Matrices

R supports the creation of 2d data structures (rows and columns) of atomic vector types.

Generally these are formed via a call to matrix().

matrix(1:4, nrow=2, ncol=2)

     [,1] [,2]
[1,]    1    3
[2,]    2    4

matrix(c(TRUE, FALSE), 2, 2)

      [,1]  [,2]
[1,]  TRUE  TRUE
[2,] FALSE FALSE

matrix(LETTERS[1:6], 2)

     [,1] [,2] [,3]
[1,] "A"  "C"  "E" 
[2,] "B"  "D"  "F" 

matrix(6:1 / 2, ncol = 2)

     [,1] [,2]
[1,]  3.0  1.5
[2,]  2.5  1.0
[3,]  2.0  0.5

Data ordering

Matrices in R use column major ordering (data is stored in column order not row order).

(m = matrix(1:6, nrow=2, ncol=3))

     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6

c(m)

[1] 1 2 3 4 5 6

(n = matrix(1:6, nrow=2, ncol=3))

     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6

c(n)

[1] 1 2 3 4 5 6

(x = matrix(1:6, nrow=2, ncol=3, byrow = TRUE))

     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    4    5    6

c(x)

[1] 1 4 2 5 3 6

(y = matrix(1:6, nrow=3, ncol=2, byrow=TRUE))

     [,1] [,2]
[1,]    1    2
[2,]    3    4
[3,]    5    6

c(y)

[1] 1 3 5 2 4 6

Matrix structure

m = matrix(1:4, ncol=2, nrow=2)

typeof(m)

[1] "integer"

mode(m)

[1] "numeric"

class(m)

[1] "matrix" "array" 

attributes(m)

$dim
[1] 2 2

n = letters[1:6]
dim(n) = c(2L, 3L)
n

     [,1] [,2] [,3]
[1,] "a"  "c"  "e" 
[2,] "b"  "d"  "f" 

o = letters[1:6]
attr(o,"dim") = c(2L, 3L)
o

     [,1] [,2] [,3]
[1,] "a"  "c"  "e" 
[2,] "b"  "d"  "f" 

Arrays

Arrays are just an \(n\)-dimensional extension of matrices and are defined by adding the appropriate dimension sizes.

array(1:8, dim = c(2,2,2))

, , 1

     [,1] [,2]
[1,]    1    3
[2,]    2    4

, , 2

     [,1] [,2]
[1,]    5    7
[2,]    6    8

array(letters[1:6], dim = c(2,1,3))

, , 1

     [,1]
[1,] "a" 
[2,] "b" 

, , 2

     [,1]
[1,] "c" 
[2,] "d" 

, , 3

     [,1]
[1,] "e" 
[2,] "f" 

Data Frames

A data frame is how R handles heterogeneous tabular data (i.e. a table of rows and columns) and is one of the most commonly used data structure in R.

(df = data.frame(
  x = 1:3, 
  y = c("a", "b", "c"),
  z = c(TRUE)
))

  x y    z
1 1 a TRUE
2 2 b TRUE
3 3 c TRUE

str(df)

'data.frame':   3 obs. of  3 variables:
 $ x: int  1 2 3
 $ y: chr  "a" "b" "c"
 $ z: logi  TRUE TRUE TRUE

Data Frame Structure

typeof(df)

[1] "list"

class(df)

[1] "data.frame"

attributes(df)

$names
[1] "x" "y" "z"

$class
[1] "data.frame"

$row.names
[1] 1 2 3

str(unclass(df))

List of 3
 $ x: int [1:3] 1 2 3
 $ y: chr [1:3] "a" "b" "c"
 $ z: logi [1:3] TRUE TRUE TRUE
 - attr(*, "row.names")= int [1:3] 1 2 3

Build your own data.frame

df = list(x = 1:3, y = c("a", "b", "c"), z = c(TRUE, TRUE, TRUE))

attr(df,"class") = "data.frame"
df

[1] x y z
<0 rows> (or 0-length row.names)

attr(df,"row.names") = 1:3
df

  x y    z
1 1 a TRUE
2 2 b TRUE
3 3 c TRUE

str(df)

'data.frame':   3 obs. of  3 variables:
 $ x: int  1 2 3
 $ y: chr  "a" "b" "c"
 $ z: logi  TRUE TRUE TRUE

is.data.frame(df)

[1] TRUE

Strings (Characters) vs Factors

Previous to R v4.0, the default behavior of data frames was to convert character data into factors. Sometimes this was useful, but mostly it wasn’t.

This behavior is controlled via the stringsAsFactors argument to data.frame (and related functions like read.csv, read.table, etc.).

df = data.frame(x = 1:3, y = c("a", "b", "c"), 
                stringsAsFactors = TRUE)
df

  x y
1 1 a
2 2 b
3 3 c

str(df)

'data.frame':   3 obs. of  2 variables:
 $ x: int  1 2 3
 $ y: Factor w/ 3 levels "a","b","c": 1 2 3

df = data.frame(x = 1:3, y = c("a", "b", "c"), 
                stringsAsFactors = FALSE)
df

  x y
1 1 a
2 2 b
3 3 c

str(df)

'data.frame':   3 obs. of  2 variables:
 $ x: int  1 2 3
 $ y: chr  "a" "b" "c"

Length Coercion

When creating a data frame from different vectors, the lengths of the component vectors will be coerced to match. However, if they not multiples of each other then there will be an error (other previous forms of length coercion would produce a warning for this case).

data.frame(x = 1:3, y = c("a"))

  x y
1 1 a
2 2 a
3 3 a

data.frame(x = 1:3, y = c("a","b"))

Error in data.frame(x = 1:3, y = c("a", "b")): arguments imply differing number of rows: 3, 2

data.frame(x = 1:3, y = character())

Error in data.frame(x = 1:3, y = character()): arguments imply differing number of rows: 3, 0

Subsetting in General

R has three subsetting operators ([, [[, and $). The behavior of these operators will depend on the object (class) they are being used with.

In general there are 6 different types of subsetting that can be performed:

Positive Integer subsetting

Returns elements at the given location(s)

x = c(1,4,7)
y = list(1,4,7)

x[1]

[1] 1

x[c(1,3)]

[1] 1 7

x[c(1,1)]

[1] 1 1

x[c(1.9,2.1)]

[1] 1 4

str( y[1] )

List of 1
 $ : num 1

str( y[c(1,3)] )

List of 2
 $ : num 1
 $ : num 7

str( y[c(1,1)] )

List of 2
 $ : num 1
 $ : num 1

str( y[c(1.9,2.1)] )

List of 2
 $ : num 1
 $ : num 4

Negative Integer subsetting

Excludes elements at the given location(s)

x = c(1,4,7)

x[-1]

[1] 4 7

x[-c(1,3)]

[1] 4

x[c(-1,-1)]

[1] 4 7

y = list(1,4,7)

str( y[-1] )

List of 2
 $ : num 4
 $ : num 7

str( y[-c(1,3)] )

List of 1
 $ : num 4

x[c(-1,2)]

Error in x[c(-1, 2)]: only 0's may be mixed with negative subscripts

y[c(-1,2)]

Error in y[c(-1, 2)]: only 0's may be mixed with negative subscripts

Logical Value Subsetting

Returns elements that correspond to TRUE in the logical vector. Length of the logical vector is coerced to be the same as the vector being subsetted.

x = c(1,4,7,12)

x[c(TRUE,TRUE,FALSE,TRUE)]

[1]  1  4 12

x[c(TRUE,FALSE)]

[1] 1 7

y = list(1,4,7,12)

str( y[c(TRUE,TRUE,FALSE,TRUE)] )

List of 3
 $ : num 1
 $ : num 4
 $ : num 12

str( y[c(TRUE,FALSE)] )

List of 2
 $ : num 1
 $ : num 7

x[x %% 2 == 0]

[1]  4 12

str( y[y %% 2 == 0] )

Error in y%%2: non-numeric argument to binary operator

Empty Subsetting

Returns the original vector, this is not the same as subsetting with NULL

x = c(1,4,7)

x[]

[1] 1 4 7

x[NULL]

numeric(0)

y = list(1,4,7)

str(y[])

List of 3
 $ : num 1
 $ : num 4
 $ : num 7

str(y[NULL])

 list()

Zero subsetting

Returns an empty vector (of the same type), this is the same as subsetting with NULL

x = c(1,4,7)

x[0]

numeric(0)

y = list(1,4,7)
str(y[0])

 list()

x[c(0,1)]

[1] 1

y[c(0,1)]

[[1]]
[1] 1

x[c(0,-1)]

[1] 4 7

y[c(0,-1)]

[[1]]
[1] 4

[[2]]
[1] 7

Character subsetting

If the vector has names, selects elements whose names correspond to the values in the name vector.

x = c(a=1, b=4, c=7)

x["a"]

a 
1 

x[c("a","a")]

a a 
1 1 

x[c("b","c")]

b c 
4 7 

y = list(a=1,b=4,c=7)

str(y["a"])

List of 1
 $ a: num 1

str(y[c("a","a")])

List of 2
 $ a: num 1
 $ a: num 1

str(y[c("b","c")])

List of 2
 $ b: num 4
 $ c: num 7

Out of bounds

x = c(1,4,7)

x[4]

[1] NA

x[-4]

[1] 1 4 7

x["a"]

[1] NA

x[c(1,4)]

[1]  1 NA

y = list(1,4,7)

str(y[4])

List of 1
 $ : NULL

str(y[-4])

List of 3
 $ : num 1
 $ : num 4
 $ : num 7

str(y["a"])

List of 1
 $ : NULL

str(y[c(1,4)])

List of 2
 $ : num 1
 $ : NULL

Missing values

x = c(1,4,7)

x[NA]

[1] NA NA NA

x[c(1,NA)]

[1]  1 NA

y = list(1,4,7)

str(y[NA])

List of 3
 $ : NULL
 $ : NULL
 $ : NULL

str(y[c(1,NA)])

List of 2
 $ : num 1
 $ : NULL

NULL and empty vectors (length 0)

This final type of subsetting follows the rules for length coercion with a 0-length vector (i.e. the vector being subset gets coerced to having length 0 if the subsetting vector has length 0)

x = c(1,4,7)

x[NULL]

numeric(0)

x[integer()]

numeric(0)

x[character()]

numeric(0)

y = list(1,4,7)

y[NULL]

list()

y[integer()]

list()

y[character()]

list()

Atomic vectors - [ vs. [[

[[ subsets like [ except it can only subset for a single value

x = c(a=1,b=4,c=7)

x[1]

a 
1 

x[[1]]

[1] 1

x[["a"]]

[1] 1

x[[1:2]]

Error in x[[1:2]]: attempt to select more than one element in vectorIndex

x[[TRUE]]

[1] 1

Generic Vectors (lists) - [ vs. [[

Subsets a single value, but returns the value - not a list containing that value. Vectors are interpreted as nested subsetting.

y = list(a=1, b=4, c=7:9)

y[2]

$b
[1] 4

str( y[2] )

List of 1
 $ b: num 4

y[[2]]

[1] 4

y[["b"]]

[1] 4

y[[1:2]]

Error in y[[1:2]]: subscript out of bounds

y[[2:1]]

[1] 4

Hadley’s Analogy (1)

Hadley’s Analogy (2)

[[ vs. $

$ is equivalent to [[ but it only works for name based subsetting of named lists (also it uses partial matching for names)

x = c("abc"=1, "def"=5)

x$abc

Error in x$abc: $ operator is invalid for atomic vectors

y = list("abc"=1, "def"=5)

y[["abc"]]

[1] 1

y$abc

[1] 1

y$d

[1] 5

A common error

Why does the following code not work?

x = list(abc = 1:10, def = 10:1)
y = "abc"

x[[y]]

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

x$y

NULL

Exercise 1

Below are 100 values,

x = c(56, 3, 17, 2, 4, 9, 6, 5, 19, 5, 2, 3, 5, 0, 13, 12, 6, 31, 10, 21, 8, 4, 1, 1, 2, 5, 16, 1, 3, 8, 1,
      3, 4, 8, 5, 2, 8, 6, 18, 40, 10, 20, 1, 27, 2, 11, 14, 5, 7, 0, 3, 0, 7, 0, 8, 10, 10, 12, 8, 82,
      21, 3, 34, 55, 18, 2, 9, 29, 1, 4, 7, 14, 7, 1, 2, 7, 4, 74, 5, 0, 3, 13, 2, 8, 1, 6, 13, 7, 1, 10,
      5, 2, 4, 4, 14, 15, 4, 17, 1, 9)

write down how you would create a subset to accomplish each of the following:

• Select every third value starting at position 2 in x.

• Remove all values with an odd index (e.g. 1, 3, etc.)

• Remove every 4th value, but only if it is odd.

Subsetting rows

As data frames have 2 dimensions, we can subset on either the rows or the columns - the subsetting values are separated by a comma.

(df = data.frame(x = 1:3, y = c("A","B","C"), z = TRUE))

  x y    z
1 1 A TRUE
2 2 B TRUE
3 3 C TRUE

df[1, ]

  x y    z
1 1 A TRUE

str( df[1, ] )

'data.frame':   1 obs. of  3 variables:
 $ x: int 1
 $ y: chr "A"
 $ z: logi TRUE

df[c(1,3), ]

  x y    z
1 1 A TRUE
3 3 C TRUE

str( df[c(1,3), ] )

'data.frame':   2 obs. of  3 variables:
 $ x: int  1 3
 $ y: chr  "A" "C"
 $ z: logi  TRUE TRUE

Subsetting Columns

df

  x y    z
1 1 A TRUE
2 2 B TRUE
3 3 C TRUE

df[, 1]

[1] 1 2 3

str( df[, 1] )

 int [1:3] 1 2 3

df[, 1:2]

  x y
1 1 A
2 2 B
3 3 C

str( df[, 1:2] )

'data.frame':   3 obs. of  2 variables:
 $ x: int  1 2 3
 $ y: chr  "A" "B" "C"

df[, -3]

  x y
1 1 A
2 2 B
3 3 C

str( df[, -3] )

'data.frame':   3 obs. of  2 variables:
 $ x: int  1 2 3
 $ y: chr  "A" "B" "C"

Subsetting both

df

  x y    z
1 1 A TRUE
2 2 B TRUE
3 3 C TRUE

df[1, 1]

[1] 1

str( df[1, 1] )

 int 1

df[1:2, 1:2]

  x y
1 1 A
2 2 B

str( df[1:2, 1:2] )

'data.frame':   2 obs. of  2 variables:
 $ x: int  1 2
 $ y: chr  "A" "B"

df[-1, 2:3]

  y    z
2 B TRUE
3 C TRUE

str( df[-1, 2:3] )

'data.frame':   2 obs. of  2 variables:
 $ y: chr  "B" "C"
 $ z: logi  TRUE TRUE

Preserving vs Simplifying

Most of the time, R’s [ subset operator is a preserving operator, in that the returned object will always have the same type/class as the object being subset.

Confusingly, when used with some classes (e.g. data frame, matrix or array) [ becomes a simplifying operator (does not preserve type) - this behavior is instead controlled by the drop argument.

Drop

df[1, ]

  x y    z
1 1 A TRUE

str(df[1, ])

'data.frame':   1 obs. of  3 variables:
 $ x: int 1
 $ y: chr "A"
 $ z: logi TRUE

df[1, , drop=TRUE]

$x
[1] 1

$y
[1] "A"

$z
[1] TRUE

str(df[1, , drop=TRUE])

List of 3
 $ x: int 1
 $ y: chr "A"
 $ z: logi TRUE

df[, 1]

[1] 1 2 3

str(df[, 1])

 int [1:3] 1 2 3

df[, 1, drop=FALSE]

  x
1 1
2 2
3 3

str(df[, 1, drop=FALSE])

'data.frame':   3 obs. of  1 variable:
 $ x: int  1 2 3

Exceptions

drop only works when the resulting value can be represented as a 1d vector (either a list or atomic).

df[1:2, 1:2]

  x y
1 1 A
2 2 B

str(df[1:2, 1:2])

'data.frame':   2 obs. of  2 variables:
 $ x: int  1 2
 $ y: chr  "A" "B"

df[1:2, 1:2, drop=TRUE]

  x y
1 1 A
2 2 B

str(df[1:2, 1:2, drop=TRUE])

'data.frame':   2 obs. of  2 variables:
 $ x: int  1 2
 $ y: chr  "A" "B"

Preserving vs Simplifying Subsets