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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+// 
+// We used the "A Divide-And-Conquer Algorithm for the Bidiagonal SVD"
+// research report written by Ming Gu and Stanley C.Eisenstat
+// The code variable names correspond to the names they used in their 
+// report
+//
+// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
+// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
+// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
+// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
+//
+// 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_BDCSVD_H
+#define EIGEN_BDCSVD_H
+
+#define EPSILON 0.0000000000000001
+
+#define ALGOSWAP 32
+
+namespace Eigen {
+/** \ingroup SVD_Module
+ *
+ *
+ * \class BDCSVD
+ *
+ * \brief class Bidiagonal Divide and Conquer SVD
+ *
+ * \param MatrixType the type of the matrix of which we are computing the SVD decomposition
+ * We plan to have a very similar interface to JacobiSVD on this class.
+ * It should be used to speed up the calcul of SVD for big matrices. 
+ */
+template<typename _MatrixType> 
+class BDCSVD : public SVDBase<_MatrixType>
+{
+  typedef SVDBase<_MatrixType> Base;
+    
+public:
+  using Base::rows;
+  using Base::cols;
+  
+  typedef _MatrixType MatrixType;
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+  typedef typename MatrixType::Index Index;
+  enum {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime, 
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime, 
+    DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime), 
+    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, 
+    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, 
+    MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime, MaxColsAtCompileTime), 
+    MatrixOptions = MatrixType::Options
+  };
+
+  typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, 
+		 MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
+  MatrixUType;
+  typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, 
+		 MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
+  MatrixVType;
+  typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
+  typedef typename internal::plain_row_type<MatrixType>::type RowType;
+  typedef typename internal::plain_col_type<MatrixType>::type ColType;
+  typedef Matrix<Scalar, Dynamic, Dynamic> MatrixX;
+  typedef Matrix<RealScalar, Dynamic, Dynamic> MatrixXr;
+  typedef Matrix<RealScalar, Dynamic, 1> VectorType;
+
+  /** \brief Default Constructor.
+   *
+   * The default constructor is useful in cases in which the user intends to
+   * perform decompositions via BDCSVD::compute(const MatrixType&).
+   */
+  BDCSVD()
+    : SVDBase<_MatrixType>::SVDBase(), 
+      algoswap(ALGOSWAP)
+  {}
+
+
+  /** \brief Default Constructor with memory preallocation
+   *
+   * Like the default constructor but with preallocation of the internal data
+   * according to the specified problem size.
+   * \sa BDCSVD()
+   */
+  BDCSVD(Index rows, Index cols, unsigned int computationOptions = 0)
+    : SVDBase<_MatrixType>::SVDBase(), 
+      algoswap(ALGOSWAP)
+  {
+    allocate(rows, cols, computationOptions);
+  }
+
+  /** \brief Constructor performing the decomposition of given matrix.
+   *
+   * \param matrix the matrix to decompose
+   * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
+   *                           By default, none is computed. This is a bit - field, the possible bits are #ComputeFullU, #ComputeThinU, 
+   *                           #ComputeFullV, #ComputeThinV.
+   *
+   * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
+   * available with the (non - default) FullPivHouseholderQR preconditioner.
+   */
+  BDCSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
+    : SVDBase<_MatrixType>::SVDBase(), 
+      algoswap(ALGOSWAP)
+  {
+    compute(matrix, computationOptions);
+  }
+
+  ~BDCSVD() 
+  {
+  }
+  /** \brief Method performing the decomposition of given matrix using custom options.
+   *
+   * \param matrix the matrix to decompose
+   * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
+   *                           By default, none is computed. This is a bit - field, the possible bits are #ComputeFullU, #ComputeThinU, 
+   *                           #ComputeFullV, #ComputeThinV.
+   *
+   * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
+   * available with the (non - default) FullPivHouseholderQR preconditioner.
+   */
+  SVDBase<MatrixType>& compute(const MatrixType& matrix, unsigned int computationOptions);
+
+  /** \brief Method performing the decomposition of given matrix using current options.
+   *
+   * \param matrix the matrix to decompose
+   *
+   * This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
+   */
+  SVDBase<MatrixType>& compute(const MatrixType& matrix)
+  {
+    return compute(matrix, this->m_computationOptions);
+  }
+
+  void setSwitchSize(int s) 
+  {
+    eigen_assert(s>3 && "BDCSVD the size of the algo switch has to be greater than 4");
+    algoswap = s;
+  }
+
+
+  /** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
+   *
+   * \param b the right - hand - side of the equation to solve.
+   *
+   * \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
+   *
+   * \note SVD solving is implicitly least - squares. Thus, this method serves both purposes of exact solving and least - squares solving.
+   * In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$.
+   */
+  template<typename Rhs>
+  inline const internal::solve_retval<BDCSVD, Rhs>
+  solve(const MatrixBase<Rhs>& b) const
+  {
+    eigen_assert(this->m_isInitialized && "BDCSVD is not initialized.");
+    eigen_assert(SVDBase<_MatrixType>::computeU() && SVDBase<_MatrixType>::computeV() && 
+		 "BDCSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
+    return internal::solve_retval<BDCSVD, Rhs>(*this, b.derived());
+  }
+
+ 
+  const MatrixUType& matrixU() const
+  {
+    eigen_assert(this->m_isInitialized && "SVD is not initialized.");
+    if (isTranspose){
+      eigen_assert(this->computeV() && "This SVD decomposition didn't compute U. Did you ask for it?");
+      return this->m_matrixV;
+    }
+    else 
+    {
+      eigen_assert(this->computeU() && "This SVD decomposition didn't compute U. Did you ask for it?");
+      return this->m_matrixU;
+    }
+     
+  }
+
+
+  const MatrixVType& matrixV() const
+  {
+    eigen_assert(this->m_isInitialized && "SVD is not initialized.");
+    if (isTranspose){
+      eigen_assert(this->computeU() && "This SVD decomposition didn't compute V. Did you ask for it?");
+      return this->m_matrixU;
+    }
+    else
+    {
+      eigen_assert(this->computeV() && "This SVD decomposition didn't compute V. Did you ask for it?");
+      return this->m_matrixV;
+    }
+  }
+ 
+private:
+  void allocate(Index rows, Index cols, unsigned int computationOptions);
+  void divide (Index firstCol, Index lastCol, Index firstRowW, 
+	       Index firstColW, Index shift);
+  void deflation43(Index firstCol, Index shift, Index i, Index size);
+  void deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size);
+  void deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift);
+  void copyUV(MatrixXr naiveU, MatrixXr naiveV, MatrixX householderU, MatrixX houseHolderV);
+
+protected:
+  MatrixXr m_naiveU, m_naiveV;
+  MatrixXr m_computed;
+  Index nRec;
+  int algoswap;
+  bool isTranspose, compU, compV;
+  
+}; //end class BDCSVD
+
+
+// Methode to allocate ans initialize matrix and attributs
+template<typename MatrixType>
+void BDCSVD<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions)
+{
+  isTranspose = (cols > rows);
+  if (SVDBase<MatrixType>::allocate(rows, cols, computationOptions)) return;
+  m_computed = MatrixXr::Zero(this->m_diagSize + 1, this->m_diagSize );
+  if (isTranspose){
+    compU = this->computeU();
+    compV = this->computeV();    
+  } 
+  else
+  {
+    compV = this->computeU();
+    compU = this->computeV();   
+  }
+  if (compU) m_naiveU = MatrixXr::Zero(this->m_diagSize + 1, this->m_diagSize + 1 );
+  else m_naiveU = MatrixXr::Zero(2, this->m_diagSize + 1 );
+  
+  if (compV) m_naiveV = MatrixXr::Zero(this->m_diagSize, this->m_diagSize);
+  
+
+  //should be changed for a cleaner implementation
+  if (isTranspose){
+    bool aux;
+    if (this->computeU()||this->computeV()){
+      aux = this->m_computeFullU;
+      this->m_computeFullU = this->m_computeFullV;
+      this->m_computeFullV = aux;
+      aux = this->m_computeThinU;
+      this->m_computeThinU = this->m_computeThinV;
+      this->m_computeThinV = aux;
+    } 
+  }
+}// end allocate
+
+// Methode which compute the BDCSVD for the int
+template<>
+SVDBase<Matrix<int, Dynamic, Dynamic> >&
+BDCSVD<Matrix<int, Dynamic, Dynamic> >::compute(const MatrixType& matrix, unsigned int computationOptions) {
+  allocate(matrix.rows(), matrix.cols(), computationOptions);
+  this->m_nonzeroSingularValues = 0;
+  m_computed = Matrix<int, Dynamic, Dynamic>::Zero(rows(), cols());
+  for (int i=0; i<this->m_diagSize; i++)   {
+    this->m_singularValues.coeffRef(i) = 0;
+  }
+  if (this->m_computeFullU) this->m_matrixU = Matrix<int, Dynamic, Dynamic>::Zero(rows(), rows());
+  if (this->m_computeFullV) this->m_matrixV = Matrix<int, Dynamic, Dynamic>::Zero(cols(), cols()); 
+  this->m_isInitialized = true;
+  return *this;
+}
+
+
+// Methode which compute the BDCSVD
+template<typename MatrixType>
+SVDBase<MatrixType>&
+BDCSVD<MatrixType>::compute(const MatrixType& matrix, unsigned int computationOptions) 
+{
+  allocate(matrix.rows(), matrix.cols(), computationOptions);
+  using std::abs;
+
+  //**** step 1 Bidiagonalization  isTranspose = (matrix.cols()>matrix.rows()) ;
+  MatrixType copy;
+  if (isTranspose) copy = matrix.adjoint();
+  else copy = matrix;
+  
+  internal::UpperBidiagonalization<MatrixX > bid(copy);
+
+  //**** step 2 Divide
+  // this is ugly and has to be redone (care of complex cast)
+  MatrixXr temp;
+  temp = bid.bidiagonal().toDenseMatrix().transpose();
+  m_computed.setZero();
+  for (int i=0; i<this->m_diagSize - 1; i++)   {
+    m_computed(i, i) = temp(i, i);
+    m_computed(i + 1, i) = temp(i + 1, i);
+  }
+  m_computed(this->m_diagSize - 1, this->m_diagSize - 1) = temp(this->m_diagSize - 1, this->m_diagSize - 1);
+  divide(0, this->m_diagSize - 1, 0, 0, 0);
+
+  //**** step 3 copy
+  for (int i=0; i<this->m_diagSize; i++)   {
+    RealScalar a = abs(m_computed.coeff(i, i));
+    this->m_singularValues.coeffRef(i) = a;
+    if (a == 0){
+      this->m_nonzeroSingularValues = i;
+      break;
+    }
+    else  if (i == this->m_diagSize - 1)
+    {
+      this->m_nonzeroSingularValues = i + 1;
+      break;
+    }
+  }
+  copyUV(m_naiveV, m_naiveU, bid.householderU(), bid.householderV());
+  this->m_isInitialized = true;
+  return *this;
+}// end compute
+
+
+template<typename MatrixType>
+void BDCSVD<MatrixType>::copyUV(MatrixXr naiveU, MatrixXr naiveV, MatrixX householderU, MatrixX householderV){
+  if (this->computeU()){
+    MatrixX temp = MatrixX::Zero(naiveU.rows(), naiveU.cols());
+    temp.real() = naiveU;
+    if (this->m_computeThinU){
+      this->m_matrixU = MatrixX::Identity(householderU.cols(), this->m_nonzeroSingularValues );
+      this->m_matrixU.block(0, 0, this->m_diagSize, this->m_nonzeroSingularValues) = 
+	temp.block(0, 0, this->m_diagSize, this->m_nonzeroSingularValues);
+      this->m_matrixU = householderU * this->m_matrixU ;
+    }
+    else
+    {
+      this->m_matrixU = MatrixX::Identity(householderU.cols(), householderU.cols());
+      this->m_matrixU.block(0, 0, this->m_diagSize, this->m_diagSize) = temp.block(0, 0, this->m_diagSize, this->m_diagSize);
+      this->m_matrixU = householderU * this->m_matrixU ;
+    }
+  }
+  if (this->computeV()){
+    MatrixX temp = MatrixX::Zero(naiveV.rows(), naiveV.cols());
+    temp.real() = naiveV;
+    if (this->m_computeThinV){
+      this->m_matrixV = MatrixX::Identity(householderV.cols(),this->m_nonzeroSingularValues );
+      this->m_matrixV.block(0, 0, this->m_nonzeroSingularValues, this->m_nonzeroSingularValues) = 
+	temp.block(0, 0, this->m_nonzeroSingularValues, this->m_nonzeroSingularValues);
+      this->m_matrixV = householderV * this->m_matrixV ;
+    }
+    else  
+    {
+      this->m_matrixV = MatrixX::Identity(householderV.cols(), householderV.cols());
+      this->m_matrixV.block(0, 0, this->m_diagSize, this->m_diagSize) = temp.block(0, 0, this->m_diagSize, this->m_diagSize);
+      this->m_matrixV = householderV * this->m_matrixV;
+    }
+  }
+}
+
+// The divide algorithm is done "in place", we are always working on subsets of the same matrix. The divide methods takes as argument the 
+// place of the submatrix we are currently working on.
+
+//@param firstCol : The Index of the first column of the submatrix of m_computed and for m_naiveU;
+//@param lastCol : The Index of the last column of the submatrix of m_computed and for m_naiveU; 
+// lastCol + 1 - firstCol is the size of the submatrix.
+//@param firstRowW : The Index of the first row of the matrix W that we are to change. (see the reference paper section 1 for more information on W)
+//@param firstRowW : Same as firstRowW with the column.
+//@param shift : Each time one takes the left submatrix, one must add 1 to the shift. Why? Because! We actually want the last column of the U submatrix 
+// to become the first column (*coeff) and to shift all the other columns to the right. There are more details on the reference paper.
+template<typename MatrixType>
+void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW, 
+				 Index firstColW, Index shift)
+{
+  // requires nbRows = nbCols + 1;
+  using std::pow;
+  using std::sqrt;
+  using std::abs;
+  const Index n = lastCol - firstCol + 1;
+  const Index k = n/2;
+  RealScalar alphaK;
+  RealScalar betaK; 
+  RealScalar r0; 
+  RealScalar lambda, phi, c0, s0;
+  MatrixXr l, f;
+  // We use the other algorithm which is more efficient for small 
+  // matrices.
+  if (n < algoswap){
+    JacobiSVD<MatrixXr> b(m_computed.block(firstCol, firstCol, n + 1, n), 
+			  ComputeFullU | (ComputeFullV * compV)) ;
+    if (compU) m_naiveU.block(firstCol, firstCol, n + 1, n + 1).real() << b.matrixU();
+    else 
+    {
+      m_naiveU.row(0).segment(firstCol, n + 1).real() << b.matrixU().row(0);
+      m_naiveU.row(1).segment(firstCol, n + 1).real() << b.matrixU().row(n);
+    }
+    if (compV) m_naiveV.block(firstRowW, firstColW, n, n).real() << b.matrixV();
+    m_computed.block(firstCol + shift, firstCol + shift, n + 1, n).setZero();
+    for (int i=0; i<n; i++)
+    {
+      m_computed(firstCol + shift + i, firstCol + shift +i) = b.singularValues().coeffRef(i);
+    }
+    return;
+  }
+  // We use the divide and conquer algorithm
+  alphaK =  m_computed(firstCol + k, firstCol + k);
+  betaK = m_computed(firstCol + k + 1, firstCol + k);
+  // The divide must be done in that order in order to have good results. Divide change the data inside the submatrices
+  // and the divide of the right submatrice reads one column of the left submatrice. That's why we need to treat the 
+  // right submatrix before the left one. 
+  divide(k + 1 + firstCol, lastCol, k + 1 + firstRowW, k + 1 + firstColW, shift);
+  divide(firstCol, k - 1 + firstCol, firstRowW, firstColW + 1, shift + 1);
+  if (compU)
+  {
+    lambda = m_naiveU(firstCol + k, firstCol + k);
+    phi = m_naiveU(firstCol + k + 1, lastCol + 1);
+  } 
+  else 
+  {
+    lambda = m_naiveU(1, firstCol + k);
+    phi = m_naiveU(0, lastCol + 1);
+  }
+  r0 = sqrt((abs(alphaK * lambda) * abs(alphaK * lambda))
+	    + abs(betaK * phi) * abs(betaK * phi));
+  if (compU)
+  {
+    l = m_naiveU.row(firstCol + k).segment(firstCol, k);
+    f = m_naiveU.row(firstCol + k + 1).segment(firstCol + k + 1, n - k - 1);
+  } 
+  else 
+  {
+    l = m_naiveU.row(1).segment(firstCol, k);
+    f = m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1);
+  }
+  if (compV) m_naiveV(firstRowW+k, firstColW) = 1;
+  if (r0 == 0)
+  {
+    c0 = 1;
+    s0 = 0;
+  }
+  else
+  {
+    c0 = alphaK * lambda / r0;
+    s0 = betaK * phi / r0;
+  }
+  if (compU)
+  {
+    MatrixXr q1 (m_naiveU.col(firstCol + k).segment(firstCol, k + 1));     
+    // we shiftW Q1 to the right
+    for (Index i = firstCol + k - 1; i >= firstCol; i--) 
+    {
+      m_naiveU.col(i + 1).segment(firstCol, k + 1) << m_naiveU.col(i).segment(firstCol, k + 1);
+    }
+    // we shift q1 at the left with a factor c0
+    m_naiveU.col(firstCol).segment( firstCol, k + 1) << (q1 * c0);
+    // last column = q1 * - s0
+    m_naiveU.col(lastCol + 1).segment(firstCol, k + 1) << (q1 * ( - s0));
+    // first column = q2 * s0
+    m_naiveU.col(firstCol).segment(firstCol + k + 1, n - k) << 
+      m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) *s0; 
+    // q2 *= c0
+    m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) *= c0; 
+  } 
+  else 
+  {
+    RealScalar q1 = (m_naiveU(0, firstCol + k));
+    // we shift Q1 to the right
+    for (Index i = firstCol + k - 1; i >= firstCol; i--) 
+    {
+      m_naiveU(0, i + 1) = m_naiveU(0, i);
+    }
+    // we shift q1 at the left with a factor c0
+    m_naiveU(0, firstCol) = (q1 * c0);
+    // last column = q1 * - s0
+    m_naiveU(0, lastCol + 1) = (q1 * ( - s0));
+    // first column = q2 * s0
+    m_naiveU(1, firstCol) = m_naiveU(1, lastCol + 1) *s0; 
+    // q2 *= c0
+    m_naiveU(1, lastCol + 1) *= c0;
+    m_naiveU.row(1).segment(firstCol + 1, k).setZero();
+    m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1).setZero();
+  }
+  m_computed(firstCol + shift, firstCol + shift) = r0;
+  m_computed.col(firstCol + shift).segment(firstCol + shift + 1, k) << alphaK * l.transpose().real();
+  m_computed.col(firstCol + shift).segment(firstCol + shift + k + 1, n - k - 1) << betaK * f.transpose().real();
+
+
+  // the line below do the deflation of the matrix for the third part of the algorithm
+  // Here the deflation is commented because the third part of the algorithm is not implemented
+  // the third part of the algorithm is a fast SVD on the matrix m_computed which works thanks to the deflation
+
+  deflation(firstCol, lastCol, k, firstRowW, firstColW, shift);
+
+  // Third part of the algorithm, since the real third part of the algorithm is not implemeted we use a JacobiSVD
+  JacobiSVD<MatrixXr> res= JacobiSVD<MatrixXr>(m_computed.block(firstCol + shift, firstCol +shift, n + 1, n), 
+					       ComputeFullU | (ComputeFullV * compV)) ;
+  if (compU) m_naiveU.block(firstCol, firstCol, n + 1, n + 1) *= res.matrixU();
+  else m_naiveU.block(0, firstCol, 2, n + 1) *= res.matrixU();
+  
+  if (compV) m_naiveV.block(firstRowW, firstColW, n, n) *= res.matrixV();
+  m_computed.block(firstCol + shift, firstCol + shift, n, n) << MatrixXr::Zero(n, n);
+  for (int i=0; i<n; i++)
+    m_computed(firstCol + shift + i, firstCol + shift +i) = res.singularValues().coeffRef(i);
+  // end of the third part
+
+
+}// end divide
+
+
+// page 12_13
+// i >= 1, di almost null and zi non null.
+// We use a rotation to zero out zi applied to the left of M
+template <typename MatrixType>
+void BDCSVD<MatrixType>::deflation43(Index firstCol, Index shift, Index i, Index size){
+  using std::abs;
+  using std::sqrt;
+  using std::pow;
+  RealScalar c = m_computed(firstCol + shift, firstCol + shift);
+  RealScalar s = m_computed(i, firstCol + shift);
+  RealScalar r = sqrt(pow(abs(c), 2) + pow(abs(s), 2));
+  if (r == 0){
+    m_computed(i, i)=0;
+    return;
+  }
+  c/=r;
+  s/=r;
+  m_computed(firstCol + shift, firstCol + shift) = r;  
+  m_computed(i, firstCol + shift) = 0;
+  m_computed(i, i) = 0;
+  if (compU){
+    m_naiveU.col(firstCol).segment(firstCol,size) = 
+      c * m_naiveU.col(firstCol).segment(firstCol, size) - 
+      s * m_naiveU.col(i).segment(firstCol, size) ;
+
+    m_naiveU.col(i).segment(firstCol, size) = 
+      (c + s*s/c) * m_naiveU.col(i).segment(firstCol, size) + 
+      (s/c) * m_naiveU.col(firstCol).segment(firstCol,size);
+  }
+}// end deflation 43
+
+
+// page 13
+// i,j >= 1, i != j and |di - dj| < epsilon * norm2(M)
+// We apply two rotations to have zj = 0;
+template <typename MatrixType>
+void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size){
+  using std::abs;
+  using std::sqrt;
+  using std::conj;
+  using std::pow;
+  RealScalar c = m_computed(firstColm, firstColm + j - 1);
+  RealScalar s = m_computed(firstColm, firstColm + i - 1);
+  RealScalar r = sqrt(pow(abs(c), 2) + pow(abs(s), 2));
+  if (r==0){
+    m_computed(firstColm + i, firstColm + i) = m_computed(firstColm + j, firstColm + j);
+    return;
+  }
+  c/=r;
+  s/=r;
+  m_computed(firstColm + i, firstColm) = r;  
+  m_computed(firstColm + i, firstColm + i) = m_computed(firstColm + j, firstColm + j);
+  m_computed(firstColm + j, firstColm) = 0;
+  if (compU){
+    m_naiveU.col(firstColu + i).segment(firstColu, size) = 
+      c * m_naiveU.col(firstColu + i).segment(firstColu, size) - 
+      s * m_naiveU.col(firstColu + j).segment(firstColu, size) ;
+
+    m_naiveU.col(firstColu + j).segment(firstColu, size) = 
+      (c + s*s/c) *  m_naiveU.col(firstColu + j).segment(firstColu, size) + 
+      (s/c) * m_naiveU.col(firstColu + i).segment(firstColu, size);
+  } 
+  if (compV){
+    m_naiveV.col(firstColW + i).segment(firstRowW, size - 1) = 
+      c * m_naiveV.col(firstColW + i).segment(firstRowW, size - 1) + 
+      s * m_naiveV.col(firstColW + j).segment(firstRowW, size - 1) ;
+
+    m_naiveV.col(firstColW + j).segment(firstRowW, size - 1)  = 
+      (c + s*s/c) * m_naiveV.col(firstColW + j).segment(firstRowW, size - 1) - 
+      (s/c) * m_naiveV.col(firstColW + i).segment(firstRowW, size - 1);
+  }
+}// end deflation 44
+
+
+
+template <typename MatrixType>
+void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift){
+  //condition 4.1
+  RealScalar EPS = EPSILON * (std::max<RealScalar>(m_computed(firstCol + shift + 1, firstCol + shift + 1), m_computed(firstCol + k, firstCol + k)));
+  const Index length = lastCol + 1 - firstCol;
+  if (m_computed(firstCol + shift, firstCol + shift) < EPS){
+    m_computed(firstCol + shift, firstCol + shift) = EPS;
+  }
+  //condition 4.2
+  for (Index i=firstCol + shift + 1;i<=lastCol + shift;i++){
+    if (std::abs(m_computed(i, firstCol + shift)) < EPS){
+      m_computed(i, firstCol + shift) = 0;
+    }
+  }
+
+  //condition 4.3
+  for (Index i=firstCol + shift + 1;i<=lastCol + shift; i++){
+    if (m_computed(i, i) < EPS){
+      deflation43(firstCol, shift, i, length);
+    }
+  }
+
+  //condition 4.4
+ 
+  Index i=firstCol + shift + 1, j=firstCol + shift + k + 1;
+  //we stock the final place of each line
+  Index *permutation = new Index[length];
+
+  for (Index p =1; p < length; p++) {
+    if (i> firstCol + shift + k){
+      permutation[p] = j;
+      j++;
+    } else if (j> lastCol + shift) 
+    {
+      permutation[p] = i;
+      i++;
+    }
+    else 
+    {
+      if (m_computed(i, i) < m_computed(j, j)){
+        permutation[p] = j;
+        j++;
+      } 
+      else
+      {
+        permutation[p] = i;
+        i++;
+      }
+    }
+  }
+  //we do the permutation
+  RealScalar aux;
+  //we stock the current index of each col
+  //and the column of each index
+  Index *realInd = new Index[length];
+  Index *realCol = new Index[length];
+  for (int pos = 0; pos< length; pos++){
+    realCol[pos] = pos + firstCol + shift;
+    realInd[pos] = pos;
+  }
+  const Index Zero = firstCol + shift;
+  VectorType temp;
+  for (int i = 1; i < length - 1; i++){
+    const Index I = i + Zero;
+    const Index realI = realInd[i];
+    const Index j  = permutation[length - i] - Zero;
+    const Index J = realCol[j];
+    
+    //diag displace
+    aux = m_computed(I, I); 
+    m_computed(I, I) = m_computed(J, J);
+    m_computed(J, J) = aux;
+    
+    //firstrow displace
+    aux = m_computed(I, Zero); 
+    m_computed(I, Zero) = m_computed(J, Zero);
+    m_computed(J, Zero) = aux;
+
+    // change columns
+    if (compU) {
+      temp = m_naiveU.col(I - shift).segment(firstCol, length + 1);
+      m_naiveU.col(I - shift).segment(firstCol, length + 1) << 
+        m_naiveU.col(J - shift).segment(firstCol, length + 1);
+      m_naiveU.col(J - shift).segment(firstCol, length + 1) << temp;
+    } 
+    else
+    {
+      temp = m_naiveU.col(I - shift).segment(0, 2);
+      m_naiveU.col(I - shift).segment(0, 2) << 
+        m_naiveU.col(J - shift).segment(0, 2);
+      m_naiveU.col(J - shift).segment(0, 2) << temp;      
+    }
+    if (compV) {
+      const Index CWI = I + firstColW - Zero;
+      const Index CWJ = J + firstColW - Zero;
+      temp = m_naiveV.col(CWI).segment(firstRowW, length);
+      m_naiveV.col(CWI).segment(firstRowW, length) << m_naiveV.col(CWJ).segment(firstRowW, length);
+      m_naiveV.col(CWJ).segment(firstRowW, length) << temp;
+    }
+
+    //update real pos
+    realCol[realI] = J;
+    realCol[j] = I;
+    realInd[J - Zero] = realI;
+    realInd[I - Zero] = j;
+  }
+  for (Index i = firstCol + shift + 1; i<lastCol + shift;i++){
+    if ((m_computed(i + 1, i + 1) - m_computed(i, i)) < EPS){
+      deflation44(firstCol , 
+		  firstCol + shift, 
+		  firstRowW, 
+		  firstColW, 
+		  i - Zero, 
+		  i + 1 - Zero, 
+		  length);
+    }
+  }
+  delete [] permutation;
+  delete [] realInd;
+  delete [] realCol;
+
+}//end deflation
+
+
+namespace internal{
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<BDCSVD<_MatrixType>, Rhs>
+  : solve_retval_base<BDCSVD<_MatrixType>, Rhs>
+{
+  typedef BDCSVD<_MatrixType> BDCSVDType;
+  EIGEN_MAKE_SOLVE_HELPERS(BDCSVDType, Rhs)
+
+  template<typename Dest> void evalTo(Dest& dst) const
+  {
+    eigen_assert(rhs().rows() == dec().rows());
+    // A = U S V^*
+    // So A^{ - 1} = V S^{ - 1} U^*    
+    Index diagSize = (std::min)(dec().rows(), dec().cols());
+    typename BDCSVDType::SingularValuesType invertedSingVals(diagSize);
+    Index nonzeroSingVals = dec().nonzeroSingularValues();
+    invertedSingVals.head(nonzeroSingVals) = dec().singularValues().head(nonzeroSingVals).array().inverse();
+    invertedSingVals.tail(diagSize - nonzeroSingVals).setZero();
+    
+    dst = dec().matrixV().leftCols(diagSize)
+      * invertedSingVals.asDiagonal()
+      * dec().matrixU().leftCols(diagSize).adjoint()
+      * rhs();	
+    return;
+  }
+};
+
+} //end namespace internal
+
+  /** \svd_module
+   *
+   * \return the singular value decomposition of \c *this computed by 
+   *  BDC Algorithm
+   *
+   * \sa class BDCSVD
+   */
+/*
+template<typename Derived>
+BDCSVD<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::bdcSvd(unsigned int computationOptions) const
+{
+  return BDCSVD<PlainObject>(*this, computationOptions);
+}
+*/
+
+} // end namespace Eigen
+
+#endif
diff --git a/eigen/unsupported/Eigen/src/SVD/CMakeLists.txt b/eigen/unsupported/Eigen/src/SVD/CMakeLists.txt
new file mode 100644
index 0000000..b40baf0
--- /dev/null
+++ b/eigen/unsupported/Eigen/src/SVD/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_SVD_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_SVD_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}unsupported/Eigen/src/SVD COMPONENT Devel
+  )
diff --git a/eigen/unsupported/Eigen/src/SVD/JacobiSVD.h b/eigen/unsupported/Eigen/src/SVD/JacobiSVD.h
new file mode 100644
index 0000000..02fac40
--- /dev/null
+++ b/eigen/unsupported/Eigen/src/SVD/JacobiSVD.h
@@ -0,0 +1,782 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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_JACOBISVD_H
+#define EIGEN_JACOBISVD_H
+
+namespace Eigen { 
+
+namespace internal {
+// forward declaration (needed by ICC)
+// the empty body is required by MSVC
+template<typename MatrixType, int QRPreconditioner,
+         bool IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>
+struct svd_precondition_2x2_block_to_be_real {};
+
+/*** QR preconditioners (R-SVD)
+ ***
+ *** Their role is to reduce the problem of computing the SVD to the case of a square matrix.
+ *** This approach, known as R-SVD, is an optimization for rectangular-enough matrices, and is a requirement for
+ *** JacobiSVD which by itself is only able to work on square matrices.
+ ***/
+
+enum { PreconditionIfMoreColsThanRows, PreconditionIfMoreRowsThanCols };
+
+template<typename MatrixType, int QRPreconditioner, int Case>
+struct qr_preconditioner_should_do_anything
+{
+  enum { a = MatrixType::RowsAtCompileTime != Dynamic &&
+             MatrixType::ColsAtCompileTime != Dynamic &&
+             MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime,
+         b = MatrixType::RowsAtCompileTime != Dynamic &&
+             MatrixType::ColsAtCompileTime != Dynamic &&
+             MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime,
+         ret = !( (QRPreconditioner == NoQRPreconditioner) ||
+                  (Case == PreconditionIfMoreColsThanRows && bool(a)) ||
+                  (Case == PreconditionIfMoreRowsThanCols && bool(b)) )
+  };
+};
+
+template<typename MatrixType, int QRPreconditioner, int Case,
+         bool DoAnything = qr_preconditioner_should_do_anything<MatrixType, QRPreconditioner, Case>::ret
+> struct qr_preconditioner_impl {};
+
+template<typename MatrixType, int QRPreconditioner, int Case>
+class qr_preconditioner_impl<MatrixType, QRPreconditioner, Case, false>
+{
+public:
+  typedef typename MatrixType::Index Index;
+  void allocate(const JacobiSVD<MatrixType, QRPreconditioner>&) {}
+  bool run(JacobiSVD<MatrixType, QRPreconditioner>&, const MatrixType&)
+  {
+    return false;
+  }
+};
+
+/*** preconditioner using FullPivHouseholderQR ***/
+
+template<typename MatrixType>
+class qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
+{
+public:
+  typedef typename MatrixType::Index Index;
+  typedef typename MatrixType::Scalar Scalar;
+  enum
+  {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime
+  };
+  typedef Matrix<Scalar, 1, RowsAtCompileTime, RowMajor, 1, MaxRowsAtCompileTime> WorkspaceType;
+
+  void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)
+  {
+    if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
+    {
+      m_qr.~QRType();
+      ::new (&m_qr) QRType(svd.rows(), svd.cols());
+    }
+    if (svd.m_computeFullU) m_workspace.resize(svd.rows());
+  }
+
+  bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
+  {
+    if(matrix.rows() > matrix.cols())
+    {
+      m_qr.compute(matrix);
+      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
+      if(svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace);
+      if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
+      return true;
+    }
+    return false;
+  }
+private:
+  typedef FullPivHouseholderQR<MatrixType> QRType;
+  QRType m_qr;
+  WorkspaceType m_workspace;
+};
+
+template<typename MatrixType>
+class qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
+{
+public:
+  typedef typename MatrixType::Index Index;
+  typedef typename MatrixType::Scalar Scalar;
+  enum
+  {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+    Options = MatrixType::Options
+  };
+  typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
+          TransposeTypeWithSameStorageOrder;
+
+  void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)
+  {
+    if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
+    {
+      m_qr.~QRType();
+      ::new (&m_qr) QRType(svd.cols(), svd.rows());
+    }
+    m_adjoint.resize(svd.cols(), svd.rows());
+    if (svd.m_computeFullV) m_workspace.resize(svd.cols());
+  }
+
+  bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
+  {
+    if(matrix.cols() > matrix.rows())
+    {
+      m_adjoint = matrix.adjoint();
+      m_qr.compute(m_adjoint);
+      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
+      if(svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace);
+      if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
+      return true;
+    }
+    else return false;
+  }
+private:
+  typedef FullPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
+  QRType m_qr;
+  TransposeTypeWithSameStorageOrder m_adjoint;
+  typename internal::plain_row_type<MatrixType>::type m_workspace;
+};
+
+/*** preconditioner using ColPivHouseholderQR ***/
+
+template<typename MatrixType>
+class qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
+{
+public:
+  typedef typename MatrixType::Index Index;
+
+  void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)
+  {
+    if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
+    {
+      m_qr.~QRType();
+      ::new (&m_qr) QRType(svd.rows(), svd.cols());
+    }
+    if (svd.m_computeFullU) m_workspace.resize(svd.rows());
+    else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
+  }
+
+  bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
+  {
+    if(matrix.rows() > matrix.cols())
+    {
+      m_qr.compute(matrix);
+      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
+      if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
+      else if(svd.m_computeThinU)
+      {
+        svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
+        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
+      }
+      if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
+      return true;
+    }
+    return false;
+  }
+
+private:
+  typedef ColPivHouseholderQR<MatrixType> QRType;
+  QRType m_qr;
+  typename internal::plain_col_type<MatrixType>::type m_workspace;
+};
+
+template<typename MatrixType>
+class qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
+{
+public:
+  typedef typename MatrixType::Index Index;
+  typedef typename MatrixType::Scalar Scalar;
+  enum
+  {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+    Options = MatrixType::Options
+  };
+
+  typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
+          TransposeTypeWithSameStorageOrder;
+
+  void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)
+  {
+    if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
+    {
+      m_qr.~QRType();
+      ::new (&m_qr) QRType(svd.cols(), svd.rows());
+    }
+    if (svd.m_computeFullV) m_workspace.resize(svd.cols());
+    else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
+    m_adjoint.resize(svd.cols(), svd.rows());
+  }
+
+  bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
+  {
+    if(matrix.cols() > matrix.rows())
+    {
+      m_adjoint = matrix.adjoint();
+      m_qr.compute(m_adjoint);
+
+      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
+      if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
+      else if(svd.m_computeThinV)
+      {
+        svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
+        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
+      }
+      if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
+      return true;
+    }
+    else return false;
+  }
+
+private:
+  typedef ColPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
+  QRType m_qr;
+  TransposeTypeWithSameStorageOrder m_adjoint;
+  typename internal::plain_row_type<MatrixType>::type m_workspace;
+};
+
+/*** preconditioner using HouseholderQR ***/
+
+template<typename MatrixType>
+class qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
+{
+public:
+  typedef typename MatrixType::Index Index;
+
+  void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)
+  {
+    if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
+    {
+      m_qr.~QRType();
+      ::new (&m_qr) QRType(svd.rows(), svd.cols());
+    }
+    if (svd.m_computeFullU) m_workspace.resize(svd.rows());
+    else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
+  }
+
+  bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)
+  {
+    if(matrix.rows() > matrix.cols())
+    {
+      m_qr.compute(matrix);
+      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
+      if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
+      else if(svd.m_computeThinU)
+      {
+        svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
+        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
+      }
+      if(svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());
+      return true;
+    }
+    return false;
+  }
+private:
+  typedef HouseholderQR<MatrixType> QRType;
+  QRType m_qr;
+  typename internal::plain_col_type<MatrixType>::type m_workspace;
+};
+
+template<typename MatrixType>
+class qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
+{
+public:
+  typedef typename MatrixType::Index Index;
+  typedef typename MatrixType::Scalar Scalar;
+  enum
+  {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+    Options = MatrixType::Options
+  };
+
+  typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
+          TransposeTypeWithSameStorageOrder;
+
+  void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)
+  {
+    if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
+    {
+      m_qr.~QRType();
+      ::new (&m_qr) QRType(svd.cols(), svd.rows());
+    }
+    if (svd.m_computeFullV) m_workspace.resize(svd.cols());
+    else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
+    m_adjoint.resize(svd.cols(), svd.rows());
+  }
+
+  bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)
+  {
+    if(matrix.cols() > matrix.rows())
+    {
+      m_adjoint = matrix.adjoint();
+      m_qr.compute(m_adjoint);
+
+      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
+      if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
+      else if(svd.m_computeThinV)
+      {
+        svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
+        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
+      }
+      if(svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());
+      return true;
+    }
+    else return false;
+  }
+
+private:
+  typedef HouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
+  QRType m_qr;
+  TransposeTypeWithSameStorageOrder m_adjoint;
+  typename internal::plain_row_type<MatrixType>::type m_workspace;
+};
+
+/*** 2x2 SVD implementation
+ ***
+ *** JacobiSVD consists in performing a series of 2x2 SVD subproblems
+ ***/
+
+template<typename MatrixType, int QRPreconditioner>
+struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, false>
+{
+  typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
+  typedef typename SVD::Index Index;
+  static void run(typename SVD::WorkMatrixType&, SVD&, Index, Index) {}
+};
+
+template<typename MatrixType, int QRPreconditioner>
+struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
+{
+  typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::RealScalar RealScalar;
+  typedef typename SVD::Index Index;
+  static void run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q)
+  {
+    using std::sqrt;
+    Scalar z;
+    JacobiRotation<Scalar> rot;
+    RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));
+    if(n==0)
+    {
+      z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
+      work_matrix.row(p) *= z;
+      if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
+      z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
+      work_matrix.row(q) *= z;
+      if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
+    }
+    else
+    {
+      rot.c() = conj(work_matrix.coeff(p,p)) / n;
+      rot.s() = work_matrix.coeff(q,p) / n;
+      work_matrix.applyOnTheLeft(p,q,rot);
+      if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());
+      if(work_matrix.coeff(p,q) != Scalar(0))
+      {
+        Scalar z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
+        work_matrix.col(q) *= z;
+        if(svd.computeV()) svd.m_matrixV.col(q) *= z;
+      }
+      if(work_matrix.coeff(q,q) != Scalar(0))
+      {
+        z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
+        work_matrix.row(q) *= z;
+        if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
+      }
+    }
+  }
+};
+
+template<typename MatrixType, typename RealScalar, typename Index>
+void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
+                            JacobiRotation<RealScalar> *j_left,
+                            JacobiRotation<RealScalar> *j_right)
+{
+  using std::sqrt;
+  Matrix<RealScalar,2,2> m;
+  m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
+       numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
+  JacobiRotation<RealScalar> rot1;
+  RealScalar t = m.coeff(0,0) + m.coeff(1,1);
+  RealScalar d = m.coeff(1,0) - m.coeff(0,1);
+  if(t == RealScalar(0))
+  {
+    rot1.c() = RealScalar(0);
+    rot1.s() = d > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
+  }
+  else
+  {
+    RealScalar u = d / t;
+    rot1.c() = RealScalar(1) / sqrt(RealScalar(1) + numext::abs2(u));
+    rot1.s() = rot1.c() * u;
+  }
+  m.applyOnTheLeft(0,1,rot1);
+  j_right->makeJacobi(m,0,1);
+  *j_left  = rot1 * j_right->transpose();
+}
+
+} // end namespace internal
+
+/** \ingroup SVD_Module
+  *
+  *
+  * \class JacobiSVD
+  *
+  * \brief Two-sided Jacobi SVD decomposition of a rectangular matrix
+  *
+  * \param MatrixType the type of the matrix of which we are computing the SVD decomposition
+  * \param QRPreconditioner this optional parameter allows to specify the type of QR decomposition that will be used internally
+  *                        for the R-SVD step for non-square matrices. See discussion of possible values below.
+  *
+  * SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
+  *   \f[ A = U S V^* \f]
+  * where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal;
+  * the diagonal entries of S are known as the \em singular \em values of \a A and the columns of \a U and \a V are known as the left
+  * and right \em singular \em vectors of \a A respectively.
+  *
+  * Singular values are always sorted in decreasing order.
+  *
+  * This JacobiSVD decomposition computes only the singular values by default. If you want \a U or \a V, you need to ask for them explicitly.
+  *
+  * You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \a m be the
+  * smaller value among \a n and \a p, there are only \a m singular vectors; the remaining columns of \a U and \a V do not correspond to actual
+  * singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix,
+  * and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving.
+  *
+  * Here's an example demonstrating basic usage:
+  * \include JacobiSVD_basic.cpp
+  * Output: \verbinclude JacobiSVD_basic.out
+  *
+  * This JacobiSVD class is a two-sided Jacobi R-SVD decomposition, ensuring optimal reliability and accuracy. The downside is that it's slower than
+  * bidiagonalizing SVD algorithms for large square matrices; however its complexity is still \f$ O(n^2p) \f$ where \a n is the smaller dimension and
+  * \a p is the greater dimension, meaning that it is still of the same order of complexity as the faster bidiagonalizing R-SVD algorithms.
+  * In particular, like any R-SVD, it takes advantage of non-squareness in that its complexity is only linear in the greater dimension.
+  *
+  * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to
+  * terminate in finite (and reasonable) time.
+  *
+  * The possible values for QRPreconditioner are:
+  * \li ColPivHouseholderQRPreconditioner is the default. In practice it's very safe. It uses column-pivoting QR.
+  * \li FullPivHouseholderQRPreconditioner, is the safest and slowest. It uses full-pivoting QR.
+  *     Contrary to other QRs, it doesn't allow computing thin unitaries.
+  * \li HouseholderQRPreconditioner is the fastest, and less safe and accurate than the pivoting variants. It uses non-pivoting QR.
+  *     This is very similar in safety and accuracy to the bidiagonalization process used by bidiagonalizing SVD algorithms (since bidiagonalization
+  *     is inherently non-pivoting). However the resulting SVD is still more reliable than bidiagonalizing SVDs because the Jacobi-based iterarive
+  *     process is more reliable than the optimized bidiagonal SVD iterations.
+  * \li NoQRPreconditioner allows not to use a QR preconditioner at all. This is useful if you know that you will only be computing
+  *     JacobiSVD decompositions of square matrices. Non-square matrices require a QR preconditioner. Using this option will result in
+  *     faster compilation and smaller executable code. It won't significantly speed up computation, since JacobiSVD is always checking
+  *     if QR preconditioning is needed before applying it anyway.
+  *
+  * \sa MatrixBase::jacobiSvd()
+  */
+template<typename _MatrixType, int QRPreconditioner> 
+class JacobiSVD : public SVDBase<_MatrixType>
+{
+  public:
+
+    typedef _MatrixType MatrixType;
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+    typedef typename MatrixType::Index Index;
+    enum {
+      RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+      DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),
+      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+      MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),
+      MatrixOptions = MatrixType::Options
+    };
+
+    typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
+                   MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
+            MatrixUType;
+    typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
+                   MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
+            MatrixVType;
+    typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
+    typedef typename internal::plain_row_type<MatrixType>::type RowType;
+    typedef typename internal::plain_col_type<MatrixType>::type ColType;
+    typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
+                   MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime>
+            WorkMatrixType;
+
+    /** \brief Default Constructor.
+      *
+      * The default constructor is useful in cases in which the user intends to
+      * perform decompositions via JacobiSVD::compute(const MatrixType&).
+      */
+    JacobiSVD()
+      : SVDBase<_MatrixType>::SVDBase()
+    {}
+
+
+    /** \brief Default Constructor with memory preallocation
+      *
+      * Like the default constructor but with preallocation of the internal data
+      * according to the specified problem size.
+      * \sa JacobiSVD()
+      */
+    JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0)
+      : SVDBase<_MatrixType>::SVDBase() 
+    {
+      allocate(rows, cols, computationOptions);
+    }
+
+    /** \brief Constructor performing the decomposition of given matrix.
+     *
+     * \param matrix the matrix to decompose
+     * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
+     *                           By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
+     *                           #ComputeFullV, #ComputeThinV.
+     *
+     * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
+     * available with the (non-default) FullPivHouseholderQR preconditioner.
+     */
+    JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
+      : SVDBase<_MatrixType>::SVDBase()
+    {
+      compute(matrix, computationOptions);
+    }
+
+    /** \brief Method performing the decomposition of given matrix using custom options.
+     *
+     * \param matrix the matrix to decompose
+     * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
+     *                           By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
+     *                           #ComputeFullV, #ComputeThinV.
+     *
+     * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
+     * available with the (non-default) FullPivHouseholderQR preconditioner.
+     */
+    SVDBase<MatrixType>& compute(const MatrixType& matrix, unsigned int computationOptions);
+
+    /** \brief Method performing the decomposition of given matrix using current options.
+     *
+     * \param matrix the matrix to decompose
+     *
+     * This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
+     */
+    SVDBase<MatrixType>& compute(const MatrixType& matrix)
+    {
+      return compute(matrix, this->m_computationOptions);
+    }
+    
+    /** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
+      *
+      * \param b the right-hand-side of the equation to solve.
+      *
+      * \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
+      *
+      * \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving.
+      * In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$.
+      */
+    template<typename Rhs>
+    inline const internal::solve_retval<JacobiSVD, Rhs>
+    solve(const MatrixBase<Rhs>& b) const
+    {
+      eigen_assert(this->m_isInitialized && "JacobiSVD is not initialized.");
+      eigen_assert(SVDBase<MatrixType>::computeU() && SVDBase<MatrixType>::computeV() && "JacobiSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
+      return internal::solve_retval<JacobiSVD, Rhs>(*this, b.derived());
+    }
+
+    
+
+  private:
+    void allocate(Index rows, Index cols, unsigned int computationOptions);
+
+  protected:
+    WorkMatrixType m_workMatrix;
+   
+    template<typename __MatrixType, int _QRPreconditioner, bool _IsComplex>
+    friend struct internal::svd_precondition_2x2_block_to_be_real;
+    template<typename __MatrixType, int _QRPreconditioner, int _Case, bool _DoAnything>
+    friend struct internal::qr_preconditioner_impl;
+
+    internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreColsThanRows> m_qr_precond_morecols;
+    internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols> m_qr_precond_morerows;
+};
+
+template<typename MatrixType, int QRPreconditioner>
+void JacobiSVD<MatrixType, QRPreconditioner>::allocate(Index rows, Index cols, unsigned int computationOptions)
+{
+  if (SVDBase<MatrixType>::allocate(rows, cols, computationOptions)) return;
+
+  if (QRPreconditioner == FullPivHouseholderQRPreconditioner)
+  {
+      eigen_assert(!(this->m_computeThinU || this->m_computeThinV) &&
+              "JacobiSVD: can't compute thin U or thin V with the FullPivHouseholderQR preconditioner. "
+              "Use the ColPivHouseholderQR preconditioner instead.");
+  }
+
+  m_workMatrix.resize(this->m_diagSize, this->m_diagSize);
+  
+  if(this->m_cols>this->m_rows) m_qr_precond_morecols.allocate(*this);
+  if(this->m_rows>this->m_cols) m_qr_precond_morerows.allocate(*this);
+}
+
+template<typename MatrixType, int QRPreconditioner>
+SVDBase<MatrixType>&
+JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsigned int computationOptions)
+{
+  using std::abs;
+  allocate(matrix.rows(), matrix.cols(), computationOptions);
+
+  // currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number of iterations,
+  // only worsening the precision of U and V as we accumulate more rotations
+  const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();
+
+  // limit for very small denormal numbers to be considered zero in order to avoid infinite loops (see bug 286)
+  const RealScalar considerAsZero = RealScalar(2) * std::numeric_limits<RealScalar>::denorm_min();
+
+  /*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */
+
+  if(!m_qr_precond_morecols.run(*this, matrix) && !m_qr_precond_morerows.run(*this, matrix))
+  {
+    m_workMatrix = matrix.block(0,0,this->m_diagSize,this->m_diagSize);
+    if(this->m_computeFullU) this->m_matrixU.setIdentity(this->m_rows,this->m_rows);
+    if(this->m_computeThinU) this->m_matrixU.setIdentity(this->m_rows,this->m_diagSize);
+    if(this->m_computeFullV) this->m_matrixV.setIdentity(this->m_cols,this->m_cols);
+    if(this->m_computeThinV) this->m_matrixV.setIdentity(this->m_cols, this->m_diagSize);
+  }
+
+  /*** step 2. The main Jacobi SVD iteration. ***/
+
+  bool finished = false;
+  while(!finished)
+  {
+    finished = true;
+
+    // do a sweep: for all index pairs (p,q), perform SVD of the corresponding 2x2 sub-matrix
+
+    for(Index p = 1; p < this->m_diagSize; ++p)
+    {
+      for(Index q = 0; q < p; ++q)
+      {
+        // if this 2x2 sub-matrix is not diagonal already...
+        // notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't
+        // keep us iterating forever. Similarly, small denormal numbers are considered zero.
+        using std::max;
+        RealScalar threshold = (max)(considerAsZero, precision * (max)(abs(m_workMatrix.coeff(p,p)),
+                                                                       abs(m_workMatrix.coeff(q,q))));
+        if((max)(abs(m_workMatrix.coeff(p,q)),abs(m_workMatrix.coeff(q,p))) > threshold)
+        {
+          finished = false;
+
+          // perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal
+          internal::svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner>::run(m_workMatrix, *this, p, q);
+          JacobiRotation<RealScalar> j_left, j_right;
+          internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right);
+
+          // accumulate resulting Jacobi rotations
+          m_workMatrix.applyOnTheLeft(p,q,j_left);
+          if(SVDBase<MatrixType>::computeU()) this->m_matrixU.applyOnTheRight(p,q,j_left.transpose());
+
+          m_workMatrix.applyOnTheRight(p,q,j_right);
+          if(SVDBase<MatrixType>::computeV()) this->m_matrixV.applyOnTheRight(p,q,j_right);
+        }
+      }
+    }
+  }
+
+  /*** step 3. The work matrix is now diagonal, so ensure it's positive so its diagonal entries are the singular values ***/
+
+  for(Index i = 0; i < this->m_diagSize; ++i)
+  {
+    RealScalar a = abs(m_workMatrix.coeff(i,i));
+    this->m_singularValues.coeffRef(i) = a;
+    if(SVDBase<MatrixType>::computeU() && (a!=RealScalar(0))) this->m_matrixU.col(i) *= this->m_workMatrix.coeff(i,i)/a;
+  }
+
+  /*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/
+
+  this->m_nonzeroSingularValues = this->m_diagSize;
+  for(Index i = 0; i < this->m_diagSize; i++)
+  {
+    Index pos;
+    RealScalar maxRemainingSingularValue = this->m_singularValues.tail(this->m_diagSize-i).maxCoeff(&pos);
+    if(maxRemainingSingularValue == RealScalar(0))
+    {
+      this->m_nonzeroSingularValues = i;
+      break;
+    }
+    if(pos)
+    {
+      pos += i;
+      std::swap(this->m_singularValues.coeffRef(i), this->m_singularValues.coeffRef(pos));
+      if(SVDBase<MatrixType>::computeU()) this->m_matrixU.col(pos).swap(this->m_matrixU.col(i));
+      if(SVDBase<MatrixType>::computeV()) this->m_matrixV.col(pos).swap(this->m_matrixV.col(i));
+    }
+  }
+
+  this->m_isInitialized = true;
+  return *this;
+}
+
+namespace internal {
+template<typename _MatrixType, int QRPreconditioner, typename Rhs>
+struct solve_retval<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs>
+  : solve_retval_base<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs>
+{
+  typedef JacobiSVD<_MatrixType, QRPreconditioner> JacobiSVDType;
+  EIGEN_MAKE_SOLVE_HELPERS(JacobiSVDType,Rhs)
+
+  template<typename Dest> void evalTo(Dest& dst) const
+  {
+    eigen_assert(rhs().rows() == dec().rows());
+
+    // A = U S V^*
+    // So A^{-1} = V S^{-1} U^*
+
+    Index diagSize = (std::min)(dec().rows(), dec().cols());
+    typename JacobiSVDType::SingularValuesType invertedSingVals(diagSize);
+
+    Index nonzeroSingVals = dec().nonzeroSingularValues();
+    invertedSingVals.head(nonzeroSingVals) = dec().singularValues().head(nonzeroSingVals).array().inverse();
+    invertedSingVals.tail(diagSize - nonzeroSingVals).setZero();
+
+    dst = dec().matrixV().leftCols(diagSize)
+        * invertedSingVals.asDiagonal()
+        * dec().matrixU().leftCols(diagSize).adjoint()
+        * rhs();
+  }
+};
+} // end namespace internal
+
+/** \svd_module
+  *
+  * \return the singular value decomposition of \c *this computed by two-sided
+  * Jacobi transformations.
+  *
+  * \sa class JacobiSVD
+  */
+template<typename Derived>
+JacobiSVD<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::jacobiSvd(unsigned int computationOptions) const
+{
+  return JacobiSVD<PlainObject>(*this, computationOptions);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_JACOBISVD_H
diff --git a/eigen/unsupported/Eigen/src/SVD/SVDBase.h b/eigen/unsupported/Eigen/src/SVD/SVDBase.h
new file mode 100644
index 0000000..fd8af3b
--- /dev/null
+++ b/eigen/unsupported/Eigen/src/SVD/SVDBase.h
@@ -0,0 +1,236 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
+// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
+// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
+// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
+//
+// 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_SVD_H
+#define EIGEN_SVD_H
+
+namespace Eigen {
+/** \ingroup SVD_Module
+ *
+ *
+ * \class SVDBase
+ *
+ * \brief Mother class of SVD classes algorithms
+ *
+ * \param MatrixType the type of the matrix of which we are computing the SVD decomposition
+ * SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
+ *   \f[ A = U S V^* \f]
+ * where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal;
+ * the diagonal entries of S are known as the \em singular \em values of \a A and the columns of \a U and \a V are known as the left
+ * and right \em singular \em vectors of \a A respectively.
+ *
+ * Singular values are always sorted in decreasing order.
+ *
+ * 
+ * You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \a m be the
+ * smaller value among \a n and \a p, there are only \a m singular vectors; the remaining columns of \a U and \a V do not correspond to actual
+ * singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix,
+ * and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving.
+ *  
+ * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to
+ * terminate in finite (and reasonable) time.
+ * \sa MatrixBase::genericSvd()
+ */
+template<typename _MatrixType> 
+class SVDBase
+{
+
+public:
+  typedef _MatrixType MatrixType;
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+  typedef typename MatrixType::Index Index;
+  enum {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+    DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),
+    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+    MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),
+    MatrixOptions = MatrixType::Options
+  };
+
+  typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
+		 MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
+  MatrixUType;
+  typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
+		 MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
+  MatrixVType;
+  typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
+  typedef typename internal::plain_row_type<MatrixType>::type RowType;
+  typedef typename internal::plain_col_type<MatrixType>::type ColType;
+  typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
+		 MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime>
+  WorkMatrixType;
+	
+
+
+
+  /** \brief Method performing the decomposition of given matrix using custom options.
+   *
+   * \param matrix the matrix to decompose
+   * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
+   *                           By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
+   *                           #ComputeFullV, #ComputeThinV.
+   *
+   * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
+   * available with the (non-default) FullPivHouseholderQR preconditioner.
+   */
+  SVDBase& compute(const MatrixType& matrix, unsigned int computationOptions);
+
+  /** \brief Method performing the decomposition of given matrix using current options.
+   *
+   * \param matrix the matrix to decompose
+   *
+   * This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
+   */
+  //virtual SVDBase& compute(const MatrixType& matrix) = 0;
+  SVDBase& compute(const MatrixType& matrix);
+
+  /** \returns the \a U matrix.
+   *
+   * For the SVDBase decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
+   * the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
+   *
+   * The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
+   *
+   * This method asserts that you asked for \a U to be computed.
+   */
+  const MatrixUType& matrixU() const
+  {
+    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    eigen_assert(computeU() && "This SVD decomposition didn't compute U. Did you ask for it?");
+    return m_matrixU;
+  }
+
+  /** \returns the \a V matrix.
+   *
+   * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
+   * the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.
+   *
+   * The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
+   *
+   * This method asserts that you asked for \a V to be computed.
+   */
+  const MatrixVType& matrixV() const
+  {
+    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    eigen_assert(computeV() && "This SVD decomposition didn't compute V. Did you ask for it?");
+    return m_matrixV;
+  }
+
+  /** \returns the vector of singular values.
+   *
+   * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
+   * returned vector has size \a m.  Singular values are always sorted in decreasing order.
+   */
+  const SingularValuesType& singularValues() const
+  {
+    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    return m_singularValues;
+  }
+
+  
+
+  /** \returns the number of singular values that are not exactly 0 */
+  Index nonzeroSingularValues() const
+  {
+    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    return m_nonzeroSingularValues;
+  }
+
+
+  /** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
+  inline bool computeU() const { return m_computeFullU || m_computeThinU; }
+  /** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
+  inline bool computeV() const { return m_computeFullV || m_computeThinV; }
+
+
+  inline Index rows() const { return m_rows; }
+  inline Index cols() const { return m_cols; }
+
+
+protected:
+  // return true if already allocated
+  bool allocate(Index rows, Index cols, unsigned int computationOptions) ;
+
+  MatrixUType m_matrixU;
+  MatrixVType m_matrixV;
+  SingularValuesType m_singularValues;
+  bool m_isInitialized, m_isAllocated;
+  bool m_computeFullU, m_computeThinU;
+  bool m_computeFullV, m_computeThinV;
+  unsigned int m_computationOptions;
+  Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
+
+
+  /** \brief Default Constructor.
+   *
+   * Default constructor of SVDBase
+   */
+  SVDBase()
+    : m_isInitialized(false),
+      m_isAllocated(false),
+      m_computationOptions(0),
+      m_rows(-1), m_cols(-1)
+  {}
+
+
+};
+
+
+template<typename MatrixType>
+bool SVDBase<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions)
+{
+  eigen_assert(rows >= 0 && cols >= 0);
+
+  if (m_isAllocated &&
+      rows == m_rows &&
+      cols == m_cols &&
+      computationOptions == m_computationOptions)
+  {
+    return true;
+  }
+
+  m_rows = rows;
+  m_cols = cols;
+  m_isInitialized = false;
+  m_isAllocated = true;
+  m_computationOptions = computationOptions;
+  m_computeFullU = (computationOptions & ComputeFullU) != 0;
+  m_computeThinU = (computationOptions & ComputeThinU) != 0;
+  m_computeFullV = (computationOptions & ComputeFullV) != 0;
+  m_computeThinV = (computationOptions & ComputeThinV) != 0;
+  eigen_assert(!(m_computeFullU && m_computeThinU) && "SVDBase: you can't ask for both full and thin U");
+  eigen_assert(!(m_computeFullV && m_computeThinV) && "SVDBase: you can't ask for both full and thin V");
+  eigen_assert(EIGEN_IMPLIES(m_computeThinU || m_computeThinV, MatrixType::ColsAtCompileTime==Dynamic) &&
+	       "SVDBase: thin U and V are only available when your matrix has a dynamic number of columns.");
+
+  m_diagSize = (std::min)(m_rows, m_cols);
+  m_singularValues.resize(m_diagSize);
+  if(RowsAtCompileTime==Dynamic)
+    m_matrixU.resize(m_rows, m_computeFullU ? m_rows
+		     : m_computeThinU ? m_diagSize
+		     : 0);
+  if(ColsAtCompileTime==Dynamic)
+    m_matrixV.resize(m_cols, m_computeFullV ? m_cols
+		     : m_computeThinV ? m_diagSize
+		     : 0);
+
+  return false;
+}
+
+}// end namespace
+
+#endif // EIGEN_SVD_H
diff --git a/eigen/unsupported/Eigen/src/SVD/TODOBdcsvd.txt b/eigen/unsupported/Eigen/src/SVD/TODOBdcsvd.txt
new file mode 100644
index 0000000..0bc9a46
--- /dev/null
+++ b/eigen/unsupported/Eigen/src/SVD/TODOBdcsvd.txt
@@ -0,0 +1,29 @@
+TO DO LIST
+
+
+
+(optional optimization) - do all the allocations in the allocate part 
+                        - support static matrices
+                        - return a error at compilation time when using integer matrices (int, long, std::complex<int>, ...)
+
+to finish the algorithm :
+			-implement the last part of the algorithm as described on the reference paper. 
+			    You may find more information on that part on this paper
+
+			-to replace the call to JacobiSVD at the end of the divide algorithm, just after the call to 
+			    deflation.
+
+(suggested step by step resolution)
+                       0) comment the call to Jacobi in the last part of the divide method and everything right after
+                               until the end of the method. What is commented can be a guideline to steps 3) 4) and 6)
+                       1) solve the secular equation (Characteristic equation) on the values that are not null (zi!=0 and di!=0), after the deflation
+                               wich should be uncommented in the divide method
+                       2) remember the values of the singular values that are already computed (zi=0)
+                       3) assign the singular values found in m_computed at the right places (with the ones found in step 2) )
+                               in decreasing order
+                       4) set the firstcol to zero (except the first element) in m_computed
+                       5) compute all the singular vectors when CompV is set to true and only the left vectors when
+                               CompV is set to false
+                       6) multiply naiveU and naiveV to the right by the matrices found, only naiveU when CompV is set to
+                               false, /!\ if CompU is false NaiveU has only 2 rows
+                       7) delete everything commented in step 0)
diff --git a/eigen/unsupported/Eigen/src/SVD/doneInBDCSVD.txt b/eigen/unsupported/Eigen/src/SVD/doneInBDCSVD.txt
new file mode 100644
index 0000000..8563dda
--- /dev/null
+++ b/eigen/unsupported/Eigen/src/SVD/doneInBDCSVD.txt
@@ -0,0 +1,21 @@
+This unsupported package is about a divide and conquer algorithm to compute SVD.
+
+The implementation follows as closely as possible the following reference paper : 
+http://www.cs.yale.edu/publications/techreports/tr933.pdf
+
+The code documentation uses the same names for variables as the reference paper. The code, deflation included, is
+working  but there are a few things that could be optimised as explained in the TODOBdsvd. 
+
+In the code comments were put at the line where would be the third step of the algorithm so one could simply add the call 
+of a function doing the last part of the algorithm and that would not require any knowledge of the part we implemented.
+
+In the TODOBdcsvd we explain what is the main difficulty of the last part and suggest a reference paper to help solve it.
+
+The implemented has trouble with fixed size matrices. 
+
+In the actual implementation, it returns matrices of zero when ask to do a svd on an int matrix. 
+
+
+Paper for the third part:
+http://www.stat.uchicago.edu/~lekheng/courses/302/classics/greengard-rokhlin.pdf
+