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cgebak

 NAME
      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 scaling
              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.

      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.

      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 CTREVC.
              On exit, V is overwritten by the transformed eigen-
              vectors.

      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 illegal
              value.