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zgbequ

ZGBEQU(l)								 )								 ZGBEQU(l)

NAME

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

SYNOPSIS

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

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

	   DOUBLE	  PRECISION AMAX, COLCND, ROWCND

	   DOUBLE	  PRECISION C( * ), R( * )

	   COMPLEX*16	  AB( LDAB, * )

PURPOSE

       ZGBEQU  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  ele-
       ments 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*16 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) DOUBLE PRECISION array, dimension (M)
	       If INFO = 0, or INFO > M, R contains the row scale factors for A.

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

       ROWCND  (output) DOUBLE PRECISION
	       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) DOUBLE PRECISION
	       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) DOUBLE PRECISION
	       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

LAPACK version 3.0						   15 June 2000 							 ZGBEQU(l)