Concrete implementation of NOX::Abstract::Group for Trilinos/Epetra. More...

#include <NOX_Epetra_Group.H>

Inheritance diagram for NOX::Epetra::Group:

Collaboration diagram for NOX::Epetra::Group:

Public Member Functions
	Group (Teuchos::ParameterList &printingParams, const Teuchos::RCP< NOX::Epetra::Interface::Required > &i, const NOX::Epetra::Vector &initialGuess)
	Constructor with NO linear system (VERY LIMITED). More...

	Group (Teuchos::ParameterList &printingParams, const Teuchos::RCP< NOX::Epetra::Interface::Required > &i, const NOX::Epetra::Vector &initialGuess, const Teuchos::RCP< NOX::Epetra::LinearSystem > &linSys)
	Standard Constructor.

	Group (const NOX::Epetra::Group &source, NOX::CopyType type=NOX::DeepCopy)
	Copy constructor. If type is DeepCopy, takes ownership of valid shared linear system.

virtual	~Group ()
	Destructor.

virtual NOX::Abstract::Group &	operator= (const NOX::Abstract::Group &source)
	Copies the source group into this group. More...

virtual NOX::Abstract::Group &	operator= (const NOX::Epetra::Group &source)
	See operator=(const NOX::Abstract::Group&);.

virtual Teuchos::RCP < NOX::Abstract::Group >	clone (CopyType type=DeepCopy) const
	Create a new Group of the same derived type as this one by cloning this one, and return a ref count pointer to the new group. More...

virtual Teuchos::RCP < NOX::Epetra::Interface::Required >	getRequiredInterface ()
	Return the userInterface.

virtual Teuchos::RCP< const NOX::Epetra::LinearSystem >	getLinearSystem () const
	Return the Linear System.

virtual Teuchos::RCP < NOX::Epetra::LinearSystem >	getLinearSystem ()
	Return the Linear System.

virtual NOX::Abstract::Group::ReturnType	computeJacobianConditionNumber (int maxIters, double tolerance, int krylovSubspaceSize=100, bool printOutput=false)

virtual double	getJacobianConditionNumber () const
	Returns the condition number of the Jacobian matrix.

virtual void	disableLinearResidualComputation (const bool disableChoice)
	Sets option to disable linear resid computation. If disabled, this saves on a MatVec per Newton but disallows inexact Newton methods.

"Compute" functions.
virtual void	setX (const NOX::Epetra::Vector &y)

virtual void	setX (const NOX::Abstract::Vector &y)
	Set the solution vector x to y. More...

virtual void	computeX (const Group &grp, const NOX::Epetra::Vector &d, double step)

virtual void	computeX (const NOX::Abstract::Group &grp, const NOX::Abstract::Vector &d, double step)
	Compute x = grp.x + step * d. More...

virtual NOX::Abstract::Group::ReturnType	computeF ()
	Compute and store F(x). More...

virtual NOX::Abstract::Group::ReturnType	computeJacobian ()
	Compute and store Jacobian. More...

virtual NOX::Abstract::Group::ReturnType	computeGradient ()
	Compute and store gradient. More...

virtual NOX::Abstract::Group::ReturnType	computeNewton (Teuchos::ParameterList &params)
	Compute the Newton direction, using parameters for the linear solve. More...

"Is" functions
Checks to see if various objects have been computed. Returns true if the corresponding "compute" function has been called since the last update to the solution vector (via instantiation or computeX).
virtual bool	isF () const
	Return true if F is valid.

virtual bool	isJacobian () const
	Return true if the Jacobian is valid. More...

virtual bool	isGradient () const
	Return true if the gradient is valid. More...

virtual bool	isNewton () const
	Return true if the Newton direction is valid. More...

virtual bool	isNormNewtonSolveResidual () const
	Returns true if the value of the Norm of the linear model for a full Newton step \|\|Js + f\|\| is valid with respect to the current solution vector.

virtual bool	isPreconditioner () const
	Returns true if an explicitly constructed preconditioner exists (i.e. one that is computed and saved for further use in multiple calls to applyRightPreconditioner).

virtual bool	isConditionNumber () const
	Returns true if the condition number has been computed.

"Get" functions
Note that these function do not check whether or not the vectors are valid. Must use the "Is" functions for that purpose.
virtual const NOX::Abstract::Vector &	getX () const
	Return solution vector.

virtual const NOX::Abstract::Vector &	getF () const
	Return F(x)

virtual double	getNormF () const
	Return 2-norm of F(x). More...

virtual const NOX::Abstract::Vector &	getGradient () const
	Return gradient.

virtual const NOX::Abstract::Vector &	getNewton () const
	Return Newton direction.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getXPtr () const
	Return RCP to solution vector.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getFPtr () const
	Return RCP to F(x)

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getGradientPtr () const
	Return RCP to gradient.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getNewtonPtr () const
	Return RCP to Newton direction.

virtual NOX::Abstract::Group::ReturnType	getNormLastLinearSolveResidual (double &residual) const
	Returns the 2-norm of the residual of the linear model used in the Newton solve computation, \|\|Js+f\|\|. This does not account for line search adjustments to the step length!

Public Member Functions inherited from NOX::Abstract::Group
	Group ()
	Constructor. More...

virtual NOX::Abstract::Group::ReturnType	applyJacobianInverse (Teuchos::ParameterList &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Applies the inverse of the Jacobian matrix to the given input vector and puts the answer in result. More...

virtual NOX::Abstract::Group::ReturnType	applyJacobianMultiVector (const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	applyJacobian for multiple right-hand sides More...

virtual NOX::Abstract::Group::ReturnType	applyJacobianTransposeMultiVector (const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	applyJacobianTranspose for multiple right-hand sides More...

virtual NOX::Abstract::Group::ReturnType	applyJacobianInverseMultiVector (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	applyJacobianInverse for multiple right-hand sides More...

virtual NOX::Abstract::Group::ReturnType	applyRightPreconditioningMultiVector (bool useTranspose, Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	applyRightPreconditioning for multiple right-hand sides More...

virtual const NOX::Abstract::Vector &	getScaledX () const

Protected Member Functions
virtual void	resetIsValid ()
	resets the isValid flags to false

virtual void	logLastLinearSolveStats (NOX::SolverStats &stats) const
	Adds statistics from last linear solve to the SovlerStats object.

virtual bool	computeNormNewtonSolveResidual ()
	Computes the 2-norm of the residual of the linear model used in the Newton solve computation, \|\|Js+f\|\|.

Protected Attributes
const NOX::Utils	utils
	Printing Utilities object.

double	normNewtonSolveResidual
	2-Norm of the Newton solve residual: \|\|Js+f\|\|

double	conditionNumber
	condition number of Jacobian

Teuchos::RCP < AztecOOConditionNumber >	azConditionNumberPtr
	Pointer to the condition number object.

bool	linearResidCompDisabled

Teuchos::RCP < NOX::Epetra::Interface::Required >	userInterfacePtr
	Reference to the user supplied interface functions.

bool	linearSolveConverged

int	numIterations

double	achievedTol

Vectors
Teuchos::RCP< NOX::Epetra::Vector >	xVectorPtr
	Solution vector pointer.

NOX::Epetra::Vector &	xVector
	Solution vector.

Teuchos::RCP< NOX::Epetra::Vector >	RHSVectorPtr
	Right-hand-side vector (function evaluation).

NOX::Epetra::Vector &	RHSVector
	Right-hand-side vector pointer (function evaluation).

Teuchos::RCP< NOX::Epetra::Vector >	gradVectorPtr
	Gradient vector pointer(steepest descent vector).

NOX::Epetra::Vector &	gradVector
	Gradient vector (steepest descent vector).

Teuchos::RCP< NOX::Epetra::Vector >	NewtonVectorPtr
	Newton direction vector pointer.

NOX::Epetra::Vector &	NewtonVector
	Newton direction vector.

Teuchos::RCP< Epetra_Vector >	tmpVectorPtr
	An extra temporary vector, only allocated if needed.

IsValid flags
True if the current solution is up-to-date with respect to the currect xVector.
bool	isValidRHS

bool	isValidJacobian

bool	isValidGrad

bool	isValidNewton

bool	isValidNormNewtonSolveResidual

bool	isValidPreconditioner

bool	isValidSolverJacOp

bool	isValidConditionNumber

Shared Operators
Teuchos::RCP < NOX::SharedObject < NOX::Epetra::LinearSystem, NOX::Epetra::Group > >	sharedLinearSystemPtr
	Pointer to shared Jacobian matrix.

NOX::SharedObject < NOX::Epetra::LinearSystem, NOX::Epetra::Group > &	sharedLinearSystem
	Reference to shared Jacobian matrix.

Jacobian operations.
Operations using the Jacobian matrix. These may not be defined in matrix-free scenarios.
virtual NOX::Abstract::Group::ReturnType	const
	Applies the inverse of the Jacobian matrix to the given input vector and puts the answer in result. More...

virtual NOX::Abstract::Group::ReturnType	applyJacobian (const NOX::Epetra::Vector &input, NOX::Epetra::Vector &result) const

virtual NOX::Abstract::Group::ReturnType	applyJacobian (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Applies Jacobian to the given input vector and puts the answer in the result. More...

virtual NOX::Abstract::Group::ReturnType	applyJacobianTranspose (const NOX::Epetra::Vector &input, NOX::Epetra::Vector &result) const

virtual NOX::Abstract::Group::ReturnType	applyJacobianTranspose (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Applies Jacobian-Transpose to the given input vector and puts the answer in the result. More...

virtual NOX::Abstract::Group::ReturnType	applyRightPreconditioning (bool useTranspose, Teuchos::ParameterList &params, const NOX::Epetra::Vector &input, NOX::Epetra::Vector &result) const

virtual NOX::Abstract::Group::ReturnType	applyRightPreconditioning (bool useTranspose, Teuchos::ParameterList &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Apply right preconditiong to the given input vector. More...

Additional Inherited Members
Public Types inherited from NOX::Abstract::Group
enum	ReturnType { Ok, NotDefined, BadDependency, NotConverged, Failed }
	The computation of, say, the Newton direction in computeNewton() may fail in many different ways, so we have included a variety of return codes to describe the failures. Of course, we also have a code for success. More...

Detailed Description

Concrete implementation of NOX::Abstract::Group for Trilinos/Epetra.

This group is set up to use the linear algebra services provided

through the Trilinos/Epetra package with AztecOO for the linear solver.

Constructor & Destructor Documentation

Group::Group	(	Teuchos::ParameterList &	printingParams,
		const Teuchos::RCP< NOX::Epetra::Interface::Required > &	i,
		const NOX::Epetra::Vector &	initialGuess
	)

Constructor with NO linear system (VERY LIMITED).

WARNING: If this constructor is used, then methods that require a Jacobian or preconditioning will not be available. You will be limited to simple algorithms like nonlinear-CG with no preconditioning.

References resetIsValid().

Member Function Documentation

Abstract::Group::ReturnType Group::applyJacobian	(	const NOX::Abstract::Vector &	input,
		NOX::Abstract::Vector &	result
	)		const

virtual

Applies Jacobian to the given input vector and puts the answer in the result.

Computes

$v = J u,$

where $J$ is the Jacobian, $u$ is the input vector, and $v$ is the result vector.

Returns

NOX::Abstract::Group::NotDefined - Returned by default implementation in NOX::Abstract::Group
NOX::Abstract::Group::BadDependency - If the Jacobian has not been computed
NOX::Abstract::Group::Failed - If the computation fails
NOX::Abstract::Group::Ok - Otherwise

Reimplemented from NOX::Abstract::Group.

Abstract::Group::ReturnType Group::applyJacobianTranspose	(	const NOX::Abstract::Vector &	input,
		NOX::Abstract::Vector &	result
	)		const

virtual

Applies Jacobian-Transpose to the given input vector and puts the answer in the result.

Computes

$v = J^T u,$

where $J$ is the Jacobian, $u$ is the input vector, and $v$ is the result vector.

Returns

NOX::Abstract::Group::NotDefined - Returned by default implementation in NOX::Abstract::Group
NOX::Abstract::Group::BadDependency - If has not been computed
NOX::Abstract::Group::Failed - If the computation fails
NOX::Abstract::Group::Ok - Otherwise

Reimplemented from NOX::Abstract::Group.

Abstract::Group::ReturnType Group::applyRightPreconditioning	(	bool	useTranspose,
		Teuchos::ParameterList &	params,
		const NOX::Abstract::Vector &	input,
		NOX::Abstract::Vector &	result
	)		const

virtual

Apply right preconditiong to the given input vector.

Let $M$ be a right preconditioner for the Jacobian $J$ ; in other words, $M$ is a matrix such that

$JM \approx I.$

Compute

$u = M^{-1} v,$

where $u$ is the input vector and $v$ is the result vector.

If useTranspose is true, then the transpose of the preconditioner is applied:

$u = {M^{-1}}^T v,$

The transpose preconditioner is currently only required for Tensor methods.

The "Tolerance" parameter specifies that the solution should be such that

$\frac{\| M v - u \|_2}{\max \{ 1, \|u\|_2\} } < \mbox{Tolerance}$

Returns

NOX::Abstract::Group::NotDefined - Returned by default implementation in NOX::Abstract::Group
NOX::Abstract::Group::NotConverged - If the linear solve fails to satisfy the "Tolerance" specified in params
NOX::Abstract::Group::Failed - If the computation fails
NOX::Abstract::Group::Ok - Otherwise

The parameters are from the "Linear %Solver" sublist of the "Direction" sublist that is passed to solver during construction.

Reimplemented from NOX::Abstract::Group.

Teuchos::RCP< NOX::Abstract::Group > Group::clone ( CopyType type = DeepCopy ) const

virtual

Create a new Group of the same derived type as this one by cloning this one, and return a ref count pointer to the new group.

If type is NOX::DeepCopy, then we need to create an exact replica of "this". Otherwise, if type is NOX::ShapeCopy, we need only replicate the shape of "this" (only the memory is allocated, the values are not copied into the vectors and Jacobian). Returns NULL if clone is not supported.

Note: Any shared data should have its ownership transfered to this group from the source for a NOX::DeepCopy.

Implements NOX::Abstract::Group.

Reimplemented in LOCA::Epetra::Group.

References Teuchos::rcp().

Abstract::Group::ReturnType Group::computeF ( )

virtual

Compute and store F(x).

Note: It's generally useful to also compute and store the 2-norm of F(x) at this point for later access by the getNormF() function.

Returns

NOX::Abstract::Group::Failed - If the computation fails in any way
NOX::Abstract::Group::Ok - Otherwise

Implements NOX::Abstract::Group.

Reimplemented in LOCA::Epetra::Group.

References NOX::Epetra::Interface::Required::computeF(), NOX::Epetra::Vector::getEpetraVector(), isF(), NOX::Abstract::Group::Ok, NOX::Epetra::Interface::Required::Residual, RHSVector, userInterfacePtr, and xVector.

Referenced by LOCA::Epetra::Group::computeF().

Abstract::Group::ReturnType Group::computeGradient ( )

virtual

Compute and store gradient.

We can pose the nonlinear equation problem $F(x) = 0$ as an optimization problem as follows:

$\min f(x) \equiv \frac{1}{2} \|F(x)\|_2^2.$

In that case, the gradient (of $f$ ) is defined as

$g \equiv J^T F.$

Returns

NOX::Abstract::Group::NotDefined - Returned by default implementation in NOX::Abstract::Group
NOX::Abstract::Group::BadDependency - If either or has not been computed
NOX::Abstract::Group::Failed - If the computation fails in any other way
NOX::Abstract::Group::Ok - Otherwise

Reimplemented from NOX::Abstract::Group.

References gradVector, isF(), isGradient(), isJacobian(), NOX::Abstract::Group::Ok, RHSVector, and sharedLinearSystem.

Abstract::Group::ReturnType Group::computeJacobian ( )

virtual

Compute and store Jacobian.

Recall that

$F(x) = \left[ \begin{array}{c} F_1(x) \\ F_2(x) \\ \vdots \\ F_n(x) \\ \end{array} \right].$

The Jacobian is denoted by $J$ and defined by

$J_{ij} = \frac{\partial F_i}{\partial x_j} (x).$

Note: If this is a shared object, this group should take ownership of the Jacobian before it computes it.

Returns

NOX::Abstract::Group::NotDefined - Returned by default implementation in NOX::Abstract::Group
NOX::Abstract::Group::Failed - If the computation fails in any other way
NOX::Abstract::Group::Ok - Otherwise

Reimplemented from NOX::Abstract::Group.

Reimplemented in LOCA::Epetra::Group.

References isJacobian(), NOX::Abstract::Group::Ok, sharedLinearSystem, and xVector.

Referenced by LOCA::Epetra::Group::computeJacobian().

Abstract::Group::ReturnType Group::computeNewton ( Teuchos::ParameterList & params )

virtual

Compute the Newton direction, using parameters for the linear solve.

The Newton direction is the solution, s, of

$J s = -F.$

The parameters are from the "Linear %Solver" sublist of the "Direction" sublist that is passed to solver during construction.

The "Tolerance" parameter may be added/modified in the sublist of "Linear Solver" parameters that is passed into this function. The solution should be such that

$\frac{\| J s - (-F) \|_2}{\max \{ 1, \|F\|_2\} } < \mbox{Tolerance}$

Returns

NOX::Abstract::Group::NotDefined - Returned by default implementation in NOX::Abstract::Group
NOX::Abstract::Group::BadDependency - If either or has not been computed
NOX::Abstract::Group::NotConverged - If the linear solve fails to satisfy the "Tolerance" specified in params
NOX::Abstract::Group::Failed - If the computation fails in any other way
NOX::Abstract::Group::Ok - Otherwise

Reimplemented from NOX::Abstract::Group.

References NOX::Abstract::Group::applyJacobianInverse(), computeNormNewtonSolveResidual(), NOX::Epetra::Vector::init(), isF(), isJacobian(), isNewton(), NewtonVector, NOX::Abstract::Group::Ok, RHSVector, and NOX::Epetra::Vector::scale().

void Group::computeX	(	const NOX::Abstract::Group &	grp,
		const NOX::Abstract::Vector &	d,
		double	step
	)

virtual

Compute x = grp.x + step * d.

Let $x$ denote this group's solution vector. Let $\hat x$ denote the result of grp.getX(). Then set

$x = \hat x + \mbox{step} \; d.$

Note: This should invalidate the function value, Jacobian, gradient, and Newton direction.; Throw an error if the copy fails.

Returns: Reference to this object

Implements NOX::Abstract::Group.

double Group::getNormF ( ) const

virtual

Return 2-norm of F(x).

In other words,

$\sqrt{\sum_{i=1}^n F_i^2}$

Implements NOX::Abstract::Group.

References isF(), NOX::Epetra::Vector::norm(), and RHSVectorPtr.

bool Group::isGradient ( ) const

virtual

Return true if the gradient is valid.

Note: Default implementation in NOX::Abstract::Group returns false.

Reimplemented from NOX::Abstract::Group.

Referenced by computeGradient(), and getGradient().

bool Group::isJacobian ( ) const

virtual

Return true if the Jacobian is valid.

Note: Default implementation in NOX::Abstract::Group returns false.

Reimplemented from NOX::Abstract::Group.

References sharedLinearSystem.

Referenced by computeGradient(), computeJacobian(), and computeNewton().

bool Group::isNewton ( ) const

virtual

Return true if the Newton direction is valid.

Note: Default implementation in NOX::Abstract::Group returns false.

Reimplemented from NOX::Abstract::Group.

Referenced by computeNewton(), and getNewton().

Abstract::Group & Group::operator= ( const NOX::Abstract::Group & source )

virtual

Copies the source group into this group.

Note: Any shared data owned by the source should have its ownership transfered to this group. This may result in a secret modification to the source object.

Implements NOX::Abstract::Group.

Reimplemented in LOCA::Epetra::Group.

Referenced by LOCA::Epetra::Group::operator=().

void Group::setX ( const NOX::Abstract::Vector & y )

virtual

Set the solution vector x to y.

Note: This should invalidate the function value, Jacobian, gradient, and Newton direction.; Throw an error if the copy fails.

Returns: Reference to this object

Implements NOX::Abstract::Group.

Member Data Documentation

NOX::Abstract::Group::ReturnType NOX::Epetra::Group::const

Applies the inverse of the Jacobian matrix to the given input vector and puts the answer in result.

 Computes

$v = J^{-1} u,$

where $J$ is the Jacobian, $u$ is the input vector, and $v$ is the result vector.

 The "Tolerance" parameter specifies that the
 solution should be such that

$\frac{\| J v - u \|_2}{\max \{ 1, \|u\|_2\} } < \mbox{Tolerance}$

\return
<ul>
<li> NOX::Abstract::Group::NotDefined - Returned by default implementation

in NOX::Abstract::Group NOX::Abstract::Group::BadDependency - If $J$ has not been computed NOX::Abstract::Group::NotConverged - If the linear solve fails to satisfy the "Tolerance" specified in params NOX::Abstract::Group::Failed - If the computation fails NOX::Abstract::Group::Ok - Otherwise

The parameter "Tolerance" may be added/modified in the list of parameters - this is the ideal solution tolerance for an iterative linear solve.

The parameter "Reuse Preconditioner" is a boolean that tells the group to turn off control of preconditioner recalculation. This is a dangerous flag but can really speed the computations if the user knows what they are doing. Toggling this flag is left to the user (ideally it should be done through a status test). Defaults to false.

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

NOX_Epetra_Group.H
NOX_Epetra_Group.C

Public Member Functions

Protected Member Functions

Protected Attributes

Jacobian operations.

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation