merge and add start/end to Eigen2Support

39 files changed, 346 insertions, 198 deletions

diff --git a/Eigen/src/Array/VectorwiseOp.h b/Eigen/src/Array/VectorwiseOp.h
index 3aaaa1ec9..eef554d8a 100644
--- a/Eigen/src/Array/VectorwiseOp.h
+++ b/Eigen/src/Array/VectorwiseOp.h
@@ -384,7 +384,7 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
     const Reverse<ExpressionType, Direction> reverse() const
     { return Reverse<ExpressionType, Direction>( _expression() ); }
 
-    const Replicate<ExpressionType,Direction==Vertical?Dynamic:1,Direction==Horizontal?Dynamic:1>
+    const Replicate<ExpressionType,(Direction==Vertical?Dynamic:1),(Direction==Horizontal?Dynamic:1)>
     replicate(int factor) const;
 
     /** \nonstableyet
diff --git a/Eigen/src/Cholesky/LDLT.h b/Eigen/src/Cholesky/LDLT.h
index c13be9ac2..4fb6d3d2c 100644
--- a/Eigen/src/Cholesky/LDLT.h
+++ b/Eigen/src/Cholesky/LDLT.h
@@ -194,7 +194,7 @@ LDLT<MatrixType>& LDLT<MatrixType>::compute(const MatrixType& a)
   {
     // Find largest diagonal element
     int index_of_biggest_in_corner;
-    biggest_in_corner = m_matrix.diagonal().end(size-j).cwiseAbs()
+    biggest_in_corner = m_matrix.diagonal().tail(size-j).cwiseAbs()
                        .maxCoeff(&index_of_biggest_in_corner);
     index_of_biggest_in_corner += j;
 
@@ -227,12 +227,12 @@ LDLT<MatrixType>& LDLT<MatrixType>::compute(const MatrixType& a)
 
     if (j == 0) {
       m_matrix.row(0) = m_matrix.row(0).conjugate();
-      m_matrix.col(0).end(size-1) = m_matrix.row(0).end(size-1) / m_matrix.coeff(0,0);
+      m_matrix.col(0).tail(size-1) = m_matrix.row(0).tail(size-1) / m_matrix.coeff(0,0);
       continue;
     }
 
-    RealScalar Djj = ei_real(m_matrix.coeff(j,j) -  m_matrix.row(j).start(j)
-                                               .dot(m_matrix.col(j).start(j)));
+    RealScalar Djj = ei_real(m_matrix.coeff(j,j) -  m_matrix.row(j).head(j)
+                                               .dot(m_matrix.col(j).head(j)));
     m_matrix.coeffRef(j,j) = Djj;
 
     // Finish early if the matrix is not full rank.
@@ -244,13 +244,13 @@ LDLT<MatrixType>& LDLT<MatrixType>::compute(const MatrixType& a)
 
     int endSize = size - j - 1;
     if (endSize > 0) {
-      _temporary.end(endSize).noalias() = m_matrix.block(j+1,0, endSize, j)
-                                * m_matrix.col(j).start(j).conjugate();
+      _temporary.tail(endSize).noalias() = m_matrix.block(j+1,0, endSize, j)
+                                * m_matrix.col(j).head(j).conjugate();
 
-      m_matrix.row(j).end(endSize) = m_matrix.row(j).end(endSize).conjugate()
-                                   - _temporary.end(endSize).transpose();
+      m_matrix.row(j).tail(endSize) = m_matrix.row(j).tail(endSize).conjugate()
+                                   - _temporary.tail(endSize).transpose();
 
-      m_matrix.col(j).end(endSize) = m_matrix.row(j).end(endSize) / Djj;
+      m_matrix.col(j).tail(endSize) = m_matrix.row(j).tail(endSize) / Djj;
     }
   }
 
diff --git a/Eigen/src/Cholesky/LLT.h b/Eigen/src/Cholesky/LLT.h
index ad737aaeb..02645b23f 100644
--- a/Eigen/src/Cholesky/LLT.h
+++ b/Eigen/src/Cholesky/LLT.h
@@ -166,7 +166,7 @@ template<> struct ei_llt_inplace<LowerTriangular>
       Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
 
       RealScalar x = ei_real(mat.coeff(k,k));
-      if (k>0) x -= mat.row(k).start(k).squaredNorm();
+      if (k>0) x -= mat.row(k).head(k).squaredNorm();
       if (x<=RealScalar(0))
         return false;
       mat.coeffRef(k,k) = x = ei_sqrt(x);
diff --git a/Eigen/src/Core/Assign.h b/Eigen/src/Core/Assign.h
index d6bf37c6e..e5c17b3f4 100644
--- a/Eigen/src/Core/Assign.h
+++ b/Eigen/src/Core/Assign.h
@@ -49,6 +49,7 @@ private:
     InnerMaxSize = int(Derived::Flags)&RowMajorBit
               ? Derived::MaxColsAtCompileTime
               : Derived::MaxRowsAtCompileTime,
+    MaxSizeAtCompileTime = ei_size_at_compile_time<Derived::MaxColsAtCompileTime,Derived::MaxRowsAtCompileTime>::ret,
     PacketSize = ei_packet_traits<typename Derived::Scalar>::size
   };
 
@@ -60,9 +61,9 @@ private:
                        && int(DstIsAligned) && int(SrcIsAligned),
     MayLinearize = StorageOrdersAgree && (int(Derived::Flags) & int(OtherDerived::Flags) & LinearAccessBit),
     MayLinearVectorize = MightVectorize && MayLinearize
-                                        && (DstIsAligned || InnerMaxSize == Dynamic),
+                                        && (DstIsAligned || MaxSizeAtCompileTime == Dynamic),
       /* If the destination isn't aligned, we have to do runtime checks and we don't unroll,
-         so it's only good for large enough sizes. See remark below about InnerMaxSize. */
+         so it's only good for large enough sizes. */
     MaySliceVectorize  = MightVectorize && int(InnerMaxSize)>=3*PacketSize
       /* slice vectorization can be slow, so we only want it if the slices are big, which is
          indicated by InnerMaxSize rather than InnerSize, think of the case of a dynamic block
@@ -385,7 +386,7 @@ struct ei_assign_impl<Derived1, Derived2, LinearVectorizedTraversal, NoUnrolling
     const int size = dst.size();
     const int packetSize = ei_packet_traits<typename Derived1::Scalar>::size;
     const int alignedStart = ei_assign_traits<Derived1,Derived2>::DstIsAligned ? 0
-                           : ei_alignmentOffset(&dst.coeffRef(0), size);
+                           : ei_first_aligned(&dst.coeffRef(0), size);
     const int alignedEnd = alignedStart + ((size-alignedStart)/packetSize)*packetSize;
 
     for(int index = 0; index < alignedStart; ++index)
@@ -430,7 +431,7 @@ struct ei_assign_impl<Derived1, Derived2, SliceVectorizedTraversal, NoUnrolling>
     const int outerSize = dst.outerSize();
     const int alignedStep = (packetSize - dst.stride() % packetSize) & packetAlignedMask;
     int alignedStart = ei_assign_traits<Derived1,Derived2>::DstIsAligned ? 0
-                     : ei_alignmentOffset(&dst.coeffRef(0,0), innerSize);
+                     : ei_first_aligned(&dst.coeffRef(0,0), innerSize);
 
     for(int i = 0; i < outerSize; ++i)
     {
@@ -480,11 +481,11 @@ EIGEN_STRONG_INLINE Derived& DenseBase<Derived>
   EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
   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)
-  ei_assert(rows() == other.rows() && cols() == other.cols());
-  ei_assign_impl<Derived, OtherDerived>::run(derived(),other.derived());
 #ifdef EIGEN_DEBUG_ASSIGN
   ei_assign_traits<Derived, OtherDerived>::debug();
 #endif
+  ei_assert(rows() == other.rows() && cols() == other.cols());
+  ei_assign_impl<Derived, OtherDerived>::run(derived(),other.derived());
 #ifndef EIGEN_NO_DEBUG
   checkTransposeAliasing(other.derived());
 #endif
diff --git a/Eigen/src/Core/Coeffs.h b/Eigen/src/Core/Coeffs.h
index b8af2531e..ebfd0c80e 100644
--- a/Eigen/src/Core/Coeffs.h
+++ b/Eigen/src/Core/Coeffs.h
@@ -379,36 +379,33 @@ EIGEN_STRONG_INLINE void DenseBase<Derived>::copyPacket(int index, const DenseBa
     other.derived().template packet<LoadMode>(index));
 }
 
-
-template<typename Derived, typename Integer, bool JustReturnZero>
-struct ei_alignmentOffset_impl
+template<typename Derived, bool JustReturnZero>
+struct ei_first_aligned_impl
 {
-  inline static Integer run(const DenseBase<Derived>&, Integer)
+  inline static int run(const DenseBase<Derived>&)
   { return 0; }
 };
 
-template<typename Derived, typename Integer>
-struct ei_alignmentOffset_impl<Derived, Integer, false>
+template<typename Derived>
+struct ei_first_aligned_impl<Derived, false>
 {
-  inline static Integer run(const DenseBase<Derived>& m, Integer maxOffset)
+  inline static int run(const DenseBase<Derived>& m)
   {
-    return ei_alignmentOffset(&m.const_cast_derived().coeffRef(0,0), maxOffset);
+    return ei_first_aligned(&m.const_cast_derived().coeffRef(0,0), m.size());
   }
 };
 
-/** \internal \returns the number of elements which have to be skipped, starting
-  * from the address of coeffRef(0,0), to find the first 16-byte aligned element.
+/** \internal \returns the index of the first element of the array that is well aligned for vectorization.
   *
-  * \note If the expression doesn't have the DirectAccessBit, this function returns 0.
-  *
-  * There is also the variant ei_alignmentOffset(const Scalar*, Integer) defined in Memory.h.
+  * There is also the variant ei_first_aligned(const Scalar*, Integer) defined in Memory.h. See it for more
+  * documentation.
   */
-template<typename Derived, typename Integer>
-inline static Integer ei_alignmentOffset(const DenseBase<Derived>& m, Integer maxOffset)
+template<typename Derived>
+inline static int ei_first_aligned(const DenseBase<Derived>& m)
 {
-  return ei_alignmentOffset_impl<Derived, Integer,
-                                 (Derived::Flags & AlignedBit) || !(Derived::Flags & DirectAccessBit)>
-                                 ::run(m, maxOffset);
+  return ei_first_aligned_impl
+           <Derived, (Derived::Flags & AlignedBit) || !(Derived::Flags & DirectAccessBit)>
+         ::run(m);
 }
 
 #endif
diff --git a/Eigen/src/Core/DenseBase.h b/Eigen/src/Core/DenseBase.h
index d47cc8876..e07b02a51 100644
--- a/Eigen/src/Core/DenseBase.h
+++ b/Eigen/src/Core/DenseBase.h
@@ -290,11 +290,11 @@ template<typename Derived> class DenseBase
     VectorBlock<Derived> segment(int start, int size);
     const VectorBlock<Derived> segment(int start, int size) const;
 
-    VectorBlock<Derived> start(int size);
-    const VectorBlock<Derived> start(int size) const;
+    VectorBlock<Derived> head(int size);
+    const VectorBlock<Derived> head(int size) const;
 
-    VectorBlock<Derived> end(int size);
-    const VectorBlock<Derived> end(int size) const;
+    VectorBlock<Derived> tail(int size);
+    const VectorBlock<Derived> tail(int size) const;
 
     typename BlockReturnType<Derived>::Type corner(CornerType type, int cRows, int cCols);
     const typename BlockReturnType<Derived>::Type corner(CornerType type, int cRows, int cCols) const;
@@ -309,11 +309,11 @@ template<typename Derived> class DenseBase
     template<int CRows, int CCols>
     const typename BlockReturnType<Derived, CRows, CCols>::Type corner(CornerType type) const;
 
-    template<int Size> VectorBlock<Derived,Size> start(void);
-    template<int Size> const VectorBlock<Derived,Size> start() const;
+    template<int Size> VectorBlock<Derived,Size> head(void);
+    template<int Size> const VectorBlock<Derived,Size> head() const;
 
-    template<int Size> VectorBlock<Derived,Size> end();
-    template<int Size> const VectorBlock<Derived,Size> end() const;
+    template<int Size> VectorBlock<Derived,Size> tail();
+    template<int Size> const VectorBlock<Derived,Size> tail() const;
 
     template<int Size> VectorBlock<Derived,Size> segment(int start);
     template<int Size> const VectorBlock<Derived,Size> segment(int start) const;
diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index 7ffddcbf8..eddabf4b9 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -218,7 +218,7 @@ inline float ei_norm1(const std::complex<float> &x) { return(ei_abs(x.real()) +
 inline std::complex<float> ei_exp(std::complex<float> x)  { return std::exp(x); }
 inline std::complex<float> ei_sin(std::complex<float> x)  { return std::sin(x); }
 inline std::complex<float> ei_cos(std::complex<float> x)  { return std::cos(x); }
-inline std::complex<float> ei_atan2(std::complex<float>, std::complex<float> )  { ei_assert(false); return 0; }
+inline std::complex<float> ei_atan2(std::complex<float>, std::complex<float> )  { ei_assert(false); return 0.f; }
 
 template<> inline std::complex<float> ei_random()
 {
@@ -255,7 +255,7 @@ inline double ei_norm1(const std::complex<double> &x) { return(ei_abs(x.real())
 inline std::complex<double> ei_exp(std::complex<double> x)  { return std::exp(x); }
 inline std::complex<double> ei_sin(std::complex<double> x)  { return std::sin(x); }
 inline std::complex<double> ei_cos(std::complex<double> x)  { return std::cos(x); }
-inline std::complex<double> ei_atan2(std::complex<double>, std::complex<double>)  { ei_assert(false); return 0; }
+inline std::complex<double> ei_atan2(std::complex<double>, std::complex<double>)  { ei_assert(false); return 0.; }
 
 template<> inline std::complex<double> ei_random()
 {
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index 8f9949b43..4c30f30ad 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/Eigen/src/Core/MatrixBase.h
@@ -397,6 +397,15 @@ template<typename Derived> class MatrixBase
     inline const Cwise<Derived> cwise() const;
     inline Cwise<Derived> cwise();
 
+    VectorBlock<Derived> start(int size);
+    const VectorBlock<Derived> start(int size) const;
+    VectorBlock<Derived> end(int size);
+    const VectorBlock<Derived> end(int size) const;
+    template<int Size> VectorBlock<Derived,Size> start();
+    template<int Size> const VectorBlock<Derived,Size> start() const;
+    template<int Size> VectorBlock<Derived,Size> end();
+    template<int Size> const VectorBlock<Derived,Size> end() const;
+
     template<typename OtherDerived>
     typename ei_plain_matrix_type_column_major<OtherDerived>::type
     solveTriangular(const MatrixBase<OtherDerived>& other) const;
diff --git a/Eigen/src/Core/MatrixStorage.h b/Eigen/src/Core/MatrixStorage.h
index 8bfa728b6..584ba8ca3 100644
--- a/Eigen/src/Core/MatrixStorage.h
+++ b/Eigen/src/Core/MatrixStorage.h
@@ -98,7 +98,7 @@ template<typename T, int _Rows, int _Cols, int _Options> class ei_matrix_storage
     inline explicit ei_matrix_storage() {}
     inline ei_matrix_storage(ei_constructor_without_unaligned_array_assert) {}
     inline ei_matrix_storage(int,int,int) {}
-    inline void swap(ei_matrix_storage& other) {}
+    inline void swap(ei_matrix_storage& ) {}
     inline static int rows(void) {return _Rows;}
     inline static int cols(void) {return _Cols;}
     inline void resize(int,int,int) {}
diff --git a/Eigen/src/Core/Redux.h b/Eigen/src/Core/Redux.h
index 92522f86c..1643f13b2 100644
--- a/Eigen/src/Core/Redux.h
+++ b/Eigen/src/Core/Redux.h
@@ -209,7 +209,7 @@ struct ei_redux_impl<Func, Derived, LinearVectorizedTraversal, NoUnrolling>
   {
     const int size = mat.size();
     const int packetSize = ei_packet_traits<Scalar>::size;
-    const int alignedStart = ei_alignmentOffset(mat,size);
+    const int alignedStart = ei_first_aligned(mat);
     enum {
       alignment = (Derived::Flags & DirectAccessBit) || (Derived::Flags & AlignedBit)
                 ? Aligned : Unaligned
diff --git a/Eigen/src/Core/SolveTriangular.h b/Eigen/src/Core/SolveTriangular.h
index 618e29828..9dc019d17 100644
--- a/Eigen/src/Core/SolveTriangular.h
+++ b/Eigen/src/Core/SolveTriangular.h
@@ -25,13 +25,27 @@
 #ifndef EIGEN_SOLVETRIANGULAR_H
 #define EIGEN_SOLVETRIANGULAR_H
 
+template<typename Lhs, typename Rhs, int Side>
+class ei_trsolve_traits
+{
+  private:
+    enum {
+      RhsIsVectorAtCompileTime = (Side==OnTheLeft ? Rhs::ColsAtCompileTime : Rhs::RowsAtCompileTime)==1
+    };
+  public:
+    enum {
+      Unrolling   = (RhsIsVectorAtCompileTime && Rhs::SizeAtCompileTime <= 8)
+                  ? CompleteUnrolling : NoUnrolling,
+      RhsVectors  = RhsIsVectorAtCompileTime ? 1 : Dynamic
+    };
+};
+
 template<typename Lhs, typename Rhs,
-  int Mode, // can be Upper/Lower | UnitDiag
   int Side, // can be OnTheLeft/OnTheRight
-  int Unrolling = Rhs::IsVectorAtCompileTime && Rhs::SizeAtCompileTime <= 8 // FIXME
-                ? CompleteUnrolling : NoUnrolling,
+  int Mode, // can be Upper/Lower | UnitDiag
+  int Unrolling = ei_trsolve_traits<Lhs,Rhs,Side>::Unrolling,
   int StorageOrder = (int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,
-  int RhsCols = Rhs::ColsAtCompileTime
+  int RhsVectors = ei_trsolve_traits<Lhs,Rhs,Side>::RhsVectors
   >
 struct ei_triangular_solver_selector;
 
@@ -142,12 +156,24 @@ struct ei_triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,NoUnrolling,ColMajor
   }
 };
 
+// transpose OnTheRight cases for vectors
+template<typename Lhs, typename Rhs, int Mode, int Unrolling, int StorageOrder>
+struct ei_triangular_solver_selector<Lhs,Rhs,OnTheRight,Mode,Unrolling,StorageOrder,1>
+{
+  static void run(const Lhs& lhs, Rhs& rhs)
+  {
+    Transpose<Rhs> rhsTr(rhs);
+    Transpose<Lhs> lhsTr(lhs);
+    ei_triangular_solver_selector<Transpose<Lhs>,Transpose<Rhs>,OnTheLeft,TriangularView<Lhs,Mode>::TransposeMode>::run(lhsTr,rhsTr);
+  }
+};
+
 template <typename Scalar, int Side, int Mode, bool Conjugate, int TriStorageOrder, int OtherStorageOrder>
 struct ei_triangular_solve_matrix;
 
 // the rhs is a matrix
-template<typename Lhs, typename Rhs, int Side, int Mode, int StorageOrder, int RhsCols>
-struct ei_triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,StorageOrder,RhsCols>
+template<typename Lhs, typename Rhs, int Side, int Mode, int StorageOrder>
+struct ei_triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,StorageOrder,Dynamic>
 {
   typedef typename Rhs::Scalar Scalar;
   typedef ei_blas_traits<Lhs> LhsProductTraits;
diff --git a/Eigen/src/Core/StableNorm.h b/Eigen/src/Core/StableNorm.h
index 2874f0fd8..b4d6aa353 100644
--- a/Eigen/src/Core/StableNorm.h
+++ b/Eigen/src/Core/StableNorm.h
@@ -65,9 +65,9 @@ MatrixBase<Derived>::stableNorm() const
   int bi=0;
   if ((int(Flags)&DirectAccessBit) && !(int(Flags)&AlignedBit))
   {
-    bi = ei_alignmentOffset(&const_cast_derived().coeffRef(0), n);
+    bi = ei_first_aligned(&const_cast_derived().coeffRef(0), n);
     if (bi>0)
-      ei_stable_norm_kernel(this->start(bi), ssq, scale, invScale);
+      ei_stable_norm_kernel(this->head(bi), ssq, scale, invScale);
   }
   for (; bi<n; bi+=blockSize)
     ei_stable_norm_kernel(this->segment(bi,std::min(blockSize, n - bi)).template forceAlignedAccessIf<Alignment>(), ssq, scale, invScale);
diff --git a/Eigen/src/Core/TriangularMatrix.h b/Eigen/src/Core/TriangularMatrix.h
index e593a468d..62d800fef 100644
--- a/Eigen/src/Core/TriangularMatrix.h
+++ b/Eigen/src/Core/TriangularMatrix.h
@@ -95,12 +95,14 @@ template<typename Derived> class TriangularBase : public AnyMatrixBase<Derived>
                 || ((Mode==StrictlyLowerTriangular || Mode==UnitLowerTriangular) && col<row));
     }
 
+    #ifdef EIGEN_INTERNAL_DEBUGGING
     void check_coordinates_internal(int row, int col)
     {
-      #ifdef EIGEN_INTERNAL_DEBUGGING
       check_coordinates(row, col);
-      #endif
     }
+    #else
+    void check_coordinates_internal(int , int ) {}
+    #endif
 
 };
 
diff --git a/Eigen/src/Core/VectorBlock.h b/Eigen/src/Core/VectorBlock.h
index 96af71b36..760c097ad 100644
--- a/Eigen/src/Core/VectorBlock.h
+++ b/Eigen/src/Core/VectorBlock.h
@@ -154,16 +154,16 @@ DenseBase<Derived>::segment(int start, int size) const
   */
 template<typename Derived>
 inline VectorBlock<Derived>
-DenseBase<Derived>::start(int size)
+DenseBase<Derived>::head(int size)
 {
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
   return VectorBlock<Derived>(derived(), 0, size);
 }
 
-/** This is the const version of start(int).*/
+/** This is the const version of head(int).*/
 template<typename Derived>
 inline const VectorBlock<Derived>
-DenseBase<Derived>::start(int size) const
+DenseBase<Derived>::head(int size) const
 {
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
   return VectorBlock<Derived>(derived(), 0, size);
@@ -186,16 +186,16 @@ DenseBase<Derived>::start(int size) const
   */
 template<typename Derived>
 inline VectorBlock<Derived>
-DenseBase<Derived>::end(int size)
+DenseBase<Derived>::tail(int size)
 {
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
   return VectorBlock<Derived>(derived(), this->size() - size, size);
 }
 
-/** This is the const version of end(int).*/
+/** This is the const version of tail(int).*/
 template<typename Derived>
 inline const VectorBlock<Derived>
-DenseBase<Derived>::end(int size) const
+DenseBase<Derived>::tail(int size) const
 {
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
   return VectorBlock<Derived>(derived(), this->size() - size, size);
@@ -247,17 +247,17 @@ DenseBase<Derived>::segment(int start) const
 template<typename Derived>
 template<int Size>
 inline VectorBlock<Derived,Size>
-DenseBase<Derived>::start()
+DenseBase<Derived>::head()
 {
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
   return VectorBlock<Derived,Size>(derived(), 0);
 }
 
-/** This is the const version of start<int>().*/
+/** This is the const version of head<int>().*/
 template<typename Derived>
 template<int Size>
 inline const VectorBlock<Derived,Size>
-DenseBase<Derived>::start() const
+DenseBase<Derived>::head() const
 {
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
   return VectorBlock<Derived,Size>(derived(), 0);
@@ -277,17 +277,17 @@ DenseBase<Derived>::start() const
 template<typename Derived>
 template<int Size>
 inline VectorBlock<Derived,Size>
-DenseBase<Derived>::end()
+DenseBase<Derived>::tail()
 {
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
   return VectorBlock<Derived, Size>(derived(), size() - Size);
 }
 
-/** This is the const version of end<int>.*/
+/** This is the const version of tail<int>.*/
 template<typename Derived>
 template<int Size>
 inline const VectorBlock<Derived,Size>
-DenseBase<Derived>::end() const
+DenseBase<Derived>::tail() const
 {
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
   return VectorBlock<Derived, Size>(derived(), size() - Size);
diff --git a/Eigen/src/Core/products/GeneralMatrixVector.h b/Eigen/src/Core/products/GeneralMatrixVector.h
index a18e5ef1d..3296f32ff 100644
--- a/Eigen/src/Core/products/GeneralMatrixVector.h
+++ b/Eigen/src/Core/products/GeneralMatrixVector.h
@@ -69,7 +69,7 @@ void ei_cache_friendly_product_colmajor_times_vector(
 
   // How many coeffs of the result do we have to skip to be aligned.
   // Here we assume data are at least aligned on the base scalar type.
-  int alignedStart = ei_alignmentOffset(res,size);
+  int alignedStart = ei_first_aligned(res,size);
   int alignedSize = PacketSize>1 ? alignedStart + ((size-alignedStart) & ~PacketAlignedMask) : 0;
   const int peeledSize  = peels>1 ? alignedStart + ((alignedSize-alignedStart) & ~PeelAlignedMask) : alignedStart;
 
@@ -79,7 +79,7 @@ void ei_cache_friendly_product_colmajor_times_vector(
                        : FirstAligned;
 
   // we cannot assume the first element is aligned because of sub-matrices
-  const int lhsAlignmentOffset = ei_alignmentOffset(lhs,size);
+  const int lhsAlignmentOffset = ei_first_aligned(lhs,size);
 
   // find how many columns do we have to skip to be aligned with the result (if possible)
   int skipColumns = 0;
@@ -282,7 +282,7 @@ static EIGEN_DONT_INLINE void ei_cache_friendly_product_rowmajor_times_vector(
   // How many coeffs of the result do we have to skip to be aligned.
   // Here we assume data are at least aligned on the base scalar type
   // if that's not the case then vectorization is discarded, see below.
-  int alignedStart = ei_alignmentOffset(rhs, size);
+  int alignedStart = ei_first_aligned(rhs, size);
   int alignedSize = PacketSize>1 ? alignedStart + ((size-alignedStart) & ~PacketAlignedMask) : 0;
   const int peeledSize  = peels>1 ? alignedStart + ((alignedSize-alignedStart) & ~PeelAlignedMask) : alignedStart;
 
@@ -292,7 +292,7 @@ static EIGEN_DONT_INLINE void ei_cache_friendly_product_rowmajor_times_vector(
                        : FirstAligned;
 
   // we cannot assume the first element is aligned because of sub-matrices
-  const int lhsAlignmentOffset = ei_alignmentOffset(lhs,size);
+  const int lhsAlignmentOffset = ei_first_aligned(lhs,size);
 
   // find how many rows do we have to skip to be aligned with rhs (if possible)
   int skipRows = 0;
diff --git a/Eigen/src/Core/products/SelfadjointMatrixMatrix.h b/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
index 5e025b90b..35efa752e 100644
--- a/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
+++ b/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
@@ -313,7 +313,6 @@ struct ei_product_selfadjoint_matrix<Scalar,LhsStorageOrder,false,ConjugateLhs,
     int size = cols;
 
     ei_const_blas_data_mapper<Scalar, LhsStorageOrder> lhs(_lhs,lhsStride);
-    ei_const_blas_data_mapper<Scalar, RhsStorageOrder> rhs(_rhs,rhsStride);
 
     if (ConjugateRhs)
       alpha = ei_conj(alpha);
diff --git a/Eigen/src/Core/products/SelfadjointMatrixVector.h b/Eigen/src/Core/products/SelfadjointMatrixVector.h
index c27454bee..32b7f220e 100644
--- a/Eigen/src/Core/products/SelfadjointMatrixVector.h
+++ b/Eigen/src/Core/products/SelfadjointMatrixVector.h
@@ -86,7 +86,7 @@ static EIGEN_DONT_INLINE void ei_product_selfadjoint_vector(
     size_t starti = FirstTriangular ? 0 : j+2;
     size_t endi   = FirstTriangular ? j : size;
     size_t alignedEnd = starti;
-    size_t alignedStart = (starti) + ei_alignmentOffset(&res[starti], endi-starti);
+    size_t alignedStart = (starti) + ei_first_aligned(&res[starti], endi-starti);
     alignedEnd = alignedStart + ((endi-alignedStart)/(PacketSize))*(PacketSize);
 
     res[j] += cj0.pmul(A0[j], t0);
diff --git a/Eigen/src/Core/products/SelfadjointRank2Update.h b/Eigen/src/Core/products/SelfadjointRank2Update.h
index 69cf1896c..1c0e503e6 100644
--- a/Eigen/src/Core/products/SelfadjointRank2Update.h
+++ b/Eigen/src/Core/products/SelfadjointRank2Update.h
@@ -41,8 +41,8 @@ struct ei_selfadjoint_rank2_update_selector<Scalar,UType,VType,LowerTriangular>
     for (int i=0; i<size; ++i)
     {
       Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+i, size-i) +=
-                        (alpha * ei_conj(u.coeff(i))) * v.end(size-i)
-                      + (alpha * ei_conj(v.coeff(i))) * u.end(size-i);
+                        (alpha * ei_conj(u.coeff(i))) * v.tail(size-i)
+                      + (alpha * ei_conj(v.coeff(i))) * u.tail(size-i);
     }
   }
 };
@@ -55,8 +55,8 @@ struct ei_selfadjoint_rank2_update_selector<Scalar,UType,VType,UpperTriangular>
     const int size = u.size();
     for (int i=0; i<size; ++i)
       Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i, i+1) +=
-                        (alpha * ei_conj(u.coeff(i))) * v.start(i+1)
-                      + (alpha * ei_conj(v.coeff(i))) * u.start(i+1);
+                        (alpha * ei_conj(u.coeff(i))) * v.head(i+1)
+                      + (alpha * ei_conj(v.coeff(i))) * u.head(i+1);
   }
 };
 
diff --git a/Eigen/src/Core/util/BlasUtil.h b/Eigen/src/Core/util/BlasUtil.h
index fa21ceebb..916a125e3 100644
--- a/Eigen/src/Core/util/BlasUtil.h
+++ b/Eigen/src/Core/util/BlasUtil.h
@@ -223,7 +223,8 @@ struct ei_blas_traits<Transpose<NestedXpr> >
   typedef typename NestedXpr::Scalar Scalar;
   typedef ei_blas_traits<NestedXpr> Base;
   typedef Transpose<NestedXpr> XprType;
-  typedef Transpose<typename Base::_ExtractType> ExtractType;
+  typedef Transpose<typename Base::_ExtractType>  ExtractType;
+  typedef Transpose<typename Base::_ExtractType> _ExtractType;
   typedef typename ei_meta_if<int(Base::ActualAccess)==HasDirectAccess,
     ExtractType,
     typename ExtractType::PlainMatrixType
diff --git a/Eigen/src/Core/util/Memory.h b/Eigen/src/Core/util/Memory.h
index 524bec2fc..bfc6ff686 100644
--- a/Eigen/src/Core/util/Memory.h
+++ b/Eigen/src/Core/util/Memory.h
@@ -209,27 +209,53 @@ template<typename T, bool Align> inline void ei_conditional_aligned_delete(T *pt
   ei_conditional_aligned_free<Align>(ptr);
 }
 
-/** \internal \returns the number of elements which have to be skipped to
-  * find the first 16-byte aligned element
+/** \internal \returns the index of the first element of the array that is well aligned for vectorization.
   *
-  * There is also the variant ei_alignmentOffset(const MatrixBase&, Integer) defined in Coeffs.h.
+  * \param array the address of the start of the array
+  * \param size the size of the array
+  *
+  * \note If no element of the array is well aligned, the size of the array is returned. Typically,
+  * for example with SSE, "well aligned" means 16-byte-aligned. If vectorization is disabled or if the
+  * packet size for the given scalar type is 1, then everything is considered well-aligned.
+  *
+  * \note If the scalar type is vectorizable, we rely on the following assumptions: sizeof(Scalar) is a
+  * power of 2, the packet size in bytes is also a power of 2, and is a multiple of sizeof(Scalar). On the
+  * other hand, we do not assume that the array address is a multiple of sizeof(Scalar), as that fails for
+  * example with Scalar=double on certain 32-bit platforms, see bug #79.
+  *
+  * There is also the variant ei_first_aligned(const MatrixBase&, Integer) defined in Coeffs.h.
   */
 template<typename Scalar, typename Integer>
-inline static Integer ei_alignmentOffset(const Scalar* ptr, Integer maxOffset)
+inline static Integer ei_first_aligned(const Scalar* array, Integer size)
 {
   typedef typename ei_packet_traits<Scalar>::type Packet;
-  const Integer PacketSize = ei_packet_traits<Scalar>::size;
-  const Integer PacketAlignedMask = PacketSize-1;
-  const bool Vectorized = PacketSize>1;
-  return Vectorized
-          ? std::min<Integer>( (PacketSize - (Integer((size_t(ptr)/sizeof(Scalar))) & PacketAlignedMask))
-                           & PacketAlignedMask, maxOffset)
-          : 0;
+  enum { PacketSize = ei_packet_traits<Scalar>::size,
+         PacketAlignedMask = PacketSize-1
+  };
+  
+  if(PacketSize==1)
+  {
+    // Either there is no vectorization, or a packet consists of exactly 1 scalar so that all elements
+    // of the array have the same aligment.
+    return 0;
+  }
+  else if(size_t(array) & (sizeof(Scalar)-1))
+  {
+    // There is vectorization for this scalar type, but the array is not aligned to the size of a single scalar.
+    // Consequently, no element of the array is well aligned.
+    return size;
+  }
+  else
+  {
+    return std::min<Integer>( (PacketSize - (Integer((size_t(array)/sizeof(Scalar))) & PacketAlignedMask))
+                           & PacketAlignedMask, size);
+  }
 }
 
 /** \internal
   * ei_aligned_stack_alloc(SIZE) allocates an aligned buffer of SIZE bytes
-  * on the stack if SIZE is smaller than EIGEN_STACK_ALLOCATION_LIMIT.
+  * on the stack if SIZE is smaller than EIGEN_STACK_ALLOCATION_LIMIT, and
+  * if stack allocation is supported by the platform (currently, this is linux only).
   * Otherwise the memory is allocated on the heap.
   * Data allocated with ei_aligned_stack_alloc \b must be freed by calling ei_aligned_stack_free(PTR,SIZE).
   * \code
@@ -381,10 +407,10 @@ public:
         ei_aligned_free( p );
     }
 
-    bool operator!=(const aligned_allocator<T>& other) const
+    bool operator!=(const aligned_allocator<T>& ) const
     { return false; }
 
-    bool operator==(const aligned_allocator<T>& other) const
+    bool operator==(const aligned_allocator<T>& ) const
     { return true; }
 };
 
diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h
index 6d4a5c7bc..4bff09252 100644
--- a/Eigen/src/Core/util/XprHelper.h
+++ b/Eigen/src/Core/util/XprHelper.h
@@ -109,23 +109,6 @@ template<int _Rows, int _Cols> struct ei_size_at_compile_time
  * whereas ei_eval is a const reference in the case of a matrix
  */
 
-// template<typename Derived> class MatrixBase;
-// template<typename Derived> class ArrayBase;
-// template<typename Object> struct ei_is_matrix_or_array
-// {
-//   struct is_matrix  {int a[1];};
-//   struct is_array   {int a[2];};
-//   struct is_none    {int a[3];};
-//
-//   template<typename T>
-//   static is_matrix testBaseClass(const MatrixBase<T>*);
-//   template<typename T>
-//   static is_array  testBaseClass(const ArrayBase<T>*);
-// //   static is_none   testBaseClass(...);
-//
-//   enum {BaseClassType = sizeof(testBaseClass(static_cast<const Object*>(0)))};
-// };
-
 template<typename T, typename StorageType = typename ei_traits<T>::StorageType> class ei_plain_matrix_type;
 template<typename T, typename BaseClassType> struct ei_plain_matrix_type_dense;
 template<typename T> struct ei_plain_matrix_type<T,Dense>
diff --git a/Eigen/src/Eigen2Support/VectorBlock.h b/Eigen/src/Eigen2Support/VectorBlock.h
new file mode 100644
index 000000000..c3be84c9b
--- /dev/null
+++ b/Eigen/src/Eigen2Support/VectorBlock.h
@@ -0,0 +1,105 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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_VECTORBLOCK2_H
+#define EIGEN_VECTORBLOCK2_H
+
+/** \deprecated use DenseMase::start(int) */
+template<typename Derived>
+inline VectorBlock<Derived>
+MatrixBase<Derived>::start(int size)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return VectorBlock<Derived>(derived(), 0, size);
+}
+
+/** \deprecated use DenseMase::start(int) */
+template<typename Derived>
+inline const VectorBlock<Derived>
+MatrixBase<Derived>::start(int size) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return VectorBlock<Derived>(derived(), 0, size);
+}
+
+/** \deprecated use DenseMase::end(int) */
+template<typename Derived>
+inline VectorBlock<Derived>
+MatrixBase<Derived>::end(int size)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return VectorBlock<Derived>(derived(), this->size() - size, size);
+}
+
+/** \deprecated use DenseMase::end(int) */
+template<typename Derived>
+inline const VectorBlock<Derived>
+MatrixBase<Derived>::end(int size) const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return VectorBlock<Derived>(derived(), this->size() - size, size);
+}
+
+/** \deprecated use DenseMase::start() */
+template<typename Derived>
+template<int Size>
+inline VectorBlock<Derived,Size>
+MatrixBase<Derived>::start()
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return VectorBlock<Derived,Size>(derived(), 0);
+}
+
+/** \deprecated use DenseMase::start() */
+template<typename Derived>
+template<int Size>
+inline const VectorBlock<Derived,Size>
+MatrixBase<Derived>::start() const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return VectorBlock<Derived,Size>(derived(), 0);
+}
+
+/** \deprecated use DenseMase::end() */
+template<typename Derived>
+template<int Size>
+inline VectorBlock<Derived,Size>
+MatrixBase<Derived>::end()
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return VectorBlock<Derived, Size>(derived(), size() - Size);
+}
+
+/** \deprecated use DenseMase::end() */
+template<typename Derived>
+template<int Size>
+inline const VectorBlock<Derived,Size>
+MatrixBase<Derived>::end() const
+{
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  return VectorBlock<Derived, Size>(derived(), size() - Size);
+}
+
+#endif // EIGEN_VECTORBLOCK2_H
diff --git a/Eigen/src/Eigenvalues/ComplexEigenSolver.h b/Eigen/src/Eigenvalues/ComplexEigenSolver.h
index 0441d4f02..d55dc2a96 100644
--- a/Eigen/src/Eigenvalues/ComplexEigenSolver.h
+++ b/Eigen/src/Eigenvalues/ComplexEigenSolver.h
@@ -133,7 +133,7 @@ void ComplexEigenSolver<MatrixType>::compute(const MatrixType& matrix)
     for (int i=0; i<n; i++)
     {
       int k;
-      m_eivalues.cwiseAbs().end(n-i).minCoeff(&k);
+      m_eivalues.cwiseAbs().tail(n-i).minCoeff(&k);
       if (k != 0)
       {
         k += i;
diff --git a/Eigen/src/Eigenvalues/EigenSolver.h b/Eigen/src/Eigenvalues/EigenSolver.h
index c9c239b98..3f9e30a6e 100644
--- a/Eigen/src/Eigenvalues/EigenSolver.h
+++ b/Eigen/src/Eigenvalues/EigenSolver.h
@@ -620,7 +620,7 @@ void EigenSolver<MatrixType>::hqr2(MatrixType& matH)
           // Overflow control
           t = ei_abs(matH.coeff(i,n));
           if ((eps * t) * t > 1)
-            matH.col(n).end(nn-i) /= t;
+            matH.col(n).tail(nn-i) /= t;
         }
       }
     }
@@ -708,7 +708,7 @@ void EigenSolver<MatrixType>::hqr2(MatrixType& matH)
     // in this algo low==0 and high==nn-1 !!
     if (i < low || i > high)
     {
-      m_eivec.row(i).end(nn-i) = matH.row(i).end(nn-i);
+      m_eivec.row(i).tail(nn-i) = matH.row(i).tail(nn-i);
     }
   }
 
diff --git a/Eigen/src/Eigenvalues/HessenbergDecomposition.h b/Eigen/src/Eigenvalues/HessenbergDecomposition.h
index 9f7df49bc..636b2f4f7 100644
--- a/Eigen/src/Eigenvalues/HessenbergDecomposition.h
+++ b/Eigen/src/Eigenvalues/HessenbergDecomposition.h
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2008-2009 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
@@ -55,25 +55,23 @@ template<typename _MatrixType> class HessenbergDecomposition
     };
 
     typedef Matrix<Scalar, SizeMinusOne, 1> CoeffVectorType;
-    typedef Matrix<RealScalar, Size, 1> DiagonalType;
-    typedef Matrix<RealScalar, SizeMinusOne, 1> SubDiagonalType;
-
-    typedef typename Diagonal<MatrixType,0>::RealReturnType DiagonalReturnType;
-
-    typedef typename Diagonal<
-        Block<MatrixType,SizeMinusOne,SizeMinusOne>,0 >::RealReturnType SubDiagonalReturnType;
 
     /** This constructor initializes a HessenbergDecomposition object for
       * further use with HessenbergDecomposition::compute()
       */
     HessenbergDecomposition(int size = Size==Dynamic ? 2 : Size)
-      : m_matrix(size,size), m_hCoeffs(size-1)
-    {}
+      : m_matrix(size,size)
+    {
+      if(size>1)
+        m_hCoeffs.resize(size-1);
+    }
 
     HessenbergDecomposition(const MatrixType& matrix)
-      : m_matrix(matrix),
-        m_hCoeffs(matrix.cols()-1)
+      : m_matrix(matrix)
     {
+      if(matrix.rows()<2)
+        return;
+      m_hCoeffs.resize(matrix.rows()-1,1);
       _compute(m_matrix, m_hCoeffs);
     }
 
@@ -84,6 +82,8 @@ template<typename _MatrixType> class HessenbergDecomposition
     void compute(const MatrixType& matrix)
     {
       m_matrix = matrix;
+      if(matrix.rows()<2)
+        return;
       m_hCoeffs.resize(matrix.rows()-1,1);
       _compute(m_matrix, m_hCoeffs);
     }
@@ -150,7 +150,7 @@ void HessenbergDecomposition<MatrixType>::_compute(MatrixType& matA, CoeffVector
     int remainingSize = n-i-1;
     RealScalar beta;
     Scalar h;
-    matA.col(i).end(remainingSize).makeHouseholderInPlace(h, beta);
+    matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);
     matA.col(i).coeffRef(i+1) = beta;
     hCoeffs.coeffRef(i) = h;
 
@@ -159,11 +159,11 @@ void HessenbergDecomposition<MatrixType>::_compute(MatrixType& matA, CoeffVector
 
     // A = H A
     matA.corner(BottomRight, remainingSize, remainingSize)
-        .applyHouseholderOnTheLeft(matA.col(i).end(remainingSize-1), h, &temp.coeffRef(0));
+        .applyHouseholderOnTheLeft(matA.col(i).tail(remainingSize-1), h, &temp.coeffRef(0));
 
     // A = A H'
     matA.corner(BottomRight, n, remainingSize)
-        .applyHouseholderOnTheRight(matA.col(i).end(remainingSize-1).conjugate(), ei_conj(h), &temp.coeffRef(0));
+        .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1).conjugate(), ei_conj(h), &temp.coeffRef(0));
   }
 }
 
@@ -178,7 +178,7 @@ HessenbergDecomposition<MatrixType>::matrixQ() const
   for (int i = n-2; i>=0; i--)
   {
     matQ.corner(BottomRight,n-i-1,n-i-1)
-        .applyHouseholderOnTheLeft(m_matrix.col(i).end(n-i-2), ei_conj(m_hCoeffs.coeff(i)), &temp.coeffRef(0,0));
+        .applyHouseholderOnTheLeft(m_matrix.col(i).tail(n-i-2), ei_conj(m_hCoeffs.coeff(i)), &temp.coeffRef(0,0));
   }
   return matQ;
 }
diff --git a/Eigen/src/Eigenvalues/Tridiagonalization.h b/Eigen/src/Eigenvalues/Tridiagonalization.h
index d8dcfb047..e43605b0f 100644
--- a/Eigen/src/Eigenvalues/Tridiagonalization.h
+++ b/Eigen/src/Eigenvalues/Tridiagonalization.h
@@ -197,25 +197,24 @@ void Tridiagonalization<MatrixType>::_compute(MatrixType& matA, CoeffVectorType&
 {
   assert(matA.rows()==matA.cols());
   int n = matA.rows();
-  Matrix<Scalar,1,Dynamic> aux(n);
   for (int i = 0; i<n-1; ++i)
   {
     int remainingSize = n-i-1;
     RealScalar beta;
     Scalar h;
-    matA.col(i).end(remainingSize).makeHouseholderInPlace(h, beta);
+    matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);
 
     // Apply similarity transformation to remaining columns,
-    // i.e., A = H A H' where H = I - h v v' and v = matA.col(i).end(n-i-1)
+    // i.e., A = H A H' where H = I - h v v' and v = matA.col(i).tail(n-i-1)
     matA.col(i).coeffRef(i+1) = 1;
 
-    hCoeffs.end(n-i-1) = (matA.corner(BottomRight,remainingSize,remainingSize).template selfadjointView<LowerTriangular>()
-                        * (ei_conj(h) * matA.col(i).end(remainingSize)));
+    hCoeffs.tail(n-i-1) = (matA.corner(BottomRight,remainingSize,remainingSize).template selfadjointView<LowerTriangular>()
+                        * (ei_conj(h) * matA.col(i).tail(remainingSize)));
 
-    hCoeffs.end(n-i-1) += (ei_conj(h)*Scalar(-0.5)*(hCoeffs.end(remainingSize).dot(matA.col(i).end(remainingSize)))) * matA.col(i).end(n-i-1);
+    hCoeffs.tail(n-i-1) += (ei_conj(h)*Scalar(-0.5)*(hCoeffs.tail(remainingSize).dot(matA.col(i).tail(remainingSize)))) * matA.col(i).tail(n-i-1);
 
     matA.corner(BottomRight, remainingSize, remainingSize).template selfadjointView<LowerTriangular>()
-      .rankUpdate(matA.col(i).end(remainingSize), hCoeffs.end(remainingSize), -1);
+      .rankUpdate(matA.col(i).tail(remainingSize), hCoeffs.tail(remainingSize), -1);
 
     matA.col(i).coeffRef(i+1) = beta;
     hCoeffs.coeffRef(i) = h;
@@ -243,7 +242,7 @@ void Tridiagonalization<MatrixType>::matrixQInPlace(MatrixBase<QDerived>* q) con
   for (int i = n-2; i>=0; i--)
   {
     matQ.corner(BottomRight,n-i-1,n-i-1)
-        .applyHouseholderOnTheLeft(m_matrix.col(i).end(n-i-2), ei_conj(m_hCoeffs.coeff(i)), &aux.coeffRef(0,0));
+        .applyHouseholderOnTheLeft(m_matrix.col(i).tail(n-i-2), ei_conj(m_hCoeffs.coeff(i)), &aux.coeffRef(0,0));
   }
 }
 
diff --git a/Eigen/src/Geometry/OrthoMethods.h b/Eigen/src/Geometry/OrthoMethods.h
index 79baeadd5..c10b6abf4 100644
--- a/Eigen/src/Geometry/OrthoMethods.h
+++ b/Eigen/src/Geometry/OrthoMethods.h
@@ -173,7 +173,7 @@ struct ei_unitOrthogonal_selector<Derived,3>
     if((!ei_isMuchSmallerThan(src.x(), src.z()))
     || (!ei_isMuchSmallerThan(src.y(), src.z())))
     {
-      RealScalar invnm = RealScalar(1)/src.template start<2>().norm();
+      RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
       perp.coeffRef(0) = -ei_conj(src.y())*invnm;
       perp.coeffRef(1) = ei_conj(src.x())*invnm;
       perp.coeffRef(2) = 0;
@@ -184,7 +184,7 @@ struct ei_unitOrthogonal_selector<Derived,3>
      */
     else
     {
-      RealScalar invnm = RealScalar(1)/src.template end<2>().norm();
+      RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
       perp.coeffRef(0) = 0;
       perp.coeffRef(1) = -ei_conj(src.z())*invnm;
       perp.coeffRef(2) = ei_conj(src.y())*invnm;
diff --git a/Eigen/src/Geometry/Quaternion.h b/Eigen/src/Geometry/Quaternion.h
index 861eff19c..24772089e 100644
--- a/Eigen/src/Geometry/Quaternion.h
+++ b/Eigen/src/Geometry/Quaternion.h
@@ -77,10 +77,10 @@ public:
   inline Scalar& w() { return this->derived().coeffs().coeffRef(3); }
 
   /** \returns a read-only vector expression of the imaginary part (x,y,z) */
-  inline const VectorBlock<Coefficients,3> vec() const { return coeffs().template start<3>(); }
+  inline const VectorBlock<Coefficients,3> vec() const { return coeffs().template head<3>(); }
 
   /** \returns a vector expression of the imaginary part (x,y,z) */
-  inline VectorBlock<Coefficients,3> vec() { return coeffs().template start<3>(); }
+  inline VectorBlock<Coefficients,3> vec() { return coeffs().template head<3>(); }
 
   /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
   inline const typename ei_traits<Derived>::Coefficients& coeffs() const { return derived().coeffs(); }
diff --git a/Eigen/src/Geometry/Transform.h b/Eigen/src/Geometry/Transform.h
index 89df73505..b945ea43f 100644
--- a/Eigen/src/Geometry/Transform.h
+++ b/Eigen/src/Geometry/Transform.h
@@ -1102,7 +1102,7 @@ struct ei_transform_right_product_impl<Other,AffineCompact, Dim,HDim, HDim,1>
   static ResultType run(const TransformType& tr, const Other& other)
   {
     ResultType res;
-    res.template start<HDim>() = tr.matrix() * other;
+    res.template head<HDim>() = tr.matrix() * other;
     res.coeffRef(Dim) = other.coeff(Dim);
   }
 };
@@ -1120,7 +1120,7 @@ struct ei_transform_right_product_impl<Other,Mode, Dim,HDim, Dim,Dim>
     res.matrix().col(Dim) = tr.matrix().col(Dim);
     res.linearExt().noalias() = (tr.linearExt() * other);
     if(Mode==Affine)
-      res.matrix().row(Dim).template start<Dim>() = tr.matrix().row(Dim).template start<Dim>();
+      res.matrix().row(Dim).template head<Dim>() = tr.matrix().row(Dim).template head<Dim>();
     return res;
   }
 };
diff --git a/Eigen/src/Geometry/Umeyama.h b/Eigen/src/Geometry/Umeyama.h
index 551a69e5b..5be098d77 100644
--- a/Eigen/src/Geometry/Umeyama.h
+++ b/Eigen/src/Geometry/Umeyama.h
@@ -170,8 +170,8 @@ umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, boo
   // Eq. (41)
   // Note that we first assign dst_mean to the destination so that there no need
   // for a temporary.
-  Rt.col(m).start(m) = dst_mean;
-  Rt.col(m).start(m).noalias() -= c*Rt.corner(TopLeft,m,m)*src_mean;
+  Rt.col(m).head(m) = dst_mean;
+  Rt.col(m).head(m).noalias() -= c*Rt.corner(TopLeft,m,m)*src_mean;
 
   if (with_scaling) Rt.block(0,0,m,m) *= c;
 
diff --git a/Eigen/src/Householder/HouseholderSequence.h b/Eigen/src/Householder/HouseholderSequence.h
index 25e962001..26e0f6a88 100644
--- a/Eigen/src/Householder/HouseholderSequence.h
+++ b/Eigen/src/Householder/HouseholderSequence.h
@@ -105,10 +105,10 @@ template<typename VectorsType, typename CoeffsType> class HouseholderSequence
       {
         if(m_trans)
           dst.corner(BottomRight, length-k, length-k)
-          .applyHouseholderOnTheRight(m_vectors.col(k).end(length-k-1), m_coeffs.coeff(k), &temp.coeffRef(0));
+          .applyHouseholderOnTheRight(m_vectors.col(k).tail(length-k-1), m_coeffs.coeff(k), &temp.coeffRef(0));
         else
           dst.corner(BottomRight, length-k, length-k)
-            .applyHouseholderOnTheLeft(m_vectors.col(k).end(length-k-1), m_coeffs.coeff(k), &temp.coeffRef(k));
+            .applyHouseholderOnTheLeft(m_vectors.col(k).tail(length-k-1), m_coeffs.coeff(k), &temp.coeffRef(k));
       }
     }
 
@@ -122,7 +122,7 @@ template<typename VectorsType, typename CoeffsType> class HouseholderSequence
       {
         int actual_k = m_trans ? vecs-k-1 : k;
         dst.corner(BottomRight, dst.rows(), length-actual_k)
-           .applyHouseholderOnTheRight(m_vectors.col(actual_k).end(length-actual_k-1), m_coeffs.coeff(actual_k), &temp.coeffRef(0));
+           .applyHouseholderOnTheRight(m_vectors.col(actual_k).tail(length-actual_k-1), m_coeffs.coeff(actual_k), &temp.coeffRef(0));
       }
     }
 
@@ -136,7 +136,7 @@ template<typename VectorsType, typename CoeffsType> class HouseholderSequence
       {
         int actual_k = m_trans ? k : vecs-k-1;
         dst.corner(BottomRight, length-actual_k, dst.cols())
-           .applyHouseholderOnTheLeft(m_vectors.col(actual_k).end(length-actual_k-1), m_coeffs.coeff(actual_k), &temp.coeffRef(0));
+           .applyHouseholderOnTheLeft(m_vectors.col(actual_k).tail(length-actual_k-1), m_coeffs.coeff(actual_k), &temp.coeffRef(0));
       }
     }
 
diff --git a/Eigen/src/Jacobi/Jacobi.h b/Eigen/src/Jacobi/Jacobi.h
index 727c97583..024a130f2 100644
--- a/Eigen/src/Jacobi/Jacobi.h
+++ b/Eigen/src/Jacobi/Jacobi.h
@@ -318,7 +318,7 @@ void /*EIGEN_DONT_INLINE*/ ei_apply_rotation_in_the_plane(VectorX& _x, VectorY&
     typedef typename ei_packet_traits<Scalar>::type Packet;
     enum { PacketSize = ei_packet_traits<Scalar>::size, Peeling = 2 };
 
-    int alignedStart = ei_alignmentOffset(y, size);
+    int alignedStart = ei_first_aligned(y, size);
     int alignedEnd = alignedStart + ((size-alignedStart)/PacketSize)*PacketSize;
 
     const Packet pc = ei_pset1(Scalar(j.c()));
@@ -336,7 +336,7 @@ void /*EIGEN_DONT_INLINE*/ ei_apply_rotation_in_the_plane(VectorX& _x, VectorY&
     Scalar* px = x + alignedStart;
     Scalar* py = y + alignedStart;
 
-    if(ei_alignmentOffset(x, size)==alignedStart)
+    if(ei_first_aligned(x, size)==alignedStart)
     {
       for(int i=alignedStart; i<alignedEnd; i+=PacketSize)
       {
diff --git a/Eigen/src/LU/FullPivLU.h b/Eigen/src/LU/FullPivLU.h
index 149af64bc..f62dcc1db 100644
--- a/Eigen/src/LU/FullPivLU.h
+++ b/Eigen/src/LU/FullPivLU.h
@@ -451,9 +451,9 @@ FullPivLU<MatrixType>& FullPivLU<MatrixType>::compute(const MatrixType& matrix)
     // bottom-right corner by Gaussian elimination.
 
     if(k<rows-1)
-      m_lu.col(k).end(rows-k-1) /= m_lu.coeff(k,k);
+      m_lu.col(k).tail(rows-k-1) /= m_lu.coeff(k,k);
     if(k<size-1)
-      m_lu.block(k+1,k+1,rows-k-1,cols-k-1).noalias() -= m_lu.col(k).end(rows-k-1) * m_lu.row(k).end(cols-k-1);
+      m_lu.block(k+1,k+1,rows-k-1,cols-k-1).noalias() -= m_lu.col(k).tail(rows-k-1) * m_lu.row(k).tail(cols-k-1);
   }
 
   // the main loop is over, we still have to accumulate the transpositions to find the
@@ -537,8 +537,8 @@ struct ei_kernel_retval<FullPivLU<_MatrixType> >
       m(dec().matrixLU().block(0, 0, rank(), cols));
     for(int i = 0; i < rank(); ++i)
     {
-      if(i) m.row(i).start(i).setZero();
-      m.row(i).end(cols-i) = dec().matrixLU().row(pivots.coeff(i)).end(cols-i);
+      if(i) m.row(i).head(i).setZero();
+      m.row(i).tail(cols-i) = dec().matrixLU().row(pivots.coeff(i)).tail(cols-i);
     }
     m.block(0, 0, rank(), rank());
     m.block(0, 0, rank(), rank()).template triangularView<StrictlyLowerTriangular>().setZero();
@@ -558,7 +558,7 @@ struct ei_kernel_retval<FullPivLU<_MatrixType> >
       m.col(i).swap(m.col(pivots.coeff(i)));
 
     // see the negative sign in the next line, that's what we were talking about above.
-    for(int i = 0; i < rank(); ++i) dst.row(dec().permutationQ().indices().coeff(i)) = -m.row(i).end(dimker);
+    for(int i = 0; i < rank(); ++i) dst.row(dec().permutationQ().indices().coeff(i)) = -m.row(i).tail(dimker);
     for(int i = rank(); i < cols; ++i) dst.row(dec().permutationQ().indices().coeff(i)).setZero();
     for(int k = 0; k < dimker; ++k) dst.coeffRef(dec().permutationQ().indices().coeff(rank()+k), k) = Scalar(1);
   }
diff --git a/Eigen/src/LU/PartialPivLU.h b/Eigen/src/LU/PartialPivLU.h
index deb29b5c6..6bb5c3ac7 100644
--- a/Eigen/src/LU/PartialPivLU.h
+++ b/Eigen/src/LU/PartialPivLU.h
@@ -229,7 +229,7 @@ struct ei_partial_lu_impl
     {
       int row_of_biggest_in_col;
       RealScalar biggest_in_corner
-        = lu.col(k).end(rows-k).cwiseAbs().maxCoeff(&row_of_biggest_in_col);
+        = lu.col(k).tail(rows-k).cwiseAbs().maxCoeff(&row_of_biggest_in_col);
       row_of_biggest_in_col += k;
 
       if(biggest_in_corner == 0) // the pivot is exactly zero: the matrix is singular
@@ -256,8 +256,8 @@ struct ei_partial_lu_impl
       {
         int rrows = rows-k-1;
         int rsize = size-k-1;
-        lu.col(k).end(rrows) /= lu.coeff(k,k);
-        lu.corner(BottomRight,rrows,rsize).noalias() -= lu.col(k).end(rrows) * lu.row(k).end(rsize);
+        lu.col(k).tail(rrows) /= lu.coeff(k,k);
+        lu.corner(BottomRight,rrows,rsize).noalias() -= lu.col(k).tail(rrows) * lu.row(k).tail(rsize);
       }
     }
     return true;
diff --git a/Eigen/src/QR/ColPivHouseholderQR.h b/Eigen/src/QR/ColPivHouseholderQR.h
index b4c1a5fcc..8b705de3c 100644
--- a/Eigen/src/QR/ColPivHouseholderQR.h
+++ b/Eigen/src/QR/ColPivHouseholderQR.h
@@ -359,14 +359,14 @@ ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const
   {
     // first, we look up in our table colSqNorms which column has the biggest squared norm
     int biggest_col_index;
-    RealScalar biggest_col_sq_norm = colSqNorms.end(cols-k).maxCoeff(&biggest_col_index);
+    RealScalar biggest_col_sq_norm = colSqNorms.tail(cols-k).maxCoeff(&biggest_col_index);
     biggest_col_index += k;
 
     // since our table colSqNorms accumulates imprecision at every step, we must now recompute
     // the actual squared norm of the selected column.
     // Note that not doing so does result in solve() sometimes returning inf/nan values
     // when running the unit test with 1000 repetitions.
-    biggest_col_sq_norm = m_qr.col(biggest_col_index).end(rows-k).squaredNorm();
+    biggest_col_sq_norm = m_qr.col(biggest_col_index).tail(rows-k).squaredNorm();
 
     // we store that back into our table: it can't hurt to correct our table.
     colSqNorms.coeffRef(biggest_col_index) = biggest_col_sq_norm;
@@ -379,7 +379,7 @@ ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const
     if(biggest_col_sq_norm < threshold_helper * (rows-k))
     {
       m_nonzero_pivots = k;
-      m_hCoeffs.end(size-k).setZero();
+      m_hCoeffs.tail(size-k).setZero();
       m_qr.corner(BottomRight,rows-k,cols-k)
           .template triangularView<StrictlyLowerTriangular>()
           .setZero();
@@ -396,7 +396,7 @@ ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const
 
     // generate the householder vector, store it below the diagonal
     RealScalar beta;
-    m_qr.col(k).end(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
+    m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
 
     // apply the householder transformation to the diagonal coefficient
     m_qr.coeffRef(k,k) = beta;
@@ -406,10 +406,10 @@ ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const
 
     // apply the householder transformation
     m_qr.corner(BottomRight, rows-k, cols-k-1)
-        .applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), m_hCoeffs.coeffRef(k), &temp.coeffRef(k+1));
+        .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &temp.coeffRef(k+1));
 
     // update our table of squared norms of the columns
-    colSqNorms.end(cols-k-1) -= m_qr.row(k).end(cols-k-1).cwiseAbs2();
+    colSqNorms.tail(cols-k-1) -= m_qr.row(k).tail(cols-k-1).cwiseAbs2();
   }
 
   m_cols_permutation.setIdentity(cols);
@@ -427,7 +427,7 @@ struct ei_solve_retval<ColPivHouseholderQR<_MatrixType>, Rhs>
   : ei_solve_retval_base<ColPivHouseholderQR<_MatrixType>, Rhs>
 {
   EIGEN_MAKE_SOLVE_HELPERS(ColPivHouseholderQR<_MatrixType>,Rhs)
-  
+
   template<typename Dest> void evalTo(Dest& dst) const
   {
     const int rows = dec().rows(), cols = dec().cols(),
diff --git a/Eigen/src/QR/FullPivHouseholderQR.h b/Eigen/src/QR/FullPivHouseholderQR.h
index 51609ca1a..598f44dc3 100644
--- a/Eigen/src/QR/FullPivHouseholderQR.h
+++ b/Eigen/src/QR/FullPivHouseholderQR.h
@@ -306,7 +306,7 @@ FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(cons
     m_rows_transpositions.coeffRef(k) = row_of_biggest_in_corner;
     cols_transpositions.coeffRef(k) = col_of_biggest_in_corner;
     if(k != row_of_biggest_in_corner) {
-      m_qr.row(k).end(cols-k).swap(m_qr.row(row_of_biggest_in_corner).end(cols-k));
+      m_qr.row(k).tail(cols-k).swap(m_qr.row(row_of_biggest_in_corner).tail(cols-k));
       ++number_of_transpositions;
     }
     if(k != col_of_biggest_in_corner) {
@@ -315,11 +315,11 @@ FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(cons
     }
 
     RealScalar beta;
-    m_qr.col(k).end(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
+    m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
     m_qr.coeffRef(k,k) = beta;
 
     m_qr.corner(BottomRight, rows-k, cols-k-1)
-        .applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), m_hCoeffs.coeffRef(k), &temp.coeffRef(k+1));
+        .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &temp.coeffRef(k+1));
   }
 
   m_cols_permutation.setIdentity(cols);
@@ -360,7 +360,7 @@ struct ei_solve_retval<FullPivHouseholderQR<_MatrixType>, Rhs>
       int remainingSize = rows-k;
       c.row(k).swap(c.row(dec().rowsTranspositions().coeff(k)));
       c.corner(BottomRight, remainingSize, rhs().cols())
-       .applyHouseholderOnTheLeft(dec().matrixQR().col(k).end(remainingSize-1),
+       .applyHouseholderOnTheLeft(dec().matrixQR().col(k).tail(remainingSize-1),
                                   dec().hCoeffs().coeff(k), &temp.coeffRef(0));
     }
 
@@ -400,7 +400,7 @@ typename FullPivHouseholderQR<MatrixType>::MatrixQType FullPivHouseholderQR<Matr
   for (int k = size-1; k >= 0; k--)
   {
     res.block(k, k, rows-k, rows-k)
-       .applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), ei_conj(m_hCoeffs.coeff(k)), &temp.coeffRef(k));
+       .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), ei_conj(m_hCoeffs.coeff(k)), &temp.coeffRef(k));
     res.row(k).swap(res.row(m_rows_transpositions.coeff(k)));
   }
   return res;
diff --git a/Eigen/src/QR/HouseholderQR.h b/Eigen/src/QR/HouseholderQR.h
index 895ae046a..24aa96e04 100644
--- a/Eigen/src/QR/HouseholderQR.h
+++ b/Eigen/src/QR/HouseholderQR.h
@@ -197,12 +197,12 @@ HouseholderQR<MatrixType>& HouseholderQR<MatrixType>::compute(const MatrixType&
     int remainingCols = cols - k - 1;
 
     RealScalar beta;
-    m_qr.col(k).end(remainingRows).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
+    m_qr.col(k).tail(remainingRows).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
     m_qr.coeffRef(k,k) = beta;
 
     // apply H to remaining part of m_qr from the left
     m_qr.corner(BottomRight, remainingRows, remainingCols)
-        .applyHouseholderOnTheLeft(m_qr.col(k).end(remainingRows-1), m_hCoeffs.coeffRef(k), &temp.coeffRef(k+1));
+        .applyHouseholderOnTheLeft(m_qr.col(k).tail(remainingRows-1), m_hCoeffs.coeffRef(k), &temp.coeffRef(k+1));
   }
   m_isInitialized = true;
   return *this;
@@ -226,7 +226,7 @@ struct ei_solve_retval<HouseholderQR<_MatrixType>, Rhs>
     // Note that the matrix Q = H_0^* H_1^*... so its inverse is Q^* = (H_0 H_1 ...)^T
     c.applyOnTheLeft(householderSequence(
       dec().matrixQR().corner(TopLeft,rows,rank),
-      dec().hCoeffs().start(rank)).transpose()
+      dec().hCoeffs().head(rank)).transpose()
     );
 
     dec().matrixQR()
diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
index 5792c5767..d2cd8e478 100644
--- a/Eigen/src/SVD/JacobiSVD.h
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -342,7 +342,7 @@ JacobiSVD<MatrixType, Options>& JacobiSVD<MatrixType, Options>::compute(const Ma
   for(int i = 0; i < diagSize; i++)
   {
     int pos;
-    m_singularValues.end(diagSize-i).maxCoeff(&pos);
+    m_singularValues.tail(diagSize-i).maxCoeff(&pos);
     if(pos)
     {
       pos += i;
diff --git a/Eigen/src/SVD/SVD.h b/Eigen/src/SVD/SVD.h
index 7a8e4f312..cd8c11b8d 100644
--- a/Eigen/src/SVD/SVD.h
+++ b/Eigen/src/SVD/SVD.h
@@ -137,7 +137,7 @@ template<typename _MatrixType> class SVD
       ei_assert(m_isInitialized && "SVD is not initialized.");
       return m_cols;
     }
-    
+
   protected:
     // Computes (a^2 + b^2)^(1/2) without destructive underflow or overflow.
     inline static Scalar pythag(Scalar a, Scalar b)
@@ -205,7 +205,7 @@ SVD<MatrixType>& SVD<MatrixType>::compute(const MatrixType& matrix)
     g = s = scale = 0.0;
     if (i < m)
     {
-      scale = A.col(i).end(m-i).cwiseAbs().sum();
+      scale = A.col(i).tail(m-i).cwiseAbs().sum();
       if (scale != Scalar(0))
       {
         for (k=i; k<m; k++)
@@ -219,18 +219,18 @@ SVD<MatrixType>& SVD<MatrixType>::compute(const MatrixType& matrix)
         A(i, i)=f-g;
         for (j=l-1; j<n; j++)
         {
-          s = A.col(j).end(m-i).dot(A.col(i).end(m-i));
+          s = A.col(j).tail(m-i).dot(A.col(i).tail(m-i));
           f = s/h;
-          A.col(j).end(m-i) += f*A.col(i).end(m-i);
+          A.col(j).tail(m-i) += f*A.col(i).tail(m-i);
         }
-        A.col(i).end(m-i) *= scale;
+        A.col(i).tail(m-i) *= scale;
       }
     }
     W[i] = scale * g;
     g = s = scale = 0.0;
     if (i+1 <= m && i+1 != n)
     {
-      scale = A.row(i).end(n-l+1).cwiseAbs().sum();
+      scale = A.row(i).tail(n-l+1).cwiseAbs().sum();
       if (scale != Scalar(0))
       {
         for (k=l-1; k<n; k++)
@@ -242,13 +242,13 @@ SVD<MatrixType>& SVD<MatrixType>::compute(const MatrixType& matrix)
         g = -sign(ei_sqrt(s),f);
         h = f*g - s;
         A(i,l-1) = f-g;
-        rv1.end(n-l+1) = A.row(i).end(n-l+1)/h;
+        rv1.tail(n-l+1) = A.row(i).tail(n-l+1)/h;
         for (j=l-1; j<m; j++)
         {
-          s = A.row(i).end(n-l+1).dot(A.row(j).end(n-l+1));
-          A.row(j).end(n-l+1) += s*rv1.end(n-l+1).transpose();
+          s = A.row(i).tail(n-l+1).dot(A.row(j).tail(n-l+1));
+          A.row(j).tail(n-l+1) += s*rv1.tail(n-l+1).transpose();
         }
-        A.row(i).end(n-l+1) *= scale;
+        A.row(i).tail(n-l+1) *= scale;
       }
     }
     anorm = std::max( anorm, (ei_abs(W[i])+ei_abs(rv1[i])) );
@@ -265,12 +265,12 @@ SVD<MatrixType>& SVD<MatrixType>::compute(const MatrixType& matrix)
           V(j, i) = (A(i, j)/A(i, l))/g;
         for (j=l; j<n; j++)
         {
-          s = V.col(j).end(n-l).dot(A.row(i).end(n-l));
-          V.col(j).end(n-l) += s * V.col(i).end(n-l);
+          s = V.col(j).tail(n-l).dot(A.row(i).tail(n-l));
+          V.col(j).tail(n-l) += s * V.col(i).tail(n-l);
         }
       }
-      V.row(i).end(n-l).setZero();
-      V.col(i).end(n-l).setZero();
+      V.row(i).tail(n-l).setZero();
+      V.col(i).tail(n-l).setZero();
     }
     V(i, i) = 1.0;
     g = rv1[i];
@@ -282,7 +282,7 @@ SVD<MatrixType>& SVD<MatrixType>::compute(const MatrixType& matrix)
     l = i+1;
     g = W[i];
     if (n-l>0)
-      A.row(i).end(n-l).setZero();
+      A.row(i).tail(n-l).setZero();
     if (g != Scalar(0.0))
     {
       g = Scalar(1.0)/g;
@@ -290,15 +290,15 @@ SVD<MatrixType>& SVD<MatrixType>::compute(const MatrixType& matrix)
       {
         for (j=l; j<n; j++)
         {
-          s = A.col(j).end(m-l).dot(A.col(i).end(m-l));
+          s = A.col(j).tail(m-l).dot(A.col(i).tail(m-l));
           f = (s/A(i,i))*g;
-          A.col(j).end(m-i) += f * A.col(i).end(m-i);
+          A.col(j).tail(m-i) += f * A.col(i).tail(m-i);
         }
       }
-      A.col(i).end(m-i) *= g;
+      A.col(i).tail(m-i) *= g;
     }
     else
-      A.col(i).end(m-i).setZero();
+      A.col(i).tail(m-i).setZero();
     ++A(i,i);
   }
   // Diagonalization of the bidiagonal form: Loop over
@@ -408,7 +408,7 @@ SVD<MatrixType>& SVD<MatrixType>::compute(const MatrixType& matrix)
     for (int i=0; i<n; i++)
     {
       int k;
-      W.end(n-i).maxCoeff(&k);
+      W.tail(n-i).maxCoeff(&k);
       if (k != 0)
       {
         k += i;
@@ -451,8 +451,8 @@ struct ei_solve_retval<SVD<_MatrixType>, Rhs>
           aux.coeffRef(i) /= si;
       }
       const int minsize = std::min(dec().rows(),dec().cols());
-      dst.col(j).start(minsize) = aux.start(minsize);
-      if(dec().cols()>dec().rows()) dst.col(j).end(cols()-minsize).setZero();
+      dst.col(j).head(minsize) = aux.head(minsize);
+      if(dec().cols()>dec().rows()) dst.col(j).tail(cols()-minsize).setZero();
       dst.col(j) = dec().matrixV() * dst.col(j);
     }
   }