Two-stage tridiagonal reduction for dense symmetric matrices using tile algorithms on multicore architectures

Proceedings - 25th IEEE International Parallel and Distributed Processing Symposium, IPDPS 2011

Volumn , Issue , 2011, Pages 944-955

  Luszczek, Piotr ^a   Ltaief, Hatem ^a   Dongarra, Jack ^a  

^a University of Tennessee   (United States)

Author keywords

Bulge Chasing; Scheduling; Tile Algorithms; Translation Layer; Tridiagonal Reduction

Indexed keywords

BIDIAGONAL; BULGE CHASING; CHOLESKY FACTORIZATIONS; DATA LOCALITY; EFFICIENT IMPLEMENTATION; MATRIX; MATRIX SIZE; MULTICORE ARCHITECTURES; MULTITHREADED; NUMERICAL LIBRARY; NUMERICAL SOFTWARE; PERFORMANCE DATA; PROCESSOR-MEMORY; RESEARCH PROBLEMS; RUNTIME SYSTEMS; SPECTRAL DECOMPOSITION; SYMMETRIC MATRICES; TRIDIAGONAL; TWO STAGE;

DISTRIBUTED PARAMETER NETWORKS; ECONOMIC ANALYSIS; FACTORIZATION; LINEAR TRANSFORMATIONS; MEMORY ARCHITECTURE; SCHEDULING ALGORITHMS; SOFTWARE ARCHITECTURE;

MATRIX ALGEBRA;

EID: 80053252490     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/IPDPS.2011.91     Document Type: Conference Paper

References (43)

1. H. W. Meuer, E. Strohmaier, J. J. Dongarra, and H. D. Simon, TOP500 Supercomputer Sites, 35th ed., June 2010, (The report can be downloaded from http://www.netlib.org/benchmark/top500.html).
2. K. Asanovic, R. Bodik, B. C. Catanzaro, J. J. Gebis, P. Husbands, K. Keutzer, D. A. Patterson, W. L. Plishker, J. Shalf, S. W. Williams, and K. A. Yelick, "The Landscape of Parallel Computing Research: A View from Berkeley," Electrical Engineering and Computer Sciences University of California at Berkeley,, Tech. Rep. Technical Report No. UCB/EECS-2006-183, December 18 2006.
3. PLASMA Users' Guide, Parallel Linear Algebra Software for Multicore Archtectures, Version 2.2, University of Tennessee, November 2009.
4. "The FLAME project," April 2010, http://z.cs.utexas.edu/wiki/ flame.wiki/FrontPage.
5. G. Golub and C. van Loan, Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.
6. L. N. Trefethen and D. Bau, Numerical Linear Algebra. Philadelphia, PA: SIAM, 1997, http://www.siam.org/books/OT50/Index.htm.
7. N. Rösch, S. Krüger, V. Nasluzov, and A. Matveev, "ParaGauss: The Density Functional Program ParaGauss for Complex Systems in Chemistry," in High Performance Computing in Science and Engineering, Garching 2004, part III. Springer, 2005, pp. 285-296, dOI: 10.1007/3-540-28555- 5-25.
8. R. Grimes, H. Krakauer, J. Lewis, H. Simon, and S.-H. Wei, "The solution of large dense generalized eigenvalue problems on the Cray X-MP/24 with SSD," J. Comput. Phys., vol. 69, pp. 471-481, April 1987. [Online]. Available: http://portal.acm.org/citation.cfm?id=32855.32865
9. R. M. Martin, "Electronic structure: Basic theory and practical methods," Cambridge University Press, 2008.
10. J. Perez, R. Badia, and J. Labarta, "A dependency-aware task-based programming environment for multi-core architectures,"in Cluster Computing, 2008 IEEE International Conference on, 29 2008-oct. 1 2008, pp. 142-151.
11. 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, 3rd ed. Philadelphia: Society for Industrial and Applied Mathematics, 1999.
12. 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. Philadelphia: Society for Industrial and Applied Mathematics, 1997.
13. J. Choi, J. J. Dongarra, S. Ostrouchov, A. Petitet, D. W. Walker, and R. C. Whaley, "The design and implementation of the ScaLAPACK LU, QR, and Cholesky factorization routines," Scientific Programming, vol. 5, pp. 173-184, 1996.
14. C. H. Bischof, B. Lang, and X. Sun, "Algorithm 807: The SBR Toolbox - software for successive band reduction," ACM Trans. Math. Softw., vol. 26, no. 4, pp. 602-616, 2000.
15. "Intel, Math Kernel Library (MKL),"http://www.intel.com/ software/products/mkl/.
16. T. A. Davis and S. Rajamanickam, "PIRO BAND, Pipelined Plane Rotations for Blocked Band Reduction."
17. B. Kågström, D. Kressner, E. Quintana-Orti, and G. Quintana-Orti, "Blocked Algorithms for the Reduction to Hessenberg-Triangular Form Revisited," BIT Numerical Mathematics, vol. 48, pp. 563-584, 2008.
18. S. Tomov, R. Nath, and J. Dongarra, "Accelerating the reduction to upper Hessenberg, tridiagonal, and bidiagonal forms through hybrid GPU-based computing," Parallel Computing, vol. DOI information: 10.1016/j.parco.2010. 06.001, 2010.
19. P. Bientinesi, F. Igual, D. Kressner, and E. Quintana-Orti, "Reduction to Condensed Forms for Symmetric Eigenvalue Problems on Multi-core Architectures," Parallel Processing and Applied Mathemetics, pp. 387-395, 2010.
20. A. Buttari, J. Langou, J. Kurzak, and J. J. Dongarra, "Parallel Tiled QR Factorization for Multicore Architectures,"Concurrency Computat.: Pract. Exper., vol. 20, no. 13, pp. 1573-1590, 2008, http://dx.doi.org/10.1002/ cpe.1301 DOI: 10.1002/cpe.1301.
21. -, "A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures," Parellel Comput. Syst. Appl., vol. 35, pp. 38-53, 2009, http://dx.doi.org/10.1016/j.parco.2008.10.002 DOI: 10.1016/j.parco.2008. 10.002.
22. E. S. Quintana-Ortí and R. A. van de Geijn, "Updating an LU Factorization with Pivoting,"ACM Trans. Math. Softw., vol. 35, no. 2, p. 11, 2008, http://doi.acm.org/10.1145/1377612.1377615 DOI: 10.1145/1377612. 1377615.
23. J. Kurzak, A. Buttari, and J. J. Dongarra, "Solving systems of linear equation on the CELL processor using Cholesky factorization," Trans. Parallel Distrib. Syst., vol. 19, no. 9, pp. 1175-1186, 2008, http://dx.doi.org/10.1109/TPDS.2007.70813 DOI: TPDS.2007.70813.
24. J. Kurzak and J. J. Dongarra, "QR factorization for the CELL processor," Scientific Programming, vol. 17, pp. 1-12, 2008, http://dx.doi.org/10.3233/SPR-2008-0268 DOI: 10.3233/SPR-2008-0268.
25. E. Agullo, B. Hadri, H. Ltaief, and J. Dongarrra, "Comparative study of one-sided factorizations with multiple software packages on multi-core hardware," in SC '09: Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis. New York, NY, USA: ACM, 2009, pp. 1-12.
26. H. Ltaief, J. Kurzak, and J. Dongarra, "Parallel block hessenberg reduction using algorithms-by-tiles for multicore architectures revisited," UT-CS-08-624 (also LAPACK Working Note 208), 2008.
27. J. A. Sharp, Ed., Data flow computing: theory and practice. Ablex Publishing Corp, 1992.
28. J. Yu and R. Buyya, "A Taxonomy of Workflow Management Systems for Grid Computing," Journal of Grid Computing, 2005.
29. O. Delannoy, N. Emad, and S. Petiton, "Workflow global computing with yml," in 7th IEEE/ACM International Conference on Grid Computing, september 2006.
30. A. Buttari, J. Dongarra, J. Kurzak, J. Langou, P. Luszczek, and S. Tomov, "The Impact of Multicore on Math Software,"in Applied Parallel Computing. State of the Art in Scientific Computing, 8th International Workshop, PARA, ser. Lecture Notes in Computer Science, B. Kågström, E. Elmroth, J. Dongarra, and J. Wasniewski, Eds., vol. 4699. Springer, 2006, pp. 1-10.
31. E. Chan, E. S. Quintana-Orti, G. Quintana-Orti, and R. van de Geijn, "Supermatrix out-of-order scheduling of matrix operations for SMP and multi-core architectures," in SPAA '07: Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures. New York, NY, USA: ACM, 2007, pp. 116-125.
32. E. Agullo, J. Demmel, J. Dongarra, B. Hadri, J. Kurzak, J. Langou, H. Ltaief, P. Luszczek, and S. Tomov, "Numerical linear algebra on emerging architectures: The PLASMA and MAGMA projects," Journal of Physics: Conference Series, vol. 180, 2009.
33. R. Dolbeau, S. Bihan, and F. Bodin, "HMPP: A hybrid multicore parallel programming environment," in Workshop on General Purpose Processing on Graphics Processing Units (GPGPU 2007), 2007.
34. C. Augonnet, S. Thibault, R. Namyst, and P.-A. Wacrenier, "StarPU: A Unified Platform for Task Scheduling on Heterogeneous Multicore Architectures," in Euro-Par 2009 Euro-par'09 Proceedings, ser. LNCS, Delft Pays-Bas, 2009. [Online]. Available: http://hal.inria.fr/inria-00384363/en/
35. F. Song, A. YarKhan, and J. Dongarra, "Dynamic task scheduling for linear algebra algorithms on distributed-memory multicore systems," in SC '09: Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis. New York, NY, USA: ACM, 2009, pp. 1-11, http://doi.acm.org/10.1145/1654059.1654079 DOI: 10.1145/1654059.1654079.
36. M. Cosnard and E. Jeannot, "Automatic Parallelization Techniques Based on Compact DAG Extraction and Symbolic Scheduling," Parallel Processing Letters, vol. 11, pp. 151-168, 2001. [Online]. Available: http://dx.doi.org/10.1142/S012962640100049X http://hal.inria.fr/inria-00000278/ en/
37. Q. Yi, K. Kennedy, H. You, K. Seymour, and J. Dongarra, "Automatic blocking of QR and LU factorizations for locality,"in 2nd ACM SIGPLAN Workshop on Memory System Performance (MSP 2004), 2004.
38. A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Manchek, and V. Sunderam, PVM: Parallel Virtual Machine. A Users'Guide and Tutorial for Networked Parallel Computing. Cambridge, MA: MIT Press, 1994.
39. M. Snir, S. W. Otto, S. Huss-Lederman, D. W. Walker, and J. J. Dongarra, MPI: The Complete Reference. Cambridge, MA: MIT Press, 1996.
40. M. P. I. Forum, "MPI: A Message-Passing Interface Standard,"The International Journal of Supercomputer Applications and High Performance Computing, vol. 8, 1994.
41. -, "MPI: A Message-Passing Interface Standard (version 1.1)," 1995, available at: http://www.mpi-forum.org/.
42. -, "MPI-2: Extensions to the Message-Passing Interface," 18 Jul. 1997, available at http://www.mpi-forum.org/docs/mpi-20.ps.
43. H. Ltaief, J. Kurzak, J. Dongarra, and R. M. Badia, "Scheduling two-sided transformations using tile algorithms on multicore architectures," Sci. Program., vol. 18, no. 1, pp. 35-50, 2010.