dgbtf2 - n band matrix A using partial pivoting with row interchanges
SUBROUTINE DGBTF2(M, N, KL, KU, AB, LDAB, IPIV, INFO) INTEGER M, N, KL, KU, LDAB, INFO INTEGER IPIV(*) DOUBLE PRECISION AB(LDAB,*) SUBROUTINE DGBTF2_64(M, N, KL, KU, AB, LDAB, IPIV, INFO) INTEGER*8 M, N, KL, KU, LDAB, INFO INTEGER*8 IPIV(*) DOUBLE PRECISION AB(LDAB,*) F95 INTERFACE SUBROUTINE GBTF2(M, N, KL, KU, AB, LDAB, IPIV, INFO) INTEGER :: M, N, KL, KU, LDAB, INFO INTEGER, DIMENSION(:) :: IPIV REAL(8), 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(8), DIMENSION(:,:) :: AB C INTERFACE #include <sunperf.h> void dgbtf2(int m, int n, int kl, int ku, double *ab, int ldab, int *ipiv, int *info); void dgbtf2_64(long m, long n, long kl, long ku, double *ab, long ldab, long *ipiv, long *info);
Oracle Solaris Studio Performance Library dgbtf2(3P) NAME dgbtf2 - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges SYNOPSIS SUBROUTINE DGBTF2(M, N, KL, KU, AB, LDAB, IPIV, INFO) INTEGER M, N, KL, KU, LDAB, INFO INTEGER IPIV(*) DOUBLE PRECISION AB(LDAB,*) SUBROUTINE DGBTF2_64(M, N, KL, KU, AB, LDAB, IPIV, INFO) INTEGER*8 M, N, KL, KU, LDAB, INFO INTEGER*8 IPIV(*) DOUBLE PRECISION AB(LDAB,*) F95 INTERFACE SUBROUTINE GBTF2(M, N, KL, KU, AB, LDAB, IPIV, INFO) INTEGER :: M, N, KL, KU, LDAB, INFO INTEGER, DIMENSION(:) :: IPIV REAL(8), 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(8), DIMENSION(:,:) :: AB C INTERFACE #include <sunperf.h> void dgbtf2(int m, int n, int kl, int ku, double *ab, int ldab, int *ipiv, int *info); void dgbtf2_64(long m, long n, long kl, long ku, double *ab, long ldab, long *ipiv, long *info); PURPOSE dgbtf2 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. ARGUMENTS M (input) The number of rows of the matrix A. M >= 0. N (input) The number of columns of the matrix A. N >= 0. KL (input) The number of subdiagonals within the band of A. KL >= 0. KU (input) The number of superdiagonals within the band of A. KU >= 0. AB (input/output) 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 fac- torization are stored in rows KL+KU+2 to 2*KL+KU+1. See below for further details. LDAB (input) The leading dimension of the array AB. LDAB >= 2*KL+KU+1. IPIV (output) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). INFO (output) = 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. 7 Nov 2015 dgbtf2(3P)