A convenience class to compute the QR factorization of a an extended multi-vector. More...

#include <LOCA_BorderedSolver_HouseholderQR.H>

Public Member Functions
	HouseholderQR (const Teuchos::RCP< LOCA::GlobalData > &global_data)
	Constructor.

virtual	~HouseholderQR ()
	Destructor.

void	computeQR (const NOX::Abstract::MultiVector::DenseMatrix &C, const NOX::Abstract::MultiVector &B, bool use_c_transpose, NOX::Abstract::MultiVector::DenseMatrix &Y1, NOX::Abstract::MultiVector &Y2, NOX::Abstract::MultiVector::DenseMatrix &T, NOX::Abstract::MultiVector::DenseMatrix &R)
	Compute QR factorization as described above.

void	applyCompactWY (const NOX::Abstract::MultiVector::DenseMatrix &Y1, const NOX::Abstract::MultiVector &Y2, const NOX::Abstract::MultiVector::DenseMatrix &T, NOX::Abstract::MultiVector::DenseMatrix &X1, NOX::Abstract::MultiVector &X2, bool isZeroX1, bool isZeroX2, bool useTranspose) const
	Applies the operator Q as described above overwriting `x` and `y`. If either of `x` or `y` are zero on input, set the corresponding `isZeroX` or `isZeroY` flags. Set\ `useTranspose` to `true` to instead apply the transpose of Q.

void	applyCompactWY (const NOX::Abstract::MultiVector::DenseMatrix &Y1, const NOX::Abstract::MultiVector &Y2, const NOX::Abstract::MultiVector::DenseMatrix &T, const NOX::Abstract::MultiVector::DenseMatrix input1, const NOX::Abstract::MultiVector input2, NOX::Abstract::MultiVector::DenseMatrix &result1, NOX::Abstract::MultiVector &result2, bool useTranspose) const
	Another version of applyCompactWY() that does not overwrite its inputs. If either input is zero, set the corresponding pointer to NULL.

Protected Member Functions
void	computeHouseholderVector (int col, const NOX::Abstract::MultiVector::DenseMatrix &A1, const NOX::Abstract::MultiVector &A2, NOX::Abstract::MultiVector::DenseMatrix &V1, NOX::Abstract::MultiVector &V2, double &beta)
	Computes the Householder vector `V1`, `V2` for column `col` of `A1` and `A2`, starting at row `col` of A1.

void	applyHouseholderVector (const NOX::Abstract::MultiVector::DenseMatrix &V1, const NOX::Abstract::MultiVector &V2, double beta, NOX::Abstract::MultiVector::DenseMatrix &A1, NOX::Abstract::MultiVector &A2)
	Applies the Householder vector `V1`, `V2` to the matrix sub-block represented by `A1` and A2.

Protected Attributes
Teuchos::RCP< LOCA::GlobalData >	globalData
	Global data object.

Teuchos::BLAS< int, double >	dblas
	BLAS Wrappers.

Detailed Description

A convenience class to compute the QR factorization of a an extended multi-vector.

This class computes the QR factorization

$Q^T \begin{bmatrix} op(C) \\ B \end{bmatrix} = \begin{bmatrix} R \\ 0 \end{bmatrix}$

where is an $m\times m$ matrix, is an $n\times m$ matrix, is an $n+m\times n+m$ matrix, is an $m\times m$ matrix, and represents either the identity operation or the transpose. The matrix is represented by a NOX::Abstract::MultiVector::DenseMatrix while is a NOX::Abstract::MultiVector. Given and , this class computes and with returned as NOX::Abstract::MultiVector::DenseMatrix. The operator is generated using the standard Householder QR algorithm (Algorithm 5.2.1, G. Golub and C. Van Loan, "Matrix Computations," 3rd Edition, Johns Hopkins, Baltimore, 1996) and is stored using the compact WY representation: (see R. Schreiver and C. Van Loan, "A Storage-Efficient WY Represntation for Products of Householder Transformations," SIAM J. Sci. Stat. Comput., Vol. 10, No. 1, pp. 53-57, January 1989).

Constructor & Destructor Documentation

◆ HouseholderQR()

LOCA::BorderedSolver::HouseholderQR::HouseholderQR ( const Teuchos::RCP< LOCA::GlobalData > & global_data )

Constructor.

Parameters

global_data [in] Global data object

Member Function Documentation

◆ computeHouseholderVector()

void LOCA::BorderedSolver::HouseholderQR::computeHouseholderVector	(	int	col,
		const NOX::Abstract::MultiVector::DenseMatrix &	A1,
		const NOX::Abstract::MultiVector &	A2,
		NOX::Abstract::MultiVector::DenseMatrix &	V1,
		NOX::Abstract::MultiVector &	V2,
		double &	beta
	)

protected

Computes the Householder vector V1, V2 for column col of A1 and A2, starting at row col of A1.

The algorithm implemented here is essentially algorithm 5.1.1 of Golub and Van Loan.

References NOX::Abstract::MultiVector::scale().

◆ computeQR()

void LOCA::BorderedSolver::HouseholderQR::computeQR	(	const NOX::Abstract::MultiVector::DenseMatrix &	C,
		const NOX::Abstract::MultiVector &	B,
		bool	use_c_transpose,
		NOX::Abstract::MultiVector::DenseMatrix &	Y1,
		NOX::Abstract::MultiVector &	Y2,
		NOX::Abstract::MultiVector::DenseMatrix &	T,
		NOX::Abstract::MultiVector::DenseMatrix &	R
	)

Compute QR factorization as described above.

Set use_c_transpose to true if the transpose of is required.

References NOX::Abstract::MultiVector::clone(), NOX::Abstract::MultiVector::multiply(), NOX::Abstract::MultiVector::numVectors(), and NOX::Abstract::MultiVector::subView().

The documentation for this class was generated from the following files:

LOCA_BorderedSolver_HouseholderQR.H
LOCA_BorderedSolver_HouseholderQR.C

Public Member Functions