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

A class for solving dense linear problems. More...

#include <Teuchos_SerialQRDenseSolver.hpp>

Inheritance diagram for Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >:
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Public Types

typedef 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 resetMatrix ()
 
void resetVectors ()
 

Protected Attributes

bool equilibrate_
 
bool shouldEquilibrate_
 
bool equilibratedA_
 
bool equilibratedB_
 
OrdinalType equilibrationModeA_
 
OrdinalType equilibrationModeB_
 
bool transpose_
 
bool factored_
 
bool solved_
 
bool matrixIsZero_
 
bool formedQ_
 
bool formedR_
 
Teuchos::ETransp TRANS_
 
OrdinalType M_
 
OrdinalType N_
 
OrdinalType Min_MN_
 
OrdinalType LDA_
 
OrdinalType LDAF_
 
OrdinalType LDQ_
 
OrdinalType LDR_
 
OrdinalType INFO_
 
OrdinalType LWORK_
 
std::vector< ScalarType > TAU_
 
MagnitudeType ANORM_
 
MagnitudeType BNORM_
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
Matrix_
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
LHS_
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
TMP_
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
RHS_
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
Factor_
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
FactorQ_
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
FactorR_
 
ScalarType * A_
 
ScalarType * AF_
 
ScalarType * Q_
 
ScalarType * R_
 
std::vector< ScalarType > WORK_
 
- Protected Attributes inherited from Teuchos::CompObject
FlopsflopCounter_
 

Private Member Functions

 SerialQRDenseSolver (const SerialQRDenseSolver< OrdinalType, ScalarType > &Source)
 
SerialQRDenseSolveroperator= (const SerialQRDenseSolver< OrdinalType, ScalarType > &Source)
 

Constructor/Destructor Methods

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

Set Methods

int setMatrix (const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > &A)
 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 solveWithTranspose (bool flag)
 If flag is true, causes all subsequent function calls to work with the adjoint of this matrix, otherwise not. More...
 
void solveWithTransposeFlag (Teuchos::ETransp trans)
 All subsequent function calls will work with the transpose-type set by this method (Teuchos::NO_TRANS or Teuchos::CONJ_TRANS). More...
 

Factor/Solve/Invert Methods

int factor ()
 Computes the in-place QR factorization of the matrix using the LAPACK routine _GETRF or the Eigen class HouseholderQR. More...
 
int solve ()
 Computes the solution X to AX = B for the this matrix and the B provided to SetVectors().. More...
 
int computeEquilibrateScaling ()
 Determines if this matrix should be scaled. More...
 
int equilibrateMatrix ()
 Equilibrates the this matrix. More...
 
int equilibrateRHS ()
 Equilibrates the current RHS. More...
 
int unequilibrateLHS ()
 Unscales the solution vectors if equilibration was used to solve the system. More...
 
int formQ ()
 Explicitly forms the unitary matrix Q. More...
 
int formR ()
 Explicitly forms the upper triangular matrix R. More...
 
int multiplyQ (ETransp transq, SerialDenseMatrix< OrdinalType, ScalarType > &C)
 Left multiply the input matrix by the unitary matrix Q or its adjoint. More...
 
int solveR (ETransp transr, SerialDenseMatrix< OrdinalType, ScalarType > &C)
 Solve input matrix on the left with the upper triangular matrix R or its adjoint. More...
 

Query methods

bool transpose ()
 Returns true if adjoint of this matrix has and will be used. More...
 
bool factored ()
 Returns true if matrix is factored (factor available via getFactoredMatrix()). More...
 
bool equilibratedA ()
 Returns true if factor is equilibrated (factor available via getFactoredMatrix()). More...
 
bool equilibratedB ()
 Returns true if RHS is equilibrated (RHS available via getRHS()). More...
 
bool shouldEquilibrate ()
 Returns true if the LAPACK general rules for equilibration suggest you should equilibrate the system. More...
 
bool solved ()
 Returns true if the current set of vectors has been solved. More...
 
bool formedQ ()
 Returns true if Q has been formed explicitly. More...
 
bool formedR ()
 Returns true if R has been formed explicitly. More...
 

Data Accessor methods

RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
getMatrix () const
 Returns pointer to current matrix. More...
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
getFactoredMatrix () const
 Returns pointer to factored matrix (assuming factorization has been performed). More...
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
getQ () const
 Returns pointer to Q (assuming factorization has been performed). More...
 
RCP< SerialDenseMatrix
< OrdinalType, ScalarType > > 
getR () const
 Returns pointer to R (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...
 
std::vector< ScalarType > tau () const
 Returns pointer to pivot vector (if factorization has been computed), zero otherwise. More...
 
MagnitudeType ANORM () const
 Returns the absolute value of the largest element of this matrix (returns -1 if not yet computed). 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, ScalarType *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 ScalarType *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...
 
TEUCHOS_DEPRECATED void POSVX (const char &FACT, const char &UPLO, const OrdinalType &n, const OrdinalType &nrhs, ScalarType *A, const OrdinalType &lda, ScalarType *AF, const OrdinalType &ldaf, const 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 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
 
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, 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, 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...
 
TEUCHOS_DEPRECATED 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, const 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 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
 
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, const 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, 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, 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
 
TEUCHOS_DEPRECATED void TREXC (const char &COMPQ, const OrdinalType &n, ScalarType *T, const OrdinalType &ldt, ScalarType *Q, const OrdinalType &ldq, const OrdinalType &ifst, const OrdinalType &ilst, ScalarType *WORK, 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, ScalarType *S, const OrdinalType &lds, 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...
 
TEUCHOS_DEPRECATED void GEBAL (const char &JOBZ, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, const OrdinalType &ilo, const 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 GEBAL (const char &JOBZ, const OrdinalType &n, ScalarType *A, const OrdinalType &lda, OrdinalType *ilo, OrdinalType *ihi, MagnitudeType *scale, OrdinalType *info) const
 
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::SerialQRDenseSolver< OrdinalType, ScalarType >

A class for solving dense linear problems.

The Teuchos::SerialQRDenseSolver class enables the definition, in terms of Teuchos::SerialDenseMatrix and Teuchos::SerialDenseVector objects, of a dense linear problem, followed by the solution of that problem via the most sophisticated techniques available in LAPACK.

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

Teuchos::SerialQRDenseSolver vs. Teuchos::LAPACK

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

Constructing Teuchos::SerialQRDenseSolver Objects

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

Setting vectors used for linear solves

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

Vector and Utility Functions

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

Strategies for Solving Linear Systems In many cases, linear least squares systems can be accurately solved by simply computing the QR 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.

Teuchos::SerialQRDenseSolver 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 to determine if equilibration might be useful.

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

Definition at line 132 of file Teuchos_SerialQRDenseSolver.hpp.

Member Typedef Documentation

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

Definition at line 138 of file Teuchos_SerialQRDenseSolver.hpp.

Constructor & Destructor Documentation

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

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

Definition at line 400 of file Teuchos_SerialQRDenseSolver.hpp.

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

SerialQRDenseSolver destructor.

Definition at line 436 of file Teuchos_SerialQRDenseSolver.hpp.

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

Member Function Documentation

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::setMatrix ( const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > &  A)

Sets the pointers for coefficient matrix.

Row dimension of A must be greater than or equal to the column dimension of A.

Definition at line 482 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialQRDenseSolver< 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.

Definition at line 509 of file Teuchos_SerialQRDenseSolver.hpp.

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

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

Note
This method must be called before the factorization is performed, otherwise it will have no effect.

Definition at line 186 of file Teuchos_SerialQRDenseSolver.hpp.

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

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

Definition at line 189 of file Teuchos_SerialQRDenseSolver.hpp.

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

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

Definition at line 192 of file Teuchos_SerialQRDenseSolver.hpp.

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

Computes the in-place QR factorization of the matrix using the LAPACK routine _GETRF or the Eigen class HouseholderQR.

Returns
Integer error code, set to 0 if successful.

Definition at line 533 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialQRDenseSolver< 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 575 of file Teuchos_SerialQRDenseSolver.hpp.

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

Determines if this matrix should be scaled.

Returns
Integer error code, set to 0 if successful.

Definition at line 661 of file Teuchos_SerialQRDenseSolver.hpp.

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

Equilibrates the this matrix.

Note
This method will be called automatically in solve() method if factorWithEquilibration( true ) is called.
Returns
Integer error code, set to 0 if successful.

Definition at line 700 of file Teuchos_SerialQRDenseSolver.hpp.

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

Equilibrates the current RHS.

Note
This method will be called automatically in solve() method if factorWithEquilibration( true ) is called.
Returns
Integer error code, set to 0 if successful.

Definition at line 746 of file Teuchos_SerialQRDenseSolver.hpp.

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

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

Note
This method will be called automatically in solve() method if factorWithEquilibration( true ) is called.
Returns
Integer error code, set to 0 if successful.

Definition at line 792 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::formQ ( )

Explicitly forms the unitary matrix Q.

Returns
Integer error code, set to 0 if successful.

Definition at line 829 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::formR ( )

Explicitly forms the upper triangular matrix R.

Returns
Integer error code, set to 0 if successful.

Definition at line 866 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::multiplyQ ( ETransp  transq,
SerialDenseMatrix< OrdinalType, ScalarType > &  C 
)

Left multiply the input matrix by the unitary matrix Q or its adjoint.

Returns
Integer error code, set to 0 if successful.

Definition at line 893 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType , typename ScalarType >
int Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::solveR ( ETransp  transr,
SerialDenseMatrix< OrdinalType, ScalarType > &  C 
)

Solve input matrix on the left with the upper triangular matrix R or its adjoint.

Returns
Integer error code, set to 0 if successful.

Definition at line 954 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::transpose ( )
inline

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

Definition at line 267 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::factored ( )
inline

Returns true if matrix is factored (factor available via getFactoredMatrix()).

Definition at line 270 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::equilibratedA ( )
inline

Returns true if factor is equilibrated (factor available via getFactoredMatrix()).

Definition at line 273 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::equilibratedB ( )
inline

Returns true if RHS is equilibrated (RHS available via getRHS()).

Definition at line 276 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::shouldEquilibrate ( )
inline

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

Definition at line 279 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::solved ( )
inline

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

Definition at line 282 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::formedQ ( )
inline

Returns true if Q has been formed explicitly.

Definition at line 285 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::formedR ( )
inline

Returns true if R has been formed explicitly.

Definition at line 288 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::getMatrix ( ) const
inline

Returns pointer to current matrix.

Definition at line 296 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::getFactoredMatrix ( ) const
inline

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

Definition at line 299 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::getQ ( ) const
inline

Returns pointer to Q (assuming factorization has been performed).

Definition at line 302 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::getR ( ) const
inline

Returns pointer to R (assuming factorization has been performed).

Definition at line 305 of file Teuchos_SerialQRDenseSolver.hpp.

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

Returns pointer to current LHS.

Definition at line 308 of file Teuchos_SerialQRDenseSolver.hpp.

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

Returns pointer to current RHS.

Definition at line 311 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::numRows ( ) const
inline

Returns row dimension of system.

Definition at line 314 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::numCols ( ) const
inline

Returns column dimension of system.

Definition at line 317 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
std::vector<ScalarType> Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::tau ( ) const
inline

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

Definition at line 320 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
MagnitudeType Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::ANORM ( ) const
inline

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

Definition at line 323 of file Teuchos_SerialQRDenseSolver.hpp.

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

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

Definition at line 1016 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 334 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 453 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 442 of file Teuchos_SerialQRDenseSolver.hpp.

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

Member Data Documentation

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

Definition at line 339 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 340 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 341 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 342 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::equilibrationModeA_
protected

Definition at line 343 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::equilibrationModeB_
protected

Definition at line 344 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 345 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 346 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 347 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::matrixIsZero_
protected

Definition at line 348 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::formedQ_
protected

Definition at line 349 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
bool Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::formedR_
protected

Definition at line 350 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
Teuchos::ETransp Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::TRANS_
protected

Definition at line 352 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::M_
protected

Definition at line 354 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::N_
protected

Definition at line 355 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::Min_MN_
protected

Definition at line 356 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 357 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 358 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::LDQ_
protected

Definition at line 359 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
OrdinalType Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::LDR_
protected

Definition at line 360 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 361 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 362 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
std::vector<ScalarType> Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::TAU_
protected

Definition at line 364 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 366 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
MagnitudeType Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::BNORM_
protected

Definition at line 367 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::Matrix_
protected

Definition at line 369 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 370 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::TMP_
protected

Definition at line 371 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 372 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::Factor_
protected

Definition at line 373 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::FactorQ_
protected

Definition at line 374 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
RCP<SerialDenseMatrix<OrdinalType, ScalarType> > Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::FactorR_
protected

Definition at line 375 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 377 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 378 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
ScalarType* Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::Q_
protected

Definition at line 379 of file Teuchos_SerialQRDenseSolver.hpp.

template<typename OrdinalType, typename ScalarType>
ScalarType* Teuchos::SerialQRDenseSolver< OrdinalType, ScalarType >::R_
protected

Definition at line 380 of file Teuchos_SerialQRDenseSolver.hpp.

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

Definition at line 381 of file Teuchos_SerialQRDenseSolver.hpp.


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