1ZGGBAK(1)                LAPACK routine (version 3.1)                ZGGBAK(1)
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NAME

6       ZGGBAK - the right or left eigenvectors of a complex generalized eigen‐
7       value problem A*x = lambda*B*x, by backward transformation on the  com‐
8       puted eigenvectors of the balanced pair of matrices output by ZGGBAL
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SYNOPSIS

11       SUBROUTINE ZGGBAK( JOB,  SIDE,  N, ILO, IHI, LSCALE, RSCALE, M, V, LDV,
12                          INFO )
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14           CHARACTER      JOB, SIDE
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16           INTEGER        IHI, ILO, INFO, LDV, M, N
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18           DOUBLE         PRECISION LSCALE( * ), RSCALE( * )
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20           COMPLEX*16     V( LDV, * )
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PURPOSE

23       ZGGBAK forms the right or left eigenvectors of  a  complex  generalized
24       eigenvalue  problem A*x = lambda*B*x, by backward transformation on the
25       computed eigenvectors of the balanced pair of matrices output  by  ZGG‐
26       BAL.
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ARGUMENTS

30       JOB     (input) CHARACTER*1
31               Specifies the type of backward transformation required:
32               = 'N':  do nothing, return immediately;
33               = 'P':  do backward transformation for permutation only;
34               = 'S':  do backward transformation for scaling only;
35               =  'B':   do  backward transformations for both permutation and
36               scaling.  JOB must be the same as the argument JOB supplied  to
37               ZGGBAL.
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39       SIDE    (input) CHARACTER*1
40               = 'R':  V contains right eigenvectors;
41               = 'L':  V contains left eigenvectors.
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43       N       (input) INTEGER
44               The number of rows of the matrix V.  N >= 0.
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46       ILO     (input) INTEGER
47               IHI      (input) INTEGER The integers ILO and IHI determined by
48               ZGGBAL.  1 <= ILO <= IHI <= N, if N > 0; ILO=1  and  IHI=0,  if
49               N=0.
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51       LSCALE  (input) DOUBLE PRECISION array, dimension (N)
52               Details  of  the permutations and/or scaling factors applied to
53               the left side of A and B, as returned by ZGGBAL.
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55       RSCALE  (input) DOUBLE PRECISION array, dimension (N)
56               Details of the permutations and/or scaling factors  applied  to
57               the right side of A and B, as returned by ZGGBAL.
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59       M       (input) INTEGER
60               The number of columns of the matrix V.  M >= 0.
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62       V       (input/output) COMPLEX*16 array, dimension (LDV,M)
63               On entry, the matrix of right or left eigenvectors to be trans‐
64               formed, as returned by ZTGEVC.  On exit, V  is  overwritten  by
65               the transformed eigenvectors.
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67       LDV     (input) INTEGER
68               The leading dimension of the matrix V. LDV >= max(1,N).
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70       INFO    (output) INTEGER
71               = 0:  successful exit.
72               < 0:  if INFO = -i, the i-th argument had an illegal value.
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FURTHER DETAILS

75       See R.C. Ward, Balancing the generalized eigenvalue problem,
76                      SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
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81 LAPACK routine (version 3.1)    November 2006                       ZGGBAK(1)
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