DSJM : a software toolkit for direct determination of sparse Jacobian matrices

Abstract

DSJM is a software toolkit written in portable C++ that enables direct determination of sparse Jacobian matrices whose sparsity pattern is a priori known. Using the seed matrix S 2 Rn×p, the Jacobian A 2 Rm×n can be determined by solving AS = B, where B 2 Rm×p has been obtained via finite difference approximation or forward automatic differentiation. Seed matrix S is defined by the nonzero unknowns in A. DSJM includes well-known as well as new column ordering heuristics. Numerical testing is highly promising both in terms of running time and the number of matrix-vector products needed to determine A.