NOX pure abstract interface to a "group"; i.e., a solution vector and the corresponding F-vector, Jacobian matrix, gradient vector, and Newton vector. More...

#include <NOX_Abstract_Group.H>

Inheritance diagram for NOX::Abstract::Group:

[legend]

Public Types
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...

Public Member Functions
	Group ()
	Constructor. More...

virtual	~Group ()
	Destructor.

virtual NOX::Abstract::Group &	operator= (const NOX::Abstract::Group &source)=0
	Copies the source group into this group. More...


virtual void	setX (const NOX::Abstract::Vector &y)=0
	Set the solution vector x to y. More...

virtual void	computeX (const NOX::Abstract::Group &grp, const NOX::Abstract::Vector &d, double step)=0
	Compute x = grp.x + step * d. More...

virtual NOX::Abstract::Group::ReturnType	computeF ()=0
	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...

Jacobian operations.
Operations using the Jacobian matrix.
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::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	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	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...

Block Jacobian operations.
Operations using the Jacobian matrix.
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...

"Is" functions.
Checks to see if various objects have been computed. Returns true if the corresponding "compute" function has been called since the last change to the solution vector.
virtual bool	isF () const =0
	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...

"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 =0
	Return solution vector.

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

virtual const NOX::Abstract::Vector &	getF () const =0
	Return F(x)

virtual double	getNormF () const =0
	Return 2-norm of F(x). More...

virtual const NOX::Abstract::Vector &	getGradient () const =0
	Return gradient.

virtual const NOX::Abstract::Vector &	getNewton () const =0
	Return Newton direction.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getXPtr () const =0
	Return RCP to solution vector.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getFPtr () const =0
	Return RCP to F(x)

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getGradientPtr () const =0
	Return RCP to gradient.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getNewtonPtr () const =0
	Return RCP to Newton direction.

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

virtual NOX::Abstract::Group::ReturnType	getNormLastLinearSolveResidual (double &residual) const
	Return the norm of the last linear solve residual as the result of either a call to computeNewton() or applyJacobianInverse(). More...


virtual Teuchos::RCP < NOX::Abstract::Group >	clone (NOX::CopyType type=NOX::DeepCopy) const =0
	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...

Detailed Description

NOX pure abstract interface to a "group"; i.e., a solution vector and the corresponding F-vector, Jacobian matrix, gradient vector, and Newton vector.

This class is a member of the namespace NOX::Abstract.

The user should implement their own concrete implementation of this class or use one of the implementations provided by us. Typically the implementation is also tied to a particular NOX::Abstract::Vector implementation.

Note: The group may be implemented so that multiple groups can share underlying memory space. This is particularly important when it comes to the Jacobian, which is often to big to be replicated for every group. Thus, we have included instructions on how shared data should be treated for the operator=() and clone() functions.

Member Enumeration Documentation

enum NOX::Abstract::Group::ReturnType

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.

Note: These return types may be expanded in future releases.

Enumerator
Ok	Computation completed successfully.
NotDefined	This function is not implemented.
BadDependency	Data dependencies not satisfied.
NotConverged	Unable to satisfy convergence criteria.
Failed	Any other type of failure.

Constructor & Destructor Documentation

NOX::Abstract::Group::Group ( )

inline

Constructor.

Note: Constructors for any derived object should always define a default x-value so that getX() is always defined.

Member Function Documentation

NOX::Abstract::Group::ReturnType NOX::Abstract::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 in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, NOX::Thyra::Group, LOCA::Homotopy::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, LOCA::MultiContinuation::ExtendedGroup, NOX::Epetra::Group, LOCA::PhaseTransition::ExtendedGroup, NOX::Petsc::Group, and NOX::LAPACK::Group.

References NotDefined.

Referenced by LOCA::DerivUtils::computeDJnDp(), LOCA::DerivUtils::computeDJnDxa(), LOCA::DerivUtils::computeDwtJnDp(), NOX::Direction::Utils::InexactNewton::computeForcingTerm(), NOX::MeritFunction::SumOfSquares::computeQuadraticMinimizer(), NOX::Thyra::WeightedMeritFunction::computeQuadraticModel(), NOX::MeritFunction::SumOfSquares::computeQuadraticModel(), NOX::Thyra::WeightedMeritFunction::computeSlope(), NOX::LineSearch::Utils::Slope::computeSlope(), NOX::Solver::TensorBased::computeTensorDirection(), NOX::Solver::TensorBased::getDirectionalDerivative(), NOX::Solver::TensorBased::getNormModelResidual(), NOX::Solver::InexactTrustRegionBased::iterateInexact(), NOX::Direction::Newton::resetForcingTerm(), and NOX::Solver::TrustRegionBased::step().

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

virtual

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

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

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::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.

Reimplemented in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, NOX::Thyra::Group, LOCA::Homotopy::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, LOCA::MultiContinuation::ExtendedGroup, LOCA::PhaseTransition::ExtendedGroup, and NOX::LAPACK::Group.

References NotDefined.

Referenced by NOX::Epetra::Group::computeNewton(), NOX::Solver::TensorBased::computeTensorDirection(), NOX::Solver::InexactTrustRegionBased::iterateInexact(), and NOX::Solver::SingleStep::try_step().

NOX::Abstract::Group::ReturnType NOX::Abstract::Group::applyJacobianInverseMultiVector	(	Teuchos::ParameterList &	params,
		const NOX::Abstract::MultiVector &	input,
		NOX::Abstract::MultiVector &	result
	)		const

virtual

applyJacobianInverse for multiple right-hand sides

The default implementation here calls applyJacobianInverse() for each right hand side serially but should be overloaded if a block solver is available.

Reimplemented in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, NOX::Thyra::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::Group, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, LOCA::MultiContinuation::ExtendedGroup, and NOX::LAPACK::Group.

References NOX::Abstract::MultiVector::numVectors(), and Ok.

Referenced by LOCA::MultiPredictor::Tangent::compute().

NOX::Abstract::Group::ReturnType NOX::Abstract::Group::applyJacobianMultiVector	(	const NOX::Abstract::MultiVector &	input,
		NOX::Abstract::MultiVector &	result
	)		const

virtual

applyJacobian for multiple right-hand sides

The default implementation here calls applyJacobian() for each right hand side serially but should be overloaded if a block method is available.

Reimplemented in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Homotopy::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, NOX::Thyra::Group, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, and LOCA::MultiContinuation::ExtendedGroup.

References NOX::Abstract::MultiVector::numVectors(), and Ok.

NOX::Abstract::Group::ReturnType NOX::Abstract::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 in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, NOX::Thyra::Group, LOCA::Homotopy::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, LOCA::MultiContinuation::ExtendedGroup, NOX::Epetra::Group, NOX::Petsc::Group, and NOX::LAPACK::Group.

References NotDefined.

Referenced by LOCA::DerivUtils::computeDwtJDp(), LOCA::DerivUtils::computeDwtJnDx(), NOX::Thyra::WeightedMeritFunction::computeGradient(), and NOX::MeritFunction::SumOfSquares::computeGradient().

NOX::Abstract::Group::ReturnType NOX::Abstract::Group::applyJacobianTransposeMultiVector	(	const NOX::Abstract::MultiVector &	input,
		NOX::Abstract::MultiVector &	result
	)		const

virtual

applyJacobianTranspose for multiple right-hand sides

The default implementation here calls applyJacobianTranspose() for each right hand side serially but should be overloaded if a block method is available.

Reimplemented in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, NOX::Thyra::Group, LOCA::Homotopy::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, and LOCA::MultiContinuation::ExtendedGroup.

References NOX::Abstract::MultiVector::numVectors(), and Ok.

Referenced by LOCA::DerivUtils::computeDwtJnDx().

NOX::Abstract::Group::ReturnType NOX::Abstract::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 in NOX::Thyra::Group, and NOX::Epetra::Group.

References NotDefined.

Referenced by NOX::Direction::NonlinearCG::compute().

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

virtual

applyRightPreconditioning for multiple right-hand sides

The default implementation here calls applyRightPreconditioning() for each right hand side serially but should be overloaded if a block method is available.

References NOX::Abstract::MultiVector::numVectors(), and Ok.

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

pure 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.

Implemented in NOX::Thyra::Group, NOX::Epetra::Group, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, NOX::Multiphysics::Group, LOCA::Epetra::Group, LOCA::TurningPoint::MooreSpence::ExtendedGroup, NOX::Petsc::Group, LOCA::Homotopy::Group, NOX::LAPACK::Group, LOCA::PhaseTransition::ExtendedGroup, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, LOCA::MultiContinuation::ArcLengthGroup, LOCA::MultiContinuation::ExtendedGroup, LOCA::LAPACK::Group, LOCA::MultiContinuation::NaturalGroup, LOCA::Thyra::Group, and LOCA::Thyra::GroupWrapper.

Referenced by NOX::Direction::Broyden::compute(), NOX::Thyra::WeightedMeritFunction::computeSlope(), NOX::LineSearch::Utils::Slope::computeSlopeWithOutJac(), NOX::Epetra::MatrixFree::setGroupForComputeF(), and NOX::Epetra::FiniteDifference::setGroupForComputeF().

virtual NOX::Abstract::Group::ReturnType NOX::Abstract::Group::computeF ( )

pure 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

Implemented in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Epetra::Group, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Homotopy::Group, NOX::Thyra::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, NOX::Multiphysics::Group, LOCA::MultiContinuation::ExtendedGroup, LOCA::LAPACK::Group, NOX::Epetra::Group, LOCA::Thyra::Group, LOCA::PhaseTransition::ExtendedGroup, NOX::Petsc::Group, and NOX::LAPACK::Group.

Referenced by NOX::Epetra::MatrixFree::Apply(), NOX::LineSearch::Backtrack::compute(), NOX::Direction::SteepestDescent::compute(), NOX::LineSearch::NonlinearCG::compute(), NOX::Direction::NonlinearCG::compute(), NOX::Direction::Newton::compute(), NOX::Direction::Broyden::compute(), LOCA::DerivUtils::computeDfDp(), NOX::Epetra::MatrixFree::computeJacobian(), NOX::Solver::TensorBased::computeTensorDirection(), NOX::Solver::TensorBased::implementGlobalStrategy(), NOX::Solver::InexactTrustRegionBased::iterateInexact(), NOX::Solver::InexactTrustRegionBased::iterateStandard(), NOX::Solver::TensorBased::performLinesearch(), NOX::Solver::PseudoTransient::step(), NOX::Solver::LineSearchBased::step(), NOX::Multiphysics::Solver::FixedPointBased::step(), NOX::Solver::TrustRegionBased::step(), NOX::Solver::TensorBased::step(), and NOX::LineSearch::Polynomial::updateGrp().

NOX::Abstract::Group::ReturnType NOX::Abstract::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 in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Homotopy::Group, NOX::Thyra::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, LOCA::MultiContinuation::ExtendedGroup, NOX::Epetra::Group, NOX::Petsc::Group, and NOX::LAPACK::Group.

References NotDefined.

NOX::Abstract::Group::ReturnType NOX::Abstract::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 in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Epetra::Group, LOCA::Homotopy::Group, NOX::Thyra::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, LOCA::MultiContinuation::ExtendedGroup, LOCA::LAPACK::Group, NOX::Epetra::Group, LOCA::Thyra::Group, LOCA::PhaseTransition::ExtendedGroup, NOX::Petsc::Group, and NOX::LAPACK::Group.

References NotDefined.

Referenced by LOCA::MultiPredictor::Tangent::compute(), NOX::Direction::SteepestDescent::compute(), NOX::Direction::NonlinearCG::compute(), NOX::Direction::Newton::compute(), NOX::Direction::Broyden::compute(), LOCA::DerivUtils::computeDJnDp(), LOCA::DerivUtils::computeDJnDxa(), LOCA::DerivUtils::computeDwtJDp(), LOCA::DerivUtils::computeDwtJnDp(), LOCA::DerivUtils::computeDwtJnDx(), NOX::Solver::TensorBased::computeTensorDirection(), LOCA::Epetra::AnasaziOperator::Floquet::Floquet(), NOX::Solver::InexactTrustRegionBased::iterateInexact(), and LOCA::AnasaziOperator::JacobianInverse::JacobianInverse().

NOX::Abstract::Group::ReturnType NOX::Abstract::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 in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Homotopy::Group, NOX::Thyra::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, LOCA::MultiContinuation::ExtendedGroup, NOX::Epetra::Group, LOCA::PhaseTransition::ExtendedGroup, NOX::Petsc::Group, and NOX::LAPACK::Group.

References NotDefined.

Referenced by NOX::Direction::Newton::compute(), and NOX::Solver::TensorBased::computeTensorDirection().

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

pure 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

Implemented in LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Homotopy::Group, NOX::Thyra::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, NOX::Multiphysics::Group, LOCA::MultiContinuation::ExtendedGroup, NOX::Epetra::Group, LOCA::PhaseTransition::ExtendedGroup, NOX::Petsc::Group, and NOX::LAPACK::Group.

Referenced by NOX::LineSearch::FullStep::compute(), NOX::LineSearch::SafeguardedDirection::compute(), NOX::LineSearch::SafeguardedStep::compute(), NOX::LineSearch::Backtrack::compute(), NOX::LineSearch::NonlinearCG::compute(), NOX::Solver::TensorBased::implementGlobalStrategy(), NOX::Solver::InexactTrustRegionBased::iterateInexact(), NOX::Solver::InexactTrustRegionBased::iterateStandard(), NOX::Solver::TensorBased::performLinesearch(), NOX::Solver::TrustRegionBased::step(), and NOX::LineSearch::Polynomial::updateGrp().

virtual double NOX::Abstract::Group::getNormF ( ) const

pure virtual

Return 2-norm of F(x).

In other words,

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

Implemented in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, NOX::Thyra::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::Group, NOX::Epetra::Group, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, LOCA::MultiContinuation::ExtendedGroup, NOX::Multiphysics::Group, NOX::Petsc::Group, NOX::LAPACK::Group, and LOCA::PhaseTransition::ExtendedGroup.

Referenced by NOX::StatusTest::FiniteValue::checkStatus(), NOX::StatusTest::Divergence::checkStatus(), NOX::StatusTest::Stagnation::checkStatus(), NOX::Direction::SteepestDescent::compute(), NOX::MeritFunction::SumOfSquares::computef(), NOX::Multiphysics::Group::computeF(), NOX::Direction::Utils::InexactNewton::computeForcingTerm(), NOX::Solver::TensorBased::computeTensorDirection(), NOX::LineSearch::Polynomial::computeValue(), NOX::Solver::TensorBased::implementGlobalStrategy(), NOX::Solver::TensorBased::performLinesearch(), NOX::Solver::TensorBased::printDirectionInfo(), NOX::Direction::Newton::resetForcingTerm(), NOX::Solver::TrustRegionBased::solve(), and NOX::Solver::TrustRegionBased::step().

NOX::Abstract::Group::ReturnType NOX::Abstract::Group::getNormLastLinearSolveResidual ( double & residual ) const

virtual

Return the norm of the last linear solve residual as the result of either a call to computeNewton() or applyJacobianInverse().

Returns

NOX::Abstract::Group::NotDefined - Returned by default implementation in NOX::Abstract::Group
NOX::Abstract::Group::BadDependency - If no linear solve has been calculated
NOX::Abstract::Group::Failed - Any other type of failure
NOX::Abstract::Group::Ok - Otherwise

Reimplemented in NOX::Epetra::Group.

References NotDefined.

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

inlinevirtual

If right scaling vector exist, return a right scaled vector.

Note: Default to getX

Reimplemented in NOX::Thyra::Group.

References getX().

Referenced by NOX::StatusTest::NormWRMS::checkStatus().

bool NOX::Abstract::Group::isGradient ( ) const

virtual

Return true if the gradient is valid.

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

Reimplemented in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, NOX::Thyra::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::Group, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, NOX::Epetra::Group, LOCA::MultiContinuation::ExtendedGroup, NOX::Petsc::Group, and NOX::LAPACK::Group.

Referenced by NOX::LineSearch::Utils::Slope::computeSlope(), and NOX::MeritFunction::SumOfSquares::computeSlope().

bool NOX::Abstract::Group::isJacobian ( ) const

virtual

Return true if the Jacobian is valid.

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

Reimplemented in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, NOX::Thyra::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::Group, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, NOX::Epetra::Group, LOCA::MultiContinuation::ExtendedGroup, NOX::Petsc::Group, NOX::LAPACK::Group, and LOCA::PhaseTransition::ExtendedGroup.

Referenced by NOX::Direction::NonlinearCG::compute(), LOCA::DerivUtils::computeDJnDxa(), NOX::Direction::Utils::InexactNewton::computeForcingTerm(), NOX::Thyra::WeightedMeritFunction::computeGradient(), NOX::MeritFunction::SumOfSquares::computeGradient(), NOX::MeritFunction::SumOfSquares::computeQuadraticMinimizer(), NOX::MeritFunction::SumOfSquares::computeSlope(), NOX::Solver::InexactTrustRegionBased::iterateInexact(), and NOX::Direction::Newton::resetForcingTerm().

bool NOX::Abstract::Group::isNewton ( ) const

virtual

Return true if the Newton direction is valid.

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

Reimplemented in LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, NOX::Thyra::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Homotopy::Group, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, NOX::Epetra::Group, LOCA::MultiContinuation::ExtendedGroup, NOX::Petsc::Group, NOX::LAPACK::Group, and LOCA::PhaseTransition::ExtendedGroup.

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

pure 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.

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

pure 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

Implemented in LOCA::Hopf::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup, LOCA::Pitchfork::MinimallyAugmented::ExtendedGroup, LOCA::TurningPoint::MooreSpence::ExtendedGroup, LOCA::Homotopy::Group, NOX::Thyra::Group, LOCA::Hopf::MooreSpence::ExtendedGroup, LOCA::Pitchfork::MooreSpence::ExtendedGroup, LOCA::Homotopy::DeflatedGroup, LOCA::MultiContinuation::ConstrainedGroup, LOCA::MultiContinuation::ExtendedGroup, NOX::Multiphysics::Group, NOX::Epetra::Group, LOCA::PhaseTransition::ExtendedGroup, NOX::Petsc::Group, and NOX::LAPACK::Group.

Referenced by NOX::Epetra::MatrixFree::Apply(), LOCA::DerivUtils::computeDCeDxa(), LOCA::DerivUtils::computeDJnDxa(), LOCA::DerivUtils::computeDwtCeDx(), LOCA::DerivUtils::computeDwtJnDx(), NOX::Epetra::MatrixFree::computeJacobian(), LOCA::DerivUtils::perturbXVec(), and NOX::Solver::TrustRegionBased::reset().

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

NOX_Abstract_Group.H
NOX_Abstract_Group.C

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