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LU factorization with partial pivoting is a canonical numerical procedure and the main component of the High Performance Linpack benchmark. This article presents an implementation of the algorithm for a hybrid, shared memory, system with standard CPU cores and GPU accelerators. The optimizations include lookahead, dynamic task scheduling, fine grain parallelism for memory-bound operations, autotuning, and data layout geared towards complex memory hierarchies. Performance in excess of one Tera flop/s is achieved using four AMD Magny Cours CPUs and four NVIDIA Fermi GPUs.

LU Factorization with Partial Pivoting for a Multi-CPU, Multi-GPU Shared Memory System