Introduction to data.table

2024-02-26

This vignette introduces the data.table syntax, its general form, how to subset rows, select and compute on columns, and perform aggregations by group. Familiarity with the data.frame data structure from base R is useful, but not essential to follow this vignette.


Data analysis using data.table

Data manipulation operations such as subset, group, update, join, etc. are all inherently related. Keeping these related operations together allows for:

Briefly, if you are interested in reducing programming and compute time tremendously, then this package is for you. The philosophy that data.table adheres to makes this possible. Our goal is to illustrate it through this series of vignettes.

Data

In this vignette, we will use NYC-flights14 data obtained from the flights package (available on GitHub only). It contains On-Time flights data from the Bureau of Transportation Statistics for all the flights that departed from New York City airports in 2014 (inspired by nycflights13). The data is available only for Jan-Oct’14.

We can use data.table’s fast-and-friendly file reader fread to load flights directly as follows:

input <- if (file.exists("flights14.csv")) {
   "flights14.csv"
} else {
  "https://raw.githubusercontent.com/Rdatatable/data.table/master/vignettes/flights14.csv"
}
flights <- fread(input)
flights
#          year month   day dep_delay arr_delay carrier origin   dest air_time distance  hour
#         <int> <int> <int>     <int>     <int>  <char> <char> <char>    <int>    <int> <int>
#      1:  2014     1     1        14        13      AA    JFK    LAX      359     2475     9
#      2:  2014     1     1        -3        13      AA    JFK    LAX      363     2475    11
#      3:  2014     1     1         2         9      AA    JFK    LAX      351     2475    19
#      4:  2014     1     1        -8       -26      AA    LGA    PBI      157     1035     7
#      5:  2014     1     1         2         1      AA    JFK    LAX      350     2475    13
#     ---                                                                                    
# 253312:  2014    10    31         1       -30      UA    LGA    IAH      201     1416    14
# 253313:  2014    10    31        -5       -14      UA    EWR    IAH      189     1400     8
# 253314:  2014    10    31        -8        16      MQ    LGA    RDU       83      431    11
# 253315:  2014    10    31        -4        15      MQ    LGA    DTW       75      502    11
# 253316:  2014    10    31        -5         1      MQ    LGA    SDF      110      659     8
dim(flights)
# [1] 253316     11

Aside: fread accepts http and https URLs directly, as well as operating system commands such as sed and awk output. See ?fread for examples.

Introduction

In this vignette, we will

  1. Start with the basics - what is a data.table, its general form, how to subset rows, how to select and compute on columns;

  2. Then we will look at performing data aggregations by group

1. Basics

a) What is data.table?

data.table is an R package that provides an enhanced version of a data.frame, the standard data structure for storing data in base R. In the Data section above, we saw how to create a data.table using fread(), but alternatively we can also create one using the data.table() function. Here is an example:

DT = data.table(
  ID = c("b","b","b","a","a","c"),
  a = 1:6,
  b = 7:12,
  c = 13:18
)
DT
#        ID     a     b     c
#    <char> <int> <int> <int>
# 1:      b     1     7    13
# 2:      b     2     8    14
# 3:      b     3     9    15
# 4:      a     4    10    16
# 5:      a     5    11    17
# 6:      c     6    12    18
class(DT$ID)
# [1] "character"

You can also convert existing objects to a data.table using setDT() (for data.frame and list structures) or as.data.table() (for other structures). For more details pertaining to the difference (goes beyond the scope of this vignette), please see ?setDT and ?as.data.table.

Note that:

b) General form - in what way is a data.table enhanced?

In contrast to a data.frame, you can do a lot more than just subsetting rows and selecting columns within the frame of a data.table, i.e., within [ ... ] (NB: we might also refer to writing things inside DT[...] as “querying DT”, as an analogy or in relevance to SQL). To understand it we will have to first look at the general form of the data.table syntax, as shown below:

DT[i, j, by]

##   R:                 i                 j        by
## SQL:  where | order by   select | update  group by

Users with an SQL background might perhaps immediately relate to this syntax.

The way to read it (out loud) is:

Take DT, subset/reorder rows using i, then calculate j, grouped by by.

Let’s begin by looking at i and j first - subsetting rows and operating on columns.

c) Subset rows in i

– Get all the flights with “JFK” as the origin airport in the month of June.

ans <- flights[origin == "JFK" & month == 6L]
head(ans)
#     year month   day dep_delay arr_delay carrier origin   dest air_time distance  hour
#    <int> <int> <int>     <int>     <int>  <char> <char> <char>    <int>    <int> <int>
# 1:  2014     6     1        -9        -5      AA    JFK    LAX      324     2475     8
# 2:  2014     6     1       -10       -13      AA    JFK    LAX      329     2475    12
# 3:  2014     6     1        18        -1      AA    JFK    LAX      326     2475     7
# 4:  2014     6     1        -6       -16      AA    JFK    LAX      320     2475    10
# 5:  2014     6     1        -4       -45      AA    JFK    LAX      326     2475    18
# 6:  2014     6     1        -6       -23      AA    JFK    LAX      329     2475    14

– Get the first two rows from flights.

ans <- flights[1:2]
ans
#     year month   day dep_delay arr_delay carrier origin   dest air_time distance  hour
#    <int> <int> <int>     <int>     <int>  <char> <char> <char>    <int>    <int> <int>
# 1:  2014     1     1        14        13      AA    JFK    LAX      359     2475     9
# 2:  2014     1     1        -3        13      AA    JFK    LAX      363     2475    11

– Sort flights first by column origin in ascending order, and then by dest in descending order:

We can use the R function order() to accomplish this.

ans <- flights[order(origin, -dest)]
head(ans)
#     year month   day dep_delay arr_delay carrier origin   dest air_time distance  hour
#    <int> <int> <int>     <int>     <int>  <char> <char> <char>    <int>    <int> <int>
# 1:  2014     1     5         6        49      EV    EWR    XNA      195     1131     8
# 2:  2014     1     6         7        13      EV    EWR    XNA      190     1131     8
# 3:  2014     1     7        -6       -13      EV    EWR    XNA      179     1131     8
# 4:  2014     1     8        -7       -12      EV    EWR    XNA      184     1131     8
# 5:  2014     1     9        16         7      EV    EWR    XNA      181     1131     8
# 6:  2014     1    13        66        66      EV    EWR    XNA      188     1131     9

order() is internally optimised

We will discuss data.table’s fast order in more detail in the data.table internals vignette.

d) Select column(s) in j

– Select arr_delay column, but return it as a vector.

ans <- flights[, arr_delay]
head(ans)
# [1]  13  13   9 -26   1   0

– Select arr_delay column, but return as a data.table instead.

ans <- flights[, list(arr_delay)]
head(ans)
#    arr_delay
#        <int>
# 1:        13
# 2:        13
# 3:         9
# 4:       -26
# 5:         1
# 6:         0

A data.table (and a data.frame too) is internally a list as well, with the stipulation that each element has the same length and the list has a class attribute. Allowing j to return a list enables converting and returning data.table very efficiently.

Tip:

As long as j-expression returns a list, each element of the list will be converted to a column in the resulting data.table. This makes j quite powerful, as we will see shortly. It is also very important to understand this for when you’d like to make more complicated queries!!

– Select both arr_delay and dep_delay columns.

ans <- flights[, .(arr_delay, dep_delay)]
head(ans)
#    arr_delay dep_delay
#        <int>     <int>
# 1:        13        14
# 2:        13        -3
# 3:         9         2
# 4:       -26        -8
# 5:         1         2
# 6:         0         4

## alternatively
# ans <- flights[, list(arr_delay, dep_delay)]

– Select both arr_delay and dep_delay columns and rename them to delay_arr and delay_dep.

Since .() is just an alias for list(), we can name columns as we would while creating a list.

ans <- flights[, .(delay_arr = arr_delay, delay_dep = dep_delay)]
head(ans)
#    delay_arr delay_dep
#        <int>     <int>
# 1:        13        14
# 2:        13        -3
# 3:         9         2
# 4:       -26        -8
# 5:         1         2
# 6:         0         4

e) Compute or do in j

– How many trips have had total delay < 0?

ans <- flights[, sum( (arr_delay + dep_delay) < 0 )]
ans
# [1] 141814

What’s happening here?

f) Subset in i and do in j

– Calculate the average arrival and departure delay for all flights with “JFK” as the origin airport in the month of June.

ans <- flights[origin == "JFK" & month == 6L,
               .(m_arr = mean(arr_delay), m_dep = mean(dep_delay))]
ans
#       m_arr    m_dep
#       <num>    <num>
# 1: 5.839349 9.807884

Because the three main components of the query (i, j and by) are together inside [...], data.table can see all three and optimise the query altogether before evaluation, rather than optimizing each separately. We are able to therefore avoid the entire subset (i.e., subsetting the columns besides arr_delay and dep_delay), for both speed and memory efficiency.

– How many trips have been made in 2014 from “JFK” airport in the month of June?

ans <- flights[origin == "JFK" & month == 6L, length(dest)]
ans
# [1] 8422

The function length() requires an input argument. We just need to compute the number of rows in the subset. We could have used any other column as the input argument to length(). This approach is reminiscent of SELECT COUNT(dest) FROM flights WHERE origin = 'JFK' AND month = 6 in SQL.

This type of operation occurs quite frequently, especially while grouping (as we will see in the next section), to the point where data.table provides a special symbol .N for it.

Special symbol .N:

.N is a special built-in variable that holds the number of observations in the current group. It is particularly useful when combined with by as we’ll see in the next section. In the absence of group by operations, it simply returns the number of rows in the subset.

Now that we now, we can now accomplish the same task by using .N as follows:

ans <- flights[origin == "JFK" & month == 6L, .N]
ans
# [1] 8422

We could have accomplished the same operation by doing nrow(flights[origin == "JFK" & month == 6L]). However, it would have to subset the entire data.table first corresponding to the row indices in i and then return the rows using nrow(), which is unnecessary and inefficient. We will cover this and other optimisation aspects in detail under the data.table design vignette.

g) Great! But how can I refer to columns by names in j (like in a data.frame)?

If you’re writing out the column names explicitly, there’s no difference compared to a data.frame (since v1.9.8).

– Select both arr_delay and dep_delay columns the data.frame way.

ans <- flights[, c("arr_delay", "dep_delay")]
head(ans)
#    arr_delay dep_delay
#        <int>     <int>
# 1:        13        14
# 2:        13        -3
# 3:         9         2
# 4:       -26        -8
# 5:         1         2
# 6:         0         4

If you’ve stored the desired columns in a character vector, there are two options: Using the .. prefix, or using the with argument.

– Select columns named in a variable using the .. prefix

select_cols = c("arr_delay", "dep_delay")
flights[ , ..select_cols]
#         arr_delay dep_delay
#             <int>     <int>
#      1:        13        14
#      2:        13        -3
#      3:         9         2
#      4:       -26        -8
#      5:         1         2
#     ---                    
# 253312:       -30         1
# 253313:       -14        -5
# 253314:        16        -8
# 253315:        15        -4
# 253316:         1        -5

For those familiar with the Unix terminal, the .. prefix should be reminiscent of the “up-one-level” command, which is analogous to what’s happening here – the .. signals to data.table to look for the select_cols variable “up-one-level”, i.e., within the global environment in this case.

– Select columns named in a variable using with = FALSE

flights[ , select_cols, with = FALSE]
#         arr_delay dep_delay
#             <int>     <int>
#      1:        13        14
#      2:        13        -3
#      3:         9         2
#      4:       -26        -8
#      5:         1         2
#     ---                    
# 253312:       -30         1
# 253313:       -14        -5
# 253314:        16        -8
# 253315:        15        -4
# 253316:         1        -5

The argument is named with after the R function with() because of similar functionality. Suppose you have a data.frame DF and you’d like to subset all rows where x > 1. In base R you can do the following:

DF = data.frame(x = c(1,1,1,2,2,3,3,3), y = 1:8)

## (1) normal way
DF[DF$x > 1, ] # data.frame needs that ',' as well
#   x y
# 4 2 4
# 5 2 5
# 6 3 6
# 7 3 7
# 8 3 8

## (2) using with
DF[with(DF, x > 1), ]
#   x y
# 4 2 4
# 5 2 5
# 6 3 6
# 7 3 7
# 8 3 8

with = TRUE is the default in data.table because we can do much more by allowing j to handle expressions - especially when combined with by, as we’ll see in a moment.

2. Aggregations

We’ve already seen i and j from data.table‘s general form in the previous section. In this section, we’ll see how they can be combined together with by to perform operations by group. Let’s look at some examples.

a) Grouping using by

– How can we get the number of trips corresponding to each origin airport?

ans <- flights[, .(.N), by = .(origin)]
ans
#    origin     N
#    <char> <int>
# 1:    JFK 81483
# 2:    LGA 84433
# 3:    EWR 87400

## or equivalently using a character vector in 'by'
# ans <- flights[, .(.N), by = "origin"]

– How can we calculate the number of trips for each origin airport for carrier code "AA"?

The unique carrier code "AA" corresponds to American Airlines Inc.

ans <- flights[carrier == "AA", .N, by = origin]
ans
#    origin     N
#    <char> <int>
# 1:    JFK 11923
# 2:    LGA 11730
# 3:    EWR  2649

– How can we get the total number of trips for each origin, dest pair for carrier code "AA"?

ans <- flights[carrier == "AA", .N, by = .(origin, dest)]
head(ans)
#    origin   dest     N
#    <char> <char> <int>
# 1:    JFK    LAX  3387
# 2:    LGA    PBI   245
# 3:    EWR    LAX    62
# 4:    JFK    MIA  1876
# 5:    JFK    SEA   298
# 6:    EWR    MIA   848

## or equivalently using a character vector in 'by'
# ans <- flights[carrier == "AA", .N, by = c("origin", "dest")]

– How can we get the average arrival and departure delay for each orig,dest pair for each month for carrier code "AA"?

ans <- flights[carrier == "AA",
        .(mean(arr_delay), mean(dep_delay)),
        by = .(origin, dest, month)]
ans
#      origin   dest month         V1         V2
#      <char> <char> <int>      <num>      <num>
#   1:    JFK    LAX     1   6.590361 14.2289157
#   2:    LGA    PBI     1  -7.758621  0.3103448
#   3:    EWR    LAX     1   1.366667  7.5000000
#   4:    JFK    MIA     1  15.720670 18.7430168
#   5:    JFK    SEA     1  14.357143 30.7500000
#  ---                                          
# 196:    LGA    MIA    10  -6.251799 -1.4208633
# 197:    JFK    MIA    10  -1.880184  6.6774194
# 198:    EWR    PHX    10  -3.032258 -4.2903226
# 199:    JFK    MCO    10 -10.048387 -1.6129032
# 200:    JFK    DCA    10  16.483871 15.5161290

Now what if we would like to order the result by those grouping columns origin, dest and month?

b) Sorted by: keyby

data.table retaining the original order of groups is intentional and by design. There are cases when preserving the original order is essential. But at times we would like to automatically sort by the variables in our grouping.

– So how can we directly order by all the grouping variables?

ans <- flights[carrier == "AA",
        .(mean(arr_delay), mean(dep_delay)),
        keyby = .(origin, dest, month)]
ans
# Key: <origin, dest, month>
#      origin   dest month         V1         V2
#      <char> <char> <int>      <num>      <num>
#   1:    EWR    DFW     1   6.427673 10.0125786
#   2:    EWR    DFW     2  10.536765 11.3455882
#   3:    EWR    DFW     3  12.865031  8.0797546
#   4:    EWR    DFW     4  17.792683 12.9207317
#   5:    EWR    DFW     5  18.487805 18.6829268
#  ---                                          
# 196:    LGA    PBI     1  -7.758621  0.3103448
# 197:    LGA    PBI     2  -7.865385  2.4038462
# 198:    LGA    PBI     3  -5.754098  3.0327869
# 199:    LGA    PBI     4 -13.966667 -4.7333333
# 200:    LGA    PBI     5 -10.357143 -6.8571429

Keys: Actually keyby does a little more than just ordering. It also sets a key after ordering by setting an attribute called sorted.

We’ll learn more about keys in the Keys and fast binary search based subset vignette; for now, all you have to know is that you can use keyby to automatically order the result by the columns specified in by.

c) Chaining

Let’s reconsider the task of getting the total number of trips for each origin, dest pair for carrier “AA”.

ans <- flights[carrier == "AA", .N, by = .(origin, dest)]

– How can we order ans using the columns origin in ascending order, and dest in descending order?

We can store the intermediate result in a variable, and then use order(origin, -dest) on that variable. It seems fairly straightforward.

ans <- ans[order(origin, -dest)]
head(ans)
#    origin   dest     N
#    <char> <char> <int>
# 1:    EWR    PHX   121
# 2:    EWR    MIA   848
# 3:    EWR    LAX    62
# 4:    EWR    DFW  1618
# 5:    JFK    STT   229
# 6:    JFK    SJU   690

But this requires having to assign the intermediate result and then overwriting that result. We can do one better and avoid this intermediate assignment to a temporary variable altogether by chaining expressions.

ans <- flights[carrier == "AA", .N, by = .(origin, dest)][order(origin, -dest)]
head(ans, 10)
#     origin   dest     N
#     <char> <char> <int>
#  1:    EWR    PHX   121
#  2:    EWR    MIA   848
#  3:    EWR    LAX    62
#  4:    EWR    DFW  1618
#  5:    JFK    STT   229
#  6:    JFK    SJU   690
#  7:    JFK    SFO  1312
#  8:    JFK    SEA   298
#  9:    JFK    SAN   299
# 10:    JFK    ORD   432

d) Expressions in by

– Can by accept expressions as well or does it just take columns?

Yes it does. As an example, if we would like to find out how many flights started late but arrived early (or on time), started and arrived late etc…

ans <- flights[, .N, .(dep_delay>0, arr_delay>0)]
ans
#    dep_delay arr_delay      N
#       <lgcl>    <lgcl>  <int>
# 1:      TRUE      TRUE  72836
# 2:     FALSE      TRUE  34583
# 3:     FALSE     FALSE 119304
# 4:      TRUE     FALSE  26593

e) Multiple columns in j - .SD

– Do we have to compute mean() for each column individually?

It is of course not practical to have to type mean(myCol) for every column one by one. What if you had 100 columns to average mean()?

How can we do this efficiently and concisely? To get there, refresh on this tip - “As long as the j-expression returns a list, each element of the list will be converted to a column in the resulting data.table. If we can refer to the data subset for each group as a variable while grouping, we can then loop through all the columns of that variable using the already- or soon-to-be-familiar base function lapply(). No new names to learn specific to data.table.

Special symbol .SD:

data.table provides a special symbol called .SD. It stands for Subset of Data. It by itself is a data.table that holds the data for the current group defined using by.

Recall that a data.table is internally a list as well with all its columns of equal length.

Let’s use the data.table DT from before to get a glimpse of what .SD looks like.

DT
#        ID     a     b     c
#    <char> <int> <int> <int>
# 1:      b     1     7    13
# 2:      b     2     8    14
# 3:      b     3     9    15
# 4:      a     4    10    16
# 5:      a     5    11    17
# 6:      c     6    12    18

DT[, print(.SD), by = ID]
#        a     b     c
#    <int> <int> <int>
# 1:     1     7    13
# 2:     2     8    14
# 3:     3     9    15
#        a     b     c
#    <int> <int> <int>
# 1:     4    10    16
# 2:     5    11    17
#        a     b     c
#    <int> <int> <int>
# 1:     6    12    18
# Empty data.table (0 rows and 1 cols): ID

To compute on (multiple) columns, we can then simply use the base R function lapply().

DT[, lapply(.SD, mean), by = ID]
#        ID     a     b     c
#    <char> <num> <num> <num>
# 1:      b   2.0   8.0  14.0
# 2:      a   4.5  10.5  16.5
# 3:      c   6.0  12.0  18.0

We are almost there. There is one little thing left to address. In our flights data.table, we only wanted to calculate the mean() of the two columns arr_delay and dep_delay. But .SD would contain all the columns other than the grouping variables by default.

– How can we specify just the columns we would like to compute the mean() on?

.SDcols

Using the argument .SDcols. It accepts either column names or column indices. For example, .SDcols = c("arr_delay", "dep_delay") ensures that .SD contains only these two columns for each group.

Similar to part g), you can also specify the columns to remove instead of columns to keep using - or !. Additionally, you can select consecutive columns as colA:colB and deselect them as !(colA:colB) or -(colA:colB).

Now let us try to use .SD along with .SDcols to get the mean() of arr_delay and dep_delay columns grouped by origin, dest and month.

flights[carrier == "AA",                       ## Only on trips with carrier "AA"
        lapply(.SD, mean),                     ## compute the mean
        by = .(origin, dest, month),           ## for every 'origin,dest,month'
        .SDcols = c("arr_delay", "dep_delay")] ## for just those specified in .SDcols
#      origin   dest month  arr_delay  dep_delay
#      <char> <char> <int>      <num>      <num>
#   1:    JFK    LAX     1   6.590361 14.2289157
#   2:    LGA    PBI     1  -7.758621  0.3103448
#   3:    EWR    LAX     1   1.366667  7.5000000
#   4:    JFK    MIA     1  15.720670 18.7430168
#   5:    JFK    SEA     1  14.357143 30.7500000
#  ---                                          
# 196:    LGA    MIA    10  -6.251799 -1.4208633
# 197:    JFK    MIA    10  -1.880184  6.6774194
# 198:    EWR    PHX    10  -3.032258 -4.2903226
# 199:    JFK    MCO    10 -10.048387 -1.6129032
# 200:    JFK    DCA    10  16.483871 15.5161290

f) Subset .SD for each group:

– How can we return the first two rows for each month?

ans <- flights[, head(.SD, 2), by = month]
head(ans)
#    month  year   day dep_delay arr_delay carrier origin   dest air_time distance  hour
#    <int> <int> <int>     <int>     <int>  <char> <char> <char>    <int>    <int> <int>
# 1:     1  2014     1        14        13      AA    JFK    LAX      359     2475     9
# 2:     1  2014     1        -3        13      AA    JFK    LAX      363     2475    11
# 3:     2  2014     1        -1         1      AA    JFK    LAX      358     2475     8
# 4:     2  2014     1        -5         3      AA    JFK    LAX      358     2475    11
# 5:     3  2014     1       -11        36      AA    JFK    LAX      375     2475     8
# 6:     3  2014     1        -3        14      AA    JFK    LAX      368     2475    11

g) Why keep j so flexible?

So that we have a consistent syntax and keep using already existing (and familiar) base functions instead of learning new functions. To illustrate, let us use the data.table DT that we created at the very beginning under the section What is a data.table?.

– How can we concatenate columns a and b for each group in ID?

DT[, .(val = c(a,b)), by = ID]
#         ID   val
#     <char> <int>
#  1:      b     1
#  2:      b     2
#  3:      b     3
#  4:      b     7
#  5:      b     8
#  6:      b     9
#  7:      a     4
#  8:      a     5
#  9:      a    10
# 10:      a    11
# 11:      c     6
# 12:      c    12

– What if we would like to have all the values of column a and b concatenated, but returned as a list column?

DT[, .(val = list(c(a,b))), by = ID]
#        ID         val
#    <char>      <list>
# 1:      b 1,2,3,7,8,9
# 2:      a  4, 5,10,11
# 3:      c        6,12

Once you start internalising usage in j, you will realise how powerful the syntax can be. A very useful way to understand it is by playing around, with the help of print().

For example:

## look at the difference between
DT[, print(c(a,b)), by = ID] # (1)
# [1] 1 2 3 7 8 9
# [1]  4  5 10 11
# [1]  6 12
# Empty data.table (0 rows and 1 cols): ID

## and
DT[, print(list(c(a,b))), by = ID] # (2)
# [[1]]
# [1] 1 2 3 7 8 9
# 
# [[1]]
# [1]  4  5 10 11
# 
# [[1]]
# [1]  6 12
# Empty data.table (0 rows and 1 cols): ID

In (1), for each group, a vector is returned, with length = 6,4,2 here. However, (2) returns a list of length 1 for each group, with its first element holding vectors of length 6,4,2. Therefore, (1) results in a length of 6+4+2 = 12, whereas (2) returns 1+1+1=3.

Summary

The general form of data.table syntax is:

DT[i, j, by]

We have seen so far that,

Using i:

We can do much more in i by keying a data.table, which allows for blazing fast subsets and joins. We will see this in the “Keys and fast binary search based subsets” and “Joins and rolling joins” vignette.

Using j:

  1. Select columns the data.table way: DT[, .(colA, colB)].

  2. Select columns the data.frame way: DT[, c("colA", "colB")].

  3. Compute on columns: DT[, .(sum(colA), mean(colB))].

  4. Provide names if necessary: DT[, .(sA =sum(colA), mB = mean(colB))].

  5. Combine with i: DT[colA > value, sum(colB)].

Using by:

And remember the tip:

As long as j returns a list, each element of the list will become a column in the resulting data.table.

We will see how to add/update/delete columns by reference and how to combine them with i and by in the next vignette.