Conditional (inequality) join in data.table

Using non-equi joins:

ans = dt1[dt2, on=.(start <= end, end > start), 
           .(i.start, i.end, counts, id, circuit, cndn = i.start < x.start & i.end >= x.end), 
           allow.cartesian=TRUE
        ][!cndn %in% TRUE]

The condition start <= end, end >= start (note the >= on both cases) would check if two intervals overlap by any means. The open interval on one side is accomplished by end > start part (> instead of >=). But still it also picks up the intervals of type:

         dt1: start=================end
   dt2: start--------------------------------end ## start < start, end > end

and

         dt1: start=================end
                dt2: start----------end          ## end == end

The cndn column is to check and remove these cases. Hopefully, those cases aren't a lot so that we don't materialise unwanted rows unnecessarily.


PS: the solution in this case is not as straightforward as I'd like to still, and that's because the solution requires an OR operation. It is possible to do two conditional joins, and then bind them together though.

Perhaps at some point, we'll have to think about the feasibility of extending joins to these kinds of operations in a more straightforward manner.


No idea if this performs faster, but here's a shot at a data table method. I reshape dt1 and use findInterval to identify where the times in dt2 line up with times in dt1.

dt1 <- data.table(structure(list(circuit = structure(c(2L, 1L, 2L, 1L, 2L, 3L, 
1L, 1L, 2L), .Label = c("a", "b", "c"), class = "factor"), start = structure(c(1393621200, 
1393627920, 1393628400, 1393631520, 1393650300, 1393646400, 1393656000, 
1393668000, 1393666200), class = c("POSIXct", "POSIXt"), tzone = ""), 
    end = structure(c(1393626600, 1393631519, 1393639200, 1393632000, 
    1393660500, 1393673400, 1393667999, 1393671600, 1393677000
    ), class = c("POSIXct", "POSIXt"), tzone = ""), id = structure(1:9, .Label = c("1001", 
    "1002", "1003", "1004", "1005", "1006", "1007", "1008", "1009"
    ), class = "factor")), .Names = c("circuit", "start", "end", 
"id"), class = "data.frame", row.names = c(NA, -9L)))

dt2 <- data.table(structure(list(start = structure(c(1393621200, 1393624800, 1393626600, 
1393627919, 1393628399, 1393632000, 1393639200, 1393646399, 1393650299, 
1393655999, 1393660500, 1393666199, 1393671600, 1393673400), class = c("POSIXct", 
"POSIXt"), tzone = ""), end = structure(c(1393624799, 1393626600, 
1393627919, 1393628399, 1393632000, 1393639200, 1393646399, 1393650299, 
1393655999, 1393660500, 1393666199, 1393671600, 1393673400, 1393677000
), class = c("POSIXct", "POSIXt"), tzone = ""), seconds = c(3599L, 
1800L, 1319L, 480L, 3601L, 7200L, 7199L, 3900L, 5700L, 4501L, 
5699L, 5401L, 1800L, 3600L), counts = c(1L, 1L, 0L, 1L, 2L, 1L, 
0L, 1L, 2L, 3L, 2L, 3L, 2L, 1L)), .Names = c("start", "end", 
"seconds", "counts"), row.names = c(1L, 3L, 4L, 5L, 6L, 7L, 8L, 
9L, 10L, 11L, 12L, 13L, 14L, 15L), class = "data.frame"))

# > dt1
   # circuit               start                 end   id
# 1:       b 2014-02-28 16:00:00 2014-02-28 17:30:00 1001
# 2:       a 2014-02-28 17:52:00 2014-02-28 18:51:59 1002
# 3:       b 2014-02-28 18:00:00 2014-02-28 21:00:00 1003
# 4:       a 2014-02-28 18:52:00 2014-02-28 19:00:00 1004
# 5:       b 2014-03-01 00:05:00 2014-03-01 02:55:00 1005
# 6:       c 2014-02-28 23:00:00 2014-03-01 06:30:00 1006
# 7:       a 2014-03-01 01:40:00 2014-03-01 04:59:59 1007
# 8:       a 2014-03-01 05:00:00 2014-03-01 06:00:00 1008
# 9:       b 2014-03-01 04:30:00 2014-03-01 07:30:00 1009

# > dt2
                  # start                 end seconds counts
 # 1: 2014-02-28 16:00:00 2014-02-28 16:59:59    3599      1
 # 2: 2014-02-28 17:00:00 2014-02-28 17:30:00    1800      1
 # 3: 2014-02-28 17:30:00 2014-02-28 17:51:59    1319      0
 # 4: 2014-02-28 17:51:59 2014-02-28 17:59:59     480      1
 # 5: 2014-02-28 17:59:59 2014-02-28 19:00:00    3601      2
 # 6: 2014-02-28 19:00:00 2014-02-28 21:00:00    7200      1
 # 7: 2014-02-28 21:00:00 2014-02-28 22:59:59    7199      0
 # 8: 2014-02-28 22:59:59 2014-03-01 00:04:59    3900      1
 # 9: 2014-03-01 00:04:59 2014-03-01 01:39:59    5700      2
# 10: 2014-03-01 01:39:59 2014-03-01 02:55:00    4501      3
# 11: 2014-03-01 02:55:00 2014-03-01 04:29:59    5699      2
# 12: 2014-03-01 04:29:59 2014-03-01 06:00:00    5401      3
# 13: 2014-03-01 06:00:00 2014-03-01 06:30:00    1800      2
# 14: 2014-03-01 06:30:00 2014-03-01 07:30:00    3600      1

## reshapes dt1 from wide to long
## puts start and end times into one column and sorts by time
## this is so that you can use findInterval later
dt3 <- dt1[,list(time = c(start,end)), by = "circuit,id"][order(time)]
dt3[,ntvl := seq_len(nrow(dt3))]
    # circuit   id                time ntvl
 # 1:       b 1001 2014-02-28 16:00:00    1
 # 2:       b 1001 2014-02-28 17:30:00    2
 # 3:       a 1002 2014-02-28 17:52:00    3
 # 4:       b 1003 2014-02-28 18:00:00    4
 # 5:       a 1002 2014-02-28 18:51:59    5
 # 6:       a 1004 2014-02-28 18:52:00    6
 # 7:       a 1004 2014-02-28 19:00:00    7
 # 8:       b 1003 2014-02-28 21:00:00    8
 # 9:       c 1006 2014-02-28 23:00:00    9
# 10:       b 1005 2014-03-01 00:05:00   10
# 11:       a 1007 2014-03-01 01:40:00   11
# 12:       b 1005 2014-03-01 02:55:00   12
# 13:       b 1009 2014-03-01 04:30:00   13
# 14:       a 1007 2014-03-01 04:59:59   14
# 15:       a 1008 2014-03-01 05:00:00   15
# 16:       a 1008 2014-03-01 06:00:00   16
# 17:       c 1006 2014-03-01 06:30:00   17
# 18:       b 1009 2014-03-01 07:30:00   18

## map interval to id
dt4 <- dt3[,list(ntvl = seq(from = min(ntvl), to = max(ntvl)-1), by = 1),by = "circuit,id"]
setkey(dt4, ntvl)
    # circuit   id ntvl
 # 1:       b 1001    1
 # 2:       a 1002    3
 # 3:       a 1002    4
 # 4:       b 1003    4
 # 5:       b 1003    5
 # 6:       b 1003    6
 # 7:       a 1004    6
 # 8:       b 1003    7
 # 9:       c 1006    9
# 10:       c 1006   10
# 11:       b 1005   10
# 12:       c 1006   11
# 13:       b 1005   11
# 14:       a 1007   11
# 15:       c 1006   12
# 16:       a 1007   12
# 17:       c 1006   13
# 18:       a 1007   13
# 19:       b 1009   13
# 20:       c 1006   14
# 21:       b 1009   14
# 22:       c 1006   15
# 23:       b 1009   15
# 24:       a 1008   15
# 25:       c 1006   16
# 26:       b 1009   16
# 27:       b 1009   17
    # circuit   id ntvl

## finds intervals in dt2
dt2[,`:=`(ntvl_start = findInterval(start, dt3[["time"]], rightmost.closed = FALSE),
    ntvl_end = findInterval(end, dt3[["time"]], rightmost.closed = FALSE))]
                  # start                 end seconds counts ntvl_start ntvl_end
 # 1: 2014-02-28 16:00:00 2014-02-28 16:59:59    3599      1          1        1
 # 2: 2014-02-28 17:00:00 2014-02-28 17:30:00    1800      1          1        2
 # 3: 2014-02-28 17:30:00 2014-02-28 17:51:59    1319      0          2        2
 # 4: 2014-02-28 17:51:59 2014-02-28 17:59:59     480      1          2        3
 # 5: 2014-02-28 17:59:59 2014-02-28 19:00:00    3601      2          3        7
 # 6: 2014-02-28 19:00:00 2014-02-28 21:00:00    7200      1          7        8
 # 7: 2014-02-28 21:00:00 2014-02-28 22:59:59    7199      0          8        8
 # 8: 2014-02-28 22:59:59 2014-03-01 00:04:59    3900      1          8        9
 # 9: 2014-03-01 00:04:59 2014-03-01 01:39:59    5700      2          9       10
# 10: 2014-03-01 01:39:59 2014-03-01 02:55:00    4501      3         10       12
# 11: 2014-03-01 02:55:00 2014-03-01 04:29:59    5699      2         12       12
# 12: 2014-03-01 04:29:59 2014-03-01 06:00:00    5401      3         12       16
# 13: 2014-03-01 06:00:00 2014-03-01 06:30:00    1800      2         16       17
# 14: 2014-03-01 06:30:00 2014-03-01 07:30:00    3600      1         17       18

## joins, by start time, then by end time
## the commented out lines may be a better alternative
## if there are many NA values
setkey(dt2, ntvl_start)
dt_ans_start <- dt4[dt2, list(start,end,counts,id,circuit),nomatch = NA]
# dt_ans_start <- dt4[dt2, list(start,end,counts,id,circuit),nomatch = 0]
# dt_ans_start_na <- dt2[!dt4]
setkey(dt2, ntvl_end)
dt_ans_end <- dt4[dt2, list(start,end,counts,id,circuit),nomatch = NA]
# dt_ans_end <- dt4[dt2, list(start,end,counts,id,circuit),nomatch = 0]
# dt_ans_end_na <- dt2[!dt4]

## bring them all together and remove duplicates
dt_ans <- unique(rbind(dt_ans_start, dt_ans_end), by = c("start", "id"))
dt_ans <- dt_ans[!(is.na(id) & counts > 0)]
dt_ans[,ntvl := NULL]
setkey(dt_ans,start)
                  # start                 end counts   id circuit
 # 1: 2014-02-28 16:00:00 2014-02-28 16:59:59      1 1001       b
 # 2: 2014-02-28 17:00:00 2014-02-28 17:30:00      1 1001       b
 # 3: 2014-02-28 17:30:00 2014-02-28 17:51:59      0   NA      NA
 # 4: 2014-02-28 17:51:59 2014-02-28 17:59:59      1 1002       a
 # 5: 2014-02-28 17:59:59 2014-02-28 19:00:00      2 1002       a
 # 6: 2014-02-28 17:59:59 2014-02-28 19:00:00      2 1003       b
 # 7: 2014-02-28 19:00:00 2014-02-28 21:00:00      1 1003       b
 # 8: 2014-02-28 21:00:00 2014-02-28 22:59:59      0   NA      NA
 # 9: 2014-02-28 22:59:59 2014-03-01 00:04:59      1 1006       c
# 10: 2014-03-01 00:04:59 2014-03-01 01:39:59      2 1006       c
# 11: 2014-03-01 00:04:59 2014-03-01 01:39:59      2 1005       b
# 12: 2014-03-01 01:39:59 2014-03-01 02:55:00      3 1006       c
# 13: 2014-03-01 01:39:59 2014-03-01 02:55:00      3 1005       b
# 14: 2014-03-01 01:39:59 2014-03-01 02:55:00      3 1007       a
# 15: 2014-03-01 02:55:00 2014-03-01 04:29:59      2 1006       c
# 16: 2014-03-01 02:55:00 2014-03-01 04:29:59      2 1007       a
# 17: 2014-03-01 04:29:59 2014-03-01 06:00:00      3 1006       c
# 18: 2014-03-01 04:29:59 2014-03-01 06:00:00      3 1007       a
# 19: 2014-03-01 04:29:59 2014-03-01 06:00:00      3 1009       b
# 20: 2014-03-01 06:00:00 2014-03-01 06:30:00      2 1006       c
# 21: 2014-03-01 06:00:00 2014-03-01 06:30:00      2 1009       b
# 22: 2014-03-01 06:30:00 2014-03-01 07:30:00      1 1009       b
                  # start                 end counts   id circuit

Tags:

R

Data.Table