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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>

Inheritance diagram for NOX::Epetra::MatrixFree:

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Collaboration diagram for NOX::Epetra::MatrixFree:
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List of all members.

Public Types

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

Public Member Functions

 MatrixFree (Interface &i, const Epetra_Vector &x, double lambda=1.0e-6)
 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 $.

Protected Attributes

string label
 Label for matrix.
Interface & interface
 User provided interface function.
Epetra_Vector currentX
 The current solution vector.
Epetra_Vector perturbX
 Perturbed solution vector.
Epetra_Vector fo
 Function evaluation at currentX.
Epetra_Vector fp
 Function evaluation at perturbX.
Epetra_Vector * fmPtr
 Optional pointer to function evaluation at -perturbX - needed only for centered finite differencing.
const Epetra_Map * epetraMap
 Epetra_Map object used in the returns of the Epetra_Operator derived methods.
bool ownsMap
 Set to true if the epetraMap is created by NOX::Epetra::MatrixFree.
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.

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 $.

Member Function Documentation

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.

Implements Epetra_Operator.

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.

Implements Epetra_Operator.

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.

Implements Epetra_Operator.

Member Data Documentation

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.

bool NOX::Epetra::MatrixFree::ownsMap [protected]
 

Set to true if the epetraMap is created by NOX::Epetra::MatrixFree.

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. This flag tells the destructor whether or not to destroy the Epetra_Map.

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