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Epetra_SerialDenseSVD Class Reference

Epetra_SerialDenseSVD: A class for SVDing dense linear problems. More...

`#include <Epetra_SerialDenseSVD.h>`

Inheritance diagram for Epetra_SerialDenseSVD:
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List of all members.

## Public Member Functions

void AllocateWORK ()
void AllocateIWORK ()
void InitPointers ()
void DeleteArrays ()
void ResetMatrix ()
void ResetVectors ()
Constructor/Destructor Methods
Epetra_SerialDenseSVD ()
Default constructor; matrix should be set using SetMatrix(), LHS and RHS set with SetVectors().
virtual ~Epetra_SerialDenseSVD ()
Epetra_SerialDenseSVD destructor.
Set Methods
int SetMatrix (Epetra_SerialDenseMatrix &A)
Sets the pointers for coefficient matrix.
int SetVectors (Epetra_SerialDenseMatrix &X, Epetra_SerialDenseMatrix &B)
Sets the pointers for left and right hand side vector(s).
Strategy modifying Methods
void SolveWithTranspose (bool Flag)
Causes equilibration to be called just before the matrix factorization as part of the call to Factor.
Factor/Solve/Invert Methods

Causes all solves to compute solution to best ability using iterative refinement.

virtual int Factor (void)
virtual int Solve (void)
Computes the solution X to AX = B for the this matrix and the B provided to SetVectors()..
virtual int Invert (double rthresh=0.0, double athresh=0.0)
Inverts the this matrix.
Query methods
bool Transpose ()
Returns true if transpose of this matrix has and will be used.
bool Factored ()
Returns true if matrix is factored (factor available via AF() and LDAF()).
bool Inverted ()
Returns true if matrix inverse has been computed (inverse available via AF() and LDAF()).
bool Solved ()
Returns true if the current set of vectors has been solved.
Data Accessor methods
Epetra_SerialDenseMatrixMatrix () const
Returns pointer to current matrix.
Epetra_SerialDenseMatrixInvertedMatrix () const
Returns pointer to inverted matrix (assuming inverse has been performed).
Epetra_SerialDenseMatrixLHS () const
Returns pointer to current LHS.
Epetra_SerialDenseMatrixRHS () const
Returns pointer to current RHS.
int M () const
Returns row dimension of system.
int N () const
Returns column dimension of system.
double * A () const
Returns pointer to the this matrix.
int LDA () const
Returns the leading dimension of the this matrix.
double * B () const
Returns pointer to current RHS.
int LDB () const
Returns the leading dimension of the RHS.
int NRHS () const
Returns the number of current right hand sides and solution vectors.
double * X () const
Returns pointer to current solution.
int LDX () const
Returns the leading dimension of the solution.
double * S () const
double * AI () const
Returns pointer to the inverted matrix (may be the same as A() if factorization done in place).
int LDAI () const
Returns the leading dimension of the inverted matrix.
double ANORM () const
Returns the 1-Norm of the this matrix (returns -1 if not yet computed).
I/O methods
virtual void Print (ostream &os) const
Print service methods; defines behavior of ostream << operator.
Additional methods for support of Epetra_SerialDenseOperator interface
virtual int SetUseTranspose (bool use_transpose)
If set true, transpose of this operator will be applied.
virtual int Apply (const Epetra_SerialDenseMatrix &Xmat, Epetra_SerialDenseMatrix &Ymat)
Returns the result of a Epetra_SerialDenseOperator applied to a Epetra_SerialDenseMatrix X in Y.
virtual int ApplyInverse (const Epetra_SerialDenseMatrix &Xmat, Epetra_SerialDenseMatrix &Ymat)
Returns the result of a Epetra_SerialDenseOperator inverse applied to an Epetra_SerialDenseMatrix X in Y.
virtual double NormInf () const
Returns the infinity norm of the global matrix.
virtual const char * Label () const
Returns a character string describing the operator.
virtual bool UseTranspose () const
Returns the current UseTranspose setting.
virtual bool HasNormInf () const
Returns true if the this object can provide an approximate Inf-norm, false otherwise.
virtual int RowDim () const
Returns the row dimension of operator.
virtual int ColDim () const
Returns the column dimension of operator.

## Public Attributes

bool Transpose_
bool Factored_
bool Solved_
bool Inverted_
char TRANS_
int M_
int N_
int Min_MN_
int NRHS_
int LDA_
int LDAI_
int LDB_
int LDX_
int INFO_
int LWORK_
int * IWORK_
double ANORM_
Epetra_SerialDenseMatrixMatrix_
Epetra_SerialDenseMatrixLHS_
Epetra_SerialDenseMatrixRHS_
Epetra_SerialDenseMatrixInverse_
double * A_
double * AI_
double * WORK_
double * U_
double * S_
double * Vt_
double * B_
double * X_
bool UseTranspose_

## Detailed Description

Epetra_SerialDenseSVD: A class for SVDing dense linear problems.

The Epetra_SerialDenseSVD class enables the definition, in terms of Epetra_SerialDenseMatrix and Epetra_SerialDenseVector objects, of a dense linear problem, followed by the solution of that problem via the most sophisticated techniques available in LAPACK.

The Epetra_SerialDenseSVD class is intended to provide full-featured support for solving linear problems for general dense rectangular (or square) matrices. It is written on top of BLAS and LAPACK and thus has excellent performance and numerical capabilities. Using this class, one can either perform simple factorizations and solves or apply all the tricks available in LAPACK to get the best possible solution for very ill-conditioned problems.

Epetra_SerialDenseSVD vs. Epetra_LAPACK

The Epetra_LAPACK class provides access to most of the same functionality as Epetra_SerialDenseSolver. The primary difference is that Epetra_LAPACK is a "thin" layer on top of LAPACK and Epetra_SerialDenseSolver attempts to provide easy access to the more sophisticated aspects of solving dense linear and eigensystems.

• When you should use Epetra_LAPACK: If you are simply looking for a convenient wrapper around the Fortran LAPACK routines and you have a well-conditioned problem, you should probably use Epetra_LAPACK directly.
• When you should use Epetra_SerialDenseSolver: If you want to (or potentially want to) solve ill-conditioned problems or want to work with a more object-oriented interface, you should probably use Epetra_SerialDenseSolver.

Constructing Epetra_SerialDenseSVD Objects

There is a single Epetra_SerialDenseSVD constructor. However, the matrix, right hand side and solution vectors must be set prior to executing most methods in this class.

Setting vectors used for linear solves

The matrix A, the left hand side X and the right hand side B (when solving AX = B, for X), can be set by appropriate set methods. Each of these three objects must be an Epetra_SerialDenseMatrix or and Epetra_SerialDenseVector object. The set methods are as follows:

Vector and Utility Functions

Once a Epetra_SerialDenseSVD is constructed, several mathematical functions can be applied to the object. Specifically:

• Factorizations.
• Solves.
• Condition estimates.
• Norms.

Counting floating point operations The Epetra_SerialDenseSVD class has Epetra_CompObject as a base class. Thus, floating point operations are counted and accumulated in the Epetra_Flop object (if any) that was set using the SetFlopCounter() method in the Epetra_CompObject base class.

Examples using Epetra_SerialDenseSVD can be found in the Epetra test directories.

## Member Function Documentation

 virtual int Epetra_SerialDenseSVD::Apply ( const Epetra_SerialDenseMatrix & Xmat, Epetra_SerialDenseMatrix & Ymat ) ` [inline, virtual]`

Returns the result of a Epetra_SerialDenseOperator applied to a Epetra_SerialDenseMatrix X in Y.

Parameters:
 In X - A Epetra_SerialDenseMatrix to multiply with operator. Out Y -A Epetra_SerialDenseMatrix containing result.
Returns:
Integer error code, set to 0 if successful.

Implements Epetra_SerialDenseOperator.

References Matrix(), and Epetra_SerialDenseMatrix::Multiply().

 virtual int Epetra_SerialDenseSVD::ApplyInverse ( const Epetra_SerialDenseMatrix & Xmat, Epetra_SerialDenseMatrix & Ymat ) ` [inline, virtual]`

Returns the result of a Epetra_SerialDenseOperator inverse applied to an Epetra_SerialDenseMatrix X in Y.

Parameters:
 In X - A Epetra_SerialDenseMatrix to solve for. Out Y -A Epetra_SerialDenseMatrix containing result.
Returns:
Integer error code, set to 0 if successful.

Implements Epetra_SerialDenseOperator.

References SetVectors(), Solve(), and SolveWithTranspose().

 virtual int Epetra_SerialDenseSVD::Invert ( double rthresh = `0.0`, double athresh = `0.0` ) ` [virtual]`

Inverts the this matrix.

Returns:
Integer error code, set to 0 if successful. Otherwise returns the LAPACK error code INFO.
 virtual int Epetra_SerialDenseSVD::SetUseTranspose ( bool use_transpose ) ` [inline, virtual]`

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.

Parameters:
 In use_transpose -If true, multiply by the transpose of operator, otherwise just use operator.
Returns:
Integer error code, set to 0 if successful. Set to -1 if this implementation does not support transpose.

Implements Epetra_SerialDenseOperator.

 int Epetra_SerialDenseSVD::SetVectors ( Epetra_SerialDenseMatrix & X, Epetra_SerialDenseMatrix & B )

Sets the pointers for left and right hand side vector(s).

Row dimension of X must match column dimension of matrix A, row dimension of B must match row dimension of A. X and B must have the same dimensions.

Referenced by ApplyInverse().

 virtual int Epetra_SerialDenseSVD::Solve ( void ) ` [virtual]`

Computes the solution X to AX = B for the this matrix and the B provided to SetVectors()..

Inverse of Matrix must be formed

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

Referenced by ApplyInverse().

 void Epetra_SerialDenseSVD::SolveWithTranspose ( bool Flag ) ` [inline]`

Causes equilibration to be called just before the matrix factorization as part of the call to Factor.

This function must be called before the factorization is performed. If Flag is true, causes all subsequent function calls to work with the transpose of this matrix, otherwise not.

Referenced by ApplyInverse().

The documentation for this class was generated from the following file:
• Epetra_SerialDenseSVD.h