Scheduling two-sided transformations using tile algorithms on multicore architectures

Scientific Programming

Volumn 18, Issue 1, 2010, Pages 35-50

  Ltaief, Hatem ^a   Kurzak, Jakub ^a   Dongarra, Jack ^a,b,c   Badia, Rosa M ^d  

^a UNIVERSITY OF TENNESSEE   (United States)

^b OAK RIDGE NATIONAL LABORATORY   (United States)

^c UNIVERSITY OF MANCHESTER   (United Kingdom)

^d BARCELONA SUPERCOMPUTING CENTER   (Spain)

Author keywords

Linear algebra; Matrix factorization; Multicore; Scheduling; Two sided transformations

Indexed keywords

ALGEBRA; COMPUTER ARCHITECTURE; DATA FLOW ANALYSIS; EIGENVALUES AND EIGENFUNCTIONS; FACTORIZATION; LINEAR ALGEBRA; LINEAR TRANSFORMATIONS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; PARALLEL PROCESSING SYSTEMS; PROGRAM PROCESSORS; SCHEDULING; SINGULAR VALUE DECOMPOSITION; SOFTWARE ARCHITECTURE;

BASIC LINEAR ALGEBRA SUBPROGRAMS; HIGH PERFORMANCE COMPUTING; MATRIX FACTORIZATIONS; MULTI CORE; MULTI-CORE PROCESSOR; MULTICORE ARCHITECTURES; SCHEDULER IMPLEMENTATION; THREAD LEVEL PARALLELISM;

MULTICORE PROGRAMMING;

EID: 77951935506     PISSN: 10589244     EISSN: None     Source Type: Journal    
DOI: 10.3233/SPR-2010-0297     Document Type: Article

References (35)

1. R. C. Agarwal and F. G. Gustavson, A parallel implementation of matrix multiplication and LU factorization on the IBM 3090, in: Proceedings of the IFIP WG 2.5 Working Conference on Aspects of Computation on Asynchronous Parallel Processors, Palo Alto, CA, August 1988, pp. 217-221.
2. R. C. Agarwal and F. G. Gustavson, Vector and parallel algorithms for Cholesky factorization on IBM 3090, in: Proceedings of the 1989 ACM/IEEE Conference on Supercomputing, Reno, NV, November 1989, pp. 225-233.
3. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney and D. Sorensen, LAPACK Users' Guide, 3rd edn, SIAM, Philadelphia, PA, USA, 1999.
4. J. L. Barlow, N. Bosner and Z. Drmač, A new stable bidiagonal reduction algorithm, Linear Algebra Appl. 397 (1) (2005), 35-84. (Pubitemid 40146312)
5. P. Bellens, J. M. Perez, R. M. Badia and J. Labarta, CellSs: A programming model for the cell BE architecture, in: Proceedings of the 2006 ACM/IEEE Conference on Supercomputing, Tampa, FL, November 11-17, 2006, p. 86.
6. N. Bosner and J. L. Barlow, Block and parallel versions of one-sided bidiagonalization, SIAM J. Matrix Anal. Appl. 29 (3) (2007), 927-953.
7. A. Buttari, J. J. Dongarra, P. Husbands, J. Kurzak and K. Yelick, Multithreading for synchronization tolerance in matrix factorization, in: Scientific Discovery Through Advanced Computing, SciDAC 2007, Boston, MA, IOP Publishing, June 24-28, 2007. (J. Phys.: Conference Series 78 012-028.)
8. A. Buttari, J. Langou, J. Kurzak and J. Dongarra, Parallel tiled QR factorization for multicore architectures, LAPACK Working Note 191, July 2007.
9. A. Buttari, J. Langou, J. Kurzak and J. J. Dongarra, Parallel tiled QR factorization for multicore architectures, Concurrency Comput. Pract. Exp. 20 (13) (2008), 1573-1590.
10. A. Buttari, J. Langou, J. Kurzak and J. J. Dongarra, A class of parallel tiled linear algebra algorithms for multicore architectures, Parellel Comput. Syst. Appl. 35 (2009), 38-53.
11. J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. Petitet, K. Stanley, D. Walker and R. C. Whaley, ScaLA-PACK, a portable linear algebra library for distributed memory computers-design issues and performance, Comput. Phys. Comm. 97 1, 2 1996, 1-15. (Pubitemid 126387751)
12. K. E. Danforth, M. Christopher and M. Takemasa, Estimating and correcting global weather model error, Mon. Weather Rev. 135 (2) (2007), 281-299. (Pubitemid 46344360)
13. E. Elmroth and F. G. Gustavson, New serial and parallel recursive QR factorization algorithms for SMP systems, in: Applied Parallel Computing, Large Scale Scientific and Industrial Problems, 4th International Workshop, PARA, Lecture Notes in Computer Science, Vol. 1541, Springer-Verlag, Berlin, 1998, pp. 120-128.
14. E. Elmroth and F. G. Gustavson, Applying recursion to serial and parallel QR factorization leads to better performance, IBM J. Res. Dev. 44 (4) (2000), 605-624.
15. E. Elmroth and F. G. Gustavson, High-performance library software for QR factorization, in: Applied Parallel Computing, New Paradigms for HPC in Industry and Academia, 5th International Workshop, PARA, Lecture Notes in Computer Science, Vol. 1947, Springer-Verlag, Berlin/Heidelberg, 2000, pp. 53-63.
16. E. Elmroth, F. G. Gustavson, I. Jonsson and B. Kågström, Recursive blocked algorithms and hybrid data structures for dense matrix library software, SIAM Rev. 46 (1) (2004), 3-45.
17. G. H. Golub and C. F. van Loan, Matrix Computation, 3rd edn, Johns Hopkins University Press, Baltimore, MD, 1996.
18. B. C. Gunter and R. A. van de Geijn, Parallel out-of-core computation and updating of the QR factorization, ACM Trans. Math. Software 31 (1) (2005), 60-78.
19. F. G. Gustavson, New generalized matrix data structures lead to a variety of high-performance algorithms, in: Proceedings of the IFIP WG 2.5 Working Conference on Software Architectures for Scientific Computing Applications, Kluwer Academic, Deventer, The Netherlands, 2000, pp. 211-234.
20. F. G. Gustavson, J. A. Gunnels and J. C. Sexton, Minimal data copy for dense linear algebra factorization, in: Applied Parallel Computing, State of the Art in Scientific Computing, 8th International Workshop, PARA, Lecture Notes in Computer Science, Vol. 4699, Springer-Verlag, Berlin/Heidelberg, 2006, pp. 540-549.
21. M. Hegland, M. Kahn and M. Osborne, A parallel algorithm for the reduction to tridiagonal form for eigendecomposition, SIAM J. Sci. Comput. 21 (3) (1999), 987-1005.
22. J. Kurzak, A. Buttari and J. J. Dongarra, Solving systems of linear equation on the CELL processor using Cholesky factorization, Trans. Parallel Distrib. Syst. 19 (9) (2008), 1175-1186.
23. J. Kurzak and J. J. Dongarra, Implementing linear algebra routines on multi-core processors with pipelining and a look ahead, in: Applied Parallel Computing, State of the Art in Scientific Computing, 8th International Workshop, PARA, Lecture Notes in Computer Science, Vol. 4699, Springer-Verlag, Berlin, June 2006, pp. 147-156.
24. J. Kurzak and J. Dongarra, QR Factorization for the CELL processor, LAPACK Working Note 201, May 2008.
25. J. Kurzak and J. J. Dongarra, QR factorization for the CELL processor, Scientific Programming, accepted.
26. R. E. Lord, J. S. Kowalik and S. P. Kumar, Solving linear algebraic equations on an MIMD computer, J. ACM 30 (1) (1983), 103-117. (Pubitemid 13504813)
27. N. Park, B. Hong and V. K. Prasanna, Analysis of memory hierarchy performance of block data layout, in: Proceedings of the 2002 International Conference on Parallel Processing, ICPP'02, IEEE Computer Society, Washington, DC, 2002, pp. 35-44.
28. N. Park, B. Hong and V. K. Prasanna, Tiling, block data layout, and memory hierarchy performance, IEEE Trans. Parallel Distrib. Syst. 14 (7) (2003), 640-654.
29. J. M. PéArez, R. M. Badia and J. Labarta, A dependency-aware task-based programming environment for multi-core architectures, in: CLUSTER, IEEE, Piscataway, NJ, 2008, pp. 142-151.
30. J. M. Perez, P. Bellens, R. M. Badia and J. Labarta, CellSs: making it easier to program the Cell Broadband Engine processor, IBM J. Res. Dev. 51 (5) (2007), 593-604. (Pubitemid 350031358)
31. PIRO-BAND: PIpelined ROtations for BAnd Reduction, available at: http://www.cise.ufl.edu/˜srajaman/.
32. G. Quintana-OrtíA, E. S. Quintana-OrtíA, E. Chan, R. A. van de Geijn and F. G. van Zee, Scheduling of QR factorization algorithms on SMP and multi-core architectures, in: PDP, IEEE Computer Society, Los Alamitos, CA, 2008, pp. 301-310.
33. R. Schreiber and C. van Loan, A storage efficient WY representation for products of householder transformations, SIAM J. Sci. Statist. Comput. 10 (1989), 53-57.
34. SMP Superscalar (SMPSs) User's Manual, Version 2.0, Barcelona Supercomputing Center, 2008.
35. L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, Philadelphia, PA, 1997.