Pate Motter
Kanika Sood
ABSTRACT
Linear algebra provides the building blocks for a wide variety of scientific and engineering simulation codes. Users of these codes face a world of continuously changing algorithms and high-performance implementations. In this paper, we describe new capabilities of our Lighthouse framework, whose goal is to match specific problems in the area of high-performance numerical computing with the best available solutions. Lighthouse's innovative strategy eliminates intensive reading of documents and automates the process for developing linear algebra software. Lighthouse provides a searchable taxonomy of popular but difficult to use numerical software for dense and sparse linear algebra while providing the user with the best algorithms for a given problem based on machine learning methods. We introduce the design of Lighthouse and show examples of its interface. We also present algorithm classification results for the preconditioned iterative linear solvers in the Parallel Extensible Toolkit for Scientific Computation (PETSc) and the Trilinos library.
- Albany. https://github.com/gahansen/albany/. https://github.com/gahansen/Albany/, 2015.Google Scholar
- Y. Ataseven, Z. Akalın-Acar, C. Acar, and N. G. Gençer. Parallel implementation of the accelerated BEM approach for EMSI of the human brain. Medical & Biological Engineering & Computing, 46(7):671--679, 2008.Google ScholarCross Ref
- S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith. Efficient management of parallelism in object oriented numerical software libraries. In E. Arge, A. M. Bruaset, and H. P. Langtangen, editors, Modern Software Tools in Scientific Computing, pages 163--202. Birkhäuser Press, 1997. Google ScholarDigital Library
- S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, L. C. McInnes, K. Rupp, B. F. Smith, S. Zampini, and H. Zhang. PETSc users manual. Technical Report ANL-95/11 - Revision 3.6, Argonne National Laboratory, 2015. URL http://www.mcs.anl.gov/petsc.Google Scholar
- S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, L. C. McInnes, K. Rupp, B. F. Smith, S. Zampini, and H. Zhang. PETSc Web page, 2015. URL http://www.mcs.anl.gov/petsc.Google Scholar
- E. Bavier, M. Hoemmen, S. Rajamanickam, and H. Thornquist. Amesos2 and Belos: Direct and iterative solvers for large sparse linear systems. Scientific . . ., pages 1--25, 2012. URL http://www.sandia.gov/~srajama/publications/Amesos2\_Belos\_2012.pdfhttp://iospress.metapress.com/index/P055118195457462.pdf. Google ScholarDigital Library
- G. Belter, E. R. Jessup, I. Karlin, and J. G. Siek. Automating the generation of composed linear algebra kernels. In SC '09: Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, pages 1--12, New York, 2009. ACM. ISBN 978-1-60558-744-8. Google ScholarDigital Library
- S. Bhowmick, V. Eijkhout, Y. Freund, E. Fuentes, and D. Keyes. Application of alternating decision trees in selecting sparse linear solvers. In Software Automatic Tuning, pages 153--173. Springer, 2010.Google Scholar
- C. Bielza and P. Larrañaga. Discrete Bayesian network classifiers: A survey. ACM Comput. Surv., 47(1):5:1--5:43, July 2014. ISSN 0360-0300. URL http://doi.acm.org/10.1145/2576868. Google ScholarDigital Library
- L. Breiman. Random forests. Mach. Learn., 45(1):5--32, Oct. 2001. ISSN 0885-6125. URL http://dx.doi.org/10.1023/A:1010933404324. Google ScholarDigital Library
- CoolFluid. http://coolfluid.github.io/. http://coolfluid.github.io/, 2015.Google Scholar
- C. Cortes and V. Vapnik. Support-vector networks. Machine learning, 20(3):273--297, 1995. Google ScholarDigital Library
- P. Cunningham and S. J. Delany. k-nearest neighbour classifiers. Multiple Classifier Systems, pages 1--17, 2007.Google Scholar
- G. Demiröz and H. A. Güvenir. Classification by voting feature intervals. In Proceedings of the 9th European Conference on Machine Learning, ECML '97, pages 85--92, London, UK, 1997. Springer-Verlag. ISBN 3-540-62858-4. URL http://dl.acm.org/citation.cfm?id=645325.649678. Google ScholarDigital Library
- Django. https://www.djangoproject.com/, 2015.Google Scholar
- J. Dongarra. Freely available software for linear algebra on the web. http://www.netlib.org/utk/people/JackDongarra/la-sw.html, 2015.Google Scholar
- P. R. Eller, J.-R. C. Cheng, and R. S. Maier. Dynamic linear solver selection for transient simulations using machine learning on distributed systems. In Parallel and Distributed Processing Symposium Workshops & PhD Forum (IPDPSW), 2012 IEEE 26th International, pages 1915--1924. IEEE, 2012. Google ScholarDigital Library
- Y. Freund and L. Mason. The alternating decision tree learning algorithm. In Proceedings of the Sixteenth International Conference on Machine Learning, ICML '99, pages 124--133, San Francisco, CA, USA, 1999. Morgan Kaufmann Publishers Inc. ISBN 1-55860-612-2. URL http://dl.acm.org/citation.cfm?id=645528.657623. Google ScholarDigital Library
- M. Hall, E. Frank, G. Holmes, B. Pfahringer, P. Reutemann, and I. H. Witten. The WEKA data mining software: An update. SIGKDD Explorations, 11, 2009. Google ScholarDigital Library
- A. Holloway and T.-Y. Chen. Neural networks for predicting the behavior of preconditioned iterative solvers. In Computational Science--ICCS 2007, pages 302--309. Springer, 2007. Google ScholarDigital Library
- G. Holmes, B. Pfahringer, R. Kirkby, E. Frank, and M. Hall. Multiclass alternating decision trees. In Machine learning: ECML 2002, pages 161--172. Springer, 2002. Google ScholarDigital Library
- W. Iba and P. Langley. Induction of one-level decision trees. In Proceedings of the Ninth International Conference on Machine Learning, pages 233--240, 1992. Google ScholarDigital Library
- Ifpack2. https://trilinos.org/packages/ifpack2/. https://trilinos.org/packages/ifpack2/, 2015.Google Scholar
- E. Jessup, B. Bolton, B. Enosh, F. Ma, and T. Nguyen. LAPACK Internet Interface and Search Engine. http://www.cs.colorado.edu/lapack, 2008.Google Scholar
- LAPACK - Linear Algebra PACKage. http://www.netlib.org/lapack/, 2015.Google Scholar
- C. Lewis. Using the" thinking-aloud" method in cognitive interface design. IBM TJ Watson Research Center, 1982.Google Scholar
- J. Nielsen. How to conduct a heuristic evaluation. http://www.useit.com/papers/heuristic/heuristic\_evaluation.html, 2007.Google Scholar
- J. Nielsen. Ten usability heuristics. http://www.useit.com/papers/heuristic/heuristic\_list.html, 2007.Google Scholar
- NIST. Guide to Available Mathematical Software. http://gams.nist.gov, 2015.Google Scholar
- U. of Colorado. Compute resources - janus. https://www.rc.colorado.edu/support/user-guide/compute-resources.html#janus, 2015.Google Scholar
- U. of Florida. The University of Florida Sparse Matrix Collection. http://www.cise.ufl.edu/research/sparse/matrices/, 2015.Google Scholar
- R. Quinlan. C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers, San Mateo, CA, 1993. Google ScholarDigital Library
- J. Rieman, M. Franzke, and D. Redmiles. Usability evaluation with the cognitive walkthrough. http://www.acm.org/sigs/sigchi/chi95/Electronic/documnts/tutors/jr\_bdy.htm, 2004.Google Scholar
- Scalable Library for Eigenvalue Problem Computations (SLEPc). http://www.grycap.upv.es/slepc/, 2015.Google Scholar
- J. G. Siek, I. Karlin, and E. R. Jessup. Build to order linear algebra kernels. In Workshop on Performance Optimization for High-Level Languages and Libraries (PO HLL 2008), pages 1--8, April 2008.Google ScholarCross Ref
- The Lighthouse Project. http://lighthousehpc.github.io/lighthouse/, 2015.Google Scholar
- Tpetra. https://trilinos.org/packages/tpetra/. https://trilinos.org/packages/tpetra/, 2015.Google Scholar
- A. D. T. van Scheltinga, P. G. Myers, and J. D. Pietrzak. A finite element sea ice model of the Canadian Arctic Archipelago. Ocean dynamics, 60(6):1539--1558, 2010.Google ScholarCross Ref
- J. Wang, Y. Wang, W.-k. Hu, and J.-k. Du. The high performance of finite element analysis and applications of surface acoustic waves in finite elastic solids. In Piezoelectricity, Acoustic Waves, and Device Applications, 2008. SPAWDA 2008. Symposium on, pages 66--71. IEEE, 2008.Google Scholar
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- Lighthouse: an automated solver selection tool
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