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