research-article

Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers

Authors:

Osni A. Marques,

Christof Vömel,

James W. Demmel, and

Beresford N. ParlettAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 35, Issue 1

Article No.: 8, Pages 1 - 13

https://doi.org/10.1145/1377603.1377611

Published: 25 July 2008 Publication History

Abstract

LAPACK is often mentioned as a positive example of a software library that encapsulates complex, robust, and widely used numerical algorithms for a wide range of applications. At installation time, the user has the option of running a (limited) number of test cases to verify the integrity of the installation process. On the algorithm developer's side, however, more exhaustive tests are usually performed to study algorithm behavior on a variety of problem settings and also computer architectures. In this process, difficult test cases need to be found that reflect particular challenges of an application or push algorithms to extreme behavior. These tests are then assembled into a comprehensive collection, therefore making it possible for any new or competing algorithm to be stressed in a similar way. This article describes an infrastructure for exhaustively testing the symmetric tridiagonal eigensolvers implemented in LAPACK. It consists of two parts: a selection of carefully chosen test matrices with particular idiosyncrasies and a portable testing framework that allows for easy testing and data processing. The tester facilitates experiments with algorithmic choices, parameter and threshold studies, and performance comparisons on different architectures.

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Wu XDi Napoli E(2023)Advancing the distributed Multi-GPU ChASE library through algorithm optimization and NCCL libraryProceedings of the SC '23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis10.1145/3624062.3624249(1688-1696)Online publication date: 12-Nov-2023
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Liao XLi SLu YRoman J(2021)A Parallel Structured Divide-and-Conquer Algorithm for Symmetric Tridiagonal Eigenvalue ProblemsIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2020.301947132:2(367-378)Online publication date: 1-Feb-2021
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Index Terms

Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices

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cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 35, Issue 1

July 2008

136 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/1377603

Issue’s Table of Contents

Copyright © 2008 ACM.

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Association for Computing Machinery

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Publication History

Published: 25 July 2008

Accepted: 01 November 2007

Revised: 01 September 2007

Received: 01 October 2006

Published in TOMS Volume 35, Issue 1

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Cited By

Wu XDi Napoli E(2023)Advancing the distributed Multi-GPU ChASE library through algorithm optimization and NCCL libraryProceedings of the SC '23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis10.1145/3624062.3624249(1688-1696)Online publication date: 12-Nov-2023
https://dl.acm.org/doi/10.1145/3624062.3624249
Wu XDavidović DAchilles SDi Napoli ERobinson T(2022)ChASEProceedings of the Platform for Advanced Scientific Computing Conference10.1145/3539781.3539792(1-12)Online publication date: 27-Jun-2022
https://dl.acm.org/doi/10.1145/3539781.3539792
Liao XLi SLu YRoman J(2021)A Parallel Structured Divide-and-Conquer Algorithm for Symmetric Tridiagonal Eigenvalue ProblemsIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2020.301947132:2(367-378)Online publication date: 1-Feb-2021
https://doi.org/10.1109/TPDS.2020.3019471
Šušnjara AKressner D(2021)A fast spectral divide‐and‐conquer method for banded matricesNumerical Linear Algebra with Applications10.1002/nla.236528:4Online publication date: 8-Mar-2021
https://doi.org/10.1002/nla.2365
Vanover JDeng XRubio-González CKhurshid SPăsăreanu C(2020)Discovering discrepancies in numerical librariesProceedings of the 29th ACM SIGSOFT International Symposium on Software Testing and Analysis10.1145/3395363.3397380(488-501)Online publication date: 18-Jul-2020
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Marques ODemmel JVasconcelos P(2020)Bidiagonal SVD Computation via an Associated Tridiagonal EigenproblemACM Transactions on Mathematical Software10.1145/336174646:2(1-25)Online publication date: 19-May-2020
https://dl.acm.org/doi/10.1145/3361746
Li SRouet FLiu JHuang CGao XChi X(2018)An efficient hybrid tridiagonal divide-and-conquer algorithm on distributed memory architecturesJournal of Computational and Applied Mathematics10.1016/j.cam.2018.05.051344(512-520)Online publication date: Dec-2018
https://doi.org/10.1016/j.cam.2018.05.051
Marques OVasconcelos P(2017)Computing the Bidiagonal SVD Through an Associated Tridiagonal EigenproblemHigh Performance Computing for Computational Science – VECPAR 201610.1007/978-3-319-61982-8_8(64-74)Online publication date: 14-Jul-2017
https://doi.org/10.1007/978-3-319-61982-8_8
Zhang WHigham N(2016)Matrix Depot: an extensible test matrix collection for JuliaPeerJ Computer Science10.7717/peerj-cs.582(e58)Online publication date: 6-Apr-2016
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Li SLiao XLiu JJiang H(2016)New fast divide‐and‐conquer algorithms for the symmetric tridiagonal eigenvalue problemNumerical Linear Algebra with Applications10.1002/nla.204623:4(656-673)Online publication date: 17-Mar-2016
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