Sparse Diagonal Matrix Adaptive SpMV Optimization Method for GPU

Sparse Matrix-Vector multiplication (SpMV) is the computational core and bottleneck of sparse linear systems, and its computational efficiency affects the overall performance of iterative solvers. Its optimization has long been a research hotspot in the fields of scientific computing and engineering applications. The discretization of partial differential equations produces sparse diagonal matrices, and because of their diverse distributions of nonzero elements, no single method can achieve optimal time performance across all matrices. To solve these problems, a Graphics Processing Unit (GPU)-based sparse diagonal matrix adaptive SpMV optimization method called Adaptive SpMV Tuning (AST) is proposed. This method designs a feature space and constructs a feature extractor to extract fine-grained features of the matrix structure. By analyzing the correlation between these features and SpMV methods, it establishes a scalable set of candidate methods and forms a mapping relationship between the features and optimal methods. Subsequently, a performance prediction tool is built to efficiently predict the optimal method for the matrix. The experimental results show that AST can achieve a prediction accuracy of 85.8%, with an average time performance loss of 0.09. Compared to Diagonal (DIA), Hacked DIA (HDIA), Hybrid of DIA and Compressed Sparse Row (HDC), DIA-Adaptive, and Divide-Rearrange and Merge (DRM), AST can achieve an average speedup in kernel runtime of 20.19, 1.86, 3.06, 3.72, and 1.53 times, respectively, and a speedup in floating-point performance of 1.05, 1.28, 12.45, 1.94, and 0.97 times, respectively.