Ifpack2 Templated Preconditioning Package  Version 1.0
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Ifpack2::ILUT< MatrixType > Class Template Reference

ILUT (incomplete LU factorization with threshold) of a Tpetra sparse matrix. More...

#include <Ifpack2_ILUT_decl.hpp>

Inheritance diagram for Ifpack2::ILUT< MatrixType >:
Inheritance graph
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Public Types

Typedefs
typedef MatrixType::scalar_type scalar_type
 The type of the entries of the input MatrixType. More...
 
typedef
MatrixType::local_ordinal_type 
local_ordinal_type
 The type of local indices in the input MatrixType. More...
 
typedef
MatrixType::global_ordinal_type 
global_ordinal_type
 The type of global indices in the input MatrixType. More...
 
typedef MatrixType::node_type node_type
 The Node type used by the input MatrixType. More...
 
typedef Teuchos::ScalarTraits
< scalar_type >::magnitudeType 
magnitude_type
 The type of the magnitude (absolute value) of a matrix entry. More...
 
typedef Tpetra::RowMatrix
< scalar_type,
local_ordinal_type,
global_ordinal_type, node_type
row_matrix_type
 Type of the Tpetra::RowMatrix specialization that this class uses. More...
 
typedef Tpetra::CrsMatrix
< scalar_type,
local_ordinal_type,
global_ordinal_type, node_type
crs_matrix_type
 Type of the Tpetra::CrsMatrix specialization that this class uses for the L and U factors. More...
 
typedef Tpetra::Map
< local_ordinal_type,
global_ordinal_type, node_type
map_type
 Type of the Tpetra::Map specialization that this class uses. More...
 
- Public Types inherited from Ifpack2::Preconditioner< MatrixType::scalar_type, MatrixType::local_ordinal_type, MatrixType::global_ordinal_type, MatrixType::node_type >
typedef Teuchos::ScalarTraits
< MatrixType::scalar_type >
::magnitudeType 
magnitude_type
 The type of the magnitude (absolute value) of a matrix entry. More...
 

Public Member Functions

Constructors and Destructors
 ILUT (const Teuchos::RCP< const row_matrix_type > &A)
 Constructor. More...
 
virtual ~ILUT ()
 Destructor. More...
 
Methods for setting up and computing the incomplete factorization
void setParameters (const Teuchos::ParameterList &params)
 Set preconditioner parameters. More...
 
void initialize ()
 Clear any previously computed factors. More...
 
bool isInitialized () const
 Returns true if the preconditioner has been successfully initialized. More...
 
void compute ()
 Compute factors L and U using the specified diagonal perturbation thresholds and relaxation parameters. More...
 
bool isComputed () const
 If compute() is completed, this query returns true, otherwise it returns false. More...
 
Implementation of Ifpack2::Details::CanChangeMatrix
virtual void setMatrix (const Teuchos::RCP< const row_matrix_type > &A)
 Change the matrix to be preconditioned. More...
 
Implementation of Tpetra::Operator
void apply (const Tpetra::MultiVector< scalar_type, local_ordinal_type, global_ordinal_type, node_type > &X, Tpetra::MultiVector< scalar_type, local_ordinal_type, global_ordinal_type, node_type > &Y, Teuchos::ETransp mode=Teuchos::NO_TRANS, scalar_type alpha=Teuchos::ScalarTraits< scalar_type >::one(), scalar_type beta=Teuchos::ScalarTraits< scalar_type >::zero()) const
 Apply the ILUT preconditioner to X, resulting in Y. More...
 
Teuchos::RCP< const map_typegetDomainMap () const
 Tpetra::Map representing the domain of this operator. More...
 
Teuchos::RCP< const map_typegetRangeMap () const
 Tpetra::Map representing the range of this operator. More...
 
bool hasTransposeApply () const
 Whether this object's apply() method can apply the transpose (or conjugate transpose, if applicable). More...
 
Mathematical functions
Teuchos::RCP< const
Teuchos::Comm< int > > 
getComm () const
 Returns the input matrix's communicator. More...
 
Teuchos::RCP< const
row_matrix_type
getMatrix () const
 Returns a reference to the matrix to be preconditioned. More...
 
Teuchos::RCP< const
crs_matrix_type
getL () const
 Returns a reference to the L factor. More...
 
Teuchos::RCP< const
crs_matrix_type
getU () const
 Returns a reference to the U factor. More...
 
int getNumInitialize () const
 Returns the number of calls to Initialize(). More...
 
int getNumCompute () const
 Returns the number of calls to Compute(). More...
 
int getNumApply () const
 Returns the number of calls to apply(). More...
 
double getInitializeTime () const
 Returns the time spent in Initialize(). More...
 
double getComputeTime () const
 Returns the time spent in Compute(). More...
 
double getApplyTime () const
 Returns the time spent in apply(). More...
 
size_t getNodeSmootherComplexity () const
 Get a rough estimate of cost per iteration. More...
 
double getLevelOfFill () const
 The level of fill. More...
 
magnitude_type getAbsoluteThreshold () const
 Get absolute threshold value. More...
 
magnitude_type getRelativeThreshold () const
 Get relative threshold value. More...
 
magnitude_type getRelaxValue () const
 Get the relax value. More...
 
magnitude_type getDropTolerance () const
 Gets the dropping tolerance. More...
 
global_size_t getGlobalNumEntries () const
 Returns the number of nonzero entries in the global graph. More...
 
size_t getNodeNumEntries () const
 Returns the number of nonzero entries in the local graph. More...
 
Implementation of Teuchos::Describable
std::string description () const
 Return a simple one-line description of this object. More...
 
void describe (Teuchos::FancyOStream &out, const Teuchos::EVerbosityLevel verbLevel=Teuchos::Describable::verbLevel_default) const
 Print the object with some verbosity level to an FancyOStream object. More...
 
- Public Member Functions inherited from Ifpack2::Preconditioner< MatrixType::scalar_type, MatrixType::local_ordinal_type, MatrixType::global_ordinal_type, MatrixType::node_type >
virtual ~Preconditioner ()
 Destructor. More...
 
- Public Member Functions inherited from Ifpack2::Details::CanChangeMatrix< Tpetra::RowMatrix< MatrixType::scalar_type, MatrixType::local_ordinal_type, MatrixType::global_ordinal_type, MatrixType::node_type > >
virtual void setMatrix (const Teuchos::RCP< const Tpetra::RowMatrix< MatrixType::scalar_type, MatrixType::local_ordinal_type, MatrixType::global_ordinal_type, MatrixType::node_type > > &A)=0
 Set the new matrix. More...
 
virtual ~CanChangeMatrix ()
 Destructor. More...
 

Detailed Description

template<class MatrixType>
class Ifpack2::ILUT< MatrixType >

ILUT (incomplete LU factorization with threshold) of a Tpetra sparse matrix.

Template Parameters
Aspecialization of Tpetra::RowMatrix.

This class computes a sparse ILUT (incomplete LU) factorization with specified fill and drop tolerance, of the local part of a given sparse matrix represented as a Tpetra::RowMatrix or Tpetra::CrsMatrix. The "local part" is the square diagonal block of the matrix owned by the calling process. Thus, if the input matrix is distributed over multiple MPI processes, this preconditioner is equivalent to nonoverlapping additive Schwarz domain decomposition over the MPI processes, with ILUT as the subdomain solver on each process.

Remarks
See the documentation of setParameters() for a list of valid parameters.
This version of ILUT is a translation of Aztec's ILUT implementation, which was written by Ray Tuminaro.
There is an important difference between this implementation and the version described in Saad's paper. See setParameters() for details.

Member Typedef Documentation

template<class MatrixType>
typedef MatrixType::scalar_type Ifpack2::ILUT< MatrixType >::scalar_type

The type of the entries of the input MatrixType.

template<class MatrixType>
typedef MatrixType::local_ordinal_type Ifpack2::ILUT< MatrixType >::local_ordinal_type

The type of local indices in the input MatrixType.

template<class MatrixType>
typedef MatrixType::global_ordinal_type Ifpack2::ILUT< MatrixType >::global_ordinal_type

The type of global indices in the input MatrixType.

template<class MatrixType>
typedef MatrixType::node_type Ifpack2::ILUT< MatrixType >::node_type

The Node type used by the input MatrixType.

template<class MatrixType>
typedef Teuchos::ScalarTraits<scalar_type>::magnitudeType Ifpack2::ILUT< MatrixType >::magnitude_type

The type of the magnitude (absolute value) of a matrix entry.

template<class MatrixType>
typedef Tpetra::RowMatrix<scalar_type, local_ordinal_type, global_ordinal_type, node_type> Ifpack2::ILUT< MatrixType >::row_matrix_type

Type of the Tpetra::RowMatrix specialization that this class uses.

template<class MatrixType>
typedef Tpetra::CrsMatrix<scalar_type, local_ordinal_type, global_ordinal_type, node_type> Ifpack2::ILUT< MatrixType >::crs_matrix_type

Type of the Tpetra::CrsMatrix specialization that this class uses for the L and U factors.

template<class MatrixType>
typedef Tpetra::Map<local_ordinal_type, global_ordinal_type, node_type> Ifpack2::ILUT< MatrixType >::map_type

Type of the Tpetra::Map specialization that this class uses.

Constructor & Destructor Documentation

template<class MatrixType >
Ifpack2::ILUT< MatrixType >::ILUT ( const Teuchos::RCP< const row_matrix_type > &  A)
explicit

Constructor.

Parameters
A[in] The sparse matrix to factor, as a Tpetra::RowMatrix. (Tpetra::CrsMatrix inherits from this, so you may use a Tpetra::CrsMatrix here instead.)

The factorization will not modify the input matrix. It stores the L and U factors in the incomplete factorization separately.

template<class MatrixType >
Ifpack2::ILUT< MatrixType >::~ILUT ( )
virtual

Destructor.

Member Function Documentation

template<class MatrixType >
void Ifpack2::ILUT< MatrixType >::setParameters ( const Teuchos::ParameterList params)
virtual

Set preconditioner parameters.

ILUT implements the following parameters:

  • "fact: ilut level-of-fill" (double)
  • "fact: drop tolerance" (magnitude_type)
  • "fact: absolute threshold" (magnitude_type)
  • "fact: relative threshold" (magnitude_type)
  • "fact: relax value" (magnitude_type)

"fact: drop tolerance" is the magnitude threshold for dropping entries. It corresponds to the \(\tau\) parameter in Saad's original description of ILUT. "fact: ilut level-of-fill" controls the number of entries to keep in the strict upper triangle of the current row, and in the strict lower triangle of the current row. It does not correspond to the \(p\) parameter in Saad's original description. This parameter represents a maximum fill fraction. In this implementation, the L and U factors always contains nonzeros corresponding to the original sparsity pattern of A, so this value should be >= 1.0. Letting \(fill = \frac{(level-of-fill - 1)*nnz(A)}{2*N}\), each row of the computed L and U factors contains at most \(fill\) nonzero elements in addition to those from the sparsity pattern of A. ILUT always keeps the diagonal entry in the current row, regardless of the drop tolerance or fill level.

The absolute and relative threshold parameters affect how this code modifies the diagonal entry of the output factor. These parameters are not part of the original ILUT algorithm, but we include them for consistency with other Ifpack2 preconditioners.

The "fact: relax value" parameter currently has no effect.

Implements Ifpack2::Preconditioner< MatrixType::scalar_type, MatrixType::local_ordinal_type, MatrixType::global_ordinal_type, MatrixType::node_type >.

template<class MatrixType >
void Ifpack2::ILUT< MatrixType >::initialize ( )
virtual

Clear any previously computed factors.

You may call this before calling compute(). The compute() method will call this automatically if it has not yet been called. If you call this after calling compute(), you must recompute the factorization (by calling compute() again) before you may call apply().

Implements Ifpack2::Preconditioner< MatrixType::scalar_type, MatrixType::local_ordinal_type, MatrixType::global_ordinal_type, MatrixType::node_type >.

template<class MatrixType>
bool Ifpack2::ILUT< MatrixType >::isInitialized ( ) const
inlinevirtual
template<class MatrixType >
void Ifpack2::ILUT< MatrixType >::compute ( )
virtual

Compute factors L and U using the specified diagonal perturbation thresholds and relaxation parameters.

This function computes the ILUT factors L and U using the current:

  1. Value for the drop tolerance
  2. Value for the level of fill
  3. Value for the a priori diagonal threshold values.

Implements Ifpack2::Preconditioner< MatrixType::scalar_type, MatrixType::local_ordinal_type, MatrixType::global_ordinal_type, MatrixType::node_type >.

template<class MatrixType>
bool Ifpack2::ILUT< MatrixType >::isComputed ( ) const
inlinevirtual
template<class MatrixType >
void Ifpack2::ILUT< MatrixType >::setMatrix ( const Teuchos::RCP< const row_matrix_type > &  A)
virtual

Change the matrix to be preconditioned.

Parameters
A[in] The new matrix.
Postcondition
! isInitialized ()
! isComputed ()

Calling this method resets the preconditioner's state. After calling this method with a nonnull input, you must first call initialize() and compute() (in that order) before you may call apply().

You may call this method with a null input. If A is null, then you may not call initialize() or compute() until you first call this method again with a nonnull input. This method invalidates any previous factorization whether or not A is null, so calling setMatrix() with a null input is one way to clear the preconditioner's state (and free any memory that it may be using).

The new matrix A need not necessarily have the same Maps or even the same communicator as the original matrix.

template<class MatrixType >
void Ifpack2::ILUT< MatrixType >::apply ( const Tpetra::MultiVector< scalar_type, local_ordinal_type, global_ordinal_type, node_type > &  X,
Tpetra::MultiVector< scalar_type, local_ordinal_type, global_ordinal_type, node_type > &  Y,
Teuchos::ETransp  mode = Teuchos::NO_TRANS,
scalar_type  alpha = Teuchos::ScalarTraits<scalar_type>::one(),
scalar_type  beta = Teuchos::ScalarTraits<scalar_type>::zero() 
) const
virtual

Apply the ILUT preconditioner to X, resulting in Y.

Parameters
X[in] Input multivector; "right-hand side" of the solve.
Y[out] Output multivector; result of the solve.

Implements Ifpack2::Preconditioner< MatrixType::scalar_type, MatrixType::local_ordinal_type, MatrixType::global_ordinal_type, MatrixType::node_type >.

template<class MatrixType >
Teuchos::RCP< const typename ILUT< MatrixType >::map_type > Ifpack2::ILUT< MatrixType >::getDomainMap ( ) const
virtual
template<class MatrixType >
Teuchos::RCP< const typename ILUT< MatrixType >::map_type > Ifpack2::ILUT< MatrixType >::getRangeMap ( ) const
virtual
template<class MatrixType >
bool Ifpack2::ILUT< MatrixType >::hasTransposeApply ( ) const

Whether this object's apply() method can apply the transpose (or conjugate transpose, if applicable).

template<class MatrixType >
Teuchos::RCP< const Teuchos::Comm< int > > Ifpack2::ILUT< MatrixType >::getComm ( ) const

Returns the input matrix's communicator.

template<class MatrixType >
Teuchos::RCP< const typename ILUT< MatrixType >::row_matrix_type > Ifpack2::ILUT< MatrixType >::getMatrix ( ) const
virtual
template<class MatrixType>
Teuchos::RCP<const crs_matrix_type> Ifpack2::ILUT< MatrixType >::getL ( ) const
inline

Returns a reference to the L factor.

template<class MatrixType>
Teuchos::RCP<const crs_matrix_type> Ifpack2::ILUT< MatrixType >::getU ( ) const
inline

Returns a reference to the U factor.

template<class MatrixType >
int Ifpack2::ILUT< MatrixType >::getNumInitialize ( ) const
virtual
template<class MatrixType >
int Ifpack2::ILUT< MatrixType >::getNumCompute ( ) const
virtual
template<class MatrixType >
int Ifpack2::ILUT< MatrixType >::getNumApply ( ) const
virtual
template<class MatrixType >
double Ifpack2::ILUT< MatrixType >::getInitializeTime ( ) const
virtual
template<class MatrixType >
double Ifpack2::ILUT< MatrixType >::getComputeTime ( ) const
virtual
template<class MatrixType >
double Ifpack2::ILUT< MatrixType >::getApplyTime ( ) const
virtual
template<class MatrixType >
size_t Ifpack2::ILUT< MatrixType >::getNodeSmootherComplexity ( ) const

Get a rough estimate of cost per iteration.

template<class MatrixType>
double Ifpack2::ILUT< MatrixType >::getLevelOfFill ( ) const
inline

The level of fill.

For ILUT, this means the maximum number of entries in each row of the resulting L and U factors (each considered separately), not including the diagonal entry in that row (which is always part of U). This has a different meaning for ILUT than it does for ILU(k).

template<class MatrixType>
magnitude_type Ifpack2::ILUT< MatrixType >::getAbsoluteThreshold ( ) const
inline

Get absolute threshold value.

template<class MatrixType>
magnitude_type Ifpack2::ILUT< MatrixType >::getRelativeThreshold ( ) const
inline

Get relative threshold value.

template<class MatrixType>
magnitude_type Ifpack2::ILUT< MatrixType >::getRelaxValue ( ) const
inline

Get the relax value.

template<class MatrixType>
magnitude_type Ifpack2::ILUT< MatrixType >::getDropTolerance ( ) const
inline

Gets the dropping tolerance.

template<class MatrixType >
global_size_t Ifpack2::ILUT< MatrixType >::getGlobalNumEntries ( ) const

Returns the number of nonzero entries in the global graph.

template<class MatrixType >
size_t Ifpack2::ILUT< MatrixType >::getNodeNumEntries ( ) const

Returns the number of nonzero entries in the local graph.

template<class MatrixType >
std::string Ifpack2::ILUT< MatrixType >::description ( ) const

Return a simple one-line description of this object.

template<class MatrixType >
void Ifpack2::ILUT< MatrixType >::describe ( Teuchos::FancyOStream out,
const Teuchos::EVerbosityLevel  verbLevel = Teuchos::Describable::verbLevel_default 
) const

Print the object with some verbosity level to an FancyOStream object.


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