BIT Numerical Mathematics

, Volume 30, Issue 1, pp 2–16 | Cite as

A general transposition method for a matrix on auxiliary store

  • Nils Andersen
Part I Computer Science

Abstract

An algorithm is developed and described for transposing a matrix larger than available working storage. If an (n×m)-matrix is stored in row-major order, and blocks ofn elements may be transferred to and from working storage at a time, the algorithm needsw=(5[m/n]+8)·n elements to be present in working storage at a time and requires [log2(2mn/w)] passages over the matrix. The algorithm is as efficient as earlier methods but needs no extra backing storage space. An algebra for mixed radix notation and a generalization of mixed radix notation is introduced for the description and verification of transposition algorithms, and earlier algorithms are briefly certified or disproved.

CR categories

E.2 F.2.1 G.4 I.1.2 

Key-words

Matrix transposition mixed radix notation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Algorithms 302, 380, 467, and 513,Collected Algorithms from CACM.Google Scholar
  2. [2]
    J. O. Eklundh:A fast computer method for matrix transposing, IEEE Transactions on Computers, VolumeC-21, Number 7 (July 1972) 801–803.Google Scholar
  3. [3]
    Patrick C. Fischer & Robert L. Probert:Storage reorganization techniques for matrix computation in a paging environment, Communications of the ACM, Volume22, Number 7 (July 1979) 405–415.CrossRefGoogle Scholar
  4. [4]
    Robert W. Floyd:Permuting information in idealized two-level storage, pp. 105–109 in Raymond E. Miller & James W. Thatcher (editors), Jean D. Bohlinger (associate editor):Complexity of Computer Computations, Plenum Press (Th IBM Research Symposia Series) 1972.Google Scholar
  5. [5]
    Geoffrey C. Goldbogen:PRIM: A fast matrix transpose method, IEEE Transactions on Software Engineering, VolumeSE-7, Number 2 (March 1981) 255–257.Google Scholar
  6. [6]
    Peter Johansen & Nils Andersen:Transposition of a matrix on auxiliary store, Rapport nr. 81/13, DIKU, University of Copenhagen, 1981.Google Scholar
  7. [7]
    P. F. Windley:Transposing matrices in a digital computer, The Computer Journal, Volume2, Number 1 (April 1959) 47–48.CrossRefGoogle Scholar

Copyright information

© BIT Foundations 1990

Authors and Affiliations

  • Nils Andersen
    • 1
  1. 1.Department of Computer ScienceUniversity of CopenhagenKøbenhavn ØDenmark

Personalised recommendations