Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3  -  forms  the  right  or  left  eigenvectors of a complex generalized eigenvalue
problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors  of  the
balanced pair of matrices output by ZGGBAL

SYNOPSIS

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

CHARACTER      JOB, SIDE

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

DOUBLE         PRECISION LSCALE( * ), RSCALE( * )

COMPLEX*16     V( LDV, * )

PURPOSE

ZGGBAK  forms  the  right or left eigenvectors of a complex generalized eigenvalue problem
A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the  balanced
pair of matrices output by ZGGBAL.

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 ZGGBAL.

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 ZGGBAL.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

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

RSCALE  (input) DOUBLE PRECISION array, dimension (N)
Details of the permutations and/or scaling factors applied
to the right side of A and B, as returned by ZGGBAL.

M       (input) INTEGER
The number of columns of the matrix V.  M >= 0.

V       (input/output) COMPLEX*16 array, dimension (LDV,M)
On entry, the matrix of right or left eigenvectors to be
transformed, as returned by ZTGEVC.
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.

FURTHERDETAILS

See R.C. Ward, Balancing the generalized eigenvalue problem,
SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

LAPACK routine (version 3.2)               April 2011                            ZGGBAK(3lapack)