Abstract
We target the development of high-performance algorithms for dense matrix operations where data resides on disk and has to be explicitly moved in and out of the main memory. We provide strong evidence that, even for a complex operation like the QR factorization, the use of a run-time system creates a separation of concerns between the matrix computations and I/O operations with the result that no significant changes need to be introduced to existing in-core algorithms. The library developer can thus focus on the design of algorithms-by-blocks, addressing disk memory as just another level of the memory hierarchy. Experimental results for the out-of-core computation of the QR factorization on a multi-core processor reveal the potential of this approach.
Chapter PDF
Similar content being viewed by others
Keywords
References
Baboulin, M., Giraud, L., Gratton, S., Langou, J.: Parallel tools for solving incremental dense least squares problems. application to space geodesy. Technical Report UT-CS-06-582; TR/PA/06/63, University of Tennessee; CERFACS (2006); To appear in J. of Algorithms and Computational Technology 3(1) (2009)
D’Azevedo, E.F., Dongarra, J.J.: The design and implementation of the parallel out-of-core scalapack LU, QR, and Cholesky factorization routines. LAPACK Working Note 118 CS-97-247, University of Tennessee, Knoxville (1997)
Reiley, W.C., van de Geijn, R.A.: POOCLAPACK: Parallel Out-of-Core Linear Algebra Package. Technical Report CS-TR-99-33, Department of Computer Sciences, The University of Texas at Austin (1999)
Toledo, S.: A survey of out-of-core algorithms in numerical linear algebra. In: DIMACS Series in Discrete Mathematics and Theoretical Computer Science (1999)
Marqués, M., Quintana-Ortí, G., Quintana-Ortí, E.S., van de Geijn, R.: Solving “large” dense matrix problems on multi-core processors. In: 10th IEEE International Workshop on Parallel and Distributed Scientific and Engineering Computing – PDSEC 2009 (to appear, 2009)
Van Zee, F.G.: The complete reference (2008) (in preparation), http://www.cs.utexas.edu/users/flame
Baboulin, M.: Solving large dense linear least squares problems on parallel distributed computers. Application to the Earth’s gravity field computation. Ph.D. dissertation, INPT, TH/PA/06/22 (2006)
Gunter, B.C.: Computational methods and processing strategies for estimating Earth’s gravity field. PhD thesis, The University of Texas at Austin (2004)
Geng, P., Oden, J.T., van de Geijn, R.: Massively parallel computation for acoustical scattering problems using boundary element methods. Journal of Sound and Vibration 191(1), 145–165 (1996)
Schafer, N., Serban, R., Negrut, D.: Implicit integration in molecular dynamics simulation. In: ASME International Mechanical Engineering Congress & Exposition (2008) (IMECE2008-66438)
Zhang, Y., Sarkar, T.K., van de Geijn, R.A., Taylor, M.C.: Parallel MoM using higher order basis function and PLAPACK in-core and out-of-core solvers for challenging EM simulations. In: IEEE AP-S & USNC/URSI Symposium (2008)
Gunter, B.C., van de Geijn, R.A.: Parallel out-of-core computation and updating the QR factorization. ACM Transactions on Mathematical Software 31(1), 60–78 (2005)
Watkins, D.S.: Fundamentals of Matrix Computations, 2nd edn. John Wiley & Sons, Inc., New York (2002)
Dongarra, J.J., Du Croz, J., Hammarling, S., Duff, I.: A set of level 3 basic linear algebra subprograms. ACM Transactions on Mathematical Software 16(1), 1–17 (1990)
Quintana-Ortí, G., Quintana-Ortí, E.S., van de Geijn, R., Zee, F.V., Chan, E.: Programming matrix algorithms-by-blocks for thread-level parallelism. ACM Transactions on Mathematical Software (2008) (to appear), FLAME Working Note #32, http://www.cs.utexas.edu/users/flame/
Anderson, E., Bai, Z., Demmel, J., Dongarra, J.E., DuCroz, J., Greenbaum, A., Hammarling, S., McKenney, A.E., Ostrouchov, S., Sorensen, D.: LAPACK Users’ Guide. SIAM, Philadelphia (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Marqués, M., Quintana-Ortí, G., Quintana-Ortí, E.S., van de Geijn, R. (2009). Out-of-Core Computation of the QR Factorization on Multi-core Processors. In: Sips, H., Epema, D., Lin, HX. (eds) Euro-Par 2009 Parallel Processing. Euro-Par 2009. Lecture Notes in Computer Science, vol 5704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03869-3_75
Download citation
DOI: https://doi.org/10.1007/978-3-642-03869-3_75
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03868-6
Online ISBN: 978-3-642-03869-3
eBook Packages: Computer ScienceComputer Science (R0)