
--- a/Eigen/src/Core/Block.h
+++ b/Eigen/src/Core/Block.h
@@ -33,10 +33,10 @@
   * \param MatrixType the type of the object in which we are taking a block
   * \param BlockRows the number of rows of the block we are taking at compile time (optional)
   * \param BlockCols the number of columns of the block we are taking at compile time (optional)
-  * \param _PacketAccess allows to enforce aligned loads and stores if set to \b ForceAligned.
-  *                      The default is \b AsRequested. This parameter is internaly used by Eigen
-  *                      in expressions such as \code mat.block() += other; \endcode and most of
-  *                      the time this is the only way it is used.
+  * \param _PacketAccess \internal used to enforce aligned loads in expressions such as
+  *                      \code mat.block() += other; \endcode. Possible values are
+  *                      \c AsRequested (default) and \c EnforceAlignedAccess.
+  *                      See class MapBase for more details.
   * \param _DirectAccessStatus \internal used for partial specialization
   *
   * This class represents an expression of either a fixed-size or dynamic-size block. It is the return
@@ -84,9 +84,9 @@ struct ei_traits<Block<MatrixType, BlockRows, BlockCols, _PacketAccess, _DirectA
     CoeffReadCost = ei_traits<MatrixType>::CoeffReadCost,
     PacketAccess = _PacketAccess
   };
-  typedef typename ei_meta_if<int(PacketAccess)==ForceAligned,
+  typedef typename ei_meta_if<int(PacketAccess)==EnforceAlignedAccess,
                  Block<MatrixType, BlockRows, BlockCols, _PacketAccess, _DirectAccessStatus>&,
-                 Block<MatrixType, BlockRows, BlockCols, ForceAligned, _DirectAccessStatus> >::ret AlignedDerivedType;
+                 Block<MatrixType, BlockRows, BlockCols, EnforceAlignedAccess, _DirectAccessStatus> >::ret AlignedDerivedType;
 };
 
 template<typename MatrixType, int BlockRows, int BlockCols, int PacketAccess, int _DirectAccessStatus> class Block
@@ -228,13 +228,13 @@ class Block<MatrixType,BlockRows,BlockCols,PacketAccess,HasDirectAccess>
 
     class InnerIterator;
     typedef typename ei_traits<Block>::AlignedDerivedType AlignedDerivedType;
-    friend class Block<MatrixType,BlockRows,BlockCols,PacketAccess==AsRequested?ForceAligned:AsRequested,HasDirectAccess>;
+    friend class Block<MatrixType,BlockRows,BlockCols,PacketAccess==EnforceAlignedAccess?AsRequested:EnforceAlignedAccess,HasDirectAccess>;
 
     EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
 
-    AlignedDerivedType _convertToForceAligned()
+    AlignedDerivedType _convertToEnforceAlignedAccess()
     {
-      return Block<MatrixType,BlockRows,BlockCols,ForceAligned,HasDirectAccess>
+      return Block<MatrixType,BlockRows,BlockCols,EnforceAlignedAccess,HasDirectAccess>
                     (m_matrix, Base::m_data, Base::m_rows.value(), Base::m_cols.value());
     }
 
diff --git a/Eigen/src/Core/ExpressionMaker.h b/Eigen/src/Core/ExpressionMaker.h
new file mode 100644
index 000000000..1d265b63c
--- /dev/null
+++ b/Eigen/src/Core/ExpressionMaker.h
@@ -0,0 +1,61 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_EXPRESSIONMAKER_H
+#define EIGEN_EXPRESSIONMAKER_H
+
+// computes the shape of a matrix from its traits flag
+template<typename XprType> struct ei_shape_of
+{
+  enum { ret = ei_traits<XprType>::Flags&SparseBit ? IsSparse : IsDense };
+};
+
+
+// Since the Sparse module is completely separated from the Core module, there is
+// no way to write the type of a generic expression working for both dense and sparse
+// matrix. Unless we change the overall design, here is a workaround.
+// There is an example in unsuported/Eigen/src/AutoDiff/AutoDiffScalar.
+
+template<typename XprType, int Shape = ei_shape_of<XprType>::ret>
+struct MakeNestByValue
+{
+  typedef NestByValue<XprType> Type;
+};
+
+template<typename Func, typename XprType, int Shape = ei_shape_of<XprType>::ret>
+struct MakeCwiseUnaryOp
+{
+  typedef CwiseUnaryOp<Func,XprType> Type;
+};
+
+template<typename Func, typename A, typename B, int Shape = ei_shape_of<A>::ret>
+struct MakeCwiseBinaryOp
+{
+  typedef CwiseBinaryOp<Func,A,B> Type;
+};
+
+// TODO complete the list
+
+
+#endif // EIGEN_EXPRESSIONMAKER_H
diff --git a/Eigen/src/Core/Map.h b/Eigen/src/Core/Map.h
index f6bc814e2..dba7e20e4 100644
--- a/Eigen/src/Core/Map.h
+++ b/Eigen/src/Core/Map.h
@@ -31,16 +31,14 @@
   * \brief A matrix or vector expression mapping an existing array of data.
   *
   * \param MatrixType the equivalent matrix type of the mapped data
-  * \param _PacketAccess allows to enforce aligned loads and stores if set to ForceAligned.
-  *                      The default is AsRequested. This parameter is internaly used by Eigen
-  *                      in expressions such as \code Map<...>(...) += other; \endcode and most
-  *                      of the time this is the only way it is used.
+  * \param PointerAlignment specifies whether the pointer is \c Aligned, or \c Unaligned.
+  *                         The default is \c Unaligned.
   *
   * This class represents a matrix or vector expression mapping an existing array of data.
   * It can be used to let Eigen interface without any overhead with non-Eigen data structures,
   * such as plain C arrays or structures from other libraries.
   *
-  * \b Tips: to change the array of data mapped by a Map object, you can use the C++
+  * \b Tip: to change the array of data mapped by a Map object, you can use the C++
   * placement new syntax:
   *
   * Example: \include Map_placement_new.cpp
@@ -48,22 +46,27 @@
   *
   * This class is the return type of Matrix::Map() but can also be used directly.
   *
+  * \b Note \b to \b Eigen \b developers: The template parameter \c PointerAlignment
+  * can also be or-ed with \c EnforceAlignedAccess in order to enforce aligned read 
+  * in expressions such as \code A += B; \endcode. See class MapBase for further details.
+  *
   * \sa Matrix::Map()
   */
-template<typename MatrixType, int _PacketAccess>
-struct ei_traits<Map<MatrixType, _PacketAccess> > : public ei_traits<MatrixType>
+template<typename MatrixType, int Options>
+struct ei_traits<Map<MatrixType, Options> > : public ei_traits<MatrixType>
 {
   enum {
-    PacketAccess = _PacketAccess,
-    Flags = ei_traits<MatrixType>::Flags & ~AlignedBit
+    PacketAccess = Options & EnforceAlignedAccess,
+    Flags = (Options&Aligned)==Aligned ? ei_traits<MatrixType>::Flags |  AlignedBit
+                                       : ei_traits<MatrixType>::Flags & ~AlignedBit
   };
-  typedef typename ei_meta_if<int(PacketAccess)==ForceAligned,
-                              Map<MatrixType, _PacketAccess>&,
-                              Map<MatrixType, ForceAligned> >::ret AlignedDerivedType;
+  typedef typename ei_meta_if<int(PacketAccess)==EnforceAlignedAccess,
+                              Map<MatrixType, Options>&,
+                              Map<MatrixType, Options|EnforceAlignedAccess> >::ret AlignedDerivedType;
 };
 
-template<typename MatrixType, int PacketAccess> class Map
-  : public MapBase<Map<MatrixType, PacketAccess> >
+template<typename MatrixType, int Options> class Map
+  : public MapBase<Map<MatrixType, Options> >
 {
   public:
 
@@ -72,9 +75,9 @@ template<typename MatrixType, int PacketAccess> class Map
 
     inline int stride() const { return this->innerSize(); }
 
-    AlignedDerivedType _convertToForceAligned()
+    AlignedDerivedType _convertToEnforceAlignedAccess()
     {
-      return Map<MatrixType,ForceAligned>(Base::m_data, Base::m_rows.value(), Base::m_cols.value());
+      return AlignedDerivedType(Base::m_data, Base::m_rows.value(), Base::m_cols.value());
     }
 
     inline Map(const Scalar* data) : Base(data) {}
diff --git a/Eigen/src/Core/MapBase.h b/Eigen/src/Core/MapBase.h
index 88a3fac1e..8770732de 100644
--- a/Eigen/src/Core/MapBase.h
+++ b/Eigen/src/Core/MapBase.h
@@ -32,11 +32,17 @@
   *
   * Expression classes inheriting MapBase must define the constant \c PacketAccess,
   * and type \c AlignedDerivedType in their respective ei_traits<> specialization structure.
-  * The value of \c PacketAccess can be either:
-  *  - \b ForceAligned which enforces both aligned loads and stores
-  *  - \b AsRequested which is the default behavior
+  * The value of \c PacketAccess can be either \b AsRequested, or set to \b EnforceAlignedAccess which
+  * enforces both aligned loads and stores.
+  * 
+  * \c EnforceAlignedAccess is automatically set in expressions such as 
+  * \code A += B; \endcode where A is either a Block or a Map. Here,
+  * this expression is transfomed into \code A = A_with_EnforceAlignedAccess + B; \endcode
+  * avoiding unaligned loads from A. Indeed, since Eigen's packet evaluation mechanism
+  * automatically align to the destination matrix, we know that loads to A will be aligned too.
+  * 
   * The type \c AlignedDerivedType should correspond to the equivalent expression type
-  * with \c PacketAccess being \c ForceAligned.
+  * with \c PacketAccess set to \c EnforceAlignedAccess.
   *
   * \sa class Map, class Block
   */
@@ -79,19 +85,19 @@ template<typename Derived> class MapBase
       * \sa MapBase::stride() */
     inline const Scalar* data() const { return m_data; }
 
-    template<bool IsForceAligned,typename Dummy> struct force_aligned_impl {
+    template<bool IsEnforceAlignedAccess,typename Dummy> struct force_aligned_impl {
       static AlignedDerivedType run(MapBase& a) { return a.derived(); }
     };
 
     template<typename Dummy> struct force_aligned_impl<false,Dummy> {
-      static AlignedDerivedType run(MapBase& a) { return a.derived()._convertToForceAligned(); }
+      static AlignedDerivedType run(MapBase& a) { return a.derived()._convertToEnforceAlignedAccess(); }
     };
 
     /** \returns an expression equivalent to \c *this but having the \c PacketAccess constant
-      * set to \c ForceAligned. Must be reimplemented by the derived class. */
+      * set to \c EnforceAlignedAccess. Must be reimplemented by the derived class. */
     AlignedDerivedType forceAligned()
     {
-      return force_aligned_impl<int(PacketAccess)==int(ForceAligned),Derived>::run(*this);
+      return force_aligned_impl<int(PacketAccess)==int(EnforceAlignedAccess),Derived>::run(*this);
     }
 
     inline const Scalar& coeff(int row, int col) const
@@ -131,7 +137,7 @@ template<typename Derived> class MapBase
     template<int LoadMode>
     inline PacketScalar packet(int row, int col) const
     {
-      return ei_ploadt<Scalar, int(PacketAccess) == ForceAligned ? Aligned : LoadMode>
+      return ei_ploadt<Scalar, int(PacketAccess) == EnforceAlignedAccess ? Aligned : LoadMode>
                (m_data + (IsRowMajor ? col + row * stride()
                                      : row + col * stride()));
     }
@@ -139,13 +145,13 @@ template<typename Derived> class MapBase
     template<int LoadMode>
     inline PacketScalar packet(int index) const
     {
-      return ei_ploadt<Scalar, int(PacketAccess) == ForceAligned ? Aligned : LoadMode>(m_data + index);
+      return ei_ploadt<Scalar, int(PacketAccess) == EnforceAlignedAccess ? Aligned : LoadMode>(m_data + index);
     }
 
     template<int StoreMode>
     inline void writePacket(int row, int col, const PacketScalar& x)
     {
-      ei_pstoret<Scalar, PacketScalar, int(PacketAccess) == ForceAligned ? Aligned : StoreMode>
+      ei_pstoret<Scalar, PacketScalar, int(PacketAccess) == EnforceAlignedAccess ? Aligned : StoreMode>
                (const_cast<Scalar*>(m_data) + (IsRowMajor ? col + row * stride()
                                                           : row + col * stride()), x);
     }
@@ -153,13 +159,14 @@ template<typename Derived> class MapBase
     template<int StoreMode>
     inline void writePacket(int index, const PacketScalar& x)
     {
-      ei_pstoret<Scalar, PacketScalar, int(PacketAccess) == ForceAligned ? Aligned : StoreMode>
+      ei_pstoret<Scalar, PacketScalar, int(PacketAccess) == EnforceAlignedAccess ? Aligned : StoreMode>
         (const_cast<Scalar*>(m_data) + index, x);
     }
 
     inline MapBase(const Scalar* data) : m_data(data), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
     {
       EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+      checkDataAlignment();
     }
 
     inline MapBase(const Scalar* data, int size)
@@ -170,6 +177,7 @@ template<typename Derived> class MapBase
       EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
       ei_assert(size >= 0);
       ei_assert(data == 0 || SizeAtCompileTime == Dynamic || SizeAtCompileTime == size);
+      checkDataAlignment();
     }
 
     inline MapBase(const Scalar* data, int rows, int cols)
@@ -178,6 +186,7 @@ template<typename Derived> class MapBase
       ei_assert( (data == 0)
               || (   rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
                   && cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)));
+      checkDataAlignment();
     }
 
     Derived& operator=(const MapBase& other)
@@ -215,6 +224,13 @@ template<typename Derived> class MapBase
     { return derived() = forceAligned() / other; }
 
   protected:
+
+    void checkDataAlignment() const
+    {
+      ei_assert( ((!(ei_traits<Derived>::Flags&AlignedBit))
+                  || ((std::size_t(m_data)&0xf)==0)) && "data is not aligned");
+    }
+    
     const Scalar* EIGEN_RESTRICT m_data;
     const ei_int_if_dynamic<RowsAtCompileTime> m_rows;
     const ei_int_if_dynamic<ColsAtCompileTime> m_cols;
diff --git a/Eigen/src/Core/Matrix.h b/Eigen/src/Core/Matrix.h
index 027e6bb70..17d2f2836 100644
--- a/Eigen/src/Core/Matrix.h
+++ b/Eigen/src/Core/Matrix.h
@@ -58,6 +58,9 @@ template <typename Derived, typename OtherDerived, bool IsVector = static_cast<b
   * \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix<float, Dynamic, Dynamic>)
   * \li \c VectorXf is a dynamic-size vector of floats (\c Matrix<float, Dynamic, 1>)
   *
+  * \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix<float, 2, Dynamic>)
+  * \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix<double, Dynamic, 3>)
+  *
   * See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs.
   *
   * You can access elements of vectors and matrices using normal subscripting:
@@ -794,11 +797,20 @@ typedef Matrix<Type, Size, 1>    Vector##SizeSuffix##TypeSuffix;  \
 /** \ingroup matrixtypedefs */                                    \
 typedef Matrix<Type, 1, Size>    RowVector##SizeSuffix##TypeSuffix;
 
+#define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size)         \
+/** \ingroup matrixtypedefs */                                    \
+typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix;  \
+/** \ingroup matrixtypedefs */                                    \
+typedef Matrix<Type, Dynamic, Size> Matrix##X##Size##TypeSuffix;
+
 #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
-EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
+EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
+EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
+EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
 
 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int,                  i)
 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float,                f)
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index 729349b6f..7b5310175 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/Eigen/src/Core/MatrixBase.h
@@ -190,6 +190,25 @@ template<typename Derived> class MatrixBase
       * i.e., the number of rows for a columns major matrix, and the number of cols otherwise */
     int innerSize() const { return (int(Flags)&RowMajorBit) ? this->cols() : this->rows(); }
 
+    /** Only plain matrices, not expressions may be resized; therefore the only useful resize method is
+      * Matrix::resize(). The present method only asserts that the new size equals the old size, and does
+      * nothing else.
+      */
+    void resize(int size)
+    {
+      ei_assert(size == this->size()
+                && "MatrixBase::resize() does not actually allow to resize.");
+    }
+    /** Only plain matrices, not expressions may be resized; therefore the only useful resize method is
+      * Matrix::resize(). The present method only asserts that the new size equals the old size, and does
+      * nothing else.
+      */
+    void resize(int rows, int cols)
+    {
+      ei_assert(rows == this->rows() && cols == this->cols()
+                && "MatrixBase::resize() does not actually allow to resize.");
+    }
+
 #ifndef EIGEN_PARSED_BY_DOXYGEN
     /** \internal the plain matrix type corresponding to this expression. Note that is not necessarily
       * exactly the return type of eval(): in the case of plain matrices, the return type of eval() is a const
diff --git a/Eigen/src/Core/StableNorm.h b/Eigen/src/Core/StableNorm.h
index 06e69c448..f2d1e7240 100644
--- a/Eigen/src/Core/StableNorm.h
+++ b/Eigen/src/Core/StableNorm.h
@@ -59,7 +59,7 @@ MatrixBase<Derived>::stableNorm() const
   RealScalar invScale = 1;
   RealScalar ssq = 0; // sum of square
   enum {
-    Alignment = (int(Flags)&DirectAccessBit) || (int(Flags)&AlignedBit) ? ForceAligned : AsRequested
+    Alignment = (int(Flags)&DirectAccessBit) || (int(Flags)&AlignedBit) ? EnforceAlignedAccess : AsRequested
   };
   int n = size();
   int bi=0;
diff --git a/Eigen/src/Core/util/Constants.h b/Eigen/src/Core/util/Constants.h
index 226a53c33..c9735b6e4 100644
--- a/Eigen/src/Core/util/Constants.h
+++ b/Eigen/src/Core/util/Constants.h
@@ -196,8 +196,8 @@ const unsigned int UnitLowerTriangular = LowerTriangularBit | UnitDiagBit;
 
 enum { DiagonalOnTheLeft, DiagonalOnTheRight };
 
-enum { Aligned, Unaligned };
-enum { ForceAligned, AsRequested };
+enum { Unaligned=0, Aligned=1 };
+enum { AsRequested=0, EnforceAlignedAccess=2 };
 enum { ConditionalJumpCost = 5 };
 enum CornerType { TopLeft, TopRight, BottomLeft, BottomRight };
 enum DirectionType { Vertical, Horizontal, BothDirections };
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 86539a64e..c8f2c4cd7 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -130,6 +130,7 @@ template<typename Scalar>     class PlanarRotation;
 // Geometry module:
 template<typename Derived, int _Dim> class RotationBase;
 template<typename Lhs, typename Rhs> class Cross;
+template<typename Derived> class QuaternionBase;
 template<typename Scalar> class Quaternion;
 template<typename Scalar> class Rotation2D;
 template<typename Scalar> class AngleAxis;
diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
index 66b9d52f4..dd41ad0e2 100644
--- a/Eigen/src/Core/util/Macros.h
+++ b/Eigen/src/Core/util/Macros.h
@@ -256,7 +256,7 @@ using Eigen::ei_cos;
 
 // C++0x features
 #if defined(__GXX_EXPERIMENTAL_CXX0X__) || (defined(_MSC_VER) && (_MSC_VER >= 1600))
-  #define EIGEN_REF_TO_TEMPORARY &&
+  #define EIGEN_REF_TO_TEMPORARY const &
 #else
   #define EIGEN_REF_TO_TEMPORARY const &
 #endif
diff --git a/Eigen/src/Core/util/StaticAssert.h b/Eigen/src/Core/util/StaticAssert.h
index 883f2d95e..6210bc91c 100644
--- a/Eigen/src/Core/util/StaticAssert.h
+++ b/Eigen/src/Core/util/StaticAssert.h
@@ -78,7 +78,8 @@
         INVALID_MATRIX_TEMPLATE_PARAMETERS,
         BOTH_MATRICES_MUST_HAVE_THE_SAME_STORAGE_ORDER,
         THIS_METHOD_IS_ONLY_FOR_DIAGONAL_MATRIX,
-        THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE
+        THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE,
+        THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES
       };
     };
 
diff --git a/Eigen/src/Geometry/Quaternion.h b/Eigen/src/Geometry/Quaternion.h
index 2f9f97807..67b040165 100644
--- a/Eigen/src/Geometry/Quaternion.h
+++ b/Eigen/src/Geometry/Quaternion.h
@@ -2,6 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>
 //
 // Eigen is free software; you can redistribute it and/or
 // modify it under the terms of the GNU Lesser General Public
@@ -25,11 +26,6 @@
 #ifndef EIGEN_QUATERNION_H
 #define EIGEN_QUATERNION_H
 
-template<typename Other,
-         int OtherRows=Other::RowsAtCompileTime,
-         int OtherCols=Other::ColsAtCompileTime>
-struct ei_quaternion_assign_impl;
-
 /** \geometry_module \ingroup Geometry_Module
   *
   * \class Quaternion
@@ -52,28 +48,33 @@ struct ei_quaternion_assign_impl;
   * \sa  class AngleAxis, class Transform
   */
 
-template<typename _Scalar> struct ei_traits<Quaternion<_Scalar> >
+template<typename Other,
+         int OtherRows=Other::RowsAtCompileTime,
+         int OtherCols=Other::ColsAtCompileTime>
+struct ei_quaternionbase_assign_impl;
+
+template<typename Scalar> class Quaternion; // [XXX] => remove when Quaternion becomes Quaternion
+
+template<typename Derived>
+struct ei_traits<QuaternionBase<Derived> >
 {
-  typedef _Scalar Scalar;
+  typedef typename ei_traits<Derived>::Scalar Scalar;
+  enum {
+    PacketAccess = ei_traits<Derived>::PacketAccess
+  };
 };
 
-template<typename _Scalar>
-class Quaternion : public RotationBase<Quaternion<_Scalar>,3>
+template<class Derived>
+class QuaternionBase : public RotationBase<Derived, 3>
 {
-  typedef RotationBase<Quaternion<_Scalar>,3> Base;
-
-
-
+  typedef RotationBase<Derived, 3> Base;
 public:
-  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,4)
-
   using Base::operator*;
 
-  /** the scalar type of the coefficients */
-  typedef _Scalar Scalar;
+  typedef typename ei_traits<QuaternionBase<Derived> >::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
 
-  /** the type of the Coefficients 4-vector */
-  typedef Matrix<Scalar, 4, 1> Coefficients;
+ // typedef typename Matrix<Scalar,4,1> Coefficients;
   /** the type of a 3D vector */
   typedef Matrix<Scalar,3,1> Vector3;
   /** the equivalent rotation matrix type */
@@ -82,114 +83,96 @@ public:
   typedef AngleAxis<Scalar> AngleAxisType;
 
   /** \returns the \c x coefficient */
-  inline Scalar x() const { return m_coeffs.coeff(0); }
+  inline Scalar x() const { return this->derived().coeffs().coeff(0); }
   /** \returns the \c y coefficient */
-  inline Scalar y() const { return m_coeffs.coeff(1); }
+  inline Scalar y() const { return this->derived().coeffs().coeff(1); }
   /** \returns the \c z coefficient */
-  inline Scalar z() const { return m_coeffs.coeff(2); }
+  inline Scalar z() const { return this->derived().coeffs().coeff(2); }
   /** \returns the \c w coefficient */
-  inline Scalar w() const { return m_coeffs.coeff(3); }
+  inline Scalar w() const { return this->derived().coeffs().coeff(3); }
 
   /** \returns a reference to the \c x coefficient */
-  inline Scalar& x() { return m_coeffs.coeffRef(0); }
+  inline Scalar& x() { return this->derived().coeffs().coeffRef(0); }
   /** \returns a reference to the \c y coefficient */
-  inline Scalar& y() { return m_coeffs.coeffRef(1); }
+  inline Scalar& y() { return this->derived().coeffs().coeffRef(1); }
   /** \returns a reference to the \c z coefficient */
-  inline Scalar& z() { return m_coeffs.coeffRef(2); }
+  inline Scalar& z() { return this->derived().coeffs().coeffRef(2); }
   /** \returns a reference to the \c w coefficient */
-  inline Scalar& w() { return m_coeffs.coeffRef(3); }
+  inline Scalar& w() { return this->derived().coeffs().coeffRef(3); }
 
   /** \returns a read-only vector expression of the imaginary part (x,y,z) */
-  inline const Block<Coefficients,3,1> vec() const { return m_coeffs.template start<3>(); }
+  inline const VectorBlock<typename ei_traits<Derived>::Coefficients,3> vec() const { return this->derived().coeffs().template start<3>(); }
 
   /** \returns a vector expression of the imaginary part (x,y,z) */
-  inline Block<Coefficients,3,1> vec() { return m_coeffs.template start<3>(); }
+  inline VectorBlock<typename ei_traits<Derived>::Coefficients,3> vec() { return this->derived().coeffs().template start<3>(); }
 
   /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
-  inline const Coefficients& coeffs() const { return m_coeffs; }
+  inline const typename ei_traits<Derived>::Coefficients& coeffs() const { return this->derived().coeffs(); }
 
   /** \returns a vector expression of the coefficients (x,y,z,w) */
-  inline Coefficients& coeffs() { return m_coeffs; }
-
-  /** Default constructor leaving the quaternion uninitialized. */
-  inline Quaternion() {}
-
-  /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from
-    * its four coefficients \a w, \a x, \a y and \a z.
-    *
-    * \warning Note the order of the arguments: the real \a w coefficient first,
-    * while internally the coefficients are stored in the following order:
-    * [\c x, \c y, \c z, \c w]
-    */
-  inline Quaternion(Scalar w, Scalar x, Scalar y, Scalar z)
-  { m_coeffs << x, y, z, w; }
+  inline typename ei_traits<Derived>::Coefficients& coeffs() { return this->derived().coeffs(); }
 
-  /** Copy constructor */
-  inline Quaternion(const Quaternion& other) { m_coeffs = other.m_coeffs; }
-
-  /** Constructs and initializes a quaternion from the angle-axis \a aa */
-  explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
-
-  /** Constructs and initializes a quaternion from either:
-    *  - a rotation matrix expression,
-    *  - a 4D vector expression representing quaternion coefficients.
-    * \sa operator=(MatrixBase<Derived>)
-    */
-  template<typename Derived>
-  explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
-
-  Quaternion& operator=(const Quaternion& other);
-  Quaternion& operator=(const AngleAxisType& aa);
-  template<typename Derived>
-  Quaternion& operator=(const MatrixBase<Derived>& m);
+  template<class OtherDerived> QuaternionBase& operator=(const QuaternionBase<OtherDerived>& other);
+  QuaternionBase& operator=(const AngleAxisType& aa);
+  template<class OtherDerived>
+  QuaternionBase& operator=(const MatrixBase<OtherDerived>& m);
 
   /** \returns a quaternion representing an identity rotation
     * \sa MatrixBase::Identity()
     */
-  inline static Quaternion Identity() { return Quaternion(1, 0, 0, 0); }
+  inline static Quaternion<Scalar> Identity() { return Quaternion<Scalar>(1, 0, 0, 0); }
 
-  /** \sa Quaternion::Identity(), MatrixBase::setIdentity()
+  /** \sa Quaternion2::Identity(), MatrixBase::setIdentity()
     */
-  inline Quaternion& setIdentity() { m_coeffs << 0, 0, 0, 1; return *this; }
+  inline QuaternionBase& setIdentity() { coeffs() << 0, 0, 0, 1; return *this; }
 
   /** \returns the squared norm of the quaternion's coefficients
-    * \sa Quaternion::norm(), MatrixBase::squaredNorm()
+    * \sa Quaternion2::norm(), MatrixBase::squaredNorm()
     */
-  inline Scalar squaredNorm() const { return m_coeffs.squaredNorm(); }
+  inline Scalar squaredNorm() const { return coeffs().squaredNorm(); }
 
   /** \returns the norm of the quaternion's coefficients
-    * \sa Quaternion::squaredNorm(), MatrixBase::norm()
+    * \sa Quaternion2::squaredNorm(), MatrixBase::norm()
     */
-  inline Scalar norm() const { return m_coeffs.norm(); }
+  inline Scalar norm() const { return coeffs().norm(); }
 
   /** Normalizes the quaternion \c *this
     * \sa normalized(), MatrixBase::normalize() */
-  inline void normalize() { m_coeffs.normalize(); }
+  inline void normalize() { coeffs().normalize(); }
   /** \returns a normalized version of \c *this
     * \sa normalize(), MatrixBase::normalized() */
-  inline Quaternion normalized() const { return Quaternion(m_coeffs.normalized()); }
+  inline Quaternion<Scalar> normalized() const { return Quaternion<Scalar>(coeffs().normalized()); }
 
-  /** \returns the dot product of \c *this and \a other
+    /** \returns the dot product of \c *this and \a other
     * Geometrically speaking, the dot product of two unit quaternions
     * corresponds to the cosine of half the angle between the two rotations.
     * \sa angularDistance()
     */
-  inline Scalar dot(const Quaternion& other) const { return m_coeffs.dot(other.m_coeffs); }
+  template<class OtherDerived> inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); }
 
-  inline Scalar angularDistance(const Quaternion& other) const;
+  template<class OtherDerived> inline Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const;
 
   Matrix3 toRotationMatrix(void) const;
 
   template<typename Derived1, typename Derived2>
-  Quaternion& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
+  QuaternionBase& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
 
-  inline Quaternion operator* (const Quaternion& q) const;
-  inline Quaternion& operator*= (const Quaternion& q);
+  template<class OtherDerived> inline Quaternion<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const;
+  template<class OtherDerived> inline QuaternionBase& operator*= (const QuaternionBase<OtherDerived>& q);
 
-  Quaternion inverse(void) const;
-  Quaternion conjugate(void) const;
+  Quaternion<Scalar> inverse(void) const;
+  Quaternion<Scalar> conjugate(void) const;
 
-  Quaternion slerp(Scalar t, const Quaternion& other) const;
+  template<class OtherDerived> Quaternion<Scalar> slerp(Scalar t, const QuaternionBase<OtherDerived>& other) const;
+
+  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+    * determined by \a prec.
+    *
+    * \sa MatrixBase::isApprox() */
+  bool isApprox(const QuaternionBase& other, RealScalar prec = precision<Scalar>()) const
+  { return coeffs().isApprox(other.coeffs(), prec); }
+
+  Vector3 _transformVector(Vector3 v) const;
 
   /** \returns \c *this with scalar type casted to \a NewScalarType
     *
@@ -197,57 +180,150 @@ public:
     * then this function smartly returns a const reference to \c *this.
     */
   template<typename NewScalarType>
-  inline typename ei_cast_return_type<Quaternion,Quaternion<NewScalarType> >::type cast() const
-  { return typename ei_cast_return_type<Quaternion,Quaternion<NewScalarType> >::type(*this); }
+  inline typename ei_cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const
+  {
+    return typename ei_cast_return_type<Derived,Quaternion<NewScalarType> >::type(
+      coeffs().template cast<NewScalarType>());
+  }
+};
 
-  /** Copy constructor with scalar type conversion */
-  template<typename OtherScalarType>
-  inline explicit Quaternion(const Quaternion<OtherScalarType>& other)
-  { m_coeffs = other.coeffs().template cast<Scalar>(); }
+template<typename _Scalar>
+struct ei_traits<Quaternion<_Scalar> >
+{
+  typedef _Scalar Scalar;
+  typedef Matrix<_Scalar,4,1> Coefficients;
+  enum{
+    PacketAccess = Aligned 
+  };
+};
 
-  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
-    * determined by \a prec.
+template<typename _Scalar>
+class Quaternion : public QuaternionBase<Quaternion<_Scalar> >{
+  typedef QuaternionBase<Quaternion<_Scalar> > Base;
+public:
+  using Base::operator=;
+
+  typedef _Scalar Scalar;
+
+  typedef typename ei_traits<Quaternion<Scalar> >::Coefficients Coefficients;
+  typedef typename Base::AngleAxisType AngleAxisType;
+
+  /** Default constructor leaving the quaternion uninitialized. */
+  inline Quaternion() {}
+
+  /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from
+    * its four coefficients \a w, \a x, \a y and \a z.
     *
-    * \sa MatrixBase::isApprox() */
-  bool isApprox(const Quaternion& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
-  { return m_coeffs.isApprox(other.m_coeffs, prec); }
+    * \warning Note the order of the arguments: the real \a w coefficient first,
+    * while internally the coefficients are stored in the following order:
+    * [\c x, \c y, \c z, \c w]
+    */
+  inline Quaternion(Scalar w, Scalar x, Scalar y, Scalar z)
+  { coeffs() << x, y, z, w; }
 
-  Vector3 _transformVector(Vector3 v) const;
+  /** Constructs and initialize a quaternion from the array data
+    * This constructor is also used to map an array */
+  inline Quaternion(const Scalar* data) : m_coeffs(data) {}
+
+  /** Copy constructor */
+//  template<class Derived> inline Quaternion(const QuaternionBase<Derived>& other) { m_coeffs = other.coeffs(); } [XXX] redundant with 703
+
+  /** Constructs and initializes a quaternion from the angle-axis \a aa */
+  explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
+
+  /** Constructs and initializes a quaternion from either:
+    *  - a rotation matrix expression,
+    *  - a 4D vector expression representing quaternion coefficients.
+    */
+  template<typename Derived>
+  explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
+
+  /** Copy constructor with scalar type conversion */
+  template<class Derived>
+  inline explicit Quaternion(const QuaternionBase<Derived>& other)
+  { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+  inline Coefficients& coeffs() { return m_coeffs;}
+  inline const Coefficients& coeffs() const { return m_coeffs;}
 
 protected:
   Coefficients m_coeffs;
 };
 
-/** \ingroup Geometry_Module
-  * single precision quaternion type */
-typedef Quaternion<float> Quaternionf;
-/** \ingroup Geometry_Module
-  * double precision quaternion type */
-typedef Quaternion<double> Quaterniond;
+/* ########### Map<Quaternion> */
+
+/** \class Map<Quaternion>
+  * \nonstableyet
+  *
+  * \brief Expression of a quaternion
+  *
+  * \param Scalar the type of the vector of diagonal coefficients
+  *
+  * \sa class Quaternion, class QuaternionBase
+  */
+template<typename _Scalar, int _PacketAccess>
+struct ei_traits<Map<Quaternion<_Scalar>, _PacketAccess> >:
+ei_traits<Quaternion<_Scalar> >
+{
+  typedef _Scalar Scalar;
+  typedef Map<Matrix<_Scalar,4,1> > Coefficients;
+  enum {
+    PacketAccess = _PacketAccess
+  };
+};
+
+template<typename _Scalar, int PacketAccess>
+class Map<Quaternion<_Scalar>, PacketAccess > : public QuaternionBase<Map<Quaternion<_Scalar>, PacketAccess> >, ei_no_assignment_operator {
+  public:
+    
+    typedef _Scalar Scalar;
+
+    typedef typename ei_traits<Map<Quaternion<Scalar>, PacketAccess> >::Coefficients Coefficients;
+
+    inline Map<Quaternion<Scalar>, PacketAccess >(const Scalar* coeffs) : m_coeffs(coeffs) {}
+    
+    inline Coefficients& coeffs() { return m_coeffs;}
+    inline const Coefficients& coeffs() const { return m_coeffs;}
+
+  protected:
+    Coefficients m_coeffs;
+};
+
+typedef Map<Quaternion<double> > QuaternionMapd;
+typedef Map<Quaternion<float> > QuaternionMapf;
+typedef Map<Quaternion<double>, Aligned> QuaternionMapAlignedd;
+typedef Map<Quaternion<float>, Aligned> QuaternionMapAlignedf;
 
 // Generic Quaternion * Quaternion product
-template<int Arch,typename Scalar> inline Quaternion<Scalar>
-ei_quaternion_product(const Quaternion<Scalar>& a, const Quaternion<Scalar>& b)
+template<int Arch, class Derived, class OtherDerived, typename Scalar, int PacketAccess> struct ei_quat_product
 {
-  return Quaternion<Scalar>
-  (
-    a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
-    a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
-    a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
-    a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
-  );
-}
+  inline static Quaternion<Scalar> run(const QuaternionBase<Derived>& a, const QuaternionBase<OtherDerived>& b){
+    return Quaternion<Scalar>
+    (
+      a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
+      a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
+      a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
+      a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
+    );
+  }
+};
 
 /** \returns the concatenation of two rotations as a quaternion-quaternion product */
-template <typename Scalar>
-inline Quaternion<Scalar> Quaternion<Scalar>::operator* (const Quaternion& other) const
+template <class Derived>
+template <class OtherDerived>
+inline Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::operator* (const QuaternionBase<OtherDerived>& other) const
 {
-  return ei_quaternion_product<EiArch>(*this,other);
+  EIGEN_STATIC_ASSERT((ei_is_same_type<typename Derived::Scalar, typename OtherDerived::Scalar>::ret),
+   YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+   return ei_quat_product<EiArch, Derived, OtherDerived, 
+                          typename ei_traits<Derived>::Scalar,
+                          ei_traits<Derived>::PacketAccess && ei_traits<OtherDerived>::PacketAccess>::run(*this, other);
 }
 
 /** \sa operator*(Quaternion) */
-template <typename Scalar>
-inline Quaternion<Scalar>& Quaternion<Scalar>::operator*= (const Quaternion& other)
+template <class Derived>
+template <class OtherDerived>
+inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
 {
   return (*this = *this * other);
 }
@@ -256,12 +332,12 @@ inline Quaternion<Scalar>& Quaternion<Scalar>::operator*= (const Quaternion& oth
   * \remarks If the quaternion is used to rotate several points (>1)
   * then it is much more efficient to first convert it to a 3x3 Matrix.
   * Comparison of the operation cost for n transformations:
-  *   - Quaternion:    30n
+  *   - Quaternion2:    30n
   *   - Via a Matrix3: 24 + 15n
   */
-template <typename Scalar>
-inline typename Quaternion<Scalar>::Vector3
-Quaternion<Scalar>::_transformVector(Vector3 v) const
+template <class Derived>
+inline typename QuaternionBase<Derived>::Vector3
+QuaternionBase<Derived>::_transformVector(Vector3 v) const
 {
     // Note that this algorithm comes from the optimization by hand
     // of the conversion to a Matrix followed by a Matrix/Vector product.
@@ -272,17 +348,18 @@ Quaternion<Scalar>::_transformVector(Vector3 v) const
     return v + this->w() * uv + this->vec().cross(uv);
 }
 
-template<typename Scalar>
-inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const Quaternion& other)
+template<class Derived>
+template<class OtherDerived>
+inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
 {
-  m_coeffs = other.m_coeffs;
+  coeffs() = other.coeffs();
   return *this;
 }
 
 /** Set \c *this from an angle-axis \a aa and returns a reference to \c *this
   */
-template<typename Scalar>
-inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const AngleAxisType& aa)
+template<class Derived>
+inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
 {
   Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
   this->w() = ei_cos(ha);
@@ -295,20 +372,23 @@ inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const AngleAxisType& aa
   *   - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
   *     and \a xpr is converted to a quaternion
   */
-template<typename Scalar>
-template<typename Derived>
-inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const MatrixBase<Derived>& xpr)
+
+template<class Derived>
+template<class MatrixDerived>
+inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)
 {
-  ei_quaternion_assign_impl<Derived>::run(*this, xpr.derived());
+  EIGEN_STATIC_ASSERT((ei_is_same_type<typename Derived::Scalar, typename MatrixDerived::Scalar>::ret),
+   YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+  ei_quaternionbase_assign_impl<MatrixDerived>::run(*this, xpr.derived());
   return *this;
 }
 
 /** Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to
   * be normalized, otherwise the result is undefined.
   */
-template<typename Scalar>
-inline typename Quaternion<Scalar>::Matrix3
-Quaternion<Scalar>::toRotationMatrix(void) const
+template<class Derived>
+inline typename QuaternionBase<Derived>::Matrix3
+QuaternionBase<Derived>::toRotationMatrix(void) const
 {
   // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
   // if not inlined then the cost of the return by value is huge ~ +35%,
@@ -352,9 +432,9 @@ Quaternion<Scalar>::toRotationMatrix(void) const
   * Note that the two input vectors do \b not have to be normalized, and
   * do not need to have the same norm.
   */
-template<typename Scalar>
+template<class Derived>
 template<typename Derived1, typename Derived2>
-inline Quaternion<Scalar>& Quaternion<Scalar>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
+inline QuaternionBase<Derived>& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
 {
   Vector3 v0 = a.normalized();
   Vector3 v1 = b.normalized();
@@ -393,19 +473,19 @@ inline Quaternion<Scalar>& Quaternion<Scalar>::setFromTwoVectors(const MatrixBas
   * Note that in most cases, i.e., if you simply want the opposite rotation,
   * and/or the quaternion is normalized, then it is enough to use the conjugate.
   *
-  * \sa Quaternion::conjugate()
+  * \sa Quaternion2::conjugate()
   */
-template <typename Scalar>
-inline Quaternion<Scalar> Quaternion<Scalar>::inverse() const
+template <class Derived>
+inline Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::inverse() const
 {
   // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite()  ??
   Scalar n2 = this->squaredNorm();
   if (n2 > 0)
-    return Quaternion(conjugate().coeffs() / n2);
+    return Quaternion<Scalar>(conjugate().coeffs() / n2);
   else
   {
     // return an invalid result to flag the error
-    return Quaternion(Coefficients::Zero());
+    return Quaternion<Scalar>(ei_traits<Derived>::Coefficients::Zero());
   }
 }
 
@@ -413,19 +493,20 @@ inline Quaternion<Scalar> Quaternion<Scalar>::inverse() const
   * if the quaternion is normalized.
   * The conjugate of a quaternion represents the opposite rotation.
   *
-  * \sa Quaternion::inverse()
+  * \sa Quaternion2::inverse()
   */
-template <typename Scalar>
-inline Quaternion<Scalar> Quaternion<Scalar>::conjugate() const
+template <class Derived>
+inline Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::conjugate() const
 {
-  return Quaternion(this->w(),-this->x(),-this->y(),-this->z());
+  return Quaternion<Scalar>(this->w(),-this->x(),-this->y(),-this->z());
 }
 
 /** \returns the angle (in radian) between two rotations
   * \sa dot()
   */
-template <typename Scalar>
-inline Scalar Quaternion<Scalar>::angularDistance(const Quaternion& other) const
+template <class Derived>
+template <class OtherDerived>
+inline typename ei_traits<QuaternionBase<Derived> >::Scalar QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
 {
   double d = ei_abs(this->dot(other));
   if (d>=1.0)
@@ -436,14 +517,15 @@ inline Scalar Quaternion<Scalar>::angularDistance(const Quaternion& other) const
 /** \returns the spherical linear interpolation between the two quaternions
   * \c *this and \a other at the parameter \a t
   */
-template <typename Scalar>
-Quaternion<Scalar> Quaternion<Scalar>::slerp(Scalar t, const Quaternion& other) const
+template <class Derived>
+template <class OtherDerived>
+Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::slerp(Scalar t, const QuaternionBase<OtherDerived>& other) const
 {
   static const Scalar one = Scalar(1) - precision<Scalar>();
   Scalar d = this->dot(other);
   Scalar absD = ei_abs(d);
   if (absD>=one)
-    return *this;
+    return Quaternion<Scalar>(*this);
 
   // theta is the angle between the 2 quaternions
   Scalar theta = std::acos(absD);
@@ -454,15 +536,15 @@ Quaternion<Scalar> Quaternion<Scalar>::slerp(Scalar t, const Quaternion& other)
   if (d<0)
     scale1 = -scale1;
 
-  return Quaternion(scale0 * m_coeffs + scale1 * other.m_coeffs);
+  return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
 }
 
 // set from a rotation matrix
 template<typename Other>
-struct ei_quaternion_assign_impl<Other,3,3>
+struct ei_quaternionbase_assign_impl<Other,3,3>
 {
   typedef typename Other::Scalar Scalar;
-  inline static void run(Quaternion<Scalar>& q, const Other& mat)
+  template<class Derived> inline static void run(QuaternionBase<Derived>& q, const Other& mat)
   {
     // This algorithm comes from  "Quaternion Calculus and Fast Animation",
     // Ken Shoemake, 1987 SIGGRAPH course notes
@@ -498,13 +580,14 @@ struct ei_quaternion_assign_impl<Other,3,3>
 
 // set from a vector of coefficients assumed to be a quaternion
 template<typename Other>
-struct ei_quaternion_assign_impl<Other,4,1>
+struct ei_quaternionbase_assign_impl<Other,4,1>
 {
   typedef typename Other::Scalar Scalar;
-  inline static void run(Quaternion<Scalar>& q, const Other& vec)
+  template<class Derived> inline static void run(QuaternionBase<Derived>& q, const Other& vec)
   {
     q.coeffs() = vec;
   }
 };
 
+
 #endif // EIGEN_QUATERNION_H
diff --git a/Eigen/src/Geometry/Transform.h b/Eigen/src/Geometry/Transform.h
index 70204f72b..4ee036140 100644
--- a/Eigen/src/Geometry/Transform.h
+++ b/Eigen/src/Geometry/Transform.h
@@ -481,6 +481,15 @@ typedef Transform<double,2> Transform2d;
 typedef Transform<double,3> Transform3d;
 
 /** \ingroup Geometry_Module */
+typedef Transform<float,2,Isometry> Isometry2f;
+/** \ingroup Geometry_Module */
+typedef Transform<float,3,Isometry> Isometry3f;
+/** \ingroup Geometry_Module */
+typedef Transform<double,2,Isometry> Isometry2d;
+/** \ingroup Geometry_Module */
+typedef Transform<double,3,Isometry> Isometry3d;
+
+/** \ingroup Geometry_Module */
 typedef Transform<float,2> Affine2f;
 /** \ingroup Geometry_Module */
 typedef Transform<float,3> Affine3f;
@@ -512,7 +521,7 @@ typedef Transform<double,3,Projective> Projective3d;
 **************************/
 
 #ifdef EIGEN_QT_SUPPORT
-/** Initialises \c *this from a QMatrix assuming the dimension is 2.
+/** Initializes \c *this from a QMatrix assuming the dimension is 2.
   *
   * This function is available only if the token EIGEN_QT_SUPPORT is defined.
   */
@@ -538,7 +547,7 @@ Transform<Scalar,Dim,Mode>& Transform<Scalar,Dim,Mode>::operator=(const QMatrix&
 
 /** \returns a QMatrix from \c *this assuming the dimension is 2.
   *
-  * \warning this convertion might loss data if \c *this is not affine
+  * \warning this conversion might loss data if \c *this is not affine
   *
   * This function is available only if the token EIGEN_QT_SUPPORT is defined.
   */
@@ -551,7 +560,7 @@ QMatrix Transform<Scalar,Dim,Mode>::toQMatrix(void) const
                  matrix.coeff(0,2), matrix.coeff(1,2));
 }
 
-/** Initialises \c *this from a QTransform assuming the dimension is 2.
+/** Initializes \c *this from a QTransform assuming the dimension is 2.
   *
   * This function is available only if the token EIGEN_QT_SUPPORT is defined.
   */
@@ -899,7 +908,7 @@ struct ei_projective_transform_inverse<TransformType, Projective>
   * \returns the inverse transformation according to some given knowledge
   * on \c *this.
   *
-  * \param traits allows to optimize the inversion process when the transformion
+  * \param traits allows to optimize the inversion process when the transformation
   * is known to be not a general transformation. The possible values are:
   *  - Projective if the transformation is not necessarily affine, i.e., if the
   *    last row is not guaranteed to be [0 ... 0 1]
@@ -968,7 +977,7 @@ struct ei_transform_take_affine_part<Transform<Scalar,Dim,AffineCompact> > {
 };
 
 /*****************************************************
-*** Specializations of construct from matix        ***
+*** Specializations of construct from matrix       ***
 *****************************************************/
 
 template<typename Other, int Mode, int Dim, int HDim>
diff --git a/Eigen/src/Geometry/Umeyama.h b/Eigen/src/Geometry/Umeyama.h
index 7652aa92e..551a69e5b 100644
--- a/Eigen/src/Geometry/Umeyama.h
+++ b/Eigen/src/Geometry/Umeyama.h
@@ -117,7 +117,7 @@ umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, boo
   enum { Dimension = EIGEN_ENUM_MIN(Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) };
 
   typedef Matrix<Scalar, Dimension, 1> VectorType;
-  typedef typename ei_plain_matrix_type<Derived>::type MatrixType;
+  typedef Matrix<Scalar, Dimension, Dimension> MatrixType;
   typedef typename ei_plain_matrix_type_row_major<Derived>::type RowMajorMatrixType;
 
   const int m = src.rows(); // dimension
@@ -131,17 +131,11 @@ umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, boo
   const VectorType dst_mean = dst.rowwise().sum() * one_over_n;
 
   // demeaning of src and dst points
-  RowMajorMatrixType src_demean(m,n);
-  RowMajorMatrixType dst_demean(m,n);
-  for (int i=0; i<n; ++i)
-  {
-    src_demean.col(i) = src.col(i) - src_mean;
-    dst_demean.col(i) = dst.col(i) - dst_mean;
-  }
+  const RowMajorMatrixType src_demean = src.colwise() - src_mean;
+  const RowMajorMatrixType dst_demean = dst.colwise() - dst_mean;
 
   // Eq. (36)-(37)
   const Scalar src_var = src_demean.rowwise().squaredNorm().sum() * one_over_n;
-  // const Scalar dst_var = dst_demean.rowwise().squaredNorm().sum() * one_over_n;
 
   // Eq. (38)
   const MatrixType sigma = one_over_n * dst_demean * src_demean.transpose();
diff --git a/Eigen/src/Geometry/arch/Geometry_SSE.h b/Eigen/src/Geometry/arch/Geometry_SSE.h
index d0342febc..1b8f6aead 100644
--- a/Eigen/src/Geometry/arch/Geometry_SSE.h
+++ b/Eigen/src/Geometry/arch/Geometry_SSE.h
@@ -26,24 +26,26 @@
 #ifndef EIGEN_GEOMETRY_SSE_H
 #define EIGEN_GEOMETRY_SSE_H
 
-template<> inline Quaternion<float>
-ei_quaternion_product<EiArch_SSE,float>(const Quaternion<float>& _a, const Quaternion<float>& _b)
+template<class Derived, class OtherDerived> struct ei_quat_product<EiArch_SSE, Derived, OtherDerived, float, Aligned>
 {
-  const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0,0,0,0x80000000));
-  Quaternion<float> res;
-  __m128 a = _a.coeffs().packet<Aligned>(0);
-  __m128 b = _b.coeffs().packet<Aligned>(0);
-  __m128 flip1 = _mm_xor_ps(_mm_mul_ps(ei_vec4f_swizzle1(a,1,2,0,2),
-                                       ei_vec4f_swizzle1(b,2,0,1,2)),mask);
-  __m128 flip2 = _mm_xor_ps(_mm_mul_ps(ei_vec4f_swizzle1(a,3,3,3,1),
-                                       ei_vec4f_swizzle1(b,0,1,2,1)),mask);
-  ei_pstore(&res.x(),
-            _mm_add_ps(_mm_sub_ps(_mm_mul_ps(a,ei_vec4f_swizzle1(b,3,3,3,3)),
-                                  _mm_mul_ps(ei_vec4f_swizzle1(a,2,0,1,0),
-                                             ei_vec4f_swizzle1(b,1,2,0,0))),
-                       _mm_add_ps(flip1,flip2)));
-  return res;
-}
+  inline static Quaternion<float> run(const QuaternionBase<Derived>& _a, const QuaternionBase<OtherDerived>& _b)
+  {
+    const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0,0,0,0x80000000));
+    Quaternion<float> res;
+    __m128 a = _a.coeffs().packet<Aligned>(0);
+    __m128 b = _b.coeffs().packet<Aligned>(0);
+    __m128 flip1 = _mm_xor_ps(_mm_mul_ps(ei_vec4f_swizzle1(a,1,2,0,2),
+                                         ei_vec4f_swizzle1(b,2,0,1,2)),mask);
+    __m128 flip2 = _mm_xor_ps(_mm_mul_ps(ei_vec4f_swizzle1(a,3,3,3,1),
+                                         ei_vec4f_swizzle1(b,0,1,2,1)),mask);
+    ei_pstore(&res.x(),
+              _mm_add_ps(_mm_sub_ps(_mm_mul_ps(a,ei_vec4f_swizzle1(b,3,3,3,3)),
+                                    _mm_mul_ps(ei_vec4f_swizzle1(a,2,0,1,0),
+                                               ei_vec4f_swizzle1(b,1,2,0,0))),
+                         _mm_add_ps(flip1,flip2)));
+    return res;
+  }
+};
 
 template<typename VectorLhs,typename VectorRhs>
 struct ei_cross3_impl<EiArch_SSE,VectorLhs,VectorRhs,float,true> {
diff --git a/Eigen/src/Sparse/SparseExpressionMaker.h b/Eigen/src/Sparse/SparseExpressionMaker.h
new file mode 100644
index 000000000..1fdcbb1f2
--- /dev/null
+++ b/Eigen/src/Sparse/SparseExpressionMaker.h
@@ -0,0 +1,48 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SPARSE_EXPRESSIONMAKER_H
+#define EIGEN_SPARSE_EXPRESSIONMAKER_H
+
+template<typename XprType>
+struct MakeNestByValue<XprType,IsSparse>
+{
+  typedef SparseNestByValue<XprType> Type;
+};
+
+template<typename Func, typename XprType>
+struct MakeCwiseUnaryOp<Func,XprType,IsSparse>
+{
+  typedef SparseCwiseUnaryOp<Func,XprType> Type;
+};
+
+template<typename Func, typename A, typename B>
+struct MakeCwiseBinaryOp<Func,A,B,IsSparse>
+{
+  typedef SparseCwiseBinaryOp<Func,A,B> Type;
+};
+
+// TODO complete the list
+
+#endif // EIGEN_SPARSE_EXPRESSIONMAKER_H