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.

• apply - When you want to apply a function to the rows or columnsof 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 toinvestigate the highly optimized, lightning-quick colMeans,rowMeans, colSums, rowSums.

• lapply - When you want to apply a function to each element of alist in turn and get a list back.

  This is the workhorse of many of the other *apply functions. Peelback 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 alist in turn, but you want a vector back, rather than a list.

  If you find yourself typing unlist(lapply(...)), stop and considersapply.

   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 theresult 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 tosqueeze some more speed out of your code or want more type safety.

  For vapply, you basically give R an example of what sort of thingyour function will return, which can save some time coercing returnedvalues 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 elementsof each, and then the 2nd elements of each, etc., coercing the resultto a vector/array as in sapply.

  This is multivariate in the sense that your function must acceptmultiple 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 avector and the subsets are defined by some other vector, usually afactor.

  The black sheep of the *apply family, of sorts. The help file's use ofthe phrase "ragged array" can be a bit confusing, but it is actuallyquite 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 definedby the unique combinations of a list of several factors. tapply issimilar in spirit to the split-apply-combine functions that arecommon in R (aggregate, by, ave, ddply, etc.) Hence itsblack sheep status.

On the side note, here is how the various plyr functions correspond to the base *apply functions (from the intro to plyr document from the plyr webpage http://had.co.nz/plyr/)

Base function   Input   Output   plyr function ---------------------------------------aggregate        d       d       ddply + colwise apply            a       a/l     aaply / alply by               d       l       dlply lapply           l       l       llply  mapply           a       a/l     maply / mlply replicate        r       a/l     raply / rlply sapply           l       a       laply 

One of the goals of plyr is to provide consistent naming conventions for each of the functions, encoding the input and output data types in the function name. It also provides consistency in output, in that output from dlply() is easily passable to ldply() to produce useful output, etc.

Conceptually, learning plyr is no more difficult than understanding the base *apply functions.

plyr and reshape functions have replaced almost all of these functions in my every day use. But, also from the Intro to Plyr document:

Related functions tapply and sweep have no corresponding function in plyr, and remain useful. merge is useful for combining summaries with the original data.

From slide 21 of http://www.slideshare.net/hadley/plyr-one-data-analytic-strategy:

(Hopefully it's clear that apply corresponds to @Hadley's aaply and aggregate corresponds to @Hadley's ddply etc. Slide 20 of the same slideshare will clarify if you don't get it from this image.)

(on the left is input, on the top is output)