Amesos_Klu Class Reference

Amesos_Klu: A serial, unblocked code ideal for getting started and for very sparse matrices, such as circuit matrces. AmesosKlu computes

A^T X = B more efficiently than

A X = B. More...

#include <Amesos_Klu.h>

Inheritance diagram for Amesos_Klu:

[legend]Collaboration diagram for Amesos_Klu:[legend]List of all members.

Public Member Functions
Constructor methods
	Amesos_Klu (const Epetra_LinearProblem &LinearProblem)
	Amesos_Klu Constructor.
	~Amesos_Klu (void)
	Amesos_Klu Destructor.
Mathematical functions.
int	SymbolicFactorization ()
	Performs SymbolicFactorization on the matrix A.
int	NumericFactorization ()
	Performs NumericFactorization on the matrix A.
int	Solve ()
	Solves A X = B (or AT X = B).
Additional methods required to support the Epetra_Operator interface.
const Epetra_LinearProblem *	GetProblem () const
	Get a pointer to the Problem.
bool	MatrixShapeOK () const
	Returns true if KLU can handle this matrix shape.
int	SetUseTranspose (bool UseTranspose)
	SetUseTranpose(true) is more efficient in Amesos_Klu.
bool	UseTranspose () const
	Returns the current UseTranspose setting.
const Epetra_Comm &	Comm () const
	Returns a pointer to the Epetra_Comm communicator associated with this matrix.
int	SetParameters (Teuchos::ParameterList &ParameterList)
	Updates internal variables.
void	PrintTiming ()
	Print timing information.
void	PrintStatus ()
	Print information about the factorization and solution phases.
Protected Attributes
int *	Lp
int *	Li
int *	Up
int *	Ui
int *	P
double *	Lx
double *	Ux
Amesos_Klu_Pimpl *	PrivateKluData_
vector< int >	Ap
vector< int >	Ai
vector< double >	Aval
int	iam
int	IsLocal_
int	numentries_
int	NumGlobalElements_
Epetra_Map *	SerialMap_
Epetra_CrsMatrix *	SerialCrsMatrixA_
Epetra_CrsMatrix *	SerialMatrix_
Epetra_CrsMatrix *	TransposeMatrix_
Epetra_CrsMatrix *	Matrix_
bool	UseTranspose_
const Epetra_LinearProblem *	Problem_
bool	PrintTiming_
bool	PrintStatus_
bool	ComputeVectorNorms_
bool	ComputeTrueResidual_
int	verbose_
int	debug_
double	ConTime_
double	SymTime_
double	NumTime_
double	SolTime_
double	VecTime_
double	MatTime_
int	NumSymbolicFact_
int	NumNumericFact_
int	NumSolve_
Epetra_Time	Time

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Detailed Description

Amesos_Klu: A serial, unblocked code ideal for getting started and for very sparse matrices, such as circuit matrces. AmesosKlu computes

A^T X = B more efficiently than

A X = B.

Amesos_Klu, an object-oriented wrapper for Klu, will solve a linear systems of equations: A X = B using Epetra objects and the Klu solver library, where A is an Epetra_RowMatrix and X and B are Epetra_MultiVector objects.

<br /><br />

AmesosKlu computes

A^T X = B more efficiently than

A X = B. The latter requires a matrix transpose - which costs both time and space.

<br /><br />

klu is Davis' implementation of Gilbert-Peierl's left-looking sparse partial pivoting algorithm, with Eisenstat & Liu's symmetric pruning. Gilbert's version appears as [L,U,P]=lu(A) in MATLAB. It doesn't exploit dense matrix kernels, but it is the only sparse LU factorization algorithm known to be asymptotically optimal, in the sense that it takes time proportional to the number of floating-point operations. It is the precursor to SuperLU, thus the name ("clark Kent LU"). For very sparse matrices that do not suffer much fill-in (such as most circuit matrices when permuted properly) dense matrix kernels do not help, and the asymptotic run-time is of practical importance.

<br /><br />

The klu_btf code first permutes the matrix to upper block triangular form (using two algorithms by Duff and Reid, MC13 and MC21, in the ACM Collected Algorithms). It then permutes each block via a symmetric minimum degree ordering (AMD, by Amestoy, Davis, and Duff). This ordering phase can be done just once for a sequence of matrices. Next, it factorizes each reordered block via the klu routine, which also attempts to preserve diagonal pivoting, but allows for partial pivoting if the diagonal is to small.

<br /><br />

Klu execution can be tuned through a variety of parameters. Amesos_Klu.h allows control of these parameters through the following named parameters, ignoring parameters with names that it does not recognize. Where possible, the parameters are common to all direct solvers (although some may ignore them). However, some parameters, in particular tuning parameters, are unique to each solver.

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Constructor & Destructor Documentation

Amesos_Klu::Amesos_Klu (  const Epetra_LinearProblem &  LinearProblem  )

Amesos_Klu Constructor. Creates an Amesos_Klu instance, using an Epetra_LinearProblem, passing in an already-defined Epetra_LinearProblem object. Note: The operator in LinearProblem must be an Epetra_RowMatrix.

Amesos_Klu::~Amesos_Klu (  void   )

Amesos_Klu Destructor. Completely deletes an Amesos_Klu object.

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Member Function Documentation

bool Amesos_Klu::MatrixShapeOK (   )  const [virtual]

Returns true if KLU can handle this matrix shape. Returns true if the matrix shape is one that KLU can handle. KLU only works with square matrices. Implements Amesos_BaseSolver.

int Amesos_Klu::NumericFactorization (   )  [virtual]

Performs NumericFactorization on the matrix A. In addition to performing numeric factorization (and symbolic factorization if necessary) on the matrix A, the call to NumericFactorization() implies that no change will be made to the underlying matrix without a subsequent call to NumericFactorization(). preconditions: GetProblem().GetOperator() != 0 (return -1) MatrixShapeOk(GetProblem().GetOperator()) == true (return -6) The non-zero structure of the matrix should not have changed since the last call to SymbolicFactorization(). The distribution of the matrix should not have changed since the last call to SymbolicFactorization() postconditions: Numeric Factorization will be performed (or marked to be performed) allowing Solve() to be performed correctly despite a potential change in in the matrix values (though not in the non-zero structure). Returns: Integer error code, set to 0 if successful. Implements Amesos_BaseSolver.

int Amesos_Klu::SetParameters (  Teuchos::ParameterList &  ParameterList  )  [virtual]

Updates internal variables. <br >Preconditions: None. <br >Postconditions: Internal variables controlling the factorization and solve will be updated and take effect on all subsequent calls to NumericFactorization() and Solve(). All parameters whose value are to differ from the default values must be included in ParameterList. Parameters not specified in ParameterList revert to their default values. Returns: Integer error code, set to 0 if successful. Implements Amesos_BaseSolver.

int Amesos_Klu::SetUseTranspose (  bool  UseTranspose  )  [inline, virtual]

SetUseTranpose(true) is more efficient in Amesos_Klu. If SetUseTranspose() is set to true, AT X = B is computed (This is the more efficient operation) else A X = B is computed (This requires a matrix transpose) Implements Amesos_BaseSolver.

int Amesos_Klu::Solve (   )  [virtual]

Solves A X = B (or AT X = B). preconditions: GetProblem().GetOperator() != 0 (return -1) MatrixShapeOk(GetProblem().GetOperator()) == true (return -6) GetProblem()->CheckInput (see Epetra_LinearProblem::CheckInput() for return values) The non-zero structure of the matrix should not have changed since the last call to SymbolicFactorization(). The distribution of the matrix should not have changed since the last call to SymbolicFactorization() The matrix should not have changed since the last call to NumericFactorization(). postconditions: X will be set such that A X = B (or AT X = B), within the limits of the accuracy of the underlying solver. Returns: Integer error code, set to 0 if successful. Implements Amesos_BaseSolver.

int Amesos_Klu::SymbolicFactorization (   )  [virtual]

Performs SymbolicFactorization on the matrix A. In addition to performing symbolic factorization on the matrix A, the call to SymbolicFactorization() implies that no change will be made to the non-zero structure of the underlying matrix without a subsequent call to SymbolicFactorization(). preconditions: GetProblem().GetOperator() != 0 (return -1) MatrixShapeOk(GetProblem().GetOperator()) == true (return -6) postconditions: Symbolic Factorization will be performed (or marked to be performed) allowing NumericFactorization() and Solve() to be called. Returns: Integer error code, set to 0 if successful. Implements Amesos_BaseSolver.

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

• Amesos_Klu.h
• Amesos_Klu.cpp

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