# zggbak.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **zggbak** (JOB, SIDE, **N**, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO)**ZGGBAK**

## Function/Subroutine Documentation

### subroutine zggbak (character JOB, character SIDE, integer N, integer ILO, integer IHI, double precision, dimension( * ) LSCALE, double precision, dimension( * ) RSCALE, integer M, complex*16, dimension( ldv, * ) V, integer LDV, integer INFO)

**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.

**Parameters:***JOB*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 INTEGER

*IHI*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.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

**Further Details:**

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

Definition at line 150 of file zggbak.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zggbak(3) is an alias of zggbak.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK