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


SYNOPSIS

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

           CHARACTER      JOB, SIDE

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

           REAL           SCALE( * )

           COMPLEX        V( LDV, * )


PURPOSE

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


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 CGEBAL.

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

       SCALE   (input) REAL array, dimension (N)
               Details of the permutation and scaling factors, as
               returned by CGEBAL.

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

       V       (input/output) COMPLEX array, dimension (LDV,M)
               On entry, the matrix of right or left eigenvectors
               to  be  transformed,  as  returned  by  CHSEIN  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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