void
Stokhos::ApproxSchurComplementPreconditioner::
multiply_block(
const Teuchos::RCP<const Stokhos::Sparse3Tensor<int,double> >& cijk,
double alpha,
const EpetraExt::BlockMultiVector& Input,
EpetraExt::BlockMultiVector& Result) const
{
// Input and Result are the whole vector/multi-vector, not just the portion
// needed for the particular sub-block
int m = Input.NumVectors();
const Teuchos::Array<double>& norms = sg_basis->norm_squared();
Cijk_type::k_iterator k_begin = cijk->k_begin();
Cijk_type::k_iterator k_end = cijk->k_end();
if (only_use_linear)
k_end = cijk->find_k(sg_basis()->dimension() + 1);
for (Cijk_type::k_iterator k_it=k_begin; k_it!=k_end; ++k_it) {
int k = index(k_it);
Cijk_type::kj_iterator j_begin = cijk->j_begin(k_it);
Cijk_type::kj_iterator j_end = cijk->j_end(k_it);
int nj = cijk->num_j(k_it);
if (nj > 0) {
int l = 0;
for (Cijk_type::kj_iterator j_it = j_begin; j_it != j_end; ++j_it) {
int j = index(j_it);
for (int mm=0; mm<m; mm++) {
j_ptr[l*m+mm] = (*(Input.GetBlock(j)))[mm];
mj_indices[l*m+mm] = l*m+mm;
}
l++;
}
Epetra_MultiVector input_tmp(View, *base_map, &j_ptr[0], nj*m);
Epetra_MultiVector result_tmp(View, *tmp, &mj_indices[0], nj*m);
(*sg_poly)[k].Apply(input_tmp, result_tmp);
l = 0;
for (Cijk_type::kj_iterator j_it = j_begin; j_it != j_end; ++j_it) {
Cijk_type::kji_iterator i_begin = cijk->i_begin(j_it);
Cijk_type::kji_iterator i_end = cijk->i_end(j_it);
for (Cijk_type::kji_iterator i_it = i_begin; i_it != i_end; ++i_it) {
int i = index(i_it);
double c = value(i_it);
if (scale_op)
c /= norms[i];
for (int mm=0; mm<m; mm++)
(*Result.GetBlock(i))(mm)->Update(alpha*c, *result_tmp(l*m+mm), 1.0);
}
l++;
}
}
}
}
int
Stokhos::MatrixFreeOperator::
Apply(const Epetra_MultiVector& Input, Epetra_MultiVector& Result) const
{
#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
TEUCHOS_FUNC_TIME_MONITOR("Stokhos: SG Operator Apply()");
#endif
// Note for transpose:
// The stochastic matrix is symmetric, however the matrix blocks may not
// be. So the algorithm here is the same whether we are using the transpose
// or not. We just apply the transpose of the blocks in the case of
// applying the global transpose, and make sure the imported Input
// vectors use the right map.
// We have to be careful if Input and Result are the same vector.
// If this is the case, the only possible solution is to make a copy
const Epetra_MultiVector *input = &Input;
bool made_copy = false;
if (Input.Values() == Result.Values() && !is_stoch_parallel) {
input = new Epetra_MultiVector(Input);
made_copy = true;
}
// Initialize
Result.PutScalar(0.0);
const Epetra_Map* input_base_map = domain_base_map.get();
const Epetra_Map* result_base_map = range_base_map.get();
if (useTranspose == true) {
input_base_map = range_base_map.get();
result_base_map = domain_base_map.get();
}
// Allocate temporary storage
int m = Input.NumVectors();
if (useTranspose == false &&
(tmp == Teuchos::null || tmp->NumVectors() != m*max_num_mat_vec))
tmp = Teuchos::rcp(new Epetra_MultiVector(*result_base_map,
m*max_num_mat_vec));
else if (useTranspose == true &&
(tmp_trans == Teuchos::null ||
tmp_trans->NumVectors() != m*max_num_mat_vec))
tmp_trans = Teuchos::rcp(new Epetra_MultiVector(*result_base_map,
m*max_num_mat_vec));
Epetra_MultiVector *tmp_result;
if (useTranspose == false)
tmp_result = tmp.get();
else
tmp_result = tmp_trans.get();
// Map input into column map
const Epetra_MultiVector *tmp_col;
if (!is_stoch_parallel)
tmp_col = input;
else {
if (useTranspose == false) {
if (input_col == Teuchos::null || input_col->NumVectors() != m)
input_col = Teuchos::rcp(new Epetra_MultiVector(*global_col_map, m));
input_col->Import(*input, *col_importer, Insert);
tmp_col = input_col.get();
}
else {
if (input_col_trans == Teuchos::null ||
input_col_trans->NumVectors() != m)
input_col_trans =
Teuchos::rcp(new Epetra_MultiVector(*global_col_map_trans, m));
input_col_trans->Import(*input, *col_importer_trans, Insert);
tmp_col = input_col_trans.get();
}
}
// Extract blocks
EpetraExt::BlockMultiVector sg_input(View, *input_base_map, *tmp_col);
EpetraExt::BlockMultiVector sg_result(View, *result_base_map, Result);
for (int i=0; i<input_block.size(); i++)
input_block[i] = sg_input.GetBlock(i);
for (int i=0; i<result_block.size(); i++)
result_block[i] = sg_result.GetBlock(i);
// Apply block SG operator via
// w_i =
// \sum_{j=0}^P \sum_{k=0}^L J_k v_j < \psi_i \psi_j \psi_k > / <\psi_i^2>
// for i=0,...,P where P = expansion_size, L = num_blocks, w_j is the jth
// input block, w_i is the ith result block, and J_k is the kth block operator
// k_begin and k_end are initialized in the constructor
const Teuchos::Array<double>& norms = sg_basis->norm_squared();
for (Cijk_type::k_iterator k_it=k_begin; k_it!=k_end; ++k_it) {
int k = index(k_it);
Cijk_type::kj_iterator j_begin = Cijk->j_begin(k_it);
Cijk_type::kj_iterator j_end = Cijk->j_end(k_it);
int nj = Cijk->num_j(k_it);
if (nj > 0) {
Teuchos::Array<double*> j_ptr(nj*m);
Teuchos::Array<int> mj_indices(nj*m);
int l = 0;
for (Cijk_type::kj_iterator j_it = j_begin; j_it != j_end; ++j_it) {
int j = index(j_it);
for (int mm=0; mm<m; mm++) {
j_ptr[l*m+mm] = (*input_block[j])[mm];
mj_indices[l*m+mm] = l*m+mm;
}
l++;
}
Epetra_MultiVector input_tmp(View, *input_base_map, &j_ptr[0], nj*m);
Epetra_MultiVector result_tmp(View, *tmp_result, &mj_indices[0], nj*m);
if (use_block_apply) {
(*block_ops)[k].Apply(input_tmp, result_tmp);
}
else {
for (int jj=0; jj<nj*m; jj++)
(*block_ops)[k].Apply(*(input_tmp(jj)), *(result_tmp(jj)));
}
l = 0;
for (Cijk_type::kj_iterator j_it = j_begin; j_it != j_end; ++j_it) {
int j = 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 = index(i_it);
double c = value(i_it);
if (scale_op) {
int i_gid;
if (useTranspose)
i_gid = epetraCijk->GCID(j);
else
i_gid = epetraCijk->GRID(i);
c /= norms[i_gid];
}
for (int mm=0; mm<m; mm++)
(*result_block[i])(mm)->Update(c, *result_tmp(l*m+mm), 1.0);
}
l++;
}
}
}
// Destroy blocks
for (int i=0; i<input_block.size(); i++)
input_block[i] = Teuchos::null;
for (int i=0; i<result_block.size(); i++)
result_block[i] = Teuchos::null;
if (made_copy)
delete input;
return 0;
}
int
Stokhos::KLMatrixFreeOperator::
Apply(const Epetra_MultiVector& Input, Epetra_MultiVector& Result) const
{
// We have to be careful if Input and Result are the same vector.
// If this is the case, the only possible solution is to make a copy
const Epetra_MultiVector *input = &Input;
bool made_copy = false;
if (Input.Values() == Result.Values() && !is_stoch_parallel) {
input = new Epetra_MultiVector(Input);
made_copy = true;
}
// Initialize
Result.PutScalar(0.0);
const Epetra_Map* input_base_map = domain_base_map.get();
const Epetra_Map* result_base_map = range_base_map.get();
if (useTranspose == true) {
input_base_map = range_base_map.get();
result_base_map = domain_base_map.get();
}
// Allocate temporary storage
int m = Input.NumVectors();
if (useTranspose == false &&
(tmp == Teuchos::null || tmp->NumVectors() != m*max_num_mat_vec))
tmp = Teuchos::rcp(new Epetra_MultiVector(*result_base_map,
m*max_num_mat_vec));
else if (useTranspose == true &&
(tmp_trans == Teuchos::null ||
tmp_trans->NumVectors() != m*max_num_mat_vec))
tmp_trans = Teuchos::rcp(new Epetra_MultiVector(*result_base_map,
m*max_num_mat_vec));
Epetra_MultiVector *tmp_result;
if (useTranspose == false)
tmp_result = tmp.get();
else
tmp_result = tmp_trans.get();
// Map input into column map
const Epetra_MultiVector *tmp_col;
if (!is_stoch_parallel)
tmp_col = input;
else {
if (useTranspose == false) {
if (input_col == Teuchos::null || input_col->NumVectors() != m)
input_col = Teuchos::rcp(new Epetra_MultiVector(*global_col_map, m));
input_col->Import(*input, *col_importer, Insert);
tmp_col = input_col.get();
}
else {
if (input_col_trans == Teuchos::null ||
input_col_trans->NumVectors() != m)
input_col_trans =
Teuchos::rcp(new Epetra_MultiVector(*global_col_map_trans, m));
input_col_trans->Import(*input, *col_importer_trans, Insert);
tmp_col = input_col_trans.get();
}
}
// Extract blocks
EpetraExt::BlockMultiVector sg_input(View, *input_base_map, *tmp_col);
EpetraExt::BlockMultiVector sg_result(View, *result_base_map, Result);
for (int i=0; i<input_block.size(); i++)
input_block[i] = sg_input.GetBlock(i);
for (int i=0; i<result_block.size(); i++)
result_block[i] = sg_result.GetBlock(i);
int N = result_block[0]->MyLength();
const Teuchos::Array<double>& norms = sg_basis->norm_squared();
int d = sg_basis->dimension();
Teuchos::Array<double> zero(d), one(d);
for(int j = 0; j<d; j++) {
zero[j] = 0.0;
one[j] = 1.0;
}
Teuchos::Array< double > phi_0(expansion_size), phi_1(expansion_size);
sg_basis->evaluateBases(zero, phi_0);
sg_basis->evaluateBases(one, phi_1);
// k_begin and k_end are initialized in the constructor
for (Cijk_type::k_iterator k_it=k_begin; k_it!=k_end; ++k_it) {
Cijk_type::kj_iterator j_begin = Cijk->j_begin(k_it);
Cijk_type::kj_iterator j_end = Cijk->j_end(k_it);
int k = index(k_it);
int nj = Cijk->num_j(k_it);
if (nj > 0) {
Teuchos::Array<double*> j_ptr(nj*m);
Teuchos::Array<int> mj_indices(nj*m);
int l = 0;
for (Cijk_type::kj_iterator j_it = j_begin; j_it != j_end; ++j_it) {
int j = index(j_it);
for (int mm=0; mm<m; mm++) {
j_ptr[l*m+mm] = input_block[j]->Values()+mm*N;
mj_indices[l*m+mm] = l*m+mm;
}
l++;
}
Epetra_MultiVector input_tmp(View, *input_base_map, &j_ptr[0], nj*m);
Epetra_MultiVector result_tmp(View, *tmp_result, &mj_indices[0], nj*m);
(*block_ops)[k].Apply(input_tmp, result_tmp);
l = 0;
for (Cijk_type::kj_iterator j_it = j_begin; j_it != j_end; ++j_it) {
int j = index(j_it);
int j_gid = epetraCijk->GCID(j);
for (Cijk_type::kji_iterator i_it = Cijk->i_begin(j_it);
i_it != Cijk->i_end(j_it); ++i_it) {
int i = index(i_it);
int i_gid = epetraCijk->GRID(i);
double c = value(i_it);
if (k == 0)
c /= phi_0[0];
else {
c /= phi_1[k];
if (i_gid == j_gid)
c -= phi_0[k]/(phi_1[k]*phi_0[0])*norms[i_gid];
}
if (scale_op) {
if (useTranspose)
c /= norms[j_gid];
else
c /= norms[i_gid];
}
for (int mm=0; mm<m; mm++)
(*result_block[i])(mm)->Update(c, *result_tmp(l*m+mm), 1.0);
}
l++;
}
}
}
// Destroy blocks
for (int i=0; i<input_block.size(); i++)
input_block[i] = Teuchos::null;
for (int i=0; i<result_block.size(); i++)
result_block[i] = Teuchos::null;
if (made_copy)
delete input;
return 0;
}