1. S-PLUS Lecture 3
Jaeyong Lee

2. Factors
A factor and a category are special types of vector, normally used to hold a categorical variable in many statistical functions.
Category is deprecated.
Factor has a class attribute, hence it is adapted to generic function mechanism.

3. Session: Factors
citizen <- c(“uk”, “us”, “no”,”au”,”uk”,”us”, “us”,”no”,”au”)
citizenf <- factor(citizen)
attributes(citizenf)
unclass(citizenf) # This is the same as category(citizen)
table(citizenf)
citizeno <- ordered(citizen, levels=“us”,”au”,”no”,”uk”)
ordered(cut(geyser$duration, breaks=0:6),levels=1:6)
income <- c(10, 20, 15, 12, 17, 13, 22, 9,14)
tapply(income, citizenf, mean)

4. Arrays
A matrix is a two dimensional collection of data and an array is a generalization of matrix.
A dimension vector of an array is an attribute of the array representing the dimension.
S arrays use column-major order: the first index moves fastest, and the last slowest.

5. Session: Arrays 1 z <- 1:150 a <- array(z,dim=c(3,5,10))
dim(z) <- c(3,5,10)
z[1,1,1]
z[2,1,1]
matrix(1:6,nrow=2,ncol=3)
z <- matrix(1:6,nrow=2, ncol=3, byrow=T)
z[1,]
z[,2]

6. Session: Arrays 2 x <- matrix(0,nc=5,nr=5); x
i <- matrix(1:5,5,2); i
x[i] <- 1; x
matrix(1:6, 3, 2)*matrix(1:6*2, 3, 2)
X <- matrix(1:6,3,2)
y <- 1:3
t(X) %*% y

7. Session: Array 3 A <- matrix(c(1,1,2,3),2,2) b <- c(2,5)
solve(A,b)
diag(rep(1,2))
solve(A,diag(rep(1,2)))
A[2, ] <- c(2,7)
chol(A)
t(chol(A)) %*% chol(A)

8. Session: Array 4 eg <- eigen(A) eg$values eg$vectors
t(eg$vectors) %*% diag(eg$values) %*% eg$vectors
X <- matrix(1:6,3,2)
s <- svd(X) s
s$u %*% diag(s$d) %*% t(s$v)