Belos  Version of the Day
epetra/example/PCPG/PCPGEpetraExFile.cpp

This is an example of how to use the Belos::PCPGSolMgr with an ML preconditioner.

// *****************************************************************************
// Belos: Block Linear Solvers Package
//
// Copyright 2004-2016 NTESS and the Belos contributors.
// *****************************************************************************
// Purpose
// The example tests the successive right-hand sides capabilities of ML
// and Belos on a heat flow u_t = u_xx problem.
//
// A sequence of linear systems with the same coefficient matrix and
// different right-hand sides is solved. A seed space is generated dynamically,
// and a deflated linear system is solved. After each solves, the first
// few Krylov vectors are saved, and used to reduce the number of iterations
// for later solves.
// The optimal numbers of vectors to deflate and save are not known.
// Presently, the maximum number of vectors to deflate (seed space dimension)
// and to save are user paraemters.
// The seed space dimension is less than or equal to total number of vectors saved.
// The difference between the seed space dimension and the total number of vectors,
// is the number of vectors used to update the seed space after each solve.
// I guess that a seed space whose dimension is a small fraction of the total space
// will be best.
//
// maxSave=1 and maxDeflate=0 uses no recycling (not tested ).
//
// TODO: Instrument with timers, so that we can tell what is going on besides
// by counting the numbers of iterations.
//
//
// \author David M. Day
//
#include "ml_include.h" //--enable-epetra --enable-teuchos.
#include "Epetra_Map.h"
#ifdef EPETRA_MPI
#include "Epetra_MpiComm.h"
#else
#include "Epetra_SerialComm.h"
#endif
#include "Epetra_Vector.h"
#include "Epetra_CrsMatrix.h"
#include "EpetraExt_MatrixMatrix.h" // build the example
#include "ml_MultiLevelPreconditioner.h" // ML
#include "Teuchos_StandardCatchMacros.hpp"
int main(int argc, char *argv[]) {
//
int MyPID = 0;
int numProc = 1;
#ifdef EPETRA_MPI
MPI_Init(&argc,&argv); // Initialize MPI
Epetra_MpiComm Comm(MPI_COMM_WORLD);
MyPID = Comm.MyPID();
numProc = Comm.NumProc();
#else
#endif
//
// Laplace's equation, homogeneous Dirichlet boundary conditions, [0,1]^2
// regular mesh, Q1 finite elements
//
typedef double ST;
typedef SCT::magnitudeType MT;
typedef Epetra_MultiVector MV;
typedef Epetra_Operator OP;
using Teuchos::ParameterList; // all of this may look fine but do not be fooled ...
using Teuchos::RCP; // it is not so clear what any of this does
using Teuchos::rcp;
bool verbose = false;
bool success = true;
try {
bool proc_verbose = false;
int frequency = -1; // frequency of status test output.
int blocksize = 1; // blocksize, PCPGIter
int numrhs = 1; // number of right-hand sides to solve for
int maxiters = 30; // maximum number of iterations allowed per linear system
int maxDeflate = 8; // maximum number of vectors deflated from the linear system;
// There is no overhead cost assoc with changing maxDeflate between solves
int maxSave = 16; // maximum number of vectors saved from current and previous .");
// If maxSave changes between solves, then re-initialize (setSize).
// Hypothesis: seed vectors are conjugate.
// Initial versions allowed users to supply a seed space et cetera, but no longer.
// The documentation it suitable for certain tasks, like defining a modules grammar,
std::string ortho("ICGS"); // The Belos documentation obscures the fact that
// IMGS is Iterated Modified Gram Schmidt,
// ICGS is Iterated Classical Gram Schmidt, and
// DKGS is another Iterated Classical Gram Schmidt.
// Mathematical issues, such as the difference between ICGS and DKGS, are not documented at all.
// UH tells me that Anasazi::SVQBOrthoManager is available; I need it for Belos
MT tol = 1.0e-8; // relative residual tolerance
// How do command line parsers work?
cmdp.setOption("verbose","quiet",&verbose,"Print messages and results");
cmdp.setOption("frequency",&frequency,"Solvers frequency for printing residuals (#iters)");
cmdp.setOption("tol",&tol,"Relative residual tolerance used by PCPG solver");
cmdp.setOption("num-rhs",&numrhs,"Number of right-hand sides to be solved for");
cmdp.setOption("max-iters",&maxiters,"Maximum number of iterations per linear system (-1 = adapted to problem/block size)");
cmdp.setOption("num-deflate",&maxDeflate,"Number of vectors deflated from the linear system");
cmdp.setOption("num-save",&maxSave,"Number of vectors saved from old Krylov subspaces");
cmdp.setOption("ortho-type",&ortho,"Orthogonalization type, either DGKS, ICGS or IMGS");
return -1;
}
if (!verbose)
frequency = -1; // reset frequency if test is not verbose
//
// *************Form the problem*********************
//
int numElePerDirection = 14*numProc; // 5 -> 20
int num_time_step = 4;
int numNodes = (numElePerDirection - 1)*(numElePerDirection - 1);
//By the way, either matrix has (3*numElePerDirection - 2)^2 nonzeros.
RCP<Epetra_Map> Map = rcp(new Epetra_Map(numNodes, 0, Comm) );
RCP<Epetra_CrsMatrix> Stiff = rcp(new Epetra_CrsMatrix(Epetra_DataAccess::Copy, *Map, 0) );
RCP<Epetra_CrsMatrix> Mass = rcp(new Epetra_CrsMatrix(Epetra_DataAccess::Copy, *Map, 0) );
RCP<Epetra_Vector> vecLHS = rcp( new Epetra_Vector(*Map) );
RCP<Epetra_Vector> vecRHS = rcp( new Epetra_Vector(*Map) );
RCP<Epetra_MultiVector> LHS, RHS;
double ko = 8.0/3.0, k1 = -1.0/3.0;
double h = 1.0/(double) numElePerDirection; // x=(iX,iY)h
double mo = h*h*4.0/9.0, m1 = h*h/9.0, m2 = h*h/36.0;
double pi = 4.0*atan(1.0), valueLHS;
int lid, node, pos, iX, iY;
for(lid = Map->MinLID(); lid <= Map->MaxLID(); lid++){
node = Map->GID(lid);
iX = node % (numElePerDirection-1);
iY = ( node - iX )/(numElePerDirection-1);
pos = node;
Stiff->InsertGlobalValues(node, 1, &ko, &pos);
Mass->InsertGlobalValues(node, 1, &mo, &pos); // init guess violates hom Dir bc
valueLHS = sin( pi*h*((double) iX+1) )*cos( 2.0 * pi*h*((double) iY+1) );
vecLHS->ReplaceGlobalValues( 1, &valueLHS, &node);
if (iY > 0) {
pos = iX + (iY-1)*(numElePerDirection-1);
Stiff->InsertGlobalValues(node, 1, &k1, &pos); //North
Mass->InsertGlobalValues(node, 1, &m1, &pos);
}
if (iY < numElePerDirection-2) {
pos = iX + (iY+1)*(numElePerDirection-1);
Stiff->InsertGlobalValues(node, 1, &k1, &pos); //South
Mass->InsertGlobalValues(node, 1, &m1, &pos);
}
if (iX > 0) {
pos = iX-1 + iY*(numElePerDirection-1);
Stiff->InsertGlobalValues(node, 1, &k1, &pos); // West
Mass->InsertGlobalValues(node, 1, &m1, &pos);
if (iY > 0) {
pos = iX-1 + (iY-1)*(numElePerDirection-1);
Stiff->InsertGlobalValues(node, 1, &k1, &pos); // North West
Mass->InsertGlobalValues(node, 1, &m2, &pos);
}
if (iY < numElePerDirection-2) {
pos = iX-1 + (iY+1)*(numElePerDirection-1);
Stiff->InsertGlobalValues(node, 1, &k1, &pos); // South West
Mass->InsertGlobalValues(node, 1, &m2, &pos);
}
}
if (iX < numElePerDirection - 2) {
pos = iX+1 + iY*(numElePerDirection-1);
Stiff->InsertGlobalValues(node, 1, &k1, &pos); // East
Mass->InsertGlobalValues(node, 1, &m1, &pos);
if (iY > 0) {
pos = iX+1 + (iY-1)*(numElePerDirection-1);
Stiff->InsertGlobalValues(node, 1, &k1, &pos); // North East
Mass->InsertGlobalValues(node, 1, &m2, &pos);
}
if (iY < numElePerDirection-2) {
pos = iX+1 + (iY+1)*(numElePerDirection-1);
Stiff->InsertGlobalValues(node, 1, &k1, &pos); // South East
Mass->InsertGlobalValues(node, 1, &m2, &pos);
}
}
}
Stiff->FillComplete();
Stiff->OptimizeStorage();
Mass->FillComplete();
Mass->OptimizeStorage();
double one = 1.0, hdt = .00005; // half time step
RCP<Epetra_CrsMatrix> A = rcp(new Epetra_CrsMatrix(*Stiff) );// A = Mass+Stiff*dt/2
int err = EpetraExt::MatrixMatrix::Add(*Mass, false, one,*A,hdt);
if (err != 0) {
std::cout << "err "<<err<<" from MatrixMatrix::Add "<<std::endl;
return(err);
}
A->FillComplete();
A->OptimizeStorage();
hdt = -hdt;
RCP<Epetra_CrsMatrix> B = rcp(new Epetra_CrsMatrix(*Stiff) );// B = Mass-Stiff*dt/2
if (err != 0) {
std::cout << "err "<<err<<" from MatrixMatrix::Add "<<std::endl;
return(err);
}
B->FillComplete();
B->OptimizeStorage();
B->Multiply(false, *vecLHS, *vecRHS); // rhs_new := B*lhs_old,
proc_verbose = verbose && (MyPID==0); /* Only print on the zero processor */
LHS = Teuchos::rcp_implicit_cast<Epetra_MultiVector>(vecLHS);
RHS = Teuchos::rcp_implicit_cast<Epetra_MultiVector>(vecRHS);
//
// ************Construct preconditioner*************
//
ParameterList MLList; // Set MLList for Smoothed Aggregation
ML_Epetra::SetDefaults("SA",MLList); // reset parameters ML User's Guide
MLList.set("smoother: type","Chebyshev"); // Chebyshev smoother ... aztec??
MLList.set("smoother: sweeps",3);
MLList.set("smoother: pre or post", "both"); // both pre- and post-smoothing
#ifdef HAVE_ML_AMESOS
MLList.set("coarse: type","Amesos-KLU"); // solve with serial direct solver KLU
#else
MLList.set("coarse: type","Jacobi"); // not recommended
puts("Warning: Iterative coarse grid solve");
#endif
//
//ML_Epetra::MultiLevelPreconditioner* Prec = new ML_Epetra::MultiLevelPreconditioner(*A, MLList);
//
RCP<Epetra_Operator> Prec = rcp( new ML_Epetra::MultiLevelPreconditioner(*A, MLList) );
assert(Prec != Teuchos::null);
// Create the Belos preconditioned operator from the preconditioner.
// NOTE: This is necessary because Belos expects an operator to apply the
// preconditioner with Apply() NOT ApplyInverse().
RCP<Belos::EpetraPrecOp> belosPrec = rcp( new Belos::EpetraPrecOp( Prec ) );
//
// *****Create parameter list for the PCPG solver manager*****
//
const int NumGlobalElements = RHS->GlobalLength();
if (maxiters == -1)
maxiters = NumGlobalElements/blocksize - 1; // maximum number of iterations to run
//
ParameterList belosList;
belosList.set( "Block Size", blocksize ); // Blocksize to be used by iterative solver
belosList.set( "Maximum Iterations", maxiters ); // Maximum number of iterations allowed
belosList.set( "Convergence Tolerance", tol ); // Relative convergence tolerance requested
belosList.set( "Num Deflated Blocks", maxDeflate ); // Number of vectors in seed space
belosList.set( "Num Saved Blocks", maxSave ); // Number of vectors saved from old spaces
belosList.set( "Orthogonalization", ortho ); // Orthogonalization type
if (numrhs > 1) {
belosList.set( "Show Maximum Residual Norm Only", true ); // although numrhs = 1.
}
if (verbose) {
belosList.set( "Verbosity", Belos::Errors + Belos::Warnings +
if (frequency > 0)
belosList.set( "Output Frequency", frequency );
}
else
belosList.set( "Verbosity", Belos::Errors + Belos::Warnings + Belos::FinalSummary );
//
// *******Construct a preconditioned linear problem********
//
RCP<Belos::LinearProblem<double,MV,OP> > problem
= rcp( new Belos::LinearProblem<double,MV,OP>( A, LHS, RHS ) );
problem->setLeftPrec( belosPrec );
bool set = problem->setProblem();
if (set == false) {
if (proc_verbose)
std::cout << std::endl << "ERROR: Belos::LinearProblem failed to set up correctly!" << std::endl;
return -1;
}
// Create an iterative solver manager.
RCP< Belos::SolverManager<double,MV,OP> > solver
= rcp( new Belos::PCPGSolMgr<double,MV,OP>(problem, rcp(&belosList,false)) );
// std::cout << LHS.Values() << std::endl
//
// *******************************************************************
// ************************* Iterate PCPG ****************************
// *******************************************************************
//
if (proc_verbose) {
std::cout << std::endl << std::endl;
std::cout << "Dimension of matrix: " << NumGlobalElements << std::endl;
std::cout << "Number of right-hand sides: " << numrhs << std::endl;
std::cout << "Block size used by solver: " << blocksize << std::endl;
std::cout << "Maximum number of iterations allowed: " << maxiters << std::endl;
std::cout << "Relative residual tolerance: " << tol << std::endl;
std::cout << std::endl;
}
for( int time_step = 0; time_step < num_time_step; time_step++){
if( time_step ){
B->Multiply(false, *LHS, *RHS); // rhs_new := B*lhs_old,
set = problem->setProblem(LHS,RHS);
if (set == false) {
if (proc_verbose)
std::cout << std::endl << "ERROR: Belos::LinearProblem failed to set up correctly!" << std::endl;
return -1;
}
} // if time_step
std::vector<double> rhs_norm( numrhs );
MVT::MvNorm( *RHS, rhs_norm );
std::cout << " RHS norm is ... " << rhs_norm[0] << std::endl;
//
// Perform solve
//
Belos::ReturnType ret = solver->solve();
//
// Compute actual residuals.
//
std::vector<double> actual_resids( numrhs );
//std::vector<double> rhs_norm( numrhs );
Epetra_MultiVector resid(*Map, numrhs);
OPT::Apply( *A, *LHS, resid );
MVT::MvAddMv( -1.0, resid, 1.0, *RHS, resid );
MVT::MvNorm( resid, actual_resids );
MVT::MvNorm( *RHS, rhs_norm );
std::cout << " RHS norm is ... " << rhs_norm[0] << std::endl;
if (proc_verbose) {
std::cout<< "---------- Actual Residuals (normalized) ----------"<<std::endl<<std::endl;
for ( int i=0; i<numrhs; i++) {
double actRes = actual_resids[i]/rhs_norm[i];
std::cout<<"Problem "<<i<<" : \t"<< actRes <<std::endl;
if (actRes > tol) badRes = true;
}
}
success = false;
break;
}
} // for time_step
if (proc_verbose) {
if (success)
std::cout << std::endl << "SUCCESS: Belos converged!" << std::endl;
else
std::cout << std::endl << "ERROR: Belos did not converge!" << std::endl;
}
}
TEUCHOS_STANDARD_CATCH_STATEMENTS(verbose, std::cerr, success);
#ifdef EPETRA_MPI
MPI_Finalize();
#endif
return success ? EXIT_SUCCESS : EXIT_FAILURE;
}

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