/// \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>::
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 EpetraOpMultiVec::MvTimesMatAddMv ( double alpha, const MultiVec<double>& A,
const Teuchos::SerialDenseMatrix<int,double>& B, double beta )
{
Epetra_LocalMap LocalMap(B.numRows(), 0, Epetra_MV->Map().Comm());
Epetra_MultiVector B_Pvec(Epetra_DataAccess::View, LocalMap, B.values(), B.stride(), B.numCols());
EpetraOpMultiVec *A_vec = dynamic_cast<EpetraOpMultiVec *>(&const_cast<MultiVec<double> &>(A));
TEUCHOS_TEST_FOR_EXCEPTION( A_vec==NULL, std::invalid_argument, "Anasazi::EpetraOpMultiVec::SetBlocks() cast of MultiVec<double> to EpetraOpMultiVec failed.");
TEUCHOS_TEST_FOR_EXCEPTION(
Epetra_MV->Multiply( 'N', 'N', alpha, *(A_vec->GetEpetraMultiVector()), B_Pvec, beta ) != 0,
EpetraSpecializedMultiVecFailure, "Anasazi::EpetraOpMultiVec::MvTimesMatAddMv() call to Epetra_MultiVec::Multiply() returned a nonzero value.");
}
void updateGuess(Teuchos::SerialDenseVector<int, std::complex<double> >& myCurrentGuess,
Teuchos::SerialDenseVector<int, std::complex<double> >& myTargetsCalculated,
Teuchos::SerialDenseMatrix<int, std::complex<double> >& myJacobian,
Teuchos::LAPACK<int, std::complex<double> >& myLAPACK
)
{
//v = J(inverse) * (-F(x))
//new guess = v + old guess
myTargetsCalculated *= -1.0;
//Perform an LU factorization of this matrix.
int ipiv[NUMDIMENSIONS], info;
char TRANS = 'N';
myLAPACK.GETRF( NUMDIMENSIONS, NUMDIMENSIONS, myJacobian.values(), myJacobian.stride(), ipiv, &info );
// Solve the linear system.
myLAPACK.GETRS( TRANS, NUMDIMENSIONS, 1, myJacobian.values(), myJacobian.stride(),
ipiv, myTargetsCalculated.values(), myTargetsCalculated.stride(), &info );
//We have overwritten myTargetsCalculated with guess update values
//myBLAS.AXPY(NUMDIMENSIONS, 1.0, myGuessAdjustment.values(), 1, myCurrentGuess.values(), 1);
myCurrentGuess += myTargetsCalculated;
}
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.");
}
}
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.");
}
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 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.");
}
}
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;
}