Sparse Matrices and Summa Matrix Multiplication Algorithm in STAPL Matrix Framework

Abstract

Applications of matrices are found in most scientific fields, such as physics, computer graphics, numerical analysis, etc. The high applicability of matrix algorithms and representations make them an important component in any parallel programming language, therefore matrix frameworks are a continuous research effort in high performance computing. This work focuses on a generic matrix framework in the STAPL library. First, we extend the STAPL library by adding a sparse matrix container. Second we implement SUMMA, the parallel matrix-multiplication algorithm, for fine grained computations. Then, implement parallel matrix-matrix algorithms for the sparse matrix container. Finally, we conduct experimental studies for each of the components we have implemented and discuss the findings. Experiments are conducted on a Cray XE6m cluster. Experimental studies consist of multiple matrix and data inputs that showcase and stress the matrix models implemented. We find that the sparse matrix container outperforms its dense counterpart in sparse in-puts, and vice versa. Both containers, and the matrix summa implementation show scalability up to 512 cores.