Sparse matrix multiplication: The distributed block-compressed sparse row library

Efficient parallel multiplication of sparse matrices is key to enabling many large-scale calculations. This article presents the DBCSR (Distributed Block Compressed Sparse Row) library for scalable sparse matrix-matrix multiplication and its use in the CP2K program for linear-scaling quantum-chemical calculations. The library combines several approaches to implement sparse matrix multiplication in a way that performs well and is demonstrably scalable. Parallel communication has well-defined limits. Data volume decreases with O(1/ √ P ) with increasing process counts P and every process communicates with at most O( √ P ) others. Local sparse matrix multiplication is handled efficiently using a combination of techniques: blocking elements together in an application-relevant way, an autotuning library for small matrix multiplications, cache-oblivious recursive multiplication, and multithreading. Additionally, on-the-fly filtering not only increases sparsity but also avoids performing calculations that fall below the filtering threshold. We demonstrate and analyze the performance of the DBCSR library and its various scaling behaviors.