DSYRFS (3lapack)

improve 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

SYNOPSIS

  SUBROUTINE DSYRFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX,
                     FERR, BERR, WORK, IWORK, INFO )

      CHARACTER      UPLO

      INTEGER        INFO, LDA, LDAF, LDB, LDX, N, NRHS

      INTEGER        IPIV( * ), IWORK( * )

      DOUBLE         PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR(
                     * ), FERR( * ), WORK( * ), X( LDX, * )

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.

ARGUMENTS

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

  N       (input) INTEGER
          The order of the matrix A.  N >= 0.

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

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

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

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

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

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

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

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

  FERR    (output) 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    (output) 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    (workspace) DOUBLE PRECISION array, dimension (3*N)

  IWORK   (workspace) INTEGER array, dimension (N)

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

PARAMETERS

  ITMAX is the maximum number of steps of iterative refinement.