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Teuchos - Trilinos Tools Package
Version of the Day
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A class for representing and solving banded dense linear systems. More...
#include <Teuchos_SerialBandDenseSolver.hpp>
Public Member Functions | |
Constructor/Destructor Methods | |
| SerialBandDenseSolver () | |
| Default constructor; matrix should be set using setMatrix(), LHS and RHS set with setVectors(). More... | |
| virtual | ~SerialBandDenseSolver () |
| SerialBandDenseSolver destructor. More... | |
Set Methods | |
| int | setMatrix (const RCP< SerialBandDenseMatrix< OrdinalType, ScalarType > > &AB) |
| Sets the pointer 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) |
| void | solveWithTranspose (bool flag) |
| void | solveWithTransposeFlag (Teuchos::ETransp trans) |
| void | solveToRefinedSolution (bool flag) |
| Set whether or not to use iterative refinement to improve solutions to linear systems. More... | |
| void | estimateSolutionErrors (bool flag) |
| Causes all solves to estimate the forward and backward solution error. More... | |
Factor/Solve Methods | |
| int | factor () |
| Computes the in-place LU factorization of the matrix using the LAPACK routine _GBTRF. More... | |
| int | solve () |
| Computes the solution X to AX = B for the this matrix and the B provided to SetVectors().. 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 | 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< SerialBandDenseMatrix < OrdinalType, ScalarType > > | getMatrix () const |
| Returns pointer to current matrix. More... | |
| RCP< SerialBandDenseMatrix < 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... | |
| OrdinalType | numLower () const |
| Returns lower bandwidth of system. More... | |
| OrdinalType | numUpper () const |
| Returns upper bandwidth of system. More... | |
| std::vector< OrdinalType > | IPIV () const |
| Returns pointer to pivot vector (if factorization has been computed), zero otherwise. 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 | ROWCND () const |
| Ratio of smallest to largest row scale factors for the this matrix (returns -1 if not yet computed). More... | |
| MagnitudeType | COLCND () const |
| Ratio of smallest to largest column 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< MagnitudeType > | FERR () const |
| Returns a pointer to the forward error estimates computed by LAPACK. More... | |
| std::vector< MagnitudeType > | BERR () const |
| Returns a pointer to the backward error estimates computed by LAPACK. More... | |
| std::vector< MagnitudeType > | R () const |
| Returns a pointer to the row scaling vector used for equilibration. More... | |
| std::vector< MagnitudeType > | C () const |
| Returns a pointer to the column scale vector used for equilibration. More... | |
I/O methods | |
| void | Print (std::ostream &os) const |
| Print service methods; defines behavior of ostream << operator. More... | |
 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... | |
| Flops * | getFlopCounter () 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 | 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... | |
| virtual void | setLabel (const char *theLabel) |
| virtual const char * | label () const |
| Access the object's label (LEGACY; return std::string instead). 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... | |
| 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... | |
| 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... | |
| 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... | |
Additional Inherited Members | |
| 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... | |
| 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... | |
| Related Functions inherited from Teuchos::Object | |
| std::ostream & | operator<< (std::ostream &os, const Teuchos::Object &obj) |
| Print the given Object to the given output stream. More... | |
A class for representing and solving banded dense linear systems.
| OrdinalType | The index type used by the linear algebra implementation. This should always be int. |
| ScalarType | The type of entries in the matrix. |
This class defines a banded dense matrix, which may have any number of rows or columns (not necessarily equal). It's called "serial" because the matrix lives in a single memory space. Thus, it's the kind of matrix that one might give to the BLAS or LAPACK, not a distributed matrix like one would give to ScaLAPACK.
This class also has methods for computing the (banded) LU factorization of the matrix, and solving linear systems with the matrix. We use instances of SerialDenseVector to represent the right-hand side b or the solution x in the linear system 
. The instance of this class used store the banded matrix must contain KL extra superdiagonals to store the L and U factors (see details below).
Users have the option to do equilibration before factoring the matrix. This may improve accuracy when solving ill-conditioned problems.
Teuchos' LAPACK class wraps LAPACK's LU factorizations, including the banded factorizations. It thus gives access to most of the same functionality as SerialBandDenseSolver. The main difference is that SerialBandDenseSolver offers a higher level of abstraction. It hides the details of which LAPACK routines to call. Furthermore, if you have built Teuchos with support for the third-party library Eigen, SerialBandDenseSolver lets you solve linear systems for ScalarType other than the four supported by the LAPACK library.
There is a single Teuchos::SerialBandDenseSolver constructor. However, the matrix, right hand side and solution vectors must be set prior to executing most methods in this class.
The matrix A, the left hand side X and the right hand side B (when solving AX = B, for X), can be set by appropriate set methods. Each of these three objects must be a SerialDenseMatrix or a SerialDenseVector object. The set methods are as follows:
The SerialBandDenseMatrix must contain KL extra superdiagonals to store the L and U factors, where KL is the upper bandwidth. Consider using the non-member conversion routines generalToBanded and bandedToGeneral if the full SerialDenseMatrix is already in storage. However, it is more efficient simply to construct the SerialBandDenseMatrix with the desired parameters and use the provided matrix access operators so that the full rectangular matrix need not be stored. The conversion routine generalToBanded has a flag to store the input Teuchos::SerialDenseMatrix in banded format with KL extra superdiagonals so this class can use it. Again, it is more efficient to simply construct a Teuchos::SerialBandDenseMatrix object with KL extra superdiagonals than are needed for the matrix data and fill the matrix using the matrix access operators.
See the documentation of Teuchos::SerialBandDenseMatrix for further details on the storage format.
Once a Teuchos::SerialBandDenseSolver is constructed, several mathematical functions can be applied to the object. Specifically:
In many cases, linear systems can be accurately solved by simply computing the LU factorization of the matrix and then performing a forward back solve with a given set of right hand side vectors. However, in some instances, the factorization may be very poorly conditioned and this simple approach may not work. In these situations, equilibration and iterative refinement may improve the accuracy, or prevent a breakdown in the factorization.
SerialBandDenseSolver will use equilibration with the factorization if, once the object is constructed and before it is factored, you call the function factorWithEquilibration(true) to force equilibration to be used. If you are uncertain if equilibration should be used, you may call the function shouldEquilibrate() which will return true if equilibration could possibly help. shouldEquilibrate() uses guidelines specified in the LAPACK User Guide, namely if SCOND < 0.1 and AMAX < Underflow or AMAX > Overflow, to determine if equilibration might be useful.
SerialBandDenseSolver will use iterative refinement after a forward/back solve if you call solveToRefinedSolution(true). It will also compute forward and backward error estimates if you call estimateSolutionErrors(true). Access to the forward (back) error estimates is available via FERR() (BERR()).
Examples using SerialBandDenseSolver can be found in the Teuchos test directories.
Definition at line 166 of file Teuchos_SerialBandDenseSolver.hpp.
| Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::SerialBandDenseSolver | ( | ) |
Default constructor; matrix should be set using setMatrix(), LHS and RHS set with setVectors().
Definition at line 464 of file Teuchos_SerialBandDenseSolver.hpp.
|
virtual |
SerialBandDenseSolver destructor.
Definition at line 501 of file Teuchos_SerialBandDenseSolver.hpp.
| int Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::setMatrix | ( | const RCP< SerialBandDenseMatrix< OrdinalType, ScalarType > > & | AB | ) |
Sets the pointer for coefficient matrix.
Definition at line 546 of file Teuchos_SerialBandDenseSolver.hpp.
| int Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::setVectors | ( | const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > & | X, |
| const RCP< SerialDenseMatrix< OrdinalType, ScalarType > > & | B | ||
| ) |
Sets the pointers for left and right hand side vector(s).
Row dimension of X must match column dimension of matrix A, row dimension of B must match row dimension of A. X and B must have the same dimensions.
Definition at line 576 of file Teuchos_SerialBandDenseSolver.hpp.
|
inline |
Set whether or not to equilibrate just before the matrix factorization. This function must be called before the factorization is performed.
Definition at line 219 of file Teuchos_SerialBandDenseSolver.hpp.
|
inline |
If flag is true, causes all subsequent function calls to work with the transpose of this matrix, otherwise not.
Definition at line 224 of file Teuchos_SerialBandDenseSolver.hpp.
|
inline |
All subsequent function calls will work with the transpose-type set by this method (Teuchos::NO_TRANS, Teuchos::TRANS, and Teuchos::CONJ_TRANS).
Definition at line 228 of file Teuchos_SerialBandDenseSolver.hpp.
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inline |
Set whether or not to use iterative refinement to improve solutions to linear systems.
Definition at line 231 of file Teuchos_SerialBandDenseSolver.hpp.
| void Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::estimateSolutionErrors | ( | bool | flag | ) |
Causes all solves to estimate the forward and backward solution error.
Error estimates will be in the arrays FERR and BERR, resp, after the solve step is complete. These arrays are accessible via the FERR() and BERR() access functions.
Definition at line 599 of file Teuchos_SerialBandDenseSolver.hpp.
| int Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::factor | ( | ) |
Computes the in-place LU factorization of the matrix using the LAPACK routine _GBTRF.
Definition at line 609 of file Teuchos_SerialBandDenseSolver.hpp.
| int Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::solve | ( | ) |
Computes the solution X to AX = B for the this matrix and the B provided to SetVectors()..
Definition at line 667 of file Teuchos_SerialBandDenseSolver.hpp.
| int Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::computeEquilibrateScaling | ( | ) |
Computes the scaling vector S(i) = 1/sqrt(A(i,i)) of the this matrix.
Definition at line 767 of file Teuchos_SerialBandDenseSolver.hpp.
| int Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::equilibrateMatrix | ( | ) |
Equilibrates the this matrix.
Definition at line 788 of file Teuchos_SerialBandDenseSolver.hpp.
| int Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::equilibrateRHS | ( | ) |
Equilibrates the current RHS.
Definition at line 844 of file Teuchos_SerialBandDenseSolver.hpp.
| int Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::applyRefinement | ( | ) |
Apply Iterative Refinement.
Definition at line 733 of file Teuchos_SerialBandDenseSolver.hpp.
| int Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::unequilibrateLHS | ( | ) |
Unscales the solution vectors if equilibration was used to solve the system.
Definition at line 876 of file Teuchos_SerialBandDenseSolver.hpp.
| int Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::reciprocalConditionEstimate | ( | MagnitudeType & | Value | ) |
Returns the reciprocal of the 1-norm condition number of the this matrix.
| Value | Out On return contains the reciprocal of the 1-norm condition number of the this matrix. |
Definition at line 902 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns true if transpose of this matrix has and will be used.
Definition at line 299 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns true if matrix is factored (factor available via AF() and LDAF()).
Definition at line 302 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns true if factor is equilibrated (factor available via AF() and LDAF()).
Definition at line 305 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns true if RHS is equilibrated (RHS available via B() and LDB()).
Definition at line 308 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns true if the LAPACK general rules for equilibration suggest you should equilibrate the system.
Definition at line 311 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns true if forward and backward error estimated have been computed (available via FERR() and BERR()).
Definition at line 314 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns true if the condition number of the this matrix has been computed (value available via ReciprocalConditionEstimate()).
Definition at line 317 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns true if the current set of vectors has been solved.
Definition at line 320 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns true if the current set of vectors has been refined.
Definition at line 323 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns pointer to current matrix.
Definition at line 330 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns pointer to factored matrix (assuming factorization has been performed).
Definition at line 333 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns pointer to current LHS.
Definition at line 336 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns pointer to current RHS.
Definition at line 339 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns row dimension of system.
Definition at line 342 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns column dimension of system.
Definition at line 345 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns lower bandwidth of system.
Definition at line 348 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns upper bandwidth of system.
Definition at line 351 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns pointer to pivot vector (if factorization has been computed), zero otherwise.
Definition at line 354 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns the 1-Norm of the this matrix (returns -1 if not yet computed).
Definition at line 357 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns the reciprocal of the condition number of the this matrix (returns -1 if not yet computed).
Definition at line 360 of file Teuchos_SerialBandDenseSolver.hpp.
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Ratio of smallest to largest row scale factors for the this matrix (returns -1 if not yet computed).
If ROWCND() is >= 0.1 and AMAX() is not close to overflow or underflow, then equilibration is not needed.
Definition at line 365 of file Teuchos_SerialBandDenseSolver.hpp.
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Ratio of smallest to largest column scale factors for the this matrix (returns -1 if not yet computed).
If COLCND() is >= 0.1 then equilibration is not needed.
Definition at line 370 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns the absolute value of the largest entry of the this matrix (returns -1 if not yet computed).
Definition at line 373 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns a pointer to the forward error estimates computed by LAPACK.
Definition at line 376 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns a pointer to the backward error estimates computed by LAPACK.
Definition at line 379 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns a pointer to the row scaling vector used for equilibration.
Definition at line 382 of file Teuchos_SerialBandDenseSolver.hpp.
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Returns a pointer to the column scale vector used for equilibration.
Definition at line 385 of file Teuchos_SerialBandDenseSolver.hpp.
| void Teuchos::SerialBandDenseSolver< OrdinalType, ScalarType >::Print | ( | std::ostream & | os | ) | const |
Print service methods; defines behavior of ostream << operator.
Definition at line 935 of file Teuchos_SerialBandDenseSolver.hpp.
1.8.5