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LOCA::Pitchfork::MooreSpence::ExtendedGroup Class Reference

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

#include <LOCA_Pitchfork_MooreSpence_ExtendedGroup.H>

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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 > &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::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 pitchfork 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
 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.
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 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

Teuchos::RCP< LOCA::GlobalDataglobalData
 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 $F$.
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.
vector< int > index_f
 Stores indices for getting f part of fMultiVec.
vector< int > index_dfdp
 Stores indices for getting df/dp part of fMultiVec.
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 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 (string 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.
double getBifParam () const
 Get bifurcation parameter.
double lTransNorm (const NOX::Abstract::Vector &n) const
 Defines null vector normalization $l^Tn$ equation.
void lTransNorm (const NOX::Abstract::MultiVector &n, NOX::Abstract::MultiVector::DenseMatrix &result) const
 null vector normalization for multivectors
void setBifParam (double param)
 Set bifurcation parameter.
void setupViews ()
 Sets up multivector views.
void init (bool perturbSoln=false, double perturbSize=0.0)
 Initializes group.

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:


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 vector< int > &  paramIDs,
NOX::Abstract::MultiVector dfdp,
bool  isValidF 
) [virtual]
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 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.

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.


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