/// \brief Verify the result of the "thin" QR factorization \f$A = QR\f$.
///
/// This method returns a list of three magnitudes:
/// - \f$\| A - QR \|_F\f$
/// - \f$\|I - Q^* Q\|_F\f$
/// - \f$\|A\|_F\f$
///
/// The notation $\f\| X \|\f$ denotes the Frobenius norm
/// (square root of sum of squares) of a matrix \f$X\f$.
/// Returning the Frobenius norm of \f$A\f$ allows you to scale
/// or not scale the residual \f$\|A - QR\|\f$ as you prefer.
virtual std::vector< magnitude_type >
verify (const multivector_type& A,
const multivector_type& Q,
const Teuchos::SerialDenseMatrix< local_ordinal_type, scalar_type >& R)
{
using Teuchos::ArrayRCP;
local_ordinal_type nrowsLocal_A, ncols_A, LDA;
local_ordinal_type nrowsLocal_Q, ncols_Q, LDQ;
fetchDims (A, nrowsLocal_A, ncols_A, LDA);
fetchDims (Q, nrowsLocal_Q, ncols_Q, LDQ);
if (nrowsLocal_A != nrowsLocal_Q)
throw std::runtime_error ("A and Q must have same number of rows");
else if (ncols_A != ncols_Q)
throw std::runtime_error ("A and Q must have same number of columns");
else if (ncols_A != R.numCols())
throw std::runtime_error ("A and R must have same number of columns");
else if (R.numRows() < R.numCols())
throw std::runtime_error ("R must have no fewer rows than columns");
// Const views suffice for verification
ArrayRCP< const scalar_type > A_ptr = fetchConstView (A);
ArrayRCP< const scalar_type > Q_ptr = fetchConstView (Q);
return global_verify (nrowsLocal_A, ncols_A, A_ptr.get(), LDA,
Q_ptr.get(), LDQ, R.values(), R.stride(),
pScalarMessenger_.get());
}
void
Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type,point_compare_type>::
transformPCE2QP_smolyak(
const value_type& alpha,
const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& input,
Teuchos::SerialDenseMatrix<ordinal_type,value_type>& result,
const value_type& beta,
bool trans) const {
Teuchos::SerialDenseMatrix<ordinal_type,value_type> op_input, op_result;
result.scale(beta);
for (ordinal_type i=0; i<operators.size(); i++) {
Teuchos::RCP<operator_type> op = operators[i];
if (trans) {
op_input.reshape(input.numRows(), op->coeff_size());
op_result.reshape(result.numRows(), op->point_size());
}
else {
op_input.reshape(op->coeff_size(), input.numCols());
op_result.reshape(op->point_size(), result.numCols());
}
gather(scatter_maps[i], input, trans, op_input);
op->transformPCE2QP(smolyak_coeffs[i], op_input, op_result, 0.0, trans);
scatter(gather_maps[i], op_result, trans, result);
}
}
// Update *this with alpha * A * B + beta * (*this).
void MvTimesMatAddMv (ScalarType alpha, const Anasazi::MultiVec<ScalarType> &A,
const Teuchos::SerialDenseMatrix<int, ScalarType> &B,
ScalarType beta)
{
assert (Length_ == A.GetVecLength());
assert (B.numRows() == A.GetNumberVecs());
assert (B.numCols() <= NumberVecs_);
MyMultiVec* MyA;
MyA = dynamic_cast<MyMultiVec*>(&const_cast<Anasazi::MultiVec<ScalarType> &>(A));
assert(MyA!=NULL);
if ((*this)[0] == (*MyA)[0]) {
// If this == A, then need additional storage ...
// This situation is a bit peculiar but it may be required by
// certain algorithms.
std::vector<ScalarType> tmp(NumberVecs_);
for (int i = 0 ; i < Length_ ; ++i) {
for (int v = 0; v < A.GetNumberVecs() ; ++v) {
tmp[v] = (*MyA)(i, v);
}
for (int v = 0 ; v < B.numCols() ; ++v) {
(*this)(i, v) *= beta;
ScalarType res = Teuchos::ScalarTraits<ScalarType>::zero();
for (int j = 0 ; j < A.GetNumberVecs() ; ++j) {
res += tmp[j] * B(j, v);
}
(*this)(i, v) += alpha * res;
}
}
}
else {
for (int i = 0 ; i < Length_ ; ++i) {
for (int v = 0 ; v < B.numCols() ; ++v) {
(*this)(i, v) *= beta;
ScalarType res = 0.0;
for (int j = 0 ; j < A.GetNumberVecs() ; ++j) {
res += (*MyA)(i, j) * B(j, v);
}
(*this)(i, v) += alpha * res;
}
}
}
}
void
Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type,point_compare_type>::
apply_direct(
const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& A,
const value_type& alpha,
const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& input,
Teuchos::SerialDenseMatrix<ordinal_type,value_type>& result,
const value_type& beta,
bool trans) const {
if (trans) {
TEUCHOS_ASSERT(input.numCols() <= A.numCols());
TEUCHOS_ASSERT(result.numCols() == A.numRows());
TEUCHOS_ASSERT(result.numRows() == input.numRows());
blas.GEMM(Teuchos::NO_TRANS, Teuchos::TRANS, input.numRows(),
A.numRows(), input.numCols(), alpha, input.values(),
input.stride(), A.values(), A.stride(), beta,
result.values(), result.stride());
}
else {
TEUCHOS_ASSERT(input.numRows() <= A.numCols());
TEUCHOS_ASSERT(result.numRows() == A.numRows());
TEUCHOS_ASSERT(result.numCols() == input.numCols());
blas.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, A.numRows(),
input.numCols(), input.numRows(), alpha, A.values(),
A.stride(), input.values(), input.stride(), beta,
result.values(), result.stride());
}
}
void assembleIRKState(
const int stageIndex,
const Teuchos::SerialDenseMatrix<int,Scalar> &A_in,
const Scalar dt,
const Thyra::VectorBase<Scalar> &x_base,
const Thyra::ProductVectorBase<Scalar> &x_stage_bar,
Teuchos::Ptr<Thyra::VectorBase<Scalar> > x_out_ptr
)
{
typedef ScalarTraits<Scalar> ST;
const int numStages_in = A_in.numRows();
TEUCHOS_ASSERT_IN_RANGE_UPPER_EXCLUSIVE( stageIndex, 0, numStages_in );
TEUCHOS_ASSERT_EQUALITY( A_in.numRows(), numStages_in );
TEUCHOS_ASSERT_EQUALITY( A_in.numCols(), numStages_in );
TEUCHOS_ASSERT_EQUALITY( x_stage_bar.productSpace()->numBlocks(), numStages_in );
Thyra::VectorBase<Scalar>& x_out = *x_out_ptr;
V_V( outArg(x_out), x_base );
for ( int j = 0; j < numStages_in; ++j ) {
Vp_StV( outArg(x_out), dt * A_in(stageIndex,j), *x_stage_bar.getVectorBlock(j) );
}
}
void EpetraMultiVec::MvTimesMatAddMv ( double alpha, const MultiVec<double>& A,
const Teuchos::SerialDenseMatrix<int,double>& B, double beta )
{
Epetra_LocalMap LocalMap(B.numRows(), 0, Map().Comm());
Epetra_MultiVector B_Pvec(View, LocalMap, B.values(), B.stride(), B.numCols());
EpetraMultiVec *A_vec = dynamic_cast<EpetraMultiVec *>(&const_cast<MultiVec<double> &>(A));
TEUCHOS_TEST_FOR_EXCEPTION( A_vec==NULL, std::invalid_argument, "Anasazi::EpetraMultiVec::SetBlocks() cast of MultiVec<double> to EpetraMultiVec failed.");
TEUCHOS_TEST_FOR_EXCEPTION(
Multiply( 'N', 'N', alpha, *A_vec, B_Pvec, beta ) != 0,
EpetraMultiVecFailure, "Anasazi::EpetraMultiVec::MvTimesMatAddMv() call to Epetra_MultiVec::Multiply() returned a nonzero value.");
}
void EpetraMultiVec::MvTransMv ( const double alpha, const MultiVec<double>& A,
Teuchos::SerialDenseMatrix<int,double>& B) const
{
EpetraMultiVec *A_vec = dynamic_cast<EpetraMultiVec *>(&const_cast<MultiVec<double> &>(A));
if (A_vec) {
Epetra_LocalMap LocalMap(B.numRows(), 0, Map().Comm());
Epetra_MultiVector B_Pvec(View, LocalMap, B.values(), B.stride(), B.numCols());
int info = B_Pvec.Multiply( 'T', 'N', alpha, *A_vec, *this, 0.0 );
TEST_FOR_EXCEPTION(info!=0, EpetraMultiVecFailure,
"Belos::EpetraMultiVec::MvTransMv call to Multiply() returned a nonzero value.");
}
}
// Generic BLAS level 3 matrix multiplication
// \f$\text{this}\leftarrow \alpha A B+\beta\text{this}\f$
void gemm(const Real alpha,
const MV& A,
const Teuchos::SerialDenseMatrix<int,Real> &B,
const Real beta) {
// Scale this by beta
this->scale(beta);
for(int i=0;i<B.numRows();++i) {
for(int j=0;j<B.numCols();++j) {
mvec_[j]->axpy(alpha*B(i,j),*A.getVector(i));
}
}
}
void EpetraMultiVec::MvTimesMatAddMv ( const double alpha, const MultiVec<double>& A,
const Teuchos::SerialDenseMatrix<int,double>& B, const double beta )
{
Epetra_LocalMap LocalMap(B.numRows(), 0, Map().Comm());
Epetra_MultiVector B_Pvec(View, LocalMap, B.values(), B.stride(), B.numCols());
EpetraMultiVec *A_vec = dynamic_cast<EpetraMultiVec *>(&const_cast<MultiVec<double> &>(A));
TEST_FOR_EXCEPTION(A_vec==NULL, EpetraMultiVecFailure,
"Belos::EpetraMultiVec::MvTimesMatAddMv cast from Belos::MultiVec<> to Belos::EpetraMultiVec failed.");
int info = Multiply( 'N', 'N', alpha, *A_vec, B_Pvec, beta );
TEST_FOR_EXCEPTION(info!=0, EpetraMultiVecFailure,
"Belos::EpetraMultiVec::MvTimesMatAddMv call to Multiply() returned a nonzero value.");
}
void
Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type,point_compare_type>::
scatter(
const Teuchos::Array<ordinal_type>& map,
const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& input,
bool trans,
Teuchos::SerialDenseMatrix<ordinal_type,value_type>& result) const {
if (trans) {
for (ordinal_type j=0; j<map.size(); j++)
for (ordinal_type i=0; i<input.numRows(); i++)
result(i,map[j]) += input(i,j);
}
else {
for (ordinal_type j=0; j<input.numCols(); j++)
for (ordinal_type i=0; i<map.size(); i++)
result(map[i],j) += input(i,j);
}
}
void EpetraMultiVec::MvTransMv ( double alpha, const MultiVec<double>& A,
Teuchos::SerialDenseMatrix<int,double>& B
#ifdef HAVE_ANASAZI_EXPERIMENTAL
, ConjType conj
#endif
) const
{
EpetraMultiVec *A_vec = dynamic_cast<EpetraMultiVec *>(&const_cast<MultiVec<double> &>(A));
if (A_vec) {
Epetra_LocalMap LocalMap(B.numRows(), 0, Map().Comm());
Epetra_MultiVector B_Pvec(View, LocalMap, B.values(), B.stride(), B.numCols());
TEUCHOS_TEST_FOR_EXCEPTION(
B_Pvec.Multiply( 'T', 'N', alpha, *A_vec, *this, 0.0 ) != 0,
EpetraMultiVecFailure, "Anasazi::EpetraMultiVec::MvTransMv() call to Epetra_MultiVec::Multiply() returned a nonzero value.");
}
}
// Compute a dense matrix B through the matrix-matrix multiply alpha * A^H * (*this).
void MvTransMv (ScalarType alpha, const Anasazi::MultiVec<ScalarType>& A,
Teuchos::SerialDenseMatrix< int, ScalarType >& B
#ifdef HAVE_ANASAZI_EXPERIMENTAL
, Anasazi::ConjType conj
#endif
) const
{
MyMultiVec* MyA;
MyA = dynamic_cast<MyMultiVec*>(&const_cast<Anasazi::MultiVec<ScalarType> &>(A));
assert (MyA != 0);
assert (A.GetVecLength() == Length_);
assert (NumberVecs_ <= B.numCols());
assert (A.GetNumberVecs() <= B.numRows());
#ifdef HAVE_ANASAZI_EXPERIMENTAL
if (conj == Anasazi::CONJ) {
#endif
for (int v = 0 ; v < A.GetNumberVecs() ; ++v) {
for (int w = 0 ; w < NumberVecs_ ; ++w) {
ScalarType value = 0.0;
for (int i = 0 ; i < Length_ ; ++i) {
value += Teuchos::ScalarTraits<ScalarType>::conjugate((*MyA)(i, v)) * (*this)(i, w);
}
B(v, w) = alpha * value;
}
}
#ifdef HAVE_ANASAZI_EXPERIMENTAL
} else {
for (int v = 0 ; v < A.GetNumberVecs() ; ++v) {
for (int w = 0 ; w < NumberVecs_ ; ++w) {
ScalarType value = 0.0;
for (int i = 0 ; i < Length_ ; ++i) {
value += (*MyA)(i, v) * (*this)(i, w);
}
B(v, w) = alpha * value;
}
}
}
#endif
}
// Compute a dense matrix B through the matrix-matrix multiply alpha * A^H * (*this).
void MvTransMv (const ScalarType alpha, const Belos::MultiVec<ScalarType>& A,
Teuchos::SerialDenseMatrix< int, ScalarType >& B) const
{
MyMultiVec* MyA;
MyA = dynamic_cast<MyMultiVec*>(&const_cast<Belos::MultiVec<ScalarType> &>(A));
TEUCHOS_ASSERT(MyA != NULL);
assert (A.GetGlobalLength() == Length_);
assert (NumberVecs_ <= B.numCols());
assert (A.GetNumberVecs() <= B.numRows());
for (int v = 0 ; v < A.GetNumberVecs() ; ++v) {
for (int w = 0 ; w < NumberVecs_ ; ++w) {
ScalarType value = 0.0;
for (int i = 0 ; i < Length_ ; ++i) {
value += Teuchos::ScalarTraits<ScalarType>::conjugate((*MyA)(i, v)) * (*this)(i, w);
}
B(v, w) = alpha * value;
}
}
}
/*! \brief Update \c mv with \f$ \alpha A B + \beta mv \f$.
*/
static void MvTimesMatAddMv( const double alpha, const _MV & A,
const Teuchos::SerialDenseMatrix<int,double>& B,
const double beta, _MV & mv )
{
// Out::os() << "MvTimesMatAddMv()" << endl;
int n = B.numCols();
// Out::os() << "B.numCols()=" << n << endl;
TEST_FOR_EXCEPT(mv.size() != n);
for (int j=0; j<mv.size(); j++)
{
Vector<double> tmp;
if (beta==one())
{
tmp = mv[j].copy();
}
else if (beta==zero())
{
tmp = mv[j].copy();
tmp.setToConstant(zero());
}
else
{
tmp = beta * mv[j];
}
if (alpha != zero())
{
for (int i=0; i<A.size(); i++)
{
tmp = tmp + alpha*B(i,j)*A[i];
}
}
mv[j].acceptCopyOf(tmp);
}
}
void EpetraOpMultiVec::MvTransMv ( double alpha, const MultiVec<double>& A,
Teuchos::SerialDenseMatrix<int,double>& B
#ifdef HAVE_ANASAZI_EXPERIMENTAL
, ConjType conj
#endif
) const
{
EpetraOpMultiVec *A_vec = dynamic_cast<EpetraOpMultiVec *>(&const_cast<MultiVec<double> &>(A));
if (A_vec) {
Epetra_LocalMap LocalMap(B.numRows(), 0, Epetra_MV->Map().Comm());
Epetra_MultiVector B_Pvec(Epetra_DataAccess::View, LocalMap, B.values(), B.stride(), B.numCols());
int info = Epetra_OP->Apply( *Epetra_MV, *Epetra_MV_Temp );
TEUCHOS_TEST_FOR_EXCEPTION( info != 0, EpetraSpecializedMultiVecFailure,
"Anasazi::EpetraOpMultiVec::MvTransMv(): Error returned from Epetra_Operator::Apply()" );
TEUCHOS_TEST_FOR_EXCEPTION(
B_Pvec.Multiply( 'T', 'N', alpha, *(A_vec->GetEpetraMultiVector()), *Epetra_MV_Temp, 0.0 ) != 0,
EpetraSpecializedMultiVecFailure, "Anasazi::EpetraOpMultiVec::MvTransMv() call to Epetra_MultiVector::Multiply() returned a nonzero value.");
}
}
void
factorExplicit (Kokkos::MultiVector<Scalar, NodeType>& A,
Kokkos::MultiVector<Scalar, NodeType>& Q,
Teuchos::SerialDenseMatrix<LocalOrdinal, Scalar>& R,
const bool contiguousCacheBlocks,
const bool forceNonnegativeDiagonal=false)
{
using Teuchos::asSafe;
typedef Kokkos::MultiVector<Scalar, NodeType> KMV;
// Tsqr currently likes LocalOrdinal ordinals, but
// Kokkos::MultiVector has size_t ordinals. Do conversions
// here.
//
// Teuchos::asSafe() can do safe conversion (e.g., checking for
// overflow when casting to a narrower integer type), if a
// custom specialization is defined for
// Teuchos::ValueTypeConversionTraits<size_t, LocalOrdinal>.
// Otherwise, this has the same (potentially) unsafe effect as
// static_cast<LocalOrdinal>(...) would have.
const LocalOrdinal A_numRows = asSafe<LocalOrdinal> (A.getNumRows());
const LocalOrdinal A_numCols = asSafe<LocalOrdinal> (A.getNumCols());
const LocalOrdinal A_stride = asSafe<LocalOrdinal> (A.getStride());
const LocalOrdinal Q_numRows = asSafe<LocalOrdinal> (Q.getNumRows());
const LocalOrdinal Q_numCols = asSafe<LocalOrdinal> (Q.getNumCols());
const LocalOrdinal Q_stride = asSafe<LocalOrdinal> (Q.getStride());
// Sanity checks for matrix dimensions
if (A_numRows < A_numCols) {
std::ostringstream os;
os << "In Tsqr::factorExplicit: input matrix A has " << A_numRows
<< " local rows, and " << A_numCols << " columns. The input "
"matrix must have at least as many rows on each processor as "
"there are columns.";
throw std::invalid_argument(os.str());
} else if (A_numRows != Q_numRows) {
std::ostringstream os;
os << "In Tsqr::factorExplicit: input matrix A and output matrix Q "
"must have the same number of rows. A has " << A_numRows << " rows"
" and Q has " << Q_numRows << " rows.";
throw std::invalid_argument(os.str());
} else if (R.numRows() < R.numCols()) {
std::ostringstream os;
os << "In Tsqr::factorExplicit: output matrix R must have at least "
"as many rows as columns. R has " << R.numRows() << " rows and "
<< R.numCols() << " columns.";
throw std::invalid_argument(os.str());
} else if (A_numCols != R.numCols()) {
std::ostringstream os;
os << "In Tsqr::factorExplicit: input matrix A and output matrix R "
"must have the same number of columns. A has " << A_numCols
<< " columns and R has " << R.numCols() << " columns.";
throw std::invalid_argument(os.str());
}
// Check for quick exit, based on matrix dimensions
if (Q_numCols == 0)
return;
// Hold on to nonconst views of A and Q. This will make TSQR
// correct (if perhaps inefficient) for all possible Kokkos Node
// types, even GPU nodes.
Teuchos::ArrayRCP<scalar_type> A_ptr = A.getValuesNonConst();
Teuchos::ArrayRCP<scalar_type> Q_ptr = Q.getValuesNonConst();
R.putScalar (STS::zero());
NodeOutput nodeResults =
nodeTsqr_->factor (A_numRows, A_numCols, A_ptr.getRawPtr(), A_stride,
R.values(), R.stride(), contiguousCacheBlocks);
// FIXME (mfh 19 Oct 2010) Replace actions on raw pointer with
// actions on the Kokkos::MultiVector or at least the ArrayRCP.
nodeTsqr_->fill_with_zeros (Q_numRows, Q_numCols,
Q_ptr.getRawPtr(), Q_stride,
contiguousCacheBlocks);
matview_type Q_rawView (Q_numRows, Q_numCols,
Q_ptr.getRawPtr(), Q_stride);
matview_type Q_top_block =
nodeTsqr_->top_block (Q_rawView, contiguousCacheBlocks);
if (Q_top_block.nrows() < R.numCols()) {
std::ostringstream os;
os << "The top block of Q has too few rows. This means that the "
<< "the intranode TSQR implementation has a bug in its top_block"
<< "() method. The top block should have at least " << R.numCols()
<< " rows, but instead has only " << Q_top_block.ncols()
<< " rows.";
throw std::logic_error (os.str());
}
{
matview_type Q_top (R.numCols(), Q_numCols, Q_top_block.get(),
Q_top_block.lda());
matview_type R_view (R.numRows(), R.numCols(), R.values(), R.stride());
distTsqr_->factorExplicit (R_view, Q_top, forceNonnegativeDiagonal);
}
nodeTsqr_->apply (ApplyType::NoTranspose,
A_numRows, A_numCols, A_ptr.getRawPtr(), A_stride,
nodeResults, Q_numCols, Q_ptr.getRawPtr(), Q_stride,
contiguousCacheBlocks);
// If necessary, force the R factor to have a nonnegative diagonal.
if (forceNonnegativeDiagonal &&
! QR_produces_R_factor_with_nonnegative_diagonal()) {
details::NonnegDiagForcer<LocalOrdinal, Scalar, STS::isComplex> forcer;
matview_type Q_mine (Q_numRows, Q_numCols, Q_ptr.getRawPtr(), Q_stride);
matview_type R_mine (R.numRows(), R.numCols(), R.values(), R.stride());
forcer.force (Q_mine, R_mine);
}
// "Commit" the changes to the multivector.
A_ptr = Teuchos::null;
Q_ptr = Teuchos::null;
}