Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  -  forms  the right or left eigenvectors of a complex general matrix by backward
transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL

```

#### SYNOPSIS

```       SUBROUTINE ZGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, INFO )

CHARACTER      JOB, SIDE

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

DOUBLE         PRECISION SCALE( * )

COMPLEX*16     V( LDV, * )

```

#### PURPOSE

```       ZGEBAK forms the right or left eigenvectors  of  a  complex  general  matrix  by  backward
transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL.

```

#### 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 ZGEBAL.

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

SCALE   (input) DOUBLE PRECISION array, dimension (N)
Details of the permutation and scaling factors, as returned
by ZGEBAL.

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 ZHSEIN or ZTREVC.
On exit, V is overwritten by the transformed eigenvectors.

LDV     (input) INTEGER
The leading dimension of the array V. LDV >= max(1,N).

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.

LAPACK routine (version 3.2)               April 2011                            ZGEBAK(3lapack)
```