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].
-----------------------------------