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Ifpack_CrsRiluk: A class for constructing and using an incomplete lower/upper (ILU) factorization of a given Epetra_RowMatrix. More...
#include <Ifpack_CrsRiluk.h>
Public Member Functions  
Ifpack_CrsRiluk (const Ifpack_IlukGraph &Graph_in)  
Ifpack_CrsRiluk constuctor with variable number of indices per row. More...  
Ifpack_CrsRiluk (const Ifpack_CrsRiluk &Matrix)  
Copy constructor. More...  
virtual  ~Ifpack_CrsRiluk () 
Ifpack_CrsRiluk Destructor. More...  
int  InitValues (const Epetra_CrsMatrix &A) 
Initialize L and U with values from user matrix A. More...  
int  InitValues (const Epetra_VbrMatrix &A) 
Initialize L and U with values from user matrix A. More...  
bool  ValuesInitialized () const 
If values have been initialized, this query returns true, otherwise it returns false. More...  
void  SetRelaxValue (double RelaxValue) 
Set RILU(k) relaxation parameter. More...  
void  SetAbsoluteThreshold (double Athresh) 
Set absolute threshold value. More...  
void  SetRelativeThreshold (double Rthresh) 
Set relative threshold value. More...  
void  SetOverlapMode (Epetra_CombineMode OverlapMode) 
Set overlap mode type. More...  
int  SetParameters (const Teuchos::ParameterList ¶meterlist, bool cerr_warning_if_unused=false) 
Set parameters using a Teuchos::ParameterList object. More...  
int  Factor () 
Compute ILU factors L and U using the specified graph, diagonal perturbation thresholds and relaxation parameters. More...  
bool  Factored () const 
If factor is completed, this query returns true, otherwise it returns false. More...  
int  Solve (bool Trans, const Epetra_MultiVector &X, Epetra_MultiVector &Y) const 
Returns the result of a Ifpack_CrsRiluk forward/back solve on a Epetra_MultiVector X in Y (works for Epetra_Vectors also). More...  
int  Multiply (bool Trans, const Epetra_MultiVector &X, Epetra_MultiVector &Y) const 
Returns the result of multiplying U, D and L in that order on an Epetra_MultiVector X in Y. More...  
int  Condest (bool Trans, double &ConditionNumberEstimate) const 
Returns the maximum over all the condition number estimate for each local ILU set of factors. More...  
double  GetRelaxValue () 
Get RILU(k) relaxation parameter. More...  
double  GetAbsoluteThreshold () 
Get absolute threshold value. More...  
double  GetRelativeThreshold () 
Get relative threshold value. More...  
Epetra_CombineMode  GetOverlapMode () 
Get overlap mode type. More...  
int  NumGlobalRows () const 
Returns the number of global matrix rows. More...  
int  NumGlobalCols () const 
Returns the number of global matrix columns. More...  
int  NumGlobalNonzeros () const 
Returns the number of nonzero entries in the global graph. More...  
virtual int  NumGlobalBlockDiagonals () const 
Returns the number of diagonal entries found in the global input graph. More...  
long long  NumGlobalRows64 () const 
long long  NumGlobalCols64 () const 
long long  NumGlobalNonzeros64 () const 
virtual long long  NumGlobalBlockDiagonals64 () const 
int  NumMyRows () const 
Returns the number of local matrix rows. More...  
int  NumMyCols () const 
Returns the number of local matrix columns. More...  
int  NumMyNonzeros () const 
Returns the number of nonzero entries in the local graph. More...  
virtual int  NumMyBlockDiagonals () const 
Returns the number of diagonal entries found in the local input graph. More...  
virtual int  NumMyDiagonals () const 
Returns the number of nonzero diagonal values found in matrix. More...  
int  IndexBase () const 
Returns the index base for row and column indices for this graph. More...  
long long  IndexBase64 () const 
const Ifpack_IlukGraph &  Graph () const 
returns the address of the Ifpack_IlukGraph associated with this factored matrix. More...  
const Epetra_CrsMatrix &  L () const 
Returns the address of the L factor associated with this factored matrix. More...  
const Epetra_Vector &  D () const 
Returns the address of the D factor associated with this factored matrix. More...  
const Epetra_CrsMatrix &  U () const 
Returns the address of the L factor associated with this factored matrix. More...  
Protected Member Functions  
void  SetFactored (bool Flag) 
void  SetValuesInitialized (bool Flag) 
bool  Allocated () const 
int  SetAllocated (bool Flag) 
int  BlockGraph2PointGraph (const Epetra_CrsGraph &BG, Epetra_CrsGraph &PG, bool Upper) 
Private Member Functions  
int  AllocateCrs () 
int  AllocateVbr () 
int  InitAllValues (const Epetra_RowMatrix &A, int MaxNumEntries) 
int  BlockMap2PointMap (const Epetra_BlockMap &BlockMap, Teuchos::RefCountPtr< Epetra_Map > *PointMap) 
int  GenerateXY (bool Trans, const Epetra_MultiVector &Xin, const Epetra_MultiVector &Yin, Teuchos::RefCountPtr< Epetra_MultiVector > *Xout, Teuchos::RefCountPtr< Epetra_MultiVector > *Yout) const 
Friends  
std::ostream &  operator<< (std::ostream &os, const Ifpack_CrsRiluk &A) 
<< operator will work for Ifpack_CrsRiluk. More...  
const char *  Label () const 
Returns a character string describing the operator. More...  
int  SetUseTranspose (bool UseTranspose_in) 
If set true, transpose of this operator will be applied. More...  
int  Apply (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const 
Returns the result of a Epetra_Operator applied to a Epetra_MultiVector X in Y. More...  
int  ApplyInverse (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const 
Returns the result of a Epetra_Operator inverse applied to an Epetra_MultiVector X in Y. More...  
double  NormInf () const 
Returns 0.0 because this class cannot compute Infnorm. More...  
bool  HasNormInf () const 
Returns false because this class cannot compute an Infnorm. More...  
bool  UseTranspose () const 
Returns the current UseTranspose setting. More...  
const Epetra_Map &  OperatorDomainMap () const 
Returns the Epetra_Map object associated with the domain of this operator. More...  
const Epetra_Map &  OperatorRangeMap () const 
Returns the Epetra_Map object associated with the range of this operator. More...  
const Epetra_Comm &  Comm () const 
Returns the Epetra_BlockMap object associated with the range of this matrix operator. More...  
Ifpack_CrsRiluk: A class for constructing and using an incomplete lower/upper (ILU) factorization of a given Epetra_RowMatrix.
The Ifpack_CrsRiluk class computes a "Relaxed" ILU factorization with level k fill of a given Epetra_CrsMatrix. The factorization that is produced is a function of several parameters:
The pattern of the matrix  All fill is derived from the original matrix nonzero structure. Level zero fill is defined as the original matrix pattern (nonzero structure), even if the matrix value at an entry is stored as a zero. (Thus it is possible to add entries to the ILU factors by adding zero entries the original matrix.)
Level of fill  Starting with the original matrix pattern as level fill of zero, the next level of fill is determined by analyzing the graph of the previous level and determining nonzero fill that is a result of combining entries that were from previous level only (not the current level). This rule limits fill to entries that are direct decendents from the previous level graph. Fill for level k is determined by applying this rule recursively. For sufficiently large values of k, the fill would eventually be complete and an exact LU factorization would be computed. Level of fill is defined during the construction of the Ifpack_IlukGraph object.
Level of overlap  All Ifpack preconditioners work on parallel distributed memory computers by using the row partitioning the user input matrix to determine the partitioning for local ILU factors. If the level of overlap is set to zero, the rows of the user matrix that are stored on a given processor are treated as a selfcontained local matrix and all column entries that reach to offprocessor entries are ignored. Setting the level of overlap to one tells Ifpack to increase the size of the local matrix by adding rows that are reached to by rows owned by this processor. Increasing levels of overlap are defined recursively in the same way. For sufficiently large levels of overlap, the entire matrix would be part of each processor's local ILU factorization process. Level of overlap is defined during the construction of the Ifpack_IlukGraph object.
Once the factorization is computed, applying the factorization (LUy = x) results in redundant approximations for any elements of y that correspond to rows that are part of more than one local ILU factor. The OverlapMode (changed by calling SetOverlapMode()) defines how these redundancies are handled using the Epetra_CombineMode enum. The default is to zero out all values of y for rows that were not part of the original matrix row distribution.
Fraction of relaxation  Ifpack_CrsRiluk computes the ILU factorization rowbyrow. As entries at a given row are computed, some number of them will be dropped because they do match the prescribed sparsity pattern. The relaxation factor determines how these dropped values will be handled. If the RelaxValue (changed by calling SetRelaxValue()) is zero, then these extra entries will by dropped. This is a classical ILU approach. If the RelaxValue is 1, then the sum of the extra entries will be added to the diagonal. This is a classical Modified ILU (MILU) approach. If RelaxValue is between 0 and 1, then RelaxValue times the sum of extra entries will be added to the diagonal.
For most situations, RelaxValue should be set to zero. For certain kinds of problems, e.g., reservoir modeling, there is a conservation principle involved such that any operator should obey a zero rowsum property. MILU was designed for these cases and you should set the RelaxValue to 1. For other situations, setting RelaxValue to some nonzero value may improve the stability of factorization, and can be used if the computed ILU factors are poorly conditioned.
Estimating Preconditioner Condition Numbers
For illconditioned matrices, we often have difficulty computing usable incomplete factorizations. The most common source of problems is that the factorization may encounter a small or zero pivot, in which case the factorization can fail, or even if the factorization succeeds, the factors may be so poorly conditioned that use of them in the iterative phase produces meaningless results. Before we can fix this problem, we must be able to detect it. To this end, we use a simple but effective condition number estimate for .
The condition of a matrix , called , is defined as in some appropriate norm . gives some indication of how many accurate floating point digits can be expected from operations involving the matrix and its inverse. A condition number approaching the accuracy of a given floating point number system, about 15 decimal digits in IEEE double precision, means that any results involving or may be meaningless.
The norm of a vector is defined as the maximum of the absolute values of the vector entries, and the norm of a matrix C is defined as . A crude lower bound for the is where . It is a lower bound because .
For our purposes, we want to estimate , where and are our incomplete factors. Edmond in his Ph.D. thesis demonstrates that provides an effective estimate for . Furthermore, since finding such that is a basic kernel for applying the preconditioner, computing this estimate of is performed by setting , calling the solve kernel to compute and then computing .
A priori Diagonal Perturbations
Given the above method to estimate the conditioning of the incomplete factors, if we detect that our factorization is too illconditioned we can improve the conditioning by perturbing the matrix diagonal and restarting the factorization using this more diagonally dominant matrix. In order to apply perturbation, prior to starting the factorization, we compute a diagonal perturbation of our matrix and perform the factorization on this perturbed matrix. The overhead cost of perturbing the diagonal is minimal since the first step in computing the incomplete factors is to copy the matrix into the memory space for the incomplete factors. We simply compute the perturbed diagonal at this point.
The actual perturbation values we use are the diagonal values with , , where is the matrix dimension and returns the sign of the diagonal entry. This has the effect of forcing the diagonal values to have minimal magnitude of and to increase each by an amount proportional to , and still keep the sign of the original diagonal entry.
Constructing Ifpack_CrsRiluk objects
Constructing Ifpack_CrsRiluk objects is a multistep process. The basic steps are as follows:
Note that, even after a matrix is constructed, it is possible to update existing matrix entries. It is not possible to create new entries.
Counting Floating Point Operations
Each Ifpack_CrsRiluk object keep track of the number of serial floating point operations performed using the specified object as the this argument to the function. The Flops() function returns this number as a double precision number. Using this information, in conjunction with the Epetra_Time class, one can get accurate parallel performance numbers. The ResetFlops() function resets the floating point counter.
Definition at line 210 of file Ifpack_CrsRiluk.h.
Ifpack_CrsRiluk::Ifpack_CrsRiluk  (  const Ifpack_IlukGraph &  Graph_in  ) 
Ifpack_CrsRiluk constuctor with variable number of indices per row.
Creates a Ifpack_CrsRiluk object and allocates storage.
In  Graph_in  Graph generated by Ifpack_IlukGraph. 
Definition at line 55 of file Ifpack_CrsRiluk.cpp.
Ifpack_CrsRiluk::Ifpack_CrsRiluk  (  const Ifpack_CrsRiluk &  Matrix  ) 
Copy constructor.
Definition at line 76 of file Ifpack_CrsRiluk.cpp.

virtual 
Ifpack_CrsRiluk Destructor.
Definition at line 105 of file Ifpack_CrsRiluk.cpp.
int Ifpack_CrsRiluk::InitValues  (  const Epetra_CrsMatrix &  A  ) 
Initialize L and U with values from user matrix A.
Copies values from the user's matrix into the nonzero pattern of L and U.
In  A  User matrix to be factored. 
Definition at line 182 of file Ifpack_CrsRiluk.cpp.
int Ifpack_CrsRiluk::InitValues  (  const Epetra_VbrMatrix &  A  ) 
Initialize L and U with values from user matrix A.
Copies values from the user's matrix into the nonzero pattern of L and U.
In  A  User matrix to be factored. 
Definition at line 212 of file Ifpack_CrsRiluk.cpp.

inline 
If values have been initialized, this query returns true, otherwise it returns false.
Definition at line 252 of file Ifpack_CrsRiluk.h.

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Set RILU(k) relaxation parameter.
Definition at line 255 of file Ifpack_CrsRiluk.h.

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Set absolute threshold value.
Definition at line 258 of file Ifpack_CrsRiluk.h.

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Set relative threshold value.
Definition at line 261 of file Ifpack_CrsRiluk.h.

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Set overlap mode type.
Definition at line 264 of file Ifpack_CrsRiluk.h.
int Ifpack_CrsRiluk::SetParameters  (  const Teuchos::ParameterList &  parameterlist, 
bool  cerr_warning_if_unused = false 

) 
Set parameters using a Teuchos::ParameterList object.
Definition at line 162 of file Ifpack_CrsRiluk.cpp.
int Ifpack_CrsRiluk::Factor  (  void  ) 
Compute ILU factors L and U using the specified graph, diagonal perturbation thresholds and relaxation parameters.
This function computes the RILU(k) factors L and U using the current:
InitValues() must be called before the factorization can proceed.
Definition at line 361 of file Ifpack_CrsRiluk.cpp.

inline 
If factor is completed, this query returns true, otherwise it returns false.
Definition at line 289 of file Ifpack_CrsRiluk.h.
int Ifpack_CrsRiluk::Solve  (  bool  Trans, 
const Epetra_MultiVector &  X,  
Epetra_MultiVector &  Y  
)  const 
Returns the result of a Ifpack_CrsRiluk forward/back solve on a Epetra_MultiVector X in Y (works for Epetra_Vectors also).
In  Trans If true, solve transpose problem. 
In  X  A Epetra_MultiVector of dimension NumVectors to solve for. 
Out  Y A Epetra_MultiVector of dimension NumVectorscontaining result. 
Definition at line 513 of file Ifpack_CrsRiluk.cpp.
int Ifpack_CrsRiluk::Multiply  (  bool  Trans, 
const Epetra_MultiVector &  X,  
Epetra_MultiVector &  Y  
)  const 
Returns the result of multiplying U, D and L in that order on an Epetra_MultiVector X in Y.
In  Trans If true, multiply by L^T, D and U^T in that order. 
In  X  A Epetra_MultiVector of dimension NumVectors to solve for. 
Out  Y A Epetra_MultiVector of dimension NumVectorscontaining result. 
Definition at line 554 of file Ifpack_CrsRiluk.cpp.
int Ifpack_CrsRiluk::Condest  (  bool  Trans, 
double &  ConditionNumberEstimate  
)  const 
Returns the maximum over all the condition number estimate for each local ILU set of factors.
This functions computes a local condition number estimate on each processor and return the maximum over all processor of the estimate.
In  Trans If true, solve transpose problem. 
Out  ConditionNumberEstimate  The maximum across all processors of the infinitynorm estimate of the condition number of the inverse of LDU. 
Definition at line 596 of file Ifpack_CrsRiluk.cpp.

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Get RILU(k) relaxation parameter.
Definition at line 334 of file Ifpack_CrsRiluk.h.

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Get absolute threshold value.
Definition at line 337 of file Ifpack_CrsRiluk.h.

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Get relative threshold value.
Definition at line 340 of file Ifpack_CrsRiluk.h.

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Get overlap mode type.
Definition at line 343 of file Ifpack_CrsRiluk.h.

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Returns the number of global matrix rows.
Definition at line 348 of file Ifpack_CrsRiluk.h.

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Returns the number of global matrix columns.
Definition at line 351 of file Ifpack_CrsRiluk.h.

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Returns the number of nonzero entries in the global graph.
Definition at line 354 of file Ifpack_CrsRiluk.h.

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Returns the number of diagonal entries found in the global input graph.
Definition at line 357 of file Ifpack_CrsRiluk.h.

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Definition at line 360 of file Ifpack_CrsRiluk.h.

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Definition at line 361 of file Ifpack_CrsRiluk.h.

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Definition at line 362 of file Ifpack_CrsRiluk.h.

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Definition at line 363 of file Ifpack_CrsRiluk.h.

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Returns the number of local matrix rows.
Definition at line 366 of file Ifpack_CrsRiluk.h.

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Returns the number of local matrix columns.
Definition at line 369 of file Ifpack_CrsRiluk.h.

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Returns the number of nonzero entries in the local graph.
Definition at line 372 of file Ifpack_CrsRiluk.h.

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Returns the number of diagonal entries found in the local input graph.
Definition at line 375 of file Ifpack_CrsRiluk.h.

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Returns the number of nonzero diagonal values found in matrix.
Definition at line 378 of file Ifpack_CrsRiluk.h.

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Returns the index base for row and column indices for this graph.
Definition at line 382 of file Ifpack_CrsRiluk.h.

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Definition at line 384 of file Ifpack_CrsRiluk.h.

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returns the address of the Ifpack_IlukGraph associated with this factored matrix.
Definition at line 387 of file Ifpack_CrsRiluk.h.

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Returns the address of the L factor associated with this factored matrix.
Definition at line 390 of file Ifpack_CrsRiluk.h.

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Returns the address of the D factor associated with this factored matrix.
Definition at line 393 of file Ifpack_CrsRiluk.h.

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Returns the address of the L factor associated with this factored matrix.
Definition at line 396 of file Ifpack_CrsRiluk.h.

inlinevirtual 
Returns a character string describing the operator.
Implements Epetra_Operator.
Definition at line 401 of file Ifpack_CrsRiluk.h.

inlinevirtual 
If set true, transpose of this operator will be applied.
This flag allows the transpose of the given operator to be used implicitly. Setting this flag affects only the Apply() and ApplyInverse() methods. If the implementation of this interface does not support transpose use, this method should return a value of 1.
In  UseTranspose_in If true, multiply by the transpose of operator, otherwise just use operator. 
Implements Epetra_Operator.
Definition at line 413 of file Ifpack_CrsRiluk.h.

inlinevirtual 
Returns the result of a Epetra_Operator applied to a Epetra_MultiVector X in Y.
Note that this implementation of Apply does NOT perform a forward back solve with the LDU factorization. Instead it applies these operators via multiplication with U, D and L respectively. The ApplyInverse() method performs a solve.
In  X  A Epetra_MultiVector of dimension NumVectors to multiply with matrix. 
Out  Y A Epetra_MultiVector of dimension NumVectors containing result. 
Implements Epetra_Operator.
Definition at line 427 of file Ifpack_CrsRiluk.h.

inlinevirtual 
Returns the result of a Epetra_Operator inverse applied to an Epetra_MultiVector X in Y.
In this implementation, we use several existing attributes to determine how virtual method ApplyInverse() should call the concrete method Solve(). We pass in the UpperTriangular(), the Epetra_CrsMatrix::UseTranspose(), and NoDiagonal() methods. The most notable warning is that if a matrix has no diagonal values we assume that there is an implicit unit diagonal that should be accounted for when doing a triangular solve.
In  X  A Epetra_MultiVector of dimension NumVectors to solve for. 
Out  Y A Epetra_MultiVector of dimension NumVectors containing result. 
Implements Epetra_Operator.
Definition at line 444 of file Ifpack_CrsRiluk.h.

inlinevirtual 
Returns 0.0 because this class cannot compute Infnorm.
Implements Epetra_Operator.
Definition at line 448 of file Ifpack_CrsRiluk.h.

inlinevirtual 
Returns false because this class cannot compute an Infnorm.
Implements Epetra_Operator.
Definition at line 451 of file Ifpack_CrsRiluk.h.

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Returns the current UseTranspose setting.
Implements Epetra_Operator.
Definition at line 454 of file Ifpack_CrsRiluk.h.

inlinevirtual 
Returns the Epetra_Map object associated with the domain of this operator.
Implements Epetra_Operator.
Definition at line 457 of file Ifpack_CrsRiluk.h.

inlinevirtual 
Returns the Epetra_Map object associated with the range of this operator.
Implements Epetra_Operator.
Definition at line 460 of file Ifpack_CrsRiluk.h.

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Returns the Epetra_BlockMap object associated with the range of this matrix operator.
Implements Epetra_Operator.
Definition at line 463 of file Ifpack_CrsRiluk.h.

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Definition at line 467 of file Ifpack_CrsRiluk.h.

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Definition at line 614 of file Ifpack_CrsRiluk.cpp.

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<< operator will work for Ifpack_CrsRiluk.
Definition at line 795 of file Ifpack_CrsRiluk.cpp.

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