test/Relaxation_LL/cxx_main.cpp

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//       Ifpack: Object-Oriented Algebraic Preconditioner Package
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#include "Ifpack_ConfigDefs.h"
 
#ifdef HAVE_MPI
#include "Epetra_MpiComm.h"
#else
#include "Epetra_SerialComm.h"
#endif
#include "Epetra_CrsMatrix.h"
#include "Epetra_Vector.h"
#include "Epetra_LinearProblem.h"
#include "Epetra_Map.h"
#include "Galeri_Maps.h"
#include "Galeri_CrsMatrices.h"
#include "Galeri_Utils.h"
#include "Teuchos_ParameterList.hpp"
#include "Teuchos_RefCountPtr.hpp"
#include "Ifpack_PointRelaxation.h"
#include "Ifpack_BlockRelaxation.h"
#include "Ifpack_SparseContainer.h"
#include "Ifpack_Amesos.h"
#include "AztecOO.h"
 
static bool verbose = false;
static bool SymmetricGallery = false;
static bool Solver = AZ_gmres;
const int NumVectors = 3;
 
// ====================================================================== 
int CompareBlockOverlap(const Teuchos::RefCountPtr<Epetra_RowMatrix>& A, int Overlap)
{
  Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
  Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
  LHS.PutScalar(0.0); RHS.Random();
 
  Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
 
  Teuchos::ParameterList List;
  List.set("relaxation: damping factor", 1.0);
  List.set("relaxation: type", "Jacobi");
  List.set("relaxation: sweeps",1);
  List.set("partitioner: overlap", Overlap);
  List.set("partitioner: type", "linear");
  List.set("partitioner: local parts", 16);
 
  RHS.PutScalar(1.0);
  LHS.PutScalar(0.0);
 
  Ifpack_BlockRelaxation<Ifpack_SparseContainer<Ifpack_Amesos> > Prec(&*A);
  Prec.SetParameters(List);
  Prec.Compute();
 
  // set AztecOO solver object
  AztecOO AztecOOSolver(Problem);
  AztecOOSolver.SetAztecOption(AZ_solver,Solver);
  if (verbose)
    AztecOOSolver.SetAztecOption(AZ_output,32);
  else
    AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
  AztecOOSolver.SetPrecOperator(&Prec);
 
  AztecOOSolver.Iterate(1550,1e-5);
 
  return(AztecOOSolver.NumIters());
}
 
// ====================================================================== 
int CompareBlockSizes(std::string PrecType, const Teuchos::RefCountPtr<Epetra_RowMatrix>& A, int NumParts)
{
  Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
  Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
  LHS.PutScalar(0.0); RHS.Random();
 
  Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
 
  Teuchos::ParameterList List;
  List.set("relaxation: damping factor", 1.0);
  List.set("relaxation: type", PrecType);
  List.set("relaxation: sweeps",1);
  List.set("partitioner: type", "linear");
  List.set("partitioner: local parts", NumParts);
 
  RHS.PutScalar(1.0);
  LHS.PutScalar(0.0);
 
  Ifpack_BlockRelaxation<Ifpack_SparseContainer<Ifpack_Amesos> > Prec(&*A);
  Prec.SetParameters(List);
  Prec.Compute();
 
  // set AztecOO solver object
  AztecOO AztecOOSolver(Problem);
  AztecOOSolver.SetAztecOption(AZ_solver,Solver);
  if (verbose)
    AztecOOSolver.SetAztecOption(AZ_output,32);
  else
    AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
  AztecOOSolver.SetPrecOperator(&Prec);
 
  AztecOOSolver.Iterate(1550,1e-5);
 
  return(AztecOOSolver.NumIters());
}
 
// ====================================================================== 
bool ComparePointAndBlock(std::string PrecType, const Teuchos::RefCountPtr<Epetra_RowMatrix>& A, int sweeps)
{
  Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
  Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
  LHS.PutScalar(0.0); RHS.Random();
 
  Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
 
  // Set up the list
  Teuchos::ParameterList List;
  List.set("relaxation: damping factor", 1.0);
  List.set("relaxation: type", PrecType);
  List.set("relaxation: sweeps",sweeps);
  List.set("partitioner: type", "linear");
  List.set("partitioner: local parts", A->NumMyRows());
 
  int ItersPoint, ItersBlock;
 
  // ================================================== //
  // get the number of iterations with point relaxation //
  // ================================================== //
  {
    RHS.PutScalar(1.0);
    LHS.PutScalar(0.0);
 
    Ifpack_PointRelaxation Point(&*A);
    Point.SetParameters(List);
    Point.Compute();
 
    // set AztecOO solver object
    AztecOO AztecOOSolver(Problem);
    AztecOOSolver.SetAztecOption(AZ_solver,Solver);
    if (verbose)
      AztecOOSolver.SetAztecOption(AZ_output,32);
    else
      AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
    AztecOOSolver.SetPrecOperator(&Point);
 
    AztecOOSolver.Iterate(1550,1e-2);
 
    double TrueResidual = AztecOOSolver.TrueResidual();
    ItersPoint = AztecOOSolver.NumIters();
    // some output
    if (verbose && Problem.GetMatrix()->Comm().MyPID() == 0) {
      cout << "Iterations  = " << ItersPoint << endl;
      cout << "Norm of the true residual = " << TrueResidual << endl;
    }
  }
 
  // ================================================== //
  // get the number of iterations with block relaxation //
  // ================================================== //
  {
 
    RHS.PutScalar(1.0);
    LHS.PutScalar(0.0);
 
    Ifpack_BlockRelaxation<Ifpack_SparseContainer<Ifpack_Amesos> > Block(&*A);
    Block.SetParameters(List);
    Block.Compute();
 
    // set AztecOO solver object
    AztecOO AztecOOSolver(Problem);
    AztecOOSolver.SetAztecOption(AZ_solver,Solver);
    if (verbose)
      AztecOOSolver.SetAztecOption(AZ_output,32);
    else
      AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
    AztecOOSolver.SetPrecOperator(&Block);
 
    AztecOOSolver.Iterate(1550,1e-2);
 
    double TrueResidual = AztecOOSolver.TrueResidual();
    ItersBlock = AztecOOSolver.NumIters();
    // some output
    if (verbose && Problem.GetMatrix()->Comm().MyPID() == 0) {
      cout << "Iterations " << ItersBlock << endl;
      cout << "Norm of the true residual = " << TrueResidual << endl;
    }
  }
 
  int diff = ItersPoint - ItersBlock;
  if (diff < 0) diff = -diff;
    
  if (diff > 10)
  {
    if (verbose)
      cout << "TEST FAILED!" << endl;
    return(false);
  }
  else {
    if (verbose)
      cout << "TEST PASSED" << endl;
    return(true);
  }
}
 
// ====================================================================== 
bool KrylovTest(std::string PrecType, const Teuchos::RefCountPtr<Epetra_RowMatrix>& A, bool backward)
{
  Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
  Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
  LHS.PutScalar(0.0); RHS.Random();
 
  Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
 
  // Set up the list
  Teuchos::ParameterList List;
  List.set("relaxation: damping factor", 1.0);
  List.set("relaxation: type", PrecType);
  if(backward) List.set("relaxation: backward mode",backward);  
 
  int Iters1, Iters10;
 
  if (verbose) {
    cout << "Krylov test: Using " << PrecType 
         << " with AztecOO" << endl;
  }
 
  // ============================================== //
  // get the number of iterations with 1 sweep only //
  // ============================================== //
  {
 
    List.set("relaxation: sweeps",1);
    Ifpack_PointRelaxation Point(&*A);
    Point.SetParameters(List);
    Point.Compute();
 
    // set AztecOO solver object
    AztecOO AztecOOSolver(Problem);
    AztecOOSolver.SetAztecOption(AZ_solver,Solver);
    AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
    AztecOOSolver.SetPrecOperator(&Point);
 
    AztecOOSolver.Iterate(1550,1e-5);
 
    double TrueResidual = AztecOOSolver.TrueResidual();
    // some output
    if (verbose && Problem.GetMatrix()->Comm().MyPID() == 0) {
      cout << "Norm of the true residual = " << TrueResidual << endl;
    }
    Iters1 = AztecOOSolver.NumIters();
  }
 
  // ======================================================== //
  // now re-run with 10 sweeps, solver should converge faster
  // ======================================================== //
  {
    List.set("relaxation: sweeps",10);
    Ifpack_PointRelaxation Point(&*A);
    Point.SetParameters(List);
    Point.Compute();
    LHS.PutScalar(0.0);
 
    // set AztecOO solver object
    AztecOO AztecOOSolver(Problem);
    AztecOOSolver.SetAztecOption(AZ_solver,Solver);
    AztecOOSolver.SetAztecOption(AZ_output,AZ_none);
    AztecOOSolver.SetPrecOperator(&Point);
    AztecOOSolver.Iterate(1550,1e-5);
 
    double TrueResidual = AztecOOSolver.TrueResidual();
    // some output
    if (verbose && Problem.GetMatrix()->Comm().MyPID() == 0) {
      cout << "Norm of the true residual = " << TrueResidual << endl;
    }
    Iters10 = AztecOOSolver.NumIters();
  }
 
  if (verbose) {
    cout << "Iters_1 = " << Iters1 << ", Iters_10 = " << Iters10 << endl;
    cout << "(second number should be smaller than first one)" << endl;
  }
 
  if (Iters10 > Iters1) {
    if (verbose)
      cout << "TEST FAILED!" << endl;
    return(false);
  }
  else {
    if (verbose)
      cout << "TEST PASSED" << endl;
    return(true);
  }
}
 
// ====================================================================== 
bool BasicTest(std::string PrecType, const Teuchos::RefCountPtr<Epetra_RowMatrix>& A,bool backward)
{
  Epetra_MultiVector LHS(A->RowMatrixRowMap(), NumVectors);
  Epetra_MultiVector RHS(A->RowMatrixRowMap(), NumVectors);
  LHS.PutScalar(0.0); RHS.Random();
 
  double starting_residual = Galeri::ComputeNorm(&*A, &LHS, &RHS);
  Epetra_LinearProblem Problem(&*A, &LHS, &RHS);
 
  // Set up the list
  Teuchos::ParameterList List;
  List.set("relaxation: damping factor", 1.0);
  List.set("relaxation: sweeps",1550);
  List.set("relaxation: type", PrecType);
  if(backward) List.set("relaxation: backward mode",backward);
  
 
  Ifpack_PointRelaxation Point(&*A);
 
  Point.SetParameters(List);
  Point.Compute();
  // use the preconditioner as solver, with 1550 iterations
  Point.ApplyInverse(RHS,LHS);
 
  // compute the real residual
 
  double residual = Galeri::ComputeNorm(&*A, &LHS, &RHS);
  
  if (A->Comm().MyPID() == 0 && verbose)
    cout << "||A * x - b||_2 (scaled) = " << residual / starting_residual << endl;
  
  // Jacobi is very slow to converge here
  if (residual / starting_residual < 1e-2) {
    if (verbose)
      cout << "Test passed" << endl;
    return(true);
  }
  else {
    if (verbose)
      cout << "Test failed!" << endl;
    return(false);
  }
}
 
// ====================================================================== 
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
  MPI_Init(&argc,&argv);
  Epetra_MpiComm Comm( MPI_COMM_WORLD );
#else
  Epetra_SerialComm Comm;
#endif
 
  verbose = (Comm.MyPID() == 0);
 
  for (int i = 1 ; i < argc ; ++i) {
    if (strcmp(argv[i],"-s") == 0) {
      SymmetricGallery = true;
      Solver = AZ_cg;
    }
  }
 
  // size of the global matrix. 
  Teuchos::ParameterList GaleriList;
  int nx = 30; 
  GaleriList.set("nx", nx);
  GaleriList.set("ny", nx * Comm.NumProc());
  GaleriList.set("mx", 1);
  GaleriList.set("my", Comm.NumProc());
  Teuchos::RefCountPtr<Epetra_Map> Map = Teuchos::rcp( Galeri::CreateMap64("Cartesian2D", Comm, GaleriList) );
  Teuchos::RefCountPtr<Epetra_CrsMatrix> A;
  if (SymmetricGallery)
    A = Teuchos::rcp( Galeri::CreateCrsMatrix("Laplace2D", &*Map, GaleriList) );
  else
    A = Teuchos::rcp( Galeri::CreateCrsMatrix("Recirc2D", &*Map, GaleriList) );
 
  // test the preconditioner
  int TestPassed = true;
 
  // ======================================== //
  // first verify that we can get convergence //
  // with all point relaxation methods        //
  // ======================================== //
 
  if(!BasicTest("Jacobi",A,false))
    TestPassed = false;
 
  if(!BasicTest("symmetric Gauss-Seidel",A,false))
    TestPassed = false;
 
  if (!SymmetricGallery) {
    if(!BasicTest("Gauss-Seidel",A,false))
      TestPassed = false;
    if(!BasicTest("Gauss-Seidel",A,true))
      TestPassed = false;  
 
  }
 
  // ============================= //
  // check uses as preconditioners //
  // ============================= //
  
  if(!KrylovTest("symmetric Gauss-Seidel",A,false))
    TestPassed = false;
 
  if (!SymmetricGallery) {
    if(!KrylovTest("Gauss-Seidel",A,false))
      TestPassed = false;
    if(!KrylovTest("Gauss-Seidel",A,true))
      TestPassed = false;
 
  }
 
  // ================================== //
  // compare point and block relaxation //
  // ================================== //
 
  //TestPassed = TestPassed && 
   // ComparePointAndBlock("Jacobi",A,1);
 
  TestPassed = TestPassed && 
    ComparePointAndBlock("Jacobi",A,10);
 
  //TestPassed = TestPassed && 
    //ComparePointAndBlock("symmetric Gauss-Seidel",A,1);
 
  TestPassed = TestPassed && 
    ComparePointAndBlock("symmetric Gauss-Seidel",A,10);
 
  if (!SymmetricGallery) {
    //TestPassed = TestPassed && 
      //ComparePointAndBlock("Gauss-Seidel",A,1);
 
    TestPassed = TestPassed && 
      ComparePointAndBlock("Gauss-Seidel",A,10);
  }
 
  // ============================ //
  // verify effect of # of blocks //
  // ============================ //
  
  {
    int Iters4, Iters8, Iters16;
    Iters4 = CompareBlockSizes("Jacobi",A,4);
    Iters8 = CompareBlockSizes("Jacobi",A,8);
    Iters16 = CompareBlockSizes("Jacobi",A,16);
 
    if ((Iters16 > Iters8) && (Iters8 > Iters4)) {
      if (verbose)
        cout << "Test passed" << endl;
    }
    else {
      if (verbose) 
        cout << "TEST FAILED!" << endl;
      TestPassed = TestPassed && false;
    }
  }
 
  // ================================== //
  // verify effect of overlap in Jacobi //
  // ================================== //
 
  {
    int Iters0, Iters2, Iters4;
    Iters0 = CompareBlockOverlap(A,0);
    Iters2 = CompareBlockOverlap(A,2);
    Iters4 = CompareBlockOverlap(A,4);
    if ((Iters4 < Iters2) && (Iters2 < Iters0)) {
      if (verbose)
        cout << "Test passed" << endl;
    }
    else {
      if (verbose) 
        cout << "TEST FAILED!" << endl;
      TestPassed = TestPassed && false;
    }
  }
 
  // ============ //
  // final output //
  // ============ //
 
  if (!TestPassed) {
    cout << "Test `TestRelaxation.exe' failed!" << endl;
    exit(EXIT_FAILURE);
  }
  
#ifdef HAVE_MPI
  MPI_Finalize(); 
#endif
  
  cout << endl;
  cout << "Test `TestRelaxation.exe' passed!" << endl;
  cout << endl;
  return(EXIT_SUCCESS);
}