NOX Development
Public Member Functions | Protected Member Functions | Protected Attributes
LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup Class Reference

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

#include <LOCA_TurningPoint_MinimallyAugmented_ExtendedGroup.H>

Inheritance diagram for LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup:
Inheritance graph
[legend]
Collaboration diagram for LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup:
Collaboration graph
[legend]

List of all members.

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 $G$.
virtual
NOX::Abstract::Group::ReturnType 
computeJacobian ()
 Compute the blocks of the Jacobian derivative of $G$.
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 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 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 (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 (string paramID) const
 Return copy of parameter indexed by paramID.
virtual
NOX::Abstract::Group::ReturnType 
computeDfDpMulti (const 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.
virtual void postProcessContinuationStep (LOCA::Abstract::Iterator::StepStatus stepStatus)
 Perform any postprocessing after a continuation step finishes.
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.
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.
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.

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.

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 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:
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends