dgbtrf(3P) Sun Performance Library dgbtrf(3P)NAMEdgbtrf - compute an LU factorization of a real m-by-n band matrix A
using partial pivoting with row interchanges
SYNOPSIS
SUBROUTINE DGBTRF(M, N, KL, KU, A, LDA, IPIVOT, INFO)
INTEGER M, N, KL, KU, LDA, INFO
INTEGER IPIVOT(MIN(M,N))
DOUBLE PRECISION A(LDA,N)
SUBROUTINE DGBTRF_64(M, N, KL, KU, A, LDA, IPIVOT, INFO)
INTEGER*8 M, N, KL, KU, LDA, INFO
INTEGER*8 IPIVOT(N)
DOUBLE PRECISION A(LDA,N)
F95 INTERFACE
SUBROUTINE GBTRF(M, [N], KL, KU, A, [LDA], IPIVOT, [INFO])
INTEGER :: M, N, KL, KU, LDA, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE GBTRF_64(M, [N], KL, KU, A, [LDA], IPIVOT, [INFO])
INTEGER(8) :: M, N, KL, KU, LDA, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dgbtrf(int m, int n, int kl, int ku, double *a, int lda, int
*ipivot, int *info);
void dgbtrf_64(long m, long n, long kl, long ku, double *a, long lda,
long *ipivot, long *info);
PURPOSEdgbtrf 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.
ARGUMENTS
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.
A (input/output) Double precision array of dimension (LDA,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 A as
follows: A(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 fac‐
torization are stored in rows KL+KU+2 to 2*KL+KU+1. See
below for further details.
LDA (input) Integer array of dimension MIN(M,N)
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 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.
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 ele‐
ments of U because of fill-in resulting from the row interchanges.
6 Mar 2009 dgbtrf(3P)
