dla_gbrpvgrw()

double precision function dla_gbrpvgrw	(	integer	n,
		integer	kl,
		integer	ku,
		integer	ncols,
		double precision, dimension( ldab, * )	ab,
		integer	ldab,
		double precision, dimension( ldafb, * )	afb,
		integer	ldafb )

DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

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

Purpose:

!>
!> DLA_GBRPVGRW computes the reciprocal pivot growth factor
!> norm(A)/norm(U). The  norm is used. If this is
!> much less than 1, the stability of the LU factorization of the
!> (equilibrated) matrix A could be poor. This also means that the
!> solution X, estimated condition numbers, and error bounds could be
!> unreliable.
!> 

Parameters

[in]	N	!> N is INTEGER !> The number of linear equations, i.e., the order 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]	NCOLS	!> NCOLS is INTEGER !> The number of columns of the matrix A. NCOLS >= 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 AB. LDAB >= KL+KU+1. !>
[in]	AFB	!> AFB is DOUBLE PRECISION array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by DGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1. !>
[in]	LDAFB	!> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.