CGBEQU man page on IRIX

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CGBEQU(3F)							    CGBEQU(3F)

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

SYNOPSIS
     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, * )

PURPOSE
     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.

									Page 1

CGBEQU(3F)							    CGBEQU(3F)

     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

									Page 2

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