* added a Tridiagonalization class for selfadjoint matrices

* added MatrixBase::real()
* added the ability to extract a selfadjoint matrix from the
  lower or upper part of a matrix, e.g.:
    m.extract<Upper|SelfAdjoint>()
  will ignore the strict lower part and return a selfadjoint.
  This is compatible with ZeroDiag and UnitDiag.

Eigen/src/Core/CwiseUnaryOp.h

@@ -139,7 +139,7 @@ MatrixBase<Derived>::cwiseAbs2() const
   return derived();
 }
 
-/** \returns an expression of the complex conjugate of *this.
+/** \returns an expression of the complex conjugate of \c *this.
   *
   * \sa adjoint() */
 template<typename Derived>
@@ -149,6 +149,16 @@ MatrixBase<Derived>::conjugate() const
   return ConjugateReturnType(derived());
 }
 
+/** \returns an expression of the real part of \c *this.
+  *
+  * \sa adjoint() */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::RealReturnType
+MatrixBase<Derived>::real() const
+{
+  return derived();
+}
+
 /** \returns an expression of *this with the \a Scalar type casted to
   * \a NewScalar.
   *

Eigen/src/Core/Extract.h

@@ -77,7 +77,7 @@ template<typename MatrixType, unsigned int Mode> class Extract
     inline Scalar _coeff(int row, int col) const
     {
       if(Flags & LowerTriangularBit ? col>row : row>col)
-        return (Scalar)0;
+        return (Flags & SelfAdjointBit) ? ei_conj(m_matrix.coeff(col, row)) : (Scalar)0;
       if(Flags & UnitDiagBit)
         return col==row ? (Scalar)1 : m_matrix.coeff(row, col);
       else if(Flags & ZeroDiagBit)

Eigen/src/Core/Functors.h

@@ -204,6 +204,19 @@ template<typename Scalar, typename NewType>
 struct ei_functor_traits<ei_scalar_cast_op<Scalar,NewType> >
 { enum { Cost = ei_is_same_type<Scalar, NewType>::ret ? 0 : NumTraits<NewType>::AddCost, IsVectorizable = false }; };
 
+/** \internal
+  * \brief Template functor to extract the real part of a complex
+  *
+  * \sa class CwiseUnaryOp, MatrixBase::real()
+  */
+template<typename Scalar>
+struct ei_scalar_real_op EIGEN_EMPTY_STRUCT {
+  typedef typename NumTraits<Scalar>::Real result_type;
+  inline result_type operator() (const Scalar& a) const { return ei_real(a); }
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_real_op<Scalar> >
+{ enum { Cost =  0, IsVectorizable = false }; };
 
 /** \internal
   * \brief Template functor to multiply a scalar by a fixed other one

Eigen/src/Core/MatrixBase.h

@@ -197,6 +197,8 @@ template<typename Derived> class MatrixBase : public ArrayBase<Derived>
                         CwiseUnaryOp<ei_scalar_conjugate_op<Scalar>, Derived>,
                         Derived&
                      >::ret ConjugateReturnType;
+    /** the return type of MatrixBase::real() */
+    typedef CwiseUnaryOp<ei_scalar_real_op<Scalar>, Derived> RealReturnType;
     /** the return type of MatrixBase::adjoint() */
     typedef Transpose<NestByValue<typename ei_unref<ConjugateReturnType>::type> >
             AdjointReturnType;
@@ -477,6 +479,7 @@ template<typename Derived> class MatrixBase : public ArrayBase<Derived>
     /// \name Coefficient-wise operations
     //@{
     const ConjugateReturnType conjugate() const;
+    const RealReturnType real() const;
 
     template<typename OtherDerived>
     const CwiseBinaryOp<ei_scalar_product_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>

Eigen/src/Core/util/Constants.h

@@ -59,8 +59,6 @@ const unsigned int Upper = UpperTriangularBit;
 const unsigned int StrictlyUpper = UpperTriangularBit | ZeroDiagBit;
 const unsigned int Lower = LowerTriangularBit;
 const unsigned int StrictlyLower = LowerTriangularBit | ZeroDiagBit;
-
-// additional possible values for the Mode parameter of part()
 const unsigned int SelfAdjoint = SelfAdjointBit;
 
 // additional possible values for the Mode parameter of extract()

Eigen/src/Core/util/ForwardDeclarations.h

@@ -59,6 +59,7 @@ template<typename Scalar> struct ei_scalar_product_op;
 template<typename Scalar> struct ei_scalar_quotient_op;
 template<typename Scalar> struct ei_scalar_opposite_op;
 template<typename Scalar> struct ei_scalar_conjugate_op;
+template<typename Scalar> struct ei_scalar_real_op;
 template<typename Scalar> struct ei_scalar_abs_op;
 template<typename Scalar> struct ei_scalar_abs2_op;
 template<typename Scalar> struct ei_scalar_sqrt_op;