Optimised sparse storage mode for symbolic analysis of large networks

Symbolic network analysis gained growing interest as it aims at producing outputs in the form of expressions that containing both variables and numbers. However, such analysis faces the primary difficulty of the exponential growth of product terms in a symbolic network function with respect to circuit size. This long-standing difficulty is only partially overcome by various symbolic approximations and hierarchical decomposition approaches. A new storage scheme called Row-Indexed Semi-Symmetric Sparse (RISS) storage mode that partially solves this difficulty is presented in this paper. Unlike other similar storage schemes, the proposed scheme requires only about twice the number of nonzero matrix elements at most. The efficiency of the proposed RISS storage mode is assessed by considering several matrices of moderate sizes and comparing the memory requirement for each matrix in full storage mode and in RISS storage mode. The overall performance of a solver that incorporates the RISS storage mode and the sparse matrix techniques is assessed by considering a typical example of a 90° phase splitting network. When compared to an alternative matrix solver based on successive matrix reduction, the proposed solver demonstrates a reduction of 65% in the operation count and a reduction of 60% in the average memory storage requirement.