# zggbal (3) - Linux Manuals

zggbal.f -

## SYNOPSIS

### Functions/Subroutines

subroutine zggbal (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

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

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