DSPRFS(l)		LAPACK routine (version	1.1)		    DSPRFS(l)

NAME
  DSPRFS - improve the computed	solution to a system of	linear equations when
  the coefficient matrix is symmetric indefinite and packed, and provides
  error	bounds and backward error estimates for	the solution

SYNOPSIS

  SUBROUTINE DSPRFS( UPLO, N, NRHS, AP,	AFP, IPIV, B, LDB, X, LDX, FERR,
		     BERR, WORK, IWORK,	INFO )

      CHARACTER	     UPLO

      INTEGER	     INFO, LDB,	LDX, N,	NRHS

      INTEGER	     IPIV( * ),	IWORK( * )

      DOUBLE	     PRECISION AFP( * ), AP( * ), B( LDB, * ), BERR( * ),
		     FERR( * ),	WORK( *	), X( LDX, * )

PURPOSE
  DSPRFS improves the computed solution	to a system of linear equations	when
  the coefficient matrix is symmetric indefinite and packed, 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.

  AP	  (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
	  The upper or lower triangle of the symmetric matrix A, packed
	  columnwise in	a linear array.	 The j-th column of A is stored	in
	  the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j)
	  for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for
	  j<=i<=n.

  AFP	  (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
	  The factored form of the matrix A.  AFP 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
	  DSPTRF, stored as a packed triangular	matrix.

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

  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 DSPTRS.  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.