Analytical Matrix Inversion and Code Generation for Labeling Flow Network Problems

Symbolic simplification and algebraic differentiation are only some of the advantages symbolic computations offer over their numerical counterparts. With a focus on sparse systems of linear equations, this contribution presents an analytical approach to a matrix inversion problem occurring in the field of Metabolic Flux Analysis. It is illustrated how the inherent complexity of the approach can be handled and how symbolic solutions can be compiled into highly performant machine code. Finally, benchmark results demonstrate that compiled analytical solutions offer comparable or even better performance than state-of-theart sparse matrix algorithms.