Sparse matrix technology tools in APL

Abstract

We have implemented sparse matrix technology tools in APL. Such tools have been conspicuously scarce, because APL has not been the language of choice for solving boundary value problems governed by partial differential equations. But when carefully coded, APL is able to tackle problems governed by partial differential equations in a way that ads flexibility and, on account of its compactness, maintainability. The main criticism of APL in numerically intensive applications has been execution speed. APL compilation addresses this drawback and shows factors of speed improvement of better than about three. Timings will be presented for some benchmark elliptical boundary value problems, both for interpretive and compiled APL. Examples are given of common tasks that are encountered in conjunction with the finite element method, such as determination of the symbolic form of the stiffness matrix, and the more universal task of solution of a sparse (symmetric) set of equations using the conjugate gradient method.