Introduction to HPC with MPI for Data Science by Frank Nielsen

Author:Frank Nielsen
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

5.4.1 Cannon’s Algorithm

In order to illustrate this matrix product algorithm, let us consider the initial configuration on the 2D torus of size :

Cannon’s algorithm require pre-processing and post-processing operations that are pre-skewing and post-skewing (inverse of pre-skewing) primitives. The algorithm sends matrix block of A and B using horizontal and vertical rotations, respectively. These rotations are simply either row or column shifts (wrapped using the 1D torus topology property).

First, let us pre-process matrices A and B by pre-skewing them horizontally and vertically, respectively:Matrix A: We shifts vertically by sliding columns the elements so that the first diagonal becomes the “leftmost” column ( preskew ),

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