Flexible Linear Algebra Development and Scheduling with Cholesky Factorization

Azzam Haidar, Chongxiao Cao, Stanimire Tomov, Asim YarKhan, Piotr Luszczek, Jack Dongarra
University of Tennessee, Knoxville, USA
7th IEEE International Conference on High Performance Computing and Communications, 2015


   title={Flexible Linear Algebra Development and Scheduling with Cholesky Factorization},

   author={Haidar, Azzam and YarKhan, Asim and Cao, Chongxiao and Luszczek, Piotr and Tomov, Stanimire and Dongarra, Jack},



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Modern high performance computing environments are composed of networks of compute nodes that often contain a variety of heterogeneous compute resources, such as multicore-CPUs, GPUs, and coprocessors. One challenge faced by domain scientists is how to efficiently use all these distributed, heterogeneous resources. In order to use the GPUs effectively, the workload parallelism needs to be much greater than the parallelism for a multicore-CPU. On the other hand, a Xeon Phi coprocessor will work most effectively with degree of parallelism between GPUs and multicore-CPUs. Additionally, effectively using distributed memory nodes brings out another level of complexity where the workload must be carefully partitioned over the nodes. In this work we are using a lightweight runtime environment to handle many of the complexities in such distributed, heterogeneous systems. The runtime environment uses task-superscalar concepts to enable the developer to write serial code while providing parallel execution. The task-programming model allows the developer to write resource-specialization code, so that each resource gets the appropriate sized workload-grain. Our taskprogramming abstraction enables the developer to write a single algorithm that will execute efficiently across the distributed heterogeneous machine. We demonstrate the effectiveness of our approach with performance results for dense linear algebra applications, specifically the Cholesky factorization.
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