# dggbal.f man page

dggbal.f

## Synopsis

### Functions/Subroutines

subroutine dggbal (JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO)
DGGBAL

## Function/Subroutine Documentation

### subroutine dggbal (character JOB, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, integer ILO, integer IHI, double precision, dimension( * ) LSCALE, double precision, dimension( * ) RSCALE, double precision, dimension( * ) WORK, integer INFO)

DGGBAL

Purpose:

``` DGGBAL balances a pair of general real 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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
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.```

WORK

```          WORK is DOUBLE PRECISION 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:

December 2016

Further Details:

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

Definition at line 179 of file dggbal.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dggbal(3) is an alias of dggbal.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK