ZLAQHB  -  equilibrate a symmetric band matrix A using the
       scaling factors in the vector S


SYNOPSIS

       SUBROUTINE ZLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND,  AMAX,
                          EQUED )

           CHARACTER      EQUED, UPLO

           INTEGER        KD, LDAB, N

           DOUBLE         PRECISION AMAX, SCOND

           DOUBLE         PRECISION S( * )

           COMPLEX*16     AB( LDAB, * )


PURPOSE

       ZLAQHB  equilibrates  a  symmetric band 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 symmetric matrix A is stored.  = 'U':
               Upper triangular
               = 'L':  Lower triangular

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

       KD      (input) INTEGER
               The number of super-diagonals of the matrix  A  if
               UPLO = 'U', or the number of sub-diagonals if UPLO
               = 'L'.  KD >= 0.

       AB      (input/output) COMPLEX*16 array, dimension
               (LDAB,N)
               On  entry, the upper or lower triangle of the sym­
               metric band matrix A, stored  in  the  first  KD+1
               rows of the array.  The j-th column of A is stored
               in the j-th column of the array AB as follows:  if
               UPLO  =  'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
               kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)    =  A(i,j)
               for j<=i<=min(n,j+kd).

               On exit, if INFO = 0, the triangular factor U or L
               from the Cholesky factorization A = U'*U  or  A  =
               L*L'  of  the  band  matrix A, in the same storage
               format as A.

       LDAB    (input) INTEGER
               The leading dimension of the array  AB.   LDAB  >=


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               = 'Y':  Equilibration was done, i.e., A  has  been
               replaced by diag(S) * A * diag(S).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


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