The Art of R Programming

14.2.3 Extended Example: Generating a Powers Matrix...................

Recall in Section 9.1.7, we needed to generate a matrix of powers of our pre-

dictor variable. We used the following code:

1 # forms matrix of powers of the vector x, through degree dg

2 powers1 <- function(x,dg) {

3 pw <- matrix(x,nrow=length(x))

4 prod <- x # current product

5 for (i in 2:dg) {

6 prod <- prod*x

7 pw <- cbind(pw,prod)

8 }

9 return(pw)

10 }

One glaring problem is thatcbind()is used to build up the output ma-

trix, column by column. This is very costly in terms of memory-allocation

time. It’s much better to allocate the full matrix at the beginning, even

though it will be empty, as this will mean incurring the cost of only one

memory-allocation operation.

1 # forms matrix of powers of the vector x, through degree dg

2 powers2 <- function(x,dg) {

3 pw <- matrix(nrow=length(x),ncol=dg)

4 prod <- x # current product

5 pw[,1] <- prod

6 for (i in 2:dg) {

7 prod <- prod*x

8 pw[,i] <- prod

9 }

10 return(pw)

11 }

And indeed,powers2()is a lot faster.

> x <- runif(1000000)

> system.time(powers1(x,8))

user system elapsed

0.776 0.356 1.334

> system.time(powers2(x,8))

user system elapsed

0.388 0.204 0.593

312 Chapter 14