Secondary indices and auto indexing

2024-04-14

This vignette assumes that the reader is familiar with data.table’s [i, j, by] syntax, and how to perform fast key based subsets. If you’re not familiar with these concepts, please read the “Introduction to data.table”, “Reference semantics” and “Keys and fast binary search based subset” vignettes first.


Data

We will use the same flights data as in the “Introduction to data.table” vignette.

flights <- fread("flights14.csv")
head(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
# 6:  2014     1     1         4         0      AA    EWR    LAX      339     2454    18
dim(flights)
# [1] 253316     11

Introduction

In this vignette, we will

1. Secondary indices

a) What are secondary indices?

Secondary indices are similar to keys in data.table, except for two major differences:

b) Set and get secondary indices

– How can we set the column origin as a secondary index in the data.table flights?

setindex(flights, origin)
head(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
# 6:  2014     1     1         4         0      AA    EWR    LAX      339     2454    18

## alternatively we can provide character vectors to the function 'setindexv()'
# setindexv(flights, "origin") # useful to program with

# 'index' attribute added
names(attributes(flights))
# [1] "names"             "row.names"         "class"             ".internal.selfref"
# [5] "index"

– How can we get all the secondary indices set so far in flights?

indices(flights)
# [1] "origin"

setindex(flights, origin, dest)
indices(flights)
# [1] "origin"       "origin__dest"

c) Why do we need secondary indices?

– Reordering a data.table can be expensive and not always ideal

Consider the case where you would like to perform a fast key based subset on origin column for the value “JFK”. We’d do this as:

## not run
setkey(flights, origin)
flights["JFK"] # or flights[.("JFK")]

setkey() requires:

a) computing the order vector for the column(s) provided, here, origin, and

b) reordering the entire data.table, by reference, based on the order vector computed.

Computing the order isn’t the time consuming part, since data.table uses true radix sorting on integer, character and numeric vectors. However, reordering the data.table could be time consuming (depending on the number of rows and columns).

Unless our task involves repeated subsetting on the same column, fast key based subsetting could effectively be nullified by the time to reorder, depending on our data.table dimensions.

– There can be only one key at the most

Now if we would like to repeat the same operation but on dest column instead, for the value “LAX”, then we have to setkey(), again.

## not run
setkey(flights, dest)
flights["LAX"]

And this reorders flights by dest, again. What we would really like is to be able to perform the fast subsetting by eliminating the reordering step.

And this is precisely what secondary indices allow for!

– Secondary indices can be reused

Since there can be multiple secondary indices, and creating an index is as simple as storing the order vector as an attribute, this allows us to even eliminate the time to recompute the order vector if an index already exists.

– The new on argument allows for cleaner syntax and automatic creation and reuse of secondary indices

As we will see in the next section, the on argument provides several advantages:

on argument

2. Fast subsetting using on argument and secondary indices

a) Fast subsets in i

– Subset all rows where the origin airport matches “JFK” using on

flights["JFK", on = "origin"]
#         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         2         1      AA    JFK    LAX      350     2475    13
#     5:  2014     1     1        -2       -18      AA    JFK    LAX      338     2475    21
#    ---                                                                                    
# 81479:  2014    10    31        -4       -21      UA    JFK    SFO      337     2586    17
# 81480:  2014    10    31        -2       -37      UA    JFK    SFO      344     2586    18
# 81481:  2014    10    31         0       -33      UA    JFK    LAX      320     2475    17
# 81482:  2014    10    31        -6       -38      UA    JFK    SFO      343     2586     9
# 81483:  2014    10    31        -6       -38      UA    JFK    LAX      323     2475    11

## alternatively
# flights[.("JFK"), on = "origin"] (or)
# flights[list("JFK"), on = "origin"]

– How can I subset based on origin and dest columns?

For example, if we want to subset "JFK", "LAX" combination, then:

flights[.("JFK", "LAX"), on = c("origin", "dest")][1:5]
#     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         2         1      AA    JFK    LAX      350     2475    13
# 5:  2014     1     1        -2       -18      AA    JFK    LAX      338     2475    21

b) Select in j

All the operations we will discuss below are no different to the ones we already saw in the Keys and fast binary search based subset vignette. Except we’ll be using the on argument instead of setting keys.

– Return arr_delay column alone as a data.table corresponding to origin = "LGA" and dest = "TPA"

flights[.("LGA", "TPA"), .(arr_delay), on = c("origin", "dest")]
#       arr_delay
#           <int>
#    1:         1
#    2:        14
#    3:       -17
#    4:        -4
#    5:       -12
#   ---          
# 1848:        39
# 1849:       -24
# 1850:       -12
# 1851:        21
# 1852:       -11

c) Chaining

– On the result obtained above, use chaining to order the column in decreasing order.

flights[.("LGA", "TPA"), .(arr_delay), on = c("origin", "dest")][order(-arr_delay)]
#       arr_delay
#           <int>
#    1:       486
#    2:       380
#    3:       351
#    4:       318
#    5:       300
#   ---          
# 1848:       -40
# 1849:       -43
# 1850:       -46
# 1851:       -48
# 1852:       -49

d) Compute or do in j

– Find the maximum arrival delay corresponding to origin = "LGA" and dest = "TPA".

flights[.("LGA", "TPA"), max(arr_delay), on = c("origin", "dest")]
# [1] 486

e) sub-assign by reference using := in j

We have seen this example already in the Reference semantics and Keys and fast binary search based subset vignette. Let’s take a look at all the hours available in the flights data.table:

# get all 'hours' in flights
flights[, sort(unique(hour))]
#  [1]  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

We see that there are totally 25 unique values in the data. Both 0 and 24 hours seem to be present. Let’s go ahead and replace 24 with 0, but this time using on instead of setting keys.

flights[.(24L), hour := 0L, on = "hour"]

Now, let’s check if 24 is replaced with 0 in the hour column.

flights[, sort(unique(hour))]
#  [1]  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

f) Aggregation using by

– Get the maximum departure delay for each month corresponding to origin = "JFK". Order the result by month

ans <- flights["JFK", max(dep_delay), keyby = month, on = "origin"]
head(ans)
# Key: <month>
#    month    V1
#    <int> <int>
# 1:     1   881
# 2:     2  1014
# 3:     3   920
# 4:     4  1241
# 5:     5   853
# 6:     6   798

g) The mult argument

The other arguments including mult work exactly the same way as we saw in the Keys and fast binary search based subset vignette. The default value for mult is “all”. We can choose, instead only the “first” or “last” matching rows should be returned.

– Subset only the first matching row where dest matches “BOS” and “DAY”

flights[c("BOS", "DAY"), on = "dest", mult = "first"]
#     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         3         1      AA    JFK    BOS       39      187    12
# 2:  2014     1     1        25        35      EV    EWR    DAY      102      533    17

– Subset only the last matching row where origin matches “LGA”, “JFK”, “EWR” and dest matches “XNA”

flights[.(c("LGA", "JFK", "EWR"), "XNA"), on = c("origin", "dest"), mult = "last"]
#     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    10    31        -5       -11      MQ    LGA    XNA      165     1147     6
# 2:    NA    NA    NA        NA        NA    <NA>    JFK    XNA       NA       NA    NA
# 3:  2014    10    31        -2       -25      EV    EWR    XNA      160     1131     6

h) The nomatch argument

We can choose if queries that do not match should return NA or be skipped altogether using the nomatch argument.

– From the previous example, subset all rows only if there’s a match

flights[.(c("LGA", "JFK", "EWR"), "XNA"), mult = "last", on = c("origin", "dest"), nomatch = NULL]
#     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    10    31        -5       -11      MQ    LGA    XNA      165     1147     6
# 2:  2014    10    31        -2       -25      EV    EWR    XNA      160     1131     6

3. Auto indexing

First we looked at how to fast subset using binary search using keys. Then we figured out that we could improve performance even further and have cleaner syntax by using secondary indices.

That is what auto indexing does. At the moment, it is only implemented for binary operators == and %in%. An index is automatically created and saved as an attribute. That is, unlike the on argument which computes the index on the fly each time (unless one already exists), a secondary index is created here.

Let’s start by creating a data.table big enough to highlight the advantage.

set.seed(1L)
dt = data.table(x = sample(1e5L, 1e7L, TRUE), y = runif(100L))
print(object.size(dt), units = "Mb")
# 114.4 Mb

When we use == or %in% on a single column for the first time, a secondary index is created automatically, and it is used to perform the subset.

## have a look at all the attribute names
names(attributes(dt))
# [1] "names"             "row.names"         "class"             ".internal.selfref"

## run thefirst time
(t1 <- system.time(ans <- dt[x == 989L]))
#    user  system elapsed 
#   0.556   0.025   0.581
head(ans)
#        x         y
#    <int>     <num>
# 1:   989 0.7757157
# 2:   989 0.6813302
# 3:   989 0.2815894
# 4:   989 0.4954259
# 5:   989 0.7885886
# 6:   989 0.5547504

## secondary index is created
names(attributes(dt))
# [1] "names"             "row.names"         "class"             ".internal.selfref"
# [5] "index"

indices(dt)
# [1] "x"

The time to subset the first time is the time to create the index + the time to subset. Since creating a secondary index involves only creating the order vector, this combined operation is faster than vector scans in many cases. But the real advantage comes in successive subsets. They are extremely fast.

## successive subsets
(t2 <- system.time(dt[x == 989L]))
#    user  system elapsed 
#   0.002   0.000   0.002
system.time(dt[x %in% 1989:2012])
#    user  system elapsed 
#   0.002   0.000   0.002

In recent version we extended auto indexing to expressions involving more than one column (combined with & operator). In the future, we plan to extend binary search to work with more binary operators like <, <=, > and >=.

We will discuss fast subsets using keys and secondary indices to joins in the next vignette, “Joins and rolling joins”.