CXML
        	    
LAPACK version 3.0
cgbequ(3)

PURPOSE
  CGBEQU - compute row and column scalings intended to equilibrate an M-by-N
  band matrix A and reduce its condition number

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

      INTEGER	     INFO, KL, KU, LDAB, M, N

      REAL	     AMAX, COLCND, ROWCND

      REAL	     C( * ), R( * )

      COMPLEX	     AB( LDAB, * )

DESCRIPTION
  CGBEQU computes row and column scalings intended to equilibrate an M-by-N
  band matrix A and reduce its condition number. R returns the row scale
  factors and C the column scale factors, chosen to try to make the largest
  element in each row and column of the matrix B with elements
  B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.

  R(i) and C(j) are restricted to be between SMLNUM = smallest safe number
  and BIGNUM = largest safe number.  Use of these scaling factors is not
  guaranteed to reduce the condition number of A but works well in practice.

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) COMPLEX array, dimension (LDAB,N)
	  The band matrix A, stored 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).

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

  R	  (output) REAL array, dimension (M)
	  If INFO = 0, or INFO > M, R contains the row scale factors for A.

  C	  (output) REAL array, dimension (N)
	  If INFO = 0, C contains the column scale factors for A.

  ROWCND  (output) REAL
	  If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest
	  R(i) to the largest R(i).  If ROWCND >= 0.1 and AMAX is neither too
	  large nor too small, it is not worth scaling by R.

  COLCND  (output) REAL
	  If INFO = 0, COLCND contains the ratio of the smallest C(i) to the
	  largest C(i).	 If COLCND >= 0.1, it is not worth scaling by C.

  AMAX	  (output) REAL
	  Absolute value of largest matrix element.  If AMAX is very close to
	  overflow or very close to underflow, the matrix should be scaled.

  INFO	  (output) INTEGER
	  = 0:	successful exit
	  < 0:	if INFO = -i, the i-th argument had an illegal value
	  > 0:	if INFO = i, and i is
	  <= M:	 the i-th row of A is exactly zero
	  >  M:	 the (i-M)-th column of A is exactly zero