Next: Computational Routines for Orthogonal Up: Computational Routines for Linear Previous: Symmetric Indefinite Linear Systems   Contents   Index

## Triangular Linear Systems

LA_TRTRS
Real and complex versions.


SUBROUTINE LA_TRTRS( UPLO, TRANS, &

DIAG, N, NRHS, A, LDA, B, LDB, INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

TRANS, UPLO

INTEGER, INTENT(IN) :: LDA, LDB, N, NRHS

INTEGER, INTENT(OUT) :: INFO
type(wp), INTENT(IN) :: A(LDA,*)
type(wp), INTENT(INOUT) :: rhs

where
type ::= REAL  COMPLEX
wp   ::= KIND(1.0)  KIND(1.0D0)
rhs  ::= B(LDB,*)  B(*)


LA_TRTRS solves a triangular system of the form , , or , where is a real /complex triangular matrix of order , and is a rectangular matrix.
References: See  [1] and [9,20].
-----------------------------------

LA_TRCON
Real version.


SUBROUTINE LA_TRCON( NORM, UPLO, &

DIAG, N, A, LDA, RCOND, WORK, &

IWORK, INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

NORM, UPLO

INTEGER, INTENT(IN) :: LDA, N

INTEGER, INTENT(OUT) :: INFO, IWORK(*)

REAL(wp), INTENT(OUT) :: RCOND

REAL(wp), INTENT(IN) :: A(LDA,*)

REAL(wp), INTENT(OUT) :: WORK(*)

where
wp   ::= KIND(1.0)  KIND(1.0D0)


Complex version.


SUBROUTINE LA_TRCON( NORM, UPLO, &

DIAG, N, A, LDA, RCOND, WORK, &

RWORK, INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

NORM, UPLO

INTEGER, INTENT(IN) :: LDA, N

INTEGER, INTENT(OUT) :: INFO

REAL(wp), INTENT(OUT) :: RCOND, RWORK(*)

COMPLEX(wp), INTENT(IN) :: A(LDA,*)

COMPLEX(wp), INTENT(OUT) :: WORK(*)

where
wp   ::= KIND(1.0)  KIND(1.0D0)


LA_TRCON estimates the reciprocal of the condition number of a real / complex triangular matrix .
References: See  [1] and [9,20,21].
-----------------------------------

LA_TRRFS
Real version.


SUBROUTINE LA_TRRFS( UPLO, TRANS, &

DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, &

FERR, BERR, WORK, IWORK, INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

TRANS, UPLO

INTEGER, INTENT(IN) :: LDA, LDB, LDX, N, &

NRHS

INTEGER, INTENT(OUT) :: INFO, IWORK(*)

REAL(wp), INTENT(OUT) :: err

REAL(wp), INTENT(IN) :: A(LDA,*), rhs

REAL(wp), INTENT(IN) :: sol

REAL(wp), INTENT(OUT) :: WORK(*)

where
wp   ::= KIND(1.0)  KIND(1.0D0)
rhs  ::= B(LDB,*)  B(*)
sol  ::= X(LDX,*)  X(*)
err  ::= FERR(*), BERR(*)  FERR, BERR


Complex version.


SUBROUTINE LA_TRRFS( UPLO, TRANS, &

DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, &

FERR, BERR, WORK, RWORK, INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

TRANS, UPLO

INTEGER, INTENT(IN) :: LDA, LDB, LDX, N, &

NRHS

INTEGER, INTENT(OUT) :: INFO

REAL(wp), INTENT(OUT) :: err, RWORK(*)

COMPLEX(wp), INTENT(IN) :: A(LDA,*), rhs

COMPLEX(wp), INTENT(INOUT) :: sol

COMPLEX(wp), INTENT(OUT) :: WORK(*)

where
wp   ::= KIND(1.0)  KIND(1.0D0)
rhs  ::= B(LDB,*)  B(*)
sol  ::= X(LDX,*)  X(*)
err  ::= FERR(*), BERR(*)  FERR, BERR


LA_TRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a real / complex triangular coefficient matrix.
References: See  [1] and [9,21,20].
-----------------------------------

LA_TRTRI
Real and complex versions.


SUBROUTINE LA_TRTRI( UPLO, DIAG, N, A, &

LDA, INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

UPLO

INTEGER, INTENT(IN) :: LDA, N

INTEGER, INTENT(OUT) :: INFO
type(wp), INTENT(INOUT) :: A( LDA, * )

where
type ::= REAL  COMPLEX
wp   ::= KIND(1.0)  KIND(1.0D0)


LA_TRTRI computes the inverse of a real / complex upper or lower triangular matrix .
References: See  [1] and [9,20].
-----------------------------------

LA_TPTRS
Real and complex versions.


SUBROUTINE LA_TPTRS( UPLO, TRANS, &

DIAG, N, NRHS, AP, B, LDB, INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

TRANS, UPLO

INTEGER, INTENT(IN) :: LDB, N, NRHS

INTEGER, INTENT(OUT) :: INFO
type(wp), INTENT(IN) :: AP(*)
type(wp), INTENT(INOUT) :: rhs

where
type ::= REAL  COMPLEX
wp   ::= KIND(1.0)  KIND(1.0D0)
rhs  ::= B(LDB,*)  B(*)



LA_TPTRS solves a triangular system of the form , , or , where is a real / complex triangular matrix of order stored in packed format, and is an matrix.
References: See  [1] and [9,20].
-----------------------------------

LA_TPCON
Real version.


SUBROUTINE LA_TPCON( NORM, UPLO, &

DIAG, N, AP, RCOND, WORK, IWORK, &

INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

NORM, UPLO

INTEGER, INTENT(IN) :: N

INTEGER, INTENT(OUT) :: INFO, IWORK(*)

REAL(wp), INTENT(OUT) :: RCOND

REAL(wp), INTENT(IN) :: AP(*)

REAL(wp), INTENT(OUT) :: WORK(*)

where
wp   ::= KIND(1.0)  KIND(1.0D0)


Complex version.


SUBROUTINE LA_TPCON( NORM, UPLO, &

DIAG, N, AP, RCOND, WORK, RWORK, &

INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

NORM, UPLO

INTEGER, INTENT(IN) :: N

INTEGER, INTENT(OUT) :: INFO

REAL(wp), INTENT(OUT) :: RCOND, RWORK(*)

COMPLEX(wp), INTENT(IN) :: AP(*)

COMPLEX(wp), INTENT(OUT) :: WORK(*)

where
wp   ::= KIND(1.0)  KIND(1.0D0)


LA_TPCON estimates the reciprocal of the condition number of a packed real / complex triangular matrix .
References: See  [1] and [9,21,20].
-----------------------------------

LA_TPRFS
Real version.


SUBROUTINE LA_TPRFS( UPLO, TRANS, &

DIAG, N, NRHS, AP, B, LDB, X, LDX, &

FERR, BERR, WORK, IWORK, INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

TRANS, UPLO

INTEGER, INTENT(IN) :: LDB, LDX, N, NRHS

INTEGER, INTENT(OUT) :: INFO, IWORK(*)

REAL(wp), INTENT(OUT) :: err

REAL(wp), INTENT(IN) :: AP(*), rhs, sol

REAL(wp), INTENT(OUT) :: WORK(*)

where
wp   ::= KIND(1.0)  KIND(1.0D0)
rhs  ::= B(LDB,*)  B(*)
sol  ::= X(LDX,*)  X(*)
err  ::= FERR(*), BERR(*)  FERR, BERR


Complex version.


SUBROUTINE LA_TPRFS( UPLO, TRANS, &

DIAG, N, NRHS, AP, B, LDB, X, LDX, &

FERR, BERR, WORK, RWORK, INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

TRANS, UPLO

INTEGER, INTENT(IN) :: LDB, LDX, N, NRHS

INTEGER, INTENT(OUT) :: INFO

REAL(wp), INTENT(OUT) :: err, RWORK(*)

COMPLEX(wp), INTENT(IN) :: AP(*), rhs, sol

COMPLEX(wp), INTENT(OUT) :: WORK(*)

where
wp   ::= KIND(1.0)  KIND(1.0D0)
rhs  ::= B(LDB,*)  B(*)
sol  ::= X(LDX,*)  X(*)
err  ::= FERR(*), BERR(*)  FERR, BERR


LA_TPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a real / complex triangular packed coefficient matrix.
References: See  [1] and [9,21,20].
-----------------------------------

LA_TPTRI
Real and complex versions.


SUBROUTINE LA_TPTRI( UPLO, DIAG, N, AP, &

INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

UPLO

INTEGER, INTENT(IN) :: N

INTEGER, INTENT(OUT) :: INFO
type(wp), INTENT(INOUT) :: AP( * )

where
type ::= REAL  COMPLEX
wp   ::= KIND(1.0)  KIND(1.0D0)


LA_TPTRI computes the inverse of a real / complex upper / lower triangular matrix stored in packed format.
References: See  [1] and [9,20].
-----------------------------------

LA_TBTRS
Real and complex versions.


SUBROUTINE LA_TBTRS( UPLO, TRANS, &

DIAG, N, KD, NRHS, AB, LDAB, B, LDB, &

INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

TRANS, UPLO

INTEGER, INTENT(IN) :: KD, LDAB, LDB, N, &

NRHS

INTEGER, INTENT(OUT) :: INFO
type(wp), INTENT(IN) :: AB(LDAB,*)
type(wp), INTENT(INOUT) :: rhs

where
type ::= REAL  COMPLEX
wp   ::= KIND(1.0)  KIND(1.0D0)
rhs  ::= B(LDB,*)  B(*)


LA_TBTRS solves a triangular system of the form , , or , where is a real / complex triangular band matrix of order , and is an matrix.
References: See  [1] and [9,20].
-----------------------------------

LA_TBCON
Real version.


SUBROUTINE LA_TBCON( NORM, UPLO, &

DIAG, N, KD, AB, LDAB, RCOND, WORK, &

IWORK, INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

NORM, UPLO

INTEGER, INTENT(IN) :: KD, LDAB, N

INTEGER, INTENT(OUT) :: INFO, IWORK(*)

REAL(wp), INTENT(OUT) :: RCOND

REAL(wp), INTENT(IN) :: AB(LDAB,*)

REAL(wp), INTENT(OUT) :: WORK(*)

where
wp   ::= KIND(1.0)  KIND(1.0D0)


Complex version.


SUBROUTINE LA_TBCON( NORM, UPLO, &

DIAG, N, KD, AB, LDAB, RCOND, WORK, &

RWORK, INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

NORM, UPLO

INTEGER, INTENT(IN) :: KD, LDAB, N

INTEGER, INTENT(OUT) :: INFO

REAL(wp), INTENT(OUT) :: RCOND, RWORK(*)

COMPLEX(wp), INTENT(IN) :: AB(LDAB,*)

COMPLEX(wp), INTENT(OUT) :: WORK(*)

where
wp   ::= KIND(1.0)  KIND(1.0D0)


LA_TBCON estimates the reciprocal of the condition number of a real / complex triangular band matrix A.
References: See  [1] and [9,21,20].
-----------------------------------

LA_TBRFS
Real version.


SUBROUTINE LA_TBRFS( UPLO, TRANS, &

DIAG, N, KD, NRHS, AB, LDAB, B, LDB, &

X, LDX, FERR, BERR, WORK, IWORK, &

INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

TRANS, UPLO

INTEGER, INTENT(IN) :: KD, LDAB, LDB, &

LDX, N, NRHS

INTEGER, INTENT(OUT) :: INFO, IWORK(*)

REAL(wp), INTENT(OUT) :: err

REAL(wp), INTENT(IN) :: AB(LDAB,*), rhs, sol

REAL(wp), INTENT(OUT) :: WORK(*)

where
wp   ::= KIND(1.0)  KIND(1.0D0)
rhs  ::= B(LDB,*)  B(*)
sol  ::= X(LDX,*)  X(*)
err  ::= FERR(*), BERR(*)  FERR, BERR


Complex version.


SUBROUTINE LA_TBRFS( UPLO, TRANS, &

DIAG, N, KD, NRHS, AB, LDAB, B, LDB, &

X, LDX, FERR, BERR, WORK, RWORK, &

INFO )

CHARACTER(LEN=1), INTENT(IN) :: DIAG, &

TRANS, UPLO

INTEGER, INTENT(IN) :: KD, LDAB, LDB, &

LDX, N, NRHS

INTEGER, INTENT(OUT) :: INFO

REAL(wp), INTENT(OUT) :: err, RWORK(*)

COMPLEX(wp), INTENT(IN) :: AB(LDAB,*), &
rhs, sol

COMPLEX(wp), INTENT(OUT) :: WORK(*)

where
wp   ::= KIND(1.0)  KIND(1.0D0)
rhs  ::= B(LDB,*)  B(*)
sol  ::= X(LDX,*)  X(*)
err  ::= BERR(*), FERR(*)  BERR, FERR


LA_TBRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a real / complex triangular band coefficient matrix.
References: See  [1] and [9,21,20].
-----------------------------------

Next: Computational Routines for Orthogonal Up: Computational Routines for Linear Previous: Symmetric Indefinite Linear Systems   Contents   Index
Susan Blackford 2001-08-19