# zggbak.f man page

zggbak.f —

## Synopsis

### Functions/Subroutines

subroutinezggbak(JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO)ZGGBAK

## Function/Subroutine Documentation

### subroutine zggbak (characterJOB, characterSIDE, integerN, integerILO, integerIHI, double precision, dimension( * )LSCALE, double precision, dimension( * )RSCALE, integerM, complex*16, dimension( ldv, * )V, integerLDV, integerINFO)

**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:**

November 2011

**Further Details:**

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

Definition at line 148 of file zggbak.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zggbak(3) is an alias of zggbak.f(3).