ZLAQHE(3)      LAPACK routine of NEC Numeric Library Collection      ZLAQHE(3)



NAME
       ZLAQHE

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



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




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

           A         (input/output)
                     A is 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 contains 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
                     triangular 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)
                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(N,1).

           S         (input)
                     S is DOUBLE PRECISION array, dimension (N)
                     The scale factors for A.

           SCOND     (input)
                     SCOND is DOUBLE PRECISION
                     Ratio of the smallest S(i) to the largest S(i).

           AMAX      (input)
                     AMAX is DOUBLE PRECISION
                     Absolute value of largest matrix entry.

           EQUED     (output)
                     EQUED is 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                     = 'Y':  Equilibration was done, i.e., A has been replaced by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).



       Internal 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.



LAPACK routine                  31 October 2017                      ZLAQHE(3)