Purpose

LA_GBSV computes the solution to a real or complex linear system of equations $AX = B$, where $A$ is a square band matrix and $X$ and $B$ are rectangular matrices or vectors. The $L\,U$ decomposition with row interchanges is used to factor $A$ as $A = L\,U$, where $L$ is a product of permutation and unit lower triangular matrices with $kl$ subdiagonals, and $U$ is upper triangular with $kl + ku$ superdiagonals. The factored form of $A$ is then used to solve the above system.