## Vector

• In R, vector includes: atomic vector and list.

## Atomic Vector

• There are 6 types of atomic vectors in R:
• Double
• Integer
• Character
• Logical
• Complex
• Raw

## Double Vector

• double means regular number.
• double data type is also called numeric.
• R will store any number you type in R as a double vector of length 1.
4.5
## [1] 4.5
is.vector(4.5)
## [1] TRUE
typeof(4.5)
## [1] "double"

## Double Vector

die <- c(1, 2, 3, 4, 5, 6)
die
## [1] 1 2 3 4 5 6
• die is a double vector of length 6.
typeof(die)
## [1] "double"
• typeof() returns the type of the data (double, integer, character, complex, or raw).

## Integer Vector

• integer refers to numbers that can be written without a decimal component.
• By default, R stores any number as double.
• To specify that you want a number to be stored as integer:
my_integer <- c(-1L, 2L, 4L)
my_integer
## [1] -1  2  4
typeof(my_integer)
## [1] "integer"

## Character Vector

• Character vector stores small pieces of text.
text <- c("Hello", 'World')
text
## [1] "Hello" "World"
typeof(text)
## [1] "character"

## Logical Vector

• Logical vector stores TRUE and FALSE, also called Boolean data type.
• When applying calculation functions to logical vector, TRUE = 1 and FALSE = 0.
my_logic <- c(TRUE, TRUE, FALSE)
my_logic
## [1]  TRUE  TRUE FALSE
sum(my_logic)
## [1] 2
typeof(my_logic)
## [1] "logical"

## Complex and Raw Vector

• Complex and raw vectors are not common in R.
• Complex vector stores complex numbers.
my_complex <- complex(real = 1, imaginary = 2)
my_complex
## [1] 1+2i
typeof(my_complex)
## [1] "complex"

## Complex and Raw Vector

• Raw vector stores raw bytes of data.
my_raw <- raw(length = 3)
my_raw
## [1] 00 00 00
typeof(my_raw)
## [1] "raw"

## List

• How are lists different from atomic vectors?
Atomic Vectors Lists
- Group data into a one-dimensional array - Group data into a one-dimensional array
- Group individual values of the same data type - Group R objects such as atomic vectors and other lists

## List

my_vector <- c(1, "one", TRUE)
my_vector
## [1] "1"    "one"  "TRUE"
my_list <- list(1, "one", TRUE)
my_list
## [[1]]
## [1] 1
##
## [[2]]
## [1] "one"
##
## [[3]]
## [1] TRUE

## Creating a List

• list() creates a list in the same way c() creates a vector.
• Elements in lists can have different lengths, dimensions, or type of objects.
big_list <- list(1:12, "2020", list("january", 2:8))
big_list
## [[1]]
##  [1]  1  2  3  4  5  6  7  8  9 10 11 12
##
## [[2]]
## [1] "2020"
##
## [[3]]
## [[3]][[1]]
## [1] "january"
##
## [[3]][[2]]
## [1] 2 3 4 5 6 7 8

## Creating a List

another_list <- list(c("stat385", "spring2020"), 1:5, list("homework", "projects"))
another_list
## [[1]]
## [1] "stat385"    "spring2020"
##
## [[2]]
## [1] 1 2 3 4 5
##
## [[3]]
## [[3]][[1]]
## [1] "homework"
##
## [[3]][[2]]
## [1] "projects"

## Creating a List

instructor <- list("Ha", 24)
students <- list(list("Alex", 20), list("Dave", 21))
stat385 <- list(instructor, students)
• How many elements does stat385 have?

## Creating a List

stat385
## [[1]]
## [[1]][[1]]
## [1] "Ha"
##
## [[1]][[2]]
## [1] 24
##
##
## [[2]]
## [[2]][[1]]
## [[2]][[1]][[1]]
## [1] "Alex"
##
## [[2]][[1]][[2]]
## [1] 20
##
##
## [[2]][[2]]
## [[2]][[2]][[1]]
## [1] "Dave"
##
## [[2]][[2]][[2]]
## [1] 21

## Selecting Values in a List

• How do we select an element of a list?
big_list
## [[1]]
##  [1]  1  2  3  4  5  6  7  8  9 10 11 12
##
## [[2]]
## [1] "2020"
##
## [[3]]
## [[3]][[1]]
## [1] "january"
##
## [[3]][[2]]
## [1] 2 3 4 5 6 7 8

## Selecting Values in a List

big_list[1]
## [[1]]
##  [1]  1  2  3  4  5  6  7  8  9 10 11 12
• big_list[1] returns a list of length 1 containing an atomic vector of type double.
big_list[[1]]
##  [1]  1  2  3  4  5  6  7  8  9 10 11 12
• big_list[[1]] returns an atomic vector of type double.

• Notes:
• [[1]] means list.
• [1] means vector.

## Selecting Values in a List

• Compare the following code segments:
another_list[[1]]
## [1] "stat385"    "spring2020"
another_list[[1]][1]
## [1] "stat385"

## Selecting Values in a List

another_list[1]
## [[1]]
## [1] "stat385"    "spring2020"
another_list[1][1]
## [[1]]
## [1] "stat385"    "spring2020"

## Selecting Values in a List

stat385
## [[1]]
## [[1]][[1]]
## [1] "Ha"
##
## [[1]][[2]]
## [1] 24
##
##
## [[2]]
## [[2]][[1]]
## [[2]][[1]][[1]]
## [1] "Alex"
##
## [[2]][[1]][[2]]
## [1] 20
##
##
## [[2]][[2]]
## [[2]][[2]][[1]]
## [1] "Dave"
##
## [[2]][[2]][[2]]
## [1] 21

## Selecting Values in a List

• Using [[]] and [], we can access any element in a list.
stat385[[2]]
## [[1]]
## [[1]][[1]]
## [1] "Alex"
##
## [[1]][[2]]
## [1] 20
##
##
## [[2]]
## [[2]][[1]]
## [1] "Dave"
##
## [[2]][[2]]
## [1] 21

## Selecting Values in a List

stat385[[2]][[1]]
## [[1]]
## [1] "Alex"
##
## [[2]]
## [1] 20
stat385[[2]][[1]][[1]]
## [1] "Alex"

## Selecting Values in a List

• Question: How do we get Ha’s age from stat385?

## Selecting Values in a List

stat385
## [[1]]
## [[1]][[1]]
## [1] "Ha"
##
## [[1]][[2]]
## [1] 24
##
##
## [[2]]
## [[2]][[1]]
## [[2]][[1]][[1]]
## [1] "Alex"
##
## [[2]][[1]][[2]]
## [1] 20
##
##
## [[2]][[2]]
## [[2]][[2]][[1]]
## [1] "Dave"
##
## [[2]][[2]][[2]]
## [1] 21

## Selecting Values in a List

• Question: How do we get Ha’s age from stat385?
stat385[[1]]
## [[1]]
## [1] "Ha"
##
## [[2]]
## [1] 24
stat385[[1]][[2]]
## [1] 24

## Matrix

• Matrix stores values of the same data type in a two-dimensional array.
m <- matrix(data = die, nrow = 2)
m
##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

## Matrix

• To create a matrix, supply matrix() with an atomic vector to reorganize into a matrix and specify the number of rows/columns.
m <- matrix(data = die, ncol = 3)
m
##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6
• What’s about specifying both the number of rows and columns?

## Matrix

m <- matrix(data = die, nrow = 2, ncol = 2)
m
##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4

## Matrix

• By default, matrix() will fill up the matrix column by column. We can fill the matrix row by row by including the argument byrow = TRUE:
m <- matrix(data = die, nrow = 2, byrow = TRUE)
m
##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6

## Selecting Elements in a Matrix

• To select element(s) in a matrix, use [ , ]:
m
##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6
m[1, 1]
## [1] 1
m[2, 2]
## [1] 5

## Selecting Elements in a Matrix

• To select element(s) in a matrix, use [ , ]:
m
##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6
m[1, ]
## [1] 1 2 3
m[, 3]
## [1] 3 6

## Selecting Elements in a Matrix

• To select element(s) in a matrix, use [ , ]:
m
##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6
m[1:2, 1:2]
##      [,1] [,2]
## [1,]    1    2
## [2,]    4    5

## Selecting Elements in a Matrix

• To select element(s) in a matrix, use [ , ]:
m
##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6
m[1, c(1, 3)]
## [1] 1 3

## Array

• The array() function creates $$n$$-dimensional array.
my_array <- array(data = 1:12, dim = c(2, 6))
my_array
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1    3    5    7    9   11
## [2,]    2    4    6    8   10   12

## Array

• What happens if we give more data points than the dimension allows?
my_array <- array(data = 1:14, dim = c(2, 6))
my_array
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1    3    5    7    9   11
## [2,]    2    4    6    8   10   12
• my_array is a two-dimensional array, which is a matrix.
• What’s about three-dimensional array?

## Array

my_array <- array(data = 1:12, dim = c(2, 2, 3))
my_array
## , , 1
##
##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4
##
## , , 2
##
##      [,1] [,2]
## [1,]    5    7
## [2,]    6    8
##
## , , 3
##
##      [,1] [,2]
## [1,]    9   11
## [2,]   10   12

## Selecting Elements in an Array

• For a three-dimensional array, use [ , , ]:
my_array[1, 1, 1]
## [1] 1
my_array[ , , 1]
##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4
my_array[ , 1, 1]
## [1] 1 2

## Summary

• Elements of an atomic vector, a matrix, or an array have to be of the same data type.
• Elements of a list can be of different R objects.
• Atomic vector and list store data in a one-dimensional array.
• Matrix stores data in a two-dimensional array.
• Array can store data in a $$n$$-dimensional array.

## Extra Question

• What is the difference between data types and R objects?
• Data types: basic elements of a programming language.
• Think double, integer, character, logical, complex, and raw.
• R objects: bigger structure, containing elements that belong to one of the data types.
• Think atomic vector, list, matrix, array, dataframe, etc.

## Attributes

• Attribute = extra information about the object.
• Attributes won’t affect the values of the object.
• Think of attributes as “metadata”.
• Use attributes() to see which attributes an object has.
attributes(die)
## NULL
• NULL means the object has no attribute.

## Names

• Names is one of the most common attributes of an R object.
• names() is the helper function associated with the names attribute.
names(die)
## NULL
names(die) <- c("one", "two", "three", "four", "five", "six")
attributes(die)
## \$names
## [1] "one"   "two"   "three" "four"  "five"  "six"
die
##   one   two three  four  five   six
##     1     2     3     4     5     6

## Names

die + 1
##   one   two three  four  five   six
##     2     3     4     5     6     7
names(die) <- c("small", "small", "small", "big", "big", "big")
die
## small small small   big   big   big
##     1     2     3     4     5     6
names(die) <- NULL
die
## [1] 1 2 3 4 5 6

## Dimension

• Another common attribute is dimension.
• dim() returns the dimension of an R Object.
dim(die)
## NULL
dim(die) <- c(2, 3)
die
##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

## To-do

• Make sure your R and RStudio are working.
• Redo in-class examples on your own.
• Continue reading Chapter 3 of Hands-On Programming with R.