Inverse Matrix using Gauss Elimination Method by OpenMP

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Author(s)

Madini O. Alassafi 1,* Yousef S. Alsenani 1

1. Computer Skills Unite, King Abdualziz University, Jeddah, 21571, Saudi Arabia

* Corresponding author.

DOI: https://doi.org/10.5815/ijitcs.2016.02.05

Received: 4 Jun. 2015 / Revised: 23 Sep. 2015 / Accepted: 17 Nov. 2015 / Published: 8 Feb. 2016

Index Terms

OpenMP in C++, Gauss elimination, Examples of OpenMP, OpenMP directives

Abstract

OpenMP is an implementation program interface that might be utilized to explicitly immediate multi-threaded and it shared memory parallelism. OpenMP platform for specifications multi-processing via concurrent work between interested parties of hardware and software industry, governments and academia. OpenMP is not needs implemented identically by all vendors and it is not proposed for distributed memory parallel systems by itself. In order to invert a matrix, there are multiple approaches. The proposed LU decomposition calculates the upper and lower triangular via Gauss elimination method. The computation can be parallelized using OpenMP technology. The proposed technique main goal is to analyze the amount of time taken for different sizes of matrices so we used 1 thread, 2 threads, 4 threads, and 8 threads which will be compared against each other to measure the efficiency of the parallelization. The result of interrupting compered the amount of time spent in all the computing using 1 thread, 2 threads, 4 threads, and 8 threads. We came up with if we raise the number of threads the performance will be increased (less amount of time required). If we use 8 threads we get around 64% performance gained. Also as the size of matrix increases, the efficiency of parallelization also increases, which is evident from the time difference between serial and parallel code. This is because, more computations are done parallel and hence the efficiency is high. Schedule type in OpenMP has different behavior, we used static, dynamic, and guided scheme.

Cite This Paper

Madini O. Alassafi, Yousef S. Alsenani, "Inverse Matrix using Gauss Elimination Method by OpenMP", International Journal of Information Technology and Computer Science(IJITCS), Vol.8, No.2, pp.41-46, 2016. DOI:10.5815/ijitcs.2016.02.05

Reference

[1]Murthy, K.N.B. and C.S.R. Murthy, Gaussian-elimination-based algorithm for solving linear equations on mesh-connected processors. Computers and Digital Techniques, IEE Proceedings -, 1996. 143(6): p. 407-412.

[2]Allande, C., et al., A Performance Model for OpenMP Memory Bound Applications in Multisocket Systems. Procedia Computer Science, 2014. 29(0): p. 2208-2218.

[3]Park, I. and S.W. Kim, Study of OpenMP applications on the InfiniBand-based software distributed shared-memory system. Parallel Computing, 2005. 31(10–12): p. 1099-1113.

[4]Guo, X., et al., Developing a scalable hybrid MPI/OpenMP unstructured finite element model. Computers & Fluids, 2015. 110(0): p. 227-234.

[5]Zhang, S., et al., Parallel computation of a dam-break flow model using OpenMP on a multi-core computer. Journal of Hydrology, 2014. 512(0): p. 126-133.

[6]Marongiu, A., P. Burgio, and L. Benini, Supporting OpenMP on a multi-cluster embedded MPSoC. Microprocessors and Microsystems, 2011. 35(8): p. 668-682.

[7]Jeun, W.-C., et al., Overcoming performance bottlenecks in using OpenMP on SMP clusters. Parallel Computing, 2008. 34(10): p. 570-592.

[8]Doroodian, S., N. Ghaemian, and M. Sharifi. Estimating overheads of OpenMP directives. in Electrical Engineering (ICEE), 2011 19th Iranian Conference on. 2011.

[9]Jian, G., Y. Su, and J. Jian-Ming, An OpenMP-CUDA Implementation of Multilevel Fast Multipole Algorithm for Electromagnetic Simulation on Multi-GPU Computing Systems. Antennas and Propagation, IEEE Transactions on, 2013. 61(7): p. 3607-3616.

[10]Barlas, G., Chapter 4 - Shared-memory programming: OpenMP, in Multicore and GPU Programming, G. Barlas, Editor. 2015, Morgan Kaufmann: Boston. p. 165-238.

[11]Shengfei, L., et al. Performance Evaluation of Multithreaded Sparse Matrix-Vector Multiplication Using OpenMP. in High Performance Computing and Communications, 2009. HPCC '09. 11th IEEE International Conference on. 2009.

[12]Jian-Jun, H. and L. Qing-Hua. Dynamic Power-Aware Scheduling Algorithms for Real-Time Task Sets with Fault-Tolerance in Parallel and Distributed Computing Environment. in Parallel and Distributed Processing Symposium, 2005. Proceedings. 19th IEEE International. 2005.

[13]S.F. McGinn and R.E. Shaw. Parallel Gaussian elimination using OpenMP and MPI. In Proceedings of the International Symposium on High Performance Computing Systems and Applications, 2002. 

[14]Sibai, Fadi N., 2013. Performance modeling and analysis of parallel Gaussian elimination on multi-core computers. Journal of King Saud University – Computer and Information Sciences. Elsevier, Vol. 26, pp. 41–54.

[15]Michailidis, P. D. and Margaritis, K. G. (2011). Parallel direct methods for solving the system of linear equations with pipelining on a multicore using OpenMP. Journal of Computational and Applied Mathematics, 236(3):326–341.