.TH ZGBTRF 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
ZGBTRF - an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
.SH SYNOPSIS
.TP 19
SUBROUTINE ZGBTRF(
M, N, KL, KU, AB, LDAB, IPIV, INFO )
.TP 19
.ti +4
INTEGER
INFO, KL, KU, LDAB, M, N
.TP 19
.ti +4
INTEGER
IPIV( * )
.TP 19
.ti +4
COMPLEX*16
AB( LDAB, * )
.SH PURPOSE
ZGBTRF computes an LU factorization of a complex m-by-n band matrix A
using partial pivoting with row interchanges.
This is the blocked version of the algorithm, calling Level 3 BLAS.
.SH ARGUMENTS
.TP 8
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
.TP 8
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
.TP 8
KL (input) INTEGER
The number of subdiagonals within the band of A. KL >= 0.
.TP 8
KU (input) INTEGER
The number of superdiagonals within the band of A. KU >= 0.
.TP 8
AB (input/output) COMPLEX*16 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.
.TP 8
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
.TP 8
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).
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
.br
> 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.
.SH FURTHER DETAILS
The band storage scheme is illustrated by the following example, when
M = N = 6, KL = 2, KU = 1:
.br
On entry: On exit:
.br
* * * + + + * * * 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.