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Amesos_Klu Class Reference

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

#include <Amesos_Klu.h>

Inheritance diagram for Amesos_Klu:
Inheritance graph
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List of all members.

Private Attributes

int SerialXlda_
Teuchos::RCP< Amesos_Klu_PimplPrivateKluData_
Teuchos::RCP
< Amesos_StandardIndex
StdIndex_
Teuchos::RCP
< Amesos_StandardIndex
StdIndexRange_
Teuchos::RCP
< Amesos_StandardIndex
StdIndexDomain_
std::vector< int > Ap
 Ap, Ai, Aval form the compressed row storage used by Klu Ai and Aval can point directly into a matrix if it is StorageOptimized(), hence they may either be in vector form or may be a pointer into Epetra_CrsMatrix internals.
std::vector< int > VecAi
std::vector< double > VecAval
double * Aval
int * Ai
int UseDataInPlace_
 1 if Problem_->GetOperator() is stored entirely on process 0
int numentries_
 Number of non-zero entries in Problem_->GetOperator()
int NumGlobalElements_
 Number of rows and columns in the Problem_->GetOperator()
Epetra_RowMatrixRowMatrixA_
 Operator converted to a RowMatrix.
Epetra_CrsMatrixCrsMatrixA_
 Operator converted to a CrsMatrix.
Teuchos::RCP< Epetra_MapSerialMap_
 Points to a Serial Map (unused if UseDataInPlace_ == 1 )
Teuchos::RCP< Epetra_CrsMatrixSerialCrsMatrixA_
 Points to a Serial Copy of A (unused if UseDataInPlace_==1)
Epetra_RowMatrixStdIndexMatrix_
 Points to a Contiguous Copy of A.
Epetra_MultiVectorStdIndexDomainVector_
Epetra_MultiVectorStdIndexRangeVector_
Epetra_RowMatrixSerialMatrix_
 Points to a Serial Copy of A.
bool TrustMe_
 If true, no checks are made and the matrix is assume to be distributed.
int NumVectors_
 Number of vectors in RHS and LHS.
double * SerialXBvalues_
 Pointer to the actual values in the serial version of X and B.
double * SerialBvalues_
Teuchos::RCP< Epetra_MultiVectorSerialB_
 Serial versions of the LHS and RHS (may point to the original vector if serial)
Teuchos::RCP< Epetra_MultiVectorSerialX_
Teuchos::RCP< Epetra_MultiVectorSerialXextract_
 Serial versions of the LHS and RHS (if necessary)
Teuchos::RCP< Epetra_MultiVectorSerialBextract_
bool UseTranspose_
 If true, the transpose of A is used.
const Epetra_LinearProblemProblem_
 Pointer to the linear system problem.
std::vector< int > ColIndicesV_
 Only used for RowMatrices to extract copies.
std::vector< double > RowValuesV_
 Only used for RowMatrices to extract copies.
Teuchos::RCP< Epetra_ImportImportToSerial_
 Importer to process 0.
Teuchos::RCP< Epetra_ImportImportRangeToSerial_
Teuchos::RCP< Epetra_ImportImportDomainToSerial_
int MtxRedistTime_
 Quick access ids for the individual timings.
int MtxConvTime_
int VecRedistTime_
int SymFactTime_
int NumFactTime_
int SolveTime_
int OverheadTime_
 Amesos_Klu (const Epetra_LinearProblem &LinearProblem)
 Amesos_Klu Constructor.
 ~Amesos_Klu (void)
 Amesos_Klu Destructor.
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)
const Epetra_LinearProblemGetProblem () const
 Get a pointer to the Problem.
bool MatrixShapeOK () const
 Returns true if KLU can handle this matrix shape.
int SetUseTranspose (bool UseTranspose_in)
 SetUseTranpose(true) is more efficient in Amesos_Klu.
bool UseTranspose () const
 Returns the current UseTranspose setting.
const Epetra_CommComm () const
 Returns a pointer to the Epetra_Comm communicator associated with this operator.
int SetParameters (Teuchos::ParameterList &ParameterList)
 Updates internal variables.
int NumSymbolicFact () const
 Returns the number of symbolic factorizations performed by this object.
int NumNumericFact () const
 Returns the number of numeric factorizations performed by this object.
int NumSolve () const
 Returns the number of solves performed by this object.
void PrintTiming () const
 Prints timing information.
void PrintStatus () const
 Prints information about the factorization and solution phases.
void GetTiming (Teuchos::ParameterList &TimingParameterList) const
 Extracts timing information and places in parameter list.
int CreateLocalMatrixAndExporters ()
int ExportToSerial ()
int ConvertToKluCRS (bool firsttime)
int PerformSymbolicFactorization ()
int PerformNumericFactorization ()

Detailed Description

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

Interface to UMFPACK.

Interface to KLU internal solver.

Class Amesos_Klu is an object-oriented wrapper for KLU. KLU, whose sources are distributed within Amesos, is a serial solver for sparse matrices. KLU will solve a linear system of equations: $A X = B$, where A is an Epetra_RowMatrix and X and B are Epetra_MultiVector objects.

Amesos_Klu computes $A^T X = B$ more efficiently than $>A X = B$. The latter requires a matrix transpose -- which costs both time and space.

KLU is Tim 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.

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.

Date:
Last updated on 24-May-05.

Definition at line 111 of file Amesos_Klu.h.


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.

Definition at line 89 of file Amesos_Klu.cpp.

Amesos_Klu::~Amesos_Klu ( void  )

Amesos_Klu Destructor.

Definition at line 111 of file Amesos_Klu.cpp.


Member Function Documentation

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().

<br >Preconditions:

<br >Postconditions:

Returns:
Integer error code, set to 0 if successful.

Implements Amesos_BaseSolver.

Definition at line 586 of file Amesos_Klu.cpp.

int Amesos_Klu::NumericFactorization ( ) [virtual]

Performs NumericFactorization on the matrix A.

In addition to performing numeric factorization 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().

<br >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(). (return -2 if the number of non-zeros changes) Other changes can have arbitrary consequences.
  • The distribution of the matrix should not have changed since the last call to SymbolicFactorization()
  • The matrix should be indexed from 0 to n-1, unless the parameter "Reindex" was set to "true" prior to the call to SymbolicFactorization(). (return -3 - if caught)
  • The paremeter "Reindex" should not be set to "true" except on CrsMatrices. (return -4)
  • The paremeter "Reindex" should not be set to "true" unless Amesos was built with EpetraExt, i.e. with --enable-epetraext on the configure line. (return -4)
  • Internal errors retur -5.

<br >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.

Definition at line 641 of file Amesos_Klu.cpp.

int Amesos_Klu::Solve ( ) [virtual]

Solves A X = B (or AT x = B)

<br >Preconditions:

<br >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.

Definition at line 680 of file Amesos_Klu.cpp.

const Epetra_LinearProblem* Amesos_Klu::GetProblem ( ) const [inline, virtual]

Get a pointer to the Problem.

Implements Amesos_BaseSolver.

Definition at line 147 of file Amesos_Klu.h.

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.

Definition at line 572 of file Amesos_Klu.cpp.

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

SetUseTranpose(true) is more efficient in Amesos_Klu.

If SetUseTranspose() is set to true, $A^T X = B$ is computed.

Implements Amesos_BaseSolver.

Definition at line 160 of file Amesos_Klu.h.

bool Amesos_Klu::UseTranspose ( ) const [inline, virtual]

Returns the current UseTranspose setting.

Implements Amesos_BaseSolver.

Definition at line 162 of file Amesos_Klu.h.

const Epetra_Comm& Amesos_Klu::Comm ( ) const [inline, virtual]

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

Implements Amesos_BaseSolver.

Definition at line 164 of file Amesos_Klu.h.

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 subseuent 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.

Definition at line 418 of file Amesos_Klu.cpp.

int Amesos_Klu::NumSymbolicFact ( ) const [inline, virtual]

Returns the number of symbolic factorizations performed by this object.

Implements Amesos_BaseSolver.

Definition at line 169 of file Amesos_Klu.h.

int Amesos_Klu::NumNumericFact ( ) const [inline, virtual]

Returns the number of numeric factorizations performed by this object.

Implements Amesos_BaseSolver.

Definition at line 172 of file Amesos_Klu.h.

int Amesos_Klu::NumSolve ( ) const [inline, virtual]

Returns the number of solves performed by this object.

Implements Amesos_BaseSolver.

Definition at line 175 of file Amesos_Klu.h.

void Amesos_Klu::PrintTiming ( ) const [virtual]

Prints timing information.

Implements Amesos_BaseSolver.

Definition at line 892 of file Amesos_Klu.cpp.

void Amesos_Klu::PrintStatus ( ) const [virtual]

Prints information about the factorization and solution phases.

Implements Amesos_BaseSolver.

Definition at line 869 of file Amesos_Klu.cpp.

void Amesos_Klu::GetTiming ( Teuchos::ParameterList TimingParameterList) const [inline, virtual]

Extracts timing information and places in parameter list.

Reimplemented from Amesos_BaseSolver.

Definition at line 184 of file Amesos_Klu.h.

int Amesos_Klu::CreateLocalMatrixAndExporters ( ) [private]

Definition at line 178 of file Amesos_Klu.cpp.

int Amesos_Klu::ExportToSerial ( ) [private]

Definition at line 119 of file Amesos_Klu.cpp.

int Amesos_Klu::ConvertToKluCRS ( bool  firsttime) [private]

Definition at line 306 of file Amesos_Klu.cpp.

int Amesos_Klu::PerformSymbolicFactorization ( ) [private]

Definition at line 447 of file Amesos_Klu.cpp.

int Amesos_Klu::PerformNumericFactorization ( ) [private]

Definition at line 485 of file Amesos_Klu.cpp.


Member Data Documentation

int Amesos_Klu::SerialXlda_ [private]

Definition at line 258 of file Amesos_Klu.h.

Definition at line 267 of file Amesos_Klu.h.

Definition at line 268 of file Amesos_Klu.h.

Definition at line 269 of file Amesos_Klu.h.

Definition at line 270 of file Amesos_Klu.h.

std::vector<int> Amesos_Klu::Ap [private]

Ap, Ai, Aval form the compressed row storage used by Klu Ai and Aval can point directly into a matrix if it is StorageOptimized(), hence they may either be in vector form or may be a pointer into Epetra_CrsMatrix internals.

Ap must always be constructed.

Definition at line 276 of file Amesos_Klu.h.

std::vector<int> Amesos_Klu::VecAi [private]

Definition at line 277 of file Amesos_Klu.h.

std::vector<double> Amesos_Klu::VecAval [private]

Definition at line 278 of file Amesos_Klu.h.

double* Amesos_Klu::Aval [private]

Definition at line 279 of file Amesos_Klu.h.

int* Amesos_Klu::Ai [private]

Definition at line 280 of file Amesos_Klu.h.

1 if Problem_->GetOperator() is stored entirely on process 0

Definition at line 283 of file Amesos_Klu.h.

int Amesos_Klu::numentries_ [private]

Number of non-zero entries in Problem_->GetOperator()

Definition at line 285 of file Amesos_Klu.h.

Number of rows and columns in the Problem_->GetOperator()

Definition at line 287 of file Amesos_Klu.h.

Operator converted to a RowMatrix.

Definition at line 290 of file Amesos_Klu.h.

Operator converted to a CrsMatrix.

Definition at line 292 of file Amesos_Klu.h.

Points to a Serial Map (unused if UseDataInPlace_ == 1 )

Definition at line 302 of file Amesos_Klu.h.

Points to a Serial Copy of A (unused if UseDataInPlace_==1)

Definition at line 304 of file Amesos_Klu.h.

Points to a Contiguous Copy of A.

Definition at line 306 of file Amesos_Klu.h.

Definition at line 307 of file Amesos_Klu.h.

Definition at line 308 of file Amesos_Klu.h.

Points to a Serial Copy of A.

Definition at line 310 of file Amesos_Klu.h.

bool Amesos_Klu::TrustMe_ [private]

If true, no checks are made and the matrix is assume to be distributed.

Definition at line 316 of file Amesos_Klu.h.

int Amesos_Klu::NumVectors_ [private]

Number of vectors in RHS and LHS.

Definition at line 318 of file Amesos_Klu.h.

double* Amesos_Klu::SerialXBvalues_ [private]

Pointer to the actual values in the serial version of X and B.

Definition at line 320 of file Amesos_Klu.h.

double* Amesos_Klu::SerialBvalues_ [private]

Definition at line 321 of file Amesos_Klu.h.

Serial versions of the LHS and RHS (may point to the original vector if serial)

Definition at line 323 of file Amesos_Klu.h.

Definition at line 324 of file Amesos_Klu.h.

Serial versions of the LHS and RHS (if necessary)

Definition at line 326 of file Amesos_Klu.h.

Definition at line 327 of file Amesos_Klu.h.

bool Amesos_Klu::UseTranspose_ [private]

If true, the transpose of A is used.

Definition at line 330 of file Amesos_Klu.h.

Pointer to the linear system problem.

Definition at line 332 of file Amesos_Klu.h.

std::vector<int> Amesos_Klu::ColIndicesV_ [private]

Only used for RowMatrices to extract copies.

Definition at line 335 of file Amesos_Klu.h.

std::vector<double> Amesos_Klu::RowValuesV_ [private]

Only used for RowMatrices to extract copies.

Definition at line 337 of file Amesos_Klu.h.

Importer to process 0.

Definition at line 339 of file Amesos_Klu.h.

Definition at line 340 of file Amesos_Klu.h.

Definition at line 341 of file Amesos_Klu.h.

Quick access ids for the individual timings.

Definition at line 343 of file Amesos_Klu.h.

int Amesos_Klu::MtxConvTime_ [private]

Definition at line 343 of file Amesos_Klu.h.

Definition at line 343 of file Amesos_Klu.h.

int Amesos_Klu::SymFactTime_ [private]

Definition at line 344 of file Amesos_Klu.h.

int Amesos_Klu::NumFactTime_ [private]

Definition at line 344 of file Amesos_Klu.h.

int Amesos_Klu::SolveTime_ [private]

Definition at line 344 of file Amesos_Klu.h.

Definition at line 344 of file Amesos_Klu.h.


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