Challenges and solutions for creating functions to manipulate arrays in R when the number of dimensions is unknown.
arrays in RBelow I am creating an array of dimensions \(3 \times 2 \times 4\) with each entry containing a unique value.
x <- array(1:24, dim = c(3, 2, 4))
x, , 1
[,1] [,2]
[1,] 1 4
[2,] 2 5
[3,] 3 6
, , 2
[,1] [,2]
[1,] 7 10
[2,] 8 11
[3,] 9 12
, , 3
[,1] [,2]
[1,] 13 16
[2,] 14 17
[3,] 15 18
, , 4
[,1] [,2]
[1,] 19 22
[2,] 20 23
[3,] 21 24class(x)[1] "array"You can access the entry \((1, 1, 1)\), i.e. the cell value in first entries of each dimension, in R by:
x[1, 1, 1][1] 1If you want the entries \((i, 1, 1)\) where \(i = 1, 2, 3\) then you can leave the first element blank in R like below:
x[, 1, 1][1] 1 2 3In the above code, the result is a vector but if you wanted to keep the array structure as is then you could add drop = FALSE like below:
x[, 1, 1, drop = FALSE], , 1
[,1]
[1,] 1
[2,] 2
[3,] 3If you want the entries \((1, j, k)\) where \(j = 1, 2\) and \(k = 1, 2, 3, 4\), then you can leave the first two entries in the square bracket like below:
x[1, , ] [,1] [,2] [,3] [,4]
[1,] 1 7 13 19
[2,] 4 10 16 22The above result isn’t actually a vector but a two dimensional array, or more specifically it has the classes matrix and array.
class(x[1, , ])[1] "matrix" "array" I can modify elements in an array by using the assignment operator (<- or =) like below:
x3 <- x2 <- x
x2[1, , ] <- NA
x2, , 1
[,1] [,2]
[1,] NA NA
[2,] 2 5
[3,] 3 6
, , 2
[,1] [,2]
[1,] NA NA
[2,] 8 11
[3,] 9 12
, , 3
[,1] [,2]
[1,] NA NA
[2,] 14 17
[3,] 15 18
, , 4
[,1] [,2]
[1,] NA NA
[2,] 20 23
[3,] 21 24x3[1, , ] <- array(1:8, dim = c(2, 4))
x3, , 1
[,1] [,2]
[1,] 1 2
[2,] 2 5
[3,] 3 6
, , 2
[,1] [,2]
[1,] 3 4
[2,] 8 11
[3,] 9 12
, , 3
[,1] [,2]
[1,] 5 6
[2,] 14 17
[3,] 15 18
, , 4
[,1] [,2]
[1,] 7 8
[2,] 20 23
[3,] 21 24Up to this point, it’s pretty straight forward. But let’s say now we create a function that returns the first element of the first dimension.
index_first <- function(x) {
x[1, , ]
}
index_first(x) [,1] [,2] [,3] [,4]
[1,] 1 7 13 19
[2,] 4 10 16 22y <- array(1, dim = c(2, 4, 2))
index_first(y) [,1] [,2]
[1,] 1 1
[2,] 1 1
[3,] 1 1
[4,] 1 1The above function works fine for the arrays x and y. But what if the number of dimension is different?
z <- array(dim = c(2, 2, 2, 2))
index_first(z)Error in x[1, , ]: incorrect number of dimensionsSo how do we change our function so it works for an array of any number of dimensions? This is where it gets quite challenging. And while I’m at it, let me throw another challenge.
Suppose now I want a function that modifies the entries in the first element of the first dimension by a user supplied value.
modify_first <- function(x, value) {
x[1, ,] <- value
}modify_first(x, NA)
modify_first(x, array(1:8, dim = c(2, 4)))Again this works fine until we have an array with different number of dimensions.
modify_first(z, 1)Error in x[1, , ] <- value: incorrect number of subscriptsSo how would you modify the function so this can be generalised for arrays with a different number of dimensions?
In the first instance, it’s useful to know that the square brackets are in fact functions so the codes below are equivalent:
`[`(x, 1, , ) [,1] [,2] [,3] [,4]
[1,] 1 7 13 19
[2,] 4 10 16 22x[1, , ] [,1] [,2] [,3] [,4]
[1,] 1 7 13 19
[2,] 4 10 16 22The assignment operator for arrays can be written like below where the last argument is the value to replace the indexed array.
`[<-`(x2, 1, , , 0), , 1
[,1] [,2]
[1,] 0 0
[2,] 2 5
[3,] 3 6
, , 2
[,1] [,2]
[1,] 0 0
[2,] 8 11
[3,] 9 12
, , 3
[,1] [,2]
[1,] 0 0
[2,] 14 17
[3,] 15 18
, , 4
[,1] [,2]
[1,] 0 0
[2,] 20 23
[3,] 21 24Below is similar.
x2[1, , ] <- 0I say similar because the above actually modifies x2 but the call before that didn’t. Below is the actual equivalent operation.
x2 <- `[<-`(x2, 1, , , 0)index_first <- function(x) {
d <- dim(x)
do.call("[", c(list(x, 1), rep(list(bquote()), length(d) - 1)))
}
index_first(x) [,1] [,2] [,3] [,4]
[1,] 1 7 13 19
[2,] 4 10 16 22index_first(z), , 1
[,1] [,2]
[1,] NA NA
[2,] NA NA
, , 2
[,1] [,2]
[1,] NA NA
[2,] NA NAmodify_first <- function(x, value) {
d <- dim(x)
do.call("[<-", c(list(x, 1), rep(list(bquote()), length(d) - 1), list(value)))
}
modify_first(x, 3), , 1
[,1] [,2]
[1,] 3 3
[2,] 2 5
[3,] 3 6
, , 2
[,1] [,2]
[1,] 3 3
[2,] 8 11
[3,] 9 12
, , 3
[,1] [,2]
[1,] 3 3
[2,] 14 17
[3,] 15 18
, , 4
[,1] [,2]
[1,] 3 3
[2,] 20 23
[3,] 21 24modify_first(z, 3), , 1, 1
[,1] [,2]
[1,] 3 3
[2,] NA NA
, , 2, 1
[,1] [,2]
[1,] 3 3
[2,] NA NA
, , 1, 2
[,1] [,2]
[1,] 3 3
[2,] NA NA
, , 2, 2
[,1] [,2]
[1,] 3 3
[2,] NA NASo you might wonder when you need such a result. I actually used this for the edibble R-package to create a kind of generalised version of Latin square design, i.e. an array that kind of stitches up multiple Latin squares.
set.seed(1)
edibble::latin_array(dim = c(3, 3, 3), nt = 3), , 1
[,1] [,2] [,3]
[1,] 1 3 2
[2,] 3 2 1
[3,] 2 1 3
, , 2
[,1] [,2] [,3]
[1,] 2 1 3
[2,] 1 3 2
[3,] 3 2 1
, , 3
[,1] [,2] [,3]
[1,] 3 2 1
[2,] 2 1 3
[3,] 1 3 2Beyond the above, I’m not sure who needs to manipulate arrays with dynamic dimensions. If you have a use case, I’d love to know.
The above challenges are sort of challenges that I hope to include in the Advanced R Programming unit that’s planned for Honours level in the Business Analytics major at Monash University. If you want to learn more about R as a programming lanuage (instead of a data analysis tool) then I’d recommend the Advanced R book by Hadley Wickham.
