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Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType > Class Template Reference

A class for constructing and using Hermitian positive definite dense matrices. More...

#include <Teuchos_SerialSpdDenseSolver.hpp>

Inheritance diagram for Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >:
Teuchos::CompObject Teuchos::Object Teuchos::BLAS< OrdinalType, ScalarType > Teuchos::LAPACK< OrdinalType, ScalarType > Teuchos::DefaultBLASImpl< OrdinalType, ScalarType >

List of all members.

Public Member Functions

Constructor/Destructor Methods
 SerialSpdDenseSolver ()
 Default constructor; matrix should be set using setMatrix(), LHS and RHS set with setVectors().
virtual ~SerialSpdDenseSolver ()
 SerialSpdDenseSolver destructor.
Set Methods
int setMatrix (const RCP< SerialSymDenseMatrix< OrdinalType, ScalarType > > &A_in)
 Sets the pointers for coefficient matrix.
int setVectors (const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > &X, const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > &B)
 Sets the pointers for left and right hand side vector(s).
Strategy Modifying Methods
void factorWithEquilibration (bool flag)
 Causes equilibration to be called just before the matrix factorization as part of the call to factor.
void solveToRefinedSolution (bool flag)
 Causes all solves to compute solution to best ability using iterative refinement.
void estimateSolutionErrors (bool flag)
 Causes all solves to estimate the forward and backward solution error.
Factor/Solve/Invert Methods
int factor ()
 Computes the in-place Cholesky factorization of the matrix using the LAPACK routine DPOTRF.
int solve ()
 Computes the solution X to AX = B for the this matrix and the B provided to SetVectors()..
int invert ()
 Inverts the this matrix.
int computeEquilibrateScaling ()
 Computes the scaling vector S(i) = 1/sqrt(A(i,i) of the this matrix.
int equilibrateMatrix ()
 Equilibrates the this matrix.
int equilibrateRHS ()
 Equilibrates the current RHS.
int applyRefinement ()
 Apply Iterative Refinement.
int unequilibrateLHS ()
 Unscales the solution vectors if equilibration was used to solve the system.
int reciprocalConditionEstimate (MagnitudeType &Value)
 Returns the reciprocal of the 1-norm condition number of 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 equilibratedA ()
 Returns true if factor is equilibrated (factor available via AF() and LDAF()).
bool equilibratedB ()
 Returns true if RHS is equilibrated (RHS available via B() and LDB()).
bool shouldEquilibrate ()
 Returns true if the LAPACK general rules for equilibration suggest you should equilibrate the system.
bool solutionErrorsEstimated ()
 Returns true if forward and backward error estimated have been computed (available via FERR() and BERR()).
bool inverted ()
 Returns true if matrix inverse has been computed (inverse available via AF() and LDAF()).
bool reciprocalConditionEstimated ()
 Returns true if the condition number of the this matrix has been computed (value available via ReciprocalConditionEstimate()).
bool solved ()
 Returns true if the current set of vectors has been solved.
bool solutionRefined ()
 Returns true if the current set of vectors has been refined.
Data Accessor methods
RCP< SerialSymDenseMatrix
< OrdinalType, ScalarType > > 
getMatrix () const
 Returns pointer to current matrix.
RCP< SerialSymDenseMatrix
< OrdinalType, ScalarType > > 
getFactoredMatrix () const
 Returns pointer to factored matrix (assuming factorization has been performed).
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
getLHS () const
 Returns pointer to current LHS.
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
getRHS () const
 Returns pointer to current RHS.
OrdinalType numRows () const
 Returns row dimension of system.
OrdinalType numCols () const
 Returns column dimension of system.
MagnitudeType ANORM () const
 Returns the 1-Norm of the this matrix (returns -1 if not yet computed).
MagnitudeType RCOND () const
 Returns the reciprocal of the condition number of the this matrix (returns -1 if not yet computed).
MagnitudeType SCOND ()
 Ratio of smallest to largest equilibration scale factors for the this matrix (returns -1 if not yet computed).
MagnitudeType AMAX () const
 Returns the absolute value of the largest entry of the this matrix (returns -1 if not yet computed).
std::vector< MagnitudeType > FERR () const
 Returns a pointer to the forward error estimates computed by LAPACK.
std::vector< MagnitudeType > BERR () const
 Returns a pointer to the backward error estimates computed by LAPACK.
std::vector< MagnitudeType > R () const
 Returns a pointer to the row scaling vector used for equilibration.
I/O methods
void Print (std::ostream &os) const
 Print service methods; defines behavior of ostream << operator.

Detailed Description

template<typename OrdinalType, typename ScalarType>
class Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >

A class for constructing and using Hermitian positive definite dense matrices.

The Teuchos::SerialSpdDenseSolver class enables the construction and use of a templated, Hermitian positive definite, double-precision dense matrices. It is built on the BLAS and LAPACK via the Teuchos::BLAS and Teuchos::LAPACK classes.

The Teuchos::SerialSpdDenseSolver class is intended to provide full-featured support for solving linear system problems for Hermitian positive definite 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.

Teuchos::SerialSpdDenseSolver vs. Teuchos::LAPACK

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

Extracting Data from Teuchos::SerialSpdDenseSolver Objects

Once a Teuchos::SerialSpdDenseSolver is constructed, it is possible to view the data via access functions.

Warning:
Use of these access functions cam be extremely dangerous from a data hiding perspective.

Vector and Utility Functions

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

Strategies for Solving Linear Systems In many cases, linear systems can be accurately solved by simply computing the Cholesky factorization of the matrix and then performing a forward back solve with a given set of right hand side vectors. However, in some instances, the factorization may be very poorly conditioned and the simple approach may not work. In these situations, equilibration and iterative refinement may improve the accuracy, or prevent a breakdown in the factorization.

Teuchos::SerialSpdDenseSolver will use equilibration with the factorization if, once the object is constructed and before it is factored, you call the function FactorWithEquilibration(true) to force equilibration to be used. If you are uncertain if equilibration should be used, you may call the function ShouldEquilibrate() which will return true if equilibration could possibly help. ShouldEquilibrate() uses guidelines specified in the LAPACK User Guide, namely if SCOND < 0.1 and AMAX < Underflow or AMAX > Overflow, to determine if equilibration might be useful.

Teuchos::SerialSpdDenseSolver will use iterative refinement after a forward/back solve if you call SolveToRefinedSolution(true). It will also compute forward and backward error estimates if you call EstimateSolutionErrors(true). Access to the forward (back) error estimates is available via FERR() (BERR()).

Examples using Teuchos::SerialSpdDenseSolver can be found in the Teuchos test directories.

Examples:

DenseMatrix/cxx_main_sym.cpp.

Definition at line 133 of file Teuchos_SerialSpdDenseSolver.hpp.


Constructor & Destructor Documentation

template<typename OrdinalType , typename ScalarType >
Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::SerialSpdDenseSolver ( )

Default constructor; matrix should be set using setMatrix(), LHS and RHS set with setVectors().

Definition at line 411 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::~SerialSpdDenseSolver ( ) [virtual]

SerialSpdDenseSolver destructor.

Definition at line 444 of file Teuchos_SerialSpdDenseSolver.hpp.


Member Function Documentation

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::setMatrix ( const RCP< SerialSymDenseMatrix< OrdinalType, ScalarType > > &  A_in)

Sets the pointers for coefficient matrix.

Definition at line 485 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::setVectors ( const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > &  X,
const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > &  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.

Definition at line 500 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
void Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::factorWithEquilibration ( 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.

Definition at line 185 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
void Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solveToRefinedSolution ( bool  flag) [inline]

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

Definition at line 188 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::estimateSolutionErrors ( bool  flag)

Causes all solves to estimate the forward and backward solution error.

Error estimates will be in the arrays FERR and BERR, resp, after the solve step is complete. These arrays are accessible via the FERR() and BERR() access functions.

Definition at line 523 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::factor ( )

Computes the in-place Cholesky factorization of the matrix using the LAPACK routine DPOTRF.

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

Definition at line 533 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solve ( )

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

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

Definition at line 580 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::invert ( )

Inverts the this matrix.

Note: This function works a little differently that DPOTRI in that it fills the entire matrix with the inverse, independent of the UPLO specification.

Returns:
Integer error code, set to 0 if successful. Otherwise returns the LAPACK error code INFO.

Definition at line 835 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::computeEquilibrateScaling ( )

Computes the scaling vector S(i) = 1/sqrt(A(i,i) of the this matrix.

Returns:
Integer error code, set to 0 if successful. Otherwise returns the LAPACK error code INFO.

Definition at line 692 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibrateMatrix ( )

Equilibrates the this matrix.

Returns:
Integer error code, set to 0 if successful. Otherwise returns the LAPACK error code INFO.

Definition at line 711 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibrateRHS ( )

Equilibrates the current RHS.

Returns:
Integer error code, set to 0 if successful. Otherwise returns the LAPACK error code INFO.

Definition at line 784 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::applyRefinement ( )

Apply Iterative Refinement.

Returns:
Integer error code, set to 0 if successful. Otherwise returns the LAPACK error code INFO.

Definition at line 657 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::unequilibrateLHS ( )

Unscales the solution vectors if equilibration was used to solve the system.

Returns:
Integer error code, set to 0 if successful. Otherwise returns the LAPACK error code INFO.

Definition at line 812 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::reciprocalConditionEstimate ( MagnitudeType &  Value)

Returns the reciprocal of the 1-norm condition number of the this matrix.

Parameters:
ValueOut On return contains the reciprocal of the 1-norm condition number of the this matrix.
Returns:
Integer error code, set to 0 if successful. Otherwise returns the LAPACK error code INFO.

Definition at line 862 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::transpose ( ) [inline]

Returns true if transpose of this matrix has and will be used.

Definition at line 265 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::factored ( ) [inline]

Returns true if matrix is factored (factor available via AF() and LDAF()).

Definition at line 268 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibratedA ( ) [inline]

Returns true if factor is equilibrated (factor available via AF() and LDAF()).

Definition at line 271 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibratedB ( ) [inline]

Returns true if RHS is equilibrated (RHS available via B() and LDB()).

Definition at line 274 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::shouldEquilibrate ( ) [inline]

Returns true if the LAPACK general rules for equilibration suggest you should equilibrate the system.

Definition at line 277 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solutionErrorsEstimated ( ) [inline]

Returns true if forward and backward error estimated have been computed (available via FERR() and BERR()).

Definition at line 280 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::inverted ( ) [inline]

Returns true if matrix inverse has been computed (inverse available via AF() and LDAF()).

Definition at line 283 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::reciprocalConditionEstimated ( ) [inline]

Returns true if the condition number of the this matrix has been computed (value available via ReciprocalConditionEstimate()).

Definition at line 286 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solved ( ) [inline]

Returns true if the current set of vectors has been solved.

Definition at line 289 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solutionRefined ( ) [inline]

Returns true if the current set of vectors has been refined.

Definition at line 292 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialSymDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::getMatrix ( ) const [inline]

Returns pointer to current matrix.

Definition at line 299 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialSymDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::getFactoredMatrix ( ) const [inline]

Returns pointer to factored matrix (assuming factorization has been performed).

Definition at line 302 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::getLHS ( ) const [inline]

Returns pointer to current LHS.

Definition at line 305 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::getRHS ( ) const [inline]

Returns pointer to current RHS.

Definition at line 308 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::numRows ( ) const [inline]

Returns row dimension of system.

Definition at line 311 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::numCols ( ) const [inline]

Returns column dimension of system.

Definition at line 314 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::ANORM ( ) const [inline]

Returns the 1-Norm of the this matrix (returns -1 if not yet computed).

Definition at line 317 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::RCOND ( ) const [inline]

Returns the reciprocal of the condition number of the this matrix (returns -1 if not yet computed).

Definition at line 320 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::SCOND ( ) [inline]

Ratio of smallest to largest equilibration scale factors for the this matrix (returns -1 if not yet computed).

If SCOND() is >= 0.1 and AMAX() is not close to overflow or underflow, then equilibration is not needed.

Definition at line 325 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::AMAX ( ) const [inline]

Returns the absolute value of the largest entry of the this matrix (returns -1 if not yet computed).

Definition at line 328 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
std::vector<MagnitudeType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::FERR ( ) const [inline]

Returns a pointer to the forward error estimates computed by LAPACK.

Definition at line 331 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
std::vector<MagnitudeType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::BERR ( ) const [inline]

Returns a pointer to the backward error estimates computed by LAPACK.

Definition at line 334 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
std::vector<MagnitudeType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::R ( ) const [inline]

Returns a pointer to the row scaling vector used for equilibration.

Definition at line 337 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::Print ( std::ostream &  os) const

Print service methods; defines behavior of ostream << operator.

Definition at line 895 of file Teuchos_SerialSpdDenseSolver.hpp.


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