All possible unique pair combinations of gamete positions - r

Question

I have some gamete data in the following format:
Ind Letter Place Position
1 A 19 23
2 B 19 23
3 B 19 23
4 B 19 23
1 B 19 34
2 A 19 34
3 B 19 34
4 B 19 34
1 C 19 52
2 T 19 52
3 C 19 52
4 T 19 52
1 T 33 15
2 T 33 15
3 T 33 15
4 C 33 15
1 C 33 26
2 T 33 26
3 T 33 26
4 C 33 26
dput of data:
structure(list(Ind = c(1L,2L,3L,4L,1L,2L,3L,4L,1L,2L,3L,4L,1L,2L,3L,4L,1L,2L,3L,4L),
Letter = structure(c(1L,2L,2L,2L,2L,1L,2L,2L,3L,4L,3L,4L,4L,4L,4L,3L,3L,4L,4L,3L),
.Label = c("A","B","C","T"), class="factor"),
Place = c(19L,19L,19L,19L,19L,19L,19L,19L,19L,19L,19L,19L,33L,33L,33L,33L,33L,33L,33L,33L),
Position = c(23L,23L,23L,23L,34L,34L,34L,34L,52L,52L,52L,52L,15L,15L,15L,15L,26L,26L,26L,26L)),
.Names = c("Ind","Letter","Place","Position"),
class="data.frame", row.names = c(NA,-20L))
I need to pair and combine them, so I get all possible unique combinations with reference to Position within a pair. I have another data-file, that contains information on the pairs, and they are paired with reference to Place. So in this file I may see, that Place 19+Place 33 is a pair, and I want the following result:
Ind Letter Place Position Ind Letter Place Position
1 A 19 23 1 T 33 15
2 B 19 23 2 T 33 15
3 B 19 23 3 T 33 15
4 B 19 23 4 C 33 15
1 A 19 23 1 C 33 26
2 B 19 23 2 T 33 26
3 B 19 23 3 T 33 26
4 B 19 23 4 C 33 26
1 B 19 34 1 T 33 15
2 A 19 34 2 T 33 15
3 B 19 34 3 T 33 15
4 B 19 34 4 C 33 15
1 B 19 34 1 C 33 26
2 A 19 34 2 T 33 26
3 B 19 34 3 T 33 26
4 B 19 34 4 C 33 26
1 C 19 52 1 T 33 15
2 T 19 52 2 T 33 15
3 C 19 52 3 T 33 15
4 T 19 52 4 C 33 15
1 C 19 52 1 C 33 26
2 T 19 52 2 T 33 26
3 C 19 52 3 T 33 26
4 T 19 52 4 C 33 26
In this case unique means that A1:A2 is equal to A2:A1.
The reason I want to do this, is because I want to do a Four-Gamete-Test on the pairs, to the see if all possible combinations of Letter is existent. So e.g. for the last combined pair above, we have the letter-pairs CC, TT, CT, TC, so this combined pair will pass the FGT.
I have tried to do the combining with expand.grid, as it seems this is quite close to what I want. However, when I require all combination of data$Position, I lose the information for Ind, Letter, and Place. Also the output includes non-unique pairs.
Can anyone point me to a tool, that is closer to what I want? Or give me some guidelines on how to modify expand.grid, to get what I need.
Should you be aware of a tool, that actually does the Four-Gamete-Test, or something similar, then that would of course also be interesting for me to look at.

Answer 1

You can use expand.grid but not directly on the Position column. The idea is to find all combinations of the "quartets" (unique Positions):
pair <- c(19, 33)
df1 <- df1[df1$Place %in% pair, ]
split1 <- split( df1, df1$Position)
vec1 <- unique(df1$Position[df1$Place == pair[1]])
vec2 <- unique(df1$Position[df1$Place == pair[2]])
combin_num <- expand.grid(vec2, vec1)[,2:1]
do.call(
rbind,
lapply(seq_len(nrow(combin_num)), function(i){
cbind( split1[[as.character(combin_num[i,1])]],
split1[[as.character(combin_num[i,2])]] )
})
)[,]
Result:
# Ind Letter Place Position Ind.1 Letter.1 Place.1 Position.1
# 1 1 A 19 23 1 T 33 15
# 2 2 B 19 23 2 T 33 15
# 3 3 B 19 23 3 T 33 15
# 4 4 B 19 23 4 C 33 15
# 5 1 A 19 23 1 C 33 26
# 6 2 B 19 23 2 T 33 26
# 7 3 B 19 23 3 T 33 26
# 8 4 B 19 23 4 C 33 26
# 51 1 B 19 34 1 T 33 15
# 61 2 A 19 34 2 T 33 15
# 71 3 B 19 34 3 T 33 15
# 81 4 B 19 34 4 C 33 15
# 52 1 B 19 34 1 C 33 26
# 62 2 A 19 34 2 T 33 26
# 72 3 B 19 34 3 T 33 26
# 82 4 B 19 34 4 C 33 26
# 9 1 C 19 52 1 T 33 15
# 10 2 T 19 52 2 T 33 15
# 11 3 C 19 52 3 T 33 15
# 12 4 T 19 52 4 C 33 15
# 91 1 C 19 52 1 C 33 26
# 101 2 T 19 52 2 T 33 26
# 111 3 C 19 52 3 T 33 26
# 121 4 T 19 52 4 C 33 26