//==============================================================================
int Ifpack_Chebyshev::
PowerMethod(const Epetra_Operator& Operator,
const Epetra_Vector& InvPointDiagonal,
const int MaximumIterations,
double& lambda_max)
{
// this is a simple power method
lambda_max = 0.0;
double RQ_top, RQ_bottom, norm;
Epetra_Vector x(Operator.OperatorDomainMap());
Epetra_Vector y(Operator.OperatorRangeMap());
x.Random();
x.Norm2(&norm);
if (norm == 0.0) IFPACK_CHK_ERR(-1);
x.Scale(1.0 / norm);
for (int iter = 0; iter < MaximumIterations; ++iter)
{
Operator.Apply(x, y);
IFPACK_CHK_ERR(y.Multiply(1.0, InvPointDiagonal, y, 0.0));
IFPACK_CHK_ERR(y.Dot(x, &RQ_top));
IFPACK_CHK_ERR(x.Dot(x, &RQ_bottom));
lambda_max = RQ_top / RQ_bottom;
IFPACK_CHK_ERR(y.Norm2(&norm));
if (norm == 0.0) IFPACK_CHK_ERR(-1);
IFPACK_CHK_ERR(x.Update(1.0 / norm, y, 0.0));
}
return(0);
}
// ============================================================================
bool ML_Epetra::MatrixFreePreconditioner::
CheckSPD(const Epetra_Operator& A, const bool UseApply,
const int NumChecks,
const int NumVectors) const
{
bool res = true;
std::vector<double> norm(NumVectors);
if (!IsComputed())
return(false);
if (MyPID() == 0)
std::cout << "Checking SPD property of the operator... " << std::endl;
Epetra_MultiVector X(A.OperatorDomainMap(), NumVectors);
Epetra_MultiVector AX(A.OperatorRangeMap(), NumVectors);
try
{
for (int i = 0; i < NumChecks; ++i)
{
int ierr;
if (X.Random()) res = false;
if (UseApply)
ierr = A.Apply(X, AX);
else
ierr = A.ApplyInverse(X, AX);
if (ierr < 0)
throw(-1);
AX.Dot(X, &norm[0]);
for (int v = 0; v < NumVectors; ++v)
{
std::cout << norm[v] << std::endl;
if (norm[v] <= 0.0)
throw(-2);
}
}
}
catch(...)
{
res = false;
}
if (MyPID() == 0)
{
if (res)
std::cout << "Passed: all x * A * x are positive." << std::endl;
else
std::cout << "Failed: some x * A * x are negative or zero!" << std::endl;
}
return(res);
}
int runOperatorTests(Epetra_Operator & A, bool verbose) {
int ierr = 0;
double residual;
EPETRA_CHK_ERR(EpetraExt::OperatorToMatrixMarketFile("Test_A1.mm", A, "Official EpetraExt test operator",
"This is the official EpetraExt test operator generated by the EpetraExt regression tests"));
EPETRA_CHK_ERR(EpetraExt::OperatorToMatlabFile("Test_A1.dat", A));
A.OperatorRangeMap().Comm().Barrier();
A.OperatorRangeMap().Comm().Barrier();
Epetra_CrsMatrix * A1;
Epetra_CrsMatrix * A2;
EPETRA_CHK_ERR(EpetraExt::MatrixMarketFileToCrsMatrix("Test_A1.mm", A.OperatorRangeMap(), A1));
EPETRA_CHK_ERR(EpetraExt::MatlabFileToCrsMatrix("Test_A1.dat", A.OperatorRangeMap().Comm(), A2));
residual = A.NormInf(); double rAInf = residual;
if (verbose) std::cout << "Inf Norm of Operator A = " << residual << std::endl;
residual = A1->NormInf(); double rA1Inf = residual;
if (verbose) std::cout << "Inf Norm of Matrix A1 = " << residual << std::endl;
ierr += checkValues(rA1Inf,rAInf,"Inf Norm of A", verbose);
Epetra_Vector x(A.OperatorDomainMap()); x.Random();
Epetra_Vector y1(A.OperatorRangeMap());
Epetra_Vector y2(A.OperatorRangeMap());
Epetra_Vector y3(A.OperatorRangeMap());
A.Apply(x,y1);
A1->Multiply(false, x, y2);
A2->Multiply(false, x, y3);
y1.Norm2(&residual); double rAx1 = residual;
if (verbose) std::cout << "Norm of A*x = " << residual << std::endl;
y2.Norm2(&residual); double rAx2 = residual;
if (verbose) std::cout << "Norm of A1*x = " << residual << std::endl;
ierr += checkValues(rAx1,rAx2,"Norm of A1*x", verbose);
y3.Norm2(&residual); double rAx3 = residual;
if (verbose) std::cout << "Norm of A2*x = " << residual << std::endl;
ierr += checkValues(rAx1,rAx3,"Norm of A2*x", verbose);
delete A1;
delete A2;
return(ierr);
}
