Fast Sparse Matrix-Vector Multiplication by Exploiting Variable Block Structure

• Published in: High Performance Computing and Communications pp. 807 - 816
• Main Authors: Vuduc, Richard W., Moon, Hyun-Jin
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005; Springer
• Edition: 1ère éd
• Series: Lecture Notes in Computer Science
• Subjects: Applied sciences; Block Size; Cache Blocking; Compression Ratio; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Dense Block; Exact sciences and technology; Software; Sparse Matrix; Finite element method; High performance; Alignment; Cache memory; Bandwidth; Matrix calculus; Sparse matrix; Tiling; Data structure; Distributed computing; Modeling; Execution time
• ISBN: 9783540290315; 3540290311
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11557654_91

We improve the performance of sparse matrix-vector multiplication(SpMV) on modern cache-based superscalar machines when the matrix structure consists of multiple, irregularly aligned rectangular blocks. Matrices from finite element modeling applications often have this structure. We split the matrix, A, into a sum, A1 + A2 + ... + As, where each term is stored in a new data structure we refer to as unaligned block compressed sparse row (UBCSR) format. A classical approach which stores A in a BCSR can also reduce execution time, but the improvements may be limited because BCSR imposes an alignment of the matrix non-zeros that leads to extra work from filled-in zeros. Combining splitting with UBCSR reduces this extra work while retaining the generally lower memory bandwidth requirements and register-level tiling opportunities of BCSR. We show speedups can be as high as 2.1× over no blocking, and as high as 1.8× over BCSR as used in prior work on a set of application matrices. Even when performance does not improve significantly, split UBCSR usually reduces matrix storage.