Stratimikos Version of the Day
|TsqrAdaptor (const Teuchos::RCP< Teuchos::ParameterList > &plist)|
|Constructor (that accepts a parameter list). |
|Constructor (that uses default parameters). |
|void||factorExplicit (MV &A, MV &Q, dense_matrix_type &R, const bool forceNonnegativeDiagonal=false)|
|Compute QR factorization [Q,R] = qr(A,0). |
|int||revealRank (MV &Q, dense_matrix_type &R, const magnitude_type &tol)|
|Rank-revealing decomposition. |
Stub adaptor from Thyra::MultiVectorBase to TSQR.
TSQR (Tall Skinny QR factorization) is an orthogonalization kernel that is as accurate as Householder QR, yet requires only messages between $P$ MPI processes, independently of the number of columns in the multivector.
TSQR works independently of the particular multivector implementation, and interfaces to the latter via an adaptor class. This class is the adaptor class for
MultiVectorBase. It templates on the MultiVector (MV) type so that it can pick up that class' typedefs. In particular, TSQR chooses its intranode implementation based on the Kokkos Node type of the multivector.
|Thyra::TsqrAdaptor< Scalar >::TsqrAdaptor||(||const Teuchos::RCP< Teuchos::ParameterList > &||plist||)||
Constructor (that accepts a parameter list).
|plist||[in] List of parameters for configuring TSQR. The specific parameter keys that are read depend on the TSQR implementation. For details, call |
|void Thyra::TsqrAdaptor< Scalar >::factorExplicit||(||MV &||A,|
|const bool||forceNonnegativeDiagonal =
Compute QR factorization [Q,R] = qr(A,0).
|A||[in/out] On input: the multivector to factor. Overwritten with garbage on output.|
|Q||[out] On output: the (explicitly stored) Q factor in the QR factorization of the (input) multivector A.|
|R||[out] On output: the R factor in the QR factorization of the (input) multivector A.|
|forceNonnegativeDiagonal||[in] If true, then (if necessary) do extra work (modifying both the Q and R factors) in order to force the R factor to have a nonnegative diagonal.|
|int Thyra::TsqrAdaptor< Scalar >::revealRank||(||MV &||Q,|
|const magnitude_type &||tol|
Using the R factor and explicit Q factor from factorExplicit(), compute the singular value decomposition (SVD) of R ( ). If R is full rank (with respect to the given relative tolerance tol), don't change Q or R. Otherwise, compute and in place (the latter may be no longer upper triangular).
|Q||[in/out] On input: explicit Q factor computed by factorExplicit(). (Must be an orthogonal resp. unitary matrix.) On output: If R is of full numerical rank with respect to the tolerance tol, Q is unmodified. Otherwise, Q is updated so that the first rank columns of Q are a basis for the column space of A (the original matrix whose QR factorization was computed by factorExplicit()). The remaining columns of Q are a basis for the null space of A.|
|R||[in/out] On input: ncols by ncols upper triangular matrix with leading dimension ldr >= ncols. On output: if input is full rank, R is unchanged on output. Otherwise, if is the SVD of R, on output R is overwritten with $ V^*$. This is also an ncols by ncols matrix, but may not necessarily be upper triangular.|
|tol||[in] Relative tolerance for computing the numerical rank of the matrix R.|