OpenMP Thread Affinity for Matrix Factorization on Multicore Systems

Abstract

Abstract-The aim of this paper is to investigate the impact of thread affinity on computing performance for matrix factorization on shared memory multicore systems with hierarchical memory. We consider two parallel block matrix factorizations (LU and WZ) and employ thread affinity to improve their performance. We study decomposition without pivoting and we compare differences between various affinity strategies for diagonally dominant matrices. Our results show that the choice of thread affinity has the measurable impact on the performance of the matrice factorizations.

Influence of loop transformations on performance and energy consumption of the multithreded WZ factorization

“…In many numerical algorithms where dependencies between data are very complicated, even such tools as efficient optimizing compilers are not able to transform the code to use the potential of modern processors. The authors of [3], [1], present algorithms for solving systems of equations, trying to improve their performance, in particular in parallel. Improvement in performance was obtained by appropriate transformation of the underlying algorithm using looping tiling and appropriate data structures.…”

“…However, to parallelize them efficiently, the programmer has to make some decisions about applying various transformations. An example of such loops is matrix algorithms, like matrix multiplication or different kinds of factorizations, widely investigated in the literature [3], [1].…”

An Experimental Evaluation of the OpenMP Thread Mapping for LU Factorisation on Xeon Phi Coprocessor and on Hybrid CPU-MIC Platform

“…In this research, we control the thread affinity using the environment variable KMP AFFINITY on CPU and PHI KMP AFFINITY on MIC. We studied the OpenMP thread mapping strategies for matrix decompositions on multicore architectures in our work [3]. The results showed that the choice of scatter has the measurable impact on the executed time of the matrix factorisations on CPU.…”

“…There is not a single thread mapping strategy that suits all the applications. We studied the OpenMP thread mapping strategies for matrix decompositions on multicore architectures in our work [3]. The results showed that the choice of thread affinity has the measurable impact on the executed time of the matrix factorisations.…”

“…3 shows the performance of the LU factorisation in the function of the number of the threads for the matrix size of 19456 on Intel Xeon Phi in native mode and on the hybrid CPU-MIC platform in automatic offload mode for KMP AFFINITY=scatter on CPU and the different values for PHI KMP AFFINITY. We can seeAn Experimental Evaluation of the OpenMP Thread Mapping for Some Factorisations on Xeon Phi Coprocessor offload, MKL LU without piv., KMP_AFFINITY=scatter/scatter number of threads = 60 number of threads = 120 number of threads = 180 number of threads = offload, MKL LU without piv., KMP_AFFINITY=scatter/none number of threads = 60 number of threads = 120 number of threads = 180 number of threads = 240 The performance of the LU factorisation without pivoting (MKL library's implementation) in the automatic offload mode -for different matrix sizes, number of the threads, and the thread mapping settings.…”