CHERFS - improve the computed solution to a system of lin­
       ear equations when the  coefficient  matrix  is  Hermitian
       indefinite,  and  provides error bounds and backward error
       estimates for the solution


SYNOPSIS

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

           CHARACTER      UPLO

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

           INTEGER        IPIV( * )

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

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


PURPOSE

       CHERFS  improves the computed solution to a system of lin­
       ear equations when the  coefficient  matrix  is  Hermitian
       indefinite,  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 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  factored  form  of the matrix A.  AF contains
               the block diagonal matrix D  and  the  multipliers
               used  to obtain the factor U or L from the factor­
               ization A = U*D*U**H or A = L*D*L**H  as  computed
               by CHETRF.

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

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

       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
               CHETRS.  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  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) REAL 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 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



PARAMETERS

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


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