Parallel Computing for Data Science

12.7. SOLVING SYSTEMS OF LINEAR EQUATIONS 271

reduces the problem to one of matrix multiplication, and thus we can par-

allelize the Jacobi algorithm by utilizing a method for doing parallel matrix

multiplication.

12.7.3 Example: R/gputools Implementation of Ja-

cobi

Here’s the R code, using gputools:

jc b <− function ( a , b , eps ) {

n <− length ( b )

d <− diag ( a ) # a ve c t o r , not a m atrix

tmp <− diag ( d ) # a matrix , not a v e c t o r

o <− a − diag ( d )

di <− 1/d

x <− b # i n i t i a l guess , co u l d be b e t t e r

repeat {

oldx <− x

tmp <− gpuMatMult ( o , x )

tmp <− b − tmp

x <− di ∗ tmp # e l e m e ntwise m u l t i p l i c a t i o n

i f (s