dgbtrf()

subroutine dgbtrf	(	integer	m,
		integer	n,
		integer	kl,
		integer	ku,
		double precision, dimension( ldab, * )	ab,
		integer	ldab,
		integer, dimension( * )	ipiv,
		integer	info )

DGBTRF

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Purpose:

!>
!> DGBTRF computes an LU factorization of a real m-by-n band matrix A
!> using partial pivoting with row interchanges.
!>
!> This is the blocked version of the algorithm, calling Level 3 BLAS.
!> 

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,out]	AB	!> AB is DOUBLE PRECISION array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows KL+1 to !> 2*KL+KU+1; rows 1 to KL of the array need not be set. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) !> !> On exit, details of the factorization: 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. !> See below for further details. !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= 2*KL+KU+1. !>
[out]	IPIV	!> IPIV is INTEGER array, dimension (min(M,N)) !> The pivot indices; for 1 <= i <= min(M,N), row i of the !> matrix was interchanged with row IPIV(i). !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = +i, U(i,i) is exactly zero. The factorization !> has been completed, but the factor U is exactly !> singular, and division by zero will occur if it is used !> to solve a system of equations. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  The band storage scheme is illustrated by the following example, when
!>  M = N = 6, KL = 2, KU = 1:
!>
!>  On entry:                       On exit:
!>
!>      *    *    *    +    +    +       *    *    *   u14  u25  u36
!>      *    *    +    +    +    +       *    *   u13  u24  u35  u46
!>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
!>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
!>     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
!>     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
!>
!>  Array elements marked * are not used by the routine; elements marked
!>  + need not be set on entry, but are required by the routine to store
!>  elements of U because of fill-in resulting from the row interchanges.
!>