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NAME
     zggbak - form the right or left eigenvectors  of  a  complex
     generalized eigenvalue problem A*x = lambda*B*x, by backward
     transformation on the computed eigenvectors of the  balanced
     pair of matrices output by ZGGBAL

SYNOPSIS
     SUBROUTINE ZGGBAK( JOB, SIDE, N, ILO, IHI,  LSCALE,  RSCALE,
               M, V, LDV, INFO )

     CHARACTER JOB, SIDE

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

     DOUBLE PRECISION LSCALE( * ), RSCALE( * )

     COMPLEX*16 V( LDV, * )



     #include <sunperf.h>

     void zggbak(char job, char side, int n, int  ilo,  int  ihi,
               double  *lscale, double *rscale, int m, doublecom-
               plex *v, int ldv, int *info) ;

PURPOSE
     ZGGBAK forms the right or left  eigenvectors  of  a  complex
     generalized eigenvalue problem A*x = lambda*B*x, by backward
     transformation on the computed eigenvectors of the  balanced
     pair of matrices output by ZGGBAL.


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  scaling
               only;
               = 'B':  do backward transformations for both  per-
               mutation and scaling.  JOB must be the same as the
               argument JOB supplied to ZGGBAL.

     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 ZGGBAL.  1 <= ILO <= IHI <= N, if N
               > 0; ILO=1 and IHI=0, if N=0.

     LSCALE    (input) DOUBLE PRECISION array, dimension (N)
               Details of the permutations and/or scaling factors
               applied  to  the left side of A and B, as returned
               by ZGGBAL.

     RSCALE    (input) DOUBLE PRECISION array, dimension (N)
               Details of the permutations and/or scaling factors
               applied  to the right side of A and B, as returned
               by ZGGBAL.

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

     V         (input/output) COMPLEX*16 array, dimension (LDV,M)
               On entry, the matrix of right or left eigenvectors
               to  be  transformed,  as  returned  by ZTGEVC.  On
               exit, V is overwritten by the  transformed  eigen-
               vectors.

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

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

FURTHER DETAILS
     See R.C. Ward, Balancing the generalized eigenvalue problem,
                    SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

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