How can I sweep the first two dimensions of an array based on the first columns of third dimension?
A simplified example:
My array:
a <- array(1:24,c(4,3,2))
> a
, , 1
[,1] [,2] [,3]
[1,] 1 5 9
[2,] 2 6 10
[3,] 3 7 11
[4,] 4 8 12
, , 2
[,1] [,2] [,3]
[1,] 13 17 21
[2,] 14 18 22
[3,] 15 19 23
[4,] 16 20 24
I would like to divide each matrix by its first column by sweep (or another) function. I would like to put the following output in a single array by using a single sweep function.
> sweep(a[,,1], 1, a[,,1][,1], "/")
[,1] [,2] [,3]
[1,] 1 5.000000 9.000000
[2,] 1 3.000000 5.000000
[3,] 1 2.333333 3.666667
[4,] 1 2.000000 3.000000
> sweep(a[,,2], 1, a[,,2][,1], "/")
[,1] [,2] [,3]
[1,] 1 1.307692 1.615385
[2,] 1 1.285714 1.571429
[3,] 1 1.266667 1.533333
[4,] 1 1.250000 1.500000
How can I achieve this?
Using a simple for loop.
res <- array(dim=dim(a))
for (i in seq_len(dim(a)[3])) res[, , i] <- a[, , i]/a[, 1, i]
res
# , , 1
#
# [,1] [,2] [,3]
# [1,] 1 5.000000 9.000000
# [2,] 1 3.000000 5.000000
# [3,] 1 2.333333 3.666667
# [4,] 1 2.000000 3.000000
#
# , , 2
#
# [,1] [,2] [,3]
# [1,] 1 1.307692 1.615385
# [2,] 1 1.285714 1.571429
# [3,] 1 1.266667 1.533333
# [4,] 1 1.250000 1.500000
This appears to outperform *apply functions.
a <- array(rnorm(1e3), c(4, 3, 20000))
microbenchmark::microbenchmark(sapply=array(sapply(seq_len(dim(a)[3]), \(x) a[, , x] / a[, 1, x]), dim=dim(a)),
vapply=array(vapply(seq_len(dim(a)[3]), \(x) a[, , x] / a[, 1, x], vector('numeric', prod(dim(a)[1:2]))), dim=dim(a)),`for`={res <- array(dim=dim(a))
for (i in seq_len(dim(a)[3])) res[, , i] <- a[, , i] / a[, 1, i]},
apply=apply(a, 3, function(x) x / x[,1]))
# Unit: milliseconds
# expr min lq mean median uq max neval cld
# sapply 73.22494 78.46897 88.27141 86.18902 90.08711 232.8461 100 b
# vapply 72.03503 78.24985 86.89068 84.87590 90.58196 226.0209 100 b
# for 58.87842 64.48287 74.33136 70.23162 77.25822 209.9818 100 a
# apply 110.48710 118.79229 130.51282 124.47029 134.64933 294.0801 100 c