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# sggbak

```
NAME
SGGBAK - 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
SGGBAL

SYNOPSIS
SUBROUTINE SGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE,
M, E, LDE, INFO )

CHARACTER      JOB, SIDE

INTEGER        IHI, ILO, INFO, LDE, M, N

REAL           E( LDE, * ), LSCALE( * ), RSCALE( * )

PURPOSE
SGGBAK 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
SGGBAL.

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 SGGBAL.

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 SGGBAL.

LSCALE  (input) REAL array, dimension (N)
Details of the permutations and/or scaling factors
applied to the left side of A and B, as returned by
SGGBAL.

RSCALE  (input) REAL array, dimension (N)

Details of the permutations and/or scaling factors
applied to the right side of A and B, as returned by
SGGBAL.

M       (input) INTEGER
The number of columns of the matrix E.

E       (input/output) REAL array, dimension (LDE,M)
On entry, the matrix of right or left eigenvectors
to be transformed, as returned by STGEVC.  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.
```