关于分块稀疏矩阵的内存占用
On Memory Footprints of Partitioned Sparse Matrices
AI总结：
研究通过分析563个稀疏矩阵在均匀分块存储下的内存占用，比较不同分块大小和存储方式，发现单精度和双精度下内存节省可达42.3%和28.7%，且平均接近理论下限。
摘要：
稀疏矩阵计算的运行特性可通过减少内存占用来优化。本文分析了563个代表性的稀疏矩阵在均匀分块下的内存占用，考虑了不同分块大小和存储方式，并进行了统计评估。内存占用还与下限和CSR存储格式进行了比较。单精度和双精度下的平均节省率分别为42.3%和28.7%，最坏情况下的节省率为25.5%和17.1%。此外，分块矩阵的内存占用平均比CSR格式更接近理论下限。基于这些结果，提供了高效的稀疏矩阵存储和分块建议。
英文摘要：
Runtime characteristics of sparse matrix computations and related processes may be often improved by reducing memory footprints of involved matrices. Such a reduction can be usually achieved when matrices are processed in a block-wise manner. The presented study analysed memory footprints of 563 representative benchmark sparse matrices with respect to their partitioning into uniformly-sized blocks. Different block sizes and different ways of storing blocks in memory were considered and statistically evaluated. Memory footprints of partitioned matrices were additionally compared with lower bounds and with the CSR storage format. The average measured memory savings against CSR in case of single and double precision were 42.3 and 28.7 percents, the corresponding worst-case savings 25.5 and 17.1 percents. Moreover, memory footprints of partitioned matrices were in average 5 times closer to their lower bounds than CSR. Based on the obtained results, generic suggestions for efficient partitioning and storage of sparse matrices in a computer memory are provided.
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