The Art of R Programming

>m

[,1] [,2]

[1,] 1 2

[2,] 7 8

> dm <- diag(m)

>dm

[1]18

> diag(dm)

[,1] [,2]

[1,] 1 0

[2,] 0 8

> diag(3)

[,1] [,2] [,3]

[1,]100

[2,]010

[3,]001

Thesweep()function is capable of fairly complex operations. As a simple

example, let’s take a 3-by-3 matrix and add 1 to row 1, 4 to row 2, and 7 to

row 3.

>m

[,1] [,2] [,3]

[1,]123

[2,]456

[3,]789

> sweep(m,1,c(1,4,7),"+")

[,1] [,2] [,3]

[1,]234

[2,] 8 9 10

[3,] 14 15 16

The first two arguments tosweep()are like those ofapply(): the array

and the margin, which is 1 for rows in this case. The fourth argument is a

function to be applied, and the third is an argument to that function (to the

"+"function).

8.4.1 Extended Example: Vector Cross Product..........................

Let’s consider the issue of vector cross products. The definition is very

simple: The cross product of vectors(x 1 ,x 2 ,x 3 )and(y 1 ,y 2 ,y 3 )in three-

dimensional space is a new three-dimensional vector, as shown in Equa-

tion 8.1.

(x 2 y 3 −x 3 y 2 ,−x 1 y 3 +x 3 y 1 ,x 1 y 2 −x 2 y 1 ) (8.1)

198 Chapter 8