LocalOrdinal
revealRank (Kokkos::MultiVector<Scalar, NodeType>& Q,
Teuchos::SerialDenseMatrix<LocalOrdinal, Scalar>& R,
const magnitude_type& tol,
const bool contiguousCacheBlocks = false) const
{
typedef Kokkos::MultiVector<Scalar, NodeType> KMV;
const LocalOrdinal nrows = static_cast<LocalOrdinal> (Q.getNumRows());
const LocalOrdinal ncols = static_cast<LocalOrdinal> (Q.getNumCols());
const LocalOrdinal ldq = static_cast<LocalOrdinal> (Q.getStride());
Teuchos::ArrayRCP<Scalar> Q_ptr = Q.getValuesNonConst();
// Take the easy exit if available.
if (ncols == 0)
return 0;
//
// FIXME (mfh 16 Jul 2010) We _should_ compute the SVD of R (as
// the copy B) on Proc 0 only. This would ensure that all
// processors get the same SVD and rank (esp. in a heterogeneous
// computing environment). For now, we just do this computation
// redundantly, and hope that all the returned rank values are
// the same.
//
matrix_type U (ncols, ncols, STS::zero());
const ordinal_type rank =
reveal_R_rank (ncols, R.values(), R.stride(),
U.get(), U.lda(), tol);
if (rank < ncols)
{
// cerr << ">>> Rank of R: " << rank << " < ncols=" << ncols << endl;
// cerr << ">>> Resulting U:" << endl;
// print_local_matrix (cerr, ncols, ncols, R, ldr);
// cerr << endl;
// If R is not full rank: reveal_R_rank() already computed
// the SVD \f$R = U \Sigma V^*\f$ of (the input) R, and
// overwrote R with \f$\Sigma V^*\f$. Now, we compute \f$Q
// := Q \cdot U\f$, respecting cache blocks of Q.
Q_times_B (nrows, ncols, Q_ptr.getRawPtr(), ldq,
U.get(), U.lda(), contiguousCacheBlocks);
}
return rank;
}
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;
}