A group representing the Moore-Spence pitchfork equations. More...

#include <LOCA_Pitchfork_MooreSpence_ExtendedGroup.H>

Inheritance diagram for LOCA::Pitchfork::MooreSpence::ExtendedGroup:

Collaboration diagram for LOCA::Pitchfork::MooreSpence::ExtendedGroup:

Public Member Functions
	ExtendedGroup (const Teuchos::RCP< LOCA::GlobalData > &global_data, const Teuchos::RCP< LOCA::Parameter::SublistParser > &topParams, const Teuchos::RCP< Teuchos::ParameterList > &pfParams, const Teuchos::RCP< LOCA::Pitchfork::MooreSpence::AbstractGroup > &g)
	Constructor with initial data passed through parameter lists.

	ExtendedGroup (const ExtendedGroup &source, NOX::CopyType type=NOX::DeepCopy)
	Copy constructor.

virtual	~ExtendedGroup ()
	Destructor.

Implementation of NOX::Abstract::Group virtual methods
virtual NOX::Abstract::Group &	operator= (const NOX::Abstract::Group &source)
	Assignment operator.

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

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

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

virtual NOX::Abstract::Group::ReturnType	computeF ()
	Compute the pitchfork equation residual . More...

virtual NOX::Abstract::Group::ReturnType	computeJacobian ()
	Compute the blocks of the Jacobian derivative of . More...

virtual NOX::Abstract::Group::ReturnType	computeGradient ()
	Gradient computation is not defined for this group.

virtual NOX::Abstract::Group::ReturnType	computeNewton (Teuchos::ParameterList &params)
	Compute Newton direction using applyJacobianInverse().

virtual NOX::Abstract::Group::ReturnType	applyJacobian (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Computes the extended Jacobian vector product. More...

virtual NOX::Abstract::Group::ReturnType	applyJacobianTranspose (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Jacobian transpose product is not defined by this group.

virtual NOX::Abstract::Group::ReturnType	applyJacobianInverse (Teuchos::ParameterList &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Applies the inverse of the extended Jacobian matrix using the bordering algorithm. More...

virtual NOX::Abstract::Group::ReturnType	applyJacobianMultiVector (const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	Applies Jacobian for extended system.

virtual NOX::Abstract::Group::ReturnType	applyJacobianTransposeMultiVector (const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	Jacobian transpose not defined for this system.

virtual NOX::Abstract::Group::ReturnType	applyJacobianInverseMultiVector (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	Applies Jacobian inverse for extended system. More...

virtual bool	isF () const
	Return `true` if the extended residual is valid.

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

virtual bool	isGradient () const
	Always returns false.

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

virtual const NOX::Abstract::Vector &	getX () const
	Return extended solution vector .

virtual const NOX::Abstract::Vector &	getF () const
	Return extended equation residual .

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

virtual const NOX::Abstract::Vector &	getGradient () const
	Vector returned is not valid.

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

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

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getFPtr () const
	Return RCP to extended equation residual .

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getGradientPtr () const
	Vector returned is not valid.

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

virtual double	getNormNewtonSolveResidual () const
	Return the norm of the Newton solve residual.

Implementation of LOCA::Extended::MultiAbstractGroup
virtual methods
virtual Teuchos::RCP< const LOCA::MultiContinuation::AbstractGroup >	getUnderlyingGroup () const
	Return underlying group.

virtual Teuchos::RCP < LOCA::MultiContinuation::AbstractGroup >	getUnderlyingGroup ()
	Return underlying group.

Public Member Functions inherited from LOCA::Extended::MultiAbstractGroup
	MultiAbstractGroup ()
	Default constructor.

virtual	~MultiAbstractGroup ()
	Destructor.

virtual Teuchos::RCP < NOX::Abstract::Group >	getNestedGroup ()
	Override from NOX::Abstract::Group base class. Calls getUnderlyingGroup() from this class.

virtual Teuchos::RCP< const NOX::Abstract::Group >	getNestedGroup () const
	Override from NOX::Abstract::Group base class. Calls getUnderlyingGroup() from this class.

virtual Teuchos::RCP< const LOCA::MultiContinuation::AbstractGroup >	getBaseLevelUnderlyingGroup () const
	Return base-level underlying group. More...

virtual Teuchos::RCP < LOCA::MultiContinuation::AbstractGroup >	getBaseLevelUnderlyingGroup ()
	Return base-level underlying group. More...

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

virtual	~Group ()
	Destructor.

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...

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

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...

Public Member Functions inherited from LOCA::MultiContinuation::AbstractGroup
	AbstractGroup ()
	Default constructor.

virtual	~AbstractGroup ()
	Destructor.

virtual double	computeScaledDotProduct (const NOX::Abstract::Vector &a, const NOX::Abstract::Vector &b) const
	Compute a scaled dot product. More...

virtual void	scaleVector (NOX::Abstract::Vector &x) const
	Scales a vector using scaling vector. More...

Implementation of LOCA::MultiContinuation::AbstractGroup
virtual methods
Teuchos::RCP< LOCA::GlobalData >	globalData
	Pointer LOCA global data object.

Teuchos::RCP < LOCA::Parameter::SublistParser >	parsedParams
	Parsed top-level parameters.

Teuchos::RCP < Teuchos::ParameterList >	pitchforkParams
	Bifurcation parameter list.

Teuchos::RCP < LOCA::Pitchfork::MooreSpence::AbstractGroup >	grpPtr
	Pointer to base group that defines .

LOCA::Pitchfork::MooreSpence::ExtendedMultiVector	xMultiVec
	Stores the extended solution vector and J^-1 df/dp.

LOCA::Pitchfork::MooreSpence::ExtendedMultiVector	fMultiVec
	Stores the extended residual vector and df/dp.

LOCA::Pitchfork::MooreSpence::ExtendedMultiVector	newtonMultiVec
	Stores the extended Newton vector.

Teuchos::RCP < NOX::Abstract::MultiVector >	asymMultiVec
	Stores the asymmetric vector.

Teuchos::RCP < NOX::Abstract::MultiVector >	lengthMultiVec
	Stores the length normalization vector.

Teuchos::RCP < LOCA::Pitchfork::MooreSpence::ExtendedVector >	xVec
	Stores view of first column of xMultiVec.

Teuchos::RCP < LOCA::Pitchfork::MooreSpence::ExtendedVector >	fVec
	Stores view of first column of fMultiVec.

Teuchos::RCP < LOCA::Pitchfork::MooreSpence::ExtendedMultiVector >	ffMultiVec
	Stores view of first column of fMultiVec as a multivec.

Teuchos::RCP < LOCA::Pitchfork::MooreSpence::ExtendedMultiVector >	dfdpMultiVec
	Stores view of df/dp columns of fMultiVec.

Teuchos::RCP < LOCA::Pitchfork::MooreSpence::ExtendedVector >	newtonVec
	Stores view of first column of newtonMultiVec.

Teuchos::RCP < NOX::Abstract::Vector >	asymVec
	Stores view of first column of asymMultiVec.

Teuchos::RCP < NOX::Abstract::Vector >	lengthVec
	Stores view of first column of lengthMultiVec.

Teuchos::RCP < LOCA::Pitchfork::MooreSpence::SolverStrategy >	solverStrategy
	Stores bordering strategy.

std::vector< int >	index_f
	Stores indices for getting f part of fMultiVec.

std::vector< int >	index_dfdp
	Stores indices for getting df/dp part of fMultiVec.

std::vector< int >	bifParamID
	Stores the bifurcation parameter index.

bool	isValidF
	Is residual vector valid.

bool	isValidJacobian
	Is Jacobian matrix valid.

bool	isValidNewton
	Is Newton vector valid.

virtual void	copy (const NOX::Abstract::Group &source)
	Assignment operator.

virtual void	setParamsMulti (const std::vector< int > &paramIDs, const NOX::Abstract::MultiVector::DenseMatrix &vals)
	Set parameters indexed by (integer) paramIDs.

virtual void	setParams (const ParameterVector &p)
	Set the parameter vector in the group to p.

virtual void	setParam (int paramID, double val)
	Set parameter indexed by paramID.

virtual void	setParam (std::string paramID, double val)
	Set parameter indexed by paramID.

virtual const ParameterVector &	getParams () const
	Return a const reference to the paramter vector owned by the group.

virtual double	getParam (int paramID) const
	Return copy of parameter indexed by paramID.

virtual double	getParam (std::string paramID) const
	Return copy of parameter indexed by paramID.

virtual NOX::Abstract::Group::ReturnType	computeDfDpMulti (const std::vector< int > &paramIDs, NOX::Abstract::MultiVector &dfdp, bool isValidF)

virtual void	preProcessContinuationStep (LOCA::Abstract::Iterator::StepStatus stepStatus)
	Perform any preprocessing before a continuation step starts. More...

virtual void	postProcessContinuationStep (LOCA::Abstract::Iterator::StepStatus stepStatus)
	Perform any postprocessing after a continuation step finishes. More...

virtual void	projectToDraw (const NOX::Abstract::Vector &x, double *px) const
	Projects solution to a few scalars for multiparameter continuation.

virtual int	projectToDrawDimension () const
	Returns the dimension of the project to draw array.

virtual void	printSolution (const double conParam) const
	Function to print out extended solution and continuation parameter after successful continuation step. More...

virtual void	printSolution (const NOX::Abstract::Vector &x_, const double conParam) const
	Function to print out extended solution and continuation parameter after successful continuation step. More...

double	getBifParam () const
	Get bifurcation parameter.

double	lTransNorm (const NOX::Abstract::Vector &n) const
	Defines null vector normalization equation.

void	lTransNorm (const NOX::Abstract::MultiVector &n, NOX::Abstract::MultiVector::DenseMatrix &result) const
	null vector normalization for multivectors More...

void	setBifParam (double param)
	Set bifurcation parameter.

void	setupViews ()
	Sets up multivector views.

void	init (bool perturbSoln=false, double perturbSize=0.0)
	Initializes group.

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

A group representing the Moore-Spence pitchfork equations.

The LOCA::Pitchfork::MooreSpence::ExtendedGroup is a concrete implementation of the NOX::Abstract::Group, LOCA::MultiContinuation::AbstractGroup and LOCA::Extended::MultiAbstractGroup that defines the following extended set of equations that are regular at a generic pitchfork bifurcation:

$G(z) = \left[ \begin{array}{c} F(x,p)+\sigma\psi \\ Jn \\ \langle x, \psi\rangle \\ l^Tn-1 \end{array} \right] = 0$

where $z = [x, n, \sigma, p]\in\Re^{2n+2}$ , $x$ is the solution vector, $n$ is the null vector, $\psi$ is the antisymmetric vector, $\sigma$ is the slack variables representing the asymmetry in the problem, $l$ is the length normalization vector and $J$ is the Jacobian of F.

The group stores an underlying group of type LOCA::Pitchfork::MooreSpence AbstractGroup to represent the equations $F(x,p) = 0$ and to manipulate the underlying Jacobian $J$ . Note that the entire extended Jacobian $D_z G$ is not stored in memory, rather a block-elimination algorithm (bordering algorithm) is used to compute linear solves of the extended Jacobian (see LOCA::Pitchfork::MooreSpence::SolverFactory for more details).

This class implements all of the NOX::Abstract::Group, LOCA::MultiContinuation::AbstractGroup, and LOCA::Extended::MultiAbstractGroup methods for this extended set of equations and therefore is a complete group which can be passed to most NOX solvers to locate a single pitchfork point or to the LOCA::Stepper to compute a family of pitchforks in a second parameter.

However, Jacobian-tranpose operations and gradient calculations cannot be implemented efficiently and therefore gradient-base nonlinear solvers such as steepest descent and Trust region methods cannot be used to solve the extended pitchfork equations.

The class is intialized via the pfParams parameter list argument to the constructor. The parameters this class recognizes are:

"Bifurcation Parameter" – [string] (Must be supplied) Name of the bifurcation parameter
"Length Normalization Vector" – [Teuchos::RCP<NOX::Abstract::Vector>] (Must be supplied) Vector storing length normalization vector
"Initial Null Vector" – [Teuchos::RCP<NOX::Abstract::Vector>] (Must be supplied) Vector storing initial guess for the null vector
"Antisymmetric Vector" – [Teuchos::RCP<NOX::Abstract::Vector>] (Must be supplied) Vector storing antisymmetric vector $\psi$
"Perturb Initial Solution" – [bool] (default: false) Flag indicating whether to perturb the initial solution
"Relative Perturbation Size" – double Relative perturbation size if perturbing the initial solution

Member Function Documentation

NOX::Abstract::Group::ReturnType LOCA::Pitchfork::MooreSpence::ExtendedGroup::applyJacobian	(	const NOX::Abstract::Vector &	input,
		NOX::Abstract::Vector &	result
	)		const

virtual

Computes the extended Jacobian vector product.

This method computes the extended Jacobian vector product

$\begin{bmatrix} J & 0 & \psi & \frac{\partial F}{\partial p} \\ \frac{\partial Jn}{\partial x} & J & 0 & \frac{\partial Jn}{\partial p} \\ \psi^T & 0 & 0 & 0 \\ 0 & l^T & 0 & 0 \end{bmatrix} \begin{bmatrix} a \\ b \\ c \\ d \end{bmatrix} = \begin{bmatrix} Ja + \psi c + \frac{\partial F}{\partial p}d \\ \frac{\partial Jn}{\partial x}a + Jb + \frac{\partial Jn}{\partial p}d \\ \langle a, \psi\rangle \\ l^T b \end{bmatrix}$

using the applyJacobian, computeDJnDxa, and innerProdut methods of the underlying group where $a$ , $b$ , $c$ , $d$ are the solution, null-vector, slack, and paramter components of the given vector input. Vectors input and result must be of type LOCA::Pitchfork::MooreSpence::ExtendedVector, otherwise an error is thrown.

Reimplemented from NOX::Abstract::Group.

References NOX::Abstract::Vector::createMultiVector(), and NOX::DeepCopy.

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

virtual

Applies the inverse of the extended Jacobian matrix using the bordering algorithm.

This method is a special case of applyJacobianInverseMultiVector() for a single right-hand-side.

Reimplemented from NOX::Abstract::Group.

References NOX::Abstract::Vector::createMultiVector(), and NOX::DeepCopy.

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

virtual

Applies Jacobian inverse for extended system.

Uses a LOCA::Pitchfork::MooreSpence::SolverStrategy instantiated by the LOCA::Pitchfork::MooreSpence::SolverFactory to implement the solve.

Reimplemented from NOX::Abstract::Group.

NOX::Abstract::Group::ReturnType LOCA::Pitchfork::MooreSpence::ExtendedGroup::computeDfDpMulti	(	const std::vector< int > &	paramIDs,
		NOX::Abstract::MultiVector &	dfdp,
		bool	isValidF
	)

virtual

Compute $\partial F/\partial p$ for each parameter $p$ indexed by paramIDs. The first column of dfdp holds F, which is valid if isValidF is true. Otherwise F must be computed.

Implements LOCA::MultiContinuation::AbstractGroup.

References LOCA::Pitchfork::MooreSpence::ExtendedMultiVector::getColumn(), LOCA::Pitchfork::MooreSpence::ExtendedMultiVector::getNullMultiVec(), LOCA::Extended::MultiVector::getScalar(), LOCA::Pitchfork::MooreSpence::ExtendedMultiVector::getXMultiVec(), NOX::Abstract::MultiVector::numVectors(), and NOX::Abstract::Group::Ok.

NOX::Abstract::Group::ReturnType LOCA::Pitchfork::MooreSpence::ExtendedGroup::computeF ( )

virtual

Compute the pitchfork equation residual $G$ .

This method fills the extended residual

$G(z) = \left[ \begin{array}{c} F(x,p)+\sigma\psi \\ Jn \\ \langle x, \psi\rangle \\ l^Tn-1 \end{array} \right] = 0$

The solution component residual $F(x,p)$ and the null-vector residual $Jn$ are calculated via the computeF and applyJacobian methods of the underlying group. The symmetry residual, $\langle x, \psi\rangle$ is computed via the innerProduct() method of the underlying group.

Implements NOX::Abstract::Group.

References NOX::Abstract::Group::Ok.

NOX::Abstract::Group::ReturnType LOCA::Pitchfork::MooreSpence::ExtendedGroup::computeJacobian ( )

virtual

Compute the blocks of the Jacobian derivative of $G$ .

This method computes the $J$ , $\partial F/\partial p$ , and $\partial Jn/\partial p$ blocks of the extended Jacobian:

$D_z G(z) = \begin{bmatrix} J & 0 & \psi & \frac{\partial F}{\partial p} \\ \frac{\partial Jn}{\partial x} & J & 0 & \frac{\partial Jn}{\partial p} \\ \psi^T & 0 & 0 & 0 \\ 0 & l^T & 0 & 0 \end{bmatrix}$

by calling the computeJacobian, computeDfDp, and computeDJnDp methods of the underlying group. The second derivative matrix $\partial Jn/\partial x$ is not calculated since only its action on vectors is needed for linear solves using the bordering algorithms.

Reimplemented from NOX::Abstract::Group.

References NOX::Abstract::Group::Ok, and Teuchos::rcp().

void LOCA::Pitchfork::MooreSpence::ExtendedGroup::lTransNorm	(	const NOX::Abstract::MultiVector &	n,
		NOX::Abstract::MultiVector::DenseMatrix &	result
	)		const

null vector normalization for multivectors

Note: result should have 1 row and n.numVectors() columns.

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

void LOCA::Pitchfork::MooreSpence::ExtendedGroup::postProcessContinuationStep ( LOCA::Abstract::Iterator::StepStatus stepStatus )

virtual

Perform any postprocessing after a continuation step finishes.

The stepStatus argument indicates whether the step was successful.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

void LOCA::Pitchfork::MooreSpence::ExtendedGroup::preProcessContinuationStep ( LOCA::Abstract::Iterator::StepStatus stepStatus )

virtual

Perform any preprocessing before a continuation step starts.

The stepStatus argument indicates whether the previous step was successful.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

void LOCA::Pitchfork::MooreSpence::ExtendedGroup::printSolution ( const double conParam ) const

virtual

Function to print out extended solution and continuation parameter after successful continuation step.

This method prints the solution, null-vector, and parameter components of the extended solution vector using the printSolution method of the underlying group.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

References NOX::Utils::StepperDetails.

void LOCA::Pitchfork::MooreSpence::ExtendedGroup::printSolution	(	const NOX::Abstract::Vector &	x_,
		const double	conParam
	)		const

virtual

Function to print out extended solution and continuation parameter after successful continuation step.

This method prints the solution, null-vector, and parameter components of the extended solution vector using the printSolution method of the underlying group.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

References LOCA::Pitchfork::MooreSpence::ExtendedVector::getBifParam(), LOCA::Pitchfork::MooreSpence::ExtendedVector::getNullVec(), LOCA::Pitchfork::MooreSpence::ExtendedVector::getSlack(), LOCA::Pitchfork::MooreSpence::ExtendedVector::getXVec(), and NOX::Utils::StepperDetails.

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

LOCA_Pitchfork_MooreSpence_ExtendedGroup.H
LOCA_Pitchfork_MooreSpence_ExtendedGroup.C

Public Member Functions

Implementation of LOCA::MultiContinuation::AbstractGroup

Additional Inherited Members

Detailed Description

Member Function Documentation