ZGGBAK(3)      LAPACK routine of NEC Numeric Library Collection      ZGGBAK(3)



NAME
       ZGGBAK

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



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




ARGUMENTS
           JOB       (input)
                     JOB is 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 ZGGBAL.

           SIDE      (input)
                     SIDE is CHARACTER*1
                     = 'R':  V contains right eigenvectors;
                     = 'L':  V contains left eigenvectors.

           N         (input)
                     N is INTEGER
                     The number of rows of the matrix V.  N >= 0.

           ILO       (input)
                     ILO is INTEGER

           IHI       (input)
                     IHI is INTEGER
                     The integers ILO and IHI determined by ZGGBAL.
                     1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

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

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

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

           V         (input/output)
                     V is COMPLEX*16 array, dimension (LDV,M)
                     On entry, the matrix of right or left eigenvectors to be
                     transformed, as returned by ZTGEVC.
                     On exit, V is overwritten by the transformed eigenvectors.

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

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



LAPACK routine                  31 October 2017                      ZGGBAK(3)