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

```
_BALANC(3F)							   _BALANC(3F)

```

### NAME[Toc][Back]

```     BALANC, SBALANC  -	 EISPACK routine.  This	subroutine balances a REAL
matrix and	isolates eigenvalues whenever possible.

```

### SYNOPSYS[Toc][Back]

```	  subroutine  balanc(nm, n, a, low, igh, scale)
integer	      nm, n, a,	low, igh
double precision a(nm,n), scale(n)

subroutine sbalanc(nm, n, a, low, igh, scale)
integer	      nm, n, a,	low, igh
real	      a(nm,n), scale(n)

```

### DESCRIPTION[Toc][Back]

```     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.

A contains	the input matrix to be balanced. On OUTPUT

A contains	the balanced matrix.

LOW and IGH are two integers such that A(I,J) is 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 BALANCE
appears in

BALANC in line.  (Note that the ALGOL roles of identifiers	K,L have been
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 1111```
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