# Basic data structures¶

In the previous chapter we saw the most basic data types in R: vectors of numeric, integer, character, factor and boolean values. These were all stored as a vector. A vector is a one dimensional structure. In this chapter we look at additional, multi-dimensional, data structures that can store basic data: the matrix, data.frame and list.

## Matrix¶

A vector is a one-dimensional array. A two-dimensional array can be represented with a matrix. Here is how you can create a matrix with two rows and three columns.

matrix(ncol=3, nrow=2)
##      [,1] [,2] [,3]
## [1,]   NA   NA   NA
## [2,]   NA   NA   NA


The matrix above did not have any values: all values were missing (NA). Let’s make a matrix with values 1 to 6.

matrix(1:6, ncol=3, nrow=2)
##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6


Note that by default the values are distributed column-wise. To go row-wise you can use the byrow=TRUE argument.

matrix(1:6, ncol=3, nrow=2, byrow=TRUE)
##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6


This can also be achieved by switching the number of columns and rows and using the t (transpose) function.

m <- matrix(1:6, ncol=2, nrow=3)
t(m)
##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6


It is common to create a matrix by column-binding and/or row-binding vectors using cbind and rbind. These are two of the most commonly used functions in R so pay close attention!

a <- c(1,2,3)
b <- 5:7


column binding

m1 <- cbind(a, b)
m1
##      a b
## [1,] 1 5
## [2,] 2 6
## [3,] 3 7


row binding

m2 <- rbind(a, b)
m2
##   [,1] [,2] [,3]
## a    1    2    3
## b    5    6    7


You can use cbind and rbind also to combine matrices, as long as the number of rows or columns of the two objects are the same.

m3 <- cbind(b, b, a)
m <- cbind(m1, m3)
m
##      a b b b a
## [1,] 1 5 5 5 1
## [2,] 2 6 6 6 2
## [3,] 3 7 7 7 3


We can get some of the structural properties of a matrix with functions such as nrow, ncol, dim and length.

nrow(m)
##  3
ncol(m)
##  5
# dimensions of m (nrow, ncol))
dim(m)
##  3 5
# number of cells, or nrow(m) * ncol(m)
length(m)
##  15


Columns have (variable) names that can be changed.

# get the column names
colnames(m)
##  "a" "b" "b" "b" "a"
# set the column names
colnames(m) <- c('ID', 'X', 'Y', 'v1', 'v2')
m
##      ID X Y v1 v2
## [1,]  1 5 5  5  1
## [2,]  2 6 6  6  2
## [3,]  3 7 7  7  3


Likewise there are row names, but these are less important.

rownames(m) <- paste0('row_', 1:nrow(m))
m
##       ID X Y v1 v2
## row_1  1 5 5  5  1
## row_2  2 6 6  6  2
## row_3  3 7 7  7  3


A matrix can only store a single data type. If you try to mix character and numeric values, all values will become character values (as the other way around may not be possible).

cbind(vchar=c('a','b'), vnumb=1:2)
##      vchar vnumb
## [1,] "a"   "1"
## [2,] "b"   "2"


You can see that 1 and 2 are character values because they are quoted. You could not use them in algebra without first converting them back to numbers. Note that the column names were set by providing them to cbind

A matrix is a two dimensional array. Higher dimensional arrays can also be created. See help(array), but these data structures are not that commonly used, so we do not discuss them here.

## List¶

A list is a very flexible container to store data. Each element of a list can contain any type of R object, e.g. a vector, matrix, data.frame, another list, or more complex data types.

A simple list:

list(1:3)
## []
##  1 2 3


It shows that the first element [] contains a vector of 1, 2, 3

Here is one with two data types.

e <- list(c(2,5), 'abc')
e
## []
##  2 5
##
## []
##  "abc"


List elements can be named.

names(e) <- c('first', 'last')
e
## $first ##  2 5 ## ##$last
##  "abc"


And a more complex list.

m <- matrix(1:6, ncol=3, nrow=2)
f <- list(e, m, 'abc')
f
## []
## []$first ##  2 5 ## ## []$last
##  "abc"
##
##
## []
##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6
##
## []
##  "abc"


Note that the first element of list f is itself a list of two elements.

## Data frame¶

The data.frame is the workhorse for statistical data analysis in R. It is rectangular like a matrix, but unlike matrices a data.frame can have columns (variables) of different data types. A data.frame is what you get when you read spreadsheet-like data into R with functions like read.table or read.csv. We’ll show that in a later chapter. We can also create a data.frame with some simple code.

# four vectors
ID <- as.integer(1:4)
name <- c('Ana', 'Rob', 'Liu', 'Veronica')
sex <- as.factor(c('F','M','M','F'))
score <- c(10.2, 9, 13.5, 18)
d <- data.frame(ID, name, sex, score, stringsAsFactors=FALSE)
d
##   ID     name sex score
## 1  1      Ana   F  10.2
## 2  2      Rob   M   9.0
## 3  3      Liu   M  13.5
## 4  4 Veronica   F  18.0


I used the argument stringsAsFactors=FALSE to avoid converting the character variable name to a factor. d is a data.frame, but individual columns can be of any class. Note that the length of a data.frame is defined as the number of variables (columns), while the length of a matrix is defined as the number of cells! This is because a matrix is a special kind of vector, while a data.frame is a special kind of list in which each element has the same size.

class(d)
##  "data.frame"
length(d)
##  4


Because a data.frame is a special kind of list, you can do with a data.frame what you can do with a list.

is.list(d)
##  TRUE
names(d)
##  "ID"    "name"  "sex"   "score"


But in other ways, a data.frame is also similar to a matrix (which normal lists are not).

nrow(d)
##  4
dim(d)
##  4 4
colnames(d)
##  "ID"    "name"  "sex"   "score"