ZGEBAK  - form the right or left eigenvectors of a complex
       general matrix by backward transformation on the  computed
       eigenvectors of the balanced matrix output by ZGEBAL


SYNOPSIS

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

           CHARACTER      JOB, SIDE

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

           DOUBLE         PRECISION SCALE( * )

           COMPLEX*16     V( LDV, * )


PURPOSE

       ZGEBAK forms the right or left eigenvectors of  a  complex
       general  matrix by backward transformation on the computed
       eigenvectors of the balanced matrix output by ZGEBAL.


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 ZGEBAL.

       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 ZGEBAL.  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 ZGEBAL.

       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  ZHSEIN  or

               formed 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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