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r - Adding values in two data.tables

I have two data.tables, and one has a subset of rows/columns of another. I'd like to add values of the smaller data.table to the values of the larger one:

DT1 <- as.data.table(matrix(c(0, 1, 2, 3), nrow=2, ncol=2, 
       dimnames=list(c("a", "b"), c("a", "b"))), keep=T)
DT2 <- as.data.table(matrix(c(0, 0, 1, 2, 2, 1, 1, 0, 3), nrow=3, ncol=3, 
       dimnames=list(c("a", "b", "c"), c("a", "b", "c"))), keep=T)

DT1
#   rn a b
#1:  a 0 2
#2:  b 1 3
DT2
#   rn a b c
#1:  a 0 2 1
#2:  b 0 2 0
#3:  c 1 1 3

I'd like to add DT1 to DT2 so that I get

#   rn a b c
#1:  a 0 4 1
#2:  b 1 5 0
#3:  c 1 1 3

I know I can overwrite values of DT2 with DT1 very easily:

DT2[DT1, names(DT1) := DT1, on="rn"]

I was hoping that something like this would work:

DT2[DT1, names(DT1) := DT1 + .SD, on="rn"]

...but it doesn't. There's probably some simple variation on this that would work, though, right?

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You can use rbindlist() to bring the two together, then sum the values based on rn

rbindlist(list(DT1, DT2), fill=TRUE)[, lapply(.SD, sum, na.rm = TRUE), by = rn]
#    rn a b c
# 1:  a 0 4 1
# 2:  b 1 5 0
# 3:  c 1 1 3

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