Towards an auto-tuning system design for optimal sparse compression format selection with user expertise

Several applications in numerical scientific computing process sparse matrices with either a regular or irregular structure. The very large size of these matrices requires to use compressing formats and target parallel/distributed architectures in order to reduce both space complexity and processing time. The optimal compression format (OCF) of such matrices may in fact vary according to both the application context of the numerical method and the target hardware architecture. In this paper, we propose a design of a system that automatically selects the OCF according to the two above cited parameters. The expert system obtained from our model targets dynamic integration of the user expertise thus allowing better performances. The optimal format selection is based on the makespan criterion. As a first validation test of our system, we studied the representative case of Horner scheme in the context of data parallel programming model and multicore cluster. Our experiments focus on the four compression formats CSR, CSC, COO and ELLPACK and their complexities in a data parallel programming model context.