bool
Albany::KLResponseFunction::
computeKL(const Stokhos::EpetraVectorOrthogPoly& sg_u,
const int NumKL,
Teuchos::Array<double>& evals,
Teuchos::RCP<Epetra_MultiVector>& evecs)
{
Teuchos::RCP<const EpetraExt::BlockVector> X_ov = sg_u.getBlockVector();
//App_sg->get_sg_model()->import_solution( *(sg_u->getBlockVector()) );
//Teuchos::RCP<const EpetraExt::BlockVector> cX_ov = X_ov;
// pceKL is object with member functions that explicitly call anasazi
Stokhos::PCEAnasaziKL pceKL(X_ov, *(sg_u.basis()), NumKL);
// Set parameters for anasazi
Teuchos::ParameterList& anasazi_params =
responseParams.sublist("Anasazi");
Teuchos::ParameterList default_params = pceKL.getDefaultParams();
anasazi_params.setParametersNotAlreadySet(default_params);
// Self explanatory
bool result = pceKL.computeKL(anasazi_params);
// Retrieve evals/evectors into return argument slots...
evals = pceKL.getEigenvalues();
evecs = pceKL.getEigenvectors();
return result;
}
void
Stokhos::KLReducedMatrixFreeOperator::
setup()
{
#ifdef HAVE_STOKHOS_ANASAZI
#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
TEUCHOS_FUNC_TIME_MONITOR("Stokhos::KLReducedMatrixFreeOperator -- Calculation/setup of KL opeator");
#endif
mean = Teuchos::rcp_dynamic_cast<Epetra_CrsMatrix>(
block_ops->getCoeffPtr(0));
// Copy matrix coefficients into vectors
for (int coeff=0; coeff<num_blocks; coeff++) {
Teuchos::RCP<const Epetra_CrsMatrix> block_coeff =
Teuchos::rcp_dynamic_cast<Epetra_CrsMatrix>
(block_ops->getCoeffPtr(coeff));
int row = 0;
for (int i=0; i<mean->NumMyRows(); i++) {
int num_col;
mean->NumMyRowEntries(i, num_col);
for (int j=0; j<num_col; j++)
(*block_vec_poly)[coeff][row++] = (*block_coeff)[i][j];
}
}
int myPID = sg_comm->MyPID();
// Compute KL expansion of solution sg_J_vec_poly
Stokhos::PCEAnasaziKL pceKL(*block_vec_poly, num_KL);
Teuchos::ParameterList anasazi_params = pceKL.getDefaultParams();
bool result = pceKL.computeKL(anasazi_params);
if (!result && myPID == 0)
std::cout << "KL Eigensolver did not converge!" << std::endl;
Teuchos::RCP<Epetra_MultiVector> evecs = pceKL.getEigenvectors();
Teuchos::Array<double> evals = pceKL.getEigenvalues();
//num_KL_computed = evecs->NumVectors();
if (myPID == 0)
std::cout << "num computed eigenvectors = "
<< evecs->NumVectors() << std::endl;
double kl_tol = params->get("KL Tolerance", 1e-6);
num_KL_computed = 0;
while (num_KL_computed < evals.size() &&
std::sqrt(evals[num_KL_computed]/evals[0]) > kl_tol)
num_KL_computed++;
if (num_KL_computed == evals.size() && myPID == 0)
std::cout << "Can't achieve KL tolerance " << kl_tol
<< ". Smallest eigenvalue / largest eigenvalue = "
<< std::sqrt(evals[num_KL_computed-1]/evals[0]) << std::endl;
if (myPID == 0)
std::cout << "num KL eigenvectors = " << num_KL_computed << std::endl;
// Compute dot products of Jacobian blocks and KL eigenvectors
dot_products.resize(num_KL_computed);
for (int rv=0; rv < num_KL_computed; rv++) {
dot_products[rv].resize(num_blocks-1);
for (int coeff=1; coeff < num_blocks; coeff++) {
double dot;
(*block_vec_poly)[coeff].Dot(*((*evecs)(rv)), &dot);
dot_products[rv][coeff-1] = dot;
}
}
// Compute KL coefficients
const Teuchos::Array<double>& norms = sg_basis->norm_squared();
sparse_kl_coeffs =
Teuchos::rcp(new Stokhos::Sparse3Tensor<int,double>);
for (Cijk_type::i_iterator i_it=Cijk->i_begin();
i_it!=Cijk->i_end(); ++i_it) {
int i = epetraCijk->GRID(index(i_it));
sparse_kl_coeffs->sum_term(i, i, 0, norms[i]);
}
Cijk_type::k_iterator l_begin = ++(Cijk->k_begin());
Cijk_type::k_iterator l_end = Cijk->k_end();
for (Cijk_type::k_iterator l_it=l_begin; l_it!=l_end; ++l_it) {
int l = index(l_it);
for (Cijk_type::kj_iterator j_it = Cijk->j_begin(l_it);
j_it != Cijk->j_end(l_it); ++j_it) {
int j = epetraCijk->GCID(index(j_it));
for (Cijk_type::kji_iterator i_it = Cijk->i_begin(j_it);
i_it != Cijk->i_end(j_it); ++i_it) {
int i = epetraCijk->GRID(index(i_it));
double c = value(i_it);
for (int k=1; k<num_KL_computed+1; k++) {
double dp = dot_products[k-1][l-1];
double v = dp*c;
if (std::abs(v) > drop_tolerance)
sparse_kl_coeffs->sum_term(i,j,k,v);
}
}
}
}
sparse_kl_coeffs->fillComplete();
bool save_tensor = params->get("Save Sparse 3 Tensor To File", false);
if (save_tensor) {
static int idx = 0;
std::string basename = params->get("Sparse 3 Tensor Base Filename",
"sparse_KL_coeffs");
std::stringstream ss;
ss << basename << "_" << idx++ << ".mm";
sparse3Tensor2MatrixMarket(*sparse_kl_coeffs,
*(epetraCijk->getStochasticRowMap()), ss.str());
}
// Transform eigenvectors back to matrices
kl_blocks.resize(num_KL_computed);
Teuchos::RCP<Epetra_BlockMap> kl_map =
Teuchos::rcp(new Epetra_LocalMap(num_KL_computed+1, 0,
sg_comm->TimeDomainComm()));
kl_ops =
Teuchos::rcp(new Stokhos::EpetraOperatorOrthogPoly(
sg_basis, kl_map, domain_base_map, range_base_map,
range_sg_map, sg_comm));
kl_ops->setCoeffPtr(0, mean);
for (int rv=0; rv<num_KL_computed; rv++) {
if (kl_blocks[rv] == Teuchos::null)
kl_blocks[rv] = Teuchos::rcp(new Epetra_CrsMatrix(*mean));
int row = 0;
for (int i=0; i<mean->NumMyRows(); i++) {
int num_col;
mean->NumMyRowEntries(i, num_col);
for (int j=0; j<num_col; j++)
(*kl_blocks[rv])[i][j] = (*evecs)[rv][row++];
}
kl_ops->setCoeffPtr(rv+1, kl_blocks[rv]);
}
Teuchos::RCP<Stokhos::EpetraSparse3Tensor> reducedEpetraCijk =
Teuchos::rcp(new Stokhos::EpetraSparse3Tensor(
sg_basis, sparse_kl_coeffs, sg_comm,
epetraCijk->getStochasticRowMap(), sparse_kl_coeffs,
0, -1));
reducedEpetraCijk->transformToLocal();
// Create matrix-free op
kl_mat_free_op = Teuchos::rcp(new Stokhos::MatrixFreeOperator(
sg_comm, sg_basis, reducedEpetraCijk,
domain_base_map, range_base_map,
domain_sg_map, range_sg_map, params));
kl_mat_free_op->setupOperator(kl_ops);
// Check accuracy of KL expansion
if (do_error_tests) {
Teuchos::Array<double> point(sg_basis->dimension());
for (int i=0; i<sg_basis->dimension(); i++)
point[i] = 0.5;
Teuchos::Array<double> basis_vals(sg_basis->size());
sg_basis->evaluateBases(point, basis_vals);
Epetra_Vector val(*block_vec_map);
Epetra_Vector val_kl(*block_vec_map);
block_vec_poly->evaluate(basis_vals, val);
val_kl.Update(1.0, (*block_vec_poly)[0], 0.0);
Teuchos::Array< Stokhos::OrthogPolyApprox<int,double> > rvs(num_KL_computed);
Teuchos::Array<double> val_rvs(num_KL_computed);
for (int rv=0; rv<num_KL_computed; rv++) {
rvs[rv].reset(sg_basis);
rvs[rv][0] = 0.0;
for (int coeff=1; coeff<num_blocks; coeff++)
rvs[rv][coeff] = dot_products[rv][coeff-1];
val_rvs[rv] = rvs[rv].evaluate(point, basis_vals);
val_kl.Update(val_rvs[rv], *((*evecs)(rv)), 1.0);
}
double nrm;
val.NormInf(&nrm);
val.Update(-1.0, val_kl, 1.0);
double diff;
val.NormInf(&diff);
if (myPID == 0)
std::cout << "Infinity norm of random field difference = " << diff/nrm
<< std::endl;
// Check accuracy of operator
Epetra_Vector op_input(*domain_sg_map), op_result(*range_sg_map), op_kl_result(*range_sg_map);
op_input.PutScalar(1.0);
Stokhos::MatrixFreeOperator op(sg_comm, sg_basis, epetraCijk,
domain_base_map, range_base_map,
domain_sg_map, range_sg_map, params);
op.setupOperator(block_ops);
op.Apply(op_input, op_result);
this->Apply(op_input, op_kl_result);
op_result.NormInf(&nrm);
op_result.Update(-1.0, op_kl_result, 1.0);
op_result.NormInf(&diff);
if (myPID == 0)
std::cout << "Infinity norm of operator difference = " << diff/nrm
<< std::endl;
}
#else
TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error,
"Stokhos::KLReducedMatrixFreeOperator is available " <<
"only when configured with Anasazi support!")
#endif
}
