- move: DerivedTraits becomes MatrixBase::Traits

- the static constants are private again in the Derived classes
- more documentation and code snippets
- new isDiagonal() method

40 files changed, 301 insertions, 174 deletions

diff --git a/Eigen/src/Core/Block.h b/Eigen/src/Core/Block.h
index 032048000..c6a41d551 100644
--- a/Eigen/src/Core/Block.h
+++ b/Eigen/src/Core/Block.h
@@ -66,10 +66,10 @@ template<typename MatrixType, int BlockRows, int BlockCols> class Block
     
     EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
     
+  private:
     static const int RowsAtCompileTime = BlockRows,
                      ColsAtCompileTime = BlockCols;
 
-  private:
     const Block& _ref() const { return *this; }
     int _rows() const { return BlockRows; }
     int _cols() const { return BlockCols; }
diff --git a/Eigen/src/Core/Cast.h b/Eigen/src/Core/Cast.h
index 74f5ce311..83cec459a 100644
--- a/Eigen/src/Core/Cast.h
+++ b/Eigen/src/Core/Cast.h
@@ -57,8 +57,8 @@ template<typename NewScalar, typename MatrixType> class Cast : NoOperatorEquals,
     Cast(const MatRef& matrix) : m_matrix(matrix) {}
     
   private:
-    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-                     ColsAtCompileTime = MatrixType::ColsAtCompileTime;
+    static const int RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = MatrixType::Traits::ColsAtCompileTime;
     const Cast& _ref() const { return *this; }
     int _rows() const { return m_matrix.rows(); }
     int _cols() const { return m_matrix.cols(); }
diff --git a/Eigen/src/Core/Column.h b/Eigen/src/Core/Column.h
index e46769fb1..97c3d7415 100644
--- a/Eigen/src/Core/Column.h
+++ b/Eigen/src/Core/Column.h
@@ -62,10 +62,9 @@ template<typename MatrixType> class Column
     
     EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Column)
     
-    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-                     ColsAtCompileTime = 1;
-
   private:
+    static const int RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = 1;
     const Column& _ref() const { return *this; }
     int _rows() const { return m_matrix.rows(); }
     int _cols() const { return 1; }
diff --git a/Eigen/src/Core/Conjugate.h b/Eigen/src/Core/Conjugate.h
index 90add873e..620f16234 100644
--- a/Eigen/src/Core/Conjugate.h
+++ b/Eigen/src/Core/Conjugate.h
@@ -48,10 +48,10 @@ template<typename MatrixType> class Conjugate : NoOperatorEquals,
     
     Conjugate(const MatRef& matrix) : m_matrix(matrix) {}
     
-    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-                     ColsAtCompileTime = MatrixType::ColsAtCompileTime;
-
   private:
+    static const int RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = MatrixType::Traits::ColsAtCompileTime;
+
     const Conjugate& _ref() const { return *this; }
     int _rows() const { return m_matrix.rows(); }
     int _cols() const { return m_matrix.cols(); }
diff --git a/Eigen/src/Core/DiagonalCoeffs.h b/Eigen/src/Core/DiagonalCoeffs.h
index d2a0af56c..8906d213c 100644
--- a/Eigen/src/Core/DiagonalCoeffs.h
+++ b/Eigen/src/Core/DiagonalCoeffs.h
@@ -50,10 +50,10 @@ template<typename MatrixType> class DiagonalCoeffs
     
     EIGEN_INHERIT_ASSIGNMENT_OPERATORS(DiagonalCoeffs)
     
-    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+  private:
+    static const int RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime,
                      ColsAtCompileTime = 1;
 
-  private:
     const DiagonalCoeffs& _ref() const { return *this; }
     int _rows() const { return std::min(m_matrix.rows(), m_matrix.cols()); }
     int _cols() const { return 1; }
diff --git a/Eigen/src/Core/DiagonalMatrix.h b/Eigen/src/Core/DiagonalMatrix.h
index b54d20829..d02fc5e62 100644
--- a/Eigen/src/Core/DiagonalMatrix.h
+++ b/Eigen/src/Core/DiagonalMatrix.h
@@ -55,10 +55,10 @@ class DiagonalMatrix : NoOperatorEquals,
           && coeffs.size() > 0);
     }
     
+  private:
     static const int RowsAtCompileTime = CoeffsVectorType::Traits::SizeAtCompileTime,
                      ColsAtCompileTime = CoeffsVectorType::Traits::SizeAtCompileTime;
-
-  private:
+    
     const DiagonalMatrix& _ref() const { return *this; }
     int _rows() const { return m_coeffs.size(); }
     int _cols() const { return m_coeffs.size(); }
@@ -79,7 +79,7 @@ class DiagonalMatrix : NoOperatorEquals,
   * Example: \include MatrixBase_asDiagonal.cpp
   * Output: \verbinclude MatrixBase_asDiagonal.out
   *
-  * \sa class DiagonalMatrix
+  * \sa class DiagonalMatrix, isDiagonal()
   **/
 template<typename Scalar, typename Derived>
 const DiagonalMatrix<Derived>
@@ -88,4 +88,32 @@ MatrixBase<Scalar, Derived>::asDiagonal() const
   return DiagonalMatrix<Derived>(ref());
 }
 
+/** \returns true if *this is approximately equal to a diagonal matrix,
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isDiagonal.cpp
+  * Output: \verbinclude MatrixBase_isDiagonal.out
+  *
+  * \sa asDiagonal()
+  */
+template<typename Scalar, typename Derived>
+bool MatrixBase<Scalar, Derived>::isDiagonal
+(typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+{
+  if(cols() != rows()) return false;
+  RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
+  for(int j = 0; j < cols(); j++)
+  {
+    RealScalar absOnDiagonal = abs(coeff(j,j));
+    if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
+  }
+  for(int j = 0; j < cols(); j++)
+    for(int i = 0; i < j; i++)
+    {
+      if(!Eigen::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
+      if(!Eigen::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
+    }
+  return true;
+}
+
 #endif // EIGEN_DIAGONALMATRIX_H
diff --git a/Eigen/src/Core/Difference.h b/Eigen/src/Core/Difference.h
index 1c72a9aa2..1f666e555 100644
--- a/Eigen/src/Core/Difference.h
+++ b/Eigen/src/Core/Difference.h
@@ -41,10 +41,10 @@ template<typename Lhs, typename Rhs> class Difference : NoOperatorEquals,
       assert(lhs.rows() == rhs.rows() && lhs.cols() == rhs.cols());
     }
 
-    static const int RowsAtCompileTime = Lhs::RowsAtCompileTime,
-                     ColsAtCompileTime = Rhs::ColsAtCompileTime;
-
   private:
+    static const int RowsAtCompileTime = Lhs::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = Rhs::Traits::ColsAtCompileTime;
+
     const Difference& _ref() const { return *this; }
     int _rows() const { return m_lhs.rows(); }
     int _cols() const { return m_lhs.cols(); }
diff --git a/Eigen/src/Core/Dot.h b/Eigen/src/Core/Dot.h
index b22fbaac8..2ae8b3093 100644
--- a/Eigen/src/Core/Dot.h
+++ b/Eigen/src/Core/Dot.h
@@ -72,10 +72,15 @@ template<typename Scalar, typename Derived>
 template<typename OtherDerived>
 Scalar MatrixBase<Scalar, Derived>::dot(const OtherDerived& other) const
 {
-  assert(Traits::IsVectorAtCompileTime && OtherDerived::Traits::IsVectorAtCompileTime && size() == other.size());
+  assert(Traits::IsVectorAtCompileTime
+      && OtherDerived::Traits::IsVectorAtCompileTime
+      && size() == other.size());
   Scalar res;
-  if(EIGEN_UNROLLED_LOOPS && Traits::SizeAtCompileTime != Dynamic && Traits::SizeAtCompileTime <= 16)
-    DotUnroller<Traits::SizeAtCompileTime-1, Traits::SizeAtCompileTime, Derived, OtherDerived>
+  if(EIGEN_UNROLLED_LOOPS
+  && Traits::SizeAtCompileTime != Dynamic
+  && Traits::SizeAtCompileTime <= 16)
+    DotUnroller<Traits::SizeAtCompileTime-1, Traits::SizeAtCompileTime,
+                Derived, OtherDerived>
       ::run(*static_cast<const Derived*>(this), other, res);
   else
   {
@@ -123,25 +128,42 @@ MatrixBase<Scalar, Derived>::normalized() const
   return (*this) / norm();
 }
 
+/** \returns true if *this is approximately orthogonal to \a other,
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isOrtho_vector.cpp
+  * Output: \verbinclude MatrixBase_isOrtho_vector.out
+  */
 template<typename Scalar, typename Derived>
 template<typename OtherDerived>
 bool MatrixBase<Scalar, Derived>::isOrtho
 (const OtherDerived& other,
- const typename NumTraits<Scalar>::Real& prec = precision<Scalar>()) const
+ typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
 {
   return abs2(dot(other)) <= prec * prec * norm2() * other.norm2();
 }
 
+/** \returns true if *this is approximately an unitary matrix,
+  *          within the precision given by \a prec. In the case where the \a Scalar
+  *          type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
+  *
+  * \note This can be used to check whether a family of vectors forms an orthonormal basis.
+  *       Indeed, \c m.isOrtho() returns true if and only if the columns of m form an
+  *       orthonormal basis.
+  *
+  * Example: \include MatrixBase_isOrtho_matrix.cpp
+  * Output: \verbinclude MatrixBase_isOrtho_matrix.out
+  */
 template<typename Scalar, typename Derived>
 bool MatrixBase<Scalar, Derived>::isOrtho
-(const typename NumTraits<Scalar>::Real& prec = precision<Scalar>()) const
+(typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
 {
   for(int i = 0; i < cols(); i++)
   {
-    if(!isApprox(col(i).norm2(), static_cast<Scalar>(1)))
+    if(!Eigen::isApprox(col(i).norm2(), static_cast<Scalar>(1), prec))
       return false;
     for(int j = 0; j < i; j++)
-      if(!isMuchSmallerThan(col(i).dot(col(j)), static_cast<Scalar>(1)))
+      if(!Eigen::isMuchSmallerThan(col(i).dot(col(j)), static_cast<Scalar>(1), prec))
         return false;
   }
   return true;
diff --git a/Eigen/src/Core/DynBlock.h b/Eigen/src/Core/DynBlock.h
index b910afcee..1d8951c11 100644
--- a/Eigen/src/Core/DynBlock.h
+++ b/Eigen/src/Core/DynBlock.h
@@ -66,11 +66,11 @@ template<typename MatrixType> class DynBlock
     
     EIGEN_INHERIT_ASSIGNMENT_OPERATORS(DynBlock)
     
+  private:
     static const int
-      RowsAtCompileTime = MatrixType::RowsAtCompileTime == 1 ? 1 : Dynamic,
-      ColsAtCompileTime = MatrixType::ColsAtCompileTime == 1 ? 1 : Dynamic;
+      RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime == 1 ? 1 : Dynamic,
+      ColsAtCompileTime = MatrixType::Traits::ColsAtCompileTime == 1 ? 1 : Dynamic;
 
-  private:
     const DynBlock& _ref() const { return *this; }
     int _rows() const { return m_blockRows; }
     int _cols() const { return m_blockCols; }
diff --git a/Eigen/src/Core/Fuzzy.h b/Eigen/src/Core/Fuzzy.h
index 3641157f7..9337cadc8 100644
--- a/Eigen/src/Core/Fuzzy.h
+++ b/Eigen/src/Core/Fuzzy.h
@@ -30,7 +30,7 @@ template<typename Scalar, typename Derived>
 template<typename OtherDerived>
 bool MatrixBase<Scalar, Derived>::isApprox(
   const OtherDerived& other,
-  const typename NumTraits<Scalar>::Real& prec = precision<Scalar>()
+  typename NumTraits<Scalar>::Real prec = precision<Scalar>()
 ) const
 {
   assert(rows() == other.rows() && cols() == other.cols());
@@ -51,7 +51,7 @@ bool MatrixBase<Scalar, Derived>::isApprox(
 template<typename Scalar, typename Derived>
 bool MatrixBase<Scalar, Derived>::isMuchSmallerThan(
   const typename NumTraits<Scalar>::Real& other,
-  const typename NumTraits<Scalar>::Real& prec = precision<Scalar>()
+  typename NumTraits<Scalar>::Real prec = precision<Scalar>()
 ) const
 {
   if(Traits::IsVectorAtCompileTime)
@@ -71,7 +71,7 @@ template<typename Scalar, typename Derived>
 template<typename OtherDerived>
 bool MatrixBase<Scalar, Derived>::isMuchSmallerThan(
   const MatrixBase<Scalar, OtherDerived>& other,
-  const typename NumTraits<Scalar>::Real& prec = precision<Scalar>()
+  typename NumTraits<Scalar>::Real prec = precision<Scalar>()
 ) const
 {
   assert(rows() == other.rows() && cols() == other.cols());
diff --git a/Eigen/src/Core/Identity.h b/Eigen/src/Core/Identity.h
index 4f8045c1e..7c1893b08 100644
--- a/Eigen/src/Core/Identity.h
+++ b/Eigen/src/Core/Identity.h
@@ -26,6 +26,12 @@
 #ifndef EIGEN_IDENTITY_H
 #define EIGEN_IDENTITY_H
 
+/** \class Identity
+  *
+  * \brief Expression of the identity matrix of some size.
+  *
+  * \sa MatrixBase::identity(int)
+  */
 template<typename MatrixType> class Identity : NoOperatorEquals,
   public MatrixBase<typename MatrixType::Scalar, Identity<MatrixType> >
 {
@@ -33,15 +39,15 @@ template<typename MatrixType> class Identity : NoOperatorEquals,
     typedef typename MatrixType::Scalar Scalar;
     friend class MatrixBase<Scalar, Identity<MatrixType> >;
     
-    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-                     ColsAtCompileTime = MatrixType::ColsAtCompileTime;
-    
     Identity(int rows) : m_rows(rows)
     {
       assert(rows > 0 && RowsAtCompileTime == ColsAtCompileTime);
     }
     
   private:
+    static const int RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = MatrixType::Traits::ColsAtCompileTime;
+    
     const Identity& _ref() const { return *this; }
     int _rows() const { return m_rows; }
     int _cols() const { return m_rows; }
@@ -55,22 +61,46 @@ template<typename MatrixType> class Identity : NoOperatorEquals,
     int m_rows;
 };
 
+/** \returns an expression of the identity matrix of given type and size.
+  *
+  * \param rows The number of rows of the identity matrix to return. If *this has
+  *             fixed size, that size is used as the default argument for \a rows
+  *             and is then the only allowed value. If *this has dynamic size,
+  *             you can use any positive value for \a rows.
+  *
+  * \note An identity matrix is a square matrix, so it is required that the type of *this
+  *       allows being a square matrix.
+  *
+  * Example: \include MatrixBase_identity_int.cpp
+  * Output: \verbinclude MatrixBase_identity_int.out
+  *
+  * \sa class Identity, isIdentity()
+  */
 template<typename Scalar, typename Derived>
 const Identity<Derived> MatrixBase<Scalar, Derived>::identity(int rows)
 {
   return Identity<Derived>(rows);
 }
 
+/** \returns true if *this is approximately equal to the identity matrix,
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isIdentity.cpp
+  * Output: \verbinclude MatrixBase_isIdentity.out
+  *
+  * \sa class Identity, identity(int)
+  */
 template<typename Scalar, typename Derived>
 bool MatrixBase<Scalar, Derived>::isIdentity
-(const typename NumTraits<Scalar>::Real& prec = precision<Scalar>()) const
+(typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
 {
-  for(int j = 0; j < col(); j++)
+  if(cols() != rows()) return false;
+  for(int j = 0; j < cols(); j++)
   {
-    if(!isApprox(coeff(j, j), static_cast<Scalar>(1)))
+    if(!Eigen::isApprox(coeff(j, j), static_cast<Scalar>(1), prec))
       return false;
     for(int i = 0; i < j; i++)
-      if(!isMuchSmallerThan(coeff(i, j), static_cast<Scalar>(1)))
+      if(!Eigen::isMuchSmallerThan(coeff(i, j), static_cast<Scalar>(1), prec))
         return false;
   }
   return true;
diff --git a/Eigen/src/Core/Map.h b/Eigen/src/Core/Map.h
index 999ae283b..899062cf3 100644
--- a/Eigen/src/Core/Map.h
+++ b/Eigen/src/Core/Map.h
@@ -46,18 +46,18 @@ template<typename MatrixType> class Map
     typedef typename MatrixType::Scalar Scalar;
     friend class MatrixBase<Scalar, Map<MatrixType> >;
 
-    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-                     ColsAtCompileTime = MatrixType::ColsAtCompileTime;
-    static const MatrixStorageOrder Order = MatrixType::Order;
-
   private:
+    static const int RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = MatrixType::Traits::ColsAtCompileTime;
+    static const MatrixStorageOrder _Order = MatrixType::StorageOrder;
+
     const Map& _ref() const { return *this; }
     int _rows() const { return m_rows; }
     int _cols() const { return m_cols; }
     
     const Scalar& _coeff(int row, int col) const
     {
-      if(Order == ColumnMajor)
+      if(_Order == ColumnMajor)
         return m_data[row + col * m_rows];
       else // RowMajor
         return m_data[col + row * m_cols];
@@ -65,7 +65,7 @@ template<typename MatrixType> class Map
     
     Scalar& _coeffRef(int row, int col)
     {
-      if(Order == ColumnMajor)
+      if(_Order == ColumnMajor)
         return const_cast<Scalar*>(m_data)[row + col * m_rows];
       else // RowMajor
         return const_cast<Scalar*>(m_data)[col + row * m_cols];
diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index 2cf28e8a7..c4b021baa 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -144,6 +144,10 @@ inline bool isMuchSmallerThan(const std::complex<float>& a, const std::complex<f
 {
   return abs2(a) <= abs2(b) * prec * prec;
 }
+inline bool isMuchSmallerThan(const std::complex<float>& a, float b, float prec = precision<float>())
+{
+  return abs2(a) <= abs2(b) * prec * prec;
+}
 inline bool isApprox(const std::complex<float>& a, const std::complex<float>& b, float prec = precision<float>())
 {
   return isApprox(std::real(a), std::real(b), prec)
@@ -165,6 +169,10 @@ inline bool isMuchSmallerThan(const std::complex<double>& a, const std::complex<
 {
   return abs2(a) <= abs2(b) * prec * prec;
 }
+inline bool isMuchSmallerThan(const std::complex<double>& a, double b, double prec = precision<double>())
+{
+  return abs2(a) <= abs2(b) * prec * prec;
+}
 inline bool isApprox(const std::complex<double>& a, const std::complex<double>& b, double prec = precision<double>())
 {
   return isApprox(std::real(a), std::real(b), prec)
diff --git a/Eigen/src/Core/Matrix.h b/Eigen/src/Core/Matrix.h
index cde5dcebf..8984f3893 100644
--- a/Eigen/src/Core/Matrix.h
+++ b/Eigen/src/Core/Matrix.h
@@ -79,6 +79,8 @@ class Matrix : public MatrixBase<_Scalar, Matrix<_Scalar, _Rows, _Cols, _Storage
 {
   public:
     friend class MatrixBase<_Scalar, Matrix>;
+    friend class Map<Matrix>;
+    
     typedef      MatrixBase<_Scalar, Matrix>            Base;
     typedef      MatrixStorage<_Scalar, _Rows, _Cols>   Storage;
     typedef      _Scalar                                Scalar;
@@ -91,16 +93,15 @@ class Matrix : public MatrixBase<_Scalar, Matrix<_Scalar, _Rows, _Cols, _Storage
     Scalar* data()
     { return Storage::m_data; }
     
-    static const MatrixStorageOrder Order = _StorageOrder;
-    static const int RowsAtCompileTime = _Rows, ColsAtCompileTime = _Cols;
-
   private:
+    static const int RowsAtCompileTime = _Rows, ColsAtCompileTime = _Cols;
+    static const MatrixStorageOrder StorageOrder = _StorageOrder;
 
     Ref _ref() const { return Ref(*this); }
     
     const Scalar& _coeff(int row, int col) const
     {
-      if(Order == ColumnMajor)
+      if(_StorageOrder == ColumnMajor)
         return (Storage::m_data)[row + col * Storage::_rows()];
       else // RowMajor
         return (Storage::m_data)[col + row * Storage::_cols()];
@@ -108,7 +109,7 @@ class Matrix : public MatrixBase<_Scalar, Matrix<_Scalar, _Rows, _Cols, _Storage
     
     Scalar& _coeffRef(int row, int col)
     {
-      if(Order == ColumnMajor)
+      if(_StorageOrder == ColumnMajor)
         return (Storage::m_data)[row + col * Storage::_rows()];
       else // RowMajor
         return (Storage::m_data)[col + row * Storage::_cols()];
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index 123cbf438..fbf17b581 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/Eigen/src/Core/MatrixBase.h
@@ -26,37 +26,6 @@
 #ifndef EIGEN_MATRIXBASE_H
 #define EIGEN_MATRIXBASE_H
 
-#include "Util.h"
-
-template <typename Derived>
-struct DerivedTraits
-{
-    /** The number of rows at compile-time. This is just a copy of the value provided
-      * by the \a Derived type. If a value is not known at compile-time,
-      * it is set to the \a Dynamic constant.
-      * \sa rows(), cols(), ColsAtCompileTime, SizeAtCompileTime */
-    static const int RowsAtCompileTime = Derived::RowsAtCompileTime;
-    
-    /** The number of columns at compile-time. This is just a copy of the value provided
-      * by the \a Derived type. If a value is not known at compile-time,
-      * it is set to the \a Dynamic constant.
-      * \sa rows(), cols(), RowsAtCompileTime, SizeAtCompileTime */
-    static const int ColsAtCompileTime = Derived::ColsAtCompileTime;
-    
-    /** This is equal to the number of coefficients, i.e. the number of
-      * rows times the number of columns, or to \a Dynamic if this is not
-      * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
-    static const int SizeAtCompileTime
-      = Derived::RowsAtCompileTime == Dynamic || Derived::ColsAtCompileTime == Dynamic
-      ? Dynamic : Derived::RowsAtCompileTime * Derived::ColsAtCompileTime;
-    
-    /** This is set to true if either the number of rows or the number of
-      * columns is known at compile-time to be equal to 1. Indeed, in that case,
-      * we are dealing with a column-vector (if there is only one column) or with
-      * a row-vector (if there is only one row). */
-    static const bool IsVectorAtCompileTime = Derived::RowsAtCompileTime == 1 || Derived::ColsAtCompileTime == 1;
-};
-
 /** \class MatrixBase
   *
   * \brief Base class for all matrices, vectors, and expressions
@@ -88,7 +57,37 @@ struct DerivedTraits
 template<typename Scalar, typename Derived> class MatrixBase
 {
   public:
-    typedef DerivedTraits<Derived> Traits;
+  
+    /** \brief Some traits provided by the Derived type.
+      * Grouping these in a nested subclass is what was needed for ICC compatibility. */
+    struct Traits
+    {
+      /** The number of rows at compile-time. This is just a copy of the value provided
+        * by the \a Derived type. If a value is not known at compile-time,
+        * it is set to the \a Dynamic constant.
+        * \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
+      static const int RowsAtCompileTime = Derived::RowsAtCompileTime;
+      
+      /** The number of columns at compile-time. This is just a copy of the value provided
+        * by the \a Derived type. If a value is not known at compile-time,
+        * it is set to the \a Dynamic constant.
+        * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
+      static const int ColsAtCompileTime = Derived::ColsAtCompileTime;
+      
+      /** This is equal to the number of coefficients, i.e. the number of
+        * rows times the number of columns, or to \a Dynamic if this is not
+        * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
+      static const int SizeAtCompileTime
+        = Derived::RowsAtCompileTime == Dynamic || Derived::ColsAtCompileTime == Dynamic
+        ? Dynamic : Derived::RowsAtCompileTime * Derived::ColsAtCompileTime;
+      
+      /** This is set to true if either the number of rows or the number of
+        * columns is known at compile-time to be equal to 1. Indeed, in that case,
+        * we are dealing with a column-vector (if there is only one column) or with
+        * a row-vector (if there is only one row). */
+      static const bool IsVectorAtCompileTime
+        = Derived::RowsAtCompileTime == 1 || Derived::ColsAtCompileTime == 1;
+    };
     
     /** This is the "reference type" used to pass objects of type MatrixBase as arguments
       * to functions. If this MatrixBase type represents an expression, then \a Ref
@@ -104,17 +103,17 @@ template<typename Scalar, typename Derived> class MatrixBase
       * \a Scalar is \a std::complex<T> then RealScalar is \a T. */
     typedef typename NumTraits<Scalar>::Real RealScalar;
     
-    /** \returns the number of rows. \sa cols(), RowsAtCompileTime */
+    /** \returns the number of rows. \sa cols(), DerivedTraits::RowsAtCompileTime */
     int rows() const { return static_cast<const Derived *>(this)->_rows(); }
-    /** \returns the number of columns. \sa row(), ColsAtCompileTime*/
+    /** \returns the number of columns. \sa row(), DerivedTraits::ColsAtCompileTime*/
     int cols() const { return static_cast<const Derived *>(this)->_cols(); }
     /** \returns the number of coefficients, which is \a rows()*cols().
-      * \sa rows(), cols(), SizeAtCompileTime. */
+      * \sa rows(), cols(), DerivedTraits::SizeAtCompileTime. */
     int size() const { return rows() * cols(); }
     /** \returns true if either the number of rows or the number of columns is equal to 1.
       * In other words, this function returns
       * \code rows()==1 || cols()==1 \endcode
-      * \sa rows(), cols(), IsVectorAtCompileTime. */
+      * \sa rows(), cols(), DerivedTraits::IsVectorAtCompileTime. */
     bool isVector() const { return rows()==1 || cols()==1; }
     /** \returns a Ref to *this. \sa Ref */
     Ref ref() const
@@ -164,9 +163,8 @@ template<typename Scalar, typename Derived> class MatrixBase
     RealScalar norm()  const;
     const ScalarMultiple<RealScalar, Derived> normalized() const;
     template<typename OtherDerived>
-    bool isOrtho(const OtherDerived& other,
-                 const typename NumTraits<Scalar>::Real& prec) const;
-    bool isOrtho(const typename NumTraits<Scalar>::Real& prec) const;
+    bool isOrtho(const OtherDerived& other, RealScalar prec) const;
+    bool isOrtho(RealScalar prec) const;
     
     static const Eval<Random<Derived> > random(int rows, int cols);
     static const Eval<Random<Derived> > random(int size);
@@ -179,9 +177,10 @@ template<typename Scalar, typename Derived> class MatrixBase
     static const Ones<Derived> ones();
     static const Identity<Derived> identity(int rows = Derived::RowsAtCompileTime);
     
-    bool isZero(const typename NumTraits<Scalar>::Real& prec) const;
-    bool isOnes(const typename NumTraits<Scalar>::Real& prec) const;
-    bool isIdentity(const typename NumTraits<Scalar>::Real& prec) const;
+    bool isZero(RealScalar prec) const;
+    bool isOnes(RealScalar prec) const;
+    bool isIdentity(RealScalar prec) const;
+    bool isDiagonal(RealScalar prec) const;
     
     const DiagonalMatrix<Derived> asDiagonal() const;
     
@@ -189,19 +188,12 @@ template<typename Scalar, typename Derived> class MatrixBase
     const DiagonalCoeffs<Derived> diagonal() const;
     
     template<typename OtherDerived>
-    bool isApprox(
-      const OtherDerived& other,
-      const typename NumTraits<Scalar>::Real& prec
-    ) const;
-    bool isMuchSmallerThan(
-      const typename NumTraits<Scalar>::Real& other,
-      const typename NumTraits<Scalar>::Real& prec
-    ) const;
+    bool isApprox(const OtherDerived& other, RealScalar prec) const;
+    bool isMuchSmallerThan
+    (const typename NumTraits<Scalar>::Real& other, RealScalar prec) const;
     template<typename OtherDerived>
-    bool isMuchSmallerThan(
-      const MatrixBase<Scalar, OtherDerived>& other,
-      const typename NumTraits<Scalar>::Real& prec
-    ) const;
+    bool isMuchSmallerThan
+    (const MatrixBase<Scalar, OtherDerived>& other, RealScalar prec) const;
     
     template<typename OtherDerived>
     const Product<Derived, OtherDerived>
diff --git a/Eigen/src/Core/MatrixRef.h b/Eigen/src/Core/MatrixRef.h
index a2613892e..e2f281fab 100644
--- a/Eigen/src/Core/MatrixRef.h
+++ b/Eigen/src/Core/MatrixRef.h
@@ -38,10 +38,10 @@ template<typename MatrixType> class MatrixRef
 
     EIGEN_INHERIT_ASSIGNMENT_OPERATORS(MatrixRef)
 
-    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-                     ColsAtCompileTime = MatrixType::ColsAtCompileTime;
-
   private:
+    static const int RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = MatrixType::Traits::ColsAtCompileTime;
+
     int _rows() const { return m_matrix.rows(); }
     int _cols() const { return m_matrix.cols(); }
 
diff --git a/Eigen/src/Core/Minor.h b/Eigen/src/Core/Minor.h
index c26c78e7f..c300e35cf 100644
--- a/Eigen/src/Core/Minor.h
+++ b/Eigen/src/Core/Minor.h
@@ -56,13 +56,13 @@ template<typename MatrixType> class Minor
     
     EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Minor)
     
+  private:
     static const int
-      RowsAtCompileTime = (MatrixType::RowsAtCompileTime != Dynamic) ?
-                           MatrixType::RowsAtCompileTime - 1 : Dynamic,
-      ColsAtCompileTime = (MatrixType::ColsAtCompileTime != Dynamic) ?
-                           MatrixType::ColsAtCompileTime - 1 : Dynamic;
+      RowsAtCompileTime = (MatrixType::Traits::RowsAtCompileTime != Dynamic) ?
+                            MatrixType::Traits::RowsAtCompileTime - 1 : Dynamic,
+      ColsAtCompileTime = (MatrixType::Traits::ColsAtCompileTime != Dynamic) ?
+                            MatrixType::Traits::ColsAtCompileTime - 1 : Dynamic;
 
-  private:
     const Minor& _ref() const { return *this; }
     int _rows() const { return m_matrix.rows() - 1; }
     int _cols() const { return m_matrix.cols() - 1; }
diff --git a/Eigen/src/Core/Ones.h b/Eigen/src/Core/Ones.h
index b0fa1daf3..30aad4c3c 100644
--- a/Eigen/src/Core/Ones.h
+++ b/Eigen/src/Core/Ones.h
@@ -39,10 +39,9 @@ template<typename MatrixType> class Ones : NoOperatorEquals,
     typedef typename MatrixType::Scalar Scalar;
     friend class MatrixBase<Scalar, Ones<MatrixType> >;
   
-    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-                     ColsAtCompileTime = MatrixType::ColsAtCompileTime;
-
   private:
+    static const int RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = MatrixType::Traits::ColsAtCompileTime;
   
     const Ones& _ref() const { return *this; }
     int _rows() const { return m_rows; }
@@ -78,7 +77,7 @@ template<typename MatrixType> class Ones : NoOperatorEquals,
   * Example: \include MatrixBase_ones_int_int.cpp
   * Output: \verbinclude MatrixBase_ones_int_int.out
   *
-  * \sa ones(), ones(int)
+  * \sa ones(), ones(int), isOnes(), class Ones
   */
 template<typename Scalar, typename Derived>
 const Ones<Derived> MatrixBase<Scalar, Derived>::ones(int rows, int cols)
@@ -100,7 +99,7 @@ const Ones<Derived> MatrixBase<Scalar, Derived>::ones(int rows, int cols)
   * Example: \include MatrixBase_ones_int.cpp
   * Output: \verbinclude MatrixBase_ones_int.out
   *
-  * \sa ones(), ones(int,int)
+  * \sa ones(), ones(int,int), isOnes(), class Ones
   */
 template<typename Scalar, typename Derived>
 const Ones<Derived> MatrixBase<Scalar, Derived>::ones(int size)
@@ -118,7 +117,7 @@ const Ones<Derived> MatrixBase<Scalar, Derived>::ones(int size)
   * Example: \include MatrixBase_ones.cpp
   * Output: \verbinclude MatrixBase_ones.out
   *
-  * \sa ones(int), ones(int,int)
+  * \sa ones(int), ones(int,int), isOnes(), class Ones
   */
 template<typename Scalar, typename Derived>
 const Ones<Derived> MatrixBase<Scalar, Derived>::ones()
@@ -126,13 +125,21 @@ const Ones<Derived> MatrixBase<Scalar, Derived>::ones()
   return Ones<Derived>(Traits::RowsAtCompileTime, Traits::ColsAtCompileTime);
 }
 
+/** \returns true if *this is approximately equal to the matrix where all coefficients
+  *          are equal to 1, within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isOnes.cpp
+  * Output: \verbinclude MatrixBase_isOnes.out
+  *
+  * \sa class Ones, ones()
+  */
 template<typename Scalar, typename Derived>
 bool MatrixBase<Scalar, Derived>::isOnes
-(const typename NumTraits<Scalar>::Real& prec = precision<Scalar>()) const
+(typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
 {
-  for(int j = 0; j < col(); j++)
-    for(int i = 0; i < row(); i++)
-      if(!isApprox(coeff(i, j), static_cast<Scalar>(1)))
+  for(int j = 0; j < cols(); j++)
+    for(int i = 0; i < rows(); i++)
+      if(!Eigen::isApprox(coeff(i, j), static_cast<Scalar>(1), prec))
         return false;
   return true;
 }
diff --git a/Eigen/src/Core/OperatorEquals.h b/Eigen/src/Core/OperatorEquals.h
index 296573953..7f86cb8f2 100644
--- a/Eigen/src/Core/OperatorEquals.h
+++ b/Eigen/src/Core/OperatorEquals.h
@@ -30,8 +30,8 @@
 template<typename Derived1, typename Derived2, int UnrollCount>
 struct MatrixOperatorEqualsUnroller
 {
-  static const int col = (UnrollCount-1) / Derived1::RowsAtCompileTime;
-  static const int row = (UnrollCount-1) % Derived1::RowsAtCompileTime;
+  static const int col = (UnrollCount-1) / Derived1::Traits::RowsAtCompileTime;
+  static const int row = (UnrollCount-1) % Derived1::Traits::RowsAtCompileTime;
 
   static void run(Derived1 &dst, const Derived2 &src)
   {
diff --git a/Eigen/src/Core/Opposite.h b/Eigen/src/Core/Opposite.h
index ab4ce4c10..f1166be16 100644
--- a/Eigen/src/Core/Opposite.h
+++ b/Eigen/src/Core/Opposite.h
@@ -36,10 +36,10 @@ template<typename MatrixType> class Opposite : NoOperatorEquals,
     
     Opposite(const MatRef& matrix) : m_matrix(matrix) {}
     
-    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-                     ColsAtCompileTime = MatrixType::ColsAtCompileTime;
-
   private:
+    static const int RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = MatrixType::Traits::ColsAtCompileTime;
+
     const Opposite& _ref() const { return *this; }
     int _rows() const { return m_matrix.rows(); }
     int _cols() const { return m_matrix.cols(); }
diff --git a/Eigen/src/Core/Product.h b/Eigen/src/Core/Product.h
index be573f416..e31320208 100644
--- a/Eigen/src/Core/Product.h
+++ b/Eigen/src/Core/Product.h
@@ -75,10 +75,9 @@ template<typename Lhs, typename Rhs> class Product : NoOperatorEquals,
       assert(lhs.cols() == rhs.rows());
     }
     
-    static const int RowsAtCompileTime = Lhs::RowsAtCompileTime,
-                     ColsAtCompileTime = Rhs::ColsAtCompileTime;
-
   private:
+    static const int RowsAtCompileTime = Lhs::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = Rhs::Traits::ColsAtCompileTime;
 
     const Product& _ref() const { return *this; }
     int _rows() const { return m_lhs.rows(); }
@@ -88,8 +87,10 @@ template<typename Lhs, typename Rhs> class Product : NoOperatorEquals,
     {
       Scalar res;
       if(EIGEN_UNROLLED_LOOPS
-      && Lhs::ColsAtCompileTime != Dynamic && Lhs::ColsAtCompileTime <= 16)
-        ProductUnroller<Lhs::ColsAtCompileTime-1, Lhs::ColsAtCompileTime, LhsRef, RhsRef>
+      && Lhs::Traits::ColsAtCompileTime != Dynamic
+      && Lhs::Traits::ColsAtCompileTime <= 16)
+        ProductUnroller<Lhs::Traits::ColsAtCompileTime-1,
+                        Lhs::Traits::ColsAtCompileTime, LhsRef, RhsRef>
           ::run(row, col, m_lhs, m_rhs, res);
       else
       {
diff --git a/Eigen/src/Core/Random.h b/Eigen/src/Core/Random.h
index cf6d44fb3..deb0dbde7 100644
--- a/Eigen/src/Core/Random.h
+++ b/Eigen/src/Core/Random.h
@@ -39,10 +39,9 @@ template<typename MatrixType> class Random : NoOperatorEquals,
     typedef typename MatrixType::Scalar Scalar;
     friend class MatrixBase<Scalar, Random<MatrixType> >;
   
-    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-                     ColsAtCompileTime = MatrixType::ColsAtCompileTime;
-  
   private:
+    static const int RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = MatrixType::Traits::ColsAtCompileTime;
   
     const Random& _ref() const { return *this; }
     int _rows() const { return m_rows; }
@@ -50,7 +49,7 @@ template<typename MatrixType> class Random : NoOperatorEquals,
     
     Scalar _coeff(int, int) const
     {
-      return random<Scalar>();
+      return Eigen::random<Scalar>();
     }
   
   public:
diff --git a/Eigen/src/Core/Row.h b/Eigen/src/Core/Row.h
index a10bf8bf5..1473e0a63 100644
--- a/Eigen/src/Core/Row.h
+++ b/Eigen/src/Core/Row.h
@@ -68,10 +68,10 @@ template<typename MatrixType> class Row
     
     EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Row)
     
+  private:
     static const int RowsAtCompileTime = 1,
-                     ColsAtCompileTime = MatrixType::ColsAtCompileTime;
+                     ColsAtCompileTime = MatrixType::Traits::ColsAtCompileTime;
 
-  private:
     const Row& _ref() const { return *this; }
     
     int _rows() const { return 1; }
diff --git a/Eigen/src/Core/ScalarMultiple.h b/Eigen/src/Core/ScalarMultiple.h
index 618fcf4dd..11b074e38 100644
--- a/Eigen/src/Core/ScalarMultiple.h
+++ b/Eigen/src/Core/ScalarMultiple.h
@@ -37,10 +37,10 @@ template<typename FactorType, typename MatrixType> class ScalarMultiple : NoOper
     ScalarMultiple(const MatRef& matrix, FactorType factor)
       : m_matrix(matrix), m_factor(factor) {}
 
-    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-                     ColsAtCompileTime = MatrixType::ColsAtCompileTime;
-
   private:
+    static const int RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = MatrixType::Traits::ColsAtCompileTime;
+
     const ScalarMultiple& _ref() const { return *this; }
     int _rows() const { return m_matrix.rows(); }
     int _cols() const { return m_matrix.cols(); }
diff --git a/Eigen/src/Core/Sum.h b/Eigen/src/Core/Sum.h
index 365c23810..b9b35cdca 100644
--- a/Eigen/src/Core/Sum.h
+++ b/Eigen/src/Core/Sum.h
@@ -41,10 +41,10 @@ template<typename Lhs, typename Rhs> class Sum : NoOperatorEquals,
       assert(lhs.rows() == rhs.rows() && lhs.cols() == rhs.cols());
     }
 
-    static const int RowsAtCompileTime = Lhs::RowsAtCompileTime,
-                     ColsAtCompileTime = Rhs::ColsAtCompileTime;
-
   private:
+    static const int RowsAtCompileTime = Lhs::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = Rhs::Traits::ColsAtCompileTime;
+
     const Sum& _ref() const { return *this; }
     int _rows() const { return m_lhs.rows(); }
     int _cols() const { return m_lhs.cols(); }
diff --git a/Eigen/src/Core/Transpose.h b/Eigen/src/Core/Transpose.h
index b12efde81..274a159e5 100644
--- a/Eigen/src/Core/Transpose.h
+++ b/Eigen/src/Core/Transpose.h
@@ -50,10 +50,10 @@ template<typename MatrixType> class Transpose
     
     EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Transpose)
     
-    static const int RowsAtCompileTime = MatrixType::ColsAtCompileTime,
-                     ColsAtCompileTime = MatrixType::RowsAtCompileTime;
-
   private:
+    static const int RowsAtCompileTime = MatrixType::Traits::ColsAtCompileTime,
+                     ColsAtCompileTime = MatrixType::Traits::RowsAtCompileTime;
+
     const Transpose& _ref() const { return *this; }
     int _rows() const { return m_matrix.cols(); }
     int _cols() const { return m_matrix.rows(); }
diff --git a/Eigen/src/Core/Zero.h b/Eigen/src/Core/Zero.h
index 72a6bd4df..ff587d886 100644
--- a/Eigen/src/Core/Zero.h
+++ b/Eigen/src/Core/Zero.h
@@ -39,10 +39,10 @@ template<typename MatrixType> class Zero : NoOperatorEquals,
     typedef typename MatrixType::Scalar Scalar;
     friend class MatrixBase<Scalar, Zero<MatrixType> >;
   
-    static const int RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-                     ColsAtCompileTime = MatrixType::ColsAtCompileTime;
-
   private:
+    static const int RowsAtCompileTime = MatrixType::Traits::RowsAtCompileTime,
+                     ColsAtCompileTime = MatrixType::Traits::ColsAtCompileTime;
+
     const Zero& _ref() const { return *this; }
     int _rows() const { return m_rows; }
     int _cols() const { return m_cols; }
@@ -125,13 +125,21 @@ const Zero<Derived> MatrixBase<Scalar, Derived>::zero()
   return Zero<Derived>(Traits::RowsAtCompileTime, Traits::ColsAtCompileTime);
 }
 
+/** \returns true if *this is approximately equal to the zero matrix,
+  *          within the precision given by \a prec.
+  *
+  * Example: \include MatrixBase_isZero.cpp
+  * Output: \verbinclude MatrixBase_isZero.out
+  *
+  * \sa class Zero, zero()
+  */
 template<typename Scalar, typename Derived>
 bool MatrixBase<Scalar, Derived>::isZero
-(const typename NumTraits<Scalar>::Real& prec = precision<Scalar>()) const
+(typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
 {
-  for(int j = 0; j < col(); j++)
-    for(int i = 0; i < row(); i++)
-      if(!isMuchSmallerThan(coeff(i, j), static_cast<Scalar>(1)))
+  for(int j = 0; j < cols(); j++)
+    for(int i = 0; i < rows(); i++)
+      if(!Eigen::isMuchSmallerThan(coeff(i, j), static_cast<Scalar>(1), prec))
         return false;
   return true;
 }
diff --git a/doc/Doxyfile.in b/doc/Doxyfile.in
index 0a250144a..dd1e57297 100644
--- a/doc/Doxyfile.in
+++ b/doc/Doxyfile.in
@@ -37,7 +37,7 @@ SEPARATE_MEMBER_PAGES  = NO
 TAB_SIZE               = 8
 ALIASES                = \
 "only_for_vectors=This is only for vectors (either row-vectors or column-vectors), \
-as determined by \link MatrixBase::IsVectorAtCompileTime \endlink."
+i.e. matrices which are known at compile-time to have either one row or one column."
 OPTIMIZE_OUTPUT_FOR_C  = NO
 OPTIMIZE_OUTPUT_JAVA   = NO
 BUILTIN_STL_SUPPORT    = NO
diff --git a/doc/snippets/MatrixBase_isDiagonal.cpp b/doc/snippets/MatrixBase_isDiagonal.cpp
new file mode 100644
index 000000000..5c2f7d4d2
--- /dev/null
+++ b/doc/snippets/MatrixBase_isDiagonal.cpp
@@ -0,0 +1,6 @@
+Matrix3d m = 10000 * Matrix3d::identity();
+m(0,2) = 1;
+cout << "Here's the matrix m:" << endl << m << endl;
+cout << "m.isDiagonal() returns: " << m.isDiagonal() << endl;
+cout << "m.isDiagonal(1e-3) returns: " << m.isDiagonal(1e-3) << endl;
+
diff --git a/doc/snippets/MatrixBase_isIdentity.cpp b/doc/snippets/MatrixBase_isIdentity.cpp
new file mode 100644
index 000000000..19d0156eb
--- /dev/null
+++ b/doc/snippets/MatrixBase_isIdentity.cpp
@@ -0,0 +1,5 @@
+Matrix3d m = Matrix3d::identity();
+m(0,2) = 1e-4;
+cout << "Here's the matrix m:" << endl << m << endl;
+cout << "m.isIdentity() returns: " << m.isIdentity() << endl;
+cout << "m.isIdentity(1e-3) returns: " << m.isIdentity(1e-3) << endl;
diff --git a/doc/snippets/MatrixBase_isOnes.cpp b/doc/snippets/MatrixBase_isOnes.cpp
new file mode 100644
index 000000000..3cd82ab7b
--- /dev/null
+++ b/doc/snippets/MatrixBase_isOnes.cpp
@@ -0,0 +1,5 @@
+Matrix3d m = Matrix3d::ones();
+m(0,2) += 1e-4;
+cout << "Here's the matrix m:" << endl << m << endl;
+cout << "m.isOnes() returns: " << m.isOnes() << endl;
+cout << "m.isOnes(1e-3) returns: " << m.isOnes(1e-3) << endl;
diff --git a/doc/snippets/MatrixBase_isOrtho_matrix.cpp b/doc/snippets/MatrixBase_isOrtho_matrix.cpp
new file mode 100644
index 000000000..a79df9202
--- /dev/null
+++ b/doc/snippets/MatrixBase_isOrtho_matrix.cpp
@@ -0,0 +1,5 @@
+Matrix3d m = Matrix3d::identity();
+m(0,2) = 1e-4;
+cout << "Here's the matrix m:" << endl << m << endl;
+cout << "m.isOrtho() returns: " << m.isOrtho() << endl;
+cout << "m.isOrtho(1e-3) returns: " << m.isOrtho(1e-3) << endl;
diff --git a/doc/snippets/MatrixBase_isOrtho_vector.cpp b/doc/snippets/MatrixBase_isOrtho_vector.cpp
new file mode 100644
index 000000000..656eaf316
--- /dev/null
+++ b/doc/snippets/MatrixBase_isOrtho_vector.cpp
@@ -0,0 +1,6 @@
+Vector3d v(1,0,0);
+Vector3d w(1e-4,0,1);
+cout << "Here's the vector v:" << endl << v << endl;
+cout << "Here's the vector w:" << endl << w << endl;
+cout << "v.isOrtho(w) returns: " << v.isOrtho(w) << endl;
+cout << "v.isOrtho(w,1e-3) returns: " << v.isOrtho(w,1e-3) << endl;
diff --git a/doc/snippets/MatrixBase_isZero.cpp b/doc/snippets/MatrixBase_isZero.cpp
new file mode 100644
index 000000000..efab3d624
--- /dev/null
+++ b/doc/snippets/MatrixBase_isZero.cpp
@@ -0,0 +1,5 @@
+Matrix3d m = Matrix3d::zero();
+m(0,2) = 1e-4;
+cout << "Here's the matrix m:" << endl << m << endl;
+cout << "m.isZero() returns: " << m.isZero() << endl;
+cout << "m.isZero(1e-3) returns: " << m.isZero(1e-3) << endl;
diff --git a/test/adjoint.cpp b/test/adjoint.cpp
index 7a33f8b73..690f0424a 100644
--- a/test/adjoint.cpp
+++ b/test/adjoint.cpp
@@ -34,7 +34,7 @@ template<typename MatrixType> void adjoint(const MatrixType& m)
   */
 
   typedef typename MatrixType::Scalar Scalar;
-  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, 1> VectorType;
   int rows = m.rows();
   int cols = m.cols();
   
@@ -42,9 +42,9 @@ template<typename MatrixType> void adjoint(const MatrixType& m)
              m2 = MatrixType::random(rows, cols),
              m3(rows, cols),
              mzero = MatrixType::zero(rows, cols),
-             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+             identity = Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, MatrixType::Traits::RowsAtCompileTime>
                               ::identity(rows),
-             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+             square = Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, MatrixType::Traits::RowsAtCompileTime>
                               ::random(rows, rows);
   VectorType v1 = VectorType::random(rows),
              v2 = VectorType::random(rows),
diff --git a/test/basicstuff.cpp b/test/basicstuff.cpp
index dcc909b4f..2c2a945c3 100644
--- a/test/basicstuff.cpp
+++ b/test/basicstuff.cpp
@@ -30,7 +30,7 @@ namespace Eigen {
 template<typename MatrixType> void basicStuff(const MatrixType& m)
 {
   typedef typename MatrixType::Scalar Scalar;
-  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, 1> VectorType;
   
   int rows = m.rows();
   int cols = m.cols();
@@ -41,9 +41,9 @@ template<typename MatrixType> void basicStuff(const MatrixType& m)
              m2 = MatrixType::random(rows, cols),
              m3(rows, cols),
              mzero = MatrixType::zero(rows, cols),
-             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+             identity = Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, MatrixType::Traits::RowsAtCompileTime>
                               ::identity(rows),
-             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+             square = Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, MatrixType::Traits::RowsAtCompileTime>
                               ::random(rows, rows);
   VectorType v1 = VectorType::random(rows),
              v2 = VectorType::random(rows),
@@ -75,8 +75,8 @@ template<typename MatrixType> void basicStuff(const MatrixType& m)
   
   // now test copying a row-vector into a (column-)vector and conversely.
   square.col(r) = square.row(r).eval();
-  Matrix<Scalar, 1, MatrixType::RowsAtCompileTime> rv(rows);
-  Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> cv(rows);
+  Matrix<Scalar, 1, MatrixType::Traits::RowsAtCompileTime> rv(rows);
+  Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, 1> cv(rows);
   rv = square.col(r);
   cv = square.row(r);
   VERIFY_IS_APPROX(rv, cv.transpose());
diff --git a/test/linearstructure.cpp b/test/linearstructure.cpp
index 2bb7a1d81..32199c5e0 100644
--- a/test/linearstructure.cpp
+++ b/test/linearstructure.cpp
@@ -34,7 +34,7 @@ template<typename MatrixType> void linearStructure(const MatrixType& m)
   */
 
   typedef typename MatrixType::Scalar Scalar;
-  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, 1> VectorType;
   
   int rows = m.rows();
   int cols = m.cols();
@@ -45,9 +45,9 @@ template<typename MatrixType> void linearStructure(const MatrixType& m)
              m2 = MatrixType::random(rows, cols),
              m3(rows, cols),
              mzero = MatrixType::zero(rows, cols),
-             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+             identity = Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, MatrixType::Traits::RowsAtCompileTime>
                               ::identity(rows),
-             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+             square = Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, MatrixType::Traits::RowsAtCompileTime>
                               ::random(rows, rows);
   VectorType v1 = VectorType::random(rows),
              v2 = VectorType::random(rows),
diff --git a/test/miscmatrices.cpp b/test/miscmatrices.cpp
index 7126266fc..e0aa13270 100644
--- a/test/miscmatrices.cpp
+++ b/test/miscmatrices.cpp
@@ -34,8 +34,8 @@ template<typename MatrixType> void miscMatrices(const MatrixType& m)
   */
 
   typedef typename MatrixType::Scalar Scalar;
-  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
-  typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;
+  typedef Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, 1, MatrixType::Traits::ColsAtCompileTime> RowVectorType;
   int rows = m.rows();
   int cols = m.cols();
   
@@ -45,7 +45,7 @@ template<typename MatrixType> void miscMatrices(const MatrixType& m)
   VERIFY_IS_APPROX(m1(r,c), static_cast<Scalar>(1));
   VectorType v1 = VectorType::random(rows);
   v1[0];
-  Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+  Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, MatrixType::Traits::RowsAtCompileTime>
   square = v1.asDiagonal();
   if(r==r2) VERIFY_IS_APPROX(square(r,r2), v1[r]);
   else VERIFY_IS_MUCH_SMALLER_THAN(square(r,r2), static_cast<Scalar>(1));
diff --git a/test/product.cpp b/test/product.cpp
index 81610d64c..e56d6aee9 100644
--- a/test/product.cpp
+++ b/test/product.cpp
@@ -34,7 +34,7 @@ template<typename MatrixType> void product(const MatrixType& m)
   */
 
   typedef typename MatrixType::Scalar Scalar;
-  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, 1> VectorType;
   
   int rows = m.rows();
   int cols = m.cols();
@@ -45,9 +45,9 @@ template<typename MatrixType> void product(const MatrixType& m)
              m2 = MatrixType::random(rows, cols),
              m3(rows, cols),
              mzero = MatrixType::zero(rows, cols),
-             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+             identity = Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, MatrixType::Traits::RowsAtCompileTime>
                               ::identity(rows),
-             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+             square = Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, MatrixType::Traits::RowsAtCompileTime>
                               ::random(rows, rows);
   VectorType v1 = VectorType::random(rows),
              v2 = VectorType::random(rows),
diff --git a/test/submatrices.cpp b/test/submatrices.cpp
index 29c83f742..e263bfb6a 100644
--- a/test/submatrices.cpp
+++ b/test/submatrices.cpp
@@ -34,8 +34,8 @@ template<typename MatrixType> void submatrices(const MatrixType& m)
   */
   
   typedef typename MatrixType::Scalar Scalar;
-  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
-  typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;
+  typedef Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, 1, MatrixType::Traits::ColsAtCompileTime> RowVectorType;
   int rows = m.rows();
   int cols = m.cols();
   
@@ -43,9 +43,9 @@ template<typename MatrixType> void submatrices(const MatrixType& m)
              m2 = MatrixType::random(rows, cols),
              m3(rows, cols),
              mzero = MatrixType::zero(rows, cols),
-             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+             identity = Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, MatrixType::Traits::RowsAtCompileTime>
                               ::identity(rows),
-             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+             square = Matrix<Scalar, MatrixType::Traits::RowsAtCompileTime, MatrixType::Traits::RowsAtCompileTime>
                               ::random(rows, rows);
   VectorType v1 = VectorType::random(rows),
              v2 = VectorType::random(rows),