DSYRFS(l)		LAPACK routine (version	1.1)		    DSYRFS(l)

NAME
  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

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 refer-
	  enced.  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 deter-
	  mined	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 bounds for each solution vector X(j)
	  (the j-th column of the solution matrix X).  If XTRUE	is the true
	  solution, FERR(j) bounds the magnitude of the	largest	entry in
	  (X(j)	- XTRUE) divided by the	magnitude of the largest entry in
	  X(j).	 The quality of	the error bound	depends	on the quality of the
	  estimate of norm(inv(A)) computed in the code; if the	estimate of
	  norm(inv(A)) is accurate, the	error bound is guaranteed.

  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 entry	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.