DGBTRF(l) LAPACK routine (version 1.1) DGBTRF(l)
DGBTRF - compute an LU factorization of a real m-by-n band matrix A using
partial pivoting with row interchanges
SUBROUTINE DGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )
INTEGER INFO, KL, KU, LDAB, M, N
INTEGER IPIV( * )
DOUBLE PRECISION AB( LDAB, * )
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.
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/output) 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 tri-
angular 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.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
IPIV (output) 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).
INFO (output) 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.
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.
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