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## man page of LAPACK-3

### LAPACK-3: forms the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward

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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.## FURTHER DETAILS

See R.C. Ward, Balancing the generalized eigenvalue problem, SIAM J. Sci. Stat. Comp. 2 (1981), 141-152. LAPACK routine (version 3.2) March 2011 LAPACK-3(3)

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