Parallel Computing for Data Science

6 CHAPTER 1. INTRODUCTION

than having to translate the R repeatedly for each line of the loop, at each

iteration.

In the code for mutoutser() above, the inner loops can be rewritten as a

matrix product, as we will see below, and that will turn out to eliminate

two of our loops.

3

To see the matrix formulation, suppose we have this matrix:













0 1 0 0 1

1 0 0 1 1

0 1 0 1 0

1 1 1 0 0

1 1 1 0 1













(1.1)

Consider the case in which i is 2 and j is 4 in the above pseudocode, Listing

1.4.1. The innermost loop, i.e., the one involving k, computes

1 · 1 + 0 · 1 + 0 · 1 + 1 · 0 + 1 · 0 = 1 (1.2)

But that is merely the inner product of rows i and j of the matrix! ...