To solve an unsymmetric banded system of linear equations. Given a unsymmetric band matrix and an -vector , this subroutine solves the system .
The matrix is factorized using Gaussian elimination with row interchanges. If the lower semibandwidth is and the upper semibandwidth is , that is, if for or , ﬁll-in is limited to additional diagonals of the upper triangle and the computation is performed within an array of size . At each pivotal step, operations are avoided on any row with a zero in the pivot column and on the columns beyond the last to have an entry in the pivot row.