herfs - Man Page

subroutine cherfs (uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CHERFS
subroutine csyrfs (uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CSYRFS
subroutine dsyrfs (uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DSYRFS
subroutine ssyrfs (uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
SSYRFS
subroutine zherfs (uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZHERFS
subroutine zsyrfs (uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZSYRFS

CHERFS  

Purpose:

 CHERFS improves the computed solution to a system of linear
 equations when the coefficient matrix is Hermitian indefinite, and
 provides error bounds and backward error estimates for the solution.

Parameters

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.

A

          A is COMPLEX array, dimension (LDA,N)
          The Hermitian matrix A.  If UPLO = 'U', the leading N-by-N
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced.  If UPLO = 'L', the leading N-by-N lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

AF

          AF is COMPLEX array, dimension (LDAF,N)
          The factored form of the matrix A.  AF contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor U or L from the factorization A = U*D*U**H or
          A = L*D*L**H as computed by CHETRF.

LDAF

          LDAF is INTEGER
          The leading dimension of the array AF.  LDAF >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by CHETRF.

B

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side matrix B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

X

          X is COMPLEX array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by CHETRS.
          On exit, the improved solution matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bound for each solution vector
          X(j) (the j-th column of the solution matrix X).
          If XTRUE is the true solution corresponding to X(j), FERR(j)
          is an estimated upper bound for the magnitude of the largest
          element in (X(j) - XTRUE) divided by the magnitude of the
          largest element in X(j).  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector X(j) (i.e., the smallest relative change in
          any element of A or B that makes X(j) an exact solution).

WORK

          WORK is COMPLEX array, dimension (2*N)

RWORK

          RWORK is REAL array, dimension (N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

  ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 190 of file cherfs.f.

CSYRFS  

Purpose:

 CSYRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is symmetric indefinite, and
 provides error bounds and backward error estimates for the solution.

Parameters

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.

A

          A is COMPLEX array, dimension (LDA,N)
          The symmetric matrix A.  If UPLO = 'U', the leading N-by-N
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced.  If UPLO = 'L', the leading N-by-N lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

AF

          AF is COMPLEX array, dimension (LDAF,N)
          The factored form of the matrix A.  AF contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor U or L from the factorization A = U*D*U**T or
          A = L*D*L**T as computed by CSYTRF.

LDAF

          LDAF is INTEGER
          The leading dimension of the array AF.  LDAF >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by CSYTRF.

B

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side matrix B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

X

          X is COMPLEX array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by CSYTRS.
          On exit, the improved solution matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bound for each solution vector
          X(j) (the j-th column of the solution matrix X).
          If XTRUE is the true solution corresponding to X(j), FERR(j)
          is an estimated upper bound for the magnitude of the largest
          element in (X(j) - XTRUE) divided by the magnitude of the
          largest element in X(j).  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector X(j) (i.e., the smallest relative change in
          any element of A or B that makes X(j) an exact solution).

WORK

          WORK is COMPLEX array, dimension (2*N)

RWORK

          RWORK is REAL array, dimension (N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

  ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 190 of file csyrfs.f.

DSYRFS  

Purpose:

 DSYRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is symmetric indefinite, and
 provides error bounds and backward error estimates for the solution.

Parameters

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          The symmetric matrix A.  If UPLO = 'U', the leading N-by-N
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced.  If UPLO = 'L', the leading N-by-N lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

AF

          AF is DOUBLE PRECISION array, dimension (LDAF,N)
          The factored form of the matrix A.  AF contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor U or L from the factorization A = U*D*U**T or
          A = L*D*L**T as computed by DSYTRF.

LDAF

          LDAF is INTEGER
          The leading dimension of the array AF.  LDAF >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by DSYTRF.

B

          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side matrix B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

X

          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by DSYTRS.
          On exit, the improved solution matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

FERR

          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bound for each solution vector
          X(j) (the j-th column of the solution matrix X).
          If XTRUE is the true solution corresponding to X(j), FERR(j)
          is an estimated upper bound for the magnitude of the largest
          element in (X(j) - XTRUE) divided by the magnitude of the
          largest element in X(j).  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error.

BERR

          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector X(j) (i.e., the smallest relative change in
          any element of A or B that makes X(j) an exact solution).

WORK

          WORK is DOUBLE PRECISION array, dimension (3*N)

IWORK

          IWORK is INTEGER array, dimension (N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

  ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 189 of file dsyrfs.f.

SSYRFS  

Purpose:

 SSYRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is symmetric indefinite, and
 provides error bounds and backward error estimates for the solution.

Parameters

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.

A

          A is REAL array, dimension (LDA,N)
          The symmetric matrix A.  If UPLO = 'U', the leading N-by-N
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced.  If UPLO = 'L', the leading N-by-N lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

AF

          AF is REAL array, dimension (LDAF,N)
          The factored form of the matrix A.  AF contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor U or L from the factorization A = U*D*U**T or
          A = L*D*L**T as computed by SSYTRF.

LDAF

          LDAF is INTEGER
          The leading dimension of the array AF.  LDAF >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by SSYTRF.

B

          B is REAL array, dimension (LDB,NRHS)
          The right hand side matrix B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

X

          X is REAL array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by SSYTRS.
          On exit, the improved solution matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bound for each solution vector
          X(j) (the j-th column of the solution matrix X).
          If XTRUE is the true solution corresponding to X(j), FERR(j)
          is an estimated upper bound for the magnitude of the largest
          element in (X(j) - XTRUE) divided by the magnitude of the
          largest element in X(j).  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector X(j) (i.e., the smallest relative change in
          any element of A or B that makes X(j) an exact solution).

WORK

          WORK is REAL array, dimension (3*N)

IWORK

          IWORK is INTEGER array, dimension (N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

  ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 189 of file ssyrfs.f.

ZHERFS  

Purpose:

 ZHERFS improves the computed solution to a system of linear
 equations when the coefficient matrix is Hermitian indefinite, and
 provides error bounds and backward error estimates for the solution.

Parameters

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          The Hermitian matrix A.  If UPLO = 'U', the leading N-by-N
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced.  If UPLO = 'L', the leading N-by-N lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

AF

          AF is COMPLEX*16 array, dimension (LDAF,N)
          The factored form of the matrix A.  AF contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor U or L from the factorization A = U*D*U**H or
          A = L*D*L**H as computed by ZHETRF.

LDAF

          LDAF is INTEGER
          The leading dimension of the array AF.  LDAF >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by ZHETRF.

B

          B is COMPLEX*16 array, dimension (LDB,NRHS)
          The right hand side matrix B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

X

          X is COMPLEX*16 array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by ZHETRS.
          On exit, the improved solution matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

FERR

          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bound for each solution vector
          X(j) (the j-th column of the solution matrix X).
          If XTRUE is the true solution corresponding to X(j), FERR(j)
          is an estimated upper bound for the magnitude of the largest
          element in (X(j) - XTRUE) divided by the magnitude of the
          largest element in X(j).  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error.

BERR

          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector X(j) (i.e., the smallest relative change in
          any element of A or B that makes X(j) an exact solution).

WORK

          WORK is COMPLEX*16 array, dimension (2*N)

RWORK

          RWORK is DOUBLE PRECISION array, dimension (N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

  ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 190 of file zherfs.f.

ZSYRFS  

Purpose:

 ZSYRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is symmetric indefinite, and
 provides error bounds and backward error estimates for the solution.

Parameters

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          The symmetric matrix A.  If UPLO = 'U', the leading N-by-N
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced.  If UPLO = 'L', the leading N-by-N lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

AF

          AF is COMPLEX*16 array, dimension (LDAF,N)
          The factored form of the matrix A.  AF contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor U or L from the factorization A = U*D*U**T or
          A = L*D*L**T as computed by ZSYTRF.

LDAF

          LDAF is INTEGER
          The leading dimension of the array AF.  LDAF >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by ZSYTRF.

B

          B is COMPLEX*16 array, dimension (LDB,NRHS)
          The right hand side matrix B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

X

          X is COMPLEX*16 array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by ZSYTRS.
          On exit, the improved solution matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

FERR

          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bound for each solution vector
          X(j) (the j-th column of the solution matrix X).
          If XTRUE is the true solution corresponding to X(j), FERR(j)
          is an estimated upper bound for the magnitude of the largest
          element in (X(j) - XTRUE) divided by the magnitude of the
          largest element in X(j).  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error.

BERR

          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector X(j) (i.e., the smallest relative change in
          any element of A or B that makes X(j) an exact solution).

WORK

          WORK is COMPLEX*16 array, dimension (2*N)

RWORK

          RWORK is DOUBLE PRECISION array, dimension (N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

  ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 190 of file zsyrfs.f.