Chapter 1 Data in R

1.1 Data Type

R has 6 data types.

logical
integer
numeric (double)
complex
character
(null)

R will save data when you assign it to the variable. With n <- 15, n is set to numeric,

n <- 15
class(n)

## [1] "numeric"

We can use various operations(methods) with numeric type variables. For example,

# addition
n + 4

## [1] 19

# multiplication
n * 3

## [1] 45

# power
n ^ 2

## [1] 225

# division
n / 7

## [1] 2.142857

# Inf, -Inf, NaN(Not a Number)
n / 0

## [1] Inf

Note also that we can get access to stored data 15 by the variable name n. In addition, we can coerce the object n to be a integer type variable.

n <- as.integer(n)
class(n)

## [1] "integer"

By enclosing a string with double quotes, we create a character type object,

ch <- "Hello"
class(ch)

## [1] "character"

ch <- "Double quotes \" \" in double quotes"
cat(ch)

## Double quotes " " in double quotes

To define a logical object, we type

bool <- TRUE
class(bool)

## [1] "logical"

R can interpret 0 as FALSE, other numbers as TRUE

m <- as.logical(1 + 5i)
m

## [1] TRUE

class(m)

## [1] "logical"

m <- as.logical(0)
m

## [1] FALSE

bool2 <- bool + bool  # implicit conversion
bool2

## [1] 2

class(bool2)

## [1] "integer"

Google NaN NULL NA in R or type ?NA ?NaN ?NULL.

1.2 Data Structure

1.2.1 Vector

Define Vectors

x <- vector("numeric", length = 10) # zero vector numeric(10)
x

##  [1] 0 0 0 0 0 0 0 0 0 0

class(x)

## [1] "numeric"

length(x)

## [1] 10

y <- 1 : 10 # by = 1
y

##  [1]  1  2  3  4  5  6  7  8  9 10

z <- seq(from = 1, to = 9, by = 2)
z

## [1] 1 3 5 7 9

w <- c(1, 3, 4, 2)  # concatenation
w

## [1] 1 3 4 2

Manipulating Vectors

x + y    # vector addition

##  [1]  1  2  3  4  5  6  7  8  9 10

z * 2    # scalar multiplication

## [1]  2  6 10 14 18

y + 1    # elementwise addition

##  [1]  2  3  4  5  6  7  8  9 10 11

y ^ 2    # elementwise exponentiation

##  [1]   1   4   9  16  25  36  49  64  81 100

w <- c(z, x)
w

##  [1] 1 3 5 7 9 0 0 0 0 0 0 0 0 0 0

w[1]     # index in R starts from 1

## [1] 1

w[c(1, 4, 2)]

## [1] 1 7 3

w[w > 5]

## [1] 7 9

mean(w)

## [1] 1.666667

Note : Vector can contain only one type

v <- c(1, "2")
# v[1] + 1

1.2.2 Lists

Unlike vectors, lists can contain several data types.

# list with names
ls_1 <- list(a = 13, b = "char", c = c(1,4,3)) 
ls_1$a         # access data using name

## [1] 13

ls_1[[1]]      # access data using index

## [1] 13

class(ls_1[1])

## [1] "list"

ls_2 <- list(1, 3, "2")           # list without names
ls_2

## [[1]]
## [1] 1
## 
## [[2]]
## [1] 3
## 
## [[3]]
## [1] "2"

names(ls_2) <- c("A", "B", "C")   # assign names to list
ls_2

## $A
## [1] 1
## 
## $B
## [1] 3
## 
## $C
## [1] "2"

str(ls_2)                 # str() : compactly display the "structure" of an object

## List of 3
##  $ A: num 1
##  $ B: num 3
##  $ C: chr "2"

rm(list = ls())           # input of the argument 'list' is not a list

1.2.3 Matrix

Define Matrix

mat <- matrix(nrow = 2, ncol = 4)
class(mat)

## [1] "matrix"

dim(mat)

## [1] 2 4

str(mat)

##  logi [1:2, 1:4] NA NA NA NA NA NA ...

attributes(mat)

## $dim
## [1] 2 4

Assign elements of a matrix

A <- matrix(1:16, nrow = 2, ncol = 8)
A  # columnwise construction

##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,]    1    3    5    7    9   11   13   15
## [2,]    2    4    6    8   10   12   14   16

dim(A) <- c(4, 4) # reshape matrix
A

##      [,1] [,2] [,3] [,4]
## [1,]    1    5    9   13
## [2,]    2    6   10   14
## [3,]    3    7   11   15
## [4,]    4    8   12   16

B <- matrix(seq(15, -30, -3), 4, 4) # argument names can be dropped
B

##      [,1] [,2] [,3] [,4]
## [1,]   15    3   -9  -21
## [2,]   12    0  -12  -24
## [3,]    9   -3  -15  -27
## [4,]    6   -6  -18  -30

diag(4)    # identity matrix of dimension 4 * 4

##      [,1] [,2] [,3] [,4]
## [1,]    1    0    0    0
## [2,]    0    1    0    0
## [3,]    0    0    1    0
## [4,]    0    0    0    1

diag(c(1, 2, 3 ,4))  # diagonal matrix with an input vector

##      [,1] [,2] [,3] [,4]
## [1,]    1    0    0    0
## [2,]    0    2    0    0
## [3,]    0    0    3    0
## [4,]    0    0    0    4

diag(B)    # diagonal part of matrix B

## [1]  15   0 -15 -30

Elementwise operations

A > B
A == B
A != B
A + B
A * B     # This is not a matrix multiplcation
A ^ 2

Examples of built-in matrix operations

A %*% B         # Matrix multiplication
A %o% B         # Outer product. AB'
crossprod(A,B)  # A'B
crossprod(A)      # A'A
t(A)              # Transpose
# solve(A, b)       # solution of b = Ax by x = inv(A)b
# solve(A)      # inv(A)

# install.packages("MASS")
library(MASS)
MASS::ginv(A)   # Moore - Penrose inverse
x <- eigen(A)     # eigenvalues
x$values
x$vectors
cbind(A,B)      # bind matrices by columns
rbind(A,B)      # bind matrices by rows
rowMeans(A)

Google Array, Factor, DataFrame in R or type ?array ?factor ?data.frame.

R Basics