Epetra_CrsSingletonFilter: A class for explicitly eliminating matrix rows and columns. More...

#include <Epetra_CrsSingletonFilter.h>

Collaboration diagram for Epetra_CrsSingletonFilter:

Public Member Functions
Constructors/Destructor
	Epetra_CrsSingletonFilter ()
	Epetra_CrsSingletonFilter default constructor.

virtual	~Epetra_CrsSingletonFilter ()
	Epetra_CrsSingletonFilter Destructor.

Analyze methods
int	Analyze (Epetra_RowMatrix *FullMatrix)
	Analyze the input matrix, removing row/column pairs that have singletons. More...

bool	SingletonsDetected () const
	Returns true if singletons were detected in this matrix (must be called after Analyze() to be effective).

Reduce methods
int	ConstructReducedProblem (Epetra_LinearProblem *Problem)
	Return a reduced linear problem based on results of Analyze(). More...

int	UpdateReducedProblem (Epetra_LinearProblem *Problem)
	Update a reduced linear problem using new values. More...

Methods to construct Full System Solution
int	ComputeFullSolution ()
	Compute a solution for the full problem using the solution of the reduced problem, put in LHS of FullProblem(). More...

Filter Statistics
int	NumRowSingletons () const
	Return number of rows that contain a single entry, returns -1 if Analysis not performed yet.

int	NumColSingletons () const
	Return number of columns that contain a single entry that are not associated with singleton row, returns -1 if Analysis not performed yet.

int	NumSingletons () const
	Return total number of singletons detected, returns -1 if Analysis not performed yet. More...

double	RatioOfDimensions () const
	Returns ratio of reduced system to full system dimensions, returns -1.0 if reduced problem not constructed.

double	RatioOfNonzeros () const
	Returns ratio of reduced system to full system nonzero count, returns -1.0 if reduced problem not constructed.

Attribute Access Methods
Epetra_LinearProblem *	FullProblem () const
	Returns pointer to the original unreduced Epetra_LinearProblem.

Epetra_LinearProblem *	ReducedProblem () const
	Returns pointer to the derived reduced Epetra_LinearProblem.

Epetra_RowMatrix *	FullMatrix () const
	Returns pointer to Epetra_CrsMatrix from full problem.

Epetra_CrsMatrix *	ReducedMatrix () const
	Returns pointer to Epetra_CrsMatrix from full problem.

Epetra_MapColoring *	RowMapColors () const
	Returns pointer to Epetra_MapColoring object: color 0 rows are part of reduced system.

Epetra_MapColoring *	ColMapColors () const
	Returns pointer to Epetra_MapColoring object: color 0 columns are part of reduced system.

Epetra_Map *	ReducedMatrixRowMap () const
	Returns pointer to Epetra_Map describing the reduced system row distribution.

Epetra_Map *	ReducedMatrixColMap () const
	Returns pointer to Epetra_Map describing the reduced system column distribution.

Epetra_Map *	ReducedMatrixDomainMap () const
	Returns pointer to Epetra_Map describing the domain map for the reduced system.

Epetra_Map *	ReducedMatrixRangeMap () const
	Returns pointer to Epetra_Map describing the range map for the reduced system.

Protected Member Functions
Epetra_CrsMatrix *	FullCrsMatrix () const

const Epetra_Map &	FullMatrixRowMap () const

const Epetra_Map &	FullMatrixColMap () const

const Epetra_Map &	FullMatrixDomainMap () const

const Epetra_Map &	FullMatrixRangeMap () const

void	InitializeDefaults ()

int	ComputeEliminateMaps ()

int	Setup (Epetra_LinearProblem *Problem)

int	InitFullMatrixAccess ()

int	GetRow (int Row, int &NumIndices, int *&Indices)

int	GetRowGCIDs (int Row, int &NumIndices, double &Values, int &GlobalIndices)

int	GetRow (int Row, int &NumIndices, double &Values, int &Indices)

int	CreatePostSolveArrays (const Epetra_IntVector &RowIDs, const Epetra_MapColoring &RowMapColors, const Epetra_IntVector &ColProfiles, const Epetra_IntVector &NewColProfiles, const Epetra_IntVector &ColHasRowWithSingleton)

int	ConstructRedistributeExporter (Epetra_Map SourceMap, Epetra_Map TargetMap, Epetra_Export &RedistributeExporter, Epetra_Map &RedistributeMap)

Protected Attributes
Epetra_LinearProblem *	FullProblem_

Epetra_LinearProblem *	ReducedProblem_

Epetra_RowMatrix *	FullMatrix_

Epetra_CrsMatrix *	FullCrsMatrix_

Epetra_CrsMatrix *	ReducedMatrix_

Epetra_MultiVector *	ReducedRHS_

Epetra_MultiVector *	ReducedLHS_

Epetra_Map *	ReducedMatrixRowMap_

Epetra_Map *	ReducedMatrixColMap_

Epetra_Map *	ReducedMatrixDomainMap_

Epetra_Map *	ReducedMatrixRangeMap_

Epetra_Map *	OrigReducedMatrixDomainMap_

Epetra_Import *	Full2ReducedRHSImporter_

Epetra_Import *	Full2ReducedLHSImporter_

Epetra_Export *	RedistributeDomainExporter_

int *	ColSingletonRowLIDs_

int *	ColSingletonColLIDs_

int *	ColSingletonPivotLIDs_

double *	ColSingletonPivots_

int	AbsoluteThreshold_

double	RelativeThreshold_

int	NumMyRowSingletons_

int	NumMyColSingletons_

int	NumGlobalRowSingletons_

int	NumGlobalColSingletons_

double	RatioOfDimensions_

double	RatioOfNonzeros_

bool	HaveReducedProblem_

bool	UserDefinedEliminateMaps_

bool	AnalysisDone_

bool	SymmetricElimination_

Epetra_MultiVector *	tempExportX_

Epetra_MultiVector *	tempX_

Epetra_MultiVector *	tempB_

Epetra_MultiVector *	RedistributeReducedLHS_

int *	Indices_

Epetra_SerialDenseVector	Values_

Epetra_MapColoring *	RowMapColors_

Epetra_MapColoring *	ColMapColors_

bool	FullMatrixIsCrsMatrix_

int	MaxNumMyEntries_

Detailed Description

Epetra_CrsSingletonFilter: A class for explicitly eliminating matrix rows and columns.

The Epetra_CrsSingletonFilter class takes an existing Epetra_LinearProblem object, analyzes
it structure and explicitly eliminates singleton rows and columns from the matrix and appropriately
modifies the RHS and LHS of the linear problem.  The result of this process is a reduced system of equations
that is itself an Epetra_LinearProblem object.  The reduced system can then be solved using any solver that
is understands an Epetra_LinearProblem.  The solution for the full system is obtained by calling ComputeFullSolution().

Singleton rows are defined to be rows that have a single nonzero entry in the matrix.  The equation associated with
this row can be explicitly eliminated because it involved only one variable.  For example if row i has a single nonzero
value in column j, call it A(i,j), we can explicitly solve for x(j) = b(i)/A(i,j), where b(i) is the ith entry of the RHS
and x(j) is the jth entry of the LHS.

Singleton columns are defined to be columns that have a single nonzero entry in the matrix.  The variable associated
with this column is fully dependent, meaning that the solution for all other variables does not depend on it.  If this
entry is A(i,j) then the ith row and jth column can be removed from the system and x(j) can be solved after the solution
for all other variables is determined.

By removing singleton rows and columns, we can often produce a reduced system that is smaller and far less dense, and in
general having better numerical properties.

The basic procedure for using this class is as follows:

Construct full problem: Construct and Epetra_LinearProblem containing the "full" matrix, RHS and LHS. This is done outside of Epetra_CrsSingletonFilter class. Presumably, you have some reason to believe that this system may contain singletons.
Construct an Epetra_CrsSingletonFilter instance: Constructor needs no arguments.
Analyze matrix: Invoke the Analyze() method, passing in the Epetra_RowMatrix object from your full linear problem mentioned in the first step above.
Go/No Go decision to construct reduced problem: Query the results of the Analyze method using the SingletonsDetected() method. This method returns "true" if there were singletons found in the matrix. You can also query any of the other methods in the Filter Statistics section to determine if you want to proceed with the construction of the reduced system.
Construct reduced problem: If, in the previous step, you determine that you want to proceed with the construction of the reduced problem, you should next call the ConstructReducedProblem() method, passing in the full linear problem object from the first step. This method will use the information from the Analyze() method to construct a reduce problem that has explicitly eliminated the singleton rows, solved for the corresponding LHS values and updated the RHS. This step will also remove singleton columns from the reduced system. Once the solution of the reduced problem is is computed (via any solver that understands an Epetra_LinearProblem), you should call the ComputeFullSolution() method to compute the LHS values assocaited with the singleton columns.
Solve reduced problem: Obtain a pointer to the reduced problem using the ReducedProblem() method. Using the solver of your choice, solve the reduced system.
Compute solution to full problem: Once the solution the reduced problem is determined, the ComputeFullSolution() method will place the reduced solution values into the appropriate locations of the full solution LHS and then compute the values associated with column singletons. At this point, you have a complete solution to the original full problem.
Solve a subsequent full problem that differs from the original problem only in values: It is often the case that the structure of a problem will be the same for a sequence of linear problems. In this case, the UpdateReducedProblem() method can be useful. After going through the above process one time, if you have a linear problem that is structural identical to the previous problem, you can minimize memory and time costs by using the UpdateReducedProblem() method, passing in the subsequent problem. Once you have called the UpdateReducedProblem() method, you can then solve the reduce problem problem as you wish, and then compute the full solution as before. The pointer generated by ReducedProblem() will not change when UpdateReducedProblem() is called.

Member Function Documentation

int Epetra_CrsSingletonFilter::Analyze ( Epetra_RowMatrix * FullMatrix )

Analyze the input matrix, removing row/column pairs that have singletons.

Analyzes the user's input matrix to determine rows and columns that should be explicitly eliminated to create the reduced system. Look for rows and columns that have single entries. These rows/columns can easily be removed from the problem. The results of calling this method are two MapColoring objects accessible via RowMapColors() and ColMapColors() accessor methods. All rows/columns that would be eliminated in the reduced system have a color of 1 in the corresponding RowMapColors/ColMapColors object. All kept rows/cols have a color of 0.

int Epetra_CrsSingletonFilter::ComputeFullSolution ( )

Compute a solution for the full problem using the solution of the reduced problem, put in LHS of FullProblem().

After solving the reduced linear system, this method can be called to compute the solution to the original problem, assuming the solution for the reduced system is valid. The solution of the unreduced, original problem will be in the LHS of the original Epetra_LinearProblem.

int Epetra_CrsSingletonFilter::ConstructReducedProblem ( Epetra_LinearProblem * Problem )

Return a reduced linear problem based on results of Analyze().

Creates a new Epetra_LinearProblem object based on the results of the Analyze phase. A pointer to the reduced problem is obtained via a call to ReducedProblem().

Returns: Error code, set to 0 if no error.

int Epetra_CrsSingletonFilter::NumSingletons ( ) const

inline

Return total number of singletons detected, returns -1 if Analysis not performed yet.

Return total number of singletons detected across all processors. This method will not return a valid result until after the Analyze() method is called. The dimension of the reduced system can be computed by subtracting this number from dimension of full system.

Warning: This method returns -1 if Analyze() method has not been called.

References NumColSingletons(), and NumRowSingletons().

int Epetra_CrsSingletonFilter::UpdateReducedProblem ( Epetra_LinearProblem * Problem )

Update a reduced linear problem using new values.

Updates an existing Epetra_LinearProblem object using new matrix, LHS and RHS values. The matrix structure must be identical to the matrix that was used to construct the original reduced problem.

Returns: Error code, set to 0 if no error.

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

Epetra_CrsSingletonFilter.h

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation