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# zgebak

```
NAME
ZGEBAK - form 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.

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.

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 eigen-
vectors.

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.
```