DGEBAK (3lapack)

form the right or left eigenvectors of a real general 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 general 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.  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
          DGEBAL.

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

  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 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 illegal value.