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LOCA::Homotopy::DeflatedGroup Class Reference

LOCA's Homotopy Algorithm. More...

#include <LOCA_Homotopy_DeflatedGroup.H>

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List of all members.

Public Member Functions

 DeflatedGroup (const Teuchos::RCP< LOCA::GlobalData > &global_data, const Teuchos::RCP< Teuchos::ParameterList > &topParams, const Teuchos::RCP< Teuchos::ParameterList > &hParams, const Teuchos::RCP< LOCA::Homotopy::AbstractGroup > &grp, const Teuchos::RCP< const NOX::Abstract::Vector > &start_vec, const std::vector< Teuchos::RCP< const NOX::Abstract::Vector > > &prev_solns, const double identity_sign=1.0)
 Constructor.
 DeflatedGroup (const DeflatedGroup &source, NOX::CopyType type=NOX::DeepCopy)
 Copy constructor.
virtual ~DeflatedGroup ()
 Destructor.
double getHomotopyParam () const
 Get homotopy parameter.
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
 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 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 (string paramID, double val)
 Set parameter indexed by (string) paramID.
virtual const ParameterVectorgetParams () 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 (string paramID) const
 Return copy of parameter indexed by (string) 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 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
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.

Protected Member Functions

virtual void resetIsValid ()
 Resets all isValid flags to false.
virtual void setupViews ()
 Sets up multivector views.
void setHomotopyParam (double param)
 Set homotopy parameter.
void setStepperParameters (Teuchos::ParameterList &topParams)
 Creates and sets the "Stepper" parameter sublist.

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
homotopyParams
 Pitchfork parameter list.
Teuchos::RCP
< LOCA::Homotopy::AbstractGroup
grpPtr
 Pointer to base group that defines $F$.
Teuchos::RCP
< LOCA::BorderedSystem::AbstractGroup
bordered_grp
 Pointer to base group as a bordered group.
LOCA::MultiContinuation::ExtendedMultiVector xMultiVec
 Stores the extended solution vector.
LOCA::MultiContinuation::ExtendedMultiVector fMultiVec
 Stores the extended residual vector.
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::ExtendedVector
newtonVec
 Stores view of first column of newtonMultiVec.
Teuchos::RCP
< LOCA::MultiContinuation::ExtendedVector
gradientVec
 Stores view of first column of gradientMultiVec.
Teuchos::RCP< const
NOX::Abstract::Vector
startVec
 Stores the starting vector, $ x^\ast $.
double identitySign
std::vector< Teuchos::RCP
< const NOX::Abstract::Vector > > 
solns
 Stores array of deflated solution vectors.
Teuchos::RCP
< NOX::Abstract::Vector
distVec
 Temporary vector for storing distance.
Teuchos::RCP
< NOX::Abstract::MultiVector
totalDistMultiVec
 Temporary vector for storing sum of distances.
Teuchos::RCP
< NOX::Abstract::Vector
totalDistVec
 Temporary vector for storing sum of distances.
Teuchos::RCP
< NOX::Abstract::MultiVector
underlyingF
 underlying group's F vector as a multivector
Teuchos::RCP
< LOCA::BorderedSolver::JacobianOperator
jacOp
Teuchos::RCP
< LOCA::BorderedSolver::AbstractStrategy
borderedSolver
 Stores bordered solver strategy.
Teuchos::RCP
< NOX::Abstract::MultiVector::DenseMatrix
minusOne
 Stores -1.
int numSolns
 Number of previous solutions.
std::vector< double > distances
 Array of distances from previous solutions.
double distProd
 Product of distances.
vector< int > index_f
 Stores indices for getting f part of fMultiVec.
LOCA::ParameterVector paramVec
 Copy of the ParameterVector for the underlying grpPtr.
double conParam
 Value of the homotopy continuation parameter.
int conParamID
 Continuatioin parameter ID number from the ParameterVector.
const string conParamLabel
 Contains the string used to identify the homotopy parameter in the ParameterVector object.
bool augmentJacForHomotopyNotImplemented
 Tracks whether the LOCA::Homotopy::Group method augmentJacobianForHomotopy is implemented. If not, the augmentation is applied during the applyJacobian assuming a matrix-free implementation.
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.

Detailed Description

LOCA's Homotopy Algorithm.

The HomotopyGroup is a concrete implementation of the LOCA::Continuation::AbstractGroup that modifies the set of nonlinear equations to be solved to allow for Homotopy to be applied to the system. This object should be used in conjunction with the LOCA::Stepper object to drive the continuation. This algorithm solves a system of nonlinear equations supplied by the user ( $ F(x) $) through continuation. An artificial parameter $ \lambda $ is used to control the continuation. The idea is to solve a simple equation starting at $ \lambda $ = 0 and, using the solution from the previous step, solve systems of equations that gets progressively closer to the true system of interest ( at $ \lambda $ = 1.0 we recover the original equations $ F(x) $). By constraining the definition of $ g(x, \lambda) $ and using artificial parameter contiuation, the continuation branch should be free of multiplicity and bifurcation phenomena.

The modified system of equations, $ g(x, \lambda) $, supplied by the HomotopyGroup is defined as:

\[ g(x, \lambda) = \lambda F(x) + (1.0 - \lambda)(x - a)(S) \]

where $x$ is the solution vector, $ \lambda $ is an artificial parameter, $ F(x) $ is the set of nonlinear equations the user supplies, $ g(x) $ is the corresponding set of homotopy equations that LOCA will solve, $ a $ is a random vector, and $ S $ is a scaling factor used to switch sign of the last term (typically valued 1.0 or -1.0).

This group requires the loca Stepper for continuation from $ \lambda $ = 0.0 (a simple set of equations to solve) to $ \lambda $ = 1.0 (the set of equations requested by the user, $ F(x) $). The Homotopy::Group will generate the Stepper parameter sublist in the parameter list that is passed in to the constructor. The user is free to modify this list (it sets default values) before passing it into the stepper object but should NOT change the starting and stopping values for the continuation parameter.

References:


Constructor & Destructor Documentation

LOCA::Homotopy::DeflatedGroup::DeflatedGroup ( const Teuchos::RCP< LOCA::GlobalData > &  global_data,
const Teuchos::RCP< Teuchos::ParameterList > &  topParams,
const Teuchos::RCP< Teuchos::ParameterList > &  hParams,
const Teuchos::RCP< LOCA::Homotopy::AbstractGroup > &  grp,
const Teuchos::RCP< const NOX::Abstract::Vector > &  start_vec,
const std::vector< Teuchos::RCP< const NOX::Abstract::Vector > > &  prev_solns,
const double  identity_sign = 1.0 
)

Constructor.

Parameters:
global_data[in] Global data object
topParams[in] Parsed top-level parameter list.
hParams[in] Homotopy parameters
grp[in] Group representing $f$.

References LOCA::ParameterVector::addParameter(), bordered_grp, borderedSolver, conParam, conParamID, conParamLabel, LOCA::ParameterVector::getIndex(), globalData, grpPtr, homotopyParams, isBordered, minusOne, paramVec, parsedParams, Teuchos::rcp(), setStepperParameters(), setupViews(), startVec, and xVec.


Member Function Documentation

NOX::Abstract::Group::ReturnType LOCA::Homotopy::DeflatedGroup::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.

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

void LOCA::Homotopy::DeflatedGroup::extractParameterComponent ( bool  use_transpose,
const NOX::Abstract::MultiVector v,
NOX::Abstract::MultiVector::DenseMatrix v_p 
) const [virtual]
void LOCA::Homotopy::DeflatedGroup::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::Homotopy::DeflatedGroup::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.

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

void LOCA::Homotopy::DeflatedGroup::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::Homotopy::DeflatedGroup::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.


Member Data Documentation

Value of the homotopy continuation parameter.

Ranges from 0.0 (easy solution) to 1.0 (solution to the system of interest).

Referenced by copy(), and DeflatedGroup().

Copy of the ParameterVector for the underlying grpPtr.

We copy this and then add the homotopy parameter to the list.

Referenced by copy(), and DeflatedGroup().


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