CXML
        	    
LAPACK version 3.0
slaqgb(3)

PURPOSE
  SLAQGB - 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

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

      CHARACTER	     EQUED

      INTEGER	     KL, KU, LDAB, M, N

      REAL	     AMAX, COLCND, ROWCND

      REAL	     AB( LDAB, * ), C( * ), R( * )

DESCRIPTION
  SLAQGB equilibrates 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.

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) REAL 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) REAL array, dimension (M)
	  The row scale factors for A.

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

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

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

  AMAX	  (input) REAL
	  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
	  postmultiplied 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	  equilibration, i.e., A has been replaced by diag(R) * A * diag(C).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.