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From tile algorithm to stripe algorithm: a CUBLAS-based parallel implementation on GPUs of Gauss method for the resolution of extremely large dense linear systems stored on an array of solid state devices

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JOURNAL OF SUPERCOMPUTING 2014年第1期68卷 365-413页

作者： Carcenac, Manuel European Univ Lefke Dept Comp Engn Gemikonagi Turkey

This paper presents an efficient algorithmic approach to the GPU-based parallel resolution of dense linear systems of extremely large size. A formal transformation of the code of Gauss method allows us to develop for matrix calculations the concept of stripe algorithm, as opposed to that of tile algorithm. Our stripe algorithm is based on the partitioning of the linear system's matrix into stripes of rows and is well suited for efficient implementation on a GPU, using cublasDgemm function of CUBLAS library as the main building block. It is also well adapted to storage of the linear system on an array of solid state devices, the PC memory being used as a cache between the SSDs and the GPU memory. We demonstrate experimentally that our code solves efficiently dense linear systems of size up to 400,000 (160 billion matrix elements) using an NIVDIA C2050 and six 240 GB SSDs.

关键词： Dense linear system Graphical processing unit (GPU) CUBLAS Stripe algorithm tile algorithm Solid state device (SSD)

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Faster method for tuning the tile size for tile matrix decomposition 10

Faster method for tuning the tile size for tile matrix decom...

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10th IEEE International Symposium on Embedded Multicore/Many-core Systems-on-Chip (MCSOC)

作者： Suzuki, Tomohiro Univ Yamanashi Dept Interdisciplinary Res Div Engn 4-3-11 Takeda Kofu Yamanashi 4008511 Japan

ISBN: (纸本)9781509035311

Matrices are frequently decomposed in various ways in order to meet the conditions of an application, and therefore, algorithms for doing this are very important in the field of numerical linear algebra. In the tile algorithm, it is very critical to find a tile size that is suitable for the size of the matrix and the run-time environment. Smaller tiles can generate many fine-grained tasks. This can resolve load imbalances, but it causes a decline in the performance of the level three Basic Linear Algebra Subprograms (L3 BLAS) because L3 BLAS routines show higher performance with a larger size of data. Agullo et al. presented a pruned search routine for determining the size of the tile and the width of the inner blocks for tile matrix decomposition routines. To further reduce the parameter search time, we reduce the candidates by considering the number of tasks, which varies with the tile size.

关键词： tile algorithm QR decomposition tile size tuning

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Improved Internode Communication for tile QR Decomposition for Multicore Cluster Systems 29

Improved Internode Communication for Tile QR Decomposition f...

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29th IEEE International Parallel and Distributed Processing Symposium (IPDPS)

作者： Suzuki, Tomohiro Univ Yamanashi Dept Interdisciplinary Res Div Engn 4-3-11 Takeda Kofu Yamanashi 4008511 Japan

ISBN: (纸本)9781467376846

tile algorithms for matrix decomposition can generate many fine-grained tasks. Therefore, their suitability for processing with multicore architecture has attracted much attention from the high-performance computing (HPC) community. Our implementation of tile QR decomposition for a cluster system has dynamic scheduling, OpenMP work-sharing, and other useful features. In this article, we discuss the problems in internode communications that were present in our previous implementation. The improved implementation has both strong and weak scalability.

关键词： tile algorithm QR decomposition Cluster system Dynamic task scheduling

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Performance tuning of tile matrix decomposition 13

Performance tuning of tile matrix decomposition

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IEEE 13th International Symposium on Embedded Multicore/Many-Core Systems-on-Chip (MCSoC)

作者： Suzuki, Tomohiro Univ Yamanashi Dept Interdisciplinary Res Div Engn 4-3-11 Takeda Kofu Yamanashi 4008511 Japan

ISBN: (纸本)9781728148823

Task parallel algorithms have attracted attention as algorithms for highly parallel architectures in recent years. The aim of such algorithms is to keep all computing resources running without stalling by executing a large number of finegrained tasks asynchronously while observing data dependencies. The tile algorithm of matrix decomposition of dense matrices is implemented using a task parallel programming model following such an approach. In this article, we will consider how to select tile size, which is an important performance parameter.

关键词： matrix decomposition tile algorithm multi-core/many-core architecture

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