sgbtf2 - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
SUBROUTINE SGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO) INTEGER M, N, KL, KU, LDAB, INFO INTEGER IPIV(*) REAL AB(LDAB,*)
SUBROUTINE SGBTF2_64( M, N, KL, KU, AB, LDAB, IPIV, INFO) INTEGER*8 M, N, KL, KU, LDAB, INFO INTEGER*8 IPIV(*) REAL AB(LDAB,*)
SUBROUTINE GBTF2( [M], [N], KL, KU, AB, [LDAB], IPIV, [INFO]) INTEGER :: M, N, KL, KU, LDAB, INFO INTEGER, DIMENSION(:) :: IPIV REAL, DIMENSION(:,:) :: AB
SUBROUTINE GBTF2_64( [M], [N], KL, KU, AB, [LDAB], IPIV, [INFO]) INTEGER(8) :: M, N, KL, KU, LDAB, INFO INTEGER(8), DIMENSION(:) :: IPIV REAL, DIMENSION(:,:) :: AB
#include <sunperf.h>
void sgbtf2(int m, int n, int kl, int ku, float *ab, int ldab, int *ipiv, int *info);
void sgbtf2_64(long m, long n, long kl, long ku, float *ab, long ldab, long *ipiv, long *info);
sgbtf2 computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges.
This is the unblocked version of the algorithm, calling Level 2 BLAS.
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.
= 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.