subroutine zggbak (JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO)
subroutine zggbak (characterJOB, characterSIDE, integerN, integerILO, integerIHI, double precision, dimension( * )LSCALE, double precision, dimension( * )RSCALE, integerM, complex*16, dimension( ldv, * )V, integerLDV, integerINFO)ZGGBAK 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.
JOB is 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
SIDE is CHARACTER*1 = 'R': V contains right eigenvectors; = 'L': V contains left eigenvectors.N
N is INTEGER The number of rows of the matrix V. N >= 0.ILO
ILO is INTEGERIHI
IHI is 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
LSCALE is 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
RSCALE is 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
M is INTEGER The number of columns of the matrix V. M >= 0.V
V is 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
LDV is INTEGER The leading dimension of the matrix V. LDV >= max(1,N).INFO
INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.
Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:
November 2011Further Details:
See R.C. Ward, Balancing the generalized eigenvalue problem, SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.