sgbtrf (l) - Linux Manuals
sgbtrf: computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
NAMESGBTRF - computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
- SUBROUTINE SGBTRF(
- M, N, KL, KU, AB, LDAB, IPIV, INFO )
- INTEGER INFO, KL, KU, LDAB, M, N
- INTEGER IPIV( * )
- REAL AB( LDAB, * )
PURPOSESGBTRF 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.
- 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) REAL 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.
- LDAB (input) INTEGER
- The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
- 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).
- 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 DETAILSThe band storage scheme is illustrated by the following example, when M = N = 6, KL = 2, KU = 1:
On entry: On exit: