NAME

       zggbak.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zggbak (JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO)
           ZGGBAK

Function/Subroutine Documentation

   subroutine zggbak (characterJOB, characterSIDE, integerN, integerILO, integerIHI, double
       precision, dimension( * )LSCALE, double precision, dimension( * )RSCALE, integerM,
       complex*16, dimension( ldv, * )V, integerLDV, integerINFO)
       ZGGBAK

       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.

       Parameters:
           JOB

                     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

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

           N

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

           ILO

                     ILO is INTEGER

           IHI

                     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

                     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

                     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

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

           V

                     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

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

           INFO

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Further Details:

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

       Definition at line 148 of file zggbak.f.

Author

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