Merged eigen/eigen into default

27 files changed, 479 insertions, 1586 deletions

diff --git a/unsupported/Eigen/AlignedVector3 b/unsupported/Eigen/AlignedVector3
index 7b45e6cce..35493e87b 100644
--- a/unsupported/Eigen/AlignedVector3
+++ b/unsupported/Eigen/AlignedVector3
@@ -57,6 +57,10 @@ template<typename _Scalar> class AlignedVector3
 
     inline Index rows() const { return 3; }
     inline Index cols() const { return 1; }
+    
+    Scalar* data() { return m_coeffs.data(); }
+    const Scalar* data() const { return m_coeffs.data(); }
+    Index innerStride() const { return 1; }
 
     inline const Scalar& coeff(Index row, Index col) const
     { return m_coeffs.coeff(row, col); }
@@ -181,8 +185,28 @@ template<typename _Scalar> class AlignedVector3
     {
       return m_coeffs.template head<3>().isApprox(other,eps);
     }
+    
+    CoeffType& coeffs() { return m_coeffs; }
+    const CoeffType& coeffs() const { return m_coeffs; }
 };
 
+namespace internal {
+
+template<typename Scalar>
+struct evaluator<AlignedVector3<Scalar> >
+  : evaluator<Matrix<Scalar,4,1> >::type
+{
+  typedef AlignedVector3<Scalar> XprType;
+  typedef typename evaluator<Matrix<Scalar,4,1> >::type Base;
+  
+  typedef evaluator type;
+  typedef evaluator nestedType;
+
+  evaluator(const XprType &m) : Base(m.coeffs()) {}  
+};
+
+}
+
 //@}
 
 }
diff --git a/unsupported/Eigen/BDCSVD b/unsupported/Eigen/BDCSVD
new file mode 100644
index 000000000..44649dbd0
--- /dev/null
+++ b/unsupported/Eigen/BDCSVD
@@ -0,0 +1,26 @@
+#ifndef EIGEN_BDCSVD_MODULE_H
+#define EIGEN_BDCSVD_MODULE_H
+
+#include <Eigen/SVD>
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+/** \defgroup BDCSVD_Module BDCSVD module
+  *
+  *
+  *
+  * This module provides Divide & Conquer SVD decomposition for matrices (both real and complex).
+  * This decomposition is accessible via the following MatrixBase method:
+  *  - MatrixBase::bdcSvd()
+  *
+  * \code
+  * #include <Eigen/BDCSVD>
+  * \endcode
+  */
+
+#include "src/BDCSVD/BDCSVD.h"
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_BDCSVD_MODULE_H
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */
diff --git a/unsupported/Eigen/IterativeSolvers b/unsupported/Eigen/IterativeSolvers
index aa15403db..ff0d59b6e 100644
--- a/unsupported/Eigen/IterativeSolvers
+++ b/unsupported/Eigen/IterativeSolvers
@@ -24,9 +24,6 @@
   */
 //@{
 
-#include "../../Eigen/src/misc/Solve.h"
-#include "../../Eigen/src/misc/SparseSolve.h"
-
 #ifndef EIGEN_MPL2_ONLY
 #include "src/IterativeSolvers/IterationController.h"
 #include "src/IterativeSolvers/ConstrainedConjGrad.h"
diff --git a/unsupported/Eigen/MPRealSupport b/unsupported/Eigen/MPRealSupport
index 632de3854..8e42965a3 100644
--- a/unsupported/Eigen/MPRealSupport
+++ b/unsupported/Eigen/MPRealSupport
@@ -159,10 +159,10 @@ int main()
       {
         if(rows==0 || cols==0 || depth==0)
           return;
-        
+
         mpreal  acc1(0,mpfr_get_prec(blockA[0].mpfr_srcptr())),
                 tmp (0,mpfr_get_prec(blockA[0].mpfr_srcptr()));
-        
+
         if(strideA==-1) strideA = depth;
         if(strideB==-1) strideB = depth;
 
diff --git a/unsupported/Eigen/MatrixFunctions b/unsupported/Eigen/MatrixFunctions
index 0b12aaffb..0320606c1 100644
--- a/unsupported/Eigen/MatrixFunctions
+++ b/unsupported/Eigen/MatrixFunctions
@@ -82,7 +82,9 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const
 \param[in]  M  a square matrix.
 \returns  expression representing \f$ \cos(M) \f$.
 
-This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::cos().
+This function computes the matrix cosine. Use ArrayBase::cos() for computing the entry-wise cosine.
+
+The implementation calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::cos().
 
 \sa \ref matrixbase_sin "sin()" for an example.
 
@@ -123,6 +125,9 @@ differential equations: the solution of \f$ y' = My \f$ with the
 initial condition \f$ y(0) = y_0 \f$ is given by
 \f$ y(t) = \exp(M) y_0 \f$.
 
+The matrix exponential is different from applying the exp function to all the entries in the matrix.
+Use ArrayBase::exp() if you want to do the latter.
+
 The cost of the computation is approximately \f$ 20 n^3 \f$ for
 matrices of size \f$ n \f$. The number 20 depends weakly on the
 norm of the matrix.
@@ -177,6 +182,9 @@ the scalar logarithm, the equation \f$ \exp(X) = M \f$ may have
 multiple solutions; this function returns a matrix whose eigenvalues
 have imaginary part in the interval \f$ (-\pi,\pi] \f$.
 
+The matrix logarithm is different from applying the log function to all the entries in the matrix.
+Use ArrayBase::log() if you want to do the latter.
+
 In the real case, the matrix \f$ M \f$ should be invertible and
 it should have no eigenvalues which are real and negative (pairs of
 complex conjugate eigenvalues are allowed). In the complex case, it
@@ -232,7 +240,8 @@ const MatrixPowerReturnValue<Derived> MatrixBase<Derived>::pow(RealScalar p) con
 
 The matrix power \f$ M^p \f$ is defined as \f$ \exp(p \log(M)) \f$,
 where exp denotes the matrix exponential, and log denotes the matrix
-logarithm.
+logarithm. This is different from raising all the entries in the matrix
+to the p-th power. Use ArrayBase::pow() if you want to do the latter.
 
 If \p p is complex, the scalar type of \p M should be the type of \p
 p . \f$ M^p \f$ simply evaluates into \f$ \exp(p \log(M)) \f$.
@@ -391,7 +400,9 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const
 \param[in]  M  a square matrix.
 \returns  expression representing \f$ \sin(M) \f$.
 
-This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::sin().
+This function computes the matrix sine. Use ArrayBase::sin() for computing the entry-wise sine.
+
+The implementation calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::sin().
 
 Example: \include MatrixSine.cpp
 Output: \verbinclude MatrixSine.out
@@ -428,7 +439,9 @@ const MatrixSquareRootReturnValue<Derived> MatrixBase<Derived>::sqrt() const
 
 The matrix square root of \f$ M \f$ is the matrix \f$ M^{1/2} \f$
 whose square is the original matrix; so if \f$ S = M^{1/2} \f$ then
-\f$ S^2 = M \f$. 
+\f$ S^2 = M \f$. This is different from taking the square root of all
+the entries in the matrix; use ArrayBase::sqrt() if you want to do the
+latter.
 
 In the <b>real case</b>, the matrix \f$ M \f$ should be invertible and
 it should have no eigenvalues which are real and negative (pairs of
diff --git a/unsupported/Eigen/SVD b/unsupported/Eigen/SVD
deleted file mode 100644
index 900a8aa60..000000000
--- a/unsupported/Eigen/SVD
+++ /dev/null
@@ -1,35 +0,0 @@
-#ifndef EIGEN_SVD_MODULE_H
-#define EIGEN_SVD_MODULE_H
-
-#include <Eigen/QR>
-#include <Eigen/Householder>
-#include <Eigen/Jacobi>
-
-#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
-
-/** \defgroup SVD_Module SVD module
-  *
-  *
-  *
-  * This module provides SVD decomposition for matrices (both real and complex).
-  * This decomposition is accessible via the following MatrixBase method:
-  *  - MatrixBase::jacobiSvd()
-  *
-  * \code
-  * #include <Eigen/SVD>
-  * \endcode
-  */
-
-#include "../../Eigen/src/misc/Solve.h"
-#include "../../Eigen/src/SVD/UpperBidiagonalization.h"
-#include "src/SVD/SVDBase.h"
-#include "src/SVD/JacobiSVD.h"
-#include "src/SVD/BDCSVD.h"
-#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)
-#include "../../Eigen/src/SVD/JacobiSVD_MKL.h"
-#endif
-
-#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
-
-#endif // EIGEN_SVD_MODULE_H
-/* vim: set filetype=cpp et sw=2 ts=2 ai: */
diff --git a/unsupported/Eigen/SparseExtra b/unsupported/Eigen/SparseExtra
index b5597902a..819cffa27 100644
--- a/unsupported/Eigen/SparseExtra
+++ b/unsupported/Eigen/SparseExtra
@@ -37,9 +37,6 @@
   */
 
 
-#include "../../Eigen/src/misc/Solve.h"
-#include "../../Eigen/src/misc/SparseSolve.h"
-
 #include "src/SparseExtra/DynamicSparseMatrix.h"
 #include "src/SparseExtra/BlockOfDynamicSparseMatrix.h"
 #include "src/SparseExtra/RandomSetter.h"
diff --git a/unsupported/Eigen/src/SVD/BDCSVD.h b/unsupported/Eigen/src/BDCSVD/BDCSVD.h
index 80006fd60..0167872af 100644
--- a/unsupported/Eigen/src/SVD/BDCSVD.h
+++ b/unsupported/Eigen/src/BDCSVD/BDCSVD.h
@@ -19,11 +19,21 @@
 #ifndef EIGEN_BDCSVD_H
 #define EIGEN_BDCSVD_H
 
-#define EPSILON 0.0000000000000001
+namespace Eigen {
 
-#define ALGOSWAP 16
+template<typename _MatrixType> class BDCSVD;
 
-namespace Eigen {
+namespace internal {
+
+template<typename _MatrixType> 
+struct traits<BDCSVD<_MatrixType> >
+{
+  typedef _MatrixType MatrixType;
+};  
+
+} // end namespace internal
+  
+  
 /** \ingroup SVD_Module
  *
  *
@@ -36,13 +46,15 @@ namespace Eigen {
  * It should be used to speed up the calcul of SVD for big matrices. 
  */
 template<typename _MatrixType> 
-class BDCSVD : public SVDBase<_MatrixType>
+class BDCSVD : public SVDBase<BDCSVD<_MatrixType> >
 {
-  typedef SVDBase<_MatrixType> Base;
+  typedef SVDBase<BDCSVD> Base;
     
 public:
   using Base::rows;
   using Base::cols;
+  using Base::computeU;
+  using Base::computeV;
   
   typedef _MatrixType MatrixType;
   typedef typename MatrixType::Scalar Scalar;
@@ -58,15 +70,10 @@ public:
     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 typename Base::MatrixUType MatrixUType;
+  typedef typename Base::MatrixVType MatrixVType;
+  typedef typename Base::SingularValuesType SingularValuesType;
+  
   typedef Matrix<Scalar, Dynamic, Dynamic> MatrixX;
   typedef Matrix<RealScalar, Dynamic, Dynamic> MatrixXr;
   typedef Matrix<RealScalar, Dynamic, 1> VectorType;
@@ -77,9 +84,7 @@ public:
    * 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), m_numIters(0)
+  BDCSVD() : m_algoswap(16), m_numIters(0)
   {}
 
 
@@ -90,8 +95,7 @@ public:
    * \sa BDCSVD()
    */
   BDCSVD(Index rows, Index cols, unsigned int computationOptions = 0)
-    : SVDBase<_MatrixType>::SVDBase(), 
-      algoswap(ALGOSWAP), m_numIters(0)
+    : m_algoswap(16), m_numIters(0)
   {
     allocate(rows, cols, computationOptions);
   }
@@ -107,8 +111,7 @@ public:
    * available with the (non - default) FullPivHouseholderQR preconditioner.
    */
   BDCSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
-    : SVDBase<_MatrixType>::SVDBase(), 
-      algoswap(ALGOSWAP), m_numIters(0)
+    : m_algoswap(16), m_numIters(0)
   {
     compute(matrix, computationOptions);
   }
@@ -116,6 +119,7 @@ public:
   ~BDCSVD() 
   {
   }
+  
   /** \brief Method performing the decomposition of given matrix using custom options.
    *
    * \param matrix the matrix to decompose
@@ -126,7 +130,7 @@ public:
    * 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);
+  BDCSVD& compute(const MatrixType& matrix, unsigned int computationOptions);
 
   /** \brief Method performing the decomposition of given matrix using current options.
    *
@@ -134,7 +138,7 @@ public:
    *
    * 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)
+  BDCSVD& compute(const MatrixType& matrix)
   {
     return compute(matrix, this->m_computationOptions);
   }
@@ -142,58 +146,7 @@ public:
   void setSwitchSize(int s) 
   {
     eigen_assert(s>3 && "BDCSVD the size of the algo switch has to be greater than 3");
-    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;
-    }
+    m_algoswap = s;
   }
  
 private:
@@ -209,15 +162,27 @@ private:
   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(const typename internal::UpperBidiagonalization<MatrixX>::HouseholderUSequenceType& householderU, 
-              const typename internal::UpperBidiagonalization<MatrixX>::HouseholderVSequenceType& householderV);
+  template<typename HouseholderU, typename HouseholderV, typename NaiveU, typename NaiveV>
+  void copyUV(const HouseholderU &householderU, const HouseholderV &householderV, const NaiveU &naiveU, const NaiveV &naivev);
+  static void structured_update(Block<MatrixXr,Dynamic,Dynamic> A, const MatrixXr &B, Index n1);
 
 protected:
   MatrixXr m_naiveU, m_naiveV;
   MatrixXr m_computed;
-  Index nRec;
-  int algoswap;
-  bool isTranspose, compU, compV;
+  Index m_nRec;
+  int m_algoswap;
+  bool m_isTranspose, m_compU, m_compV;
+  
+  using Base::m_singularValues;
+  using Base::m_diagSize;
+  using Base::m_computeFullU;
+  using Base::m_computeFullV;
+  using Base::m_computeThinU;
+  using Base::m_computeThinV;
+  using Base::m_matrixU;
+  using Base::m_matrixV;
+  using Base::m_isInitialized;
+  using Base::m_nonzeroSingularValues;
 
 public:  
   int m_numIters;
@@ -228,117 +193,147 @@ public:
 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 );
+  m_isTranspose = (cols > rows);
+  if (Base::allocate(rows, cols, computationOptions))
+    return;
   
-  if (compV) m_naiveV = MatrixXr::Zero(this->m_diagSize, this->m_diagSize);
+  m_computed = MatrixXr::Zero(m_diagSize + 1, m_diagSize );
+  m_compU = computeV();
+  m_compV = computeU();
+  if (m_isTranspose)
+    std::swap(m_compU, m_compV);
   
-
-  //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;
-    } 
-  }
+  if (m_compU) m_naiveU = MatrixXr::Zero(m_diagSize + 1, m_diagSize + 1 );
+  else         m_naiveU = MatrixXr::Zero(2, m_diagSize + 1 );
+  
+  if (m_compV) m_naiveV = MatrixXr::Zero(m_diagSize, m_diagSize);
 }// 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) {
+BDCSVD<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_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;
+  
+  m_singularValues.head(m_diagSize).setZero();
+  
+  if (m_computeFullU) m_matrixU.setZero(rows(), rows());
+  if (m_computeFullV) m_matrixV.setZero(cols(), cols()); 
+  m_isInitialized = true;
   return *this;
 }
 
 
 // Methode which compute the BDCSVD
 template<typename MatrixType>
-SVDBase<MatrixType>&
-BDCSVD<MatrixType>::compute(const MatrixType& matrix, unsigned int computationOptions) 
+BDCSVD<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()) ;
+  //**** step 1 Bidiagonalization  m_isTranspose = (matrix.cols()>matrix.rows()) ;
   MatrixType copy;
-  if (isTranspose) copy = matrix.adjoint();
-  else copy = matrix;
+  if (m_isTranspose) copy = matrix.adjoint();
+  else               copy = matrix;
   
   internal::UpperBidiagonalization<MatrixX> bid(copy);
 
   //**** step 2 Divide
-  m_computed.topRows(this->m_diagSize) = bid.bidiagonal().toDenseMatrix().transpose();
+  m_naiveU.setZero();
+  m_naiveV.setZero();
+  m_computed.topRows(m_diagSize) = bid.bidiagonal().toDenseMatrix().transpose();
   m_computed.template bottomRows<1>().setZero();
-  divide(0, this->m_diagSize - 1, 0, 0, 0);
+  divide(0, m_diagSize - 1, 0, 0, 0);
 
   //**** step 3 copy
-  for (int i=0; i<this->m_diagSize; i++)   {
+  for (int i=0; i<m_diagSize; i++)
+  {
     RealScalar a = abs(m_computed.coeff(i, i));
-    this->m_singularValues.coeffRef(i) = a;
-    if (a == 0){
-      this->m_nonzeroSingularValues = i;
-      this->m_singularValues.tail(this->m_diagSize - i - 1).setZero();
+    m_singularValues.coeffRef(i) = a;
+    if (a == 0)
+    {
+      m_nonzeroSingularValues = i;
+      m_singularValues.tail(m_diagSize - i - 1).setZero();
       break;
     }
-    else  if (i == this->m_diagSize - 1)
+    else if (i == m_diagSize - 1)
     {
-      this->m_nonzeroSingularValues = i + 1;
+      m_nonzeroSingularValues = i + 1;
       break;
     }
   }
-  copyUV(bid.householderU(), bid.householderV());
-  this->m_isInitialized = true;
+  if(m_isTranspose) copyUV(bid.householderV(), bid.householderU(), m_naiveV, m_naiveU);
+  else              copyUV(bid.householderU(), bid.householderV(), m_naiveU, m_naiveV);
+  m_isInitialized = true;
   return *this;
 }// end compute
 
 
 template<typename MatrixType>
-void BDCSVD<MatrixType>::copyUV(const typename internal::UpperBidiagonalization<MatrixX>::HouseholderUSequenceType& householderU, 
-                                const typename internal::UpperBidiagonalization<MatrixX>::HouseholderVSequenceType& householderV)
+template<typename HouseholderU, typename HouseholderV, typename NaiveU, typename NaiveV>
+void BDCSVD<MatrixType>::copyUV(const HouseholderU &householderU, const HouseholderV &householderV, const NaiveU &naiveU, const NaiveV &naiveV)
 {
   // Note exchange of U and V: m_matrixU is set from m_naiveV and vice versa
-  if (this->computeU()){
-    Index Ucols = this->m_computeThinU ? this->m_nonzeroSingularValues : householderU.cols();
-    this->m_matrixU = MatrixX::Identity(householderU.cols(), Ucols);
-    Index blockCols = this->m_computeThinU ? this->m_nonzeroSingularValues : this->m_diagSize;
-    this->m_matrixU.block(0, 0, this->m_diagSize, blockCols) = 
-        m_naiveV.template cast<Scalar>().block(0, 0, this->m_diagSize, blockCols);
-    this->m_matrixU = householderU * this->m_matrixU;
+  if (computeU())
+  {
+    Index Ucols = m_computeThinU ? m_nonzeroSingularValues : householderU.cols();
+    m_matrixU = MatrixX::Identity(householderU.cols(), Ucols);
+    Index blockCols = m_computeThinU ? m_nonzeroSingularValues : m_diagSize;
+    m_matrixU.topLeftCorner(m_diagSize, blockCols) = naiveV.template cast<Scalar>().topLeftCorner(m_diagSize, blockCols);
+    householderU.applyThisOnTheLeft(m_matrixU);
+  }
+  if (computeV())
+  {
+    Index Vcols = m_computeThinV ? m_nonzeroSingularValues : householderV.cols();
+    m_matrixV = MatrixX::Identity(householderV.cols(), Vcols);
+    Index blockCols = m_computeThinV ? m_nonzeroSingularValues : m_diagSize;
+    m_matrixV.topLeftCorner(m_diagSize, blockCols) = naiveU.template cast<Scalar>().topLeftCorner(m_diagSize, blockCols);
+    householderV.applyThisOnTheLeft(m_matrixV);
   }
-  if (this->computeV()){
-    Index Vcols = this->m_computeThinV ? this->m_nonzeroSingularValues : householderV.cols();
-    this->m_matrixV = MatrixX::Identity(householderV.cols(), Vcols);
-    Index blockCols = this->m_computeThinV ? this->m_nonzeroSingularValues : this->m_diagSize;
-    this->m_matrixV.block(0, 0, this->m_diagSize, blockCols) = 
-        m_naiveU.template cast<Scalar>().block(0, 0, this->m_diagSize, blockCols);
-    this->m_matrixV = householderV * this->m_matrixV;
+}
+
+/** \internal
+  * Performs A = A * B exploiting the special structure of the matrix A. Splitting A as:
+  *  A = [A1]
+  *      [A2]
+  * such that A1.rows()==n1, then we assume that at least half of the columns of A1 and A2 are zeros.
+  * We can thus pack them prior to the the matrix product. However, this is only worth the effort if the matrix is large
+  * enough.
+  */
+template<typename MatrixType>
+void BDCSVD<MatrixType>::structured_update(Block<MatrixXr,Dynamic,Dynamic> A, const MatrixXr &B, Index n1)
+{
+  Index n = A.rows();
+  if(n>100)
+  {
+    // If the matrices are large enough, let's exploit the sparse strucure of A by
+    // splitting it in half (wrt n1), and packing the non-zero columns.
+    DenseIndex n2 = n - n1;
+    MatrixXr A1(n1,n), A2(n2,n), B1(n,n), B2(n,n);
+    Index k1=0, k2=0;
+    for(Index j=0; j<n; ++j)
+    {
+      if( (A.col(j).head(n1).array()!=0).any() )
+      {
+        A1.col(k1) = A.col(j).head(n1);
+        B1.row(k1) = B.row(j);
+        ++k1;
+      }
+      if( (A.col(j).tail(n2).array()!=0).any() )
+      {
+        A2.col(k2) = A.col(j).tail(n2);
+        B2.row(k2) = B.row(j);
+        ++k2;
+      }
+    }
+  
+    A.topRows(n1).noalias()    = A1.leftCols(k1) * B1.topRows(k1);
+    A.bottomRows(n2).noalias() = A2.leftCols(k2) * B2.topRows(k2);
   }
+  else
+    A *= B;  // FIXME this requires a temporary
 }
 
 // The divide algorithm is done "in place", we are always working on subsets of the same matrix. The divide methods takes as argument the 
@@ -352,8 +347,7 @@ void BDCSVD<MatrixType>::copyUV(const typename internal::UpperBidiagonalization<
 //@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)
+void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW, Index firstColW, Index shift)
 {
   // requires nbRows = nbCols + 1;
   using std::pow;
@@ -365,24 +359,22 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
   RealScalar betaK; 
   RealScalar r0; 
   RealScalar lambda, phi, c0, s0;
-  MatrixXr l, f;
+  VectorType 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();
+  if (n < m_algoswap)
+  {
+    JacobiSVD<MatrixXr> b(m_computed.block(firstCol, firstCol, n + 1, n), ComputeFullU | (m_compV ? ComputeFullV : 0)) ;
+    if (m_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);
+      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();
+    if (m_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);
-    }
+    m_computed.diagonal().segment(firstCol + shift, n) = b.singularValues().head(n);
     return;
   }
   // We use the divide and conquer algorithm
@@ -393,7 +385,7 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
   // 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)
+  if (m_compU)
   {
     lambda = m_naiveU(firstCol + k, firstCol + k);
     phi = m_naiveU(firstCol + k + 1, lastCol + 1);
@@ -403,9 +395,8 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
     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)
+  r0 = sqrt((abs(alphaK * lambda) * abs(alphaK * lambda)) + abs(betaK * phi) * abs(betaK * phi));
+  if (m_compU)
   {
     l = m_naiveU.row(firstCol + k).segment(firstCol, k);
     f = m_naiveU.row(firstCol + k + 1).segment(firstCol + k + 1, n - k - 1);
@@ -415,7 +406,7 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
     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 (m_compV) m_naiveV(firstRowW+k, firstColW) = 1;
   if (r0 == 0)
   {
     c0 = 1;
@@ -426,32 +417,27 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
     c0 = alphaK * lambda / r0;
     s0 = betaK * phi / r0;
   }
-  if (compU)
+  if (m_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);
-    }
+      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);
+    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));
+    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; 
+    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; 
+    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
@@ -464,9 +450,8 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
     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();
-
+  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();
 
   // Second part: try to deflate singular values in combined matrix
   deflation(firstCol, lastCol, k, firstRowW, firstColW, shift);
@@ -475,9 +460,12 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
   MatrixXr UofSVD, VofSVD;
   VectorType singVals;
   computeSVDofM(firstCol + shift, n, UofSVD, singVals, VofSVD);
-  if (compU) m_naiveU.block(firstCol, firstCol, n + 1, n + 1) *= UofSVD;
-  else m_naiveU.block(0, firstCol, 2, n + 1) *= UofSVD;
-  if (compV) m_naiveV.block(firstRowW, firstColW, n, n) *= VofSVD;
+  
+  if (m_compU)  structured_update(m_naiveU.block(firstCol, firstCol, n + 1, n + 1), UofSVD, (n+2)/2);
+  else          m_naiveU.middleCols(firstCol, n + 1) *= UofSVD; // FIXME this requires a temporary, and exploit that there are 2 rows at compile time
+  
+  if (m_compV)  structured_update(m_naiveV.block(firstRowW, firstColW, n, n), VofSVD, (n+1)/2);
+  
   m_computed.block(firstCol + shift, firstCol + shift, n, n).setZero();
   m_computed.block(firstCol + shift, firstCol + shift, n, n).diagonal() = singVals;
 }// end divide
@@ -485,7 +473,7 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
 // Compute SVD of m_computed.block(firstCol, firstCol, n + 1, n); this block only has non-zeros in
 // the first column and on the diagonal and has undergone deflation, so diagonal is in increasing
 // order except for possibly the (0,0) entry. The computed SVD is stored U, singVals and V, except
-// that if compV is false, then V is not computed. Singular values are sorted in decreasing order.
+// that if m_compV is false, then V is not computed. Singular values are sorted in decreasing order.
 //
 // TODO Opportunities for optimization: better root finding algo, better stopping criterion, better
 // handling of round-off errors, be consistent in ordering
@@ -493,26 +481,28 @@ template <typename MatrixType>
 void BDCSVD<MatrixType>::computeSVDofM(Index firstCol, Index n, MatrixXr& U, VectorType& singVals, MatrixXr& V)
 {
   // TODO Get rid of these copies (?)
-  ArrayXr col0 = m_computed.block(firstCol, firstCol, n, 1);
+  // FIXME at least preallocate them
+  ArrayXr col0 = m_computed.col(firstCol).segment(firstCol, n);
   ArrayXr diag = m_computed.block(firstCol, firstCol, n, n).diagonal();
   diag(0) = 0;
 
   // compute singular values and vectors (in decreasing order)
   singVals.resize(n);
   U.resize(n+1, n+1);
-  if (compV) V.resize(n, n);
+  if (m_compV) V.resize(n, n);
 
   if (col0.hasNaN() || diag.hasNaN()) return;
 
   ArrayXr shifts(n), mus(n), zhat(n);
+  
   computeSingVals(col0, diag, singVals, shifts, mus);
   perturbCol0(col0, diag, singVals, shifts, mus, zhat);
   computeSingVecs(zhat, diag, singVals, shifts, mus, U, V);
 
   // Reverse order so that singular values in increased order
   singVals.reverseInPlace();
-  U.leftCols(n) = U.leftCols(n).rowwise().reverse().eval();
-  if (compV) V = V.rowwise().reverse().eval();
+  U.leftCols(n) = U.leftCols(n).rowwise().reverse().eval(); // FIXME this requires a temporary
+  if (m_compV) V = V.rowwise().reverse().eval();            // FIXME this requires a temporary
 }
 
 template <typename MatrixType>
@@ -521,10 +511,13 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayXr& col0, const ArrayXr& dia
 {
   using std::abs;
   using std::swap;
+  using std::max;
 
   Index n = col0.size();
-  for (Index k = 0; k < n; ++k) {
-    if (col0(k) == 0) {
+  for (Index k = 0; k < n; ++k)
+  {
+    if (col0(k) == 0)
+    {
       // entry is deflated, so singular value is on diagonal
       singVals(k) = diag(k);
       mus(k) = 0;
@@ -540,27 +533,29 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayXr& col0, const ArrayXr& dia
     RealScalar mid = left + (right-left) / 2;
     RealScalar fMid = 1 + (col0.square() / ((diag + mid) * (diag - mid))).sum();
 
-    RealScalar shift;
-    if (k == n-1 || fMid > 0) shift = left;
-    else shift = right;
+    RealScalar shift = (k == n-1 || fMid > 0) ? left : right;
     
     // measure everything relative to shift
     ArrayXr diagShifted = diag - shift;
     
     // initial guess
     RealScalar muPrev, muCur;
-    if (shift == left) {
+    if (shift == left)
+    {
       muPrev = (right - left) * 0.1;
       if (k == n-1) muCur = right - left;
-      else muCur = (right - left) * 0.5; 
-    } else {
+      else          muCur = (right - left) * 0.5; 
+    }
+    else
+    {
       muPrev = -(right - left) * 0.1;
       muCur = -(right - left) * 0.5;
     }
 
     RealScalar fPrev = 1 + (col0.square() / ((diagShifted - muPrev) * (diag + shift + muPrev))).sum();
     RealScalar fCur = 1 + (col0.square() / ((diagShifted - muCur) * (diag + shift + muCur))).sum();
-    if (abs(fPrev) < abs(fCur)) {
+    if (abs(fPrev) < abs(fCur))
+    {
       swap(fPrev, fCur);
       swap(muPrev, muCur);
     }
@@ -568,7 +563,8 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayXr& col0, const ArrayXr& dia
     // rational interpolation: fit a function of the form a / mu + b through the two previous
     // iterates and use its zero to compute the next iterate
     bool useBisection = false;
-    while (abs(muCur - muPrev) > 8 * NumTraits<RealScalar>::epsilon() * (std::max)(abs(muCur), abs(muPrev)) && fCur != fPrev && !useBisection) {
+    while (abs(muCur - muPrev) > 8 * NumTraits<RealScalar>::epsilon() * (max)(abs(muCur), abs(muPrev)) && fCur != fPrev && !useBisection)
+    {
       ++m_numIters;
 
       RealScalar a = (fCur - fPrev) / (1/muCur - 1/muPrev);
@@ -584,13 +580,17 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayXr& col0, const ArrayXr& dia
     }
 
     // fall back on bisection method if rational interpolation did not work
-    if (useBisection) {
+    if (useBisection)
+    {
       RealScalar leftShifted, rightShifted;
-      if (shift == left) {
+      if (shift == left)
+      {
         leftShifted = 1e-30;
         if (k == 0) rightShifted = right - left;
-        else rightShifted = (right - left) * 0.6; // theoretically we can take 0.5, but let's be safe
-      } else {
+        else        rightShifted = (right - left) * 0.6; // theoretically we can take 0.5, but let's be safe
+      }
+      else
+      {
         leftShifted = -(right - left) * 0.6;
         rightShifted = -1e-30;
       }
@@ -599,13 +599,17 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayXr& col0, const ArrayXr& dia
       RealScalar fRight = 1 + (col0.square() / ((diagShifted - rightShifted) * (diag + shift + rightShifted))).sum();
       assert(fLeft * fRight < 0);
       
-      while (rightShifted - leftShifted > 2 * NumTraits<RealScalar>::epsilon() * (std::max)(abs(leftShifted), abs(rightShifted))) {
+      while (rightShifted - leftShifted > 2 * NumTraits<RealScalar>::epsilon() * (max)(abs(leftShifted), abs(rightShifted)))
+      {
         RealScalar midShifted = (leftShifted + rightShifted) / 2;
         RealScalar fMid = 1 + (col0.square() / ((diagShifted - midShifted) * (diag + shift + midShifted))).sum();
-        if (fLeft * fMid < 0) {
+        if (fLeft * fMid < 0)
+        {
           rightShifted = midShifted;
           fRight = fMid;
-        } else {
+        }
+        else
+        {
           leftShifted = midShifted;
           fLeft = fMid;
         }
@@ -632,13 +636,15 @@ void BDCSVD<MatrixType>::perturbCol0
    (const ArrayXr& col0, const ArrayXr& diag, const VectorType& singVals,
     const ArrayXr& shifts, const ArrayXr& mus, ArrayXr& zhat)
 {
+  using std::sqrt;
   Index n = col0.size();
-  for (Index k = 0; k < n; ++k) {
+  for (Index k = 0; k < n; ++k)
+  {
     if (col0(k) == 0) 
       zhat(k) = 0;
-    else {
+    else
+    {
       // see equation (3.6)
-      using std::sqrt;
       RealScalar tmp = 
         sqrt(
              (singVals(n-1) + diag(k)) * (mus(n-1) + (shifts(n-1) - diag(k)))
@@ -664,16 +670,21 @@ void BDCSVD<MatrixType>::computeSingVecs
     const ArrayXr& shifts, const ArrayXr& mus, MatrixXr& U, MatrixXr& V)
 {
   Index n = zhat.size();
-  for (Index k = 0; k < n; ++k) {
-    if (zhat(k) == 0) {
+  for (Index k = 0; k < n; ++k)
+  {
+    if (zhat(k) == 0)
+    {
       U.col(k) = VectorType::Unit(n+1, k);
-      if (compV) V.col(k) = VectorType::Unit(n, k);
-    } else {
+      if (m_compV) V.col(k) = VectorType::Unit(n, k);
+    }
+    else
+    {
       U.col(k).head(n) = zhat / (((diag - shifts(k)) - mus(k)) * (diag + singVals[k]));
       U(n,k) = 0;
       U.col(k).normalize();
     
-      if (compV) {
+      if (m_compV)
+      {
         V.col(k).tail(n-1) = (diag * zhat / (((diag - shifts(k)) - mus(k)) * (diag + singVals[k]))).tail(n-1);
         V(0,k) = -1;
         V.col(k).normalize();
@@ -688,15 +699,17 @@ void BDCSVD<MatrixType>::computeSingVecs
 // 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){
+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;
+  if (r == 0)
+  {
+    m_computed(i, i) = 0;
     return;
   }
   c/=r;
@@ -704,7 +717,8 @@ void BDCSVD<MatrixType>::deflation43(Index firstCol, Index shift, Index i, Index
   m_computed(firstCol + shift, firstCol + shift) = r;  
   m_computed(i, firstCol + shift) = 0;
   m_computed(i, i) = 0;
-  if (compU){
+  if (m_compU)
+  {
     m_naiveU.col(firstCol).segment(firstCol,size) = 
       c * m_naiveU.col(firstCol).segment(firstCol, size) - 
       s * m_naiveU.col(i).segment(firstCol, size) ;
@@ -720,7 +734,8 @@ void BDCSVD<MatrixType>::deflation43(Index firstCol, Index shift, Index i, Index
 // 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){
+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;
@@ -728,7 +743,8 @@ void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index fi
   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){
+  if (r==0)
+  {
     m_computed(firstColm + i, firstColm + i) = m_computed(firstColm + j, firstColm + j);
     return;
   }
@@ -737,7 +753,8 @@ void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index fi
   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){
+  if (m_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) ;
@@ -746,7 +763,8 @@ void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index fi
       (c + s*s/c) *  m_naiveU.col(firstColu + j).segment(firstColu, size) + 
       (s/c) * m_naiveU.col(firstColu + i).segment(firstColu, size);
   } 
-  if (compV){
+  if (m_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) ;
@@ -760,72 +778,56 @@ void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index fi
 
 // acts on block from (firstCol+shift, firstCol+shift) to (lastCol+shift, lastCol+shift) [inclusive]
 template <typename MatrixType>
-void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift){
+void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift)
+{
   //condition 4.1
   using std::sqrt;
+  using std::abs;
   const Index length = lastCol + 1 - firstCol;
   RealScalar norm1 = m_computed.block(firstCol+shift, firstCol+shift, length, 1).squaredNorm();
   RealScalar norm2 = m_computed.block(firstCol+shift, firstCol+shift, length, length).diagonal().squaredNorm();
-  RealScalar EPS = 10 * NumTraits<RealScalar>::epsilon() * sqrt(norm1 + norm2);
-  if (m_computed(firstCol + shift, firstCol + shift) < EPS){
-    m_computed(firstCol + shift, firstCol + shift) = EPS;
-  }
+  RealScalar epsilon = 10 * NumTraits<RealScalar>::epsilon() * sqrt(norm1 + norm2);
+  if (m_computed(firstCol + shift, firstCol + shift) < epsilon)
+    m_computed(firstCol + shift, firstCol + shift) = epsilon;
 
   //condition 4.2
-  for (Index i=firstCol + shift + 1;i<=lastCol + shift;i++){
-    if (std::abs(m_computed(i, firstCol + shift)) < EPS){
+  for (Index i=firstCol + shift + 1;i<=lastCol + shift;i++)
+    if (abs(m_computed(i, firstCol + shift)) < epsilon)
       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){
+  for (Index i=firstCol + shift + 1;i<=lastCol + shift; i++)
+    if (m_computed(i, i) < epsilon)
       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];
+  Index *permutation = new Index[length]; // FIXME avoid repeated dynamic memory allocation
 
-  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++;
-      }
-    }
+  for (Index p =1; p < length; p++)
+  {
+         if (i> firstCol + shift + k)             permutation[p] = j++;
+    else if (j> lastCol + shift)                  permutation[p] = i++;
+    else if (m_computed(i, i) < m_computed(j, j)) permutation[p] = j++;
+    else                                          permutation[p] = 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++){
+  Index *realInd = new Index[length];  // FIXME avoid repeated dynamic memory allocation
+  Index *realCol = new Index[length];  // FIXME avoid repeated dynamic memory allocation
+  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++){
+  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;
@@ -842,25 +844,25 @@ void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index
     m_computed(J, Zero) = aux;
 
     // change columns
-    if (compU) {
+    if (m_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;
+      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;      
+      m_naiveU.col(I - shift).template head<2>() = m_naiveU.col(J - shift).segment(0, 2);
+      m_naiveU.col(J - shift).template head<2>() = temp;      
     }
-    if (compV) {
+    if (m_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;
+      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
@@ -869,53 +871,16 @@ void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index
     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;
+  for (Index i = firstCol + shift + 1; i<lastCol + shift;i++)
+    if ((m_computed(i + 1, i + 1) - m_computed(i, i)) < epsilon)
+      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 
diff --git a/unsupported/Eigen/src/BDCSVD/CMakeLists.txt b/unsupported/Eigen/src/BDCSVD/CMakeLists.txt
new file mode 100644
index 000000000..73b89ea18
--- /dev/null
+++ b/unsupported/Eigen/src/BDCSVD/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_BDCSVD_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_BDCSVD_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}unsupported/Eigen/src/BDCSVD COMPONENT Devel
+  )
diff --git a/unsupported/Eigen/src/SVD/TODOBdcsvd.txt b/unsupported/Eigen/src/BDCSVD/TODOBdcsvd.txt
index 0bc9a46e6..0bc9a46e6 100644
--- a/unsupported/Eigen/src/SVD/TODOBdcsvd.txt
+++ b/unsupported/Eigen/src/BDCSVD/TODOBdcsvd.txt
diff --git a/unsupported/Eigen/src/SVD/doneInBDCSVD.txt b/unsupported/Eigen/src/BDCSVD/doneInBDCSVD.txt
index 8563ddab8..8563ddab8 100644
--- a/unsupported/Eigen/src/SVD/doneInBDCSVD.txt
+++ b/unsupported/Eigen/src/BDCSVD/doneInBDCSVD.txt
diff --git a/unsupported/Eigen/src/CMakeLists.txt b/unsupported/Eigen/src/CMakeLists.txt
index 8eb2808e3..654a2327f 100644
--- a/unsupported/Eigen/src/CMakeLists.txt
+++ b/unsupported/Eigen/src/CMakeLists.txt
@@ -12,3 +12,4 @@ ADD_SUBDIRECTORY(Skyline)
 ADD_SUBDIRECTORY(SparseExtra)
 ADD_SUBDIRECTORY(KroneckerProduct)
 ADD_SUBDIRECTORY(Splines)
+ADD_SUBDIRECTORY(BDCSVD)
diff --git a/unsupported/Eigen/src/IterativeSolvers/DGMRES.h b/unsupported/Eigen/src/IterativeSolvers/DGMRES.h
index 9fcc8a8d9..0e1b7d977 100644
--- a/unsupported/Eigen/src/IterativeSolvers/DGMRES.h
+++ b/unsupported/Eigen/src/IterativeSolvers/DGMRES.h
@@ -108,6 +108,7 @@ class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> >
     using Base::m_isInitialized;
     using Base::m_tolerance; 
   public:
+    using Base::_solve_impl;
     typedef _MatrixType MatrixType;
     typedef typename MatrixType::Scalar Scalar;
     typedef typename MatrixType::Index Index;
@@ -138,25 +139,9 @@ class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> >
 
   ~DGMRES() {}
   
-  /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A
-    * \a x0 as an initial solution.
-    *
-    * \sa compute()
-    */
-  template<typename Rhs,typename Guess>
-  inline const internal::solve_retval_with_guess<DGMRES, Rhs, Guess>
-  solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const
-  {
-    eigen_assert(m_isInitialized && "DGMRES is not initialized.");
-    eigen_assert(Base::rows()==b.rows()
-              && "DGMRES::solve(): invalid number of rows of the right hand side matrix b");
-    return internal::solve_retval_with_guess
-            <DGMRES, Rhs, Guess>(*this, b.derived(), x0);
-  }
-  
   /** \internal */
   template<typename Rhs,typename Dest>
-  void _solveWithGuess(const Rhs& b, Dest& x) const
+  void _solve_with_guess_impl(const Rhs& b, Dest& x) const
   {    
     bool failed = false;
     for(int j=0; j<b.cols(); ++j)
@@ -175,10 +160,10 @@ class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> >
 
   /** \internal */
   template<typename Rhs,typename Dest>
-  void _solve(const Rhs& b, Dest& x) const
+  void _solve_impl(const Rhs& b, MatrixBase<Dest>& x) const
   {
     x = b;
-    _solveWithGuess(b,x);
+    _solve_with_guess_impl(b,x.derived());
   }
   /** 
    * Get the restart value
@@ -522,21 +507,5 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresApplyDeflation(const RhsType &x,
   return 0; 
 }
 
-namespace internal {
-
-  template<typename _MatrixType, typename _Preconditioner, typename Rhs>
-struct solve_retval<DGMRES<_MatrixType, _Preconditioner>, Rhs>
-  : solve_retval_base<DGMRES<_MatrixType, _Preconditioner>, Rhs>
-{
-  typedef DGMRES<_MatrixType, _Preconditioner> Dec;
-  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
-
-  template<typename Dest> void evalTo(Dest& dst) const
-  {
-    dec()._solve(rhs(),dst);
-  }
-};
-} // end namespace internal
-
 } // end namespace Eigen
 #endif 
diff --git a/unsupported/Eigen/src/IterativeSolvers/GMRES.h b/unsupported/Eigen/src/IterativeSolvers/GMRES.h
index 67498705b..cd15ce0bf 100644
--- a/unsupported/Eigen/src/IterativeSolvers/GMRES.h
+++ b/unsupported/Eigen/src/IterativeSolvers/GMRES.h
@@ -281,6 +281,7 @@ private:
   int m_restart;
 
 public:
+  using Base::_solve_impl;
   typedef _MatrixType MatrixType;
   typedef typename MatrixType::Scalar Scalar;
   typedef typename MatrixType::Index Index;
@@ -315,25 +316,9 @@ public:
     */
   void set_restart(const int restart) { m_restart=restart; }
 
-  /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A
-    * \a x0 as an initial solution.
-    *
-    * \sa compute()
-    */
-  template<typename Rhs,typename Guess>
-  inline const internal::solve_retval_with_guess<GMRES, Rhs, Guess>
-  solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const
-  {
-    eigen_assert(m_isInitialized && "GMRES is not initialized.");
-    eigen_assert(Base::rows()==b.rows()
-              && "GMRES::solve(): invalid number of rows of the right hand side matrix b");
-    return internal::solve_retval_with_guess
-            <GMRES, Rhs, Guess>(*this, b.derived(), x0);
-  }
-
   /** \internal */
   template<typename Rhs,typename Dest>
-  void _solveWithGuess(const Rhs& b, Dest& x) const
+  void _solve_with_guess_impl(const Rhs& b, Dest& x) const
   {
     bool failed = false;
     for(int j=0; j<b.cols(); ++j)
@@ -353,35 +338,17 @@ public:
 
   /** \internal */
   template<typename Rhs,typename Dest>
-  void _solve(const Rhs& b, Dest& x) const
+  void _solve_impl(const Rhs& b, MatrixBase<Dest> &x) const
   {
     x = b;
     if(x.squaredNorm() == 0) return; // Check Zero right hand side
-    _solveWithGuess(b,x);
+    _solve_with_guess_impl(b,x.derived());
   }
 
 protected:
 
 };
 
-
-namespace internal {
-
-  template<typename _MatrixType, typename _Preconditioner, typename Rhs>
-struct solve_retval<GMRES<_MatrixType, _Preconditioner>, Rhs>
-  : solve_retval_base<GMRES<_MatrixType, _Preconditioner>, Rhs>
-{
-  typedef GMRES<_MatrixType, _Preconditioner> Dec;
-  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
-
-  template<typename Dest> void evalTo(Dest& dst) const
-  {
-    dec()._solve(rhs(),dst);
-  }
-};
-
-} // end namespace internal
-
 } // end namespace Eigen
 
 #endif // EIGEN_GMRES_H
diff --git a/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h b/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
index 661c1f2e0..dd43de6b3 100644
--- a/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
+++ b/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
@@ -27,8 +27,11 @@ namespace Eigen {
  */
 
 template <typename Scalar, int _UpLo = Lower, typename _OrderingType = NaturalOrdering<int> >
-class IncompleteCholesky : internal::noncopyable
+class IncompleteCholesky : public SparseSolverBase<IncompleteCholesky<Scalar,_UpLo,_OrderingType> >
 {
+  protected:
+    typedef SparseSolverBase<IncompleteCholesky<Scalar,_UpLo,_OrderingType> > Base;
+    using Base::m_isInitialized;
   public:
     typedef SparseMatrix<Scalar,ColMajor> MatrixType;
     typedef _OrderingType OrderingType;
@@ -89,7 +92,7 @@ class IncompleteCholesky : internal::noncopyable
     }
     
     template<typename Rhs, typename Dest>
-    void _solve(const Rhs& b, Dest& x) const
+    void _solve_impl(const Rhs& b, Dest& x) const
     {
       eigen_assert(m_factorizationIsOk && "factorize() should be called first");
       if (m_perm.rows() == b.rows())
@@ -103,22 +106,13 @@ class IncompleteCholesky : internal::noncopyable
         x = m_perm * x;
       x = m_scal.asDiagonal() * x;
     }
-    template<typename Rhs> inline const internal::solve_retval<IncompleteCholesky, Rhs>
-    solve(const MatrixBase<Rhs>& b) const
-    {
-      eigen_assert(m_factorizationIsOk && "IncompleteLLT did not succeed");
-      eigen_assert(m_isInitialized && "IncompleteLLT is not initialized.");
-      eigen_assert(cols()==b.rows()
-                && "IncompleteLLT::solve(): invalid number of rows of the right hand side matrix b");
-      return internal::solve_retval<IncompleteCholesky, Rhs>(*this, b.derived());
-    }
+
   protected:
     SparseMatrix<Scalar,ColMajor> m_L;  // The lower part stored in CSC
     ScalarType m_scal; // The vector for scaling the matrix 
     Scalar m_shift; //The initial shift parameter
     bool m_analysisIsOk; 
     bool m_factorizationIsOk; 
-    bool m_isInitialized;
     ComputationInfo m_info;
     PermutationType m_perm; 
     
@@ -256,22 +250,6 @@ inline void IncompleteCholesky<Scalar,_UpLo, OrderingType>::updateList(const Idx
     listCol[rowIdx(jk)].push_back(col);
   }
 }
-namespace internal {
-
-template<typename _Scalar, int _UpLo, typename OrderingType, typename Rhs>
-struct solve_retval<IncompleteCholesky<_Scalar,  _UpLo, OrderingType>, Rhs>
-  : solve_retval_base<IncompleteCholesky<_Scalar, _UpLo, OrderingType>, Rhs>
-{
-  typedef IncompleteCholesky<_Scalar, _UpLo, OrderingType> Dec;
-  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
-
-  template<typename Dest> void evalTo(Dest& dst) const
-  {
-    dec()._solve(rhs(),dst);
-  }
-};
-
-} // end namespace internal
 
 } // end namespace Eigen 
 
diff --git a/unsupported/Eigen/src/IterativeSolvers/IncompleteLU.h b/unsupported/Eigen/src/IterativeSolvers/IncompleteLU.h
index 67e780181..7d08c3515 100644
--- a/unsupported/Eigen/src/IterativeSolvers/IncompleteLU.h
+++ b/unsupported/Eigen/src/IterativeSolvers/IncompleteLU.h
@@ -13,8 +13,12 @@
 namespace Eigen { 
 
 template <typename _Scalar>
-class IncompleteLU
+class IncompleteLU : public SparseSolverBase<IncompleteLU<_Scalar> >
 {
+  protected:
+    typedef SparseSolverBase<IncompleteLU<_Scalar> > Base;
+    using Base::m_isInitialized;
+    
     typedef _Scalar Scalar;
     typedef Matrix<Scalar,Dynamic,1> Vector;
     typedef typename Vector::Index Index;
@@ -23,10 +27,10 @@ class IncompleteLU
   public:
     typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
 
-    IncompleteLU() : m_isInitialized(false) {}
+    IncompleteLU() {}
 
     template<typename MatrixType>
-    IncompleteLU(const MatrixType& mat) : m_isInitialized(false)
+    IncompleteLU(const MatrixType& mat)
     {
       compute(mat);
     }
@@ -71,43 +75,16 @@ class IncompleteLU
     }
 
     template<typename Rhs, typename Dest>
-    void _solve(const Rhs& b, Dest& x) const
+    void _solve_impl(const Rhs& b, Dest& x) const
     {
       x = m_lu.template triangularView<UnitLower>().solve(b);
       x = m_lu.template triangularView<Upper>().solve(x);
     }
 
-    template<typename Rhs> inline const internal::solve_retval<IncompleteLU, Rhs>
-    solve(const MatrixBase<Rhs>& b) const
-    {
-      eigen_assert(m_isInitialized && "IncompleteLU is not initialized.");
-      eigen_assert(cols()==b.rows()
-                && "IncompleteLU::solve(): invalid number of rows of the right hand side matrix b");
-      return internal::solve_retval<IncompleteLU, Rhs>(*this, b.derived());
-    }
-
   protected:
     FactorType m_lu;
-    bool m_isInitialized;
-};
-
-namespace internal {
-
-template<typename _MatrixType, typename Rhs>
-struct solve_retval<IncompleteLU<_MatrixType>, Rhs>
-  : solve_retval_base<IncompleteLU<_MatrixType>, Rhs>
-{
-  typedef IncompleteLU<_MatrixType> Dec;
-  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
-
-  template<typename Dest> void evalTo(Dest& dst) const
-  {
-    dec()._solve(rhs(),dst);
-  }
 };
 
-} // end namespace internal
-
 } // end namespace Eigen
 
 #endif // EIGEN_INCOMPLETE_LU_H
diff --git a/unsupported/Eigen/src/IterativeSolvers/MINRES.h b/unsupported/Eigen/src/IterativeSolvers/MINRES.h
index 98f9ecc17..aaf42c78a 100644
--- a/unsupported/Eigen/src/IterativeSolvers/MINRES.h
+++ b/unsupported/Eigen/src/IterativeSolvers/MINRES.h
@@ -2,7 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2012 Giacomo Po <gpo@ucla.edu>
-// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.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
@@ -217,6 +217,7 @@ namespace Eigen {
         using Base::m_info;
         using Base::m_isInitialized;
     public:
+        using Base::_solve_impl;
         typedef _MatrixType MatrixType;
         typedef typename MatrixType::Scalar Scalar;
         typedef typename MatrixType::Index Index;
@@ -244,26 +245,10 @@ namespace Eigen {
         
         /** Destructor. */
         ~MINRES(){}
-		
-        /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A
-         * \a x0 as an initial solution.
-         *
-         * \sa compute()
-         */
-        template<typename Rhs,typename Guess>
-        inline const internal::solve_retval_with_guess<MINRES, Rhs, Guess>
-        solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const
-        {
-            eigen_assert(m_isInitialized && "MINRES is not initialized.");
-            eigen_assert(Base::rows()==b.rows()
-                         && "MINRES::solve(): invalid number of rows of the right hand side matrix b");
-            return internal::solve_retval_with_guess
-            <MINRES, Rhs, Guess>(*this, b.derived(), x0);
-        }
-        
+
         /** \internal */
         template<typename Rhs,typename Dest>
-        void _solveWithGuess(const Rhs& b, Dest& x) const
+        void _solve_with_guess_impl(const Rhs& b, Dest& x) const
         {
             m_iterations = Base::maxIterations();
             m_error = Base::m_tolerance;
@@ -284,33 +269,16 @@ namespace Eigen {
         
         /** \internal */
         template<typename Rhs,typename Dest>
-        void _solve(const Rhs& b, Dest& x) const
+        void _solve_impl(const Rhs& b, MatrixBase<Dest> &x) const
         {
             x.setZero();
-            _solveWithGuess(b,x);
+            _solve_with_guess_impl(b,x.derived());
         }
         
     protected:
         
     };
-    
-    namespace internal {
-        
-        template<typename _MatrixType, int _UpLo, typename _Preconditioner, typename Rhs>
-        struct solve_retval<MINRES<_MatrixType,_UpLo,_Preconditioner>, Rhs>
-        : solve_retval_base<MINRES<_MatrixType,_UpLo,_Preconditioner>, Rhs>
-        {
-            typedef MINRES<_MatrixType,_UpLo,_Preconditioner> Dec;
-            EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
-            
-            template<typename Dest> void evalTo(Dest& dst) const
-            {
-                dec()._solve(rhs(),dst);
-            }
-        };
-        
-    } // end namespace internal
-    
+
 } // end namespace Eigen
 
 #endif // EIGEN_MINRES_H
diff --git a/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h b/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h
index b8f2cba17..72e25db19 100644
--- a/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h
+++ b/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h
@@ -154,16 +154,41 @@ void KroneckerProductSparse<Lhs,Rhs>::evalTo(Dest& dst) const
   dst.resize(this->rows(), this->cols());
   dst.resizeNonZeros(0);
   
+  // 1 - evaluate the operands if needed:
+  typedef typename internal::nested_eval<Lhs,10>::type Lhs1;
+  typedef typename internal::remove_all<Lhs1>::type Lhs1Cleaned;
+  const Lhs1 lhs1(m_A);
+  typedef typename internal::nested_eval<Rhs,10>::type Rhs1;
+  typedef typename internal::remove_all<Rhs1>::type Rhs1Cleaned;
+  const Rhs1 rhs1(m_B);
+  
+  // 2 - construct a SparseView for dense operands
+  typedef typename internal::conditional<internal::is_same<typename internal::traits<Lhs1Cleaned>::StorageKind,Sparse>::value, Lhs1, SparseView<const Lhs1Cleaned> >::type Lhs2;
+  typedef typename internal::remove_all<Lhs2>::type Lhs2Cleaned;
+  const Lhs2 lhs2(lhs1);
+  typedef typename internal::conditional<internal::is_same<typename internal::traits<Rhs1Cleaned>::StorageKind,Sparse>::value, Rhs1, SparseView<const Rhs1Cleaned> >::type Rhs2;
+  typedef typename internal::remove_all<Rhs2>::type Rhs2Cleaned;
+  const Rhs2 rhs2(rhs1);
+  
+  // 3 - construct respective evaluators
+  typedef typename internal::evaluator<Lhs2Cleaned>::type LhsEval;
+  LhsEval lhsEval(lhs2);
+  typedef typename internal::evaluator<Rhs2Cleaned>::type RhsEval;
+  RhsEval rhsEval(rhs2);
+  
+  typedef typename LhsEval::InnerIterator LhsInnerIterator;
+  typedef typename RhsEval::InnerIterator RhsInnerIterator;
+  
   // compute number of non-zeros per innervectors of dst
   {
     VectorXi nnzA = VectorXi::Zero(Dest::IsRowMajor ? m_A.rows() : m_A.cols());
     for (Index kA=0; kA < m_A.outerSize(); ++kA)
-      for (typename Lhs::InnerIterator itA(m_A,kA); itA; ++itA)
+      for (LhsInnerIterator itA(lhsEval,kA); itA; ++itA)
         nnzA(Dest::IsRowMajor ? itA.row() : itA.col())++;
       
     VectorXi nnzB = VectorXi::Zero(Dest::IsRowMajor ? m_B.rows() : m_B.cols());
     for (Index kB=0; kB < m_B.outerSize(); ++kB)
-      for (typename Rhs::InnerIterator itB(m_B,kB); itB; ++itB)
+      for (RhsInnerIterator itB(rhsEval,kB); itB; ++itB)
         nnzB(Dest::IsRowMajor ? itB.row() : itB.col())++;
     
     Matrix<int,Dynamic,Dynamic,ColMajor> nnzAB = nnzB * nnzA.transpose();
@@ -174,9 +199,9 @@ void KroneckerProductSparse<Lhs,Rhs>::evalTo(Dest& dst) const
   {
     for (Index kB=0; kB < m_B.outerSize(); ++kB)
     {
-      for (typename Lhs::InnerIterator itA(m_A,kA); itA; ++itA)
+      for (LhsInnerIterator itA(lhsEval,kA); itA; ++itA)
       {
-        for (typename Rhs::InnerIterator itB(m_B,kB); itB; ++itB)
+        for (RhsInnerIterator itB(rhsEval,kB); itB; ++itB)
         {
           const Index i = itA.row() * Br + itB.row(),
                       j = itA.col() * Bc + itB.col();
@@ -201,8 +226,7 @@ struct traits<KroneckerProduct<_Lhs,_Rhs> >
     Rows = size_at_compile_time<traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime>::ret,
     Cols = size_at_compile_time<traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime>::ret,
     MaxRows = size_at_compile_time<traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime>::ret,
-    MaxCols = size_at_compile_time<traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime>::ret,
-    CoeffReadCost = Lhs::CoeffReadCost + Rhs::CoeffReadCost + NumTraits<Scalar>::MulCost
+    MaxCols = size_at_compile_time<traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime>::ret
   };
 
   typedef Matrix<Scalar,Rows,Cols> ReturnType;
@@ -215,7 +239,7 @@ struct traits<KroneckerProductSparse<_Lhs,_Rhs> >
   typedef typename remove_all<_Lhs>::type Lhs;
   typedef typename remove_all<_Rhs>::type Rhs;
   typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
-  typedef typename promote_storage_type<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind>::ret StorageKind;
+  typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind, scalar_product_op<typename Lhs::Scalar, typename Rhs::Scalar> >::ret StorageKind;
   typedef typename promote_index_type<typename Lhs::Index, typename Rhs::Index>::type Index;
 
   enum {
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
index 160120d03..9e0545660 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
@@ -392,14 +392,15 @@ template<typename Derived> struct MatrixExponentialReturnValue
     template <typename ResultType>
     inline void evalTo(ResultType& result) const
     {
-      internal::matrix_exp_compute(m_src, result);
+      const typename internal::nested_eval<Derived, 10>::type tmp(m_src);
+      internal::matrix_exp_compute(tmp, result);
     }
 
     Index rows() const { return m_src.rows(); }
     Index cols() const { return m_src.cols(); }
 
   protected:
-    const typename internal::nested<Derived, 10>::type m_src;
+    const typename internal::nested<Derived>::type m_src;
 };
 
 namespace internal {
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
index a35c11be5..b68aae5e8 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
@@ -485,7 +485,7 @@ template<typename Derived> class MatrixFunctionReturnValue
     typedef typename internal::stem_function<Scalar>::type StemFunction;
 
   protected:
-    typedef typename internal::nested<Derived, 10>::type DerivedNested;
+    typedef typename internal::nested<Derived>::type DerivedNested;
 
   public:
 
@@ -503,18 +503,19 @@ template<typename Derived> class MatrixFunctionReturnValue
     template <typename ResultType>
     inline void evalTo(ResultType& result) const
     {
-      typedef typename internal::remove_all<DerivedNested>::type DerivedNestedClean;
-      typedef internal::traits<DerivedNestedClean> Traits;
+      typedef typename internal::nested_eval<Derived, 10>::type NestedEvalType;
+      typedef typename internal::remove_all<NestedEvalType>::type NestedEvalTypeClean;
+      typedef internal::traits<NestedEvalTypeClean> Traits;
       static const int RowsAtCompileTime = Traits::RowsAtCompileTime;
       static const int ColsAtCompileTime = Traits::ColsAtCompileTime;
-      static const int Options = DerivedNestedClean::Options;
+      static const int Options = NestedEvalTypeClean::Options;
       typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;
       typedef Matrix<ComplexScalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType;
 
       typedef internal::MatrixFunctionAtomic<DynMatrixType> AtomicType;
       AtomicType atomic(m_f);
 
-      internal::matrix_function_compute<DerivedNestedClean>::run(m_A, atomic, result);
+      internal::matrix_function_compute<NestedEvalTypeClean>::run(m_A, atomic, result);
     }
 
     Index rows() const { return m_A.rows(); }
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h b/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
index d46ccc145..42b60b9b1 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
@@ -310,7 +310,7 @@ public:
   typedef typename Derived::Index Index;
 
 protected:
-  typedef typename internal::nested<Derived, 10>::type DerivedNested;
+  typedef typename internal::nested<Derived>::type DerivedNested;
 
 public:
 
@@ -327,17 +327,18 @@ public:
   template <typename ResultType>
   inline void evalTo(ResultType& result) const
   {
-    typedef typename internal::remove_all<DerivedNested>::type DerivedNestedClean;
-    typedef internal::traits<DerivedNestedClean> Traits;
+    typedef typename internal::nested_eval<Derived, 10>::type DerivedEvalType;
+    typedef typename internal::remove_all<DerivedEvalType>::type DerivedEvalTypeClean;
+    typedef internal::traits<DerivedEvalTypeClean> Traits;
     static const int RowsAtCompileTime = Traits::RowsAtCompileTime;
     static const int ColsAtCompileTime = Traits::ColsAtCompileTime;
-    static const int Options = DerivedNestedClean::Options;
+    static const int Options = DerivedEvalTypeClean::Options;
     typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;
     typedef Matrix<ComplexScalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType;
     typedef internal::MatrixLogarithmAtomic<DynMatrixType> AtomicType;
     AtomicType atomic;
     
-    internal::matrix_function_compute<DerivedNestedClean>::run(m_A, atomic, result);
+    internal::matrix_function_compute<DerivedEvalTypeClean>::run(m_A, atomic, result);
   }
 
   Index rows() const { return m_A.rows(); }
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h b/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h
index 8ca4f4864..3a4d6eb3f 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h
@@ -320,7 +320,7 @@ template<typename Derived> class MatrixSquareRootReturnValue
 {
   protected:
     typedef typename Derived::Index Index;
-    typedef typename internal::nested<Derived, 10>::type DerivedNested;
+    typedef typename internal::nested<Derived>::type DerivedNested;
 
   public:
     /** \brief Constructor.
@@ -338,8 +338,10 @@ template<typename Derived> class MatrixSquareRootReturnValue
     template <typename ResultType>
     inline void evalTo(ResultType& result) const
     {
-      typedef typename internal::remove_all<DerivedNested>::type DerivedNestedClean;
-      internal::matrix_sqrt_compute<DerivedNestedClean>::run(m_src, result);
+      typedef typename internal::nested_eval<Derived, 10>::type DerivedEvalType;
+      typedef typename internal::remove_all<DerivedEvalType>::type DerivedEvalTypeClean;
+      DerivedEvalType tmp(m_src);
+      internal::matrix_sqrt_compute<DerivedEvalTypeClean>::run(tmp, result);
     }
 
     Index rows() const { return m_src.rows(); }
diff --git a/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h b/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
index ecb8dccf4..69106ddc5 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
@@ -45,18 +45,24 @@ namespace LevenbergMarquardtSpace {
 template<typename FunctorType, typename Scalar=double>
 class LevenbergMarquardt
 {
+    static Scalar sqrt_epsilon()
+    {
+      using std::sqrt;
+      return sqrt(NumTraits<Scalar>::epsilon());
+    }
+    
 public:
     LevenbergMarquardt(FunctorType &_functor)
         : functor(_functor) { nfev = njev = iter = 0;  fnorm = gnorm = 0.; useExternalScaling=false; }
 
     typedef DenseIndex Index;
-
+    
     struct Parameters {
         Parameters()
             : factor(Scalar(100.))
             , maxfev(400)
-            , ftol(sqrt_(NumTraits<Scalar>::epsilon()))
-            , xtol(sqrt_(NumTraits<Scalar>::epsilon()))
+            , ftol(sqrt_epsilon())
+            , xtol(sqrt_epsilon())
             , gtol(Scalar(0.))
             , epsfcn(Scalar(0.)) {}
         Scalar factor;
@@ -72,7 +78,7 @@ public:
 
     LevenbergMarquardtSpace::Status lmder1(
             FVectorType &x,
-            const Scalar tol = sqrt_(NumTraits<Scalar>::epsilon())
+            const Scalar tol = sqrt_epsilon()
             );
 
     LevenbergMarquardtSpace::Status minimize(FVectorType &x);
@@ -83,12 +89,12 @@ public:
             FunctorType &functor,
             FVectorType &x,
             Index *nfev,
-            const Scalar tol = sqrt_(NumTraits<Scalar>::epsilon())
+            const Scalar tol = sqrt_epsilon()
             );
 
     LevenbergMarquardtSpace::Status lmstr1(
             FVectorType  &x,
-            const Scalar tol = sqrt_(NumTraits<Scalar>::epsilon())
+            const Scalar tol = sqrt_epsilon()
             );
 
     LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType  &x);
@@ -109,7 +115,6 @@ public:
 
     Scalar lm_param(void) { return par; }
 private:
-    static Scalar sqrt_(const Scalar& x) { using std::sqrt; return sqrt(x); }
     
     FunctorType &functor;
     Index n;
diff --git a/unsupported/Eigen/src/SVD/CMakeLists.txt b/unsupported/Eigen/src/SVD/CMakeLists.txt
deleted file mode 100644
index b40baf092..000000000
--- a/unsupported/Eigen/src/SVD/CMakeLists.txt
+++ /dev/null
@@ -1,6 +0,0 @@
-FILE(GLOB Eigen_SVD_SRCS "*.h")
-
-INSTALL(FILES
-  ${Eigen_SVD_SRCS}
-  DESTINATION ${INCLUDE_INSTALL_DIR}unsupported/Eigen/src/SVD COMPONENT Devel
-  )
diff --git a/unsupported/Eigen/src/SVD/JacobiSVD.h b/unsupported/Eigen/src/SVD/JacobiSVD.h
deleted file mode 100644
index 02fac409e..000000000
--- a/unsupported/Eigen/src/SVD/JacobiSVD.h
+++ /dev/null
@@ -1,782 +0,0 @@
-// 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/unsupported/Eigen/src/SVD/SVDBase.h b/unsupported/Eigen/src/SVD/SVDBase.h
deleted file mode 100644
index fd8af3b8c..000000000
--- a/unsupported/Eigen/src/SVD/SVDBase.h
+++ /dev/null
@@ -1,236 +0,0 @@
-// 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/unsupported/Eigen/src/SparseExtra/DynamicSparseMatrix.h b/unsupported/Eigen/src/SparseExtra/DynamicSparseMatrix.h
index dec16df28..e4dc1c1de 100644
--- a/unsupported/Eigen/src/SparseExtra/DynamicSparseMatrix.h
+++ b/unsupported/Eigen/src/SparseExtra/DynamicSparseMatrix.h
@@ -352,6 +352,36 @@ class DynamicSparseMatrix<Scalar,_Options,_Index>::ReverseInnerIterator : public
     const Index m_outer;
 };
 
+namespace internal {
+
+template<typename _Scalar, int _Options, typename _Index>
+struct evaluator<DynamicSparseMatrix<_Scalar,_Options,_Index> >
+  : evaluator_base<DynamicSparseMatrix<_Scalar,_Options,_Index> >
+{
+  typedef _Scalar Scalar;
+  typedef _Index Index;
+  typedef DynamicSparseMatrix<_Scalar,_Options,_Index> SparseMatrixType;
+  typedef typename SparseMatrixType::InnerIterator InnerIterator;
+  typedef typename SparseMatrixType::ReverseInnerIterator ReverseInnerIterator;
+  
+  enum {
+    CoeffReadCost = NumTraits<_Scalar>::ReadCost,
+    Flags = SparseMatrixType::Flags
+  };
+  
+  evaluator() : m_matrix(0) {}
+  evaluator(const SparseMatrixType &mat) : m_matrix(&mat) {}
+  
+  operator SparseMatrixType&() { return m_matrix->const_cast_derived(); }
+  operator const SparseMatrixType&() const { return *m_matrix; }
+  
+  Scalar coeff(Index row, Index col) const { return m_matrix->coeff(row,col); }
+
+  const SparseMatrixType *m_matrix;
+};
+
+}
+
 } // end namespace Eigen
 
 #endif // EIGEN_DYNAMIC_SPARSEMATRIX_H