Contents
zgbtrf - compute an LU factorization of a complex m-by-n
band matrix A using partial pivoting with row interchanges
SUBROUTINE ZGBTRF(M, N, KL, KU, AB, LDAB, IPIVOT, INFO)
DOUBLE COMPLEX AB(LDAB,N)
INTEGER M, N, KL, KU, LDAB, INFO
INTEGER IPIVOT(MIN(M,N))
SUBROUTINE ZGBTRF_64(M, N, KL, KU, AB, LDAB, IPIVOT, INFO)
DOUBLE COMPLEX AB(LDAB,N)
INTEGER*8 M, N, KL, KU, LDAB, INFO
INTEGER*8 IPIVOT(MIN(M,N))
F95 INTERFACE
SUBROUTINE GBTRF(M, [N], KL, KU, AB, [LDAB], IPIVOT, [INFO])
COMPLEX(8), DIMENSION(:,:) :: AB
INTEGER :: M, N, KL, KU, LDAB, INFO
INTEGER, DIMENSION(:) :: IPIVOT
SUBROUTINE GBTRF_64(M, [N], KL, KU, AB, [LDAB], IPIVOT, [INFO])
COMPLEX(8), DIMENSION(:,:) :: AB
INTEGER(8) :: M, N, KL, KU, LDAB, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
C INTERFACE
#include <sunperf.h>
void zgbtrf(int m, int n, int kl, int ku, doublecomplex *ab,
int ldab, int *ipivot, int *info);
void zgbtrf_64(long m, long n, long kl, long ku, doublecom-
plex *ab, long ldab, long *ipivot, long *info);
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.
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 complex array of 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 mul-
tipliers 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 A. LDA >=
2*KL+KU+1.
IPIVOT (output) Integer array of dimension MIN(M,N)
The pivot indices; for 1 <= I <= min(M,N), row I
of the matrix was interchanged with row IPIVOT(I).
INFO (output) Integer
= 0: successful exit
< 0: if INFO = -I, the I-th argument had an ille-
gal 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 equa-
tions.
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; ele-
ments 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.