libtrilinos-ifpack-dev 12.4.2-2 / usr / include / trilinos / Ifpack_BlockRelaxation.h

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#ifndef IFPACK_BLOCKPRECONDITIONER_H
#define IFPACK_BLOCKPRECONDITIONER_H

#include "Ifpack_ConfigDefs.h"
#include "Ifpack_Preconditioner.h"
#include "Ifpack_Partitioner.h"
#include "Ifpack_LinePartitioner.h"
#include "Ifpack_LinearPartitioner.h"
#include "Ifpack_GreedyPartitioner.h"
#include "Ifpack_METISPartitioner.h"
#include "Ifpack_EquationPartitioner.h"
#include "Ifpack_UserPartitioner.h"
#include "Ifpack_Graph_Epetra_RowMatrix.h"
#include "Ifpack_DenseContainer.h"
#include "Ifpack_Utils.h"
#include "Teuchos_ParameterList.hpp"
#include "Teuchos_RefCountPtr.hpp"

#include "Epetra_Map.h"
#include "Epetra_RowMatrix.h"
#include "Epetra_MultiVector.h"
#include "Epetra_Vector.h"
#include "Epetra_Time.h"
#include "Epetra_Import.h"

static const int IFPACK_JACOBI = 0;
static const int IFPACK_GS = 1;
static const int IFPACK_SGS = 2;


//! Ifpack_BlockRelaxation: a class to define block relaxation preconditioners of Epetra_RowMatrix's.

/*! The Ifpack_BlockRelaxation class enables the construction of
  block relaxation
  preconditioners of an Epetra_RowMatrix. Ifpack_PointRelaxation
  is derived from
  the Ifpack_Preconditioner class, which is derived from Epetra_Operator.
  Therefore this object can be used as preconditioner everywhere an
  ApplyInverse() method is required in the preconditioning step.

  The class currently support:
  - block Jacobi;
  - block Gauss-Seidel;
  - symmetric block Gauss-Seidel.

  The idea of block relaxation method is to extend their point relaxation
  counterpart (implemented in Ifpack_PointRelaxation), by working on a
  group of equation simulteneously. Generally, larger blocks result
  in better convergence and increased robusteness.

  The user can decide:
  - the number of blocks (say, NumBlocks). If NumBlocks is equal to the
    number of rows, then the resulting scheme is equivalent to
    a point relaxation scheme;
  - how to apply the inverse of each diagonal block, by choosing a dense
    container or a sparse container. The implementation of
    block relaxation schemes requires the application of the
    inverse of each diagonal block. This can be done using LAPACK (dense
    container), or any Ifpack_Preconditioner derived class (sparse
    container);
  - blocks can be defined using a linear decomposition, by a simple greedy
    algorithm, or by resorting to METIS.

The following is an example of usage of this preconditioner with dense
containers. First, we include the header files:
\code
#include "Ifpack_AdditiveSchwarz.h"
#include "Ifpack_BlockPreconditioner.h"
#include "Ifpack_DenseContainer.h"
\endcode

Then, we declare the preconditioner. Note that this is done through
the class Ifpack_AdditiveSchwarz (see note below in this section).
\code
// A is an Epetra_RowMatrix
// List is a Teuchos::ParameterList
Ifpack_AdditiveSchwarz<Ifpack_BlockRelaxation<Ifpack_DenseContainer> > > Prec(A);
IFPACK_CHK_ERR(Prec.SetParameters(List));
IFPACK_CHK_ERR(Prec.Initialize());
IFPACK_CHK_ERR(Prec.Compute());

// action of the preconditioner is given by ApplyInverse()
// Now use it in AztecOO, solver is an AztecOO object
solver.SetPrecOperator(&Prec);
\endcode

<P>The complete list of supported parameters is reported in page \ref ifp_params. For a presentation of basic relaxation schemes, please refer to page
\ref Ifpack_PointRelaxation.

\author Marzio Sala, SNL 9214.

\date Last modified on 25-Jan-05.

*/
template<typename T>
class Ifpack_BlockRelaxation : public Ifpack_Preconditioner {

public:

  //@{ \name Constructors/Destructors
  //! Ifpack_BlockRelaxation constructor with given Epetra_RowMatrix.
  /*! Creates an Ifpack_Preconditioner preconditioner.
   *
   * \param In
   * Matrix - Pointer to matrix to be preconditioned.
   */
  Ifpack_BlockRelaxation(const Epetra_RowMatrix* Matrix);

  virtual ~Ifpack_BlockRelaxation();

  //@}

  //@{ \name Mathematical functions.

  //! Applies the matrix to an Epetra_MultiVector.
  /*!
    \param In
    X - A Epetra_MultiVector of dimension NumVectors to multiply with matrix.
    \param Out
    Y -A Epetra_MultiVector of dimension NumVectors containing the result.

    \return Integer error code, set to 0 if successful.
    */
  virtual int Apply(const Epetra_MultiVector& X,
                    Epetra_MultiVector& Y) const;

  //! Applies the block Jacobi preconditioner to X, returns the result in Y.
  /*!
    \param In
    X - A Epetra_MultiVector of dimension NumVectors to be preconditioned.
    \param Out
    Y -A Epetra_MultiVector of dimension NumVectors containing result.

    \return Integer error code, set to 0 if successful.

    */
  virtual int ApplyInverse(const Epetra_MultiVector& X,
                           Epetra_MultiVector& Y) const;

  //! Returns the infinity norm of the global matrix (not implemented)
  virtual double NormInf() const
  {
    return(-1.0);
  }
  //@}

  //@{ \name Attribute access functions

  virtual int SetUseTranspose(bool UseTranspose_in)
  {
    if (UseTranspose_in)
      IFPACK_CHK_ERR(-98); // FIXME: can I work with the transpose?
    return(0);
  }

  virtual const char* Label() const;

  //! Returns the current UseTranspose setting.
  virtual bool UseTranspose() const
  {
    return(false);
  }

  //! Returns true if the \e this object can provide an approximate Inf-norm, false otherwise.
  virtual bool HasNormInf() const
  {
    return(false);
  }

  //! Returns a pointer to the Epetra_Comm communicator associated with this operator.
  virtual const Epetra_Comm & Comm() const;

  //! Returns the Epetra_Map object associated with the domain of this operator.
  virtual const Epetra_Map & OperatorDomainMap() const;

  //! Returns the Epetra_Map object associated with the range of this operator.
  virtual const Epetra_Map & OperatorRangeMap() const;
  //@}

  //! Returns the number local blocks.
  int NumLocalBlocks() const
  {
    return(NumLocalBlocks_);
  }

  //! Returns \c true if the preconditioner has been successfully computed.
  virtual bool IsInitialized() const
  {
    return(IsInitialized_);
  }

  //! Returns \c true if the preconditioner has been successfully computed.
  virtual bool IsComputed() const
  {
    return(IsComputed_);
  }

  //! Sets all the parameters for the preconditioner.
  virtual int SetParameters(Teuchos::ParameterList& List);

  //! Initializes the preconditioner.
  virtual int Initialize();

  //! Computes the preconditioner.
  virtual int Compute();

  virtual const Epetra_RowMatrix& Matrix() const
  {
    return(*Matrix_);
  }

  virtual double Condest(const Ifpack_CondestType CT = Ifpack_Cheap,
                         const int MaxIters = 1550,
                         const double Tol = 1e-9,
                         Epetra_RowMatrix* Matrix_in = 0)
  {
    return(-1.0);
  }

  virtual double Condest() const
  {
    return(-1.0);
  }

  std::ostream& Print(std::ostream& os) const;

  //! Returns the number of calls to Initialize().
  virtual int NumInitialize() const
  {
    return(NumInitialize_);
  }

  //! Returns the number of calls to Compute().
  virtual int NumCompute() const
  {
    return(NumCompute_);
  }

  //! Returns the number of calls to ApplyInverse().
  virtual int NumApplyInverse() const
  {
    return(NumApplyInverse_);
  }

  //! Returns the time spent in Initialize().
  virtual double InitializeTime() const
  {
    return(InitializeTime_);
  }

  //! Returns the time spent in Compute().
  virtual double ComputeTime() const
  {
    return(ComputeTime_);
  }

  //! Returns the time spent in ApplyInverse().
  virtual double ApplyInverseTime() const
  {
    return(ApplyInverseTime_);
  }

  //! Returns the number of flops in the initialization phase.
  virtual double InitializeFlops() const
  {
#ifdef IFPACK_FLOPCOUNTERS
    if (Containers_.size() == 0)
      return(0.0);

    // the total number of flops is computed each time InitializeFlops() is
    // called. This is becase I also have to add the contribution from each
    // container.
    double total = InitializeFlops_;
    for (unsigned int i = 0 ; i < Containers_.size() ; ++i)
      if(Containers_[i]) total += Containers_[i]->InitializeFlops();
    return(total);
#else
    return(0.0);
#endif
  }

  virtual double ComputeFlops() const
  {
#ifdef IFPACK_FLOPCOUNTERS
    if (Containers_.size() == 0)
      return(0.0);

    double total = ComputeFlops_;
    for (unsigned int i = 0 ; i < Containers_.size() ; ++i)
      if(Containers_[i]) total += Containers_[i]->ComputeFlops();
    return(total);
#else
    return(0.0);
#endif
  }

  virtual double ApplyInverseFlops() const
  {
#ifdef IFPACK_FLOPCOUNTERS
    if (Containers_.size() == 0)
      return(0.0);

    double total = ApplyInverseFlops_;
    for (unsigned int i = 0 ; i < Containers_.size() ; ++i) {
      if(Containers_[i]) total += Containers_[i]->ApplyInverseFlops();
    }
    return(total);
#else
    return(0.0);
#endif
  }

private:

  //! Copy constructor (PRIVATE, should not be used).
  Ifpack_BlockRelaxation(const Ifpack_BlockRelaxation& rhs);

  //! operator= (PRIVATE, should not be used).
  Ifpack_BlockRelaxation & operator=(const Ifpack_BlockRelaxation& rhs)
  {
    return(*this);
  }

  virtual int ApplyInverseJacobi(const Epetra_MultiVector& X,
                                 Epetra_MultiVector& Y) const;

  virtual int DoJacobi(const Epetra_MultiVector& X,
                                  Epetra_MultiVector& Y) const;

  virtual int ApplyInverseGS(const Epetra_MultiVector& X,
                             Epetra_MultiVector& Y) const;

  virtual int DoGaussSeidel(Epetra_MultiVector& X,
                            Epetra_MultiVector& Y) const;

  virtual int ApplyInverseSGS(const Epetra_MultiVector& X,
                              Epetra_MultiVector& Y) const;

  virtual int DoSGS(const Epetra_MultiVector& X,
                    Epetra_MultiVector& Xtmp,
                    Epetra_MultiVector& Y) const;

  int ExtractSubmatrices();

  // @{ Initializations, timing and flops

  //! If true, the preconditioner has been successfully initialized.
  bool IsInitialized_;
  //! If true, the preconditioner has been successfully computed.
  bool IsComputed_;
  //! Contains the number of successful calls to Initialize().
  int NumInitialize_;
  //! Contains the number of successful call to Compute().
  int NumCompute_;
  //! Contains the number of successful call to ApplyInverse().
  mutable int NumApplyInverse_;
  //! Contains the time for all successful calls to Initialize().
  double InitializeTime_;
  //! Contains the time for all successful calls to Compute().
  double ComputeTime_;
  //! Contains the time for all successful calls to ApplyInverse().
  mutable double ApplyInverseTime_;
  //! Contains the number of flops for Initialize().
  double InitializeFlops_;
  //! Contains the number of flops for Compute().
  double ComputeFlops_;
  //! Contain sthe number of flops for ApplyInverse().
  mutable double ApplyInverseFlops_;
  // @}

  // @{ Settings
  //! Number of preconditioning sweeps.
  int NumSweeps_;
  //! Damping parameter.
  double DampingFactor_;
  //! Number of local blocks
  int NumLocalBlocks_;
  //! Parameters list to be used to solve on each subblock
  Teuchos::ParameterList List_;
  // @}

  // @{ Other data
  //! Containers_[i] contains all the necessary information to solve on each subblock.
  //! Pointers to the matrix to be preconditioned.
  Teuchos::RefCountPtr< const Epetra_RowMatrix > Matrix_;
  mutable std::vector<Teuchos::RefCountPtr<T> > Containers_;
  Epetra_Vector Diagonal_ ;

  //! Contains information about non-overlapping partitions.
  Teuchos::RefCountPtr<Ifpack_Partitioner> Partitioner_;
  std::string PartitionerType_;
  int PrecType_;
  //! Label for \c this object
  std::string Label_;
  //! If \c true, starting solution is the zero vector.
  bool ZeroStartingSolution_;
  Teuchos::RefCountPtr<Ifpack_Graph> Graph_;
  //! Weights for overlapping Jacobi only.
  Teuchos::RefCountPtr<Epetra_Vector> W_;
  // Level of overlap among blocks (for Jacobi only).
  int OverlapLevel_;
  mutable Epetra_Time Time_;
  bool IsParallel_;
  Teuchos::RefCountPtr<Epetra_Import> Importer_;
  // @}

}; // class Ifpack_BlockRelaxation

//==============================================================================
template<typename T>
Ifpack_BlockRelaxation<T>::
Ifpack_BlockRelaxation(const Epetra_RowMatrix* Matrix_in) :
  IsInitialized_(false),
  IsComputed_(false),
  NumInitialize_(0),
  NumCompute_(0),
  NumApplyInverse_(0),
  InitializeTime_(0.0),
  ComputeTime_(0.0),
  ApplyInverseTime_(0.0),
  InitializeFlops_(0.0),
  ComputeFlops_(0.0),
  ApplyInverseFlops_(0.0),
  NumSweeps_(1),
  DampingFactor_(1.0),
  NumLocalBlocks_(1),
  Matrix_(Teuchos::rcp(Matrix_in,false)),
  Diagonal_( Matrix_in->Map()),
  PartitionerType_("greedy"),
  PrecType_(IFPACK_JACOBI),
  ZeroStartingSolution_(true),
  OverlapLevel_(0),
  Time_(Comm()),
  IsParallel_(false)
{
  if (Matrix_in->Comm().NumProc() != 1)
    IsParallel_ = true;
}

//==============================================================================
template<typename T>
Ifpack_BlockRelaxation<T>::~Ifpack_BlockRelaxation()
{
}

//==============================================================================
template<typename T>
const char* Ifpack_BlockRelaxation<T>::Label() const
{
  return(Label_.c_str());
}

//==============================================================================
template<typename T>
int Ifpack_BlockRelaxation<T>::
Apply(const Epetra_MultiVector& X, Epetra_MultiVector& Y) const
{
  int ierr = Matrix().Apply(X,Y);
  IFPACK_RETURN(ierr);
}

//==============================================================================
template<typename T>
const Epetra_Comm& Ifpack_BlockRelaxation<T>::
Comm() const
{
  return(Matrix().Comm());
}

//==============================================================================
template<typename T>
const Epetra_Map& Ifpack_BlockRelaxation<T>::
OperatorDomainMap() const
{
  return(Matrix().OperatorDomainMap());
}

//==============================================================================
template<typename T>
const Epetra_Map& Ifpack_BlockRelaxation<T>::
OperatorRangeMap() const
{
  return(Matrix().OperatorRangeMap());
}

//==============================================================================
template<typename T>
int Ifpack_BlockRelaxation<T>::ExtractSubmatrices()
{

  if (Partitioner_ == Teuchos::null)
    IFPACK_CHK_ERR(-3);

  NumLocalBlocks_ = Partitioner_->NumLocalParts();

  Containers_.resize(NumLocalBlocks());

  Diagonal_ = Epetra_Vector(Matrix_->Map());
  Matrix_->ExtractDiagonalCopy(Diagonal_);

  for (int i = 0 ; i < NumLocalBlocks() ; ++i) {

    int rows = Partitioner_->NumRowsInPart(i);
    // if rows == 1, then this is a singleton block, and should not be
    // created. For now, allow creation, and just force the compute step below.

    if( rows != 1 ) {
      Containers_[i] = Teuchos::rcp( new T(rows) );

      IFPACK_CHK_ERR(Containers_[i]->SetParameters(List_));
      IFPACK_CHK_ERR(Containers_[i]->Initialize());
      // flops in Initialize() will be computed on-the-fly in method InitializeFlops().

      // set "global" ID of each partitioner row
      for (int j = 0 ; j < rows ; ++j) {
        int LRID = (*Partitioner_)(i,j);
        Containers_[i]->ID(j) = LRID;
      }

    IFPACK_CHK_ERR(Containers_[i]->Compute(*Matrix_));
    }
    // otherwise leave Containers_[i] as null
  }

#ifdef SINGLETON_DEBUG
  int issing = 0;

  for (int i = 0 ; i < NumLocalBlocks() ; ++i)
    issing += (int) ( Partitioner_->NumRowsInPart(i) == 1);
  printf( " %d of %d containers are singleton \n",issing,NumLocalBlocks());
#endif

  return(0);
}

//==============================================================================
template<typename T>
int Ifpack_BlockRelaxation<T>::Compute()
{

  if (!IsInitialized())
    IFPACK_CHK_ERR(Initialize());

  Time_.ResetStartTime();

  IsComputed_ = false;

  if (Matrix().NumGlobalRows64() != Matrix().NumGlobalCols64())
    IFPACK_CHK_ERR(-2); // only square matrices

  IFPACK_CHK_ERR(ExtractSubmatrices());

  if (IsParallel_ && PrecType_ != IFPACK_JACOBI) {
    // not needed by Jacobi (done by matvec)
    Importer_ = Teuchos::rcp( new Epetra_Import(Matrix().RowMatrixColMap(),
                                                Matrix().RowMatrixRowMap()) );

    if (Importer_ == Teuchos::null) IFPACK_CHK_ERR(-5);
  }
  IsComputed_ = true;
  ComputeTime_ += Time_.ElapsedTime();
  ++NumCompute_;

  return(0);

}

//==============================================================================
template<typename T>
int Ifpack_BlockRelaxation<T>::
ApplyInverse(const Epetra_MultiVector& X, Epetra_MultiVector& Y) const
{
  if (!IsComputed())
    IFPACK_CHK_ERR(-3);

  if (X.NumVectors() != Y.NumVectors())
    IFPACK_CHK_ERR(-2);

  Time_.ResetStartTime();

  // AztecOO gives X and Y pointing to the same memory location,
  // need to create an auxiliary vector, Xcopy
  Teuchos::RefCountPtr< const Epetra_MultiVector > Xcopy;
  if (X.Pointers()[0] == Y.Pointers()[0])
    Xcopy = Teuchos::rcp( new Epetra_MultiVector(X) );
  else
    Xcopy = Teuchos::rcp( &X, false );

  switch (PrecType_) {
  case IFPACK_JACOBI:
    IFPACK_CHK_ERR(ApplyInverseJacobi(*Xcopy,Y));
    break;
  case IFPACK_GS:
    IFPACK_CHK_ERR(ApplyInverseGS(*Xcopy,Y));
    break;
  case IFPACK_SGS:
    IFPACK_CHK_ERR(ApplyInverseSGS(*Xcopy,Y));
    break;
  }

  ApplyInverseTime_ += Time_.ElapsedTime();
  ++NumApplyInverse_;

  return(0);
}

//==============================================================================
// This method in general will not work with AztecOO if used
// outside Ifpack_AdditiveSchwarz and OverlapLevel_ != 0
//
template<typename T>
int Ifpack_BlockRelaxation<T>::
ApplyInverseJacobi(const Epetra_MultiVector& X,
                   Epetra_MultiVector& Y) const
{

  if (ZeroStartingSolution_)
    Y.PutScalar(0.0);

  // do not compute the residual in this case
  if (NumSweeps_ == 1 && ZeroStartingSolution_) {
    int ierr = DoJacobi(X,Y);
    IFPACK_RETURN(ierr);
  }

  Epetra_MultiVector AX(Y);

  for (int j = 0; j < NumSweeps_ ; j++) {
    IFPACK_CHK_ERR(Apply(Y,AX));
    ApplyInverseFlops_ += X.NumVectors() * 2 * Matrix_->NumGlobalNonzeros64();
    IFPACK_CHK_ERR(AX.Update(1.0,X,-1.0));
    ApplyInverseFlops_ += X.NumVectors() * 2 * Matrix_->NumGlobalRows64();
    IFPACK_CHK_ERR(DoJacobi(AX,Y));
    // flops counted in DoJacobi()
  }


  return(0);
}

//==============================================================================
template<typename T>
int Ifpack_BlockRelaxation<T>::
DoJacobi(const Epetra_MultiVector& X, Epetra_MultiVector& Y) const
{
  int NumVectors = X.NumVectors();

  if (OverlapLevel_ == 0) {

    for (int i = 0 ; i < NumLocalBlocks() ; ++i) {

      int rows = Partitioner_->NumRowsInPart(i);
      // may happen that a partition is empty
      if (rows == 0)
        continue;

      if(rows != 1) {
        int LID;

        // extract RHS from X
        for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
          LID = Containers_[i]->ID(j);
          for (int k = 0 ; k < NumVectors ; ++k) {
            Containers_[i]->RHS(j,k) = X[k][LID];
          }
        }

        // apply the inverse of each block. NOTE: flops occurred
        // in ApplyInverse() of each block are summed up in method
        // ApplyInverseFlops().

        IFPACK_CHK_ERR(Containers_[i]->ApplyInverse());

        // copy back into solution vector Y
        for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
          LID = Containers_[i]->ID(j);
          for (int k = 0 ; k < NumVectors ; ++k) {
            Y[k][LID] += DampingFactor_ * Containers_[i]->LHS(j,k);
          }
        }
      } //end if(rows !=1)
      else {
        // rows == 1, this is a singleton. compute directly.
        int LRID = (*Partitioner_)(i,0);
        double b = X[0][LRID];
        double a = Diagonal_[LRID];
        Y[0][LRID] += DampingFactor_* b/a;
      }
        // NOTE: flops for ApplyInverse() of each block are summed up
        // in method ApplyInverseFlops()
#ifdef IFPACK_FLOPCOUNTERS
        ApplyInverseFlops_ += NumVectors * 2 * Matrix_->NumGlobalRows();
#endif

    }
  }
  else { // overlap test

    for (int i = 0 ; i < NumLocalBlocks() ; ++i) {

      int rows = Partitioner_->NumRowsInPart(i);

      // may happen that a partition is empty
      if (rows == 0)
        continue;
      if(rows != 1) {
        int LID;

        // extract RHS from X
        for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
          LID = Containers_[i]->ID(j);
          for (int k = 0 ; k < NumVectors ; ++k) {
            Containers_[i]->RHS(j,k) = (*W_)[LID] * X[k][LID];
          }
        }

        // apply the inverse of each block
        //      if(rows != 1)
        IFPACK_CHK_ERR(Containers_[i]->ApplyInverse());

        // copy back into solution vector Y
        for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
          LID = Containers_[i]->ID(j);
          for (int k = 0 ; k < NumVectors ; ++k) {
            Y[k][LID] += DampingFactor_ * (*W_)[LID] * Containers_[i]->LHS(j,k);
          }
        }
      } // end   if(rows != 1)
      else {    // rows == 1, this is a singleton. compute directly.
        int LRID = (*Partitioner_)(i,0);
        double w = (*W_)[LRID];
        double b = w * X[0][LRID];
        double a = Diagonal_[LRID];

        Y[0][LRID] += DampingFactor_ * w * b / a;
      }
    }
    // NOTE: flops for ApplyInverse() of each block are summed up
    // in method ApplyInverseFlops()
    // NOTE: do not count for simplicity the flops due to overlapping rows
#ifdef IFPACK_FLOPCOUNTERS
    ApplyInverseFlops_ += NumVectors * 4 * Matrix_->NumGlobalRows();
#endif
  }

  return(0);
}

//==============================================================================
template<typename T>
int Ifpack_BlockRelaxation<T>::
ApplyInverseGS(const Epetra_MultiVector& X,
               Epetra_MultiVector& Y) const
{

  if (ZeroStartingSolution_)
    Y.PutScalar(0.0);

  Epetra_MultiVector Xcopy(X);
  for (int j = 0; j < NumSweeps_ ; j++) {
    IFPACK_CHK_ERR(DoGaussSeidel(Xcopy,Y));
    if (j != NumSweeps_ - 1)
      Xcopy = X;
  }

  return(0);

}

//==============================================================================
template<typename T>
int Ifpack_BlockRelaxation<T>::
DoGaussSeidel(Epetra_MultiVector& X, Epetra_MultiVector& Y) const
{

  // cycle over all local subdomains

  int Length = Matrix().MaxNumEntries();
  std::vector<int> Indices(Length);
  std::vector<double> Values(Length);

  int NumMyRows = Matrix().NumMyRows();
  int NumVectors = X.NumVectors();

  // an additonal vector is needed by parallel computations
  // (note that applications through Ifpack_AdditiveSchwarz
  // are always seen are serial)
  Teuchos::RefCountPtr< Epetra_MultiVector > Y2;
  if (IsParallel_)
    Y2 = Teuchos::rcp( new Epetra_MultiVector(Importer_->TargetMap(), NumVectors) );
  else
    Y2 = Teuchos::rcp( &Y, false );

  double** y_ptr;
  double** y2_ptr;
  Y.ExtractView(&y_ptr);
  Y2->ExtractView(&y2_ptr);

  // data exchange is here, once per sweep
  if (IsParallel_)
    IFPACK_CHK_ERR(Y2->Import(Y,*Importer_,Insert));

  for (int i = 0 ; i < NumLocalBlocks() ; ++i) {
    int rows = Partitioner_->NumRowsInPart(i);

    // may happen that a partition is empty, but if rows == 1, the container is null
    if (rows!=1 && Containers_[i]->NumRows() == 0)
      continue;

    int LID;

    // update from previous block

    for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
      LID = (*Partitioner_)(i,j);

      int NumEntries;
      IFPACK_CHK_ERR(Matrix().ExtractMyRowCopy(LID, Length,NumEntries,
                                               &Values[0], &Indices[0]));

      for (int k = 0 ; k < NumEntries ; ++k) {
        int col = Indices[k];

        for (int kk = 0 ; kk < NumVectors ; ++kk) {
          X[kk][LID] -= Values[k] * y2_ptr[kk][col];
        }
      }
    }

    if(rows != 1) {
      // solve with this block

      for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
        LID = Containers_[i]->ID(j);
        for (int k = 0 ; k < NumVectors ; ++k) {
          Containers_[i]->RHS(j,k) = X[k][LID];
        }
      }

      IFPACK_CHK_ERR(Containers_[i]->ApplyInverse());
#ifdef IFPACK_FLOPCOUNTERS
      ApplyInverseFlops_ += Containers_[i]->ApplyInverseFlops();
#endif

      for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
        LID = Containers_[i]->ID(j);
        for (int k = 0 ; k < NumVectors ; ++k) {
          double temp = DampingFactor_ * Containers_[i]->LHS(j,k);
          y2_ptr[k][LID] +=  temp;
        }
      }
    } // end if(rows != 1)
    else {
      int LRID = (*Partitioner_)(i,0);
      double b =  X[0][LRID];
      double a = Diagonal_[LRID];
      y2_ptr[0][LRID]+= DampingFactor_* b/a;
    }
  }
    // operations for all getrow()'s
    // NOTE: flops for ApplyInverse() of each block are summed up
    // in method ApplyInverseFlops()
#ifdef IFPACK_FLOPCOUNTERS
    ApplyInverseFlops_ += NumVectors * 2 * Matrix_->NumGlobalNonzeros();
    ApplyInverseFlops_ += NumVectors * 2 * Matrix_->NumGlobalRows();
#endif

    // Attention: this is delicate... Not all combinations
    // of Y2 and Y will always work (tough for ML it should be ok)
    if (IsParallel_)
      for (int m = 0 ; m < NumVectors ; ++m)
        for (int i = 0 ; i < NumMyRows ; ++i)
          y_ptr[m][i] = y2_ptr[m][i];

    return(0);
  }

//==============================================================================
template<typename T>
int Ifpack_BlockRelaxation<T>::
ApplyInverseSGS(const Epetra_MultiVector& X, Epetra_MultiVector& Y) const
{

  if (ZeroStartingSolution_)
    Y.PutScalar(0.0);

  Epetra_MultiVector Xcopy(X);
  for (int j = 0; j < NumSweeps_ ; j++) {
    IFPACK_CHK_ERR(DoSGS(X,Xcopy,Y));
    if (j != NumSweeps_ - 1)
      Xcopy = X;
  }
  return(0);
}

//==============================================================================
template<typename T>
int Ifpack_BlockRelaxation<T>::
DoSGS(const Epetra_MultiVector& X, Epetra_MultiVector& Xcopy,
      Epetra_MultiVector& Y) const
{

  int NumMyRows = Matrix().NumMyRows();
  int NumVectors = X.NumVectors();

  int Length = Matrix().MaxNumEntries();
  std::vector<int> Indices;
  std::vector<double> Values;
  Indices.resize(Length);
  Values.resize(Length);

  // an additonal vector is needed by parallel computations
  // (note that applications through Ifpack_AdditiveSchwarz
  // are always seen are serial)
  Teuchos::RefCountPtr< Epetra_MultiVector > Y2;
  if (IsParallel_)
    Y2 = Teuchos::rcp( new Epetra_MultiVector(Importer_->TargetMap(), NumVectors) );
  else
    Y2 = Teuchos::rcp( &Y, false );

  double** y_ptr;
  double** y2_ptr;
  Y.ExtractView(&y_ptr);
  Y2->ExtractView(&y2_ptr);

  // data exchange is here, once per sweep
  if (IsParallel_)
    IFPACK_CHK_ERR(Y2->Import(Y,*Importer_,Insert));

  for (int i = 0 ; i < NumLocalBlocks() ; ++i) {
    int rows =  Partitioner_->NumRowsInPart(i);
    // may happen that a partition is empty
    if (rows !=1 && Containers_[i]->NumRows() == 0)
      continue;

    int LID;

    // update from previous block

    for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
      LID = (*Partitioner_)(i,j);
      int NumEntries;
      IFPACK_CHK_ERR(Matrix().ExtractMyRowCopy(LID, Length,NumEntries,
                                               &Values[0], &Indices[0]));

      for (int k = 0 ; k < NumEntries ; ++k) {
        int col = Indices[k];

        for (int kk = 0 ; kk < NumVectors ; ++kk) {
          Xcopy[kk][LID] -= Values[k] * y2_ptr[kk][col];
        }
      }
    }

    // solve with this block

    if(rows != 1) {
      for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
        LID = Containers_[i]->ID(j);
        for (int k = 0 ; k < NumVectors ; ++k) {
          Containers_[i]->RHS(j,k) = Xcopy[k][LID];
        }
      }

      IFPACK_CHK_ERR(Containers_[i]->ApplyInverse());
#ifdef IFPACK_FLOPCOUNTERS
      ApplyInverseFlops_ += Containers_[i]->ApplyInverseFlops();
#endif

      for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
        LID = Containers_[i]->ID(j);
        for (int k = 0 ; k < NumVectors ; ++k) {
          y2_ptr[k][LID] += DampingFactor_ * Containers_[i]->LHS(j,k);
        }
      }
    }
    else {
      int LRID = (*Partitioner_)(i,0);
      double b =  Xcopy[0][LRID];
      double a = Diagonal_[LRID];
      y2_ptr[0][LRID]+= DampingFactor_* b/a;
    }
  }

#ifdef IFPACK_FLOPCOUNTERS
  // operations for all getrow()'s
  ApplyInverseFlops_ += NumVectors * 2 * Matrix_->NumGlobalNonzeros();
  ApplyInverseFlops_ += NumVectors * 2 * Matrix_->NumGlobalRows();
#endif

  Xcopy = X;

  for (int i = NumLocalBlocks() - 1; i >=0 ; --i) {
    int rows = Partitioner_->NumRowsInPart(i);
    if (rows != 1 &&Containers_[i]->NumRows() == 0)
      continue;

    int LID;

    // update from previous block

    for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
      LID = (*Partitioner_)(i,j);

      int NumEntries;
      IFPACK_CHK_ERR(Matrix().ExtractMyRowCopy(LID, Length,NumEntries,
                                               &Values[0], &Indices[0]));

      for (int k = 0 ; k < NumEntries ; ++k) {
        int col = Indices[k];

          for (int kk = 0 ; kk < NumVectors ; ++kk) {
            Xcopy[kk][LID] -= Values[k] * y2_ptr[kk][col];
          }
      }
    }

    // solve with this block
    if(rows != 1) {
      for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
        LID = Containers_[i]->ID(j);
        for (int k = 0 ; k < NumVectors ; ++k) {
          Containers_[i]->RHS(j,k) = Xcopy[k][LID];
        }
      }

      IFPACK_CHK_ERR(Containers_[i]->ApplyInverse());
#ifdef IFPACK_FLOPCOUNTERS
      ApplyInverseFlops_ += Containers_[i]->ApplyInverseFlops();
#endif

      for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
        LID = Containers_[i]->ID(j);
        for (int k = 0 ; k < NumVectors ; ++k) {
          y2_ptr[k][LID] += DampingFactor_ * Containers_[i]->LHS(j,k);
        }
      }
    }
    else {
      int LRID = (*Partitioner_)(i,0);
      double b =  Xcopy[0][LRID];
      double a = Diagonal_[LRID];
      y2_ptr[0][LRID]+= DampingFactor_* b/a;
    }
  }

#ifdef IFPACK_FLOPCOUNTERS
  // operations for all getrow()'s
  ApplyInverseFlops_ += NumVectors * 2 * Matrix_->NumGlobalNonzeros();
  ApplyInverseFlops_ += NumVectors * 2 * Matrix_->NumGlobalRows();
#endif

  // Attention: this is delicate... Not all combinations
  // of Y2 and Y will always work (tough for ML it should be ok)
  if (IsParallel_)
    for (int m = 0 ; m < NumVectors ; ++m)
      for (int i = 0 ; i < NumMyRows ; ++i)
        y_ptr[m][i] = y2_ptr[m][i];

  return(0);
}

//==============================================================================
template<typename T>
std::ostream& Ifpack_BlockRelaxation<T>::Print(std::ostream & os) const
{
  using std::endl;

  std::string PT;
  if (PrecType_ == IFPACK_JACOBI)
    PT = "Jacobi";
  else if (PrecType_ == IFPACK_GS)
    PT = "Gauss-Seidel";
  else if (PrecType_ == IFPACK_SGS)
    PT = "symmetric Gauss-Seidel";

  if (!Comm().MyPID()) {
    os << endl;
    os << "================================================================================" << endl;
    os << "Ifpack_BlockRelaxation, " << PT << endl;
    os << "Sweeps = " << NumSweeps_ << endl;
    os << "Damping factor = " << DampingFactor_;
    if (ZeroStartingSolution_)
      os << ", using zero starting solution" << endl;
    else
      os << ", using input starting solution" << endl;
    os << "Number of local blocks = " << Partitioner_->NumLocalParts() << endl;
    //os << "Condition number estimate = " << Condest_ << endl;
    os << "Global number of rows            = " << Matrix_->NumGlobalRows64() << endl;
    os << endl;
    os << "Phase           # calls   Total Time (s)       Total MFlops     MFlops/s" << endl;
    os << "-----           -------   --------------       ------------     --------" << endl;
    os << "Initialize()    "   << std::setw(5) << NumInitialize()
       << "  " << std::setw(15) << InitializeTime()
       << "  " << std::setw(15) << 1.0e-6 * InitializeFlops();
    if (InitializeTime() != 0.0)
      os << "  " << std::setw(15) << 1.0e-6 * InitializeFlops() / InitializeTime() << endl;
    else
      os << "  " << std::setw(15) << 0.0 << endl;
    os << "Compute()       "   << std::setw(5) << NumCompute()
       << "  " << std::setw(15) << ComputeTime()
       << "  " << std::setw(15) << 1.0e-6 * ComputeFlops();
    if (ComputeTime() != 0.0)
      os << "  " << std::setw(15) << 1.0e-6 * ComputeFlops() / ComputeTime() << endl;
    else
      os << "  " << std::setw(15) << 0.0 << endl;
    os << "ApplyInverse()  "   << std::setw(5) << NumApplyInverse()
       << "  " << std::setw(15) << ApplyInverseTime()
       << "  " << std::setw(15) << 1.0e-6 * ApplyInverseFlops();
    if (ApplyInverseTime() != 0.0)
      os << "  " << std::setw(15) << 1.0e-6 * ApplyInverseFlops() / ApplyInverseTime() << endl;
    else
      os << "  " << std::setw(15) << 0.0 << endl;
    os << "================================================================================" << endl;
    os << endl;
  }

  return(os);
}

//==============================================================================
template<typename T>
int Ifpack_BlockRelaxation<T>::SetParameters(Teuchos::ParameterList& List)
{
  using std::cerr;
  using std::endl;

  std::string PT;
  if (PrecType_ == IFPACK_JACOBI)
    PT = "Jacobi";
  else if (PrecType_ == IFPACK_GS)
    PT = "Gauss-Seidel";
  else if (PrecType_ == IFPACK_SGS)
    PT = "symmetric Gauss-Seidel";

  PT = List.get("relaxation: type", PT);

  if (PT == "Jacobi") {
    PrecType_ = IFPACK_JACOBI;
  }
  else if (PT == "Gauss-Seidel") {
    PrecType_ = IFPACK_GS;
  }
  else if (PT == "symmetric Gauss-Seidel") {
    PrecType_ = IFPACK_SGS;
  } else {
    cerr << "Option `relaxation: type' has an incorrect value ("
      << PT << ")'" << endl;
    cerr << "(file " << __FILE__ << ", line " << __LINE__ << ")" << endl;
    exit(EXIT_FAILURE);
  }

  NumSweeps_            = List.get("relaxation: sweeps", NumSweeps_);
  DampingFactor_        = List.get("relaxation: damping factor",
                                   DampingFactor_);
  ZeroStartingSolution_ = List.get("relaxation: zero starting solution",
                                   ZeroStartingSolution_);
  PartitionerType_      = List.get("partitioner: type",
                                   PartitionerType_);
  NumLocalBlocks_       = List.get("partitioner: local parts",
                                   NumLocalBlocks_);
  // only Jacobi can work with overlap among local domains,
  OverlapLevel_         = List.get("partitioner: overlap",
                                   OverlapLevel_);

  // check parameters
  if (PrecType_ != IFPACK_JACOBI)
    OverlapLevel_ = 0;
  if (NumLocalBlocks_ < 0)
    NumLocalBlocks_ = Matrix().NumMyRows() / (-NumLocalBlocks_);
  // other checks are performed in Partitioner_

  // copy the list as each subblock's constructor will
  // require it later
  List_ = List;

  // set the label
  std::string PT2;
  if (PrecType_ == IFPACK_JACOBI)
    PT2 = "BJ";
  else if (PrecType_ == IFPACK_GS)
    PT2 = "BGS";
  else if (PrecType_ == IFPACK_SGS)
    PT2 = "BSGS";
  Label_ = "IFPACK (" + PT2 + ", sweeps="
    + Ifpack_toString(NumSweeps_) + ", damping="
    + Ifpack_toString(DampingFactor_) + ", blocks="
    + Ifpack_toString(NumLocalBlocks()) + ")";

  return(0);
}

//==============================================================================
template<typename T>
int Ifpack_BlockRelaxation<T>::Initialize()
{
  IsInitialized_ = false;
  Time_.ResetStartTime();

  Graph_ = Teuchos::rcp( new Ifpack_Graph_Epetra_RowMatrix(Teuchos::rcp(&Matrix(),false)) );
  if (Graph_ == Teuchos::null) IFPACK_CHK_ERR(-5);

  if (PartitionerType_ == "linear")
    Partitioner_ = Teuchos::rcp( new Ifpack_LinearPartitioner(&*Graph_) );
  else if (PartitionerType_ == "greedy")
    Partitioner_ = Teuchos::rcp( new Ifpack_GreedyPartitioner(&*Graph_) );
  else if (PartitionerType_ == "metis")
    Partitioner_ = Teuchos::rcp( new Ifpack_METISPartitioner(&*Graph_) );
  else if (PartitionerType_ == "equation")
    Partitioner_ = Teuchos::rcp( new Ifpack_EquationPartitioner(&*Graph_) );
  else if (PartitionerType_ == "user")
    Partitioner_ = Teuchos::rcp( new Ifpack_UserPartitioner(&*Graph_) );
  else if (PartitionerType_ == "line")
    Partitioner_ = Teuchos::rcp( new Ifpack_LinePartitioner(&*Graph_) );
  else
    IFPACK_CHK_ERR(-2);

  if (Partitioner_ == Teuchos::null) IFPACK_CHK_ERR(-5);

  // need to partition the graph of A
  IFPACK_CHK_ERR(Partitioner_->SetParameters(List_));
  IFPACK_CHK_ERR(Partitioner_->Compute());

  // get actual number of partitions
  NumLocalBlocks_ = Partitioner_->NumLocalParts();

  // weight of each vertex
  W_ = Teuchos::rcp( new Epetra_Vector(Matrix().RowMatrixRowMap()) );
  W_->PutScalar(0.0);

  for (int i = 0 ; i < NumLocalBlocks() ; ++i) {

    for (int j = 0 ; j < Partitioner_->NumRowsInPart(i) ; ++j) {
      int LID = (*Partitioner_)(i,j);
      (*W_)[LID]++;
    }
  }
  W_->Reciprocal(*W_);

  // Update Label_ if line smoothing
  if (PartitionerType_ == "line") {
    // set the label
    std::string PT2;
    if (PrecType_ == IFPACK_JACOBI)
      PT2 = "BJ";
    else if (PrecType_ == IFPACK_GS)
      PT2 = "BGS";
    else if (PrecType_ == IFPACK_SGS)
      PT2 = "BSGS";
    Label_ = "IFPACK (" + PT2 + ", auto-line, sweeps="
      + Ifpack_toString(NumSweeps_) + ", damping="
      + Ifpack_toString(DampingFactor_) + ", blocks="
      + Ifpack_toString(NumLocalBlocks()) + ")";
  }

  InitializeTime_ += Time_.ElapsedTime();
  IsInitialized_ = true;
  ++NumInitialize_;

  return(0);
}

//==============================================================================
#endif // IFPACK_BLOCKPRECONDITIONER_H