SGGBAK(3) forms the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL

## SYNOPSIS

SUBROUTINE SGGBAK(
JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO )

CHARACTER JOB, SIDE

INTEGER IHI, ILO, INFO, LDV, M, N

REAL LSCALE( * ), RSCALE( * ), V( LDV, * )

## PURPOSE

SGGBAK forms the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices 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 permutation and scaling. JOB must be the same as the argument JOB supplied to SGGBAL.
SIDE (input) CHARACTER*1
= 'R': V contains right eigenvectors;
= 'L': V contains left eigenvectors.
N (input) INTEGER
The number of rows of the matrix V. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER The integers ILO and IHI determined by SGGBAL. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
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 V. M >= 0.
V (input/output) REAL array, dimension (LDV,M)
On entry, the matrix of right or left eigenvectors to be transformed, as returned by STGEVC. On exit, V is overwritten by the transformed eigenvectors.
LDV (input) INTEGER
The leading dimension of the matrix V. LDV >= 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.