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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@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
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PASTIXSUPPORT_H
+#define EIGEN_PASTIXSUPPORT_H
+
+namespace Eigen { 
+
+#if defined(DCOMPLEX)
+  #define PASTIX_COMPLEX  COMPLEX
+  #define PASTIX_DCOMPLEX DCOMPLEX
+#else
+  #define PASTIX_COMPLEX  std::complex<float>
+  #define PASTIX_DCOMPLEX std::complex<double>
+#endif
+
+/** \ingroup PaStiXSupport_Module
+  * \brief Interface to the PaStix solver
+  * 
+  * This class is used to solve the linear systems A.X = B via the PaStix library. 
+  * The matrix can be either real or complex, symmetric or not.
+  *
+  * \sa TutorialSparseDirectSolvers
+  */
+template<typename _MatrixType, bool IsStrSym = false> class PastixLU;
+template<typename _MatrixType, int Options> class PastixLLT;
+template<typename _MatrixType, int Options> class PastixLDLT;
+
+namespace internal
+{
+    
+  template<class Pastix> struct pastix_traits;
+
+  template<typename _MatrixType>
+  struct pastix_traits< PastixLU<_MatrixType> >
+  {
+    typedef _MatrixType MatrixType;
+    typedef typename _MatrixType::Scalar Scalar;
+    typedef typename _MatrixType::RealScalar RealScalar;
+    typedef typename _MatrixType::Index Index;
+  };
+
+  template<typename _MatrixType, int Options>
+  struct pastix_traits< PastixLLT<_MatrixType,Options> >
+  {
+    typedef _MatrixType MatrixType;
+    typedef typename _MatrixType::Scalar Scalar;
+    typedef typename _MatrixType::RealScalar RealScalar;
+    typedef typename _MatrixType::Index Index;
+  };
+
+  template<typename _MatrixType, int Options>
+  struct pastix_traits< PastixLDLT<_MatrixType,Options> >
+  {
+    typedef _MatrixType MatrixType;
+    typedef typename _MatrixType::Scalar Scalar;
+    typedef typename _MatrixType::RealScalar RealScalar;
+    typedef typename _MatrixType::Index Index;
+  };
+  
+  void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, float *vals, int *perm, int * invp, float *x, int nbrhs, int *iparm, double *dparm)
+  {
+    if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
+    if (nbrhs == 0) {x = NULL; nbrhs=1;}
+    s_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm); 
+  }
+  
+  void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, double *vals, int *perm, int * invp, double *x, int nbrhs, int *iparm, double *dparm)
+  {
+    if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
+    if (nbrhs == 0) {x = NULL; nbrhs=1;}
+    d_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm); 
+  }
+  
+  void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<float> *vals, int *perm, int * invp, std::complex<float> *x, int nbrhs, int *iparm, double *dparm)
+  {
+    if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
+    if (nbrhs == 0) {x = NULL; nbrhs=1;}
+    c_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<PASTIX_COMPLEX*>(vals), perm, invp, reinterpret_cast<PASTIX_COMPLEX*>(x), nbrhs, iparm, dparm); 
+  }
+  
+  void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<double> *vals, int *perm, int * invp, std::complex<double> *x, int nbrhs, int *iparm, double *dparm)
+  {
+    if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
+    if (nbrhs == 0) {x = NULL; nbrhs=1;}
+    z_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<PASTIX_DCOMPLEX*>(vals), perm, invp, reinterpret_cast<PASTIX_DCOMPLEX*>(x), nbrhs, iparm, dparm); 
+  }
+
+  // Convert the matrix  to Fortran-style Numbering
+  template <typename MatrixType>
+  void c_to_fortran_numbering (MatrixType& mat)
+  {
+    if ( !(mat.outerIndexPtr()[0]) ) 
+    { 
+      int i;
+      for(i = 0; i <= mat.rows(); ++i)
+        ++mat.outerIndexPtr()[i];
+      for(i = 0; i < mat.nonZeros(); ++i)
+        ++mat.innerIndexPtr()[i];
+    }
+  }
+  
+  // Convert to C-style Numbering
+  template <typename MatrixType>
+  void fortran_to_c_numbering (MatrixType& mat)
+  {
+    // Check the Numbering
+    if ( mat.outerIndexPtr()[0] == 1 ) 
+    { // Convert to C-style numbering
+      int i;
+      for(i = 0; i <= mat.rows(); ++i)
+        --mat.outerIndexPtr()[i];
+      for(i = 0; i < mat.nonZeros(); ++i)
+        --mat.innerIndexPtr()[i];
+    }
+  }
+}
+
+// This is the base class to interface with PaStiX functions. 
+// Users should not used this class directly. 
+template <class Derived>
+class PastixBase : internal::noncopyable
+{
+  public:
+    typedef typename internal::pastix_traits<Derived>::MatrixType _MatrixType;
+    typedef _MatrixType MatrixType;
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename MatrixType::RealScalar RealScalar;
+    typedef typename MatrixType::Index Index;
+    typedef Matrix<Scalar,Dynamic,1> Vector;
+    typedef SparseMatrix<Scalar, ColMajor> ColSpMatrix;
+    
+  public:
+    
+    PastixBase() : m_initisOk(false), m_analysisIsOk(false), m_factorizationIsOk(false), m_isInitialized(false), m_pastixdata(0), m_size(0)
+    {
+      init();
+    }
+    
+    ~PastixBase() 
+    {
+      clean();
+    }
+
+    /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+      *
+      * \sa compute()
+      */
+    template<typename Rhs>
+    inline const internal::solve_retval<PastixBase, Rhs>
+    solve(const MatrixBase<Rhs>& b) const
+    {
+      eigen_assert(m_isInitialized && "Pastix solver is not initialized.");
+      eigen_assert(rows()==b.rows()
+                && "PastixBase::solve(): invalid number of rows of the right hand side matrix b");
+      return internal::solve_retval<PastixBase, Rhs>(*this, b.derived());
+    }
+    
+    template<typename Rhs,typename Dest>
+    bool _solve (const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const;
+    
+    Derived& derived()
+    {
+      return *static_cast<Derived*>(this);
+    }
+    const Derived& derived() const
+    {
+      return *static_cast<const Derived*>(this);
+    }
+
+    /** Returns a reference to the integer vector IPARM of PaStiX parameters
+      * to modify the default parameters. 
+      * The statistics related to the different phases of factorization and solve are saved here as well
+      * \sa analyzePattern() factorize()
+      */
+    Array<Index,IPARM_SIZE,1>& iparm()
+    {
+      return m_iparm; 
+    }
+    
+    /** Return a reference to a particular index parameter of the IPARM vector 
+     * \sa iparm()
+     */
+    
+    int& iparm(int idxparam)
+    {
+      return m_iparm(idxparam);
+    }
+    
+     /** Returns a reference to the double vector DPARM of PaStiX parameters 
+      * The statistics related to the different phases of factorization and solve are saved here as well
+      * \sa analyzePattern() factorize()
+      */
+    Array<RealScalar,IPARM_SIZE,1>& dparm()
+    {
+      return m_dparm; 
+    }
+    
+    
+    /** Return a reference to a particular index parameter of the DPARM vector 
+     * \sa dparm()
+     */
+    double& dparm(int idxparam)
+    {
+      return m_dparm(idxparam);
+    }
+    
+    inline Index cols() const { return m_size; }
+    inline Index rows() const { return m_size; }
+    
+     /** \brief Reports whether previous computation was successful.
+      *
+      * \returns \c Success if computation was succesful,
+      *          \c NumericalIssue if the PaStiX reports a problem
+      *          \c InvalidInput if the input matrix is invalid
+      *
+      * \sa iparm()          
+      */
+    ComputationInfo info() const
+    {
+      eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+      return m_info;
+    }
+    
+    /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+      *
+      * \sa compute()
+      */
+    template<typename Rhs>
+    inline const internal::sparse_solve_retval<PastixBase, Rhs>
+    solve(const SparseMatrixBase<Rhs>& b) const
+    {
+      eigen_assert(m_isInitialized && "Pastix LU, LLT or LDLT is not initialized.");
+      eigen_assert(rows()==b.rows()
+                && "PastixBase::solve(): invalid number of rows of the right hand side matrix b");
+      return internal::sparse_solve_retval<PastixBase, Rhs>(*this, b.derived());
+    }
+    
+  protected:
+
+    // Initialize the Pastix data structure, check the matrix
+    void init(); 
+    
+    // Compute the ordering and the symbolic factorization
+    void analyzePattern(ColSpMatrix& mat);
+    
+    // Compute the numerical factorization
+    void factorize(ColSpMatrix& mat);
+    
+    // Free all the data allocated by Pastix
+    void clean()
+    {
+      eigen_assert(m_initisOk && "The Pastix structure should be allocated first"); 
+      m_iparm(IPARM_START_TASK) = API_TASK_CLEAN;
+      m_iparm(IPARM_END_TASK) = API_TASK_CLEAN;
+      internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar*)0,
+                             m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());
+    }
+    
+    void compute(ColSpMatrix& mat);
+    
+    int m_initisOk; 
+    int m_analysisIsOk;
+    int m_factorizationIsOk;
+    bool m_isInitialized;
+    mutable ComputationInfo m_info; 
+    mutable pastix_data_t *m_pastixdata; // Data structure for pastix
+    mutable int m_comm; // The MPI communicator identifier
+    mutable Matrix<int,IPARM_SIZE,1> m_iparm; // integer vector for the input parameters
+    mutable Matrix<double,DPARM_SIZE,1> m_dparm; // Scalar vector for the input parameters
+    mutable Matrix<Index,Dynamic,1> m_perm;  // Permutation vector
+    mutable Matrix<Index,Dynamic,1> m_invp;  // Inverse permutation vector
+    mutable int m_size; // Size of the matrix 
+}; 
+
+ /** Initialize the PaStiX data structure. 
+   *A first call to this function fills iparm and dparm with the default PaStiX parameters
+   * \sa iparm() dparm()
+   */
+template <class Derived>
+void PastixBase<Derived>::init()
+{
+  m_size = 0; 
+  m_iparm.setZero(IPARM_SIZE);
+  m_dparm.setZero(DPARM_SIZE);
+  
+  m_iparm(IPARM_MODIFY_PARAMETER) = API_NO;
+  pastix(&m_pastixdata, MPI_COMM_WORLD,
+         0, 0, 0, 0,
+         0, 0, 0, 1, m_iparm.data(), m_dparm.data());
+  
+  m_iparm[IPARM_MATRIX_VERIFICATION] = API_NO;
+  m_iparm[IPARM_VERBOSE]             = 2;
+  m_iparm[IPARM_ORDERING]            = API_ORDER_SCOTCH;
+  m_iparm[IPARM_INCOMPLETE]          = API_NO;
+  m_iparm[IPARM_OOC_LIMIT]           = 2000;
+  m_iparm[IPARM_RHS_MAKING]          = API_RHS_B;
+  m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;
+  
+  m_iparm(IPARM_START_TASK) = API_TASK_INIT;
+  m_iparm(IPARM_END_TASK) = API_TASK_INIT;
+  internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar*)0,
+                         0, 0, 0, 0, m_iparm.data(), m_dparm.data());
+  
+  // Check the returned error
+  if(m_iparm(IPARM_ERROR_NUMBER)) {
+    m_info = InvalidInput;
+    m_initisOk = false;
+  }
+  else { 
+    m_info = Success;
+    m_initisOk = true;
+  }
+}
+
+template <class Derived>
+void PastixBase<Derived>::compute(ColSpMatrix& mat)
+{
+  eigen_assert(mat.rows() == mat.cols() && "The input matrix should be squared");
+  
+  analyzePattern(mat);  
+  factorize(mat);
+  
+  m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;
+  m_isInitialized = m_factorizationIsOk;
+}
+
+
+template <class Derived>
+void PastixBase<Derived>::analyzePattern(ColSpMatrix& mat)
+{                         
+  eigen_assert(m_initisOk && "The initialization of PaSTiX failed");
+  
+  // clean previous calls
+  if(m_size>0)
+    clean();
+  
+  m_size = mat.rows();
+  m_perm.resize(m_size);
+  m_invp.resize(m_size);
+  
+  m_iparm(IPARM_START_TASK) = API_TASK_ORDERING;
+  m_iparm(IPARM_END_TASK) = API_TASK_ANALYSE;
+  internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),
+               mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());
+  
+  // Check the returned error
+  if(m_iparm(IPARM_ERROR_NUMBER))
+  {
+    m_info = NumericalIssue;
+    m_analysisIsOk = false;
+  }
+  else
+  { 
+    m_info = Success;
+    m_analysisIsOk = true;
+  }
+}
+
+template <class Derived>
+void PastixBase<Derived>::factorize(ColSpMatrix& mat)
+{
+//   if(&m_cpyMat != &mat) m_cpyMat = mat;
+  eigen_assert(m_analysisIsOk && "The analysis phase should be called before the factorization phase");
+  m_iparm(IPARM_START_TASK) = API_TASK_NUMFACT;
+  m_iparm(IPARM_END_TASK) = API_TASK_NUMFACT;
+  m_size = mat.rows();
+  
+  internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),
+               mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());
+  
+  // Check the returned error
+  if(m_iparm(IPARM_ERROR_NUMBER))
+  {
+    m_info = NumericalIssue;
+    m_factorizationIsOk = false;
+    m_isInitialized = false;
+  }
+  else
+  {
+    m_info = Success;
+    m_factorizationIsOk = true;
+    m_isInitialized = true;
+  }
+}
+
+/* Solve the system */
+template<typename Base>
+template<typename Rhs,typename Dest>
+bool PastixBase<Base>::_solve (const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const
+{
+  eigen_assert(m_isInitialized && "The matrix should be factorized first");
+  EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,
+                     THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+  int rhs = 1;
+  
+  x = b; /* on return, x is overwritten by the computed solution */
+  
+  for (int i = 0; i < b.cols(); i++){
+    m_iparm[IPARM_START_TASK]          = API_TASK_SOLVE;
+    m_iparm[IPARM_END_TASK]            = API_TASK_REFINE;
+  
+    internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, x.rows(), 0, 0, 0,
+                           m_perm.data(), m_invp.data(), &x(0, i), rhs, m_iparm.data(), m_dparm.data());
+  }
+  
+  // Check the returned error
+  m_info = m_iparm(IPARM_ERROR_NUMBER)==0 ? Success : NumericalIssue;
+  
+  return m_iparm(IPARM_ERROR_NUMBER)==0;
+}
+
+/** \ingroup PaStiXSupport_Module
+  * \class PastixLU
+  * \brief Sparse direct LU solver based on PaStiX library
+  * 
+  * This class is used to solve the linear systems A.X = B with a supernodal LU 
+  * factorization in the PaStiX library. The matrix A should be squared and nonsingular
+  * PaStiX requires that the matrix A has a symmetric structural pattern. 
+  * This interface can symmetrize the input matrix otherwise. 
+  * The vectors or matrices X and B can be either dense or sparse.
+  * 
+  * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+  * \tparam IsStrSym Indicates if the input matrix has a symmetric pattern, default is false
+  * NOTE : Note that if the analysis and factorization phase are called separately, 
+  * the input matrix will be symmetrized at each call, hence it is advised to 
+  * symmetrize the matrix in a end-user program and set \p IsStrSym to true
+  * 
+  * \sa \ref TutorialSparseDirectSolvers
+  * 
+  */
+template<typename _MatrixType, bool IsStrSym>
+class PastixLU : public PastixBase< PastixLU<_MatrixType> >
+{
+  public:
+    typedef _MatrixType MatrixType;
+    typedef PastixBase<PastixLU<MatrixType> > Base;
+    typedef typename Base::ColSpMatrix ColSpMatrix;
+    typedef typename MatrixType::Index Index;
+    
+  public:
+    PastixLU() : Base()
+    {
+      init();
+    }
+    
+    PastixLU(const MatrixType& matrix):Base()
+    {
+      init();
+      compute(matrix);
+    }
+    /** Compute the LU supernodal factorization of \p matrix. 
+      * iparm and dparm can be used to tune the PaStiX parameters. 
+      * see the PaStiX user's manual
+      * \sa analyzePattern() factorize()
+      */
+    void compute (const MatrixType& matrix)
+    {
+      m_structureIsUptodate = false;
+      ColSpMatrix temp;
+      grabMatrix(matrix, temp);
+      Base::compute(temp);
+    }
+    /** Compute the LU symbolic factorization of \p matrix using its sparsity pattern. 
+      * Several ordering methods can be used at this step. See the PaStiX user's manual. 
+      * The result of this operation can be used with successive matrices having the same pattern as \p matrix
+      * \sa factorize()
+      */
+    void analyzePattern(const MatrixType& matrix)
+    {
+      m_structureIsUptodate = false;
+      ColSpMatrix temp;
+      grabMatrix(matrix, temp);
+      Base::analyzePattern(temp);
+    }
+
+    /** Compute the LU supernodal factorization of \p matrix
+      * WARNING The matrix \p matrix should have the same structural pattern 
+      * as the same used in the analysis phase.
+      * \sa analyzePattern()
+      */ 
+    void factorize(const MatrixType& matrix)
+    {
+      ColSpMatrix temp;
+      grabMatrix(matrix, temp);
+      Base::factorize(temp);
+    }
+  protected:
+    
+    void init()
+    {
+      m_structureIsUptodate = false;
+      m_iparm(IPARM_SYM) = API_SYM_NO;
+      m_iparm(IPARM_FACTORIZATION) = API_FACT_LU;
+    }
+    
+    void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)
+    {
+      if(IsStrSym)
+        out = matrix;
+      else
+      {
+        if(!m_structureIsUptodate)
+        {
+          // update the transposed structure
+          m_transposedStructure = matrix.transpose();
+          
+          // Set the elements of the matrix to zero 
+          for (Index j=0; j<m_transposedStructure.outerSize(); ++j) 
+            for(typename ColSpMatrix::InnerIterator it(m_transposedStructure, j); it; ++it)
+              it.valueRef() = 0.0;
+
+          m_structureIsUptodate = true;
+        }
+        
+        out = m_transposedStructure + matrix;
+      }
+      internal::c_to_fortran_numbering(out);
+    }
+    
+    using Base::m_iparm;
+    using Base::m_dparm;
+    
+    ColSpMatrix m_transposedStructure;
+    bool m_structureIsUptodate;
+};
+
+/** \ingroup PaStiXSupport_Module
+  * \class PastixLLT
+  * \brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library
+  * 
+  * This class is used to solve the linear systems A.X = B via a LL^T supernodal Cholesky factorization
+  * available in the PaStiX library. The matrix A should be symmetric and positive definite
+  * WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX
+  * The vectors or matrices X and B can be either dense or sparse
+  * 
+  * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+  * \tparam UpLo The part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX
+  * 
+  * \sa \ref TutorialSparseDirectSolvers
+  */
+template<typename _MatrixType, int _UpLo>
+class PastixLLT : public PastixBase< PastixLLT<_MatrixType, _UpLo> >
+{
+  public:
+    typedef _MatrixType MatrixType;
+    typedef PastixBase<PastixLLT<MatrixType, _UpLo> > Base;
+    typedef typename Base::ColSpMatrix ColSpMatrix;
+    
+  public:
+    enum { UpLo = _UpLo };
+    PastixLLT() : Base()
+    {
+      init();
+    }
+    
+    PastixLLT(const MatrixType& matrix):Base()
+    {
+      init();
+      compute(matrix);
+    }
+
+    /** Compute the L factor of the LL^T supernodal factorization of \p matrix 
+      * \sa analyzePattern() factorize()
+      */
+    void compute (const MatrixType& matrix)
+    {
+      ColSpMatrix temp;
+      grabMatrix(matrix, temp);
+      Base::compute(temp);
+    }
+
+     /** Compute the LL^T symbolic factorization of \p matrix using its sparsity pattern
+      * The result of this operation can be used with successive matrices having the same pattern as \p matrix
+      * \sa factorize()
+      */
+    void analyzePattern(const MatrixType& matrix)
+    {
+      ColSpMatrix temp;
+      grabMatrix(matrix, temp);
+      Base::analyzePattern(temp);
+    }
+      /** Compute the LL^T supernodal numerical factorization of \p matrix 
+        * \sa analyzePattern()
+        */
+    void factorize(const MatrixType& matrix)
+    {
+      ColSpMatrix temp;
+      grabMatrix(matrix, temp);
+      Base::factorize(temp);
+    }
+  protected:
+    using Base::m_iparm;
+    
+    void init()
+    {
+      m_iparm(IPARM_SYM) = API_SYM_YES;
+      m_iparm(IPARM_FACTORIZATION) = API_FACT_LLT;
+    }
+    
+    void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)
+    {
+      // Pastix supports only lower, column-major matrices 
+      out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>();
+      internal::c_to_fortran_numbering(out);
+    }
+};
+
+/** \ingroup PaStiXSupport_Module
+  * \class PastixLDLT
+  * \brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library
+  * 
+  * This class is used to solve the linear systems A.X = B via a LDL^T supernodal Cholesky factorization
+  * available in the PaStiX library. The matrix A should be symmetric and positive definite
+  * WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX
+  * The vectors or matrices X and B can be either dense or sparse
+  * 
+  * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+  * \tparam UpLo The part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX
+  * 
+  * \sa \ref TutorialSparseDirectSolvers
+  */
+template<typename _MatrixType, int _UpLo>
+class PastixLDLT : public PastixBase< PastixLDLT<_MatrixType, _UpLo> >
+{
+  public:
+    typedef _MatrixType MatrixType;
+    typedef PastixBase<PastixLDLT<MatrixType, _UpLo> > Base; 
+    typedef typename Base::ColSpMatrix ColSpMatrix;
+    
+  public:
+    enum { UpLo = _UpLo };
+    PastixLDLT():Base()
+    {
+      init();
+    }
+    
+    PastixLDLT(const MatrixType& matrix):Base()
+    {
+      init();
+      compute(matrix);
+    }
+
+    /** Compute the L and D factors of the LDL^T factorization of \p matrix 
+      * \sa analyzePattern() factorize()
+      */
+    void compute (const MatrixType& matrix)
+    {
+      ColSpMatrix temp;
+      grabMatrix(matrix, temp);
+      Base::compute(temp);
+    }
+
+    /** Compute the LDL^T symbolic factorization of \p matrix using its sparsity pattern
+      * The result of this operation can be used with successive matrices having the same pattern as \p matrix
+      * \sa factorize()
+      */
+    void analyzePattern(const MatrixType& matrix)
+    { 
+      ColSpMatrix temp;
+      grabMatrix(matrix, temp);
+      Base::analyzePattern(temp);
+    }
+    /** Compute the LDL^T supernodal numerical factorization of \p matrix 
+      * 
+      */
+    void factorize(const MatrixType& matrix)
+    {
+      ColSpMatrix temp;
+      grabMatrix(matrix, temp);
+      Base::factorize(temp);
+    }
+
+  protected:
+    using Base::m_iparm;
+    
+    void init()
+    {
+      m_iparm(IPARM_SYM) = API_SYM_YES;
+      m_iparm(IPARM_FACTORIZATION) = API_FACT_LDLT;
+    }
+    
+    void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)
+    {
+      // Pastix supports only lower, column-major matrices 
+      out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>();
+      internal::c_to_fortran_numbering(out);
+    }
+};
+
+namespace internal {
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<PastixBase<_MatrixType>, Rhs>
+  : solve_retval_base<PastixBase<_MatrixType>, Rhs>
+{
+  typedef PastixBase<_MatrixType> Dec;
+  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+  template<typename Dest> void evalTo(Dest& dst) const
+  {
+    dec()._solve(rhs(),dst);
+  }
+};
+
+template<typename _MatrixType, typename Rhs>
+struct sparse_solve_retval<PastixBase<_MatrixType>, Rhs>
+  : sparse_solve_retval_base<PastixBase<_MatrixType>, Rhs>
+{
+  typedef PastixBase<_MatrixType> Dec;
+  EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
+
+  template<typename Dest> void evalTo(Dest& dst) const
+  {
+    this->defaultEvalTo(dst);
+  }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif