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zlaqgb

 NAME
      ZLAQGB - equilibrate a general M by N band matrix A with KL
      subdiagonals and KU superdiagonals using the row and scaling
      factors in the vectors R and C

 SYNOPSIS
      SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND,
                         COLCND, AMAX, EQUED )

          CHARACTER      EQUED

          INTEGER        KL, KU, LDAB, M, N

          DOUBLE         PRECISION AMAX, COLCND, ROWCND

          DOUBLE         PRECISION C( * ), R( * )

          COMPLEX*16     AB( LDAB, * )

 PURPOSE
      ZLAQGB equilibrates a general M by N band matrix A with KL
      subdiagonals and KU superdiagonals using the row and scaling
      factors in the vectors R and C.

 ARGUMENTS
      M       (input) INTEGER
              The number of rows of the matrix A.  M >= 0.

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

      KL      (input) INTEGER
              The number of subdiagonals within the band of A.  KL
              >= 0.

      KU      (input) INTEGER
              The number of superdiagonals within the band of A.
              KU >= 0.

      AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
              On entry, the matrix A in band storage, in rows 1 to
              KL+KU+1.  The j-th column of A is stored in the j-th
              column of the array AB as follows: AB(ku+1+i-j,j) =
              A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)

              On exit, the equilibrated matrix, in the same
              storage format as A.  See EQUED for the form of the
              equilibrated matrix.

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

              KL+KU+1.

      R       (output) DOUBLE PRECISION array, dimension (M)
              The row scale factors for A.

      C       (output) DOUBLE PRECISION array, dimension (N)
              The column scale factors for A.

      ROWCND  (output) DOUBLE PRECISION
              Ratio of the smallest R(i) to the largest R(i).

      COLCND  (output) DOUBLE PRECISION
              Ratio of the smallest C(i) to the largest C(i).

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

      EQUED   (output) CHARACTER*1
              Specifies the form of equilibration that was done.
              = 'N':  No equilibration
              = 'R':  Row equilibration, i.e., A has been premul-
              tiplied by diag(R).  = 'C':  Column equilibration,
              i.e., A has been postmultiplied by diag(C).  = 'B':
              Both row and column equilibration, i.e., A has been
              replaced by diag(R) * A * diag(C).

 PARAMETERS
      THRESH is a threshold value used to decide if row or column
      scaling should be done based on the ratio of the row or
      column scaling factors.  If ROWCND < THRESH, row scaling is
      done, and if COLCND < THRESH, column scaling is done.

      LARGE and SMALL are threshold values used to decide if row
      scaling should be done based on the absolute size of the
      largest matrix element.  If AMAX > LARGE or AMAX < SMALL,
      row scaling is done.