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A Parallel, In-Place, Rectangular Matrix Transpose Algorithm / submitted by Stefan Amberger
AuthorAmberger, Stefan
CensorPaule, Peter
Thesis advisorPaule, Peter ; Strumpen, Volker ; Schreiner, Wolfgang
PublishedLinz, 2019
DescriptionIV, 62 Blätter : Illustrationen
Institutional NoteUniversität Linz, Masterarbeit, 2019
Document typeMaster Thesis
Keywords (EN)in-place / rectangular matrix transposition / parallel algorithm / Cilk
URNurn:nbn:at:at-ubl:1-26797 Persistent Identifier (URN)
 The work is publicly available
A Parallel, In-Place, Rectangular Matrix Transpose Algorithm [2.53 mb]
Abstract (English)

This thesis presents a novel algorithm for Transposing Rectangular matrices In-place and in Parallel (TRIP) including a proof of correctness and an analysis of work, span and parallelism. After almost 60 years since its introduction, the problem of in-place rectangular matrix transposition still does not have a satisfying solution. Increased concurrency in todays computers, and the need for low-overhead algorithms to solve memory-intense challenges are motivating the development of algorithms like TRIP. The algorithm is based on recursive splitting of the matrix into sub-matrices, independent, parallel transposition of these sub-matrices, and subsequent combining of the results by a parallel, perfect shuffle. We prove correctness of the algorithm for different matrix shapes (ratios of dimensions), and analyze work and span: For an $M\times N$ matrix, where $M>N$, and both $M$ and $N$ are powers of two, TRIP has work \[W_1 \trip(M,N)=\Theta\left(MN\log\frac

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