dgbequ()

subroutine dgbequ	(	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 )

DGBEQU

Download DGBEQU + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> DGBEQU 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.
!> 

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) !> 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). !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !>
[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.