CLAQHE  - equilibrate a Hermitian matrix A using the scal­
       ing factors in the vector S


SYNOPSIS

       SUBROUTINE CLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX,  EQUED
                          )

           CHARACTER      EQUED, UPLO

           INTEGER        LDA, N

           REAL           AMAX, SCOND

           REAL           S( * )

           COMPLEX        A( LDA, * )


PURPOSE

       CLAQHE equilibrates a Hermitian matrix A using the scaling
       factors in the vector S.


ARGUMENTS

       UPLO    (input) CHARACTER*1
               Specifies whether the upper  or  lower  triangular
               part  of the Hermitian matrix A is stored.  = 'U':
               Upper triangular
               = 'L':  Lower triangular

       N       (input) INTEGER
               The order of the matrix A.  N >= 0.

       A       (input/output) COMPLEX array, dimension (LDA,N)
               On entry, the Hermitian matrix A.  If UPLO =  'U',
               the leading n by n upper triangular part of A con­
               tains the upper triangular part of the  matrix  A,
               and the strictly lower triangular part of A is not
               referenced.  If UPLO = 'L', the  leading  n  by  n
               lower triangular part of A contains the lower tri­
               angular part of the matrix  A,  and  the  strictly
               upper triangular part of A is not referenced.

               On  exit, if EQUED = 'Y', the equilibrated matrix:
               diag(S) * A * diag(S).

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

       S       (input) REAL array, dimension (N)
               The scale factors for A.

       SCOND   (input) REAL
               Ratio of the smallest S(i) to the largest S(i).

               Absolute value of largest matrix entry.

       EQUED   (output) CHARACTER*1
               Specifies  whether  or not equilibration was done.
               = 'N':  No equilibration.
               = 'Y':  Equilibration was done, i.e., A  has  been
               replaced by diag(S) * A * diag(S).


PARAMETERS

       THRESH  is  a  threshold  value  used to decide if scaling
       should be done based on the ratio of the scaling  factors.
       If SCOND < THRESH, scaling is done.

       LARGE  and  SMALL  are  threshold values used to decide if
       scaling should be done based on the absolute size  of  the
       largest  matrix element.  If AMAX > LARGE or AMAX < SMALL,
       scaling is done.


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