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



NAME
       ZLAQHP

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



PURPOSE
            ZLAQHP 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.

           AP        (input/output)
                     AP is 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)
                     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                     = 'Y':  Equilibration was done, i.e., A has been replaced by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                      ZLAQHP(3)