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CHPRFS(l)			       )			     CHPRFS(l)

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

SYNOPSIS
       SUBROUTINE CHPRFS( 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( * )

	   REAL		  BERR( * ), FERR( * ), RWORK( * )

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

PURPOSE
       CHPRFS  improves	 the computed solution to a system of linear equations
       when the coefficient matrix is Hermitian	 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 array, dimension (N*(N+1)/2)
	       The upper or lower triangle of the Hermitian 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 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**H or A =  L*D*L**H  as
	       computed by CHPTRF, 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 CHPTRF.

       B       (input) COMPLEX 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 array, dimension (LDX,NRHS)
	       On entry, the solution matrix X, as  computed  by  CHPTRS.   On
	       exit, the improved solution matrix X.

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

       FERR    (output) REAL 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) REAL array, dimension (NRHS)
	       The componentwise relative backward error of each solution vec‐
	       tor 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 array, dimension (2*N)

       RWORK   (workspace) REAL 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.

LAPACK version 3.0		 15 June 2000			     CHPRFS(l)
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