void Stokhos::BasisInteractionGraph::initialize(const Stokhos::OrthogPolyBasis<int,double> & max_basis,
const Stokhos::Sparse3Tensor<int,double> & Cijk,
int porder)
{
using Teuchos::RCP;
typedef Stokhos::Sparse3Tensor<int,double> Cijk_type;
// // max it out if defaulted
// if(porder<0)
// porder = max_basis.size();
// RCP<Stokhos::Sparse3Tensor<int,double> > Cijk = max_basis.computeTripleProductTensor(porder);
Cijk_type::k_iterator k_end = Cijk.k_end();
if (onlyUseLinear_) {
int dim = max_basis.dimension();
k_end = Cijk.find_k(dim+1);
}
vecLookup_.resize(max_basis.size()); // defines number of rows
numCols_ = vecLookup_.size(); // set number of columns
// Loop over Cijk entries including a non-zero in the graph at
// indices (i,j) if there is any k for which Cijk is non-zero
for(Cijk_type::k_iterator k_it=Cijk.k_begin(); k_it!=k_end; ++k_it) {
for(Cijk_type::kj_iterator j_it = Cijk.j_begin(k_it); j_it != Cijk.j_end(k_it); ++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);
vecLookup_[i].push_back(j);
}
}
}
}
Teuchos::RCP<Epetra_CrsGraph>
sparse3Tensor2CrsGraph(
const Stokhos::Sparse3Tensor<ordinal_type,value_type>& Cijk,
const Epetra_BlockMap& map)
{
typedef Stokhos::Sparse3Tensor<ordinal_type,value_type> Cijk_type;
// Graph to be created
Teuchos::RCP<Epetra_CrsGraph> graph =
Teuchos::rcp(new Epetra_CrsGraph(Copy, map, 0));
// Loop over Cijk entries including a non-zero in the graph at
// indices (i,j) if there is any k for which Cijk is non-zero
for (typename Cijk_type::k_iterator k_it=Cijk.k_begin();
k_it!=Cijk.k_end(); ++k_it) {
for (typename Cijk_type::kj_iterator j_it = Cijk.j_begin(k_it);
j_it != Cijk.j_end(k_it); ++j_it) {
ordinal_type j = index(j_it);
for (typename Cijk_type::kji_iterator i_it = Cijk.i_begin(j_it);
i_it != Cijk.i_end(j_it); ++i_it) {
ordinal_type i = index(i_it);
graph->InsertGlobalIndices(i, 1, &j);
}
}
}
// Sort, remove redundencies, transform to local, ...
graph->FillComplete();
return graph;
}
Teuchos::RCP<Epetra_CrsGraph>
sparse3Tensor2CrsGraph(
const Stokhos::OrthogPolyBasis<ordinal_type,value_type>& basis,
const Stokhos::Sparse3Tensor<ordinal_type,value_type>& Cijk,
const Epetra_Comm& comm)
{
// Number of stochastic rows
ordinal_type num_rows = basis.size();
// Replicated local map
Epetra_LocalMap map(num_rows, 0, comm);
// Graph to be created
Teuchos::RCP<Epetra_CrsGraph> graph =
Teuchos::rcp(new Epetra_CrsGraph(Copy, map, 0));
// Loop over Cijk entries including a non-zero in the graph at
// indices (i,j) if there is any k for which Cijk is non-zero
ordinal_type Cijk_size = Cijk.size();
for (ordinal_type k=0; k<Cijk_size; k++) {
ordinal_type nj = Cijk.num_j(k);
const Teuchos::Array<int>& j_indices = Cijk.Jindices(k);
for (ordinal_type jj=0; jj<nj; jj++) {
ordinal_type j = j_indices[jj];
const Teuchos::Array<int>& i_indices = Cijk.Iindices(k,jj);
ordinal_type ni = i_indices.size();
for (ordinal_type ii=0; ii<ni; ii++) {
ordinal_type i = i_indices[ii];
graph->InsertGlobalIndices(i, 1, &j);
}
}
}
// Sort, remove redundencies, transform to local, ...
graph->FillComplete();
return graph;
}
Stokhos::AdaptivityManager::Sparse3TensorHash::Sparse3TensorHash(const Stokhos::Sparse3Tensor<int,double> & Cijk)
{
typedef Stokhos::Sparse3Tensor<int,double>::k_iterator k_iterator;
typedef Stokhos::Sparse3Tensor<int,double>::kj_iterator kj_iterator;
typedef Stokhos::Sparse3Tensor<int,double>::kji_iterator kji_iterator;
for(k_iterator k_it = Cijk.k_begin();k_it!=Cijk.k_end();k_it++) {
int k = *k_it;
for(kj_iterator j_it = Cijk.j_begin(k_it);j_it!=Cijk.j_end(k_it);j_it++) {
int j = *j_it;
for(kji_iterator i_it = Cijk.i_begin(j_it);i_it!=Cijk.i_end(j_it);i_it++) {
int i = *i_it;
hashMap_[IJK(i,j,k)] = i_it.value();
}
}
}
}
Stokhos::MonoProjPCEBasis<ordinal_type, value_type>::
MonoProjPCEBasis(
ordinal_type p,
const Stokhos::OrthogPolyApprox<ordinal_type, value_type>& pce,
const Stokhos::Quadrature<ordinal_type, value_type>& quad,
const Stokhos::Sparse3Tensor<ordinal_type, value_type>& Cijk,
bool limit_integration_order_) :
RecurrenceBasis<ordinal_type, value_type>("Monomial Projection", p, true),
limit_integration_order(limit_integration_order_),
pce_sz(pce.basis()->size()),
pce_norms(pce.basis()->norm_squared()),
a(pce_sz),
b(pce_sz),
basis_vecs(pce_sz, p+1),
new_pce(p+1)
{
// If the original basis is normalized, we can use the standard QR
// factorization. For simplicity, we renormalize the PCE coefficients
// for a normalized basis
Stokhos::OrthogPolyApprox<ordinal_type, value_type> normalized_pce(pce);
for (ordinal_type i=0; i<pce_sz; i++) {
pce_norms[i] = std::sqrt(pce_norms[i]);
normalized_pce[i] *= pce_norms[i];
}
// Evaluate PCE at quad points
ordinal_type nqp = quad.size();
Teuchos::Array<value_type> pce_vals(nqp);
const Teuchos::Array<value_type>& weights = quad.getQuadWeights();
const Teuchos::Array< Teuchos::Array<value_type> >& quad_points =
quad.getQuadPoints();
const Teuchos::Array< Teuchos::Array<value_type> >& basis_values =
quad.getBasisAtQuadPoints();
for (ordinal_type i=0; i<nqp; i++) {
pce_vals[i] = normalized_pce.evaluate(quad_points[i], basis_values[i]);
}
// Form Kylov matrix up to order pce_sz
matrix_type K(pce_sz, pce_sz);
// Compute matrix
matrix_type A(pce_sz, pce_sz);
typedef Stokhos::Sparse3Tensor<ordinal_type, value_type> Cijk_type;
for (typename Cijk_type::k_iterator k_it = Cijk.k_begin();
k_it != Cijk.k_end(); ++k_it) {
ordinal_type k = index(k_it);
for (typename Cijk_type::kj_iterator j_it = Cijk.j_begin(k_it);
j_it != Cijk.j_end(k_it); ++j_it) {
ordinal_type j = index(j_it);
value_type val = 0;
for (typename Cijk_type::kji_iterator i_it = Cijk.i_begin(j_it);
i_it != Cijk.i_end(j_it); ++i_it) {
ordinal_type i = index(i_it);
value_type c = value(i_it) / (pce_norms[j]*pce_norms[k]);
val += pce[i]*c;
}
A(k,j) = val;
}
}
// Each column i is given by projection of the i-th order monomial
// onto original basis
vector_type u0 = Teuchos::getCol(Teuchos::View, K, 0);
u0(0) = 1.0;
for (ordinal_type i=1; i<pce_sz; i++)
u0(i) = 0.0;
for (ordinal_type k=1; k<pce_sz; k++) {
vector_type u = Teuchos::getCol(Teuchos::View, K, k);
vector_type up = Teuchos::getCol(Teuchos::View, K, k-1);
u.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, A, up, 0.0);
}
/*
for (ordinal_type j=0; j<pce_sz; j++) {
for (ordinal_type i=0; i<pce_sz; i++) {
value_type val = 0.0;
for (ordinal_type k=0; k<nqp; k++)
val += weights[k]*std::pow(pce_vals[k],j)*basis_values[k][i];
K(i,j) = val;
}
}
*/
std::cout << K << std::endl << std::endl;
// Compute QR factorization of K
ordinal_type ws_size, info;
value_type ws_size_query;
Teuchos::Array<value_type> tau(pce_sz);
Teuchos::LAPACK<ordinal_type,value_type> lapack;
lapack.GEQRF(pce_sz, pce_sz, K.values(), K.stride(), &tau[0],
&ws_size_query, -1, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::logic_error,
"GEQRF returned value " << info);
ws_size = static_cast<ordinal_type>(ws_size_query);
Teuchos::Array<value_type> work(ws_size);
lapack.GEQRF(pce_sz, pce_sz, K.values(), K.stride(), &tau[0],
&work[0], ws_size, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::logic_error,
"GEQRF returned value " << info);
// Get Q
lapack.ORGQR(pce_sz, pce_sz, pce_sz, K.values(), K.stride(), &tau[0],
&ws_size_query, -1, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::logic_error,
"ORGQR returned value " << info);
ws_size = static_cast<ordinal_type>(ws_size_query);
work.resize(ws_size);
lapack.ORGQR(pce_sz, pce_sz, pce_sz, K.values(), K.stride(), &tau[0],
&work[0], ws_size, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::logic_error,
"ORGQR returned value " << info);
// Get basis vectors
for (ordinal_type j=0; j<p+1; j++)
for (ordinal_type i=0; i<pce_sz; i++)
basis_vecs(i,j) = K(i,j);
// Compute T = Q'*A*Q
matrix_type prod(pce_sz,pce_sz);
prod.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, K, A, 0.0);
matrix_type T(pce_sz,pce_sz);
T.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, prod, K, 0.0);
//std::cout << T << std::endl;
// Recursion coefficients are diagonal and super diagonal
b[0] = 1.0;
for (ordinal_type i=0; i<pce_sz-1; i++) {
a[i] = T(i,i);
b[i+1] = T(i,i+1);
}
a[pce_sz-1] = T(pce_sz-1,pce_sz-1);
// Setup rest of basis
this->setup();
// Project original PCE into the new basis
vector_type u(pce_sz);
for (ordinal_type i=0; i<pce_sz; i++)
u[i] = normalized_pce[i];
new_pce.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, basis_vecs, u,
0.0);
for (ordinal_type i=0; i<=p; i++)
new_pce[i] /= this->norms[i];
}
static FlatSparse3Tensor_kji
create( const Stokhos::ProductBasis<OrdinalType,ValueType>& basis,
const Stokhos::Sparse3Tensor<OrdinalType,ValueType>& Cijk,
const Teuchos::ParameterList& params = Teuchos::ParameterList())
{
typedef Stokhos::Sparse3Tensor<OrdinalType,ValueType> Cijk_type;
// Compute number of j's for each k
const size_type dimension = basis.size();
const size_type nk = Cijk.num_k();
std::vector< size_t > j_coord_work( nk , (size_t) 0 );
size_type j_entry_count = 0 ;
for (typename Cijk_type::k_iterator k_it=Cijk.k_begin();
k_it!=Cijk.k_end(); ++k_it) {
OrdinalType k = index(k_it);
for (typename Cijk_type::kj_iterator j_it = Cijk.j_begin(k_it);
j_it != Cijk.j_end(k_it); ++j_it) {
OrdinalType j = index(j_it);
if (j >= k) {
++j_coord_work[k];
++j_entry_count;
}
}
}
// Compute number of i's for each k and j
std::vector< size_t > i_coord_work( j_entry_count , (size_t) 0 );
size_type i_entry_count = 0 ;
size_type j_entry = 0 ;
for (typename Cijk_type::k_iterator k_it=Cijk.k_begin();
k_it!=Cijk.k_end(); ++k_it) {
OrdinalType k = index(k_it);
for (typename Cijk_type::kj_iterator j_it = Cijk.j_begin(k_it);
j_it != Cijk.j_end(k_it); ++j_it) {
OrdinalType j = index(j_it);
if (j >= k) {
for (typename Cijk_type::kji_iterator i_it = Cijk.i_begin(j_it);
i_it != Cijk.i_end(j_it); ++i_it) {
++i_coord_work[j_entry];
++i_entry_count;
}
++j_entry;
}
}
}
/*
// Pad each row to have size divisible by alignment size
enum { Align = Kokkos::Impl::is_same<ExecutionSpace,Kokkos::Cuda>::value ? 32 : 2 };
for ( size_type i = 0 ; i < dimension ; ++i ) {
const size_t rem = coord_work[i] % Align;
if (rem > 0) {
const size_t pad = Align - rem;
coord_work[i] += pad;
entry_count += pad;
}
}
*/
// Allocate tensor data
FlatSparse3Tensor_kji tensor ;
tensor.m_dim = dimension;
tensor.m_j_coord = coord_array_type( "j_coord" , j_entry_count );
tensor.m_i_coord = coord_array_type( "i_coord" , i_entry_count );
tensor.m_value = value_array_type( "value" , i_entry_count );
tensor.m_num_j = entry_array_type( "num_j" , nk );
tensor.m_num_i = entry_array_type( "num_i" , j_entry_count );
tensor.m_j_row_map = row_map_array_type( "j_row_map" , nk+1 );
tensor.m_i_row_map = row_map_array_type( "i_row_map" , j_entry_count+1 );
tensor.m_flops = 3*j_entry_count + 2*i_entry_count;
// Create mirror, is a view if is host memory
typename coord_array_type::HostMirror
host_j_coord = Kokkos::create_mirror_view( tensor.m_j_coord );
typename coord_array_type::HostMirror
host_i_coord = Kokkos::create_mirror_view( tensor.m_i_coord );
typename value_array_type::HostMirror
host_value = Kokkos::create_mirror_view( tensor.m_value );
typename entry_array_type::HostMirror
host_num_j = Kokkos::create_mirror_view( tensor.m_num_j );
typename entry_array_type::HostMirror
host_num_i = Kokkos::create_mirror_view( tensor.m_num_i );
typename entry_array_type::HostMirror
host_j_row_map = Kokkos::create_mirror_view( tensor.m_j_row_map );
typename entry_array_type::HostMirror
host_i_row_map = Kokkos::create_mirror_view( tensor.m_i_row_map );
// Compute j row map
size_type sum = 0;
host_j_row_map(0) = 0;
for ( size_type k = 0 ; k < nk ; ++k ) {
sum += j_coord_work[k];
host_j_row_map(k+1) = sum;
host_num_j(k) = 0;
}
// Compute i row map
sum = 0;
host_i_row_map(0) = 0;
for ( size_type j = 0 ; j < j_entry_count ; ++j ) {
sum += i_coord_work[j];
host_i_row_map(j+1) = sum;
host_num_i(j) = 0;
}
for ( size_type k = 0 ; k < nk ; ++k ) {
j_coord_work[k] = host_j_row_map[k];
}
for ( size_type j = 0 ; j < j_entry_count ; ++j ) {
i_coord_work[j] = host_i_row_map[j];
}
for (typename Cijk_type::k_iterator k_it=Cijk.k_begin();
k_it!=Cijk.k_end(); ++k_it) {
OrdinalType k = index(k_it);
for (typename Cijk_type::kj_iterator j_it = Cijk.j_begin(k_it);
j_it != Cijk.j_end(k_it); ++j_it) {
OrdinalType j = index(j_it);
if (j >= k) {
const size_type jEntry = j_coord_work[k];
++j_coord_work[k];
host_j_coord(jEntry) = j ;
++host_num_j(k);
for (typename Cijk_type::kji_iterator i_it = Cijk.i_begin(j_it);
i_it != Cijk.i_end(j_it); ++i_it) {
OrdinalType i = index(i_it);
ValueType c = Stokhos::value(i_it);
const size_type iEntry = i_coord_work[jEntry];
++i_coord_work[jEntry];
host_value(iEntry) = (j != k) ? c : 0.5*c;
host_i_coord(iEntry) = i ;
++host_num_i(jEntry);
++tensor.m_nnz;
}
}
}
}
// Copy data to device if necessary
Kokkos::deep_copy( tensor.m_j_coord , host_j_coord );
Kokkos::deep_copy( tensor.m_i_coord , host_i_coord );
Kokkos::deep_copy( tensor.m_value , host_value );
Kokkos::deep_copy( tensor.m_num_j , host_num_j );
Kokkos::deep_copy( tensor.m_num_i , host_num_i );
Kokkos::deep_copy( tensor.m_j_row_map , host_j_row_map );
Kokkos::deep_copy( tensor.m_i_row_map , host_i_row_map );
return tensor ;
}
static FlatSparse3Tensor
create( const Stokhos::ProductBasis<OrdinalType,ValueType>& basis,
const Stokhos::Sparse3Tensor<OrdinalType,ValueType>& Cijk )
{
typedef Stokhos::Sparse3Tensor<OrdinalType,ValueType> Cijk_type;
// Compute number of k's for each i
const size_type dimension = basis.size();
std::vector< size_t > k_coord_work( dimension , (size_t) 0 );
size_type k_entry_count = 0 ;
for (typename Cijk_type::i_iterator i_it=Cijk.i_begin();
i_it!=Cijk.i_end(); ++i_it) {
OrdinalType i = index(i_it);
k_coord_work[i] = Cijk.num_k(i_it);
k_entry_count += Cijk.num_k(i_it);
}
// Compute number of j's for each i and k
std::vector< size_t > j_coord_work( k_entry_count , (size_t) 0 );
size_type j_entry_count = 0 ;
size_type k_entry = 0 ;
for (typename Cijk_type::i_iterator i_it=Cijk.i_begin();
i_it!=Cijk.i_end(); ++i_it) {
for (typename Cijk_type::ik_iterator k_it = Cijk.k_begin(i_it);
k_it != Cijk.k_end(i_it); ++k_it, ++k_entry) {
OrdinalType k = index(k_it);
for (typename Cijk_type::ikj_iterator j_it = Cijk.j_begin(k_it);
j_it != Cijk.j_end(k_it); ++j_it) {
OrdinalType j = index(j_it);
if (j >= k) {
++j_coord_work[k_entry];
++j_entry_count;
}
}
}
}
/*
// Pad each row to have size divisible by alignment size
enum { Align = KokkosArray::Impl::is_same<DeviceType,KokkosArray::Cuda>::value ? 32 : 2 };
for ( size_type i = 0 ; i < dimension ; ++i ) {
const size_t rem = coord_work[i] % Align;
if (rem > 0) {
const size_t pad = Align - rem;
coord_work[i] += pad;
entry_count += pad;
}
}
*/
// Allocate tensor data
FlatSparse3Tensor tensor ;
tensor.m_k_coord = coord_array_type( "k_coord" , k_entry_count );
tensor.m_j_coord = coord_array_type( "j_coord" , j_entry_count );
tensor.m_value = value_array_type( "value" , j_entry_count );
tensor.m_num_k = entry_array_type( "num_k" , dimension );
tensor.m_num_j = entry_array_type( "num_j" , k_entry_count );
tensor.m_k_row_map = row_map_array_type( "k_row_map" , dimension+1 );
tensor.m_j_row_map = row_map_array_type( "j_row_map" , k_entry_count+1 );
// Create mirror, is a view if is host memory
typename coord_array_type::HostMirror
host_k_coord = KokkosArray::create_mirror_view( tensor.m_k_coord );
typename coord_array_type::HostMirror
host_j_coord = KokkosArray::create_mirror_view( tensor.m_j_coord );
typename value_array_type::HostMirror
host_value = KokkosArray::create_mirror_view( tensor.m_value );
typename entry_array_type::HostMirror
host_num_k = KokkosArray::create_mirror_view( tensor.m_num_k );
typename entry_array_type::HostMirror
host_num_j = KokkosArray::create_mirror_view( tensor.m_num_j );
typename entry_array_type::HostMirror
host_k_row_map = KokkosArray::create_mirror_view( tensor.m_k_row_map );
typename entry_array_type::HostMirror
host_j_row_map = KokkosArray::create_mirror_view( tensor.m_j_row_map );
// Compute k row map
size_type sum = 0;
host_k_row_map(0) = 0;
for ( size_type i = 0 ; i < dimension ; ++i ) {
sum += k_coord_work[i];
host_k_row_map(i+1) = sum;
}
// Compute j row map
sum = 0;
host_j_row_map(0) = 0;
for ( size_type i = 0 ; i < k_entry_count ; ++i ) {
sum += j_coord_work[i];
host_j_row_map(i+1) = sum;
}
for ( size_type i = 0 ; i < dimension ; ++i ) {
k_coord_work[i] = host_k_row_map[i];
}
for ( size_type i = 0 ; i < k_entry_count ; ++i ) {
j_coord_work[i] = host_j_row_map[i];
}
for (typename Cijk_type::i_iterator i_it=Cijk.i_begin();
i_it!=Cijk.i_end(); ++i_it) {
OrdinalType i = index(i_it);
for (typename Cijk_type::ik_iterator k_it = Cijk.k_begin(i_it);
k_it != Cijk.k_end(i_it); ++k_it) {
OrdinalType k = index(k_it);
const size_type kEntry = k_coord_work[i];
++k_coord_work[i];
host_k_coord(kEntry) = k ;
++host_num_k(i);
for (typename Cijk_type::ikj_iterator j_it = Cijk.j_begin(k_it);
j_it != Cijk.j_end(k_it); ++j_it) {
OrdinalType j = index(j_it);
ValueType c = Stokhos::value(j_it);
if (j >= k) {
const size_type jEntry = j_coord_work[kEntry];
++j_coord_work[kEntry];
host_value(jEntry) = (j != k) ? c : 0.5*c;
host_j_coord(jEntry) = j ;
++host_num_j(kEntry);
++tensor.m_nnz;
}
}
}
}
// Copy data to device if necessary
KokkosArray::deep_copy( tensor.m_k_coord , host_k_coord );
KokkosArray::deep_copy( tensor.m_j_coord , host_j_coord );
KokkosArray::deep_copy( tensor.m_value , host_value );
KokkosArray::deep_copy( tensor.m_num_k , host_num_k );
KokkosArray::deep_copy( tensor.m_num_j , host_num_j );
KokkosArray::deep_copy( tensor.m_k_row_map , host_k_row_map );
KokkosArray::deep_copy( tensor.m_j_row_map , host_j_row_map );
tensor.m_flops = 5*tensor.m_nnz + dimension;
return tensor ;
}