Grouping functions (tapply, by, aggregate) and the *apply family
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
tapplyandsweephave no corresponding function inplyr, and remain useful.mergeis useful for combining summaries with the original data.
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 48If 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
lapplyunderneath.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] 5005sapply - 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 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 5005In more advanced uses of
sapplyit will attempt to coerce the result to a multi-dimensional array, if appropriate. For example, if our function returns vectors of the same length,sapplywill use them as columns of a matrix:sapply(1:5,function(x) rnorm(3,x))If our function returns a 2 dimensional matrix,
sapplywill 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
sapplybut 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 91mapply - 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] 4Map - A wrapper to
mapplywithSIMPLIFY = 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] 15rapply - 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
rapplyis, I forgot about it when first posting this answer! Obviously, I'm sure many people use it, but YMMV.rapplyis 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 <- 1:20A factor (of the same length!) defining groups:
y <- factor(rep(letters[1:5], each = 4))Add up the values in
xwithin each subgroup defined byy:tapply(x, y, sum) a b c d e 10 26 42 58 74More complex examples can be handled where the subgroups are defined by the unique combinations of a list of several factors.
tapplyis similar in spirit to the split-apply-combine functions that are common in R (aggregate,by,ave,ddply, etc.) Hence its black sheep status.