"A Parallel, In-Place, Rectangular Matrix Transpose Algorithm"
, RISC, JKU, Hagenberg, Linz, 3-2019
A Parallel, In-Place, Rectangular Matrix Transpose Algorithm
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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 today's 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 . Compared to out-of-place algorithms, TRIP, implemented in Cilk, trades work-efficiency for parallelism and for being in-place.