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zlaqsb

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

 SYNOPSIS
      SUBROUTINE ZLAQSB( 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
      ZLAQSB 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 >=
              KD+1.

      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              = 'Y':  Equilibration was done, i.e., A has been
              replaced by diag(S) * A * diag(S).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 scal-
      ing should be done based on the absolute size of the largest
      matrix element.  If AMAX > LARGE or AMAX < SMALL, scaling is
      done.