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CPPRFS(l)			       )			     CPPRFS(l)

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

SYNOPSIS
       SUBROUTINE CPPRFS( UPLO,	 N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR,
			  WORK, RWORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDB, LDX, N, NRHS

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

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

PURPOSE
       CPPRFS  improves	 the computed solution to a system of linear equations
       when the coefficient matrix is Hermitian positive definite and  packed,
       and  provides  error  bounds and backward error estimates for the solu‐
       tion.

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)*(2n-j)/2)  =
	       A(i,j) for j<=i<=n.

       AFP     (input) COMPLEX array, dimension (N*(N+1)/2)
	       The  triangular factor U or L from the Cholesky factorization A
	       = U**H*U or A = L*L**H, as computed  by	SPPTRF/CPPTRF,	packed
	       columnwise in a linear array in the same format as A (see AP).

       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 CPPTRS.  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			     CPPRFS(l)
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