skip to main content
article

SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems

Published: 01 September 2005 Publication History

Abstract

The Scalable Library for Eigenvalue Problem Computations (SLEPc) is a software library for computing a few eigenvalues and associated eigenvectors of a large sparse matrix or matrix pencil. It has been developed on top of PETSc and enforces the same programming paradigm.The emphasis of the software is on methods and techniques appropriate for problems in which the associated matrices are sparse, for example, those arising after the discretization of partial differential equations. Therefore, most of the methods offered by the library are projection methods such as Arnoldi or Lanczos, or other methods with similar properties. SLEPc provides basic methods as well as more sophisticated algorithms. It also provides built-in support for spectral transformations such as the shift-and-invert technique. SLEPc is a general library in the sense that it covers standard and generalized eigenvalue problems, both Hermitian and non-Hermitian, with either real or complex arithmetic.SLEPc can be easily applied to real world problems. To illustrate this, several case studies arising from real applications are presented and solved with SLEPc with little programming effort. The addressed problems include a matrix-free standard problem, a complex generalized problem, and a singular value decomposition. The implemented codes exhibit good properties regarding flexibility as well as parallel performance.

References

[1]
Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., and van der Vorst, H., Eds. 2000. Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. SIAM Press, Philadelphia, PA. Available online at http://www.netlib.org/etemplates.
[2]
Balay, S., Buschelman, K., Gropp, W., Kaushik, D., Knepley, M., McInnes, L. C., Smith, B., and Zhang, H. 2004. PETSc users manual. Tech. rep. ANL-95/11, Rev. 2.2.1. Argonne National Laboratory, Argonne, IL.
[3]
Berry, M. W. and Browne, M. 1999. Understanding Search Engines: Mathematical Modeling and Text Retrieval. SIAM Press, Philadelphia, PA.
[4]
Hernandez, V., Roman, J. E., and Vidal, V. 2004. SLEPc users manual. Tech. rep. DSIC-II/24/02---Rev. 2.2.1. D. Sist. Inform. y Comp., Universidad Politécnica de Valencia, Valencia, Spain.
[5]
Hernandez, V., Roman, J. E., Vidal, V., Verdu, G., and Ginestar, D. 2003. Resolution of the neutron diffusion equation with SLEPc, the Scalable Library for Eigenvalue Problem Computations. In Nuclear Mathematical and Computational Sciences: A Century in Review, A Century Anew. American Nuclear Society, Gatlinburg, TN.
[6]
Lehoucq, R. B., Sorensen, D. C., and Yang, C. 1998. ARPACK Users' Guide, Solution of Large-Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods. SIAM Press, Philadelphia, PA.
[7]
Marques, O. A. 1995. BLZPACK: Description and user's guide. Tech. rep. TR/PA/95/30. CERFACS, Toulouse, France.
[8]
Simoncini, V. 2003. Algebraic formulations for the solution of the nullspace-free eigenvalue problem using the inexact Shift-and-Invert Lanczos method. Numer. Lin. Algebra Appl. 10, 357--375.
[9]
Wu, K. and Simon, H. 1997. A parallel Lanczos method for symmetric generalized eigenvalue problems. Tech. rep. LBNL-41284. Lawrence Berkeley National Laboratory, Berkeley, CA.
[10]
Wu, K. and Simon, H. 2001. Thick-restart Lanczos method for large symmetric eigenvalue problems. In SIAM J. Matrix Anal. Appl. 22, 2, 602--616.

Cited By

View all
  • (2025)DanceQ: High-performance library for number conserving basesSciPost Physics Codebases10.21468/SciPostPhysCodeb.48Online publication date: 5-Feb-2025
  • (2025)Propagation of two-particle correlations across the chaotic phase for interacting bosonsPhysical Review Research10.1103/PhysRevResearch.7.L0120317:1Online publication date: 10-Feb-2025
  • (2025) Many-body localization in the age of classical computing * Reports on Progress in Physics10.1088/1361-6633/ad975688:2(026502)Online publication date: 20-Jan-2025
  • Show More Cited By

Recommendations

Reviews

Grigore Albeanu

A new package to be used on parallel platforms for the solution of standard and generalized eigenproblems, either in real or complex arithmetic, is presented. The authors offer a clear and well-structured presentation, giving basic information concerning the scalable library for the eigenvalue problem computations (SLEPc) package and three case studies to illustrate the software performances in different situations. The paper contains very good references and useful links for free documentation about SLEPc, examples, and the SLEPc library. SLEPc is portable, scalable, efficient, and flexible, and extends the well-known portable extensible toolkit for scientific computation (PETSc) library. It provides support for existing libraries, such as ARPACK, BLZPACK, PLANSO, TRLAN, and LAPACK, and future developments. The development team designed two objects: the eigenvalue problem solver (EPS) and the spectral transformation (ST). The package provides the following spectral transformations: shift to origin, shift and invert, and the Cayley transformation. These operators are available for solving standard and generalized eigenvalue problems. Both shell matrices and shell transformations are supported for user-defined matrix operations and spectral transformations. As the paper's fourth section shows, both command line and procedural approaches can be used. Extensibility and interoperability are other important features of SLEPc. Using the library does not require any experience in parallel programming. Each case study provides details about the SLEPc-based implementation, and includes the results concerning performance tests: running with one processor is not a good idea, but speedup and efficiency are obtained with two processors. Online Computing Reviews Service

Access critical reviews of Computing literature here

Become a reviewer for Computing Reviews.

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software  Volume 31, Issue 3
Special issue on the Advanced CompuTational Software (ACTS) Collection
September 2005
143 pages
ISSN:0098-3500
EISSN:1557-7295
DOI:10.1145/1089014
Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 2005
Published in TOMS Volume 31, Issue 3

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. Eigenvalue computation
  2. singular values
  3. spectral transform

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)126
  • Downloads (Last 6 weeks)22
Reflects downloads up to 11 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2025)DanceQ: High-performance library for number conserving basesSciPost Physics Codebases10.21468/SciPostPhysCodeb.48Online publication date: 5-Feb-2025
  • (2025)Propagation of two-particle correlations across the chaotic phase for interacting bosonsPhysical Review Research10.1103/PhysRevResearch.7.L0120317:1Online publication date: 10-Feb-2025
  • (2025) Many-body localization in the age of classical computing * Reports on Progress in Physics10.1088/1361-6633/ad975688:2(026502)Online publication date: 20-Jan-2025
  • (2025)Application of the Krylov-Schur method in three-dimensional nuclear reactor discrete ordinates criticality calculationsProgress in Nuclear Energy10.1016/j.pnucene.2024.105530178(105530)Online publication date: Jan-2025
  • (2025)Analysis and comparison of high-performance computing solvers for minimisation problems in signal processingMathematics and Computers in Simulation10.1016/j.matcom.2024.10.003229(525-538)Online publication date: Mar-2025
  • (2025)Scalable resolvent analysis for three-dimensional flowsJournal of Computational Physics10.1016/j.jcp.2024.113695524(113695)Online publication date: Mar-2025
  • (2025)A highly parallelized multiscale preconditioner for Darcy flow in high-contrast mediaJournal of Computational Physics10.1016/j.jcp.2024.113603522:COnline publication date: 1-Feb-2025
  • (2025)A scalable method with synchronous parallelization for computing selected eigenvalues of large-scale power system modelElectric Power Systems Research10.1016/j.epsr.2024.111085238(111085)Online publication date: Jan-2025
  • (2025)Parallel finite-element codes for the Bogoliubov-de Gennes stability analysis of Bose-Einstein condensatesComputer Physics Communications10.1016/j.cpc.2024.109378306(109378)Online publication date: Jan-2025
  • (2025)A robust monolithic nonlinear Newton method for the compressible Reynolds averaged Navier-Stokes EquationsComputers & Fluids10.1016/j.compfluid.2025.106549(106549)Online publication date: Jan-2025
  • Show More Cited By

View Options

Login options

Full Access

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media