R - Given a matrix and a power, produce multiple matrices containing all unique combinations of matrix columns

Question

Based on my related question linked below (see @Aleh solution): I am looking to calculate only unique products between columns in a matrix for a given power.

E.g., for N=5,M=3, p=2, we get the product of columns (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3). I want to modify (@Aleh's) code to only calculate products between columns (1,1), (1,2), (1,3), (2,2), (2,3), (3,3). But I would want to do this for each p-th order.

Can someone help me accomplish this in R?

Many thanks in advance!

Related questions question: R - Given a matrix and a power, produce multiple matrices containing all combinations of matrix columns

Answer 1

We create the following function, that takes all the "unique" permutations with chosen p and multiply the relevant columns of the matrix :

fun <- function(mat,p) {
  mat <- as.data.frame(mat)
  combs <- do.call(expand.grid,rep(list(seq(ncol(mat))),p)) # all combinations including permutations of same values
  combs <- combs[!apply(combs,1,is.unsorted),]              # "unique" permutations only
  rownames(combs) <- apply(combs,1,paste,collapse="-")      # Just for display of output, we keep info of combinations in rownames
  combs <- combs[order(rownames(combs)),]                   # sort to have desired column order on output
  apply(combs,1,function(x) Reduce(`*`,mat[,x]))            # multiply the relevant columns
}

examples

N = 5
M = 3
mat1 = matrix(1:(N*M),N,M)
#      [,1] [,2] [,3]
# [1,]    1    6   11
# [2,]    2    7   12
# [3,]    3    8   13
# [4,]    4    9   14
# [5,]    5   10   15

M = 4
mat2 = matrix(1:(N*M),N,M)
#      [,1] [,2] [,3] [,4]
# [1,]    1    6   11   16
# [2,]    2    7   12   17
# [3,]    3    8   13   18
# [4,]    4    9   14   19
# [5,]    5   10   15   20

lapply(2:4,fun,mat=mat1)
# [[1]]
#      1-1 1-2 1-3 2-2 2-3 3-3
# [1,]   1   6  11  36  66 121
# [2,]   4  14  24  49  84 144
# [3,]   9  24  39  64 104 169
# [4,]  16  36  56  81 126 196
# [5,]  25  50  75 100 150 225
# 
# [[2]]
#      1-1-1 1-1-2 1-1-3 1-2-2 1-2-3 1-3-3 2-2-2 2-2-3 2-3-3 3-3-3
# [1,]     1     6    11    36    66   121   216   396   726  1331
# [2,]     8    28    48    98   168   288   343   588  1008  1728
# [3,]    27    72   117   192   312   507   512   832  1352  2197
# [4,]    64   144   224   324   504   784   729  1134  1764  2744
# [5,]   125   250   375   500   750  1125  1000  1500  2250  3375
# 
# [[3]]
#      1-1-1-1 1-1-1-2 1-1-1-3 1-1-2-2 1-1-2-3 1-1-3-3 1-2-2-2 1-2-2-3 1-2-3-3 1-3-3-3 2-2-2-2 2-2-2-3 2-2-3-3 2-3-3-3 3-3-3-3
# [1,]       1       6      11      36      66     121     216     396     726    1331    1296    2376    4356    7986   14641
# [2,]      16      56      96     196     336     576     686    1176    2016    3456    2401    4116    7056   12096   20736
# [3,]      81     216     351     576     936    1521    1536    2496    4056    6591    4096    6656   10816   17576   28561
# [4,]     256     576     896    1296    2016    3136    2916    4536    7056   10976    6561   10206   15876   24696   38416
# [5,]     625    1250    1875    2500    3750    5625    5000    7500   11250   16875   10000   15000   22500   33750   50625

fun(mat2,2)
#      1-1 1-2 1-3 1-4 2-2 2-3 2-4 3-3 3-4 4-4
# [1,]   1   6  11  16  36  66  96 121 176 256
# [2,]   4  14  24  34  49  84 119 144 204 289
# [3,]   9  24  39  54  64 104 144 169 234 324
# [4,]  16  36  56  76  81 126 171 196 266 361
# [5,]  25  50  75 100 100 150 200 225 300 400