A group representing the minimally augemented Hopf equations. More...

#include <LOCA_Hopf_MinimallyAugmented_ExtendedGroup.H>

Inheritance diagram for LOCA::Hopf::MinimallyAugmented::ExtendedGroup:

Collaboration diagram for LOCA::Hopf::MinimallyAugmented::ExtendedGroup:

Public Member Functions
	ExtendedGroup (const Teuchos::RCP< LOCA::GlobalData > &global_data, const Teuchos::RCP< LOCA::Parameter::SublistParser > &topParams, const Teuchos::RCP< Teuchos::ParameterList > &hpfParams, const Teuchos::RCP< LOCA::Hopf::MinimallyAugmented::AbstractGroup > &grp)
	Constructor. More...

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

virtual	~ExtendedGroup ()
	Destructor.

double	getBifParam () const
	Get bifurcation parameter.

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
	Clone function.

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

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

virtual NOX::Abstract::Group::ReturnType	computeF ()
	Compute extended continuation equations.

virtual NOX::Abstract::Group::ReturnType	computeJacobian ()
	Compute extended continuation jacobian.

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

virtual NOX::Abstract::Group::ReturnType	computeNewton (Teuchos::ParameterList &params)
	Compute Newton direction for extended continuation system.

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

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

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

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.

virtual bool	isF () const
	Return `true` if 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 residual.

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

virtual const NOX::Abstract::Vector &	getGradient () const
	Gradient is never 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 residual.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getGradientPtr () const
	Gradient is never valid.

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

virtual double	getNormNewtonSolveResidual () const
	Returns 2-norm of extended 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.

Implementation of LOCA::MultiContinuation::AbstractGroup
virtual methods
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 (pVector = p).

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

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

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

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

virtual double	getParam (std::string paramID) const
	Return copy of parameter indexed by (std::string) 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 double	computeScaledDotProduct (const NOX::Abstract::Vector &a, const NOX::Abstract::Vector &b) const
	Compute a scaled dot product.

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

virtual void	printSolution (const NOX::Abstract::Vector &x, const double conParam) const
	Function to print out a vector and parameter after successful step.

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

Implementation of
LOCA::BorderedSystem::AbstractGroup virtual methods
virtual int	getBorderedWidth () const
	Return the total width of the bordered rows/columns.

virtual Teuchos::RCP< const NOX::Abstract::Group >	getUnborderedGroup () const
	Get bottom-level unbordered group.

virtual bool	isCombinedAZero () const
	Indicates whether combined A block is zero.

virtual bool	isCombinedBZero () const
	Indicates whether combined B block is zero.

virtual bool	isCombinedCZero () const
	Indicates whether combined C block is zero.

virtual void	extractSolutionComponent (const NOX::Abstract::MultiVector &v, NOX::Abstract::MultiVector &v_x) const

virtual void	extractParameterComponent (bool use_transpose, const NOX::Abstract::MultiVector &v, NOX::Abstract::MultiVector::DenseMatrix &v_p) const

virtual void	loadNestedComponents (const NOX::Abstract::MultiVector &v_x, const NOX::Abstract::MultiVector::DenseMatrix &v_p, NOX::Abstract::MultiVector &v) const

virtual void	fillA (NOX::Abstract::MultiVector &A) const
	Fill the combined A block as described above.

virtual void	fillB (NOX::Abstract::MultiVector &B) const
	Fill the combined B block as described above.

virtual void	fillC (NOX::Abstract::MultiVector::DenseMatrix &C) const
	Fill the combined C block as described above.

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

virtual	~MultiAbstractGroup ()
	Destructor.

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.

Public Member Functions inherited from LOCA::BorderedSystem::AbstractGroup
	AbstractGroup ()
	Constructor.

virtual	~AbstractGroup ()
	Destructor.

Protected Member Functions
virtual void	resetIsValid ()
	Resets all isValid flags to false.

virtual void	setupViews ()
	Sets up multivector views.

void	setBifParam (double param)
	Set bifurcation parameter.

void	getInitialVectors (Teuchos::RCP< NOX::Abstract::Vector > &aVecPtr_real, Teuchos::RCP< NOX::Abstract::Vector > &aVecPtr_imag, Teuchos::RCP< NOX::Abstract::Vector > &bVecPtr_real, Teuchos::RCP< NOX::Abstract::Vector > &bVecPtr_imag, bool isSymmetric)
	Computes initial "a" and "b" vectors.

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

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

Teuchos::RCP < Teuchos::ParameterList >	hopfParams
	Hopf parameter list.

Teuchos::RCP < LOCA::Hopf::MinimallyAugmented::AbstractGroup >	grpPtr
	Pointer to base group that defines .

Teuchos::RCP < LOCA::BorderedSystem::AbstractGroup >	bordered_grp
	Pointer to base group as a bordered group.

Teuchos::RCP < LOCA::Hopf::MinimallyAugmented::Constraint >	constraintsPtr
	Pointer to constraint object.

LOCA::MultiContinuation::ExtendedMultiVector	xMultiVec
	Stores the extended solution vector.

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

LOCA::MultiContinuation::ExtendedMultiVector	newtonMultiVec
	Stores the extended Newton vector.

LOCA::MultiContinuation::ExtendedMultiVector	gradientMultiVec
	Stores the extended gradient vector.

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

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

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

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

Teuchos::RCP < LOCA::MultiContinuation::ExtendedMultiVector >	fBifMultiVec
	Stores view of f and first column of df/dp.

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

Teuchos::RCP < LOCA::MultiContinuation::ExtendedVector >	gradientVec
	Stores view of first column of gradientMultiVec.

Teuchos::RCP < LOCA::BorderedSolver::JacobianOperator >	jacOp

Teuchos::RCP < LOCA::BorderedSolver::AbstractStrategy >	borderedSolver
	Stores bordered solver 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.

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.

bool	isValidGradient
	Is Gradient vector valid.

bool	isBordered
	Flag that indicates whether underlying group is a bordered 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 minimally augemented Hopf equations.

The LOCA::Hopf::MinimallyAugmented::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 Hopf:

$G(z) = \left[ \begin{array}{c} F(x,p)\\ \sigma \end{array} \right] = 0$

where $z = [x, p, \omega]\in\Re^{n+2}$ , $ x$ is the solution vector, $ p$ is the bifurcation parameter, $\omega$ is the Hopf frequency and $\sigma\in\Re$ is a measure of the singularity of $J+i\omega M$ and is defined via

$\begin{bmatrix} J+i\omega M & a \\ b^H & 0 \end{bmatrix} \begin{bmatrix} v \\ \sigma_1 \end{bmatrix} = \begin{bmatrix} 0 \\ n \end{bmatrix},$

$\begin{bmatrix} J^T-i\omega M^T & b \\ a^H & 0 \end{bmatrix} \begin{bmatrix} w \\ \sigma_2 \end{bmatrix} = \begin{bmatrix} 0 \\ n \end{bmatrix},$

$\sigma = w^H J+i\omega M v/n$

for any vectors $ a$ and $ b$ in $\mathbb{C}^n$ . Using these relationships, it is easy to show

$\begin{split} \sigma_x &= (w^H(J+i\omega M)v)_x/n = w^H(J+i\omega M)_x v/n \\ \sigma_p &= (w^H(J+i\omega M)v)_p/n = w^H(J+i\omega M)_p v/n \end{split}$

The group stores an underlying group of type LOCA::Hopf::MinimallyAugmented::AbstractGroup to represent the equations $ F(x,p) = 0$ and to manipulate the underlying complex matrix $C = J+i\omega M$ . This interface defines methods for computing the derivatives $(w^H C v)_x$ and $(w^H C v)_p$ . Since LOCA is not able to deal with complex vectors and matrices directly, the real-equivalent formulation is used for all complex calculations.

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 or to the LOCA::Stepper to compute a family of pitchforks in a second parameter.

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

"Bifurcation Parameter" – [string] (Must be supplied) - Name of the bifurcation parameter
"Initial Frequency" – [double] (Must be supplied) Initial guess for the Hopf frequency $\omega$ .
"Bordered Solver Method" – [string] (default "Bordering") Method for solving bordered systems of equations. See LOCA::BorderedSolver::Factory for a description.
"Symmetric Jacobian" – [bool] (default: false) - Flag indicating whether Jacobian matrix is symmetric, in which case we force and therefore the second tranpose solve for is unnecessary
"Initial Null Vector Compuation" – [string] (default: "User Provided") - Method to compute initial and vectors. Valid choices are:
- "User Provided" - Initial vectors are provided in the parameter list, in which case the following parameters are relevant:
  - "Initial Real A Vector" – [Teuchos::RCP<NOX::Abstract::Vector>] (Must be supplied) - Vector storing initial value for the real component of the vector
  - "Initial Imaginary A Vector" – [Teuchos::RCP<NOX::Abstract::Vector>] (Must be supplied) - Vector storing initial value for the imaginary component of the vector
  - "Initial Real B Vector" – [Teuchos::RCP<NOX::Abstract::Vector>] (Must be supplied for nonsymmetric Jacobians) - Vector storing initial value for the real component of the vector
  - "Initial Imaginary B Vector" – [Teuchos::RCP<NOX::Abstract::Vector>] (Must be supplied) - Vector storing initial value for the imaginary component of the vector
- "Solve df/dp" - Compute $a = J^{-T}df/dp$ and $b = J^{-1} df/dp$ where is the bifurcation parameter.
"Update Null Vectors Every Continuation Step" – [bool] (default: true) - Flag indicating whether to update and vectors via and every continuation step
"Update Null Vectors Every Nonlinear Iteration" – [bool] (default: false) - Flag indicating whether to update and vectors via and every nonlinear iteration

Constructor & Destructor Documentation

LOCA::Hopf::MinimallyAugmented::ExtendedGroup::ExtendedGroup	(	const Teuchos::RCP< LOCA::GlobalData > &	global_data,
		const Teuchos::RCP< LOCA::Parameter::SublistParser > &	topParams,
		const Teuchos::RCP< Teuchos::ParameterList > &	hpfParams,
		const Teuchos::RCP< LOCA::Hopf::MinimallyAugmented::AbstractGroup > &	grp
	)

Constructor.

Parameters

global_data	[in] Global data object
topParams	[in] Parsed top-level parameter list.
hpfParams	[in] Parameter list determining the bordered solver method.
grp	[in] Group representing .

References bifParamID, bordered_grp, borderedSolver, constraintsPtr, Teuchos::ParameterList::get(), Teuchos::RCP< T >::get(), LOCA::ParameterVector::getIndex(), getInitialVectors(), LOCA::Extended::Vector::getScalar(), LOCA::MultiContinuation::ExtendedVector::getXVec(), globalData, grpPtr, hopfParams, isBordered, Teuchos::ParameterList::isParameter(), LOCA::GlobalData::locaErrorCheck, LOCA::GlobalData::locaFactory, parsedParams, Teuchos::rcp(), setupViews(), and xVec.

Member Function Documentation

NOX::Abstract::Group::ReturnType LOCA::Hopf::MinimallyAugmented::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::Extended::MultiVector::getScalars(), LOCA::MultiContinuation::ExtendedMultiVector::getXMultiVec(), and NOX::Abstract::Group::Ok.

void LOCA::Hopf::MinimallyAugmented::ExtendedGroup::extractParameterComponent	(	bool	use_transpose,
		const NOX::Abstract::MultiVector &	v,
		NOX::Abstract::MultiVector::DenseMatrix &	v_p
	)		const

virtual

Given the vector v, extract the parameter components of all of the nested subvectors in v down to the solution component for the unbordered group.

Implements LOCA::BorderedSystem::AbstractGroup.

References Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::assign(), LOCA::Extended::MultiVector::getScalars(), LOCA::MultiContinuation::ExtendedMultiVector::getXMultiVec(), Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::numCols(), Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::numRows(), and Teuchos::View.

void LOCA::Hopf::MinimallyAugmented::ExtendedGroup::extractSolutionComponent	(	const NOX::Abstract::MultiVector &	v,
		NOX::Abstract::MultiVector &	v_x
	)		const

virtual

Given the vector v, extract the underlying solution component corresponding to the unbordered group.

Implements LOCA::BorderedSystem::AbstractGroup.

References LOCA::MultiContinuation::ExtendedMultiVector::getXMultiVec().

void LOCA::Hopf::MinimallyAugmented::ExtendedGroup::loadNestedComponents	(	const NOX::Abstract::MultiVector &	v_x,
		const NOX::Abstract::MultiVector::DenseMatrix &	v_p,
		NOX::Abstract::MultiVector &	v
	)		const