rolling joins in data.table with multiple matches

Question

I have a remark/question about rolling joins
Let X,Y be:

set.seed(123);
X <- data.table(x=c(1,1,1,2,2),y=c(T,T,F,F,F),t=as.POSIXct("08:00:00.000",format="%H:%M:%OS")+sample(0:999,5,TRUE)/1e3)
Y <- copy(X)
set.seed(123)
Y[,`:=`(IDX=.I,t=t+sample(c(-5:5)/1e3,5,T))]
Y <- rbindlist(list(Y, X[5,][,IDX:=6][,t:=t+0.001], X[5,][,IDX:=7][,t:=t+0.002]))
setkey(X,x,y,t)
setkey(Y,x,y,t)

here X and Y are sorted by x,y,t

R) X
   x     y                       t
1: 1 FALSE 2013-06-20 08:00:00.407
2: 1  TRUE 2013-06-20 08:00:00.286
3: 1  TRUE 2013-06-20 08:00:00.788
4: 2 FALSE 2013-06-20 08:00:00.882
5: 2 FALSE 2013-06-20 08:00:00.940
R) Y
   x     y                       t IDX
1: 1 FALSE 2013-06-20 08:00:00.407   3
2: 1  TRUE 2013-06-20 08:00:00.284   1
3: 1  TRUE 2013-06-20 08:00:00.791   2
4: 2 FALSE 2013-06-20 08:00:00.886   4
5: 2 FALSE 2013-06-20 08:00:00.940   6
6: 2 FALSE 2013-06-20 08:00:00.942   7
7: 2 FALSE 2013-06-20 08:00:00.945   5

From

executing Y[X, roll=-0.005] gets you

R) Y[X, roll=-0.005]
       x     y                       t IDX
    1: 1 FALSE 2013-06-20 08:00:00.407  NA => due to precision the roll is no match
    2: 1  TRUE 2013-06-20 08:00:00.286  NA => ok 
    3: 1  TRUE 2013-06-20 08:00:00.788   2 => ok (x,y) matched and 788-791=-3
    4: 2 FALSE 2013-06-20 08:00:00.882   4 => same
    5: 2 FALSE 2013-06-20 08:00:00.940   6 => NOT AN EXACT MATCH (precision)

So I would have expected to get more lines FOR THE LAST LINE as the default behaviour of "mult" is "all" and the last line of X is matched by lines 5,6, may be 7 of Y

Answer 1

First Row

For the first row of X only the first row of Y has matching x and y so the first row of Y will match iff Y$t[1] is between X$t[1] and X$t[1] + 0.005 but in fact Y$t[1] < X$t[1] as seen here:

> X$t[1] - Y$t[1]
Time difference of 0.0009999275 secs

One would need a positive roll= value whose magnitude is at least equal to the above difference in order to get a non-NA in row 1. e.g.

> Y[X, roll=0.001]
   x     y                   t IDX
1: 1 FALSE 2013-06-20 08:00:00   3
2: 1  TRUE 2013-06-20 08:00:00  NA
3: 1  TRUE 2013-06-20 08:00:00  NA
4: 2 FALSE 2013-06-20 08:00:00  NA
5: 2 FALSE 2013-06-20 08:00:00  NA

Note that you could force it by using rollends= like this:

> Y[X, roll = -0.005, rollends = TRUE]
   x     y                   t IDX
1: 1 FALSE 2013-06-20 08:00:00   3
2: 1  TRUE 2013-06-20 08:00:00  NA
3: 1  TRUE 2013-06-20 08:00:00   2
4: 2 FALSE 2013-06-20 08:00:00   4
5: 2 FALSE 2013-06-20 08:00:00   6

Last Row

For the last row of X only row 5 of Y matches, not 5, 6 and 7, since only the nearest eligible row is a match. mult= only applies to multiple matches and usually does not apply with roll= (see example at the bottom for an exception):

Note also that rows 5, 6 and 7 of Y do not have the same times. They have increasing times so there is no possibility that they all match:

> dput(Y[["t"]])
structure(c(1371729600.407, 1371729600.285, 1371729600.791, 1371729600.887, 
1371729600.941, 1371729600.942, 1371729600.945), class = c("POSIXct", 
"POSIXt"))

Even if rows 5, 6 and 7 of Y have identical times if those times are not the same as the time in the last row of X then one only gets one row out.

> # times in rows 5, 6 and 7 of Y2 are same
> Y2 <- copy(Y)
> Y2[, t:= t[c(1:4, 5, 5, 5)]]
> setkey(Y2, x, y, t)
> Y2[X, roll = -0.005]
   x     y                   t IDX
1: 1 FALSE 2013-06-20 08:00:00  NA
2: 1  TRUE 2013-06-20 08:00:00  NA
3: 1  TRUE 2013-06-20 08:00:00   2
4: 2 FALSE 2013-06-20 08:00:00   4
5: 2 FALSE 2013-06-20 08:00:00   6

Its only if rows 5, 6 and 7 of 'Y' have the same times and the last row of X also has that time that one gets multiple times out and in that case mult= can apply:

> # time in row 5 of X2 same as the times in rows 5, 6 and 7 of Y2
> X2 <- copy(X)
> X2[, t:=c(t[1:4], Y2[["t"]][5])]
> Y2[X2, roll = -0.005]
   x     y                   t IDX
1: 1 FALSE 2013-06-20 08:00:00  NA
2: 1  TRUE 2013-06-20 08:00:00  NA
3: 1  TRUE 2013-06-20 08:00:00   2
4: 2 FALSE 2013-06-20 08:00:00   4
5: 2 FALSE 2013-06-20 08:00:00   6
6: 2 FALSE 2013-06-20 08:00:00   7
7: 2 FALSE 2013-06-20 08:00:00   5
> 
> Y2[X, roll = -0.005, mult = "first"]
   x     y                   t IDX
1: 1 FALSE 2013-06-20 08:00:00  NA
2: 1  TRUE 2013-06-20 08:00:00  NA
3: 1  TRUE 2013-06-20 08:00:00   2
4: 2 FALSE 2013-06-20 08:00:00   4
5: 2 FALSE 2013-06-20 08:00:00   6

How it works is not so clear from the documentation and I had to use trial and error to discover how it functions. ?data.table does say that "Usually, there should be no duplicates in x's key" (in our example here x is Y) so it may be that the developers wished to leave it undefined for this situation and open to future change.

The idea of using mult= as you describe does seem like a very interesting idea but it seems not to be the way it currently works. Maybe it could in the future.