# zggbal.f man page

zggbal.f —

## Synopsis

### Functions/Subroutines

subroutinezggbal(JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO)ZGGBAL

## Function/Subroutine Documentation

### subroutine zggbal (characterJOB, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, integerILO, integerIHI, double precision, dimension( * )LSCALE, double precision, dimension( * )RSCALE, double precision, dimension( * )WORK, integerINFO)

**ZGGBAL**

**Purpose:**

```
ZGGBAL balances a pair of general complex matrices (A,B). This
involves, first, permuting A and B by similarity transformations to
isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N
elements on the diagonal; and second, applying a diagonal similarity
transformation to rows and columns ILO to IHI to make the rows
and columns as close in norm as possible. Both steps are optional.
Balancing may reduce the 1-norm of the matrices, and improve the
accuracy of the computed eigenvalues and/or eigenvectors in the
generalized eigenvalue problem A*x = lambda*B*x.
```

**Parameters:**

*JOB*

```
JOB is CHARACTER*1
Specifies the operations to be performed on A and B:
= 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0
and RSCALE(I) = 1.0 for i=1,...,N;
= 'P': permute only;
= 'S': scale only;
= 'B': both permute and scale.
```

*N*

```
N is INTEGER
The order of the matrices A and B. N >= 0.
```

*A*

```
A is COMPLEX*16 array, dimension (LDA,N)
On entry, the input matrix A.
On exit, A is overwritten by the balanced matrix.
If JOB = 'N', A is not referenced.
```

*LDA*

```
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
```

*B*

```
B is COMPLEX*16 array, dimension (LDB,N)
On entry, the input matrix B.
On exit, B is overwritten by the balanced matrix.
If JOB = 'N', B is not referenced.
```

*LDB*

```
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
```

*ILO*

`ILO is INTEGER`

*IHI*

```
IHI is INTEGER
ILO and IHI are set to integers such that on exit
A(i,j) = 0 and B(i,j) = 0 if i > j and
j = 1,...,ILO-1 or i = IHI+1,...,N.
If JOB = 'N' or 'S', ILO = 1 and IHI = N.
```

*LSCALE*

```
LSCALE is DOUBLE PRECISION array, dimension (N)
Details of the permutations and scaling factors applied
to the left side of A and B. If P(j) is the index of the
row interchanged with row j, and D(j) is the scaling factor
applied to row j, then
LSCALE(j) = P(j) for J = 1,...,ILO-1
= D(j) for J = ILO,...,IHI
= P(j) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.
```

*RSCALE*

```
RSCALE is DOUBLE PRECISION array, dimension (N)
Details of the permutations and scaling factors applied
to the right side of A and B. If P(j) is the index of the
column interchanged with column j, and D(j) is the scaling
factor applied to column j, then
RSCALE(j) = P(j) for J = 1,...,ILO-1
= D(j) for J = ILO,...,IHI
= P(j) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.
```

*WORK*

```
WORK is REAL array, dimension (lwork)
lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and
at least 1 when JOB = 'N' or 'P'.
```

*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 177 of file zggbal.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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