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_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


									PPPPaaaaggggeeee 2222
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