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.
Similar content being viewed by others
References
Algorithms 302, 380, 467, and 513,Collected Algorithms from CACM.
J. O. Eklundh:A fast computer method for matrix transposing, IEEE Transactions on Computers, VolumeC-21, Number 7 (July 1972) 801–803.
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.
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.
Geoffrey C. Goldbogen:PRIM: A fast matrix transpose method, IEEE Transactions on Software Engineering, VolumeSE-7, Number 2 (March 1981) 255–257.
Peter Johansen & Nils Andersen:Transposition of a matrix on auxiliary store, Rapport nr. 81/13, DIKU, University of Copenhagen, 1981.
P. F. Windley:Transposing matrices in a digital computer, The Computer Journal, Volume2, Number 1 (April 1959) 47–48.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Andersen, N. A general transposition method for a matrix on auxiliary store. BIT 30, 2–16 (1990). https://doi.org/10.1007/BF01932126
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01932126