CXML
        	    
LAPACK version 3.0
dsyrfs(3)

PURPOSE
  DSYRFS - 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

SYNTAX
  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, * )

DESCRIPTION
  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.