A QDWH-based SVD software framework on distributed-memory manycore systems
KAUST DepartmentApplied Mathematics and Computational Science
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Extreme Computing Research Center
Online Publication Date2019-04-29
Print Publication Date2019-04-26
Permanent link to this recordhttp://hdl.handle.net/10754/626212
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AbstractThis article presents a high-performance software framework for computing a dense SVD on distributed-memory manycore systems. Originally introduced by Nakatsukasa et al. (2010) and Nakatsukasa and Higham (2013), the SVD solver relies on the polar decomposition using the QR Dynamically Weighted Halley algorithm (QDWH). Although the QDWH-based SVD algorithm performs a significant amount of extra floating-point operations compared to the traditional SVD with the one-stage bidiagonal reduction, the inherent high level of concurrency associated with Level 3 BLAS compute-bound kernels ultimately compensates for the arithmetic complexity overhead. Using the ScaLAPACK two-dimensional block cyclic data distribution with a rectangular processor topology, the resulting QDWH-SVD further reduces excessive communications during the panel factorization, while increasing the degree of parallelism during the update of the trailing submatrix, as opposed to relying on the default square processor grid. After detailing the algorithmic complexity and the memory footprint of the algorithm, we conduct a thorough performance analysis and study the impact of the grid topology on the performance by looking at the communication and computation profiling trade-offs. We report performance results against state-of-the-art existing QDWH software implementations (e.g., Elemental) and their SVD extensions on large-scale distributed-memory manycore systems based on commodity Intel x86 Haswell processors and Knights Landing (KNL) architecture. The QDWH-SVD framework achieves up to 3/8-fold speedups on the Haswell/KNL-based platforms, respectively, against ScaLAPACK PDGESVD and turns out to be a competitive alternative for well- and ill-conditioned matrices. We finally come up herein with a performance model based on these empirical results. Our QDWH-based polar decomposition and its SVD extension are freely available at https://github.com/ecrc/qdwh.git and https://github.com/ecrc/ksvd.git, respectively, and have been integrated into the Cray Scientific numerical library LibSci v17.11.1.
SponsorsThe authors would like to thank Jack Poulson from Google Inc. for his help in tuning Elemental and the vendor Cray for systems' remote accesses in the context of the Cray Center of Excellence awarded to the Extreme Computing Research Center at KAUST. The authors would like also to thank Mohammad Hadi and Nick Hill from Cray for their help integrating QDWH-based SVD solver into Cray LibSci library. For computer time, this research used the resources from KAUST Supercomputing Laboratory for Shaheen-2 core hour allocations.