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.