Algorithmic Redistribution Methods for Block Cyclic Decompositions

This research aims at creating and providing a framework to describe algorithmic redistribution methods for various block cyclic decompositions. To do so properties of this data distribution scheme are formally exhibited. The examination of a number of basic dense linear algebra operations illustrates the application of those properties. This study analyzes the extent to which the general two-dimensional block cyclic data distribution allows for the expression of efficient as well as flexible matrix operations. This study also quantifies theoretically and practically how much of the efficiency of optimal block cyclic data layouts can be maintained. The general block cyclic decomposition scheme is shown to allow for the expression of flexible basic matrix operations with little impact on the performance and efficiency delivered by optimal and restricted kernels available today. Second, block cyclic data layouts, such as the purely scattered distribution, which seem less promising as far..