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man pages->IRIX man pages -> complib/dggbal (3)
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### Contents

```
DGGBAL(3F)							    DGGBAL(3F)

```

### NAME[Toc][Back]

```     DGGBAL - balance a	pair of	general	real matrices (A,B)
```

### SYNOPSIS[Toc][Back]

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

CHARACTER	JOB

INTEGER	IHI, ILO, INFO,	LDA, LDB, N

DOUBLE		PRECISION A( LDA, * ), B( LDB, * ), LSCALE( * ),
RSCALE(	* ), WORK( * )
```

### PURPOSE[Toc][Back]

```     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.

```

### ARGUMENTS[Toc][Back]

```     JOB     (input) 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	     (input) INTEGER
The order of the matrices A and B.	 N >= 0.

A	     (input/output) 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     (input) INTEGER
The leading dimension of the array	A. LDA >= max(1,N).

B	     (input/output) 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     (input) INTEGER
The leading dimension of the array	B. LDB >= max(1,N).

Page 1

DGGBAL(3F)							    DGGBAL(3F)

ILO     (output) INTEGER
IHI     (output) 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  (output) 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  (output) 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    (workspace) DOUBLE	PRECISION array, dimension (6*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.

FURTHER	DETAILS
See R.C. WARD, Balancing the generalized eigenvalue problem,
SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
DGGBAL(3F)							    DGGBAL(3F)

```

### NAME[Toc][Back]

```     DGGBAL - balance a	pair of	general	real matrices (A,B)
```

### SYNOPSIS[Toc][Back]

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

CHARACTER	JOB

INTEGER	IHI, ILO, INFO,	LDA, LDB, N

DOUBLE		PRECISION A( LDA, * ), B( LDB, * ), LSCALE( * ),
RSCALE(	* ), WORK( * )
```

### PURPOSE[Toc][Back]

```     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.

```

### ARGUMENTS[Toc][Back]

```     JOB     (input) 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	     (input) INTEGER
The order of the matrices A and B.	 N >= 0.

A	     (input/output) 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     (input) INTEGER
The leading dimension of the array	A. LDA >= max(1,N).

B	     (input/output) 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     (input) INTEGER
The leading dimension of the array	B. LDB >= max(1,N).

Page 1

DGGBAL(3F)							    DGGBAL(3F)

ILO     (output) INTEGER
IHI     (output) 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  (output) 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  (output) 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    (workspace) DOUBLE	PRECISION array, dimension (6*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.

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

PPPPaaaaggggeeee 2222```
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