Advertisement

Introduction to StarNEig—A Task-Based Library for Solving Nonsymmetric Eigenvalue Problems

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12043)

Abstract

In this paper, we present the StarNEig library for solving dense nonsymmetric (generalized) eigenvalue problems. The library is built on top of the StarPU runtime system and targets both shared and distributed memory machines. Some components of the library support GPUs. The library is currently in an early beta state and only real arithmetic is supported. Support for complex data types is planned for a future release. This paper is aimed at potential users of the library. We describe the design choices and capabilities of the library, and contrast them to existing software such as ScaLAPACK. StarNEig implements a ScaLAPACK compatibility layer that should make it easy for new users to transition to StarNEig. We demonstrate the performance of the library with a small set of computational experiments.

Keywords

Eigenvalue problem Task-based Library 

Notes

Acknowledgements

StarNEig has been developed by the authors, Angelika Schwarz (who has written the standard eigenvector solver), Lars Karlsson, and Bo Kågström. This work is part of a project (NLAFET) that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 671633. This work was supported by the Swedish strategic research programme eSSENCE. We thank the High Performance Computing Center North (HPC2N) at Umeå University for providing computational resources and valuable support during test and performance runs. Finally, the author thanks the anonymous reviewers for their valuable feedback.

References

  1. 1.
    LAPACK: Linear Algebra PACKage. http://www.netlib.org/lapack
  2. 2.
    PLASMA: Parallel Linear Algebra Software for Multicore Architectures. http://icl.cs.utk.edu/plasma/software
  3. 3.
    ScaLAPACK: Scalable Linear Algebra PACKage. http://www.netlib.org/scalapack
  4. 4.
    SLEPc: The Scalable Library for Eigenvalue Problem Computations. http://slepc.upv.es
  5. 5.
    StarNEig: A task-based library for solving nonsymmetric eigenvalue problems. https://github.com/NLAFET/StarNEig
  6. 6.
    StarPU: A unified runtime system for heterogeneous multicore architectures. http://starpu.gforge.inria.fr
  7. 7.
    Braman, K., Byers, R., Mathias, R.: The multishift \(QR\) algorithm. I. Maintaining well-focused shifts and level 3 performance. SIAM J. Matrix Anal. Appl. 23(4), 929–947 (2002).  https://doi.org/10.1137/S0895479801384573MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Braman, K., Byers, R., Mathias, R.: The multishift \(QR\) algorithm. II. Aggressive early deflation. SIAM J. Matrix Anal. Appl. 23(4), 948–973 (2002).  https://doi.org/10.1137/S0895479801384585MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Buttari, A., Langou, J., Kurzak, J., Dongarra, J.: A class of parallel tiled linear algebra algorithms for multicore architectures. Parallel Comput. 35(1), 38–53 (2009).  https://doi.org/10.1016/j.parco.2008.10.002MathSciNetCrossRefGoogle Scholar
  10. 10.
    Dongarra, J., Whaley, R.C.: A User’s Guide to the BLACS, LAWN 94 (1997)Google Scholar
  11. 11.
    Golub, G.H., Van Loan, C.F.: Matrix Computations, 4th edn. Johns Hopkins University Press, Baltimore (2012)zbMATHGoogle Scholar
  12. 12.
    Granat, R., Kågström, B., Kressner, D.: Parallel eigenvalue reordering in real Schur forms. Concurr. Comput.: Pract. Exp. 21(9), 1225–1250 (2009), http://dx.doi.org/10.1002/cpe.1386
  13. 13.
    Granat, R., Kågström, B., Kressner, D., Shao, M.: ALGORITHM 953: parallel library software for the multishift QR algorithm with aggressive early deflation. ACM Trans. Math. Softw. 41(4), 1–23 (2015).  https://doi.org/10.1145/2699471MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Imachi, H., Hoshi, T.: Hybrid numerical solvers for massively parallel eigenvalue computations and their benchmark with electronic structure calculations. J. Inf. Process. 24(1), 164–172 (2016).  https://doi.org/10.2197/ipsjjip.24.164CrossRefGoogle Scholar
  15. 15.
    Kjelgaard Mikkelsen, C.C., Myllykoski, M.: Parallel robust computation of generalized eigenvectors of matrix pencils in real Schur form. Accepted to PPAM 2019 (2019)Google Scholar
  16. 16.
    Kjelgaard Mikkelsen, C.C., Schwarz, A.B., Karlsson, L.: Parallel robust solution of triangular linear systems. Concurr. Comput.: Pract. Exp. 1–19 (2018).  https://doi.org/10.1002/cpe.5064
  17. 17.
    Luszczek, P., Ltaief, H., Dongarra, J.: Two-stage tridiagonal reduction for dense symmetric matrices using tile algorithms on multicore architectures. In: 2011 IEEE International Parallel & Distributed Processing Symposium (IPDPS), pp. 944–955. IEEE (2011).  https://doi.org/10.1109/IPDPS.2011.91
  18. 18.
    Marek, A., et al.: The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science. J. Phys.: Condens. Matter 26(21), 201–213 (2014).  https://doi.org/10.1088/0953-8984/26/21/213201CrossRefGoogle Scholar
  19. 19.
    Myllykoski, M.: A task-based algorithm for reordering the eigenvalues of a matrix in real Schur form. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds.) PPAM 2017. LNCS, vol. 10777, pp. 207–216. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78024-5_19CrossRefGoogle Scholar
  20. 20.
    Myllykoski, M., Kjelgaard Mikkelsen, C.C., Schwarz, A., Kågström, B.: D2.7: eigenvalue solvers for nonsymmetric problems. Technical report, Umeå University (2019). http://www.nlafet.eu/wp-content/uploads/2019/04/D2.7-EVP-solvers-evaluation-final.pdf
  21. 21.
    Thibault, S.: On runtime systems for task-based programming on heterogeneous platforms, Habilitation à diriger des recherches, Université de Bordeaux (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Computing Science and HPC2NUmeå UniversityUmeåSweden

Personalised recommendations