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)|
|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_|
|Epetra_MultiVector * ||tempExportX_|
|Epetra_MultiVector * ||tempX_|
|Epetra_MultiVector * ||tempB_|
|Epetra_MultiVector * ||RedistributeReducedLHS_|
|int * ||Indices_|
|Epetra_MapColoring * ||RowMapColors_|
|Epetra_MapColoring * ||ColMapColors_|
Private Member Functions
| ||Epetra_CrsSingletonFilter (const Epetra_CrsSingletonFilter &Problem)|
| ||Copy constructor (defined as private so it is unavailable to user). |
|Epetra_CrsSingletonFilter & ||operator= (const Epetra_CrsSingletonFilter &Problem)|
| ||Epetra_CrsSingletonFilter ()|
| ||Epetra_CrsSingletonFilter default constructor. |
|virtual ||~Epetra_CrsSingletonFilter ()|
| ||Epetra_CrsSingletonFilter Destructor. |
|int ||Analyze (Epetra_RowMatrix *FullMatrix)|
| ||Analyze the input matrix, removing row/column pairs that have singletons. |
|bool ||SingletonsDetected () const |
| ||Returns true if singletons were detected in this matrix (must be called after Analyze() to be effective). |
|int ||ConstructReducedProblem (Epetra_LinearProblem *Problem)|
| ||Return a reduced linear problem based on results of Analyze(). |
|int ||UpdateReducedProblem (Epetra_LinearProblem *Problem)|
| ||Update a reduced linear problem using new values. |
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(). |
|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. |
|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. |
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.
Definition at line 115 of file Epetra_CrsSingletonFilter.h.