dgbequb()

subroutine dgbequb	(	integer	m,
		integer	n,
		integer	kl,
		integer	ku,
		double precision, dimension( ldab, * )	ab,
		integer	ldab,
		double precision, dimension( * )	r,
		double precision, dimension( * )	c,
		double precision	rowcnd,
		double precision	colcnd,
		double precision	amax,
		integer	info )

DGBEQUB

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Purpose:

!>
!> DGBEQUB computes row and column scalings intended to equilibrate an
!> M-by-N 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 an absolute value of at most
!> the radix.
!>
!> R(i) and C(j) are restricted to be a power of the radix 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.
!>
!> This routine differs from DGEEQU by restricting the scaling factors
!> to a power of the radix.  Barring over- and underflow, scaling by
!> these factors introduces no additional rounding errors.  However, the
!> scaled entries' magnitudes are no longer approximately 1 but lie
!> between sqrt(radix) and 1/sqrt(radix).
!> 

Parameters

[in]	M	!> M is INTEGER !> The number of rows of the matrix A. M >= 0. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrix A. N >= 0. !>
[in]	KL	!> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !>
[in]	KU	!> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !>
[in]	AB	!> AB is DOUBLE PRECISION 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(N,j+kl) !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array A. LDAB >= max(1,M). !>
[out]	R	!> R is DOUBLE PRECISION array, dimension (M) !> If INFO = 0 or INFO > M, R contains the row scale factors !> for A. !>
[out]	C	!> C is DOUBLE PRECISION array, dimension (N) !> If INFO = 0, C contains the column scale factors for A. !>
[out]	ROWCND	!> ROWCND is 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. !>
[out]	COLCND	!> COLCND is 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. !>
[out]	AMAX	!> AMAX is 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. !>
[out]	INFO	!> INFO is 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 !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.