Introduction to the R Language

apply is used to a evaluate a function (often an anonymous one) over the margins of an array.

• It is most often used to apply a function to the rows or columns of a matrix

• It can be used with general arrays, e.g. taking the average of an array of matrices

• It is not really faster than writing a loop, but it works in one line!

> str(apply)
function (X, MARGIN, FUN, ...)

• X is an array
• MARGIN is an integer vector indicating which margins should be “retained”.
• FUN is a function to be applied
• ... is for other arguments to be passed to FUN

> x <- matrix(rnorm(200), 20, 10)
> apply(x, 2, mean)
 [1]  0.04868268  0.35743615 -0.09104379
 [4] -0.05381370 -0.16552070 -0.18192493
 [7]  0.10285727  0.36519270  0.14898850
[10]  0.26767260

> apply(x, 1, sum)
 [1] -1.94843314  2.60601195  1.51772391
 [4] -2.80386816  3.73728682 -1.69371360
 [7]  0.02359932  3.91874808 -2.39902859
[10]  0.48685925 -1.77576824 -3.34016277
[13]  4.04101009  0.46515429  1.83687755
[16]  4.36744690  2.21993789  2.60983764
[19] -1.48607630  3.58709251

For sums and means of matrix dimensions, we have some shortcuts.

• rowSums = apply(x, 1, sum)
• rowMeans = apply(x, 1, mean)
• colSums = apply(x, 2, sum)
• colMeans = apply(x, 2, mean)

The shortcut functions are much faster, but you won’t notice unless you’re using a large matrix.

Quantiles of the rows of a matrix.

> x <- matrix(rnorm(200), 20, 10)
> apply(x, 1, quantile, probs = c(0.25, 0.75))
          [,1]        [,2]       [,3]        [,4]
25% -0.3304284 -0.99812467 -0.9186279 -0.49711686
75%  0.9258157  0.07065724  0.3050407 -0.06585436
           [,5]       [,6]      [,7]       [,8]
25% -0.05999553 -0.6588380 -0.653250 0.01749997
75%  0.52928743  0.3727449  1.255089 0.72318419
          [,9]      [,10]      [,11]      [,12]
25% -1.2467955 -0.8378429 -1.0488430 -0.7054902
75%  0.3352377  0.7297176  0.3113434  0.4581150
         [,13]      [,14]      [,15]      [,16]
25% -0.1895108 -0.5729407 -0.5968578 -0.9517069
75%  0.5326299  0.5064267  0.4933852  0.8868922
         [,17]      [,18]      [,19]     [,20]

Average matrix in an array

> a <- array(rnorm(2 * 2 * 10), c(2, 2, 10))
> apply(a, c(1, 2), mean)
           [,1]        [,2]
[1,] -0.2353245 -0.03980211
[2,] -0.3339748  0.04364908

> rowMeans(a, dims = 2)
           [,1]        [,2]
[1,] -0.2353245 -0.03980211
[2,] -0.3339748  0.04364908