Skip to main content

Rapid Development of High-Performance Linear Algebra Libraries

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3732))

Abstract

We present a systematic methodology for deriving and implementing linear algebra libraries. It is quite common that an application requires a library of routines for the computation of linear algebra operations that are not (exactly) supported by commonly used libraries like LAPACK. In this situation, the application developer has the option of casting the operation into one supported by an existing library, often at the expense of performance, or implementing a custom library, often requiring considerable effort. Our recent discovery of a methodology based on formal derivation of algorithm allows such a user to quickly derive proven correct algorithms. Furthermore it provides an API that allows the so-derived algorithms to be quickly translated into high-performance implementations.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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)

    MATH  Google Scholar 

  2. Bientinesi, P., Gunnels, J.A., Myers, M.E., Quintana-Ortí, E.S., van de Geijn, R.A.: The science of deriving dense linear algebra algorithms. ACM Transactions on Mathematical Software 31(1) (March 2005)

    Google Scholar 

  3. Bientinesi, P., Quintana-Ortí, E.S., van de Geijn, R.A.: Representing linear algebra algorithms in code: The FLAME application programming interfaces. ACM Transactions on Mathematical Software 31(1) (March 2005)

    Google Scholar 

  4. Dongarra, J.J., Croz, J.D., Hammarling, S., Duff, I.: A set of level 3 basic linear algebra subprograms. ACM Trans. Math. Soft. 16(1), 1–17 (1990)

    Article  MATH  Google Scholar 

  5. Dongarra, J.J., Croz, J.D., Hammarling, S., Hanson, R.J.: An extended set of FORTRAN basic linear algebra subprograms. ACM Trans. Math. Soft. 14(1), 1–17 (1988)

    Article  MATH  Google Scholar 

  6. Goto, K., van de Geijn, R.A.: On reducing tlb misses in matrix multiplication. Technical Report CS-TR-02-55, Department of Computer Sciences, The University of Texas at Austin (2002)

    Google Scholar 

  7. Gunnels, J.A., Gustavson, F.G., Henry, G.M., van de Geijn, R.A.: FLAME: Formal linear algebra methods environment. ACM Trans. Math. Soft. 27(4), 422–455 (2001)

    Article  MATH  Google Scholar 

  8. Jonsson, I.: Recursive Blocked Algorithms, Data Structures, and High-Performance Software for Solving Linear Systems and Matrix Equations. PhD thesis, Dept. Computing Science, Umeå University, SE-901 87, Sweden (2003)

    Google Scholar 

  9. Lawson, C.L., Hanson, R.J., Kincaid, D.R., Krogh, F.T.: Basic linear algebra subprograms for Fortran usage. ACM Trans. Math. Soft. 5(3), 308–323 (1979)

    Article  MATH  Google Scholar 

  10. Moler, C., Little, J., Bangert, S.: Pro-Matlab, User’s Guide. The Mathworks, Inc. (1987)

    Google Scholar 

  11. Quintana-Ortí, E.S., van de Geijn, R.A.: Formal derivation of algorithms: The triangular Sylvester equation. ACM Transactions on Mathematical Software 29(2), 218–243 (2003)

    Article  MATH  Google Scholar 

  12. van de Geijn, R.A.: Using PLAPACK: Parallel Linear Algebra Package. The MIT Press, Cambridge (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bientinesi, P. et al. (2006). Rapid Development of High-Performance Linear Algebra Libraries. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_45

Download citation

  • DOI: https://doi.org/10.1007/11558958_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29067-4

  • Online ISBN: 978-3-540-33498-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics