I am trying to understand the way sweep function works with multidimensional arrays(4d, 5d ...) specifically when margin equals tuple of dims c(1,2), c(1,3) ...
for example:
x<-array(1,dim = c(2,3,4,5))
sweep(x, STATS=_, MARGIN= c(1,2), FUN='*')
What should the dimensions of STATS here? and how it works?
The dimensions of the statistics given in STATS should be the same as the dimensions resulting from MARGINalizing the data in the input array or, although not recommended, a size that is a sub-multiple of the number of elements in that result (e.g. length 2 in a 2x3 array; or a 2x4 array in a 2x4x3 array; or 2x2 array in a 2x4x3 array, etc.).
In order to understand the dimensions resulting from MARGINalizing the data, let's look at an example:
# Example data in a 3D array of size 2x3x4
set.seed(1717)
x = array(runif(2*3*4), c(2,3,4))
# We MARGINalize the data by computing the mean on all dimensions *other than*
# the stated ones: (1, 3)
# This gives a 2D result whose dimension is of size
# "length of dim 1" x "length of dim 3", i.e. 2x4
marginalize_on_dims = c(1,3)
m = apply(x, marginalize_on_dims, mean)
which results in the following 2x4 "means" array:
> m
[,1] [,2] [,3] [,4]
[1,] 0.3662613 0.2971481 0.155660 0.5121214
[2,] 0.5808111 0.7322553 0.662044 0.4984720
We now sweep out the computed means m from the original x array:
x_swept_out_of_means_m = sweep(x, STATS=m, MARGIN=marginalize_on_dims)
which results in:
> x_swept_out_of_means_m
, , 1
[,1] [,2] [,3]
[1,] -0.2934119 -0.3224825 0.6158943
[2,] -0.4540748 0.1814070 0.2726678
, , 2
[,1] [,2] [,3]
[1,] -0.1452443 0.3631910 -0.21794673
[2,] -0.1205201 0.0873856 0.03313448
, , 3
[,1] [,2] [,3]
[1,] -0.0766162667 -0.14700413 0.22362039
[2,] 0.0006661599 0.05828265 -0.05894881
, , 4
[,1] [,2] [,3]
[1,] 0.2341822 -0.4071083 0.1729261
[2,] -0.2680816 0.4772658 -0.2091843
We now note that the summary on the swept-out result shows a mean of 0 which is consistent to having substracted the mean:
> summary(x_swept_out_of_means_m)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-0.45407 -0.21137 -0.02914 0.00000 0.19196 0.61589
Therefore in your example, since you are marginalizing on dimensions 1 and 2, you should use a STATS value that is of dimension 2x3, for instance:
x <- array(1, dim=c(2,3,4,5))
sweep(x, STATS=matrix(nrow=c(2,3), data=c(2,3,-2,4,0,-3)), MARGIN=c(1,2), FUN='*')
where the result should be a 2x3x4x5 array with the following 2x3 array repeated 4x5 times:
[,1] [,2] [,3]
[1,] 2 -2 0
[2,] 3 4 -3
Session Info:
> sessionInfo()
R version 3.5.2 (2018-12-20)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows >= 8 x64 (build 9200)
