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


SYNOPSIS

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

           CHARACTER      EQUED, UPLO

           INTEGER        LDA, N

           DOUBLE         PRECISION AMAX, SCOND

           DOUBLE         PRECISION S( * )

           COMPLEX*16     A( LDA, * )


PURPOSE

       ZLAQHE 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*16 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) DOUBLE PRECISION array, dimension (N)
               The scale factors for A.

       SCOND   (input) DOUBLE PRECISION
               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               =  'Y':   Equilibration was done, i.e., A has been
               replaced by diag(S) * A * diag(S).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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