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NAME ZGGBAK - form the right or left eigenvectors of the general- ized eigenvalue problem by backward transformation on the computed eigenvectors of the balanced matrix output by ZGGBAL SYNOPSIS SUBROUTINE ZGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, E, LDE, INFO ) CHARACTER JOB, SIDE INTEGER IHI, ILO, INFO, LDE, M, N DOUBLE PRECISION LSCALE( * ), RSCALE( * ) COMPLEX*16 E( LDE, * ) PURPOSE ZGGBAK forms the right or left eigenvectors of the general- ized eigenvalue problem by backward transformation on the computed eigenvectors of the balanced matrix output by ZGGBAL. 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 permu- tation and scaling. JOB must be the same as the argument JOB supplied to ZGGBAL. SIDE (input) CHARACTER*1 = 'R': E contains right eigenvectors; = 'L': E contains left eigenvectors. N (input) INTEGER The number of rows of the matrix E. N >= 0. ILO (input) INTEGER IHI (input) INTEGER The integers ILO and IHI determined by ZGGBAL. LSCALE (input) 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) 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) INTEGER The number of columns of the matrix E. E (input/output) COMPLEX*16 array, dimension (LDE,M) On entry, the matrix of right or left eigenvectors to be transformed, as returned by ZTGEVC. On exit, E is overwritten by the transformed eigenvectors. LDE (input) INTEGER The leading dimension of the matrix E. LDE >= 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.