x <- c(2,1)Types of objects
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As we have demonstrated, you can use the R console like a calculator. However, the capabilities of R extend far beyond arithmetic! The first topic we will cover in exploring these capabilities is the various types of “objects” we can create in R.
Vectors
A vector in R is a list either of numbers, character strings, or logical values. We can create a vector using the command c():
Numeric vectors
A vector with the numbers 2 and 1 can be created by the command
We can see what is in the vector x by typing x or print(x) into the console:
x[1] 2 1print(x)[1] 2 1Note that we can define objects using = instead of <- if we wish (the <- is referred to as the assignment operator, and this is peculiar to R. Most languages just use =. If you don’t like using <- just use =.):
x = c(1,2)
x[1] 1 2A numeric vector with all the integers in a sequence can be created by
a <- -1
b <- 10
int <- a:b
int [1] -1 0 1 2 3 4 5 6 7 8 9 10A numeric vector with equally spaced values between any numbers can be created as
a <- 0
b <- 1
vals <- seq(a,b,length=11)
vals [1] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0or
a <- 0
b <- 1
vals <- seq(a,b,by=0.05)
vals [1] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70
[16] 0.75 0.80 0.85 0.90 0.95 1.00Character vectors
A character vector with the strings “cat”, “dog”, and “fish” is created as
pets <- c("dog","cat","fish")
pets[1] "dog" "cat" "fish"If we mix numbers and character strings we end up with a character vector:
v <- c(1,"fish")
v[1] "1" "fish"The paste() function is useful for putting together character strings:
paste("fish",1:3)[1] "fish 1" "fish 2" "fish 3"paste(seq(0,10,by=2),"\u00B0","C",sep="")[1] "0°C" "2°C" "4°C" "6°C" "8°C" "10°C"n <- 10
paste("n = ", n, sep = "")[1] "n = 10"paste(1:10, collapse = "-") # collapse into a single string[1] "1-2-3-4-5-6-7-8-9-10"Logical vectors
Create a logical vector with the values FALSE, TRUE, F, or T. These are called logical values or boolean values.
tf <- c(TRUE,FALSE,F,T)
tf[1] TRUE FALSE FALSE TRUEIf we include a numeric value, the logicals are “coerced” to numeric values so that the whole vector will becomes a numeric vector; TRUE is coerced to 1 and FALSE to 0:
tf2 <- c(TRUE,FALSE,F,pi)
tf2[1] 1.000000 0.000000 0.000000 3.141593If we include a character string, the vector becomes a character string, with the logical entries converted to the strings “TRUE” and “FALSE”.
tf3 <- c(TRUE,FALSE,F,"pi")
tf3[1] "TRUE" "FALSE" "FALSE" "pi" Accessing vector elements
To access an element of a vector, we use square brackets:
x <- seq(0.01,0.99,by = 0.01)
x[2][1] 0.02We can select more than one element like this:
pets <- c("dog","cat","fish")
pets[2:3][1] "cat" "fish"We can replace an entry with a new value, for example, with:
pets[3] <- "snake"
pets[1] "dog" "cat" "snake"We can also exclude an element or a set of elements from a vector by putting a negative subscript or a vector of negative subscripts in the brackets:
pets[-1][1] "cat" "snake"pets[-c(1,3)][1] "cat"Another useful function for defining vectors is the rep() function for repeating a numeric, character, or logical value (or vector) a number of times:
z <- rep(pi,3)
z[1] 3.141593 3.141593 3.141593rep(pets,2)[1] "dog" "cat" "snake" "dog" "cat" "snake"Matrices
A matrix is a table of numbers, character strings, or logical values with a number of rows and columns.
One way to construct a matrix is by populating the rows and columns with the entries of a vector using the matrix() function:
A <- matrix(1:8,nrow = 2, ncol = 4)
A [,1] [,2] [,3] [,4]
[1,] 1 3 5 7
[2,] 2 4 6 8If we want to fill the values across the rows we add the option byrow = T:
A <- matrix(1:8,nrow = 2,,ncol = 4, byrow = T)
A [,1] [,2] [,3] [,4]
[1,] 1 2 3 4
[2,] 5 6 7 8The matrix() function will “recycle” the given values if fewer values are given than can fit into the matrix.
A <- matrix(1:2,nrow = 4, ncol = 2)
A [,1] [,2]
[1,] 1 1
[2,] 2 2
[3,] 1 1
[4,] 2 2If the given values do not recycle a whole number of times a warning is issued:
A <- matrix(1:3,nrow = 4, ncol = 2)Warning in matrix(1:3, nrow = 4, ncol = 2): data length [3] is not a
sub-multiple or multiple of the number of rows [4]A [,1] [,2]
[1,] 1 2
[2,] 2 3
[3,] 3 1
[4,] 1 2We can also use the cbind() or rbind() functions to build matrices from vectors given as the columns or the rows:
x <- c(1,2,3)
y <- -x
X <- cbind(x,y)
X x y
[1,] 1 -1
[2,] 2 -2
[3,] 3 -3Xt <- rbind(x,y)
Xt [,1] [,2] [,3]
x 1 2 3
y -1 -2 -3Note that the cbind() and rbind() operations result in a matrix with columns or rows having names given by the vectors. We can access the names of the columns or rows of a matrix with the colnames() and rownames() functions, respectively:
colnames(X)[1] "x" "y"rownames(Xt)[1] "x" "y"If the rows or columns of a matrix are unnamed, these functions will return the NULL value:
rownames(X)NULLcolnames(Xt)NULLWe can have matrices of character values:
B <- matrix(letters[1:12],nrow = 3, byrow = T)
B [,1] [,2] [,3] [,4]
[1,] "a" "b" "c" "d"
[2,] "e" "f" "g" "h"
[3,] "i" "j" "k" "l" The above used the built-in vector letters.
We can access elements or sub-matrices with square brackets:
B[2,3][1] "g"B[1:2,3:4] [,1] [,2]
[1,] "c" "d"
[2,] "g" "h" B[c(1,3),c(1:4)] [,1] [,2] [,3] [,4]
[1,] "a" "b" "c" "d"
[2,] "i" "j" "k" "l" We can select all rows or all columns by leaving the index blank:
B[,3] # select column 3 of B[1] "c" "g" "k"B[c(1,3),] # select rows 1 and 3 [,1] [,2] [,3] [,4]
[1,] "a" "b" "c" "d"
[2,] "i" "j" "k" "l" Matrices once defined as character matrices remain charactor matrices:
B[1,2] <- 1
B [,1] [,2] [,3] [,4]
[1,] "a" "1" "c" "d"
[2,] "e" "f" "g" "h"
[3,] "i" "j" "k" "l" We can query the dimension of a matrix with the dim() function:
dim(B)[1] 3 4We can get the transpose a matrix (rows become columns and vice versa) with t():
t(X) [,1] [,2] [,3]
x 1 2 3
y -1 -2 -3Later on we will cover how to perform matrix operations such as matrix multiplication and inversion in R.
Arrays
An array consists of several matrices of the same dimension “stacked” as it were as “slices”, on top of each other. These behave just like matrices except that they have row, column, and “slice” indices.
Define an array with the array() function:
M <- array(c(1:24),dim = c(3,4,2))
M, , 1
[,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
, , 2
[,1] [,2] [,3] [,4]
[1,] 13 16 19 22
[2,] 14 17 20 23
[3,] 15 18 21 24We access elements with row, column, and “slice” indices.
M[1,3,2][1] 19M[1:2,1:2,1] [,1] [,2]
[1,] 1 4
[2,] 2 5Data frames
A data frame is like a matrix except that its columns can be vectors of different types. The data frame is a like the R version of a “spreadsheet”, and its columns are typically given names.
We can construct a data frame with the data.frame() function.
df <- data.frame(pets = pets, population = c(30,12,34), mammal = c(T,T,F))
df pets population mammal
1 dog 30 TRUE
2 cat 12 TRUE
3 snake 34 FALSEWe can access a column of a data frame using its name like this:
df$pets[1] "dog" "cat" "snake"We can get a summary of the columns in a data frame with the summary() function:
summary(df) pets population mammal
Length:3 Min. :12.00 Mode :logical
Class :character 1st Qu.:21.00 FALSE:1
Mode :character Median :30.00 TRUE :2
Mean :25.33
3rd Qu.:32.00
Max. :34.00 Lists
A list is a collection of objects of any type. If you have several matrices or vectors of different sizes, a list can be a convenient place to store and access them.
We can construct a list with the list() function:
mylist <- list(pets = pets,int = int)
mylist$pets
[1] "dog" "cat" "snake"
$int
[1] -1 0 1 2 3 4 5 6 7 8 9 10We can access the elements in a list using the name or with a double-bracketed index [[]].
mylist$pets[1] "dog" "cat" "snake"mylist[[1]][1] "dog" "cat" "snake"mylist[[1]][3][1] "snake"Functions
A function is a set of commands which execute on some user-supplied arguments, or input values. We have seen some functions above such as the c(), print(), seq(), paste(), and so on. Later on we will discuss how to define new functions.
To access the help documentation for a function, just execute ?<nameoffunction>. For example:
?pasteYou will do this very often, even after you become proficient in R.
Checking the type of an object
For any of these object classes, we can check whether an object belongs to the class with the functions is.vector(), is.matrix(), etc., which return a logical value:
is.vector(pets)[1] TRUEis.character(pets)[1] TRUEis.matrix(df)[1] FALSEis.data.frame(X)[1] FALSEis.numeric(X)[1] TRUEis.data.frame(df)[1] TRUEis.function(paste)[1] TRUECoercion of one type of object to another type
It is also possible to “coerce” one type of object to another type. For example, we can choose to read numeric vectors as character vectors or to read a matrix as a vector with the functions as.character(), as.vector(). There are several such functions beginning with as. for coercing one type of object to another type.
Here we coerce a numeric vector to a character vector:
as.character(int) [1] "-1" "0" "1" "2" "3" "4" "5" "6" "7" "8" "9" "10"If the coercion does not make sense, we will get missing values, which R represents as NA. A warning may be issued. For example, this happens when we try to convert certain character vectors to a numeric vector:
as.numeric(pets)Warning: NAs introduced by coercion[1] NA NA NAIf a character string can be converted to a number, the coercion will work:
ch <- c("1.234","1e04")
as.numeric(ch)[1] 1.234 10000.000When logical vectors are coerced to numeric vectors, the values TRUE and FALSE are converted to 1 and 0, respectively:
tf[1] TRUE FALSE FALSE TRUEas.numeric(tf)[1] 1 0 0 1If we convert a numeric vector to a logical vector, nonzero values are converted to TRUE and zeroes are converted to FALSE:
int [1] -1 0 1 2 3 4 5 6 7 8 9 10as.logical(int) [1] TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUEIf we convert a matrix to a vector the operation “vectorizes” the matrix, which means that it returns a vector containing all the columns of the matrix concatenated into one long vector.
X x y
[1,] 1 -1
[2,] 2 -2
[3,] 3 -3as.vector(X)[1] 1 2 3 -1 -2 -3Coercion of an object to an object of another type can also be induced by an attempted operation. For example, if one tries to add logical and numeric vectors, the logical vector will be coerced to a numeric vector.
tf[1] TRUE FALSE FALSE TRUEtf + 1:4[1] 2 2 3 5Practice
Practice writing code and anticipating the output of code with the following exercises.
Write code
Write your own R code to create the following:
- A numeric vector like this:
[1] -50 -40 -30 -20 -10 0 10 20 30 40 50- A matrix like this:
[,1] [,2] [,3]
[1,] 0.0 0.5 1.0
[2,] 1.5 2.0 2.5
[3,] 3.0 3.5 4.0
[4,] 4.5 5.0 5.5
[5,] 6.0 6.5 7.0
[6,] 7.5 8.0 8.5- A character vector like this:
[1] "Plan A" "Plan B" "Plan C" "Plan D" "Plan E" "Plan F" "Plan G" "Plan H"
[9] "Plan I" "Plan J" "Plan K" "Plan L" "Plan M" "Plan N" "Plan O" "Plan P"
[17] "Plan Q" "Plan R" "Plan S" "Plan T" "Plan U" "Plan V" "Plan W" "Plan X"
[25] "Plan Y" "Plan Z"- A data frame as below, with column names as given and having appropriate column classes (character, logical, and numeric):
item have cost
1 tent TRUE 600
2 stove FALSE 200
3 sleeping bag FALSE 100- A list with two data frames as below:
$trips
destination been
1 Poinsett TRUE
2 Table Rock TRUE
3 Hunting Island TRUE
4 Congaree TRUE
5 Edisto FALSE
$gear
item have cost
1 tent TRUE 600
2 stove FALSE 200
3 sleeping bag FALSE 100Read code
Anticipate the output of the following code chunks:
as.logical((-2):2)A <- matrix(seq(0.1,1,length = 10),nrow = 2, byrow = T)
A[2,3]paste(seq(0,10,by=2),"F",sep="\u00B0")rep(LETTERS[1:5],3)i <- c(19,20,1,20,19,18,21,12,5,19)
paste(letters[i],collapse="_")