# Grouping functions (tapply, by, aggregate) and the *apply family

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.

• applyWhen 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`.

• lapplyWhen 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
``````
• sapplyWhen 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.

• vapplyWhen you want to use `sapply` but perhaps need to
squeeze some more speed out of your code or want more type safety.

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
``````
• mapplyFor 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
``````
• MapA 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
``````
• rapplyFor 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")
``````
• tapplyFor 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.