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## dsyrfs()

subroutine dsyrfs | ( | character | uplo,
|  | integer | n,
|  | integer | nrhs,
|  | double precision, dimension( lda, * ) | a,
|  | integer | lda,
|  | double precision, dimension( ldaf, * ) | af,
|  | integer | ldaf,
|  | integer, dimension( * ) | ipiv,
|  | double precision, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | double precision, dimension( ldx, * ) | x,
|  | integer | ldx,
|  | double precision, dimension( * ) | ferr,
|  | double precision, dimension( * ) | berr,
|  | double precision, dimension( * ) | work,
|  | integer, dimension( * ) | iwork,
|  | integer | info )

DSYRFS

Download DSYRFS + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  UPLO

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

  [in]

  N

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

  [in]

  NRHS

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

  [in]

  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.
      !>

  [in]

  LDA

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

  [in]

  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.
      !>

  [in]

  LDAF

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

  [in]

  IPIV

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

  [in]

  B

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

  [in]

  LDB

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

  [in,out]

  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.
      !>

  [in]

  LDX

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

  [out]

  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.
      !>

  [out]

  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).
      !>

  [out]

  WORK

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

  [out]

  IWORK

      !>          IWORK is INTEGER array, dimension (N)
      !>

  [out]

  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.