Algorithms for in-place matrix transposition: Algorithms for In-Place Matrix Transposition

This paper presents implementations of in-place algorithms for transposing rectangular matrices. One implementation is a swap-based algorithm described by Tretyakov and Tyrtyshnikov,(1) to which we have introduced a number of variations. In particular, we show how the original algorithm can be modified to require constant additional memory. A proof of correctness is also sketched. This algorithm is compared with cycle-following approaches and with the swap-based GCD Transpose algorithm that partitions the matrix into a hierarchy of square submatrices. The performance of parallel implementations on a multicore system is also investigated.