LOCA::Epetra::HouseholderJacOp Class Reference

Epetra operator representing a $n+1$

bordered matrix. More...

#include <LOCA_Epetra_HouseholderJacOp.H>

Inheritance diagram for LOCA::Epetra::HouseholderJacOp:

[legend]Collaboration diagram for LOCA::Epetra::HouseholderJacOp:[legend]List of all members.


Public Member Functions
	HouseholderJacOp (const Epetra_Operator &jac, const Epetra_MultiVector &dfdpVec, const Epetra_MultiVector &houseVec_x, double houseVec_p, double b)
	Constructor.
virtual	~HouseholderJacOp ()
	Destructor.
virtual int	SetUseTranspose (bool UseTranspose)
	This operator does not support a transpose.
virtual int	Apply (const Epetra_MultiVector &Input, Epetra_MultiVector &Result) const
	Returns the result of a Epetra_Operator applied to a Epetra_MultiVector Input in Result as described above.
virtual int	ApplyInverse (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
	This method does nothing.
virtual double	NormInf () const
	Returns an approximate infinity norm of the Householder jac matrix.
virtual const char *	Label () const
	Returns a character string describing the operator.
virtual bool	UseTranspose () const
	Returns the current UseTranspose setting. Always returns false.
virtual bool	HasNormInf () const
	Returns true if the this object can provide an approximate Inf-norm, false otherwise.
virtual const Epetra_Comm &	Comm () const
	Returns a reference to the Epetra_Comm communicator associated with this operator.
virtual const Epetra_Map &	OperatorDomainMap () const
	Returns the Epetra_Map object associated with the domain of this matrix operator.
virtual const Epetra_Map &	OperatorRangeMap () const
	Returns the Epetra_Map object associated with the range of this matrix operator.
void	init (const Epetra_MultiVector &x)
	Initialize operator. Call this before starting a linear solve. The Epetra_MultiVector argument x must be of the same size and distribution as arguments to Apply().
void	finish ()
	Finish up solve. Call this after a linear solve is finished to inform the operator that the solve is completed.
void	applyHouse (Epetra_MultiVector &x, double &p) const
	This method applies the Housholder transformation from $\Re^{n+1}$ to $\Re^{n+1}$ and overwrites its arguments.
void	applyHouse (const Epetra_MultiVector &x, double p, Epetra_MultiVector &result_x, double &result_p) const
	This version of applyHouse does not overwrite its arguments.
Protected Attributes
string	label
	Label for operator.
const Epetra_Operator &	jacOperator
	Stores operator representing .
const Epetra_MultiVector &	dfdp
	Stores reference to vector.
const Epetra_MultiVector &	house_x
	Stores reference to x component of Householder vector.
double	house_p
	Stores parameter component of Householder vector.
double	beta
	Stores constant in Householder transformation.
Epetra_MultiVector *	tmp
	Temporary multi-vec used in Apply().

Detailed Description

Epetra operator representing a $n+1$

bordered matrix.

The LOCA::Epetra::HouseholderJacOp is an Epetra_Operator representing the matrix

$\begin{bmatrix} J & \frac{df}{dp} \end{bmatrix} Q$

where $J$ is an Epetra_Operator representing an $n\times n$ Jacobian matrix $\frac{df}{dx}$ , and $Q\in\Re^{n+1\times n}$ is orthogonal and whose columns span $v^{\perp}$ with $v\in\Re^{n+1}$ a supplied vector. The action of $Q$ is defined for any $z\in\Re^n$ by

$Q z = P \begin{bmatrix} z \\ 0 \end{bmatrix}.$

Here $P = I - \beta u u^T\in\Re^{n+1\times n+1}$ is a Householder transformation such that $P v = \|v\|_2 e_{n+1}$ and $u_{n+1} = 1$ where $e_{n+1}$ is the $n+1$ column of the identity.

The Apply() method performs the matrix-vector multiplication using the Householder transformation $P$ and the matrix operator $J$ . ApplyInverse() is not implemented.

This operator is used to compute solutions to the system of equations

$\begin{bmatrix} J & \frac{df}{dp} \end{bmatrix} \begin{bmatrix} \Delta x \\ \Delta p \end{bmatrix} = f \quad \text{s.t.}\quad v^T\begin{bmatrix}\Delta x \\ \Delta p\end{bmatrix} = 0$

in an iterative solver context for pseudo-arclength continuation where $v$ is the predictor vector.

Constructor & Destructor Documentation

LOCA::Epetra::HouseholderJacOp::HouseholderJacOp ( const Epetra_Operator & jac,

const Epetra_MultiVector & dfdpVec,

const Epetra_MultiVector & houseVec_x,

double houseVec_p,

double b

)

Constructor.
Builds the operator using the supplied operator jac and Epetra_Vector's dfdpVec and houseVec_x. Here houseVec_x is the x (solution) component of the Householder vector, houseVec_p is the parameter component, and b is the scalar in the Householder transformation.

Member Function Documentation

double LOCA::Epetra::HouseholderJacOp::NormInf ( ) const [virtual]

Returns an approximate infinity norm of the Householder jac matrix.
This is defined only if NormInf() of the underlying operator $J$ is defined and is given by $\|J\|_\infty+\|\frac{df}{dp}\|_\infty$ .
Implements Epetra_Operator.

int LOCA::Epetra::HouseholderJacOp::SetUseTranspose ( bool UseTranspose ) [virtual]

This operator does not support a transpose.
Setting this to true throws an error.
Implements Epetra_Operator.

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

LOCA_Epetra_HouseholderJacOp.H
LOCA_Epetra_HouseholderJacOp.C

Generated on Thu Sep 18 12:40:44 2008 for NOX by

1.3.9.1

LOCA::Epetra::HouseholderJacOp Class Reference

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation