1CGGBAK(1)                LAPACK routine (version 3.2)                CGGBAK(1)
2
3
4

NAME

6       CGGBAK  - forms the right or left eigenvectors of a complex generalized
7       eigenvalue problem A*x = lambda*B*x, by backward transformation on  the
8       computed eigenvectors of the balanced pair of matrices output by CGGBAL
9

SYNOPSIS

11       SUBROUTINE CGGBAK( JOB,  SIDE,  N, ILO, IHI, LSCALE, RSCALE, M, V, LDV,
12                          INFO )
13
14           CHARACTER      JOB, SIDE
15
16           INTEGER        IHI, ILO, INFO, LDV, M, N
17
18           REAL           LSCALE( * ), RSCALE( * )
19
20           COMPLEX        V( LDV, * )
21

PURPOSE

23       CGGBAK 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  CGG‐
26       BAL.
27

ARGUMENTS

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

FURTHER DETAILS

74       See R.C. Ward, Balancing the generalized eigenvalue problem,
75                      SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
76
77
78
79 LAPACK routine (version 3.2)    November 2008                       CGGBAK(1)
Impressum