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dgebak

 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, * )

 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 scaling
              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.

      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.

      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 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.