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

A class for representing and solving banded dense linear systems. More...

#include <Teuchos_SerialBandDenseSolver.hpp>

Inheritance diagram for Teuchos::SerialBandDenseSolver< 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
 SerialBandDenseSolver ()
 Default constructor; matrix should be set using setMatrix(), LHS and RHS set with setVectors().
virtual ~SerialBandDenseSolver ()
 SerialBandDenseSolver destructor.
Set Methods
int setMatrix (const RCP< SerialBandDenseMatrix< OrdinalType, ScalarType > > &AB)
 Sets the pointer 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)
void solveWithTranspose (bool flag)
void solveWithTransposeFlag (Teuchos::ETransp trans)
void solveToRefinedSolution (bool flag)
 Set whether or not to use iterative refinement to improve solutions to linear systems.
void estimateSolutionErrors (bool flag)
 Causes all solves to estimate the forward and backward solution error.
Factor/Solve Methods
int factor ()
 Computes the in-place LU factorization of the matrix using the LAPACK routine _GBTRF.
int solve ()
 Computes the solution X to AX = B for the this matrix and the B provided to SetVectors()..
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 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< SerialBandDenseMatrix
< OrdinalType, ScalarType > > 
getMatrix () const
 Returns pointer to current matrix.
RCP< SerialBandDenseMatrix
< 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.
OrdinalType numLower () const
 Returns lower bandwidth of system.
OrdinalType numUpper () const
 Returns upper bandwidth of system.
std::vector< OrdinalType > IPIV () const
 Returns pointer to pivot vector (if factorization has been computed), zero otherwise.
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 ROWCND () const
 Ratio of smallest to largest row scale factors for the this matrix (returns -1 if not yet computed).
MagnitudeType COLCND () const
 Ratio of smallest to largest column 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.
std::vector< MagnitudeType > C () const
 Returns a pointer to the column scale 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::SerialBandDenseSolver< OrdinalType, ScalarType >

A class for representing and solving banded dense linear systems.

Template Parameters:
OrdinalTypeThe index type used by the linear algebra implementation. This should always be int.
ScalarTypeThe type of entries in the matrix.

Introduction

This class defines a banded dense matrix, which may have any number of rows or columns (not necessarily equal). It's called "serial" because the matrix lives in a single memory space. Thus, it's the kind of matrix that one might give to the BLAS or LAPACK, not a distributed matrix like one would give to ScaLAPACK.

This class also has methods for computing the (banded) LU factorization of the matrix, and solving linear systems with the matrix. We use instances of SerialDenseVector to represent the right-hand side b or the solution x in the linear system $Ax=b$. The instance of this class used store the banded matrix must contain KL extra superdiagonals to store the L and U factors (see details below).

Users have the option to do equilibration before factoring the matrix. This may improve accuracy when solving ill-conditioned problems.

SerialBandDenseSolver and LAPACK

Teuchos' LAPACK class wraps LAPACK's LU factorizations, including the banded factorizations. It thus gives access to most of the same functionality as SerialBandDenseSolver. The main difference is that SerialBandDenseSolver offers a higher level of abstraction. It hides the details of which LAPACK routines to call. Furthermore, if you have built Teuchos with support for the third-party library Eigen, SerialBandDenseSolver lets you solve linear systems for ScalarType other than the four supported by the LAPACK library.

Constructing SerialBandDenseSolver objects

There is a single Teuchos::SerialBandDenseSolver 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 a SerialDenseMatrix or a SerialDenseVector object. The set methods are as follows:

Format of the matrix A

The SerialBandDenseMatrix must contain KL extra superdiagonals to store the L and U factors, where KL is the upper bandwidth. Consider using the non-member conversion routines generalToBanded and bandedToGeneral if the full SerialDenseMatrix is already in storage. However, it is more efficient simply to construct the SerialBandDenseMatrix with the desired parameters and use the provided matrix access operators so that the full rectangular matrix need not be stored. The conversion routine generalToBanded has a flag to store the input Teuchos::SerialDenseMatrix in banded format with KL extra superdiagonals so this class can use it. Again, it is more efficient to simply construct a Teuchos::SerialBandDenseMatrix object with KL extra superdiagonals than are needed for the matrix data and fill the matrix using the matrix access operators.

See the documentation of Teuchos::SerialBandDenseMatrix for further details on the storage format.

Vector and Utility Functions

Once a Teuchos::SerialBandDenseSolver 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 LU 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 this simple approach may not work. In these situations, equilibration and iterative refinement may improve the accuracy, or prevent a breakdown in the factorization.

SerialBandDenseSolver 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.

SerialBandDenseSolver 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 SerialBandDenseSolver can be found in the Teuchos test directories.

Definition at line 166 of file Teuchos_SerialBandDenseSolver.hpp.


Constructor & Destructor Documentation

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

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

Definition at line 464 of file Teuchos_SerialBandDenseSolver.hpp.

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

SerialBandDenseSolver destructor.

Definition at line 501 of file Teuchos_SerialBandDenseSolver.hpp.


Member Function Documentation

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::setMatrix ( const RCP< SerialBandDenseMatrix< OrdinalType, ScalarType > > &  AB)

Sets the pointer for coefficient matrix.

Definition at line 546 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialBandDenseSolver< 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 576 of file Teuchos_SerialBandDenseSolver.hpp.

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

Set whether or not to equilibrate just before the matrix factorization. This function must be called before the factorization is performed.

Definition at line 219 of file Teuchos_SerialBandDenseSolver.hpp.

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

If flag is true, causes all subsequent function calls to work with the transpose of this matrix, otherwise not.

Note:
This interface will not work correctly for complex-valued linear systems, use solveWithTransposeFlag().

Definition at line 224 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::solveWithTransposeFlag ( Teuchos::ETransp  trans) [inline]

All subsequent function calls will work with the transpose-type set by this method (Teuchos::NO_TRANS, Teuchos::TRANS, and Teuchos::CONJ_TRANS).

Note:
This interface will allow correct behavior for complex-valued linear systems, solveWithTranspose() will not.

Definition at line 228 of file Teuchos_SerialBandDenseSolver.hpp.

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

Set whether or not to use iterative refinement to improve solutions to linear systems.

Definition at line 231 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
void Teuchos::SerialBandDenseSolver< 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 599 of file Teuchos_SerialBandDenseSolver.hpp.

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

Computes the in-place LU factorization of the matrix using the LAPACK routine _GBTRF.

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

Definition at line 609 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialBandDenseSolver< 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 667 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialBandDenseSolver< 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 767 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialBandDenseSolver< 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 788 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialBandDenseSolver< 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 844 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialBandDenseSolver< 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 733 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialBandDenseSolver< 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 876 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialBandDenseSolver< 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 902 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 299 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 302 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 305 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 308 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 311 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 314 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 317 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 320 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 323 of file Teuchos_SerialBandDenseSolver.hpp.

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

Returns pointer to current matrix.

Definition at line 330 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 333 of file Teuchos_SerialBandDenseSolver.hpp.

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

Returns pointer to current LHS.

Definition at line 336 of file Teuchos_SerialBandDenseSolver.hpp.

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

Returns pointer to current RHS.

Definition at line 339 of file Teuchos_SerialBandDenseSolver.hpp.

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

Returns row dimension of system.

Definition at line 342 of file Teuchos_SerialBandDenseSolver.hpp.

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

Returns column dimension of system.

Definition at line 345 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
OrdinalType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::numLower ( ) const [inline]

Returns lower bandwidth of system.

Definition at line 348 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
OrdinalType Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::numUpper ( ) const [inline]

Returns upper bandwidth of system.

Definition at line 351 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
std::vector<OrdinalType> Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::IPIV ( ) const [inline]

Returns pointer to pivot vector (if factorization has been computed), zero otherwise.

Definition at line 354 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 357 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
MagnitudeType Teuchos::SerialBandDenseSolver< 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 360 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

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

Definition at line 365 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

If COLCND() is >= 0.1 then equilibration is not needed.

Definition at line 370 of file Teuchos_SerialBandDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
MagnitudeType Teuchos::SerialBandDenseSolver< 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 373 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 376 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 379 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 382 of file Teuchos_SerialBandDenseSolver.hpp.

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

Returns a pointer to the column scale vector used for equilibration.

Definition at line 385 of file Teuchos_SerialBandDenseSolver.hpp.

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

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

Definition at line 935 of file Teuchos_SerialBandDenseSolver.hpp.


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