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NAME
     zlaqhe - equilibrate a Hermitian matrix A using the  scaling
     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, * )



     #include <sunperf.h>

     void zlaqhe(char uplo, int n, doublecomplex  *za,  int  lda,
               double   *s,   double  scond,  double  amax,  char
               *equed);

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).

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               = 'Y':  Equilibration was done, i.e., A  has  been
               replaced by diag(S) * A * diag(S).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