diff --git a/Eigen/src/Eigenvalues/Tridiagonalization.h b/Eigen/src/Eigenvalues/Tridiagonalization.h
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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIDIAGONALIZATION_H
+#define EIGEN_TRIDIAGONALIZATION_H
+
+namespace Eigen { 
+
+namespace internal {
+  
+template<typename MatrixType> struct TridiagonalizationMatrixTReturnType;
+template<typename MatrixType>
+struct traits<TridiagonalizationMatrixTReturnType<MatrixType> >
+{
+  typedef typename MatrixType::PlainObject ReturnType;
+};
+
+template<typename MatrixType, typename CoeffVectorType>
+void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs);
+}
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+  *
+  *
+  * \class Tridiagonalization
+  *
+  * \brief Tridiagonal decomposition of a selfadjoint matrix
+  *
+  * \tparam _MatrixType the type of the matrix of which we are computing the
+  * tridiagonal decomposition; this is expected to be an instantiation of the
+  * Matrix class template.
+  *
+  * This class performs a tridiagonal decomposition of a selfadjoint matrix \f$ A \f$ such that:
+  * \f$ A = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real symmetric tridiagonal matrix.
+  *
+  * A tridiagonal matrix is a matrix which has nonzero elements only on the
+  * main diagonal and the first diagonal below and above it. The Hessenberg
+  * decomposition of a selfadjoint matrix is in fact a tridiagonal
+  * decomposition. This class is used in SelfAdjointEigenSolver to compute the
+  * eigenvalues and eigenvectors of a selfadjoint matrix.
+  *
+  * Call the function compute() to compute the tridiagonal decomposition of a
+  * given matrix. Alternatively, you can use the Tridiagonalization(const MatrixType&)
+  * constructor which computes the tridiagonal Schur decomposition at
+  * construction time. Once the decomposition is computed, you can use the
+  * matrixQ() and matrixT() functions to retrieve the matrices Q and T in the
+  * decomposition.
+  *
+  * The documentation of Tridiagonalization(const MatrixType&) contains an
+  * example of the typical use of this class.
+  *
+  * \sa class HessenbergDecomposition, class SelfAdjointEigenSolver
+  */
+template<typename _MatrixType> class Tridiagonalization
+{
+  public:
+
+    /** \brief Synonym for the template parameter \p _MatrixType. */
+    typedef _MatrixType MatrixType;
+
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+    typedef typename MatrixType::Index Index;
+
+    enum {
+      Size = MatrixType::RowsAtCompileTime,
+      SizeMinusOne = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1),
+      Options = MatrixType::Options,
+      MaxSize = MatrixType::MaxRowsAtCompileTime,
+      MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1)
+    };
+
+    typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;
+    typedef typename internal::plain_col_type<MatrixType, RealScalar>::type DiagonalType;
+    typedef Matrix<RealScalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> SubDiagonalType;
+    typedef typename internal::remove_all<typename MatrixType::RealReturnType>::type MatrixTypeRealView;
+    typedef internal::TridiagonalizationMatrixTReturnType<MatrixTypeRealView> MatrixTReturnType;
+
+    typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
+              typename internal::add_const_on_value_type<typename Diagonal<const MatrixType>::RealReturnType>::type,
+              const Diagonal<const MatrixType>
+            >::type DiagonalReturnType;
+
+    typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
+              typename internal::add_const_on_value_type<typename Diagonal<
+                Block<const MatrixType,SizeMinusOne,SizeMinusOne> >::RealReturnType>::type,
+              const Diagonal<
+                Block<const MatrixType,SizeMinusOne,SizeMinusOne> >
+            >::type SubDiagonalReturnType;
+
+    /** \brief Return type of matrixQ() */
+    typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type> HouseholderSequenceType;
+
+    /** \brief Default constructor.
+      *
+      * \param [in]  size  Positive integer, size of the matrix whose tridiagonal
+      * decomposition will be computed.
+      *
+      * The default constructor is useful in cases in which the user intends to
+      * perform decompositions via compute().  The \p size parameter is only
+      * used as a hint. It is not an error to give a wrong \p size, but it may
+      * impair performance.
+      *
+      * \sa compute() for an example.
+      */
+    Tridiagonalization(Index size = Size==Dynamic ? 2 : Size)
+      : m_matrix(size,size),
+        m_hCoeffs(size > 1 ? size-1 : 1),
+        m_isInitialized(false)
+    {}
+
+    /** \brief Constructor; computes tridiagonal decomposition of given matrix.
+      *
+      * \param[in]  matrix  Selfadjoint matrix whose tridiagonal decomposition
+      * is to be computed.
+      *
+      * This constructor calls compute() to compute the tridiagonal decomposition.
+      *
+      * Example: \include Tridiagonalization_Tridiagonalization_MatrixType.cpp
+      * Output: \verbinclude Tridiagonalization_Tridiagonalization_MatrixType.out
+      */
+    Tridiagonalization(const MatrixType& matrix)
+      : m_matrix(matrix),
+        m_hCoeffs(matrix.cols() > 1 ? matrix.cols()-1 : 1),
+        m_isInitialized(false)
+    {
+      internal::tridiagonalization_inplace(m_matrix, m_hCoeffs);
+      m_isInitialized = true;
+    }
+
+    /** \brief Computes tridiagonal decomposition of given matrix.
+      *
+      * \param[in]  matrix  Selfadjoint matrix whose tridiagonal decomposition
+      * is to be computed.
+      * \returns    Reference to \c *this
+      *
+      * The tridiagonal decomposition is computed by bringing the columns of
+      * the matrix successively in the required form using Householder
+      * reflections. The cost is \f$ 4n^3/3 \f$ flops, where \f$ n \f$ denotes
+      * the size of the given matrix.
+      *
+      * This method reuses of the allocated data in the Tridiagonalization
+      * object, if the size of the matrix does not change.
+      *
+      * Example: \include Tridiagonalization_compute.cpp
+      * Output: \verbinclude Tridiagonalization_compute.out
+      */
+    Tridiagonalization& compute(const MatrixType& matrix)
+    {
+      m_matrix = matrix;
+      m_hCoeffs.resize(matrix.rows()-1, 1);
+      internal::tridiagonalization_inplace(m_matrix, m_hCoeffs);
+      m_isInitialized = true;
+      return *this;
+    }
+
+    /** \brief Returns the Householder coefficients.
+      *
+      * \returns a const reference to the vector of Householder coefficients
+      *
+      * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+      * the member function compute(const MatrixType&) has been called before
+      * to compute the tridiagonal decomposition of a matrix.
+      *
+      * The Householder coefficients allow the reconstruction of the matrix
+      * \f$ Q \f$ in the tridiagonal decomposition from the packed data.
+      *
+      * Example: \include Tridiagonalization_householderCoefficients.cpp
+      * Output: \verbinclude Tridiagonalization_householderCoefficients.out
+      *
+      * \sa packedMatrix(), \ref Householder_Module "Householder module"
+      */
+    inline CoeffVectorType householderCoefficients() const
+    {
+      eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+      return m_hCoeffs;
+    }
+
+    /** \brief Returns the internal representation of the decomposition
+      *
+      *	\returns a const reference to a matrix with the internal representation
+      *	         of the decomposition.
+      *
+      * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+      * the member function compute(const MatrixType&) has been called before
+      * to compute the tridiagonal decomposition of a matrix.
+      *
+      * The returned matrix contains the following information:
+      *  - the strict upper triangular part is equal to the input matrix A.
+      *  - the diagonal and lower sub-diagonal represent the real tridiagonal
+      *    symmetric matrix T.
+      *  - the rest of the lower part contains the Householder vectors that,
+      *    combined with Householder coefficients returned by
+      *    householderCoefficients(), allows to reconstruct the matrix Q as
+      *       \f$ Q = H_{N-1} \ldots H_1 H_0 \f$.
+      *    Here, the matrices \f$ H_i \f$ are the Householder transformations
+      *       \f$ H_i = (I - h_i v_i v_i^T) \f$
+      *    where \f$ h_i \f$ is the \f$ i \f$th Householder coefficient and
+      *    \f$ v_i \f$ is the Householder vector defined by
+      *       \f$ v_i = [ 0, \ldots, 0, 1, M(i+2,i), \ldots, M(N-1,i) ]^T \f$
+      *    with M the matrix returned by this function.
+      *
+      * See LAPACK for further details on this packed storage.
+      *
+      * Example: \include Tridiagonalization_packedMatrix.cpp
+      * Output: \verbinclude Tridiagonalization_packedMatrix.out
+      *
+      * \sa householderCoefficients()
+      */
+    inline const MatrixType& packedMatrix() const
+    {
+      eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+      return m_matrix;
+    }
+
+    /** \brief Returns the unitary matrix Q in the decomposition
+      *
+      * \returns object representing the matrix Q
+      *
+      * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+      * the member function compute(const MatrixType&) has been called before
+      * to compute the tridiagonal decomposition of a matrix.
+      *
+      * This function returns a light-weight object of template class
+      * HouseholderSequence. You can either apply it directly to a matrix or
+      * you can convert it to a matrix of type #MatrixType.
+      *
+      * \sa Tridiagonalization(const MatrixType&) for an example,
+      *     matrixT(), class HouseholderSequence
+      */
+    HouseholderSequenceType matrixQ() const
+    {
+      eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+      return HouseholderSequenceType(m_matrix, m_hCoeffs.conjugate())
+             .setLength(m_matrix.rows() - 1)
+             .setShift(1);
+    }
+
+    /** \brief Returns an expression of the tridiagonal matrix T in the decomposition
+      *
+      * \returns expression object representing the matrix T
+      *
+      * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+      * the member function compute(const MatrixType&) has been called before
+      * to compute the tridiagonal decomposition of a matrix.
+      *
+      * Currently, this function can be used to extract the matrix T from internal
+      * data and copy it to a dense matrix object. In most cases, it may be
+      * sufficient to directly use the packed matrix or the vector expressions
+      * returned by diagonal() and subDiagonal() instead of creating a new
+      * dense copy matrix with this function.
+      *
+      * \sa Tridiagonalization(const MatrixType&) for an example,
+      * matrixQ(), packedMatrix(), diagonal(), subDiagonal()
+      */
+    MatrixTReturnType matrixT() const
+    {
+      eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+      return MatrixTReturnType(m_matrix.real());
+    }
+
+    /** \brief Returns the diagonal of the tridiagonal matrix T in the decomposition.
+      *
+      * \returns expression representing the diagonal of T
+      *
+      * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+      * the member function compute(const MatrixType&) has been called before
+      * to compute the tridiagonal decomposition of a matrix.
+      *
+      * Example: \include Tridiagonalization_diagonal.cpp
+      * Output: \verbinclude Tridiagonalization_diagonal.out
+      *
+      * \sa matrixT(), subDiagonal()
+      */
+    DiagonalReturnType diagonal() const;
+
+    /** \brief Returns the subdiagonal of the tridiagonal matrix T in the decomposition.
+      *
+      * \returns expression representing the subdiagonal of T
+      *
+      * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+      * the member function compute(const MatrixType&) has been called before
+      * to compute the tridiagonal decomposition of a matrix.
+      *
+      * \sa diagonal() for an example, matrixT()
+      */
+    SubDiagonalReturnType subDiagonal() const;
+
+  protected:
+
+    MatrixType m_matrix;
+    CoeffVectorType m_hCoeffs;
+    bool m_isInitialized;
+};
+
+template<typename MatrixType>
+typename Tridiagonalization<MatrixType>::DiagonalReturnType
+Tridiagonalization<MatrixType>::diagonal() const
+{
+  eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+  return m_matrix.diagonal();
+}
+
+template<typename MatrixType>
+typename Tridiagonalization<MatrixType>::SubDiagonalReturnType
+Tridiagonalization<MatrixType>::subDiagonal() const
+{
+  eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+  Index n = m_matrix.rows();
+  return Block<const MatrixType,SizeMinusOne,SizeMinusOne>(m_matrix, 1, 0, n-1,n-1).diagonal();
+}
+
+namespace internal {
+
+/** \internal
+  * Performs a tridiagonal decomposition of the selfadjoint matrix \a matA in-place.
+  *
+  * \param[in,out] matA On input the selfadjoint matrix. Only the \b lower triangular part is referenced.
+  *                     On output, the strict upper part is left unchanged, and the lower triangular part
+  *                     represents the T and Q matrices in packed format has detailed below.
+  * \param[out]    hCoeffs returned Householder coefficients (see below)
+  *
+  * On output, the tridiagonal selfadjoint matrix T is stored in the diagonal
+  * and lower sub-diagonal of the matrix \a matA.
+  * The unitary matrix Q is represented in a compact way as a product of
+  * Householder reflectors \f$ H_i \f$ such that:
+  *       \f$ Q = H_{N-1} \ldots H_1 H_0 \f$.
+  * The Householder reflectors are defined as
+  *       \f$ H_i = (I - h_i v_i v_i^T) \f$
+  * where \f$ h_i = hCoeffs[i]\f$ is the \f$ i \f$th Householder coefficient and
+  * \f$ v_i \f$ is the Householder vector defined by
+  *       \f$ v_i = [ 0, \ldots, 0, 1, matA(i+2,i), \ldots, matA(N-1,i) ]^T \f$.
+  *
+  * Implemented from Golub's "Matrix Computations", algorithm 8.3.1.
+  *
+  * \sa Tridiagonalization::packedMatrix()
+  */
+template<typename MatrixType, typename CoeffVectorType>
+void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)
+{
+  using numext::conj;
+  typedef typename MatrixType::Index Index;
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::RealScalar RealScalar;
+  Index n = matA.rows();
+  eigen_assert(n==matA.cols());
+  eigen_assert(n==hCoeffs.size()+1 || n==1);
+  
+  for (Index i = 0; i<n-1; ++i)
+  {
+    Index remainingSize = n-i-1;
+    RealScalar beta;
+    Scalar h;
+    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).tail(n-i-1)
+    matA.col(i).coeffRef(i+1) = 1;
+
+    hCoeffs.tail(n-i-1).noalias() = (matA.bottomRightCorner(remainingSize,remainingSize).template selfadjointView<Lower>()
+                                  * (conj(h) * matA.col(i).tail(remainingSize)));
+
+    hCoeffs.tail(n-i-1) += (conj(h)*Scalar(-0.5)*(hCoeffs.tail(remainingSize).dot(matA.col(i).tail(remainingSize)))) * matA.col(i).tail(n-i-1);
+
+    matA.bottomRightCorner(remainingSize, remainingSize).template selfadjointView<Lower>()
+      .rankUpdate(matA.col(i).tail(remainingSize), hCoeffs.tail(remainingSize), -1);
+
+    matA.col(i).coeffRef(i+1) = beta;
+    hCoeffs.coeffRef(i) = h;
+  }
+}
+
+// forward declaration, implementation at the end of this file
+template<typename MatrixType,
+         int Size=MatrixType::ColsAtCompileTime,
+         bool IsComplex=NumTraits<typename MatrixType::Scalar>::IsComplex>
+struct tridiagonalization_inplace_selector;
+
+/** \brief Performs a full tridiagonalization in place
+  *
+  * \param[in,out]  mat  On input, the selfadjoint matrix whose tridiagonal
+  *    decomposition is to be computed. Only the lower triangular part referenced.
+  *    The rest is left unchanged. On output, the orthogonal matrix Q
+  *    in the decomposition if \p extractQ is true.
+  * \param[out]  diag  The diagonal of the tridiagonal matrix T in the
+  *    decomposition.
+  * \param[out]  subdiag  The subdiagonal of the tridiagonal matrix T in
+  *    the decomposition.
+  * \param[in]  extractQ  If true, the orthogonal matrix Q in the
+  *    decomposition is computed and stored in \p mat.
+  *
+  * Computes the tridiagonal decomposition of the selfadjoint matrix \p mat in place
+  * such that \f$ mat = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real
+  * symmetric tridiagonal matrix.
+  *
+  * The tridiagonal matrix T is passed to the output parameters \p diag and \p subdiag. If
+  * \p extractQ is true, then the orthogonal matrix Q is passed to \p mat. Otherwise the lower
+  * part of the matrix \p mat is destroyed.
+  *
+  * The vectors \p diag and \p subdiag are not resized. The function
+  * assumes that they are already of the correct size. The length of the
+  * vector \p diag should equal the number of rows in \p mat, and the
+  * length of the vector \p subdiag should be one left.
+  *
+  * This implementation contains an optimized path for 3-by-3 matrices
+  * which is especially useful for plane fitting.
+  *
+  * \note Currently, it requires two temporary vectors to hold the intermediate
+  * Householder coefficients, and to reconstruct the matrix Q from the Householder
+  * reflectors.
+  *
+  * Example (this uses the same matrix as the example in
+  *    Tridiagonalization::Tridiagonalization(const MatrixType&)):
+  *    \include Tridiagonalization_decomposeInPlace.cpp
+  * Output: \verbinclude Tridiagonalization_decomposeInPlace.out
+  *
+  * \sa class Tridiagonalization
+  */
+template<typename MatrixType, typename DiagonalType, typename SubDiagonalType>
+void tridiagonalization_inplace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
+{
+  eigen_assert(mat.cols()==mat.rows() && diag.size()==mat.rows() && subdiag.size()==mat.rows()-1);
+  tridiagonalization_inplace_selector<MatrixType>::run(mat, diag, subdiag, extractQ);
+}
+
+/** \internal
+  * General full tridiagonalization
+  */
+template<typename MatrixType, int Size, bool IsComplex>
+struct tridiagonalization_inplace_selector
+{
+  typedef typename Tridiagonalization<MatrixType>::CoeffVectorType CoeffVectorType;
+  typedef typename Tridiagonalization<MatrixType>::HouseholderSequenceType HouseholderSequenceType;
+  typedef typename MatrixType::Index Index;
+  template<typename DiagonalType, typename SubDiagonalType>
+  static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
+  {
+    CoeffVectorType hCoeffs(mat.cols()-1);
+    tridiagonalization_inplace(mat,hCoeffs);
+    diag = mat.diagonal().real();
+    subdiag = mat.template diagonal<-1>().real();
+    if(extractQ)
+      mat = HouseholderSequenceType(mat, hCoeffs.conjugate())
+            .setLength(mat.rows() - 1)
+            .setShift(1);
+  }
+};
+
+/** \internal
+  * Specialization for 3x3 real matrices.
+  * Especially useful for plane fitting.
+  */
+template<typename MatrixType>
+struct tridiagonalization_inplace_selector<MatrixType,3,false>
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::RealScalar RealScalar;
+
+  template<typename DiagonalType, typename SubDiagonalType>
+  static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
+  {
+    using std::sqrt;
+    diag[0] = mat(0,0);
+    RealScalar v1norm2 = numext::abs2(mat(2,0));
+    if(v1norm2 == RealScalar(0))
+    {
+      diag[1] = mat(1,1);
+      diag[2] = mat(2,2);
+      subdiag[0] = mat(1,0);
+      subdiag[1] = mat(2,1);
+      if (extractQ)
+        mat.setIdentity();
+    }
+    else
+    {
+      RealScalar beta = sqrt(numext::abs2(mat(1,0)) + v1norm2);
+      RealScalar invBeta = RealScalar(1)/beta;
+      Scalar m01 = mat(1,0) * invBeta;
+      Scalar m02 = mat(2,0) * invBeta;
+      Scalar q = RealScalar(2)*m01*mat(2,1) + m02*(mat(2,2) - mat(1,1));
+      diag[1] = mat(1,1) + m02*q;
+      diag[2] = mat(2,2) - m02*q;
+      subdiag[0] = beta;
+      subdiag[1] = mat(2,1) - m01 * q;
+      if (extractQ)
+      {
+        mat << 1,   0,    0,
+               0, m01,  m02,
+               0, m02, -m01;
+      }
+    }
+  }
+};
+
+/** \internal
+  * Trivial specialization for 1x1 matrices
+  */
+template<typename MatrixType, bool IsComplex>
+struct tridiagonalization_inplace_selector<MatrixType,1,IsComplex>
+{
+  typedef typename MatrixType::Scalar Scalar;
+
+  template<typename DiagonalType, typename SubDiagonalType>
+  static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType&, bool extractQ)
+  {
+    diag(0,0) = numext::real(mat(0,0));
+    if(extractQ)
+      mat(0,0) = Scalar(1);
+  }
+};
+
+/** \internal
+  * \eigenvalues_module \ingroup Eigenvalues_Module
+  *
+  * \brief Expression type for return value of Tridiagonalization::matrixT()
+  *
+  * \tparam MatrixType type of underlying dense matrix
+  */
+template<typename MatrixType> struct TridiagonalizationMatrixTReturnType
+: public ReturnByValue<TridiagonalizationMatrixTReturnType<MatrixType> >
+{
+    typedef typename MatrixType::Index Index;
+  public:
+    /** \brief Constructor.
+      *
+      * \param[in] mat The underlying dense matrix
+      */
+    TridiagonalizationMatrixTReturnType(const MatrixType& mat) : m_matrix(mat) { }
+
+    template <typename ResultType>
+    inline void evalTo(ResultType& result) const
+    {
+      result.setZero();
+      result.template diagonal<1>() = m_matrix.template diagonal<-1>().conjugate();
+      result.diagonal() = m_matrix.diagonal();
+      result.template diagonal<-1>() = m_matrix.template diagonal<-1>();
+    }
+
+    Index rows() const { return m_matrix.rows(); }
+    Index cols() const { return m_matrix.cols(); }
+
+  protected:
+    typename MatrixType::Nested m_matrix;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIDIAGONALIZATION_H