SGGBAK (3lapack)

form the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL

SYNOPSIS

  SUBROUTINE SGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO
                     )

      CHARACTER      JOB, SIDE

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

      REAL           LSCALE( * ), RSCALE( * ), V( LDV, * )

PURPOSE

  SGGBAK forms the right or left eigenvectors of a real generalized
  eigenvalue problem A*x = lambda*B*x, by backward transformation on the
  computed eigenvectors of the balanced pair of matrices output by SGGBAL.

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
          SGGBAL.

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

  LSCALE  (input) REAL array, dimension (N)
          Details of the permutations and/or scaling factors applied to the
          left side of A and B, as returned by SGGBAL.

  RSCALE  (input) REAL array, dimension (N)
          Details of the permutations and/or scaling factors applied to the
          right side of A and B, as returned by SGGBAL.

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

  V       (input/output) REAL array, dimension (LDV,M)
          On entry, the matrix of right or left eigenvectors to be
          transformed, as returned by STGEVC.  On exit, V is overwritten by
          the transformed eigenvectors.

  LDV     (input) INTEGER
          The leading dimension of the matrix V. LDV >= max(1,N).

  INFO    (output) INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.

FURTHER DETAILS

  See R.C. Ward, Balancing the generalized eigenvalue problem,
                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.