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NAME
     dgebak - form the right or left eigenvectors of a real  gen-
     eral  matrix  by  backward  transformation  on  the computed
     eigenvectors of the balanced matrix output by DGEBAL

SYNOPSIS
     SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
               INFO )

     CHARACTER JOB, SIDE

     INTEGER IHI, ILO, INFO, LDV, M, N

     DOUBLE PRECISION SCALE( * ), V( LDV, * )



     #include <sunperf.h>

     void dgebak(char job, char side, int n, int  ilo,  int  ihi,
               double  *dscale,  int  m,  double *v, int ldv, int
               *info) ;

PURPOSE
     DGEBAK forms the right or left eigenvectors of a  real  gen-
     eral  matrix  by  backward  transformation  on  the computed
     eigenvectors of the balanced matrix output by DGEBAL.


ARGUMENTS
     JOB       (input) CHARACTER*1
               Specifies  the  type  of  backward  transformation
               required:   = 'N', do nothing, return immediately;
               = 'P', do backward transformation for  permutation
               only;  = 'S', do backward transformation for scal-
               ing only; = 'B', do backward  transformations  for
               both  permutation  and  scaling.   JOB must be the
               same as the argument JOB supplied to DGEBAL.

     SIDE      (input) CHARACTER*1
               = 'R':  V contains right eigenvectors;
               = 'L':  V contains left eigenvectors.

     N         (input) INTEGER
               The number of rows of the matrix V.  N >= 0.

     ILO       (input) INTEGER
               IHI     (input) INTEGER The integers ILO  and  IHI
               determined  by DGEBAL.  1 <= ILO <= IHI <= N, if N
               > 0; ILO=1 and IHI=0, if N=0.

     SCALE     (input) DOUBLE PRECISION array, dimension (N)
               Details of the permutation and scaling factors, as
               returned by DGEBAL.

     M         (input) INTEGER
               The number of columns of the matrix V.  M >= 0.

     V         (input/output) DOUBLE PRECISION  array,  dimension
               (LDV,M)
               On entry, the matrix of right or left eigenvectors
               to  be  transformed,  as  returned  by  DHSEIN  or
               DTREVC.   On  exit,  V  is  overwritten   by   the
               transformed eigenvectors.

     LDV       (input) INTEGER
               The leading dimension  of  the  array  V.  LDV  >=
               max(1,N).

     INFO      (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value.

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