ZLAQGB(l)								 )								 ZLAQGB(l)

NAME

       ZLAQGB  -  equilibrate  a  general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the
       vectors R and C

SYNOPSIS

       SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED )

	   CHARACTER	  EQUED

	   INTEGER	  KL, KU, LDAB, M, N

	   DOUBLE	  PRECISION AMAX, COLCND, ROWCND

	   DOUBLE	  PRECISION C( * ), R( * )

	   COMPLEX*16	  AB( LDAB, * )

PURPOSE

       ZLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vec-
       tors R and C.

ARGUMENTS

       M       (input) INTEGER
	       The number of rows of the matrix A.  M >= 0.

       N       (input) INTEGER
	       The number of columns of the matrix A.  N >= 0.

       KL      (input) INTEGER
	       The number of subdiagonals within the band of A.  KL >= 0.

       KU      (input) INTEGER
	       The number of superdiagonals within the band of A.  KU >= 0.

       AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
	       On entry, the matrix A in band storage, in rows 1 to KL+KU+1.  The j-th column of A is stored in the j-th column of the array AB as
	       follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)

	       On exit, the equilibrated matrix, in the same storage format as A.  See EQUED for the form of the equilibrated matrix.

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDA >= KL+KU+1.

       R       (output) DOUBLE PRECISION array, dimension (M)
	       The row scale factors for A.

       C       (output) DOUBLE PRECISION array, dimension (N)
	       The column scale factors for A.

       ROWCND  (output) DOUBLE PRECISION
	       Ratio of the smallest R(i) to the largest R(i).

       COLCND  (output) DOUBLE PRECISION
	       Ratio of the smallest C(i) to the largest C(i).

       AMAX    (input) DOUBLE PRECISION
	       Absolute value of largest matrix entry.

       EQUED   (output) CHARACTER*1
	       Specifies the form of equilibration that was done.  = 'N':  No equilibration
	       = 'R':  Row equilibration, i.e., A has been premultiplied by diag(R).  = 'C':  Column equilibration, i.e., A  has  been	postmulti-
	       plied by diag(C).  = 'B':  Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).

PARAMETERS

       THRESH is a threshold value used to decide if row or column scaling should be done based on the ratio of the row or column scaling factors.
       If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column scaling is done.

       LARGE and SMALL are threshold values used to decide if row scaling should be done based on the absolute size of the largest matrix element.
       If AMAX > LARGE or AMAX < SMALL, row scaling is done.

LAPACK version 3.0						   15 June 2000 							 ZLAQGB(l)