In this lecture we will learn about 3 different apply() functions. The basic idea of an apply() is to apply a function over some iterable object.
Let's start with lapply():
lapply() will apply a function over a list or vector:
lapply(X, FUN, ...)
where X is your list/vector and FUN is your function. For more info you can use:
help(lapply)
Let's see how we can use this in its most practical use case, apply a custom function to a vector. First I want to show you a quick function (we will go over more utilities like this one later) which will allow us to pick a random sample from a vector:
# sample just 1 random number between 1 and 10
sample(x = 1:10,1)
# vector
v <- c(1,2,3,4,5)
# our custom function
addrand <- function(x){
# Get a random number
ran <-sample(x=1:10,1)
# return x plus the random number
return(x+ran)
}
# lapply()
lapply(v,addrand)
So you noticed that in the last example we had to write out an entire function to apply to the vector, but in reality that function is just doing something pretty simple, adding a random number. Do we really want to have to formally define an entire function for this? We don't want to, especially if we only plan to use this function a single time!
To address this issue, we can create an anonymous function (called this because we won't ever name it). Here's the syntax for an anonymous function in R:
function(a){code here}
This is a similar idea to lambda expressions in Python. So for example we can rewrite the previous function as an anonymous function and use lapply() with it:
v
# Anon func with lapply()
lapply(v, function(a){a+sample(x=1:10,1)})
Notice how its kind of implied that everything inside of the curly brackets {} will be returned. Here's a simpler example:
# adds two to every element
lapply(v,function(x){x+2})
Now what if our original function had multiple arguments? lapply() actually let's us deal with that by simply adding them in like this:
add_choice <- function(num,choice){
return(num+choice)
}
add_choice(2,3)
# Uh oh! Forgot to add other arguments!
lapply(v,add_choice)
# Nice!
lapply(v,add_choice,choice=10)
You can do this with several arguments,you just keep adding them.
Notice that lapply returned a list, we can use sapply, which simplifies the process by returning a vector or matrix. For example:
help(sapply)
# Nice! A vector returned
sapply(v,add_choice,choice=10)
# let's prove it to ourselves
lapp <- lapply(v,add_choice,choice=10)
sapp <- sapply(v,add_choice,choice=10)
class(lapp) # a list
class(sapp) # vector of numerics
sapply() won't be able to automatically return a vector if your applied function doesn't return something for all elements in that vector. For example:
# Checks for even numbers
even <- function(x) {
return(x[(x %% 2 == 0)])
}
nums <- c(1,2,3,4,5)
sapply(nums,even)
lapply(nums,even)
There are actually quite a few different apply() type functions in R. We've gone over everything you need to know for now. But if your curious in finding out more about them you can check out this documentation or this excellent StackOverflow answer, copied here below:
R has many *apply functions which are ably described in the help files (e.g. ?apply). There are enough of them, though, that beginning useRs may have difficulty deciding which one is appropriate for their situation or even remembering them all. They may have a general sense that "I should be using an *apply function here", but it can be tough to keep them all straight at first.
Despite the fact (noted in other answers) that much of the functionality of the *apply family is covered by the extremely popular plyr package, the base functions remain useful and worth knowing.
This answer is intended to act as a sort of signpost for new useRs to help direct them to the correct *apply function for their particular problem. Note, this is not intended to simply regurgitate or replace the R documentation! The hope is that this answer helps you to decide which *apply function suits your situation and then it is up to you to research it further. With one exception, performance differences will not be addressed.
apply - When you want to apply a function to the rows or columns of a matrix (and higher-dimensional analogues); not generally advisable for data frames as it will coerce to a matrix first.
# Two dimensional matrix
M <- matrix(seq(1,16), 4, 4)
# apply min to rows
apply(M, 1, min)
[1] 1 2 3 4
# apply max to columns
apply(M, 2, max)
[1] 4 8 12 16
# 3 dimensional array
M <- array( seq(32), dim = c(4,4,2))
# Apply sum across each M[*, , ] - i.e Sum across 2nd and 3rd dimension
apply(M, 1, sum)
# Result is one-dimensional
[1] 120 128 136 144
# Apply sum across each M[*, *, ] - i.e Sum across 3rd dimension
apply(M, c(1,2), sum)
# Result is two-dimensional
[,1] [,2] [,3] [,4]
[1,] 18 26 34 42
[2,] 20 28 36 44
[3,] 22 30 38 46
[4,] 24 32 40 48
If you want row/column means or sums for a 2D matrix, be sure to
investigate the highly optimized, lightning-quick colMeans,
rowMeans, colSums, rowSums.
lapply - When you want to apply a function to each element of a list in turn and get a list back.
This is the workhorse of many of the other *apply functions. Peel
back their code and you will often find lapply underneath.
x <- list(a = 1, b = 1:3, c = 10:100)
lapply(x, FUN = length)
$a
[1] 1
$b
[1] 3
$c
[1] 91
lapply(x, FUN = sum)
$a
[1] 1
$b
[1] 6
$c
[1] 5005
sapply - When you want to apply a function to each element of a list in turn, but you want a vector back, rather than a list.
If you find yourself typing unlist(lapply(...)), stop and consider
sapply.
x <- list(a = 1, b = 1:3, c = 10:100)
#Compare with above; a named vector, not a list
sapply(x, FUN = length)
a b c
1 3 91
sapply(x, FUN = sum)
a b c
1 6 5005
In more advanced uses of sapply it will attempt to coerce the
result to a multi-dimensional array, if appropriate. For example, if our function returns vectors of the same length, sapply will use them as columns of a matrix:
sapply(1:5,function(x) rnorm(3,x))
If our function returns a 2 dimensional matrix, sapply will do essentially the same thing, treating each returned matrix as a single long vector:
sapply(1:5,function(x) matrix(x,2,2))
Unless we specify simplify = "array", in which case it will use the individual matrices to build a multi-dimensional array:
sapply(1:5,function(x) matrix(x,2,2), simplify = "array")
Each of these behaviors is of course contingent on our function returning vectors or matrices of the same length or dimension.
vapply - When you want to use sapply but perhaps need to
squeeze some more speed out of your code.
For vapply, you basically give R an example of what sort of thing
your function will return, which can save some time coercing returned
values to fit in a single atomic vector.
x <- list(a = 1, b = 1:3, c = 10:100)
#Note that since the advantage here is mainly speed, this
# example is only for illustration. We're telling R that
# everything returned by length() should be an integer of
# length 1.
vapply(x, FUN = length, FUN.VALUE = 0L)
a b c
1 3 91
mapply - For when you have several data structures (e.g.
vectors, lists) and you want to apply a function to the 1st elements
of each, and then the 2nd elements of each, etc., coercing the result
to a vector/array as in sapply.
This is multivariate in the sense that your function must accept multiple arguments.
#Sums the 1st elements, the 2nd elements, etc.
mapply(sum, 1:5, 1:5, 1:5)
[1] 3 6 9 12 15
#To do rep(1,4), rep(2,3), etc.
mapply(rep, 1:4, 4:1)
[[1]]
[1] 1 1 1 1
[[2]]
[1] 2 2 2
[[3]]
[1] 3 3
[[4]]
[1] 4
Map - A wrapper to mapply with SIMPLIFY = FALSE, so it is guaranteed to return a list.
Map(sum, 1:5, 1:5, 1:5)
[[1]]
[1] 3
[[2]]
[1] 6
[[3]]
[1] 9
[[4]]
[1] 12
[[5]]
[1] 15
rapply - For when you want to apply a function to each element of a nested list structure, recursively.
To give you some idea of how uncommon rapply is, I forgot about it when first posting this answer! Obviously, I'm sure many people use it, but YMMV. rapply is best illustrated with a user-defined function to apply:
#Append ! to string, otherwise increment
myFun <- function(x){
if (is.character(x)){
return(paste(x,"!",sep=""))
}
else{
return(x + 1)
}
}
#A nested list structure
l <- list(a = list(a1 = "Boo", b1 = 2, c1 = "Eeek"),
b = 3, c = "Yikes",
d = list(a2 = 1, b2 = list(a3 = "Hey", b3 = 5)))
#Result is named vector, coerced to character
rapply(l,myFun)
#Result is a nested list like l, with values altered
rapply(l, myFun, how = "replace")
tapply - For when you want to apply a function to subsets of a vector and the subsets are defined by some other vector, usually a factor.
The black sheep of the *apply family, of sorts. The help file's use of the phrase "ragged array" can be a bit confusing, but it is actually quite simple.
A vector:
x <- 1:20
A factor (of the same length!) defining groups:
y <- factor(rep(letters[1:5], each = 4))
Add up the values in x within each subgroup defined by y:
tapply(x, y, sum)
a b c d e
10 26 42 58 74
More complex examples can be handled where the subgroups are defined
by the unique combinations of a list of several factors. tapply is
similar in spirit to the split-apply-combine functions that are
common in R (aggregate, by, ave, ddply, etc.) Hence its
black sheep status.