data.table versus tidyr::expand_grid - r

Question

I have
XIa <- diag(1, 3)
colnames(XIa) <- rownames(XIa) <- c("a0", "a1", "a2")
XIb <- diag(1, 2)
colnames(XIb) <- rownames(XIb) <- c("b0", "b1")
XIc <- diag(1, 2)
colnames(XIc) <- rownames(XIc) <- c("c0", "c1")
tidyr::expand_grid gives me:
tidyr::expand_grid(as.data.frame(XIa), as.data.frame(XIb), as.data.frame(XIc))
# A tibble: 12 x 7
a0 a1 a2 b0 b1 c0 c1
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 1 0 0 1 0 1 0
2 1 0 0 1 0 0 1
3 1 0 0 0 1 1 0
4 1 0 0 0 1 0 1
5 0 1 0 1 0 1 0
6 0 1 0 1 0 0 1
7 0 1 0 0 1 1 0
8 0 1 0 0 1 0 1
9 0 0 1 1 0 1 0
10 0 0 1 1 0 0 1
11 0 0 1 0 1 1 0
12 0 0 1 0 1 0 1
How do I achieve the same result using data.table?
Clearly, there is this way:
dXIa <- data.table(XIa)
dXIb <- data.table(XIb)
dXIc <- data.table(XIc)
cbind(
dXIa[c(rep(1:3, each = 4))],
dXIb[c(rep(1:2, each = 2))],
dXIc[c(rep(1:2, len = 12))]
)
a0 a1 a2 b0 b1 c0 c1
1: 1 0 0 1 0 1 0
2: 1 0 0 1 0 0 1
3: 1 0 0 0 1 1 0
4: 1 0 0 0 1 0 1
5: 0 1 0 1 0 1 0
6: 0 1 0 1 0 0 1
7: 0 1 0 0 1 1 0
8: 0 1 0 0 1 0 1
9: 0 0 1 1 0 1 0
10: 0 0 1 1 0 0 1
11: 0 0 1 0 1 1 0
12: 0 0 1 0 1 0 1
but that is probably not optimal/ideal.

Answer 1

You can use CJ but it does not work with data.table directly. Using the function cjdt from this answer you can do -
library(data.table)
dXIa <- data.table(XIa)
dXIb <- data.table(XIb)
dXIc <- data.table(XIc)
cjdt <- function(a,b){
cj = CJ(1:nrow(a),1:nrow(b))
cbind(a[cj[[1]],],b[cj[[2]],])
}
Reduce(cjdt, list(dXIa, dXIb, dXIc))
# a0 a1 a2 b0 b1 c0 c1
# 1: 1 0 0 1 0 1 0
# 2: 1 0 0 1 0 0 1
# 3: 1 0 0 0 1 1 0
# 4: 1 0 0 0 1 0 1
# 5: 0 1 0 1 0 1 0
# 6: 0 1 0 1 0 0 1
# 7: 0 1 0 0 1 1 0
# 8: 0 1 0 0 1 0 1
# 9: 0 0 1 1 0 1 0
#10: 0 0 1 1 0 0 1
#11: 0 0 1 0 1 1 0
#12: 0 0 1 0 1 0 1

Answer 2

As an alternative to RonakShah's use of cjdt, here's a modified version that has two more features:
Guards against 0-row frames, which should really be a no-op for the 0-row frame;
Uses a single call to cbind instead of Reduce; while reduce isn't evil here, there may be benefits with a much longer list of frames/tables; and
While not a stated constraint here, it works with data.frame and data.table alike.
cjdt2 <- function(...) {
dots <- Filter(nrow, list(...))
eg <- do.call(expand.grid, lapply(sapply(dots, nrow), seq_len))
do.call(cbind, Map(function(x, i) x[i,], dots, eg))
}
cjdt2(XIa, XIb, XIc)
# a0 a1 a2 b0 b1 c0 c1
# a0 1 0 0 1 0 1 0
# a1 0 1 0 1 0 1 0
# a2 0 0 1 1 0 1 0
# a0 1 0 0 0 1 1 0
# a1 0 1 0 0 1 1 0
# a2 0 0 1 0 1 1 0
# a0 1 0 0 1 0 0 1
# a1 0 1 0 1 0 0 1
# a2 0 0 1 1 0 0 1
# a0 1 0 0 0 1 0 1
# a1 0 1 0 0 1 0 1
# a2 0 0 1 0 1 0 1
Which you can easily wrap with setDT (either externally or mod the function).

Answer 3

Here's another approach that uses data.table merge
expgridDT<-function(...) {
DTs<-list(...)
for(jj in 1:(length(DTs)-1)) {
DTs[[jj+1]]<-merge(DTs[[1]][,c(kfjekflj=1,.SD)], DTs[[2]][,c(kfjekflj=1,.SD)],by=.EACHI, allow.cartesian=TRUE)[,!"kfjekflj",with=FALSE]
}
return(DTs[[length(DTs)]][])
}
Essentially what this does is create's a dummy column on each data.table with a non-sense name (kfjekflj) to make a collision with a real column name unlikely. It sets that dummy column as the join by column. Then it merges two tables at a time with allow.cartesian turned on. It does that for every data.table that is passed to the function.
Here's a benchmark:
XIa <- diag(1, 50)
colnames(XIa) <- rownames(XIa) <- paste0("a",1:ncol(XIa))
XIb <- diag(1, 72)
colnames(XIb) <- rownames(XIb) <- paste0("b",1:ncol(XIb))
XIc <- diag(1, 80)
colnames(XIc) <- rownames(XIc) <- paste0("c",1:ncol(XIc))
XIa <- as.data.table(XIa)
XIb <- as.data.table(XIb)
XIc <- as.data.table(XIc)
microbenchmark(expgridDT(XIa, XIb, XIc), Reduce(cjdt, list(XIa, XIb, XIc)), cjdt2(XIa, XIb, XIc))
Unit: milliseconds
expr min lq mean median uq max neval
expgridDT(XIa, XIb, XIc) 167.5827 191.6542 264.8172 203.8769 231.6937 852.2033 100
Reduce(cjdt, list(XIa, XIb, XIc)) 164.4640 217.2215 252.2262 230.7276 255.6974 689.1763 100
cjdt2(XIa, XIb, XIc) 65611.1425 67829.0407 77024.1458 77151.0220 84385.0727 95048.6625 100