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

```
_CBAL(3F)							     _CBAL(3F)

```

### NAME[Toc][Back]

```     CBAL, SCBAL    -  EISPACK routine.	 This subroutine is a complex version
of	BALANCE.

```

### SYNOPSYS[Toc][Back]

```	  subroutine  cbal(nm, n, ar, ai, low, igh, scale)
integer	   nm, n, low, igh
double precision ar(nm,n), ai(nm,n), scale(n)

subroutine scbal(nm, n, ar, ai, low, igh, scale)
integer	   nm, n, low, igh
real		   ar(nm,n), ai(nm,n), scale(n)

```

### DESCRIPTION[Toc][Back]

```     This subroutine balances a	COMPLEX	matrix and isolates eigenvalues
whenever possible.

On	INPUT

NM	must be	set to the row dimension of two-dimensional array parameters
as	declared in the	calling	program	dimension statement.

N is the order of the matrix.

AR	and AI contain the real	and imaginary parts, respectively, of the
complex matrix to be balanced.  On	OUTPUT

AR	and AI contain the real	and imaginary parts, respectively, of the
balanced matrix.

LOW and IGH are two integers such that AR(I,J) and	AI(I,J)	are equal to
zero if
(1) I is greater than J	and
(2) J=1,...,LOW-1 or I=IGH+1,...,N.

SCALE contains information	determining the
permutations and scaling factors used.	Suppose	that the principal
submatrix in rows LOW through IGH has been	balanced, that P(J) denotes
the index interchanged with J during the permutation step,	and that the
elements of the diagonal matrix used are denoted by D(I,J).  Then

SCALE (J) = P(J),	  for J	= 1,...,LOW-1
= D(J,J)       J = LOW,...,IGH
= P(J)	       J = IGH+1,...,N.	 The order in which the	interchanges
are made is N to IGH+1, then 1 to LOW-1.  Note that 1 is returned for IGH
if	IGH is zero formally.  The ALGOL procedure EXC contained in CBALANCE
appears in

CBAL in line.  (Note that the ALGOL roles of identifiers K,L have been

Page 1

_CBAL(3F)							     _CBAL(3F)

reversed.)	 Questions and comments	should be directed to B. S. Garbow,
APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY

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