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 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:

  • concise and consistent syntax irrespective of the set of operations you would like to perform to achieve your end goal.

  • performing analysis fluidly without the cognitive burden of having to map each operation to a particular function from a potentially huge set of functions available before performing the analysis.

  • automatically optimising operations internally, and very effectively, by knowing precisely the data required for each operation, leading to very fast and memory efficient code.

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.

Introduction

In this vignette, we will

  1. Start with 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 data.frames, which are the standard data structure for storing data in base R. In the Data section above, we already created a data.table using fread(). We can also create one using the data.table() function. Here is an example:

You can also convert existing objects to a data.table using setDT() (for data.frames and lists) and as.data.table() (for other structures); the difference is beyond the scope of this vignette, see ?setDT and ?as.data.table for more details.

Note that:

  • Unlike data.frames, columns of character type are never converted to factors by default.

  • Row numbers are printed with a : in order to visually separate the row number from the first column.

  • When the number of rows to print exceeds the global option datatable.print.nrows (default = 100), it automatically prints only the top 5 and bottom 5 rows (as can be seen in the Data section). If you’ve had a lot of experience with data.frames, you may have found yourself waiting around while larger tables print-and-page, sometimes seemingly endlessly. You can query the default number like so:

    getOption("datatable.print.nrows")
  • data.table doesn’t set or use row names, ever. We will see why in the “Keys and fast binary search based subset” vignette.

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”, in analogy to SQL). To understand it we will have to first look at the general form of data.table syntax, as shown below:

Users who have 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

  • Within the frame of a data.table, columns can be referred to as if they are variables, much like in SQL or Stata. Therefore, we simply refer to origin and month as if they are variables. We do not need to add the prefix flights$ each time. Nevertheless, using flights$origin and flights$month would work just fine.

  • The row indices that satisfy the condition origin == "JFK" & month == 6L are computed, and since there is nothing else left to do, all columns from flights at rows corresponding to those row indices are simply returned as a data.table.

  • A comma after the condition in i is not required. But flights[origin == "JFK" & month == 6L, ] would work just fine. In data.frames, however, the comma is necessary.

  • In this case, there is no condition. The row indices are already provided in i. We therefore return a data.table with all columns from flights at rows for those row indices.

order() is internally optimised

  • We can use “-” on a character columns within the frame of a data.table to sort in decreasing order.

  • In addition, order(...) within the frame of a data.table uses data.table’s internal fast radix order forder(). This sort provided such a compelling improvement over R’s base::order that the R project adopted the data.table algorithm as its default sort in 2016 for R 3.3.0, see ?sort and the R Release NEWS.

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.

  • Since columns can be referred to as if they are variables within the frame of data.tables, we directly refer to the variable we want to subset. Since we want all the rows, we simply skip i.

  • It returns all the rows for the column arr_delay.

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

  • We wrap the variables (column names) within list(), which ensures that a data.table is returned. In case of a single column name, not wrapping with list() returns a vector instead, as seen in the previous example.

  • data.table also allows wrapping columns with .() instead of list(). It is an alias to list(); they both mean the same. Feel free to use whichever you prefer; we have noticed most users seem to prefer .() for conciseness, so we will continue to use .() hereafter.

data.tables (and data.frames) are internally lists 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!!

  • Wrap both columns within .(), or list(). That’s it.

– 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.

That’s it.

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?

  • data.table’s j can handle more than just selecting columns - it can handle expressions, i.e., computing on columns. This shouldn’t be surprising, as columns can be referred to as if they are variables. Then we should be able to compute by calling functions on those variables. And that’s what precisely happens 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.

  • We first subset in i to find matching row indices where origin airport equals "JFK", and month equals 6L. We do not subset the entire data.table corresponding to those rows yet.

  • Now, we look at j and find that it uses only two columns. And what we have to do is to compute their mean(). Therefore we subset just those columns corresponding to the matching rows, and compute their mean().

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, not 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?

The function length() requires an input argument. We just needed to compute the number of rows in the subset. We could have used any other column as input argument to length() really. 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.

So we can now accomplish the same task by using .N as follows:

  • Once again, we subset in i to get the row indices where origin airport equals “JFK”, and month equals 6.

  • We see that j uses only .N and no other columns. Therefore the entire subset is not materialised. We simply return the number of rows in the subset (which is just the length of row indices).

  • Note that we did not wrap .N with list() or .(). Therefore a vector is returned.

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 vis-a-vis data.frame (since v1.9.8).

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

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

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., in the global environment in this case.

– Select columns named in a variable using with = FALSE

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:

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

  • We know .N is a special variable that holds the number of rows in the current group. Grouping by origin obtains the number of rows, .N, for each group.

  • By doing head(flights) you can see that the origin airports occur in the order “JFK”, “LGA” and “EWR”. The original order of grouping variables is preserved in the result. This is important to keep in mind!

  • Since we did not provide a name for the column returned in j, it was named N automatically by recognising the special symbol .N.

  • by also accepts a character vector of column names. This is particularly useful for coding programmatically, e.g., designing a function with the grouping columns as a (character vector) function argument.

  • When there’s only one column or expression to refer to in j and by, we can drop the .() notation. This is purely for convenience. We could instead do:

    We’ll use this convenient form wherever applicable hereafter.

– 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.

  • We first obtain the row indices for the expression carrier == "AA" from i.

  • Using those row indices, we obtain the number of rows while grouped by origin. Once again no columns are actually materialised here, because the j-expression does not require any columns to be actually subsetted and is therefore fast and memory efficient.

  • by accepts multiple columns. We just provide all the columns by which to group by. Note the use of .() again in by – again, this is just shorthand for list(), and list() can be used here as well. Again, we’ll stick with .() in this vignette.

  • Since we did not provide column names for the expressions in j, they were automatically generated as V1 and V2.

  • Once again, note that the input order of grouping columns is preserved in the result.

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.

  • All we did was to change by to keyby. This automatically orders the result by the grouping variables in increasing order. In fact, due to the internal implementation of by first requiring a sort before recovering the original table’s order, keyby is typically faster than by because it doesn’t require this second step.

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”.

– 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.

  • Recall that we can use - on a character column in order() within the frame of a data.table. This is possible to due data.table’s internal query optimisation.

  • Also recall that order(...) with the frame of a data.table is automatically optimised to use data.table’s internal fast radix order forder() for speed.

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.

  • We can tack expressions one after another, forming a chain of operations, i.e., DT[ ... ][ ... ][ ... ].

  • Or you can also chain them vertically:

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…

  • The last row corresponds to dep_delay > 0 = TRUE and arr_delay > 0 = FALSE. We can see that 26593 flights started late but arrived early (or on time).

  • Note that we did not provide any names to by-expression. Therefore, names have been automatically assigned in the result. As with j, you can name these expressions as you would elements of any list, e.g. DT[, .N, .(dep_delayed = dep_delay>0, arr_delayed = arr_delay>0)].

  • You can provide other columns along with expressions, for example: DT[, .N, by = .(a, b>0)].

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, 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. Suppose we can refer to the data subset for each group as a variable while grouping, then we can 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.

  • .SD contains all the columns except the grouping columns by default.

  • It is also generated by preserving the original order - data corresponding to ID = "b", then ID = "a", and then ID = "c".

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

  • .SD holds the rows corresponding to columns a, b and c for that group. We compute the mean() on each of these columns using the already-familiar base function lapply().

  • Each group returns a list of three elements containing the mean value which will become the columns of the resulting data.table.

  • Since lapply() returns a list, so there is no need to wrap it with an additional .() (if necessary, refer to this tip).

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 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 provide the columns to remove instead of columns to keep using - or ! sign as well as select consecutive columns as colA:colB and deselect consecutive columns 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.

f) Subset .SD for each group:

  • .SD is a data.table that holds all the rows for that group. We simply subset the first two rows as we have seen here already.

  • For each group, head(.SD, 2) returns the first two rows as a data.table, which is also a list, so we do not have to wrap it with .().

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 What is a data.table? section.

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

  • That’s it. There is no special syntax required. All we need to know is the base function c() which concatenates vectors and the tip from before.

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

  • Here, we first concatenate the values with c(a,b) for each group, and wrap that with list(). So for each group, we return a list of all concatenated values.

  • Note those commas are for display only. A list column can contain any object in each cell, and in this example, each cell is itself a vector and some cells contain longer vectors than others.

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:

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:

We have seen so far that,

Using i:

  • We can subset rows similar to a data.frame- except you don’t have to use DT$ repetitively since columns within the frame of a data.table are seen as if they are variables.

  • We can also sort a data.table using order(), which internally uses data.table’s fast order for performance.

We can do much more in i by keying a data.table, which allows 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:

  • Using by, we can group by columns by specifying a list of columns or a character vector of column names or even expressions. The flexibility of j, combined with by and i makes for a very powerful syntax.

  • by can handle multiple columns and also expressions.

  • We can keyby grouping columns to automatically sort the grouped result.

  • We can use .SD and .SDcols in j to operate on multiple columns using already familiar base functions. Here are some examples:

    1. DT[, lapply(.SD, fun), by = ..., .SDcols = ...] - applies fun to all columns specified in .SDcols while grouping by the columns specified in by.

    2. DT[, head(.SD, 2), by = ...] - return the first two rows for each group.

    3. DT[col > val, head(.SD, 1), by = ...] - combine i along with j and 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.