Is there a way in R to create binary sets of m, filled with all combinations of n by columns, while by row only 1 value can be "1"?
For example, for n=2 and m=2, we would have the following combinations of m each:
(00, 00), (10,00), (01,00), (00,10), (00,01), (10,01), (01,10), (10,10), (01,01)
But these, for example, are not allowed: (11,00), (01,11), (00,11), (11,10), (11,11)
This is very similar to your other question. In my answer to that question, we see that rephrasing the question, makes it much easier to attack. So for this question, we can reduce it to: "How to generate all pairwise permutations of powers of 2 with repeats?"
We can use almost exactly the same setup as before, only this time we set the argument repeats.allowed = TRUE.
library(gtools)
bitPairwise2 <- function(numBits, groupSize) {
t(sapply(t(permutations(numBits + 1, groupSize,
c(0, 2^(0:(numBits-1))), repeats.allowed = TRUE)),
function(x) {as.integer(intToBits(x))})[1:numBits, ])
}
bitPairwise2(2,2)
[,1] [,2]
[1,] 0 0 ## (00,00)
[2,] 0 0
[3,] 0 0 ## (00,10)
[4,] 1 0
[5,] 0 0 ## (00,01)
[6,] 0 1
[7,] 1 0 ## (10,00)
[8,] 0 0
[9,] 1 0 ## (10,10)
[10,] 1 0
[11,] 1 0 ## (10,01)
[12,] 0 1
This function generalizes to any number of bits as well as any number of groups. For example, all possible 3-tuples of 3 bits is given by:
## first 9 groups
bitPairwise2(3, 3)[1:27, ]
[,1] [,2] [,3]
[1,] 0 0 0 ## (000,000,000)
[2,] 0 0 0
[3,] 0 0 0
[4,] 0 0 0 ## (000,000,100)
[5,] 0 0 0
[6,] 1 0 0
[7,] 0 0 0 ## (000,000,010)
[8,] 0 0 0
[9,] 0 1 0
[10,] 0 0 0 ## (000,000,001)
[11,] 0 0 0
[12,] 0 0 1
[13,] 0 0 0 ## (000,100,000)
[14,] 1 0 0
[15,] 0 0 0
[16,] 0 0 0 ## (000,100,100)
[17,] 1 0 0
[18,] 1 0 0
[19,] 0 0 0 ## (000,100,010)
[20,] 1 0 0
[21,] 0 1 0
[22,] 0 0 0 ## (000,100,001)
[23,] 1 0 0
[24,] 0 0 1
[25,] 0 0 0 ## (000,010,000)
[26,] 0 1 0
[27,] 0 0 0
And here are the last 9 groups:
a <- bitPairwise2(3, 3)[166:192, ]
row.names(a) <- 166:192
a
[,1] [,2] [,3]
166 0 0 1 ## (001,100,001)
167 1 0 0
168 0 0 1
169 0 0 1 ## (001,010,000)
170 0 1 0
171 0 0 0
172 0 0 1 ## (001,010,100)
173 0 1 0
174 1 0 0
175 0 0 1 ## (001,010,010)
176 0 1 0
177 0 1 0
178 0 0 1 ## (001,010,001)
179 0 1 0
180 0 0 1
181 0 0 1 ## (001,001,000)
182 0 0 1
183 0 0 0
184 0 0 1 ## (001,001,100)
185 0 0 1
186 1 0 0
187 0 0 1 ## (001,001,010)
188 0 0 1
189 0 1 0
190 0 0 1 ## (001,001,001)
191 0 0 1
192 0 0 1
If you need the output in a list, try this:
test <- bitPairwise2(4, 3)
numGroups <- nrow(test)/3
makeGroupList <- function(mat, nG, groupSize) {
lapply(1:nG, function(x) {
s <- groupSize*(x-1) + 1
e <- s + (groupSize - 1)
mat[s:e, ]
})
}
makeGroupList(test, numGroups, 3)
[[1]]
[,1] [,2] [,3] [,4]
[1,] 0 0 0 0
[2,] 0 0 0 0
[3,] 0 0 0 0
[[2]]
[,1] [,2] [,3] [,4]
[1,] 0 0 0 0
[2,] 0 0 0 0
[3,] 1 0 0 0
[[3]]
[,1] [,2] [,3] [,4]
[1,] 0 0 0 0
[2,] 0 0 0 0
[3,] 0 1 0 0
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