High performance matrix inversion based on LU factorization for multicore architectures

MTAGS'11 - Proceedings of the 2011 ACM International Workshop on Many Task Computing on Grids and Supercomputers, Co-located with SC'11

Volumn , Issue , 2011, Pages 33-42

  Dongarra, Jack ^a,c,d   Faverge, Mathieu ^a   Ltaief, Hatem ^b   Luszczek, Piotr ^a  

^a UNIVERSITY OF TENNESSEE   (United States)

^b KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Saudi Arabia)

^c OAK RIDGE NATIONAL LABORATORY   (United States)

^d UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

LU factorization; multicore parallel performance; runtime DAG scheduling

Indexed keywords

ALGORITHMIC APPROACH; COMPUTATIONAL TASK; DATA DEPENDENCIES; DATA FLOW; DATA LAYOUTS; DIRECTED ACYCLIC GRAPHS; EFFICIENT IMPLEMENTATION; ENERGY EFFICIENT; INVERSION PROCEDURE; LOOSE SYNCHRONIZATIONS; LU FACTORIZATION; MATRIX; MATRIX INVERSIONS; MULTI CORE; MULTICORE ARCHITECTURES; NUMERICAL LIBRARY; ON THE FLIES; PERFORMANCE IMPLEMENTATION; PERFORMANCE MATRICES; POWER CONSUMPTION ANALYSIS; PROCESSING UNITS; RUNTIME DAG SCHEDULING; RUNTIME ENVIRONMENTS; SCALAPACK; SQUARE MATRICES; SYNCHRONIZATION POINTS; SYSTEM MEMORY;

ENERGY EFFICIENCY; FACTORIZATION; LINEAR SYSTEMS; SOFTWARE ARCHITECTURE; SUPERCOMPUTERS;

MATRIX ALGEBRA;

EID: 84857663656     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2132876.2132885     Document Type: Conference Paper

References (38)

1. E. Agullo, H. Bouwmeester, J. Dongarra, J. Kurzak, J. Langou, and L. Rosenberg. Towards an efficient tile matrix inversion of symmetric positive definite matrices on multicore architectures. In VECPAR'10. 9th International Meeting High Performance Computing for Computational Science, Berkeley, CA (USA), June 22-25 2010.
2. E. Anderson, Z. Bai, C. Bischof, S. L. Blackford, J. W. Demmel, J. J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. C. Sorensen. LAPACK User's Guide. Society for Industrial and Applied Mathematics, Philadelphia, Third edition, 1999.
3. Y. Bard. Nonlinear Parameter Estimation. Academic Press, 1974.
4. L. S. Blackford, J. Choi, A. Cleary, E. F. D'Azevedo, J. W. Demmel, I. S. Dhillon, J. J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. W. Walker, and R. C. Whaley. ScaLAPACK Users' Guide. Society for Industrial and Applied Mathematics, Philadelphia, 1997.
5. G. Bosilca, A. Bouteiller, A. Danalis, M. Faverge, A. Haidar, T. Herault, J. b Kurzak, J. Langou, P. Lemarinier, H. Ltaief, P. Luszczek, A. YarKhan, and J. Dongarra. Flexible development of dense linear algebra algorithms on massively parallel architectures with DPLASMA. In 12th IEEE International Workshop on Parallel and Distributed Scientific and Engineering Computing (PDSEC-11), page to appear, Anchorage, AK, May 2011.
6. G. Bosilca, A. Bouteiller, A. Danalis, M. Faverge, H. Haidar, T. Herault, J. Kurzak, J. Langou, P. Le marinier, H. Ltaief, P. Luszczek, A. YarKhan, and J. Dongarra. Distributed-memory task execution and dependence tracking within DAGuE and the DPLASMA project. Technical Report 232, LAPACK Working Note, Sept. 2010.
7. G. Bosilca, A. Bouteiller, A. Danalis, T. Herault, P. Lemarinier, and J. Dongarra. DAGuE: A generic distributed DAG engine for high performance computing. Technical Report 231, LAPACK Working Note, Sept. 2010.
8. G. Bosilca, A. Bouteiller, A. Danalis, T. Herault, P. Lemarinier, and J. Dongarra. DAGuE: A generic distributed DAG engine for high performance computing. In Proceedings of the 16th International Workshop on High-Level Parallel Programming Models and Supportive Environments (HIPS'11), Anchorage, AL, USA, May, 20 2011. to appear.
9. G. Bosilca, A. Bouteiller, A. Danalis, T. Herault, P. Lemarinier, and J. Dongarra. DAGuE: A generic distributed dag engine for high performance computing. In 16th International Workshop on High-Level Parallel Programming Models and Supportive Environments (HIPS-11), page to appear, Anchorage, AK, May 2011.
10. C. Boulanger and L. Ouvry. Multistage linear DS-CDMA receivers. In Proc. IEEE ISSSTA 98, volume 2, pages 663-667, Sept. 1998.
11. H. Bouwmeester and J. Langou. A critical path approach to analyzing parallelism of algorithmic variants. Application to Cholesky inversion. Technical Report arXiv:1010.2000v1 [cs.DC], arXiv online archive, Oct 11 2010. Submitted to Parallel Computing. Available at arxiv.org/pdf/1010.2000.
12. R. Byers. Solving the algebraic Riccati equation with the matrix sign function. Linear Algebra and Appl., 85:267-279, 1987.
13. A. M. Castaldo and R. C. Whaley. Scaling LAPACK panel operations using Parallel Cache Assignment. Proceedings of the 15th ACM SIGPLAN symposium on Principles and practice of parallel programming, pages 223-232, 2010.
14. J. Choi, J. Demmel, I. Dhillon, J. Dongarra, Ostrouchov, S., A. Petitet, K. Stanley, D. Walker, and R. C. Whaley. ScaLAPACK, a portable linear algebra library for distributed memory computers-design issues and performance. Computer Physics Communications, 97(1-2):1-15, 1996. (Pubitemid 126387751)
15. J. J. D. Croz and N. J. Higham. Stability methods for matrix inversion. IMA J. Numer. Anal., 12, January 1992.
16. J. Dongarra, J. Du Croz, I. Duff, and S. Hammarling. Algorithm 679: A set of Level 3 Basic Linear Algebra Subprograms. ACM Trans. Math. Soft., 16(1):18-28, March 1990. (Pubitemid 20684795)
17. J. Dongarra, M. Faverge, H. Ltaief, and P. Luszczek. Exploiting Fine-Grain Parallelism in Recursive LU Factorization. Accepted at the International Conference on Parallel Computing, 2011.
18. J. J. Dongarra, I. S. Duff, J. D. Croz, and S. Hammarling. A set of level 3 basic linear algebra subprograms. ACM TOMS, 16(1):1-17, March 1990. (Pubitemid 20684794)
19. S. L. Fagin. Measurement matrix partitioning theorem. IEEE Trans. Autom. Control, AC-14(6):773-774, Dec. 1969.
20. G. E. Forsythe, M. A. Malcolm, and C. B. Moler. Computer Methods for Mathematical Computations. Prentice-Hall, Englewood Cliffs, New Jersey, 1977.
21. D. A. S. Fraser. Statistics, An Introduction. Wiley, NewYork, 1958.
22. R. Ge, X. Feng, S. Song, H.-C. Chang, D. Li, and K. W. Cameron. Powerpack: Energy profiling and analysis of high-performance systems and applications. IEEE Transactions on Parallel and Distributed Systems, PDS-21(5):658-671, May 2010.
23. B. Goglin, J. Squyres, and S. Thibault. Hardware Locality: Peering under the hood of your server. Linux Pro Magazine, 128:28-33, July 2011.
24. G. H. Golub and C. F. Van Loan. Matrix Computation. John Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, Maryland, third edition, 1996.
25. A. Haidar, H. Ltaief, A. YarKhan, and J. J. Dongarra. Analysis of Dynamically Scheduled Tile Algorithms for Dense Linear Algebra on Multicore Architectures. ICL Technical Report UT-CS-11-666, LAPACK working note #243, Submitted to Concurrency and Computations, 2010.
26. N. J. Higham. Computing the polar decomposition - with applications. SIAM J. Sci. Stat. Comput., 7:1160-1174, 1986.
27. G. H. Jowett. Applications of Jordan's procedure for matrix inversion in multiple regression and multivariate distance analysis. Journal of the Royal Statistical Society. Series B (Methodological), 25(2):352-357, 1963.
28. Z. Lei and T. Lim. Simplified polynomial-expansion linear detectors for DS-CDMA receivers. IEEE Elec. Lett., 34(16):1561-1563, 1998. (Pubitemid 128610604)
29. H. Ltaief, P. Luszczek, and J. Dongarra. Profiling high performance dense linear algebra algorithms on multicore architectures for power and energy efficiency. In EnA-HPC 2011: International Conference on Energy-Aware High Performance Computing, Hamburg, Germany, September 07-09 2011.
30. P. McCullagh and J. A. Nelder. Generalized Linear Models. Chapman and Hall, second edition edition, 1989.
31. Intel, Math Kernel Library (MKL). http://www.intel.com/software/products/ mkl/.
32. S. Moshavi, E. Kanterakis, and D. Schilling. Multistage linear receivers for DS-CDMA systems. Int. J. Wireless Inf. Networks, 3(1):1-17, Jan. 1996. (Pubitemid 126711392)
33. R. T. M. Mozaffaripour. Suboptimum search algorithm in conjunction with polynomial expanded multiuser detection for uplink. Wireless Personnal Comm., 24(1):1-9, 2003.
34. D. Simon. Optimal State Estimation. Wiley, New York, 2006.
35. D. C. Sorensen. Analysis of pairwise pivoting in Gaussian elimination. IEEE Transactions on Computers, C-34(3):274-278, 1985. http://dx.doi.org/10. 1109/ TC.1985.1676570DOI: 10.1109/TC.1985.1676570.
36. Q. Xie and N. xian Chen. Matrix-inversion method: Applications to Möbius inversion deconvolution. Physical Review E, 52(6):6055-6065, December 1995.
37. A. YarKhan, J. Kurzak, and J. Dongarra. QUARK Users'Guide: QUeueing And Runtime for Kernels. University of Tennessee Innovative Computing Laboratory Technical Report ICL-UT-11-02, 2011.
38. Ioan Raicu, Ian Foster, and Yong Zhao. Many-Task Computing for Grids and Supercomputers. IEEE Workshop on Many-Task Computing on Grids and Supercomputers (MTAGS08), 2008