Find all combinations of n1 elements from vector1 and n2 elements from vector2 in R?
Question
I have two vectors and I am trying to find all unique combinations of 3 elements from vector1 and 2 elements from vector2. I have tried the following code.
V1 = combn(1:5, 3) # 10 combinations in total
V2 = combn(6:11, 2) # 15 combinations in total
How to combine V1 and V2 so that there are 10 * 15 = 150 combinations in total? Thanks.
5 answers
solution1
6 2022-12-02 21:47:25
The function comboGrid from RcppAlgos (I am the author) does just the trick:
library(RcppAlgos)
grid <- comboGrid(c(rep(list(1:5), 3), rep(list(6:11), 2)),
repetition = FALSE)
head(grid)
#> Var1 Var2 Var3 Var4 Var5
#> [1,] 1 2 3 6 7
#> [2,] 1 2 3 6 8
#> [3,] 1 2 3 6 9
#> [4,] 1 2 3 6 10
#> [5,] 1 2 3 6 11
#> [6,] 1 2 3 7 8
tail(grid)
#> Var1 Var2 Var3 Var4 Var5
#> [145,] 3 4 5 8 9
#> [146,] 3 4 5 8 10
#> [147,] 3 4 5 8 11
#> [148,] 3 4 5 9 10
#> [149,] 3 4 5 9 11
#> [150,] 3 4 5 10 11
It is quite efficient as well. It is written in C++ and pulls together many ideas from the excellent question: Picking unordered combinations from pools with overlap . The underlying algorithm avoids generating duplicates that would need to be filtered out.
Consider the following example where generating the Cartesian product contains more than 10 billion results:
system.time(huge <- comboGrid(c(rep(list(1:20), 5), rep(list(21:35), 3)),
repetition = FALSE))
#> user system elapsed
#> 0.990 0.087 1.077
dim(huge)
#> [1] 7054320 8
solution2
6 2022-12-02 22:13:56
You can try expand.grid along with asplit , eg,
expand.grid(asplit(V1,2), asplit(V2,2))
or
with(
expand.grid(asplit(V1, 2), asplit(V2, 2)),
t(mapply(c, Var1, Var2))
)
solution3
3 ACCPTED 2022-12-02 21:28:48
You can use expand.grid() :
g <- expand.grid(seq_len(ncol(V1)), seq_len(ncol(V2)))
V3 <- rbind(V1[, g[, 1]], V2[, g[, 2]])
The result is in a similar format as V1 and V2 , ie a 5 × 150 matrix (here printed transposed):
head(t(V3))
# [,1] [,2] [,3] [,4] [,5]
# [1,] 1 2 3 6 7
# [2,] 1 2 4 6 7
# [3,] 1 2 5 6 7
# [4,] 1 3 4 6 7
# [5,] 1 3 5 6 7
# [6,] 1 4 5 6 7
dim(unique(t(V3)))
# [1] 150 5
And a generalized approach that can handle more than two initial matrices of combinations, stored in a list V :
V <- list(V1, V2)
g <- do.call(expand.grid, lapply(V, \(x) seq_len(ncol(x))))
V.comb <- do.call(rbind, mapply('[', V, T, g))
identical(V.comb, V3)
[1] TRUE
solution4
3 2022-12-02 21:35:07
After some helpful refactoring guidance from @onyambu, here is a shorter solution based on base::merge() :
merge(t(combn(1:5, 3)),t(combn(6:11, 2)),by.x=NULL,by.y = NULL)
...and the first 20 rows of output:
> merge(t(combn(1:5, 3)),t(combn(6:11, 2)),by.x=NULL,by.y = NULL)
V1.x V2.x V3 V1.y V2.y
1 1 2 3 6 7
2 1 2 4 6 7
3 1 2 5 6 7
4 1 3 4 6 7
5 1 3 5 6 7
6 1 4 5 6 7
7 2 3 4 6 7
8 2 3 5 6 7
9 2 4 5 6 7
10 3 4 5 6 7
11 1 2 3 6 8
12 1 2 4 6 8
13 1 2 5 6 8
14 1 3 4 6 8
15 1 3 5 6 8
16 1 4 5 6 8
17 2 3 4 6 8
18 2 3 5 6 8
19 2 4 5 6 8
20 3 4 5 6 8
original solution
A base R solution to create a Cartesian product with merge() looks like this:
df1 <- data.frame(t(combn(1:5, 3)))
df2 <- data.frame(t(combn(6:11, 2)))
colnames(df2) <- paste("y",1:2,sep=""))
merge(df1,df2,by.x=NULL,by.y = NULL)
...and the first 25 rows of output:
> merge(df1,df2,by.x=NULL,by.y = NULL)
X1 X2 X3 y1 y2
1 1 2 3 6 7
2 1 2 4 6 7
3 1 2 5 6 7
4 1 3 4 6 7
5 1 3 5 6 7
6 1 4 5 6 7
7 2 3 4 6 7
8 2 3 5 6 7
9 2 4 5 6 7
10 3 4 5 6 7
11 1 2 3 6 8
12 1 2 4 6 8
13 1 2 5 6 8
14 1 3 4 6 8
15 1 3 5 6 8
16 1 4 5 6 8
17 2 3 4 6 8
18 2 3 5 6 8
19 2 4 5 6 8
20 3 4 5 6 8
21 1 2 3 6 9
22 1 2 4 6 9
23 1 2 5 6 9
24 1 3 4 6 9
25 1 3 5 6 9
solution5
2 2022-12-02 21:33:10
Similar idea, using apply
apply(expand.grid(seq(ncol(V1)), seq(ncol(V2))), 1, function(i) {
c(V1[,i[1]], V2[,i[2]])})
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] 1 1 1 1 1 1 2 2 2 3 1 1 1 1
#> [2,] 2 2 2 3 3 4 3 3 4 4 2 2 2 3
#> [3,] 3 4 5 4 5 5 4 5 5 5 3 4 5 4
#> [4,] 6 6 6 6 6 6 6 6 6 6 6 6 6 6
#> [5,] 7 7 7 7 7 7 7 7 7 7 8 8 8 8
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 1 1 2 2 2 3 1 1 1 1 1 1
#> [2,] 3 4 3 3 4 4 2 2 2 3 3 4
#> [3,] 5 5 4 5 5 5 3 4 5 4 5 5
#> [4,] 6 6 6 6 6 6 6 6 6 6 6 6
#> [5,] 8 8 8 8 8 8 9 9 9 9 9 9
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 2 2 2 3 1 1 1 1 1 1 2 2
#> [2,] 3 3 4 4 2 2 2 3 3 4 3 3
#> [3,] 4 5 5 5 3 4 5 4 5 5 4 5
#> [4,] 6 6 6 6 6 6 6 6 6 6 6 6
#> [5,] 9 9 9 9 10 10 10 10 10 10 10 10
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 2 3 1 1 1 1 1 1 2 2 2 3
#> [2,] 4 4 2 2 2 3 3 4 3 3 4 4
#> [3,] 5 5 3 4 5 4 5 5 4 5 5 5
#> [4,] 6 6 6 6 6 6 6 6 6 6 6 6
#> [5,] 10 10 11 11 11 11 11 11 11 11 11 11
#> [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62]
#> [1,] 1 1 1 1 1 1 2 2 2 3 1 1
#> [2,] 2 2 2 3 3 4 3 3 4 4 2 2
#> [3,] 3 4 5 4 5 5 4 5 5 5 3 4
#> [4,] 7 7 7 7 7 7 7 7 7 7 7 7
#> [5,] 8 8 8 8 8 8 8 8 8 8 9 9
#> [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74]
#> [1,] 1 1 1 1 2 2 2 3 1 1 1 1
#> [2,] 2 3 3 4 3 3 4 4 2 2 2 3
#> [3,] 5 4 5 5 4 5 5 5 3 4 5 4
#> [4,] 7 7 7 7 7 7 7 7 7 7 7 7
#> [5,] 9 9 9 9 9 9 9 9 10 10 10 10
#> [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] [,86]
#> [1,] 1 1 2 2 2 3 1 1 1 1 1 1
#> [2,] 3 4 3 3 4 4 2 2 2 3 3 4
#> [3,] 5 5 4 5 5 5 3 4 5 4 5 5
#> [4,] 7 7 7 7 7 7 7 7 7 7 7 7
#> [5,] 10 10 10 10 10 10 11 11 11 11 11 11
#> [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] [,98]
#> [1,] 2 2 2 3 1 1 1 1 1 1 2 2
#> [2,] 3 3 4 4 2 2 2 3 3 4 3 3
#> [3,] 4 5 5 5 3 4 5 4 5 5 4 5
#> [4,] 7 7 7 7 8 8 8 8 8 8 8 8
#> [5,] 11 11 11 11 9 9 9 9 9 9 9 9
#> [,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106] [,107] [,108]
#> [1,] 2 3 1 1 1 1 1 1 2 2
#> [2,] 4 4 2 2 2 3 3 4 3 3
#> [3,] 5 5 3 4 5 4 5 5 4 5
#> [4,] 8 8 8 8 8 8 8 8 8 8
#> [5,] 9 9 10 10 10 10 10 10 10 10
#> [,109] [,110] [,111] [,112] [,113] [,114] [,115] [,116] [,117] [,118]
#> [1,] 2 3 1 1 1 1 1 1 2 2
#> [2,] 4 4 2 2 2 3 3 4 3 3
#> [3,] 5 5 3 4 5 4 5 5 4 5
#> [4,] 8 8 8 8 8 8 8 8 8 8
#> [5,] 10 10 11 11 11 11 11 11 11 11
#> [,119] [,120] [,121] [,122] [,123] [,124] [,125] [,126] [,127] [,128]
#> [1,] 2 3 1 1 1 1 1 1 2 2
#> [2,] 4 4 2 2 2 3 3 4 3 3
#> [3,] 5 5 3 4 5 4 5 5 4 5
#> [4,] 8 8 9 9 9 9 9 9 9 9
#> [5,] 11 11 10 10 10 10 10 10 10 10
#> [,129] [,130] [,131] [,132] [,133] [,134] [,135] [,136] [,137] [,138]
#> [1,] 2 3 1 1 1 1 1 1 2 2
#> [2,] 4 4 2 2 2 3 3 4 3 3
#> [3,] 5 5 3 4 5 4 5 5 4 5
#> [4,] 9 9 9 9 9 9 9 9 9 9
#> [5,] 10 10 11 11 11 11 11 11 11 11
#> [,139] [,140] [,141] [,142] [,143] [,144] [,145] [,146] [,147] [,148]
#> [1,] 2 3 1 1 1 1 1 1 2 2
#> [2,] 4 4 2 2 2 3 3 4 3 3
#> [3,] 5 5 3 4 5 4 5 5 4 5
#> [4,] 9 9 10 10 10 10 10 10 10 10
#> [5,] 11 11 11 11 11 11 11 11 11 11
#> [,149] [,150]
#> [1,] 2 3
#> [2,] 4 4
#> [3,] 5 5
#> [4,] 10 10
#> [5,] 11 11
Created on 2022-12-02 with reprex v2.0.2
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