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Performance of Dense Eigensolvers on BlueGene/Q

  • Inge GutheilEmail author
  • Jan Felix Münchhalfen
  • Johannes Grotendorst
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8384)

Abstract

Many scientific applications require the computation of about 10–30 % of the eigenvalues and eigenvectors of large dense symmetric or complex hermitian matrices. In this paper we will present performance evaluation results of the eigensolvers of the three libraries Elemental, ELPA, and ScaLAPACK on the BlueGene/Q architecture. All libraries include solvers for the computation of only a part of the spectrum. The most time-consuming part of the eigensolver is the reduction of the full eigenproblem to a tridiagonal one. Whereas Elemental and ScaLAPACK only offer routines to directly reduce the full matrix to a tridiagonal one, which only allows the use of BLAS 2 matrix-vector operations and needs a lot of communication, ELPA also offers a two-step reduction routine, first transforming the full matrix to banded form and thereafter to tridiagonal form. This two-step reduction shortens the reduction time significantly but at the cost of a higher complexity of the back transformation step. We will show up to which part of the eigenspectrum the use of the two-step reduction pays off.

Keywords

Eigenvalue and eigenvector computation Elemental ELPA ScaLAPACK BlueGene/Q 

Notes

Acknowledgements

The authors thank Jack Poulson, the author of the Elemental library and the ELPA team, especially Thomas Auckenthaler, for their immediate responses to problem reports.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Inge Gutheil
    • 1
    Email author
  • Jan Felix Münchhalfen
    • 2
  • Johannes Grotendorst
    • 1
  1. 1.Institute for Advanced SimulationJülich Supercomputing Centre, Forschungszentrum Jülich GmbHJülichGermany
  2. 2.IT Center of RWTH Aachen UniversityAachenGermany

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