next up previous contents index
Next: Symmetric Indefinite Linear Systems Up: Computational Routines for Linear Previous: General Linear Systems   Contents   Index

Symmetric/Hermitian Positive Definite Linear Systems

LA_POTRF
Real and complex Hermitian versions.


SUBROUTINE LA_POTRF( UPLO, N, A, LDA, & 

INFO )
CHARACTER(LEN=1), INTENT(IN) :: 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_POTRF computes the Cholesky factorization of a real symmetric / complex Hermitian positive definite matrix $A$.
References: See  [1] and [9,20].
-----------------------------------

LA_POTRS
Real and complex Hermitian versions.


SUBROUTINE LA_POTRS( UPLO, N, NRHS, & 

A, LDA, B, LDB, INFO )
CHARACTER(LEN=1), INTENT(IN) :: 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_POTRS solves a system of linear equations $AX = B$ with a a real symmetric / complex Hermitian positive definite matrix $A$ using the Cholesky factorization computed by LA_POTRF.
References: See  [1] and [9,20].
-----------------------------------

LA_POCON
Real version.


SUBROUTINE LA_POCON( UPLO, N, A, LDA, & 

ANORM, RCOND, WORK, IWORK, INFO )
CHARACTER(LEN=1), INTENT(IN) :: &
UPLO
INTEGER, INTENT(IN) :: LDA, N
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(IN) :: ANORM
REAL(wp), INTENT(OUT) :: RCOND
INTEGER, INTENT(OUT) :: IWORK( * )
REAL(wp), INTENT(IN) :: A( LDA, * )
REAL(wp), INTENT(OUT) :: WORK( * )
where
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)


Complex Hermitian version.


 SUBROUTINE LA_POCON( UPLO, N, A, LDA, & 

ANORM, RCOND, WORK, RWORK, INFO )
CHARACTER(LEN=1), INTENT(IN) :: &
UPLO
INTEGER, INTENT(IN) :: LDA, N
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(IN) :: ANORM
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_POCON estimates the reciprocal of the condition number of a real symmetric / complex Hermitian positive definite matrix using the Cholesky factorization computed by POTRF.
References: See  [1] and [9,21,20].
-----------------------------------

LA_PORFS
Real version.


SUBROUTINE LA_PORFS( UPLO, N, NRHS, & 

A, LDA, AF, LDAF, B, LDB, X, LDX, &
FERR, BERR, WORK, IWORK, INFO )
CHARACTER(LEN=1), INTENT(IN) :: &
UPLO
INTEGER, INTENT(IN) :: LDA, LDAF, &
LDB, LDX, N, NRHS
INTEGER, INTENT(OUT) :: INFO, &
IWORK(*)
REAL(wp), INTENT(OUT) :: err
REAL(wp), INTENT(IN) :: A( LDA,*), &
AF( LDAF,*), rhs
REAL(wp), INTENT(INOUT) :: 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 Hermitian version.


SUBROUTINE LA_PORFS( UPLO, N, NRHS, & 

A, LDA, AF, LDAF, B, LDB, X, LDX, &
FERR, BERR, WORK, RWORK, INFO )
CHARACTER(LEN=1), INTENT(IN) :: &
UPLO
INTEGER, INTENT(IN) :: LDA, LDAF, &
LDB, LDX, N, NRHS
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(OUT) :: err, RWORK(*)
COMPLEX(wp), INTENT(IN) :: A( LDA,*), &
AF( LDAF,*), 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_PORFS improves the computed solution to a system of linear equations when the coefficient matrix is a real symmetric / complex Hermitian positive definite, and provides error bounds and backward error estimates for the solution.
References: See  [1] and [9,21,20].
-----------------------------------

LA_POTRI
Real and complex Hermitian versions.


SUBROUTINE LA_POTRI( UPLO, N, A, LDA, & 

INFO )
CHARACTER(LEN=1), INTENT(IN) :: 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_POTRI computes the inverse of a real symmetric / complex Hermitian positive definite matrix $A$ using the Cholesky factorization computed by LA_POTRF.
References: See  [1] and [9,20].
-----------------------------------

LA_POEQU
Real and complex Hermitian versions.


 SUBROUTINE LA_POEQU( N, A, LDA, S, & 

SCOND, AMAX, INFO )
INTEGER, INTENT(IN) :: LDA, N
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(OUT) :: AMAX, &
SCOND, S(*)
type(wp), INTENT(IN) :: A( LDA,*)
where
type ::= REAL $\mid$ COMPLEX
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)


LA_POEQU computes row and column scalings intended to equilibrate a real symmetric / complex Hermitian positive definite matrix $A$ and reduce its condition number.
References: See  [1] and [9,21,20].
-----------------------------------

LA_PPTRF
Real and complex Hermitian versions.


SUBROUTINE LA_PPTRF( UPLO, N, AP, & 

INFO )
CHARACTER(LEN=1), INTENT(IN) :: 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_PPTRF computes the Cholesky factorization of a real symmetric / complex Hermitian positive definite matrix $A$ stored in packed format.
References: See  [1] and [9,20].
-----------------------------------

LA_PPTRS
Real and complex Hermitian versions.


SUBROUTINE LA_PPTRS( UPLO, N, NRHS, & 

AP, B, LDB, INFO )
CHARACTER(LEN=1), INTENT(IN) :: 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_PPTRS solves a system of linear equations $AX = B$ with a real symmetric / complex Hermitian positive definite matrix $A$ in packed storage using the Cholesky factorization computed by LA_PPTRF.
References: See  [1] and [9,20].
-----------------------------------

LA_PPCON
Real version.


SUBROUTINE LA_PPCON( UPLO, N, AP, & 

ANORM, RCOND, WORK, IWORK, INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: N
INTEGER, INTENT(OUT) :: INFO, IWORK(*)
REAL(wp), INTENT(IN) :: ANORM
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 Hermitian version.


 SUBROUTINE LA_PPCON( UPLO, N, AP, & 

ANORM, RCOND, WORK, RWORK, INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: N
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(IN) :: ANORM
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_PPCON estimates the reciprocal of the condition number of a real symmetric / complex Hermitian positive definite packed matrix using the Cholesky factorization computed by LA_PPTRF.
References: See  [1] and [9,21,20].
-----------------------------------

LA_PPRFS
Real version.


 SUBROUTINE LA_PPRFS( UPLO, N, NRHS, & 

AP, AFP, B, LDB, X, LDX, FERR, BERR, &
WORK, IWORK, INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: LDB, LDX, N, NRHS
INTEGER, INTENT(OUT) :: INFO, IWORK(*)
REAL(wp), INTENT(OUT) :: err
REAL(wp), INTENT(IN) :: AFP(*), AP(*), rhs
REAL(wp), INTENT(INOUT) :: 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 Hermitian version.


 SUBROUTINE LA_PPRFS( UPLO, N, NRHS, & 

AP, AFP, B, LDB, X, LDX, FERR, BERR, &
WORK, RWORK, INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: LDB, LDX, N, NRHS
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(OUT) :: err, RWORK(*)
COMPLEX(wp), INTENT(IN) :: AFP(*), AP(*), &
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_PPRFS improves the computed solution to a system of linear equations when the coefficient matrix is a real symmetric / complex Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution.
References: See  [1] and [9,21,20].
-----------------------------------

LA_PPTRI
Real and complex Hermitian versions.


 SUBROUTINE LA_PPTRI( UPLO, N, AP, INFO ) 

CHARACTER(LEN=1), INTENT(IN) :: 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_PPTRI computes the inverse of real symmetric / complex Hermitian positive definite matrix $A$ in packed storage format using the Cholesky factorization computed by LA_PPTRF.
References: See  [1] and [9,20].
-----------------------------------

LA_PPEQU
Real and complex Hermitian versions.


 SUBROUTINE LA_PPEQU( UPLO, N, AP, S, & 

SCOND, AMAX, INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: N
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(OUT) :: AMAX, SCOND, &
S(*)
type(wp), INTENT(IN) :: AP(*)
where
type ::= REAL $\mid$ COMPLEX
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)


LA_PPEQU computes row and column scalings intended to equilibrate a real symmetric / complex Hermitian positive definite matrix $A$ in packed storage and reduce its condition number.
References: See  [1] and [9,21,20].
-----------------------------------

LA_PBTRF
Real and complex Hermitian versions.


 SUBROUTINE LA_PBTRF( UPLO, N, KD, AB, & 

LDAB, INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: KD, LDAB, N
INTEGER, INTENT(OUT) :: INFO
type(wp), INTENT(INOUT) :: AB( LDAB,*)
where
type ::= REAL $\mid$ COMPLEX
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)


LA_PBTRF computes the Cholesky factorization of a real symmetric / complex Hermitian positive definite band matrix $A$.
References: See  [1] and [9,20].
-----------------------------------

LA_PBTRS
Real and complex Hermitian versions.


SUBROUTINE LA_PBTRS( UPLO, N, KD, & 

NRHS, AB, LDAB, B, LDB, INFO )
CHARACTER(LEN=1), INTENT(IN) :: 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_PBTRS solves a system of linear equations $AX = B$ with a real symmetric / complex Hermitian positive definite band matrix $A$ using the Cholesky factorization computed by LA_PBTRF.
References: See  [1] and [9,20].
-----------------------------------

LA_PBCON
Real version.


SUBROUTINE LA_PBCON( UPLO, N, KD, AB, & 

LDAB, ANORM, RCOND, WORK, IWORK, &
INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: KD, LDAB, N
INTEGER, INTENT(OUT) :: INFO, IWORK(*)
REAL(wp), INTENT(IN) :: ANORM
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 Hermitian version.


 SUBROUTINE LA_PBCON( UPLO, N, KD, AB, & 

LDAB, ANORM, RCOND, WORK, RWORK, &
INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: KD, LDAB, N
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(IN) :: ANORM
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_PBCON estimates the reciprocal of the condition number of a real symmetric / complex Hermitian positive definite band matrix using the Cholesky factorization computed by LA_PBTRF.
References: See  [1] and [9,21,20].
-----------------------------------

LA_PBRFS
Real version.


 SUBROUTINE LA_PBRFS( UPLO, N, KD, & 

NRHS, AB, LDAB, AFB, LDAFB, B, LDB, &
X, LDX, FERR, BERR, WORK, IWORK, &
INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: KD, LDAB, LDAFB, &
LDB, LDX, N, NRHS
INTEGER, INTENT(OUT) :: INFO, IWORK(*)
REAL(wp), INTENT(OUT) :: err
REAL(wp), INTENT(IN) :: AB( LDAB,*), &
AFB( LDAFB,*), rhs
REAL(wp), INTENT(INOUT) :: 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 Hermitian version.


 SUBROUTINE LA_PBRFS( UPLO, N, KD, & 

NRHS, AB, LDAB, AFB, LDAFB, B, LDB, &
X, LDX, FERR, BERR, WORK, RWORK, &
INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: KD, LDAB, LDAFB, &
LDB, LDX, N, NRHS
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(OUT) :: err, RWORK(*),
COMPLEX(wp), INTENT(IN) :: AB( LDAB,*), &
AFB( LDAFB,*), 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_PBRFS improves the computed solution to a system of linear equations when the coefficient matrix is a real symmetric / complex Hermitian positive definite banded, and provides error bounds and backward error estimates for the solution.
References: See  [1] and [9,21,20].
-----------------------------------

LA_PBEQU
Real and complex Hermitian versions.


 SUBROUTINE LA_PBEQU( UPLO, N, KD, AB, & 

LDAB, S, SCOND, AMAX, INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: KD, LDAB, N
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(OUT) :: AMAX, SCOND, &
S(*)
type(wp), INTENT(IN) :: AB( LDAB,*)
where
type ::= REAL $\mid$ COMPLEX
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)


LA_PBEQU computes row and column scalings intended to equilibrate a real symmetric / complex Hermitian positive definite band matrix A and reduce its condition number.
References: See  [1] and [9,21,20].
-----------------------------------

LA_PTTRF
Real and complex Hermitian versions.


 SUBROUTINE LA_PTTRF( N, D, E, INFO ) 

INTEGER, INTENT(IN) :: N
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(INOUT) :: D( * )
type(wp), INTENT(INOUT) :: E( * )
where
type ::= REAL $\mid$ COMPLEX
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)


LA_PTTRF computes the $L D L^T$ factorization of a real symmetric / complex Hermitian positive definite tridiagonal matrix $A$. The factorization may also be regarded as having the form $A = U^T D U$.
References: See  [1] and [9,20].
-----------------------------------

LA_PTTRS
Real version.


SUBROUTINE LA_PTTRS( N, NRHS, D, E, B, & 

LDB, INFO )
INTEGER, INTENT(IN) :: LDB, N, NRHS
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(IN) :: D(*)
REAL(wp), INTENT(IN) :: E(*)
REAL(wp), INTENT(INOUT) :: rhs
where
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)
rhs ::= B(LDB,*) $\mid$ B(*)

Complex Hermitian version.


 SUBROUTINE LA_PTTRS( UPLO, N, NRHS, D, & 

E, B, LDB, INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: LDB, N, NRHS
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(IN) :: D(*)
COMPLEX(wp), INTENT(IN) :: E(*)
COMPLEX(wp), INTENT(INOUT) :: rhs
where
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)
rhs ::= B(LDB,*) $\mid$ B(*)


LA_PTTRS solves a real symmetric / complex Hermitian positive definite tridiagonal system of the form $AX = B$, using the factorization computed by LA_PTTRF.
References: See  [1] and [9,20].
-----------------------------------

LA_PTCON
Real and complex Hermitian versions.


SUBROUTINE LA_PTCON( N, D, E, ANORM, & 

RCOND, RWORK, INFO )
INTEGER, INTENT(IN) :: N
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(IN) :: ANORM, D(*)
REAL(wp), INTENT(OUT) :: RCOND, &
RWORK(*)
type(wp), INTENT(IN) :: E(*)
where
type ::= REAL $\mid$ COMPLEX
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)


LA_PTCON computes the reciprocal of the condition number of a real symmetric / complex Hermitian positive definite tridiagonal matrix using the factorization computed by LA_PTTRF.
References: See  [1] and [9,21,20].
-----------------------------------

LA_PTRFS
Real version.


 SUBROUTINE LA_PTRFS( N, NRHS, D, E, DF, & 

EF, B, LDB, X, LDX, FERR, BERR, WORK, &
INFO )
INTEGER, INTENT(IN) :: LDB, LDX, N, NRHS
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(IN) :: D(*), DF(*)
REAL(wp), INTENT(OUT) :: err
REAL(wp), INTENT(IN) :: rhs, E(*), EF(*)
REAL(wp), INTENT(INOUT) :: 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 Hermitian version.


 SUBROUTINE LA_PTRFS( UPLO, N, NRHS, D, & 

E, DF, EF, B, LDB, X, LDX, FERR, BERR, &
WORK, RWORK, INFO )
CHARACTER(LEN=1), INTENT(IN) :: UPLO
INTEGER, INTENT(IN) :: LDB, LDX, N, NRHS
INTEGER, INTENT(OUT) :: INFO
REAL(wp), INTENT(IN) :: D(*), DF(*)
REAL(wp), INTENT(OUT) :: err, &
RWORK(*)
COMPLEX(wp), INTENT(IN) :: rhs, E(*), EF(*)
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_PTRFS improves the computed solution to a system of linear equations when the coefficient matrix is a real symmetric / complex Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution.
References: See  [1] and [9,21,20].
-----------------------------------


next up previous contents index
Next: Symmetric Indefinite Linear Systems Up: Computational Routines for Linear Previous: General Linear Systems   Contents   Index
Susan Blackford 2001-08-19