1SGGBAK(1)                LAPACK routine (version 3.2)                SGGBAK(1)
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NAME

6       SGGBAK - forms the right or left eigenvectors of a real generalized ei‐
7       genvalue problem A*x = lambda*B*x, by backward  transformation  on  the
8       computed eigenvectors of the balanced pair of matrices output by SGGBAL
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SYNOPSIS

11       SUBROUTINE SGGBAK( 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           REAL           LSCALE( * ), RSCALE( * ), V( LDV, * )
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PURPOSE

21       SGGBAK forms the right or left eigenvectors of a real  generalized  ei‐
22       genvalue  problem  A*x  = lambda*B*x, by backward transformation on the
23       computed eigenvectors of the balanced pair of matrices output  by  SGG‐
24       BAL.
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ARGUMENTS

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

72       See R.C. Ward, Balancing the generalized eigenvalue problem,
73                      SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
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77 LAPACK routine (version 3.2)    November 2008                       SGGBAK(1)
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