ZPORFS - improve the computed solution to a system of lin­
       ear equations when the  coefficient  matrix  is  Hermitian
       positive definite,


SYNOPSIS

       SUBROUTINE ZPORFS( UPLO,  N,  NRHS,  A,  LDA, AF, LDAF, B,
                          LDB, X, LDX, FERR, BERR,  WORK,  RWORK,
                          INFO )

           CHARACTER      UPLO

           INTEGER        INFO, LDA, LDAF, LDB, LDX, N, NRHS

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

           COMPLEX*16     A( LDA, * ), AF( LDAF, * ), B(  LDB,  *
                          ), WORK( * ), X( LDX, * )


PURPOSE

       ZPORFS  improves the computed solution to a system of lin­
       ear equations when the  coefficient  matrix  is  Hermitian
       positive  definite, 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) COMPLEX*16 array, dimension (LDA,N)
               The  Hermitian matrix A.  If UPLO = 'U', the lead­
               ing 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 tri­
               angular part of A is not referenced.

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

               The  triangular  factor  U  or L from the Cholesky
               factorization A = U**H*U or A =  L*L**H,  as  com­
               puted by ZPOTRF.

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

       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
               ZPOTRS.   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 solu­
               tion vector X(j) (the j-th column of the  solution
               matrix  X).   If XTRUE is the true solution corre­
               sponding 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 reli­
               able 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 ille­
               gal value


PARAMETERS

       ITMAX  is the maximum number of steps of iterative refine­
       ment.


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