Performance Analysis and Optimization of the Vector-Kronecker Product Multiplication

The Kronecker product, also called tensor product, is a fundamental matrix algebra operation, used to model complex systems using structured descriptions. This operation needs to be computed efficiently, since it is a critical kernel for iterative algorithms. In this work, we focus on the vector-kronecker product operation, where we present an in-depth performance analysis of a sequential and a parallel algorithm previously proposed. Based on this analysis, we proposed three optimizations: changing the memory access pattern, reducing load imbalance and manually vectorizing some portions of the code with Intel SSE4.2 intrinsics. The obtained results show better cache usage and load balance, thus improving the performance, especially for larger matrices.