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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, * )



     #include <sunperf.h>

     void zlaqgb(int m, int n,  int  kl,  int  ku,  doublecomplex
               *zab,  int  ldab,  double  *r,  double *dc, double
               *rowcnd,  double  *colcnd,   double   amax,   char
               *equed);

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
               premultiplied  by diag(R).  = 'C':  Column equili-
               bration,  i.e.,  A  has  been  postmultiplied   by
               diag(C).   =  'B':  Both row and column equilibra-
               tion, 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.

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