CXML
        	    
LAPACK version 3.0
zsprfs(3)

PURPOSE
  ZSPRFS - 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

SYNTAX
  SUBROUTINE ZSPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR,
		     BERR, WORK, RWORK, INFO )

      CHARACTER	     UPLO

      INTEGER	     INFO, LDB, LDX, N, NRHS

      INTEGER	     IPIV( * )

      DOUBLE	     PRECISION BERR( * ), FERR( * ), RWORK( * )

      COMPLEX*16     AFP( * ), AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )

DESCRIPTION
  ZSPRFS 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) COMPLEX*16 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)*(2*n-j)/2) = A(i,j) for
	  j<=i<=n.

  AFP	  (input) COMPLEX*16 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
	  ZSPTRF, 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 ZSPTRF.

  B	  (input) COMPLEX*16 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) COMPLEX*16 array, dimension (LDX,NRHS)
	  On entry, the solution matrix X, as computed by ZSPTRS.  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) COMPLEX*16 array, dimension (2*N)

  RWORK	  (workspace) DOUBLE PRECISION 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.