int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HCURL_TET_In_FEM) |\n" \
<< "| |\n" \
<< "| 1) Patch test involving H(curl) matrices |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Robert Kirby ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n" \
<< "| TEST 2: Patch test for mass matrices |\n" \
<< "===============================================================================\n";
int errorFlag = 0;
outStream -> precision(16);
try {
DefaultCubatureFactory<double> cubFactory; // create cubature factory
shards::CellTopology cell(shards::getCellTopologyData< shards::Tetrahedron<> >()); // create parent cell topology
int cellDim = cell.getDimension();
int min_order = 1;
int max_order = 5;
int numIntervals = max_order;
int numInterpPoints = ((numIntervals + 1)*(numIntervals + 2)*(numIntervals+3))/6;
FieldContainer<double> interp_points_ref(numInterpPoints, cellDim);
int counter = 0;
for (int j=0; j<=numIntervals; j++) {
for (int i=0; i<=numIntervals-j; i++) {
for (int k=0;k<numIntervals-j-i;k++) {
interp_points_ref(counter,0) = i*(1.0/numIntervals);
interp_points_ref(counter,1) = j*(1.0/numIntervals);
interp_points_ref(counter,2) = k*(1.0/numIntervals);
counter++;
}
}
}
for (int basis_order=min_order;basis_order<=max_order;basis_order++) {
// create basis
Teuchos::RCP<Basis<double,FieldContainer<double> > > basis =
Teuchos::rcp(new Basis_HCURL_TET_In_FEM<double,FieldContainer<double> >(basis_order,POINTTYPE_EQUISPACED) );
int numFields = basis->getCardinality();
// create cubatures
Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*(basis_order+1));
int numCubPointsCell = cellCub->getNumPoints();
// hold cubature information
FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim);
FieldContainer<double> cub_weights_cell(numCubPointsCell);
// hold basis function information on refcell
FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim );
FieldContainer<double> w_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
// holds rhs data
FieldContainer<double> rhs_at_cub_points_cell(1,numCubPointsCell,cellDim);
// FEM mass matrix
FieldContainer<double> fe_matrix_bak(1,numFields,numFields);
FieldContainer<double> fe_matrix(1,numFields,numFields);
FieldContainer<double> rhs_and_soln_vec(1,numFields);
FieldContainer<int> ipiv(numFields);
FieldContainer<double> value_of_basis_at_interp_points( numFields , numInterpPoints , cellDim);
FieldContainer<double> interpolant( 1, numInterpPoints , cellDim );
int info = 0;
Teuchos::LAPACK<int, double> solver;
// set test tolerance
double zero = (basis_order+1)*(basis_order+1)*1000*INTREPID_TOL;
// build matrices outside the loop, and then just do the rhs
// for each iteration
cellCub->getCubature(cub_points_cell, cub_weights_cell);
// need the vector basis
basis->getValues(value_of_basis_at_cub_points_cell,
cub_points_cell,
OPERATOR_VALUE);
basis->getValues( value_of_basis_at_interp_points ,
interp_points_ref ,
OPERATOR_VALUE );
// construct mass matrix
cub_weights_cell.resize(1,numCubPointsCell);
FunctionSpaceTools::multiplyMeasure<double>(w_value_of_basis_at_cub_points_cell ,
cub_weights_cell ,
value_of_basis_at_cub_points_cell );
cub_weights_cell.resize(numCubPointsCell);
value_of_basis_at_cub_points_cell.resize( 1 , numFields , numCubPointsCell , cellDim );
FunctionSpaceTools::integrate<double>(fe_matrix_bak,
w_value_of_basis_at_cub_points_cell ,
value_of_basis_at_cub_points_cell ,
COMP_BLAS );
value_of_basis_at_cub_points_cell.resize( numFields , numCubPointsCell , cellDim );
//std::cout << fe_matrix_bak << std::endl;
for (int x_order=0;x_order<basis_order;x_order++) {
for (int y_order=0;y_order<basis_order-x_order;y_order++) {
for (int z_order=0;z_order<basis_order-x_order-y_order;z_order++) {
for (int comp=0;comp<cellDim;comp++) {
fe_matrix.initialize();
// copy mass matrix
for (int i=0;i<numFields;i++) {
for (int j=0;j<numFields;j++) {
fe_matrix(0,i,j) = fe_matrix_bak(0,i,j);
}
}
// clear old vector data
rhs_and_soln_vec.initialize();
// now get rhs vector
cub_points_cell.resize(1,numCubPointsCell,cellDim);
rhs_at_cub_points_cell.initialize();
rhsFunc(rhs_at_cub_points_cell,
cub_points_cell,
comp,
x_order,
y_order,
z_order);
cub_points_cell.resize(numCubPointsCell,cellDim);
cub_weights_cell.resize(numCubPointsCell);
FunctionSpaceTools::integrate<double>(rhs_and_soln_vec,
rhs_at_cub_points_cell,
w_value_of_basis_at_cub_points_cell,
COMP_BLAS);
// solve linear system
// solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vec[0],
// numFields, &info);
solver.POTRF('L',numFields,&fe_matrix[0],numFields,&info);
solver.POTRS('L',numFields,1,&fe_matrix[0],numFields,&rhs_and_soln_vec[0],numFields,&info);
interp_points_ref.resize(1,numInterpPoints,cellDim);
// get exact solution for comparison
FieldContainer<double> exact_solution(1,numInterpPoints,cellDim);
exact_solution.initialize();
u_exact( exact_solution , interp_points_ref , comp , x_order, y_order, z_order);
interp_points_ref.resize(numInterpPoints,cellDim);
// compute interpolant
// first evaluate basis at interpolation points
value_of_basis_at_interp_points.resize(1,numFields,numInterpPoints,cellDim);
FunctionSpaceTools::evaluate<double>( interpolant ,
rhs_and_soln_vec ,
value_of_basis_at_interp_points );
value_of_basis_at_interp_points.resize(numFields,numInterpPoints,cellDim);
RealSpaceTools<double>::subtract(interpolant,exact_solution);
double nrm= RealSpaceTools<double>::vectorNorm(&interpolant[0],interpolant.dimension(1), NORM_TWO);
*outStream << "\nNorm-2 error between scalar components of exact solution of order ("
<< x_order << ", " << y_order << ", " << z_order
<< ") in component " << comp
<< " and finite element interpolant of order " << basis_order << ": "
<< nrm << "\n";
if (nrm > zero) {
*outStream << "\n\nPatch test failed for solution polynomial order ("
<< x_order << ", " << y_order << ", " << z_order << ") and basis order (scalar, vector) ("
<< basis_order << ", " << basis_order+1 << ")\n\n";
errorFlag++;
}
}
}
}
}
}
}
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
void BlockCGIter<ScalarType,MV,OP>::iterate()
{
//
// Allocate/initialize data structures
//
if (initialized_ == false) {
initialize();
}
// Allocate data needed for LAPACK work.
int info = 0;
char UPLO = 'U';
Teuchos::LAPACK<int,ScalarType> lapack;
// Allocate memory for scalars.
Teuchos::SerialDenseMatrix<int,ScalarType> alpha( blockSize_, blockSize_ );
Teuchos::SerialDenseMatrix<int,ScalarType> beta( blockSize_, blockSize_ );
Teuchos::SerialDenseMatrix<int,ScalarType> rHz( blockSize_, blockSize_ ),
rHz_old( blockSize_, blockSize_ ), pAp( blockSize_, blockSize_ );
// Create convenience variables for zero and one.
const ScalarType one = Teuchos::ScalarTraits<ScalarType>::one();
// Get the current solution std::vector.
Teuchos::RCP<MV> cur_soln_vec = lp_->getCurrLHSVec();
// Check that the current solution std::vector has blockSize_ columns.
TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetNumberVecs(*cur_soln_vec) != blockSize_, CGIterateFailure,
"Belos::BlockCGIter::iterate(): current linear system does not have the right number of vectors!" );
int rank = ortho_->normalize( *P_, Teuchos::null );
TEUCHOS_TEST_FOR_EXCEPTION(rank != blockSize_,CGIterationOrthoFailure,
"Belos::BlockCGIter::iterate(): Failed to compute initial block of orthonormal direction vectors.");
////////////////////////////////////////////////////////////////
// Iterate until the status test tells us to stop.
//
while (stest_->checkStatus(this) != Passed) {
// Increment the iteration
iter_++;
// Multiply the current direction std::vector by A and store in Ap_
lp_->applyOp( *P_, *AP_ );
// Compute alpha := <P_,R_> / <P_,AP_>
// 1) Compute P^T * A * P = pAp and P^T * R
// 2) Compute the Cholesky Factorization of pAp
// 3) Back and forward solves to compute alpha
//
MVT::MvTransMv( one, *P_, *R_, alpha );
MVT::MvTransMv( one, *P_, *AP_, pAp );
// Compute Cholesky factorization of pAp
lapack.POTRF(UPLO, blockSize_, pAp.values(), blockSize_, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0,CGIterationLAPACKFailure,
"Belos::BlockCGIter::iterate(): Failed to compute Cholesky factorization using LAPACK routine POTRF.");
// Compute alpha by performing a back and forward solve with the Cholesky factorization in pAp.
lapack.POTRS(UPLO, blockSize_, blockSize_, pAp.values(), blockSize_,
alpha.values(), blockSize_, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0,CGIterationLAPACKFailure,
"Belos::BlockCGIter::iterate(): Failed to compute alpha using Cholesky factorization (POTRS).");
//
// Update the solution std::vector X := X + alpha * P_
//
MVT::MvTimesMatAddMv( one, *P_, alpha, one, *cur_soln_vec );
lp_->updateSolution();
//
// Compute the new residual R_ := R_ - alpha * AP_
//
MVT::MvTimesMatAddMv( -one, *AP_, alpha, one, *R_ );
//
// Compute the new preconditioned residual, Z_.
if ( lp_->getLeftPrec() != Teuchos::null ) {
lp_->applyLeftPrec( *R_, *Z_ );
if ( lp_->getRightPrec() != Teuchos::null ) {
Teuchos::RCP<MV> tmp = MVT::Clone( *Z_, blockSize_ );
lp_->applyRightPrec( *Z_, *tmp );
Z_ = tmp;
}
}
else if ( lp_->getRightPrec() != Teuchos::null ) {
lp_->applyRightPrec( *R_, *Z_ );
}
else {
Z_ = R_;
}
//
// Compute beta := <AP_,Z_> / <P_,AP_>
// 1) Compute AP_^T * Z_
// 2) Compute the Cholesky Factorization of pAp (already have)
// 3) Back and forward solves to compute beta
// Compute <AP_,Z>
MVT::MvTransMv( -one, *AP_, *Z_, beta );
//
lapack.POTRS(UPLO, blockSize_, blockSize_, pAp.values(), blockSize_,
beta.values(), blockSize_, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0,CGIterationLAPACKFailure,
"Belos::BlockCGIter::iterate(): Failed to compute beta using Cholesky factorization (POTRS).");
//
// Compute the new direction vectors P_ = Z_ + P_ * beta
//
Teuchos::RCP<MV> Pnew = MVT::CloneCopy( *Z_ );
MVT::MvTimesMatAddMv(one, *P_, beta, one, *Pnew);
P_ = Pnew;
// Compute orthonormal block of new direction vectors.
rank = ortho_->normalize( *P_, Teuchos::null );
TEUCHOS_TEST_FOR_EXCEPTION(rank != blockSize_,CGIterationOrthoFailure,
"Belos::BlockCGIter::iterate(): Failed to compute block of orthonormal direction vectors.");
} // end while (sTest_->checkStatus(this) != Passed)
}