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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 $\mid$ COMPLEX
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)
rhs ::= B(LDB,*) $\mid$ B(*)


LA_TRTRS solves a triangular system of the form $AX = B$, $A^T X = B$, or $A^H X = B$, where $A$ is a real /complex triangular matrix of order $n$, and $B$ 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) $\mid$ 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) $\mid$ KIND(1.0D0)


LA_TRCON estimates the reciprocal of the condition number of a real / complex triangular matrix $A$.
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) $\mid$ KIND(1.0D0)
rhs ::= B(LDB,*) $\mid$ B(*)
sol ::= X(LDX,*) $\mid$ X(*)
err ::= FERR(*), BERR(*) $\mid$ 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) $\mid$ KIND(1.0D0)
rhs ::= B(LDB,*) $\mid$ B(*)
sol ::= X(LDX,*) $\mid$ X(*)
err ::= FERR(*), BERR(*) $\mid$ 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 $\mid$ COMPLEX
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)


LA_TRTRI computes the inverse of a real / complex upper or lower triangular matrix $A$.
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 $\mid$ COMPLEX
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)
rhs ::= B(LDB,*) $\mid$ B(*)


LA_TPTRS solves a triangular system of the form $AX = B$, $A^T X = B$, or $A^H X = B$, where $A$ is a real / complex triangular matrix of order $n$ stored in packed format, and $B$ is an $N\times nrhs$ 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) $\mid$ 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) $\mid$ KIND(1.0D0)


LA_TPCON estimates the reciprocal of the condition number of a packed real / complex triangular matrix $A$.
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) $\mid$ KIND(1.0D0)
rhs ::= B(LDB,*) $\mid$ B(*)
sol ::= X(LDX,*) $\mid$ X(*)
err ::= FERR(*), BERR(*) $\mid$ 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) $\mid$ KIND(1.0D0)
rhs ::= B(LDB,*) $\mid$ B(*)
sol ::= X(LDX,*) $\mid$ X(*)
err ::= FERR(*), BERR(*) $\mid$ 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 $\mid$ COMPLEX
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)


LA_TPTRI computes the inverse of a real / complex upper / lower triangular matrix $A$ 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 $\mid$ COMPLEX
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)
rhs ::= B(LDB,*) $\mid$ B(*)


LA_TBTRS solves a triangular system of the form $AX = B$, $A^T X = B$, or $A^H X = B$, where $A$ is a real / complex triangular band matrix of order $n$, and $B$ is an $n\times nrhs$ 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) $\mid$ 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) $\mid$ 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) $\mid$ KIND(1.0D0)
rhs ::= B(LDB,*) $\mid$ B(*)
sol ::= X(LDX,*) $\mid$ X(*)
err ::= FERR(*), BERR(*) $\mid$ 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) $\mid$ KIND(1.0D0)
rhs ::= B(LDB,*) $\mid$ B(*)
sol ::= X(LDX,*) $\mid$ X(*)
err ::= BERR(*), FERR(*) $\mid$ 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 up previous contents index
Next: Computational Routines for Orthogonal Up: Computational Routines for Linear Previous: Symmetric Indefinite Linear Systems   Contents   Index
Susan Blackford 2001-08-19