.TH ZGGBAK 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME ZGGBAK - 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 .SH SYNOPSIS .TP 19 SUBROUTINE ZGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO ) .TP 19 .ti +4 CHARACTER JOB, SIDE .TP 19 .ti +4 INTEGER IHI, ILO, INFO, LDV, M, N .TP 19 .ti +4 DOUBLE PRECISION LSCALE( * ), RSCALE( * ) .TP 19 .ti +4 COMPLEX*16 V( LDV, * ) .SH 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. .SH ARGUMENTS .TP 8 JOB (input) CHARACTER*1 Specifies the type of backward transformation required: .br = \(aqN\(aq: do nothing, return immediately; .br = \(aqP\(aq: do backward transformation for permutation only; .br = \(aqS\(aq: do backward transformation for scaling only; .br = \(aqB\(aq: do backward transformations for both permutation and scaling. JOB must be the same as the argument JOB supplied to ZGGBAL. .TP 8 SIDE (input) CHARACTER*1 = \(aqR\(aq: V contains right eigenvectors; .br = \(aqL\(aq: V contains left eigenvectors. .TP 8 N (input) INTEGER The number of rows of the matrix V. N >= 0. .TP 8 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. .TP 8 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. .TP 8 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. .TP 8 M (input) INTEGER The number of columns of the matrix V. M >= 0. .TP 8 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. .TP 8 LDV (input) INTEGER The leading dimension of the matrix V. LDV >= max(1,N). .TP 8 INFO (output) INTEGER = 0: successful exit. .br < 0: if INFO = -i, the i-th argument had an illegal value. .SH FURTHER DETAILS See R.C. Ward, Balancing the generalized eigenvalue problem, SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.