doc/html/BlockKrylovSchur_2BlockKrylovSchurEpetraExGenAztecOO_8cpp-example.html

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//                 Anasazi: Block Eigensolvers Package

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// This example computes the eigenvalues of smallest magnitude of a

// generalized eigenvalue problem $K x = \lambda M x$, using Anasazi's

// implementation of the block Krylov-Schur method.  It implements

// inverse iteration using an AztecOO iterative linear solver with an

// Ifpack preconditioner.

//

// Anasazi computes the smallest-magnitude eigenvalues using a

// shift-and-invert strategy.  For simplicity, the code below uses a

// shift of zero.  It illustrates the general pattern for using

// Anasazi for this problem:

//

//   1. Construct an "operator" A such that $Az = K^{-1} M z$.

//   2. Use Anasazi to solve $Az = \sigma z$, which is a spectral

//      transformation of the original problem $K x = \lambda M x$.

//   3. The eigenvalues $\lambda$ of the original problem are the

//      inverses of the eigenvalues $\sigma$ of the transformed

//      problem.

//

// The "operator A such that $A z = K^{-1} M z$" is a subclass of

// Epetra_Operator.  The Apply method of that operator takes the

// vector b, and computes $x = K^{-1} M b$.  It does so first by

// applying the matrix M, and then by solving the linear system $K x =

// M b$ for x.  Trilinos implements many different ways to solve

// linear systems.  The example below uses an iterative linear solver

// provided by the AztecOO package, with an Ifpack preconditioner, to

// solve linear systems.


// Include header for block Krylov-Schur solver

#include "AnasaziBlockKrylovSchurSolMgr.hpp"

// Include header to define basic eigenproblem Ax = \lambda*Bx

#include "AnasaziBasicEigenproblem.hpp"

// Include header to provide Anasazi with Epetra adapters.  If you

// plan to use Tpetra objects instead of Epetra objects, include

// AnasaziTpetraAdapter.hpp instead; do analogously if you plan to use

// Thyra objects instead of Epetra objects.

#include "AnasaziEpetraAdapter.hpp"

// Include header for Epetra sparse matrix, Map (representation of

// parallel distributions), and linear problem.  AztecOO uses the

// latter to encapsulate linear systems to solve.

#include "Epetra_Map.h"

#include "Epetra_CrsMatrix.h"

#include "Epetra_LinearProblem.h"

// Include header for AztecOO iterative linear solver, and

// AztecOO_Operator.  The latter wraps an AztecOO solver in an

// Epetra_Operator.

#include "AztecOO.h"

#include "AztecOO_Operator.h"

// Include header for Ifpack preconditioner factory

#include "Ifpack.h"

// Include header for Teuchos serial dense matrix, which we use to

// compute the eigenvectors.

#include "Teuchos_SerialDenseMatrix.hpp"

// Include header for the problem definition

#include "ModeLaplace2DQ2.h"


// Include selected communicator class and map required by Epetra objects

#ifdef EPETRA_MPI

#  include "Epetra_MpiComm.h"

#else

#  include "Epetra_SerialComm.h"

#endif // EPETRA_MPI


// ****************************************************************************

// BEGIN MAIN ROUTINE

// ****************************************************************************


int

main (int argc, char *argv[])

{

  using Teuchos::RCP;

  using Teuchos::rcp;

  using std::cerr;

  using std::cout;

  using std::endl;

  // Anasazi solvers have the following template parameters:

  //

  //   - Scalar: The type of dot product results.

  //   - MV: The type of (multi)vectors.

  //   - OP: The type of operators (functions from multivector to

  //     multivector).  A matrix (like Epetra_CrsMatrix) is an example

  //     of an operator; an Ifpack preconditioner is another example.

  //

  // Here, Scalar is double, MV is Epetra_MultiVector, and OP is

  // Epetra_Operator.

  typedef Epetra_MultiVector MV;

  typedef Epetra_Operator OP;

  typedef Anasazi::MultiVecTraits<double, MV> MVT;


#ifdef EPETRA_MPI

  // Initialize MPI

  MPI_Init (&argc, &argv);

  Epetra_MpiComm Comm (MPI_COMM_WORLD);

#else

  Epetra_SerialComm Comm;

#endif // EPETRA_MPI


  const int MyPID = Comm.MyPID ();


  //

  // Set up the test problem

  //


  // Dimensionality of the spatial domain to discretize

  const int space_dim = 2;


  // Size of each of the dimensions of the (discrete) domain

  std::vector<double> brick_dim (space_dim);

  brick_dim[0] = 1.0;

  brick_dim[1] = 1.0;


  // Number of elements in each of the dimensions of the domain

  std::vector<int> elements (space_dim);

  elements[0] = 10;

  elements[1] = 10;


  // Create the test problem

  RCP<ModalProblem> testCase =

    rcp (new ModeLaplace2DQ2 (Comm, brick_dim[0], elements[0],

                              brick_dim[1], elements[1]));


  // Get the stiffness and mass matrices.

  //

  // rcp (T*, false) returns a nonowning (doesn't deallocate) RCP.

  RCP<Epetra_CrsMatrix> K =

    rcp (const_cast<Epetra_CrsMatrix* > (testCase->getStiffness ()), false);

  RCP<Epetra_CrsMatrix> M =

    rcp (const_cast<Epetra_CrsMatrix*> (testCase->getMass ()), false);


  //

  // Create linear solver for linear systems with K

  //

  // Anasazi uses shift and invert, with a "shift" of zero, to find

  // the eigenvalues of least magnitude.  In this example, we

  // implement the "invert" part of shift and invert by using an

  // AztecOO iterative linear solver with an Ifpack preconditioner.

  //


  //

  // Construct Ifpack preconditioner

  //


  // An Ifpack "factory" knows how to create Ifpack preconditioners.

  Ifpack Factory;


  // Use the Factory to create the preconditioner.  Factory.Create()

  // returns a raw Ifpack2_Preconditioner pointer.  The caller (that's

  // us!) is responsible for deallocation, so we use an owning RCP to

  // deallocate it automatically.

  //

  // The Factory needs a string name of the preconditioner, and the

  // overlap level.  (Almost) all Ifpack preconditioners are local to

  // each MPI process.  Ifpack automatically does an additive Schwarz

  // decomposition across processes.  The default overlap level for

  // additive Schwarz is zero, but you can use a different overlap

  // level here if you want.  The overlap level must be nonnegative,

  // and only matters if running with more than one MPI process.

  std::string PrecType = "ICT"; // incomplete Cholesky

  const int OverlapLevel = 0;

  // Create the preconditioner.

  RCP<Ifpack_Preconditioner> Prec =

    rcp (Factory.Create (PrecType, &*K, OverlapLevel));

  if (Prec.is_null ()) {

    throw std::logic_error ("Ifpack's factory returned a NULL preconditioner!");

  }


  //

  // Set Ifpack preconditioner parameters.

  //

  // Set parameters after creating the preconditioner.  Please refer

  // to Ifpack's documentation for a list of valid parameters.

  //

  Teuchos::ParameterList ifpackList;

  ifpackList.set ("fact: drop tolerance", 1e-4);

  ifpackList.set ("fact: ict level-of-fill", 0.0);

  // The "combine mode" describes how to combine contributions from

  // other MPI processes.  It only matters if the overlap level is

  // nonzero.  See Epetra_CombineMode.h for documentation of of the

  // various combine modes.

  ifpackList.set ("schwarz: combine mode", "Add");


  // Set the parameters.

  IFPACK_CHK_ERR(Prec->SetParameters(ifpackList));


  // Initialize the preconditioner.  This only looks at the structure

  // of the matrix, not the values.  Nevertheless, the matrix must

  // generally be fill complete at this point.  Compare Initialize()

  // to a symbolic factorization, and Compute() (see below) to a

  // numeric factorization.

  IFPACK_CHK_ERR(Prec->Initialize());


  // Compute the preconditioner.  This looks at both the structure and

  // the values of the matrix.  Compare Initialize() (see above) to a

  // symbolic factorization, and Compute() (see below) to a numeric

  // factorization.

  IFPACK_CHK_ERR(Prec->Compute());


  //

  // Set up AztecOO iterative solver for solving linear systems with K.

  //


  // Create Epetra linear problem class for solving linear systems

  // with K.  This implements the inverse operator for shift and

  // invert.

  Epetra_LinearProblem precProblem;

  // Tell the linear problem about the matrix K.  Epetra_LinearProblem

  // doesn't know about RCP, so we have to give it a raw pointer.

  precProblem.SetOperator (K.getRawPtr ());


  // Create AztecOO iterative solver for solving linear systems with K.

  AztecOO precSolver (precProblem);

  // Tell the solver to use the Ifpack preconditioner we created above.

  precSolver.SetPrecOperator (Prec.get ());

  // Set AztecOO solver options.

  precSolver.SetAztecOption (AZ_output, AZ_none); // Don't print output

  precSolver.SetAztecOption (AZ_solver, AZ_cg); // Use CG


  // Use the above AztecOO solver to create the AztecOO_Operator.

  // This is the place where we tell the AztecOO solver the maximum

  // number of iterations (here, we use the matrix dimension; in

  // practice, you'll want a smaller number) and the convergence

  // tolerance (here, 1e-12).

  RCP<AztecOO_Operator> precOperator =

    rcp (new AztecOO_Operator (&precSolver, K->NumGlobalRows (), 1e-12));


  // Create an Operator that computes y = K^{-1} M x.

  //

  // This Operator object is the operator we give to Anasazi.  Thus,

  // Anasazi just sees an operator that computes y = K^{-1} M x.  The

  // matrix K got absorbed into precOperator via precProblem (the

  // Epetra_LinearProblem object).  Later, when we set up the Anasazi

  // eigensolver, we will need to tell it about M, so that it can

  // orthogonalize basis vectors with respect to the inner product

  // defined by M (since it is symmetric positive definite).

  RCP<Anasazi::EpetraGenOp> Aop = rcp (new Anasazi::EpetraGenOp (precOperator, M));


  //

  // Set parameters for the block Krylov-Schur eigensolver

  //


  double tol = 1.0e-8;

  int nev = 10;

  int blockSize = 3;

  int numBlocks = 3 * nev / blockSize;

  int maxRestarts = 10;


  // We're looking for the largest-magnitude eigenvalues of the

  // _inverse_ operator, thus, the smallest-magnitude eigenvalues of

  // the original operator.

  std::string which = "LM";

  int verbosity = Anasazi::Errors + Anasazi::Warnings + Anasazi::FinalSummary;


  // Create ParameterList to pass into eigensolver

  Teuchos::ParameterList MyPL;

  MyPL.set ("Verbosity", verbosity);

  MyPL.set ("Which", which);

  MyPL.set ("Block Size", blockSize);

  MyPL.set ("Num Blocks", numBlocks);

  MyPL.set ("Maximum Restarts", maxRestarts);

  MyPL.set ("Convergence Tolerance", tol);


  // Create an initial set of vectors to start the eigensolver.  Note:

  // This needs to have the same number of columns as the block size.

  RCP<MV> ivec = rcp (new MV (K->Map (), blockSize));

  MVT::MvRandom (*ivec);


  // This object holds all the stuff about your problem that Anasazi

  // will see.

  //

  // Anasazi only needs M so that it can orthogonalize basis vectors

  // with respect to the M inner product.  Wouldn't it be nice if

  // Anasazi didn't require M in two different places?  Alas, this is

  // not currently the case.

  RCP<Anasazi::BasicEigenproblem<double,MV,OP> > MyProblem =

    rcp (new Anasazi::BasicEigenproblem<double,MV,OP> (Aop, M, ivec));


  // Tell the eigenproblem that the matrix pencil (K,M) is symmetric.

  MyProblem->setHermitian (true);


  // Set the number of eigenvalues requested

  MyProblem->setNEV (nev);


  // Tell the eigenproblem that you are finished passing it information.

  bool boolret = MyProblem->setProblem();

  if (boolret != true) {

    if (MyPID == 0) {

      cout << "Anasazi::BasicEigenproblem::setProblem() returned with error." << endl;

    }

#ifdef EPETRA_MPI

    MPI_Finalize ();

#endif // EPETRA_MPI

    return -1;

  }


  // Create the Block Krylov-Schur eigensolver.

  Anasazi::BlockKrylovSchurSolMgr<double, MV, OP> MySolverMgr (MyProblem, MyPL);


  // Solve the eigenvalue problem.

  //

  // Note that creating the eigensolver is separate from solving it.

  // After creating the eigensolver, you may call solve() multiple

  // times with different parameters or initial vectors.  This lets

  // you reuse intermediate state, like allocated basis vectors.

  Anasazi::ReturnType returnCode = MySolverMgr.solve ();

  if (returnCode != Anasazi::Converged && MyPID == 0) {

    cout << "Anasazi::EigensolverMgr::solve() returned unconverged." << endl;

  }


  // Get the eigenvalues and eigenvectors from the eigenproblem.

  Anasazi::Eigensolution<double,MV> sol = MyProblem->getSolution ();

  // Anasazi returns eigenvalues as Anasazi::Value, so that if

  // Anasazi's Scalar type is real-valued (as it is in this case), but

  // some eigenvalues are complex, you can still access the

  // eigenvalues correctly.  In this case, there are no complex

  // eigenvalues, since the matrix pencil is symmetric.

  std::vector<Anasazi::Value<double> > evals = sol.Evals;

  Teuchos::RCP<MV> evecs = sol.Evecs;

  int numev = sol.numVecs;


  if (numev > 0) {

    // Reconstruct the eigenvalues.  The ones that Anasazi gave back

    // are the inverses of the original eigenvalues.  Reconstruct the

    // eigenvectors too.

    Teuchos::SerialDenseMatrix<int,double> dmatr(numev,numev);

    MV tempvec (K->Map (), MVT::GetNumberVecs (*evecs));

    K->Apply (*evecs, tempvec);

    MVT::MvTransMv (1.0, tempvec, *evecs, dmatr);


    if (MyPID == 0) {

      double compeval = 0.0;

      cout.setf (std::ios_base::right, std::ios_base::adjustfield);

      cout << "Actual Eigenvalues (obtained by Rayleigh quotient) : " << endl;

      cout << "------------------------------------------------------" << endl;

      cout << std::setw(16) << "Real Part"

           << std::setw(16) << "Rayleigh Error" << endl;

      cout << "------------------------------------------------------" << endl;

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

        compeval = dmatr(i,i);

        cout << std::setw(16) << compeval

             << std::setw(16)

             << std::fabs (compeval - 1.0/evals[i].realpart)

             << endl;

      }

      cout << "------------------------------------------------------" << endl;

    }


  }


#ifdef EPETRA_MPI

  MPI_Finalize ();

#endif // EPETRA_MPI


  return 0;

}