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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 >:
Inheritance graph
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Public Types

typedef Teuchos::ScalarTraits
< ScalarType >::magnitudeType 
MagnitudeType
 
- Public Types inherited from Teuchos::DefaultBLASImpl< OrdinalType, ScalarType >
typedef details::GivensRotator
< ScalarType >::c_type 
rotg_c_type
 The type used for c in ROTG. More...
 
- Public Types inherited from Teuchos::LAPACK< OrdinalType, ScalarType >
typedef Teuchos::ScalarTraits
< ScalarType >::magnitudeType 
MagnitudeType
 

Protected Member Functions

void allocateWORK ()
 
void allocateIWORK ()
 
void resetMatrix ()
 
void resetVectors ()
 

Protected Attributes

bool equilibrate_
 
bool shouldEquilibrate_
 
bool equilibratedA_
 
bool equilibratedB_
 
bool transpose_
 
bool factored_
 
bool estimateSolutionErrors_
 
bool solutionErrorsEstimated_
 
bool solved_
 
bool inverted_
 
bool reciprocalConditionEstimated_
 
bool refineSolution_
 
bool solutionRefined_
 
OrdinalType numRowCols_
 
OrdinalType LDA_
 
OrdinalType LDAF_
 
OrdinalType INFO_
 
OrdinalType LWORK_
 
std::vector< int > IWORK_
 
MagnitudeType ANORM_
 
MagnitudeType RCOND_
 
MagnitudeType SCOND_
 
MagnitudeType AMAX_
 
RCP< SerialSymDenseMatrix
< OrdinalType, ScalarType > > 
Matrix_
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
LHS_
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
RHS_
 
RCP< SerialSymDenseMatrix
< OrdinalType, ScalarType > > 
Factor_
 
ScalarType * A_
 
ScalarType * AF_
 
std::vector< MagnitudeTypeFERR_
 
std::vector< MagnitudeTypeBERR_
 
std::vector< ScalarType > WORK_
 
std::vector< MagnitudeTypeR_
 
- Protected Attributes inherited from Teuchos::CompObject
FlopsflopCounter_
 

Private Member Functions

 SerialSpdDenseSolver (const SerialSpdDenseSolver< OrdinalType, ScalarType > &Source)
 
SerialSpdDenseSolveroperator= (const SerialSpdDenseSolver< OrdinalType, ScalarType > &Source)
 

Constructor/Destructor Methods

 SerialSpdDenseSolver ()
 Default constructor; matrix should be set using setMatrix(), LHS and RHS set with setVectors(). More...
 
virtual ~SerialSpdDenseSolver ()
 SerialSpdDenseSolver destructor. More...
 

Set Methods

int setMatrix (const RCP< SerialSymDenseMatrix< OrdinalType, ScalarType > > &A_in)
 Sets the pointers for coefficient matrix. More...
 
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). More...
 

Strategy Modifying Methods

void factorWithEquilibration (bool flag)
 Causes equilibration to be called just before the matrix factorization as part of the call to factor. More...
 
void solveToRefinedSolution (bool flag)
 Causes all solves to compute solution to best ability using iterative refinement. More...
 
void estimateSolutionErrors (bool flag)
 Causes all solves to estimate the forward and backward solution error. More...
 

Factor/Solve/Invert Methods

int factor ()
 Computes the in-place Cholesky factorization of the matrix using the LAPACK routine DPOTRF. More...
 
int solve ()
 Computes the solution X to AX = B for the this matrix and the B provided to SetVectors().. More...
 
int invert ()
 Inverts the this matrix. More...
 
int computeEquilibrateScaling ()
 Computes the scaling vector S(i) = 1/sqrt(A(i,i) of the this matrix. More...
 
int equilibrateMatrix ()
 Equilibrates the this matrix. More...
 
int equilibrateRHS ()
 Equilibrates the current RHS. More...
 
int applyRefinement ()
 Apply Iterative Refinement. More...
 
int unequilibrateLHS ()
 Unscales the solution vectors if equilibration was used to solve the system. More...
 
int reciprocalConditionEstimate (MagnitudeType &Value)
 Returns the reciprocal of the 1-norm condition number of the this matrix. More...
 

Query methods

bool transpose ()
 Returns true if transpose of this matrix has and will be used. More...
 
bool factored ()
 Returns true if matrix is factored (factor available via AF() and LDAF()). More...
 
bool equilibratedA ()
 Returns true if factor is equilibrated (factor available via AF() and LDAF()). More...
 
bool equilibratedB ()
 Returns true if RHS is equilibrated (RHS available via B() and LDB()). More...
 
bool shouldEquilibrate ()
 Returns true if the LAPACK general rules for equilibration suggest you should equilibrate the system. More...
 
bool solutionErrorsEstimated ()
 Returns true if forward and backward error estimated have been computed (available via FERR() and BERR()). More...
 
bool inverted ()
 Returns true if matrix inverse has been computed (inverse available via AF() and LDAF()). More...
 
bool reciprocalConditionEstimated ()
 Returns true if the condition number of the this matrix has been computed (value available via ReciprocalConditionEstimate()). More...
 
bool solved ()
 Returns true if the current set of vectors has been solved. More...
 
bool solutionRefined ()
 Returns true if the current set of vectors has been refined. More...
 

Data Accessor methods

RCP< SerialSymDenseMatrix
< OrdinalType, ScalarType > > 
getMatrix () const
 Returns pointer to current matrix. More...
 
RCP< SerialSymDenseMatrix
< OrdinalType, ScalarType > > 
getFactoredMatrix () const
 Returns pointer to factored matrix (assuming factorization has been performed). More...
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
getLHS () const
 Returns pointer to current LHS. More...
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
getRHS () const
 Returns pointer to current RHS. More...
 
OrdinalType numRows () const
 Returns row dimension of system. More...
 
OrdinalType numCols () const
 Returns column dimension of system. More...
 
MagnitudeType ANORM () const
 Returns the 1-Norm of the this matrix (returns -1 if not yet computed). More...
 
MagnitudeType RCOND () const
 Returns the reciprocal of the condition number of the this matrix (returns -1 if not yet computed). More...
 
MagnitudeType SCOND ()
 Ratio of smallest to largest equilibration scale factors for the this matrix (returns -1 if not yet computed). More...
 
MagnitudeType AMAX () const
 Returns the absolute value of the largest entry of the this matrix (returns -1 if not yet computed). More...
 
std::vector< MagnitudeTypeFERR () const
 Returns a pointer to the forward error estimates computed by LAPACK. More...
 
std::vector< MagnitudeTypeBERR () const
 Returns a pointer to the backward error estimates computed by LAPACK. More...
 
std::vector< MagnitudeTypeR () const
 Returns a pointer to the row scaling vector used for equilibration. More...
 

I/O methods

void Print (std::ostream &os) const
 Print service methods; defines behavior of ostream << operator. More...
 

Additional Inherited Members

- Public Member Functions inherited from Teuchos::CompObject
 CompObject ()
 Default constructor. More...
 
 CompObject (const CompObject &source)
 Copy Constructor. More...
 
virtual ~CompObject ()
 Destructor. More...
 
void setFlopCounter (const Flops &FlopCounter)
 Set the internal Teuchos::Flops() pointer. More...
 
void setFlopCounter (const CompObject &compObject)
 Set the internal Teuchos::Flops() pointer to the flop counter of another Teuchos::CompObject. More...
 
void unsetFlopCounter ()
 Set the internal Teuchos::Flops() pointer to 0 (no flops counted). More...
 
FlopsgetFlopCounter () const
 Get the pointer to the Teuchos::Flops() object associated with this object, returns 0 if none. More...
 
void resetFlops () const
 Resets the number of floating point operations to zero for this multi-std::vector. More...
 
double getFlops () const
 Returns the number of floating point operations with this multi-std::vector. More...
 
void updateFlops (int addflops) const
 Increment Flop count for this object. More...
 
void updateFlops (long int addflops) const
 Increment Flop count for this object. More...
 
void updateFlops (double addflops) const
 Increment Flop count for this object. More...
 
void updateFlops (float addflops) const
 Increment Flop count for this object. More...
 
- Public Member Functions inherited from Teuchos::Object
 Object (int tracebackModeIn=-1)
 Default Constructor. More...
 
 Object (const char *label, int tracebackModeIn=-1)
 Labeling Constructor. More...
 
 Object (const std::string &label, int tracebackModeIn=-1)
 Create an Object with the given label, and optionally, with the given traceback mode. More...
 
virtual ~Object ()
 Destructor (virtual, for safety of derived classes). More...
 
virtual void setLabel (const char *theLabel)
 
virtual const char * label () const
 Access the object's label (LEGACY; return std::string instead). More...
 
virtual void print (std::ostream &os) const
 Print the object to the given output stream. More...
 
virtual int reportError (const std::string message, int errorCode) const
 Report an error with this Object. More...
 
- Public Member Functions inherited from Teuchos::BLAS< OrdinalType, ScalarType >
 BLAS (void)
 Default constructor. More...
 
 BLAS (const BLAS< OrdinalType, ScalarType > &)
 Copy constructor. More...
 
virtual ~BLAS (void)
 Destructor. More...
 
- Public Member Functions inherited from Teuchos::DefaultBLASImpl< OrdinalType, ScalarType >
 DefaultBLASImpl (void)
 Default constructor. More...
 
 DefaultBLASImpl (const DefaultBLASImpl< OrdinalType, ScalarType > &)
 Copy constructor. More...
 
virtual ~DefaultBLASImpl (void)
 Destructor. More...
 
void ROTG (ScalarType *da, ScalarType *db, rotg_c_type *c, ScalarType *s) const
 Computes a Givens plane rotation. More...
 
void ROT (const OrdinalType &n, ScalarType *dx, const OrdinalType &incx, ScalarType *dy, const OrdinalType &incy, MagnitudeType *c, ScalarType *s) const
 Applies a Givens plane rotation. More...
 
void SCAL (const OrdinalType &n, const ScalarType &alpha, ScalarType *x, const OrdinalType &incx) const
 Scale the vector x by the constant alpha. More...
 
void COPY (const OrdinalType &n, const ScalarType *x, const OrdinalType &incx, ScalarType *y, const OrdinalType &incy) const
 Copy the vector x to the vector y. More...
 
template<typename alpha_type , typename x_type >
void AXPY (const OrdinalType &n, const alpha_type alpha, const x_type *x, const OrdinalType &incx, ScalarType *y, const OrdinalType &incy) const
 Perform the operation: y <- y+alpha*x. More...
 
ScalarTraits< ScalarType >
::magnitudeType 
ASUM (const OrdinalType &n, const ScalarType *x, const OrdinalType &incx) const
 Sum the absolute values of the entries of x. More...
 
template<typename x_type , typename y_type >
ScalarType DOT (const OrdinalType &n, const x_type *x, const OrdinalType &incx, const y_type *y, const OrdinalType &incy) const
 Form the dot product of the vectors x and y. More...
 
ScalarTraits< ScalarType >
::magnitudeType 
NRM2 (const OrdinalType &n, const ScalarType *x, const OrdinalType &incx) const
 Compute the 2-norm of the vector x. More...
 
OrdinalType IAMAX (const OrdinalType &n, const ScalarType *x, const OrdinalType &incx) const
 Return the index of the element of x with the maximum magnitude. More...
 
template<typename alpha_type , typename A_type , typename x_type , typename beta_type >
void GEMV (ETransp trans, const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const A_type *A, const OrdinalType &lda, const x_type *x, const OrdinalType &incx, const beta_type beta, ScalarType *y, const OrdinalType &incy) const
 Performs the matrix-vector operation: y <- alpha*A*x+beta*y or y <- alpha*A'*x+beta*y where A is a general m by n matrix. More...
 
template<typename A_type >
void TRMV (EUplo uplo, ETransp trans, EDiag diag, const OrdinalType &n, const A_type *A, const OrdinalType &lda, ScalarType *x, const OrdinalType &incx) const
 Performs the matrix-vector operation: x <- A*x or x <- A'*x where A is a unit/non-unit n by n upper/lower triangular matrix. More...
 
template<typename alpha_type , typename x_type , typename y_type >
void GER (const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const x_type *x, const OrdinalType &incx, const y_type *y, const OrdinalType &incy, ScalarType *A, const OrdinalType &lda) const
 Performs the rank 1 operation: A <- alpha*x*y'+A. More...
 
template<typename alpha_type , typename A_type , typename B_type , typename beta_type >
void GEMM (ETransp transa, ETransp transb, const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, const alpha_type alpha, const A_type *A, const OrdinalType &lda, const B_type *B, const OrdinalType &ldb, const beta_type beta, ScalarType *C, const OrdinalType &ldc) const
 General matrix-matrix multiply. More...
 
void SWAP (const OrdinalType &n, ScalarType *const x, const OrdinalType &incx, ScalarType *const y, const OrdinalType &incy) const
 Swap the entries of x and y. More...
 
template<typename alpha_type , typename A_type , typename B_type , typename beta_type >
void SYMM (ESide side, EUplo uplo, const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const A_type *A, const OrdinalType &lda, const B_type *B, const OrdinalType &ldb, const beta_type beta, ScalarType *C, const OrdinalType &ldc) const
 Performs the matrix-matrix operation: C <- alpha*A*B+beta*C or C <- alpha*B*A+beta*C where A is an m by m or n by n symmetric matrix and B is a general matrix. More...
 
template<typename alpha_type , typename A_type , typename beta_type >
void SYRK (EUplo uplo, ETransp trans, const OrdinalType &n, const OrdinalType &k, const alpha_type alpha, const A_type *A, const OrdinalType &lda, const beta_type beta, ScalarType *C, const OrdinalType &ldc) const
 Performs the symmetric rank k operation: C <- alpha*A*A'+beta*C or C <- alpha*A'*A+beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case or k by n matrix in the second case. More...
 
template<typename alpha_type , typename A_type >
void TRMM (ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const A_type *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb) const
 Performs the matrix-matrix operation: B <- alpha*op(A)*B or B <- alpha*B*op(A) where op(A) is an unit/non-unit, upper/lower triangular matrix and B is a general matrix. More...
 
template<typename alpha_type , typename A_type >
void TRSM (ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType &m, const OrdinalType &n, const alpha_type alpha, const A_type *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb) const
 Solves the matrix equations: op(A)*X=alpha*B or X*op(A)=alpha*B where X and B are m by n matrices, A is a unit/non-unit, upper/lower triangular matrix and op(A) is A or A'. The matrix X is overwritten on B. More...
 
- Public Member Functions inherited from Teuchos::LAPACK< OrdinalType, ScalarType >
 LAPACK (void)
 Default Constructor. More...
 
 LAPACK (const LAPACK< OrdinalType, ScalarType > &lapack)
 Copy Constructor. More...
 
virtual ~LAPACK (void)
 Destructor. More...
 
void PTTRF (const OrdinalType &n, MagnitudeType *d, ScalarType *e, OrdinalType *info) const
 Computes the L*D*L' factorization of a Hermitian/symmetric positive definite tridiagonal matrix A. More...
 
void PTTRS (const OrdinalType &n, const OrdinalType &nrhs, const MagnitudeType *d, const ScalarType *e, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
 Solves a tridiagonal system A*X=B using the *D*L' factorization of A computed by PTTRF. More...
 
void POTRF (const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *info) const
 Computes Cholesky factorization of a real symmetric positive definite matrix A. More...
 
void POTRS (const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
 Solves a system of linear equations A*X=B, where A is a symmetric positive definite matrix factored by POTRF and the nrhs solutions are returned in B. More...
 
void POTRI (const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *info) const
 Computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A from POTRF. More...
 
void POCON (const char &UPLO, const OrdinalType &n, const ScalarType *A, const OrdinalType &lda, const ScalarType &anorm, ScalarType *rcond, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
 Estimates the reciprocal of the condition number (1-norm) of a real symmetric positive definite matrix A using the Cholesky factorization from POTRF. More...
 
void POSV (const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
 Computes the solution to a real system of linear equations A*X=B, where A is a symmetric positive definite matrix and the nrhs solutions are returned in B. More...
 
void POEQU (const OrdinalType &n, const ScalarType *A, const OrdinalType &lda, MagnitudeType *S, MagnitudeType *scond, MagnitudeType *amax, OrdinalType *info) const
 Computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (w.r.t. 2-norm). More...
 
void PORFS (const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, const ScalarType *AF, const OrdinalType &ldaf, const ScalarType *B, const OrdinalType &ldb, ScalarType *X, const OrdinalType &ldx, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
 Improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, and provides error bounds and backward error estimates for the solution. More...
 
void POSVX (const char &FACT, const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, ScalarType *AF, const OrdinalType &ldaf, char *EQUED, ScalarType *S, ScalarType *B, const OrdinalType &ldb, ScalarType *X, const OrdinalType &ldx, ScalarType *rcond, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
 Uses the Cholesky factorization to compute the solution to a real system of linear equations A*X=B, where A is symmetric positive definite. System can be equilibrated by POEQU and iteratively refined by PORFS, if requested. More...
 
void GELS (const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Solves an over/underdetermined real m by n linear system A using QR or LQ factorization of A. More...
 
void GELSS (const OrdinalType &m, const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, MagnitudeType *S, const MagnitudeType rcond, OrdinalType *rank, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *info) const
 Use the SVD to solve a possibly rank-deficient linear least-squares problem. More...
 
void GELSS (const OrdinalType &m, const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, ScalarType *S, const ScalarType &rcond, OrdinalType *rank, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Legacy GELSS interface for real-valued ScalarType. More...
 
void GGLSE (const OrdinalType &m, const OrdinalType &n, const OrdinalType &p, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, ScalarType *C, ScalarType *D, ScalarType *X, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Solves the linear equality-constrained least squares (LSE) problem where A is an m by n matrix,B is a p by n matrix C is a given m-vector, and D is a given p-vector. More...
 
void GEQRF (const OrdinalType &m, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Computes a QR factorization of a general m by n matrix A. More...
 
void GEQR2 (const OrdinalType &m, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *TAU, ScalarType *WORK, OrdinalType *const info) const
 BLAS 2 version of GEQRF, with known workspace size. More...
 
void GETRF (const OrdinalType &m, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *IPIV, OrdinalType *info) const
 Computes an LU factorization of a general m by n matrix A using partial pivoting with row interchanges. More...
 
void GETRS (const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, const OrdinalType *IPIV, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
 Solves a system of linear equations A*X=B or A'*X=B with a general n by n matrix A using the LU factorization computed by GETRF. More...
 
void LASCL (const char &TYPE, const OrdinalType &kl, const OrdinalType &ku, const MagnitudeType cfrom, const MagnitudeType cto, const OrdinalType &m, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *info) const
 Multiplies the m by n matrix A by the real scalar cto/cfrom. More...
 
void GEQP3 (const OrdinalType &m, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *jpvt, ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *info) const
 Computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS. More...
 
void LASWP (const OrdinalType &N, ScalarType *A, const OrdinalType &LDA, const OrdinalType &K1, const OrdinalType &K2, const OrdinalType *IPIV, const OrdinalType &INCX) const
 Apply a series of row interchanges to the matrix A. More...
 
void GBTRF (const OrdinalType &m, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, ScalarType *A, const OrdinalType &lda, OrdinalType *IPIV, OrdinalType *info) const
 Computes an LU factorization of a general banded m by n matrix A using partial pivoting with row interchanges. More...
 
void GBTRS (const char &TRANS, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, const OrdinalType *IPIV, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
 Solves a system of linear equations A*X=B or A'*X=B with a general banded n by n matrix A using the LU factorization computed by GBTRF. More...
 
void GTTRF (const OrdinalType &n, ScalarType *dl, ScalarType *d, ScalarType *du, ScalarType *du2, OrdinalType *IPIV, OrdinalType *info) const
 Computes an LU factorization of a n by n tridiagonal matrix A using partial pivoting with row interchanges. More...
 
void GTTRS (const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *dl, const ScalarType *d, const ScalarType *du, const ScalarType *du2, const OrdinalType *IPIV, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
 Solves a system of linear equations A*X=B or A'*X=B or A^H*X=B with a tridiagonal matrix A using the LU factorization computed by GTTRF. More...
 
void GETRI (const OrdinalType &n, ScalarType *A, const OrdinalType &lda, const OrdinalType *IPIV, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Computes the inverse of a matrix A using the LU factorization computed by GETRF. More...
 
void LATRS (const char &UPLO, const char &TRANS, const char &DIAG, const char &NORMIN, const OrdinalType &N, const ScalarType *A, const OrdinalType &LDA, ScalarType *X, MagnitudeType *SCALE, MagnitudeType *CNORM, OrdinalType *INFO) const
 Robustly solve a possibly singular triangular linear system. More...
 
void GECON (const char &NORM, const OrdinalType &n, const ScalarType *A, const OrdinalType &lda, const ScalarType &anorm, ScalarType *rcond, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
 Estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by GETRF. More...
 
void GBCON (const char &NORM, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const ScalarType *A, const OrdinalType &lda, const OrdinalType *IPIV, const ScalarType &anorm, ScalarType *rcond, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
 Estimates the reciprocal of the condition number of a general banded real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by GETRF. More...
 
ScalarTraits< ScalarType >
::magnitudeType 
LANGB (const char &NORM, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const ScalarType *A, const OrdinalType &lda, MagnitudeType *WORK) const
 Returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals. More...
 
void GESV (const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, OrdinalType *IPIV, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
 Computes the solution to a real system of linear equations A*X=B, where A is factored through GETRF and the nrhs solutions are computed through GETRS. More...
 
void GEEQU (const OrdinalType &m, const OrdinalType &n, const ScalarType *A, const OrdinalType &lda, ScalarType *R, ScalarType *C, ScalarType *rowcond, ScalarType *colcond, ScalarType *amax, OrdinalType *info) const
 Computes row and column scalings intended to equilibrate an m by n matrix A and reduce its condition number. More...
 
void GERFS (const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, const ScalarType *AF, const OrdinalType &ldaf, const OrdinalType *IPIV, const ScalarType *B, const OrdinalType &ldb, ScalarType *X, const OrdinalType &ldx, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
 Improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. Use after GETRF/GETRS. More...
 
void GBEQU (const OrdinalType &m, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const ScalarType *A, const OrdinalType &lda, MagnitudeType *R, MagnitudeType *C, MagnitudeType *rowcond, MagnitudeType *colcond, MagnitudeType *amax, OrdinalType *info) const
 Computes row and column scalings intended to equilibrate an m by n banded matrix A and reduce its condition number. More...
 
void GBRFS (const char &TRANS, const OrdinalType &n, const OrdinalType &kl, const OrdinalType &ku, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, const ScalarType *AF, const OrdinalType &ldaf, const OrdinalType *IPIV, const ScalarType *B, const OrdinalType &ldb, ScalarType *X, const OrdinalType &ldx, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
 Improves the computed solution to a banded system of linear equations and provides error bounds and backward error estimates for the solution. Use after GBTRF/GBTRS. More...
 
void GESVX (const char &FACT, const char &TRANS, const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, ScalarType *AF, const OrdinalType &ldaf, OrdinalType *IPIV, char *EQUED, ScalarType *R, ScalarType *C, ScalarType *B, const OrdinalType &ldb, ScalarType *X, const OrdinalType &ldx, ScalarType *rcond, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const
 Uses the LU factorization to compute the solution to a real system of linear equations A*X=B, returning error bounds on the solution and a condition estimate. More...
 
void SYTRD (const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *D, ScalarType *E, ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Reduces a real symmetric matrix A to tridiagonal form by orthogonal similarity transformations. More...
 
void GEHRD (const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, ScalarType *A, const OrdinalType &lda, ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Reduces a real general matrix A to upper Hessenberg form by orthogonal similarity transformations. More...
 
void TRTRS (const char &UPLO, const char &TRANS, const char &DIAG, const OrdinalType &n, const OrdinalType &nrhs, const ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, OrdinalType *info) const
 Solves a triangular linear system of the form A*X=B or A**T*X=B, where A is a triangular matrix. More...
 
void TRTRI (const char &UPLO, const char &DIAG, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *info) const
 Computes the inverse of an upper or lower triangular matrix A. More...
 
void SPEV (const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType *AP, ScalarType *W, ScalarType *Z, const OrdinalType &ldz, ScalarType *WORK, OrdinalType *info) const
 Computes the eigenvalues and, optionally, eigenvectors of a symmetric n by n matrix A in packed storage. More...
 
void SYEV (const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *W, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Computes all the eigenvalues and, optionally, eigenvectors of a symmetric n by n matrix A. More...
 
void SYGV (const OrdinalType &itype, const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, ScalarType *W, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Computes all the eigenvalues and, optionally, eigenvectors of a symmetric n by n matrix pencil {A,B}, where A is symmetric and B is symmetric positive-definite. More...
 
void HEEV (const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, MagnitudeType *W, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *info) const
 Computes all the eigenvalues and, optionally, eigenvectors of a Hermitian n by n matrix A. More...
 
void HEGV (const OrdinalType &itype, const char &JOBZ, const char &UPLO, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, MagnitudeType *W, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *info) const
 Computes all the eigenvalues and, optionally, eigenvectors of a generalized Hermitian-definite n by n matrix pencil {A,B}, where A is Hermitian and B is Hermitian positive-definite. More...
 
void STEQR (const char &COMPZ, const OrdinalType &n, MagnitudeType *D, MagnitudeType *E, ScalarType *Z, const OrdinalType &ldz, MagnitudeType *WORK, OrdinalType *info) const
 Computes the eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal n by n matrix A using implicit QL/QR. The eigenvectors can only be computed if A was reduced to tridiagonal form by SYTRD. More...
 
void PTEQR (const char &COMPZ, const OrdinalType &n, MagnitudeType *D, MagnitudeType *E, ScalarType *Z, const OrdinalType &ldz, MagnitudeType *WORK, OrdinalType *info) const
 Computes the eigenvalues and, optionally, eigenvectors of a symmetric positive-definite tridiagonal n by n matrix A using BDSQR, after factoring the matrix with PTTRF. More...
 
void HSEQR (const char &JOB, const char &COMPZ, const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, ScalarType *H, const OrdinalType &ldh, ScalarType *WR, ScalarType *WI, ScalarType *Z, const OrdinalType &ldz, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Computes the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition, where T is an upper quasi-triangular matrix and Z contains the Schur vectors. More...
 
void GEES (const char &JOBVS, const char &SORT, OrdinalType &(*ptr2func)(ScalarType *, ScalarType *), const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *sdim, ScalarType *WR, ScalarType *WI, ScalarType *VS, const OrdinalType &ldvs, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *BWORK, OrdinalType *info) const
 
void GEES (const char &JOBVS, const char &SORT, OrdinalType &(*ptr2func)(ScalarType *), const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *sdim, ScalarType *W, ScalarType *VS, const OrdinalType &ldvs, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *BWORK, OrdinalType *info) const
 
void GEES (const char &JOBVS, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *sdim, MagnitudeType *WR, MagnitudeType *WI, ScalarType *VS, const OrdinalType &ldvs, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *BWORK, OrdinalType *info) const
 
void GEEV (const char &JOBVL, const char &JOBVR, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, MagnitudeType *WR, MagnitudeType *WI, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *info) const
 Computes for an n by n real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. More...
 
void GEEVX (const char &BALANC, const char &JOBVL, const char &JOBVR, const char &SENSE, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *WR, ScalarType *WI, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, OrdinalType *ilo, OrdinalType *ihi, MagnitudeType *SCALE, MagnitudeType *abnrm, MagnitudeType *RCONDE, MagnitudeType *RCONDV, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *IWORK, OrdinalType *info) const
 
void GGEVX (const char &BALANC, const char &JOBVL, const char &JOBVR, const char &SENSE, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, ScalarType *BETA, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, OrdinalType *ilo, OrdinalType *ihi, MagnitudeType *lscale, MagnitudeType *rscale, MagnitudeType *abnrm, MagnitudeType *bbnrm, MagnitudeType *RCONDE, MagnitudeType *RCONDV, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *IWORK, OrdinalType *BWORK, OrdinalType *info) const
 
void GGEV (const char &JOBVL, const char &JOBVR, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, ScalarType *BETA, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 
void TRSEN (const char &JOB, const char &COMPQ, const OrdinalType *SELECT, const OrdinalType &n, ScalarType *T, const OrdinalType &ldt, ScalarType *Q, const OrdinalType &ldq, MagnitudeType *WR, MagnitudeType *WI, OrdinalType *M, ScalarType *S, MagnitudeType *SEP, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *IWORK, const OrdinalType &liwork, OrdinalType *info) const
 
void TGSEN (const OrdinalType &ijob, const OrdinalType &wantq, const OrdinalType &wantz, const OrdinalType *SELECT, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, MagnitudeType *BETA, ScalarType *Q, const OrdinalType &ldq, ScalarType *Z, const OrdinalType &ldz, OrdinalType *M, MagnitudeType *PL, MagnitudeType *PR, MagnitudeType *DIF, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *IWORK, const OrdinalType &liwork, OrdinalType *info) const
 
void GGES (const char &JOBVL, const char &JOBVR, const char &SORT, OrdinalType &(*ptr2func)(ScalarType *, ScalarType *, ScalarType *), const OrdinalType &n, ScalarType *A, const OrdinalType &lda, ScalarType *B, const OrdinalType &ldb, OrdinalType *sdim, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, MagnitudeType *BETA, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *BWORK, OrdinalType *info) const
 
void GESVD (const char &JOBU, const char &JOBVT, const OrdinalType &m, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, MagnitudeType *S, ScalarType *U, const OrdinalType &ldu, ScalarType *V, const OrdinalType &ldv, ScalarType *WORK, const OrdinalType &lwork, MagnitudeType *RWORK, OrdinalType *info) const
 Computes the singular values (and optionally, vectors) of a real matrix A. More...
 
void ORMQR (const char &SIDE, const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, const ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *C, const OrdinalType &ldc, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 
void ORM2R (const char &SIDE, const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, const ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *C, const OrdinalType &ldc, ScalarType *WORK, OrdinalType *const info) const
 BLAS 2 version of ORMQR; known workspace size. More...
 
void UNMQR (const char &SIDE, const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, const ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *C, const OrdinalType &ldc, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Apply Householder reflectors (complex case). More...
 
void UNM2R (const char &SIDE, const char &TRANS, const OrdinalType &M, const OrdinalType &N, const OrdinalType &K, const ScalarType *A, const OrdinalType &LDA, const ScalarType *TAU, ScalarType *C, const OrdinalType &LDC, ScalarType *WORK, OrdinalType *const INFO) const
 BLAS 2 version of UNMQR; known workspace size. More...
 
void ORGQR (const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Compute explicit Q factor from QR factorization (GEQRF) (real case). More...
 
void UNGQR (const OrdinalType &m, const OrdinalType &n, const OrdinalType &k, ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Compute explicit QR factor from QR factorization (GEQRF) (complex case). More...
 
void ORGHR (const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Generates a real orthogonal matrix Q which is the product of ihi-ilo elementary reflectors of order n, as returned by GEHRD. On return Q is stored in A. More...
 
void ORMHR (const char &SIDE, const char &TRANS, const OrdinalType &m, const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, const ScalarType *A, const OrdinalType &lda, const ScalarType *TAU, ScalarType *C, const OrdinalType &ldc, ScalarType *WORK, const OrdinalType &lwork, OrdinalType *info) const
 Overwrites the general real m by n matrix C with the product of C and Q, which is a product of ihi-ilo elementary reflectors, as returned by GEHRD. More...
 
void TREVC (const char &SIDE, const char &HOWMNY, OrdinalType *select, const OrdinalType &n, const ScalarType *T, const OrdinalType &ldt, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, const OrdinalType &mm, OrdinalType *m, ScalarType *WORK, OrdinalType *info) const
 
void TREVC (const char &SIDE, const OrdinalType &n, const ScalarType *T, const OrdinalType &ldt, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, const OrdinalType &mm, OrdinalType *m, ScalarType *WORK, MagnitudeType *RWORK, OrdinalType *info) const
 
void TREXC (const char &COMPQ, const OrdinalType &n, ScalarType *T, const OrdinalType &ldt, ScalarType *Q, const OrdinalType &ldq, OrdinalType *ifst, OrdinalType *ilst, ScalarType *WORK, OrdinalType *info) const
 
void TGEVC (const char &SIDE, const char &HOWMNY, const OrdinalType *SELECT, const OrdinalType &n, const ScalarType *S, const OrdinalType &lds, const ScalarType *P, const OrdinalType &ldp, ScalarType *VL, const OrdinalType &ldvl, ScalarType *VR, const OrdinalType &ldvr, const OrdinalType &mm, OrdinalType *M, ScalarType *WORK, OrdinalType *info) const
 
void LARTG (const ScalarType &f, const ScalarType &g, MagnitudeType *c, ScalarType *s, ScalarType *r) const
 Gnerates a plane rotation that zeros out the second component of the input vector. More...
 
void LARFG (const OrdinalType &n, ScalarType *alpha, ScalarType *x, const OrdinalType &incx, ScalarType *tau) const
 Generates an elementary reflector of order n that zeros out the last n-1 components of the input vector. More...
 
void GEBAL (const char &JOBZ, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *ilo, OrdinalType *ihi, MagnitudeType *scale, OrdinalType *info) const
 Balances a general matrix A, through similarity transformations to make the rows and columns as close in norm as possible. More...
 
void GEBAK (const char &JOBZ, const char &SIDE, const OrdinalType &n, const OrdinalType &ilo, const OrdinalType &ihi, const MagnitudeType *scale, const OrdinalType &m, ScalarType *V, const OrdinalType &ldv, OrdinalType *info) const
 Forms the left or right eigenvectors of a general matrix that has been balanced by GEBAL by backward transformation of the computed eigenvectors V. More...
 
ScalarType LARND (const OrdinalType &idist, OrdinalType *seed) const
 Returns a random number from a uniform or normal distribution. More...
 
void LARNV (const OrdinalType &idist, OrdinalType *seed, const OrdinalType &n, ScalarType *v) const
 Returns a vector of random numbers from a chosen distribution. More...
 
ScalarType LAMCH (const char &CMACH) const
 Determines machine parameters for floating point characteristics. More...
 
OrdinalType ILAENV (const OrdinalType &ispec, const std::string &NAME, const std::string &OPTS, const OrdinalType &N1=-1, const OrdinalType &N2=-1, const OrdinalType &N3=-1, const OrdinalType &N4=-1) const
 Chooses problem-dependent parameters for the local environment. More...
 
ScalarType LAPY2 (const ScalarType &x, const ScalarType &y) const
 Computes x^2 + y^2 safely, to avoid overflow. More...
 
- Static Public Member Functions inherited from Teuchos::Object
static void setTracebackMode (int tracebackModeValue)
 Set the value of the Object error traceback report mode. More...
 
static int getTracebackMode ()
 Get the value of the Object error traceback report mode. More...
 
- Static Public Attributes inherited from Teuchos::Object
static int tracebackMode = -1
 

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.

Definition at line 101 of file Teuchos_SerialSpdDenseSolver.hpp.

Member Typedef Documentation

template<typename OrdinalType, typename ScalarType>
typedef Teuchos::ScalarTraits<ScalarType>::magnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::MagnitudeType

Definition at line 106 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 378 of file Teuchos_SerialSpdDenseSolver.hpp.

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

SerialSpdDenseSolver destructor.

Definition at line 410 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::SerialSpdDenseSolver ( const SerialSpdDenseSolver< OrdinalType, ScalarType > &  Source)
private

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 451 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 466 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 153 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 156 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 489 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 499 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 546 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 805 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 662 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 681 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 754 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 627 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 782 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 832 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 232 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 235 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 238 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 241 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 244 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 247 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 250 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 253 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 256 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 259 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 266 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 269 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 272 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 275 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 278 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 281 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 284 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 287 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 292 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 295 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 298 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 301 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 304 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 865 of file Teuchos_SerialSpdDenseSolver.hpp.

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

Definition at line 316 of file Teuchos_SerialSpdDenseSolver.hpp.

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

Definition at line 317 of file Teuchos_SerialSpdDenseSolver.hpp.

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

Definition at line 429 of file Teuchos_SerialSpdDenseSolver.hpp.

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

Definition at line 416 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
SerialSpdDenseSolver& Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::operator= ( const SerialSpdDenseSolver< OrdinalType, ScalarType > &  Source)
private

Member Data Documentation

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibrate_
protected

Definition at line 321 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::shouldEquilibrate_
protected

Definition at line 322 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibratedA_
protected

Definition at line 323 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::equilibratedB_
protected

Definition at line 324 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::transpose_
protected

Definition at line 325 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::factored_
protected

Definition at line 326 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::estimateSolutionErrors_
protected

Definition at line 327 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solutionErrorsEstimated_
protected

Definition at line 328 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solved_
protected

Definition at line 329 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::inverted_
protected

Definition at line 330 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::reciprocalConditionEstimated_
protected

Definition at line 331 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::refineSolution_
protected

Definition at line 332 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::solutionRefined_
protected

Definition at line 333 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::numRowCols_
protected

Definition at line 335 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::LDA_
protected

Definition at line 336 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::LDAF_
protected

Definition at line 337 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::INFO_
protected

Definition at line 338 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::LWORK_
protected

Definition at line 339 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
std::vector<int> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::IWORK_
protected

Definition at line 341 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::ANORM_
protected

Definition at line 343 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::RCOND_
protected

Definition at line 344 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::SCOND_
protected

Definition at line 345 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
MagnitudeType Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::AMAX_
protected

Definition at line 346 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialSymDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::Matrix_
protected

Definition at line 348 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::LHS_
protected

Definition at line 349 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::RHS_
protected

Definition at line 350 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialSymDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::Factor_
protected

Definition at line 351 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
ScalarType* Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::A_
protected

Definition at line 353 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
ScalarType* Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::AF_
protected

Definition at line 354 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
std::vector<MagnitudeType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::FERR_
protected

Definition at line 355 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
std::vector<MagnitudeType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::BERR_
protected

Definition at line 356 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
std::vector<ScalarType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::WORK_
protected

Definition at line 357 of file Teuchos_SerialSpdDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
std::vector<MagnitudeType> Teuchos::SerialSpdDenseSolver< OrdinalType, ScalarType >::R_
protected

Definition at line 358 of file Teuchos_SerialSpdDenseSolver.hpp.


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