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


SYNOPSIS

       SUBROUTINE ZLAQHP( UPLO, N, AP, S, SCOND, AMAX, EQUED )

           CHARACTER      EQUED, UPLO

           INTEGER        N

           DOUBLE         PRECISION AMAX, SCOND

           DOUBLE         PRECISION S( * )

           COMPLEX*16     AP( * )


PURPOSE

       ZLAQHP 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.

       AP      (input/output) COMPLEX*16 array, dimension
               (N*(N+1)/2)
               On entry, the upper or lower triangle of the  Her­
               mitian  matrix  A,  packed  columnwise in a linear
               array.  The j-th column of  A  is  stored  in  the
               array  AP  as  follows:  if  UPLO  =  'U',  AP(i +
               (j-1)*j/2) = A(i,j) for 1<=i<=j; if  UPLO  =  'L',
               AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

               On  exit,  the equilibrated matrix:  diag(S) * A *
               diag(S), in the same storage format as A.

       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.

               =  'Y':   Equilibration was done, i.e., A has been
               replaced by diag(S) * A * diag(S).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