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LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup Class Reference

A group representing the minimally augemented turning point equations. More...

#include <LOCA_TurningPoint_MinimallyAugmented_ExtendedGroup.H>

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Public Member Functions

 ExtendedGroup (const Teuchos::RCP< LOCA::GlobalData > &global_data, const Teuchos::RCP< LOCA::Parameter::SublistParser > &topParams, const Teuchos::RCP< Teuchos::ParameterList > &tpParams, const Teuchos::RCP< LOCA::TurningPoint::MinimallyAugmented::AbstractGroup > &g)
 Constructor with initial data passed through parameter lists.
 
 ExtendedGroup (const ExtendedGroup &source, NOX::CopyType type=NOX::DeepCopy)
 Copy constructor.
 
virtual ~ExtendedGroup ()
 Destructor.
 
double getBifParam () const
 Get bifurcation parameter.
 
Teuchos::RCP< const
NOX::Abstract::Vector
getLeftNullVec () const
 Returns left null vector.
 
Teuchos::RCP< const
NOX::Abstract::Vector
getRightNullVec () const
 Returns right null vector v.
 
Teuchos::RCP< const
NOX::Abstract::Vector
getAVec () const
 Returns "A" vector.
 
Teuchos::RCP< const
NOX::Abstract::Vector
getBVec () const
 Returns "B".
 
Implementation of NOX::Abstract::Group virtual methods
virtual NOX::Abstract::Groupoperator= (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 turning point equation residual $G$. More...
 
virtual
NOX::Abstract::Group::ReturnType 
computeJacobian ()
 Compute the blocks of the Jacobian derivative of $G$. 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.
 
virtual
NOX::Abstract::Group::ReturnType 
applyJacobianTranspose (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
 Computes the extended Jacobian transpose vector product.
 
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.
 
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 for extended 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 the extended residual $G$ 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 $z$.
 
virtual const
NOX::Abstract::Vector
getF () const
 Return extended equation residual $G(z)$.
 
virtual double getNormF () const
 Return 2-norm of $G(z)$.
 
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 $z$.
 
virtual Teuchos::RCP< const
NOX::Abstract::Vector
getFPtr () const
 Return RCP to extended equation residual $G(z)$.
 
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.
 
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.
 
virtual void setParam (std::string paramID, double val)
 Set parameter indexed by paramID.
 
virtual void setParam (int paramID, double val)
 Set parameter indexed by paramID.
 
virtual const ParameterVectorgetParams () 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...
 
Implementation of
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.
 
Implementation of LOCA::Abstract::TransposeSolveGroup

virtual methods

virtual
NOX::Abstract::Group::ReturnType 
applyJacobianTransposeInverse (Teuchos::ParameterList &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
 Solve Jacobian-tranpose system.
 
virtual
NOX::Abstract::Group::ReturnType 
applyJacobianTransposeInverseMultiVector (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
 Solve Jacobian-tranpose system with multiple right-hand sides.
 
- 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.
 
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...
 
- Public Member Functions inherited from LOCA::BorderedSystem::AbstractGroup
 AbstractGroup ()
 Constructor.
 
virtual ~AbstractGroup ()
 Destructor.
 
- Public Member Functions inherited from LOCA::Abstract::TransposeSolveGroup
 TransposeSolveGroup ()
 Constructor.
 
virtual ~TransposeSolveGroup ()
 Destructor.
 

Protected Member Functions

void setBifParam (double param)
 Set bifurcation parameter.
 

Protected Attributes

Teuchos::RCP< LOCA::GlobalDataglobalData
 Pointer LOCA global data object.
 
Teuchos::RCP
< LOCA::Parameter::SublistParser
parsedParams
 Parsed top-level parameters.
 
Teuchos::RCP
< Teuchos::ParameterList
turningPointParams
 Bifurcation parameter list.
 
Teuchos::RCP
< LOCA::TurningPoint::MinimallyAugmented::AbstractGroup
grpPtr
 Pointer to base group that defines $F$.
 
Teuchos::RCP
< LOCA::TurningPoint::MinimallyAugmented::Constraint
constraint
 Pointer to the constraint equation.
 
Teuchos::RCP
< LOCA::MultiContinuation::ConstrainedGroup
conGroup
 Pointer to constrained group implementation.
 
int bifParamID
 Stores the bifurcation parameter index.
 

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 turning point equations.

The LOCA::TurningPoint::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 turning point:

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

where $z = [x, p]\in\Re^{n+1}$, $x$ is the solution vector, $p$ is the bifurcation parameter, $J$ is the Jacobian of $F$, and $\sigma\in\Re$ is a measure of the singularity of $F$ and is defined via

\[ \begin{bmatrix} J & a \\ b^T & 0 \end{bmatrix} \begin{bmatrix} v \\ \sigma_1 \end{bmatrix} = \begin{bmatrix} 0 \\ n \end{bmatrix}, \]

\[ \begin{bmatrix} J^T & b \\ a^T & 0 \end{bmatrix} \begin{bmatrix} w \\ \sigma_2 \end{bmatrix} = \begin{bmatrix} 0 \\ n \end{bmatrix}, \]

\[ \sigma = w^T J v/n \]

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

\[ \begin{split} \sigma_x &= (w^T J v)_x/n = w^T J_x v/n \\ \sigma_p &= (w^T J v)_p/n = w^T J_p v/n \end{split} \]

The group stores an underlying group of type LOCA::TurningPoint::MinimallyAugmented::AbstractGroup to represent the equations $F(x,p) = 0$ and to manipulate the underlying Jacobian $J$. This interface defines methods for computing the derivatives $(w^T J v)_x$ and $(w^T J v)_p$ as well.

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 turning point or to the LOCA::Stepper to compute a family of turning points in a second parameter.

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

Member Function Documentation

NOX::Abstract::Group::ReturnType LOCA::TurningPoint::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.

NOX::Abstract::Group::ReturnType LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup::computeF ( )
virtual

Compute the turning point equation residual $G$.

This method fills the extended residual

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

Implements NOX::Abstract::Group.

NOX::Abstract::Group::ReturnType LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup::computeJacobian ( )
virtual

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

This method computes the $J$, $F_p$, $\sigma_x$ and $\sigma_p$ blocks of the extended Jacobian:

\[ D_z G(z) = \begin{bmatrix} J & F_p \\ \sigma_x & \sigma_p \end{bmatrix} \]

Reimplemented from NOX::Abstract::Group.

void LOCA::TurningPoint::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.

void LOCA::TurningPoint::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.

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

Given the solution component v_x and combined parameter components v_p, distribute these components through the nested sub-vectors in v.

Implements LOCA::BorderedSystem::AbstractGroup.

void LOCA::TurningPoint::MinimallyAugmented::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::TurningPoint::MinimallyAugmented::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::TurningPoint::MinimallyAugmented::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::TurningPoint::MinimallyAugmented::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::Extended::Vector::getScalar(), LOCA::MultiContinuation::ExtendedVector::getXVec(), and NOX::Utils::StepperDetails.


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