zlaqhp(3F)

NAME
     ZLAQHP - equilibrate a Hermitian matrix A using the scaling 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 Hermitian 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.  = '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             = 'Y':  Equilibration was done, i.e., A has been replaced by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.