DGEBF

DGEBF is a double-precision LAPACK routine that computes the LU factorization with partial pivoting of a general banded square matrix. It factors the input matrix A, which is stored in band storage with lower bandwidth KL and upper bandwidth KU, overwriting A with the factors L and U in a compact form. The multipliers for the elimination process are stored below the diagonal and the upper triangular part contains the U factors, while the unit diagonal of L is implicit. Pivot information from the row interchanges is returned in the integer array IPIV.

Input to DGEBF includes the matrix A in band storage, the leading dimension LDAB that must satisfy LDAB >= KL+KU+1, the order of the matrix N, and the bandwidth parameters KL and KU. On exit, IPIV records the permutations performed during factorization. The routine adheres to the LAPACK convention of using column-major storage.

On successful completion, INFO equals 0. If INFO equals a positive value k, the k-th diagonal element of the factorization is exactly zero, indicating that the matrix is singular to working precision at that step and the factorization may be incomplete. The primary use of DGEBF is to provide LU factors that can be used to solve systems A X = B for banded matrices via a companion solver, such as DGBSL, which applies the stored factors and pivoting to compute the solution.

DGEBF is part of a family of banded matrix routines in LAPACK. It offers reduced storage and computation for banded problems compared with dense approaches, while maintaining compatibility with the common LAPACK workflow for solving linear systems.