ZLAQGE  -  equilibrate a general M by N matrix A using the
       row and scaling factors in the vectors R and C


SYNOPSIS

       SUBROUTINE ZLAQGE( M, N, A, LDA,  R,  C,  ROWCND,  COLCND,
                          AMAX, EQUED )

           CHARACTER      EQUED

           INTEGER        LDA, M, N

           DOUBLE         PRECISION AMAX, COLCND, ROWCND

           DOUBLE         PRECISION C( * ), R( * )

           COMPLEX*16     A( LDA, * )


PURPOSE

       ZLAQGE  equilibrates  a  general M by N matrix A 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.

       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
               On entry, the M by N matrix A.  On exit, the equi­
               librated matrix.  See EQUED for the  form  of  the
               equilibrated matrix.

       LDA     (input) INTEGER
               The  leading  dimension  of  the  array A.  LDA >=
               max(M,1).

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

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

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

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

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

               Specifies the form of equilibration that was done.
               = 'N':  No equilibration
               =  'R':   Row equilibration, i.e., A has been pre­
               multiplied by diag(R).  = 'C':  Column  equilibra­
               tion,  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               has been replaced by diag(R) * A * diag(C).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 col­
       umn scaling should be done based on the ratio of  the  row
       or  column scaling factors.  If ROWCND < THRESH, row scal­
       ing 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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