NOX::Epetra::MatrixFree Class Reference

Concrete implementation for creating an Epetra_Operator Jacobian based on the Matrix-Free Newton-Krylov method. More...

#include <NOX_Epetra_MatrixFree.H>

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List of all members.

Public Types

enum  DifferenceType { Forward, Backward, Centered }
 Define types for use of the perturbation parameter $ \delta$. More...

Public Member Functions

 MatrixFree (Teuchos::ParameterList &printParams, const Teuchos::RCP< NOX::Epetra::Interface::Required > &i, const NOX::Epetra::Vector &cloneVector, bool useNewPerturbation=false)
 Constructor.
virtual ~MatrixFree ()
 Pure virtual destructor.
virtual int SetUseTranspose (bool UseTranspose)
 If set true, transpose of this operator will be applied.
virtual int Apply (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
 Returns the result of a Epetra_Operator applied to a Epetra_MultiVector X in Y.
virtual int ApplyInverse (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
 Returns the result of a Epetra_Operator inverse applied to an Epetra_MultiVector X in Y.
virtual double NormInf () const
 Returns the infinity norm of the global matrix.
virtual const char * Label () const
 Returns a character string describing the operator.
virtual bool UseTranspose () const
 Returns the current UseTranspose setting.
virtual bool HasNormInf () const
 Returns true if the this object can provide an approximate Inf-norm, false otherwise.
virtual const Epetra_Comm & Comm () const
 Returns a reference to the Epetra_Comm communicator associated with this operator.
virtual const Epetra_Map & OperatorDomainMap () const
 Returns the Epetra_BlockMap object associated with the domain of this matrix operator.
virtual const Epetra_Map & OperatorRangeMap () const
 Returns the Epetra_BlockMap object associated with the range of this matrix operator.
virtual bool computeJacobian (const Epetra_Vector &x, Epetra_Operator &Jac)
 Compute Jacobian given the specified input vector, x. Returns true if computation was successful.
virtual void setDifferenceMethod (DifferenceType type)
 Set the type of perturbation method used (default is Forward).
void setLambda (double lambda_)
 Allows the user to change the value of $ \lambda $ in the perturbation calculation.
void setComputePerturbation (bool bVal)
 Flag that toggles whether MatrixFree should compute the perturbation parameter $ \eta $ or use a value supplied by the user through setPerturbation().
void setPerturbation (double eta_)
 Set the perturbation parameter $ \eta $.
double getPerturbation () const
 Returns the most recently used value of the perturbation parameter $ \eta $.
void setGroupForComputeF (const NOX::Abstract::Group &group)
 Clone a NOX::Abstract::Group derived object and use the computeF() method of that group for the perturbation instead of the NOX::Epetra::Interface::Required::computeF() method. This is required for LOCA to get the operators correct during homotopy.

Protected Attributes

string label
 Label for matrix.
Teuchos::RCP
< NOX::Epetra::Interface::Required
interface
 User provided interface function.
NOX::Epetra::Vector currentX
 The current solution vector.
NOX::Epetra::Vector perturbX
 Perturbed solution vector.
NOX::Epetra::Vector fo
 Function evaluation at currentX.
NOX::Epetra::Vector fp
 Function evaluation at perturbX.
Teuchos::RCP< NOX::Epetra::VectorfmPtr
 Optional pointer to function evaluation at -perturbX - needed only for centered finite differencing.
Teuchos::RCP< const Epetra_Map > epetraMap
 Epetra_Map object used in the returns of the Epetra_Operator derived methods.
DifferenceType diffType
 Define types for use of the perturbation parameter $ \delta$.
double lambda
 Scale factor for eta calculation.
double eta
 Perturbation value to use in the directional derivative.
double userEta
 User specified perturbation value to use in the directional derivative. Set by setPerturbation().
bool computeEta
 Flag that determines if we should calculate eta or use a value set by the user.
bool useGroupForComputeF
 Flag to enables the use of a group instead of the interface for the computeF() calls in the directional difference calculation.
bool useNewPerturbation
 A new perturbation formulation developed by C. T. Kelley and A. G. Salinger can be used by the constructor flag useNewPerturbation = true.
Teuchos::RCP
< NOX::Abstract::Group
groupPtr
 Pointer to the group for possible use in computeF() calls.
NOX::Utils utils
 Printing utilities.


Detailed Description

Concrete implementation for creating an Epetra_Operator Jacobian based on the Matrix-Free Newton-Krylov method.

Matrix-Free Newton-Krylov is a method that takes advantage of the fact the Newton Krylov solvers do not require an explicit Jacobian matrix. Newton-Krylov solvers only require the matrix-vector product $Jy$ in the iteration sequence. This product can approximated by the following:

\[ Jy = \frac{F(x + \delta y) - F(x)}{\delta} \]

where $J$ is the Jacobian, $F$ is the function evaluation, $x$ is the solution vector, $y$ is the vector to be operated on, and $\delta$ is a scalar perturbation calculated by:

\[ \delta = \lambda * (\lambda + \frac{\| x\|}{\| y\|} ) \]

where $ \lambda = 1.0e-6 $.

Definition at line 84 of file NOX_Epetra_MatrixFree.H.


Member Enumeration Documentation

Define types for use of the perturbation parameter $ \delta$.

Definition at line 90 of file NOX_Epetra_MatrixFree.H.


Constructor & Destructor Documentation

MatrixFree::MatrixFree ( Teuchos::ParameterList &  printParams,
const Teuchos::RCP< NOX::Epetra::Interface::Required > &  i,
const NOX::Epetra::Vector cloneVector,
bool  useNewPerturbation = false 
)

Constructor.

The vector x is used to clone the solution vector.

Definition at line 54 of file NOX_Epetra_MatrixFree.C.

References currentX, epetraMap, fo, fp, NOX::Epetra::Vector::getEpetraVector(), NOX::Epetra::Vector::init(), and perturbX.

MatrixFree::~MatrixFree (  )  [virtual]

Pure virtual destructor.

Definition at line 95 of file NOX_Epetra_MatrixFree.C.


Member Function Documentation

int MatrixFree::SetUseTranspose ( bool  UseTranspose  )  [virtual]

If set true, transpose of this operator will be applied.

This flag allows the transpose of the given operator to be used implicitly. Setting this flag affects only the Apply() and ApplyInverse() methods. If the implementation of this interface does not support transpose use, this method should return a value of -1.

Parameters:
UseTranspose -If true, multiply by the transpose of operator, otherwise just use operator.
Returns:
Integer error code, set to 0 if successful. Set to -1 if this implementation does not support transpose.

Definition at line 100 of file NOX_Epetra_MatrixFree.C.

References NOX::Utils::out(), and utils.

int MatrixFree::Apply ( const Epetra_MultiVector &  X,
Epetra_MultiVector &  Y 
) const [virtual]

Returns the result of a Epetra_Operator applied to a Epetra_MultiVector X in Y.

Parameters:
X - A Epetra_MultiVector of dimension NumVectors to multiply with matrix.
Y -A Epetra_MultiVector of dimension NumVectors containing result.
Returns:
Integer error code, set to 0 if successful.

Definition at line 110 of file NOX_Epetra_MatrixFree.C.

References computeEta, NOX::Epetra::Vector::CreateView, currentX, diffType, eta, fmPtr, fo, fp, NOX::Epetra::Vector::getEpetraVector(), NOX::Epetra::Vector::getVectorSpace(), groupPtr, interface, lambda, NOX::Epetra::Interface::Required::MF_Res, NOX::Epetra::Vector::norm(), perturbX, NOX::Epetra::Vector::scale(), useGroupForComputeF, useNewPerturbation, and userEta.

int MatrixFree::ApplyInverse ( const Epetra_MultiVector &  X,
Epetra_MultiVector &  Y 
) const [virtual]

Returns the result of a Epetra_Operator inverse applied to an Epetra_MultiVector X in Y.

Parameters:
X - A Epetra_MultiVector of dimension NumVectors to solve for.
Y -A Epetra_MultiVector of dimension NumVectors containing result.
Returns:
Integer error code, set to 0 if successful.
Warning:
In order to work with AztecOO, any implementation of this method must support the case where X and Y are the same object.

Definition at line 217 of file NOX_Epetra_MatrixFree.C.

References NOX::Utils::out(), and utils.

double MatrixFree::NormInf (  )  const [virtual]

Returns the infinity norm of the global matrix.

Definition at line 225 of file NOX_Epetra_MatrixFree.C.

References NOX::Utils::out(), and utils.

const char * MatrixFree::Label (  )  const [virtual]

Returns a character string describing the operator.

Definition at line 234 of file NOX_Epetra_MatrixFree.C.

References label.

bool MatrixFree::UseTranspose (  )  const [virtual]

Returns the current UseTranspose setting.

Definition at line 239 of file NOX_Epetra_MatrixFree.C.

bool MatrixFree::HasNormInf (  )  const [virtual]

Returns true if the this object can provide an approximate Inf-norm, false otherwise.

Definition at line 244 of file NOX_Epetra_MatrixFree.C.

const Epetra_Comm & MatrixFree::Comm (  )  const [virtual]

Returns a reference to the Epetra_Comm communicator associated with this operator.

Definition at line 249 of file NOX_Epetra_MatrixFree.C.

References currentX, and NOX::Epetra::Vector::getEpetraVector().

const Epetra_Map & MatrixFree::OperatorDomainMap (  )  const [virtual]

Returns the Epetra_BlockMap object associated with the domain of this matrix operator.

Definition at line 253 of file NOX_Epetra_MatrixFree.C.

References epetraMap.

const Epetra_Map & MatrixFree::OperatorRangeMap (  )  const [virtual]

Returns the Epetra_BlockMap object associated with the range of this matrix operator.

Definition at line 258 of file NOX_Epetra_MatrixFree.C.

References epetraMap.

bool MatrixFree::computeJacobian ( const Epetra_Vector &  x,
Epetra_Operator &  Jac 
) [virtual]

Compute Jacobian given the specified input vector, x. Returns true if computation was successful.

Implements NOX::Epetra::Interface::Jacobian.

Definition at line 263 of file NOX_Epetra_MatrixFree.C.

References currentX, fo, NOX::Epetra::Vector::getEpetraVector(), groupPtr, interface, NOX::Epetra::Interface::Required::MF_Jac, and useGroupForComputeF.

void MatrixFree::setDifferenceMethod ( DifferenceType  type  )  [virtual]

Set the type of perturbation method used (default is Forward).

Definition at line 285 of file NOX_Epetra_MatrixFree.C.

References diffType.

void MatrixFree::setLambda ( double  lambda_  ) 

Allows the user to change the value of $ \lambda $ in the perturbation calculation.

Definition at line 290 of file NOX_Epetra_MatrixFree.C.

References lambda.

void MatrixFree::setComputePerturbation ( bool  bVal  ) 

Flag that toggles whether MatrixFree should compute the perturbation parameter $ \eta $ or use a value supplied by the user through setPerturbation().

Definition at line 295 of file NOX_Epetra_MatrixFree.C.

References computeEta.

void MatrixFree::setPerturbation ( double  eta_  ) 

Set the perturbation parameter $ \eta $.

Definition at line 300 of file NOX_Epetra_MatrixFree.C.

References computeEta, and userEta.

double MatrixFree::getPerturbation (  )  const

Returns the most recently used value of the perturbation parameter $ \eta $.

Definition at line 306 of file NOX_Epetra_MatrixFree.C.

References eta.

void MatrixFree::setGroupForComputeF ( const NOX::Abstract::Group group  ) 

Clone a NOX::Abstract::Group derived object and use the computeF() method of that group for the perturbation instead of the NOX::Epetra::Interface::Required::computeF() method. This is required for LOCA to get the operators correct during homotopy.

Definition at line 311 of file NOX_Epetra_MatrixFree.C.

References NOX::Abstract::Group::clone(), groupPtr, and useGroupForComputeF.


Member Data Documentation

string NOX::Epetra::MatrixFree::label [protected]

Label for matrix.

Definition at line 184 of file NOX_Epetra_MatrixFree.H.

Referenced by Label().

User provided interface function.

Definition at line 187 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply(), and computeJacobian().

The current solution vector.

Definition at line 190 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply(), Comm(), computeJacobian(), and MatrixFree().

Perturbed solution vector.

Definition at line 193 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply(), and MatrixFree().

Function evaluation at currentX.

Definition at line 196 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply(), computeJacobian(), and MatrixFree().

Function evaluation at perturbX.

Definition at line 199 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply(), and MatrixFree().

Teuchos::RCP<NOX::Epetra::Vector> NOX::Epetra::MatrixFree::fmPtr [mutable, protected]

Optional pointer to function evaluation at -perturbX - needed only for centered finite differencing.

Definition at line 202 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply().

Teuchos::RCP<const Epetra_Map> NOX::Epetra::MatrixFree::epetraMap [protected]

Epetra_Map object used in the returns of the Epetra_Operator derived methods.

If the user is using Epetra_BlockMaps, then NOX::Epetra::MatrixFree must create an equivalent Epetra_Map from the Epetra_BlockMap that can be used as the return object of the OperatorDomainMap() and OperatorRangeMap() methods.

Definition at line 207 of file NOX_Epetra_MatrixFree.H.

Referenced by MatrixFree(), OperatorDomainMap(), and OperatorRangeMap().

Define types for use of the perturbation parameter $ \delta$.

Definition at line 210 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply(), and setDifferenceMethod().

double NOX::Epetra::MatrixFree::lambda [protected]

Scale factor for eta calculation.

Definition at line 213 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply(), and setLambda().

double NOX::Epetra::MatrixFree::eta [mutable, protected]

Perturbation value to use in the directional derivative.

Definition at line 216 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply(), and getPerturbation().

User specified perturbation value to use in the directional derivative. Set by setPerturbation().

Definition at line 219 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply(), and setPerturbation().

Flag that determines if we should calculate eta or use a value set by the user.

Definition at line 222 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply(), setComputePerturbation(), and setPerturbation().

Flag to enables the use of a group instead of the interface for the computeF() calls in the directional difference calculation.

Definition at line 225 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply(), computeJacobian(), and setGroupForComputeF().

A new perturbation formulation developed by C. T. Kelley and A. G. Salinger can be used by the constructor flag useNewPerturbation = true.

Definition at line 228 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply().

Pointer to the group for possible use in computeF() calls.

Definition at line 231 of file NOX_Epetra_MatrixFree.H.

Referenced by Apply(), computeJacobian(), and setGroupForComputeF().

Printing utilities.

Definition at line 234 of file NOX_Epetra_MatrixFree.H.

Referenced by ApplyInverse(), NormInf(), and SetUseTranspose().


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

Generated on Thu Dec 17 11:03:06 2009 for Nonlinear Solver Project by  doxygen 1.5.9